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@@ -0,0 +1,2741 @@
+1
+00:00:00,000 --> 00:00:02,680
+موسيقى
+
+2
+00:00:16,600 --> 00:00:21,960
+بسم الله الرحمن الرحيم، المرة الماضية بدأنا في
+
+3
+00:00:21,960 --> 00:00:26,740
+chapter 14، واخذنا أول section وهو الـ functions of
+
+4
+00:00:26,740 --> 00:00:30,860
+several variables. عرفنا هذه الـ functions، جيبنا الـ
+
+5
+00:00:30,860 --> 00:00:35,010
+domain والـ range لهذه الـ functions، جيبنا ما يسمى
+
+6
+00:00:35,010 --> 00:00:40,830
+بالـ level surface والـ level curves للمنحنى في
+
+7
+00:00:40,830 --> 00:00:44,790
+الإحداثيات الديكارتية، سواء كان في متغيرين أو في
+
+8
+00:00:44,790 --> 00:00:50,250
+ثلاثة متغيرات. اليوم إن شاء الله، هنجي لهذه الـ
+
+9
+00:00:50,250 --> 00:00:54,230
+functions، نجيب الـ limits والـ continuity لهذه
+
+10
+00:00:54,230 --> 00:00:58,850
+الدوال. هنبدأ بأول نقطة، يعني هنقسم هذا section إلى
+
+11
+00:00:58,850 --> 00:01:03,490
+نقطتين. النقطة الأولى بدنا ناخد فيها الـ limits،
+
+12
+00:01:03,490 --> 00:01:08,630
+والنقطة الثانية بدنا ناخد فيها الـ continuity. يعني
+
+13
+00:01:08,630 --> 00:01:13,470
+هنقسم محاضرتنا إلى جزئين، إن شاء الله تبارك وتعالى.
+
+14
+00:01:13,470 --> 00:01:18,770
+لو رجعنا بالذاكرة إلى الدرس في calculus A أو
+
+15
+00:01:18,770 --> 00:01:22,230
+calculus B، كنا بنقول limit لـ function
+
+16
+00:01:43,520 --> 00:01:46,320
+فيه متغير واحد.
+
+17
+00:01:55,410 --> 00:02:00,810
+هذا ما كنا ندرسه في calculus A وB. الآن نقول لو
+
+18
+00:02:00,810 --> 00:02:06,050
+كان الـ function فيه متغيرين، شو اللي بده يحصل؟ يبقى
+
+19
+00:02:06,050 --> 00:02:11,270
+باجي بقول هنا f، الـ f is a function of two
+
+20
+00:02:11,270 --> 00:02:19,170
+variables، في متغيرين، then باجي بقول limit
+
+21
+00:02:22,050 --> 00:02:29,250
+لما x وy بدها تروح إلى x
+
+22
+00:02:29,250 --> 00:02:34,970
+nought و y nought، بده يساوي الـ L. طب لو كانت في
+
+23
+00:02:34,970 --> 00:02:40,630
+ثلاثة متغيرات، يبقى لو كانت الدالة function of
+
+24
+00:02:40,630 --> 00:02:50,890
+three variables، في ثلاثة متغيرات، then limit للـ f
+
+25
+00:02:50,890 --> 00:02:58,790
+of x وy وz، لما الـ x والـ y والـ z بدها تروح إلى
+
+26
+00:02:58,790 --> 00:03:06,010
+x nought، y nought، z nought. يبقى ناتج
+
+27
+00:03:06,010 --> 00:03:12,650
+هذا بده يساوي L. يبقى
+
+28
+00:03:12,650 --> 00:03:18,210
+بده يساوي مين؟ بده يساوي L. وهكذا. يبقى لو عندي
+
+29
+00:03:18,210 --> 00:03:23,170
+متغيرين، ثلاثة، أربعة من المتغيرات، كله بنفس الفورمة.
+
+30
+00:03:23,170 --> 00:03:28,170
+يبقى نفس المفهوم اللي احنا اتعلمناه بالنسبة لمين؟
+
+31
+00:03:28,170 --> 00:03:35,510
+لكالكولاس A. بناء عليه، يبقى هنا لو جيت قلت لك: اه
+
+32
+00:03:45,750 --> 00:03:48,950
+يبقى أول خطوة في إيجاد limit هو التعويض المباشر.
+
+33
+00:03:48,950 --> 00:03:53,710
+يبقى هذه قداشها تساوي؟ x nought. طب والـ y؟ ما عنديش y.
+
+34
+00:03:53,710 --> 00:03:58,510
+يبقى لا، ولا قيمة لها، مش موجودة أصلاً. طب لو قلت
+
+35
+00:03:58,510 --> 00:04:05,270
+limit للـ y، لما الـ x والـ y بدها تروح لـ x nought و y
+
+36
+00:04:05,270 --> 00:04:12,570
+nought، برضه كمان y nought. طب لو قلت limit لـ constant k
+
+37
+00:04:12,570 --> 00:04:18,810
+لما الـ x والـ y بدها تروح إلى x nought و y nought، limit
+
+38
+00:04:18,810 --> 00:04:22,470
+للمقدار الثابت، الثابت نفسه، اللي درسناه في
+
+39
+00:04:22,470 --> 00:04:28,010
+calculus A وB وC، هو نفس الشيء بقوله:
+
+40
+00:04:28,010 --> 00:04:34,810
+هنا where حيث الـ k is constant.
+
+41
+00:04:39,200 --> 00:04:43,540
+بنفس النتيجة الخاصة بالمنطقة التي درسناها في
+
+42
+00:04:43,540 --> 00:04:48,000
+calculus A، على الـ limits للـ function نفسها، هي على
+
+43
+00:04:48,000 --> 00:04:51,400
+الـ functions of two variables, of three variables,
+
+44
+00:04:51,860 --> 00:04:57,340
+of n variables، الآخرين. بعد ذلك، نبدأ نذكر بهذا
+
+45
+00:04:57,340 --> 00:05:01,580
+الكلام لـ function of two variables، وما ينطبق على
+
+46
+00:05:01,580 --> 00:05:04,860
+الـ function of two variables، نفسه تماماً على الـ
+
+47
+00:05:04,860 --> 00:05:09,360
+functions of three variables أو more variables أو
+
+48
+00:05:09,360 --> 00:05:14,180
+أكثر من ذلك. لو كان أربعة متغيرات، خمس متغيرات، إن من
+
+49
+00:05:14,180 --> 00:05:19,900
+المتغيرات الآخرين. يبقى هذا هنحطه على صيغة النظرية
+
+50
+00:05:19,900 --> 00:05:20,720
+التالية.
+
+51
+00:05:25,840 --> 00:05:34,120
+بنقول اللي هي الـ properties، الخاص بـ properties of
+
+52
+00:05:34,120 --> 00:05:42,660
+limits of functions of
+
+53
+00:05:42,660 --> 00:05:45,820
+two variables.
+
+54
+00:05:55,220 --> 00:06:01,540
+الـ M، الـ M، الـ M، الـ M، الـ M، الـ M، الـ M، الـ M،
+
+55
+00:06:01,540 --> 00:06:05,480
+الـ M، الـ M، الـ M، الـ M، الـ M، الـ M، الـ M، الـ M،
+
+56
+00:06:05,480 --> 00:06:05,860
+الـ M، الـ M، الـ M، الـ M، الـ M، الـ M، الـ M، الـ M،
+
+57
+00:06:05,860 --> 00:06:05,880
+الـ M، الـ M، الـ M، الـ M، الـ M، الـ M، الـ M، الـ M،
+
+58
+00:06:05,880 --> 00:06:06,040
+الـ M، الـ M، الـ M، الـ M، الـ M، الـ M، الـ M، الـ M،
+
+59
+00:06:06,040 --> 00:06:12,740
+الـ M، الـ M، الـ M، الـ
+
+60
+00:06:12,740 --> 00:06:24,120
+M، للـ f of x وy، لما الـ x والـ y بدها تروح إلى
+
+61
+00:06:24,120 --> 00:06:35,620
+x nought و y nought، تساوي الـ L، and الـ limit للـ g of x
+
+62
+00:06:35,620 --> 00:06:42,120
+وy، لما الـ x والـ y بدها تروح إلى x nought و y nought،
+
+63
+00:06:42,120 --> 00:06:45,140
+بده يساوي الـ M مثلاً.
+
+64
+00:06:48,650 --> 00:06:52,810
+النقطة الأولى، limit
+
+65
+00:07:04,000 --> 00:07:08,780
+عندما تذهب الـ x والـ y إلى الـ x nought والـ y
+
+66
+00:07:08,780 --> 00:07:17,520
+nought، يبقى هذا الكلام زائد أو ناقص M. النقطة الثانية،
+
+67
+00:07:17,520 --> 00:07:23,580
+limit لكيف
+
+68
+00:07:23,580 --> 00:07:25,720
+تتغير الـ x والـ y.
+
+69
+00:07:28,690 --> 00:07:37,630
+بدها تروح إلى x nought و y nought، بده يساوي K في L. and
+
+70
+00:07:37,630 --> 00:07:48,530
+بناء عليه، limit لمين؟ للـ F of x و y، للـ G of x و y، لما
+
+71
+00:07:48,530 --> 00:07:54,690
+x و y بدها تروح إلى x nought و y nought، يبقى هذا الكلام
+
+72
+00:07:54,690 --> 00:08:03,930
+بده يساوي الـ L في M. النقطة الثالثة، بدي الـ limit للـ F
+
+73
+00:08:03,930 --> 00:08:11,770
+of x وy، على الـ G of x وy، لما الـ x والـ y بدها
+
+74
+00:08:11,770 --> 00:08:17,910
+تروح إلى x nought و y nought.
+
+75
+00:08:17,910 --> 00:08:25,270
+يبقى هذا الكلام بده يساوي L على M، بشرط أن الـ M
+
+76
+00:08:25,270 --> 00:08:38,090
+ممنوع تساوي zero. والنقطة الرابعة، limit للـ F من x و
+
+77
+00:08:38,090 --> 00:08:45,910
+y، كله to the power n، لما الـ x والـ y بدها تروح إلى
+
+78
+00:08:45,910 --> 00:08:53,150
+x nought و y nought، يبقى هذا بده يساوي الـ L أس n، والـ
+
+79
+00:08:53,150 --> 00:08:58,630
+n is a positive integer.
+
+80
+00:09:10,240 --> 00:09:15,860
+لما الـ x والـ y بدها تروح إلى x nought و y nought،
+
+81
+00:09:15,860 --> 00:09:27,400
+للجذر النوني للـ F of x وy، بده يساوي الجذر النوني
+
+82
+00:09:27,400 --> 00:09:36,100
+لـ L، وله بده يساوي L أس واحد على n، والـ n as a
+
+83
+00:09:36,100 --> 00:09:37,440
+positive integer.
+
+84
+00:10:28,780 --> 00:10:36,600
+أقل من أو يساوي الـ F of x y، أقل من أو يساوي الـ H
+
+85
+00:10:36,600 --> 00:10:49,520
+of x y، for all x y التي لا تساوي x nought و y nought،
+
+86
+00:10:53,570 --> 00:11:06,230
+in a disk، and a disk centered at x nought و y nought،
+
+87
+00:11:06,230 --> 00:11:14,190
+and if وإذا
+
+88
+00:11:14,190 --> 00:11:24,830
+كان limit للـ g of x و y، لما الـ x والـ y إلى x nought
+
+89
+00:11:24,830 --> 00:11:35,030
+و y nought، بده يساوي limit لما الـ x والـ y بدها تروح لـ x
+
+90
+00:11:35,030 --> 00:11:43,250
+nought و y nought، للـ h of x و y، بده يساوي الـ L، then
+
+91
+00:11:43,250 --> 00:11:52,610
+limit للـ f of x و y، لما الـ x والـ y بدها تروح إلى
+
+92
+00:11:52,610 --> 00:11:57,270
+x nought و y nought، يبقى بده يساوي الـ L كذلك.
+
+93
+00:12:43,190 --> 00:12:48,170
+لو راجعنا إلى هذه الخواص الست اللي قدامنا، لن نجد
+
+94
+00:12:48,170 --> 00:12:53,690
+أنها تختلف مع الست خواص تبع الـ calculus A التي
+
+95
+00:12:53,690 --> 00:12:59,270
+درستها في أول ما دخلت الجامعة، في الفصل الأول، أثناء
+
+96
+00:12:59,270 --> 00:13:03,310
+دراسة الـ  يبقى المعلومات اللي كانت على function of one
+
+97
+00:13:03,310 --> 00:13:07,690
+variable، نفسها على function of two variables.
+
+98
+00:13:08,180 --> 00:13:13,000
+الخواص بتقول لي ما يأتي: افترض أن عندي L وM وK
+
+99
+00:13:13,000 --> 00:13:19,700
+كانت أعداد حقيقية. limit f of x و y يساوي L، limit g
+
+100
+00:13:19,700 --> 00:13:23,900
+of x و y يساوي
+
+101
+00:13:23,900 --> 00:13:30,140
+M. النقطة الأولى، درسنا في calculus A نهاية المجموع
+
+102
+00:13:30,140 --> 00:13:34,700
+الجبري لدالتين، يساوي المجموع الجبري للنهايتين. إيش
+
+103
+00:13:34,700 --> 00:13:38,960
+معناه؟ معناه كإن الـ limit بتدخل على الدالة الأولى،
+
+104
+00:13:38,960 --> 00:13:42,600
+زائد أو ناقص الـ limit لما تدخل على الدالة الثانية.
+
+105
+00:13:42,600 --> 00:13:46,420
+يبقى limit الدالة الأولى بـ L، limit الدالة الثانية
+
+106
+00:13:46,420 --> 00:13:51,600
+بـ M. هل في خلاف بينها وبين calculus A؟ لا خلاف. نقطة
+
+107
+00:13:51,600 --> 00:13:57,530
+ثانية: limit حاصل ضرب مقدار ثابت في دالة، يبقى المقدار
+
+108
+00:13:57,530 --> 00:14:02,930
+الثابت في نهاية الدالة. لأن limit الـ constant، قبل
+
+109
+00:14:02,930 --> 00:14:06,890
+قليل، كتبناها بالـ constant itself. يعني لو اعتبرت هذا
+
+110
+00:14:06,890 --> 00:14:11,550
+limit لحاصل ضرب دالتين، بيكون limit المقدار الثابت
+
+111
+00:14:11,550 --> 00:14:15,270
+بالمقدار الثابت نفسه، في limit الدالة اللي هو بالـ L.
+
+112
+00:14:15,270 --> 00:14:20,960
+يبقى حاصل الضرب K في L. وكذلك لو بدل الـ K كانت
+
+113
+00:14:20,960 --> 00:14:25,520
+function أخرى، ولتكن اللي هو الدالة F والدالة G.
+
+114
+00:14:25,520 --> 00:14:30,000
+limit حاصل ضرب two functions، يساوي limit الدالة
+
+115
+00:14:30,000 --> 00:14:35,380
+الأولى مضروب في limit الدالة الثانية، وL في M بالمثل.
+
+116
+00:14:35,380 --> 00:14:40,960
+لو كانت قسمة، يبقى limit للـ F of x وy على الـ G of x
+
+117
+00:14:40,960 --> 00:14:45,140
+وy، لما الـ x والـ y بتروح لـ x nought و y nought، يساوي limit
+
+118
+00:14:45,140 --> 00:14:49,760
+البسط على limit المقام. يعني بقدر أوزع limit لكل
+
+119
+00:14:49,760 --> 00:14:55,720
+من البسط والمقام. يبقى بناء عليه، يساوي L على M، بشرط
+
+120
+00:14:56,800 --> 00:15:00,760
+المقام ممنوع يساوي صفر. يعني ممنوع الـ M تساوي zero،
+
+121
+00:15:00,760 --> 00:15:05,400
+لأن الـ M لو كانت بـ zero، بصير الـ limit غير معرّفة.
+
+122
+00:15:05,400 --> 00:15:10,520
+does not exist، مش موجودة، تمام؟ طيب، النقطة
+
+123
+00:15:10,520 --> 00:15:15,520
+الرابعة، لما الـ expression مرفوعة to the power n، الـ
+
+124
+00:15:15,520 --> 00:15:20,860
+limit، قلت لكم معها VIP، تدخل على الجزء تربيع، تكعيب،
+
+125
+00:15:20,860 --> 00:15:25,600
+أس n، تدخل تحت الجذر، تدخل على الزاوية تبع النسبة
+
+126
+00:15:25,600 --> 00:15:30,160
+المثلثية، تدخل على العدد داخل الـ n، أو على الدالة
+
+127
+00:15:30,160 --> 00:15:33,620
+داخل الـ n، إلى الأعلى. يبقى معنى هذا الكلام أن الـ
+
+128
+00:15:33,620 --> 00:15:38,440
+limit دخلت داخل القوس، لكل أس n. limit الدالة اللي
+
+129
+00:15:38,440 --> 00:15:44,000
+داخل القوس هو L، بصير أس n، بحيث n عدد صحيح موجب.
+
+130
+00:15:44,000 --> 00:15:48,260
+اللي بعدها، limit الجذر، يبقى ما بتصير عصري، بتصير
+
+131
+00:15:48,260 --> 00:15:54,120
+كسرية. يبقى الـ limit بـ تعتبر واحد على n الجذر
+
+132
+00:15:54,120 --> 00:15:58,120
+النوني. يعني 1 إلى n. يبقى دخلت على الدالة اللي جوا،
+
+133
+00:15:58,120 --> 00:16:04,360
+فصلت اللي جوا بـ L، تحت الجذر النوني، يعني L أس 1
+
+134
+00:16:04,360 --> 00:16:10,180
+إلى n، و n عدد صحيح موجب. طب السؤال هو: طب افترض كان
+
+135
+00:16:10,180 --> 00:16:16,170
+سالباً، يعني أنت جبت للعدد الكسري، وجبت للعدد الموجب،
+
+136
+00:16:16,170 --> 00:16:20,190
+بس ما جبتش للعدد السالب الصحيح، صح ولا لا؟ أو للعدد
+
+137
+00:16:20,190 --> 00:16:25,710
+السالب الكسري. كيف نساوي؟ لو كان مثلاً f of x أس
+
+138
+00:16:25,710 --> 00:16:32,860
+سالب عشرة مثلاً؟ نقول واحد على x أس عشرة، و
+
+139
+00:16:32,860 --> 00:16:36,440
+بنأخذ limit الكسر الصحيح اللي فوق بواحد زي ما هو، و
+
+140
+00:16:36,440 --> 00:16:39,980
+limit اللي تحت بنأخذها، limit، بنطبق عليها ميم اللي
+
+141
+00:16:39,980 --> 00:16:43,560
+هي الحالة اللي عندنا دي، وبالمثل تماماً بالنسبة
+
+142
+00:16:43,560 --> 00:16:47,340
+للحالة اللي عندنا. يبقى ما عندنا مشكلة. يبقى الـ limit
+
+143
+00:16:47,340 --> 00:16:52,200
+الصحيح على الأس، سواء كان موجب، أو سالب، أو
+
+144
+00:16:52,200 --> 00:16:56,700
+كسري، كسري كمان موجب أو سالب، على الشكلتين. كلامنا هذا
+
+145
+00:16:56,700 --> 00:17:01,790
+ما له صحيح. طيب، شو اسمها هذه؟ آخر نقطة: sandwich
+
+146
+00:17:01,790 --> 00:17:05,610
+theorem أو squeezing theorem؟ هذه وهذه الاثنين
+
+147
+00:17:05,610 --> 00:17:08,370
+نفس المعنى. طب، إحنا اخذنا sandwich theorem في
+
+148
+00:17:08,370 --> 00:17:12,190
+calculus A، مظبوط؟ نفس المعلومة، إحنا اخذناها في
+
+149
+00:17:12,190 --> 00:17:17,290
+calculus A، هيجتنا في calculus C. إيش بتقول؟ بتقول:
+
+150
+00:17:17,290 --> 00:17:23,210
+لو كان عندك ثلاث دوال، مرتبة بهذا الشكل: الأولى أقل
+
+151
+00:17:23,210 --> 00:17:26,030
+من أو تساوي الثانية، والثانية أقل من أو تساوي
+
+152
+00:17:26,030 --> 00:17:32,550
+الثالثة. هذا الكلام صحيح لكل الـ x y اللي ما بتساويش x
+
+153
+00:17:32,550 --> 00:17:37,950
+nought و y nought، وهذا الكلام صحيح على disk course مركز
+
+154
+00:17:37,950 --> 00:17:41,570
+في نقطة x nought و y nought. يبقى لما آخذ الـ limit، لما
+
+155
+00:17:41,570 --> 00:17:46,410
+الـ x والـ y كلها بدأت تروح إلى x nought و y nought، في هذه
+
+156
+00:17:46,410 --> 00:17:51,430
+الحالة، إذا حدث أن limit الدالة الأولى هي limit
+
+157
+00:17:51,430 --> 00:17:55,510
+الدالة الثالثة، يساوي نفس الرقم، إذا الـ limit
+
+158
+00:17:55,510 --> 00:18:01,350
+اللي في النص بيكون نفس الرقم. يبقى limit اللي
+
+159
+00:18:01,350 --> 00:18:07,230
+في النص، f of x و y، لما الـ x والـ y والـ y والـ y والـ y والـ y والـ y
+
+160
+00:18:07,230 --> 00:18:07,810
+والـ y والـ y والـ y والـ y والـ y والـ y والـ y والـ y والـ y والـ y
+
+161
+00:18:07,810 --> 00:18:09,210
+والـ y والـ y والـ y والـ y والـ y والـ y والـ y والـ y والـ y والـ y
+
+162
+00:18:09,210 --> 00:18:09,450
+والـ y والـ y والـ y والـ y والـ y والـ y والـ y والـ y والـ y والـ y
+
+163
+00:18:09,450 --> 00:18:09,550
+والـ y والـ y والـ y والـ y والـ y والـ y والـ y والـ y والـ y والـ y
+
+164
+00:18:09,550 --> 00:18:09,570
+والـ y والـ y والـ y والـ y والـ y والـ y والـ y والـ y والـ y والـ y
+
+165
+00:18:09,570 --> 00:18:09,610
+والـ y والـ y والـ y والـ y والـ y والـ y والـ y والـ y والـ y والـ y
+
+166
+00:18:09,720 --> 00:18:15,040
+هل فعلياً اختلفت عن ما سبق دراستنا في كل calculus؟ هو
+
+167
+00:18:15,040 --> 00:18:21,780
+هو حرفياً نفسه. طب نشوف الآن تطبيق العملي لهذه المفاهيم.
+
+168
+00:18:21,780 --> 00:18:33,840
+نعطي مثال توضيحي على ذلك. يبقى example نحسبه.
+
+169
+00:18:33,84
+
+223
+00:24:27,040 --> 00:24:32,520
+سوى 4 شو بدي يحصل يبقى بتصير general 4 اللي هو ب 2
+
+224
+00:24:32,520 --> 00:24:38,900
+ناقص 2 ب 0 و 4 ناقص 4 بصير 0 على 0 طب ايش بدنا نسوي
+
+225
+00:24:38,900 --> 00:24:40,040
+في هذه الدالة
+
+226
+00:24:50,580 --> 00:24:54,760
+تحليل الـ bus كفارق
+
+227
+00:24:54,760 --> 00:25:03,740
+بين المربعين كما
+
+228
+00:25:03,740 --> 00:25:06,420
+اقتصدنا في السؤال السابق
+
+229
+00:25:10,330 --> 00:25:14,310
+الـ bus أو المقام بيروح بضرورة مين في المرافق
+
+230
+00:25:14,310 --> 00:25:18,830
+للمقدار اللي فيه الجذر يبقى هذا الكلام بيساوي
+
+231
+00:25:18,830 --> 00:25:26,480
+limit لما الـ X و الـ Y بدا تروح ل 2 و 2 بشرط إن
+
+232
+00:25:26,480 --> 00:25:32,880
+الـ X زائد الـ Y ما يساوي 4 لمن؟ للـ X زائد الـ Y
+
+233
+00:25:32,880 --> 00:25:39,940
+ناقص 4 على الجذر التربيعي للـ X زائد الـ Y ناقص
+
+234
+00:25:39,940 --> 00:25:46,220
+2 تمثل الجذر التربيعي للـ X زائد Y زائد 2
+
+235
+00:25:46,220 --> 00:25:53,760
+على الجذر التربيعي للـ X زائد Y زائد 2 هذا
+
+236
+00:25:53,760 --> 00:25:59,740
+الكلام بده يساوي limit لما الـ X و الـ Y بدها تروح لل
+
+237
+00:25:59,740 --> 00:26:04,920
+2 و 2 بشرط إن الـ X زائد الـ Y ما يساوي
+
+238
+00:26:04,920 --> 00:26:12,740
+الـ 4 طبعا بصير عامل مشترك الـ X زائد الـ Y ناقص الـ 4
+
+239
+00:26:12,740 --> 00:26:20,560
+في الجذر التربيعي للـ X زائد Y زائد 2 كل هذا
+
+240
+00:26:20,560 --> 00:26:26,440
+مقسوما على هل ليس هذا هو تحليل الفرق بين المربعين؟
+
+241
+00:26:26,440 --> 00:26:29,760
+يجب أن أعود إلى أصله يجب أن يكون مرفوع الكمية
+
+242
+00:26:29,760 --> 00:26:35,480
+الأولى الحمد لله الجذر مع السلامة يطير ويبقى لدي X
+
+243
+00:26:35,480 --> 00:26:41,140
+زائد Y هنا ناقص 4 المقدار هذا هو نفس المقدار
+
+244
+00:26:41,140 --> 00:26:47,860
+لأن هذا يتم اختصاره وبالتالي تقول المسألة إلى limit
+
+245
+00:26:47,860 --> 00:26:54,070
+عندما X و Y بعدها تذهب إلى الـ 2 و 2 بشرط أن X زائد
+
+246
+00:26:54,070 --> 00:27:03,900
+Y لا يساوي 4 لـ square root X زائد Y زائد 2 بنروح
+
+247
+00:27:03,900 --> 00:27:07,880
+لعوض تعويض مباشر يبقى هذا الكلام بيساوي الجذر
+
+248
+00:27:07,880 --> 00:27:13,560
+التربيعي للـ 2 زائد 2 زائد 2 و لو كله
+
+249
+00:27:13,560 --> 00:27:18,220
+على بعضه بيساوي جذر بيساوي 4 إذا نهاية هذا
+
+250
+00:27:18,220 --> 00:27:24,460
+المقدار بيساوي جذر بيساوي 4 يبقى عليها بناء
+
+251
+00:27:24,460 --> 00:27:30,060
+الـ limit لهذه الـ function أعطتني 4 وحلينا عن
+
+252
+00:27:30,060 --> 00:27:31,300
+طريق أحد الطرق
+
+253
+00:27:37,380 --> 00:27:45,260
+بين المربعين واختصرنا سوف نصل إلى نفس النتيجة.
+
+254
+00:27:45,260 --> 00:27:55,820
+السؤال الذي يليه سؤال خمسة يجري بالـ limit لما
+
+255
+00:27:55,820 --> 00:28:06,290
+الـ X و Y بدأت تروح لـ 0 0 لمن؟ ل 1 ناقص cos
+
+256
+00:28:06,290 --> 00:28:23,830
+sin XY مقسومة على XY  اتسأل كو
+
+257
+00:28:23,830 --> 00:28:28,870
+sin XY مقسومة
+
+258
+00:28:28,870 --> 00:28:33,240
+على XY يعني نضرب في ايش؟ مرافق البسط ويجب نضرب
+
+259
+00:28:33,240 --> 00:28:37,400
+باسمية مائة بالمائة أنا عندي 1 ناقص cos xy
+
+260
+00:28:37,400 --> 00:28:41,260
+يبقى بدها ضرب في 1 زائد cos xy واقسم على
+
+261
+00:28:41,260 --> 00:28:45,380
+1 زائد cos xy وروح اكمل عادي جدا يبقى هذا
+
+262
+00:28:45,380 --> 00:28:48,520
+ضرب في المرافق لكن السؤال اللي جابله ضربنا في
+
+263
+00:28:48,520 --> 00:28:52,280
+المرافق إذا دانيلي خاطر أفكر بطريقة ثانية الكلام
+
+264
+00:28:52,280 --> 00:28:56,180
+اللي قلته صح وبيحل السؤال مائة بالمائة ولا واحد
+
+265
+00:28:56,180 --> 00:29:00,840
+يَقدر يعترض عليكم تمام؟ لكن أنا بفكر في شغلة ثانية
+
+266
+00:29:00,840 --> 00:29:06,380
+أنا بعرف شوية حساب مثلثات وبالتالي بدأ أفكر بهذه
+
+267
+00:29:06,380 --> 00:29:11,620
+المسألة في حية حُطها في شكل آخر باستخدام قواعد
+
+268
+00:29:11,620 --> 00:29:18,620
+حساب المثلثات اللي دُرست في calculus A سؤال هذي
+
+269
+00:29:18,620 --> 00:29:26,500
+مين؟ هذي cos xy cos تربيع كلام اذا بص مضروبة في
+
+270
+00:29:26,500 --> 00:29:32,720
+2 لأن cos تربيع الـ X يساوي نصف في 1 ناقص cos 2X
+
+271
+00:29:32,720 --> 00:29:38,320
+إذا أنا لو رجعت إلى حساب المثلثات بقدر أقول limit
+
+272
+00:29:38,320 --> 00:29:45,380
+لما الـ X و الـ Y بدها تروح إلى 0 و 0 لـ
+
+273
+00:29:45,380 --> 00:29:54,200
+2 sin تربيع XY على 2 كل هذا الكلام على X
+
+274
+00:29:54,200 --> 00:29:56,360
+تمين في الـ Y
+
+275
+00:30:00,670 --> 00:30:06,690
+طيب تعال نشوف شو بنسويه بجى بقول لو 2 اللي
+
+276
+00:30:06,690 --> 00:30:11,450
+فوق شُجِلبت أو نُزلت تحت ايش بيصير؟ XY على 2
+
+277
+00:30:11,450 --> 00:30:17,790
+صحيح ولا لأ؟ يبقى هذه بدها تصير limit لما الـ X و
+
+278
+00:30:17,790 --> 00:30:26,230
+الـ Y بدها تروح لـ 0 0 لـ sin تربيع XY على 2 على
+
+279
+00:30:26,230 --> 00:30:27,870
+XY على 2
+
+280
+00:30:30,550 --> 00:30:36,370
+هذا مثل ايه؟ 100% صارت الزاوية لأنها XY على 2 وهذا
+
+281
+00:30:36,370 --> 00:30:46,670
+XY على 2 بس هذا ايه؟ XY مش XY ده قيمة كذا يبقى رتب
+
+282
+00:30:46,670 --> 00:30:51,410
+أمورك شوف ليش بصير فيها هذه لأن لو عوضنا تعويضا
+
+283
+00:30:51,410 --> 00:30:56,510
+مباشرا ايش بتبقى 0 على 0 صحيح ولا لأ؟ كويس
+
+284
+00:30:56,510 --> 00:30:59,530
+يبقى لو عملتها بشكل آخر
+
+285
+00:31:04,920 --> 00:31:13,440
+هتروح للـ 0 0 وروح نقول هذه عبارة عن sin xy
+
+286
+00:31:13,440 --> 00:31:21,500
+على 2 على xy على 2 في sin xy على 2
+
+287
+00:31:21,500 --> 00:31:27,440
+مظبوط طب اللي بتقوله كده هيطلع؟ 1 طب والثانية
+
+288
+00:31:27,440 --> 00:31:33,320
+0 يبقى هنا في قيمة في 0 يبقى النتيجة تساوي
+
+289
+00:31:33,320 --> 00:31:38,020
+0 الآن لو رحت ضربت في المرافق لازم تطلع نتيجة
+
+290
+00:31:38,020 --> 00:31:42,440
+0 لو ما طلعتش 0 معناته هذا حلنا غلط يبقى
+
+291
+00:31:42,440 --> 00:31:47,340
+good exercise لك تروح تحل المسألة بطريقة ضرب في
+
+292
+00:31:47,340 --> 00:31:53,950
+مرافق البسط وهو 1 زائد cos XY حلّيه في البيت
+
+293
+00:31:53,950 --> 00:32:01,190
+بالطريقة الثانية وهي الجواب معك سؤال السادس VI
+
+294
+00:32:01,190 --> 00:32:09,770
+بدي limit لما الـ X و الـ Y و الـ Z بدل المتغيرين بدي
+
+295
+00:32:09,770 --> 00:32:17,150
+أخليهم ثلاثة هنا لمن؟ لـ  tan<sup>-1</sup>  و بقى على 2
+
+296
+00:32:17,150 --> 00:32:32,430
+و 2 لمن؟ لـ tan<sup>-1</sup> xyz أقول
+
+297
+00:32:32,430 --> 00:32:36,590
+كويس أعود تعويض مباشرة ويلا نشوف شو اللي بده يطلع
+
+298
+00:32:36,590 --> 00:32:44,030
+يبقى هذه ويساوي tan<sup>-1</sup> لمن؟ للـ X اللي يساوي
+
+299
+00:32:44,030 --> 00:32:51,840
+ربعها مضروبة في π/2 في 2  الـ 2 مع الـ 2
+
+300
+00:32:51,840 --> 00:32:58,460
+بتروح بيصير tan<sup>-1</sup> π/2 بس π/
+
+301
+00:32:58,460 --> 00:33:01,900
+4 طبعا مش π/2 π/4 و
+
+302
+00:33:01,900 --> 00:33:03,300
+بيشارت سالم
+
+303
+00:33:19,030 --> 00:33:25,090
+لمن؟ لـ π/4 ويساوي ناقص كم؟ فالـ tan<sup>-1</sup>
+
+304
+00:33:25,090 --> 00:33:31,850
+π/4؟ كم؟ كم يمثل الـ 45؟ 1
+
+305
+00:33:31,850 --> 00:33:35,570
+إذا tan<sup>-1</sup> π/4 يبقى يساوي 1 يبقى
+
+306
+00:33:35,570 --> 00:33:38,870
+limit تساوي كم؟ سالب 1
+
+307
+00:33:41,270 --> 00:33:44,250
+إذا اللي قبلها زي ما أنتم شايفين المعلومات اللي
+
+308
+00:33:44,250 --> 00:33:47,530
+درسناها على functions of two variables في حالة الـ
+
+309
+00:33:47,530 --> 00:33:51,690
+limit صحيحة لـ functions of three variables أو
+
+310
+00:33:51,690 --> 00:33:56,470
+variables أو الـ n variables مهما كان شكل الـ main
+
+311
+00:33:56,470 --> 00:34:07,130
+شكل المتغيرات اللي عندنا tan
+
+312
+00:34:07,130 --> 00:34:17,120
+<sup>-1</sup>π/4 تقع
+
+313
+00:34:17,120 --> 00:34:20,360
+في الـ domain تبعها لأن الـ domain لـ tan<sup>-1</sup> يساوي
+
+314
+00:34:20,360 --> 00:34:23,360
+من −∞ إلى ∞  هي tan<sup>-1</sup> 1
+
+315
+00:34:26,020 --> 00:34:30,860
+صحيح بنات هذه قيمة سالب tan<sup>-1</sup> π/4
+
+316
+00:34:30,860 --> 00:34:35,160
+كمية بدك تطلع قيمة عددية على الجهاز ما لكش  بلاش
+
+317
+00:34:35,160 --> 00:34:39,740
+خليها زي ما هي إذا بدناها المهم نوصل إلى نتيجة
+
+318
+00:34:39,740 --> 00:34:48,020
+كويس نجي الآن لسؤال رقم 2 سؤال رقم 2 على
+
+319
+00:34:48,020 --> 00:34:56,720
+نفس الموضوع بقول if إذا كان 2 |XY|
+
+320
+00:34:56,720 --> 00:35:06,360
+−X²−Y²/6  أقل من 4 − 4
+
+321
+00:35:06,360 --> 00:35:13,760
+cos√|XY|  أقل من 2|XY|
+
+322
+00:35:13,760 --> 00:35:17,900
+أقل من 2|XY|
+
+323
+00:35:34,400 --> 00:35:39,840
+للـ 4 − 4 cos للجذر التربيعي لـ
+
+324
+00:35:39,840 --> 00:35:40,920
+|XY|
+
+325
+00:36:16,650 --> 00:36:23,610
+السؤال مرة ثانية بيقول لو عندك ثلاث دوال، الدالة
+
+326
+00:36:23,610 --> 00:36:27,490
+الأولى أقل من الدالة الثانية أقل من الدالة
+
+327
+00:36:27,490 --> 00:36:32,070
+الثالثة في الـ limit للدالة اللي في الوسط مقسومة
+
+328
+00:36:32,070 --> 00:36:37,290
+على |XY| للأولى من حد ما شوف
+
+329
+00:36:37,290 --> 00:36:41,660
+السؤال بهذا الشكل شوفوا كم سنة وشتيرة لأن هذه
+
+330
+00:36:41,660 --> 00:36:46,260
+كأنها مقارنة بين الـ limits لمن؟ لثلاث دوال إذا
+
+331
+00:36:46,260 --> 00:36:51,660
+أنا بدأت أروح أستخدم خواصي في حل هذه المسألة
+
+332
+00:36:51,660 --> 00:36:56,660
+كون فيها دي |XY| إذا احتمال الـ XY الـ
+
+333
+00:36:56,660 --> 00:37:02,610
+absolute  لها ليطلع منها يكون الرقم موجب يكون
+
+334
+00:37:02,610 --> 00:37:09,390
+الرقم
+
+335
+00:37:09,390 --> 00:37:11,470
+موجب يكون الرقم موجب يكون الرقم موجب يكون الرقم
+
+336
+00:37:11,470 --> 00:37:12,810
+موجب يكون الرقم موجب يكون الرقم موجب يكون الرقم
+
+337
+00:37:12,810 --> 00:37:13,550
+موجب يكون الرقم موجب يكون الرقم موجب يكون الرقم
+
+338
+00:37:13,550 --> 00:37:13,590
+موجب يكون الرقم موجب يكون الرقم موجب يكون الرقم
+
+339
+00:37:13,590 --> 00:37:13,690
+موجب يكون الرقم موجب يكون الرقم موجب يكون الرقم
+
+340
+00:37:13,690 --> 00:37:19,090
+موجب يكون الرقم موجب يكون الرقم موجب يكون الرقم
+
+341
+00:37:19,090 --> 00:37:28,870
+موجب يكون الرقم موجب يكون الرقم موجب إذا لو كانت
+
+342
+00:37:28,870 --> 00:37:33,870
+الـ x,y قيمة موجبة ايش اللي بده يحصل في هذه
+
+343
+00:37:33,870 --> 00:37:40,110
+الحالة؟ يبقى بدهاجة يقول بده يصير الـ absolute
+
+344
+00:37:40,110 --> 00:37:46,690
+value  لـ x,y دائما وأبدا موجبة صحيح ولا لا؟ يبقى
+
+345
+00:37:46,690 --> 00:37:54,930
+بصير المسألة سهلة يبقى بصير عندنا 2 2 x
+
+346
+00:37:54,930 --> 00:37:55,630
+,y
+
+347
+00:38:17,940 --> 00:38:24,160
+إذا ما دام الـ XY موجبة بقدر أقسم عليها كلها
+
+348
+00:38:26,340 --> 00:38:27,480
+يبقى الـ
+
+349
+00:38:30,950 --> 00:38:38,030
+−X²/6Y  أقل من 4 − 4 cos للجذر التربيعي
+
+350
+00:38:38,030 --> 00:38:42,110
+لتربيعيها يعني لأن هذه حطيت الـ absolute مدى موجب
+
+351
+00:38:42,110 --> 00:38:46,110
+والله ما حطيتهاش سيئة يعني لو شيلتها والله حد إنها
+
+352
+00:38:46,110 --> 00:38:54,010
+موجبة ما عنديش مشكلة فيها على مين؟ على الـ XY مقسوما
+
+353
+00:38:54,010 --> 00:39:03,900
+على XY يبقى هنا أقل من 2 أقل من 2 طيب خديني الـ
+
+354
+00:39:03,900 --> 00:39:07,880
+limit لثلاثة أطراف ناخد الـ limit لثلاثة أطراف
+
+355
+00:39:07,880 --> 00:39:12,800
+ممكنش لما الـ x و y بده يروح للـ 0 0 يبقى بده
+
+356
+00:39:12,800 --> 00:39:18,140
+يصير عندي هنا limit لما الـ x و الـ y راح للـ 0
+
+357
+00:39:18,140 --> 00:39:25,780
+0 لـ 2 − X²−Y²/6XY
+
+358
+00:39:25,780 --> 00:39:28,540
+طبعا لو اختصرنا هنا ماذا يصير عندي هنا
+
+359
+00:39:34,820 --> 00:39:42,560
+أقل من أو يساوي الـ limit لما X و Y بدها تروح للـ 0 0
+
+360
+00:39:42,560 --> 00:39:50,920
+لـ 4 − 4 cos√|XY|/XY
+
+361
+00:39:50,920 --> 00:39:58,120
+أقل من أو يساوي limit لما الـ X و Y بده يروح للـ 0 0
+
+362
+00:39:58,120 --> 00:40:03,520
+لمن؟ للـ 2 طب ما لما الـ X و الـ Y بتروح لـ 0،0
+
+363
+00:40:03,520 --> 00:40:09,240
+هذا الـ term ممكن تهمليه يا بنات يبقى صار الـ 2 بدأ
+
+364
+00:40:09,240 --> 00:40:19,450
+أقل من limit لما الـ X و الـ Y بدي أروح إلى 0 0 لـ 4 − 4
+
+365
+00:40:19,450 --> 00:40:26,130
+cos√|XY|/XY لو حطيت الـ
+
+366
+00:40:26,130 --> 00:40:31,110
+absolute  في مشكلة لأ هي بالموجب بس مشان شكل اللي
+
+367
+00:40:31,110 --> 00:40:35,110
+هو المطلوب ليس إلا أقل من 2
+
+368
+00:40:39,260 --> 00:40:49,270
+يبقى باجي بقوله باي ساندوتش ثيوريم بصير الـ limit لـ
+
+369
+00:40:49,270 --> 00:40:53,710
+الـ 4 − 4 cos للجذر التربيعي لـ
+
+370
+00:40:53,710 --> 00:40:57,930
+|XY|/|XY| لما الـ X و Y بدها تروح لـ 0 0 بده يساوي 2
+
+371
+00:40:57,930 --> 00:41:03,690
+نقل هذا لو كانت X و Y أكبر من من الـ 0 بدالي
+
+372
+00:41:03,690 --> 00:41:10,610
+أخذ F
+
+373
+00:41:10,610 --> 00:41:11,930
+من الـ 0 يعني حاصل ضربه ما كان كمية سالبة و
+
+374
+00:41:15,750 --> 00:41:21,610
+يحدث هذا الكلام لو كانت X بالسالب و Y بالموجب أو
+
+375
+00:41:21,610 --> 00:41:26,610
+العكس X بالموجب و Y بالسالب يبقى المسألة تبعتي هذا
+
+376
+00:41:26,610 --> 00:41:31,970
+بقدر أكتبها على الشكل التالي يبقى 2 − X
+
+377
+00:41:31,970 --> 00:41:39,210
+تربيع
+
+378
+00:41:39,210 --> 00:41:39,870
+Y تربيع/6
+
+379
+00:41:46,220 --> 00:41:52,720
+أقل من 4 − 4 cos للجذر التربيعي لـ
+
+380
+00:41:52,720 --> 00:41:59,000
+|XY| كله مقسوما على |XY|
+
+381
+00:41:59,000 --> 00:42:07,080
+أقل من 2 بالأقل لما تبقى هذا
+
+382
+00:42:07,080 --> 00:42:12,240
+سالب بقدر أتخلص من هذا الـ absolute وبالتالي بيصير
+
+383
+00:42:12,240 --> 00:42:24,080
+المسألة 2 − X²−Y²/6XY يعني شيلت
+
+384
+00:42:24,080 --> 00:42:28,480
+الـ absolute و حطيت إشارة سالب مع السالب ما يحصل
+
+385
+00:42:28,480 --> 00:42:39,430
+بالموجب أقل من 4 − 4 cos للجذر التربيعي لـ
+
+386
+00:42:39,430 --> 00:42:49,190
+XY/|XY| أقل من من الـ 2 بعد ذلك ناخد
+
+387
+00:42:49,190 --> 00:42:52,290
+الـ
+
+388
+00:43:09,820 --> 00:43:16,940
+خد الـ limit للثلاثة أطراف بيصير limit للـ 2
+
+389
+00:43:16,940 --> 00:43:25,520
+زائد لو اختصرنا هذه بدها تصير XY/6 لما X و
+
+390
+00:43:25,520 --> 00:43:33,220
+Y بدها تروح لـ 0 و 0 أقل من limit لما الـ X و
+
+391
+00:43:33,220 --> 00:43:41,510
+الـ Y بدها تروح لـ 0 0 لـ 4 − 4 للجذر
+
+392
+00:43:41,510 --> 00:43:47,810
+التربيعي cos للجذر التربيعي cos للجذر
+
+393
+00:43:47,810 --> 00:43:52,330
+التربيعي لـ |XY|/|XY|
+
+394
+00:43:5
+
+445
+00:51:15,340 --> 00:51:18,920
+العشري يعطي نتيجة مختلفة because it does not exist على
+
+446
+00:51:18,920 --> 00:51:25,020
+طول الخط does not exist بدل كل جميع المسارات التي تمر بهذه
+
+447
+00:51:25,020 --> 00:51:32,340
+النقطة. بناء عليه، واضحة الصورة التي عندنا هذه مش
+
+448
+00:51:32,340 --> 00:51:35,500
+تأخذين مساراً لا يمر بالنقطة و تروحين تحجبين وتقولين that
+
+449
+00:51:35,500 --> 00:51:39,020
+it does not exist ولا  يوجد المسار الذي تأخذينه يجب أن
+
+450
+00:51:39,020 --> 00:51:44,800
+تتأكدين فعلاً أنه يمر بهذه النقطة. لو أخذتي مساراً آخر لا
+
+451
+00:51:44,800 --> 00:51:50,380
+يمر، سيصير كلامك غلط. نعطي أمثلة توضيحية على ذلك.
+
+452
+00:52:01,580 --> 00:52:12,540
+التّقْدِيرات التّالية تُظهر أن التّقْدِيرات
+
+453
+00:52:12,540 --> 00:52:16,660
+التالية ليست
+
+454
+00:52:16,660 --> 00:52:23,260
+موجودة، ليست
+
+455
+00:52:23,260 --> 00:52:25,980
+موجودة كـ
+
+456
+00:52:39,960 --> 00:52:49,580
+Limit لمن؟ لـ X تربيع ناقص Y على X ناقص Y طبعاً
+
+457
+00:52:49,580 --> 00:52:58,940
+لما X و Y يذهبان إلى  Zero، أنا عندي
+
+458
+00:52:58,940 --> 00:53:04,160
+function و أريد حساب  Limit لهذه function عند
+
+459
+00:53:04,160 --> 00:53:10,670
+نقطة الأصل. أُعيد وأقول:  شو ممكن نقطة الأصل؟ محور X،
+
+460
+00:53:10,670 --> 00:53:18,930
+محور Y، Y تساوي X تربيع، Y تساوي X تكعيب، Y تساوي
+
+461
+00:53:18,930 --> 00:53:24,910
+الجذر التكعيبي لـ X،  Y تساوي X تربيع زائد واحد
+
+462
+00:53:24,910 --> 00:53:30,830
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+463
+00:53:30,830 --> 00:53:30,910
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+464
+00:53:30,910 --> 00:53:31,530
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+465
+00:53:31,530 --> 00:53:33,310
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ ل
+
+466
+00:53:36,220 --> 00:53:40,100
+إذا جئتِ بمسارات لا تمر بهذه النقطة، إذا قلتِ هذا
+
+467
+00:53:40,100 --> 00:53:44,640
+غلط، يجب أن المسارات التي أريد أن آخذها تتأكد فعلاً أنها تمر
+
+468
+00:53:44,640 --> 00:53:49,500
+بهذه النقطة حتى يكون كلامنا صحيحاً. طيب خليني
+
+469
+00:53:49,500 --> 00:53:54,120
+أختار مسارات، ما هو شوفوا ماذا ستقولون لو أخذنا مثلاً على
+
+470
+00:53:54,120 --> 00:54:03,030
+سبيل المثال عبر محور X، يبقى أبدأ بقول هذا path
+
+471
+00:54:03,030 --> 00:54:09,610
+آخذ للمسار Y تساوي صفر، من هو Y تساوي صفر؟ الذي هو
+
+472
+00:54:09,610 --> 00:54:15,210
+الـ X axis، الذي هو الـ X axis، يبقى يصبح هذا يا بنات
+
+473
+00:54:15,210 --> 00:54:24,210
+limit لما الـ X والـ Y يذهبان إلى؟ إلى الـ 0 والـ
+
+474
+00:54:24,210 --> 00:54:30,370
+0 والـ 0، لمن؟ أريد أن أشيل الـ Y وأضع مكانها 0،
+
+475
+00:54:30,370 --> 00:54:36,170
+ماذا يحصل؟ عندك X تربيع على X، يعني limit لما الـ X
+
+476
+00:54:36,170 --> 00:54:47,090
+والـ Y ذهبا إلى 0 والـ 0 فقط لـ X، كم يصبح عندي؟ 0 طيب
+
+477
+00:54:47,520 --> 00:54:56,600
+الآن أبدأ بقول take the path، خذي المسار مثلاً X
+
+478
+00:54:56,600 --> 00:55:07,580
+تساوي صفر، الـ Y axis، يعني الـ Y axis، ماذا سيحدث؟
+
+479
+00:55:07,580 --> 00:55:17,760
+limit لما الـ X والـ Y يذهبان إلى 0,0، لمن؟ لـ X
+
+480
+00:55:17,760 --> 00:55:24,160
+تربيع ناقص 0، ما طالع عندي؟  ناقص
+
+481
+00:55:24,160 --> 00:55:31,520
+Y على ناقص Y،  كذا يطلع الـ limit واحد صحيح، يبقى هنا
+
+482
+00:55:31,520 --> 00:55:37,480
+واحد صحيح، ماذا ترون في النتيجتين؟ النتيجتين
+
+483
+00:55:37,480 --> 00:55:44,120
+مختلفتان، يبقى هنا أذهب وأقول سواءً الـ limit لـ X
+
+484
+00:55:44,120 --> 00:55:52,270
+تربيع ناقص Y على X ناقص Y، لما الـ X والـ Y يذهبان
+
+485
+00:55:52,270 --> 00:55:59,290
+إلى 0 و 0، لا يوجد
+
+486
+00:55:59,290 --> 00:56:03,330
+لأن
+
+487
+00:56:03,330 --> 00:56:08,790
+الـ 0 لا يساوي الـ 1
+
+488
+00:56:36,950 --> 00:56:42,450
+لنعطي مثالاً للبنات، نبرهن
+
+489
+00:56:42,450 --> 00:56:54,170
+بهِ أن الـ limit لما الـ X والـ Y يذهبان من 0،0، لما الـ X
+
+490
+00:56:54,170 --> 00:56:58,390
+والـ Y تقع على X تربيع
+
+491
+00:57:11,560 --> 00:57:15,020
+طبعاً أنا أنظر، المؤشر يُعطي لي 0 على 0، يقول هذا
+
+492
+00:57:15,020 --> 00:57:20,900
+اختاري مساراً فعلاً يمر بنقطة الأصل، مثلاً لو قلتِ Y
+
+493
+00:57:20,900 --> 00:57:24,920
+تساوي X، خط
+
+494
+00:57:24,920 --> 00:57:29,740
+مستقيم يُقسم الذي هو الزاوية بين محور X ومحور Y،
+
+495
+00:57:29,740 --> 00:57:34,460
+الربع الأول، يُقسمه ويَمرُ بنقطة الأصل، يبقى آتي
+
+496
+00:57:34,460 --> 00:57:36,560
+بأقول مثلاً P
+
+497
+00:57:46,740 --> 00:57:53,140
+يجب أن أشيل
+
+498
+00:57:53,140 --> 00:57:57,680
+كل Y وأضع مكانها X أو أشيل كل X وأضع مكانها Y
+
+499
+00:57:57,680 --> 00:58:02,880
+سواءً كانت هذه أو تلك، الاثنان are the same، يجب أن
+
+500
+00:58:02,880 --> 00:58:03,640
+أشيل كل Y وأضع مكانها X أو أشيل كل X وأضع مكانها
+
+501
+00:58:10,730 --> 00:58:17,570
+يبقى يا بنات صارت هذه كأنها ماذا؟ لـ limit لما الـ X والـ Y
+
+502
+00:58:17,570 --> 00:58:25,390
+تذهبان إلى 0،0، لـ X أس 4 على X تربيع، عامل مشترك
+
+503
+00:58:25,390 --> 00:58:28,890
+يظل X تربيع
+
+504
+00:58:36,510 --> 00:58:43,790
+تبدأ تذهب إلى 0،0، لـ X تربيع على 1 زائد X أس
+
+505
+00:58:43,790 --> 00:58:50,590
+4، نشيل كل X ونحط مكانها 0، يصبح 0 على
+
+506
+00:58:50,590 --> 00:58:59,190
+واحد زائد 0، ويساوي 0، نجرب أي مسار آخر بحيث
+
+507
+00:58:59,190 --> 00:59:02,390
+المسار يمر بنقطة الأصل
+
+508
+00:59:06,170 --> 00:59:13,830
+take the path، مثلاً على سبيل المثال Y يساوي الجذر
+
+509
+00:59:13,830 --> 00:59:20,650
+التكعيبي لـ X، يعني X أس ثلث، هل تعرفين هذه الملعونة أم
+
+510
+00:59:20,650 --> 00:59:29,850
+لا؟ تعرفونها أم لا؟ نقول plus A، هذا محور X، هذا Y،
+
+511
+00:59:29,850 --> 00:59:36,280
+هذا أصل الملعونة، يأتي كـ... يأتي بالشكل هذا، يبقى هذا
+
+512
+00:59:36,280 --> 00:59:42,980
+Y تساوي X أس ثلث، يبقى فعلاً يمر بنقطة الأصل التي
+
+513
+00:59:42,980 --> 00:59:46,940
+عندنا، يبقى انظروا ماذا سيحدث، سيحدث limit
+
+514
+00:59:46,940 --> 00:59:54,260
+لما الـ X والـ Y يذهبان إلى 0،0، لمن؟ للدالة التي
+
+515
+00:59:54,260 --> 00:59:56,500
+عندنا هذه، يبقى هذه X
+
+516
+01:00:13,210 --> 01:00:19,430
+والـ Y تذهب إلى الـ 0 والـ 0، هذا برنامج
+
+517
+01:00:19,430 --> 01:00:25,790
+باعتباره X أس ثلث،  لكل تكعيب بـ X أس واحد، وعند X
+
+518
+01:00:25,790 --> 01:00:32,530
+يجب أن يكون X تربيع فقط، لغاية X تربيع، وهذه X أس
+
+519
+01:00:32,530 --> 01:00:39,490
+ثلث أس ستة، يبقى أس مركب بسيط جداً X تربيع، يبقى
+
+520
+01:00:39,490 --> 01:00:45,810
+صارت هذه الـ limit لما الـ X والـ Y تذهبان إلى
+
+521
+01:00:45,810 --> 01:00:51,870
+الـ 0،0، للـ X تربيع على 2 X تربيع، يبقى الـ Limit
+
+522
+01:00:51,870 --> 01:00:56,350
+هذه تساوي كم؟ نصف، باختصار X تربيع مع X
+
+523
+01:00:56,350 --> 01:01:02,010
+تربيع، تعطي نصف، تطلع هنا نصف وهنا 0، يبقى الـ
+
+524
+01:01:02,010 --> 01:01:04,770
+Limit يضمن Exact، يبقى الـ Limit
+
+525
+01:01:20,700 --> 01:01:31,480
+does not exist because  الذي هو الـ 0 لا يساوي
+
+526
+01:01:31,480 --> 01:01:36,660
+نصف، ولا يشبه تماماً كما كنا في الـ calculation
+
+527
+01:01:36,660 --> 01:01:40,160
+نأخذ الـ limit من اليمين ومن الشمال، إذا اختلفت
+
+528
+01:01:40,160 --> 01:01:43,920
+اليمين عن الشمال، يكون الـ limit does not exist، إذا
+
+529
+01:01:43,920 --> 01:01:48,720
+هنا لدينا مسارين مختلفين، مشينا مع الأول ومشينا مع
+
+530
+01:01:48,720 --> 01:01:52,300
+الثاني، وأخذنا نتيجتين different limits، نتيجتين
+
+531
+01:01:52,300 --> 01:01:55,740
+مختلفتين، إذا أذهب وأقول أن الـ limit الذي عندي هذا
+
+532
+01:01:55,740 --> 01:01:58,960
+لا يجب أن exists
+
+533
+01:02:01,490 --> 01:02:09,130
+كيف؟ بمسارين، ليس سبعة، بمسارين فقط، كافيين، إن شاء
+
+534
+01:02:09,130 --> 01:02:13,890
+الله، يكون فيه خمسة، سمعتِ ماذا قلنا لكم؟ قلنا لكم
+
+535
+01:02:13,890 --> 01:02:18,850
+افترضي أن عندي عشرة مسارات، ولما شرحتُ الجزء النظري
+
+536
+01:02:18,850 --> 01:02:25,250
+قبل الأمثلة، وجئتُ بتسعة مسارات أعطتني نفس القيمة
+
+537
+01:02:25,250 --> 01:02:29,490
+لكن المسار العاشر لم يُعطِني نفس القيمة، إذا الـ limit
+
+538
+01:02:29,490 --> 01:02:37,160
+ماذا قلنا؟ does not exist يعني
+
+539
+01:02:37,160 --> 01:02:40,260
+عندي خمسة وثلاثون طالباً، الذي يجي لي ثمانية عشر على
+
+540
+01:02:40,260 --> 01:02:58,320
+النصف، عزيزي.
+
+541
+01:03:02,040 --> 01:03:06,880
+هذا الكلام الذي رأيته قبل قليل، كله موجود في جزء
+
+542
+01:03:06,880 --> 01:03:09,440
+النظرية
+
+543
+01:03:09,440 --> 01:03:11,500
+ 
+
+544
+01:03:11,500 --> 01:03:14,680
+ 
+
+545
+01:03:14,680 --> 01:03:14,980
+ 
+
+546
+01:03:14,980 --> 01:03:16,240
+ 
+
+547
+01:03:16,240 --> 01:03:17,440
+ 
+
+548
+01:03:17,440 --> 01:03:24,520
+للتابع، الآن آتي بقول لو جئنا نعمل مباشرة كما
+
+549
+01:03:24,520 --> 01:03:28,860
+كنا نعمل في كل الأمثلة السابقة وطلع الذي هو 0
+
+550
+01:03:28,860 --> 01:03:33,080
+على 0، مالها نهاية، مالها نهاية، 0 في مالها نهاية
+
+551
+01:03:33,080 --> 01:03:38,120
+يعني شغلات does not exist، و لست قادرة أن أتحرك
+
+552
+01:03:38,120 --> 01:03:41,760
+أو أتحرك مع المسألة الموجودة، ماذا نفعل في مثل هذه
+
+553
+01:03:41,760 --> 01:03:46,400
+الحالة؟ قال لي بسيطة، انقل إلى polar coordinates
+
+554
+01:03:47,040 --> 01:03:53,440
+حولْ مثلتك إلى إحداثيات قطبية، تصبح المسألة
+
+555
+01:03:53,440 --> 01:03:59,440
+سهلة، ونحل المسألة بكل سهولة طبعاً، طيب كيف تتحول
+
+556
+01:03:59,440 --> 01:04:03,420
+إلى polar coordinates؟ هذا ما سنضعه في صيغة الـ
+
+557
+01:04:03,420 --> 01:04:08,080
+remark التالية، نبدأ بالكثير من remarks
+
+558
+01:04:18,840 --> 01:04:31,580
+we cannot find، إذا لم نستطع إيجاد الـ limit للـ f of
+
+559
+01:04:31,580 --> 01:04:39,660
+x و y لما الـ x والـ y يذهبان إلى x node و y
+
+560
+01:04:39,660 --> 01:04:45,040
+node، ماذا نفعل فيها الآن؟ way to change
+
+561
+01:04:49,200 --> 01:05:00,440
+will change to the polar coordinates، يجب أن ننتقل
+
+562
+01:05:00,440 --> 01:05:07,500
+إلى الإحداثيات القطبية، من الإحداثيات القطبية، الـ X
+
+563
+01:05:07,500 --> 01:05:15,280
+يساوي R Cos θ والـ y يساوي r Sin θ وعندك الـ r
+
+564
+01:05:15,280 --> 01:05:23,000
+يساوي الجذر التربيعي لـ X تربيع زائد Y تربيع، ونَقِضْ
+
+565
+01:05:23,000 --> 01:05:27,940
+أنّ الـ
+
+566
+01:05:27,940 --> 01:05:35,180
+r تذهب إلى الصفر if and only if الـ x والـ y تذهبان
+
+567
+01:05:35,180 --> 01:05:36,460
+إلى الصفر
+
+568
+01:05:43,520 --> 01:05:47,200
+دعيني أوضح الكلام الذي نقوله بالرسم ثم
+
+569
+01:05:47,200 --> 01:05:52,760
+نبدأ نعمل به، ابق لو جئتِ أخذتِ محاور بهذا الشكل
+
+570
+01:05:52,760 --> 01:06:00,400
+يا بنات، وقلت هذا محور X وهذا محور Y وهذه نقطة
+
+571
+01:06:00,400 --> 01:06:08,420
+الأصل، جئنا ورسمنا دائرة مركزها نقطة الأصل ونصف
+
+572
+01:06:08,420 --> 01:06:16,090
+قطرها يساوي R، على سبيل المثال، يبقى هذا لو R نصف
+
+573
+01:06:16,090 --> 01:06:24,550
+القطر تبع هذه الدائرة، هذه النقطة عند محيط الدائرة
+
+574
+01:06:24,550 --> 01:06:30,830
+أريد أن أسميها X وY في الـ Cartesian coordinates، لو
+
+575
+01:06:30,830 --> 01:06:35,910
+كانت الزاوية هذه، التي هي الزاوية θ، ونزلت من هنا
+
+576
+01:06:35,910 --> 01:06:43,280
+عمودياً، يبقى هذا X وهذا Y، يبقى X الذي عندي يساوي R
+
+577
+01:06:43,280 --> 01:06:49,260
+Cos θ والـ Y الذي عندي هذا بـ R Sin θ، لأن الزاوية
+
+578
+01:06:49,260 --> 01:06:56,460
+هذه زاوية قائمة، طيب لو ربعنا وجمعنا، أليس يصبح عندي X
+
+579
+01:06:56,460 --> 01:07:00,420
+تربيع زائد Y تربيع تساوي R تربيع Cos تربيع زائد R
+
+580
+01:07:00,420 --> 01:07:03,540
+تربيع Sin تربيع، آخذ R تربيع وأعمل Cos تربيع زائد Sin تربيع
+
+581
+01:07:03,540 --> 01:07:07,300
+من هذا واحد، يبقى يصبح X
+
+582
+01:07:07,300 --> 01:07:12,140
+تربيع زائد Y تربيع تساوي R تربيع، إذا أريد R أقول
+
+583
+01:07:12,140 --> 01:07:16,100
+square root لـ X تربيع زائد Y تربيع، إذا عرفنا
+
+584
+01:07:16,100 --> 01:07:20,940
+العلاقة الأخيرة، من أين جاءت؟ طيب لو يا بنات الـ X
+
+585
+01:07:20,940 --> 01:07:28,970
+ذهبت إلى الصفر، وY نزلت للصفر، يعني لو هنا وصلت هنا
+
+586
+01:07:28,970 --> 01:07:35,060
+هي بـ X صغيرة وY صغيرة، R تزيد أم تنقص أصلاً؟ يعني
+
+587
+01:07:35,060 --> 01:07:41,660
+افترض هنا وصلت لهنا، كيف يعني؟ أشعر النقطة هكذا أصبحت
+
+588
+01:07:41,660 --> 01:07:45,740
+الـ Y صغيرة والـ X أكبر قليلاً مثلاً، على سبيل المثال
+
+589
+01:07:45,740 --> 01:07:50,340
+يبقى إذا الـ X ذهبت إلى 0 والـ Y ذهبت إلى 0
+
+590
+01:07:50,340 --> 01:07:54,740
+فتذهب إلى 0 طبيعياً، يبقى الـ R تذهب إلى 0 لو كان
+
+591
+01:07:54,740 --> 01:07:56,920
+الـ X والـ Y ذهبا إلى 0
+
+592
+01:08:06,260 --> 01:08:14,600
+الصورة، نعطي أمثلة توضيحية على هذا الكلام for
+
+593
+01:08:14,600 --> 01:08:22,280
+example find
+
+594
+01:08:22,280 --> 01:08:23,460
+the following limits
+
+595
+01:08:34,720 --> 01:08:40,100
+فإذا كانت موجودة
+
+596
+01:08:40,100 --> 01:08:45,780
+إذا كانت
+
+597
+01:08:45,780 --> 01:08:50,560
+موجودة، إذا كانت موجودة
+
+598
+01:09:17,050 --> 01:09:21,670
+طبعاً أول ما يُخطر ببالي أقول أريد أن أحلل الزاوية
+
+599
+01:09:21,670 --> 01:09:25,710
+التي لدينا كفرق بين مكعبين، أفترض حالة أن هناك
+
+600
+01:09:25,710 --> 01:09:30,490
+اختصارات بينهما وبين المقام، هل يمكن تحليل
+
+601
+01:09:30,490 --> 01:09:35,410
+المقام؟ لا لا لا لا لا لا لا لا لا لا لا لا لا لا
+
+602
+01:09:35,410 --> 01:09:37,350
+لا لا لا لا لا لا لا لا لا لا لا لا لا لا لا لا
+
+603
+01:09:37,350 --> 01:09:43,310
+لا لا لا لا لا لا لا
+
+604
+01:09:43,700 --> 01:09:49,240
+يصبح عندي cosine كم؟ 0 على 0، أليس
+
+605
+01:09:49,240 --> 01:09:52,740
+تعرفون؟ لا أعرف، ما هو 0 على 0، كمية غير معينة
+
+606
+01:09:52,950 --> 01:09:57,110
+إذا كـكمية غير معينة، أيضاً لا أعرف، طيب كيف أريد
+
+607
+01:09:57,110 --> 01:10:01,590
+أن أفعل التحليل؟ لست قادرة على الاختصار وهكذا ليست ثابتة أبداً
+
+608
+01:10:01,590 --> 01:10:06,250
+بالمرة؟ صحيح؟ يبقى لا إمكانية في هذه الحالة
+
+609
+01:10:06,250 --> 01:10:10,890
+بالطرق التي سبقت دراستها في الـ Cartesian Curve
+
+610
+01:10:10,890 --> 01:10:15,490
+لنحل هذه المسألة، أحد الأمثلة التي تخطر ببالك في
+
+611
+01:10:15,490 --> 01:10:19,230
+التمرين، تمام، طيب كيف نفعل في هذه الحالة؟ إذا الـ
+
+612
+01:10:19,230 --> 01:10:23,790
+automatic، ليس لدي إلا أن أتحول إلى polar coordinates
+
+613
+01:10:23,790 --> 01:10:26,430
+إذا لما أتحول إلى polar
+
+614
+01:10:34,270 --> 01:10:41,610
+R تكعيب Cos تكعيب θ ناقص R تكعيب Sin تكعيب θ
+
+615
+01:10:41,610 --> 01:10:48,990
+كله على R تربيع Cos تربيع θ زائد R تربيع في
+
+667
+01:17:42,800 --> 01:17:52,660
+node و Y node لما
+
+668
+01:17:52,660 --> 01:17:57,710
+نمر إلى الشروط التالية هذه اختلافات عن الشروط
+
+669
+01:17:57,710 --> 01:18:01,130
+الثلاثة تبع الـcontinuity  الـ function فيه one
+
+670
+01:18:01,130 --> 01:18:06,850
+variable تبع calculus A يجعلها الله إلا حولناها
+
+671
+01:18:06,850 --> 01:18:14,450
+بمعادلة تناسب معدلة في متغيرين أو ثلاثة متغيرات أو أن
+
+672
+01:18:14,450 --> 01:18:18,360
+من المتغيرات وهكذا يبقى الدالة بيقول أنَّها
+
+673
+01:18:18,360 --> 01:18:23,140
+continuous عند نقطة x0 و y0 إذا كانت الدالة معرفة
+
+674
+01:18:23,140 --> 01:18:28,780
+عند هذه النقطة أو f of x0 و y0 exist  مش هذا نفس
+
+675
+01:18:28,780 --> 01:18:33,880
+المعنى، من الثاني الـ limit cannot exist ثلاثة
+
+676
+01:18:33,880 --> 01:18:38,280
+اثنين هذول بدهم يساووا بعض، يبقى الـ f of x0 و y0
+
+677
+01:18:38,280 --> 01:18:41,550
+بده يساوي الـ limit تبع الـ F of X و Y لما الـ X Y
+
+678
+01:18:41,550 --> 01:18:45,350
+بتروح لـ X0 و Y0 إذا تحققت الشروط الثلاثة فإن
+
+679
+01:18:45,350 --> 01:18:51,010
+الواحد بيقول الدالة متصلة عند هذه النقطة، طيب في
+
+680
+01:18:51,010 --> 01:18:55,510
+الخلاصة أخذنا بعض الشغلات أو بعض النظريات أو بعض
+
+681
+01:18:55,510 --> 01:19:00,040
+القواعد لأن كنت ريوز الـ functions صحيحة هنا، زي إذا
+
+682
+01:19:00,040 --> 01:19:04,700
+عندي two functions و الاثنين كانوا متصلتين في المجموعة
+
+683
+01:19:04,700 --> 01:19:08,460
+التالية وحاصل الضرب و القسمة و الجمع في المجال دابل
+
+684
+01:19:08,460 --> 01:19:13,100
+إلى آخرين كثيرات الحدود دوال متصلة، الـ rational
+
+685
+01:19:13,100 --> 01:19:16,960
+function بحيث المقام ما يساوي zero كذلك كلها دوال
+
+686
+01:19:16,960 --> 01:19:22,800
+متصلة، إذا هذا الكلام ينطبق على الكلام في حالة الـ
+
+687
+01:19:22,800 --> 01:19:23,840
+functions of
+
+688
+01:19:37,480 --> 01:19:48,080
+in your functions دوال متصلة، then  النقطة الأولى الـ
+
+689
+01:19:48,080 --> 01:19:57,500
+F زائد أو ناقص الـ G، الـ F في G، الـ F على G، و بشرط أن
+
+690
+01:19:57,500 --> 01:19:58,020
+الـ G
+
+691
+01:20:21,600 --> 01:20:27,940
+rational functions are
+
+692
+01:20:27,940 --> 01:20:39,720
+continuous تبقى دوال متصلة، in which بحيث أن these
+
+693
+01:20:39,720 --> 01:20:48,540
+functions are defined حتكون
+
+694
+01:20:48,540 --> 01:20:57,020
+دوال معرفة،  الأمر الثالث، كثيرات الحدود polynomials
+
+695
+01:20:57,020 --> 01:21:04,400
+are continuous functions.
+
+696
+01:21:07,140 --> 01:21:13,380
+Examples كال
+
+697
+01:21:13,380 --> 01:21:21,940
+الأول، و أسأل هل ده اللي قابل للاتصال ولا لا، as the
+
+698
+01:21:21,940 --> 01:21:30,840
+function، as the function f of x y أحقها
+
+699
+01:21:48,530 --> 01:21:56,650
+زيرو زيرو، و هنا بتساوي زيرو لما X و Y بدها تساوي
+
+700
+01:21:56,650 --> 01:22:05,890
+زيرو زيرو، هل الدالة هذه continuous at
+
+701
+01:22:05,890 --> 01:22:09,850
+زيرو زيرو أم لا؟
+
+702
+01:22:44,450 --> 01:22:48,370
+يقول لي هل الدالة اللي عندنا هذه متصلة عند النقطة
+
+703
+01:22:48,370 --> 01:22:52,970
+00 ولا لا؟ طبعاً الدالة مُجَزَّأة إلى من؟ مُجَزَّأة إلى هنا
+
+704
+01:22:52,970 --> 01:22:56,790
+فأقول لك: تعال نشوف الشروط مُتحققة ولا لا
+
+705
+01:22:56,790 --> 01:23:03,310
+الآن، F of 00، كده مُعرفة صح ولا لا؟ يبقى
+
+706
+01:23:03,310 --> 01:23:12,450
+بأجي بقول له هنا الـ solution، النقطة الأولى الـ F
+
+707
+01:23:12,450 --> 01:23:19,830
+of 0 0 بيبقى يساوي 0، فهذا معناه أن الـ F is defined
+
+708
+01:23:19,830 --> 01:23:25,610
+defined at
+
+709
+01:23:25,610 --> 01:23:32,510
+اللي هو 0 و 0، إذا بتروح لمين؟ للشرط الثاني
+
+710
+01:23:49,120 --> 01:23:56,790
+لو أخذت مثلاً عبر محور X، يبقى Y بقد إيش؟ بزيرو
+
+711
+01:23:56,790 --> 01:24:02,330
+يبقى إيش بيصير عندي؟ واحد، طب لو أنا سلكت عبر محور X
+
+712
+01:24:02,330 --> 01:24:09,590
+عبر محور Y، يبقى X بزيرو بيطلع الجواب يساوي واحد
+
+713
+01:24:09,590 --> 01:24:17,850
+يبقى limit does not exist يبقى هنا take the path
+
+714
+01:24:20,350 --> 01:24:27,130
+مسارين X يساوي 0 و Y يساوي 0، و نحن نحن نحن نحن نحن
+
+715
+01:24:27,130 --> 01:24:30,570
+نحن نحن
+
+716
+01:24:30,570 --> 01:24:31,550
+نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن
+
+717
+01:24:31,550 --> 01:24:32,710
+نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن
+
+718
+01:24:32,710 --> 01:24:35,250
+نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن
+
+719
+01:24:35,250 --> 01:24:40,570
+نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن
+
+720
+01:24:40,570 --> 01:24:48,430
+نحن
+
+721
+01:24:48,430 --> 01:24:55,030
+نحل، لما الـ X و الـ Y بدها تروح لـ 0 و الـ 0، و Y
+
+722
+01:24:55,030 --> 01:24:59,790
+تساوي 0، إيش بيظل عندي؟ X تربيع على X تربيع يساوي
+
+723
+01:24:59,790 --> 01:25:04,850
+1؟ هنا واحد عبر المسار الأول، واحد عبر المسار
+
+724
+01:25:04,850 --> 01:25:09,250
+الثاني، يبقى الـ limit ما له لازم، not exist، يبقى
+
+725
+01:25:09,250 --> 01:25:15,350
+هنا سواء الـ limit لما الـ X و Y بدها تروح للـ Zero و
+
+726
+01:25:15,350 --> 01:25:22,190
+Zero للـ X تربيع ناقص Y تربيع على X تربيع زائد Y
+
+727
+01:25:22,190 --> 01:25:27,570
+تربيع لا يوجد
+
+728
+01:25:27,570 --> 01:25:38,010
+لأنه واحد لا تساوي واحد، يبقى Therefore
+
+729
+01:25:46,220 --> 01:26:09,480
+is not continuous at zero zero مثال آخر، اتنين و قول
+
+730
+01:26:09,480 --> 01:26:21,930
+is the function، هل الدالة f of x و y تساوي ثلاثة x
+
+731
+01:26:21,930 --> 01:26:30,610
+تربيع y على x تربيع زائد y تربيع لما الـ x و الـ y
+
+732
+01:26:30,610 --> 01:26:41,950
+لا تساوي 0 0، و تساوي 0 لما الـ x و الـ y بدها تساوي 0
+
+733
+01:26:41,950 --> 01:26:44,870
+0 continuous
+
+734
+01:26:48,370 --> 01:26:54,210
+at zero zero هذا
+
+735
+01:26:54,210 --> 01:26:58,310
+السؤال، solution
+
+736
+01:26:58,310 --> 01:27:03,350
+إذاً
+
+737
+01:27:03,350 --> 01:27:08,070
+نأتي نشوف شروط الـ continuity الثلاثة هل هي متحققة
+
+738
+01:27:08,070 --> 01:27:10,790
+والله غير متحققة
+
+739
+01:27:34,520 --> 01:27:39,420
+الدالة واضحة أنها معرفة عند 00، مضبوط؟ يبقى بقول له
+
+740
+01:27:39,420 --> 01:27:45,460
+الخطوة الأولى، تأخذ الـ F of 00، ده بيساوي Zero، هذا
+
+741
+01:27:45,460 --> 01:27:58,080
+بيقول أن الـ F is defined at 00، بعد هيك تأخذ الـ
+
+742
+01:27:58,080 --> 01:28:05,140
+limit للدالة اللي عندنا، يبقى ببدأ آخذ الـ limit، النقطة
+
+743
+01:28:05,140 --> 01:28:12,700
+الثانية، آخذ الـ limit لمن؟ لما الـ X و الـ Y بدها
+
+744
+01:28:12,700 --> 01:28:20,160
+تروح للـ Zero و الـ Zero لمن؟ لثلاثة X تربيع Y على X
+
+745
+01:28:20,160 --> 01:28:26,460
+تربيع زائد Y تربيع، يبقى بتروح آخذ مسارات، ده كل
+
+746
+01:28:26,460 --> 01:28:29,680
+واحد أذكى مني شوية بيقول: طيب جرب الـ polar يمكن تكون
+
+747
+01:28:29,680 --> 01:28:35,220
+أسرع، بصراحة بدك تاخذ مرتين بس في الـ polar، مرة واحدة
+
+748
+01:28:35,220 --> 01:28:40,880
+بقول له: ماشي، يبقى هذا الكلام بيساوي limit لما الـ X
+
+749
+01:28:40,880 --> 01:28:49,780
+و الـ Y، أو بدل X و Y، R بدها تروح للـ zero، يبقى R
+
+750
+01:28:49,780 --> 01:28:58,370
+بدها تروح للـ zero، لثلاثة R تربيع Sin تربيع ثيتا في
+
+751
+01:28:58,370 --> 01:29:05,350
+R في Sine الزاوية ثيتا على R تربيع Cos تربيع
+
+752
+01:29:05,350 --> 01:29:12,310
+ثيتا زائد R تربيع Sine تربيع ثيتا، بهذا الكلام يبدو
+
+753
+01:29:12,310 --> 01:29:21,700
+يساوي limit لما الـ R بدأت تذهب إلى Zero لثلاثة R
+
+754
+01:29:21,700 --> 01:29:27,800
+تكعيب مع الـ R تربيع اللي تحت، بصير ثلاثة R في Cos
+
+755
+01:29:27,800 --> 01:29:34,620
+تربيع تيتا في Sine تيتا، و لتحت الله يسهل عليه، طبعاً
+
+756
+01:29:34,620 --> 01:29:40,460
+R مع R تربيع بـ R تكعيب، R تربيع مع R تكعيب بيضل R، Cos
+
+757
+01:29:40,460 --> 01:29:44,320
+تربيع زي الـ Sine تربيع تيتا اللي هو قد إيش؟ هو قديش؟
+
+758
+01:29:47,250 --> 01:29:54,590
+يبقى الـ limit exist و يساوي كده؟ و يساوي zero، و
+
+759
+01:29:54,590 --> 01:29:59,070
+الدالة لو معرفة و تساوي كده؟ إذا هذه دالة
+
+760
+01:29:59,070 --> 01:29:59,790
+continuous
+
+761
+01:30:09,210 --> 01:30:15,950
+0 و 0، يعني بالنسبة لك، تفهموا، إذا قلت عند 0 و 0 ليس
+
+762
+01:30:15,950 --> 01:30:21,550
+معناه هذا الكلام أن الـ limit does not exist أو في
+
+763
+01:30:21,550 --> 01:30:26,490
+عندي discord في اللي ممكن أعرفه، آخذ لك مثال رقم
+
+764
+01:30:26,490 --> 01:30:35,630
+ثلاثة، شو رأيك؟ دي functions الـ E أس X ناقص Y و Cos
+
+765
+01:30:35,630 --> 01:30:51,600
+X زائد Y على X تربيع زائد واحد زائد ثلاثة و Ln خمسة
+
+766
+01:30:51,600 --> 01:30:59,040
+زائد X تربيع زائد Y تربيع، هل هناك نقطة الدالة
+
+767
+01:30:59,040 --> 01:31:04,260
+عندها مش معرفة؟ أي واحد من دول الثلاثة؟ تولى يا
+
+768
+01:31:04,260 --> 01:31:04,680
+عزفي
+
+769
+01:31:11,290 --> 01:31:15,390
+لأ، كل واحد لحاله، هذول ثلاثة دوال، يعني ثلاثة مسائل
+
+770
+01:31:15,390 --> 01:31:18,830
+باعتبارها، أي واحدة فيهم، حتلاقي نقطة دليل عندها
+
+771
+01:31:18,830 --> 01:31:25,330
+معرفة، كلها معرفة، اثنين، الثانية الأولى هي exponential
+
+772
+01:31:25,330 --> 01:31:30,330
+فهي متصلة، و الثالثة Cosine متصلة مثلاً من هنا إلى
+
+773
+01:31:30,330 --> 01:31:36,230
+هنا، و الثالثة من هنا إلى هنا كمان متصلة، صحيح ولا
+
+774
+01:31:36,230 --> 01:31:42,290
+لأ؟ إذا هذه continuous for all x y بلا استثناء، يبقى
+
+775
+01:31:42,290 --> 01:31:46,710
+هذه الـ functions اللي عندنا دول ما لهم؟ are
+
+776
+01:31:46,710 --> 01:31:50,150
+continuous
+
+777
+01:31:52,420 --> 01:32:04,940
+for all x y بلا استثناء، not I remark the
+
+778
+01:32:04,940 --> 01:32:13,600
+previous rule، the previous rules القواعد السابقة
+
+779
+01:32:13,600 --> 01:32:27,470
+on the functions of two variables are
+
+780
+01:32:27,470 --> 01:32:31,710
+true صحيحة
+
+781
+01:32:31,710 --> 01:32:41,730
+are true for the functions or the functions of
+
+782
+01:32:41,730 --> 01:32:51,650
+three or more variables يعني لثلاثة متغيرات أو
+
+783
+01:32:51,650 --> 01:32:59,750
+أكثر أيضاً صحيحة، examples نمر لأيه؟
+
+784
+01:32:59,750 --> 01:33:09,130
+أيه؟ قولي at what points؟ at what points؟ من من
+
+785
+01:33:09,130 --> 01:33:14,650
+النقاط does the following
+
+786
+01:33:36,300 --> 01:33:46,520
+x و y يساوي x زائد الـ y على ثلاثة ناقص sign اللي هو
+
+787
+01:33:46,520 --> 01:33:50,380
+الـ x هل
+
+788
+01:33:50,380 --> 01:33:56,520
+في نقطة يا بنات هذه الدالة عندها غير قابلة للاتصال
+
+789
+01:33:56,520 --> 01:33:58,400
+إذا في قولوا لي عنها
+
+790
+01:34:26,180 --> 01:34:31,400
+في ولا حاجة، يبقى دي continuous for all x و y، يبقى
+
+791
+01:34:31,400 --> 01:34:40,840
+دي continuous for all x و y، طيب، انتقل للكلمة شوية
+
+792
+01:34:40,840 --> 01:34:54,140
+النقطة الثانية، f of x و y تساوي Ln اللي هو ln x
+
+793
+01:34:54,140 --> 01:35:02,230
+تربيع زائد Y تربيع، في نقطة عندها الدالة غير معرفة
+
+794
+01:35:02,230 --> 01:35:09,970
+أو مُمَتَّصَة، اللي هي معرفة، القيم الموجبة، صح ولا لأ؟ فـ Sin X
+
+795
+01:35:09,970 --> 01:35:14,430
+تربيع و Y تربيع إن كان X و Y بالسالب و رميهم موجبة
+
+796
+01:35:14,430 --> 01:35:20,830
+في المربع، يبقى ضل اثنين بس، نقطة الأصل، تجيء هذه الدالة
+
+797
+01:35:20,830 --> 01:35:27,560
+continuous ما عدا نقطة الأصل، يبقى هذه continuous
+
+798
+01:35:27,560 --> 01:35:31,360
+for
+
+799
+01:35:31,360 --> 01:35:44,200
+all x و y except ما عدا 0.000
+
+800
+01:35:44,200 --> 01:35:49,520
+أو الـ origin، النقطة التالية
+
+801
+01:35:57,160 --> 01:36:07,020
+اللي هي f of x و y، f of x و y بدها تساوي sign واحد
+
+802
+01:36:07,020 --> 01:36:16,180
+على x y يالا
+
+803
+01:36:16,180 --> 01:36:24,620
+وين الدالة مش معرفة؟ عند صفر و صفر، و أي واحد صفر و أي
+
+804
+01:36:24,620 --> 01:36:36,790
+رقم آخر، الرقم بصفر تمام، يبقى هنا continuous except
+
+805
+01:36:45,430 --> 01:37:09,930
+أكثر بوينتس، أكثر
+
+806
+01:37:09,930 --> 01:37:10,090
+بوينتس، أكثر بوينتس، أكثر بوينتس، أكثر بوينتس،
+
+807
+01:37:14,120 --> 01:37:24,460
+يقول F of X, Y, Z، X, Y, Z بيساوي الجذر التربيعي X
+
+808
+01:37:24,460 --> 01:37:40,420
+تربيع زائد Y تربيع ناقص واحد، النقاط
+
+809
+01:37:40,420 --> 01:37:46,840
+اللي بتبقى  ده اللي عندها continuous، يبقى هذا يكون
+
+810
+01:37:46,840 --> 01:37:58,220
+في نواص for all x, y, z except at
+
+811
+01:37:58,220 --> 01:38:07,860
+x تربيع زائد y تربيع ناقص واحد، منها أقل من الـ 0
+
+812
+01:38:11,090 --> 01:38:14,190
+ذا أكبر من Zero مافي مشكلة، مُعرَّفة، لكن إذا أقل من
+
+813
+01:38:14,190 --> 01:38:21,590
+Zero، مُعرَّفة أو إن شئتم فقولوا ها الـ X تربيع زائد
+
+814
+01:38:21,590 --> 01:38:26,950
+Y تربيع أقل من واحد، طب مين هم النقاط هذول يا
+
+815
+01:38:26,950 --> 01:38:34,790
+بنات؟ بس Zero Zero داخل الدائرة، احنا في الفراغ X Y
+
+816
+01:38:34,790 --> 01:38:42,120
+و Z، سيلندر، يبقى كل النقاط اللي داخل الـ except ما
+
+817
+01:38:42,120 --> 01:38:48,760
+عدا النقاط اللي داخل الـ cylinder، يبقى هنا هذا
+
+818
+01:38:48,760 --> 01:38:57,440
+معناه أن الـ continuous for
+
+819
+01:38:57,440 --> 01:39:04,780
+all x, y, z except the
+
+820
+01:39:04,780 --> 01:39:06,520
+points
+
+821
+01:39:11,550 --> 01:39:22,750
+داخل السيلندر X تربيع زائد Y تربيع يساوي واحد، يعني
+
+822
+01:39:22,750 --> 01:39:26,910
+عند كل النقاط داخل السيلندر الدالة غير مُعَرَّفة، لكن برا
+
+823
+01:39:26,910 --> 01:39:39,960
+كلها بتبقى مُعَرَّفة، النقطة الثانية، لو قلت لك F X Y Z X
+
+824
+01:39:39,960 --> 01:39:53,140
+Y Z X Y Z X Y Z X
+
+825
+01:39:53,140 --> 01:39:57,120
+Y Z X Y Z X Y Z X Y Z X Y Z X Y Z X Y Z X Y Z X Y
+
+826
+01:39:57,120 --> 01:40:05,680
+Z X Y Z X Y Z X Y Z X Y Z X Y Z X Y Z X Y Z X Y Z
+
+827
+01:40:05,680 --> 01:40:06,180
+X Y Z X Y Z X Y Z X Y Z X Y Z X Y Z X Y Z X Y Z X
+
+828
+01:40:06,180 --> 01:40:08,770
+X X X X X X X X X X X لو كانت الـ X و الـ Y بزيرو مش
+
+829
+01:40:08,770 --> 01:40:12,530
+مشكلة، لكن الـ Z ممنوع تساوي زيرو، واحد على 0، إذا كانت في
+
+830
+01:40:12,530 --> 01:40:15,630
+مقامها نهاية غير معرفة
+
+831
+01:40:25,880 --> 01:40:35,100
+Y زائد بدها تساوي الواحد على زد ناقص الجذر
+
+832
+01:40:35,100 --> 01:40:47,820
+التربيعي لـ X تربيع زائد Y تربيع، يبقى
+
+833
+01:40:47,820 --> 01:40:54,200
+continuous for
+
+834
+01:40:54,200 --> 01:40:54,820
+all
+
+835
+01:40:59,260 --> 01:41:07,520
+بحيث أن المقام ممنوع يساوي Zero، يبقى Z ناقص
+
+836
+01:41:07,520 --> 01:41:13,780
+الجذر التربيعي X تربيع زائد Y تربيع لا يساوي Zero
+
+837
+01:41:13,780 --> 01:41:23,760
+أو Z لا يساوي الجذر التربيعي X تربيع زائد Y تربيع
+
+838
+01:41:23,760 --> 01:41:32,550
+أو Z تربيع لا يساوي X تربيع زائد Y تربيع، معادلة تُشَكِّل
+
+839
+01:41:32,550 --> 01:41:40,450
+يا ابنها لو كانت تساوي مخروط دائري صحيح Circular cone
+
+840
+01:41:40,450 --> 01:41:47,490
+الدائرية التابعة
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/-aEoMwQERo4_postprocess.srt b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/-aEoMwQERo4_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..8a5e6bddfbabf23fef5518abd0321be900fde9a6
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/-aEoMwQERo4_postprocess.srt
@@ -0,0 +1,3392 @@
+1
+00:00:00,000 --> 00:00:02,680
+موسيقى
+
+2
+00:00:16,600 --> 00:00:21,960
+بسم الله الرحمن الرحيم المرة الماضية بدأنا في
+
+3
+00:00:21,960 --> 00:00:26,740
+chapter 14 واخدنا اول section وهو ال functions of
+
+4
+00:00:26,740 --> 00:00:30,860
+several variables عرفنا هذه ال functions جيبنا ال
+
+5
+00:00:30,860 --> 00:00:35,010
+domain و ال range لهذه ال functionsجيبنا ما يسمى
+
+6
+00:00:35,010 --> 00:00:40,830
+بال level surface و level curves لمين للمنحنة في
+
+7
+00:00:40,830 --> 00:00:44,790
+الأحداثيات الكارثية سواء كان في متغيرين أو في
+
+8
+00:00:44,790 --> 00:00:50,250
+ثلاثة متغيرات اليوم ان شاء الله هنجي لهذه ال
+
+9
+00:00:50,250 --> 00:00:54,230
+functions نجيب ال limits و ال continuity لهذه
+
+10
+00:00:54,230 --> 00:00:58,850
+الدولة هنبدأ بأول لقطة يعني هنقسم هذا section إلى
+
+11
+00:00:58,850 --> 00:01:03,490
+لقطتينالنقطة الأولى بدنا ناخد فيها ال limits
+
+12
+00:01:03,490 --> 00:01:08,630
+والنقطة الثانية بدنا ناخد فيها ال continuity يعني
+
+13
+00:01:08,630 --> 00:01:13,470
+هنقسم محاضرتنا إلى جزئين ان شاء الله تبارك وتعالى
+
+14
+00:01:13,470 --> 00:01:18,770
+لو رجعنا بالذاكرة إلى الورق إلى calculus A أو
+
+15
+00:01:18,770 --> 00:01:22,230
+calculus B كنا بنقول limit ل function
+
+16
+00:01:43,520 --> 00:01:46,320
+يبقى فيه متغير واحد
+
+17
+00:01:55,410 --> 00:02:00,810
+هذا ما كنا ندرسه في calculus a و b الان نقول لو
+
+18
+00:02:00,810 --> 00:02:06,050
+كان ال function فيه متغيرين شو اللي بده يحصل يبقى
+
+19
+00:02:06,050 --> 00:02:11,270
+باجي بقول هنا f ال f is a function of two
+
+20
+00:02:11,270 --> 00:02:19,170
+variables في متغيرين then باجي بقول limit
+
+21
+00:02:22,050 --> 00:02:29,250
+بصارت متغيرات لتحت بيصير x و y بدها تروح الى x
+
+22
+00:02:29,250 --> 00:02:34,970
+node و y node بده يساوي ال مثلة طب لو كانت في
+
+23
+00:02:34,970 --> 00:02:40,630
+ثلاثة متغيرات يبقى لو كانت الدالة function of
+
+24
+00:02:40,630 --> 00:02:50,890
+three variables في ثلاثة متغيرات then limitللـ f
+
+25
+00:02:50,890 --> 00:02:58,790
+of x و y و z لما ال x و ال y و ال z بدها تروح الى
+
+26
+00:02:58,790 --> 00:03:06,010
+x node turns to x node و y node و z node يبقى ناتج
+
+27
+00:03:06,010 --> 00:03:12,650
+هذا بده يساوي L يبقى
+
+28
+00:03:12,650 --> 00:03:18,210
+بده يساوي من؟ بده يساوي Lوهكذا يبقى لو عندى
+
+29
+00:03:18,210 --> 00:03:23,170
+متغيرين تلاتة اربع من المتغيرين كله بنفس الفورمة
+
+30
+00:03:23,170 --> 00:03:28,170
+يبقى نفس المفهوم اللى احنا اتعلمناه بالنسبة لمين
+
+31
+00:03:28,170 --> 00:03:35,510
+لكالكولاس ايه بناء عليه يبقى هنا لو جيت قلتلك اه
+
+32
+00:03:45,750 --> 00:03:48,950
+يبقى أول خطوة في إيجاد limit هو التعويض المباشر
+
+33
+00:03:48,950 --> 00:03:53,710
+يبقى هذه قداشها تساوي X node طب و ال Y ماعنديش Y
+
+34
+00:03:53,710 --> 00:03:58,510
+يبقى لا و لا قتلها كإلها مش موجودة أصلا طب لو قلت
+
+35
+00:03:58,510 --> 00:04:05,270
+limit لل Y لما ال X هو Y بدها تروح لل X node و Y
+
+36
+00:04:05,270 --> 00:04:12,570
+node برضه كمان Y nodeطب لو قلت limit ل constant k
+
+37
+00:04:12,570 --> 00:04:18,810
+لما ال x و y بدها تروح الى x node و y node limit
+
+38
+00:04:18,810 --> 00:04:22,470
+المقدرة ثابت بالمقدرة ثابت itself اللي درس فيه
+
+39
+00:04:22,470 --> 00:04:28,010
+calculus a و الله b و الله c هو نفس الشيء بقوله
+
+40
+00:04:28,010 --> 00:04:34,810
+هنا where حيثم ال k is constant
+
+41
+00:04:39,200 --> 00:04:43,540
+بنفس النتيجة الخاصة المنطقة التي دُرسها في
+
+42
+00:04:43,540 --> 00:04:48,000
+Calculus A على ال limits للfunction نفسها هي على
+
+43
+00:04:48,000 --> 00:04:51,400
+ال functions of two variables, of three variables,
+
+44
+00:04:51,860 --> 00:04:57,340
+of n variables الاخرينبعد ذلك نبدأ نذكر بهذا
+
+45
+00:04:57,340 --> 00:05:01,580
+الكلام لـ function of two variables وما ينطبق على
+
+46
+00:05:01,580 --> 00:05:04,860
+ال function of two variables نفسه تماما على ال
+
+47
+00:05:04,860 --> 00:05:09,360
+functions of three variables او more variables او
+
+48
+00:05:09,360 --> 00:05:14,180
+اكتر من ذلك لو كان اربع متغيرات خمس متغيرات ان من
+
+49
+00:05:14,180 --> 00:05:19,900
+المتغيرات الاخرين يبقى هذا هنحطه على صيغة النظرية
+
+50
+00:05:19,900 --> 00:05:20,720
+التالية
+
+51
+00:05:25,840 --> 00:05:34,120
+بنقول اللي هي ال properties الخاص properties of
+
+52
+00:05:34,120 --> 00:05:42,660
+limits of functions of
+
+53
+00:05:42,660 --> 00:05:45,820
+two variables
+
+54
+00:05:55,220 --> 00:06:01,540
+الـ M الـ M الـ M الـ M الـ M الـ M الـ M الـ M
+
+55
+00:06:01,540 --> 00:06:05,480
+الـ M الـ M الـ M الـ M الـ M الـ M الـ M الـ M
+
+56
+00:06:05,480 --> 00:06:05,860
+الـ M الـ M الـ M الـ M الـ M الـ M الـ M الـ M
+
+57
+00:06:05,860 --> 00:06:05,880
+الـ M الـ M الـ M الـ M الـ M الـ M الـ M الـ M
+
+58
+00:06:05,880 --> 00:06:06,040
+الـ M الـ M الـ M الـ M الـ M الـ M الـ M الـ M
+
+59
+00:06:06,040 --> 00:06:12,740
+الـ M الـ M الـ M الـ
+
+60
+00:06:12,740 --> 00:06:24,120
+M الـ Mلل f of x و y لما ال x و ال y بدها تروح إلى
+
+61
+00:06:24,120 --> 00:06:35,620
+x node و y node تساوي ال L and ال limit لل g of x
+
+62
+00:06:35,620 --> 00:06:42,120
+و y لما ال x و ال y بدها تروح إلى x node و y node
+
+63
+00:06:42,120 --> 00:06:45,140
+بده يساوي ال M مثلا
+
+64
+00:06:48,650 --> 00:06:52,810
+النقطة الأولى limit
+
+65
+00:07:04,000 --> 00:07:08,780
+عندما تذهب الـ x و الـ y إلى الـ x node و الـ y
+
+66
+00:07:08,780 --> 00:07:17,520
+node يبقى هذا الكلام زائد او ناقص M النقطة الثانية
+
+67
+00:07:17,520 --> 00:07:23,580
+limit لكيف
+
+68
+00:07:23,580 --> 00:07:25,720
+تفهم الـ x و الـ y
+
+69
+00:07:28,690 --> 00:07:37,630
+بدها تروح الى X node وY node بده ساوي K في L and
+
+70
+00:07:37,630 --> 00:07:48,530
+بناء عليه limit لمن؟ لل F of X وY لل G of X وY لما
+
+71
+00:07:48,530 --> 00:07:54,690
+X وY بدها تروح الى X node وY node يبقى هذا الكلام
+
+72
+00:07:54,690 --> 00:08:03,930
+بده ساوي ال L في Mالمقطة الثالثة بدي ال limit لل F
+
+73
+00:08:03,930 --> 00:08:11,770
+of X و Y على ال G of X و Y لما ال X و ال Y بدها
+
+74
+00:08:11,770 --> 00:08:17,910
+تروح إلى X node و Y node
+
+75
+00:08:17,910 --> 00:08:25,270
+يبقى هذا الكلام بده يساوي L على M بشرط ان ال M
+
+76
+00:08:25,270 --> 00:08:38,090
+ممنوع تساوي Zeroوالنقطة الرابعة limit لل F من X و
+
+77
+00:08:38,090 --> 00:08:45,910
+Y كله to the power N لما ال X و ال Y بدها تروح إلى
+
+78
+00:08:45,910 --> 00:08:53,150
+X node و Y node يبقى هذا بده يساوي ال L أس N و ال
+
+79
+00:08:53,150 --> 00:08:58,630
+N is a positive integer
+
+80
+00:09:10,240 --> 00:09:15,860
+لما ال X و ال Y بدها تروح الى X naught و Y naught
+
+81
+00:09:15,860 --> 00:09:27,400
+للجذر النوني لل F of X و Y بده يساوي الجذر النوني
+
+82
+00:09:27,400 --> 00:09:36,100
+ل L و له بده يساوي L اصول واحد على M و ال M as a
+
+83
+00:09:36,100 --> 00:09:37,440
+positive integer
+
+84
+00:10:28,780 --> 00:10:36,600
+أقل من أو يساوي ال F of X Y أقل من أو يساوي ال H
+
+85
+00:10:36,600 --> 00:10:49,520
+of X Y for all X Y التي لا تساوي X node وY node
+
+86
+00:10:53,570 --> 00:11:06,230
+in a disk and a disk centered at x node و y node
+
+87
+00:11:06,230 --> 00:11:14,190
+and if وإذا
+
+88
+00:11:14,190 --> 00:11:24,830
+كان limit للـ g of x و y لما ال x و ال yإلى x non
+
+89
+00:11:24,830 --> 00:11:35,030
+و y non بده يساوي limit لما ال x و y بدها تروح ل x
+
+90
+00:11:35,030 --> 00:11:43,250
+non و y non لل h of x و y بده يساوي ال L then
+
+91
+00:11:43,250 --> 00:11:52,610
+limitللـ f of x و y لما ال x و ال y بدها تروح الى
+
+92
+00:11:52,610 --> 00:11:57,270
+x نهض و y نهض يبقى بده يساوي ال L كذلك
+
+93
+00:12:43,190 --> 00:12:48,170
+لو راجعنا الى هذه الخواص الست اللى قدامنا لن نجد
+
+94
+00:12:48,170 --> 00:12:53,690
+انها تختلف مع الست خواص تبع ال calculus A التي
+
+95
+00:12:53,690 --> 00:12:59,270
+درست في أول ما دخلت الجامعة في الفصل الأول أثناء
+
+96
+00:12:59,270 --> 00:13:03,310
+دراسة يبقى المعلومات اللى كانت على function of one
+
+97
+00:13:03,310 --> 00:13:07,690
+variable نفسها على function of two variables
+
+98
+00:13:08,180 --> 00:13:13,000
+الخواصة بتقول لي ما يأتي افترض ان عندي L و M و K
+
+99
+00:13:13,000 --> 00:13:19,700
+كانت اعداد حقيقية limit f of x و y يساوي L limit g
+
+100
+00:13:19,700 --> 00:13:23,900
+of x و y يساوي
+
+101
+00:13:23,900 --> 00:13:30,140
+Mالنقطة الأولى درسنا في calculus A نهاية المجموع
+
+102
+00:13:30,140 --> 00:13:34,700
+الجبري لدالتين يساوي المجموع الجبري للنهايتين ايش
+
+103
+00:13:34,700 --> 00:13:38,960
+معناه؟ معناه كإن ال limit بتدخش على الدالة الأولى
+
+104
+00:13:38,960 --> 00:13:42,600
+زيد أو نقص ال limit لما تدخش على الدالة الثانية
+
+105
+00:13:42,600 --> 00:13:46,420
+يبقى limit الدالة الأولى بL limit الدالة الثانية
+
+106
+00:13:46,420 --> 00:13:51,600
+بM هل في خلاف بينها و بين calculus A؟ لا خلاف نقطة
+
+107
+00:13:51,600 --> 00:13:57,530
+تانيةLimit حاصل ضرب مقدار ثابت في دلة يبقى المقدار
+
+108
+00:13:57,530 --> 00:14:02,930
+الثابت في نهاية الدلة لأن limit ال constant قبل
+
+109
+00:14:02,930 --> 00:14:06,890
+قليل كتبنا بال constant itself يعني لو اعتبرت هذا
+
+110
+00:14:06,890 --> 00:14:11,550
+limit لحاصل ضرب دلتين بديكون limit المقدار الثابت
+
+111
+00:14:11,550 --> 00:14:15,270
+بالمقدار الثابت itself في limit الدلة اللي هو بالL
+
+112
+00:14:15,270 --> 00:14:20,960
+يبقى حاصل الضرب K في Lو كذلك لو بدل ال K كانت
+
+113
+00:14:20,960 --> 00:14:25,520
+function أخرى و لتكن اللي هو الدالة F والدالة G
+
+114
+00:14:25,520 --> 00:14:30,000
+limit حصل ضارب two functions سوى limit الدالة
+
+115
+00:14:30,000 --> 00:14:35,380
+الأولى مضروب في limit الدالة ثانية و L في M بالمثل
+
+116
+00:14:35,380 --> 00:14:40,960
+لو كانت قسمةيبقى limit لل F of X وY على ال G of X
+
+117
+00:14:40,960 --> 00:14:45,140
+وY لما ال X وY بتروح ال X node وY node يسوى limit
+
+118
+00:14:45,140 --> 00:14:49,760
+ال bus على limit المقام يعني بقدر اوزع limit لكل
+
+119
+00:14:49,760 --> 00:14:55,720
+من ال bus والمقام يبقى بناء عليها يسوى L على M بشر
+
+120
+00:14:56,800 --> 00:15:00,760
+المقام ممنوع يساوي صفر يعني ممنوع ال M تساوي Zero
+
+121
+00:15:00,760 --> 00:15:05,400
+لأن ال M لو كانت ب Zero بصير ال demand غير معادلة
+
+122
+00:15:05,400 --> 00:15:10,520
+ف does not exist مش موجودة تمام؟ طيب النقطة
+
+123
+00:15:10,520 --> 00:15:15,520
+الرابعة لمة ال alphabets مرفوعة to the power Nالـ
+
+124
+00:15:15,520 --> 00:15:20,860
+limit قلت لكم معها Vip تدخل على الجزء تربيه تكعيب
+
+125
+00:15:20,860 --> 00:15:25,600
+أُس N تدخل تحت الجذر تدخل على الزاوية تبع النسبة
+
+126
+00:15:25,600 --> 00:15:30,160
+المثلثية تدخل على العدد داخل ال N أو على الدلة
+
+127
+00:15:30,160 --> 00:15:33,620
+داخل ال N إلى أقلينيبقى المعنى هذا الكلام ان ال
+
+128
+00:15:33,620 --> 00:15:38,440
+limit دخلت داخل القوس لكل أُس N limit الدلة اللي
+
+129
+00:15:38,440 --> 00:15:44,000
+داخل القوس هو L بصير أُس N بحيث N عدد صحيح موجب
+
+130
+00:15:44,000 --> 00:15:48,260
+اللي بعدها limit الجذر يبقى بطل يصير عصري اشصار
+
+131
+00:15:48,260 --> 00:15:54,120
+كاسري يبقى ال limit لميل باعتبار واحد على N الجذر
+
+132
+00:15:54,120 --> 00:15:58,120
+النونيتعني 1 إلى N يبقى دخلت على الدالة اللي جوا
+
+133
+00:15:58,120 --> 00:16:04,360
+فصلمت اللي جوا ب L تحت الجذر النوني يعني L أس 1
+
+134
+00:16:04,360 --> 00:16:10,180
+إلى N و N عدد صحيح موجة طب السؤال هو طب افترض كان
+
+135
+00:16:10,180 --> 00:16:16,170
+سالميعني انت جبت للعدد الكاسري وجبت للعدد الموجب
+
+136
+00:16:16,170 --> 00:16:20,190
+بس ما جبتش للعدد السالب صحيح ولا لا؟ او للعدد
+
+137
+00:16:20,190 --> 00:16:25,710
+السالب الكاسري كيف نسوي لو كان مثلا f of x أُس
+
+138
+00:16:25,710 --> 00:16:32,860
+سالب عشرة مثلا؟نقول واحد عالى الزمن واسعاشر و
+
+139
+00:16:32,860 --> 00:16:36,440
+بنخلق limit الكون الصحيح اللي فوق بواحد زي ما هو و
+
+140
+00:16:36,440 --> 00:16:39,980
+limit اللي تحت باخدنا limit بنطبق عليها ميم اللي
+
+141
+00:16:39,980 --> 00:16:43,560
+هي الحالة اللي عندنا دي و مثله تماما بالنسبة
+
+142
+00:16:43,560 --> 00:16:47,340
+للحالة اللي عندنا يبقى ماعنا مشكلة يبقى ال limit
+
+143
+00:16:47,340 --> 00:16:52,200
+صحيح على الأس سواء كان موجب و الله سالب و الله
+
+144
+00:16:52,200 --> 00:16:56,700
+كسري كسري كمان موجب أو سالب على الشكتين كلامنا هذا
+
+145
+00:16:56,700 --> 00:17:01,790
+مالهم صحيحطيب، شو اسمها هذه أخر نقطة؟ sandwich
+
+146
+00:17:01,790 --> 00:17:05,610
+theorem أو squeezing theorem؟ هذه و هذه الأثنين
+
+147
+00:17:05,610 --> 00:17:08,370
+نفس المعنى طب أنا خدنا sandwich theorem في
+
+148
+00:17:08,370 --> 00:17:12,190
+calculus E، مظبوط؟ نفس المعلومة، أنا خدناها في
+
+149
+00:17:12,190 --> 00:17:17,290
+calculus E، هيجتنا في calculus Cأيش بتقولي بتقولي
+
+150
+00:17:17,290 --> 00:17:23,210
+لو كان عندك ثلاث دوال مرتبة بهذا الشكل الأولى أقل
+
+151
+00:17:23,210 --> 00:17:26,030
+من أو تساوي التانية و التانية أقل من أو تساوي
+
+152
+00:17:26,030 --> 00:17:32,550
+التالتة هذا الكلام صحيح لكل ال X Y اللي مابسويش X
+
+153
+00:17:32,550 --> 00:17:37,950
+node و Y node و هذا كلام صحيح على desk course مركز
+
+154
+00:17:37,950 --> 00:17:41,570
+و نقطة X node و Y node يبقى لما أخد ال limit لما
+
+155
+00:17:41,570 --> 00:17:46,410
+ال X و Y كلها بدأت تروح إلى X nodeو why not في هذه
+
+156
+00:17:46,410 --> 00:17:51,430
+الحالة إذا حدث ان limit الدالة الأولى هي limit
+
+157
+00:17:51,430 --> 00:17:55,510
+الدالة التالتة سوى نفس الرقم إذا ال automatic
+
+158
+00:17:55,510 --> 00:18:01,350
+limit اللي في النص بيكون نفس الرقم يبقى limit اللي
+
+159
+00:18:01,350 --> 00:18:07,230
+في النص f of x و y لما ال x هو y هو y هو y هو y هو
+
+160
+00:18:07,230 --> 00:18:07,810
+y هو y هو y هو y هو y هو y هو y هو y هو y هو y هو
+
+161
+00:18:07,810 --> 00:18:09,210
+y هو y هو y هو y هو y هو y هو y هو y هو y هو y هو
+
+162
+00:18:09,210 --> 00:18:09,450
+y هو y هو y هو y هو y هو y هو y هو y هو y هو y هو
+
+163
+00:18:09,450 --> 00:18:09,550
+y هو y هو y هو y هو y هو y هو y هو y هو y هو y هو
+
+164
+00:18:09,550 --> 00:18:09,570
+y هو y هو y هو y هو y هو y هو y هو y هو y هو y هو
+
+165
+00:18:09,570 --> 00:18:09,610
+y هو y هو y هو y هو y هو y هو y هو y هو y هو y هو
+
+166
+00:18:09,720 --> 00:18:15,040
+هل فعليا اختلفت عن ما سبق الدراسة في كل كناسة هو
+
+167
+00:18:15,040 --> 00:18:21,780
+هو حرفيا طب نشوف الأن تطبيق العملي لهذه المفاهيم
+
+168
+00:18:21,780 --> 00:18:33,840
+نعطي مثال توضيحي على ذلك يبقى example نحسبيه
+
+169
+00:18:33,840 --> 00:18:43,160
+للنهايات التالية evaluate دهfollowing limits
+
+170
+00:18:43,160 --> 00:18:49,740
+المقطة
+
+171
+00:18:49,740 --> 00:18:57,400
+الأولى the limit لما ال X و ال Y بدها تروح إلى
+
+172
+00:18:57,400 --> 00:19:06,340
+ثلاثة وأربعة limit للجذر التربيعي لل X تربيع زائد
+
+173
+00:19:06,340 --> 00:19:07,400
+Y تربيع
+
+174
+00:19:14,060 --> 00:19:19,120
+زي ما دراسة في calculus ايه؟ اول خطوة في حساب ال
+
+175
+00:19:19,120 --> 00:19:22,840
+limits هي التعويير المشيزي يعني زي ال polynomial
+
+176
+00:19:22,840 --> 00:19:26,840
+بالضغط تماما يبقى baggage يبقى جول بدي اشيل X و
+
+177
+00:19:26,840 --> 00:19:33,540
+احط مكانها تلاتة لكل تربيع وهذه بدي احط بدالها
+
+178
+00:19:33,540 --> 00:19:40,230
+أربعة لكل تربيع وهذه الناقص يساويتسعة وستة عشر
+
+179
+00:19:40,230 --> 00:19:44,530
+وخمسة وعشرين شيل واحد بيظل جذر التربيه اليمن
+
+180
+00:19:44,530 --> 00:19:50,970
+للاربع وعشرين لو اربع في ستة يعني اتنين ال square
+
+181
+00:19:50,970 --> 00:20:00,210
+root لستة قيمة هذه النهاية السؤال الثاني ال
+
+182
+00:20:00,210 --> 00:20:07,630
+delimit لمن لما ال X وYيجب ان تذهب الى الـ 0 و الـ
+
+183
+00:20:07,630 --> 00:20:15,970
+0 الى ماين الى الـ E of Y بصين X على ماين على X
+
+184
+00:20:15,970 --> 00:20:23,350
+تعويض
+
+185
+00:20:23,350 --> 00:20:28,550
+المباشر شوفوا ايش بيجيب هنا سفر على سفر تبقى تدبر
+
+186
+00:20:28,550 --> 00:20:34,110
+حالك و تظبط أمورك بحيث تقدر تحسب هذه ال limit
+
+187
+00:20:39,770 --> 00:20:50,170
+عشان تفترحوا علينا كيف يكون شكل الحل انا
+
+188
+00:20:50,170 --> 00:20:54,670
+ماتكلمش عن نتيجة نهائية باتكلم على الطريقة كيف بنا
+
+189
+00:20:54,670 --> 00:21:00,130
+نحل المثالات طبعا هذه بواحد وهذه zero على zero
+
+190
+00:21:00,130 --> 00:21:03,490
+يعني
+
+191
+00:21:03,490 --> 00:21:09,130
+نفصل هذه الى اللي هي اعصر ضروف دالتي تمام تماميبقى
+
+192
+00:21:09,130 --> 00:21:14,970
+هذا limit لما ال X و ال Y بدها تروح إلى Zero و
+
+193
+00:21:14,970 --> 00:21:23,010
+Zero لل E أُس Y في limit لما ال X و ال Y بدها تروح
+
+194
+00:21:23,010 --> 00:21:32,510
+ل Zero Zero ل Sin X على X و يسار ماعنديش ال X كإن
+
+195
+00:21:32,510 --> 00:21:38,680
+ال Y بدها تروح ل Zero التعرض المباشربيعطيكي EOS
+
+196
+00:21:38,680 --> 00:21:44,500
+Zeroطب و هذه ماعنديش ويب كأنه ال X بده تروح لمين
+
+197
+00:21:44,500 --> 00:21:51,380
+لزرع عظم المعروف فهذه من Calculus A وقداش واحد إذا
+
+198
+00:21:51,380 --> 00:21:55,980
+ماكنتش Calculus A بروح ل Calculus B بقول Zero على
+
+199
+00:21:55,980 --> 00:22:00,580
+Zero بقعدة نوبة المشتقة تبص على مشتقين المقام يبقى
+
+200
+00:22:00,580 --> 00:22:04,300
+Cos X على واحد Cos صفر بواحد على واحد اللي همين
+
+201
+00:22:04,300 --> 00:22:09,740
+بواحد صحية يبقى نتيجة تزاوي واحد فقط لغير
+
+202
+00:22:14,390 --> 00:22:22,810
+ثالث يبقى يحلى بالنا limit لما ال X وال Y بدأت
+
+203
+00:22:22,810 --> 00:22:31,190
+تروح لمين للواحد وواحد ل X تربيع ناقص Y تربيع على
+
+204
+00:22:31,190 --> 00:22:33,090
+X ناقص Y
+
+205
+00:22:35,990 --> 00:22:43,570
+عاوزة ان انا اشر شو بيجيب ليه لكن لو انا طلعت في
+
+206
+00:22:43,570 --> 00:22:47,890
+ال bus بلاقي هو عبارة عن فرق بين المربعين يبقى هذا
+
+207
+00:22:47,890 --> 00:22:53,890
+الكلام بده يساوي limit لما ال x و ال y بده تروح
+
+208
+00:22:53,890 --> 00:23:02,200
+للواحدة واحد بحلل هذا x ناقص y في x زائد yعلى مين
+
+209
+00:23:02,200 --> 00:23:06,900
+على x نقص y طبعا الجو السادة بيروح مع الجو السادة
+
+210
+00:23:06,900 --> 00:23:12,220
+وبالتالي تقول المسألة الى limit لما ال x و ال y
+
+211
+00:23:12,220 --> 00:23:18,460
+يروح واحد و واحد فضل اني كداش x زائد y يبقى واحد
+
+212
+00:23:18,460 --> 00:23:24,010
+زائد واحد يساوي كداش اتنين إذا يا بنات إذا كانفي
+
+213
+00:23:24,010 --> 00:23:29,650
+عندي rational function في البسط والمقام بحلل كل من
+
+214
+00:23:29,650 --> 00:23:34,030
+البسط والمقام وبجري الاقتصاد اللي موجودة وبعد هيك
+
+215
+00:23:34,030 --> 00:23:38,490
+بروح بعض و اتطوير مباشرة بنحصل على مين على النتيجة
+
+216
+00:23:38,490 --> 00:23:46,810
+كما في هذا المثال نعطي مثالة مرابعا بدنا
+
+217
+00:23:46,810 --> 00:23:53,850
+limit لما ال X و ال Y بدها تروح لمين؟ لاثنينو
+
+218
+00:23:53,850 --> 00:24:01,770
+اتنين بشرط ان ال X زائد ال Y ما تسويش اربعة لل X
+
+219
+00:24:01,770 --> 00:24:08,070
+زائد ال Y ناقص اربعة على الجدرى الترابيع ل X زائد
+
+220
+00:24:08,070 --> 00:24:14,650
+Y ناقص اتنين السؤال
+
+221
+00:24:14,650 --> 00:24:21,060
+مرة تاليةLimit لدالة قدامنا هي عندي ال X و ال Y
+
+222
+00:24:21,060 --> 00:24:27,040
+بتروح ل 2 و 2 بشرط ان ال X زاد Y ماتسويش 4 طب لو
+
+223
+00:24:27,040 --> 00:24:32,520
+سوى 4 شو بدي يحصل يبقى بتصير general 4 اللي هو ب2
+
+224
+00:24:32,520 --> 00:24:38,900
+ناقص 2 ب0 و 4 ناقص 4 بصير 0 على 0 طب ايش بدنا نسوي
+
+225
+00:24:38,900 --> 00:24:40,040
+في هذه الدالة
+
+226
+00:24:50,580 --> 00:24:54,760
+تحليل ال bus كفارق
+
+227
+00:24:54,760 --> 00:25:03,740
+بين المرابعين كما
+
+228
+00:25:03,740 --> 00:25:06,420
+اقتصدنا في السؤال السابق
+
+229
+00:25:10,330 --> 00:25:14,310
+الـ bus أو المقام بيروح بضرورة مين في المرافق
+
+230
+00:25:14,310 --> 00:25:18,830
+للمقدار اللي فيه الجدر يبقى هذا الكلام بيساوي
+
+231
+00:25:18,830 --> 00:25:26,480
+limit لما ال X و ال Y بدا تروح لليه 2 و 2بشرط إن
+
+232
+00:25:26,480 --> 00:25:32,880
+ال X زائد ال Y ما نسويش أربعة لمن؟ لل X زائد ال Y
+
+233
+00:25:32,880 --> 00:25:39,940
+ناقص أربعة على الجدر التربيعي لل X زائد ال Y ناقص
+
+234
+00:25:39,940 --> 00:25:46,220
+اتنين تمين للجدر التربيعي لل X زائد Y زائد اتنين
+
+235
+00:25:46,220 --> 00:25:53,760
+على الجدر التربيعي لل X زائد Y زائد اتنينهذا
+
+236
+00:25:53,760 --> 00:25:59,740
+الكلام بده يسوي limit لما ال X و ال Y بدها تروح لل
+
+237
+00:25:59,740 --> 00:26:04,920
+إتنين و إتنين بشرط إن ال X زائد ال Y مايسويش
+
+238
+00:26:04,920 --> 00:26:12,740
+الأربعة طبعا بصير علمين ال X زائد ال Y نقص الأربعة
+
+239
+00:26:12,740 --> 00:26:20,560
+في الجدري التربيعي لل X زائد Y زائد 2 كل هذا
+
+240
+00:26:20,560 --> 00:26:26,440
+مقسوما علىهل ليس هذا هو تحليل الفرق بين المربعين؟
+
+241
+00:26:26,440 --> 00:26:29,760
+يجب أن أعود إلى أصله يجب أن يكون مرفع الكمية
+
+242
+00:26:29,760 --> 00:26:35,480
+الأولى الحمد لله الجدر مع السلامة يطير ويبقى لدي X
+
+243
+00:26:35,480 --> 00:26:41,140
+زائد Y هنا ناقص أربع المقدار هذا هو نفس المقدار
+
+244
+00:26:41,140 --> 00:26:47,860
+لأن هذا يتم اختصار وبالتالي تقول المسألة إلى limit
+
+245
+00:26:47,860 --> 00:26:54,070
+عندما X وYبعدها تذهب إلى الـ 2 و 2 بشرط أن X زائد
+
+246
+00:26:54,070 --> 00:27:03,900
+Y لا يساوي 4 لـ square root X زائد Y زائد 2بنروح
+
+247
+00:27:03,900 --> 00:27:07,880
+لعوض تعويض مباشر يبقى هذا الكلام بيساوي الجدرى
+
+248
+00:27:07,880 --> 00:27:13,560
+التربيعى للإتنين زائد اتنين زائد اتنين و لو كله
+
+249
+00:27:13,560 --> 00:27:18,220
+على بعضه بيساوي جداري بيساوي أربعة إذا نهاية هذا
+
+250
+00:27:18,220 --> 00:27:24,460
+المقدار بيساوي جداري بيساوي أربعة يبقى عليها بناء
+
+251
+00:27:24,460 --> 00:27:30,060
+ال limit لهذه ال function أعطتنى أربعة وحلينا عن
+
+252
+00:27:30,060 --> 00:27:31,300
+طريق أحد الطرق
+
+253
+00:27:37,380 --> 00:27:45,260
+بين المربعين واختصرنا سوف نصل إلى نفس النتيجة .
+
+254
+00:27:45,260 --> 00:27:55,820
+السؤال الذي يليه سؤال خمسة يجري بالـ delimit لما
+
+255
+00:27:55,820 --> 00:28:06,290
+ال X وY بدأت تروح لـ Zero Zero لمن ؟ لواحد ناقصكو
+
+256
+00:28:06,290 --> 00:28:23,830
+ساين XY مقسومة على XY اتسالد كو
+
+257
+00:28:23,830 --> 00:28:28,870
+ساين XY مقسومة
+
+258
+00:28:28,870 --> 00:28:33,240
+على XYيعني نضرم في ايش؟ مرافق البصمة ويجب نضر
+
+259
+00:28:33,240 --> 00:28:37,400
+سميمة مائة بالمائة أنا عندي واحد نقص cosine xy
+
+260
+00:28:37,400 --> 00:28:41,260
+يبقى بدها ضرم في واحد زائد cosine xy واقسم على
+
+261
+00:28:41,260 --> 00:28:45,380
+واحد زائد cosine xy وروح اكمل عادي جدا يبقى هذا
+
+262
+00:28:45,380 --> 00:28:48,520
+ضرب في المرافق لكن السؤال اللي جابله ضربنا في
+
+263
+00:28:48,520 --> 00:28:52,280
+المرافق إذا دانيلي خاطر افكر بقنية تانية الكلام
+
+264
+00:28:52,280 --> 00:28:56,180
+اللي قلته صح وبيحل السؤال مائة بالمائة ولا واحد
+
+265
+00:28:56,180 --> 00:29:00,840
+يقدر يعترض عليكم تمام؟لكن انا بفكر في شغلة تانية
+
+266
+00:29:00,840 --> 00:29:06,380
+انا بعرف شوية حساب مثلثات وبالتالي بدأ فابرك هذه
+
+267
+00:29:06,380 --> 00:29:11,620
+المثلة في حيطة حُطها في شكل اخر باستخدام قواعد
+
+268
+00:29:11,620 --> 00:29:18,620
+حساب المثلثات اللي دُرست في calculus A سؤال هذي
+
+269
+00:29:18,620 --> 00:29:26,500
+مين؟ هذي cos xy cos تربيع كلام اذا بص مضلوبة في
+
+270
+00:29:26,500 --> 00:29:32,720
+اتنينلأن cos تربيع ال X يسوى نص في واحد نقص cos 2X
+
+271
+00:29:32,720 --> 00:29:38,320
+إذا أنا لو رجعت إلى حساب المثلثات بقدر أقول limit
+
+272
+00:29:38,320 --> 00:29:45,380
+لما ال X و ال Y بدها تروح إلى Zero و Zero للي
+
+273
+00:29:45,380 --> 00:29:54,200
+اتنين sin تربيع XY على اتنين كل هذا الكلام على X
+
+274
+00:29:54,200 --> 00:29:56,360
+تمين في ال Y
+
+275
+00:30:00,670 --> 00:30:06,690
+طيب تعالى نشوف شو بنسويه بجى بقول لو اتنين اللى
+
+276
+00:30:06,690 --> 00:30:11,450
+فوق شجلبت او نزلت اتعب ايش بيصير؟ XY على اتنين
+
+277
+00:30:11,450 --> 00:30:17,790
+صحيح ولا لأ؟ يبقى هذه بدها تصير limit لما ال X و
+
+278
+00:30:17,790 --> 00:30:26,230
+ال Y بدها تروح ل 00 لصينة تربية XY على اتنين على
+
+279
+00:30:26,230 --> 00:30:27,870
+XY على اتنين
+
+280
+00:30:30,550 --> 00:30:36,370
+هذا مثل ايه؟ 100% صارت الزاوية لأننا XY على 2 وهذا
+
+281
+00:30:36,370 --> 00:30:46,670
+XY على 2 بس هذا ايه؟ XY مش XY ده دولة كذا يبقى رتب
+
+282
+00:30:46,670 --> 00:30:51,410
+أمورك شوف ليش بصير فيها هذه لأن لو عوضنا تعويضا
+
+283
+00:30:51,410 --> 00:30:56,510
+مباشرا ايش بتبقى Zero على Zero صحيح ولا لأ؟ كويس
+
+284
+00:30:56,510 --> 00:30:59,530
+يبقى لو عملتها بشكل اخر
+
+285
+00:31:04,920 --> 00:31:13,440
+هتروح لل zero zero وروح نقول هدى عبارة عن sin xy
+
+286
+00:31:13,440 --> 00:31:21,500
+على اتنين على xy على اتنين في sin xy على اتنين
+
+287
+00:31:21,500 --> 00:31:27,440
+مظبوط طب اللى بتقوله كدهش بنتى؟ واحدطب والتانية
+
+288
+00:31:27,440 --> 00:31:33,320
+Zero يبقى هنا في قدر في Zero يبقى النتيجة تساوي
+
+289
+00:31:33,320 --> 00:31:38,020
+Zero الان لو روحت ضربت في المرافق لازم تطلع نتيجة
+
+290
+00:31:38,020 --> 00:31:42,440
+Zero لو ما طلعتش Zero معناته هذا حلنا غلط يبقى
+
+291
+00:31:42,440 --> 00:31:47,340
+good exercise لك تروح تحل المثلة بطريقة ضرب في
+
+292
+00:31:47,340 --> 00:31:53,950
+مرافق البصر وهو واحد زائد cosine XYحلّيه في البيت
+
+293
+00:31:53,950 --> 00:32:01,190
+بالطريقة الثانية وهي الجواب معاك سؤال السادس V I
+
+294
+00:32:01,190 --> 00:32:09,770
+بدي limit لما ال X و ال Y و ال Z بدل المتغيرين بدي
+
+295
+00:32:09,770 --> 00:32:17,150
+اخليهم تلاتة هنا لمن؟ لاناقص رابع و بقى على اتنين
+
+296
+00:32:17,150 --> 00:32:32,430
+و اتنين لمن؟لتان انفرست اكس YZ اقول
+
+297
+00:32:32,430 --> 00:32:36,590
+كويس اعود تعويض مباشرة ويلا نشوف شو اللي بده يطلع
+
+298
+00:32:36,590 --> 00:32:44,030
+يبقى هادي ويساوي تان انفرست لمينة لل X اللي يساوي
+
+299
+00:32:44,030 --> 00:32:51,840
+بربعه مضروبة في Pi على اتنين في اتنينتنين مع اتنين
+
+300
+00:32:51,840 --> 00:32:58,460
+بتروح بيصير تان انفرز باية على اتنين بس باية على
+
+301
+00:32:58,460 --> 00:33:01,900
+اربعة طبعا مش باية على اتنين باية على اربعة و
+
+302
+00:33:01,900 --> 00:33:03,300
+بيشارت سالم
+
+303
+00:33:19,030 --> 00:33:25,090
+لمين؟ لـ πاية على أربعة ويسوى ناقص. كم فالتان انفس
+
+304
+00:33:25,090 --> 00:33:31,850
+باية على أربعة؟ كم؟ كم يظل الخمسة واربعين؟ واحد
+
+305
+00:33:31,850 --> 00:33:35,570
+إذا تان انفس لباية على أربعة يبقى ساوى واحد يبقى
+
+306
+00:33:35,570 --> 00:33:38,870
+limit تسوى كم؟ سالف واحد
+
+307
+00:33:41,270 --> 00:33:44,250
+إذا اللي قبلها زي ما انتوا شايفين المعلومات اللي
+
+308
+00:33:44,250 --> 00:33:47,530
+درسناها على functions of two variables في حالة ال
+
+309
+00:33:47,530 --> 00:33:51,690
+limit صحيحة لل functions of three variables او
+
+310
+00:33:51,690 --> 00:33:56,470
+variables او ال invariables مهما كان شكل ال main
+
+311
+00:33:56,470 --> 00:34:07,130
+شكل المتغيرات اللي عندنا تان
+
+312
+00:34:07,130 --> 00:34:17,120
+انفرسباي على أربعة تقع
+
+313
+00:34:17,120 --> 00:34:20,360
+في ال domain تبعها لأن ال domain ten inverse نسالي
+
+314
+00:34:20,360 --> 00:34:23,360
+من infinity لإنفينتي هي ten inverse one
+
+315
+00:34:26,020 --> 00:34:30,860
+صحيح بنات هذه مضالة سالب تان انفرست باي على اربعة
+
+316
+00:34:30,860 --> 00:34:35,160
+كمهية بدك تطلع قيمة عددية على الجهاز مالكيش بلاش
+
+317
+00:34:35,160 --> 00:34:39,740
+خليها زي ما هي اذا بدناها المهم نوصل الى نتيجة
+
+318
+00:34:39,740 --> 00:34:48,020
+كويس نجي الان لسؤال رقم اتنين سؤال رقم اتنين على
+
+319
+00:34:48,020 --> 00:34:56,720
+نفس الموضوع بقول ما if إذا كان2 absolute value ل X
+
+320
+00:34:56,720 --> 00:35:06,360
+Y ناقص X تربيع وY تربيع على 6 أقل من 4 ناقص 4
+
+321
+00:35:06,360 --> 00:35:13,760
+كوصاي الجذري التربيعي ل absolute value ل X Y أقل
+
+322
+00:35:13,760 --> 00:35:17,900
+من 2 absolute value ل X Y
+
+323
+00:35:34,400 --> 00:35:39,840
+للأربعة ناقص أربعة كوصين الجذري الترابيعي لـ
+
+324
+00:35:39,840 --> 00:35:40,920
+absolute value
+
+325
+00:36:16,650 --> 00:36:23,610
+السؤال مرة تانية بيقول لو عندك تلت دوال، الدالة
+
+326
+00:36:23,610 --> 00:36:27,490
+الأولى، أقل من الدالة التانية، أقل من الدالة
+
+327
+00:36:27,490 --> 00:36:32,070
+التالتة، في ال delimit للدالة اللي في المصم مقسومة
+
+328
+00:36:32,070 --> 00:36:37,290
+على absolute value ل X Y، لأول واحدة من حد ما شوف
+
+329
+00:36:37,290 --> 00:36:41,660
+السؤال بهذا الشكل، شوفوا كم سنة وشتيرةلأن هذه
+
+330
+00:36:41,660 --> 00:36:46,260
+كانها مقارنة بين ال limits لمين لثلاث دواد، إذا
+
+331
+00:36:46,260 --> 00:36:51,660
+أنا بدأ أروح أستخدم صلاحياتي في حل هذه المثلة،
+
+332
+00:36:51,660 --> 00:36:56,660
+كونوا فيين دي absolute value، إذا احتمال ال X Y ال
+
+333
+00:36:56,660 --> 00:37:02,610
+absolute بالإلها ليطلع منهايكون الرقم موجب يكون
+
+334
+00:37:02,610 --> 00:37:09,390
+الرقم
+
+335
+00:37:09,390 --> 00:37:11,470
+موجب يكون الرقم موجب يكون الرقم موجب يكون الرقم
+
+336
+00:37:11,470 --> 00:37:12,810
+موجب يكون الرقم موجب يكون الرقم موجب يكون الرقم
+
+337
+00:37:12,810 --> 00:37:13,550
+موجب يكون الرقم موجب يكون الرقم موجب يكون الرقم
+
+338
+00:37:13,550 --> 00:37:13,590
+موجب يكون الرقم موجب يكون الرقم موجب يكون الرقم
+
+339
+00:37:13,590 --> 00:37:13,690
+موجب يكون الرقم موجب يكون الرقم موجب يكون الرقم
+
+340
+00:37:13,690 --> 00:37:19,090
+موجب يكون الرقم موجب يكون الرقم موجب يكون الرقم
+
+341
+00:37:19,090 --> 00:37:28,870
+موجب يكون الرقم موجب يكون الرقم موجبإذا لو كانت
+
+342
+00:37:28,870 --> 00:37:33,870
+الـ x,y قيمة موجبة إيش اللي بده يحصل في هذه
+
+343
+00:37:33,870 --> 00:37:40,110
+الحلقة؟ يبقى بدهاجة يقول بده يصير ال absolute
+
+344
+00:37:40,110 --> 00:37:46,690
+value الـ x,y دائما و أبدا موجبة صحيح ولا لا؟ يبقى
+
+345
+00:37:46,690 --> 00:37:54,930
+بصيري المسألة كتالة يبقى بصير عندنا اتنين اتنين x
+
+346
+00:37:54,930 --> 00:37:55,630
+,y
+
+347
+00:38:17,940 --> 00:38:24,160
+إذا ما دام ال X Y موجة بقدر أقسم عليها كلها
+
+348
+00:38:26,340 --> 00:38:27,480
+يبقى الـ
+
+349
+00:38:30,950 --> 00:38:38,030
+على 6xy أقل من أربعة ناقص أربعة كوصيني الجدري
+
+350
+00:38:38,030 --> 00:38:42,110
+بتربيها يعني لإن هذه حطيت ال absolute مدى موجب
+
+351
+00:38:42,110 --> 00:38:46,110
+والله ماحطيتهاش سيئة يعني لو شيلتها والله حد إنها
+
+352
+00:38:46,110 --> 00:38:54,010
+موجبة ماعنديش مشكلة فيها على مين على ال XY مخسوما
+
+353
+00:38:54,010 --> 00:39:03,900
+على XY يبقى هنا أقل من 2 أقل من 2طيب خديني ال
+
+354
+00:39:03,900 --> 00:39:07,880
+limit لثلاثة أطراف ناخد ال limit لثلاثة أطراف
+
+355
+00:39:07,880 --> 00:39:12,800
+ممكنش لما ال x و y بده يروح لل zero zero يبقى بده
+
+356
+00:39:12,800 --> 00:39:18,140
+يصير عندي هنا limit لما ال x و ال y راح لل zero
+
+357
+00:39:18,140 --> 00:39:25,780
+zero للي اتنين ناقص x تربيع و y تربيع على ستة x y
+
+358
+00:39:25,780 --> 00:39:28,540
+طبعا لو اختصرنا هنا ماذا يصير عندي هنا
+
+359
+00:39:34,820 --> 00:39:42,560
+أقل من أو يسوى ال limit لما X وY بدها تروح لل 0 0
+
+360
+00:39:42,560 --> 00:39:50,920
+لل 4 ناقص 4 cosine absolute value لل X Y على ال X
+
+361
+00:39:50,920 --> 00:39:58,120
+Y أقل من أو يسوى limit لما ال X وY بده يروح لل 0 0
+
+362
+00:39:58,120 --> 00:40:03,520
+لمين؟ لل إتنينطب ما لما ال X و ال Y بتروح ل 0،0
+
+363
+00:40:03,520 --> 00:40:09,240
+هذا ال term ممكن تدريش يا بنات يبقى صار ال E2 بدأ
+
+364
+00:40:09,240 --> 00:40:19,450
+أقل من limit لما ال X و ال Yبدي اروح الى 00 لل4-4
+
+365
+00:40:19,450 --> 00:40:26,130
+cos absolute value لل X Y على ال X Y لو حطيت ال
+
+366
+00:40:26,130 --> 00:40:31,110
+absolute في مشكلة لأ مهي بالموجة بس مشان شكل اللي
+
+367
+00:40:31,110 --> 00:40:35,110
+هو المطلوب ليس الا اقل من اتنين
+
+368
+00:40:39,260 --> 00:40:49,270
+يبقى باجي بقوله باي ساندوش تيريم بصير ال limitلأ
+
+369
+00:40:49,270 --> 00:40:53,710
+الاربعة ناقص اربعة كوصين الجدري الترابيعي ال
+
+370
+00:40:53,710 --> 00:40:57,930
+absolute value ل X و Y على ال absolute value ل X و
+
+371
+00:40:57,930 --> 00:41:03,690
+Y لما ال X و Y بدها تروح ل Zero Zero بده يسوي قدر
+
+372
+00:41:03,690 --> 00:41:10,610
+نقل هذا لو كانت X و Y أكبر من مين من ال Zero بدالي
+
+373
+00:41:10,610 --> 00:41:11,930
+أخد F
+
+374
+00:41:15,750 --> 00:41:21,610
+من الـ zero يعني حاصل ضربه ما كان كمية سالبة و
+
+375
+00:41:21,610 --> 00:41:26,610
+يحدث هذا الكلام لو كانت X بالسالب و Y بالموجة أو
+
+376
+00:41:26,610 --> 00:41:31,970
+العكس X بالموجة و Y بالسالب يبقى المثلة تبعتي هذا
+
+377
+00:41:31,970 --> 00:41:39,210
+بقدر اكتفها على الشكل التالي يبقى اتنين ناقص X
+
+378
+00:41:39,210 --> 00:41:39,870
+تربيع
+
+379
+00:41:46,220 --> 00:41:52,720
+أقل من أربعة ناقص أربعة كوصين الجذري التربيعي ل
+
+380
+00:41:52,720 --> 00:41:59,000
+absolute value ل X Y كله مبسوما على absolute value
+
+381
+00:41:59,000 --> 00:42:07,080
+ل X Y أقل من جداش أقل من اتنينبالأقل لما تبقى هذا
+
+382
+00:42:07,080 --> 00:42:12,240
+سالب بقدر أتخلص من هذا ال absolute وبالتالي بيصير
+
+383
+00:42:12,240 --> 00:42:24,080
+المسألة E2 زائد X تربيع Y تربيع على 6XY يعني شيلت
+
+384
+00:42:24,080 --> 00:42:28,480
+ال absolute و حطيت إشارة سالب مع السلب مايحصل
+
+385
+00:42:28,480 --> 00:42:39,430
+بالموجب أقل من 4نقص أربعة كوصين الجذري التربيعي لل
+
+386
+00:42:39,430 --> 00:42:49,190
+X في Y على absolute value لل X Y أقل من مين أقل من
+
+387
+00:42:49,190 --> 00:42:52,290
+الأتنين بعد ذلك ناخد
+
+388
+00:43:09,820 --> 00:43:16,940
+خُد ال limit للثلاثة أطراف بيصير limit للإتنين
+
+389
+00:43:16,940 --> 00:43:25,520
+زائد لو اختصرنا هذه بلدش بصير x y على ستة لما x و
+
+390
+00:43:25,520 --> 00:43:33,220
+y بدها تروح ل zero و zero أقل من limit لما ال x و
+
+391
+00:43:33,220 --> 00:43:41,510
+ال y بدها تروحلزيرو زيرو للاربعة ناقص أربعة الجدري
+
+392
+00:43:41,510 --> 00:43:47,810
+التربيعي ال cosine الجدري التربيعي cosine الجدري
+
+393
+00:43:47,810 --> 00:43:52,330
+التربيعي ال absolute value لل X Y على absolute
+
+394
+00:43:52,330 --> 00:44:00,170
+value لل X Y أقل من limit للإتنين لما ال X والY
+
+395
+00:44:00,170 --> 00:44:00,970
+بدها
+
+396
+00:44:08,820 --> 00:44:19,080
+تاني هتديلي قداش؟ اتنين اقل من limit x y بدها تروح
+
+397
+00:44:19,080 --> 00:44:24,320
+لل zero و ال zero لل أربعة ناقص أربعة قصين الجدري
+
+398
+00:44:24,320 --> 00:44:31,560
+التربيعي لل x y absolute value x y اقل من أو يساوي
+
+399
+00:44:31,560 --> 00:44:38,480
+اتنين برضه بيسألت و اشتغلهم ايه؟ ساندوش
+
+400
+00:44:39,230 --> 00:44:46,830
+سيُرِم الـ Limit لما الـ X والـ Y بدها تروح للـ
+
+401
+00:44:46,830 --> 00:44:52,690
+Zero والـ Zero كل هذا الكلام للمقدار أربعة ناقص
+
+402
+00:44:52,690 --> 00:44:57,970
+أربعة Cos ل Square Root لل absolute value لل X وY
+
+403
+00:44:57,970 --> 00:45:03,250
+على ال absolute value لل X وY بده سوى كده اتنين
+
+404
+00:45:03,630 --> 00:45:09,510
+الطالعين في العلاقة رقم واحد وهي واحد وهذا العلاقة
+
+405
+00:45:09,510 --> 00:45:15,410
+رقم اتنين إذا سواء كانت X وY موجب والله سالبة
+
+406
+00:45:15,410 --> 00:45:25,490
+مايفرقش علنا يبقى thus وهكذا او from thus اللي هو
+
+407
+00:45:25,490 --> 00:45:25,910
+ال limit
+
+408
+00:45:51,000 --> 00:45:57,940
+يبقى هذا مثال عملي على استخدامالنقطة السادسة من
+
+409
+00:45:57,940 --> 00:46:02,940
+خواص ال limits على ال functions of several
+
+410
+00:46:02,940 --> 00:46:04,040
+variables
+
+411
+00:46:47,010 --> 00:46:59,090
+F of X Y F of X Y has different
+
+412
+00:46:59,090 --> 00:47:02,790
+limits
+
+413
+00:47:19,890 --> 00:47:31,810
+path is عبر مصارين مختلفين as x و y بدها تروح الى
+
+414
+00:47:31,810 --> 00:47:43,490
+x node و y node then limit f of x و y لما x و y
+
+415
+00:47:43,490 --> 00:47:47,350
+بدها تروح الى x node و y node
+
+416
+00:48:22,430 --> 00:48:28,930
+كفينها مرة ثانية نقرأ شوي المكتوب نحاول نفهمه
+
+417
+00:48:28,930 --> 00:48:36,310
+تماما ايش بقولي بقول لو عندك ال F of X و Y has
+
+418
+00:48:36,310 --> 00:48:42,630
+different limits نهايات مختلفة along two different
+
+419
+00:48:42,630 --> 00:48:48,930
+paths عبر مسارين مختلفين لما ال X و Y بدأت تروح لل
+
+420
+00:48:48,930 --> 00:48:55,050
+X node و Y nodeLimit لـ f of x و y لما الـ x و y
+
+421
+00:48:55,050 --> 00:49:00,510
+بتروح الأكسنون does not exist يبقى هذه وسيلة من
+
+422
+00:49:00,510 --> 00:49:04,630
+إحدى الوسيلة بتثبت ان limit هذه مالها does not
+
+423
+00:49:04,630 --> 00:49:09,470
+exist غير موجة كيف هذا الكلام ممولة كويسة افترضي
+
+424
+00:49:09,470 --> 00:49:17,510
+عندنا محاول يقولون هذا محور x وهذا محور y أخدنا
+
+425
+00:49:17,510 --> 00:49:23,700
+نقطة زي النقطة هذه مثلاهذا ليحدثي تبعه X node وY
+
+426
+00:49:23,700 --> 00:49:32,720
+node. أي منحنى.يمروا بهذه النقطة ممكن اخدوا مسار
+
+427
+00:49:32,720 --> 00:49:36,660
+من المسارات اللي احنا بنحكي عنها وبالتالي قد يكون
+
+428
+00:49:36,660 --> 00:49:42,940
+المسار خط مستقيم أفق قد يكون خط مستقيم رأسي قد
+
+429
+00:49:42,940 --> 00:49:49,340
+يكون خط مستقيم مائم قد يكون منحنى على سبيل المثال
+
+430
+00:49:49,340 --> 00:49:55,700
+يعني ممكن اقول هذا مسار ممكن اقول هذا مسار ممكن
+
+431
+00:49:55,700 --> 00:50:00,960
+اقول هذا مسارأجي واحد تاني قال لي لأ ممكن يكون هذا
+
+432
+00:50:00,960 --> 00:50:05,900
+ما صار أنا رايح فيه على النقفة ممكن من تحت ماعناه
+
+433
+00:50:05,900 --> 00:50:11,000
+مشكلة واحد قال لي لأ انا في عندي منحنى المنحنى
+
+434
+00:50:11,000 --> 00:50:17,260
+ممكن ييجي هيك يبقى أنا رايح على النقفة لأن هذا اجي
+
+435
+00:50:17,260 --> 00:50:22,280
+واحد تاني قال لي لأ انا ممكن اطبع المنحنى بالشكل
+
+436
+00:50:22,280 --> 00:50:29,390
+هذا هيكالمهم المسار يكون رايح على النقطةيبقى لو
+
+437
+00:50:29,390 --> 00:50:33,770
+أخدت مسارين اتنين أخدت ال limit مع المسار الأول
+
+438
+00:50:33,770 --> 00:50:39,270
+لما ال XY بيروح لنفس النقطة هذه لقيته سوا رقم مشيت
+
+439
+00:50:39,270 --> 00:50:43,750
+على مسار تاني و أخدت ال limit يعطاني رقم ثاني غير
+
+440
+00:50:43,750 --> 00:50:47,610
+رقم الأولان يبقى في هذا الحالة بيقول ال limit مانع
+
+441
+00:50:47,610 --> 00:50:54,410
+does not exist مشان ال limit إذا بدوا كل المسارات
+
+442
+00:50:54,410 --> 00:50:57,790
+التي سامروا بهذه النقطة بتأدي إلى نفس النتيجة
+
+443
+00:51:05,600 --> 00:51:10,220
+أفرض في هذه النقطة أنا بس عندي عشر مسارات قلتلها
+
+444
+00:51:10,220 --> 00:51:15,340
+أيوة جلت تسع مسارات أقن نفس النتيجة و المسار
+
+445
+00:51:15,340 --> 00:51:18,920
+العشري أقن نتيجة مختلفة because does not exist على
+
+446
+00:51:18,920 --> 00:51:25,020
+طول الخط exist بدل كل جميع المسارات التي تمور بهذه
+
+447
+00:51:25,020 --> 00:51:32,340
+النقطةبناء عليه واضحة الصورة اللى عندنا هذه مش
+
+448
+00:51:32,340 --> 00:51:35,500
+تاخدى بمسار لا يمر بالنقطة و تروح تحجب تقول that
+
+449
+00:51:35,500 --> 00:51:39,020
+does not exist ولا exist المسار اللى بتاخده يجب ان
+
+450
+00:51:39,020 --> 00:51:44,800
+تتأكد فعلا انه يمر بهذه النقطة لو أخدت مسار آخر لا
+
+451
+00:51:44,800 --> 00:51:50,380
+يمر بصير كلامك غلط نعطي أمثلة توضحية على ذلك
+
+452
+00:52:01,580 --> 00:52:12,540
+التقاليدات التالية تظهر ان التقاليدات
+
+453
+00:52:12,540 --> 00:52:16,660
+التالية ليست
+
+454
+00:52:16,660 --> 00:52:23,260
+موجودة ليست
+
+455
+00:52:23,260 --> 00:52:25,980
+موجودة ك
+
+456
+00:52:39,960 --> 00:52:49,580
+Limit لمن ؟ لـ X تربيع ناقص Y على X ناقص Y طبعاً
+
+457
+00:52:49,580 --> 00:52:58,940
+لما X و Y بدها تروح للـ Zero أنا عندي
+
+458
+00:52:58,940 --> 00:53:04,160
+function و بدى أحسب بـ Limit لهذه function عند مين
+
+459
+00:53:04,160 --> 00:53:10,670
+عنده نقطة الأصل برجع أقول شو ممكن نقطة الأصلمحور X
+
+460
+00:53:10,670 --> 00:53:18,930
+محور Y Y تساوي X تربية Y تساوي X تكيب Y تساوي
+
+461
+00:53:18,930 --> 00:53:24,910
+الجذر التالت ل X الاخر Y تساوي X تربية زائد واحد
+
+462
+00:53:24,910 --> 00:53:30,830
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+463
+00:53:30,830 --> 00:53:30,910
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+464
+00:53:30,910 --> 00:53:31,530
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+465
+00:53:31,530 --> 00:53:33,310
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ ل
+
+466
+00:53:36,220 --> 00:53:40,100
+إذا جيت مع مصار لا يمروا بهذه النقطة إذا قولت هذا
+
+467
+00:53:40,100 --> 00:53:44,640
+غلط يبقى المصار اللي بدي أخد اتأكد فعلا انه يمروا
+
+468
+00:53:44,640 --> 00:53:49,500
+بهذه النقطة حتى يكون كلامنا معلوم صحيح طيب خليني
+
+469
+00:53:49,500 --> 00:53:54,120
+اختار مصار ما هو شوف ايش بتقوله لو اخد مثلا على
+
+470
+00:53:54,120 --> 00:54:03,030
+سبيل المثال عبر محور X يبقى بدأت اقوله تكذى path
+
+471
+00:54:03,030 --> 00:54:09,610
+خد للمصار y تساوي zero مين y تساوي zero؟ اللي هو
+
+472
+00:54:09,610 --> 00:54:15,210
+ال x axis اللي هو ال x axis يبقى بصير هذه يا بنات
+
+473
+00:54:15,210 --> 00:54:24,210
+limit لما ال x وال y بدها تروحلمن؟ لل a لل 0 و لل
+
+474
+00:54:24,210 --> 00:54:30,370
+0 لل 0 و لل 0 لمن؟ بدي أشيل ال y و أضع مكانها 0
+
+475
+00:54:30,370 --> 00:54:36,170
+ماذا يحصل؟ عندك x تربيع على x يعني limit لما ال x
+
+476
+00:54:36,170 --> 00:54:47,090
+و ال y راحت لل 0 و لل 0 فقط ل x كم يصبح عندي 0 طيب
+
+477
+00:54:47,520 --> 00:54:56,600
+الان بدأت أقوله take the path خد المسافة مثلا x
+
+478
+00:54:56,600 --> 00:55:07,580
+تساوي زيرو ال y axis يعني ال y axis إيش بده يصير
+
+479
+00:55:07,580 --> 00:55:17,760
+limit لما ال x و ال y بدها تروح ل 0,0لمن ؟ ل X
+
+480
+00:55:17,760 --> 00:55:24,160
+تربيع ال X كنتش قولنا Zero ما طالع عندي قداشر ناقص
+
+481
+00:55:24,160 --> 00:55:31,520
+Y على ناقص Y كدهش بطلع ال limit واحد صحيح يبقى هنا
+
+482
+00:55:31,520 --> 00:55:37,480
+واحد صحيح شو رأيكوا في سنتين الأثنين هدول سنتين
+
+483
+00:55:37,480 --> 00:55:44,120
+مختلفتين يبقى هنا بروح بقوله سواء ال limit لل X
+
+484
+00:55:44,120 --> 00:55:52,270
+تربيعناقص y على x ناقص y لما ال x و ال y بدنا يروح
+
+485
+00:55:52,270 --> 00:55:59,290
+ل zero و zero لا يوجد
+
+486
+00:55:59,290 --> 00:56:03,330
+لأن
+
+487
+00:56:03,330 --> 00:56:08,790
+ال zero لا يساوي ال واحد
+
+488
+00:56:36,950 --> 00:56:42,450
+عشان نعطي مثال لبنات نبرى
+
+489
+00:56:42,450 --> 00:56:54,170
+بيه ان ال limit لما ال x و y يتقع من 0،0 لما ال x
+
+490
+00:56:54,170 --> 00:56:58,390
+و y تقع على x ترمية
+
+491
+00:57:11,560 --> 00:57:15,020
+طبعا انا اتفرج من المؤشر يجيب لي 0 على 0 يقول ده
+
+492
+00:57:15,020 --> 00:57:20,900
+اختار مسار فعلا يمر بنقطة الأصل مثلا لو يقول Y
+
+493
+00:57:20,900 --> 00:57:24,920
+تساوي X خط
+
+494
+00:57:24,920 --> 00:57:29,740
+مستقيم بنصف اللي هو الزاوية بين محور X و محور Y
+
+495
+00:57:29,740 --> 00:57:34,460
+الرابع الأول بنصف و تمر بنقطة الأصل يبقى باجي
+
+496
+00:57:34,460 --> 00:57:36,560
+بقوله مثلا P
+
+497
+00:57:46,740 --> 00:57:53,140
+يجب ان اشيل
+
+498
+00:57:53,140 --> 00:57:57,680
+كل Y و اضع مكانها X او اشيل كل X و اضع مكانها Y
+
+499
+00:57:57,680 --> 00:58:02,880
+سواء كانت هذه او تلت اتنين are the same يجب ان
+
+500
+00:58:02,880 --> 00:58:03,640
+اشيل كل Y و اضع مكانها X او اشيل كل X و اضع مكانها
+
+501
+00:58:10,730 --> 00:58:17,570
+يبقى بنات صارت هذه كإنها إيش لمل لما ال X وال Y
+
+502
+00:58:17,570 --> 00:58:25,390
+بدها تروح ل 00 ل X أُس 4 على X تربيه عامل مشترك
+
+503
+00:58:25,390 --> 00:58:28,890
+يظل 1 زي X أُس 4
+
+504
+00:58:36,510 --> 00:58:43,790
+بدا تروح للـ 0 والـ 0 لل X تربيع على 1 زايد X أُس
+
+505
+00:58:43,790 --> 00:58:50,590
+4 نشيل كل X ونحط مكانها Zero يبقاش مصير Zero على
+
+506
+00:58:50,590 --> 00:58:59,190
+واحد زايد Zero ويساوي Zero نجرب أي مسار آخر بحيث
+
+507
+00:58:59,190 --> 00:59:02,390
+المسار يمر بنقطة الأصل
+
+508
+00:59:06,170 --> 00:59:13,830
+take the path مثلًا على سبيل المثال Y يسوى الجذر
+
+509
+00:59:13,830 --> 00:59:20,650
+التالت ل X يعني X أسطول هل تعرفين الملحانة دي أم
+
+510
+00:59:20,650 --> 00:59:29,850
+لا؟ عارفين او لا؟ تقول plus A هاي هذا محور X هذا Y
+
+511
+00:59:29,850 --> 00:59:36,280
+هذا أصل الملحانة بيجي ك .. بيجي بالشكل هذايبقى هذا
+
+512
+00:59:36,280 --> 00:59:42,980
+Y تساوي X أسطل يبقى فعلا يمر بنقطة الأصل اللي
+
+513
+00:59:42,980 --> 00:59:46,940
+عندنا يبقى شوف ايش اللي بده يصير بده يصير limit
+
+514
+00:59:46,940 --> 00:59:54,260
+لما ال X و ال Y بده يروح ل 0 0 لمين للدالة اللي
+
+515
+00:59:54,260 --> 00:59:56,500
+عندنا هذه يبقى هذه X
+
+516
+01:00:13,210 --> 01:00:19,430
+والـ Y بدها تذهب الى الـ 0 و الـ 0 هذه برنامج
+
+517
+01:00:19,430 --> 01:00:25,790
+بعتبارها X أُس تلت لكل تكييب بـ X أُس واحد وعند X
+
+518
+01:00:25,790 --> 01:00:32,530
+يجب أن يكون X تربيع فقط لغاية X تربيع وهذه X أُس
+
+519
+01:00:32,530 --> 01:00:39,490
+تلت أُس ستة يبقى أُس مركب بسيط جدا X تربيع يبقى
+
+520
+01:00:39,490 --> 01:00:45,810
+صارت هذه الـ limitلما الـ X و الـ Y بدها تروح إلى
+
+521
+01:00:45,810 --> 01:00:51,870
+الـ 0,0 للـ X تربيع على 2 X تربيع يبقى الـ Limit
+
+522
+01:00:51,870 --> 01:00:56,350
+هذي تساوي قدر شبلها؟ نص لإختصار X تربيها مع X
+
+523
+01:00:56,350 --> 01:01:02,010
+تربيها بتعطي نص تطلع هنا نص وهنا Zero يبقى ال
+
+524
+01:01:02,010 --> 01:01:04,770
+Limit تضمن Exact يبقى ال Limit
+
+525
+01:01:20,700 --> 01:01:31,480
+does not exist because اللي هو الـ zero لا يساوي
+
+526
+01:01:31,480 --> 01:01:36,660
+نص ولا تشبيه تماما زي ما كنا في الcalculation
+
+527
+01:01:36,660 --> 01:01:40,160
+بناخد ال limit من اليمين و من الشمال إذا اختلفت
+
+528
+01:01:40,160 --> 01:01:43,920
+اليمين عن الشمال يكون ال limit does not exist إذا
+
+529
+01:01:43,920 --> 01:01:48,720
+هنا لهم مسارين مختلفينمشينا مع الأول ومشينا مع
+
+530
+01:01:48,720 --> 01:01:52,300
+التاني واخدنا المتوطالي different limits، خمتين
+
+531
+01:01:52,300 --> 01:01:55,740
+مختلفتين، إذا بروح بقوله إن ال limit اللي عندي هذه
+
+532
+01:01:55,740 --> 01:01:58,960
+مالها لازم ت exist
+
+533
+01:02:01,490 --> 01:02:09,130
+كيف؟ بس مسارين مش سبع بس مسارين كفين اتنين ان شاء
+
+534
+01:02:09,130 --> 01:02:13,890
+الله يكون فيه خمس طاقم سمعت ايش قلنالك لول قلنالك
+
+535
+01:02:13,890 --> 01:02:18,850
+افترضي انه عندي عشر مسارات و لما شرحت الجزء النظري
+
+536
+01:02:18,850 --> 01:02:25,250
+قبل الأمثلة و لجيت تسع مسارات اعطاني نفس القيمة
+
+537
+01:02:25,250 --> 01:02:29,490
+لكن المسار العاشر ماعطانيش نفس القيمة اذا ال limit
+
+538
+01:02:29,490 --> 01:02:37,160
+ايش قلناها؟does not exist يعني
+
+539
+01:02:37,160 --> 01:02:40,260
+عندي خمسة و تلاتين طالب اللي أجيلا تمانتاش على
+
+540
+01:02:40,260 --> 01:02:58,320
+النص يعزيزي
+
+541
+01:03:02,040 --> 01:03:06,880
+هذا الكلام اللي شفته قبل قليل كله موجود في جزء
+
+542
+01:03:06,880 --> 01:03:09,440
+النظر التابع للتابع للتابع للتابع للتابع للتابع
+
+543
+01:03:09,440 --> 01:03:11,500
+للتابع للتابع للتابع للتابع للتابع للتابع للتابع
+
+544
+01:03:11,500 --> 01:03:14,680
+للتابع للتابع للتابع للتابع للتابع للتابع للتابع
+
+545
+01:03:14,680 --> 01:03:14,980
+للتابع للتابع للتابع للتابع للتابع للتابع للتابع
+
+546
+01:03:14,980 --> 01:03:16,240
+للتابع للتابع للتابع للتابع للتابع للتابع للتابع
+
+547
+01:03:16,240 --> 01:03:17,440
+للتابع للتابع للتابع للتابع للتابع للتابع للتابع
+
+548
+01:03:17,440 --> 01:03:24,520
+للتابع للتالان باجي بقول لو جينا نشتغل مباشر زي ما
+
+549
+01:03:24,520 --> 01:03:28,860
+كنا بنشتغل في كل الأمثلة السابقة وطلع اللي مت zero
+
+550
+01:03:28,860 --> 01:03:33,080
+على zero مالة نهاية مالة نهاية zero في مالة نهاية
+
+551
+01:03:33,080 --> 01:03:38,120
+يعني شغلات does not exist ومش قادرة أتلحح أو أحرك
+
+552
+01:03:38,120 --> 01:03:41,760
+حالي مع المسألة اللي موجودة شو نعمل في مثل هذه
+
+553
+01:03:41,760 --> 01:03:46,400
+الحالة؟ قال لي بسيطة اتحول إلى polar coordinates
+
+554
+01:03:47,040 --> 01:03:53,440
+تحول مثلتك إلى احداثيات او قطبية بيصير المسألة
+
+555
+01:03:53,440 --> 01:03:59,440
+سهلة وبنحل المسألة بكل سهولة طبعا طيب كيفك تتحول
+
+556
+01:03:59,440 --> 01:04:03,420
+لل polar coordinates هذا ما سنضعه في صيغة ال
+
+557
+01:04:03,420 --> 01:04:08,080
+remark التالية نبدأ بكتير remark
+
+558
+01:04:18,840 --> 01:04:31,580
+we cannot find إذا مش قادرين نوجد ال limit لل f of
+
+559
+01:04:31,580 --> 01:04:39,660
+x و y لما ال x و ال y بدها تروح إلى x node و y
+
+560
+01:04:39,660 --> 01:04:45,040
+node شو نعمل فيها دلوقتي way to change
+
+561
+01:04:49,200 --> 01:05:00,440
+will change to the polar coordinates يجب أن نتحول
+
+562
+01:05:00,440 --> 01:05:07,500
+إلى الإحداثيات القطبية من الإحداثيات القطبية ال X
+
+563
+01:05:07,500 --> 01:05:15,280
+يساوي R Cos Thetaوالـ y يسوي r sin θ وعندك الـ r
+
+564
+01:05:15,280 --> 01:05:23,000
+تسوي الجذري التربيعي ل x تربيع زائد y تربيع ونقض
+
+565
+01:05:23,000 --> 01:05:27,940
+ان الـ
+
+566
+01:05:27,940 --> 01:05:35,180
+r بدها تروح للزيرو if and only if ال x و ال y بدها
+
+567
+01:05:35,180 --> 01:05:36,460
+تروح للزيرو
+
+568
+01:05:43,520 --> 01:05:47,200
+خلّيني اوضّح الكلام اللي احنا بنقوله بالرسم ثم
+
+569
+01:05:47,200 --> 01:05:52,760
+نبدأ نشتغل بيه ابقى لو جيت اخدت محاور بهذا الشكل
+
+570
+01:05:52,760 --> 01:06:00,400
+يا بنات وقولت هذا محور X وهذا محور Y وهذه نقطة
+
+571
+01:06:00,400 --> 01:06:08,420
+الأصل جينا رسمنا دائرة اللي مركزها نقطة الأصل ونصف
+
+572
+01:06:08,420 --> 01:06:16,090
+قطرها يساوي R على سبيل المثاليبقى هذا لو R نصف
+
+573
+01:06:16,090 --> 01:06:24,550
+القطر تبع هذه الدائرة هذه النقطة عند محيط الدائرة
+
+574
+01:06:24,550 --> 01:06:30,830
+بدي أسميها X وY في الـ Cartesian coordinates لو
+
+575
+01:06:30,830 --> 01:06:35,910
+كانت الزاوية هذه اللي هي الزاوية ثيتا ونزلت من هنا
+
+576
+01:06:35,910 --> 01:06:43,280
+عمودي يبقى هذا X و هذا Yيبقى X اللي عندي تساوي R
+
+577
+01:06:43,280 --> 01:06:49,260
+Cos θ و ال Y اللي عندي هذي بR Sin θ لإن الزاوية
+
+578
+01:06:49,260 --> 01:06:56,460
+هذه زاوية قائمة طب لو ربعته وجمعت مش بصير عنديX
+
+579
+01:06:56,460 --> 01:07:00,420
+تربيع زائد Y تربيع تساوي R تربيع Cos تربيع زائد R
+
+580
+01:07:00,420 --> 01:07:03,540
+تربيع Sine تربيع باخد R على التربيع و اشتغل بقى
+
+581
+01:07:03,540 --> 01:07:07,300
+Cos تربيع زائد Sine تربيع من دين واحد يبقى بيصير X
+
+582
+01:07:07,300 --> 01:07:12,140
+تربيع زائد Y تربيع تساوي R تربيع إذا بدي R بقول
+
+583
+01:07:12,140 --> 01:07:16,100
+square root ل X تربيع زائد Y تربيع إذا عرفنا
+
+584
+01:07:16,100 --> 01:07:20,940
+العلاقة الأخيرة من أين جاءت طيب لو يا بنات ال X
+
+585
+01:07:20,940 --> 01:07:28,970
+راحت لل ZeroوY نزلت للزيرو يعني لو هاني وصلت هنا
+
+586
+01:07:28,970 --> 01:07:35,060
+هي ب X نقصة و Y نقصة R تزيد ولا تنجح اصلا؟يعني
+
+587
+01:07:35,060 --> 01:07:41,660
+افترض هنا وصلت لهنا كيف يعني احس النقطة هيك صارت
+
+588
+01:07:41,660 --> 01:07:45,740
+ال Y صغيرة و ال X أكبر شوية مثلا على سبيل المثال
+
+589
+01:07:45,740 --> 01:07:50,340
+يبقى إذا ال X راحت ل Zero و ال Y راحت ل Zero
+
+590
+01:07:50,340 --> 01:07:54,740
+فبتروح ل Zero طبيعي يبقى ال R بتروح ل Zero لو كان
+
+591
+01:07:54,740 --> 01:07:56,920
+ال X و Y راحت ل Zero
+
+592
+01:08:06,260 --> 01:08:14,600
+الصورة نعطي أمثلة توضيحية على هذا الكلام for
+
+593
+01:08:14,600 --> 01:08:22,280
+example find
+
+594
+01:08:22,280 --> 01:08:23,460
+the following limits
+
+595
+01:08:34,720 --> 01:08:40,100
+فإذا كانت موجودة
+
+596
+01:08:40,100 --> 01:08:45,780
+إذا كانت
+
+597
+01:08:45,780 --> 01:08:50,560
+موجودة إذا كانت موجودة
+
+598
+01:09:17,050 --> 01:09:21,670
+طبعا اول مجلة في ذهن نفسي اقول بدي احلل الزاوية
+
+599
+01:09:21,670 --> 01:09:25,710
+اللي عندناها كفرق بين المكعبين افترض حالة انها في
+
+600
+01:09:25,710 --> 01:09:30,490
+اختصارات بينهم و بين المقام لأ هل يمكن تحليل
+
+601
+01:09:30,490 --> 01:09:35,410
+المقام؟ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+602
+01:09:35,410 --> 01:09:37,350
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+603
+01:09:37,350 --> 01:09:43,310
+لأ لأ لأ لأ لأ لأ لأ
+
+604
+01:09:43,700 --> 01:09:49,240
+مش مصيري عندي cosine قداش؟ Zero على Zero، مش
+
+605
+01:09:49,240 --> 01:09:52,740
+عارفين؟ ماعرفش ما هو Zero على Zero، كمية غير معينة
+
+606
+01:09:52,950 --> 01:09:57,110
+إذا كوصيلة كمية غير معينة برضه بعرفاش طب كيف بدي
+
+607
+01:09:57,110 --> 01:10:01,590
+أسوي للتحليل مش قادر يختصر و هيك مش ثابتة أبدا
+
+608
+01:10:01,590 --> 01:10:06,250
+بالمرة؟ مظبوط؟ يبقى فيش إمكانية في هذه الحالة
+
+609
+01:10:06,250 --> 01:10:10,890
+بالطرق التي سبقت دراستها في ال Cartesian Curve
+
+610
+01:10:10,890 --> 01:10:15,490
+لنحل هذه المثلة أحد المثال اللي ابتدى لبالك في
+
+611
+01:10:15,490 --> 01:10:19,230
+التمرينتمام طب كيف نسوي في هذه الحالة إذا ال
+
+612
+01:10:19,230 --> 01:10:23,790
+automatic ماليش إلا اتحول إلى polar coordinates
+
+613
+01:10:23,790 --> 01:10:26,430
+إذا لما اتحول إلى polar
+
+614
+01:10:34,270 --> 01:10:41,610
+R تكييب Cos تكييب ثيتا ناقص R تكييب Sin تكييب ثيتا
+
+615
+01:10:41,610 --> 01:10:48,990
+كله على R تربيع Cos تربيع ثيتا زائد R تربيع في Sin
+
+616
+01:10:48,990 --> 01:10:55,870
+تربيع ثيتا كله ال limit لما ال R بتروح لوين؟ لزيرو
+
+617
+01:10:56,410 --> 01:11:01,030
+الان صار في عندى اختصارات بقدر اخد R تكييب عمل
+
+618
+01:11:01,030 --> 01:11:06,810
+مشترك او بقدر اخد R تربيع عمل مشترك وبالتالي بتقول
+
+619
+01:11:06,810 --> 01:11:12,350
+المسألة الى الشكل التالي limit لما ال R بدها تروح
+
+620
+01:11:12,350 --> 01:11:17,930
+لل zero ليه cosine هنا يا بنات R تكييب
+
+621
+01:11:20,930 --> 01:11:28,710
+فى مين فى cosine تكييب ثيتا نقص sin تكييب ثيتا على
+
+622
+01:11:28,710 --> 01:11:37,190
+R تربيع فقط لغير فى cosine تربيع ثيتا زائد sin
+
+623
+01:11:37,190 --> 01:11:39,870
+تربيع ثيتا بالشكل اللى عالى
+
+624
+01:11:43,460 --> 01:11:48,960
+لما نختصر هذا ما يحصل؟ يحصل limit لما الار بدها
+
+625
+01:11:48,960 --> 01:11:57,260
+تروح ل zero ل cosine ار في cosine تكييب تيتا ناقص
+
+626
+01:11:57,260 --> 01:12:05,240
+صيني تكييب تيتا على كده؟ اه السلامة راح تبقى شايفة
+
+627
+01:12:05,240 --> 01:12:09,500
+كيف لما حولت إلى ال polar coordinates اتبسطت المثل
+
+628
+01:12:09,500 --> 01:12:13,800
+عندى وصرت بالشكل اللي عندنا هذاطب لما الار بدت
+
+629
+01:12:13,800 --> 01:12:18,800
+ساوي بدت تروح للزيرو يبقى كده ايش بيصير كوصين صفر
+
+630
+01:12:18,800 --> 01:12:23,420
+في الجسد بيعطي كوصين زيرو له بقدام واحد إذا المثل
+
+631
+01:12:23,420 --> 01:12:26,380
+اللي ماكنتش قادر اتلخلح فيه في ال Cartesian
+
+632
+01:12:26,380 --> 01:12:30,020
+coordinates لما حولت إلى ال polar coordinates صارت
+
+633
+01:12:30,020 --> 01:12:36,600
+عملية عملية سهلة وبالتالي حصلت على كده مقدار هذه
+
+634
+01:12:36,600 --> 01:12:39,680
+ال element ناخد كمان مثال
+
+635
+01:12:44,900 --> 01:12:55,680
+بدنا limit لما ال X و ال Y بدها تروح ل 00 لتان
+
+636
+01:12:55,680 --> 01:13:01,100
+inverse اللي همين absolute value ل X و absolute
+
+637
+01:13:01,100 --> 01:13:06,860
+value ل Y على X تربيع زائد Y تربيع
+
+638
+01:13:11,990 --> 01:13:16,050
+برضه التعويض المباشر بيجيب لـ 0 يا عزيزي صح؟ إذا
+
+639
+01:13:16,050 --> 01:13:21,210
+بتحول ل 100 من ال polar coordinates يبقى هذي بيصير
+
+640
+01:13:21,210 --> 01:13:27,590
+ال limit لما ال R بدأ تروح ل 0 لتان inverse و هي
+
+641
+01:13:27,590 --> 01:13:32,810
+القوة هذا absolute value لل R في sin θ absolute
+
+642
+01:13:32,810 --> 01:13:41,190
+value لل R sin θ كله على R تربية في sin تربية ثتا
+
+643
+01:13:47,710 --> 01:13:54,450
+هذا الكلام بده يساوي limit لما ال R بدها تروح
+
+644
+01:14:00,640 --> 01:14:06,180
+الـ absolute value لـ R في absolute value للـ
+
+645
+01:14:06,180 --> 01:14:12,540
+cosine عمر المسافة يا بنات هذه كانت سالبة و ليست
+
+646
+01:14:12,540 --> 01:14:17,900
+جبهة يبقى ال absolute لل cosine وهذا R بره يبقى لو
+
+647
+01:14:17,900 --> 01:14:24,920
+أخدت R عامل مشترك يبقى cosine θ زائد sin θ ك
+
+648
+01:14:24,920 --> 01:14:35,130
+absolute وهذا ك absoluteهذه R تربيع في كوصين تربيع
+
+649
+01:14:35,130 --> 01:14:41,730
+تيتا زائد صين تربيع تيتا بالشكل اللي علناه يبقى
+
+650
+01:14:41,730 --> 01:14:47,270
+هذا الكلام يسمي limit لما ال R بدها تروح ل zero
+
+651
+01:14:47,270 --> 01:14:54,150
+لمن لتان inverse absolute value لكوصين تيتا زائد
+
+652
+01:14:54,150 --> 01:14:58,550
+absolute value لصين تيتا كله على R
+
+653
+01:15:00,980 --> 01:15:04,960
+يبقى R تربيع وSin تربيع زي الـSin تربيع اللي هي
+
+654
+01:15:04,960 --> 01:15:10,860
+أبواحد طب لما الـR بدها تروح لـinfinity يبقى ايش
+
+655
+01:15:10,860 --> 01:15:20,900
+بيصير يا بنات تان انفرز شكل على زيرو كده انفرز تان
+
+656
+01:15:20,900 --> 01:15:26,800
+انفرز يعني كده باي على اتن يبقى limit
+
+657
+01:15:29,840 --> 01:15:34,620
+لحد هنا أستاذ يكفينا على النقطة الأولى من هذا ال
+
+658
+01:15:34,620 --> 01:15:40,320
+section نروح للنقطة الثانية اللي مرتبطة مع هذه
+
+659
+01:15:40,320 --> 01:15:44,080
+النقطة تماما اللي هو ال continuity
+
+660
+01:16:22,540 --> 01:16:34,420
+is sent to the continuous المتصلة
+
+661
+01:16:34,420 --> 01:16:42,720
+at the point عند النقطة x0
+
+662
+01:16:58,600 --> 01:17:08,960
+defined at x non و y non الشرط التاني لو كانت ال
+
+663
+01:17:08,960 --> 01:17:19,020
+limit لل f of x و y لما ال x و ال y بدها تروح ال x
+
+664
+01:17:19,020 --> 01:17:22,640
+non و y non exist
+
+665
+01:17:25,100 --> 01:17:35,160
+الشرط التالف لو كانت ال F of X node و Y node بتسوي
+
+666
+01:17:35,160 --> 01:17:42,800
+limit F of X و Y لما ال X و ال Y بده يروح إلى X
+
+667
+01:17:42,800 --> 01:17:52,660
+node و Y node لما
+
+668
+01:17:52,660 --> 01:17:57,710
+نمر إلى الشروط التالفهذه اختلافات عن الشروط
+
+669
+01:17:57,710 --> 01:18:01,130
+التلاتة تبع الcontinuity الـ function فيه one
+
+670
+01:18:01,130 --> 01:18:06,850
+variable تبع calculus A يجهيها اللهم إلا حولناها
+
+671
+01:18:06,850 --> 01:18:14,450
+بعدة تناسب معدلة في متغيرين أو ثلاثة متغيرات أو ان
+
+672
+01:18:14,450 --> 01:18:18,360
+من المتغيرات وهكذايبقى الدالة بيقول انها
+
+673
+01:18:18,360 --> 01:18:23,140
+continuous عند نقطة x0 و y0 إذا الدالة كانت معرفة
+
+674
+01:18:23,140 --> 01:18:28,780
+عند هذه النقطة او f of x0 و y0 exist مش هذا نفس
+
+675
+01:18:28,780 --> 01:18:33,880
+المعنى، من الثاني ال limit cannot exist تلاتة
+
+676
+01:18:33,880 --> 01:18:38,280
+اتنين هدول بدهم يسووا بعض، يبقى ال f of x0 و y0
+
+677
+01:18:38,280 --> 01:18:41,550
+بده يسووا ال limitتبعت ال F of X و Y لما ال X Y
+
+678
+01:18:41,550 --> 01:18:45,350
+بتروح ل X0 و Y0 إذا تحققت الشروط التلاتة في أن
+
+679
+01:18:45,350 --> 01:18:51,010
+الواحد بقول الدالة متصلة عند هذه النقطة طيب في
+
+680
+01:18:51,010 --> 01:18:55,510
+كالخلصية أخدنا بعض الشغلات أو بعض النظريات أو بعض
+
+681
+01:18:55,510 --> 01:19:00,040
+القواعدلان كنت ريوز ال functions صحيحة هنا زي اذا
+
+682
+01:19:00,040 --> 01:19:04,700
+عندى two functions وتنتين كانوا متصلات في المجموعة
+
+683
+01:19:04,700 --> 01:19:08,460
+التاصلة وحاصلة الدرب والقسمة والضغط في المجلد دابل
+
+684
+01:19:08,460 --> 01:19:13,100
+الى اخرين كثيرات الحدود دوال متصلة ال rational
+
+685
+01:19:13,100 --> 01:19:16,960
+function بحيث المقام مايسوي zero كذلك كلها دوال
+
+686
+01:19:16,960 --> 01:19:22,800
+متصلة اذا هذا الكلام ينطبق على الكلام في حالة ال
+
+687
+01:19:22,800 --> 01:19:23,840
+functions of
+
+688
+01:19:37,480 --> 01:19:48,080
+in your functions دوال متصلة then المقطة الأولى ال
+
+689
+01:19:48,080 --> 01:19:57,500
+F زائد أو ناقص ال G ال F في G ال F على G وبشرط ان
+
+690
+01:19:57,500 --> 01:19:58,020
+ال G
+
+691
+01:20:21,600 --> 01:20:27,940
+rational functions are
+
+692
+01:20:27,940 --> 01:20:39,720
+continuous تبقى دوال متصلة in which بحيث ان these
+
+693
+01:20:39,720 --> 01:20:48,540
+functions are defined هتكون
+
+694
+01:20:48,540 --> 01:20:57,020
+دوال معرفةالأمرة التلاتة كثيرات الحدود polynomials
+
+695
+01:20:57,020 --> 01:21:04,400
+are continuous functions.
+
+696
+01:21:07,140 --> 01:21:13,380
+Examples كال
+
+697
+01:21:13,380 --> 01:21:21,940
+الأولواسأل هل ده اللي قابل اتصال ولا لا as the
+
+698
+01:21:21,940 --> 01:21:30,840
+function as the function f of x y أحقها
+
+699
+01:21:48,530 --> 01:21:56,650
+زيرو زيرو وهنا بتساوي زيرو لما X وY بدها تساوي
+
+700
+01:21:56,650 --> 01:22:05,890
+زيرو زيرو هل الدالة هذه continuous at
+
+701
+01:22:05,890 --> 01:22:09,850
+زيرو زيرو ام لا؟
+
+702
+01:22:44,450 --> 01:22:48,370
+يقول لي هل الدلة اللي عندنا هذه متصلة عندنا نقطة
+
+703
+01:22:48,370 --> 01:22:52,970
+00 ولا لا طبعا الدلة مجزة إلى مين ؟ مجزة إلى هنا
+
+704
+01:22:52,970 --> 01:22:56,790
+فأقول لك تاجر الشروب انت لا تشوف متحققة ولا لا
+
+705
+01:22:56,790 --> 01:23:03,310
+الان F of 00 كده شبنات إذا معرفة صح ولا لا يبقى
+
+706
+01:23:03,310 --> 01:23:12,450
+باجي بقوله هنا ال solution تاجر النقطة الأولىالـ F
+
+707
+01:23:12,450 --> 01:23:19,830
+of 0 0 بيبقى سوية 0 فهذا معناته ان ال F is defined
+
+708
+01:23:19,830 --> 01:23:25,610
+defined at
+
+709
+01:23:25,610 --> 01:23:32,510
+اللي هو 0 و 0 اذا بتروح لمين لل condition التاني
+
+710
+01:23:49,120 --> 01:23:56,790
+لو أخدت مثلًا عبرة محور X يبقى وايه بقداشبزيرو
+
+711
+01:23:56,790 --> 01:24:02,330
+يبقى ايش بيصير عندى؟ واحد طب لو انا شكت عبر محور X
+
+712
+01:24:02,330 --> 01:24:09,590
+عبر محور Y يبقى X بزيرو بيطلع الجواب سنة بواحد
+
+713
+01:24:09,590 --> 01:24:17,850
+يبقى limit does not exist يبقى هنا take the path
+
+714
+01:24:20,350 --> 01:24:27,130
+مسارين X يساوي 0 و Y يساوي 0 و نحن نحن نحن نحن نحن
+
+715
+01:24:27,130 --> 01:24:30,570
+نحن نحن
+
+716
+01:24:30,570 --> 01:24:31,550
+نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن
+
+717
+01:24:31,550 --> 01:24:32,710
+نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن
+
+718
+01:24:32,710 --> 01:24:35,250
+نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن
+
+719
+01:24:35,250 --> 01:24:40,570
+نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن
+
+720
+01:24:40,570 --> 01:24:48,430
+نحن
+
+721
+01:24:48,430 --> 01:24:55,030
+نحلما الـ X و الـ Y بدها تروح لـ 0 و الـ 0 و Y
+
+722
+01:24:55,030 --> 01:24:59,790
+تساوي 0، إيش بيظل عندي X تربيه علي X تربيه تساوي
+
+723
+01:24:59,790 --> 01:25:04,850
+1؟ هنا سالف واحد عبر المسار الأول، واحد عبر المسار
+
+724
+01:25:04,850 --> 01:25:09,250
+التاني، يبقى ال limit ما له لازم not exist يبقى
+
+725
+01:25:09,250 --> 01:25:15,350
+هنا سواء ال limit لما ال X و Yذا تروح للـ Zero و
+
+726
+01:25:15,350 --> 01:25:22,190
+Zero لل X تربيع ناقص Y تربيع على X تربيع زائد Y
+
+727
+01:25:22,190 --> 01:25:27,570
+تربيع لا يوجد
+
+728
+01:25:27,570 --> 01:25:38,010
+سبب لأنه سالم واحد لاتساوي واحد يبقى Therefore
+
+729
+01:25:46,220 --> 01:26:09,480
+is not continuous at zero zero مثال أقم اتنين وقول
+
+730
+01:26:09,480 --> 01:26:21,930
+is the function هل الدالةf of x و y تساوي تلاتة x
+
+731
+01:26:21,930 --> 01:26:30,610
+تربيع y على x تربيع زائد y تربيع لما ال x و ال y
+
+732
+01:26:30,610 --> 01:26:41,950
+لا تساوي 0 0 وتساوي 0 لما ال x و ال y بدها تساوي 0
+
+733
+01:26:41,950 --> 01:26:44,870
+0 continuous
+
+734
+01:26:48,370 --> 01:26:54,210
+at zero zero هذا
+
+735
+01:26:54,210 --> 01:26:58,310
+السؤال solution
+
+736
+01:26:58,310 --> 01:27:03,350
+إذا
+
+737
+01:27:03,350 --> 01:27:08,070
+نيجي نشوف شروط ال continuity التلاتة هل هي متحققة
+
+738
+01:27:08,070 --> 01:27:10,790
+و الله غير متحقق
+
+739
+01:27:34,520 --> 01:27:39,420
+الدالة واضحة انها معرفة عند 00 مظبوط يبقى بقوله
+
+740
+01:27:39,420 --> 01:27:45,460
+الخطوة الأولى فتاخد ال F of 00 ده الساوية Zero هذا
+
+741
+01:27:45,460 --> 01:27:58,080
+بيقول ان ال F is defined at 00 بعد هيك فتاخد ال
+
+742
+01:27:58,080 --> 01:28:05,140
+limit لدالة اللي عندنايبقى بدأ اخد ال limit النقطة
+
+743
+01:28:05,140 --> 01:28:12,700
+الثانية تاخد ال limit لمن؟ لما ال X و ال Y بدها
+
+744
+01:28:12,700 --> 01:28:20,160
+تروح لل Zero و ال Zero لمن؟ لتلاتة X تربيع Y عن X
+
+745
+01:28:20,160 --> 01:28:26,460
+تربيع زائد Y تربيع يبقى بتروح اخد مسارات ده كل
+
+746
+01:28:26,460 --> 01:28:29,680
+واحد اشطر مني شوية يقول طيب جرب ال polar يمكن تكون
+
+747
+01:28:29,680 --> 01:28:35,220
+أسرعبصراحة بدك تاخد مرتين بس في ال polar مرة واحدة
+
+748
+01:28:35,220 --> 01:28:40,880
+مقول له ماشي يبقى هذا الكلام بيساوي limit لما ال X
+
+749
+01:28:40,880 --> 01:28:49,780
+و ال Y او بداش X و Y R بدها تروح لل zero يبقى R
+
+750
+01:28:49,780 --> 01:28:58,370
+بدها تروح لل zero لتلاتة R ترميعوSin تربيع ثيتا في
+
+751
+01:28:58,370 --> 01:29:05,350
+R في Sine الزاوية ثيتا على R تربيع CoSin تربيع
+
+752
+01:29:05,350 --> 01:29:12,310
+ثيتا زائد R تربيع Sine تربيع ثيتا بهذا الكلام يبدو
+
+753
+01:29:12,310 --> 01:29:21,700
+يساوي limit لما ال R بدأت تذهب الى Zeroلتلاتة R
+
+754
+01:29:21,700 --> 01:29:27,800
+تكيب مع ال R تربيع اللي تحت تصيب تلاتة R في Cos
+
+755
+01:29:27,800 --> 01:29:34,620
+تربيع تيتا في Sine تيتا و لتحت الله يسهل عليه طبعا
+
+756
+01:29:34,620 --> 01:29:40,460
+R مع R تربيع بR تكيب R تربيع مع R تكيب بغلق R Cos
+
+757
+01:29:40,460 --> 01:29:44,320
+تربيع زي ال Sine تربيع تيتا اللي هو قداش هو حصيا
+
+758
+01:29:47,250 --> 01:29:54,590
+يبقى ال limit exist و تساوي كده؟ و تساوي zero و
+
+759
+01:29:54,590 --> 01:29:59,070
+الدالة لو معرفة و تساوي كده؟ اذا هذه دالة
+
+760
+01:29:59,070 --> 01:29:59,790
+continuous
+
+761
+01:30:09,210 --> 01:30:15,950
+0 و 0 يعني بالنسبة لك تفهموا إذا قلت عند 0 و 0 ليس
+
+762
+01:30:15,950 --> 01:30:21,550
+معناه هذا الكلام ان ال limit does not exist او في
+
+763
+01:30:21,550 --> 01:30:26,490
+عندي discord في اللي ممكن اعرفه اخدي لك مثال رقم
+
+764
+01:30:26,490 --> 01:30:35,630
+تلاتة شو رايك دي functions ال E أس X ناقص Y و Cos
+
+765
+01:30:35,630 --> 01:30:51,600
+Xزائد Y على X تربية زائد واحد زائد تلاتة وLin خمسة
+
+766
+01:30:51,600 --> 01:30:59,040
+زائد X تربية زائد Y تربية هل هناك نقطة الدالة
+
+767
+01:30:59,040 --> 01:31:04,260
+عندها مش معرفة اي واحد من دول التلاتة اتولى يا
+
+768
+01:31:04,260 --> 01:31:04,680
+عزفي
+
+769
+01:31:11,290 --> 01:31:15,390
+لأ كل واحد لحاله هذول تلات دوال يعني تلات مسائل
+
+770
+01:31:15,390 --> 01:31:18,830
+باعتبارها أي واحدة فيهم هتيله نقطة دليل عندها
+
+771
+01:31:18,830 --> 01:31:25,330
+معاها كله معاها اتنينالثانية الأولى هي exponential
+
+772
+01:31:25,330 --> 01:31:30,330
+فهي متصلة والتالتة كروسايم متصلة مثلا من هنا إلى
+
+773
+01:31:30,330 --> 01:31:36,230
+هنا والتالتة من هنا إلى هنا كمان متصلة، صحيح ولا
+
+774
+01:31:36,230 --> 01:31:42,290
+لأ؟ إذا هذه continuous for all x y بلاستينة يبقى
+
+775
+01:31:42,290 --> 01:31:46,710
+هذه ال functions اللي عندنا دول مالهم are
+
+776
+01:31:46,710 --> 01:31:50,150
+continuous
+
+777
+01:31:52,420 --> 01:32:04,940
+for all x y belasted not I remark the
+
+778
+01:32:04,940 --> 01:32:13,600
+previous rule the previous rules القواعد السابقة
+
+779
+01:32:13,600 --> 01:32:27,470
+on the functions of twovariables are
+
+780
+01:32:27,470 --> 01:32:31,710
+true صحيحة
+
+781
+01:32:31,710 --> 01:32:41,730
+are true for the functions or the functions of
+
+782
+01:32:41,730 --> 01:32:51,650
+three or more variablesيعني ليه ثلاثة متغيرات او
+
+783
+01:32:51,650 --> 01:32:59,750
+اكتر برضه صحيحة examples نمرأ
+
+784
+01:32:59,750 --> 01:33:09,130
+ايه؟ قولي at what points؟ at what points؟ من من
+
+785
+01:33:09,130 --> 01:33:14,650
+النقاط does the following
+
+786
+01:33:36,300 --> 01:33:46,520
+x و y يسوى x زائد ال y على تلاتة ناقص sign اللي هو
+
+787
+01:33:46,520 --> 01:33:50,380
+ال x هل
+
+788
+01:33:50,380 --> 01:33:56,520
+في نقطة يا بنات هذه الدالة عندها غير قابلة للاتصال
+
+789
+01:33:56,520 --> 01:33:58,400
+إذا في قولوني عنها
+
+790
+01:34:26,180 --> 01:34:31,400
+فى ولا حاجة يبقى دى continuous for all x و y يبقى
+
+791
+01:34:31,400 --> 01:34:40,840
+دى continuous for all x و y طيب انتقل الكلمة شوية
+
+792
+01:34:40,840 --> 01:34:54,140
+النقطة الثانية f of x و y تسبب لين اللي هو main x
+
+793
+01:34:54,140 --> 01:35:02,230
+تربيعزائد Y تربية في نقطة عندها الدالة غير معرفة
+
+794
+01:35:02,230 --> 01:35:09,970
+أو ممتصدة اللي المعرف نقيه موجبة صح ولا لأ فSin X
+
+795
+01:35:09,970 --> 01:35:14,430
+تربيه وY تربيه إن كان X وY بالسالب ورمه مموجة
+
+796
+01:35:14,430 --> 01:35:20,830
+فالمربع يبقى ضل أثنين بس نقطة الأصل يجي هذه الدالة
+
+797
+01:35:20,830 --> 01:35:27,560
+continuous ما عادة نقطة الأصليبقى هذه continuous
+
+798
+01:35:27,560 --> 01:35:31,360
+for
+
+799
+01:35:31,360 --> 01:35:44,200
+all x و y except ماعدا 0.000
+
+800
+01:35:44,200 --> 01:35:49,520
+أو ال origin النقطة التالفة
+
+801
+01:35:57,160 --> 01:36:07,020
+اللي هي f of x و y f of x و y بدها تساوي sign واحد
+
+802
+01:36:07,020 --> 01:36:16,180
+على x y يالا
+
+803
+01:36:16,180 --> 01:36:24,620
+وين الدلة مش معرفة عن صفر و صفر و أي واحد صفر و أي
+
+804
+01:36:24,620 --> 01:36:36,790
+رقم آخرالرقم مصفر تمام يبقى هنا continuous except
+
+805
+01:36:45,430 --> 01:37:09,930
+أكترين فوينتز أكترين
+
+806
+01:37:09,930 --> 01:37:10,090
+فوينتز أكترين فوينتز أكترين فوينتز أكترين فوينتز
+
+807
+01:37:14,120 --> 01:37:24,460
+يقول F of X, Y, Z X, Y, Z بيساوي الجدري التربيعي X
+
+808
+01:37:24,460 --> 01:37:40,420
+تربيع زائد Y تربيع ناقص واحد النقاط
+
+809
+01:37:40,420 --> 01:37:46,840
+اللي بتبقى ده اللي عندها continuousيبقى هذا يكون
+
+810
+01:37:46,840 --> 01:37:58,220
+في نواص for all x, y, z except at
+
+811
+01:37:58,220 --> 01:38:07,860
+x تربية زي y تربية ناقص واحدة منها أقل من الـ 0
+
+812
+01:38:11,090 --> 01:38:14,190
+ذا أكبر من Zero مافي مشكلة مُعرّفة لكن إذا أقل من
+
+813
+01:38:14,190 --> 01:38:21,590
+Zero مُعرّفة أو إن شئتم فاقولوا ها ال X تربيع زي
+
+814
+01:38:21,590 --> 01:38:26,950
+دورة تربيع أقل من واحد طب مين هم النقاط هذول يا
+
+815
+01:38:26,950 --> 01:38:34,790
+بنات بس Zero Zero داخل الدائرة احنا في الفراغ X Y
+
+816
+01:38:34,790 --> 01:38:42,120
+و Z سيلندر يبقىكل النقاط اللي داخل الـ except ما
+
+817
+01:38:42,120 --> 01:38:48,760
+عدا النقاط اللي داخل الـ cylinder يبقى هنا هذا
+
+818
+01:38:48,760 --> 01:38:57,440
+معناه ان ال continuous for
+
+819
+01:38:57,440 --> 01:39:04,780
+all x, y, z except the
+
+820
+01:39:04,780 --> 01:39:06,520
+points
+
+821
+01:39:11,550 --> 01:39:22,750
+انترال لسيلندر X تربية زي Y تربية يسوى واحد يعني
+
+822
+01:39:22,750 --> 01:39:26,910
+عند كل النقاط داخل السيلندر الدالة غير مضة لكن برا
+
+823
+01:39:26,910 --> 01:39:39,960
+كلها بتبقى A معارض النقطة الثانية لو قلتك FX Y Z X
+
+824
+01:39:39,960 --> 01:39:53,140
+Y Z X Y Z X Y Z X
+
+825
+01:39:53,140 --> 01:39:57,120
+Y Z X Y Z X Y Z X Y Z X Y Z X Y Z X Y Z X Y Z X Y
+
+826
+01:39:57,120 --> 01:40:05,680
+Z X Y Z X Y Z X Y Z X Y Z X Y Z X Y Z X Y Z X Y Z
+
+827
+01:40:05,680 --> 01:40:06,180
+X Y Z X Y Z X Y Z X Y Z X Y Z X Y Z X Y Z X Y Z X
+
+828
+01:40:06,180 --> 01:40:08,770
+X X X X X X X X X X Xلو كانت ال X و Y بيزيروا مش
+
+829
+01:40:08,770 --> 01:40:12,530
+مشكلة لكن ال Z ممنوع تساوي زي 1 على 0 إذا كانت في
+
+830
+01:40:12,530 --> 01:40:15,630
+مالة نهاية غير معرفة
+
+831
+01:40:25,880 --> 01:40:35,100
+Y زاد بدها تساوي الومين واحد على زد ناقص الجدري
+
+832
+01:40:35,100 --> 01:40:47,820
+التربيعي ل X تربيع زائد Y تربيع يبقى
+
+833
+01:40:47,820 --> 01:40:54,200
+continuous for
+
+834
+01:40:54,200 --> 01:40:54,820
+all
+
+835
+01:40:59,260 --> 01:41:07,520
+بحيث ان المقام له ممنوع يساوي Zero يبقى Z ناقص
+
+836
+01:41:07,520 --> 01:41:13,780
+الجدري التربيعي X تربيع زائد Y تربيع لا يساوي Zero
+
+837
+01:41:13,780 --> 01:41:23,760
+أو Z لا يساوي الجدري التربيعي X تربيع زائد Y تربيع
+
+838
+01:41:23,760 --> 01:41:32,550
+او Z تربيعلا يساوي X تربيع زاد Y تربيع معادلة تشهد
+
+839
+01:41:32,550 --> 01:41:40,450
+يا ابنها لو كانت تساوي كون مخروض صحيح Circular كون
+
+840
+01:41:40,450 --> 01:41:47,490
+القاعة التابعة عبارة عن أي دائرة يبقى هنا except
+
+841
+01:41:47,490 --> 01:41:55,150
+the points on the
+
+842
+01:41:57,760 --> 01:42:08,740
+circular cone Z تربيع X تربيع زائد Y تربيع كل
+
+843
+01:42:08,740 --> 01:42:13,620
+النقاط داخل ال circular cone أو الخارج ال circular
+
+844
+01:42:13,620 --> 01:42:17,720
+cone بعد ما تقعش عليه من الخارج لأنه إذا وقعت عليه
+
+845
+01:42:17,720 --> 01:42:26,650
+مصير كلامي هذا ما هوش صحيح طيب exercisesاربعتاشر
+
+846
+01:42:26,650 --> 01:42:36,770
+وانين المسائل التالية من واحد الى خمسين Multiple
+
+847
+01:42:36,770 --> 01:42:46,070
+of three وزياد عليهم سؤال خمسة وخمسين وسبعة وخمسين
+
+848
+01:42:46,070 --> 01:42:55,170
+ومن واحد وستين لغاية ستة وستين in all
+
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/-aEoMwQERo4_raw.srt b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/-aEoMwQERo4_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..4c4970c16373acddd65ab3fc30ac077082ac622e
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/-aEoMwQERo4_raw.srt
@@ -0,0 +1,3476 @@
+1
+00:00:00,000 --> 00:00:02,680
+موسيقى
+
+2
+00:00:16,600 --> 00:00:21,960
+بسم الله الرحمن الرحيم المرة الماضية بدأنا في
+
+3
+00:00:21,960 --> 00:00:26,740
+chapter 14 واخدنا اول section وهو ال functions of
+
+4
+00:00:26,740 --> 00:00:30,860
+several variables عرفنا هذه ال functions جيبنا ال
+
+5
+00:00:30,860 --> 00:00:35,010
+domain و ال range لهذه ال functionsجيبنا ما يسمى
+
+6
+00:00:35,010 --> 00:00:40,830
+بال level surface و level curves لمين للمنحنة في
+
+7
+00:00:40,830 --> 00:00:44,790
+الأحداثيات الكارثية سواء كان في متغيرين أو في
+
+8
+00:00:44,790 --> 00:00:50,250
+ثلاثة متغيرات اليوم ان شاء الله هنجي لهذه ال
+
+9
+00:00:50,250 --> 00:00:54,230
+functions نجيب ال limits و ال continuity لهذه
+
+10
+00:00:54,230 --> 00:00:58,850
+الدولة هنبدأ بأول لقطة يعني هنقسم هذا section إلى
+
+11
+00:00:58,850 --> 00:01:03,490
+لقطتينالنقطة الأولى بدنا ناخد فيها ال limits
+
+12
+00:01:03,490 --> 00:01:08,630
+والنقطة الثانية بدنا ناخد فيها ال continuity يعني
+
+13
+00:01:08,630 --> 00:01:13,470
+هنقسم محاضرتنا إلى جزئين ان شاء الله تبارك وتعالى
+
+14
+00:01:13,470 --> 00:01:18,770
+لو رجعنا بالذاكرة إلى الورق إلى calculus A أو
+
+15
+00:01:18,770 --> 00:01:22,230
+calculus B كنا بنقول limit ل function
+
+16
+00:01:43,520 --> 00:01:46,320
+يبقى فيه متغير واحد
+
+17
+00:01:55,410 --> 00:02:00,810
+هذا ما كنا ندرسه في calculus a و b الان نقول لو
+
+18
+00:02:00,810 --> 00:02:06,050
+كان ال function فيه متغيرين شو اللي بده يحصل يبقى
+
+19
+00:02:06,050 --> 00:02:11,270
+باجي بقول هنا f ال f is a function of two
+
+20
+00:02:11,270 --> 00:02:19,170
+variables في متغيرين then باجي بقول limit
+
+21
+00:02:22,050 --> 00:02:29,250
+بصارت متغيرات لتحت بيصير x و y بدها تروح الى x
+
+22
+00:02:29,250 --> 00:02:34,970
+node و y node بده يساوي ال مثلة طب لو كانت في
+
+23
+00:02:34,970 --> 00:02:40,630
+ثلاثة متغيرات يبقى لو كانت الدالة function of
+
+24
+00:02:40,630 --> 00:02:50,890
+three variables في ثلاثة متغيرات then limitللـ f
+
+25
+00:02:50,890 --> 00:02:58,790
+of x و y و z لما ال x و ال y و ال z بدها تروح الى
+
+26
+00:02:58,790 --> 00:03:06,010
+x node turns to x node و y node و z node يبقى ناتج
+
+27
+00:03:06,010 --> 00:03:12,650
+هذا بده يساوي L يبقى
+
+28
+00:03:12,650 --> 00:03:18,210
+بده يساوي من؟ بده يساوي Lوهكذا يبقى لو عندى
+
+29
+00:03:18,210 --> 00:03:23,170
+متغيرين تلاتة اربع من المتغيرين كله بنفس الفورمة
+
+30
+00:03:23,170 --> 00:03:28,170
+يبقى نفس المفهوم اللى احنا اتعلمناه بالنسبة لمين
+
+31
+00:03:28,170 --> 00:03:35,510
+لكالكولاس ايه بناء عليه يبقى هنا لو جيت قلتلك اه
+
+32
+00:03:45,750 --> 00:03:48,950
+يبقى أول خطوة في إيجاد limit هو التعويض المباشر
+
+33
+00:03:48,950 --> 00:03:53,710
+يبقى هذه قداشها تساوي X node طب و ال Y ماعنديش Y
+
+34
+00:03:53,710 --> 00:03:58,510
+يبقى لا و لا قتلها كإلها مش موجودة أصلا طب لو قلت
+
+35
+00:03:58,510 --> 00:04:05,270
+limit لل Y لما ال X هو Y بدها تروح لل X node و Y
+
+36
+00:04:05,270 --> 00:04:12,570
+node برضه كمان Y nodeطب لو قلت limit ل constant k
+
+37
+00:04:12,570 --> 00:04:18,810
+لما ال x و y بدها تروح الى x node و y node limit
+
+38
+00:04:18,810 --> 00:04:22,470
+المقدرة ثابت بالمقدرة ثابت itself اللي درس فيه
+
+39
+00:04:22,470 --> 00:04:28,010
+calculus a و الله b و الله c هو نفس الشيء بقوله
+
+40
+00:04:28,010 --> 00:04:34,810
+هنا where حيثم ال k is constant
+
+41
+00:04:39,200 --> 00:04:43,540
+بنفس النتيجة الخاصة المنطقة التي دُرسها في
+
+42
+00:04:43,540 --> 00:04:48,000
+Calculus A على ال limits للfunction نفسها هي على
+
+43
+00:04:48,000 --> 00:04:51,400
+ال functions of two variables, of three variables,
+
+44
+00:04:51,860 --> 00:04:57,340
+of n variables الاخرينبعد ذلك نبدأ نذكر بهذا
+
+45
+00:04:57,340 --> 00:05:01,580
+الكلام لـ function of two variables وما ينطبق على
+
+46
+00:05:01,580 --> 00:05:04,860
+ال function of two variables نفسه تماما على ال
+
+47
+00:05:04,860 --> 00:05:09,360
+functions of three variables او more variables او
+
+48
+00:05:09,360 --> 00:05:14,180
+اكتر من ذلك لو كان اربع متغيرات خمس متغيرات ان من
+
+49
+00:05:14,180 --> 00:05:19,900
+المتغيرات الاخرين يبقى هذا هنحطه على صيغة النظرية
+
+50
+00:05:19,900 --> 00:05:20,720
+التالية
+
+51
+00:05:25,840 --> 00:05:34,120
+بنقول اللي هي ال properties الخاص properties of
+
+52
+00:05:34,120 --> 00:05:42,660
+limits of functions of
+
+53
+00:05:42,660 --> 00:05:45,820
+two variables
+
+54
+00:05:55,220 --> 00:06:01,540
+الـ M الـ M الـ M الـ M الـ M الـ M الـ M الـ M
+
+55
+00:06:01,540 --> 00:06:05,480
+الـ M الـ M الـ M الـ M الـ M الـ M الـ M الـ M
+
+56
+00:06:05,480 --> 00:06:05,860
+الـ M الـ M الـ M الـ M الـ M الـ M الـ M الـ M
+
+57
+00:06:05,860 --> 00:06:05,860
+الـ M الـ M الـ M الـ M الـ M الـ M الـ M الـ M
+
+58
+00:06:05,860 --> 00:06:05,880
+الـ M الـ M الـ M الـ M الـ M الـ M الـ M الـ M
+
+59
+00:06:05,880 --> 00:06:06,040
+الـ M الـ M الـ M الـ M الـ M الـ M الـ M الـ M
+
+60
+00:06:06,040 --> 00:06:06,040
+الـ M الـ M الـ M الـ M الـ M الـ M الـ M الـ M
+
+61
+00:06:06,040 --> 00:06:12,740
+الـ M الـ M الـ M الـ
+
+62
+00:06:12,740 --> 00:06:24,120
+M الـ Mلل f of x و y لما ال x و ال y بدها تروح إلى
+
+63
+00:06:24,120 --> 00:06:35,620
+x node و y node تساوي ال L and ال limit لل g of x
+
+64
+00:06:35,620 --> 00:06:42,120
+و y لما ال x و ال y بدها تروح إلى x node و y node
+
+65
+00:06:42,120 --> 00:06:45,140
+بده يساوي ال M مثلا
+
+66
+00:06:48,650 --> 00:06:52,810
+النقطة الأولى limit
+
+67
+00:07:04,000 --> 00:07:08,780
+عندما تذهب الـ x و الـ y إلى الـ x node و الـ y
+
+68
+00:07:08,780 --> 00:07:17,520
+node يبقى هذا الكلام زائد او ناقص M النقطة الثانية
+
+69
+00:07:17,520 --> 00:07:23,580
+limit لكيف
+
+70
+00:07:23,580 --> 00:07:25,720
+تفهم الـ x و الـ y
+
+71
+00:07:28,690 --> 00:07:37,630
+بدها تروح الى X node وY node بده ساوي K في L and
+
+72
+00:07:37,630 --> 00:07:48,530
+بناء عليه limit لمن؟ لل F of X وY لل G of X وY لما
+
+73
+00:07:48,530 --> 00:07:54,690
+X وY بدها تروح الى X node وY node يبقى هذا الكلام
+
+74
+00:07:54,690 --> 00:08:03,930
+بده ساوي ال L في Mالمقطة الثالثة بدي ال limit لل F
+
+75
+00:08:03,930 --> 00:08:11,770
+of X و Y على ال G of X و Y لما ال X و ال Y بدها
+
+76
+00:08:11,770 --> 00:08:17,910
+تروح إلى X node و Y node
+
+77
+00:08:17,910 --> 00:08:25,270
+يبقى هذا الكلام بده يساوي L على M بشرط ان ال M
+
+78
+00:08:25,270 --> 00:08:38,090
+ممنوع تساوي Zeroوالنقطة الرابعة limit لل F من X و
+
+79
+00:08:38,090 --> 00:08:45,910
+Y كله to the power N لما ال X و ال Y بدها تروح إلى
+
+80
+00:08:45,910 --> 00:08:53,150
+X node و Y node يبقى هذا بده يساوي ال L أس N و ال
+
+81
+00:08:53,150 --> 00:08:58,630
+N is a positive integer
+
+82
+00:09:10,240 --> 00:09:15,860
+لما ال X و ال Y بدها تروح الى X naught و Y naught
+
+83
+00:09:15,860 --> 00:09:27,400
+للجذر النوني لل F of X و Y بده يساوي الجذر النوني
+
+84
+00:09:27,400 --> 00:09:36,100
+ل L و له بده يساوي L اصول واحد على M و ال M as a
+
+85
+00:09:36,100 --> 00:09:37,440
+positive integer
+
+86
+00:10:28,780 --> 00:10:36,600
+أقل من أو يساوي ال F of X Y أقل من أو يساوي ال H
+
+87
+00:10:36,600 --> 00:10:49,520
+of X Y for all X Y التي لا تساوي X node وY node
+
+88
+00:10:53,570 --> 00:11:06,230
+in a disk and a disk centered at x node و y node
+
+89
+00:11:06,230 --> 00:11:14,190
+and if وإذا
+
+90
+00:11:14,190 --> 00:11:24,830
+كان limit للـ g of x و y لما ال x و ال yإلى x non
+
+91
+00:11:24,830 --> 00:11:35,030
+و y non بده يساوي limit لما ال x و y بدها تروح ل x
+
+92
+00:11:35,030 --> 00:11:43,250
+non و y non لل h of x و y بده يساوي ال L then
+
+93
+00:11:43,250 --> 00:11:52,610
+limitللـ f of x و y لما ال x و ال y بدها تروح الى
+
+94
+00:11:52,610 --> 00:11:57,270
+x نهض و y نهض يبقى بده يساوي ال L كذلك
+
+95
+00:12:43,190 --> 00:12:48,170
+لو راجعنا الى هذه الخواص الست اللى قدامنا لن نجد
+
+96
+00:12:48,170 --> 00:12:53,690
+انها تختلف مع الست خواص تبع ال calculus A التي
+
+97
+00:12:53,690 --> 00:12:59,270
+درست في أول ما دخلت الجامعة في الفصل الأول أثناء
+
+98
+00:12:59,270 --> 00:13:03,310
+دراسة يبقى المعلومات اللى كانت على function of one
+
+99
+00:13:03,310 --> 00:13:07,690
+variable نفسها على function of two variables
+
+100
+00:13:08,180 --> 00:13:13,000
+الخواصة بتقول لي ما يأتي افترض ان عندي L و M و K
+
+101
+00:13:13,000 --> 00:13:19,700
+كانت اعداد حقيقية limit f of x و y يساوي L limit g
+
+102
+00:13:19,700 --> 00:13:23,900
+of x و y يساوي
+
+103
+00:13:23,900 --> 00:13:30,140
+Mالنقطة الأولى درسنا في calculus A نهاية المجموع
+
+104
+00:13:30,140 --> 00:13:34,700
+الجبري لدالتين يساوي المجموع الجبري للنهايتين ايش
+
+105
+00:13:34,700 --> 00:13:38,960
+معناه؟ معناه كإن ال limit بتدخش على الدالة الأولى
+
+106
+00:13:38,960 --> 00:13:42,600
+زيد أو نقص ال limit لما تدخش على الدالة الثانية
+
+107
+00:13:42,600 --> 00:13:46,420
+يبقى limit الدالة الأولى بL limit الدالة الثانية
+
+108
+00:13:46,420 --> 00:13:51,600
+بM هل في خلاف بينها و بين calculus A؟ لا خلاف نقطة
+
+109
+00:13:51,600 --> 00:13:57,530
+تانيةLimit حاصل ضرب مقدار ثابت في دلة يبقى المقدار
+
+110
+00:13:57,530 --> 00:14:02,930
+الثابت في نهاية الدلة لأن limit ال constant قبل
+
+111
+00:14:02,930 --> 00:14:06,890
+قليل كتبنا بال constant itself يعني لو اعتبرت هذا
+
+112
+00:14:06,890 --> 00:14:11,550
+limit لحاصل ضرب دلتين بديكون limit المقدار الثابت
+
+113
+00:14:11,550 --> 00:14:15,270
+بالمقدار الثابت itself في limit الدلة اللي هو بالL
+
+114
+00:14:15,270 --> 00:14:20,960
+يبقى حاصل الضرب K في Lو كذلك لو بدل ال K كانت
+
+115
+00:14:20,960 --> 00:14:25,520
+function أخرى و لتكن اللي هو الدالة F والدالة G
+
+116
+00:14:25,520 --> 00:14:30,000
+limit حصل ضارب two functions سوى limit الدالة
+
+117
+00:14:30,000 --> 00:14:35,380
+الأولى مضروب في limit الدالة ثانية و L في M بالمثل
+
+118
+00:14:35,380 --> 00:14:40,960
+لو كانت قسمةيبقى limit لل F of X وY على ال G of X
+
+119
+00:14:40,960 --> 00:14:45,140
+وY لما ال X وY بتروح ال X node وY node يسوى limit
+
+120
+00:14:45,140 --> 00:14:49,760
+ال bus على limit المقام يعني بقدر اوزع limit لكل
+
+121
+00:14:49,760 --> 00:14:55,720
+من ال bus والمقام يبقى بناء عليها يسوى L على M بشر
+
+122
+00:14:56,800 --> 00:15:00,760
+المقام ممنوع يساوي صفر يعني ممنوع ال M تساوي Zero
+
+123
+00:15:00,760 --> 00:15:05,400
+لأن ال M لو كانت ب Zero بصير ال demand غير معادلة
+
+124
+00:15:05,400 --> 00:15:10,520
+ف does not exist مش موجودة تمام؟ طيب النقطة
+
+125
+00:15:10,520 --> 00:15:15,520
+الرابعة لمة ال alphabets مرفوعة to the power Nالـ
+
+126
+00:15:15,520 --> 00:15:20,860
+limit قلت لكم معها Vip تدخل على الجزء تربيه تكعيب
+
+127
+00:15:20,860 --> 00:15:25,600
+أُس N تدخل تحت الجذر تدخل على الزاوية تبع النسبة
+
+128
+00:15:25,600 --> 00:15:30,160
+المثلثية تدخل على العدد داخل ال N أو على الدلة
+
+129
+00:15:30,160 --> 00:15:33,620
+داخل ال N إلى أقلينيبقى المعنى هذا الكلام ان ال
+
+130
+00:15:33,620 --> 00:15:38,440
+limit دخلت داخل القوس لكل أُس N limit الدلة اللي
+
+131
+00:15:38,440 --> 00:15:44,000
+داخل القوس هو L بصير أُس N بحيث N عدد صحيح موجب
+
+132
+00:15:44,000 --> 00:15:48,260
+اللي بعدها limit الجذر يبقى بطل يصير عصري اشصار
+
+133
+00:15:48,260 --> 00:15:54,120
+كاسري يبقى ال limit لميل باعتبار واحد على N الجذر
+
+134
+00:15:54,120 --> 00:15:58,120
+النونيتعني 1 إلى N يبقى دخلت على الدالة اللي جوا
+
+135
+00:15:58,120 --> 00:16:04,360
+فصلمت اللي جوا ب L تحت الجذر النوني يعني L أس 1
+
+136
+00:16:04,360 --> 00:16:10,180
+إلى N و N عدد صحيح موجة طب السؤال هو طب افترض كان
+
+137
+00:16:10,180 --> 00:16:16,170
+سالميعني انت جبت للعدد الكاسري وجبت للعدد الموجب
+
+138
+00:16:16,170 --> 00:16:20,190
+بس ما جبتش للعدد السالب صحيح ولا لا؟ او للعدد
+
+139
+00:16:20,190 --> 00:16:25,710
+السالب الكاسري كيف نسوي لو كان مثلا f of x أُس
+
+140
+00:16:25,710 --> 00:16:32,860
+سالب عشرة مثلا؟نقول واحد عالى الزمن واسعاشر و
+
+141
+00:16:32,860 --> 00:16:36,440
+بنخلق limit الكون الصحيح اللي فوق بواحد زي ما هو و
+
+142
+00:16:36,440 --> 00:16:39,980
+limit اللي تحت باخدنا limit بنطبق عليها ميم اللي
+
+143
+00:16:39,980 --> 00:16:43,560
+هي الحالة اللي عندنا دي و مثله تماما بالنسبة
+
+144
+00:16:43,560 --> 00:16:47,340
+للحالة اللي عندنا يبقى ماعنا مشكلة يبقى ال limit
+
+145
+00:16:47,340 --> 00:16:52,200
+صحيح على الأس سواء كان موجب و الله سالب و الله
+
+146
+00:16:52,200 --> 00:16:56,700
+كسري كسري كمان موجب أو سالب على الشكتين كلامنا هذا
+
+147
+00:16:56,700 --> 00:17:01,790
+مالهم صحيحطيب، شو اسمها هذه أخر نقطة؟ sandwich
+
+148
+00:17:01,790 --> 00:17:05,610
+theorem أو squeezing theorem؟ هذه و هذه الأثنين
+
+149
+00:17:05,610 --> 00:17:08,370
+نفس المعنى طب أنا خدنا sandwich theorem في
+
+150
+00:17:08,370 --> 00:17:12,190
+calculus E، مظبوط؟ نفس المعلومة، أنا خدناها في
+
+151
+00:17:12,190 --> 00:17:17,290
+calculus E، هيجتنا في calculus Cأيش بتقولي بتقولي
+
+152
+00:17:17,290 --> 00:17:23,210
+لو كان عندك ثلاث دوال مرتبة بهذا الشكل الأولى أقل
+
+153
+00:17:23,210 --> 00:17:26,030
+من أو تساوي التانية و التانية أقل من أو تساوي
+
+154
+00:17:26,030 --> 00:17:32,550
+التالتة هذا الكلام صحيح لكل ال X Y اللي مابسويش X
+
+155
+00:17:32,550 --> 00:17:37,950
+node و Y node و هذا كلام صحيح على desk course مركز
+
+156
+00:17:37,950 --> 00:17:41,570
+و نقطة X node و Y node يبقى لما أخد ال limit لما
+
+157
+00:17:41,570 --> 00:17:46,410
+ال X و Y كلها بدأت تروح إلى X nodeو why not في هذه
+
+158
+00:17:46,410 --> 00:17:51,430
+الحالة إذا حدث ان limit الدالة الأولى هي limit
+
+159
+00:17:51,430 --> 00:17:55,510
+الدالة التالتة سوى نفس الرقم إذا ال automatic
+
+160
+00:17:55,510 --> 00:18:01,350
+limit اللي في النص بيكون نفس الرقم يبقى limit اللي
+
+161
+00:18:01,350 --> 00:18:07,230
+في النص f of x و y لما ال x هو y هو y هو y هو y هو
+
+162
+00:18:07,230 --> 00:18:07,810
+y هو y هو y هو y هو y هو y هو y هو y هو y هو y هو
+
+163
+00:18:07,810 --> 00:18:09,210
+y هو y هو y هو y هو y هو y هو y هو y هو y هو y هو
+
+164
+00:18:09,210 --> 00:18:09,450
+y هو y هو y هو y هو y هو y هو y هو y هو y هو y هو
+
+165
+00:18:09,450 --> 00:18:09,550
+y هو y هو y هو y هو y هو y هو y هو y هو y هو y هو
+
+166
+00:18:09,550 --> 00:18:09,570
+y هو y هو y هو y هو y هو y هو y هو y هو y هو y هو
+
+167
+00:18:09,570 --> 00:18:09,570
+y هو y هو y هو y هو y هو y هو y هو y هو y هو y هو
+
+168
+00:18:09,570 --> 00:18:09,610
+y هو y هو y هو y هو y هو y هو y هو y هو y هو y هو
+
+169
+00:18:09,720 --> 00:18:15,040
+هل فعليا اختلفت عن ما سبق الدراسة في كل كناسة هو
+
+170
+00:18:15,040 --> 00:18:21,780
+هو حرفيا طب نشوف الأن تطبيق العملي لهذه المفاهيم
+
+171
+00:18:21,780 --> 00:18:33,840
+نعطي مثال توضيحي على ذلك يبقى example نحسبيه
+
+172
+00:18:33,840 --> 00:18:43,160
+للنهايات التالية evaluate دهfollowing limits
+
+173
+00:18:43,160 --> 00:18:49,740
+المقطة
+
+174
+00:18:49,740 --> 00:18:57,400
+الأولى the limit لما ال X و ال Y بدها تروح إلى
+
+175
+00:18:57,400 --> 00:19:06,340
+ثلاثة وأربعة limit للجذر التربيعي لل X تربيع زائد
+
+176
+00:19:06,340 --> 00:19:07,400
+Y تربيع
+
+177
+00:19:14,060 --> 00:19:19,120
+زي ما دراسة في calculus ايه؟ اول خطوة في حساب ال
+
+178
+00:19:19,120 --> 00:19:22,840
+limits هي التعويير المشيزي يعني زي ال polynomial
+
+179
+00:19:22,840 --> 00:19:26,840
+بالضغط تماما يبقى baggage يبقى جول بدي اشيل X و
+
+180
+00:19:26,840 --> 00:19:33,540
+احط مكانها تلاتة لكل تربيع وهذه بدي احط بدالها
+
+181
+00:19:33,540 --> 00:19:40,230
+أربعة لكل تربيع وهذه الناقص يساويتسعة وستة عشر
+
+182
+00:19:40,230 --> 00:19:44,530
+وخمسة وعشرين شيل واحد بيظل جذر التربيه اليمن
+
+183
+00:19:44,530 --> 00:19:50,970
+للاربع وعشرين لو اربع في ستة يعني اتنين ال square
+
+184
+00:19:50,970 --> 00:20:00,210
+root لستة قيمة هذه النهاية السؤال الثاني ال
+
+185
+00:20:00,210 --> 00:20:07,630
+delimit لمن لما ال X وYيجب ان تذهب الى الـ 0 و الـ
+
+186
+00:20:07,630 --> 00:20:15,970
+0 الى ماين الى الـ E of Y بصين X على ماين على X
+
+187
+00:20:15,970 --> 00:20:23,350
+تعويض
+
+188
+00:20:23,350 --> 00:20:28,550
+المباشر شوفوا ايش بيجيب هنا سفر على سفر تبقى تدبر
+
+189
+00:20:28,550 --> 00:20:34,110
+حالك و تظبط أمورك بحيث تقدر تحسب هذه ال limit
+
+190
+00:20:39,770 --> 00:20:50,170
+عشان تفترحوا علينا كيف يكون شكل الحل انا
+
+191
+00:20:50,170 --> 00:20:54,670
+ماتكلمش عن نتيجة نهائية باتكلم على الطريقة كيف بنا
+
+192
+00:20:54,670 --> 00:21:00,130
+نحل المثالات طبعا هذه بواحد وهذه zero على zero
+
+193
+00:21:00,130 --> 00:21:03,490
+يعني
+
+194
+00:21:03,490 --> 00:21:09,130
+نفصل هذه الى اللي هي اعصر ضروف دالتي تمام تماميبقى
+
+195
+00:21:09,130 --> 00:21:14,970
+هذا limit لما ال X و ال Y بدها تروح إلى Zero و
+
+196
+00:21:14,970 --> 00:21:23,010
+Zero لل E أُس Y في limit لما ال X و ال Y بدها تروح
+
+197
+00:21:23,010 --> 00:21:32,510
+ل Zero Zero ل Sin X على X و يسار ماعنديش ال X كإن
+
+198
+00:21:32,510 --> 00:21:38,680
+ال Y بدها تروح ل Zero التعرض المباشربيعطيكي EOS
+
+199
+00:21:38,680 --> 00:21:44,500
+Zeroطب و هذه ماعنديش ويب كأنه ال X بده تروح لمين
+
+200
+00:21:44,500 --> 00:21:51,380
+لزرع عظم المعروف فهذه من Calculus A وقداش واحد إذا
+
+201
+00:21:51,380 --> 00:21:55,980
+ماكنتش Calculus A بروح ل Calculus B بقول Zero على
+
+202
+00:21:55,980 --> 00:22:00,580
+Zero بقعدة نوبة المشتقة تبص على مشتقين المقام يبقى
+
+203
+00:22:00,580 --> 00:22:04,300
+Cos X على واحد Cos صفر بواحد على واحد اللي همين
+
+204
+00:22:04,300 --> 00:22:09,740
+بواحد صحية يبقى نتيجة تزاوي واحد فقط لغير
+
+205
+00:22:14,390 --> 00:22:22,810
+ثالث يبقى يحلى بالنا limit لما ال X وال Y بدأت
+
+206
+00:22:22,810 --> 00:22:31,190
+تروح لمين للواحد وواحد ل X تربيع ناقص Y تربيع على
+
+207
+00:22:31,190 --> 00:22:33,090
+X ناقص Y
+
+208
+00:22:35,990 --> 00:22:43,570
+عاوزة ان انا اشر شو بيجيب ليه لكن لو انا طلعت في
+
+209
+00:22:43,570 --> 00:22:47,890
+ال bus بلاقي هو عبارة عن فرق بين المربعين يبقى هذا
+
+210
+00:22:47,890 --> 00:22:53,890
+الكلام بده يساوي limit لما ال x و ال y بده تروح
+
+211
+00:22:53,890 --> 00:23:02,200
+للواحدة واحد بحلل هذا x ناقص y في x زائد yعلى مين
+
+212
+00:23:02,200 --> 00:23:06,900
+على x نقص y طبعا الجو السادة بيروح مع الجو السادة
+
+213
+00:23:06,900 --> 00:23:12,220
+وبالتالي تقول المسألة الى limit لما ال x و ال y
+
+214
+00:23:12,220 --> 00:23:18,460
+يروح واحد و واحد فضل اني كداش x زائد y يبقى واحد
+
+215
+00:23:18,460 --> 00:23:24,010
+زائد واحد يساوي كداش اتنين إذا يا بنات إذا كانفي
+
+216
+00:23:24,010 --> 00:23:29,650
+عندي rational function في البسط والمقام بحلل كل من
+
+217
+00:23:29,650 --> 00:23:34,030
+البسط والمقام وبجري الاقتصاد اللي موجودة وبعد هيك
+
+218
+00:23:34,030 --> 00:23:38,490
+بروح بعض و اتطوير مباشرة بنحصل على مين على النتيجة
+
+219
+00:23:38,490 --> 00:23:46,810
+كما في هذا المثال نعطي مثالة مرابعا بدنا
+
+220
+00:23:46,810 --> 00:23:53,850
+limit لما ال X و ال Y بدها تروح لمين؟ لاثنينو
+
+221
+00:23:53,850 --> 00:24:01,770
+اتنين بشرط ان ال X زائد ال Y ما تسويش اربعة لل X
+
+222
+00:24:01,770 --> 00:24:08,070
+زائد ال Y ناقص اربعة على الجدرى الترابيع ل X زائد
+
+223
+00:24:08,070 --> 00:24:14,650
+Y ناقص اتنين السؤال
+
+224
+00:24:14,650 --> 00:24:21,060
+مرة تاليةLimit لدالة قدامنا هي عندي ال X و ال Y
+
+225
+00:24:21,060 --> 00:24:27,040
+بتروح ل 2 و 2 بشرط ان ال X زاد Y ماتسويش 4 طب لو
+
+226
+00:24:27,040 --> 00:24:32,520
+سوى 4 شو بدي يحصل يبقى بتصير general 4 اللي هو ب2
+
+227
+00:24:32,520 --> 00:24:38,900
+ناقص 2 ب0 و 4 ناقص 4 بصير 0 على 0 طب ايش بدنا نسوي
+
+228
+00:24:38,900 --> 00:24:40,040
+في هذه الدالة
+
+229
+00:24:50,580 --> 00:24:54,760
+تحليل ال bus كفارق
+
+230
+00:24:54,760 --> 00:25:03,740
+بين المرابعين كما
+
+231
+00:25:03,740 --> 00:25:06,420
+اقتصدنا في السؤال السابق
+
+232
+00:25:10,330 --> 00:25:14,310
+الـ bus أو المقام بيروح بضرورة مين في المرافق
+
+233
+00:25:14,310 --> 00:25:18,830
+للمقدار اللي فيه الجدر يبقى هذا الكلام بيساوي
+
+234
+00:25:18,830 --> 00:25:26,480
+limit لما ال X و ال Y بدا تروح لليه 2 و 2بشرط إن
+
+235
+00:25:26,480 --> 00:25:32,880
+ال X زائد ال Y ما نسويش أربعة لمن؟ لل X زائد ال Y
+
+236
+00:25:32,880 --> 00:25:39,940
+ناقص أربعة على الجدر التربيعي لل X زائد ال Y ناقص
+
+237
+00:25:39,940 --> 00:25:46,220
+اتنين تمين للجدر التربيعي لل X زائد Y زائد اتنين
+
+238
+00:25:46,220 --> 00:25:53,760
+على الجدر التربيعي لل X زائد Y زائد اتنينهذا
+
+239
+00:25:53,760 --> 00:25:59,740
+الكلام بده يسوي limit لما ال X و ال Y بدها تروح لل
+
+240
+00:25:59,740 --> 00:26:04,920
+إتنين و إتنين بشرط إن ال X زائد ال Y مايسويش
+
+241
+00:26:04,920 --> 00:26:12,740
+الأربعة طبعا بصير علمين ال X زائد ال Y نقص الأربعة
+
+242
+00:26:12,740 --> 00:26:20,560
+في الجدري التربيعي لل X زائد Y زائد 2 كل هذا
+
+243
+00:26:20,560 --> 00:26:26,440
+مقسوما علىهل ليس هذا هو تحليل الفرق بين المربعين؟
+
+244
+00:26:26,440 --> 00:26:29,760
+يجب أن أعود إلى أصله يجب أن يكون مرفع الكمية
+
+245
+00:26:29,760 --> 00:26:35,480
+الأولى الحمد لله الجدر مع السلامة يطير ويبقى لدي X
+
+246
+00:26:35,480 --> 00:26:41,140
+زائد Y هنا ناقص أربع المقدار هذا هو نفس المقدار
+
+247
+00:26:41,140 --> 00:26:47,860
+لأن هذا يتم اختصار وبالتالي تقول المسألة إلى limit
+
+248
+00:26:47,860 --> 00:26:54,070
+عندما X وYبعدها تذهب إلى الـ 2 و 2 بشرط أن X زائد
+
+249
+00:26:54,070 --> 00:27:03,900
+Y لا يساوي 4 لـ square root X زائد Y زائد 2بنروح
+
+250
+00:27:03,900 --> 00:27:07,880
+لعوض تعويض مباشر يبقى هذا الكلام بيساوي الجدرى
+
+251
+00:27:07,880 --> 00:27:13,560
+التربيعى للإتنين زائد اتنين زائد اتنين و لو كله
+
+252
+00:27:13,560 --> 00:27:18,220
+على بعضه بيساوي جداري بيساوي أربعة إذا نهاية هذا
+
+253
+00:27:18,220 --> 00:27:24,460
+المقدار بيساوي جداري بيساوي أربعة يبقى عليها بناء
+
+254
+00:27:24,460 --> 00:27:30,060
+ال limit لهذه ال function أعطتنى أربعة وحلينا عن
+
+255
+00:27:30,060 --> 00:27:31,300
+طريق أحد الطرق
+
+256
+00:27:37,380 --> 00:27:45,260
+بين المربعين واختصرنا سوف نصل إلى نفس النتيجة .
+
+257
+00:27:45,260 --> 00:27:55,820
+السؤال الذي يليه سؤال خمسة يجري بالـ delimit لما
+
+258
+00:27:55,820 --> 00:28:06,290
+ال X وY بدأت تروح لـ Zero Zero لمن ؟ لواحد ناقصكو
+
+259
+00:28:06,290 --> 00:28:23,830
+ساين XY مقسومة على XY اتسالد كو
+
+260
+00:28:23,830 --> 00:28:28,870
+ساين XY مقسومة
+
+261
+00:28:28,870 --> 00:28:33,240
+على XYيعني نضرم في ايش؟ مرافق البصمة ويجب نضر
+
+262
+00:28:33,240 --> 00:28:37,400
+سميمة مائة بالمائة أنا عندي واحد نقص cosine xy
+
+263
+00:28:37,400 --> 00:28:41,260
+يبقى بدها ضرم في واحد زائد cosine xy واقسم على
+
+264
+00:28:41,260 --> 00:28:45,380
+واحد زائد cosine xy وروح اكمل عادي جدا يبقى هذا
+
+265
+00:28:45,380 --> 00:28:48,520
+ضرب في المرافق لكن السؤال اللي جابله ضربنا في
+
+266
+00:28:48,520 --> 00:28:52,280
+المرافق إذا دانيلي خاطر افكر بقنية تانية الكلام
+
+267
+00:28:52,280 --> 00:28:56,180
+اللي قلته صح وبيحل السؤال مائة بالمائة ولا واحد
+
+268
+00:28:56,180 --> 00:29:00,840
+يقدر يعترض عليكم تمام؟لكن انا بفكر في شغلة تانية
+
+269
+00:29:00,840 --> 00:29:06,380
+انا بعرف شوية حساب مثلثات وبالتالي بدأ فابرك هذه
+
+270
+00:29:06,380 --> 00:29:11,620
+المثلة في حيطة حُطها في شكل اخر باستخدام قواعد
+
+271
+00:29:11,620 --> 00:29:18,620
+حساب المثلثات اللي دُرست في calculus A سؤال هذي
+
+272
+00:29:18,620 --> 00:29:26,500
+مين؟ هذي cos xy cos تربيع كلام اذا بص مضلوبة في
+
+273
+00:29:26,500 --> 00:29:32,720
+اتنينلأن cos تربيع ال X يسوى نص في واحد نقص cos 2X
+
+274
+00:29:32,720 --> 00:29:38,320
+إذا أنا لو رجعت إلى حساب المثلثات بقدر أقول limit
+
+275
+00:29:38,320 --> 00:29:45,380
+لما ال X و ال Y بدها تروح إلى Zero و Zero للي
+
+276
+00:29:45,380 --> 00:29:54,200
+اتنين sin تربيع XY على اتنين كل هذا الكلام على X
+
+277
+00:29:54,200 --> 00:29:56,360
+تمين في ال Y
+
+278
+00:30:00,670 --> 00:30:06,690
+طيب تعالى نشوف شو بنسويه بجى بقول لو اتنين اللى
+
+279
+00:30:06,690 --> 00:30:11,450
+فوق شجلبت او نزلت اتعب ايش بيصير؟ XY على اتنين
+
+280
+00:30:11,450 --> 00:30:17,790
+صحيح ولا لأ؟ يبقى هذه بدها تصير limit لما ال X و
+
+281
+00:30:17,790 --> 00:30:26,230
+ال Y بدها تروح ل 00 لصينة تربية XY على اتنين على
+
+282
+00:30:26,230 --> 00:30:27,870
+XY على اتنين
+
+283
+00:30:30,550 --> 00:30:36,370
+هذا مثل ايه؟ 100% صارت الزاوية لأننا XY على 2 وهذا
+
+284
+00:30:36,370 --> 00:30:46,670
+XY على 2 بس هذا ايه؟ XY مش XY ده دولة كذا يبقى رتب
+
+285
+00:30:46,670 --> 00:30:51,410
+أمورك شوف ليش بصير فيها هذه لأن لو عوضنا تعويضا
+
+286
+00:30:51,410 --> 00:30:56,510
+مباشرا ايش بتبقى Zero على Zero صحيح ولا لأ؟ كويس
+
+287
+00:30:56,510 --> 00:30:59,530
+يبقى لو عملتها بشكل اخر
+
+288
+00:31:04,920 --> 00:31:13,440
+هتروح لل zero zero وروح نقول هدى عبارة عن sin xy
+
+289
+00:31:13,440 --> 00:31:21,500
+على اتنين على xy على اتنين في sin xy على اتنين
+
+290
+00:31:21,500 --> 00:31:27,440
+مظبوط طب اللى بتقوله كدهش بنتى؟ واحدطب والتانية
+
+291
+00:31:27,440 --> 00:31:33,320
+Zero يبقى هنا في قدر في Zero يبقى النتيجة تساوي
+
+292
+00:31:33,320 --> 00:31:38,020
+Zero الان لو روحت ضربت في المرافق لازم تطلع نتيجة
+
+293
+00:31:38,020 --> 00:31:42,440
+Zero لو ما طلعتش Zero معناته هذا حلنا غلط يبقى
+
+294
+00:31:42,440 --> 00:31:47,340
+good exercise لك تروح تحل المثلة بطريقة ضرب في
+
+295
+00:31:47,340 --> 00:31:53,950
+مرافق البصر وهو واحد زائد cosine XYحلّيه في البيت
+
+296
+00:31:53,950 --> 00:32:01,190
+بالطريقة الثانية وهي الجواب معاك سؤال السادس V I
+
+297
+00:32:01,190 --> 00:32:09,770
+بدي limit لما ال X و ال Y و ال Z بدل المتغيرين بدي
+
+298
+00:32:09,770 --> 00:32:17,150
+اخليهم تلاتة هنا لمن؟ لاناقص رابع و بقى على اتنين
+
+299
+00:32:17,150 --> 00:32:32,430
+و اتنين لمن؟لتان انفرست اكس YZ اقول
+
+300
+00:32:32,430 --> 00:32:36,590
+كويس اعود تعويض مباشرة ويلا نشوف شو اللي بده يطلع
+
+301
+00:32:36,590 --> 00:32:44,030
+يبقى هادي ويساوي تان انفرست لمينة لل X اللي يساوي
+
+302
+00:32:44,030 --> 00:32:51,840
+بربعه مضروبة في Pi على اتنين في اتنينتنين مع اتنين
+
+303
+00:32:51,840 --> 00:32:58,460
+بتروح بيصير تان انفرز باية على اتنين بس باية على
+
+304
+00:32:58,460 --> 00:33:01,900
+اربعة طبعا مش باية على اتنين باية على اربعة و
+
+305
+00:33:01,900 --> 00:33:03,300
+بيشارت سالم
+
+306
+00:33:19,030 --> 00:33:25,090
+لمين؟ لـ πاية على أربعة ويسوى ناقص. كم فالتان انفس
+
+307
+00:33:25,090 --> 00:33:31,850
+باية على أربعة؟ كم؟ كم يظل الخمسة واربعين؟ واحد
+
+308
+00:33:31,850 --> 00:33:35,570
+إذا تان انفس لباية على أربعة يبقى ساوى واحد يبقى
+
+309
+00:33:35,570 --> 00:33:38,870
+limit تسوى كم؟ سالف واحد
+
+310
+00:33:41,270 --> 00:33:44,250
+إذا اللي قبلها زي ما انتوا شايفين المعلومات اللي
+
+311
+00:33:44,250 --> 00:33:47,530
+درسناها على functions of two variables في حالة ال
+
+312
+00:33:47,530 --> 00:33:51,690
+limit صحيحة لل functions of three variables او
+
+313
+00:33:51,690 --> 00:33:56,470
+variables او ال invariables مهما كان شكل ال main
+
+314
+00:33:56,470 --> 00:34:07,130
+شكل المتغيرات اللي عندنا تان
+
+315
+00:34:07,130 --> 00:34:17,120
+انفرسباي على أربعة تقع
+
+316
+00:34:17,120 --> 00:34:20,360
+في ال domain تبعها لأن ال domain ten inverse نسالي
+
+317
+00:34:20,360 --> 00:34:23,360
+من infinity لإنفينتي هي ten inverse one
+
+318
+00:34:26,020 --> 00:34:30,860
+صحيح بنات هذه مضالة سالب تان انفرست باي على اربعة
+
+319
+00:34:30,860 --> 00:34:35,160
+كمهية بدك تطلع قيمة عددية على الجهاز مالكيش بلاش
+
+320
+00:34:35,160 --> 00:34:39,740
+خليها زي ما هي اذا بدناها المهم نوصل الى نتيجة
+
+321
+00:34:39,740 --> 00:34:48,020
+كويس نجي الان لسؤال رقم اتنين سؤال رقم اتنين على
+
+322
+00:34:48,020 --> 00:34:56,720
+نفس الموضوع بقول ما if إذا كان2 absolute value ل X
+
+323
+00:34:56,720 --> 00:35:06,360
+Y ناقص X تربيع وY تربيع على 6 أقل من 4 ناقص 4
+
+324
+00:35:06,360 --> 00:35:13,760
+كوصاي الجذري التربيعي ل absolute value ل X Y أقل
+
+325
+00:35:13,760 --> 00:35:17,900
+من 2 absolute value ل X Y
+
+326
+00:35:34,400 --> 00:35:39,840
+للأربعة ناقص أربعة كوصين الجذري الترابيعي لـ
+
+327
+00:35:39,840 --> 00:35:40,920
+absolute value
+
+328
+00:36:16,650 --> 00:36:23,610
+السؤال مرة تانية بيقول لو عندك تلت دوال، الدالة
+
+329
+00:36:23,610 --> 00:36:27,490
+الأولى، أقل من الدالة التانية، أقل من الدالة
+
+330
+00:36:27,490 --> 00:36:32,070
+التالتة، في ال delimit للدالة اللي في المصم مقسومة
+
+331
+00:36:32,070 --> 00:36:37,290
+على absolute value ل X Y، لأول واحدة من حد ما شوف
+
+332
+00:36:37,290 --> 00:36:41,660
+السؤال بهذا الشكل، شوفوا كم سنة وشتيرةلأن هذه
+
+333
+00:36:41,660 --> 00:36:46,260
+كانها مقارنة بين ال limits لمين لثلاث دواد، إذا
+
+334
+00:36:46,260 --> 00:36:51,660
+أنا بدأ أروح أستخدم صلاحياتي في حل هذه المثلة،
+
+335
+00:36:51,660 --> 00:36:56,660
+كونوا فيين دي absolute value، إذا احتمال ال X Y ال
+
+336
+00:36:56,660 --> 00:37:02,610
+absolute بالإلها ليطلع منهايكون الرقم موجب يكون
+
+337
+00:37:02,610 --> 00:37:09,390
+الرقم
+
+338
+00:37:09,390 --> 00:37:11,470
+موجب يكون الرقم موجب يكون الرقم موجب يكون الرقم
+
+339
+00:37:11,470 --> 00:37:12,810
+موجب يكون الرقم موجب يكون الرقم موجب يكون الرقم
+
+340
+00:37:12,810 --> 00:37:13,550
+موجب يكون الرقم موجب يكون الرقم موجب يكون الرقم
+
+341
+00:37:13,550 --> 00:37:13,590
+موجب يكون الرقم موجب يكون الرقم موجب يكون الرقم
+
+342
+00:37:13,590 --> 00:37:13,690
+موجب يكون الرقم موجب يكون الرقم موجب يكون الرقم
+
+343
+00:37:13,690 --> 00:37:13,690
+موجب يكون الرقم موجب يكون الرقم موجب يكون الرقم
+
+344
+00:37:13,690 --> 00:37:13,690
+موجب يكون الرقم موجب يكون الرقم موجب يكون الرقم
+
+345
+00:37:13,690 --> 00:37:19,090
+موجب يكون الرقم موجب يكون الرقم موجب يكون الرقم
+
+346
+00:37:19,090 --> 00:37:28,870
+موجب يكون الرقم موجب يكون الرقم موجبإذا لو كانت
+
+347
+00:37:28,870 --> 00:37:33,870
+الـ x,y قيمة موجبة إيش اللي بده يحصل في هذه
+
+348
+00:37:33,870 --> 00:37:40,110
+الحلقة؟ يبقى بدهاجة يقول بده يصير ال absolute
+
+349
+00:37:40,110 --> 00:37:46,690
+value الـ x,y دائما و أبدا موجبة صحيح ولا لا؟ يبقى
+
+350
+00:37:46,690 --> 00:37:54,930
+بصيري المسألة كتالة يبقى بصير عندنا اتنين اتنين x
+
+351
+00:37:54,930 --> 00:37:55,630
+,y
+
+352
+00:38:17,940 --> 00:38:24,160
+إذا ما دام ال X Y موجة بقدر أقسم عليها كلها
+
+353
+00:38:26,340 --> 00:38:27,480
+يبقى الـ
+
+354
+00:38:30,950 --> 00:38:38,030
+على 6xy أقل من أربعة ناقص أربعة كوصيني الجدري
+
+355
+00:38:38,030 --> 00:38:42,110
+بتربيها يعني لإن هذه حطيت ال absolute مدى موجب
+
+356
+00:38:42,110 --> 00:38:46,110
+والله ماحطيتهاش سيئة يعني لو شيلتها والله حد إنها
+
+357
+00:38:46,110 --> 00:38:54,010
+موجبة ماعنديش مشكلة فيها على مين على ال XY مخسوما
+
+358
+00:38:54,010 --> 00:39:03,900
+على XY يبقى هنا أقل من 2 أقل من 2طيب خديني ال
+
+359
+00:39:03,900 --> 00:39:07,880
+limit لثلاثة أطراف ناخد ال limit لثلاثة أطراف
+
+360
+00:39:07,880 --> 00:39:12,800
+ممكنش لما ال x و y بده يروح لل zero zero يبقى بده
+
+361
+00:39:12,800 --> 00:39:18,140
+يصير عندي هنا limit لما ال x و ال y راح لل zero
+
+362
+00:39:18,140 --> 00:39:25,780
+zero للي اتنين ناقص x تربيع و y تربيع على ستة x y
+
+363
+00:39:25,780 --> 00:39:28,540
+طبعا لو اختصرنا هنا ماذا يصير عندي هنا
+
+364
+00:39:34,820 --> 00:39:42,560
+أقل من أو يسوى ال limit لما X وY بدها تروح لل 0 0
+
+365
+00:39:42,560 --> 00:39:50,920
+لل 4 ناقص 4 cosine absolute value لل X Y على ال X
+
+366
+00:39:50,920 --> 00:39:58,120
+Y أقل من أو يسوى limit لما ال X وY بده يروح لل 0 0
+
+367
+00:39:58,120 --> 00:40:03,520
+لمين؟ لل إتنينطب ما لما ال X و ال Y بتروح ل 0،0
+
+368
+00:40:03,520 --> 00:40:09,240
+هذا ال term ممكن تدريش يا بنات يبقى صار ال E2 بدأ
+
+369
+00:40:09,240 --> 00:40:19,450
+أقل من limit لما ال X و ال Yبدي اروح الى 00 لل4-4
+
+370
+00:40:19,450 --> 00:40:26,130
+cos absolute value لل X Y على ال X Y لو حطيت ال
+
+371
+00:40:26,130 --> 00:40:31,110
+absolute في مشكلة لأ مهي بالموجة بس مشان شكل اللي
+
+372
+00:40:31,110 --> 00:40:35,110
+هو المطلوب ليس الا اقل من اتنين
+
+373
+00:40:39,260 --> 00:40:49,270
+يبقى باجي بقوله باي ساندوش تيريم بصير ال limitلأ
+
+374
+00:40:49,270 --> 00:40:53,710
+الاربعة ناقص اربعة كوصين الجدري الترابيعي ال
+
+375
+00:40:53,710 --> 00:40:57,930
+absolute value ل X و Y على ال absolute value ل X و
+
+376
+00:40:57,930 --> 00:41:03,690
+Y لما ال X و Y بدها تروح ل Zero Zero بده يسوي قدر
+
+377
+00:41:03,690 --> 00:41:10,610
+نقل هذا لو كانت X و Y أكبر من مين من ال Zero بدالي
+
+378
+00:41:10,610 --> 00:41:11,930
+أخد F
+
+379
+00:41:15,750 --> 00:41:21,610
+من الـ zero يعني حاصل ضربه ما كان كمية سالبة و
+
+380
+00:41:21,610 --> 00:41:26,610
+يحدث هذا الكلام لو كانت X بالسالب و Y بالموجة أو
+
+381
+00:41:26,610 --> 00:41:31,970
+العكس X بالموجة و Y بالسالب يبقى المثلة تبعتي هذا
+
+382
+00:41:31,970 --> 00:41:39,210
+بقدر اكتفها على الشكل التالي يبقى اتنين ناقص X
+
+383
+00:41:39,210 --> 00:41:39,870
+تربيع
+
+384
+00:41:46,220 --> 00:41:52,720
+أقل من أربعة ناقص أربعة كوصين الجذري التربيعي ل
+
+385
+00:41:52,720 --> 00:41:59,000
+absolute value ل X Y كله مبسوما على absolute value
+
+386
+00:41:59,000 --> 00:42:07,080
+ل X Y أقل من جداش أقل من اتنينبالأقل لما تبقى هذا
+
+387
+00:42:07,080 --> 00:42:12,240
+سالب بقدر أتخلص من هذا ال absolute وبالتالي بيصير
+
+388
+00:42:12,240 --> 00:42:24,080
+المسألة E2 زائد X تربيع Y تربيع على 6XY يعني شيلت
+
+389
+00:42:24,080 --> 00:42:28,480
+ال absolute و حطيت إشارة سالب مع السلب مايحصل
+
+390
+00:42:28,480 --> 00:42:39,430
+بالموجب أقل من 4نقص أربعة كوصين الجذري التربيعي لل
+
+391
+00:42:39,430 --> 00:42:49,190
+X في Y على absolute value لل X Y أقل من مين أقل من
+
+392
+00:42:49,190 --> 00:42:52,290
+الأتنين بعد ذلك ناخد
+
+393
+00:43:09,820 --> 00:43:16,940
+خُد ال limit للثلاثة أطراف بيصير limit للإتنين
+
+394
+00:43:16,940 --> 00:43:25,520
+زائد لو اختصرنا هذه بلدش بصير x y على ستة لما x و
+
+395
+00:43:25,520 --> 00:43:33,220
+y بدها تروح ل zero و zero أقل من limit لما ال x و
+
+396
+00:43:33,220 --> 00:43:41,510
+ال y بدها تروحلزيرو زيرو للاربعة ناقص أربعة الجدري
+
+397
+00:43:41,510 --> 00:43:47,810
+التربيعي ال cosine الجدري التربيعي cosine الجدري
+
+398
+00:43:47,810 --> 00:43:52,330
+التربيعي ال absolute value لل X Y على absolute
+
+399
+00:43:52,330 --> 00:44:00,170
+value لل X Y أقل من limit للإتنين لما ال X والY
+
+400
+00:44:00,170 --> 00:44:00,970
+بدها
+
+401
+00:44:08,820 --> 00:44:19,080
+تاني هتديلي قداش؟ اتنين اقل من limit x y بدها تروح
+
+402
+00:44:19,080 --> 00:44:24,320
+لل zero و ال zero لل أربعة ناقص أربعة قصين الجدري
+
+403
+00:44:24,320 --> 00:44:31,560
+التربيعي لل x y absolute value x y اقل من أو يساوي
+
+404
+00:44:31,560 --> 00:44:38,480
+اتنين برضه بيسألت و اشتغلهم ايه؟ ساندوش
+
+405
+00:44:39,230 --> 00:44:46,830
+سيُرِم الـ Limit لما الـ X والـ Y بدها تروح للـ
+
+406
+00:44:46,830 --> 00:44:52,690
+Zero والـ Zero كل هذا الكلام للمقدار أربعة ناقص
+
+407
+00:44:52,690 --> 00:44:57,970
+أربعة Cos ل Square Root لل absolute value لل X وY
+
+408
+00:44:57,970 --> 00:45:03,250
+على ال absolute value لل X وY بده سوى كده اتنين
+
+409
+00:45:03,630 --> 00:45:09,510
+الطالعين في العلاقة رقم واحد وهي واحد وهذا العلاقة
+
+410
+00:45:09,510 --> 00:45:15,410
+رقم اتنين إذا سواء كانت X وY موجب والله سالبة
+
+411
+00:45:15,410 --> 00:45:25,490
+مايفرقش علنا يبقى thus وهكذا او from thus اللي هو
+
+412
+00:45:25,490 --> 00:45:25,910
+ال limit
+
+413
+00:45:51,000 --> 00:45:57,940
+يبقى هذا مثال عملي على استخدامالنقطة السادسة من
+
+414
+00:45:57,940 --> 00:46:02,940
+خواص ال limits على ال functions of several
+
+415
+00:46:02,940 --> 00:46:04,040
+variables
+
+416
+00:46:47,010 --> 00:46:59,090
+F of X Y F of X Y has different
+
+417
+00:46:59,090 --> 00:47:02,790
+limits
+
+418
+00:47:19,890 --> 00:47:31,810
+path is عبر مصارين مختلفين as x و y بدها تروح الى
+
+419
+00:47:31,810 --> 00:47:43,490
+x node و y node then limit f of x و y لما x و y
+
+420
+00:47:43,490 --> 00:47:47,350
+بدها تروح الى x node و y node
+
+421
+00:48:22,430 --> 00:48:28,930
+كفينها مرة ثانية نقرأ شوي المكتوب نحاول نفهمه
+
+422
+00:48:28,930 --> 00:48:36,310
+تماما ايش بقولي بقول لو عندك ال F of X و Y has
+
+423
+00:48:36,310 --> 00:48:42,630
+different limits نهايات مختلفة along two different
+
+424
+00:48:42,630 --> 00:48:48,930
+paths عبر مسارين مختلفين لما ال X و Y بدأت تروح لل
+
+425
+00:48:48,930 --> 00:48:55,050
+X node و Y nodeLimit لـ f of x و y لما الـ x و y
+
+426
+00:48:55,050 --> 00:49:00,510
+بتروح الأكسنون does not exist يبقى هذه وسيلة من
+
+427
+00:49:00,510 --> 00:49:04,630
+إحدى الوسيلة بتثبت ان limit هذه مالها does not
+
+428
+00:49:04,630 --> 00:49:09,470
+exist غير موجة كيف هذا الكلام ممولة كويسة افترضي
+
+429
+00:49:09,470 --> 00:49:17,510
+عندنا محاول يقولون هذا محور x وهذا محور y أخدنا
+
+430
+00:49:17,510 --> 00:49:23,700
+نقطة زي النقطة هذه مثلاهذا ليحدثي تبعه X node وY
+
+431
+00:49:23,700 --> 00:49:32,720
+node. أي منحنى.يمروا بهذه النقطة ممكن اخدوا مسار
+
+432
+00:49:32,720 --> 00:49:36,660
+من المسارات اللي احنا بنحكي عنها وبالتالي قد يكون
+
+433
+00:49:36,660 --> 00:49:42,940
+المسار خط مستقيم أفق قد يكون خط مستقيم رأسي قد
+
+434
+00:49:42,940 --> 00:49:49,340
+يكون خط مستقيم مائم قد يكون منحنى على سبيل المثال
+
+435
+00:49:49,340 --> 00:49:55,700
+يعني ممكن اقول هذا مسار ممكن اقول هذا مسار ممكن
+
+436
+00:49:55,700 --> 00:50:00,960
+اقول هذا مسارأجي واحد تاني قال لي لأ ممكن يكون هذا
+
+437
+00:50:00,960 --> 00:50:05,900
+ما صار أنا رايح فيه على النقفة ممكن من تحت ماعناه
+
+438
+00:50:05,900 --> 00:50:11,000
+مشكلة واحد قال لي لأ انا في عندي منحنى المنحنى
+
+439
+00:50:11,000 --> 00:50:17,260
+ممكن ييجي هيك يبقى أنا رايح على النقفة لأن هذا اجي
+
+440
+00:50:17,260 --> 00:50:22,280
+واحد تاني قال لي لأ انا ممكن اطبع المنحنى بالشكل
+
+441
+00:50:22,280 --> 00:50:29,390
+هذا هيكالمهم المسار يكون رايح على النقطةيبقى لو
+
+442
+00:50:29,390 --> 00:50:33,770
+أخدت مسارين اتنين أخدت ال limit مع المسار الأول
+
+443
+00:50:33,770 --> 00:50:39,270
+لما ال XY بيروح لنفس النقطة هذه لقيته سوا رقم مشيت
+
+444
+00:50:39,270 --> 00:50:43,750
+على مسار تاني و أخدت ال limit يعطاني رقم ثاني غير
+
+445
+00:50:43,750 --> 00:50:47,610
+رقم الأولان يبقى في هذا الحالة بيقول ال limit مانع
+
+446
+00:50:47,610 --> 00:50:54,410
+does not exist مشان ال limit إذا بدوا كل المسارات
+
+447
+00:50:54,410 --> 00:50:57,790
+التي سامروا بهذه النقطة بتأدي إلى نفس النتيجة
+
+448
+00:51:05,600 --> 00:51:10,220
+أفرض في هذه النقطة أنا بس عندي عشر مسارات قلتلها
+
+449
+00:51:10,220 --> 00:51:15,340
+أيوة جلت تسع مسارات أقن نفس النتيجة و المسار
+
+450
+00:51:15,340 --> 00:51:18,920
+العشري أقن نتيجة مختلفة because does not exist على
+
+451
+00:51:18,920 --> 00:51:25,020
+طول الخط exist بدل كل جميع المسارات التي تمور بهذه
+
+452
+00:51:25,020 --> 00:51:32,340
+النقطةبناء عليه واضحة الصورة اللى عندنا هذه مش
+
+453
+00:51:32,340 --> 00:51:35,500
+تاخدى بمسار لا يمر بالنقطة و تروح تحجب تقول that
+
+454
+00:51:35,500 --> 00:51:39,020
+does not exist ولا exist المسار اللى بتاخده يجب ان
+
+455
+00:51:39,020 --> 00:51:44,800
+تتأكد فعلا انه يمر بهذه النقطة لو أخدت مسار آخر لا
+
+456
+00:51:44,800 --> 00:51:50,380
+يمر بصير كلامك غلط نعطي أمثلة توضحية على ذلك
+
+457
+00:52:01,580 --> 00:52:12,540
+التقاليدات التالية تظهر ان التقاليدات
+
+458
+00:52:12,540 --> 00:52:16,660
+التالية ليست
+
+459
+00:52:16,660 --> 00:52:23,260
+موجودة ليست
+
+460
+00:52:23,260 --> 00:52:25,980
+موجودة ك
+
+461
+00:52:39,960 --> 00:52:49,580
+Limit لمن ؟ لـ X تربيع ناقص Y على X ناقص Y طبعاً
+
+462
+00:52:49,580 --> 00:52:58,940
+لما X و Y بدها تروح للـ Zero أنا عندي
+
+463
+00:52:58,940 --> 00:53:04,160
+function و بدى أحسب بـ Limit لهذه function عند مين
+
+464
+00:53:04,160 --> 00:53:10,670
+عنده نقطة الأصل برجع أقول شو ممكن نقطة الأصلمحور X
+
+465
+00:53:10,670 --> 00:53:18,930
+محور Y Y تساوي X تربية Y تساوي X تكيب Y تساوي
+
+466
+00:53:18,930 --> 00:53:24,910
+الجذر التالت ل X الاخر Y تساوي X تربية زائد واحد
+
+467
+00:53:24,910 --> 00:53:30,830
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+468
+00:53:30,830 --> 00:53:30,910
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+469
+00:53:30,910 --> 00:53:31,530
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+470
+00:53:31,530 --> 00:53:31,530
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+471
+00:53:31,530 --> 00:53:33,310
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ ل
+
+472
+00:53:36,220 --> 00:53:40,100
+إذا جيت مع مصار لا يمروا بهذه النقطة إذا قولت هذا
+
+473
+00:53:40,100 --> 00:53:44,640
+غلط يبقى المصار اللي بدي أخد اتأكد فعلا انه يمروا
+
+474
+00:53:44,640 --> 00:53:49,500
+بهذه النقطة حتى يكون كلامنا معلوم صحيح طيب خليني
+
+475
+00:53:49,500 --> 00:53:54,120
+اختار مصار ما هو شوف ايش بتقوله لو اخد مثلا على
+
+476
+00:53:54,120 --> 00:54:03,030
+سبيل المثال عبر محور X يبقى بدأت اقوله تكذى path
+
+477
+00:54:03,030 --> 00:54:09,610
+خد للمصار y تساوي zero مين y تساوي zero؟ اللي هو
+
+478
+00:54:09,610 --> 00:54:15,210
+ال x axis اللي هو ال x axis يبقى بصير هذه يا بنات
+
+479
+00:54:15,210 --> 00:54:24,210
+limit لما ال x وال y بدها تروحلمن؟ لل a لل 0 و لل
+
+480
+00:54:24,210 --> 00:54:30,370
+0 لل 0 و لل 0 لمن؟ بدي أشيل ال y و أضع مكانها 0
+
+481
+00:54:30,370 --> 00:54:36,170
+ماذا يحصل؟ عندك x تربيع على x يعني limit لما ال x
+
+482
+00:54:36,170 --> 00:54:47,090
+و ال y راحت لل 0 و لل 0 فقط ل x كم يصبح عندي 0 طيب
+
+483
+00:54:47,520 --> 00:54:56,600
+الان بدأت أقوله take the path خد المسافة مثلا x
+
+484
+00:54:56,600 --> 00:55:07,580
+تساوي زيرو ال y axis يعني ال y axis إيش بده يصير
+
+485
+00:55:07,580 --> 00:55:17,760
+limit لما ال x و ال y بدها تروح ل 0,0لمن ؟ ل X
+
+486
+00:55:17,760 --> 00:55:24,160
+تربيع ال X كنتش قولنا Zero ما طالع عندي قداشر ناقص
+
+487
+00:55:24,160 --> 00:55:31,520
+Y على ناقص Y كدهش بطلع ال limit واحد صحيح يبقى هنا
+
+488
+00:55:31,520 --> 00:55:37,480
+واحد صحيح شو رأيكوا في سنتين الأثنين هدول سنتين
+
+489
+00:55:37,480 --> 00:55:44,120
+مختلفتين يبقى هنا بروح بقوله سواء ال limit لل X
+
+490
+00:55:44,120 --> 00:55:52,270
+تربيعناقص y على x ناقص y لما ال x و ال y بدنا يروح
+
+491
+00:55:52,270 --> 00:55:59,290
+ل zero و zero لا يوجد
+
+492
+00:55:59,290 --> 00:56:03,330
+لأن
+
+493
+00:56:03,330 --> 00:56:08,790
+ال zero لا يساوي ال واحد
+
+494
+00:56:36,950 --> 00:56:42,450
+عشان نعطي مثال لبنات نبرى
+
+495
+00:56:42,450 --> 00:56:54,170
+بيه ان ال limit لما ال x و y يتقع من 0،0 لما ال x
+
+496
+00:56:54,170 --> 00:56:58,390
+و y تقع على x ترمية
+
+497
+00:57:11,560 --> 00:57:15,020
+طبعا انا اتفرج من المؤشر يجيب لي 0 على 0 يقول ده
+
+498
+00:57:15,020 --> 00:57:20,900
+اختار مسار فعلا يمر بنقطة الأصل مثلا لو يقول Y
+
+499
+00:57:20,900 --> 00:57:24,920
+تساوي X خط
+
+500
+00:57:24,920 --> 00:57:29,740
+مستقيم بنصف اللي هو الزاوية بين محور X و محور Y
+
+501
+00:57:29,740 --> 00:57:34,460
+الرابع الأول بنصف و تمر بنقطة الأصل يبقى باجي
+
+502
+00:57:34,460 --> 00:57:36,560
+بقوله مثلا P
+
+503
+00:57:46,740 --> 00:57:53,140
+يجب ان اشيل
+
+504
+00:57:53,140 --> 00:57:57,680
+كل Y و اضع مكانها X او اشيل كل X و اضع مكانها Y
+
+505
+00:57:57,680 --> 00:58:02,880
+سواء كانت هذه او تلت اتنين are the same يجب ان
+
+506
+00:58:02,880 --> 00:58:03,640
+اشيل كل Y و اضع مكانها X او اشيل كل X و اضع مكانها
+
+507
+00:58:03,640 --> 00:58:03,640
+Y
+
+508
+00:58:10,730 --> 00:58:17,570
+يبقى بنات صارت هذه كإنها إيش لمل لما ال X وال Y
+
+509
+00:58:17,570 --> 00:58:25,390
+بدها تروح ل 00 ل X أُس 4 على X تربيه عامل مشترك
+
+510
+00:58:25,390 --> 00:58:28,890
+يظل 1 زي X أُس 4
+
+511
+00:58:36,510 --> 00:58:43,790
+بدا تروح للـ 0 والـ 0 لل X تربيع على 1 زايد X أُس
+
+512
+00:58:43,790 --> 00:58:50,590
+4 نشيل كل X ونحط مكانها Zero يبقاش مصير Zero على
+
+513
+00:58:50,590 --> 00:58:59,190
+واحد زايد Zero ويساوي Zero نجرب أي مسار آخر بحيث
+
+514
+00:58:59,190 --> 00:59:02,390
+المسار يمر بنقطة الأصل
+
+515
+00:59:06,170 --> 00:59:13,830
+take the path مثلًا على سبيل المثال Y يسوى الجذر
+
+516
+00:59:13,830 --> 00:59:20,650
+التالت ل X يعني X أسطول هل تعرفين الملحانة دي أم
+
+517
+00:59:20,650 --> 00:59:29,850
+لا؟ عارفين او لا؟ تقول plus A هاي هذا محور X هذا Y
+
+518
+00:59:29,850 --> 00:59:36,280
+هذا أصل الملحانة بيجي ك .. بيجي بالشكل هذايبقى هذا
+
+519
+00:59:36,280 --> 00:59:42,980
+Y تساوي X أسطل يبقى فعلا يمر بنقطة الأصل اللي
+
+520
+00:59:42,980 --> 00:59:46,940
+عندنا يبقى شوف ايش اللي بده يصير بده يصير limit
+
+521
+00:59:46,940 --> 00:59:54,260
+لما ال X و ال Y بده يروح ل 0 0 لمين للدالة اللي
+
+522
+00:59:54,260 --> 00:59:56,500
+عندنا هذه يبقى هذه X
+
+523
+01:00:13,210 --> 01:00:19,430
+والـ Y بدها تذهب الى الـ 0 و الـ 0 هذه برنامج
+
+524
+01:00:19,430 --> 01:00:25,790
+بعتبارها X أُس تلت لكل تكييب بـ X أُس واحد وعند X
+
+525
+01:00:25,790 --> 01:00:32,530
+يجب أن يكون X تربيع فقط لغاية X تربيع وهذه X أُس
+
+526
+01:00:32,530 --> 01:00:39,490
+تلت أُس ستة يبقى أُس مركب بسيط جدا X تربيع يبقى
+
+527
+01:00:39,490 --> 01:00:45,810
+صارت هذه الـ limitلما الـ X و الـ Y بدها تروح إلى
+
+528
+01:00:45,810 --> 01:00:51,870
+الـ 0,0 للـ X تربيع على 2 X تربيع يبقى الـ Limit
+
+529
+01:00:51,870 --> 01:00:56,350
+هذي تساوي قدر شبلها؟ نص لإختصار X تربيها مع X
+
+530
+01:00:56,350 --> 01:01:02,010
+تربيها بتعطي نص تطلع هنا نص وهنا Zero يبقى ال
+
+531
+01:01:02,010 --> 01:01:04,770
+Limit تضمن Exact يبقى ال Limit
+
+532
+01:01:20,700 --> 01:01:31,480
+does not exist because اللي هو الـ zero لا يساوي
+
+533
+01:01:31,480 --> 01:01:36,660
+نص ولا تشبيه تماما زي ما كنا في الcalculation
+
+534
+01:01:36,660 --> 01:01:40,160
+بناخد ال limit من اليمين و من الشمال إذا اختلفت
+
+535
+01:01:40,160 --> 01:01:43,920
+اليمين عن الشمال يكون ال limit does not exist إذا
+
+536
+01:01:43,920 --> 01:01:48,720
+هنا لهم مسارين مختلفينمشينا مع الأول ومشينا مع
+
+537
+01:01:48,720 --> 01:01:52,300
+التاني واخدنا المتوطالي different limits، خمتين
+
+538
+01:01:52,300 --> 01:01:55,740
+مختلفتين، إذا بروح بقوله إن ال limit اللي عندي هذه
+
+539
+01:01:55,740 --> 01:01:58,960
+مالها لازم ت exist
+
+540
+01:02:01,490 --> 01:02:09,130
+كيف؟ بس مسارين مش سبع بس مسارين كفين اتنين ان شاء
+
+541
+01:02:09,130 --> 01:02:13,890
+الله يكون فيه خمس طاقم سمعت ايش قلنالك لول قلنالك
+
+542
+01:02:13,890 --> 01:02:18,850
+افترضي انه عندي عشر مسارات و لما شرحت الجزء النظري
+
+543
+01:02:18,850 --> 01:02:25,250
+قبل الأمثلة و لجيت تسع مسارات اعطاني نفس القيمة
+
+544
+01:02:25,250 --> 01:02:29,490
+لكن المسار العاشر ماعطانيش نفس القيمة اذا ال limit
+
+545
+01:02:29,490 --> 01:02:37,160
+ايش قلناها؟does not exist يعني
+
+546
+01:02:37,160 --> 01:02:40,260
+عندي خمسة و تلاتين طالب اللي أجيلا تمانتاش على
+
+547
+01:02:40,260 --> 01:02:58,320
+النص يعزيزي
+
+548
+01:03:02,040 --> 01:03:06,880
+هذا الكلام اللي شفته قبل قليل كله موجود في جزء
+
+549
+01:03:06,880 --> 01:03:09,440
+النظر التابع للتابع للتابع للتابع للتابع للتابع
+
+550
+01:03:09,440 --> 01:03:11,500
+للتابع للتابع للتابع للتابع للتابع للتابع للتابع
+
+551
+01:03:11,500 --> 01:03:14,680
+للتابع للتابع للتابع للتابع للتابع للتابع للتابع
+
+552
+01:03:14,680 --> 01:03:14,980
+للتابع للتابع للتابع للتابع للتابع للتابع للتابع
+
+553
+01:03:14,980 --> 01:03:16,240
+للتابع للتابع للتابع للتابع للتابع للتابع للتابع
+
+554
+01:03:16,240 --> 01:03:16,240
+للتابع للتابع للتابع للتابع للتابع للتابع للتابع
+
+555
+01:03:16,240 --> 01:03:17,440
+للتابع للتابع للتابع للتابع للتابع للتابع للتابع
+
+556
+01:03:17,440 --> 01:03:24,520
+للتابع للتالان باجي بقول لو جينا نشتغل مباشر زي ما
+
+557
+01:03:24,520 --> 01:03:28,860
+كنا بنشتغل في كل الأمثلة السابقة وطلع اللي مت zero
+
+558
+01:03:28,860 --> 01:03:33,080
+على zero مالة نهاية مالة نهاية zero في مالة نهاية
+
+559
+01:03:33,080 --> 01:03:38,120
+يعني شغلات does not exist ومش قادرة أتلحح أو أحرك
+
+560
+01:03:38,120 --> 01:03:41,760
+حالي مع المسألة اللي موجودة شو نعمل في مثل هذه
+
+561
+01:03:41,760 --> 01:03:46,400
+الحالة؟ قال لي بسيطة اتحول إلى polar coordinates
+
+562
+01:03:47,040 --> 01:03:53,440
+تحول مثلتك إلى احداثيات او قطبية بيصير المسألة
+
+563
+01:03:53,440 --> 01:03:59,440
+سهلة وبنحل المسألة بكل سهولة طبعا طيب كيفك تتحول
+
+564
+01:03:59,440 --> 01:04:03,420
+لل polar coordinates هذا ما سنضعه في صيغة ال
+
+565
+01:04:03,420 --> 01:04:08,080
+remark التالية نبدأ بكتير remark
+
+566
+01:04:18,840 --> 01:04:31,580
+we cannot find إذا مش قادرين نوجد ال limit لل f of
+
+567
+01:04:31,580 --> 01:04:39,660
+x و y لما ال x و ال y بدها تروح إلى x node و y
+
+568
+01:04:39,660 --> 01:04:45,040
+node شو نعمل فيها دلوقتي way to change
+
+569
+01:04:49,200 --> 01:05:00,440
+will change to the polar coordinates يجب أن نتحول
+
+570
+01:05:00,440 --> 01:05:07,500
+إلى الإحداثيات القطبية من الإحداثيات القطبية ال X
+
+571
+01:05:07,500 --> 01:05:15,280
+يساوي R Cos Thetaوالـ y يسوي r sin θ وعندك الـ r
+
+572
+01:05:15,280 --> 01:05:23,000
+تسوي الجذري التربيعي ل x تربيع زائد y تربيع ونقض
+
+573
+01:05:23,000 --> 01:05:27,940
+ان الـ
+
+574
+01:05:27,940 --> 01:05:35,180
+r بدها تروح للزيرو if and only if ال x و ال y بدها
+
+575
+01:05:35,180 --> 01:05:36,460
+تروح للزيرو
+
+576
+01:05:43,520 --> 01:05:47,200
+خلّيني اوضّح الكلام اللي احنا بنقوله بالرسم ثم
+
+577
+01:05:47,200 --> 01:05:52,760
+نبدأ نشتغل بيه ابقى لو جيت اخدت محاور بهذا الشكل
+
+578
+01:05:52,760 --> 01:06:00,400
+يا بنات وقولت هذا محور X وهذا محور Y وهذه نقطة
+
+579
+01:06:00,400 --> 01:06:08,420
+الأصل جينا رسمنا دائرة اللي مركزها نقطة الأصل ونصف
+
+580
+01:06:08,420 --> 01:06:16,090
+قطرها يساوي R على سبيل المثاليبقى هذا لو R نصف
+
+581
+01:06:16,090 --> 01:06:24,550
+القطر تبع هذه الدائرة هذه النقطة عند محيط الدائرة
+
+582
+01:06:24,550 --> 01:06:30,830
+بدي أسميها X وY في الـ Cartesian coordinates لو
+
+583
+01:06:30,830 --> 01:06:35,910
+كانت الزاوية هذه اللي هي الزاوية ثيتا ونزلت من هنا
+
+584
+01:06:35,910 --> 01:06:43,280
+عمودي يبقى هذا X و هذا Yيبقى X اللي عندي تساوي R
+
+585
+01:06:43,280 --> 01:06:49,260
+Cos θ و ال Y اللي عندي هذي بR Sin θ لإن الزاوية
+
+586
+01:06:49,260 --> 01:06:56,460
+هذه زاوية قائمة طب لو ربعته وجمعت مش بصير عنديX
+
+587
+01:06:56,460 --> 01:07:00,420
+تربيع زائد Y تربيع تساوي R تربيع Cos تربيع زائد R
+
+588
+01:07:00,420 --> 01:07:03,540
+تربيع Sine تربيع باخد R على التربيع و اشتغل بقى
+
+589
+01:07:03,540 --> 01:07:07,300
+Cos تربيع زائد Sine تربيع من دين واحد يبقى بيصير X
+
+590
+01:07:07,300 --> 01:07:12,140
+تربيع زائد Y تربيع تساوي R تربيع إذا بدي R بقول
+
+591
+01:07:12,140 --> 01:07:16,100
+square root ل X تربيع زائد Y تربيع إذا عرفنا
+
+592
+01:07:16,100 --> 01:07:20,940
+العلاقة الأخيرة من أين جاءت طيب لو يا بنات ال X
+
+593
+01:07:20,940 --> 01:07:28,970
+راحت لل ZeroوY نزلت للزيرو يعني لو هاني وصلت هنا
+
+594
+01:07:28,970 --> 01:07:35,060
+هي ب X نقصة و Y نقصة R تزيد ولا تنجح اصلا؟يعني
+
+595
+01:07:35,060 --> 01:07:41,660
+افترض هنا وصلت لهنا كيف يعني احس النقطة هيك صارت
+
+596
+01:07:41,660 --> 01:07:45,740
+ال Y صغيرة و ال X أكبر شوية مثلا على سبيل المثال
+
+597
+01:07:45,740 --> 01:07:50,340
+يبقى إذا ال X راحت ل Zero و ال Y راحت ل Zero
+
+598
+01:07:50,340 --> 01:07:54,740
+فبتروح ل Zero طبيعي يبقى ال R بتروح ل Zero لو كان
+
+599
+01:07:54,740 --> 01:07:56,920
+ال X و Y راحت ل Zero
+
+600
+01:08:06,260 --> 01:08:14,600
+الصورة نعطي أمثلة توضيحية على هذا الكلام for
+
+601
+01:08:14,600 --> 01:08:22,280
+example find
+
+602
+01:08:22,280 --> 01:08:23,460
+the following limits
+
+603
+01:08:34,720 --> 01:08:40,100
+فإذا كانت موجودة
+
+604
+01:08:40,100 --> 01:08:45,780
+إذا كانت
+
+605
+01:08:45,780 --> 01:08:50,560
+موجودة إذا كانت موجودة
+
+606
+01:09:17,050 --> 01:09:21,670
+طبعا اول مجلة في ذهن نفسي اقول بدي احلل الزاوية
+
+607
+01:09:21,670 --> 01:09:25,710
+اللي عندناها كفرق بين المكعبين افترض حالة انها في
+
+608
+01:09:25,710 --> 01:09:30,490
+اختصارات بينهم و بين المقام لأ هل يمكن تحليل
+
+609
+01:09:30,490 --> 01:09:35,410
+المقام؟ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+610
+01:09:35,410 --> 01:09:37,350
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+611
+01:09:37,350 --> 01:09:37,350
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+612
+01:09:37,350 --> 01:09:37,350
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+613
+01:09:37,350 --> 01:09:43,310
+لأ لأ لأ لأ لأ لأ لأ
+
+614
+01:09:43,700 --> 01:09:49,240
+مش مصيري عندي cosine قداش؟ Zero على Zero، مش
+
+615
+01:09:49,240 --> 01:09:52,740
+عارفين؟ ماعرفش ما هو Zero على Zero، كمية غير معينة
+
+616
+01:09:52,950 --> 01:09:57,110
+إذا كوصيلة كمية غير معينة برضه بعرفاش طب كيف بدي
+
+617
+01:09:57,110 --> 01:10:01,590
+أسوي للتحليل مش قادر يختصر و هيك مش ثابتة أبدا
+
+618
+01:10:01,590 --> 01:10:06,250
+بالمرة؟ مظبوط؟ يبقى فيش إمكانية في هذه الحالة
+
+619
+01:10:06,250 --> 01:10:10,890
+بالطرق التي سبقت دراستها في ال Cartesian Curve
+
+620
+01:10:10,890 --> 01:10:15,490
+لنحل هذه المثلة أحد المثال اللي ابتدى لبالك في
+
+621
+01:10:15,490 --> 01:10:19,230
+التمرينتمام طب كيف نسوي في هذه الحالة إذا ال
+
+622
+01:10:19,230 --> 01:10:23,790
+automatic ماليش إلا اتحول إلى polar coordinates
+
+623
+01:10:23,790 --> 01:10:26,430
+إذا لما اتحول إلى polar
+
+624
+01:10:34,270 --> 01:10:41,610
+R تكييب Cos تكييب ثيتا ناقص R تكييب Sin تكييب ثيتا
+
+625
+01:10:41,610 --> 01:10:48,990
+كله على R تربيع Cos تربيع ثيتا زائد R تربيع في Sin
+
+626
+01:10:48,990 --> 01:10:55,870
+تربيع ثيتا كله ال limit لما ال R بتروح لوين؟ لزيرو
+
+627
+01:10:56,410 --> 01:11:01,030
+الان صار في عندى اختصارات بقدر اخد R تكييب عمل
+
+628
+01:11:01,030 --> 01:11:06,810
+مشترك او بقدر اخد R تربيع عمل مشترك وبالتالي بتقول
+
+629
+01:11:06,810 --> 01:11:12,350
+المسألة الى الشكل التالي limit لما ال R بدها تروح
+
+630
+01:11:12,350 --> 01:11:17,930
+لل zero ليه cosine هنا يا بنات R تكييب
+
+631
+01:11:20,930 --> 01:11:28,710
+فى مين فى cosine تكييب ثيتا نقص sin تكييب ثيتا على
+
+632
+01:11:28,710 --> 01:11:37,190
+R تربيع فقط لغير فى cosine تربيع ثيتا زائد sin
+
+633
+01:11:37,190 --> 01:11:39,870
+تربيع ثيتا بالشكل اللى عالى
+
+634
+01:11:43,460 --> 01:11:48,960
+لما نختصر هذا ما يحصل؟ يحصل limit لما الار بدها
+
+635
+01:11:48,960 --> 01:11:57,260
+تروح ل zero ل cosine ار في cosine تكييب تيتا ناقص
+
+636
+01:11:57,260 --> 01:12:05,240
+صيني تكييب تيتا على كده؟ اه السلامة راح تبقى شايفة
+
+637
+01:12:05,240 --> 01:12:09,500
+كيف لما حولت إلى ال polar coordinates اتبسطت المثل
+
+638
+01:12:09,500 --> 01:12:13,800
+عندى وصرت بالشكل اللي عندنا هذاطب لما الار بدت
+
+639
+01:12:13,800 --> 01:12:18,800
+ساوي بدت تروح للزيرو يبقى كده ايش بيصير كوصين صفر
+
+640
+01:12:18,800 --> 01:12:23,420
+في الجسد بيعطي كوصين زيرو له بقدام واحد إذا المثل
+
+641
+01:12:23,420 --> 01:12:26,380
+اللي ماكنتش قادر اتلخلح فيه في ال Cartesian
+
+642
+01:12:26,380 --> 01:12:30,020
+coordinates لما حولت إلى ال polar coordinates صارت
+
+643
+01:12:30,020 --> 01:12:36,600
+عملية عملية سهلة وبالتالي حصلت على كده مقدار هذه
+
+644
+01:12:36,600 --> 01:12:39,680
+ال element ناخد كمان مثال
+
+645
+01:12:44,900 --> 01:12:55,680
+بدنا limit لما ال X و ال Y بدها تروح ل 00 لتان
+
+646
+01:12:55,680 --> 01:13:01,100
+inverse اللي همين absolute value ل X و absolute
+
+647
+01:13:01,100 --> 01:13:06,860
+value ل Y على X تربيع زائد Y تربيع
+
+648
+01:13:11,990 --> 01:13:16,050
+برضه التعويض المباشر بيجيب لـ 0 يا عزيزي صح؟ إذا
+
+649
+01:13:16,050 --> 01:13:21,210
+بتحول ل 100 من ال polar coordinates يبقى هذي بيصير
+
+650
+01:13:21,210 --> 01:13:27,590
+ال limit لما ال R بدأ تروح ل 0 لتان inverse و هي
+
+651
+01:13:27,590 --> 01:13:32,810
+القوة هذا absolute value لل R في sin θ absolute
+
+652
+01:13:32,810 --> 01:13:41,190
+value لل R sin θ كله على R تربية في sin تربية ثتا
+
+653
+01:13:47,710 --> 01:13:54,450
+هذا الكلام بده يساوي limit لما ال R بدها تروح
+
+654
+01:14:00,640 --> 01:14:06,180
+الـ absolute value لـ R في absolute value للـ
+
+655
+01:14:06,180 --> 01:14:12,540
+cosine عمر المسافة يا بنات هذه كانت سالبة و ليست
+
+656
+01:14:12,540 --> 01:14:17,900
+جبهة يبقى ال absolute لل cosine وهذا R بره يبقى لو
+
+657
+01:14:17,900 --> 01:14:24,920
+أخدت R عامل مشترك يبقى cosine θ زائد sin θ ك
+
+658
+01:14:24,920 --> 01:14:35,130
+absolute وهذا ك absoluteهذه R تربيع في كوصين تربيع
+
+659
+01:14:35,130 --> 01:14:41,730
+تيتا زائد صين تربيع تيتا بالشكل اللي علناه يبقى
+
+660
+01:14:41,730 --> 01:14:47,270
+هذا الكلام يسمي limit لما ال R بدها تروح ل zero
+
+661
+01:14:47,270 --> 01:14:54,150
+لمن لتان inverse absolute value لكوصين تيتا زائد
+
+662
+01:14:54,150 --> 01:14:58,550
+absolute value لصين تيتا كله على R
+
+663
+01:15:00,980 --> 01:15:04,960
+يبقى R تربيع وSin تربيع زي الـSin تربيع اللي هي
+
+664
+01:15:04,960 --> 01:15:10,860
+أبواحد طب لما الـR بدها تروح لـinfinity يبقى ايش
+
+665
+01:15:10,860 --> 01:15:20,900
+بيصير يا بنات تان انفرز شكل على زيرو كده انفرز تان
+
+666
+01:15:20,900 --> 01:15:26,800
+انفرز يعني كده باي على اتن يبقى limit
+
+667
+01:15:29,840 --> 01:15:34,620
+لحد هنا أستاذ يكفينا على النقطة الأولى من هذا ال
+
+668
+01:15:34,620 --> 01:15:40,320
+section نروح للنقطة الثانية اللي مرتبطة مع هذه
+
+669
+01:15:40,320 --> 01:15:44,080
+النقطة تماما اللي هو ال continuity
+
+670
+01:16:22,540 --> 01:16:34,420
+is sent to the continuous المتصلة
+
+671
+01:16:34,420 --> 01:16:42,720
+at the point عند النقطة x0
+
+672
+01:16:58,600 --> 01:17:08,960
+defined at x non و y non الشرط التاني لو كانت ال
+
+673
+01:17:08,960 --> 01:17:19,020
+limit لل f of x و y لما ال x و ال y بدها تروح ال x
+
+674
+01:17:19,020 --> 01:17:22,640
+non و y non exist
+
+675
+01:17:25,100 --> 01:17:35,160
+الشرط التالف لو كانت ال F of X node و Y node بتسوي
+
+676
+01:17:35,160 --> 01:17:42,800
+limit F of X و Y لما ال X و ال Y بده يروح إلى X
+
+677
+01:17:42,800 --> 01:17:52,660
+node و Y node لما
+
+678
+01:17:52,660 --> 01:17:57,710
+نمر إلى الشروط التالفهذه اختلافات عن الشروط
+
+679
+01:17:57,710 --> 01:18:01,130
+التلاتة تبع الcontinuity الـ function فيه one
+
+680
+01:18:01,130 --> 01:18:06,850
+variable تبع calculus A يجهيها اللهم إلا حولناها
+
+681
+01:18:06,850 --> 01:18:14,450
+بعدة تناسب معدلة في متغيرين أو ثلاثة متغيرات أو ان
+
+682
+01:18:14,450 --> 01:18:18,360
+من المتغيرات وهكذايبقى الدالة بيقول انها
+
+683
+01:18:18,360 --> 01:18:23,140
+continuous عند نقطة x0 و y0 إذا الدالة كانت معرفة
+
+684
+01:18:23,140 --> 01:18:28,780
+عند هذه النقطة او f of x0 و y0 exist مش هذا نفس
+
+685
+01:18:28,780 --> 01:18:33,880
+المعنى، من الثاني ال limit cannot exist تلاتة
+
+686
+01:18:33,880 --> 01:18:38,280
+اتنين هدول بدهم يسووا بعض، يبقى ال f of x0 و y0
+
+687
+01:18:38,280 --> 01:18:41,550
+بده يسووا ال limitتبعت ال F of X و Y لما ال X Y
+
+688
+01:18:41,550 --> 01:18:45,350
+بتروح ل X0 و Y0 إذا تحققت الشروط التلاتة في أن
+
+689
+01:18:45,350 --> 01:18:51,010
+الواحد بقول الدالة متصلة عند هذه النقطة طيب في
+
+690
+01:18:51,010 --> 01:18:55,510
+كالخلصية أخدنا بعض الشغلات أو بعض النظريات أو بعض
+
+691
+01:18:55,510 --> 01:19:00,040
+القواعدلان كنت ريوز ال functions صحيحة هنا زي اذا
+
+692
+01:19:00,040 --> 01:19:04,700
+عندى two functions وتنتين كانوا متصلات في المجموعة
+
+693
+01:19:04,700 --> 01:19:08,460
+التاصلة وحاصلة الدرب والقسمة والضغط في المجلد دابل
+
+694
+01:19:08,460 --> 01:19:13,100
+الى اخرين كثيرات الحدود دوال متصلة ال rational
+
+695
+01:19:13,100 --> 01:19:16,960
+function بحيث المقام مايسوي zero كذلك كلها دوال
+
+696
+01:19:16,960 --> 01:19:22,800
+متصلة اذا هذا الكلام ينطبق على الكلام في حالة ال
+
+697
+01:19:22,800 --> 01:19:23,840
+functions of
+
+698
+01:19:37,480 --> 01:19:48,080
+in your functions دوال متصلة then المقطة الأولى ال
+
+699
+01:19:48,080 --> 01:19:57,500
+F زائد أو ناقص ال G ال F في G ال F على G وبشرط ان
+
+700
+01:19:57,500 --> 01:19:58,020
+ال G
+
+701
+01:20:21,600 --> 01:20:27,940
+rational functions are
+
+702
+01:20:27,940 --> 01:20:39,720
+continuous تبقى دوال متصلة in which بحيث ان these
+
+703
+01:20:39,720 --> 01:20:48,540
+functions are defined هتكون
+
+704
+01:20:48,540 --> 01:20:57,020
+دوال معرفةالأمرة التلاتة كثيرات الحدود polynomials
+
+705
+01:20:57,020 --> 01:21:04,400
+are continuous functions.
+
+706
+01:21:07,140 --> 01:21:13,380
+Examples كال
+
+707
+01:21:13,380 --> 01:21:21,940
+الأولواسأل هل ده اللي قابل اتصال ولا لا as the
+
+708
+01:21:21,940 --> 01:21:30,840
+function as the function f of x y أحقها
+
+709
+01:21:48,530 --> 01:21:56,650
+زيرو زيرو وهنا بتساوي زيرو لما X وY بدها تساوي
+
+710
+01:21:56,650 --> 01:22:05,890
+زيرو زيرو هل الدالة هذه continuous at
+
+711
+01:22:05,890 --> 01:22:09,850
+زيرو زيرو ام لا؟
+
+712
+01:22:44,450 --> 01:22:48,370
+يقول لي هل الدلة اللي عندنا هذه متصلة عندنا نقطة
+
+713
+01:22:48,370 --> 01:22:52,970
+00 ولا لا طبعا الدلة مجزة إلى مين ؟ مجزة إلى هنا
+
+714
+01:22:52,970 --> 01:22:56,790
+فأقول لك تاجر الشروب انت لا تشوف متحققة ولا لا
+
+715
+01:22:56,790 --> 01:23:03,310
+الان F of 00 كده شبنات إذا معرفة صح ولا لا يبقى
+
+716
+01:23:03,310 --> 01:23:12,450
+باجي بقوله هنا ال solution تاجر النقطة الأولىالـ F
+
+717
+01:23:12,450 --> 01:23:19,830
+of 0 0 بيبقى سوية 0 فهذا معناته ان ال F is defined
+
+718
+01:23:19,830 --> 01:23:25,610
+defined at
+
+719
+01:23:25,610 --> 01:23:32,510
+اللي هو 0 و 0 اذا بتروح لمين لل condition التاني
+
+720
+01:23:49,120 --> 01:23:56,790
+لو أخدت مثلًا عبرة محور X يبقى وايه بقداشبزيرو
+
+721
+01:23:56,790 --> 01:24:02,330
+يبقى ايش بيصير عندى؟ واحد طب لو انا شكت عبر محور X
+
+722
+01:24:02,330 --> 01:24:09,590
+عبر محور Y يبقى X بزيرو بيطلع الجواب سنة بواحد
+
+723
+01:24:09,590 --> 01:24:17,850
+يبقى limit does not exist يبقى هنا take the path
+
+724
+01:24:20,350 --> 01:24:27,130
+مسارين X يساوي 0 و Y يساوي 0 و نحن نحن نحن نحن نحن
+
+725
+01:24:27,130 --> 01:24:30,570
+نحن نحن
+
+726
+01:24:30,570 --> 01:24:31,550
+نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن
+
+727
+01:24:31,550 --> 01:24:32,710
+نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن
+
+728
+01:24:32,710 --> 01:24:35,250
+نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن
+
+729
+01:24:35,250 --> 01:24:35,250
+نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن
+
+730
+01:24:35,250 --> 01:24:40,570
+نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن
+
+731
+01:24:40,570 --> 01:24:48,430
+نحن
+
+732
+01:24:48,430 --> 01:24:55,030
+نحلما الـ X و الـ Y بدها تروح لـ 0 و الـ 0 و Y
+
+733
+01:24:55,030 --> 01:24:59,790
+تساوي 0، إيش بيظل عندي X تربيه علي X تربيه تساوي
+
+734
+01:24:59,790 --> 01:25:04,850
+1؟ هنا سالف واحد عبر المسار الأول، واحد عبر المسار
+
+735
+01:25:04,850 --> 01:25:09,250
+التاني، يبقى ال limit ما له لازم not exist يبقى
+
+736
+01:25:09,250 --> 01:25:15,350
+هنا سواء ال limit لما ال X و Yذا تروح للـ Zero و
+
+737
+01:25:15,350 --> 01:25:22,190
+Zero لل X تربيع ناقص Y تربيع على X تربيع زائد Y
+
+738
+01:25:22,190 --> 01:25:27,570
+تربيع لا يوجد
+
+739
+01:25:27,570 --> 01:25:38,010
+سبب لأنه سالم واحد لاتساوي واحد يبقى Therefore
+
+740
+01:25:46,220 --> 01:26:09,480
+is not continuous at zero zero مثال أقم اتنين وقول
+
+741
+01:26:09,480 --> 01:26:21,930
+is the function هل الدالةf of x و y تساوي تلاتة x
+
+742
+01:26:21,930 --> 01:26:30,610
+تربيع y على x تربيع زائد y تربيع لما ال x و ال y
+
+743
+01:26:30,610 --> 01:26:41,950
+لا تساوي 0 0 وتساوي 0 لما ال x و ال y بدها تساوي 0
+
+744
+01:26:41,950 --> 01:26:44,870
+0 continuous
+
+745
+01:26:48,370 --> 01:26:54,210
+at zero zero هذا
+
+746
+01:26:54,210 --> 01:26:58,310
+السؤال solution
+
+747
+01:26:58,310 --> 01:27:03,350
+إذا
+
+748
+01:27:03,350 --> 01:27:08,070
+نيجي نشوف شروط ال continuity التلاتة هل هي متحققة
+
+749
+01:27:08,070 --> 01:27:10,790
+و الله غير متحقق
+
+750
+01:27:34,520 --> 01:27:39,420
+الدالة واضحة انها معرفة عند 00 مظبوط يبقى بقوله
+
+751
+01:27:39,420 --> 01:27:45,460
+الخطوة الأولى فتاخد ال F of 00 ده الساوية Zero هذا
+
+752
+01:27:45,460 --> 01:27:58,080
+بيقول ان ال F is defined at 00 بعد هيك فتاخد ال
+
+753
+01:27:58,080 --> 01:28:05,140
+limit لدالة اللي عندنايبقى بدأ اخد ال limit النقطة
+
+754
+01:28:05,140 --> 01:28:12,700
+الثانية تاخد ال limit لمن؟ لما ال X و ال Y بدها
+
+755
+01:28:12,700 --> 01:28:20,160
+تروح لل Zero و ال Zero لمن؟ لتلاتة X تربيع Y عن X
+
+756
+01:28:20,160 --> 01:28:26,460
+تربيع زائد Y تربيع يبقى بتروح اخد مسارات ده كل
+
+757
+01:28:26,460 --> 01:28:29,680
+واحد اشطر مني شوية يقول طيب جرب ال polar يمكن تكون
+
+758
+01:28:29,680 --> 01:28:35,220
+أسرعبصراحة بدك تاخد مرتين بس في ال polar مرة واحدة
+
+759
+01:28:35,220 --> 01:28:40,880
+مقول له ماشي يبقى هذا الكلام بيساوي limit لما ال X
+
+760
+01:28:40,880 --> 01:28:49,780
+و ال Y او بداش X و Y R بدها تروح لل zero يبقى R
+
+761
+01:28:49,780 --> 01:28:58,370
+بدها تروح لل zero لتلاتة R ترميعوSin تربيع ثيتا في
+
+762
+01:28:58,370 --> 01:29:05,350
+R في Sine الزاوية ثيتا على R تربيع CoSin تربيع
+
+763
+01:29:05,350 --> 01:29:12,310
+ثيتا زائد R تربيع Sine تربيع ثيتا بهذا الكلام يبدو
+
+764
+01:29:12,310 --> 01:29:21,700
+يساوي limit لما ال R بدأت تذهب الى Zeroلتلاتة R
+
+765
+01:29:21,700 --> 01:29:27,800
+تكيب مع ال R تربيع اللي تحت تصيب تلاتة R في Cos
+
+766
+01:29:27,800 --> 01:29:34,620
+تربيع تيتا في Sine تيتا و لتحت الله يسهل عليه طبعا
+
+767
+01:29:34,620 --> 01:29:40,460
+R مع R تربيع بR تكيب R تربيع مع R تكيب بغلق R Cos
+
+768
+01:29:40,460 --> 01:29:44,320
+تربيع زي ال Sine تربيع تيتا اللي هو قداش هو حصيا
+
+769
+01:29:47,250 --> 01:29:54,590
+يبقى ال limit exist و تساوي كده؟ و تساوي zero و
+
+770
+01:29:54,590 --> 01:29:59,070
+الدالة لو معرفة و تساوي كده؟ اذا هذه دالة
+
+771
+01:29:59,070 --> 01:29:59,790
+continuous
+
+772
+01:30:09,210 --> 01:30:15,950
+0 و 0 يعني بالنسبة لك تفهموا إذا قلت عند 0 و 0 ليس
+
+773
+01:30:15,950 --> 01:30:21,550
+معناه هذا الكلام ان ال limit does not exist او في
+
+774
+01:30:21,550 --> 01:30:26,490
+عندي discord في اللي ممكن اعرفه اخدي لك مثال رقم
+
+775
+01:30:26,490 --> 01:30:35,630
+تلاتة شو رايك دي functions ال E أس X ناقص Y و Cos
+
+776
+01:30:35,630 --> 01:30:51,600
+Xزائد Y على X تربية زائد واحد زائد تلاتة وLin خمسة
+
+777
+01:30:51,600 --> 01:30:59,040
+زائد X تربية زائد Y تربية هل هناك نقطة الدالة
+
+778
+01:30:59,040 --> 01:31:04,260
+عندها مش معرفة اي واحد من دول التلاتة اتولى يا
+
+779
+01:31:04,260 --> 01:31:04,680
+عزفي
+
+780
+01:31:11,290 --> 01:31:15,390
+لأ كل واحد لحاله هذول تلات دوال يعني تلات مسائل
+
+781
+01:31:15,390 --> 01:31:18,830
+باعتبارها أي واحدة فيهم هتيله نقطة دليل عندها
+
+782
+01:31:18,830 --> 01:31:25,330
+معاها كله معاها اتنينالثانية الأولى هي exponential
+
+783
+01:31:25,330 --> 01:31:30,330
+فهي متصلة والتالتة كروسايم متصلة مثلا من هنا إلى
+
+784
+01:31:30,330 --> 01:31:36,230
+هنا والتالتة من هنا إلى هنا كمان متصلة، صحيح ولا
+
+785
+01:31:36,230 --> 01:31:42,290
+لأ؟ إذا هذه continuous for all x y بلاستينة يبقى
+
+786
+01:31:42,290 --> 01:31:46,710
+هذه ال functions اللي عندنا دول مالهم are
+
+787
+01:31:46,710 --> 01:31:50,150
+continuous
+
+788
+01:31:52,420 --> 01:32:04,940
+for all x y belasted not I remark the
+
+789
+01:32:04,940 --> 01:32:13,600
+previous rule the previous rules القواعد السابقة
+
+790
+01:32:13,600 --> 01:32:27,470
+on the functions of twovariables are
+
+791
+01:32:27,470 --> 01:32:31,710
+true صحيحة
+
+792
+01:32:31,710 --> 01:32:41,730
+are true for the functions or the functions of
+
+793
+01:32:41,730 --> 01:32:51,650
+three or more variablesيعني ليه ثلاثة متغيرات او
+
+794
+01:32:51,650 --> 01:32:59,750
+اكتر برضه صحيحة examples نمرأ
+
+795
+01:32:59,750 --> 01:33:09,130
+ايه؟ قولي at what points؟ at what points؟ من من
+
+796
+01:33:09,130 --> 01:33:14,650
+النقاط does the following
+
+797
+01:33:36,300 --> 01:33:46,520
+x و y يسوى x زائد ال y على تلاتة ناقص sign اللي هو
+
+798
+01:33:46,520 --> 01:33:50,380
+ال x هل
+
+799
+01:33:50,380 --> 01:33:56,520
+في نقطة يا بنات هذه الدالة عندها غير قابلة للاتصال
+
+800
+01:33:56,520 --> 01:33:58,400
+إذا في قولوني عنها
+
+801
+01:34:26,180 --> 01:34:31,400
+فى ولا حاجة يبقى دى continuous for all x و y يبقى
+
+802
+01:34:31,400 --> 01:34:40,840
+دى continuous for all x و y طيب انتقل الكلمة شوية
+
+803
+01:34:40,840 --> 01:34:54,140
+النقطة الثانية f of x و y تسبب لين اللي هو main x
+
+804
+01:34:54,140 --> 01:35:02,230
+تربيعزائد Y تربية في نقطة عندها الدالة غير معرفة
+
+805
+01:35:02,230 --> 01:35:09,970
+أو ممتصدة اللي المعرف نقيه موجبة صح ولا لأ فSin X
+
+806
+01:35:09,970 --> 01:35:14,430
+تربيه وY تربيه إن كان X وY بالسالب ورمه مموجة
+
+807
+01:35:14,430 --> 01:35:20,830
+فالمربع يبقى ضل أثنين بس نقطة الأصل يجي هذه الدالة
+
+808
+01:35:20,830 --> 01:35:27,560
+continuous ما عادة نقطة الأصليبقى هذه continuous
+
+809
+01:35:27,560 --> 01:35:31,360
+for
+
+810
+01:35:31,360 --> 01:35:44,200
+all x و y except ماعدا 0.000
+
+811
+01:35:44,200 --> 01:35:49,520
+أو ال origin النقطة التالفة
+
+812
+01:35:57,160 --> 01:36:07,020
+اللي هي f of x و y f of x و y بدها تساوي sign واحد
+
+813
+01:36:07,020 --> 01:36:16,180
+على x y يالا
+
+814
+01:36:16,180 --> 01:36:24,620
+وين الدلة مش معرفة عن صفر و صفر و أي واحد صفر و أي
+
+815
+01:36:24,620 --> 01:36:36,790
+رقم آخرالرقم مصفر تمام يبقى هنا continuous except
+
+816
+01:36:45,430 --> 01:37:09,930
+أكترين فوينتز أكترين
+
+817
+01:37:09,930 --> 01:37:10,090
+فوينتز أكترين فوينتز أكترين فوينتز أكترين فوينتز
+
+818
+01:37:10,090 --> 01:37:10,090
+أكترين فوينتز أكترين فوينتز أكترين فوينتز أكترين
+
+819
+01:37:10,090 --> 01:37:10,090
+فوينتز أكترين فوينتز أكترين فوينتز أكترين فوينتز
+
+820
+01:37:10,090 --> 01:37:10,090
+أكترين فوينتز أكترين فوينتز أكترين فوينتز أكترين
+
+821
+01:37:10,090 --> 01:37:10,090
+فوينتز أكترين فوينتز أكترين فوينتز أكترين فوينتز
+
+822
+01:37:10,090 --> 01:37:10,090
+أكترين فوينتز أكترين فوينتز أكترين فوينتز أكتر
+
+823
+01:37:14,120 --> 01:37:24,460
+يقول F of X, Y, Z X, Y, Z بيساوي الجدري التربيعي X
+
+824
+01:37:24,460 --> 01:37:40,420
+تربيع زائد Y تربيع ناقص واحد النقاط
+
+825
+01:37:40,420 --> 01:37:46,840
+اللي بتبقى ده اللي عندها continuousيبقى هذا يكون
+
+826
+01:37:46,840 --> 01:37:58,220
+في نواص for all x, y, z except at
+
+827
+01:37:58,220 --> 01:38:07,860
+x تربية زي y تربية ناقص واحدة منها أقل من الـ 0
+
+828
+01:38:11,090 --> 01:38:14,190
+ذا أكبر من Zero مافي مشكلة مُعرّفة لكن إذا أقل من
+
+829
+01:38:14,190 --> 01:38:21,590
+Zero مُعرّفة أو إن شئتم فاقولوا ها ال X تربيع زي
+
+830
+01:38:21,590 --> 01:38:26,950
+دورة تربيع أقل من واحد طب مين هم النقاط هذول يا
+
+831
+01:38:26,950 --> 01:38:34,790
+بنات بس Zero Zero داخل الدائرة احنا في الفراغ X Y
+
+832
+01:38:34,790 --> 01:38:42,120
+و Z سيلندر يبقىكل النقاط اللي داخل الـ except ما
+
+833
+01:38:42,120 --> 01:38:48,760
+عدا النقاط اللي داخل الـ cylinder يبقى هنا هذا
+
+834
+01:38:48,760 --> 01:38:57,440
+معناه ان ال continuous for
+
+835
+01:38:57,440 --> 01:39:04,780
+all x, y, z except the
+
+836
+01:39:04,780 --> 01:39:06,520
+points
+
+837
+01:39:11,550 --> 01:39:22,750
+انترال لسيلندر X تربية زي Y تربية يسوى واحد يعني
+
+838
+01:39:22,750 --> 01:39:26,910
+عند كل النقاط داخل السيلندر الدالة غير مضة لكن برا
+
+839
+01:39:26,910 --> 01:39:39,960
+كلها بتبقى A معارض النقطة الثانية لو قلتك FX Y Z X
+
+840
+01:39:39,960 --> 01:39:53,140
+Y Z X Y Z X Y Z X
+
+841
+01:39:53,140 --> 01:39:57,120
+Y Z X Y Z X Y Z X Y Z X Y Z X Y Z X Y Z X Y Z X Y
+
+842
+01:39:57,120 --> 01:40:05,680
+Z X Y Z X Y Z X Y Z X Y Z X Y Z X Y Z X Y Z X Y Z
+
+843
+01:40:05,680 --> 01:40:06,180
+X Y Z X Y Z X Y Z X Y Z X Y Z X Y Z X Y Z X Y Z X
+
+844
+01:40:06,180 --> 01:40:06,180
+Y Z X Y Z X Y Z X Y Z X Y Z X Y Z X Y Z X Y Z X Y
+
+845
+01:40:06,180 --> 01:40:06,180
+Z X Y Z X Y Z X Y Z X Y Z X Y Z X Y Z X Y Z X Y Z
+
+846
+01:40:06,180 --> 01:40:06,180
+X Y Z X Y Z X Y Z X Y Z X Y Z X Y Z X Y Z X Y Z X
+
+847
+01:40:06,180 --> 01:40:06,180
+Y Z X Y Z X Y Z X X Y Z X Y Z X X Y Z X X Y Z X X
+
+848
+01:40:06,180 --> 01:40:06,180
+X X X X X X X X X X X X X X X X X X X X X X X X X
+
+849
+01:40:06,180 --> 01:40:08,770
+X X X X X X X X X X Xلو كانت ال X و Y بيزيروا مش
+
+850
+01:40:08,770 --> 01:40:12,530
+مشكلة لكن ال Z ممنوع تساوي زي 1 على 0 إذا كانت في
+
+851
+01:40:12,530 --> 01:40:15,630
+مالة نهاية غير معرفة
+
+852
+01:40:25,880 --> 01:40:35,100
+Y زاد بدها تساوي الومين واحد على زد ناقص الجدري
+
+853
+01:40:35,100 --> 01:40:47,820
+التربيعي ل X تربيع زائد Y تربيع يبقى
+
+854
+01:40:47,820 --> 01:40:54,200
+continuous for
+
+855
+01:40:54,200 --> 01:40:54,820
+all
+
+856
+01:40:59,260 --> 01:41:07,520
+بحيث ان المقام له ممنوع يساوي Zero يبقى Z ناقص
+
+857
+01:41:07,520 --> 01:41:13,780
+الجدري التربيعي X تربيع زائد Y تربيع لا يساوي Zero
+
+858
+01:41:13,780 --> 01:41:23,760
+أو Z لا يساوي الجدري التربيعي X تربيع زائد Y تربيع
+
+859
+01:41:23,760 --> 01:41:32,550
+او Z تربيعلا يساوي X تربيع زاد Y تربيع معادلة تشهد
+
+860
+01:41:32,550 --> 01:41:40,450
+يا ابنها لو كانت تساوي كون مخروض صحيح Circular كون
+
+861
+01:41:40,450 --> 01:41:47,490
+القاعة التابعة عبارة عن أي دائرة يبقى هنا except
+
+862
+01:41:47,490 --> 01:41:55,150
+the points on the
+
+863
+01:41:57,760 --> 01:42:08,740
+circular cone Z تربيع X تربيع زائد Y تربيع كل
+
+864
+01:42:08,740 --> 01:42:13,620
+النقاط داخل ال circular cone أو الخارج ال circular
+
+865
+01:42:13,620 --> 01:42:17,720
+cone بعد ما تقعش عليه من الخارج لأنه إذا وقعت عليه
+
+866
+01:42:17,720 --> 01:42:26,650
+مصير كلامي هذا ما هوش صحيح طيب exercisesاربعتاشر
+
+867
+01:42:26,650 --> 01:42:36,770
+وانين المسائل التالية من واحد الى خمسين Multiple
+
+868
+01:42:36,770 --> 01:42:46,070
+of three وزياد عليهم سؤال خمسة وخمسين وسبعة وخمسين
+
+869
+01:42:46,070 --> 01:42:55,170
+ومن واحد وستين لغاية ستة وستين in all
+
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/0xeRGhgbabI_postprocess.srt b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/0xeRGhgbabI_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..3fffd944ca0a0a4a36fd3ffb7f55fbef87dad15d
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/0xeRGhgbabI_postprocess.srt
@@ -0,0 +1,3296 @@
+1
+00:00:00,000 --> 00:00:02,680
+موسيقى
+
+2
+00:00:16,200 --> 00:00:21,720
+بسم الله الرحمن الرحيم بمناسبة حلول اليوم الأول من
+
+3
+00:00:21,720 --> 00:00:28,620
+شهر رمضان مبارك نهنئكم بقدومي هذا الشهر ونوصيكم أن
+
+4
+00:00:28,620 --> 00:00:35,610
+تجددوا حياتكم من جديديعني بتغير نمط التعامل
+
+5
+00:00:35,610 --> 00:00:42,090
+الأولاني لإن رمضان فرصة للتغيير من الأسوأ إلى
+
+6
+00:00:42,090 --> 00:00:47,170
+الأحسن و من الأحسن إلى الأحسن منه و هكذا طبعا هذه
+
+7
+00:00:47,170 --> 00:00:51,970
+طبيعة الحياة سنن التغيير موجودة في الكون منذ بدء
+
+8
+00:00:51,970 --> 00:00:58,600
+الخليقة و إلى يومنا هذاكل واحد اتفكر ان في شغل كنت
+
+9
+00:00:58,600 --> 00:01:02,460
+بعملها غلط قبل هيك يبقى بنعملها الصح مشان الله
+
+10
+00:01:02,460 --> 00:01:06,860
+سبحانه و تعالى يغفرنا و نصير في الطريق الصحيح و
+
+11
+00:01:06,860 --> 00:01:11,980
+طبعا ان الذين آمنوا و عملوا الصالحات يهديهم ربهم
+
+12
+00:01:11,980 --> 00:01:18,420
+بإيمانهم يعني شفتوا في الثانوية العامة النتيجة
+
+13
+00:01:18,420 --> 00:01:22,880
+الأوائل او البنات الأوائل من حفظة القرآن الكريم
+
+14
+00:01:23,580 --> 00:01:30,040
+يبقى الذي يتدين يكون هذا سببا في تفوقه مش سببا في
+
+15
+00:01:30,040 --> 00:01:35,420
+تأخره ونحن المسلمين مطالبين دائما و أبدا أن نكون
+
+16
+00:01:35,420 --> 00:01:42,140
+في المقدمة و لن ترتفع لنا قائمة إلا إذا التزمنا
+
+17
+00:01:42,140 --> 00:01:48,000
+بديننا قولا و عملامش قول، لذا القرآن الكريم بيقول
+
+18
+00:01:48,000 --> 00:01:52,160
+إن الذين آمنوا وقالوا الصالحات والله إن الذين
+
+19
+00:01:52,160 --> 00:01:56,580
+آمنوا وعملوا الصالحات يبقى وعملوا الصالحات إذا
+
+20
+00:01:56,580 --> 00:02:05,510
+مطلوب مننا أن نعمل وأن نجدد وأننتذكر الأشياء اللى
+
+21
+00:02:05,510 --> 00:02:08,890
+ممكن نعملها غلط أو اللى عملناها غلط فهيك و نعزم
+
+22
+00:02:08,890 --> 00:02:13,930
+على أن لا نعود إليها ثانية بارك الله فيكم و نرجع
+
+23
+00:02:13,930 --> 00:02:18,850
+لموضوعنا طيب بذكر تذكير قبل كل شيء بالشيء اللى
+
+24
+00:02:18,850 --> 00:02:22,510
+أخدناه المرة الماضية في ال directional derivative
+
+25
+00:02:23,130 --> 00:02:27,230
+طبعا عرفنا ال gradient vector عرفنا ال directional
+
+26
+00:02:27,230 --> 00:02:32,530
+derivative ثم كتبنا أخر حاجة بعد ما أخذنا ميثالين
+
+27
+00:02:32,530 --> 00:02:37,710
+الخواف S ثلاثة تبعت ال directional derivative بذكر
+
+28
+00:02:37,710 --> 00:02:42,110
+صادقين قولنا ال directional derivative هديله رمز
+
+29
+00:02:42,110 --> 00:02:45,470
+اللي هو DUF
+
+30
+00:02:48,500 --> 00:02:55,560
+لجراد ال F عند النقطة P نُط بط اللي هو متجه الوحدة
+
+31
+00:02:55,560 --> 00:03:04,720
+U وفكنا هذا الكلام وقلنا ان هذا يعتبر طول لجراد F
+
+32
+00:03:05,070 --> 00:03:11,090
+فيقول ال U P Cos الزاوية تيتا لكن لما كان متجه
+
+33
+00:03:11,090 --> 00:03:16,450
+الوحدة طوله يساوي واحد صحيح إذا هذا كله بده يساوي
+
+34
+00:03:16,450 --> 00:03:23,050
+طول جراد ال F P Cos الزاوية ثانية الآن بدنا نيجي
+
+35
+00:03:23,050 --> 00:03:27,700
+لخواص هذا ال direction ال derivativeكتبنا المرة
+
+36
+00:03:27,700 --> 00:03:32,120
+اللي فاتت أنه ممكن يكون موجب ممكن يكون سالب ممكن
+
+37
+00:03:32,120 --> 00:03:38,200
+يكون صفر ممكن يكون أكبر ما يمكن ممكن أن يكون أقل
+
+38
+00:03:38,200 --> 00:03:42,800
+ما يمكن و ممكن يكون zero روحنا قولنا ال F
+
+39
+00:03:42,800 --> 00:03:47,720
+increases most strategically اللي هي النقطة هذه
+
+40
+00:03:47,720 --> 00:03:54,220
+إذا كان والله ال U grade ال V2 في نفس الاتجاه يحدث
+
+41
+00:03:54,220 --> 00:04:00,660
+هذاإن كانت θ تساوي زيرو، ثتا تساوي زيرو يعني اتنين
+
+42
+00:04:00,660 --> 00:04:05,040
+في نفس الاتجاه وبالتالي ال cosine صفر واحد وهي
+
+43
+00:04:05,040 --> 00:04:10,660
+أكبر قيمة بياخدها ال cosine وبالتالي هي أكبر قيمة
+
+44
+00:04:10,660 --> 00:04:17,520
+لل directional derivativeتمام وهي قيمة موجبة يبقى
+
+45
+00:04:17,520 --> 00:04:21,680
+positive و أكبر ما يمكن أن نحصل عليه هو اكترش لو
+
+46
+00:04:21,680 --> 00:04:25,460
+كان ال U اجراد ال F اتنين في نفس الاتجاه in the
+
+47
+00:04:25,460 --> 00:04:29,960
+same direction هذه الحالة الأولى الحالة الثانية
+
+48
+00:04:29,960 --> 00:04:35,940
+باجي بقول لو كانت ال U اجراد ال V اتجاهين متضادين
+
+49
+00:04:36,230 --> 00:04:40,830
+يبقى الزاوية بينهم كمية و تمانين درجة كسايم مية و
+
+50
+00:04:40,830 --> 00:04:47,350
+تمانين بسالب واحد وهي أصغر قيمة بياخدها كسايم ثيتا
+
+51
+00:04:47,350 --> 00:04:51,890
+يبقى بالتالي بحصل على أقل قيمة لل directional
+
+52
+00:04:51,890 --> 00:04:57,510
+derivative وقتاش لما ثيتا تساوي باي لأن كسايم باي
+
+53
+00:04:57,510 --> 00:05:03,130
+بسالب واحد في الحالة الأولى قيمة ال directional
+
+54
+00:05:03,130 --> 00:05:08,630
+derivativeبيبقى فقط قدرة جبلات في الحالة اللي طول
+
+55
+00:05:08,630 --> 00:05:13,630
+grade ال F وفي الحالة الثانية قيمة ال derivation
+
+56
+00:05:13,630 --> 00:05:19,770
+derivative اللي هو سالب grade ال F طبعا؟ طب الحالة
+
+57
+00:05:19,770 --> 00:05:25,610
+التالتةالحالة التالتة لو كان ال U وما اجراد ال V
+
+58
+00:05:25,610 --> 00:05:30,810
+اتنين are orthogonal اتنين مالهم متعامدين يبقى
+
+59
+00:05:30,810 --> 00:05:36,350
+الزاوية بينهم تسعين درجة كصين تسعين بزيرو وفي هذه
+
+60
+00:05:36,350 --> 00:05:39,610
+الحالة بقول ان ال directional derivative بدي ساوي
+
+61
+00:05:39,610 --> 00:05:44,730
+من؟ بدي ساوي زيرو يبقى لو كان ال theta تساوي pi
+
+62
+00:05:44,730 --> 00:05:52,140
+على اتنين في هذه الحالةبيكون مقدار الـ DUF كله
+
+63
+00:05:52,140 --> 00:05:56,660
+بيديه سوا قداش 0 إذا قيمة ال direction derivative
+
+64
+00:05:56,660 --> 00:06:00,760
+أحيانا ممكن تكون موجبة أحيانا ممكن تكون سالبة
+
+65
+00:06:00,760 --> 00:06:06,440
+أحيانا ممكن تكون 0أكبر قيمة بيأخدها الـ TASH إذا
+
+66
+00:06:06,440 --> 00:06:09,960
+كان الـ U قيمة الـ P في نفس الإتاجة الجزائية بينهم
+
+67
+00:06:09,960 --> 00:06:15,160
+Zero وقيمة الـ Direction Derivative عدديا يسوى فقط
+
+68
+00:06:15,160 --> 00:06:21,330
+طول قيمة الـ F وهي قيمة موجبةإذا كان اتنين في
+
+69
+00:06:21,330 --> 00:06:25,990
+اتجاهين متضادين فالـ grad الف هياخد قيمة سالبة
+
+70
+00:06:25,990 --> 00:06:29,610
+ومقدار ال direction of the derivative بدي يكون
+
+71
+00:06:29,610 --> 00:06:34,590
+سالب اللي هو طول grad الف الحالة التالتة والاخيرة
+
+72
+00:06:34,590 --> 00:06:36,830
+ان ال direction of the derivative بدي يساوي zero
+
+73
+00:06:36,830 --> 00:06:42,330
+واكتش اذا U و grad الف اتنين are orthogonal بدنا
+
+74
+00:06:42,330 --> 00:06:46,530
+نبدأ بمثال توضيحي على ذلك يبقى اكتشافي
+
+75
+00:06:52,900 --> 00:06:56,560
+طبعا هذا مكتوب معاكم من المرة الماضية اه مكتوب بس
+
+76
+00:06:56,560 --> 00:07:04,480
+انا بتذكر بتذكر لان بيقول let f of x y بده ساوي ال
+
+77
+00:07:04,480 --> 00:07:14,360
+square root لل x square زائد اتنين y نمره a find
+
+78
+00:07:14,360 --> 00:07:22,260
+the direction find the direction of
+
+79
+00:07:23,490 --> 00:07:29,510
+increasing if
+
+80
+00:07:29,510 --> 00:07:37,890
+most rapidly at
+
+81
+00:07:37,890 --> 00:07:46,870
+عند النقطة P node اللي هي أربعة وعشرة number B
+
+82
+00:07:46,870 --> 00:07:51,850
+find the direction of decreasing
+
+83
+00:07:54,170 --> 00:08:01,910
+F مصطرى بدليا من النقطة 14 نمرى C find a unit
+
+84
+00:08:01,910 --> 00:08:16,510
+vector find a unit vector تجه وحدة such that بحيث
+
+85
+00:08:16,510 --> 00:08:27,490
+ان ال DUFبدو يساوي zero at عند نفس النقطة P naught
+
+86
+00:08:27,490 --> 00:08:30,410
+of أربعة و عشر
+
+87
+00:08:47,610 --> 00:08:53,090
+يبقى هذا المثال يجيب على التلات خواب سبعة المرة
+
+88
+00:08:53,090 --> 00:08:58,210
+الماضية و اللي ذكرنا أبهم قبل قليل السؤال بيقول خد
+
+89
+00:08:58,210 --> 00:09:01,370
+ال F of X و Y بيبقى سوى ال square root لل X square
+
+90
+00:09:01,370 --> 00:09:06,010
+زي ال 2Y بيقول هاتلي ال direction of increasing F
+
+91
+00:09:06,010 --> 00:09:11,010
+most rapidly عن النقطة اللي هي 14بعدها كمالها to
+
+92
+00:09:11,010 --> 00:09:16,070
+the action of decreasing if most rapidly when عند
+
+93
+00:09:16,070 --> 00:09:21,020
+النفطة اربعة و عشرة و بعدها كانت لمتجهة الوحدةعند
+
+94
+00:09:21,020 --> 00:09:22,940
+النقطة اللي عندنا دي بيحط ال directional
+
+95
+00:09:22,940 --> 00:09:27,360
+derivative بيبقى تساوي مين؟ بيبقى تساوي Zero بقولك
+
+96
+00:09:27,360 --> 00:09:31,980
+خيص يبقى مشان أجيب أي واحد من التلات لازم ل grade
+
+97
+00:09:31,980 --> 00:09:36,160
+ال F مشان أ grade ال F أجيبها يبقى بال D مشتقة ال
+
+98
+00:09:36,160 --> 00:09:40,940
+F بالنسبة ل X و مشتقة ال F بالنسبة ل Y عند النقطة
+
+99
+00:09:40,940 --> 00:09:46,400
+من أربعة و عشرة إذا هبدأ بمين بال F X
+
+100
+00:09:50,720 --> 00:09:56,660
+مشتقة الجدر واحد على اتنين الجدر زي ما تعلمنا في
+
+101
+00:09:56,660 --> 00:10:02,760
+كل قلص ا في مشتقة ما داكل الجدر بالنسبة للعكس اللي
+
+102
+00:10:02,760 --> 00:10:03,380
+هو بيبقى
+
+103
+00:10:07,820 --> 00:10:11,600
+طيب اتنين مع اتنين الله يسهل عليها يبقى قصير
+
+104
+00:10:11,600 --> 00:10:18,160
+الناتج x على ال general تربيعي ل x تربيع زائد
+
+105
+00:10:18,160 --> 00:10:21,840
+اتنين وات بالمرة نقدر نحسب
+
+106
+00:10:41,910 --> 00:10:49,450
+يبقى الناتج 4 على 6 يبقى 2 على 3 بال middle بدنا
+
+107
+00:10:49,450 --> 00:10:58,400
+نجيب F1يجب ان يكون fy هو واحد على اتنين الجدري
+
+108
+00:10:58,400 --> 00:11:04,660
+التربيعي ل X تربيع زائدي اتنين Y في مشتقة ما تحت
+
+109
+00:11:04,660 --> 00:11:08,340
+الجدر بالنسبة الى Y لو جداش اتنين
+
+110
+00:11:22,640 --> 00:11:27,040
+عنده نقطة اربعة و عشرة اذا ماجي بيقول هذا الكلام
+
+111
+00:11:27,040 --> 00:11:33,300
+يساوي واحد على الجنري التربيهي لاربع تربيع اللي هي
+
+112
+00:11:33,300 --> 00:11:41,800
+ستاشر زائد اتنين في عشرة لعشرين ستة و تلاتين يبقى
+
+113
+00:11:41,800 --> 00:11:48,440
+الصوت بناء عليه حسبنا له قدش ل gradientللدالة R
+
+114
+00:11:48,440 --> 00:11:54,480
+عند النقطة أربعة و عشرة و اللي هي بتساوي طولتين في
+
+115
+00:11:54,480 --> 00:12:01,180
+اتجاه I زائد سُد في اتجاه M في اتجاه J إذا هذا
+
+116
+00:12:01,180 --> 00:12:05,660
+اللي هي بتلعب دور أساسي عند حساب ال directional
+
+117
+00:12:05,660 --> 00:12:11,100
+derivative للدالة اللي عندنا هنا حتى الآن لم نجيب
+
+118
+00:12:11,100 --> 00:12:17,370
+على المطلوب الأول تبع المثلمن هنا بدأت إجابة
+
+119
+00:12:17,370 --> 00:12:21,170
+المطلوب الأولى للنمرية قال هنا the direction of
+
+120
+00:12:21,170 --> 00:12:27,050
+increasing F most rapidly يبقى
+
+121
+00:12:27,050 --> 00:12:36,450
+الاتزاق اربعة و عشرة صحيح
+
+122
+00:12:36,450 --> 00:12:37,970
+طيب
+
+123
+00:12:44,070 --> 00:12:48,950
+التزايد most rapidly بيحصل وقتاش لو كان المتجه هو
+
+124
+00:12:48,950 --> 00:12:54,090
+grade ال F في نفس الاتجاه اذا انا لو جبت ال unit
+
+125
+00:12:54,090 --> 00:12:59,270
+vector تبع grade ال F بكون جبت ال direction صحيح
+
+126
+00:12:59,270 --> 00:13:06,030
+ولا لأ يبقى باجي بقول هنا ال F increasing
+
+127
+00:13:08,450 --> 00:13:17,350
+most rapidly N
+
+128
+00:13:17,350 --> 00:13:28,730
+أو F الـ U and اجراد الـ F are in the same
+
+129
+00:13:28,730 --> 00:13:33,570
+direction يبقى
+
+130
+00:13:33,570 --> 00:13:36,490
+لو كانوا في نفس الاتجاه
+
+131
+00:13:40,380 --> 00:13:48,080
+معنى هذا الكلام أن المتجه U لأنه هو grade F على
+
+132
+00:13:48,080 --> 00:13:56,150
+قول grade Fطبعا يبقى هذا الكلام بده يساوي grade ال
+
+133
+00:13:56,150 --> 00:14:01,750
+F اللي وطلعناه بروزناه يبقى تلتين في اتجاه ال I
+
+134
+00:14:01,750 --> 00:14:08,430
+زائد ست في اتجاه ال J مقسوما على ال square root
+
+135
+00:14:08,430 --> 00:14:14,150
+لاربع أتساع زائد واحد على ستة و تلاتين
+
+136
+00:14:16,550 --> 00:14:20,970
+طبعا المضاعف المشرك ستة وتلاتين على تسعة فيها
+
+137
+00:14:20,970 --> 00:14:25,870
+الأربعة في أربعة في ستاشر واحد سبعتاشر يبقى هذا
+
+138
+00:14:25,870 --> 00:14:33,030
+الكلام تلتين I زي ست جي على الجانري التربيعي
+
+139
+00:14:33,030 --> 00:14:40,190
+لسبعتاشر على ستة وتلاتينطبعا بتطلع من تحت الجدر 36
+
+140
+00:14:40,190 --> 00:14:46,150
+بال6 بتنقلبه تطلع فوق فبصير عندنا هنا 6 في هذه
+
+141
+00:14:46,150 --> 00:14:57,090
+بصير عندى قداش 4 على جدر 17 I زائد 1 على جدر 17 J
+
+142
+00:14:59,600 --> 00:15:04,280
+يبقى الاتجاه اللذي تتزيد فيه F مصر Rapidly عند
+
+143
+00:15:04,280 --> 00:15:08,000
+النقطة أربعة أو عشرة هو ال vector اللي عندنا هذا
+
+144
+00:15:08,000 --> 00:15:13,800
+كويس طب قداش مقدار ال direction ال derivative في
+
+145
+00:15:13,800 --> 00:15:18,940
+هذه الحالة وما طلبوش مني بس انا لو ادعى اسمه هو
+
+146
+00:15:18,940 --> 00:15:26,420
+مين قول ال V وين قول ال V هل تماميبقى هذا بيكون
+
+147
+00:15:26,420 --> 00:15:30,900
+طول اللي عندنا هذا فيما لو طلبه لنا نقول القيمة
+
+148
+00:15:30,900 --> 00:15:35,320
+تساوي طول جراد ال F طول جراد ال F اللي هي القيمة
+
+149
+00:15:35,320 --> 00:15:40,280
+اللي عندنا هنا يبقى جدر سبعتاشر على ستة ما علينا
+
+150
+00:15:40,280 --> 00:15:47,720
+نمرى بيه نمرى بيه نقلب ال D اتجاه التناقص يبقى
+
+151
+00:15:47,720 --> 00:15:51,780
+باجي بقوله ال F decreasing
+
+152
+00:15:56,550 --> 00:16:05,470
+decreasing most rapidly at
+
+153
+00:16:05,470 --> 00:16:14,990
+النقطة أربعة و عشرة in the direction في اتجاه مين
+
+154
+00:16:14,990 --> 00:16:21,100
+يا بنات سالب أربعةعلى سبعتاشر I على جدر سبعتاشر I
+
+155
+00:16:21,100 --> 00:16:27,780
+سالب واحد على جدر سبعتاشر J يعني عكس من؟ عكس
+
+156
+00:16:27,780 --> 00:16:33,000
+لاتجاه الأولاني تماما لأنه قلنا في اتجاه معاكس
+
+157
+00:16:33,000 --> 00:16:38,200
+لمن؟ لجراد ال F الاتجاه الأولاني هذا هو مفتجه
+
+158
+00:16:38,200 --> 00:16:43,320
+الوحدة في اتجاه جراد ال F إذا هدفي عكس تماما بكتب
+
+159
+00:16:43,320 --> 00:16:51,250
+نفس المتجه بس بإشارة مخالفةعام نمرى C و قال لي في
+
+160
+00:16:51,250 --> 00:16:53,470
+دقيقة ايه انت بتبقى بسطشان ال directional
+
+161
+00:16:53,470 --> 00:16:59,530
+derivative عنده النقطة هذه اللي هو بده ساوي زيرو
+
+162
+00:16:59,530 --> 00:17:06,610
+باجي بقولك عندنا D U F بده ساوي زيرو هذا معناته
+
+163
+00:17:06,610 --> 00:17:16,700
+انه grade ال F ضد ال U بده ساوي زيروحيث ال U
+
+164
+00:17:16,700 --> 00:17:25,220
+بسويول في اتجاه I زي U في اتجاه J is a unit vector
+
+165
+00:17:25,220 --> 00:17:31,460
+تمام؟ طيب باجي بقول لهم قعدوا اللي فيها جاهزة
+
+166
+00:17:31,460 --> 00:17:40,280
+عندنا اللي يمين تلتين I زي ست جيه كله Dot U واحد
+
+167
+00:17:40,280 --> 00:17:45,410
+في اتجاه Iيو اتنين في اتجاه الجهد كله بده يساوي
+
+168
+00:17:45,410 --> 00:17:57,030
+زيرو او بمعنى اخر تلتين يو اتنين زيادة سادس يوتو
+
+169
+00:17:57,030 --> 00:18:03,510
+بده يساوي كده؟ بده يساوي زيرو لو ضربت كله في ستة
+
+170
+00:18:03,510 --> 00:18:11,070
+عشان اتخلص من الكثور اربع يو اتنين زيادة سادسيوتو
+
+171
+00:18:11,070 --> 00:18:16,510
+بدل ساوي زيك ضربت المعادلة كلها في ستة يبقى هذا
+
+172
+00:18:16,510 --> 00:18:25,630
+بدي أقيني أن يوتو بدل ساوي سالب أربعة في اليوة طيب
+
+173
+00:18:25,630 --> 00:18:31,590
+هذه أولاق بتربط بين مجهولين يواحد و يتنين عشان
+
+174
+00:18:31,590 --> 00:18:37,110
+أقدر أجيب القيمة هذه بلزمني كمان معادلة من أين بدي
+
+175
+00:18:37,110 --> 00:18:42,280
+أجيب المعادلة؟قول متجه الواحدة المعروف الواحد صحيح
+
+176
+00:18:42,280 --> 00:18:49,660
+بروح بقوله ب .. ولكن ب .. اللي هو U واحد تربيع
+
+177
+00:18:49,660 --> 00:18:55,340
+زائد U اتنين تربيع تحت الجدر التربيعي كله بتتساوي
+
+178
+00:18:55,340 --> 00:19:01,780
+واحد رابع الطرفين بصير U واحد تربيع زائد U اتنين
+
+179
+00:19:01,780 --> 00:19:06,020
+تربيع تتساوي واحد طيب
+
+180
+00:19:06,440 --> 00:19:13,740
+يبقى ال U واحد تربيع زاد ال U اتنين لو سالف اربع U
+
+181
+00:19:13,740 --> 00:19:20,540
+واحد يبقى سالف اربع U واحد يبقى تربيع يساوي واحد
+
+182
+00:19:20,540 --> 00:19:24,060
+يبقى
+
+183
+00:19:24,060 --> 00:19:35,030
+سبعتاش يبقى سبعتاش U تربيع يساوي واحدالـ U1 تساوي
+
+184
+00:19:35,030 --> 00:19:43,910
+زائد أو ناقص واحد على ال square root لمين ل 17 إذا
+
+185
+00:19:43,910 --> 00:19:48,490
+طلع عندي مش مستجد واحد و أنا ما جداش اتنين فبجي
+
+186
+00:19:48,490 --> 00:20:00,710
+بقوله if ال U1 يساوي واحد على جدر 17 then ال U2
+
+187
+00:20:00,710 --> 00:20:09,060
+تساويسالف أربعة في واحد على جذر السبعتاشر المعادلة
+
+188
+00:20:09,060 --> 00:20:12,100
+من أين؟ المعادلة اللي عندك فيها دي اللي هي star
+
+189
+00:20:12,100 --> 00:20:21,360
+منها بشيل ال U وال و بحط قمتها يبقى بناء عليه هذا
+
+190
+00:20:21,360 --> 00:20:31,190
+أعطاني أن المتجه U هو عبارة عنU1 على جذر 17 في
+
+191
+00:20:31,190 --> 00:20:41,150
+اتجاه I ماقص 4 على جذر 17 في اتجاه J الحالة
+
+192
+00:20:41,150 --> 00:20:51,310
+التانية لو كان U1 سالب 1 على جذر 17يو اتنين يسوى
+
+193
+00:20:51,310 --> 00:20:59,370
+سالب اربع في سالب واحد على جذر سبعتاشر ويسوى اربع
+
+194
+00:20:59,370 --> 00:21:07,270
+على من اربع على جذر سبعتاشر
+
+195
+00:21:07,270 --> 00:21:15,030
+هو يبقى بناء عليه المتجه يو هو عبارة عن اللي هو
+
+196
+00:21:15,030 --> 00:21:24,360
+السالب1 على جدر 17 في اتجاه I زائد 4 على جدر 17 في
+
+197
+00:21:24,360 --> 00:21:31,360
+اتجاه J يعني عندي بدل المتجه اتنين بيحققولي هذه
+
+198
+00:21:31,360 --> 00:21:34,900
+المعادلة بيخيلولي ال direction derivative عند هذه
+
+199
+00:21:34,900 --> 00:21:37,800
+النقطة بده ساوي Zero
+
+200
+00:22:16,060 --> 00:22:20,660
+بنجي لعنوان جديد برضه في نفس ال section نجي لحاجات
+
+201
+00:22:20,660 --> 00:22:26,740
+يسمى gradients gradients
+
+202
+00:22:26,740 --> 00:22:31,420
+and tangents
+
+203
+00:22:31,420 --> 00:22:37,920
+والممثل
+
+204
+00:22:37,920 --> 00:22:39,720
+في level curves
+
+205
+00:22:58,440 --> 00:23:07,620
+f of x1 as a
+
+206
+00:23:07,620 --> 00:23:16,400
+constant value والتي تكون c على سبيل المثال along
+
+207
+00:23:16,400 --> 00:23:19,500
+a
+
+208
+00:23:19,500 --> 00:23:20,660
+smooth curve
+
+209
+00:23:26,290 --> 00:23:37,570
+العلم اللي اسمه R R of T هو G of T في اتجاه I زائد
+
+210
+00:23:37,570 --> 00:23:41,190
+H of T في اتجاه J
+
+211
+00:23:48,400 --> 00:23:56,080
+اللي هو G of T وكذلك H of T كله بده يساوي constant
+
+212
+00:23:56,080 --> 00:24:02,000
+C as A level K
+
+213
+00:24:40,980 --> 00:24:53,460
+هذا هو قيمة
+
+214
+00:24:53,460 --> 00:24:58,600
+الدلة يسوي مقدارا ثابتا along a small curve R of T
+
+215
+00:24:58,600 --> 00:25:03,320
+يسوي G of T في اتجاه I زادتش من T في اتجاه T كل من
+
+216
+00:25:03,320 --> 00:25:11,060
+X وY هي function في T كأن X هي G of T وYهي H of T
+
+217
+00:25:11,060 --> 00:25:16,040
+ثم F of G of T و H of T بدل ساوية ماذا؟ بدل ساوية
+
+218
+00:25:16,040 --> 00:25:21,820
+الكنستنسي بالضبط تماماو في هذه الحالة بسميها level
+
+219
+00:25:21,820 --> 00:25:26,300
+k طبعا لو راجعنا بالذاكره الى الوراء الى section
+
+220
+00:25:26,300 --> 00:25:31,140
+14-1 فقنا بنقوله بنجي على ال function و بنسويها
+
+221
+00:25:31,140 --> 00:25:37,080
+كنصة إذا سوناها كنصة فهذا بيكون level k بشرط انه
+
+222
+00:25:37,080 --> 00:25:41,340
+تبقى ال function ده اللي فيه متغيرين أما إن كانت
+
+223
+00:25:41,340 --> 00:25:44,380
+ده اللي فيه ثلاثة متغيرات بسميها
+
+224
+00:25:54,320 --> 00:26:02,030
+يبقى سارة اندي تدالها لما سويها بـCيبقى هذا بيسميه
+
+225
+00:26:02,030 --> 00:26:06,210
+level K يعني طيب تعالوا فنفضلها و نشوف كده شهدها
+
+226
+00:26:06,210 --> 00:26:11,490
+الساوية ففضلها كيف؟ اه احنا خدنا chain rule لو
+
+227
+00:26:11,490 --> 00:26:17,350
+كانت F ده اللي فيه متغيرين و كل متغير ده اللي فيه
+
+228
+00:26:17,350 --> 00:26:22,690
+متغير اخر مظبوط فكنا بنقول ايش؟ كنا بنقول
+
+229
+00:26:39,450 --> 00:26:48,430
+متغير واحد بشتقة كلية يبقى في dx على dt زائد
+
+230
+00:26:48,430 --> 00:26:58,730
+partial f على partial y في dy على dt ممتاز
+
+231
+00:26:58,730 --> 00:27:06,560
+جدا طيب الآن ال x مين عندي؟من أجابة كانت؟ G of T
+
+232
+00:27:06,560 --> 00:27:15,380
+يبقى هذي كإنهاراش partial F على partial X في DG
+
+233
+00:27:15,380 --> 00:27:27,240
+على DT زائد partial F على partial Y في DH على DT
+
+234
+00:27:27,240 --> 00:27:28,160
+بيبقى سوى Z
+
+235
+00:27:31,670 --> 00:27:35,910
+مابيقش رأيك هذا dot product بين متجهين وانا مش
+
+236
+00:27:35,910 --> 00:27:42,650
+داري كيف dot product بين متجهين بقول اه تعالي شوفي
+
+237
+00:27:42,650 --> 00:27:47,170
+هذه المدرسة اكتفها على الشكل التالي partial F على
+
+238
+00:27:47,170 --> 00:27:54,150
+partial X في اتجاه I زائد partial F على partial Y
+
+239
+00:27:54,150 --> 00:27:57,350
+في اتجاه G dot
+
+240
+00:28:12,050 --> 00:28:16,310
+على دي تي في اتجاه اللي هي بده يساوي زيرو لو عملت
+
+241
+00:28:16,310 --> 00:28:21,010
+ضغط مرضي الملتنة مش هفتطعلي فوق هالي صح ولا لأ طيب
+
+242
+00:28:21,010 --> 00:28:27,930
+ده جنهان هي تعريف مين يا بناها ليه grade يعني
+
+243
+00:28:27,930 --> 00:28:33,990
+grade تبع الدل اف تمام يبقى هذه هي grade الاف
+
+244
+00:28:41,810 --> 00:28:46,170
+صح ولا لأ؟ إذا بقدر أشيل هذه و أكتب عليها DR على
+
+245
+00:28:46,170 --> 00:28:55,890
+DT يبقى هذا معناته DR على DT قداش ما تش ساوي0 إذا
+
+246
+00:28:55,890 --> 00:29:01,230
+انا عندي متجهين واحد اسمه Gradle F والثاني DR على
+
+247
+00:29:01,230 --> 00:29:05,450
+DT بطل product بينهم بسوق ال Dates بسوق Gradle
+
+248
+00:29:05,450 --> 00:29:10,710
+الاتنين مالهم تقولك يبقى اتنين هذول مالهم متعامدين
+
+249
+00:29:10,710 --> 00:29:14,130
+طب شوفي هذا إيش بفيدني ساعدني أخلي بالكم معايا
+
+250
+00:29:14,130 --> 00:29:21,910
+طلعوا عينيك كويس الان DR على DT مش هي مستقلتها دي
+
+251
+00:29:21,910 --> 00:29:27,550
+طب مستقلتها دي شو بتفيدنيال V ممتاز جدا يبقى هذا
+
+252
+00:29:27,550 --> 00:29:32,490
+مشتقتها هذا عبارة عن ال velocity طب ال velocity و
+
+253
+00:29:32,490 --> 00:29:36,690
+اتجاه الحركة و ال tangent مش كله في اتجاه الواحد
+
+254
+00:29:36,690 --> 00:29:43,410
+يبقى هذا كأنه مين كأنه tangent لمين لو ال tangent
+
+255
+00:29:43,410 --> 00:29:50,860
+vector لجسم يتحرك في الفراغ عند نقطة ماكويس؟ يبقى
+
+256
+00:29:50,860 --> 00:29:56,440
+هذا كأنه إيش؟ كأنه grade ال F و ال tangent مالهم
+
+257
+00:29:56,440 --> 00:30:04,620
+اتنين R Orthogonal يبقى هذا هو V وبالتالي هذا هو
+
+258
+00:30:04,620 --> 00:30:08,720
+ال unit هو ال tangent vector و ليس ال unit او ال
+
+259
+00:30:08,720 --> 00:30:14,260
+tangent vector و اتنين هذا R Orthogonal هذا معناته
+
+260
+00:30:14,260 --> 00:30:22,080
+ان grade ال Fand the
+
+261
+00:30:22,080 --> 00:30:37,140
+tangent to the curve are orthogonal كيف
+
+262
+00:30:37,140 --> 00:30:42,720
+هذا الكلام؟ يعني عملت لو جيت تخيلت على سبيل المثال
+
+263
+00:30:42,720 --> 00:30:52,440
+أن هذا كان level curveهذا كان level care هذا
+
+264
+00:30:52,440 --> 00:30:55,980
+واحد منهم من ال level cares كويس و بجيت عنده نقطة
+
+265
+00:30:55,980 --> 00:31:03,860
+مثل هذه النقطة كويس و روحت رسام ال tangent يبقى
+
+266
+00:31:03,860 --> 00:31:12,800
+هذا كان ال tangent اللي عندنا اللي هو من ال T إذا
+
+267
+00:31:13,430 --> 00:31:18,870
+العمودي علي إجراد ال F بيكون بالشكل اللي عندنا هذا
+
+268
+00:31:18,870 --> 00:31:26,310
+الزاوية قائمة وهذا بيكون بهمين إجراد ال F يبقى
+
+269
+00:31:26,310 --> 00:31:31,490
+إجراد ال F والT اتنين are orthogonal من هنا كان
+
+270
+00:31:31,490 --> 00:31:32,950
+بالشكل اللي عندنا
+
+271
+00:31:35,790 --> 00:31:40,690
+ماذا في عندي tangent line عند نقطة على level
+
+272
+00:31:40,690 --> 00:31:46,230
+surface إذا بروح أدور على معادلة هذا ال tangent
+
+273
+00:31:46,230 --> 00:31:52,310
+كويس إذا بروح أحط عنوان جانب صغير اللي هو equation
+
+274
+00:31:52,310 --> 00:31:54,010
+of the tangent line
+
+275
+00:31:57,740 --> 00:32:07,740
+equation of the tangent line
+
+276
+00:32:07,740 --> 00:32:11,920
+to a level k
+
+277
+00:32:31,410 --> 00:32:39,050
+الان بحاول احسب معادلة تانجنت
+
+278
+00:32:39,050 --> 00:32:46,330
+lineعند النقطة اللى عندنا هذا كيف بنحسب هذه
+
+279
+00:32:46,330 --> 00:32:51,710
+المعادلة بقول بسيطة جدا بدي استخدم فكرة dot
+
+280
+00:32:51,710 --> 00:32:57,690
+product في main في إيجاد هذه المعادلة تبعت من تبعت
+
+281
+00:32:57,690 --> 00:33:03,690
+tangent line يبقى بنروح نستخدم هذه في اللى هو
+
+282
+00:33:03,690 --> 00:33:09,540
+إيجاد هذه المعادلة و العمودي عندنا هنا mainاللي هو
+
+283
+00:33:09,540 --> 00:33:15,660
+ال gradient vector مظبوط او لا؟ طيب انا بدي اروح
+
+284
+00:33:15,660 --> 00:33:20,100
+احنا دلوقتي ال tangent line مش ال tangent vector
+
+285
+00:33:20,100 --> 00:33:23,640
+يبقى ال tangent line بقى الوسط ال parametric
+
+286
+00:33:23,640 --> 00:33:29,960
+equations تمام؟ يبقى ال parametric equations هدول
+
+287
+00:33:29,960 --> 00:33:37,990
+بتكون من نقطةاللي هي نقطة التماس هذه على سبيل
+
+288
+00:33:37,990 --> 00:33:43,150
+المثال يعني لو قلت هذه النقطة هي X node وY node
+
+289
+00:33:43,150 --> 00:33:51,190
+وانا بدي معادلة المماس الموازي لل unit tangent
+
+290
+00:33:51,190 --> 00:33:57,530
+vector بيض موازي لل unit tangent vector إذا بدي
+
+291
+00:33:57,530 --> 00:34:04,990
+أجيب المعادلة كتاليكويس؟ يبقى بتروح اخد اي نقطة
+
+292
+00:34:04,990 --> 00:34:09,890
+موجودة على هذا ال line على سبيل المثال و التكن
+
+293
+00:34:09,890 --> 00:34:17,730
+النقطة هذه النقطة هذه ليه اكس او اكس و واي كان
+
+294
+00:34:17,730 --> 00:34:25,470
+اعدادي تبعك كويس؟ طيب الانالـ unit tangent vector
+
+295
+00:34:25,470 --> 00:34:30,390
+مش ال unit tangent line مش عفر مش ال .. ال .. ال
+
+296
+00:34:30,390 --> 00:34:33,690
+.. مش ال .. فش حاجة اسمها unit tangent line يبقى
+
+297
+00:34:33,690 --> 00:34:37,150
+بقول ال tangent line ماعنديش هنا يبقى انا باجي
+
+298
+00:34:37,150 --> 00:34:41,210
+بقول ال unit tangent vector مع ال grade لف اتنين
+
+299
+00:34:41,210 --> 00:34:46,290
+مالهم are orthogonal اتنين اخر مالهم متعاملين اذا
+
+300
+00:34:46,290 --> 00:34:51,350
+نضبطي product بينهم دي سوى كده؟ zero بناء انا عليه
+
+301
+00:34:51,350 --> 00:34:58,970
+فبروح بقوله ايش؟عندنا هنا اللي هو مين؟ العقود اللي
+
+302
+00:34:58,970 --> 00:35:04,390
+هو grade ال F احنا اه هنا باجي بقوله هنا grade ال
+
+303
+00:35:04,390 --> 00:35:12,290
+F بارة ضغط مين؟ المتجه اللي عندنا هذا اللي هو بدي
+
+304
+00:35:12,290 --> 00:35:18,930
+اسميه على سبيل المثال المتجه N بدي اسوي مين؟ Zero
+
+305
+00:35:18,930 --> 00:35:27,180
+كويس، يبقى هذا شو معناه؟زادة fx عند النقطة x node
+
+306
+00:35:27,180 --> 00:35:32,580
+و y node في اتجاه الـ I زادة fy عند النقطة x node
+
+307
+00:35:32,580 --> 00:35:40,960
+و y node في اتجاه الـ J كله Dot دل
+
+308
+00:35:40,960 --> 00:35:46,880
+المتجه اللي عالنا هذا اللي هو مين؟ x ماقص x node
+
+309
+00:35:46,880 --> 00:35:53,550
+في اتجاه الـ IY نقص Y node في اتجاه الـ J كله ساوي
+
+310
+00:35:53,550 --> 00:36:02,270
+0 لو روحت فكرة هذه ليس بيصير Fx عند نقطة X node وY
+
+311
+00:36:02,270 --> 00:36:11,310
+node في X نقص X node زائد Fy عند نقطة X node وY
+
+312
+00:36:11,310 --> 00:36:19,980
+node في Y نقص Y node كله ساوي مين؟ ساوي 0السؤال هو
+
+313
+00:36:19,980 --> 00:36:27,260
+هل هذه معادلة خط مستقيم؟ تعالوا نشوف ال Fx عندها
+
+314
+00:36:27,260 --> 00:36:31,000
+نقطة يا بنات هذا دلة ولا رقم number؟
+
+315
+00:36:46,900 --> 00:36:53,580
+معادلة خاط المستقيم يبقى هذه معادلة الخاط المستقيم
+
+316
+00:36:53,580 --> 00:36:58,940
+اللي احنا قاعدين ندور عليها او اللي احنا بدنا يعني
+
+317
+00:36:58,940 --> 00:37:00,680
+يبقى هذه ال equation
+
+318
+00:37:16,170 --> 00:37:24,670
+نبقى هذه المعادلة المطلوبة ناخد مثال عليه نبقى
+
+319
+00:37:24,670 --> 00:37:25,170
+example
+
+320
+00:37:38,770 --> 00:37:46,370
+the curve ورسم المنحنى x تربيه على ناقص واي تساوي
+
+321
+00:37:46,370 --> 00:37:55,110
+واحد together with two together with تقري هاد ال F
+
+322
+00:37:55,110 --> 00:38:06,110
+and the tangent line and the tangent line وخط
+
+323
+00:38:06,110 --> 00:38:15,290
+التمامat the point at the point عند النقطة اللي هو
+
+324
+00:38:15,290 --> 00:38:23,050
+جذر اتنين و واحد and write an equation and write
+
+325
+00:38:23,050 --> 00:38:29,890
+an equation و بده نكتب معادلة for the tangent line
+
+326
+00:38:29,890 --> 00:38:36,830
+for the tangent line
+
+327
+00:38:39,590 --> 00:38:44,450
+وبنقدرش او ما هو شكل معادلة خط التماس
+
+328
+00:39:09,620 --> 00:39:14,140
+برجع للسؤال مرة تانية بقول لي ارسم للمنحنة اللي
+
+329
+00:39:14,140 --> 00:39:18,950
+عندنا هذامع مين؟ together with degree of F ترسم
+
+330
+00:39:18,950 --> 00:39:25,050
+على الرسمة degree of F and tangent line وخط التماس
+
+331
+00:39:25,050 --> 00:39:28,870
+عند النقطة يبقى with degree of F وخط التماس عند
+
+332
+00:39:28,870 --> 00:39:32,690
+النقطة للملحنة اللي موجودة عندنا وبعد هيك نجيب
+
+333
+00:39:32,690 --> 00:39:38,170
+المعادلة يبقى مطلوبين يهم الرسم زائد معادلة
+
+334
+00:39:38,170 --> 00:39:43,070
+tangent line لمين؟ للخط المستقبل اللي عندنا أو خط
+
+335
+00:39:43,070 --> 00:39:46,770
+التماسبقوله قويس هو ال function اللي عندي وين هي
+
+336
+00:39:46,770 --> 00:39:50,690
+عشان اجيب له grade ال F بالزمن ال function وين ال
+
+337
+00:39:50,690 --> 00:39:54,230
+function هذه؟ مش ماطيني ال function لكن ماطيني
+
+338
+00:39:54,230 --> 00:39:58,330
+مين؟ اللي بال curve اللي بال curve ال function
+
+339
+00:39:58,330 --> 00:40:02,250
+بسويها بمين؟ ب constant يبقى ال function الأساسية
+
+340
+00:40:02,250 --> 00:40:09,310
+مين هي يا بنات؟ F of X Y تساوي X تربيه ناقص Y يبقى
+
+341
+00:40:09,310 --> 00:40:14,540
+باجي بقوله هناهذا level curve يبقى المعادلة
+
+342
+00:40:14,540 --> 00:40:20,420
+الأصلية أو ال function الأصلية هي من هنا ال f of x
+
+343
+00:40:20,420 --> 00:40:27,240
+و y اللي هو بدها تساوي x تربيه ناقص y لأنه أنا لما
+
+344
+00:40:27,240 --> 00:40:31,200
+بجيبي level curve بساوي المعادلة اللي عندي أو
+
+345
+00:40:31,200 --> 00:40:36,500
+الدالة اللي عندي بمقدار ثابت بمقدار ثابت يبقى هذه
+
+346
+00:40:36,500 --> 00:40:41,560
+أصل المعادلة اللي موجود عنديبقول له خيص اذا احنا
+
+347
+00:40:41,560 --> 00:40:46,600
+مشان نجيب المعادلة اللى عندنا بلزم نجد كله من Fx و
+
+348
+00:40:46,600 --> 00:40:51,880
+Fy وين عند النقطة المعطاعة هبروح بقول له هنا بدي
+
+349
+00:40:51,880 --> 00:41:00,260
+اجيب له Fx يبقى تفاضل F نسم ال X له كده؟ ب2X و
+
+350
+00:41:00,260 --> 00:41:00,980
+بالمرة
+
+351
+00:41:04,170 --> 00:41:09,250
+عند النقطة جدري اتنين واحد المعطاع يبقى قدر ما
+
+352
+00:41:09,250 --> 00:41:16,490
+تساوي اتنين جدري اتنين بعد هيك بيروح اجيب له fy
+
+353
+00:41:16,490 --> 00:41:25,560
+كده يبقى له قدروهذا بده يعطيك انه fy عند النقطة
+
+354
+00:41:25,560 --> 00:41:29,260
+جدري اتنين وواحد والسالي بواحد كل وصف انت مالوش
+
+355
+00:41:29,260 --> 00:41:34,940
+دعوة بمين بالمتغيرات اذا البناء عليها حصلت على مين
+
+356
+00:41:34,940 --> 00:41:40,560
+على grade ال F اللي بدنا يها أوي للزمان على اي حال
+
+357
+00:41:40,560 --> 00:41:43,740
+هل مطلوب اكتبها و الله اذا كان مطلوب اكتبها مش
+
+358
+00:41:43,740 --> 00:41:48,440
+مطلوبها اي مركبة انت خلاص جاهزة طب كويس قال هو ايش
+
+359
+00:41:48,440 --> 00:41:53,310
+ارسم المنحنةوارسوم ل grade ال F اذا انا بتروح
+
+360
+00:41:53,310 --> 00:41:59,910
+اقوله grade ال F عند النقطة جذر اتنين او واحد هي
+
+361
+00:41:59,910 --> 00:42:07,250
+اتنين جذر اتنين في اتجاه I ناقص G يبقى هذه اللي
+
+362
+00:42:07,250 --> 00:42:13,390
+بتلعب دور كبير وياه في المسألة ابتعدطيب خليني اروح
+
+363
+00:42:13,390 --> 00:42:18,410
+نرسم اللي هو التسلسل في الترتيب تبع المطلوب تبع
+
+364
+00:42:18,410 --> 00:42:23,790
+المثلة خليني اروح نرسم وبعد هيك بصير خير ايوة
+
+365
+00:42:23,790 --> 00:42:31,290
+فبجيب درسم ايش بقوله هنا ال level level
+
+366
+00:42:31,290 --> 00:42:34,370
+KF
+
+367
+00:42:34,370 --> 00:42:38,230
+S
+
+368
+00:42:38,230 --> 00:42:40,210
+اللي هو مين؟
+
+369
+00:42:43,480 --> 00:42:51,840
+ممكن اكتبه بشكل اخر وهو y تساوي x ترمية نقص واحد
+
+370
+00:42:51,840 --> 00:42:55,340
+معادلة ايش دي يا بنات برابرها بس في الأول ماكنتش
+
+371
+00:42:55,340 --> 00:43:00,540
+واضحة لكن عكت ترتيبها صارت المعادلة سهلة وميسورة
+
+372
+00:43:00,540 --> 00:43:07,120
+لو روحت ارسلها بقيت بقول هي المحاول هي ان محور x
+
+373
+00:43:07,950 --> 00:43:13,550
+هذا محور Y وهذا نقطة الاصل اللي هي Zero يمكن هذه
+
+374
+00:43:13,550 --> 00:43:19,250
+أصل الدالة Y تساوي X تربيع بس Shift لأسفل بمقدار
+
+375
+00:43:19,250 --> 00:43:26,850
+واحد طب بدأ أجيب نقطة تقاطعها مع محور X يبقى بحط Y
+
+376
+00:43:26,850 --> 00:43:32,750
+بدأت Zero بصير X زاد أو ناقص واحد يبقى البرامج
+
+377
+00:43:32,750 --> 00:43:37,700
+هتمار غير نقطة واحدوهتمر بالنقطة مين؟ اللي هو سالب
+
+378
+00:43:37,700 --> 00:43:43,580
+واحد وهنا بتجينا من وين؟ من عند السالب واحد يبقى
+
+379
+00:43:43,580 --> 00:43:48,880
+هذه الفرابنة اللي عندنا ومن هنا بتجينا بالشكل اللي
+
+380
+00:43:48,880 --> 00:43:56,500
+عندنا درجة يبقى هذه الفرابنة Y تساوي X تربيع ماقص
+
+381
+00:43:56,500 --> 00:44:03,000
+واحدطيب تمام تمام بدي أجل النقطة جذري اتنين و واحد
+
+382
+00:44:03,000 --> 00:44:06,320
+جذري اتنين و واحد واربعة من عشرة يعني وين بدها
+
+383
+00:44:06,320 --> 00:44:09,720
+تجيلي هاي واحد واربعة من عشرة نفسها بدها تجي
+
+384
+00:44:09,720 --> 00:44:13,940
+تقريبا هنا و أطلع بتكون عندنا مية النقطة اللي
+
+385
+00:44:13,940 --> 00:44:17,820
+عندنا هي جيبكي النقطة هذه اللي هي جذري اتنين و
+
+386
+00:44:17,820 --> 00:44:22,800
+واحد بالشكل اللي عندنا هنا الان في مماس المماس
+
+387
+00:44:22,800 --> 00:44:24,220
+اللي عندنا بهذا الشكل
+
+388
+00:44:32,570 --> 00:44:39,670
+الخطة الأزرق اللي انت شايفينها هي
+
+389
+00:44:39,670 --> 00:44:45,790
+عمّجناها بالأزرق لكي نبين للكون لأن
+
+390
+00:44:45,790 --> 00:44:51,170
+هذا خط التماسك مثل المنحنة عند النقطة اللي عندنا
+
+391
+00:44:51,170 --> 00:44:51,770
+هذه
+
+392
+00:44:54,770 --> 00:44:58,250
+الان قال لي ارسم المنحنى و رسمنا له المنحنى ارسم
+
+393
+00:44:58,250 --> 00:45:02,530
+الماس و رسمنا له الماس مين ضايقني جراد ال F اه
+
+394
+00:45:02,530 --> 00:45:07,970
+جراد ال F جراد ال F قاللي له اتنين جذري اتنين في
+
+395
+00:45:07,970 --> 00:45:14,710
+اتجاه ال I ناقص J إذا بدي أجي أرسم هذا بدي أنسبه
+
+396
+00:45:14,710 --> 00:45:19,710
+إلى نقطة الأصل و بعدين بحركه زي ما بدي صحيح؟ يبقى
+
+397
+00:45:19,710 --> 00:45:24,010
+لو J تتحرك اتنين جذري اتنين اه اتنين جذري اتنين
+
+398
+00:45:24,330 --> 00:45:27,650
+يبقى يا بنات جدر اتنين اللي هو واحد واربعة من عشرة
+
+399
+00:45:27,650 --> 00:45:34,250
+هذي جدر اتنين تمام اتنين جدر اتنين كمان جدها مرتين
+
+400
+00:45:34,250 --> 00:45:40,950
+يبقى بدي امد هذا محور X امشي على طول الخط يبقى هذا
+
+401
+00:45:40,950 --> 00:45:46,990
+محور X بتاخد مسافة جد هذه مرتين يبقى بتجيك نقطة
+
+402
+00:45:46,990 --> 00:45:52,510
+تقريبا هنا يبقى هذا النقطة اللي هي اتنين جدر اتنين
+
+403
+00:45:52,970 --> 00:45:58,370
+بدي أنزل كده؟ سالب واحد يبقى بدي أنزل سالب واحد
+
+404
+00:45:58,370 --> 00:46:03,910
+الى النقطة اللى عندنا طبعا يبقى لو جيت ووصلت من
+
+405
+00:46:03,910 --> 00:46:09,670
+نقطة الأصل هيك بيكون هذا اتنين جدري اتنين في اتجاه
+
+406
+00:46:09,670 --> 00:46:18,210
+الاي ناقص جي هذا كله main اللى هو اجراد ال F لكن
+
+407
+00:46:18,210 --> 00:46:21,800
+اجراد ال F هو اللى بدرسوه بهاعند النقطة احنا بنعرف
+
+408
+00:46:21,800 --> 00:46:27,600
+ان المتجه ممكن يساوي متجه اول و تاني و تالت و زي
+
+409
+00:46:27,600 --> 00:46:34,020
+ما بدي مادام في نفس المقدار و في نفس الاتجاه يبقى
+
+410
+00:46:34,020 --> 00:46:38,480
+بقدر احرك المتجه هذا زي ما بدي اذا المتجه هذا بدي
+
+411
+00:46:38,480 --> 00:46:44,380
+تكون هيحرك بالازرق يا بنات بهذا الشكل بديكون هو
+
+412
+00:46:44,380 --> 00:46:51,820
+المتجه العمودي تقريبا يا اللهيبقى هذا main هذا
+
+413
+00:46:51,820 --> 00:46:57,440
+المتجه اللي عندنا هذا يبقى هذا اللي هو grade ال F
+
+414
+00:46:57,440 --> 00:47:03,630
+كذلك هذا grade ال F و هذا الموازي بالضبط تمامطيب
+
+415
+00:47:03,630 --> 00:47:09,390
+هاي رسمنا المنتجة رسمنا المنحنة رسمنا grad فاش
+
+416
+00:47:09,390 --> 00:47:13,990
+ضايل عليه المعادلة هاي المعادلة قدامي بس بداتي
+
+417
+00:47:13,990 --> 00:47:18,870
+اعوض فيها يبقى ال F X حسبتها عند النقطة اللي هي
+
+418
+00:47:18,870 --> 00:47:24,110
+كدوش كانت اتنين جادريك اتنين يبقى باجي بقوله that
+
+419
+00:47:24,110 --> 00:47:37,880
+equation of the tangent line Sإتنين جدري اتنين هي
+
+420
+00:47:37,880 --> 00:47:44,880
+قيمة ال Fx في مين؟ في ال X ناقص X naught اللي جدري
+
+421
+00:47:44,880 --> 00:47:49,760
+اتنين زائد و الله ناقص طبعا لأن هذا الحظ
+
+422
+00:48:09,840 --> 00:48:15,560
+زائد واحد بده يساوي قدرت بده يساوي Zero او ال Y
+
+423
+00:48:15,560 --> 00:48:22,400
+بده يساوي اللي هو اتنين جذري اتنين X و هنا ناقص
+
+424
+00:48:22,400 --> 00:48:26,900
+تلت اذا هنا ناقص تلت انا مش شايف اللي اقنعه و زي
+
+425
+00:48:26,900 --> 00:48:31,320
+ما انت شايفها معادلة من الدرجة الاولى في كل من X و
+
+426
+00:48:31,320 --> 00:48:36,540
+Y إذا هي معادلة ايش معادلة خاط مستقيم
+
+427
+00:49:02,220 --> 00:49:06,960
+زي ما تشوفون يا بنات ال gradient vector كأنه مؤثر
+
+428
+00:49:06,960 --> 00:49:11,860
+تفاضلي، ليه؟ لأنه grad F partial F by partial X في
+
+429
+00:49:11,860 --> 00:49:15,160
+اتجاه ال I partial F by partial Y في اتجاه ال Z،
+
+430
+00:49:15,160 --> 00:49:20,760
+تمام؟ طيب، إذا هذا له قواعد لاشتقاق العادية
+
+431
+00:49:20,760 --> 00:49:25,920
+المتعرف عليها بالنسبة للدوال العادية، هروح نذكر
+
+432
+00:49:25,920 --> 00:49:34,380
+بهذه القواعد كالتالي الgebra rulesالجيبرا rules
+
+433
+00:49:34,380 --> 00:49:46,080
+القواعد الجابرية for gradients نمري
+
+434
+00:49:46,080 --> 00:49:54,300
+واحد لو بدي إجراء لمن؟ لل K في ال F طبعا ال K مقدر
+
+435
+00:49:54,300 --> 00:50:01,910
+ثابت يبقى هذا K في جراد ال Fوالـ K is a real
+
+436
+00:50:01,910 --> 00:50:13,510
+number بعدد حقيقي اتنين Gradient ل ال F زائد او
+
+437
+00:50:13,510 --> 00:50:18,850
+ناقص G يعني كأنه مشتقة ال F زائد او ناقص G يبقى
+
+438
+00:50:18,850 --> 00:50:24,510
+مشتقة الدالة الأولى زائد او ناقص مشتقة الدالة
+
+439
+00:50:24,510 --> 00:50:32,060
+الثانية نمرها تلاتةمشتقة F في G أو الـ Gradient
+
+440
+00:50:32,060 --> 00:50:38,200
+للـ F في G ماجي بقول الدالة الأولى في ال Gradient
+
+441
+00:50:38,200 --> 00:50:44,140
+Vector للدالة الثانية زائد الدالة الثانية لل
+
+442
+00:50:44,140 --> 00:50:49,040
+Gradient Vector لمن؟ للدالة الأولى، فلو كان ضرب،
+
+443
+00:50:49,040 --> 00:50:56,640
+لو كان قسمة اما اربع ال Gradient لل F على Gبقيت
+
+444
+00:50:56,640 --> 00:50:59,800
+أقول المقام في مجتقة ال bus نقص ال bus في مجتقة
+
+445
+00:50:59,800 --> 00:51:03,740
+المقام على مربع المقام الأصلي يبقى نفس النتجة بدأت
+
+446
+00:51:03,740 --> 00:51:10,000
+أقول المقام في ال gradient لل F نقص ال F في ال
+
+447
+00:51:10,000 --> 00:51:17,800
+gradient ل G كله على مين على G تربيع وبشرط إن ال G
+
+448
+00:51:17,800 --> 00:51:25,200
+هذه ما لها ممنوعة ساوي زيو طيب
+
+449
+00:51:26,420 --> 00:51:31,060
+من أول مبادرة المحاضرة الماضية وحتى هذه اللحظة و
+
+450
+00:51:31,060 --> 00:51:35,960
+احنا بنتكلم على functions في مين؟ في two variables
+
+451
+00:51:35,960 --> 00:51:41,380
+فقط هل هذا الكلام صحيح ل three variables او
+
+452
+00:51:41,380 --> 00:51:48,580
+invariables هذا ما سنشير اليه الآن طبعا صحيح ولا
+
+453
+00:51:48,580 --> 00:51:55,140
+مشكلة في ذلك فبتقول ال functions of three
+
+454
+00:51:55,140 --> 00:52:05,100
+variablesof three variables الدول في ثلاثة متغيرات
+
+455
+00:52:05,100 --> 00:52:14,680
+f ال f of x y و z is a differentiable function
+
+456
+00:52:14,680 --> 00:52:17,740
+دلقابل
+
+457
+00:52:17,740 --> 00:52:24,330
+الاشتقاق andالـ U كان U1 في اتجاه الـ I U2 في
+
+458
+00:52:24,330 --> 00:52:30,410
+اتجاه الـ J U3 في اتجاه الـ K is a unit vector as
+
+459
+00:52:30,410 --> 00:52:45,090
+a unit vector كان متجه واحدة then اجراد ال Fاللي
+
+460
+00:52:45,090 --> 00:52:49,890
+بدأ يتساوي partial F على partial X في اتجاه I
+
+461
+00:52:49,890 --> 00:52:55,210
+partial F على partial Y في اتجاه G partial F على
+
+462
+00:52:55,210 --> 00:53:00,730
+partial Z في اتجاه K يعني أضفنا بس المراكبة في
+
+463
+00:53:00,730 --> 00:53:06,030
+اتجاه مين؟ في اتجاه K وبعدين بقول هنا Z
+
+464
+00:53:06,030 --> 00:53:11,570
+directional derivative
+
+465
+00:53:16,340 --> 00:53:29,040
+S الـ D U F بدي أساوي جراد ال F بطي ال U اللي هو
+
+466
+00:53:29,040 --> 00:53:35,160
+بدي أساوي الدرجة من هنا اللي هو partial F على
+
+467
+00:53:35,160 --> 00:53:42,860
+partial X ال U1 partial F على partial Y ال U2 زايد
+
+468
+00:53:42,860 --> 00:53:49,740
+partial Fعلى partial z في ال U3 هذه مركبات ال U
+
+469
+00:53:49,740 --> 00:53:56,480
+وهذه مركبات ال F يبقى كل واحدة في نظيرتها وبنجمع
+
+470
+00:53:56,480 --> 00:54:02,340
+بطلع جداش المقدار اللي عندك ياريت أقدركوا بس also
+
+471
+00:54:02,340 --> 00:54:08,360
+وكذلك for originally D U F
+
+472
+00:54:17,750 --> 00:54:25,370
+لو جبتها بلغة الأطوال تبقى باجي بقول هذا طول اجراد
+
+473
+00:54:25,370 --> 00:54:32,530
+ال F فطول ال U في Cos الزاوية بينهم اه ايه كده طول
+
+474
+00:54:32,530 --> 00:54:37,630
+ال U؟ لإن انا جاي ال unit vector هناك تمام؟ إذا
+
+475
+00:54:37,630 --> 00:54:43,160
+هذا الكلام بده يساوي طول اجراد ال Fفي cosine
+
+476
+00:54:43,160 --> 00:54:52,460
+الزواياتي باش بدينا محاضرتنا اليومبالتذكير باخرها
+
+477
+00:54:52,460 --> 00:54:57,920
+ادخلناها في المحاضرة الماضية و هي خواص ال product
+
+478
+00:54:57,920 --> 00:55:02,960
+أو خواص ال directional derivative والان احنا
+
+479
+00:55:02,960 --> 00:55:07,780
+رايحين وين على نفس الخواص يعني ما بدنا نعيدها كمان
+
+480
+00:55:07,780 --> 00:55:13,520
+اه كمان مرة تبقى احنا نذكرها ب اه باختصار فقط لغية
+
+481
+00:55:13,520 --> 00:55:18,540
+يعني يا بنات الخواص اللي كان تبتغن طبع على ال
+
+482
+00:55:18,540 --> 00:55:19,860
+directional derivative
+
+483
+00:55:22,430 --> 00:55:29,050
+متغيرين هي صحيحة بالضبط تماما على ال function اللي
+
+484
+00:55:29,050 --> 00:55:35,970
+فيه ثلاثة متغيرات لذلك أقعد باختصار بصيغة ال
+
+485
+00:55:35,970 --> 00:55:42,830
+remark التالي ال
+
+486
+00:55:42,830 --> 00:55:43,890
+three properties
+
+487
+00:55:50,260 --> 00:55:58,760
+اللي بدنا نفهم محاضرة اليوم of equation star طبعا
+
+488
+00:55:58,760 --> 00:56:05,560
+سمينا هذه ال equation star are
+
+489
+00:56:05,560 --> 00:56:14,140
+the same are the same نفسهم
+
+490
+00:56:14,140 --> 00:56:26,820
+in the caseكما في حالة of function of two
+
+491
+00:56:26,820 --> 00:56:32,020
+variables that
+
+492
+00:56:32,020 --> 00:56:39,660
+is I N ال
+
+493
+00:56:39,660 --> 00:56:46,820
+F increases most rapidly
+
+494
+00:56:49,020 --> 00:56:55,920
+يقرر أكثر بسرعة في الاتجاه
+
+495
+00:56:55,920 --> 00:57:08,380
+.. في اتجاه F عظيم ويقرر
+
+496
+00:57:08,380 --> 00:57:12,200
+.. و F يقرر
+
+497
+00:57:16,020 --> 00:57:22,200
+most rapidly and the direction of سالب جراد ال F
+
+498
+00:57:22,200 --> 00:57:25,720
+finally
+
+499
+00:57:25,720 --> 00:57:29,840
+ال
+
+500
+00:57:29,840 --> 00:57:41,140
+DUF بدل ساوي zero F LU and جراد ال F are
+
+501
+00:57:41,140 --> 00:57:42,880
+orthogonal
+
+502
+00:57:47,070 --> 00:57:52,210
+يبقى احنا كأنه بنعمم الشغلات اللي حصلنا عليها قبل
+
+503
+00:57:52,210 --> 00:58:01,870
+هيك تعميم نعطي مثال توضيحيا على درجة example find
+
+504
+00:58:01,870 --> 00:58:14,610
+the directions find the directions find
+
+505
+00:58:14,610 --> 00:58:20,300
+the directionsin which
+
+506
+00:58:20,300 --> 00:58:32,700
+the function f of x و y و z بدل سوى لن x تربيع
+
+507
+00:58:32,700 --> 00:58:42,100
+زائد y تربيع ناقص واحد زائد y زائد ستة z
+
+508
+00:58:48,620 --> 00:58:59,480
+increases and decreases most
+
+509
+00:58:59,480 --> 00:59:06,860
+rapidly most
+
+510
+00:59:06,860 --> 00:59:22,210
+rapidly at P0 of 1 و 1 و 0then find ومن ثم أوجد
+
+511
+00:59:22,210 --> 00:59:30,690
+the derivatives of
+
+512
+00:59:30,690 --> 00:59:35,930
+the function in these directions
+
+513
+01:00:17,510 --> 01:00:20,570
+يبقى المعلومات اللي خدناها على functions of two
+
+514
+01:00:20,570 --> 01:00:25,450
+variables صحيحة على functions of three variables
+
+515
+01:00:25,450 --> 01:00:31,890
+ناخد مثال عظيح ينهي هذه الاتجاهات بحيث الدلل عن
+
+516
+01:00:31,890 --> 01:00:37,730
+هذه increases و كذلك decreases مصطلح بدي أن نقطع
+
+517
+01:00:37,730 --> 01:00:42,040
+عنها و من ثمفاشل قدش ال derivatives في هذه
+
+518
+01:00:42,040 --> 01:00:45,240
+الاتجاهات لما يقول هذه ال derivatives في هذه
+
+519
+01:00:45,240 --> 01:00:48,500
+الاتجاهات يعني كأنه يقول هذه الظاهرة شينا ليها
+
+520
+01:00:48,500 --> 01:00:52,360
+derivatives لمن؟ لل function اللي عامة
+
+521
+01:01:00,110 --> 01:01:08,710
+عند نقطة المعطاة فانت تجيب فكرة في الاسئلة فانت
+
+522
+01:01:08,710 --> 01:01:12,270
+تجيب فكرة في الاسئلة
+
+523
+01:01:18,820 --> 01:01:24,700
+نقص واحد في مجتكط مداخل الـ N بالنسبة إلى X اللي
+
+524
+01:01:24,700 --> 01:01:33,000
+هو باتنين X برة ماعنديش X يبقى كله بالصفات بالمرة
+
+525
+01:01:33,000 --> 01:01:40,360
+نحسبها ال F X عند النقطة واحد واحد و Zero يبقى
+
+526
+01:01:40,360 --> 01:01:46,120
+بدأت ساوي اتنين على واحد زائد واحد نقص واحد بساوي
+
+527
+01:01:46,120 --> 01:01:52,520
+قداش اتنينبعد هيك بتروح أجيبله fy اللي هي بدها
+
+528
+01:01:52,520 --> 01:02:00,360
+تساوي واحد على x تربيع زائد y تربيع ناقص واحد كله
+
+529
+01:02:00,360 --> 01:02:04,620
+في مشتقة ما داخل الليل و باتبعين y
+
+530
+01:02:11,730 --> 01:02:17,590
+يبقى هذا الكلام يعطينا ان if y عندنا نقطة واحدة
+
+531
+01:02:17,590 --> 01:02:26,350
+واحدة وزيرو يساوي اتنين على واحد زائد واحد ناقص
+
+532
+01:02:26,350 --> 01:02:31,790
+واحد وكله زائد واحد يبقى اتنين زائد واحد يساوي كم؟
+
+533
+01:02:31,790 --> 01:02:33,150
+يساوي تلتة
+
+534
+01:02:36,320 --> 01:02:42,480
+يبقى مشتقة ال F بالنسبة إلى Z يبقى لإن هذا كله قدر
+
+535
+01:02:42,480 --> 01:02:47,960
+Zero لأنه لا يحتوي على Zero ومشتقة هذه ب Zero يبقى
+
+536
+01:02:47,960 --> 01:02:56,300
+مشتقة هذا قدر ب6 هذا يؤكدك أن مشتقة ال FZ عند 1 و1
+
+537
+01:02:56,300 --> 01:03:03,140
+و0 ملاش دعوة لإنه مقدارا ثابتايبقى عند اي لحظة
+
+538
+01:03:03,140 --> 01:03:07,960
+بيكون المشتقة دائما within moment ب 6 بناء عليه
+
+539
+01:03:07,960 --> 01:03:17,680
+قدرنا نجيب مين ال M اجراد ال M هو 2I زائد 3J زائد
+
+540
+01:03:17,680 --> 01:03:23,420
+6K يبقى
+
+541
+01:03:23,420 --> 01:03:27,080
+هذا هو العمودي الفقري تبع المثلة اش بقول المطلوب
+
+542
+01:03:27,720 --> 01:03:32,040
+قال لهذا ال directions بها تتدلع انكريز موست
+
+543
+01:03:32,040 --> 01:03:37,800
+رابدلي اذا انكريز موست رابدلي يبقى المتجه هي جراد
+
+544
+01:03:37,800 --> 01:03:41,700
+ال V اتنين واحد جراد ال F اتنين واحد يكون في نفسي
+
+545
+01:03:41,700 --> 01:03:48,640
+الاتجاه يبقى انا ها لو جبت ال unit vector تبع جراد
+
+546
+01:03:48,640 --> 01:03:53,640
+ال F يكون هو المطموع عارف ولا لأ يبقى باجي بقوله
+
+547
+01:03:53,640 --> 01:04:13,270
+هنا ال Fincreases most rapidly in the
+
+548
+01:04:13,270 --> 01:04:23,730
+direction of grad F على طول grad F اللي هو بدي
+
+549
+01:04:23,730 --> 01:04:31,230
+أعطيني المتجه UWhite بمعنى هذا الكلام ان ال U هذه
+
+550
+01:04:31,230 --> 01:04:40,470
+تساوي اتنين I زائد تلاتة J زائد ستة K مقسومة على
+
+551
+01:04:40,470 --> 01:04:49,570
+طول المتجد اربعة زائد تسعة زائد ستة و تلاتين ستة و
+
+552
+01:04:49,570 --> 01:04:55,940
+تلاتين و تسعة خمسة و اربعين و اربعة تحت الجدليبقى
+
+553
+01:04:55,940 --> 01:05:02,220
+هذه بدها تساوي سبعين في اتجاه ال I ثلاث أسبوع في
+
+554
+01:05:02,220 --> 01:05:08,460
+اتجاه ال J ست أسباع في اتجاه مين؟ في اتجاه ال E
+
+555
+01:05:08,460 --> 01:05:13,540
+يبقى
+
+556
+01:05:13,540 --> 01:05:18,420
+جبت الاتجاه اللي الدالة بتبقى فيه مالها increases
+
+557
+01:05:18,420 --> 01:05:23,260
+most rapidly تبقى decreasing most rapidly؟ ممتازة،
+
+558
+01:05:23,260 --> 01:05:26,570
+طب إيش رأيك؟طلب كمان طبعا قال لي هاتلي derivative
+
+559
+01:05:26,570 --> 01:05:36,150
+في هذا الاتجاه يبقى باجي بقوله ال derivative in
+
+560
+01:05:36,150 --> 01:05:48,070
+this direction قداش يا فنان ال duf قداش بتساوي طول
+
+561
+01:05:48,070 --> 01:05:56,070
+جراد ال F طول جراد ال Fقداش طولى جراد ال F؟ سبعة
+
+562
+01:05:56,070 --> 01:06:00,290
+نجى
+
+563
+01:06:00,290 --> 01:06:07,930
+الآن ال F decreases most
+
+564
+01:06:07,930 --> 01:06:13,990
+rapidly at
+
+565
+01:06:13,990 --> 01:06:21,750
+ال 1 و 1 و 0 in the direction
+
+566
+01:06:24,850 --> 01:06:32,130
+مين؟ عكس في اتجاه الـ I اللي هو سالب سبعين في
+
+567
+01:06:32,130 --> 01:06:39,750
+اتجاه الـ I سالب تلت أسباع في اتجاه الـ G سالب ست
+
+568
+01:06:39,750 --> 01:06:49,870
+أسباع في اتجاه مين؟ ال K كمان ال derivative in
+
+569
+01:06:49,870 --> 01:06:51,170
+this
+
+570
+01:06:55,330 --> 01:07:04,530
+direction is سالب اولى grade ال F سوى ده سالب سبع
+
+571
+01:07:04,530 --> 01:07:13,510
+خلاصنا و احنا خلاصنا ال section طبعا وبالتالى بروح
+
+572
+01:07:13,510 --> 01:07:22,010
+ل exercises اليمين اربعتاشر خمسةالمسائل من واحد
+
+573
+01:07:22,010 --> 01:07:28,330
+لخمسة و تلاتين القادة
+
+574
+01:07:28,330 --> 01:07:31,030
+حد بتسمع أي سؤال هنا؟
+
+575
+01:07:58,040 --> 01:08:01,500
+ببناء زي ما شايفين ال directional derivative فيها
+
+576
+01:08:01,500 --> 01:08:05,440
+معلومات قيمة وبالتالي يعني دائما و أبدا في
+
+577
+01:08:05,440 --> 01:08:10,840
+الامتحانات النهائية بنحاول نجيب سؤال مرتبط فيها
+
+578
+01:08:10,840 --> 01:08:15,780
+ننتقل لل section اللذي يليه يا خالد اللي هو
+
+579
+01:08:15,780 --> 01:08:24,520
+section اربعة عشر ستة اربعة عشر ستة اللي هو تانجين
+
+580
+01:08:29,670 --> 01:08:48,750
+Tangent players and differentials نمسى
+
+581
+01:08:48,750 --> 01:08:51,770
+حد منك كله؟ خلاص؟
+
+582
+01:09:07,370 --> 01:09:11,370
+أحنا قبل شويه بجينا نقول الـ tangent line in ده
+
+583
+01:09:11,370 --> 01:09:16,470
+نقطة مظبوط لمين؟ لل level كام؟ طب لو صار level
+
+584
+01:09:16,470 --> 01:09:20,450
+surface اللي ببطل يصير عندي tangent line و انا
+
+585
+01:09:20,450 --> 01:09:24,730
+بصير tangent plane طبعا افضل ان اعطيله definition
+
+586
+01:09:24,730 --> 01:09:30,110
+و بعدين نشوف كيف ان نحسب المعادلة تبعه انا بجي
+
+587
+01:09:30,110 --> 01:09:35,370
+بقول definition ال
+
+588
+01:09:35,370 --> 01:09:35,810
+tangent
+
+589
+01:09:41,640 --> 01:09:47,800
+الـ tangent plane at the point
+
+590
+01:09:47,800 --> 01:09:55,860
+عند النقطة الـ P naught of X naught و Y naught و Z
+
+591
+01:09:55,860 --> 01:10:00,120
+naught on
+
+592
+01:10:00,120 --> 01:10:01,460
+the level surface
+
+593
+01:10:11,460 --> 01:10:22,440
+F of X و Y و Z يساوي Constancy of a differentiable
+
+594
+01:10:22,440 --> 01:10:35,420
+function F is the plane هو عبارة عن المستوى إضرار
+
+595
+01:10:35,420 --> 01:10:43,710
+الذي يمر بالنقطةP نوت و X نوت و Y نوت و Z نوت
+
+596
+01:10:43,710 --> 01:10:47,590
+Normal
+
+597
+01:10:47,590 --> 01:10:56,970
+و يكون عموديًا to grade ال F عند النقطة اليمين P
+
+598
+01:10:56,970 --> 01:10:57,910
+نوت
+
+599
+01:11:13,660 --> 01:11:21,440
+وحد يعطيني دفتر من دفتر اي دفتر لو جيت تخيلت يا
+
+600
+01:11:21,440 --> 01:11:26,700
+ابنات ان ايدي هذه level surface تبقى مجسم في الفرق
+
+601
+01:11:26,700 --> 01:11:32,820
+قبضة اليد هذه هي level surface خلت مماسي يمسها
+
+602
+01:11:32,820 --> 01:11:40,140
+يمسها في نقطة واحدةيبقى هذه النقطة اسمها X node و
+
+603
+01:11:40,140 --> 01:11:44,860
+Y node و Z node انا بدي اجيب معادلة ال plane هذا
+
+604
+01:11:44,860 --> 01:11:50,480
+من العمودي على ال plane هو ال grade ال F زي ما
+
+605
+01:11:50,480 --> 01:11:54,920
+كانت في حتة level curve قبل قليل كان العمودي على
+
+606
+01:11:54,920 --> 01:11:59,880
+ال tangent main هو grade ال F وهناك العمودي على ال
+
+607
+01:11:59,880 --> 01:12:04,460
+tangent P plane هي grade ال F زي ما هو L U على A
+
+608
+01:12:04,460 --> 01:12:12,450
+على Lمرة تانية بقول تانجينت بلين مستوى التماس عندي
+
+609
+01:12:12,450 --> 01:12:16,770
+النقطة P نقطة X نقطة Y نقطة و Z نقطة على ال level
+
+610
+01:12:16,770 --> 01:12:22,030
+surface F و X و Y و Z بدي اسمه كونه C لدفينشف و
+
+611
+01:12:22,030 --> 01:12:27,200
+Function F هو عبارة عن بلين اللي يمربهذه النقطة
+
+612
+01:12:27,200 --> 01:12:32,980
+ويكون عمودي علمين على الجراد ال F طب إذا نص مرسمة
+
+613
+01:12:32,980 --> 01:12:37,380
+فوضيحية طب أنا أعطيكم مثال بقفض اليد التباتي لكن
+
+614
+01:12:37,380 --> 01:12:42,580
+بقول أنا عندي فيه level surface على سبيل المثال لو
+
+615
+01:12:42,580 --> 01:12:49,680
+كان عندي محاور بهذا الشكل وقول هذا محور X هذا محور
+
+616
+01:12:49,680 --> 01:12:57,180
+Y هذا محور Z وروحت رسمتالـ level surface اللي عندي
+
+617
+01:12:57,180 --> 01:13:05,840
+هذا و نفترض ان ال level surface كان بهذا الشكل على
+
+618
+01:13:05,840 --> 01:13:11,140
+سبيل المثال جبت
+
+619
+01:13:11,140 --> 01:13:17,140
+مستوى و خلته يمس هذا ال level surface المستوى هذا
+
+620
+01:13:17,140 --> 01:13:22,680
+حرصه بلون آخر بنات يبقى لو جب مستوى بالشكل اللي
+
+621
+01:13:22,680 --> 01:13:23,420
+عندنا هذا
+
+622
+01:13:27,390 --> 01:13:32,410
+راح اشترك معاه في نقطة واحدة زي النقطة اللى عناها
+
+623
+01:13:32,410 --> 01:13:38,770
+يبقى هذا بدراسمه مظلل مظلل يبقى هو اللى فوق
+
+624
+01:13:38,770 --> 01:13:44,410
+والمجسم اللى بيصير باسمه منه او منها منه اسفل طبعا
+
+625
+01:13:44,410 --> 01:13:51,730
+يبقى هذا الأسود بدهرش بيكون منقط لأنه مظهر ليش
+
+626
+01:13:51,730 --> 01:13:58,620
+وكذلك هذا كمان بدهرشلأنه اه دراسة ملقطة لإن ليه
+
+627
+01:13:58,620 --> 01:14:04,360
+plane غطى طيب ليه plane و هذا ال surface اشتركوا
+
+628
+01:14:04,360 --> 01:14:10,640
+في نقطة واحدة؟ مين هي النقطة هذه؟ هي النقطة P نوض
+
+629
+01:14:10,640 --> 01:14:18,460
+و X نوض و Y نوض و Z نوض العمودي عند النقطة هذا غطى
+
+630
+01:14:18,460 --> 01:14:30,800
+العمودي على ال plane كان من نجراد ال Fعندنا نرجع
+
+631
+01:14:30,800 --> 01:14:37,480
+بالذاكرة الى الوراء الى section 12-5 معادة لطلينة
+
+632
+01:14:37,480 --> 01:14:42,860
+إذا نالت نقطة تقع فيه والذكر العمودي عليه grade F
+
+633
+01:14:42,860 --> 01:14:47,360
+هو العمودي عليه هو النقطة الحمد لله موجودة إذا
+
+634
+01:14:47,360 --> 01:14:52,900
+المعادلة القديمة هيطب اشكرت المعادلة القديمة عزيزي
+
+635
+01:14:52,900 --> 01:14:59,960
+AX أو AX ناقص X naught زائد B في Y ناقص Y naught
+
+636
+01:14:59,960 --> 01:15:05,980
+زائد Z زائد C زائد Z ناقص Z naught بيسوء من Zero
+
+637
+01:15:05,980 --> 01:15:11,140
+يعني إيه؟ يعني بنروح ناخد أي نقطة أخرى في ليه
+
+638
+01:15:11,140 --> 01:15:19,950
+planeوالتكن هذه النقطة مثلا ل P X Y و Z وبنعتبر ان
+
+639
+01:15:19,950 --> 01:15:25,870
+في عندى vector اسمه P node P يبقى هذا ال vector
+
+640
+01:15:25,870 --> 01:15:36,110
+اللي هو P node P يبقى باجب اقوله هنا from section
+
+641
+01:15:36,110 --> 01:15:39,530
+أتناشر خمسة
+
+642
+01:15:45,740 --> 01:15:54,160
+Tangent A Plane S المركبة
+
+643
+01:15:54,160 --> 01:15:59,880
+الأولى تبع المتجهة grade ال F مش هي عبارة عن F X
+
+644
+01:15:59,880 --> 01:16:07,280
+عند النقطة F of X node و Y node و Z node في ال X
+
+645
+01:16:07,280 --> 01:16:09,220
+ناقص ال X node
+
+646
+01:16:38,850 --> 01:16:48,150
+الـ Fx والـ Fy والـ Fz المركبة المفتجه العموديهذه
+
+647
+01:16:48,150 --> 01:16:59,250
+المراكبات المتجهة العمودي Fx Fy Fz Fz Fz Fz Fz Fz
+
+648
+01:16:59,250 --> 01:16:59,550
+Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz
+
+649
+01:16:59,550 --> 01:16:59,730
+Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz
+
+650
+01:16:59,730 --> 01:17:04,970
+Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz
+
+651
+01:17:04,970 --> 01:17:05,030
+Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz
+
+652
+01:17:05,030 --> 01:17:09,510
+Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz
+
+653
+01:17:15,440 --> 01:17:19,700
+طيب كويس، في حاجة كمان قدناها بنات اسمها normal
+
+654
+01:17:19,700 --> 01:17:24,940
+line، ال normal line على ال plane عند اللقطة،
+
+655
+01:17:24,940 --> 01:17:30,960
+طبعا، ال normal line على ال plane عند اللقطة،
+
+656
+01:17:30,960 --> 01:17:36,720
+يبقوا خط موازي لمين؟لكن هذا ال F إذا بقدر أجيب ال
+
+657
+01:17:36,720 --> 01:17:41,740
+parametric equations لهذا ال line بدلالة مركبة ل
+
+658
+01:17:41,740 --> 01:17:46,060
+gradient هنحطها تعريف و بعدين نوجد المعادلات
+
+659
+01:17:46,060 --> 01:17:49,280
+تبعدها فبجيب اقول command definition
+
+660
+01:18:05,190 --> 01:18:17,290
+الخط العملي to the surface to the surface at P0 or
+
+661
+01:18:17,290 --> 01:18:27,210
+X0 or Y0 or Z0 as the line through as the line
+
+662
+01:18:27,210 --> 01:18:31,890
+through P0
+
+663
+01:18:31,890 --> 01:18:34,310
+parallel
+
+664
+01:18:43,650 --> 01:18:48,690
+اللي هي البينو برضه
+
+665
+01:18:48,690 --> 01:18:59,630
+من سيكشن أتناشر خمسة from section أتناشر خمسة the
+
+666
+01:18:59,630 --> 01:19:03,370
+parametric
+
+667
+01:19:03,370 --> 01:19:05,710
+equations
+
+668
+01:19:06,410 --> 01:19:20,350
+of this line R ال X بدي ساوي ال X node زائد المتجه
+
+669
+01:19:20,350 --> 01:19:27,050
+الموازي لل gradient ال F
+
+670
+01:19:27,050 --> 01:19:34,930
+X زائد ال F X عند النقطة P node في T ال Y بدي ساوي
+
+671
+01:19:34,930 --> 01:19:42,770
+Y nodeزائد fy عند النقطة P0 في T ال Z بتسوي Z0
+
+672
+01:19:42,770 --> 01:19:51,890
+زائد FZ عند النقطة P0 في Main في اتجاه Aيبقى هؤلاء
+
+673
+01:19:51,890 --> 01:19:55,870
+الـparameters لمين؟ للـnormal line يبقى صح اننا
+
+674
+01:19:55,870 --> 01:20:00,910
+جيبنا ال tangent plane لمين؟ لل level surface و
+
+675
+01:20:00,910 --> 01:20:05,170
+جيبنا العمودي على level surface اللي هو هو العمودي
+
+676
+01:20:05,170 --> 01:20:09,390
+على tangent plane يعني العمودي على level surface
+
+677
+01:20:09,390 --> 01:20:15,710
+هو نفس العمود على مين؟ على tangent plane لل level
+
+678
+01:20:15,710 --> 01:20:21,510
+surface اللي موجود عندنانعطي أمثلة توضيحية على ذلك
+
+679
+01:20:21,510 --> 01:20:30,390
+أول مثال مثلا نقول
+
+680
+01:20:30,390 --> 01:20:33,010
+find the equations of the tangent plane
+
+681
+01:20:47,660 --> 01:21:01,940
+and normal line and normal line and normal line at
+
+682
+01:21:01,940 --> 01:21:15,180
+the point at the point عند النقطة ال P نوت of واحد
+
+683
+01:21:15,470 --> 01:21:23,610
+و سالب واحد و تلاتة on the surface on the surface
+
+684
+01:21:23,610 --> 01:21:33,110
+على السطر اللي همين x تربيع زائدي اتنين x y ناقص y
+
+685
+01:21:33,110 --> 01:21:39,170
+تربيع زائد 6 تربيع كله بده يساوي سبع
+
+686
+01:21:56,450 --> 01:22:01,810
+السؤال مرة تانية طلب مني معادلة مستوى التماس
+
+687
+01:22:01,810 --> 01:22:07,390
+ومعادلة الخط العمودي عند النقطة التي تقع على ال
+
+688
+01:22:07,390 --> 01:22:11,530
+level surface لمين للمنحنة اللي عندنا يبقى هذه
+
+689
+01:22:11,530 --> 01:22:15,670
+معادلة إيش يا بنات level surface مين الدالة
+
+690
+01:22:15,670 --> 01:22:21,730
+الأصلية الدالة هذه بدون السبعة بسميها F of X وY
+
+691
+01:22:21,730 --> 01:22:25,510
+يبقى باجي بقوله هنا ال F
+
+692
+01:22:28,480 --> 01:22:37,380
+اللي هي level surface هي x تربيع زائد اتنين اكس
+
+693
+01:22:37,380 --> 01:22:39,000
+واي ناقص واي
+
+694
+01:22:44,050 --> 01:22:47,310
+يبقى برضه grade ال F بتلعب دور الأساسي عندنا بدنا
+
+695
+01:22:47,310 --> 01:22:52,550
+نروح نجيبله grade ال F يبقى بدنا نجيبله ال Fx يبقى
+
+696
+01:22:52,550 --> 01:22:59,110
+مشتقة الدالة F بالنسبة ل X يعني يبقى 2X زائد 2Y
+
+697
+01:22:59,110 --> 01:23:01,790
+الباقى كله Zero ايوة
+
+698
+01:23:08,580 --> 01:23:13,660
+يعني هذي كانت z مقص واحد لكل تربية؟ اه ممكن المقص
+
+699
+01:23:13,660 --> 01:23:18,160
+واحد ورق سبعة لازم تفكر و تقدر أفهم ال .. لأ ليس
+
+700
+01:23:18,160 --> 01:23:21,800
+بالضرورة ليس بالضرورة طبعا شو رأيك؟ انا لو جيبت
+
+701
+01:23:21,800 --> 01:23:27,160
+السبعة على الشجرة التانية و قلت كله يسوى zero يسوى
+
+702
+01:23:27,160 --> 01:23:31,500
+هذا برضه level surface او zero level surface لو
+
+703
+01:23:31,500 --> 01:23:34,380
+كتبته و ماحدش اللي و الكلام عندي و انا الاشتراك
+
+704
+01:23:34,380 --> 01:23:36,460
+مبينش لهذا و هناك كله بروح
+
+705
+01:23:41,330 --> 01:23:46,810
+يبقى هذا سواء كتبت في الشكل هذا ستة نت السبعة أو
+
+706
+01:23:46,810 --> 01:23:52,890
+دخلت بالعصابن اشتقاق لا قيمة لها تمام جبنا ال Fx
+
+707
+01:23:52,890 --> 01:23:59,230
+المدين X زي دي اتنين Y بدي احسب هذا المقدار Fx عند
+
+708
+01:23:59,230 --> 01:24:05,180
+النقطة الموطنة واحد وثاني واحد وتلريبقى x بواحد
+
+709
+01:24:05,180 --> 01:24:09,560
+يبقى قصيري اتنين و هنا سالب اتنين يبقى الحمد لله
+
+710
+01:24:09,560 --> 01:24:15,820
+قداش بزيره بدي اروح ليبقى ال fy يبقى ال x تلفية مع
+
+711
+01:24:15,820 --> 01:24:23,380
+السلامة يطلع اتنين x مقص اتنين y يبقى هذا بدي
+
+712
+01:24:23,380 --> 01:24:29,740
+يعطينا ان ال fy عند النقطة واحد و سالب واحد يكون
+
+713
+01:24:29,740 --> 01:24:36,280
+تلاتة يساويالـ x هذه باتنين وهنا زائدي اتنين يبقى
+
+714
+01:24:36,280 --> 01:24:42,080
+قداش اربع ناقص ناقص يبقى بتطلع قداش اللي هو اربع
+
+715
+01:24:42,080 --> 01:24:49,540
+بتجيب ال fz يساوي zero zero zero يبقى بس قداش
+
+716
+01:24:49,540 --> 01:24:56,740
+اتنين z يبقى اتنين z هذا بدي يعطيناإن F زده عند
+
+717
+01:24:56,740 --> 01:25:02,520
+الواحد و سالب واحد و تلاته بده يساوي اتنين في
+
+718
+01:25:02,520 --> 01:25:08,700
+تلاته في قدر بيه ستة من هدولي التلاتة مع بعض بقدر
+
+719
+01:25:08,700 --> 01:25:14,600
+أجيب له ال gradient لدالة F اللي هو اتجاه ال I ب
+
+720
+01:25:14,600 --> 01:25:21,860
+Zero يبقى أربعة J زائد ستة K طيب
+
+721
+01:25:24,110 --> 01:25:27,650
+هذه المراكبة في اتجاه ال X هذه المراكبة في اتجاه
+
+722
+01:25:27,650 --> 01:25:32,710
+ال Y وهذه المراكبة في اتجاه ال K نجي للمعادلة اللي
+
+723
+01:25:32,710 --> 01:25:39,290
+عندناها هذه حسبناها في Zero هذه أربعة، هذه بسنتة X
+
+724
+01:25:39,290 --> 01:25:43,610
+نقطة وY نقطة وZ نقطة المعروفة وماضلش عليها إلا
+
+725
+01:25:43,610 --> 01:25:49,590
+المعادلة يبقى عندنا أنا عليه بقول المعادلة كتالة
+
+726
+01:26:32,870 --> 01:26:39,710
+زائد اربعة في ال Y زائد واحد زائد ز
+
+727
+01:26:52,920 --> 01:26:59,840
+نقص تمانتاشة بدو يساوي Zero او ان شئتم فقولوا هذا
+
+728
+01:26:59,840 --> 01:27:08,260
+اربعة Y زائد ستة Z اربعة من نقص تمانتاشة بضل نقص
+
+729
+01:27:08,260 --> 01:27:13,640
+اربعتاش على الشجرة التانية بيساوي اربعتاش لو قسمنا
+
+730
+01:27:13,640 --> 01:27:16,120
+كله على اتنين بيصير اتنين
+
+731
+01:27:18,620 --> 01:27:25,380
+هذا الـ Z بيكون ساوية سبعة هذا ال equation of the
+
+732
+01:27:25,380 --> 01:27:31,920
+tangent plane قلّي بعد ذلك بدي ال equation of the
+
+733
+01:27:31,920 --> 01:27:40,000
+normal line قبل ما بدي بقول هنا دي equations of
+
+734
+01:27:40,000 --> 01:27:45,120
+the normal line
+
+735
+01:27:48,420 --> 01:27:55,820
+الـ X بدي يسوى X نُض الـ E بواحد زائد كدهش؟ زائد
+
+736
+01:27:55,820 --> 01:28:01,560
+Zero لإن ال F X عندى كدهش؟ Zero يبقى معاه سلامة و
+
+737
+01:28:01,560 --> 01:28:08,660
+ال Y بدي يسوى كدهش؟ سالب واحد زائد
+
+738
+01:28:08,660 --> 01:28:17,350
+أربعة T و هنا ال Z بيسوى تلاتة عظم النقريبقى تلاتة
+
+739
+01:28:17,350 --> 01:28:37,710
+وانا زائد ستة T مثال أخير في محاضرة اليوم five
+
+740
+01:28:37,710 --> 01:28:39,450
+parametric equations
+
+741
+01:28:48,420 --> 01:28:56,260
+للتانجين الطريق للتانجين
+
+742
+01:28:56,260 --> 01:29:10,380
+الطريق للتانجين الطريق للتانجين
+
+743
+01:29:10,380 --> 01:29:19,490
+الطريقintersection of the surfaces of the surfaces
+
+744
+01:29:19,490 --> 01:29:29,450
+للسطحين الو X Y Z يساوي واحد والتاني الو X تربيع
+
+745
+01:29:29,450 --> 01:29:37,590
+زائد اتنين Y تربيع زائد تلاتة Z تربيع بده يساوي
+
+746
+01:29:37,590 --> 01:29:48,670
+ستة at thepoint عند النقطة اللي بين واحد وواحد
+
+747
+01:29:48,670 --> 01:29:49,890
+وواحد
+
+748
+01:30:31,300 --> 01:30:36,640
+سؤال مرة ثانية، عشان نقدر نتصور الموضوع، انا في
+
+749
+01:30:36,640 --> 01:30:40,880
+only two surfaces و الاتنين متقاطعين، يعني لو
+
+750
+01:30:40,880 --> 01:30:44,660
+افترضت ان ايدي اليمين هي surface و القطب تبعت ايدي
+
+751
+01:30:44,660 --> 01:30:49,260
+الشمال هي surface اخر، اتنين صار بينهم متقاطع،
+
+752
+01:30:49,260 --> 01:31:06,920
+قضعوا في من؟ من حلبالمنحنة تبقى
+
+753
+01:31:06,920 --> 01:31:16,840
+تقاطع تقاطع تقاطع تقاطع تقاطع تقاطع
+
+754
+01:31:19,550 --> 01:31:25,210
+نقطة موجودة عليه
+
+755
+01:31:25,210 --> 01:31:41,290
+مستجه يوازي نقطة موجودة عليه مستجه يوازي نقطة
+
+756
+01:31:41,290 --> 01:31:44,690
+موجودة عليه مستجه يوازي
+
+757
+01:31:50,090 --> 01:31:57,670
+طب مذاكرين كيف كنا نجيب معادلة خط التقاطة لمستويين
+
+758
+01:31:57,670 --> 01:32:05,010
+متقاطعين كنا نجيب ال normal على الأول نجيب ال
+
+759
+01:32:05,010 --> 01:32:11,310
+normal على التاني اطلع المنتجة الموازي لخط التقاطة
+
+760
+01:32:11,310 --> 01:32:15,070
+هنا نفس الفكرة من المنتجة العمودي على ال surface
+
+761
+01:32:15,070 --> 01:32:21,430
+الأوللجراد تبع ال level service اللي عندنا و
+
+762
+01:32:21,430 --> 01:32:26,850
+التانية لجراد التانية لو اتلب cross product بجيب
+
+763
+01:32:26,850 --> 01:32:31,610
+الخط الموازية tangent بقى لجرادها من الدالة الأولى
+
+764
+01:32:31,610 --> 01:32:34,850
+و لجرادها من الدالة الثانية هدول دلتين او two
+
+765
+01:32:34,850 --> 01:32:39,370
+surfaces مختلفين يبقى انا في عندي بدل ال function
+
+766
+01:32:39,370 --> 01:32:44,350
+تنتهي هنا يا بنات ال function الأولى اللي هي f of
+
+767
+01:32:44,350 --> 01:32:44,770
+x
+
+768
+01:32:52,100 --> 01:32:55,440
+YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ
+
+769
+01:32:55,440 --> 01:32:56,920
+YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ
+
+770
+01:32:56,920 --> 01:32:58,840
+YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ
+
+771
+01:32:58,840 --> 01:33:00,620
+YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ
+
+772
+01:33:00,620 --> 01:33:00,740
+YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ
+
+773
+01:33:00,740 --> 01:33:01,240
+YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ
+
+774
+01:33:01,240 --> 01:33:01,460
+YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ
+
+775
+01:33:16,780 --> 01:33:21,640
+عند النقطة واحد و واحد و واحد يسوي واحد في واحد و
+
+776
+01:33:21,640 --> 01:33:24,540
+يسوي واحد و يسوي واحد و يسوي واحد و يسوي واحد و
+
+777
+01:33:24,540 --> 01:33:25,100
+يسوي واحد و يسوي واحد و يسوي واحد و يسوي واحد و
+
+778
+01:33:25,100 --> 01:33:28,520
+يسوي واحد و يسوي واحد و يسوي واحد و يسوي واحد و
+
+779
+01:33:28,520 --> 01:33:32,700
+يسوي واحد و يسوي واحد و يسوي واحد و يسوي واحد و
+
+780
+01:33:32,700 --> 01:33:33,340
+يسوي واحد و يسوي واحد و يسوي واحد و يسوي واحد و
+
+781
+01:33:33,340 --> 01:33:33,560
+يسوي واحد و يسوي واحد و يسوي واحد و يسوي واحد و
+
+782
+01:33:33,560 --> 01:33:34,360
+يسوي واحد و يسوي واحد و يسوي واحد و يسوي واحد و
+
+783
+01:33:34,360 --> 01:33:38,000
+يسوي واحد و يسوي واحد و يسوي واحد و يسوي واحد و
+
+784
+01:33:38,000 --> 01:33:40,280
+يسوي واحد و يسوي وا
+
+785
+01:33:47,460 --> 01:33:53,760
+فز عند نقطة واحد و واحد و واحد هي جداش واحد اللي
+
+786
+01:33:53,760 --> 01:34:00,340
+عملناه لف يروح نعمله لمين؟ لجي يبقى بدي أجيب كمان
+
+787
+01:34:00,340 --> 01:34:06,140
+الجي اكس والجي واي والجي زد عند نفس النقطة يبقى
+
+788
+01:34:06,140 --> 01:34:08,640
+بدي أجيب له هنا جي اكس
+
+789
+01:34:16,680 --> 01:34:23,140
+جي اكس عند النقطة واحد و واحد و واحد يساوي اتنين
+
+790
+01:34:23,140 --> 01:34:29,460
+في واحد و يساوي قداش اتنين بدي ال جي واي اللي هو
+
+791
+01:34:29,460 --> 01:34:35,440
+اربعة واي هذا بدي اقولك ان جي واي عند النقطة واحد
+
+792
+01:34:48,850 --> 01:34:55,650
+GZ عند النقطة واحد وواحد وواحد يساوي 6 في واحد
+
+793
+01:34:55,650 --> 01:35:06,490
+ويساوي 6 إذا حصلنا على مين؟ على Grad F عند النقطة
+
+794
+01:35:06,490 --> 01:35:14,150
+من الـEP node اللي عندنا مين هي يا بنات؟ I زائد G
+
+795
+01:35:14,150 --> 01:35:18,310
+زائد K كل المركبات زي بعض
+
+796
+01:35:24,910 --> 01:35:29,190
+عند نفس النقطة P node هي ما تغيرتش
+
+797
+01:35:32,080 --> 01:35:38,000
+بقولك هي النقطة واحد و واحد و واحد وهنا نفس النقطة
+
+798
+01:35:38,000 --> 01:35:43,360
+اللي واحد و واحد و واحد يبقى هذا الكلام بدرساوي
+
+799
+01:35:43,360 --> 01:35:53,200
+فانا عندنا اتنين I زائد اربع G زائد ستة K بدي اعمل
+
+800
+01:35:53,200 --> 01:35:58,240
+cross product فيما بينهم يقدروا احجيب له اجراد ال
+
+801
+01:36:02,990 --> 01:36:14,930
+محدد IJK مركبات ال F 1111 مركبات ال G 246 و 9
+
+802
+01:36:23,510 --> 01:36:29,050
+يبقى 6-4 في اتجاه ال I ناقص
+
+803
+01:36:33,930 --> 01:36:40,410
+يبقى هنا ستة نقص اتنين في اتجاه ال J اللي بقعده
+
+804
+01:36:40,410 --> 01:36:47,490
+أشطر صفر عموده اربعة نقص اتنين في اتجاه ال K زائد
+
+805
+01:36:47,490 --> 01:36:54,650
+اربعة نقص اتنين في اتجاه ال K و اتنين I نقص اربعة
+
+806
+01:36:54,650 --> 01:37:02,550
+J زائد اتنين K هذا this vector
+
+807
+01:37:06,240 --> 01:37:14,960
+Parallel to the tangent line
+
+808
+01:37:14,960 --> 01:37:27,080
+of the curve of intersection of
+
+809
+01:37:27,080 --> 01:37:32,580
+the two level surfaces
+
+810
+01:37:39,490 --> 01:37:43,990
+يبقى جبنة قراءة ال Fالمتجه العمودي على ال surface
+
+811
+01:37:43,990 --> 01:37:48,070
+الأول جبنا grade الجيه المتجه العمودي على ال
+
+812
+01:37:48,070 --> 01:37:52,370
+surface التاني عملنا cross product طلعني متجه
+
+813
+01:37:52,370 --> 01:37:58,630
+يوازي المماس لمين لمنحنة التقاطع تبع المستوين
+
+814
+01:37:58,630 --> 01:38:04,190
+المتجه موجود والحمد لله النقطة موجودة إذا بقدر
+
+815
+01:38:04,190 --> 01:38:10,290
+أجيب المعادات البرامترية لخط التماثر فبقدر أقولهم
+
+816
+01:38:10,290 --> 01:38:15,890
+ما يأتيthe parametric
+
+817
+01:38:15,890 --> 01:38:33,090
+equations of the tangent line up X سوى X0 زائد AT
+
+818
+01:38:33,090 --> 01:38:40,310
+Y سوى Y0 زائد BT Z سوى Z
+
+819
+01:38:59,390 --> 01:39:06,190
+طب لحد هنا stop لسه مكملناشمرة قادمة ان شاء الله
+
+820
+01:39:06,190 --> 01:39:13,010
+بنكمل هذا ال section وبرضه بندخل ال section اللي
+
+821
+01:39:13,010 --> 01:39:18,270
+بعده ان تمكننا ان شاء الله تعالى لأن هذا ال
+
+822
+01:39:18,270 --> 01:39:31,650
+section قويل شوية يعطيكوا
+
+823
+01:39:31,650 --> 01:39:31,970
+العافية
+
+824
+01:39:41,730 --> 01:39:43,710
+السلام عليكم و رحمه الله
+
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/0xeRGhgbabI_raw.json b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/0xeRGhgbabI_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..1bc01938b895a9b2e9c68ab0a01d4bab90f5052a
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/0xeRGhgbabI_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 268, "start": 0.0, "end": 2.68, "text": "موسيقى", "tokens": [2304, 41779, 1829, 4587, 7578], "avg_logprob": -0.3916015724341075, "compression_ratio": 0.5714285714285714, "no_speech_prob": 0.0036106109619140625, "words": [{"start": 0.0, "end": 2.68, "word": "موسيقى", "probability": 0.72783203125}], "temperature": 1.0}, {"id": 2, "seek": 3256, "start": 16.2, "end": 32.56, "text": "بسم الله الرحمن الرحيم بمناسبة حلول اليوم الأول من شهر رمضان مبارك نهنئكم بقدومي هذا الشهر ونوصيكم أن تجددوا حياتكم من جديد", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 4724, 2304, 8315, 35457, 3660, 11331, 1211, 12610, 45595, 20498, 16247, 12610, 9154, 13412, 3224, 2288, 12602, 2304, 11242, 7649, 3714, 3555, 9640, 4117, 8717, 3224, 1863, 19986, 24793, 4724, 28543, 20498, 1829, 23758, 25124, 3224, 2288, 4032, 1863, 2407, 9381, 1829, 24793, 14739, 6055, 7435, 3215, 3215, 14407, 11331, 1829, 9307, 24793, 9154, 10874, 16254, 3215], "avg_logprob": 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{"start": 22.48, "end": 23.12, "word": " مبارك", "probability": 0.9503173828125}, {"start": 23.12, "end": 24.44, "word": " نهنئكم", "probability": 0.8373046875}, {"start": 24.44, "end": 25.64, "word": " بقدومي", "probability": 0.947998046875}, {"start": 25.64, "end": 25.9, "word": " هذا", "probability": 0.98388671875}, {"start": 25.9, "end": 26.56, "word": " الشهر", "probability": 0.9957682291666666}, {"start": 26.56, "end": 27.86, "word": " ونوصيكم", "probability": 0.8982747395833334}, {"start": 27.86, "end": 28.62, "word": " أن", "probability": 0.6572265625}, {"start": 28.62, "end": 29.94, "word": " تجددوا", "probability": 0.990625}, {"start": 29.94, "end": 31.2, "word": " حياتكم", "probability": 0.97802734375}, {"start": 31.2, "end": 31.8, "word": " من", "probability": 0.98779296875}, {"start": 31.8, "end": 32.56, "word": " جديد", "probability": 0.9944661458333334}], "temperature": 1.0}, {"id": 3, "seek": 5475, "start": 32.99, "end": 54.75, "text": "يعني بتغير نمط التعامل الأولاني 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{"start": 133.57, "end": 133.65, "word": " و", "probability": 0.7841796875}, {"start": 133.65, "end": 133.93, "word": " نرجع", "probability": 0.6627604166666666}, {"start": 133.93, "end": 134.69, "word": " لموضوعنا", "probability": 0.90458984375}, {"start": 134.69, "end": 135.63, "word": " طيب", "probability": 0.7903645833333334}, {"start": 135.63, "end": 136.29, "word": " بذكر", "probability": 0.7431640625}, {"start": 136.29, "end": 136.99, "word": " تذكير", "probability": 0.9483642578125}, {"start": 136.99, "end": 137.31, "word": " قبل", "probability": 0.97998046875}, {"start": 137.31, "end": 137.59, "word": " كل", "probability": 0.97412109375}, {"start": 137.59, "end": 138.01, "word": " شيء", "probability": 0.81494140625}, {"start": 138.01, "end": 138.61, "word": " بالشيء", "probability": 0.9495849609375}, {"start": 138.61, "end": 138.85, "word": " اللى", "probability": 0.962646484375}, {"start": 138.85, "end": 139.33, "word": " أخدناه", "probability": 0.907421875}, {"start": 139.33, "end": 139.67, "word": " المرة", "probability": 0.970458984375}, {"start": 139.67, "end": 140.69, "word": " الماضية", "probability": 0.9951171875}, {"start": 140.69, "end": 141.11, "word": " في", "probability": 0.91845703125}, {"start": 141.11, "end": 141.49, "word": " ال", "probability": 0.81005859375}, {"start": 141.49, "end": 142.03, "word": " directional", "probability": 0.365966796875}, {"start": 142.03, "end": 142.51, "word": " derivative", "probability": 0.54296875}], "temperature": 1.0}, {"id": 8, "seek": 16547, "start": 143.13, "end": 165.47, "text": "طبعا عرفنا ال gradient vector عرفنا ال directional derivative ثم كتبنا أخر حاجة بعد ما أخذنا ميثالين الخواف S ثلاثة تبعت ال directional derivative بذكر صادقين قولنا ال directional derivative هديله رمز اللي هو DUF", "tokens": [9566, 3555, 3615, 995, 6225, 28480, 8315, 2423, 16235, 8062, 6225, 28480, 8315, 2423, 42242, 13760, 38637, 2304, 9122, 2655, 3555, 8315, 5551, 34740, 11331, 26108, 3660, 39182, 19446, 5551, 9778, 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0.94921875}, {"start": 175.86, "end": 178.64, "word": " وفكنا", "probability": 0.7889404296875}, {"start": 178.64, "end": 178.96, "word": " هذا", "probability": 0.97314453125}, {"start": 178.96, "end": 179.72, "word": " الكلام", "probability": 0.9415690104166666}, {"start": 179.72, "end": 180.6, "word": " وقلنا", "probability": 0.8486328125}, {"start": 180.6, "end": 180.86, "word": " ان", "probability": 0.615234375}, {"start": 180.86, "end": 181.3, "word": " هذا", "probability": 0.8955078125}, {"start": 181.3, "end": 182.2, "word": " يعتبر", "probability": 0.9191080729166666}, {"start": 182.2, "end": 183.0, "word": " طول", "probability": 0.97607421875}, {"start": 183.0, "end": 184.08, "word": " لجراد", "probability": 0.968994140625}, {"start": 184.08, "end": 184.72, "word": " F", "probability": 0.2054443359375}], "temperature": 1.0}, {"id": 10, "seek": 20547, "start": 185.07, "end": 205.47, "text": "فيقول ال U P Cos الزاوية تيتا لكن لما كان متجه الوحدة طوله يساوي واحد صحيح إذا هذا كله بده يساوي طول جراد ال F P Cos الزاوية ثانية الآن بدنا نيجي لخواص هذا ال direction ال derivative", "tokens": [5172, 1829, 39648, 2423, 624, 430, 15855, 6024, 110, 995, 2407, 10632, 6055, 36081, 995, 44381, 5296, 15042, 25961, 44650, 7435, 3224, 2423, 2407, 24401, 3660, 23032, 12610, 3224, 7251, 3794, 995, 45865, 36764, 24401, 20328, 5016, 1829, 5016, 11933, 15730, 23758, 28242, 3224, 47525, 3224, 7251, 3794, 995, 45865, 23032, 12610, 10874, 2288, 18513, 2423, 479, 430, 15855, 6024, 110, 995, 2407, 10632, 38637, 7649, 10632, 6024, 48506, 47525, 8315, 8717, 1829, 7435, 1829, 5296, 9778, 2407, 33546, 23758, 2423, 3513, 2423, 13760], "avg_logprob": -0.26985294257893283, "compression_ratio": 1.6555555555555554, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 185.07, "end": 185.77, "word": "فيقول", "probability": 0.5556640625}, {"start": 185.77, "end": 186.05, "word": " ال", "probability": 0.833984375}, {"start": 186.05, "end": 186.39, "word": " U", "probability": 0.6904296875}, 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"probability": 0.9583984375}, {"start": 200.95, "end": 201.71, "word": " ثانية", "probability": 0.6800130208333334}, {"start": 201.71, "end": 202.47, "word": " الآن", "probability": 0.65869140625}, {"start": 202.47, "end": 202.81, "word": " بدنا", "probability": 0.5799560546875}, {"start": 202.81, "end": 203.05, "word": " نيجي", "probability": 0.86541748046875}, {"start": 203.05, "end": 203.87, "word": " لخواص", "probability": 0.9388427734375}, {"start": 203.87, "end": 204.25, "word": " هذا", "probability": 0.85595703125}, {"start": 204.25, "end": 204.39, "word": " ال", "probability": 0.93505859375}, {"start": 204.39, "end": 204.83, "word": " direction", "probability": 0.47802734375}, {"start": 204.83, "end": 205.11, "word": " ال", "probability": 0.64599609375}, {"start": 205.11, "end": 205.47, "word": " derivative", "probability": 0.95947265625}], "temperature": 1.0}, {"id": 11, "seek": 23476, "start": 206.82, "end": 234.76, "text": "كتبنا المرة اللي فاتت أنه ممكن يكون موجب ممكن يكون سالب ممكن يكون صفر ممكن يكون أكبر ما يمكن ممكن أن يكون أقل ما يمكن و ممكن يكون zero روحنا قولنا ال F increases most strategically اللي هي النقطة هذه إذا كان والله ال U grade ال V2 في نفس الاتجاه يحدث هذا", "tokens": [4117, 2655, 3555, 8315, 9673, 25720, 13672, 1829, 6156, 9307, 2655, 14739, 3224, 3714, 43020, 7251, 30544, 3714, 29245, 3555, 3714, 43020, 7251, 30544, 8608, 6027, 3555, 3714, 43020, 7251, 30544, 20328, 5172, 2288, 3714, 43020, 7251, 30544, 5551, 4117, 26890, 19446, 7251, 43020, 3714, 43020, 14739, 7251, 30544, 5551, 4587, 1211, 19446, 7251, 43020, 4032, 3714, 43020, 7251, 30544, 4018, 12602, 2407, 5016, 8315, 12174, 12610, 8315, 2423, 479, 8637, 881, 38061, 13672, 1829, 39896, 28239, 47432, 3660, 29538, 11933, 15730, 25961, 16070, 43761, 2423, 624, 7204, 2423, 691, 17, 8978, 8717, 36178, 2423, 9307, 7435, 40294, 7251, 24401, 12984, 23758], "avg_logprob": -0.17809465787943127, "compression_ratio": 1.8783783783783783, "no_speech_prob": 0.0, "words": [{"start": 206.82, 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"end": 362.82, "text": "بيكون مقدار الـ DUF كله بيديه سوا قداش 0 إذا قيمة ال direction derivative أحيانا ممكن تكون موجبة أحيانا ممكن تكون سالبة أحيانا ممكن تكون 0", "tokens": [3555, 1829, 30544, 3714, 28543, 9640, 2423, 39184, 28423, 37, 28242, 3224, 4724, 1829, 16254, 3224, 8608, 14407, 12174, 3215, 33599, 1958, 11933, 15730, 12174, 32640, 3660, 2423, 3513, 13760, 5551, 5016, 1829, 7649, 995, 3714, 43020, 6055, 30544, 3714, 29245, 49401, 5551, 5016, 1829, 7649, 995, 3714, 43020, 6055, 30544, 8608, 6027, 49401, 5551, 5016, 1829, 7649, 995, 3714, 43020, 6055, 30544, 1958], "avg_logprob": -0.36923076923076925, "compression_ratio": 1.6099290780141844, "no_speech_prob": 0.0, "words": [{"start": 347.78, "end": 348.62, "word": "بيكون", "probability": 0.58837890625}, {"start": 348.62, "end": 350.3, "word": " مقدار", "probability": 0.6772054036458334}, {"start": 350.3, "end": 350.5, "word": " الـ", "probability": 0.33306884765625}, {"start": 350.5, "end": 351.76, "word": " DUF", "probability": 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81649, "start": 788.45, "end": 816.49, "text": "most rapidly N أو F الـ U and اجراد الـ F are in the same direction يبقى لو كانوا في نفس الاتجاه", "tokens": [1761, 12910, 426, 34051, 479, 2423, 39184, 624, 293, 1975, 7435, 2288, 18513, 2423, 39184, 479, 366, 294, 264, 912, 3513, 7251, 3555, 4587, 7578, 45164, 25961, 14407, 8978, 8717, 36178, 2423, 9307, 7435, 40294], "avg_logprob": -0.3129340335726738, "compression_ratio": 1.0731707317073171, "no_speech_prob": 0.0, "words": [{"start": 788.45, "end": 788.91, "word": "most", "probability": 0.67041015625}, {"start": 788.91, "end": 789.69, "word": " rapidly", "probability": 0.890625}, {"start": 789.69, "end": 797.35, "word": " N", "probability": 0.2034912109375}, {"start": 797.35, "end": 799.09, "word": " أو", "probability": 0.57568359375}, {"start": 799.09, "end": 799.65, "word": " F", "probability": 0.9638671875}, {"start": 799.65, "end": 800.69, "word": " الـ", "probability": 0.417236328125}, {"start": 800.69, "end": 801.05, "word": " 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اللي بال curve اللي بال curve ال function بسويها بمين؟ ب constant يبقى ال function الأساسية مين هي يا بنات؟ F of X Y تساوي X تربيه ناقص Y يبقى باجي بقوله هنا", "tokens": [3555, 39648, 3224, 12174, 45865, 3794, 31439, 2423, 2445, 13672, 1829, 18871, 16254, 4032, 9957, 39896, 6225, 8592, 7649, 1975, 7435, 1829, 3555, 46740, 7204, 2423, 479, 20666, 11622, 27842, 2423, 2445, 4032, 9957, 2423, 2445, 29538, 22807, 37893, 3714, 41193, 9957, 1829, 2423, 2445, 44381, 3714, 41193, 9957, 1829, 3714, 9957, 22807, 13672, 1829, 20666, 7605, 13672, 1829, 20666, 7605, 2423, 2445, 4724, 3794, 45865, 11296, 4724, 2304, 9957, 22807, 4724, 5754, 7251, 3555, 4587, 7578, 2423, 2445, 16247, 3794, 32277, 10632, 3714, 9957, 39896, 35186, 4724, 8315, 2655, 22807, 479, 295, 1783, 398, 6055, 3794, 995, 45865, 1783, 6055, 2288, 21292, 3224, 8717, 995, 4587, 9381, 398, 7251, 3555, 4587, 7578, 4724, 26108, 1829, 4724, 39648, 3224, 34105], "avg_logprob": -0.2897727390951362, "compression_ratio": 1.9578059071729959, 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يا", "probability": 0.92236328125}, {"start": 2402.77, "end": 2403.23, "word": " بنات؟", "probability": 0.7930908203125}, {"start": 2403.23, "end": 2403.85, "word": " F", "probability": 0.71240234375}, {"start": 2403.85, "end": 2404.11, "word": " of", "probability": 0.8232421875}, {"start": 2404.11, "end": 2404.27, "word": " X", "probability": 0.5537109375}, {"start": 2404.27, "end": 2404.57, "word": " Y", "probability": 0.544921875}, {"start": 2404.57, "end": 2405.21, "word": " تساوي", "probability": 0.928466796875}, {"start": 2405.21, "end": 2406.35, "word": " X", "probability": 0.77490234375}, {"start": 2406.35, "end": 2407.01, "word": " تربيه", "probability": 0.574737548828125}, {"start": 2407.01, "end": 2407.89, "word": " ناقص", "probability": 0.9295654296875}, {"start": 2407.89, "end": 2408.47, "word": " Y", "probability": 0.98388671875}, {"start": 2408.47, "end": 2409.31, "word": " يبقى", "probability": 0.9468994140625}, {"start": 2409.31, "end": 2409.69, "word": " باجي", 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unit vector هناك تمام؟ إذا هذا الكلام بده يساوي طول اجراد ال F", "tokens": [1211, 2407, 10874, 3555, 2655, 11296, 4724, 1211, 17082, 3660, 16247, 9566, 2407, 6027, 6055, 3555, 4587, 7578, 4724, 26108, 1829, 4724, 39648, 23758, 23032, 12610, 1975, 7435, 2288, 18513, 2423, 479, 6156, 9566, 12610, 2423, 624, 8978, 15855, 6024, 110, 995, 2407, 10632, 49374, 16095, 1975, 3224, 1975, 1829, 3224, 9122, 3215, 3224, 23032, 12610, 2423, 624, 22807, 5296, 28814, 1863, 1975, 8315, 10874, 47302, 2423, 4985, 8062, 34105, 4117, 46811, 10943, 22807, 11933, 15730, 23758, 2423, 28820, 10943, 47525, 3224, 7251, 3794, 995, 45865, 23032, 12610, 1975, 7435, 2288, 18513, 2423, 479], "avg_logprob": -0.3411184154058758, "compression_ratio": 1.6864864864864866, "no_speech_prob": 0.0, "words": [{"start": 3257.75, "end": 3258.73, "word": "لو", "probability": 0.217315673828125}, {"start": 3258.73, "end": 3259.71, "word": " جبتها", "probability": 0.781494140625}, {"start": 3259.71, "end": 3260.37, "word": " بلغة", 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بالضبط تماما على ال function اللي فيه ثلاثة متغيرات لذلك أقعد باختصار بصيغة ال remark التالي ال three properties", "tokens": [2304, 2655, 17082, 13546, 9957, 39896, 20328, 5016, 1829, 5016, 3660, 20666, 11242, 3555, 9566, 46811, 10943, 995, 15844, 2423, 2445, 13672, 1829, 8978, 3224, 38637, 1211, 5718, 104, 3660, 44650, 17082, 13546, 9307, 5296, 8848, 23275, 5551, 4587, 22488, 4724, 47283, 2655, 9381, 9640, 4724, 9381, 1829, 17082, 3660, 2423, 7942, 16712, 6027, 1829, 2423, 1045, 7221], "avg_logprob": -0.25675317493535704, "compression_ratio": 1.3419354838709678, "no_speech_prob": 5.364418029785156e-07, "words": [{"start": 3322.43, "end": 3323.57, "word": "متغيرين", "probability": 0.8029052734375}, {"start": 3323.57, "end": 3324.17, "word": " هي", "probability": 0.57666015625}, {"start": 3324.17, "end": 3324.95, "word": " صحيحة", "probability": 0.96025390625}, {"start": 3324.95, "end": 3325.59, "word": " بالضبط", "probability": 0.896484375}, {"start": 3325.59, "end": 3326.31, "word": " 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"يبقى المعلومات اللي خدناها على functions of two variables صحيحة على functions of three variables ناخد مثال عظيح ينهي هذه الاتجاهات بحيث الدلل عن هذه increases و كذلك decreases مصطلح بدي أن نقطع عنها و من ثم", "tokens": [1829, 3555, 4587, 7578, 9673, 30241, 20498, 9307, 13672, 1829, 16490, 3215, 8315, 11296, 15844, 6828, 295, 732, 9102, 20328, 5016, 1829, 5016, 3660, 15844, 6828, 295, 1045, 9102, 8717, 47283, 3215, 50113, 6027, 6225, 19913, 1829, 5016, 7251, 1863, 3224, 1829, 29538, 2423, 9307, 7435, 40294, 9307, 4724, 5016, 1829, 12984, 32748, 1211, 1211, 18871, 29538, 8637, 4032, 9122, 8848, 23275, 24108, 3714, 9381, 9566, 1211, 5016, 4724, 16254, 14739, 8717, 47432, 3615, 18871, 11296, 4032, 9154, 38637, 2304], "avg_logprob": -0.3310185302922755, "compression_ratio": 1.6062176165803108, "no_speech_prob": 0.0, "words": [{"start": 3617.51, "end": 3617.85, "word": "يبقى", "probability": 0.633636474609375}, {"start": 3617.85, "end": 3618.61, "word": " المعلومات", "probability": 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"end": 5905.93, "word": " up", "probability": 0.68359375}, {"start": 5905.93, "end": 5908.85, "word": " X", "probability": 0.371826171875}, {"start": 5908.85, "end": 5909.91, "word": " سوى", "probability": 0.4563802083333333}, {"start": 5909.91, "end": 5910.93, "word": " X0", "probability": 0.58551025390625}, {"start": 5910.93, "end": 5912.25, "word": " زائد", "probability": 0.615234375}, {"start": 5912.25, "end": 5913.09, "word": " AT", "probability": 0.8984375}, {"start": 5913.09, "end": 5914.19, "word": " Y", "probability": 0.80517578125}, {"start": 5914.19, "end": 5914.89, "word": " سوى", "probability": 0.8271484375}, {"start": 5914.89, "end": 5915.75, "word": " Y0", "probability": 0.93701171875}, {"start": 5915.75, "end": 5916.79, "word": " زائد", "probability": 0.9519856770833334}, {"start": 5916.79, "end": 5917.51, "word": " BT", "probability": 0.83837890625}, {"start": 5917.51, "end": 5919.25, "word": " Z", "probability": 0.70703125}, {"start": 5919.25, "end": 5919.93, "word": " سوى", "probability": 0.9638671875}, {"start": 5919.93, "end": 5920.31, "word": " Z", "probability": 0.9765625}], "temperature": 1.0}, {"id": 219, "seek": 594335, "start": 5939.39, "end": 5943.35, "text": "طب لحد هنا stop لسه مكملناش", "tokens": [9566, 3555, 5296, 24401, 34105, 1590, 5296, 3794, 3224, 3714, 24793, 1211, 1863, 33599], "avg_logprob": -0.46223957935969034, "compression_ratio": 0.9183673469387755, "no_speech_prob": 0.0, "words": [{"start": 5939.39, "end": 5940.63, "word": "طب", "probability": 0.3073272705078125}, {"start": 5940.63, "end": 5940.91, "word": " لحد", "probability": 0.90869140625}, {"start": 5940.91, "end": 5941.13, "word": " هنا", "probability": 0.8935546875}, {"start": 5941.13, "end": 5941.57, "word": " stop", "probability": 0.2978515625}, {"start": 5941.57, "end": 5942.37, "word": " لسه", "probability": 0.9220377604166666}, {"start": 5942.37, "end": 5943.35, "word": " مكملناش", "probability": 0.792041015625}], "temperature": 1.0}, {"id": 220, "seek": 597197, "start": 5944.45, "end": 5971.97, "text": "مرة قادمة ان شاء الله بنكمل هذا ال section وبرضه بندخل ال section اللي بعده ان تمكننا ان شاء الله تعالى لأن هذا ال section قويل شوية يعطيكوا العافية", "tokens": [2304, 25720, 12174, 18513, 46007, 16472, 13412, 16606, 21984, 44945, 24793, 1211, 23758, 2423, 3541, 4032, 26890, 11242, 3224, 44945, 3215, 9778, 1211, 2423, 3541, 13672, 1829, 39182, 3224, 16472, 46811, 19452, 8315, 16472, 13412, 16606, 21984, 37279, 6027, 7578, 5296, 33456, 23758, 2423, 3541, 12174, 2407, 26895, 13412, 2407, 10632, 37495, 9566, 1829, 4117, 14407, 18863, 31845, 10632], "avg_logprob": -0.16197916393478712, "compression_ratio": 1.6917808219178083, "no_speech_prob": 0.0, "words": [{"start": 5944.45, "end": 5944.91, "word": "مرة", "probability": 0.724853515625}, {"start": 5944.91, "end": 5945.51, "word": " قادمة", "probability": 0.9471028645833334}, {"start": 5945.51, "end": 5945.75, "word": " ان", "probability": 0.68896484375}, {"start": 5945.75, "end": 5945.91, "word": " شاء", "probability": 0.988037109375}, {"start": 5945.91, "end": 5946.19, "word": " الله", "probability": 0.9580078125}, {"start": 5946.19, "end": 5947.43, "word": " بنكمل", "probability": 0.9230143229166666}, {"start": 5947.43, "end": 5948.13, "word": " هذا", "probability": 0.83740234375}, {"start": 5948.13, "end": 5948.61, "word": " ال", "probability": 0.69091796875}, {"start": 5948.61, "end": 5949.03, "word": " section", "probability": 0.916015625}, {"start": 5949.03, "end": 5950.17, "word": " وبرضه", "probability": 0.86181640625}, {"start": 5950.17, "end": 5950.91, "word": " بندخل", "probability": 0.9803466796875}, {"start": 5950.91, "end": 5951.45, "word": " ال", "probability": 0.63818359375}, {"start": 5951.45, "end": 5952.13, "word": " section", "probability": 0.91943359375}, {"start": 5952.13, "end": 5953.01, "word": " اللي", "probability": 0.8486328125}, {"start": 5953.01, "end": 5953.81, "word": " بعده", "probability": 0.9248046875}, {"start": 5953.81, "end": 5954.25, "word": " ان", "probability": 0.72314453125}, {"start": 5954.25, "end": 5955.63, "word": " تمكننا", "probability": 0.7747395833333334}, {"start": 5955.63, "end": 5956.07, "word": " ان", "probability": 0.91845703125}, {"start": 5956.07, "end": 5956.41, "word": " شاء", "probability": 0.99072265625}, {"start": 5956.41, "end": 5956.75, "word": " الله", "probability": 0.9365234375}, {"start": 5956.75, "end": 5957.33, "word": " تعالى", "probability": 0.95849609375}, {"start": 5957.33, "end": 5957.89, "word": " لأن", "probability": 0.58154296875}, {"start": 5957.89, "end": 5958.13, "word": " هذا", "probability": 0.77294921875}, {"start": 5958.13, "end": 5958.27, "word": " ال", "probability": 0.449951171875}, {"start": 5958.27, "end": 5958.59, "word": " section", "probability": 0.8994140625}, {"start": 5958.59, "end": 5959.27, "word": " قويل", "probability": 0.8468424479166666}, {"start": 5959.27, "end": 5960.33, "word": " شوية", "probability": 0.8740234375}, {"start": 5960.33, "end": 5971.65, "word": " يعطيكوا", "probability": 0.8853515625}, {"start": 5971.65, "end": 5971.97, "word": " العافية", "probability": 0.9405924479166666}], "temperature": 1.0}, {"id": 221, "seek": 598371, "start": 5981.73, "end": 5983.71, "text": "السلام عليكم و رحمه الله", "tokens": [6027, 3794, 37440, 25894, 24793, 4032, 12602, 35571, 3224, 21984], "avg_logprob": -0.7162641937082465, "compression_ratio": 0.8979591836734694, "no_speech_prob": 0.0006761550903320312, "words": [{"start": 5981.73, "end": 5982.37, "word": "السلام", "probability": 0.28369140625}, {"start": 5982.37, "end": 5982.69, "word": " عليكم", "probability": 0.908203125}, {"start": 5982.69, "end": 5983.15, "word": " و", "probability": 0.90234375}, {"start": 5983.15, "end": 5983.45, "word": " رحمه", "probability": 0.5323893229166666}, {"start": 5983.45, "end": 5983.71, "word": " الله", "probability": 0.96923828125}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 5991.584, "duration_after_vad": 5261.87284375003}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/0xeRGhgbabI_raw.srt b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/0xeRGhgbabI_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..2d184d1b5bb6b9e4b4ff5d62691aa74fd4069bc5
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/0xeRGhgbabI_raw.srt
@@ -0,0 +1,3300 @@
+1
+00:00:00,000 --> 00:00:02,680
+موسيقى
+
+2
+00:00:16,200 --> 00:00:21,720
+بسم الله الرحمن الرحيم بمناسبة حلول اليوم الأول من
+
+3
+00:00:21,720 --> 00:00:28,620
+شهر رمضان مبارك نهنئكم بقدومي هذا الشهر ونوصيكم أن
+
+4
+00:00:28,620 --> 00:00:35,610
+تجددوا حياتكم من جديديعني بتغير نمط التعامل
+
+5
+00:00:35,610 --> 00:00:42,090
+الأولاني لإن رمضان فرصة للتغيير من الأسوأ إلى
+
+6
+00:00:42,090 --> 00:00:47,170
+الأحسن و من الأحسن إلى الأحسن منه و هكذا طبعا هذه
+
+7
+00:00:47,170 --> 00:00:51,970
+طبيعة الحياة سنن التغيير موجودة في الكون منذ بدء
+
+8
+00:00:51,970 --> 00:00:58,600
+الخليقة و إلى يومنا هذاكل واحد اتفكر ان في شغل كنت
+
+9
+00:00:58,600 --> 00:01:02,460
+بعملها غلط قبل هيك يبقى بنعملها الصح مشان الله
+
+10
+00:01:02,460 --> 00:01:06,860
+سبحانه و تعالى يغفرنا و نصير في الطريق الصحيح و
+
+11
+00:01:06,860 --> 00:01:11,980
+طبعا ان الذين آمنوا و عملوا الصالحات يهديهم ربهم
+
+12
+00:01:11,980 --> 00:01:18,420
+بإيمانهم يعني شفتوا في الثانوية العامة النتيجة
+
+13
+00:01:18,420 --> 00:01:22,880
+الأوائل او البنات الأوائل من حفظة القرآن الكريم
+
+14
+00:01:23,580 --> 00:01:30,040
+يبقى الذي يتدين يكون هذا سببا في تفوقه مش سببا في
+
+15
+00:01:30,040 --> 00:01:35,420
+تأخره ونحن المسلمين مطالبين دائما و أبدا أن نكون
+
+16
+00:01:35,420 --> 00:01:42,140
+في المقدمة و لن ترتفع لنا قائمة إلا إذا التزمنا
+
+17
+00:01:42,140 --> 00:01:48,000
+بديننا قولا و عملامش قول، لذا القرآن الكريم بيقول
+
+18
+00:01:48,000 --> 00:01:52,160
+إن الذين آمنوا وقالوا الصالحات والله إن الذين
+
+19
+00:01:52,160 --> 00:01:56,580
+آمنوا وعملوا الصالحات يبقى وعملوا الصالحات إذا
+
+20
+00:01:56,580 --> 00:02:05,510
+مطلوب مننا أن نعمل وأن نجدد وأننتذكر الأشياء اللى
+
+21
+00:02:05,510 --> 00:02:08,890
+ممكن نعملها غلط أو اللى عملناها غلط فهيك و نعزم
+
+22
+00:02:08,890 --> 00:02:13,930
+على أن لا نعود إليها ثانية بارك الله فيكم و نرجع
+
+23
+00:02:13,930 --> 00:02:18,850
+لموضوعنا طيب بذكر تذكير قبل كل شيء بالشيء اللى
+
+24
+00:02:18,850 --> 00:02:22,510
+أخدناه المرة الماضية في ال directional derivative
+
+25
+00:02:23,130 --> 00:02:27,230
+طبعا عرفنا ال gradient vector عرفنا ال directional
+
+26
+00:02:27,230 --> 00:02:32,530
+derivative ثم كتبنا أخر حاجة بعد ما أخذنا ميثالين
+
+27
+00:02:32,530 --> 00:02:37,710
+الخواف S ثلاثة تبعت ال directional derivative بذكر
+
+28
+00:02:37,710 --> 00:02:42,110
+صادقين قولنا ال directional derivative هديله رمز
+
+29
+00:02:42,110 --> 00:02:45,470
+اللي هو DUF
+
+30
+00:02:48,500 --> 00:02:55,560
+لجراد ال F عند النقطة P نُط بط اللي هو متجه الوحدة
+
+31
+00:02:55,560 --> 00:03:04,720
+U وفكنا هذا الكلام وقلنا ان هذا يعتبر طول لجراد F
+
+32
+00:03:05,070 --> 00:03:11,090
+فيقول ال U P Cos الزاوية تيتا لكن لما كان متجه
+
+33
+00:03:11,090 --> 00:03:16,450
+الوحدة طوله يساوي واحد صحيح إذا هذا كله بده يساوي
+
+34
+00:03:16,450 --> 00:03:23,050
+طول جراد ال F P Cos الزاوية ثانية الآن بدنا نيجي
+
+35
+00:03:23,050 --> 00:03:27,700
+لخواص هذا ال direction ال derivativeكتبنا المرة
+
+36
+00:03:27,700 --> 00:03:32,120
+اللي فاتت أنه ممكن يكون موجب ممكن يكون سالب ممكن
+
+37
+00:03:32,120 --> 00:03:38,200
+يكون صفر ممكن يكون أكبر ما يمكن ممكن أن يكون أقل
+
+38
+00:03:38,200 --> 00:03:42,800
+ما يمكن و ممكن يكون zero روحنا قولنا ال F
+
+39
+00:03:42,800 --> 00:03:47,720
+increases most strategically اللي هي النقطة هذه
+
+40
+00:03:47,720 --> 00:03:54,220
+إذا كان والله ال U grade ال V2 في نفس الاتجاه يحدث
+
+41
+00:03:54,220 --> 00:04:00,660
+هذاإن كانت θ تساوي زيرو، ثتا تساوي زيرو يعني اتنين
+
+42
+00:04:00,660 --> 00:04:05,040
+في نفس الاتجاه وبالتالي ال cosine صفر واحد وهي
+
+43
+00:04:05,040 --> 00:04:10,660
+أكبر قيمة بياخدها ال cosine وبالتالي هي أكبر قيمة
+
+44
+00:04:10,660 --> 00:04:17,520
+لل directional derivativeتمام وهي قيمة موجبة يبقى
+
+45
+00:04:17,520 --> 00:04:21,680
+positive و أكبر ما يمكن أن نحصل عليه هو اكترش لو
+
+46
+00:04:21,680 --> 00:04:25,460
+كان ال U اجراد ال F اتنين في نفس الاتجاه in the
+
+47
+00:04:25,460 --> 00:04:29,960
+same direction هذه الحالة الأولى الحالة الثانية
+
+48
+00:04:29,960 --> 00:04:35,940
+باجي بقول لو كانت ال U اجراد ال V اتجاهين متضادين
+
+49
+00:04:36,230 --> 00:04:40,830
+يبقى الزاوية بينهم كمية و تمانين درجة كسايم مية و
+
+50
+00:04:40,830 --> 00:04:47,350
+تمانين بسالب واحد وهي أصغر قيمة بياخدها كسايم ثيتا
+
+51
+00:04:47,350 --> 00:04:51,890
+يبقى بالتالي بحصل على أقل قيمة لل directional
+
+52
+00:04:51,890 --> 00:04:57,510
+derivative وقتاش لما ثيتا تساوي باي لأن كسايم باي
+
+53
+00:04:57,510 --> 00:05:03,130
+بسالب واحد في الحالة الأولى قيمة ال directional
+
+54
+00:05:03,130 --> 00:05:08,630
+derivativeبيبقى فقط قدرة جبلات في الحالة اللي طول
+
+55
+00:05:08,630 --> 00:05:13,630
+grade ال F وفي الحالة الثانية قيمة ال derivation
+
+56
+00:05:13,630 --> 00:05:19,770
+derivative اللي هو سالب grade ال F طبعا؟ طب الحالة
+
+57
+00:05:19,770 --> 00:05:25,610
+التالتةالحالة التالتة لو كان ال U وما اجراد ال V
+
+58
+00:05:25,610 --> 00:05:30,810
+اتنين are orthogonal اتنين مالهم متعامدين يبقى
+
+59
+00:05:30,810 --> 00:05:36,350
+الزاوية بينهم تسعين درجة كصين تسعين بزيرو وفي هذه
+
+60
+00:05:36,350 --> 00:05:39,610
+الحالة بقول ان ال directional derivative بدي ساوي
+
+61
+00:05:39,610 --> 00:05:44,730
+من؟ بدي ساوي زيرو يبقى لو كان ال theta تساوي pi
+
+62
+00:05:44,730 --> 00:05:52,140
+على اتنين في هذه الحالةبيكون مقدار الـ DUF كله
+
+63
+00:05:52,140 --> 00:05:56,660
+بيديه سوا قداش 0 إذا قيمة ال direction derivative
+
+64
+00:05:56,660 --> 00:06:00,760
+أحيانا ممكن تكون موجبة أحيانا ممكن تكون سالبة
+
+65
+00:06:00,760 --> 00:06:06,440
+أحيانا ممكن تكون 0أكبر قيمة بيأخدها الـ TASH إذا
+
+66
+00:06:06,440 --> 00:06:09,960
+كان الـ U قيمة الـ P في نفس الإتاجة الجزائية بينهم
+
+67
+00:06:09,960 --> 00:06:15,160
+Zero وقيمة الـ Direction Derivative عدديا يسوى فقط
+
+68
+00:06:15,160 --> 00:06:21,330
+طول قيمة الـ F وهي قيمة موجبةإذا كان اتنين في
+
+69
+00:06:21,330 --> 00:06:25,990
+اتجاهين متضادين فالـ grad الف هياخد قيمة سالبة
+
+70
+00:06:25,990 --> 00:06:29,610
+ومقدار ال direction of the derivative بدي يكون
+
+71
+00:06:29,610 --> 00:06:34,590
+سالب اللي هو طول grad الف الحالة التالتة والاخيرة
+
+72
+00:06:34,590 --> 00:06:36,830
+ان ال direction of the derivative بدي يساوي zero
+
+73
+00:06:36,830 --> 00:06:42,330
+واكتش اذا U و grad الف اتنين are orthogonal بدنا
+
+74
+00:06:42,330 --> 00:06:46,530
+نبدأ بمثال توضيحي على ذلك يبقى اكتشافي
+
+75
+00:06:52,900 --> 00:06:56,560
+طبعا هذا مكتوب معاكم من المرة الماضية اه مكتوب بس
+
+76
+00:06:56,560 --> 00:07:04,480
+انا بتذكر بتذكر لان بيقول let f of x y بده ساوي ال
+
+77
+00:07:04,480 --> 00:07:14,360
+square root لل x square زائد اتنين y نمره a find
+
+78
+00:07:14,360 --> 00:07:22,260
+the direction find the direction of
+
+79
+00:07:23,490 --> 00:07:29,510
+increasing if
+
+80
+00:07:29,510 --> 00:07:37,890
+most rapidly at
+
+81
+00:07:37,890 --> 00:07:46,870
+عند النقطة P node اللي هي أربعة وعشرة number B
+
+82
+00:07:46,870 --> 00:07:51,850
+find the direction of decreasing
+
+83
+00:07:54,170 --> 00:08:01,910
+F مصطرى بدليا من النقطة 14 نمرى C find a unit
+
+84
+00:08:01,910 --> 00:08:16,510
+vector find a unit vector تجه وحدة such that بحيث
+
+85
+00:08:16,510 --> 00:08:27,490
+ان ال DUFبدو يساوي zero at عند نفس النقطة P naught
+
+86
+00:08:27,490 --> 00:08:30,410
+of أربعة و عشر
+
+87
+00:08:47,610 --> 00:08:53,090
+يبقى هذا المثال يجيب على التلات خواب سبعة المرة
+
+88
+00:08:53,090 --> 00:08:58,210
+الماضية و اللي ذكرنا أبهم قبل قليل السؤال بيقول خد
+
+89
+00:08:58,210 --> 00:09:01,370
+ال F of X و Y بيبقى سوى ال square root لل X square
+
+90
+00:09:01,370 --> 00:09:06,010
+زي ال 2Y بيقول هاتلي ال direction of increasing F
+
+91
+00:09:06,010 --> 00:09:11,010
+most rapidly عن النقطة اللي هي 14بعدها كمالها to
+
+92
+00:09:11,010 --> 00:09:16,070
+the action of decreasing if most rapidly when عند
+
+93
+00:09:16,070 --> 00:09:21,020
+النفطة اربعة و عشرة و بعدها كانت لمتجهة الوحدةعند
+
+94
+00:09:21,020 --> 00:09:22,940
+النقطة اللي عندنا دي بيحط ال directional
+
+95
+00:09:22,940 --> 00:09:27,360
+derivative بيبقى تساوي مين؟ بيبقى تساوي Zero بقولك
+
+96
+00:09:27,360 --> 00:09:31,980
+خيص يبقى مشان أجيب أي واحد من التلات لازم ل grade
+
+97
+00:09:31,980 --> 00:09:36,160
+ال F مشان أ grade ال F أجيبها يبقى بال D مشتقة ال
+
+98
+00:09:36,160 --> 00:09:40,940
+F بالنسبة ل X و مشتقة ال F بالنسبة ل Y عند النقطة
+
+99
+00:09:40,940 --> 00:09:46,400
+من أربعة و عشرة إذا هبدأ بمين بال F X
+
+100
+00:09:50,720 --> 00:09:56,660
+مشتقة الجدر واحد على اتنين الجدر زي ما تعلمنا في
+
+101
+00:09:56,660 --> 00:10:02,760
+كل قلص ا في مشتقة ما داكل الجدر بالنسبة للعكس اللي
+
+102
+00:10:02,760 --> 00:10:03,380
+هو بيبقى
+
+103
+00:10:07,820 --> 00:10:11,600
+طيب اتنين مع اتنين الله يسهل عليها يبقى قصير
+
+104
+00:10:11,600 --> 00:10:18,160
+الناتج x على ال general تربيعي ل x تربيع زائد
+
+105
+00:10:18,160 --> 00:10:21,840
+اتنين وات بالمرة نقدر نحسب
+
+106
+00:10:41,910 --> 00:10:49,450
+يبقى الناتج 4 على 6 يبقى 2 على 3 بال middle بدنا
+
+107
+00:10:49,450 --> 00:10:58,400
+نجيب F1يجب ان يكون fy هو واحد على اتنين الجدري
+
+108
+00:10:58,400 --> 00:11:04,660
+التربيعي ل X تربيع زائدي اتنين Y في مشتقة ما تحت
+
+109
+00:11:04,660 --> 00:11:08,340
+الجدر بالنسبة الى Y لو جداش اتنين
+
+110
+00:11:22,640 --> 00:11:27,040
+عنده نقطة اربعة و عشرة اذا ماجي بيقول هذا الكلام
+
+111
+00:11:27,040 --> 00:11:33,300
+يساوي واحد على الجنري التربيهي لاربع تربيع اللي هي
+
+112
+00:11:33,300 --> 00:11:41,800
+ستاشر زائد اتنين في عشرة لعشرين ستة و تلاتين يبقى
+
+113
+00:11:41,800 --> 00:11:48,440
+الصوت بناء عليه حسبنا له قدش ل gradientللدالة R
+
+114
+00:11:48,440 --> 00:11:54,480
+عند النقطة أربعة و عشرة و اللي هي بتساوي طولتين في
+
+115
+00:11:54,480 --> 00:12:01,180
+اتجاه I زائد سُد في اتجاه M في اتجاه J إذا هذا
+
+116
+00:12:01,180 --> 00:12:05,660
+اللي هي بتلعب دور أساسي عند حساب ال directional
+
+117
+00:12:05,660 --> 00:12:11,100
+derivative للدالة اللي عندنا هنا حتى الآن لم نجيب
+
+118
+00:12:11,100 --> 00:12:17,370
+على المطلوب الأول تبع المثلمن هنا بدأت إجابة
+
+119
+00:12:17,370 --> 00:12:21,170
+المطلوب الأولى للنمرية قال هنا the direction of
+
+120
+00:12:21,170 --> 00:12:27,050
+increasing F most rapidly يبقى
+
+121
+00:12:27,050 --> 00:12:36,450
+الاتزاق اربعة و عشرة صحيح
+
+122
+00:12:36,450 --> 00:12:37,970
+طيب
+
+123
+00:12:44,070 --> 00:12:48,950
+التزايد most rapidly بيحصل وقتاش لو كان المتجه هو
+
+124
+00:12:48,950 --> 00:12:54,090
+grade ال F في نفس الاتجاه اذا انا لو جبت ال unit
+
+125
+00:12:54,090 --> 00:12:59,270
+vector تبع grade ال F بكون جبت ال direction صحيح
+
+126
+00:12:59,270 --> 00:13:06,030
+ولا لأ يبقى باجي بقول هنا ال F increasing
+
+127
+00:13:08,450 --> 00:13:17,350
+most rapidly N
+
+128
+00:13:17,350 --> 00:13:28,730
+أو F الـ U and اجراد الـ F are in the same
+
+129
+00:13:28,730 --> 00:13:33,570
+direction يبقى
+
+130
+00:13:33,570 --> 00:13:36,490
+لو كانوا في نفس الاتجاه
+
+131
+00:13:40,380 --> 00:13:48,080
+معنى هذا الكلام أن المتجه U لأنه هو grade F على
+
+132
+00:13:48,080 --> 00:13:56,150
+قول grade Fطبعا يبقى هذا الكلام بده يساوي grade ال
+
+133
+00:13:56,150 --> 00:14:01,750
+F اللي وطلعناه بروزناه يبقى تلتين في اتجاه ال I
+
+134
+00:14:01,750 --> 00:14:08,430
+زائد ست في اتجاه ال J مقسوما على ال square root
+
+135
+00:14:08,430 --> 00:14:14,150
+لاربع أتساع زائد واحد على ستة و تلاتين
+
+136
+00:14:16,550 --> 00:14:20,970
+طبعا المضاعف المشرك ستة وتلاتين على تسعة فيها
+
+137
+00:14:20,970 --> 00:14:25,870
+الأربعة في أربعة في ستاشر واحد سبعتاشر يبقى هذا
+
+138
+00:14:25,870 --> 00:14:33,030
+الكلام تلتين I زي ست جي على الجانري التربيعي
+
+139
+00:14:33,030 --> 00:14:40,190
+لسبعتاشر على ستة وتلاتينطبعا بتطلع من تحت الجدر 36
+
+140
+00:14:40,190 --> 00:14:46,150
+بال6 بتنقلبه تطلع فوق فبصير عندنا هنا 6 في هذه
+
+141
+00:14:46,150 --> 00:14:57,090
+بصير عندى قداش 4 على جدر 17 I زائد 1 على جدر 17 J
+
+142
+00:14:59,600 --> 00:15:04,280
+يبقى الاتجاه اللذي تتزيد فيه F مصر Rapidly عند
+
+143
+00:15:04,280 --> 00:15:08,000
+النقطة أربعة أو عشرة هو ال vector اللي عندنا هذا
+
+144
+00:15:08,000 --> 00:15:13,800
+كويس طب قداش مقدار ال direction ال derivative في
+
+145
+00:15:13,800 --> 00:15:18,940
+هذه الحالة وما طلبوش مني بس انا لو ادعى اسمه هو
+
+146
+00:15:18,940 --> 00:15:26,420
+مين قول ال V وين قول ال V هل تماميبقى هذا بيكون
+
+147
+00:15:26,420 --> 00:15:30,900
+طول اللي عندنا هذا فيما لو طلبه لنا نقول القيمة
+
+148
+00:15:30,900 --> 00:15:35,320
+تساوي طول جراد ال F طول جراد ال F اللي هي القيمة
+
+149
+00:15:35,320 --> 00:15:40,280
+اللي عندنا هنا يبقى جدر سبعتاشر على ستة ما علينا
+
+150
+00:15:40,280 --> 00:15:47,720
+نمرى بيه نمرى بيه نقلب ال D اتجاه التناقص يبقى
+
+151
+00:15:47,720 --> 00:15:51,780
+باجي بقوله ال F decreasing
+
+152
+00:15:56,550 --> 00:16:05,470
+decreasing most rapidly at
+
+153
+00:16:05,470 --> 00:16:14,990
+النقطة أربعة و عشرة in the direction في اتجاه مين
+
+154
+00:16:14,990 --> 00:16:21,100
+يا بنات سالب أربعةعلى سبعتاشر I على جدر سبعتاشر I
+
+155
+00:16:21,100 --> 00:16:27,780
+سالب واحد على جدر سبعتاشر J يعني عكس من؟ عكس
+
+156
+00:16:27,780 --> 00:16:33,000
+لاتجاه الأولاني تماما لأنه قلنا في اتجاه معاكس
+
+157
+00:16:33,000 --> 00:16:38,200
+لمن؟ لجراد ال F الاتجاه الأولاني هذا هو مفتجه
+
+158
+00:16:38,200 --> 00:16:43,320
+الوحدة في اتجاه جراد ال F إذا هدفي عكس تماما بكتب
+
+159
+00:16:43,320 --> 00:16:51,250
+نفس المتجه بس بإشارة مخالفةعام نمرى C و قال لي في
+
+160
+00:16:51,250 --> 00:16:53,470
+دقيقة ايه انت بتبقى بسطشان ال directional
+
+161
+00:16:53,470 --> 00:16:59,530
+derivative عنده النقطة هذه اللي هو بده ساوي زيرو
+
+162
+00:16:59,530 --> 00:17:06,610
+باجي بقولك عندنا D U F بده ساوي زيرو هذا معناته
+
+163
+00:17:06,610 --> 00:17:16,700
+انه grade ال F ضد ال U بده ساوي زيروحيث ال U
+
+164
+00:17:16,700 --> 00:17:25,220
+بسويول في اتجاه I زي U في اتجاه J is a unit vector
+
+165
+00:17:25,220 --> 00:17:31,460
+تمام؟ طيب باجي بقول لهم قعدوا اللي فيها جاهزة
+
+166
+00:17:31,460 --> 00:17:40,280
+عندنا اللي يمين تلتين I زي ست جيه كله Dot U واحد
+
+167
+00:17:40,280 --> 00:17:45,410
+في اتجاه Iيو اتنين في اتجاه الجهد كله بده يساوي
+
+168
+00:17:45,410 --> 00:17:57,030
+زيرو او بمعنى اخر تلتين يو اتنين زيادة سادس يوتو
+
+169
+00:17:57,030 --> 00:18:03,510
+بده يساوي كده؟ بده يساوي زيرو لو ضربت كله في ستة
+
+170
+00:18:03,510 --> 00:18:11,070
+عشان اتخلص من الكثور اربع يو اتنين زيادة سادسيوتو
+
+171
+00:18:11,070 --> 00:18:16,510
+بدل ساوي زيك ضربت المعادلة كلها في ستة يبقى هذا
+
+172
+00:18:16,510 --> 00:18:25,630
+بدي أقيني أن يوتو بدل ساوي سالب أربعة في اليوة طيب
+
+173
+00:18:25,630 --> 00:18:31,590
+هذه أولاق بتربط بين مجهولين يواحد و يتنين عشان
+
+174
+00:18:31,590 --> 00:18:37,110
+أقدر أجيب القيمة هذه بلزمني كمان معادلة من أين بدي
+
+175
+00:18:37,110 --> 00:18:42,280
+أجيب المعادلة؟قول متجه الواحدة المعروف الواحد صحيح
+
+176
+00:18:42,280 --> 00:18:49,660
+بروح بقوله ب .. ولكن ب .. اللي هو U واحد تربيع
+
+177
+00:18:49,660 --> 00:18:55,340
+زائد U اتنين تربيع تحت الجدر التربيعي كله بتتساوي
+
+178
+00:18:55,340 --> 00:19:01,780
+واحد رابع الطرفين بصير U واحد تربيع زائد U اتنين
+
+179
+00:19:01,780 --> 00:19:06,020
+تربيع تتساوي واحد طيب
+
+180
+00:19:06,440 --> 00:19:13,740
+يبقى ال U واحد تربيع زاد ال U اتنين لو سالف اربع U
+
+181
+00:19:13,740 --> 00:19:20,540
+واحد يبقى سالف اربع U واحد يبقى تربيع يساوي واحد
+
+182
+00:19:20,540 --> 00:19:24,060
+يبقى
+
+183
+00:19:24,060 --> 00:19:35,030
+سبعتاش يبقى سبعتاش U تربيع يساوي واحدالـ U1 تساوي
+
+184
+00:19:35,030 --> 00:19:43,910
+زائد أو ناقص واحد على ال square root لمين ل 17 إذا
+
+185
+00:19:43,910 --> 00:19:48,490
+طلع عندي مش مستجد واحد و أنا ما جداش اتنين فبجي
+
+186
+00:19:48,490 --> 00:20:00,710
+بقوله if ال U1 يساوي واحد على جدر 17 then ال U2
+
+187
+00:20:00,710 --> 00:20:09,060
+تساويسالف أربعة في واحد على جذر السبعتاشر المعادلة
+
+188
+00:20:09,060 --> 00:20:12,100
+من أين؟ المعادلة اللي عندك فيها دي اللي هي star
+
+189
+00:20:12,100 --> 00:20:21,360
+منها بشيل ال U وال و بحط قمتها يبقى بناء عليه هذا
+
+190
+00:20:21,360 --> 00:20:31,190
+أعطاني أن المتجه U هو عبارة عنU1 على جذر 17 في
+
+191
+00:20:31,190 --> 00:20:41,150
+اتجاه I ماقص 4 على جذر 17 في اتجاه J الحالة
+
+192
+00:20:41,150 --> 00:20:51,310
+التانية لو كان U1 سالب 1 على جذر 17يو اتنين يسوى
+
+193
+00:20:51,310 --> 00:20:59,370
+سالب اربع في سالب واحد على جذر سبعتاشر ويسوى اربع
+
+194
+00:20:59,370 --> 00:21:07,270
+على من اربع على جذر سبعتاشر
+
+195
+00:21:07,270 --> 00:21:15,030
+هو يبقى بناء عليه المتجه يو هو عبارة عن اللي هو
+
+196
+00:21:15,030 --> 00:21:24,360
+السالب1 على جدر 17 في اتجاه I زائد 4 على جدر 17 في
+
+197
+00:21:24,360 --> 00:21:31,360
+اتجاه J يعني عندي بدل المتجه اتنين بيحققولي هذه
+
+198
+00:21:31,360 --> 00:21:34,900
+المعادلة بيخيلولي ال direction derivative عند هذه
+
+199
+00:21:34,900 --> 00:21:37,800
+النقطة بده ساوي Zero
+
+200
+00:22:16,060 --> 00:22:20,660
+بنجي لعنوان جديد برضه في نفس ال section نجي لحاجات
+
+201
+00:22:20,660 --> 00:22:26,740
+يسمى gradients gradients
+
+202
+00:22:26,740 --> 00:22:31,420
+and tangents
+
+203
+00:22:31,420 --> 00:22:37,920
+والممثل
+
+204
+00:22:37,920 --> 00:22:39,720
+في level curves
+
+205
+00:22:58,440 --> 00:23:07,620
+f of x1 as a
+
+206
+00:23:07,620 --> 00:23:16,400
+constant value والتي تكون c على سبيل المثال along
+
+207
+00:23:16,400 --> 00:23:19,500
+a
+
+208
+00:23:19,500 --> 00:23:20,660
+smooth curve
+
+209
+00:23:26,290 --> 00:23:37,570
+العلم اللي اسمه R R of T هو G of T في اتجاه I زائد
+
+210
+00:23:37,570 --> 00:23:41,190
+H of T في اتجاه J
+
+211
+00:23:48,400 --> 00:23:56,080
+اللي هو G of T وكذلك H of T كله بده يساوي constant
+
+212
+00:23:56,080 --> 00:24:02,000
+C as A level K
+
+213
+00:24:40,980 --> 00:24:53,460
+هذا هو قيمة
+
+214
+00:24:53,460 --> 00:24:58,600
+الدلة يسوي مقدارا ثابتا along a small curve R of T
+
+215
+00:24:58,600 --> 00:25:03,320
+يسوي G of T في اتجاه I زادتش من T في اتجاه T كل من
+
+216
+00:25:03,320 --> 00:25:11,060
+X وY هي function في T كأن X هي G of T وYهي H of T
+
+217
+00:25:11,060 --> 00:25:16,040
+ثم F of G of T و H of T بدل ساوية ماذا؟ بدل ساوية
+
+218
+00:25:16,040 --> 00:25:21,820
+الكنستنسي بالضبط تماماو في هذه الحالة بسميها level
+
+219
+00:25:21,820 --> 00:25:26,300
+k طبعا لو راجعنا بالذاكره الى الوراء الى section
+
+220
+00:25:26,300 --> 00:25:31,140
+14-1 فقنا بنقوله بنجي على ال function و بنسويها
+
+221
+00:25:31,140 --> 00:25:37,080
+كنصة إذا سوناها كنصة فهذا بيكون level k بشرط انه
+
+222
+00:25:37,080 --> 00:25:41,340
+تبقى ال function ده اللي فيه متغيرين أما إن كانت
+
+223
+00:25:41,340 --> 00:25:44,380
+ده اللي فيه ثلاثة متغيرات بسميها
+
+224
+00:25:54,320 --> 00:26:02,030
+يبقى سارة اندي تدالها لما سويها بـCيبقى هذا بيسميه
+
+225
+00:26:02,030 --> 00:26:06,210
+level K يعني طيب تعالوا فنفضلها و نشوف كده شهدها
+
+226
+00:26:06,210 --> 00:26:11,490
+الساوية ففضلها كيف؟ اه احنا خدنا chain rule لو
+
+227
+00:26:11,490 --> 00:26:17,350
+كانت F ده اللي فيه متغيرين و كل متغير ده اللي فيه
+
+228
+00:26:17,350 --> 00:26:22,690
+متغير اخر مظبوط فكنا بنقول ايش؟ كنا بنقول
+
+229
+00:26:39,450 --> 00:26:48,430
+متغير واحد بشتقة كلية يبقى في dx على dt زائد
+
+230
+00:26:48,430 --> 00:26:58,730
+partial f على partial y في dy على dt ممتاز
+
+231
+00:26:58,730 --> 00:27:06,560
+جدا طيب الآن ال x مين عندي؟من أجابة كانت؟ G of T
+
+232
+00:27:06,560 --> 00:27:15,380
+يبقى هذي كإنهاراش partial F على partial X في DG
+
+233
+00:27:15,380 --> 00:27:27,240
+على DT زائد partial F على partial Y في DH على DT
+
+234
+00:27:27,240 --> 00:27:28,160
+بيبقى سوى Z
+
+235
+00:27:31,670 --> 00:27:35,910
+مابيقش رأيك هذا dot product بين متجهين وانا مش
+
+236
+00:27:35,910 --> 00:27:42,650
+داري كيف dot product بين متجهين بقول اه تعالي شوفي
+
+237
+00:27:42,650 --> 00:27:47,170
+هذه المدرسة اكتفها على الشكل التالي partial F على
+
+238
+00:27:47,170 --> 00:27:54,150
+partial X في اتجاه I زائد partial F على partial Y
+
+239
+00:27:54,150 --> 00:27:57,350
+في اتجاه G dot
+
+240
+00:28:12,050 --> 00:28:16,310
+على دي تي في اتجاه اللي هي بده يساوي زيرو لو عملت
+
+241
+00:28:16,310 --> 00:28:21,010
+ضغط مرضي الملتنة مش هفتطعلي فوق هالي صح ولا لأ طيب
+
+242
+00:28:21,010 --> 00:28:27,930
+ده جنهان هي تعريف مين يا بناها ليه grade يعني
+
+243
+00:28:27,930 --> 00:28:33,990
+grade تبع الدل اف تمام يبقى هذه هي grade الاف
+
+244
+00:28:41,810 --> 00:28:46,170
+صح ولا لأ؟ إذا بقدر أشيل هذه و أكتب عليها DR على
+
+245
+00:28:46,170 --> 00:28:55,890
+DT يبقى هذا معناته DR على DT قداش ما تش ساوي0 إذا
+
+246
+00:28:55,890 --> 00:29:01,230
+انا عندي متجهين واحد اسمه Gradle F والثاني DR على
+
+247
+00:29:01,230 --> 00:29:05,450
+DT بطل product بينهم بسوق ال Dates بسوق Gradle
+
+248
+00:29:05,450 --> 00:29:10,710
+الاتنين مالهم تقولك يبقى اتنين هذول مالهم متعامدين
+
+249
+00:29:10,710 --> 00:29:14,130
+طب شوفي هذا إيش بفيدني ساعدني أخلي بالكم معايا
+
+250
+00:29:14,130 --> 00:29:21,910
+طلعوا عينيك كويس الان DR على DT مش هي مستقلتها دي
+
+251
+00:29:21,910 --> 00:29:27,550
+طب مستقلتها دي شو بتفيدنيال V ممتاز جدا يبقى هذا
+
+252
+00:29:27,550 --> 00:29:32,490
+مشتقتها هذا عبارة عن ال velocity طب ال velocity و
+
+253
+00:29:32,490 --> 00:29:36,690
+اتجاه الحركة و ال tangent مش كله في اتجاه الواحد
+
+254
+00:29:36,690 --> 00:29:43,410
+يبقى هذا كأنه مين كأنه tangent لمين لو ال tangent
+
+255
+00:29:43,410 --> 00:29:50,860
+vector لجسم يتحرك في الفراغ عند نقطة ماكويس؟ يبقى
+
+256
+00:29:50,860 --> 00:29:56,440
+هذا كأنه إيش؟ كأنه grade ال F و ال tangent مالهم
+
+257
+00:29:56,440 --> 00:30:04,620
+اتنين R Orthogonal يبقى هذا هو V وبالتالي هذا هو
+
+258
+00:30:04,620 --> 00:30:08,720
+ال unit هو ال tangent vector و ليس ال unit او ال
+
+259
+00:30:08,720 --> 00:30:14,260
+tangent vector و اتنين هذا R Orthogonal هذا معناته
+
+260
+00:30:14,260 --> 00:30:22,080
+ان grade ال Fand the
+
+261
+00:30:22,080 --> 00:30:37,140
+tangent to the curve are orthogonal كيف
+
+262
+00:30:37,140 --> 00:30:42,720
+هذا الكلام؟ يعني عملت لو جيت تخيلت على سبيل المثال
+
+263
+00:30:42,720 --> 00:30:52,440
+أن هذا كان level curveهذا كان level care هذا
+
+264
+00:30:52,440 --> 00:30:55,980
+واحد منهم من ال level cares كويس و بجيت عنده نقطة
+
+265
+00:30:55,980 --> 00:31:03,860
+مثل هذه النقطة كويس و روحت رسام ال tangent يبقى
+
+266
+00:31:03,860 --> 00:31:12,800
+هذا كان ال tangent اللي عندنا اللي هو من ال T إذا
+
+267
+00:31:13,430 --> 00:31:18,870
+العمودي علي إجراد ال F بيكون بالشكل اللي عندنا هذا
+
+268
+00:31:18,870 --> 00:31:26,310
+الزاوية قائمة وهذا بيكون بهمين إجراد ال F يبقى
+
+269
+00:31:26,310 --> 00:31:31,490
+إجراد ال F والT اتنين are orthogonal من هنا كان
+
+270
+00:31:31,490 --> 00:31:32,950
+بالشكل اللي عندنا
+
+271
+00:31:35,790 --> 00:31:40,690
+ماذا في عندي tangent line عند نقطة على level
+
+272
+00:31:40,690 --> 00:31:46,230
+surface إذا بروح أدور على معادلة هذا ال tangent
+
+273
+00:31:46,230 --> 00:31:52,310
+كويس إذا بروح أحط عنوان جانب صغير اللي هو equation
+
+274
+00:31:52,310 --> 00:31:54,010
+of the tangent line
+
+275
+00:31:57,740 --> 00:32:07,740
+equation of the tangent line
+
+276
+00:32:07,740 --> 00:32:11,920
+to a level k
+
+277
+00:32:31,410 --> 00:32:39,050
+الان بحاول احسب معادلة تانجنت
+
+278
+00:32:39,050 --> 00:32:46,330
+lineعند النقطة اللى عندنا هذا كيف بنحسب هذه
+
+279
+00:32:46,330 --> 00:32:51,710
+المعادلة بقول بسيطة جدا بدي استخدم فكرة dot
+
+280
+00:32:51,710 --> 00:32:57,690
+product في main في إيجاد هذه المعادلة تبعت من تبعت
+
+281
+00:32:57,690 --> 00:33:03,690
+tangent line يبقى بنروح نستخدم هذه في اللى هو
+
+282
+00:33:03,690 --> 00:33:09,540
+إيجاد هذه المعادلة و العمودي عندنا هنا mainاللي هو
+
+283
+00:33:09,540 --> 00:33:15,660
+ال gradient vector مظبوط او لا؟ طيب انا بدي اروح
+
+284
+00:33:15,660 --> 00:33:20,100
+احنا دلوقتي ال tangent line مش ال tangent vector
+
+285
+00:33:20,100 --> 00:33:23,640
+يبقى ال tangent line بقى الوسط ال parametric
+
+286
+00:33:23,640 --> 00:33:29,960
+equations تمام؟ يبقى ال parametric equations هدول
+
+287
+00:33:29,960 --> 00:33:37,990
+بتكون من نقطةاللي هي نقطة التماس هذه على سبيل
+
+288
+00:33:37,990 --> 00:33:43,150
+المثال يعني لو قلت هذه النقطة هي X node وY node
+
+289
+00:33:43,150 --> 00:33:51,190
+وانا بدي معادلة المماس الموازي لل unit tangent
+
+290
+00:33:51,190 --> 00:33:57,530
+vector بيض موازي لل unit tangent vector إذا بدي
+
+291
+00:33:57,530 --> 00:34:04,990
+أجيب المعادلة كتاليكويس؟ يبقى بتروح اخد اي نقطة
+
+292
+00:34:04,990 --> 00:34:09,890
+موجودة على هذا ال line على سبيل المثال و التكن
+
+293
+00:34:09,890 --> 00:34:17,730
+النقطة هذه النقطة هذه ليه اكس او اكس و واي كان
+
+294
+00:34:17,730 --> 00:34:25,470
+اعدادي تبعك كويس؟ طيب الانالـ unit tangent vector
+
+295
+00:34:25,470 --> 00:34:30,390
+مش ال unit tangent line مش عفر مش ال .. ال .. ال
+
+296
+00:34:30,390 --> 00:34:33,690
+.. مش ال .. فش حاجة اسمها unit tangent line يبقى
+
+297
+00:34:33,690 --> 00:34:37,150
+بقول ال tangent line ماعنديش هنا يبقى انا باجي
+
+298
+00:34:37,150 --> 00:34:41,210
+بقول ال unit tangent vector مع ال grade لف اتنين
+
+299
+00:34:41,210 --> 00:34:46,290
+مالهم are orthogonal اتنين اخر مالهم متعاملين اذا
+
+300
+00:34:46,290 --> 00:34:51,350
+نضبطي product بينهم دي سوى كده؟ zero بناء انا عليه
+
+301
+00:34:51,350 --> 00:34:58,970
+فبروح بقوله ايش؟عندنا هنا اللي هو مين؟ العقود اللي
+
+302
+00:34:58,970 --> 00:35:04,390
+هو grade ال F احنا اه هنا باجي بقوله هنا grade ال
+
+303
+00:35:04,390 --> 00:35:12,290
+F بارة ضغط مين؟ المتجه اللي عندنا هذا اللي هو بدي
+
+304
+00:35:12,290 --> 00:35:18,930
+اسميه على سبيل المثال المتجه N بدي اسوي مين؟ Zero
+
+305
+00:35:18,930 --> 00:35:27,180
+كويس، يبقى هذا شو معناه؟زادة fx عند النقطة x node
+
+306
+00:35:27,180 --> 00:35:32,580
+و y node في اتجاه الـ I زادة fy عند النقطة x node
+
+307
+00:35:32,580 --> 00:35:40,960
+و y node في اتجاه الـ J كله Dot دل
+
+308
+00:35:40,960 --> 00:35:46,880
+المتجه اللي عالنا هذا اللي هو مين؟ x ماقص x node
+
+309
+00:35:46,880 --> 00:35:53,550
+في اتجاه الـ IY نقص Y node في اتجاه الـ J كله ساوي
+
+310
+00:35:53,550 --> 00:36:02,270
+0 لو روحت فكرة هذه ليس بيصير Fx عند نقطة X node وY
+
+311
+00:36:02,270 --> 00:36:11,310
+node في X نقص X node زائد Fy عند نقطة X node وY
+
+312
+00:36:11,310 --> 00:36:19,980
+node في Y نقص Y node كله ساوي مين؟ ساوي 0السؤال هو
+
+313
+00:36:19,980 --> 00:36:27,260
+هل هذه معادلة خط مستقيم؟ تعالوا نشوف ال Fx عندها
+
+314
+00:36:27,260 --> 00:36:31,000
+نقطة يا بنات هذا دلة ولا رقم number؟
+
+315
+00:36:46,900 --> 00:36:53,580
+معادلة خاط المستقيم يبقى هذه معادلة الخاط المستقيم
+
+316
+00:36:53,580 --> 00:36:58,940
+اللي احنا قاعدين ندور عليها او اللي احنا بدنا يعني
+
+317
+00:36:58,940 --> 00:37:00,680
+يبقى هذه ال equation
+
+318
+00:37:16,170 --> 00:37:24,670
+نبقى هذه المعادلة المطلوبة ناخد مثال عليه نبقى
+
+319
+00:37:24,670 --> 00:37:25,170
+example
+
+320
+00:37:38,770 --> 00:37:46,370
+the curve ورسم المنحنى x تربيه على ناقص واي تساوي
+
+321
+00:37:46,370 --> 00:37:55,110
+واحد together with two together with تقري هاد ال F
+
+322
+00:37:55,110 --> 00:38:06,110
+and the tangent line and the tangent line وخط
+
+323
+00:38:06,110 --> 00:38:15,290
+التمامat the point at the point عند النقطة اللي هو
+
+324
+00:38:15,290 --> 00:38:23,050
+جذر اتنين و واحد and write an equation and write
+
+325
+00:38:23,050 --> 00:38:29,890
+an equation و بده نكتب معادلة for the tangent line
+
+326
+00:38:29,890 --> 00:38:36,830
+for the tangent line
+
+327
+00:38:39,590 --> 00:38:44,450
+وبنقدرش او ما هو شكل معادلة خط التماس
+
+328
+00:39:09,620 --> 00:39:14,140
+برجع للسؤال مرة تانية بقول لي ارسم للمنحنة اللي
+
+329
+00:39:14,140 --> 00:39:18,950
+عندنا هذامع مين؟ together with degree of F ترسم
+
+330
+00:39:18,950 --> 00:39:25,050
+على الرسمة degree of F and tangent line وخط التماس
+
+331
+00:39:25,050 --> 00:39:28,870
+عند النقطة يبقى with degree of F وخط التماس عند
+
+332
+00:39:28,870 --> 00:39:32,690
+النقطة للملحنة اللي موجودة عندنا وبعد هيك نجيب
+
+333
+00:39:32,690 --> 00:39:38,170
+المعادلة يبقى مطلوبين يهم الرسم زائد معادلة
+
+334
+00:39:38,170 --> 00:39:43,070
+tangent line لمين؟ للخط المستقبل اللي عندنا أو خط
+
+335
+00:39:43,070 --> 00:39:46,770
+التماسبقوله قويس هو ال function اللي عندي وين هي
+
+336
+00:39:46,770 --> 00:39:50,690
+عشان اجيب له grade ال F بالزمن ال function وين ال
+
+337
+00:39:50,690 --> 00:39:54,230
+function هذه؟ مش ماطيني ال function لكن ماطيني
+
+338
+00:39:54,230 --> 00:39:58,330
+مين؟ اللي بال curve اللي بال curve ال function
+
+339
+00:39:58,330 --> 00:40:02,250
+بسويها بمين؟ ب constant يبقى ال function الأساسية
+
+340
+00:40:02,250 --> 00:40:09,310
+مين هي يا بنات؟ F of X Y تساوي X تربيه ناقص Y يبقى
+
+341
+00:40:09,310 --> 00:40:14,540
+باجي بقوله هناهذا level curve يبقى المعادلة
+
+342
+00:40:14,540 --> 00:40:20,420
+الأصلية أو ال function الأصلية هي من هنا ال f of x
+
+343
+00:40:20,420 --> 00:40:27,240
+و y اللي هو بدها تساوي x تربيه ناقص y لأنه أنا لما
+
+344
+00:40:27,240 --> 00:40:31,200
+بجيبي level curve بساوي المعادلة اللي عندي أو
+
+345
+00:40:31,200 --> 00:40:36,500
+الدالة اللي عندي بمقدار ثابت بمقدار ثابت يبقى هذه
+
+346
+00:40:36,500 --> 00:40:41,560
+أصل المعادلة اللي موجود عنديبقول له خيص اذا احنا
+
+347
+00:40:41,560 --> 00:40:46,600
+مشان نجيب المعادلة اللى عندنا بلزم نجد كله من Fx و
+
+348
+00:40:46,600 --> 00:40:51,880
+Fy وين عند النقطة المعطاعة هبروح بقول له هنا بدي
+
+349
+00:40:51,880 --> 00:41:00,260
+اجيب له Fx يبقى تفاضل F نسم ال X له كده؟ ب2X و
+
+350
+00:41:00,260 --> 00:41:00,980
+بالمرة
+
+351
+00:41:04,170 --> 00:41:09,250
+عند النقطة جدري اتنين واحد المعطاع يبقى قدر ما
+
+352
+00:41:09,250 --> 00:41:16,490
+تساوي اتنين جدري اتنين بعد هيك بيروح اجيب له fy
+
+353
+00:41:16,490 --> 00:41:25,560
+كده يبقى له قدروهذا بده يعطيك انه fy عند النقطة
+
+354
+00:41:25,560 --> 00:41:29,260
+جدري اتنين وواحد والسالي بواحد كل وصف انت مالوش
+
+355
+00:41:29,260 --> 00:41:34,940
+دعوة بمين بالمتغيرات اذا البناء عليها حصلت على مين
+
+356
+00:41:34,940 --> 00:41:40,560
+على grade ال F اللي بدنا يها أوي للزمان على اي حال
+
+357
+00:41:40,560 --> 00:41:43,740
+هل مطلوب اكتبها و الله اذا كان مطلوب اكتبها مش
+
+358
+00:41:43,740 --> 00:41:48,440
+مطلوبها اي مركبة انت خلاص جاهزة طب كويس قال هو ايش
+
+359
+00:41:48,440 --> 00:41:53,310
+ارسم المنحنةوارسوم ل grade ال F اذا انا بتروح
+
+360
+00:41:53,310 --> 00:41:59,910
+اقوله grade ال F عند النقطة جذر اتنين او واحد هي
+
+361
+00:41:59,910 --> 00:42:07,250
+اتنين جذر اتنين في اتجاه I ناقص G يبقى هذه اللي
+
+362
+00:42:07,250 --> 00:42:13,390
+بتلعب دور كبير وياه في المسألة ابتعدطيب خليني اروح
+
+363
+00:42:13,390 --> 00:42:18,410
+نرسم اللي هو التسلسل في الترتيب تبع المطلوب تبع
+
+364
+00:42:18,410 --> 00:42:23,790
+المثلة خليني اروح نرسم وبعد هيك بصير خير ايوة
+
+365
+00:42:23,790 --> 00:42:31,290
+فبجيب درسم ايش بقوله هنا ال level level
+
+366
+00:42:31,290 --> 00:42:34,370
+KF
+
+367
+00:42:34,370 --> 00:42:38,230
+S
+
+368
+00:42:38,230 --> 00:42:40,210
+اللي هو مين؟
+
+369
+00:42:43,480 --> 00:42:51,840
+ممكن اكتبه بشكل اخر وهو y تساوي x ترمية نقص واحد
+
+370
+00:42:51,840 --> 00:42:55,340
+معادلة ايش دي يا بنات برابرها بس في الأول ماكنتش
+
+371
+00:42:55,340 --> 00:43:00,540
+واضحة لكن عكت ترتيبها صارت المعادلة سهلة وميسورة
+
+372
+00:43:00,540 --> 00:43:07,120
+لو روحت ارسلها بقيت بقول هي المحاول هي ان محور x
+
+373
+00:43:07,950 --> 00:43:13,550
+هذا محور Y وهذا نقطة الاصل اللي هي Zero يمكن هذه
+
+374
+00:43:13,550 --> 00:43:19,250
+أصل الدالة Y تساوي X تربيع بس Shift لأسفل بمقدار
+
+375
+00:43:19,250 --> 00:43:26,850
+واحد طب بدأ أجيب نقطة تقاطعها مع محور X يبقى بحط Y
+
+376
+00:43:26,850 --> 00:43:32,750
+بدأت Zero بصير X زاد أو ناقص واحد يبقى البرامج
+
+377
+00:43:32,750 --> 00:43:37,700
+هتمار غير نقطة واحدوهتمر بالنقطة مين؟ اللي هو سالب
+
+378
+00:43:37,700 --> 00:43:43,580
+واحد وهنا بتجينا من وين؟ من عند السالب واحد يبقى
+
+379
+00:43:43,580 --> 00:43:48,880
+هذه الفرابنة اللي عندنا ومن هنا بتجينا بالشكل اللي
+
+380
+00:43:48,880 --> 00:43:56,500
+عندنا درجة يبقى هذه الفرابنة Y تساوي X تربيع ماقص
+
+381
+00:43:56,500 --> 00:44:03,000
+واحدطيب تمام تمام بدي أجل النقطة جذري اتنين و واحد
+
+382
+00:44:03,000 --> 00:44:06,320
+جذري اتنين و واحد واربعة من عشرة يعني وين بدها
+
+383
+00:44:06,320 --> 00:44:09,720
+تجيلي هاي واحد واربعة من عشرة نفسها بدها تجي
+
+384
+00:44:09,720 --> 00:44:13,940
+تقريبا هنا و أطلع بتكون عندنا مية النقطة اللي
+
+385
+00:44:13,940 --> 00:44:17,820
+عندنا هي جيبكي النقطة هذه اللي هي جذري اتنين و
+
+386
+00:44:17,820 --> 00:44:22,800
+واحد بالشكل اللي عندنا هنا الان في مماس المماس
+
+387
+00:44:22,800 --> 00:44:24,220
+اللي عندنا بهذا الشكل
+
+388
+00:44:32,570 --> 00:44:39,670
+الخطة الأزرق اللي انت شايفينها هي
+
+389
+00:44:39,670 --> 00:44:45,790
+عمّجناها بالأزرق لكي نبين للكون لأن
+
+390
+00:44:45,790 --> 00:44:51,170
+هذا خط التماسك مثل المنحنة عند النقطة اللي عندنا
+
+391
+00:44:51,170 --> 00:44:51,770
+هذه
+
+392
+00:44:54,770 --> 00:44:58,250
+الان قال لي ارسم المنحنى و رسمنا له المنحنى ارسم
+
+393
+00:44:58,250 --> 00:45:02,530
+الماس و رسمنا له الماس مين ضايقني جراد ال F اه
+
+394
+00:45:02,530 --> 00:45:07,970
+جراد ال F جراد ال F قاللي له اتنين جذري اتنين في
+
+395
+00:45:07,970 --> 00:45:14,710
+اتجاه ال I ناقص J إذا بدي أجي أرسم هذا بدي أنسبه
+
+396
+00:45:14,710 --> 00:45:19,710
+إلى نقطة الأصل و بعدين بحركه زي ما بدي صحيح؟ يبقى
+
+397
+00:45:19,710 --> 00:45:24,010
+لو J تتحرك اتنين جذري اتنين اه اتنين جذري اتنين
+
+398
+00:45:24,330 --> 00:45:27,650
+يبقى يا بنات جدر اتنين اللي هو واحد واربعة من عشرة
+
+399
+00:45:27,650 --> 00:45:34,250
+هذي جدر اتنين تمام اتنين جدر اتنين كمان جدها مرتين
+
+400
+00:45:34,250 --> 00:45:40,950
+يبقى بدي امد هذا محور X امشي على طول الخط يبقى هذا
+
+401
+00:45:40,950 --> 00:45:46,990
+محور X بتاخد مسافة جد هذه مرتين يبقى بتجيك نقطة
+
+402
+00:45:46,990 --> 00:45:52,510
+تقريبا هنا يبقى هذا النقطة اللي هي اتنين جدر اتنين
+
+403
+00:45:52,970 --> 00:45:58,370
+بدي أنزل كده؟ سالب واحد يبقى بدي أنزل سالب واحد
+
+404
+00:45:58,370 --> 00:46:03,910
+الى النقطة اللى عندنا طبعا يبقى لو جيت ووصلت من
+
+405
+00:46:03,910 --> 00:46:09,670
+نقطة الأصل هيك بيكون هذا اتنين جدري اتنين في اتجاه
+
+406
+00:46:09,670 --> 00:46:18,210
+الاي ناقص جي هذا كله main اللى هو اجراد ال F لكن
+
+407
+00:46:18,210 --> 00:46:21,800
+اجراد ال F هو اللى بدرسوه بهاعند النقطة احنا بنعرف
+
+408
+00:46:21,800 --> 00:46:27,600
+ان المتجه ممكن يساوي متجه اول و تاني و تالت و زي
+
+409
+00:46:27,600 --> 00:46:34,020
+ما بدي مادام في نفس المقدار و في نفس الاتجاه يبقى
+
+410
+00:46:34,020 --> 00:46:38,480
+بقدر احرك المتجه هذا زي ما بدي اذا المتجه هذا بدي
+
+411
+00:46:38,480 --> 00:46:44,380
+تكون هيحرك بالازرق يا بنات بهذا الشكل بديكون هو
+
+412
+00:46:44,380 --> 00:46:51,820
+المتجه العمودي تقريبا يا اللهيبقى هذا main هذا
+
+413
+00:46:51,820 --> 00:46:57,440
+المتجه اللي عندنا هذا يبقى هذا اللي هو grade ال F
+
+414
+00:46:57,440 --> 00:47:03,630
+كذلك هذا grade ال F و هذا الموازي بالضبط تمامطيب
+
+415
+00:47:03,630 --> 00:47:09,390
+هاي رسمنا المنتجة رسمنا المنحنة رسمنا grad فاش
+
+416
+00:47:09,390 --> 00:47:13,990
+ضايل عليه المعادلة هاي المعادلة قدامي بس بداتي
+
+417
+00:47:13,990 --> 00:47:18,870
+اعوض فيها يبقى ال F X حسبتها عند النقطة اللي هي
+
+418
+00:47:18,870 --> 00:47:24,110
+كدوش كانت اتنين جادريك اتنين يبقى باجي بقوله that
+
+419
+00:47:24,110 --> 00:47:37,880
+equation of the tangent line Sإتنين جدري اتنين هي
+
+420
+00:47:37,880 --> 00:47:44,880
+قيمة ال Fx في مين؟ في ال X ناقص X naught اللي جدري
+
+421
+00:47:44,880 --> 00:47:49,760
+اتنين زائد و الله ناقص طبعا لأن هذا الحظ
+
+422
+00:48:09,840 --> 00:48:15,560
+زائد واحد بده يساوي قدرت بده يساوي Zero او ال Y
+
+423
+00:48:15,560 --> 00:48:22,400
+بده يساوي اللي هو اتنين جذري اتنين X و هنا ناقص
+
+424
+00:48:22,400 --> 00:48:26,900
+تلت اذا هنا ناقص تلت انا مش شايف اللي اقنعه و زي
+
+425
+00:48:26,900 --> 00:48:31,320
+ما انت شايفها معادلة من الدرجة الاولى في كل من X و
+
+426
+00:48:31,320 --> 00:48:36,540
+Y إذا هي معادلة ايش معادلة خاط مستقيم
+
+427
+00:49:02,220 --> 00:49:06,960
+زي ما تشوفون يا بنات ال gradient vector كأنه مؤثر
+
+428
+00:49:06,960 --> 00:49:11,860
+تفاضلي، ليه؟ لأنه grad F partial F by partial X في
+
+429
+00:49:11,860 --> 00:49:15,160
+اتجاه ال I partial F by partial Y في اتجاه ال Z،
+
+430
+00:49:15,160 --> 00:49:20,760
+تمام؟ طيب، إذا هذا له قواعد لاشتقاق العادية
+
+431
+00:49:20,760 --> 00:49:25,920
+المتعرف عليها بالنسبة للدوال العادية، هروح نذكر
+
+432
+00:49:25,920 --> 00:49:34,380
+بهذه القواعد كالتالي الgebra rulesالجيبرا rules
+
+433
+00:49:34,380 --> 00:49:46,080
+القواعد الجابرية for gradients نمري
+
+434
+00:49:46,080 --> 00:49:54,300
+واحد لو بدي إجراء لمن؟ لل K في ال F طبعا ال K مقدر
+
+435
+00:49:54,300 --> 00:50:01,910
+ثابت يبقى هذا K في جراد ال Fوالـ K is a real
+
+436
+00:50:01,910 --> 00:50:13,510
+number بعدد حقيقي اتنين Gradient ل ال F زائد او
+
+437
+00:50:13,510 --> 00:50:18,850
+ناقص G يعني كأنه مشتقة ال F زائد او ناقص G يبقى
+
+438
+00:50:18,850 --> 00:50:24,510
+مشتقة الدالة الأولى زائد او ناقص مشتقة الدالة
+
+439
+00:50:24,510 --> 00:50:32,060
+الثانية نمرها تلاتةمشتقة F في G أو الـ Gradient
+
+440
+00:50:32,060 --> 00:50:38,200
+للـ F في G ماجي بقول الدالة الأولى في ال Gradient
+
+441
+00:50:38,200 --> 00:50:44,140
+Vector للدالة الثانية زائد الدالة الثانية لل
+
+442
+00:50:44,140 --> 00:50:49,040
+Gradient Vector لمن؟ للدالة الأولى، فلو كان ضرب،
+
+443
+00:50:49,040 --> 00:50:56,640
+لو كان قسمة اما اربع ال Gradient لل F على Gبقيت
+
+444
+00:50:56,640 --> 00:50:59,800
+أقول المقام في مجتقة ال bus نقص ال bus في مجتقة
+
+445
+00:50:59,800 --> 00:51:03,740
+المقام على مربع المقام الأصلي يبقى نفس النتجة بدأت
+
+446
+00:51:03,740 --> 00:51:10,000
+أقول المقام في ال gradient لل F نقص ال F في ال
+
+447
+00:51:10,000 --> 00:51:17,800
+gradient ل G كله على مين على G تربيع وبشرط إن ال G
+
+448
+00:51:17,800 --> 00:51:25,200
+هذه ما لها ممنوعة ساوي زيو طيب
+
+449
+00:51:26,420 --> 00:51:31,060
+من أول مبادرة المحاضرة الماضية وحتى هذه اللحظة و
+
+450
+00:51:31,060 --> 00:51:35,960
+احنا بنتكلم على functions في مين؟ في two variables
+
+451
+00:51:35,960 --> 00:51:41,380
+فقط هل هذا الكلام صحيح ل three variables او
+
+452
+00:51:41,380 --> 00:51:48,580
+invariables هذا ما سنشير اليه الآن طبعا صحيح ولا
+
+453
+00:51:48,580 --> 00:51:55,140
+مشكلة في ذلك فبتقول ال functions of three
+
+454
+00:51:55,140 --> 00:52:05,100
+variablesof three variables الدول في ثلاثة متغيرات
+
+455
+00:52:05,100 --> 00:52:14,680
+f ال f of x y و z is a differentiable function
+
+456
+00:52:14,680 --> 00:52:17,740
+دلقابل
+
+457
+00:52:17,740 --> 00:52:24,330
+الاشتقاق andالـ U كان U1 في اتجاه الـ I U2 في
+
+458
+00:52:24,330 --> 00:52:30,410
+اتجاه الـ J U3 في اتجاه الـ K is a unit vector as
+
+459
+00:52:30,410 --> 00:52:45,090
+a unit vector كان متجه واحدة then اجراد ال Fاللي
+
+460
+00:52:45,090 --> 00:52:49,890
+بدأ يتساوي partial F على partial X في اتجاه I
+
+461
+00:52:49,890 --> 00:52:55,210
+partial F على partial Y في اتجاه G partial F على
+
+462
+00:52:55,210 --> 00:53:00,730
+partial Z في اتجاه K يعني أضفنا بس المراكبة في
+
+463
+00:53:00,730 --> 00:53:06,030
+اتجاه مين؟ في اتجاه K وبعدين بقول هنا Z
+
+464
+00:53:06,030 --> 00:53:11,570
+directional derivative
+
+465
+00:53:16,340 --> 00:53:29,040
+S الـ D U F بدي أساوي جراد ال F بطي ال U اللي هو
+
+466
+00:53:29,040 --> 00:53:35,160
+بدي أساوي الدرجة من هنا اللي هو partial F على
+
+467
+00:53:35,160 --> 00:53:42,860
+partial X ال U1 partial F على partial Y ال U2 زايد
+
+468
+00:53:42,860 --> 00:53:49,740
+partial Fعلى partial z في ال U3 هذه مركبات ال U
+
+469
+00:53:49,740 --> 00:53:56,480
+وهذه مركبات ال F يبقى كل واحدة في نظيرتها وبنجمع
+
+470
+00:53:56,480 --> 00:54:02,340
+بطلع جداش المقدار اللي عندك ياريت أقدركوا بس also
+
+471
+00:54:02,340 --> 00:54:08,360
+وكذلك for originally D U F
+
+472
+00:54:17,750 --> 00:54:25,370
+لو جبتها بلغة الأطوال تبقى باجي بقول هذا طول اجراد
+
+473
+00:54:25,370 --> 00:54:32,530
+ال F فطول ال U في Cos الزاوية بينهم اه ايه كده طول
+
+474
+00:54:32,530 --> 00:54:37,630
+ال U؟ لإن انا جاي ال unit vector هناك تمام؟ إذا
+
+475
+00:54:37,630 --> 00:54:43,160
+هذا الكلام بده يساوي طول اجراد ال Fفي cosine
+
+476
+00:54:43,160 --> 00:54:52,460
+الزواياتي باش بدينا محاضرتنا اليومبالتذكير باخرها
+
+477
+00:54:52,460 --> 00:54:57,920
+ادخلناها في المحاضرة الماضية و هي خواص ال product
+
+478
+00:54:57,920 --> 00:55:02,960
+أو خواص ال directional derivative والان احنا
+
+479
+00:55:02,960 --> 00:55:07,780
+رايحين وين على نفس الخواص يعني ما بدنا نعيدها كمان
+
+480
+00:55:07,780 --> 00:55:13,520
+اه كمان مرة تبقى احنا نذكرها ب اه باختصار فقط لغية
+
+481
+00:55:13,520 --> 00:55:18,540
+يعني يا بنات الخواص اللي كان تبتغن طبع على ال
+
+482
+00:55:18,540 --> 00:55:19,860
+directional derivative
+
+483
+00:55:22,430 --> 00:55:29,050
+متغيرين هي صحيحة بالضبط تماما على ال function اللي
+
+484
+00:55:29,050 --> 00:55:35,970
+فيه ثلاثة متغيرات لذلك أقعد باختصار بصيغة ال
+
+485
+00:55:35,970 --> 00:55:42,830
+remark التالي ال
+
+486
+00:55:42,830 --> 00:55:43,890
+three properties
+
+487
+00:55:50,260 --> 00:55:58,760
+اللي بدنا نفهم محاضرة اليوم of equation star طبعا
+
+488
+00:55:58,760 --> 00:56:05,560
+سمينا هذه ال equation star are
+
+489
+00:56:05,560 --> 00:56:14,140
+the same are the same نفسهم
+
+490
+00:56:14,140 --> 00:56:26,820
+in the caseكما في حالة of function of two
+
+491
+00:56:26,820 --> 00:56:32,020
+variables that
+
+492
+00:56:32,020 --> 00:56:39,660
+is I N ال
+
+493
+00:56:39,660 --> 00:56:46,820
+F increases most rapidly
+
+494
+00:56:49,020 --> 00:56:55,920
+يقرر أكثر بسرعة في الاتجاه
+
+495
+00:56:55,920 --> 00:57:08,380
+.. في اتجاه F عظيم ويقرر
+
+496
+00:57:08,380 --> 00:57:12,200
+.. و F يقرر
+
+497
+00:57:16,020 --> 00:57:22,200
+most rapidly and the direction of سالب جراد ال F
+
+498
+00:57:22,200 --> 00:57:25,720
+finally
+
+499
+00:57:25,720 --> 00:57:29,840
+ال
+
+500
+00:57:29,840 --> 00:57:41,140
+DUF بدل ساوي zero F LU and جراد ال F are
+
+501
+00:57:41,140 --> 00:57:42,880
+orthogonal
+
+502
+00:57:47,070 --> 00:57:52,210
+يبقى احنا كأنه بنعمم الشغلات اللي حصلنا عليها قبل
+
+503
+00:57:52,210 --> 00:58:01,870
+هيك تعميم نعطي مثال توضيحيا على درجة example find
+
+504
+00:58:01,870 --> 00:58:14,610
+the directions find the directions find
+
+505
+00:58:14,610 --> 00:58:20,300
+the directionsin which
+
+506
+00:58:20,300 --> 00:58:32,700
+the function f of x و y و z بدل سوى لن x تربيع
+
+507
+00:58:32,700 --> 00:58:42,100
+زائد y تربيع ناقص واحد زائد y زائد ستة z
+
+508
+00:58:48,620 --> 00:58:59,480
+increases and decreases most
+
+509
+00:58:59,480 --> 00:59:06,860
+rapidly most
+
+510
+00:59:06,860 --> 00:59:22,210
+rapidly at P0 of 1 و 1 و 0then find ومن ثم أوجد
+
+511
+00:59:22,210 --> 00:59:30,690
+the derivatives of
+
+512
+00:59:30,690 --> 00:59:35,930
+the function in these directions
+
+513
+01:00:17,510 --> 01:00:20,570
+يبقى المعلومات اللي خدناها على functions of two
+
+514
+01:00:20,570 --> 01:00:25,450
+variables صحيحة على functions of three variables
+
+515
+01:00:25,450 --> 01:00:31,890
+ناخد مثال عظيح ينهي هذه الاتجاهات بحيث الدلل عن
+
+516
+01:00:31,890 --> 01:00:37,730
+هذه increases و كذلك decreases مصطلح بدي أن نقطع
+
+517
+01:00:37,730 --> 01:00:42,040
+عنها و من ثمفاشل قدش ال derivatives في هذه
+
+518
+01:00:42,040 --> 01:00:45,240
+الاتجاهات لما يقول هذه ال derivatives في هذه
+
+519
+01:00:45,240 --> 01:00:48,500
+الاتجاهات يعني كأنه يقول هذه الظاهرة شينا ليها
+
+520
+01:00:48,500 --> 01:00:52,360
+derivatives لمن؟ لل function اللي عامة
+
+521
+01:01:00,110 --> 01:01:08,710
+عند نقطة المعطاة فانت تجيب فكرة في الاسئلة فانت
+
+522
+01:01:08,710 --> 01:01:12,270
+تجيب فكرة في الاسئلة
+
+523
+01:01:18,820 --> 01:01:24,700
+نقص واحد في مجتكط مداخل الـ N بالنسبة إلى X اللي
+
+524
+01:01:24,700 --> 01:01:33,000
+هو باتنين X برة ماعنديش X يبقى كله بالصفات بالمرة
+
+525
+01:01:33,000 --> 01:01:40,360
+نحسبها ال F X عند النقطة واحد واحد و Zero يبقى
+
+526
+01:01:40,360 --> 01:01:46,120
+بدأت ساوي اتنين على واحد زائد واحد نقص واحد بساوي
+
+527
+01:01:46,120 --> 01:01:52,520
+قداش اتنينبعد هيك بتروح أجيبله fy اللي هي بدها
+
+528
+01:01:52,520 --> 01:02:00,360
+تساوي واحد على x تربيع زائد y تربيع ناقص واحد كله
+
+529
+01:02:00,360 --> 01:02:04,620
+في مشتقة ما داخل الليل و باتبعين y
+
+530
+01:02:11,730 --> 01:02:17,590
+يبقى هذا الكلام يعطينا ان if y عندنا نقطة واحدة
+
+531
+01:02:17,590 --> 01:02:26,350
+واحدة وزيرو يساوي اتنين على واحد زائد واحد ناقص
+
+532
+01:02:26,350 --> 01:02:31,790
+واحد وكله زائد واحد يبقى اتنين زائد واحد يساوي كم؟
+
+533
+01:02:31,790 --> 01:02:33,150
+يساوي تلتة
+
+534
+01:02:36,320 --> 01:02:42,480
+يبقى مشتقة ال F بالنسبة إلى Z يبقى لإن هذا كله قدر
+
+535
+01:02:42,480 --> 01:02:47,960
+Zero لأنه لا يحتوي على Zero ومشتقة هذه ب Zero يبقى
+
+536
+01:02:47,960 --> 01:02:56,300
+مشتقة هذا قدر ب6 هذا يؤكدك أن مشتقة ال FZ عند 1 و1
+
+537
+01:02:56,300 --> 01:03:03,140
+و0 ملاش دعوة لإنه مقدارا ثابتايبقى عند اي لحظة
+
+538
+01:03:03,140 --> 01:03:07,960
+بيكون المشتقة دائما within moment ب 6 بناء عليه
+
+539
+01:03:07,960 --> 01:03:17,680
+قدرنا نجيب مين ال M اجراد ال M هو 2I زائد 3J زائد
+
+540
+01:03:17,680 --> 01:03:23,420
+6K يبقى
+
+541
+01:03:23,420 --> 01:03:27,080
+هذا هو العمودي الفقري تبع المثلة اش بقول المطلوب
+
+542
+01:03:27,720 --> 01:03:32,040
+قال لهذا ال directions بها تتدلع انكريز موست
+
+543
+01:03:32,040 --> 01:03:37,800
+رابدلي اذا انكريز موست رابدلي يبقى المتجه هي جراد
+
+544
+01:03:37,800 --> 01:03:41,700
+ال V اتنين واحد جراد ال F اتنين واحد يكون في نفسي
+
+545
+01:03:41,700 --> 01:03:48,640
+الاتجاه يبقى انا ها لو جبت ال unit vector تبع جراد
+
+546
+01:03:48,640 --> 01:03:53,640
+ال F يكون هو المطموع عارف ولا لأ يبقى باجي بقوله
+
+547
+01:03:53,640 --> 01:04:13,270
+هنا ال Fincreases most rapidly in the
+
+548
+01:04:13,270 --> 01:04:23,730
+direction of grad F على طول grad F اللي هو بدي
+
+549
+01:04:23,730 --> 01:04:31,230
+أعطيني المتجه UWhite بمعنى هذا الكلام ان ال U هذه
+
+550
+01:04:31,230 --> 01:04:40,470
+تساوي اتنين I زائد تلاتة J زائد ستة K مقسومة على
+
+551
+01:04:40,470 --> 01:04:49,570
+طول المتجد اربعة زائد تسعة زائد ستة و تلاتين ستة و
+
+552
+01:04:49,570 --> 01:04:55,940
+تلاتين و تسعة خمسة و اربعين و اربعة تحت الجدليبقى
+
+553
+01:04:55,940 --> 01:05:02,220
+هذه بدها تساوي سبعين في اتجاه ال I ثلاث أسبوع في
+
+554
+01:05:02,220 --> 01:05:08,460
+اتجاه ال J ست أسباع في اتجاه مين؟ في اتجاه ال E
+
+555
+01:05:08,460 --> 01:05:13,540
+يبقى
+
+556
+01:05:13,540 --> 01:05:18,420
+جبت الاتجاه اللي الدالة بتبقى فيه مالها increases
+
+557
+01:05:18,420 --> 01:05:23,260
+most rapidly تبقى decreasing most rapidly؟ ممتازة،
+
+558
+01:05:23,260 --> 01:05:26,570
+طب إيش رأيك؟طلب كمان طبعا قال لي هاتلي derivative
+
+559
+01:05:26,570 --> 01:05:36,150
+في هذا الاتجاه يبقى باجي بقوله ال derivative in
+
+560
+01:05:36,150 --> 01:05:48,070
+this direction قداش يا فنان ال duf قداش بتساوي طول
+
+561
+01:05:48,070 --> 01:05:56,070
+جراد ال F طول جراد ال Fقداش طولى جراد ال F؟ سبعة
+
+562
+01:05:56,070 --> 01:06:00,290
+نجى
+
+563
+01:06:00,290 --> 01:06:07,930
+الآن ال F decreases most
+
+564
+01:06:07,930 --> 01:06:13,990
+rapidly at
+
+565
+01:06:13,990 --> 01:06:21,750
+ال 1 و 1 و 0 in the direction
+
+566
+01:06:24,850 --> 01:06:32,130
+مين؟ عكس في اتجاه الـ I اللي هو سالب سبعين في
+
+567
+01:06:32,130 --> 01:06:39,750
+اتجاه الـ I سالب تلت أسباع في اتجاه الـ G سالب ست
+
+568
+01:06:39,750 --> 01:06:49,870
+أسباع في اتجاه مين؟ ال K كمان ال derivative in
+
+569
+01:06:49,870 --> 01:06:51,170
+this
+
+570
+01:06:55,330 --> 01:07:04,530
+direction is سالب اولى grade ال F سوى ده سالب سبع
+
+571
+01:07:04,530 --> 01:07:13,510
+خلاصنا و احنا خلاصنا ال section طبعا وبالتالى بروح
+
+572
+01:07:13,510 --> 01:07:22,010
+ل exercises اليمين اربعتاشر خمسةالمسائل من واحد
+
+573
+01:07:22,010 --> 01:07:28,330
+لخمسة و تلاتين القادة
+
+574
+01:07:28,330 --> 01:07:31,030
+حد بتسمع أي سؤال هنا؟
+
+575
+01:07:58,040 --> 01:08:01,500
+ببناء زي ما شايفين ال directional derivative فيها
+
+576
+01:08:01,500 --> 01:08:05,440
+معلومات قيمة وبالتالي يعني دائما و أبدا في
+
+577
+01:08:05,440 --> 01:08:10,840
+الامتحانات النهائية بنحاول نجيب سؤال مرتبط فيها
+
+578
+01:08:10,840 --> 01:08:15,780
+ننتقل لل section اللذي يليه يا خالد اللي هو
+
+579
+01:08:15,780 --> 01:08:24,520
+section اربعة عشر ستة اربعة عشر ستة اللي هو تانجين
+
+580
+01:08:29,670 --> 01:08:48,750
+Tangent players and differentials نمسى
+
+581
+01:08:48,750 --> 01:08:51,770
+حد منك كله؟ خلاص؟
+
+582
+01:09:07,370 --> 01:09:11,370
+أحنا قبل شويه بجينا نقول الـ tangent line in ده
+
+583
+01:09:11,370 --> 01:09:16,470
+نقطة مظبوط لمين؟ لل level كام؟ طب لو صار level
+
+584
+01:09:16,470 --> 01:09:20,450
+surface اللي ببطل يصير عندي tangent line و انا
+
+585
+01:09:20,450 --> 01:09:24,730
+بصير tangent plane طبعا افضل ان اعطيله definition
+
+586
+01:09:24,730 --> 01:09:30,110
+و بعدين نشوف كيف ان نحسب المعادلة تبعه انا بجي
+
+587
+01:09:30,110 --> 01:09:35,370
+بقول definition ال
+
+588
+01:09:35,370 --> 01:09:35,810
+tangent
+
+589
+01:09:41,640 --> 01:09:47,800
+الـ tangent plane at the point
+
+590
+01:09:47,800 --> 01:09:55,860
+عند النقطة الـ P naught of X naught و Y naught و Z
+
+591
+01:09:55,860 --> 01:10:00,120
+naught on
+
+592
+01:10:00,120 --> 01:10:01,460
+the level surface
+
+593
+01:10:11,460 --> 01:10:22,440
+F of X و Y و Z يساوي Constancy of a differentiable
+
+594
+01:10:22,440 --> 01:10:35,420
+function F is the plane هو عبارة عن المستوى إضرار
+
+595
+01:10:35,420 --> 01:10:43,710
+الذي يمر بالنقطةP نوت و X نوت و Y نوت و Z نوت
+
+596
+01:10:43,710 --> 01:10:47,590
+Normal
+
+597
+01:10:47,590 --> 01:10:56,970
+و يكون عموديًا to grade ال F عند النقطة اليمين P
+
+598
+01:10:56,970 --> 01:10:57,910
+نوت
+
+599
+01:11:13,660 --> 01:11:21,440
+وحد يعطيني دفتر من دفتر اي دفتر لو جيت تخيلت يا
+
+600
+01:11:21,440 --> 01:11:26,700
+ابنات ان ايدي هذه level surface تبقى مجسم في الفرق
+
+601
+01:11:26,700 --> 01:11:32,820
+قبضة اليد هذه هي level surface خلت مماسي يمسها
+
+602
+01:11:32,820 --> 01:11:40,140
+يمسها في نقطة واحدةيبقى هذه النقطة اسمها X node و
+
+603
+01:11:40,140 --> 01:11:44,860
+Y node و Z node انا بدي اجيب معادلة ال plane هذا
+
+604
+01:11:44,860 --> 01:11:50,480
+من العمودي على ال plane هو ال grade ال F زي ما
+
+605
+01:11:50,480 --> 01:11:54,920
+كانت في حتة level curve قبل قليل كان العمودي على
+
+606
+01:11:54,920 --> 01:11:59,880
+ال tangent main هو grade ال F وهناك العمودي على ال
+
+607
+01:11:59,880 --> 01:12:04,460
+tangent P plane هي grade ال F زي ما هو L U على A
+
+608
+01:12:04,460 --> 01:12:12,450
+على Lمرة تانية بقول تانجينت بلين مستوى التماس عندي
+
+609
+01:12:12,450 --> 01:12:16,770
+النقطة P نقطة X نقطة Y نقطة و Z نقطة على ال level
+
+610
+01:12:16,770 --> 01:12:22,030
+surface F و X و Y و Z بدي اسمه كونه C لدفينشف و
+
+611
+01:12:22,030 --> 01:12:27,200
+Function F هو عبارة عن بلين اللي يمربهذه النقطة
+
+612
+01:12:27,200 --> 01:12:32,980
+ويكون عمودي علمين على الجراد ال F طب إذا نص مرسمة
+
+613
+01:12:32,980 --> 01:12:37,380
+فوضيحية طب أنا أعطيكم مثال بقفض اليد التباتي لكن
+
+614
+01:12:37,380 --> 01:12:42,580
+بقول أنا عندي فيه level surface على سبيل المثال لو
+
+615
+01:12:42,580 --> 01:12:49,680
+كان عندي محاور بهذا الشكل وقول هذا محور X هذا محور
+
+616
+01:12:49,680 --> 01:12:57,180
+Y هذا محور Z وروحت رسمتالـ level surface اللي عندي
+
+617
+01:12:57,180 --> 01:13:05,840
+هذا و نفترض ان ال level surface كان بهذا الشكل على
+
+618
+01:13:05,840 --> 01:13:11,140
+سبيل المثال جبت
+
+619
+01:13:11,140 --> 01:13:17,140
+مستوى و خلته يمس هذا ال level surface المستوى هذا
+
+620
+01:13:17,140 --> 01:13:22,680
+حرصه بلون آخر بنات يبقى لو جب مستوى بالشكل اللي
+
+621
+01:13:22,680 --> 01:13:23,420
+عندنا هذا
+
+622
+01:13:27,390 --> 01:13:32,410
+راح اشترك معاه في نقطة واحدة زي النقطة اللى عناها
+
+623
+01:13:32,410 --> 01:13:38,770
+يبقى هذا بدراسمه مظلل مظلل يبقى هو اللى فوق
+
+624
+01:13:38,770 --> 01:13:44,410
+والمجسم اللى بيصير باسمه منه او منها منه اسفل طبعا
+
+625
+01:13:44,410 --> 01:13:51,730
+يبقى هذا الأسود بدهرش بيكون منقط لأنه مظهر ليش
+
+626
+01:13:51,730 --> 01:13:58,620
+وكذلك هذا كمان بدهرشلأنه اه دراسة ملقطة لإن ليه
+
+627
+01:13:58,620 --> 01:14:04,360
+plane غطى طيب ليه plane و هذا ال surface اشتركوا
+
+628
+01:14:04,360 --> 01:14:10,640
+في نقطة واحدة؟ مين هي النقطة هذه؟ هي النقطة P نوض
+
+629
+01:14:10,640 --> 01:14:18,460
+و X نوض و Y نوض و Z نوض العمودي عند النقطة هذا غطى
+
+630
+01:14:18,460 --> 01:14:30,800
+العمودي على ال plane كان من نجراد ال Fعندنا نرجع
+
+631
+01:14:30,800 --> 01:14:37,480
+بالذاكرة الى الوراء الى section 12-5 معادة لطلينة
+
+632
+01:14:37,480 --> 01:14:42,860
+إذا نالت نقطة تقع فيه والذكر العمودي عليه grade F
+
+633
+01:14:42,860 --> 01:14:47,360
+هو العمودي عليه هو النقطة الحمد لله موجودة إذا
+
+634
+01:14:47,360 --> 01:14:52,900
+المعادلة القديمة هيطب اشكرت المعادلة القديمة عزيزي
+
+635
+01:14:52,900 --> 01:14:59,960
+AX أو AX ناقص X naught زائد B في Y ناقص Y naught
+
+636
+01:14:59,960 --> 01:15:05,980
+زائد Z زائد C زائد Z ناقص Z naught بيسوء من Zero
+
+637
+01:15:05,980 --> 01:15:11,140
+يعني إيه؟ يعني بنروح ناخد أي نقطة أخرى في ليه
+
+638
+01:15:11,140 --> 01:15:19,950
+planeوالتكن هذه النقطة مثلا ل P X Y و Z وبنعتبر ان
+
+639
+01:15:19,950 --> 01:15:25,870
+في عندى vector اسمه P node P يبقى هذا ال vector
+
+640
+01:15:25,870 --> 01:15:36,110
+اللي هو P node P يبقى باجب اقوله هنا from section
+
+641
+01:15:36,110 --> 01:15:39,530
+أتناشر خمسة
+
+642
+01:15:45,740 --> 01:15:54,160
+Tangent A Plane S المركبة
+
+643
+01:15:54,160 --> 01:15:59,880
+الأولى تبع المتجهة grade ال F مش هي عبارة عن F X
+
+644
+01:15:59,880 --> 01:16:07,280
+عند النقطة F of X node و Y node و Z node في ال X
+
+645
+01:16:07,280 --> 01:16:09,220
+ناقص ال X node
+
+646
+01:16:38,850 --> 01:16:48,150
+الـ Fx والـ Fy والـ Fz المركبة المفتجه العموديهذه
+
+647
+01:16:48,150 --> 01:16:59,250
+المراكبات المتجهة العمودي Fx Fy Fz Fz Fz Fz Fz Fz
+
+648
+01:16:59,250 --> 01:16:59,250
+Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz
+
+649
+01:16:59,250 --> 01:16:59,550
+Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz
+
+650
+01:16:59,550 --> 01:16:59,730
+Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz
+
+651
+01:16:59,730 --> 01:17:04,970
+Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz
+
+652
+01:17:04,970 --> 01:17:05,030
+Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz
+
+653
+01:17:05,030 --> 01:17:09,510
+Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz Fz
+
+654
+01:17:15,440 --> 01:17:19,700
+طيب كويس، في حاجة كمان قدناها بنات اسمها normal
+
+655
+01:17:19,700 --> 01:17:24,940
+line، ال normal line على ال plane عند اللقطة،
+
+656
+01:17:24,940 --> 01:17:30,960
+طبعا، ال normal line على ال plane عند اللقطة،
+
+657
+01:17:30,960 --> 01:17:36,720
+يبقوا خط موازي لمين؟لكن هذا ال F إذا بقدر أجيب ال
+
+658
+01:17:36,720 --> 01:17:41,740
+parametric equations لهذا ال line بدلالة مركبة ل
+
+659
+01:17:41,740 --> 01:17:46,060
+gradient هنحطها تعريف و بعدين نوجد المعادلات
+
+660
+01:17:46,060 --> 01:17:49,280
+تبعدها فبجيب اقول command definition
+
+661
+01:18:05,190 --> 01:18:17,290
+الخط العملي to the surface to the surface at P0 or
+
+662
+01:18:17,290 --> 01:18:27,210
+X0 or Y0 or Z0 as the line through as the line
+
+663
+01:18:27,210 --> 01:18:31,890
+through P0
+
+664
+01:18:31,890 --> 01:18:34,310
+parallel
+
+665
+01:18:43,650 --> 01:18:48,690
+اللي هي البينو برضه
+
+666
+01:18:48,690 --> 01:18:59,630
+من سيكشن أتناشر خمسة from section أتناشر خمسة the
+
+667
+01:18:59,630 --> 01:19:03,370
+parametric
+
+668
+01:19:03,370 --> 01:19:05,710
+equations
+
+669
+01:19:06,410 --> 01:19:20,350
+of this line R ال X بدي ساوي ال X node زائد المتجه
+
+670
+01:19:20,350 --> 01:19:27,050
+الموازي لل gradient ال F
+
+671
+01:19:27,050 --> 01:19:34,930
+X زائد ال F X عند النقطة P node في T ال Y بدي ساوي
+
+672
+01:19:34,930 --> 01:19:42,770
+Y nodeزائد fy عند النقطة P0 في T ال Z بتسوي Z0
+
+673
+01:19:42,770 --> 01:19:51,890
+زائد FZ عند النقطة P0 في Main في اتجاه Aيبقى هؤلاء
+
+674
+01:19:51,890 --> 01:19:55,870
+الـparameters لمين؟ للـnormal line يبقى صح اننا
+
+675
+01:19:55,870 --> 01:20:00,910
+جيبنا ال tangent plane لمين؟ لل level surface و
+
+676
+01:20:00,910 --> 01:20:05,170
+جيبنا العمودي على level surface اللي هو هو العمودي
+
+677
+01:20:05,170 --> 01:20:09,390
+على tangent plane يعني العمودي على level surface
+
+678
+01:20:09,390 --> 01:20:15,710
+هو نفس العمود على مين؟ على tangent plane لل level
+
+679
+01:20:15,710 --> 01:20:21,510
+surface اللي موجود عندنانعطي أمثلة توضيحية على ذلك
+
+680
+01:20:21,510 --> 01:20:30,390
+أول مثال مثلا نقول
+
+681
+01:20:30,390 --> 01:20:33,010
+find the equations of the tangent plane
+
+682
+01:20:47,660 --> 01:21:01,940
+and normal line and normal line and normal line at
+
+683
+01:21:01,940 --> 01:21:15,180
+the point at the point عند النقطة ال P نوت of واحد
+
+684
+01:21:15,470 --> 01:21:23,610
+و سالب واحد و تلاتة on the surface on the surface
+
+685
+01:21:23,610 --> 01:21:33,110
+على السطر اللي همين x تربيع زائدي اتنين x y ناقص y
+
+686
+01:21:33,110 --> 01:21:39,170
+تربيع زائد 6 تربيع كله بده يساوي سبع
+
+687
+01:21:56,450 --> 01:22:01,810
+السؤال مرة تانية طلب مني معادلة مستوى التماس
+
+688
+01:22:01,810 --> 01:22:07,390
+ومعادلة الخط العمودي عند النقطة التي تقع على ال
+
+689
+01:22:07,390 --> 01:22:11,530
+level surface لمين للمنحنة اللي عندنا يبقى هذه
+
+690
+01:22:11,530 --> 01:22:15,670
+معادلة إيش يا بنات level surface مين الدالة
+
+691
+01:22:15,670 --> 01:22:21,730
+الأصلية الدالة هذه بدون السبعة بسميها F of X وY
+
+692
+01:22:21,730 --> 01:22:25,510
+يبقى باجي بقوله هنا ال F
+
+693
+01:22:28,480 --> 01:22:37,380
+اللي هي level surface هي x تربيع زائد اتنين اكس
+
+694
+01:22:37,380 --> 01:22:39,000
+واي ناقص واي
+
+695
+01:22:44,050 --> 01:22:47,310
+يبقى برضه grade ال F بتلعب دور الأساسي عندنا بدنا
+
+696
+01:22:47,310 --> 01:22:52,550
+نروح نجيبله grade ال F يبقى بدنا نجيبله ال Fx يبقى
+
+697
+01:22:52,550 --> 01:22:59,110
+مشتقة الدالة F بالنسبة ل X يعني يبقى 2X زائد 2Y
+
+698
+01:22:59,110 --> 01:23:01,790
+الباقى كله Zero ايوة
+
+699
+01:23:08,580 --> 01:23:13,660
+يعني هذي كانت z مقص واحد لكل تربية؟ اه ممكن المقص
+
+700
+01:23:13,660 --> 01:23:18,160
+واحد ورق سبعة لازم تفكر و تقدر أفهم ال .. لأ ليس
+
+701
+01:23:18,160 --> 01:23:21,800
+بالضرورة ليس بالضرورة طبعا شو رأيك؟ انا لو جيبت
+
+702
+01:23:21,800 --> 01:23:27,160
+السبعة على الشجرة التانية و قلت كله يسوى zero يسوى
+
+703
+01:23:27,160 --> 01:23:31,500
+هذا برضه level surface او zero level surface لو
+
+704
+01:23:31,500 --> 01:23:34,380
+كتبته و ماحدش اللي و الكلام عندي و انا الاشتراك
+
+705
+01:23:34,380 --> 01:23:36,460
+مبينش لهذا و هناك كله بروح
+
+706
+01:23:41,330 --> 01:23:46,810
+يبقى هذا سواء كتبت في الشكل هذا ستة نت السبعة أو
+
+707
+01:23:46,810 --> 01:23:52,890
+دخلت بالعصابن اشتقاق لا قيمة لها تمام جبنا ال Fx
+
+708
+01:23:52,890 --> 01:23:59,230
+المدين X زي دي اتنين Y بدي احسب هذا المقدار Fx عند
+
+709
+01:23:59,230 --> 01:24:05,180
+النقطة الموطنة واحد وثاني واحد وتلريبقى x بواحد
+
+710
+01:24:05,180 --> 01:24:09,560
+يبقى قصيري اتنين و هنا سالب اتنين يبقى الحمد لله
+
+711
+01:24:09,560 --> 01:24:15,820
+قداش بزيره بدي اروح ليبقى ال fy يبقى ال x تلفية مع
+
+712
+01:24:15,820 --> 01:24:23,380
+السلامة يطلع اتنين x مقص اتنين y يبقى هذا بدي
+
+713
+01:24:23,380 --> 01:24:29,740
+يعطينا ان ال fy عند النقطة واحد و سالب واحد يكون
+
+714
+01:24:29,740 --> 01:24:36,280
+تلاتة يساويالـ x هذه باتنين وهنا زائدي اتنين يبقى
+
+715
+01:24:36,280 --> 01:24:42,080
+قداش اربع ناقص ناقص يبقى بتطلع قداش اللي هو اربع
+
+716
+01:24:42,080 --> 01:24:49,540
+بتجيب ال fz يساوي zero zero zero يبقى بس قداش
+
+717
+01:24:49,540 --> 01:24:56,740
+اتنين z يبقى اتنين z هذا بدي يعطيناإن F زده عند
+
+718
+01:24:56,740 --> 01:25:02,520
+الواحد و سالب واحد و تلاته بده يساوي اتنين في
+
+719
+01:25:02,520 --> 01:25:08,700
+تلاته في قدر بيه ستة من هدولي التلاتة مع بعض بقدر
+
+720
+01:25:08,700 --> 01:25:14,600
+أجيب له ال gradient لدالة F اللي هو اتجاه ال I ب
+
+721
+01:25:14,600 --> 01:25:21,860
+Zero يبقى أربعة J زائد ستة K طيب
+
+722
+01:25:24,110 --> 01:25:27,650
+هذه المراكبة في اتجاه ال X هذه المراكبة في اتجاه
+
+723
+01:25:27,650 --> 01:25:32,710
+ال Y وهذه المراكبة في اتجاه ال K نجي للمعادلة اللي
+
+724
+01:25:32,710 --> 01:25:39,290
+عندناها هذه حسبناها في Zero هذه أربعة، هذه بسنتة X
+
+725
+01:25:39,290 --> 01:25:43,610
+نقطة وY نقطة وZ نقطة المعروفة وماضلش عليها إلا
+
+726
+01:25:43,610 --> 01:25:49,590
+المعادلة يبقى عندنا أنا عليه بقول المعادلة كتالة
+
+727
+01:26:32,870 --> 01:26:39,710
+زائد اربعة في ال Y زائد واحد زائد ز
+
+728
+01:26:52,920 --> 01:26:59,840
+نقص تمانتاشة بدو يساوي Zero او ان شئتم فقولوا هذا
+
+729
+01:26:59,840 --> 01:27:08,260
+اربعة Y زائد ستة Z اربعة من نقص تمانتاشة بضل نقص
+
+730
+01:27:08,260 --> 01:27:13,640
+اربعتاش على الشجرة التانية بيساوي اربعتاش لو قسمنا
+
+731
+01:27:13,640 --> 01:27:16,120
+كله على اتنين بيصير اتنين
+
+732
+01:27:18,620 --> 01:27:25,380
+هذا الـ Z بيكون ساوية سبعة هذا ال equation of the
+
+733
+01:27:25,380 --> 01:27:31,920
+tangent plane قلّي بعد ذلك بدي ال equation of the
+
+734
+01:27:31,920 --> 01:27:40,000
+normal line قبل ما بدي بقول هنا دي equations of
+
+735
+01:27:40,000 --> 01:27:45,120
+the normal line
+
+736
+01:27:48,420 --> 01:27:55,820
+الـ X بدي يسوى X نُض الـ E بواحد زائد كدهش؟ زائد
+
+737
+01:27:55,820 --> 01:28:01,560
+Zero لإن ال F X عندى كدهش؟ Zero يبقى معاه سلامة و
+
+738
+01:28:01,560 --> 01:28:08,660
+ال Y بدي يسوى كدهش؟ سالب واحد زائد
+
+739
+01:28:08,660 --> 01:28:17,350
+أربعة T و هنا ال Z بيسوى تلاتة عظم النقريبقى تلاتة
+
+740
+01:28:17,350 --> 01:28:37,710
+وانا زائد ستة T مثال أخير في محاضرة اليوم five
+
+741
+01:28:37,710 --> 01:28:39,450
+parametric equations
+
+742
+01:28:48,420 --> 01:28:56,260
+للتانجين الطريق للتانجين
+
+743
+01:28:56,260 --> 01:29:10,380
+الطريق للتانجين الطريق للتانجين
+
+744
+01:29:10,380 --> 01:29:19,490
+الطريقintersection of the surfaces of the surfaces
+
+745
+01:29:19,490 --> 01:29:29,450
+للسطحين الو X Y Z يساوي واحد والتاني الو X تربيع
+
+746
+01:29:29,450 --> 01:29:37,590
+زائد اتنين Y تربيع زائد تلاتة Z تربيع بده يساوي
+
+747
+01:29:37,590 --> 01:29:48,670
+ستة at thepoint عند النقطة اللي بين واحد وواحد
+
+748
+01:29:48,670 --> 01:29:49,890
+وواحد
+
+749
+01:30:31,300 --> 01:30:36,640
+سؤال مرة ثانية، عشان نقدر نتصور الموضوع، انا في
+
+750
+01:30:36,640 --> 01:30:40,880
+only two surfaces و الاتنين متقاطعين، يعني لو
+
+751
+01:30:40,880 --> 01:30:44,660
+افترضت ان ايدي اليمين هي surface و القطب تبعت ايدي
+
+752
+01:30:44,660 --> 01:30:49,260
+الشمال هي surface اخر، اتنين صار بينهم متقاطع،
+
+753
+01:30:49,260 --> 01:31:06,920
+قضعوا في من؟ من حلبالمنحنة تبقى
+
+754
+01:31:06,920 --> 01:31:16,840
+تقاطع تقاطع تقاطع تقاطع تقاطع تقاطع
+
+755
+01:31:19,550 --> 01:31:25,210
+نقطة موجودة عليه
+
+756
+01:31:25,210 --> 01:31:41,290
+مستجه يوازي نقطة موجودة عليه مستجه يوازي نقطة
+
+757
+01:31:41,290 --> 01:31:44,690
+موجودة عليه مستجه يوازي
+
+758
+01:31:50,090 --> 01:31:57,670
+طب مذاكرين كيف كنا نجيب معادلة خط التقاطة لمستويين
+
+759
+01:31:57,670 --> 01:32:05,010
+متقاطعين كنا نجيب ال normal على الأول نجيب ال
+
+760
+01:32:05,010 --> 01:32:11,310
+normal على التاني اطلع المنتجة الموازي لخط التقاطة
+
+761
+01:32:11,310 --> 01:32:15,070
+هنا نفس الفكرة من المنتجة العمودي على ال surface
+
+762
+01:32:15,070 --> 01:32:21,430
+الأوللجراد تبع ال level service اللي عندنا و
+
+763
+01:32:21,430 --> 01:32:26,850
+التانية لجراد التانية لو اتلب cross product بجيب
+
+764
+01:32:26,850 --> 01:32:31,610
+الخط الموازية tangent بقى لجرادها من الدالة الأولى
+
+765
+01:32:31,610 --> 01:32:34,850
+و لجرادها من الدالة الثانية هدول دلتين او two
+
+766
+01:32:34,850 --> 01:32:39,370
+surfaces مختلفين يبقى انا في عندي بدل ال function
+
+767
+01:32:39,370 --> 01:32:44,350
+تنتهي هنا يا بنات ال function الأولى اللي هي f of
+
+768
+01:32:44,350 --> 01:32:44,770
+x
+
+769
+01:32:52,100 --> 01:32:55,440
+YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ
+
+770
+01:32:55,440 --> 01:32:56,920
+YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ
+
+771
+01:32:56,920 --> 01:32:58,840
+YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ
+
+772
+01:32:58,840 --> 01:33:00,620
+YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ
+
+773
+01:33:00,620 --> 01:33:00,740
+YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ
+
+774
+01:33:00,740 --> 01:33:01,240
+YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ
+
+775
+01:33:01,240 --> 01:33:01,460
+YZ YZ YZ YZ YZ YZ YZ YZ YZ YZ
+
+776
+01:33:16,780 --> 01:33:21,640
+عند النقطة واحد و واحد و واحد يسوي واحد في واحد و
+
+777
+01:33:21,640 --> 01:33:24,540
+يسوي واحد و يسوي واحد و يسوي واحد و يسوي واحد و
+
+778
+01:33:24,540 --> 01:33:25,100
+يسوي واحد و يسوي واحد و يسوي واحد و يسوي واحد و
+
+779
+01:33:25,100 --> 01:33:28,520
+يسوي واحد و يسوي واحد و يسوي واحد و يسوي واحد و
+
+780
+01:33:28,520 --> 01:33:32,700
+يسوي واحد و يسوي واحد و يسوي واحد و يسوي واحد و
+
+781
+01:33:32,700 --> 01:33:33,340
+يسوي واحد و يسوي واحد و يسوي واحد و يسوي واحد و
+
+782
+01:33:33,340 --> 01:33:33,560
+يسوي واحد و يسوي واحد و يسوي واحد و يسوي واحد و
+
+783
+01:33:33,560 --> 01:33:34,360
+يسوي واحد و يسوي واحد و يسوي واحد و يسوي واحد و
+
+784
+01:33:34,360 --> 01:33:38,000
+يسوي واحد و يسوي واحد و يسوي واحد و يسوي واحد و
+
+785
+01:33:38,000 --> 01:33:40,280
+يسوي واحد و يسوي وا
+
+786
+01:33:47,460 --> 01:33:53,760
+فز عند نقطة واحد و واحد و واحد هي جداش واحد اللي
+
+787
+01:33:53,760 --> 01:34:00,340
+عملناه لف يروح نعمله لمين؟ لجي يبقى بدي أجيب كمان
+
+788
+01:34:00,340 --> 01:34:06,140
+الجي اكس والجي واي والجي زد عند نفس النقطة يبقى
+
+789
+01:34:06,140 --> 01:34:08,640
+بدي أجيب له هنا جي اكس
+
+790
+01:34:16,680 --> 01:34:23,140
+جي اكس عند النقطة واحد و واحد و واحد يساوي اتنين
+
+791
+01:34:23,140 --> 01:34:29,460
+في واحد و يساوي قداش اتنين بدي ال جي واي اللي هو
+
+792
+01:34:29,460 --> 01:34:35,440
+اربعة واي هذا بدي اقولك ان جي واي عند النقطة واحد
+
+793
+01:34:48,850 --> 01:34:55,650
+GZ عند النقطة واحد وواحد وواحد يساوي 6 في واحد
+
+794
+01:34:55,650 --> 01:35:06,490
+ويساوي 6 إذا حصلنا على مين؟ على Grad F عند النقطة
+
+795
+01:35:06,490 --> 01:35:14,150
+من الـEP node اللي عندنا مين هي يا بنات؟ I زائد G
+
+796
+01:35:14,150 --> 01:35:18,310
+زائد K كل المركبات زي بعض
+
+797
+01:35:24,910 --> 01:35:29,190
+عند نفس النقطة P node هي ما تغيرتش
+
+798
+01:35:32,080 --> 01:35:38,000
+بقولك هي النقطة واحد و واحد و واحد وهنا نفس النقطة
+
+799
+01:35:38,000 --> 01:35:43,360
+اللي واحد و واحد و واحد يبقى هذا الكلام بدرساوي
+
+800
+01:35:43,360 --> 01:35:53,200
+فانا عندنا اتنين I زائد اربع G زائد ستة K بدي اعمل
+
+801
+01:35:53,200 --> 01:35:58,240
+cross product فيما بينهم يقدروا احجيب له اجراد ال
+
+802
+01:36:02,990 --> 01:36:14,930
+محدد IJK مركبات ال F 1111 مركبات ال G 246 و 9
+
+803
+01:36:23,510 --> 01:36:29,050
+يبقى 6-4 في اتجاه ال I ناقص
+
+804
+01:36:33,930 --> 01:36:40,410
+يبقى هنا ستة نقص اتنين في اتجاه ال J اللي بقعده
+
+805
+01:36:40,410 --> 01:36:47,490
+أشطر صفر عموده اربعة نقص اتنين في اتجاه ال K زائد
+
+806
+01:36:47,490 --> 01:36:54,650
+اربعة نقص اتنين في اتجاه ال K و اتنين I نقص اربعة
+
+807
+01:36:54,650 --> 01:37:02,550
+J زائد اتنين K هذا this vector
+
+808
+01:37:06,240 --> 01:37:14,960
+Parallel to the tangent line
+
+809
+01:37:14,960 --> 01:37:27,080
+of the curve of intersection of
+
+810
+01:37:27,080 --> 01:37:32,580
+the two level surfaces
+
+811
+01:37:39,490 --> 01:37:43,990
+يبقى جبنة قراءة ال Fالمتجه العمودي على ال surface
+
+812
+01:37:43,990 --> 01:37:48,070
+الأول جبنا grade الجيه المتجه العمودي على ال
+
+813
+01:37:48,070 --> 01:37:52,370
+surface التاني عملنا cross product طلعني متجه
+
+814
+01:37:52,370 --> 01:37:58,630
+يوازي المماس لمين لمنحنة التقاطع تبع المستوين
+
+815
+01:37:58,630 --> 01:38:04,190
+المتجه موجود والحمد لله النقطة موجودة إذا بقدر
+
+816
+01:38:04,190 --> 01:38:10,290
+أجيب المعادات البرامترية لخط التماثر فبقدر أقولهم
+
+817
+01:38:10,290 --> 01:38:15,890
+ما يأتيthe parametric
+
+818
+01:38:15,890 --> 01:38:33,090
+equations of the tangent line up X سوى X0 زائد AT
+
+819
+01:38:33,090 --> 01:38:40,310
+Y سوى Y0 زائد BT Z سوى Z
+
+820
+01:38:59,390 --> 01:39:06,190
+طب لحد هنا stop لسه مكملناشمرة قادمة ان شاء الله
+
+821
+01:39:06,190 --> 01:39:13,010
+بنكمل هذا ال section وبرضه بندخل ال section اللي
+
+822
+01:39:13,010 --> 01:39:18,270
+بعده ان تمكننا ان شاء الله تعالى لأن هذا ال
+
+823
+01:39:18,270 --> 01:39:31,650
+section قويل شوية يعطيكوا
+
+824
+01:39:31,650 --> 01:39:31,970
+العافية
+
+825
+01:39:41,730 --> 01:39:43,710
+السلام عليكم و رحمه الله
+
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/481Vfp-Apr4.srt b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/481Vfp-Apr4.srt
new file mode 100644
index 0000000000000000000000000000000000000000..3e409a7c02a04868463235638db5ab2b9eb6546f
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/481Vfp-Apr4.srt
@@ -0,0 +1,2157 @@
+1
+00:00:00,000 --> 00:00:02,680
+موسيقى
+
+2
+00:00:15,840 --> 00:00:20,180
+بسم الله الرحمن الرحيم ابتدأنا في شبطر أربعة عشر
+
+3
+00:00:20,180 --> 00:00:24,540
+وأخذنا فيه two sections، الـ two sections بتحدث عن
+
+4
+00:00:24,540 --> 00:00:29,560
+الـ functions of several variables. أخذنا كيف نجيب
+
+5
+00:00:29,560 --> 00:00:32,880
+الـ domain و الـ range لهذه الـ functions، وتعرفنا
+
+6
+00:00:32,880 --> 00:00:37,460
+كذلك على level curves و level surfaces للمنحنيات
+
+7
+00:00:37,460 --> 00:00:44,780
+أو الأسطح. بعد ذلك ننتقل إلى جد الـ limit و الـ
+
+8
+00:00:44,780 --> 00:00:49,760
+continuity للدالة of several variables. الآن في
+
+9
+00:00:49,760 --> 00:00:55,260
+section 14-3 سنذهب إلى derivatives of functions of
+
+10
+00:00:55,260 --> 00:00:59,660
+several variables. نبدأ بمتغيرين ثم نذهب لثلاثة
+
+11
+00:00:59,660 --> 00:01:05,440
+متغيرات أو أكثر لنتدرج في فهم الموضوع. فعندي
+
+12
+00:01:05,440 --> 00:01:10,980
+partial derivatives، يعني المشتقات الجزئية. في
+
+13
+00:01:10,980 --> 00:01:15,440
+مشتقة كلية وفي مشتقة جزئية. الإجابة نعم. متى تكون
+
+14
+00:01:15,440 --> 00:01:20,860
+المشتقة الكلية ومتى تكون المشتقة الجزئية؟ تكون
+
+15
+00:01:20,860 --> 00:01:24,900
+المشتقة الكلية إذا عندي function في one variable،
+
+16
+00:01:24,900 --> 00:01:29,220
+يبقى أقول هذا اسمه اشتقاق كلي (total differentiation).
+
+17
+00:01:29,220 --> 00:01:34,580
+يبقى أقول dy على dx، سواء f prime of x. عندي تبقى
+
+18
+00:01:34,580 --> 00:01:38,880
+الدالة y في متغير واحد. أما إذا كانت الدالة في
+
+19
+00:01:38,880 --> 00:01:43,180
+متغيرين أو ثلاثة أو أربعة، ففي هذه الحالة الاشتقاق
+
+20
+00:01:43,180 --> 00:01:47,600
+بيكون اشتقاق جزئي، اللي هو موضوع اليوم. فبقى دي
+
+21
+00:01:47,600 --> 00:01:51,800
+أقول في partial derivative، المشتقة الجزئية للدالة
+
+22
+00:01:51,800 --> 00:01:57,420
+f of x و y بالنسبة للمتغير x عند النقطة x<sub>0</sub> و y<sub>0</sub>.
+
+23
+00:01:57,420 --> 00:02:02,940
+أعطى لها الرمز f، وحكم تحته اللي هو الـ index
+
+24
+00:02:02,940 --> 00:02:08,340
+x، اللي هو الدليل x. يعني إيش معناها؟ معناها المشتقة
+
+25
+00:02:08,340 --> 00:02:12,440
+بالنسبة لـ x، وأكتبها على الصورة partial f على
+
+26
+00:02:12,440 --> 00:02:15,700
+partial x. هذه كمان اللي بقيت أكتب دي عادية.
+
+27
+00:02:19,890 --> 00:02:24,450
+يبقى وتقرأ partial F على partial X، ويُفهم منها
+
+28
+00:02:24,450 --> 00:02:29,550
+أننا نريد أن نشتق الدالة بالنسبة إلى X. طب إذا
+
+29
+00:02:29,550 --> 00:02:34,850
+جئنا لنشتق X، ما أخبار الـ Y؟ يبقى الـ Y بنعتبرها
+
+30
+00:02:34,850 --> 00:02:40,890
+مقدارًا ثابتًا. تمام. أطلع الكلام اللي أنا بقوله
+
+31
+00:02:40,890 --> 00:02:46,910
+هيضعنا عليها على التعريف. هذا هو الـ Limit عندما الـ
+
+32
+00:02:46,910 --> 00:02:53,730
+H تذهب إلى الـ 0 لـ F of X<sub>0</sub> زائد H وY<sub>0</sub>. يبقى ثبتنا
+
+33
+00:02:53,730 --> 00:02:59,430
+الـ Y<sub>0</sub> وعملنا تغيير في الـ X، لأننا نقص F of X<sub>0</sub> وY<sub>0</sub>
+
+34
+00:02:59,430 --> 00:03:05,330
+على H. هل شكل التعريف اختلف فيه مضمونه عن التعريف
+
+35
+00:03:05,330 --> 00:03:08,950
+تبع الـ function of one variable؟ مش هو نفس التعريف
+
+36
+00:03:08,950 --> 00:03:12,770
+الـ derivative العادي؟ طيب، هذا لو كان الاشتقاق
+
+37
+00:03:12,770 --> 00:03:17,510
+بالنسبة لـ X. طب لو كان الاشتقاق بالنسبة لـ Y، يبقى
+
+38
+00:03:17,510 --> 00:03:22,310
+نفس المفهوم. إذا أقول F<sub>Y</sub> أو partial F على partial
+
+39
+00:03:22,310 --> 00:03:29,210
+Y عند النقطة X<sub>0</sub> وY<sub>0</sub> هو limit. بثبت الـ X<sub>0</sub>
+
+40
+00:03:29,210 --> 00:03:33,370
+كأنه مقدار ثابت وأروح آخذ التغيير اللي بيحصل في
+
+41
+00:03:33,370 --> 00:03:38,490
+الـ Y. فبقول Y<sub>0</sub> زائد H ناقص F of X<sub>0</sub> و Y<sub>0</sub>
+
+42
+00:03:38,490 --> 00:03:43,750
+على مين؟ على H. بشرط أن الـ limit في كلتا الحالتين
+
+43
+00:03:43,750 --> 00:03:49,670
+exist، يعني الـ derivative هذا بيحصل إذا كان عندي
+
+44
+00:03:49,670 --> 00:03:56,220
+إذا كان الـ limit هذه ما لها exist. نروح نحط هذا على
+
+45
+00:03:56,220 --> 00:04:08,180
+أرض الواقع. فآجي أقول فـ f(w) مثلاً تساوي f of x و y
+
+46
+00:04:08,180 --> 00:04:18,520
+وذهب. يبقى آجي أقول to find، لإيجاد، نمرّة واحد.
+
+47
+00:04:28,130 --> 00:04:38,030
+Y and Z are constants. يبقى
+
+48
+00:04:38,030 --> 00:04:44,410
+دول بنعتبرهم ثوابت. طيب، نمرّة اثنين، لو بدي partial F
+
+49
+00:04:44,410 --> 00:04:49,030
+على partial Y، يبقى هنا آجي أقول
+
+50
+00:04:59,080 --> 00:05:05,380
+لو بدنا الـ partial F على partial Z، و consider
+
+51
+00:05:05,380 --> 00:05:15,900
+بنروح نعتبر أن الـ X والـ Y are constants، وهكذا.
+
+52
+00:05:18,560 --> 00:05:23,940
+بدأ من الآن فصاعدًا، يا بنات، لو كانت الدالة في متغيرين
+
+53
+00:05:23,940 --> 00:05:29,960
+وبدي مشتقة بالنسبة لأحد المتغيرين، فبعتبر المتغير
+
+54
+00:05:29,960 --> 00:05:34,720
+الثاني ماله؟ ثابت عند الاشتقاق. إذا والله الدالة في
+
+55
+00:05:34,720 --> 00:05:39,840
+ثلاثة متغيرات، بدي أشتق بالنسبة لأحدهم، يبقى بعتبر
+
+56
+00:05:39,840 --> 00:05:44,200
+الاثنين الآخرين مقادير ثابتة. يعني مشتقة كل واحد
+
+57
+00:05:44,200 --> 00:05:49,180
+فيهم بجد إيش؟ بصفر (zero). يعني بعتبره مقدار ثابت، و
+
+58
+00:05:49,180 --> 00:06:02,480
+هكذا. نعطي أمثلة توضيحية على ذلك. مثال الأول:
+
+59
+00:06:02,480 --> 00:06:06,580
+find f<sub>x</sub>
+
+60
+00:06:06,580 --> 00:06:14,860
+and f<sub>y</sub> for the following
+
+61
+00:06:22,270 --> 00:06:33,290
+F of X Y يساوي Y في tan X<sup>2</sup> Y<sup>3</sup>
+
+62
+00:06:39,010 --> 00:06:49,270
+بدها تساوي e<sup>XY</sup> في sin (X<sup>2</sup> + Y<sup>2</sup> + ⅓XY)
+
+63
+00:06:49,270 --> 00:07:00,530
+نمرّة ثلاثة: e<sup>F of X وY</sup> بدها تساوي integration من X<sup>2</sup> + 1 إلى Y
+
+64
+00:07:00,530 --> 00:07:05,970
+مرة ثانية. المعلومة النظرية اللي أخذناها بالنسبة
+
+65
+00:07:31,900 --> 00:07:37,090
+للمشتقة الدالة بالنسبة لأحد المتغيرات. نعطي أمثلة
+
+66
+00:07:37,090 --> 00:07:41,670
+توضيحية عليها. المثال بيقول: هات المشتقة الدالة
+
+67
+00:07:41,670 --> 00:07:46,450
+بالنسبة لـ X، وكذلك مشتقة الدالة بالنسبة لـ Y لكل من
+
+68
+00:07:46,450 --> 00:07:51,330
+الدوال التالية.
+
+70
+00:08:16,440 --> 00:08:24,240
+نبدأ بالنقطة الأولى. يبدأ يجيب مشتقتها بالنسبة إلى
+
+71
+00:08:24,240 --> 00:08:31,780
+X، يبقى يجي إلى F<sub>X</sub>، يعني مشتقة الـ F بالنسبة إلى X.
+
+72
+00:08:31,780 --> 00:08:36,960
+ونفهمها، يبقى الـ Y تعتبر، يا بنات، مقدار ثابت.
+
+73
+00:08:36,960 --> 00:08:41,400
+بقول يا Y، خليك زي ما أنتِ، ما لكِش دعوة. وتفضل الـ tan
+
+74
+00:08:42,140 --> 00:08:49,580
+قد إيش؟ بـ 6<sup>2</sup>، الزاوية، الزاوية اللي هي من X<sup>2</sup> و Y<sup>3</sup>
+
+75
+00:08:49,580 --> 00:08:53,700
+طبقًا لقاعدة chain rule، في مشتقة الزاوية
+
+76
+00:08:53,700 --> 00:08:59,800
+بالنسبة لـ X. يبقى Y<sup>3</sup> مقدار ثابت مالوش دعوة.
+
+77
+00:08:59,800 --> 00:09:07,640
+مشتقة الـ X<sup>2</sup> بـ 2X، والـ Y<sup>3</sup> تبقى كما هي. واضحة؟
+
+78
+00:09:07,640 --> 00:09:16,550
+الآن هذه؟ طيب، نجيب f<sub>y</sub> تساوي، اللي هو تفاضل الـ f
+
+79
+00:09:16,550 --> 00:09:25,210
+بالنسبة إلى y، partial f by partial y. أيوة، هذه y وهذه y
+
+80
+00:09:25,210 --> 00:09:30,770
+يبقى هذه مشتقتها قاعدة ضرب دالتين. نرجع لقاعدة
+
+81
+00:09:30,770 --> 00:09:35,150
+الضرب أو للثانوية الأولى، في مشتقة الثانية في مشتقة الأولى. يبقى الأولى
+
+82
+00:09:35,150 --> 00:09:40,940
+مشتقة الثانية، تفاضل
+
+83
+00:09:40,940 --> 00:09:50,200
+الـ tan X<sup>2</sup> Y<sup>3</sup> في مشتقة الزاوية. ليه؟
+
+84
+00:09:50,200 --> 00:09:55,880
+ثلاثة Y<sup>2</sup>، والـ X<sup>2</sup> مقدار ثابت. يبقى فيه
+
+85
+00:09:55,880 --> 00:10:01,840
+ثلاثة X<sup>2</sup> و Y<sup>2</sup>، هذه الأولى في مشتقة الثانية
+
+86
+00:10:01,840 --> 00:10:06,300
+زائد الدالة الثانية في مشتقة الأولى. مشتقة الأولى
+
+87
+00:10:06,300 --> 00:10:13,580
+في قد إيش؟ بواحد صحيح، يبقى زائد tan X<sup>2</sup> Y<sup>3</sup>
+
+88
+00:10:13,580 --> 00:10:15,800
+نمرّة ب
+
+89
+00:10:18,840 --> 00:10:23,880
+برضه بنفس الطريقة، هذه تعتبر function وتحتوي على الـ
+
+90
+00:10:23,880 --> 00:10:28,840
+X والـ Y، وهذه function تحتوي على الـ X والـ Y. يبقى
+
+91
+00:10:28,840 --> 00:10:33,760
+عليكِ بأمرين سواء كان بدنا F<sub>x</sub> أو F<sub>y</sub> فهي مشتقة
+
+92
+00:10:33,760 --> 00:10:37,860
+قاعدة ضرب. ده اللي يتم بجد الدالة الأولى اللي هي
+
+93
+00:10:37,860 --> 00:10:44,800
+e<sup>XY</sup> ومشتقة الأولى بقد إيش يا بنات؟ الـ X بنمشيها زي
+
+94
+00:10:44,800 --> 00:10:54,450
+ما هي. ضرب مشتقة الأس بالنسبة لـ X، اللي هو بقد إيش؟ مشتقة
+
+95
+00:10:54,450 --> 00:11:01,670
+الأس بالنسبة لإيش؟ لـ X، يعني Y ثابت. بقد إيش؟ Y. تمام.
+
+96
+00:11:01,670 --> 00:11:07,190
+فاهمين؟ هي مشتقة الأولى في الثانية في sin<sup>3</sup> X<sup>2</sup>
+
+97
+00:11:07,190 --> 00:11:15,050
++Y<sup>2</sup> + ⅓XY + الدالة الأولى
+
+98
+00:11:15,050 --> 00:11:21,290
+زي ما هي e<sup>XY</sup> في تفاضل الدالة الثانية. يبقى تفاضل
+
+99
+00:11:21,290 --> 00:11:29,550
+الثانية: الثلاثة sin<sup>2</sup> في مين؟ في X<sup>2</sup> + Y<sup>2</sup>
+
+100
+00:11:29,550 --> 00:11:36,050
++ ⅓XY في تفاضل الـ sin اللي هو مين؟
+
+101
+00:11:36,050 --> 00:11:40,590
+بـ cos، يبقى cos نفس الزاوية.
+
+102
+00:11:47,060 --> 00:11:51,940
+لأ، ما خلصناش لسه. بدك تضربي في تفاضل الزاوية بالنسبة
+
+103
+00:11:51,940 --> 00:11:57,720
+لمين؟ بالنسبة لمين؟ لـ X، يبقى هذا بده يضرب يا بنات
+
+104
+00:11:57,720 --> 00:12:04,840
+في مين؟ في تفاضل الزاوية اللي هو 2X فقط زائد
+
+105
+00:12:04,840 --> 00:12:14,240
+⅓Y. شكلها طويلة. يبقى أنا اشتقيتها اشتقاقًا كاملًا. طبعًا
+
+106
+00:12:14,240 --> 00:12:20,160
+ممكن يكون عندي اختصار، إن الثلاثة داخلة بصير 6X و
+
+107
+00:12:20,160 --> 00:12:26,000
+هنا زائد Y، تفرجش مش كتير. طيب، هذا الـ F<sub>x</sub>. بدنا نروح
+
+108
+00:12:26,000 --> 00:12:32,140
+نجيب الـ F<sub>yy</sub> يساوي، يبقى بنشتق الدالة بالنسبة لـ Y، يبقى
+
+109
+00:12:32,140 --> 00:12:37,740
+الـ exponential زي ما هو، e<sup>XY</sup>. مشتقة الأس بالنسبة لإيش؟ لـ Y
+
+110
+00:12:37,740 --> 00:12:47,440
+فهو كده بـ X. فاهمين؟ في sin<sup>3</sup> (X<sup>2</sup> + Y<sup>2</sup>
+
+111
+00:12:47,440 --> 00:12:54,980
++ ⅓XY). جاية مشتقة الأولى في الثانية زائد
+
+112
+00:12:54,980 --> 00:13:02,160
+الأولى كما هي في مشتقة الثانية، sin<sup>3</sup> لثلاثة
+
+113
+00:13:02,160 --> 00:13:11,480
+sin<sup>2</sup> الزاوية، (X<sup>2</sup> + ⅓XY) في تفاضل
+
+114
+00:13:11,480 --> 00:13:16,940
+الـ sin اللي هو الـ cos، (X<sup>2</sup> + Y<sup>2</sup> +
+
+115
+00:13:16,940 --> 00:13:25,760
+⅓XY). ضرب مشتقة الزاوية بالنسبة لـ Y اللي هي 2Y
+
+116
+00:13:25,760 --> 00:13:33,440
+زائد ⅓X. هيك اشتقيناها اشتقاقًا كاملًا.
+
+117
+00:13:58,800 --> 00:14:07,100
+طيب، نجي لمين؟ للنمرّة ثلاثة. النمرّة ثلاثة بدها مشتقة هذه وهذه
+
+118
+00:14:07,100 --> 00:14:11,080
+عندي تكامل، إذا نروح نكامل الدالة وبعدين نشتق،
+
+119
+00:14:11,080 --> 00:14:17,150
+كويس؟ لأ، أروح اللي ما أنصحش أطبق التكامل. أيوة، أروح
+
+120
+00:14:17,150 --> 00:14:21,650
+تكامل. يعني مثلًا بتقدرّيش تتكاملها زي المثل اللي
+
+121
+00:14:21,650 --> 00:14:26,370
+قدامنا. هذا صعب تكاملها (very difficult). يبقى المقصود
+
+122
+00:14:26,370 --> 00:14:30,030
+مش تروحي تكاملي. أنا بدي أشتق، أصدقائي. آه، أخذنا على
+
+123
+00:14:30,030 --> 00:14:33,550
+ذلك اللي هي مين في الكالكولس؟ شو اسمها النظرية؟
+
+124
+00:14:33,550 --> 00:14:37,930
+fundamental theorem of calculus. يبقى أنا بدي أروح
+
+125
+00:14:37,930 --> 00:14:42,560
+أطبق الـ fundamental theorem of calculus مع مراعاة
+
+126
+00:14:42,560 --> 00:14:48,960
+مين ثابت ومين المتغير. يبقى أنا بدي F<sub>x</sub>، بدي اشتقاق
+
+127
+00:14:48,960 --> 00:14:53,800
+بالنسبة لـ X، يبقى الـ Y إيش تعتبر؟ ثابت. إذا هذا يعتبر
+
+128
+00:14:53,800 --> 00:15:01,860
+مقدارًا ثابتًا. يبقى هذا بدي أقول اللي فوق B<sub>0</sub> ناقص
+
+129
+00:15:01,860 --> 00:15:09,530
+يبقى هذه الـ 0، ناقص... notes mean... بدي أشيل كل T وأحط
+
+130
+00:15:09,530 --> 00:15:14,190
+مكانها X<sup>2</sup> + 1. إذا هذا إيش بتصير؟
+
+131
+00:15:14,190 --> 00:15:25,210
+sin(X<sup>2</sup> + 1). fill in... بدي أشيل الـ T وأحط
+
+132
+00:15:25,210 --> 00:15:32,360
+مكانها X<sup>2</sup> + 1. لكل T<sup>3</sup> ناقص 1 ضرب
+
+133
+00:15:32,360 --> 00:15:46,740
+مشتقة تمين الدالة، اللي هو بقد إيش؟ بـ 2X. طبعًا
+
+134
+00:15:46,740 --> 00:15:51,200
+يمكن اختصاره، أفك هذا. وقت مش مشكلة. المهم أن أعرف
+
+135
+00:15:51,200 --> 00:15:58,010
+كيف أطبق النظرية. طب لو بدها f<sub>y</sub> يا بنات، يبقى هذا
+
+136
+00:15:58,010 --> 00:16:03,770
+يعتبر كله كأنه مقدار ثابت. يبقى إيش آجي أقول؟ بشيل
+
+137
+00:16:03,770 --> 00:16:12,750
+كل T وبحط مكانها Y. يبقى إيش بصير؟ sin Y<sup>3</sup>. تمام.
+
+138
+00:16:12,750 --> 00:16:18,170
+يبقى شلت الـ T وحطيت مكانها اللي هو Y<sup>3</sup>، لن
+
+139
+00:16:30,810 --> 00:16:34,850
+أبقى، يا بنات، لو كانت هذه دالة في X وهذه دالة في X
+
+140
+00:16:34,850 --> 00:16:41,870
+وطلبت المشتقة بالنسبة لـ Y، زيرو. ممتاز جدًا. يبقى لو
+
+141
+00:16:41,870 --> 00:16:45,590
+كانت الدالة اللي فوق بدلالة X والدالة تحت الـ index
+
+142
+00:16:45,590 --> 00:16:50,230
+التابع للتكامل بدلالة X وطلبت المشتقة بالنسبة إلى
+
+143
+00:16:50,230 --> 00:16:56,070
+Y، إذًا أوتوماتيك المشتقة تساوي قد إيش؟ Zero. وبالمثل لو
+
+144
+00:16:56,070 --> 00:17:01,870
+كانت الدالة الاثنين متغيرين في Y وطلبت المشتقة
+
+145
+00:17:01,870 --> 00:17:07,610
+بالنسبة لـ X، الناتج يساوي Zero. تمام تمام. طيب، بعد ما
+
+146
+00:17:07,610 --> 00:17:13,590
+انتهينا من هذا المثال، نروح ناخد مثال آخر. مثال
+
+147
+00:17:13,590 --> 00:17:18,070
+اثنين بيقول
+
+148
+00:17:18,070 --> 00:17:31,270
+find الـ f<sub>x</sub>، الـ f<sub>x</sub>، والـ f<sub>y</sub>، والـ f<sub>z</sub>
+
+149
+00:17:49,650 --> 00:18:03,510
+Y و Z تساوي X في e<sup>Y</sup> زائد Y في e<sup>Z</sup> زائد Z
+
+150
+00:18:03,510 --> 00:18:15,870
+في e<sup>X</sup>. لمين؟ F of X و Y و Z يساوي tan<sup>-1</sup>
+
+151
+00:18:15,870 --> 00:18:22,250
+لمين؟ لـ (XY + YZ)
+
+152
+00:18:54,230 --> 00:18:59,470
+الفرق بين المثال رقم اثنين والمثال رقم واحد أن
+
+153
+00:18:59,470 --> 00:19:03,130
+المثال رقم واحد كان function في two variables بس
+
+154
+00:19:03,130 --> 00:19:07,910
+ده function في three variables. طلب المشتقة بالنسبة
+
+155
+00:19:07,910 --> 00:19:11,910
+لـ X والمشتقة بالنسبة لـ Y والمشتقة بالنسبة لـ Z. إذا
+
+156
+00:19:11,910 --> 00:19:15,450
+بدنا نعمل السؤال بنفس الطريقة اللي عملنا فيها
+
+157
+00:19:15,450 --> 00:19:27,570
+السؤال السابق. بدنا نعتبر الـ Y و
+
+158
+00:19:27,570 --> 00:19:35,850
+Z ثابت وX هو المتغير. يبقى e<sup>Y</sup> كله مقدار ثابت، تفضل X
+
+159
+00:19:35,850 --> 00:19:44,650
+بجد واحد. يبقى e<sup>Y</sup> هذا كله صفر. هذا Z ثابت ومشتقة
+
+160
+00:19:44,650 --> 00:19:52,620
+e<sup>Z</sup> بـ e<sup>Z</sup> itself. طبعًا طبعًا هذا الـ f<sub>x</sub>. بدي الـ f<sub>y</sub>
+
+161
+00:19:52,620 --> 00:20:01,600
+يساوي الـ X ثابت، ما لكش دعوة. مشتقة الـ e<sup>Y</sup> بـ e<sup>Y</sup>
+
+162
+00:20:01,600 --> 00:20:02,480
+itself.
+
+163
+00:20:18,880 --> 00:20:25,300
+مشتقتها صفر. هذه الـ Y كما هي، مشتقة الـ e<sup>Z</sup> بالـ
+
+164
+00:20:25,300 --> 00:20:32,360
+e<sup>Z</sup>، والـ Z. اتصلت، مشتقة الـ Z بواحد. زائد e<sup>X</sup>
+
+165
+00:20:32,360 --> 00:20:36,900
+طيب، وجبنا المشتقات الثلاثة للنقطة الأولى. النقطة
+
+166
+00:20:36,900 --> 00:20:43,960
+الثانية اللي نمرّة بها، فنج
+
+223
+00:27:57,250 --> 00:28:06,640
+تاني بسكتر بيه XYZ في مشتقة الزاوية
+
+224
+00:28:06,640 --> 00:28:17,720
+كده مشتقة هذا بالنسبة ل X؟ بYZ تمام زائد هذه كأنها
+
+225
+00:28:17,720 --> 00:28:23,780
+دالة وهذه دالة تانية فبجي بقول مشتقة هذه بواحد وYZ
+
+226
+00:28:23,780 --> 00:28:30,100
+كما هي زائد الدالة الأولى زي ما هي، الـ Y مقدار ثابت
+
+227
+00:28:30,100 --> 00:28:34,480
+الـ Z لـ partial Z by partial X
+
+228
+00:28:37,220 --> 00:28:43,080
+واضحات مرة تانية، بدأ أقولها، هذا الاشتقاق أفعلته
+
+229
+00:28:43,080 --> 00:28:47,660
+اسمه اشتقاق ضمني، تمام، يبقى بدأ أفضل كل شيء في
+
+230
+00:28:47,660 --> 00:28:51,820
+موقعه مع مراعاة قواعد التفاضل المختلفة، أنا بفضل
+
+231
+00:28:51,820 --> 00:28:55,920
+بالنسبة لـ X أولا، لأن بدي partial Z by partial X
+
+232
+00:28:55,920 --> 00:29:00,930
+يبقى باجي بقول التفاضل كسبيا باتنين X، هذا كله الـ Y
+
+233
+00:29:00,930 --> 00:29:04,670
+تربية صغيرة، مقنعة، ثابت، تفاضل الـ Z له partial Z by
+
+234
+00:29:04,670 --> 00:29:08,770
+partial X، نجي الـ Y مقنعة، ثابت، مانوش داورة، تفاضل
+
+235
+00:29:08,770 --> 00:29:14,180
+التان بسكت تربيع، ضرب مشتقة الزاوية، أعتبر هذه دالة
+
+236
+00:29:14,180 --> 00:29:20,060
+و هذه دالة تانية، يبقى مشتقة الأولى بواحد في YZ، هاي
+
+237
+00:29:20,060 --> 00:29:25,220
+الـ YZ زائد الأولى زي ما هي، الـ X مشتقة التانية
+
+238
+00:29:25,220 --> 00:29:29,840
+مشتقة الـ YZ، Y مقدر ثابت، مشتقة الـ Z اللي هو partial
+
+239
+00:29:29,840 --> 00:29:36,270
+Z by partial X، عاد بعد هيك فكي وطلعيلي partial z
+
+240
+00:29:36,270 --> 00:29:41,450
+by partial x على شجة، وساعمليلي هيك و روحي أخليها
+
+241
+00:29:41,450 --> 00:29:48,430
+باقي الشغل الشغل الروتيني، يعني هدف، يعني هدفي أنا
+
+242
+00:29:48,430 --> 00:29:51,310
+أجيب الـ partial z على partial x عن بعض، وأخد عامل
+
+243
+00:29:51,310 --> 00:29:55,690
+مشترك، وأنقل هذا على شكل تاني، وأجسم شغل روتيني، لا
+
+244
+00:29:55,690 --> 00:30:00,650
+قيمة له، وإن غلط فيه بنحاسبك، يبقى لا، بس فاضليه من
+
+245
+00:30:00,650 --> 00:30:03,490
+الأول للآخر في الـ implicit differentiation هذا
+
+246
+00:30:03,490 --> 00:30:07,910
+فاضليه من الأول للآخر، صح، وروح وخليني، تمام؟ مش
+
+247
+00:30:07,910 --> 00:30:11,410
+هنضيع وقت وإحنا نقعد نحس فيه، لأن إحنا اشتقينا اشتقاقا
+
+248
+00:30:11,410 --> 00:30:17,210
+صحيح، اللي هو الاشتقاق بالنسبة إلى X، بالذالك ياخد
+
+249
+00:30:17,210 --> 00:30:22,210
+الاشتقاق بالنسبة لمن؟ لـ Y، بقولك كذلك كذلك، مستقل الـ
+
+250
+00:30:22,210 --> 00:30:30,470
+X ترميه Zero، تمام، مستقل تاني نين Y، زائد
+
+251
+00:30:32,520 --> 00:30:39,600
+خلصت؟ لسه، الـ Y متغير والـ Z متغير، يبقى 2Y في Z
+
+252
+00:30:39,600 --> 00:30:47,480
+زائد Y تربيع partial Z by partial Y، شوفت كيف
+
+253
+00:30:47,480 --> 00:30:52,120
+اترجعت عن بعض وعن اللي فوق؟ طيب، هذا الكلام
+
+254
+00:30:52,120 --> 00:30:57,420
+بالتسابق بنا نشتقت ده لاني بالنسبة لمين؟ لـ Y، يبقى
+
+255
+00:30:57,420 --> 00:31:05,110
+مشتقة الأولى واحد، وظلتان X Y Z زائد Y في تفاضلي
+
+256
+00:31:05,110 --> 00:31:11,530
+التان بسكتر بيه الزاوية ضرب مشتقة الزاوية بالنسبة
+
+257
+00:31:11,530 --> 00:31:17,370
+لمين؟ بالنسبة إلى Y، يبقى الـ X ايش يُعتبر البلاد؟
+
+258
+00:31:17,370 --> 00:31:25,150
+المقدار ثابت، ومشتقة الـ Y زد بالنسبة لـ Y؟ بزد، لأن
+
+259
+00:31:25,150 --> 00:31:26,990
+مشتقة الـ Y بتساوي واحد
+
+260
+00:31:41,490 --> 00:31:45,130
+مرة تانية بقول، المشتقة الأخيرة لأن هو اللي ممكن
+
+261
+00:31:45,130 --> 00:31:51,110
+تلخبط فيها، طلعيلي كويس، هذه دالة وهذه كلها تعتبر
+
+262
+00:31:51,110 --> 00:31:56,100
+دالة تانية، يبقى مشتقة الأولى بواحد في تان هذه زي دي
+
+263
+00:31:56,100 --> 00:32:00,220
+دالة الأولى ليه Y، مشتقة التان بصيك تربيع في مشتقة
+
+264
+00:32:00,220 --> 00:32:05,060
+الزاوية، الـ X والـ Y ثوابت، لكن إحنا بنشتق بالنسبة لـ Y
+
+265
+00:32:05,060 --> 00:32:10,560
+يبقى X فقط هو ثابت، و Y و Z هو المتغير، يبقى باجي
+
+266
+00:32:10,560 --> 00:32:15,080
+بقول، يبقى الأولى X في Z لإنه مشتقة الـ Y بواحد
+
+267
+00:32:15,080 --> 00:32:21,440
+بعدين X في Y مشتقة الـ Z، لو partial z by partial y
+
+268
+00:32:21,440 --> 00:32:26,040
+هيك اشتقينا اشتقاقا كاملا، وماحدش اللي اعتراض عندنا
+
+269
+00:32:26,040 --> 00:32:31,560
+تمام، طيب، على أي حال، بدنا نيجي هذا بالنسبة لمهم
+
+270
+00:32:31,560 --> 00:32:39,200
+للمشتقة الأولى، بدأس السؤال الآن، إحنا في calculus A
+
+271
+00:32:39,200 --> 00:32:42,860
+فبناخد المشتقة الأولى والثانية والثالثة والـ
+
+272
+00:32:42,860 --> 00:32:47,930
+رابعة، والمشتقة النونية، مظبوط، هل يوجد عندنا في الـ
+
+273
+00:32:47,930 --> 00:32:52,370
+partial derivatives، مشتقات أولى وثانية وثالثة و
+
+274
+00:32:52,370 --> 00:32:59,390
+رابعة، نونية، الإجابة نعم، كالتالي، يبقى بداجي
+
+275
+00:32:59,390 --> 00:33:05,530
+لحاجة اسمها second second
+
+276
+00:33:05,530 --> 00:33:13,530
+and higher order
+
+277
+00:33:17,830 --> 00:33:27,510
+partial derivatives يعني
+
+278
+00:33:27,510 --> 00:33:31,430
+المشتقة الثانية أو الأعلى، المشتقة الثالثة،
+
+279
+00:33:31,430 --> 00:33:33,130
+الرابعة، الخامسة، السادسة
+
+280
+00:33:43,970 --> 00:33:48,590
+يبقى دي تعتبر مشتقة مين؟ يعني بتشتق مرتين بالنسبة
+
+281
+00:33:48,590 --> 00:33:55,230
+لمين؟ بالنسبة للـ X، أو معناها partial by partial X
+
+282
+00:33:55,230 --> 00:34:03,170
+لـ partial F by partial X، الشكل هذا يعني بتشتقوا
+
+283
+00:34:03,170 --> 00:34:06,570
+بالنسبة للـ F أولا بالنسبة للـ X، واللي هو إنت
+
+284
+00:34:06,570 --> 00:34:12,850
+بتشتقه كمان مرة، ومن جهة الرموز مكتوبة FXX
+
+285
+00:34:16,140 --> 00:34:25,180
+similarly، بنفس الطريقة، fyy يعني partial square f
+
+286
+00:34:25,180 --> 00:34:33,740
+by partial y squared، يعني partial على partial y لـ
+
+287
+00:34:33,740 --> 00:34:40,280
+partial f by partial y هذا
+
+288
+00:34:40,280 --> 00:34:47,510
+النقطة الأولى، النقطة الثانية، طب لو عندي partial x
+
+289
+00:34:47,510 --> 00:34:53,670
+partial y، مش كله زي بعضه، مختلفين، يعني عندي partial
+
+290
+00:34:53,670 --> 00:35:01,010
+square f على partial x partial y، إيش معناها هذه؟
+
+291
+00:35:01,010 --> 00:35:08,470
+معناها إنه partial على partial x لـ partial f by
+
+292
+00:35:08,470 --> 00:35:13,660
+partial y، يعني إيش معناها يا بنات؟ بدي أشتق أولا
+
+293
+00:35:13,660 --> 00:35:21,660
+بالنسبة لـ Y، ولا بالنسبة لـ X؟ لـ Y أولا، ثم لـ X، يعني
+
+294
+00:35:21,660 --> 00:35:29,220
+هذه كيانها إيش؟ كيانها partial على partial X للـ FY
+
+295
+00:35:29,220 --> 00:35:32,520
+تمام؟
+
+296
+00:35:32,520 --> 00:35:37,480
+يعني أشتق بالنسبة لـ Y أولا، ثم بالنسبة لـ X، أو إن شئتم
+
+297
+00:35:37,480 --> 00:35:38,500
+فقولوا
+
+298
+00:35:46,220 --> 00:36:03,160
+يبقى partial by partial
+
+299
+00:36:03,160 --> 00:36:09,060
+y لـ Fx، يبقى Fxy
+
+300
+00:36:13,090 --> 00:36:20,730
+قبل ما أكمل، جاي في بالي سؤال، هل الـ Fxy هي نفس الـ
+
+301
+00:36:20,730 --> 00:36:29,830
+Fyx؟ زي بعض؟ لأ، ليس بالضرورة، ممكن يحصل، تمام؟ لكن
+
+302
+00:36:29,830 --> 00:36:31,790
+in general، لأ
+
+303
+00:36:34,810 --> 00:36:39,690
+ممكن أقول، ممكن، وقتها، هذا ما سنعرفه في نهاية هذا
+
+304
+00:36:39,690 --> 00:36:45,570
+الـ section، بنظرية: إذا كانت الدالة متصلة ومشتقتها دوال
+
+305
+00:36:45,570 --> 00:36:51,590
+متصلة بالنسبة لـ X وكذلك بالنسبة إلى Y، وهذه كلها
+
+306
+00:36:51,590 --> 00:36:58,370
+معرفة، بيحصل التساوي اللي إحنا بنسأل عليه، طيب افترض
+
+307
+00:36:58,370 --> 00:36:59,090
+يا بنات
+
+308
+00:37:17,050 --> 00:37:24,730
+partial تربيع F على partial x partial y يعني هذه كأنها
+
+309
+00:37:24,730 --> 00:37:37,450
+partial على partial Y للـ FXX، يبقى الـ FXXY لو
+
+310
+00:37:37,450 --> 00:37:38,150
+عندك
+
+311
+00:37:50,280 --> 00:37:57,540
+يعني هذه partial تربيع على partial X تربيع لـ
+
+312
+00:37:57,540 --> 00:38:04,960
+partial تربيع F على partial Y تربيع، يعني هذه
+
+313
+00:38:04,960 --> 00:38:11,420
+partial تربيع على partial X تربيع لمين؟ للـ FYY
+
+314
+00:38:11,420 --> 00:38:14,340
+يعني هاني هان
+
+315
+00:38:20,010 --> 00:38:25,950
+بتعرف في أول رقم أو أول متغير قريب على الـ F، أول
+
+316
+00:38:25,950 --> 00:38:30,110
+اشتقاق بالنسبة له، وبعدين بنروح للبعد وللبعد وهكذا
+
+317
+00:38:30,110 --> 00:38:43,170
+طيب، نبدأ ناخد بعض الأمثلة التوضيحية، طيب
+
+318
+00:38:43,170 --> 00:38:47,790
+قبل الأمثلة التوضيحية، بقول لك لو كانت ثلاثة متغيرات
+
+319
+00:38:47,790 --> 00:38:49,130
+على سبيل المثال
+
+320
+00:39:10,090 --> 00:39:16,610
+يبقى هذه تساوي partial على partial X لمن؟ لـ partial
+
+321
+00:39:16,610 --> 00:39:22,830
+على partial Y لـ partial F على partial Z، يعني بنت
+
+322
+00:39:22,830 --> 00:39:30,010
+هذه تساوي من؟ FZ في الأول، وبعدها تفضل بالنسبة لـ Y
+
+323
+00:39:30,010 --> 00:39:34,830
+وبعدها تفضل بالنسبة لـ X، وهكذا
+
+324
+00:39:43,220 --> 00:39:55,060
+السؤال الأول يقول لي: let f of x, y و z بدها تساوي x
+
+325
+00:39:55,060 --> 00:40:04,740
+أس خمسة زائد x أس أربعة و y أس أربعة زائد زائد
+
+326
+00:40:04,740 --> 00:40:23,180
+y زائد تربيع، find FXY، FYX،
+
+327
+00:40:23,180 --> 00:40:28,860
+FXYY،
+
+328
+00:40:28,860 --> 00:40:35,300
+FZXY
+
+329
+00:41:23,620 --> 00:41:39,240
+يبقى Fxy، يبقى فيه ثلاثة متغيرات، يبقى
+
+330
+00:41:39,240 --> 00:41:44,340
+Fxy، يبقى فيه ثلاثة متغيرات
+
+331
+00:42:06,030 --> 00:42:13,390
+يجب أن نجيب fxy، يبقى بالفضل هو الاسم لمن؟ للـ one
+
+332
+00:42:13,390 --> 00:42:19,870
+يبقى هذا؟ Zero، مع السلامة، يبقى هذا Zero وهذا أربعة
+
+333
+00:42:19,870 --> 00:42:29,150
+X تكعيب، ما لها داوة، وهذه أربعة Y تكعيب، وهنا في Z تكعيب
+
+334
+00:42:29,150 --> 00:42:32,930
+والباقي بـ Zero، يبقى النتيجة سارة تقدر
+
+335
+00:42:40,620 --> 00:42:51,100
+بتركيب، نمري بيه، نمري بيه، يبقى في الأول بالاسم الأمين
+
+336
+00:42:51,100 --> 00:42:57,160
+للـ FY، يبقى بالذاتي للـ FY، وسبعة يبقى بالذاتي الـ
+
+337
+00:42:57,160 --> 00:43:00,820
+function اللي عندنا، يبقى الـ X أس خمسة بالدرجة بـ
+
+338
+00:43:00,820 --> 00:43:09,680
+Zero، يبقى هذه أربعة X أس أربعة زي ما هو، Y تكعيب، فزي
+
+339
+00:43:09,680 --> 00:43:15,760
+التكعيب، بقى المشتقة بالنسبة لـ Y زائد زي التربية
+
+340
+00:43:15,760 --> 00:43:22,020
+بيروح اشتقها بالنسبة لمن؟ لـ X، يبقى هذا بدي يعطيكي
+
+341
+00:43:22,020 --> 00:43:29,360
+إن FYX يساوي، اشتق بالنسبة لـ X يبقى إيش مصير عندك؟
+
+342
+00:43:29,360 --> 00:43:46,240
+16 X تكعيب Y تكعيب Z تكعيب، زائد Zero، بقدر
+
+343
+00:43:46,240 --> 00:43:51,320
+الله، تمام، هذا يتفق مع نظرية اللي قلت لكوا بعد قليل
+
+344
+00:43:51,320 --> 00:43:56,660
+الدالة هذه كثيرة حدود، إلى أن هي دالة متصلة، ومشتقتها
+
+345
+00:43:56,660 --> 00:43:59,520
+بالنسبة لك كثيرة حدود، دالة متصلة
+
+346
+00:44:01,930 --> 00:44:07,070
+دالة متصلة، الـ X Y كثيرة حدود، متصلة، وهذه متصلة، من
+
+347
+00:44:07,070 --> 00:44:11,990
+هنا جاء من جاء هذا التساوي اللي إحنا تسألنا عليه
+
+348
+00:44:11,990 --> 00:44:19,230
+قبل قليل، يبقى هذا بيه بدأي لنمري الـ C، نمري الـ C
+
+349
+00:44:19,230 --> 00:44:29,730
+قال لي بدي FXY، يعني FXY، FXY جاهزة، عادي
+
+350
+00:44:34,200 --> 00:44:40,580
+بدي اشتقها كمان مرة بالنسبة لمين؟ بالنسبة لـ Y، يعني
+
+351
+00:44:40,580 --> 00:44:49,340
+هذه كأنها partial على partial Y لـ 16 X تكعيب و Y
+
+352
+00:44:49,340 --> 00:44:56,020
+تكعيب، يبقى Z تكعيب، نشتق بالنسبة لـ Y يبقى يدى ثلاثة
+
+353
+00:44:56,020 --> 00:45:02,200
+في ستاشر، ثمانية وأربعين X تكعيب زي ما هي، وهدي Y
+
+354
+00:45:02,200 --> 00:45:12,820
+تربيع، وهدي Z تكعيب، نمري دي، نمري دي، بده F Z X Y
+
+355
+00:45:12,820 --> 00:45:16,480
+اللي هو الخطوة تفضل بالنسبة لـ Z
+
+356
+00:45:23,450 --> 00:45:31,390
+هذه خالية من Z بـ Zero، هذه مصير ثلاثة X أس أربعة
+
+357
+00:45:31,390 --> 00:45:42,570
+Y أس أربعة Z تربيع زائد اثنين Y زائد اثنين Y زائد
+
+358
+00:45:42,570 --> 00:45:49,010
+اثنين Y زائد اثنين Y زائد اثنين
+
+359
+00:45:49,010 --> 00:45:49,530
+Y زائد اثنين Y زائد اثنين Y زائد اثنين Y زائد
+
+360
+00:45:49,530 --> 00:45:50,170
+اثنين Y زائد اثنين Y زائد اثنين Y زائد اثنين Y
+
+361
+00:45:50,170 --> 00:45:50,190
+Y زائد اثنين Y زائد اثنين Y زائد اثنين Y زائد
+
+362
+00:45:50,190 --> 00:45:51,170
+اثنين Y زائد اثنين Y زائد اثنين Y زائد اثنين Y
+
+363
+00:45:51,170 --> 00:46:00,740
+زائد اف زد اكس اشتغل اسم الـ X يبقى اثناشر X تكعيب Y
+
+364
+00:46:00,740 --> 00:46:06,400
+أس أربعة Z تربيع، وهذا بالاسم الـ X، مع السلامة، بـ
+
+365
+00:46:06,400 --> 00:46:16,360
+Zero، الله، سؤال عليه، اللي بعدها بدي F Z X Y، هشتغل
+
+366
+00:46:16,360 --> 00:46:20,720
+نتيجة اللي حصلت عليها بالاسم الأمين الـ Y، أربعة في
+
+367
+00:46:20,720 --> 00:46:21,380
+اثناشر
+
+368
+00:46:29,480 --> 00:46:36,180
+تبقى عرفنا كيف تتم عملية الاشتقاق، طيب هذا المثال
+
+369
+00:46:36,180 --> 00:46:41,340
+الأول، المثال الثاني، show
+
+370
+00:46:41,340 --> 00:46:48,540
+that the function، show that the function
+
+371
+00:46:51,310 --> 00:47:05,750
+F of X و Y و Z، وسبعة E أس ثلاثة X زائد أربعة Y، زائد خمسة Z satisfies
+
+372
+00:47:05,750 --> 00:47:10,490
+خمسة Z، satisfies
+
+373
+00:47:21,920 --> 00:47:27,600
+وهذا اللي اتلاف لازم اللي partial تربيع F by
+
+374
+00:47:27,600 --> 00:47:32,880
+partial X تربيع، partial تربيع F by partial Y تربيع،
+
+375
+00:47:32,880 --> 00:47:39,460
+partial تربيع F by partial Z تربيع
+
+376
+00:48:03,890 --> 00:48:04,830
+ساعدني كثير
+
+377
+00:48:20,070 --> 00:48:25,170
+سؤال مرة تانية، يعطيني function في ثلاثة متغيرات
+
+378
+00:48:25,170 --> 00:48:30,170
+exponential أس ثلاثة X زائد أربعة Y في Cos خمسة Z
+
+379
+00:48:30,170 --> 00:48:34,310
+وقال لي أثبت لي أن هذه المعادلة بحقها معادلة
+
+380
+00:48:34,310 --> 00:48:39,290
+Laplace، يروي بركة بنات، معادلة Laplace في متغيرين
+
+381
+00:48:39,290 --> 00:48:44,130
+يكون هذا مش موجود، يبقى المشتقة الثانية بالنسبة لـ X
+
+382
+00:48:44,130 --> 00:48:47,250
+والمشتقة الثانية بالنسبة لـ Y تستوي Zero، إذا ثلاثة
+
+383
+00:48:47,250 --> 00:48:51,950
+متغيرات، بنضيف المشتقة الثانية متغيرة تانية، أربعة
+
+384
+00:48:51,950 --> 00:48:56,110
+متغيرات، خمس متغيرات، إن من المتغيرات كله بنفس
+
+385
+00:48:56,110 --> 00:48:56,710
+الطريقة
+
+386
+00:49:02,440 --> 00:49:07,380
+ومرتين بالنسبة لـ Y، و مرتين بالنسبة لـ Z، ونجمع، بدل
+
+387
+00:49:07,380 --> 00:49:12,080
+النتج يكون جداش Zero، إن حدث ذلك بقول فعلا هذه
+
+388
+00:49:12,080 --> 00:49:17,000
+الدالة تحقق معادلة Laplace equation، لم و جمعنا
+
+389
+00:49:17,000 --> 00:49:24,480
+عليه، بضروحه جيد، اللي هو partial F by partial X، هذه
+
+390
+00:49:24,480 --> 00:49:30,240
+فيهاش X، يبقى X بس فيه الاربعة Y كله مقدار ثابت
+
+391
+00:49:30,240 --> 00:49:34,620
+يبقى الـ X مو ننشي نفسها بس مضروبة في جذر في ثلاثة
+
+392
+00:49:34,620 --> 00:49:41,520
+يبقى هاي ثلاثة E أس ثلاثة X زائد أربعة Y
+
+393
+00:49:45,720 --> 00:49:
+
+445
+00:57:02,490 --> 00:57:03,550
+هل العكس صحيح؟
+
+446
+00:57:19,820 --> 00:57:25,160
+بالتالي دالة متصلة صحية لكنها دالة غير قابلة
+
+447
+00:57:25,160 --> 00:57:25,940
+للاشتقاق
+
+448
+00:57:31,850 --> 00:57:35,930
+أو Vertical Tangent أو الدالة نفسها ما تكونش معرّفة
+
+449
+00:57:35,930 --> 00:57:40,270
+عندها مظبوط تبقى هذه الأربع مواقع اللي تجعل الدالة فيها
+
+450
+00:57:40,270 --> 00:57:45,810
+غير قابلة للاشتقاق، فبنعطي مثال على ذلك example
+
+451
+00:57:45,810 --> 00:57:54,930
+يقول
+
+452
+00:57:54,930 --> 00:58:06,880
+إنّ الـ F of X  هو Y يساوي X في cos Y زائد Y في
+
+453
+00:58:06,880 --> 00:58:19,980
+cos X زائد XY  نجد أن الـ Fxy  يُساوي
+
+454
+00:58:19,980 --> 00:58:26,590
+الـ Fyx  لجميع قيم x و y  باستثناء
+
+455
+00:58:26,590 --> 00:58:32,170
+نقطة واحدة فقط، وإنما لجميع النقاط على المستوى plane  أو
+
+456
+00:58:32,170 --> 00:58:35,950
+النقاط المعرفة عليها الدالة، فهذان المقداران
+
+457
+00:58:35,950 --> 00:58:43,010
+متساويان،  يبقى الحل solution  أروح أجيب له
+
+458
+00:58:43,010 --> 00:58:54,110
+مشتقة fx  أولاً، يبقى fx  بمَ؟ cos y + cos x
+
+459
+00:58:54,110 --> 00:59:04,110
+زائد y  أجيب له مشتقة Fxy ،  أشتقها بالنسبة
+
+460
+00:59:04,110 --> 00:59:14,530
+لـ y، cos y  زائد cos x  زائد
+
+461
+00:59:14,530 --> 00:59:18,050
+1، أروح أجيب من
+
+462
+00:59:24,250 --> 00:59:36,130
+x، cos y  زائد sin x  زائد x،  بعد ذلك نشتغل بالنسبة
+
+463
+00:59:36,130 --> 00:59:44,550
+إلى x، f<sub>yx</sub>،  أشتق بالنسبة إلى x، cos y بالنسبة
+
+464
+00:59:44,550 --> 00:59:50,970
+إلى x، cos x بالنسبة إلى x، اللي هو −sin x  
+
+465
+00:59:50,970 --> 00:59:57,690
+واحد واثنين from واحد
+
+466
+00:59:57,690 --> 01:00:04,850
+and اثنين we have أنّ
+
+467
+01:00:04,850 --> 01:00:13,510
+الـ Fxy  يُساوي الـ Fyx  لكل قيم x و y بلا استثناء، طيب ما
+
+468
+01:00:13,510 --> 01:00:19,750
+هو السبب يا جماعة؟ لماذا هذه دالة متصلة
+
+469
+01:00:19,750 --> 01:00:24,070
+أم لا؟  في نقطة واحدة تستطيعون أن تجدوا لي نقطة تجعل الدالة
+
+470
+01:00:24,070 --> 01:00:29,850
+غير متصلة؟ لا، هذه  polynomial ، هذه sin ، هذه cos
+
+471
+01:00:29,850 --> 01:00:33,850
+polynomial في sin و polynomial في cos ، يبقى هذه
+
+472
+01:00:33,850 --> 01:00:40,790
+متصلة على طول الخط، مشتقة Fx نفس القصة متصلة، Fxy
+
+473
+01:00:40,790 --> 01:00:48,710
+متصلة، Fy متصلة، f<sub>yx</sub> متصلة، وكذلك كلهم معرفات
+
+474
+01:00:48,710 --> 01:00:54,470
+إذا انطبقت كل شروط النظرية، مدام انطبقت إذا غصب عن
+
+475
+01:00:54,470 --> 01:00:59,950
+اللي ما يرضى بتطلع المقداران هذان متساويان
+
+476
+01:00:59,950 --> 01:01:06,270
+هنا انتهى هذا الـ section وإليكم مجموعة المسائل الـ
+
+477
+01:01:06,270 --> 01:01:11,350
+exercises، أربعة عشر، ثلاثة مسائل
+
+478
+01:01:13,300 --> 01:01:21,540
+من واحد إلى ثمانية وثلاثين، والقدر، وسؤال خمسة وستون
+
+479
+01:01:21,540 --> 01:01:28,960
+وسة وستون، عفواً، عفواً، لسة جايبينها، جايبينها من
+
+480
+01:01:28,960 --> 01:01:33,760
+واحد إلى ثمانية وثلاثين والقدر، ومن واحد وأربعين
+
+481
+01:01:33,760 --> 01:01:42,360
+إلى أربعة وخمسين كذلك، والقدر، وكذلك من اللي هو
+
+482
+01:01:42,360 --> 01:01:52,540
+خمسة وستون، وكذلك خمسة وستة وستون
+
+483
+01:01:52,540 --> 01:02:01,220
+وكذلك من ثلاثة وسبعين إلى ثمانين والقدر
+
+484
+01:02:01,220 --> 01:02:01,840
+كذلك
+
+485
+01:02:11,920 --> 01:02:15,660
+ننتقل هنا إلى الـ section الذي يليه وهو
+
+486
+01:02:15,660 --> 01:02:19,820
+the chain rule، وهي قاعدة السلسلة، نروح نأخذ
+
+487
+01:02:19,820 --> 01:02:23,920
+قاعدة السلسلة في functions of several variables
+
+488
+01:02:23,920 --> 01:02:27,500
+كما درسناها في one variable في Calculus A، في
+
+489
+01:02:27,500 --> 01:02:30,980
+Calculus C، نأخذها في functions of several
+
+490
+01:02:30,980 --> 01:02:35,760
+variables، وسنتدرج فيها من متغيرين إلى ثلاثة
+
+491
+01:02:35,760 --> 01:02:40,740
+متغيرات إلى أربعة إلى نحو ذلك، يبقى أبدأ بنظرية
+
+492
+01:02:40,740 --> 01:02:41,420
+UM
+
+493
+01:03:02,230 --> 01:03:11,550
+continuous partial derivatives
+
+494
+01:03:11,550 --> 01:03:19,390
+Fx
+
+495
+01:03:19,390 --> 01:03:36,330
+و Fy، و F<sub>x</sub> كانت هي x(t) و الـ y هي
+
+496
+01:03:36,330 --> 01:03:43,350
+function of t، وكذلك كلاهما هما are
+
+497
+01:03:43,350 --> 01:03:48,910
+differentiable functions، are differentiable
+
+498
+01:03:48,910 --> 01:03:57,230
+functions of متغير، اسمه t، of t
+
+499
+01:03:59,960 --> 01:04:13,240
+و متساوي f(x(t), y(t)) as a differentiable
+
+500
+01:04:13,240 --> 01:04:17,980
+function، دالة
+
+501
+01:04:17,980 --> 01:04:31,090
+قابلة للاشتقاق of t، و dw/dt  يساوي ∂w/
+
+502
+01:04:31,090 --> 01:04:40,030
+∂x dx/dt  زي ∂w/
+
+503
+01:04:40,030 --> 01:04:48,690
+∂y dy/dt . النظرية الثانية
+
+504
+01:04:48,690 --> 01:04:58,960
+وسأعود إلى النظرية الثانية. تقول إنّ الـ W function في
+
+505
+01:04:58,960 --> 01:05:12,980
+x, y و z is is
+
+506
+01:05:12,980 --> 01:05:20,220
+differentiable، and x,
+
+507
+01:05:20,700 --> 01:05:32,110
+y and z differentiable functions، are differentiable
+
+508
+01:05:32,110 --> 01:05:40,150
+functions of t، then
+
+509
+01:05:40,150 --> 01:05:52,530
+W is a differentiable function of
+
+510
+01:05:52,530 --> 01:05:55,170
+t، and
+
+511
+01:05:58,030 --> 01:06:10,830
+dW/dt  يساوي ∂W/∂x dx/dt  زائد
+
+512
+01:06:10,830 --> 01:06:19,930
+∂W/∂y dy/dt  زائد ∂W/∂z
+
+513
+01:06:19,930 --> 01:06:20,950
+dz/dt
+
+514
+01:07:25,020 --> 01:07:29,980
+طيب نرجع للنظريتين اللي كتبناها مرة ثانية، النظرية
+
+515
+01:07:29,980 --> 01:07:36,880
+الأولى تقول: لو W function في متغيرين x و y، وأخذنا
+
+516
+01:07:36,880 --> 01:07:42,160
+المشتقة الأولى بالنسبة لـ x، والمشتقة الأولى بالنسبة لـ
+
+517
+01:07:42,160 --> 01:07:48,760
+y، وكانتا دالتين متصلتين، وكانت كل من x و y كل واحدة
+
+518
+01:07:48,760 --> 01:07:55,330
+فيهما دالة في متغير آخر، يعني W دالة في من؟ كل واحد
+
+519
+01:07:55,330 --> 01:07:58,710
+من المتغيرين دالة في متغير آخر
+
+520
+01:08:07,390 --> 01:08:17,010
+يعني كان W هو function في t فقط،  dw/dt
+
+521
+01:08:17,010 --> 01:08:22,410
+ماذا يُساوي؟  أقول: ∂w/∂x
+
+522
+01:08:22,410 --> 01:08:29,130
+لماذا قلت ∂  وليس  d ؟ لأني أقول تفاضل جزئي، لأنّ w  فيه
+
+523
+01:08:29,130 --> 01:08:37,000
+متغيرين، لكن عند dx/dt  قلت تفاضل عادي، لماذا؟ لأنّ
+
+524
+01:08:37,000 --> 01:08:41,960
+x  بس function في متغير واحد، يبقى في حالة
+
+525
+01:08:41,960 --> 01:08:46,360
+المتغيرين أو ثلاثة أقول ∂ ، في حالة متغير واحد
+
+526
+01:08:46,360 --> 01:08:52,360
+أقول تفاضل عادي dx/dt  زائد،  ∂w/∂y
+
+527
+01:08:52,360 --> 01:08:55,460
+dy/dt
+
+528
+01:09:01,850 --> 01:09:07,330
+كل واحد من المتغيرات الثلاثة دالة في متغير جديد
+
+529
+01:09:07,330 --> 01:09:11,210
+اللي هو المتغير t، ما شكل المشتقة في هذه
+
+530
+01:09:11,210 --> 01:09:15,290
+الحالة، أو ما شكل الـ general ؟ أقول dw/dt
+
+531
+01:09:15,290 --> 01:09:24,910
+( تكرار لفظ "دي" )
+
+532
+01:09:24,910 --> 01:09:29,590
+دي
+
+533
+01:09:31,840 --> 01:09:37,640
+الكلام من خلال الأمثلة، نيجي لبعض الأمثلة
+
+534
+01:09:37,640 --> 01:09:44,660
+أول
+
+535
+01:09:44,660 --> 01:09:54,100
+مثال يقول لي: express  عبّر لي
+
+536
+01:09:54,100 --> 01:09:59,200
+عن dw/dt
+
+537
+01:10:04,320 --> 01:10:11,360
+function of t by two
+
+538
+01:10:11,360 --> 01:10:16,280
+methods، بطريقة
+
+539
+01:10:16,280 --> 01:10:20,200
+ثانية، طريقة
+
+540
+01:10:20,200 --> 01:10:28,280
+الأولى، by using chain
+
+541
+01:10:28,280 --> 01:10:29,800
+rule
+
+542
+01:10:38,360 --> 01:10:47,080
+الثانية، by expressing... by expressing
+
+543
+01:10:47,080 --> 01:10:52,060
+w
+
+544
+01:10:52,060 --> 01:11:00,480
+as a function of t directly
+
+545
+01:11:08,830 --> 01:11:15,870
+السؤال B، احسب
+
+546
+01:11:15,870 --> 01:11:26,730
+dW/dt at the given value
+
+547
+01:11:26,730 --> 01:11:35,550
+of t، السؤال
+
+548
+01:11:35,550 --> 01:11:50,760
+الأول، يقول:  W = x<sup>2</sup> + y<sup>2</sup>، والـ
+
+549
+01:11:50,760 --> 01:12:04,100
+x = cos t + sin t، والـ y = cos t − sin t، و t = 0
+
+550
+01:12:04,100 --> 01:12:07,960
+. t = 0
+
+551
+01:12:31,760 --> 01:12:37,520
+قبل أن نبدأ المثال، حابب أضع ما أخذناه على
+
+552
+01:12:37,520 --> 01:12:43,180
+أرض الواقع عملياً، من خلال رسم، بمعنى أنه ممكن تنسى
+
+553
+01:12:43,180 --> 01:12:47,960
+ممكن تنسى، ممكن تخطئ، لكن الرسم دائماً يجعلك
+
+554
+01:12:47,960 --> 01:12:52,820
+معلوماتك دقيقة مئة بالمئة، فبالنسبة للمشتقة
+
+555
+01:12:52,820 --> 01:12:57,120
+الأولى، أكتبها على شكل رسم، وبعدين أكمل وأحصل
+
+556
+01:12:57,120 --> 01:13:02,300
+على السؤال، هذه الجهة لنبدأ عملية الحل، هذا بدأ، أحاول
+
+557
+01:13:02,300 --> 01:13:07,760
+أرسم، من النقطة، النقطة الأولى، الآن بدأت، أقول: الـ
+
+558
+01:13:07,760 --> 01:13:12,760
+W هي function في من؟ في متغيرين، هذا ما أقوله
+
+559
+01:13:12,760 --> 01:13:18,080
+أقول هي النقطة، عندها أقول: W هي function
+
+560
+01:13:18,080 --> 01:13:23,520
+في x و y، إذن هنا أبدأ أضع خطاً وهنا خطاً، أبدأ أضع هنا x
+
+561
+01:13:23,520 --> 01:13:34,720
+وهنا y، بعد ذلك، كل من x و y في متغير واحد، يبقى
+
+562
+01:13:34,720 --> 01:13:43,420
+هذا t، بعد ذلك بالنسبة لـ x و W فيهما متغيرين، إذن
+
+563
+01:13:43,420 --> 01:13:49,120
+الاشتقاق هذا يكون اشتقاق جزئي، ∂W/∂x
+
+564
+01:13:49,120 --> 01:13:53,880
+بنفس الطريقة، هذا اشتقاق جزئي، ∂W/∂y
+
+565
+01:13:53,880 --> 01:14:00,550
+لكن من x إلى t  هذا متغير واحد يبقى
+
+566
+01:14:00,550 --> 01:14:09,190
+dx/dt  وهذا dy/dt  الذي سنضربه في هذا، في هذا زائد هذا في هذا،  ماذا يعطيك الآن
+
+567
+01:14:09,190 --> 01:14:18,150
+هذا في هذا زائد هذا في هذا، ماذا يُعطيك؟ الآن هذا بالضبط، صحيح أم لا؟
+
+568
+01:14:18,150 --> 01:14:19,590
+هذا بالضبط، صحيح أم لا؟
+
+569
+01:14:27,350 --> 01:14:31,070
+طيب، هذا بالنسبة للحالة التي و... الحالة
+
+570
+01:14:31,070 --> 01:14:35,550
+الثانية، لو كان ثلاثة متغيرات، أعملها بنفس الطريقة
+
+571
+01:14:35,550 --> 01:14:42,050
+يبقى أقول: W هي function في x و y و z، إذن
+
+572
+01:14:42,050 --> 01:14:48,700
+أكون عندي ثلاثة متغيرات، هذا الـ x وهذا الـ y وهذا
+
+573
+01:14:48,700 --> 01:14:55,760
+الـ z، كل واحد منهم دالة في نفس المتغير الذي هو t
+
+574
+01:15:00,160 --> 01:15:06,300
+هذه الدالة في ثلاثة متغيرات xyz، يبقى هذا اشتقاق جزئي
+
+575
+01:15:06,300 --> 01:15:11,220
+وهذا ∂W/∂y وهذا ∂W/∂z
+
+576
+01:15:11,220 --> 01:15:21,960
+الباقي اشتقاق عادي، يبقى dx/dt، dy/dt، dz/dt
+
+577
+01:15:21,960 --> 01:15:30,460
+نضربهم في بعض، هذه في هذه، هذه في هذه، ونجمع
+
+578
+01:15:30,460 --> 01:15:35,920
+بتعرفين القاعدة الثانية تماماً؟ يعني لو أنا
+
+579
+01:15:35,920 --> 01:15:41,080
+نسيت،  لا أعرف كيف أحفظها، أو حفظ الطلاب من خلال
+
+580
+01:15:41,080 --> 01:15:44,800
+الـ diagram الذي أمامنا هذا أو الشكل الهندسي الذي
+
+581
+01:15:44,800 --> 01:15:52,920
+أمامنا أستطيع أن أجيب على السؤال حتى لو نسيتها،  نيجي
+
+582
+01:15:52,920 --> 01:15:56,900
+أضع هذه المعلومة لأن عندنا سؤال و نأتي
+
+583
+01:15:56,900 --> 01:16:07,600
+إلى solution  السؤال،  لدينا W function في x
+
+584
+01:16:07,600 --> 01:16:13,080
+و y، والـ x function في t، والـ y function في t، و
+
+585
+01:16:13,080 --> 01:16:17,640
+قال لي احسب عند t = 0، ماذا سأحسب؟
+
+586
+01:16:18,290 --> 01:16:25,830
+قال لي عبّر عن dw/dt  بدلالة t بطريقة ثانية،
+
+587
+01:16:25,830 --> 01:16:30,070
+الطريقة الأولى باستخدام chain rule، كما نحن
+
+588
+01:16:30,070 --> 01:16:38,410
+كاتبونه، إذا جئت أقول له: dw/dt  = ∂w/∂x
+
+589
+01:16:38,410 --> 01:16:46,990
+dx/dt + ∂w/∂y dy/dt
+
+590
+01:17:03,230 --> 01:17:12,770
+مشتقة W بالنسبة لـ x، يبقى y ثابتة،  مشتقة
+
+591
+01:17:12,770 --> 01:17:24,970
+x بالنسبة إلى t، = −sin t + cos t
+
+592
+01:17:24,970 --> 01:17:33,110
+من الشطر الأول dx/dt، الذي بعدها زائد، مشتقة W
+
+593
+01:17:33,110 --> 01:17:41,030
+بالنسبة لـ y، = 2y، مشتقة y بالنسبة لـ t، = −sin t + cos t
+
+594
+01:17:41,030 --> 01:17:49,530
+ماذا قال؟ قال إنه يريد هذا الكلام
+
+595
+01:17:49,530 --> 01:17:55,130
+كدالة في t،  يبقى لا يريد x و y  أن يكونوا في النتيجة
+
+596
+01:17:55,130 --> 01:17:59,510
+مرة واحدة، يريد النتيجة كلها بدلالة t، طيب ماهي
+
+597
+01:17:59,510 --> 01:18:03,970
+المشكلة، ماهو الشيء لديك؟ يبقى هذا يساوي 2x
+
+598
+01:18:03,970 --> 01:18:13,140
+الذي فوق، وهو ماذا؟  الذي هو cos t + sin t
+
+599
+01:18:13,140 --> 01:18:24,000
+وهذا، الذي هو cos t − sin t، + 2، والـ y  التي فوق
+
+600
+01:18:24,000 --> 01:18:38,060
+cos t + sin t  × (−sin t + cos t)
+
+601
+01:18:38,470 --> 01:18:44,150
+غير صحيح، فماذا سيحدث؟  السالب مع السالب نخرجهما، فيصبح الذي
+
+602
+01:18:44,150 --> 01:18:50,030
+خارج هذا ماذا؟ سالب، ويصبح لدينا من؟ يصبح لدينا
+
+603
+01:18:50,030 --> 01:18:58,750
+cos t + sin t ، إذاً
+
+604
+01:18:58,750 --> 01:19:05,530
+تريدين تفكينها؟ تفكينها، لكن بمجرد النظر، هذا هو
+
+605
+01:19:05,530 --> 01:19:14,210
+هذا صحيح أم لا؟  يُريد المشتقة، تُساوي هذا، الفرق بين
+
+606
+01:19:14,210 --> 01:19:21,530
+المربعين، مربع الأول ناقص مربع الثاني، مربع
+
+607
+01:19:21,530 --> 01:19:24,690
+الأول ناقص مربع الثاني، مربع الأول ناقص مربع
+
+608
+01:19:24,690 --> 01:19:30,910
+الثاني، مربع الأول ناقص مربع الثاني، مربع الأول
+
+609
+01:19:30,910 --> 01:19:32,370
+ناقص مربع الثاني
+
+610
+01:19:35,440 --> 01:19:41,740
+حسب طريقة حلّها من البداية، إذا أعطيتني W
+
+611
+01:19:41,740 --> 01:19:45,400
+كـ function في t، وأثبت أن المشتقة هذه تُساوي
+
+612
+01:19:45,400 --> 01:19:50,980
+صفر، تُساوي صفر،  صفر بسيطة، وجبتِ
+
+613
+01:19:50,980 --> 01:19:55,750
+النقطة الثانية، يجب أن أقول:  يجب أن أقول
+
+614
+01:19:55,750 --> 01:20:00,410
+يجب أن أقول: يجب
+
+615
+01:20:00,410 --> 01:20:07,830
+أن أقول: يجب
+
+616
+01:20:07,830 --> 01:20:11,090
+أن
+
+617
+01:20:11,090 --> 01:20:12,830
+أقول:
+
+618
+01:20:19,960 --> 01:20:31,540
+2 sin t cos t + sin<sup>2</sup> t + cos<sup>2</sup> t
+
+619
+01:21:06,440 --> 01:21:13,600
+هذه بالموجب وهذه بالموجب عند cos<sup>2</sup> و cos
+
+620
+01:21:13,600 --> 01:21:15,620
+تربيع
+
+621
+01:21:25,430 --> 01:21:30,830
+يبقى cos<sup>2</sup> t + sin<sup>2</sup> t أو أيضاً sin
+
+622
+01:21:30,830 --> 01:21:38,470
+<sup>2</sup> 2 sin<sup>2</sup> t لو أخذنا 2  عاملاً مشتركاً
+
+623
+01:21:38,470 --> 01:21:42,630
+
+667
+01:28:17,580 --> 01:28:24,880
+ناقص واحد ناقص sign XYT
+
+668
+01:28:25,630 --> 01:28:31,530
+Limit T يبقى بطلة تصير الدالة هذه مانها Function
+
+669
+01:28:31,530 --> 01:28:38,310
+في X وY وإنما صارت دالة في مين؟ في متغير واحد اللي
+
+670
+01:28:38,310 --> 01:28:43,870
+هو T، يبقى مجتق مباشرة إذا لو جاءت اشتقها دي برضه،
+
+671
+01:28:43,870 --> 01:28:51,890
+إيش سيحصل؟ DW by DT بده يساوي ال exponential زي ما
+
+672
+01:28:51,890 --> 01:28:54,270
+هي ضرب مشتقة الأس
+
+673
+01:28:59,890 --> 01:29:12,070
+ب cos T لن T ضرب مشتقة الزاوية T في واحد على T
+
+674
+01:29:12,070 --> 01:29:22,150
+زائد لن الـ T نختصر يبقى هذه E أس T ناقص واحد ناقص
+
+675
+01:29:22,150 --> 01:29:30,880
+cos T لن T في واحد زائد لن T هل اختلفوا الإجابتين
+
+676
+01:29:30,880 --> 01:29:35,040
+على البعض هنا؟ طلع الإجابة اللي مبروزة والإجابة
+
+677
+01:29:35,040 --> 01:29:39,600
+اللي قدامها دنتين نفس الشيء لذلك على كل الأمرين
+
+678
+01:29:39,600 --> 01:29:46,660
+كله بيعطينا نفس النتيجة طيب نقرأ فيه قال لي بدي
+
+679
+01:29:46,660 --> 01:29:53,720
+تحسبلي DW على DT عند T تساوي درجة واحد فبعدين
+
+680
+01:29:53,720 --> 01:30:01,850
+بقوله DW على DT عند T تساوي واحد فهذا بيصير ايه
+
+681
+01:30:01,850 --> 01:30:11,230
+و لكنه كما ناقص ناقص cosine واحد لن الواحد مصبوط
+
+682
+01:30:11,230 --> 01:30:20,550
+هيك لن الواحد وعندك هنا في واحد زائد لن الواحد
+
+683
+01:30:20,550 --> 01:30:24,730
+فهذا بيقدر واحد لن الواحد
+
+684
+01:30:30,390 --> 01:30:37,750
+لأن هذا يصير النتيجة يساوي واحد ناقص كده يبقى
+
+685
+01:30:37,750 --> 01:30:44,530
+الجواب كمان يساوي صفر إذا عند T تساوي واحد قيمة
+
+686
+01:30:44,530 --> 01:30:51,250
+هذه المشتقة تساوي صفر لحد هنا stop و بنكمل إن شاء
+
+687
+01:30:51,250 --> 01:30:56,660
+الله المرة القادمة لسه بننتقل الآن بدل ال X و ال Y
+
+688
+01:30:56,660 --> 01:31:03,160
+بدل ما يكون متغير واحد بنخليها في main يعني W دالة
+
+689
+01:31:03,160 --> 01:31:11,020
+في X و Y و Z وكل من X و Y و Z دالة في متغيرين و
+
+690
+01:31:11,020 --> 01:31:16,000
+بعدين ناخد special cases كمان يعني لسه لنا شغل في
+
+691
+01:31:16,000 --> 01:31:21,240
+هذا ال section سنكمله إن شاء الله في المرة القادمة
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/481Vfp-Apr4_postprocess.srt b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/481Vfp-Apr4_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..4a6685def5c57f9199b1d3f98f9b80d83f2be79e
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/481Vfp-Apr4_postprocess.srt
@@ -0,0 +1,2764 @@
+1
+00:00:00,000 --> 00:00:02,680
+موسيقى
+
+2
+00:00:15,840 --> 00:00:20,180
+بسم الله الرحمن الرحيم ابتدنا في شبطر اربعة عشر
+
+3
+00:00:20,180 --> 00:00:24,540
+واخدنا فيه two sections ال two sections بتحدث عن
+
+4
+00:00:24,540 --> 00:00:29,560
+ال functions of several variables أخدنا كيف بنجيب
+
+5
+00:00:29,560 --> 00:00:32,880
+ال domain و ال range لهذه ال functions و اتعرفنا
+
+6
+00:00:32,880 --> 00:00:37,460
+كذلك على level curves و level surfaces للمنحنيات
+
+7
+00:00:37,460 --> 00:00:44,780
+او الصطوحبعد ذلك ننتقل إلى جد ال limit و ال
+
+8
+00:00:44,780 --> 00:00:49,760
+continuity للدالة of several variables الان في
+
+9
+00:00:49,760 --> 00:00:55,260
+section 14-3 سنذهب إلى derivatives of functions of
+
+10
+00:00:55,260 --> 00:00:59,660
+several variablesبنبدأ بمتغيرين ثم نذهب لثلاث
+
+11
+00:00:59,660 --> 00:01:05,440
+متغيرات أو أكتر لنتدرج في فهم الموضوع فعندي
+
+12
+00:01:05,440 --> 00:01:10,980
+partially derivatives يعني المشتقات الجزئية في
+
+13
+00:01:10,980 --> 00:01:15,440
+مشتقة كلية و في مشتقة جزئية الإجابة نعم متى تكون
+
+14
+00:01:15,440 --> 00:01:20,860
+المشتقة الكلية و متى تكون المشتقة الجزئيةبتكون
+
+15
+00:01:20,860 --> 00:01:24,900
+المشتقة الكلية إذا عندي function في one variable
+
+16
+00:01:24,900 --> 00:01:29,220
+يبقى بقول هذا اسم اشتقاق كلي total differentiation
+
+17
+00:01:29,220 --> 00:01:34,580
+يبقى بقول dy على dx سوى f prime of x عندي تبقى
+
+18
+00:01:34,580 --> 00:01:38,880
+الدالة y في متغير واحد أما إذا كانت الدالة في
+
+19
+00:01:38,880 --> 00:01:43,180
+متغيرين أو ثلاثة أو أربعة ففي هذه الحالة الاشتقاق
+
+20
+00:01:43,180 --> 00:01:47,600
+بيكون اشتقاق جزءياللي هو الموضوع لليوم فبقى دي
+
+21
+00:01:47,600 --> 00:01:51,800
+بقول في partial derivative المشتقة الجزئية للدالة
+
+22
+00:01:51,800 --> 00:01:57,420
+f of x و y بالنسبة للمتغير x عند النقطة x node و y
+
+23
+00:01:57,420 --> 00:02:02,940
+node as هديها الرمز f و حكم تحتها اللي هو ال index
+
+24
+00:02:02,940 --> 00:02:08,340
+x اللي هو الدليل x يعني ايش معناها؟ معناها المشتقة
+
+25
+00:02:08,340 --> 00:02:12,440
+بالنسبة ل x و بكتبها على الصورة partial f على
+
+26
+00:02:12,440 --> 00:02:15,700
+partial x هدى كمان اللي بقيت اكتب دي عادية
+
+27
+00:02:19,890 --> 00:02:24,450
+يبقى و تقرأ partial F على partial X و يُفهَم منها
+
+28
+00:02:24,450 --> 00:02:29,550
+أننا نريد أن نشتغل الدالة بالنسبة إلى X طب إذا
+
+29
+00:02:29,550 --> 00:02:34,850
+جئنا لنشتغل X ما أخبار ال Y يبقى ال Y بنعتبرها
+
+30
+00:02:34,850 --> 00:02:40,890
+مقدارا ثابتا تمام اتطلع الكلام اللي أنا بقوله
+
+31
+00:02:40,890 --> 00:02:46,910
+هيحطنا عليها على التعريفهذا هو الـ Limit عندما الـ
+
+32
+00:02:46,910 --> 00:02:53,730
+H تذهب إلى الـ 0 لـ F of X0 زائد H وY0 يبقى ثبتنا
+
+33
+00:02:53,730 --> 00:02:59,430
+الـ Y0 وعملنا تغيير في الـ X لأننا نقص F of X0 وY0
+
+34
+00:02:59,430 --> 00:03:05,330
+على H هل شكل التعريف اختلف فيه مضمونه عن التعريف
+
+35
+00:03:05,330 --> 00:03:08,950
+تبع الـ function of one variable؟مش هو نفس التعريف
+
+36
+00:03:08,950 --> 00:03:12,770
+الـ derivative العادى؟ طيب هذا لو كان الاشتقاق
+
+37
+00:03:12,770 --> 00:03:17,510
+بالنسبة ل X طب لو كان الاشتقاق بالنسبة ل Y يبقى
+
+38
+00:03:17,510 --> 00:03:22,310
+نفسي المفهوم اذا اقول FY أو partial F على partial
+
+39
+00:03:22,310 --> 00:03:29,210
+Y عند النقطة X node وY node هو limitبثبت ال X node
+
+40
+00:03:29,210 --> 00:03:33,370
+كإنه مقدار ثابت و بروح باخد التغيير اللي بيحصل في
+
+41
+00:03:33,370 --> 00:03:38,490
+مهم في ال Y فبقول Y node زي ال H نقص of X node و Y
+
+42
+00:03:38,490 --> 00:03:43,750
+node على مين على H بشرط إن ال limit في كلتل حالتين
+
+43
+00:03:43,750 --> 00:03:49,670
+exist يعني ال derivative هذا بيحصل إذا كان عندى
+
+44
+00:03:49,670 --> 00:03:56,220
+إذا كان ال limit هذه مالها existالروح نحط هذا على
+
+45
+00:03:56,220 --> 00:04:08,180
+أرض الواقع فباجي بقول ف f w مثلا تساوي f of x و y
+
+46
+00:04:08,180 --> 00:04:18,520
+و ذهب يبقى باجي بقول to find لإيجاب نمر راحة
+
+47
+00:04:28,130 --> 00:04:38,030
+Y and Z are constants يبقى
+
+48
+00:04:38,030 --> 00:04:44,410
+دول بنعتبرهم ثوابت طيب نمر اتنين لو بدي partial F
+
+49
+00:04:44,410 --> 00:04:49,030
+على partial Y يبقى هنا باجي بقول
+
+50
+00:04:59,080 --> 00:05:05,380
+لو بدنا ال partial F على partial Z و ي consider
+
+51
+00:05:05,380 --> 00:05:15,900
+بنروح نعتبر ان ال X and ال Y are constants و هكذا
+
+52
+00:05:18,560 --> 00:05:23,940
+بدا من الأن فصعدنا بنات لو كانت الدالة في متغيرين
+
+53
+00:05:23,940 --> 00:05:29,960
+و بدى مشتقة بالنسبة لأحد المتغيرين فبعتبر المتغير
+
+54
+00:05:29,960 --> 00:05:34,720
+الثاني ماله ثابت عند الاشتقاء إذا و الله الدالة في
+
+55
+00:05:34,720 --> 00:05:39,840
+ثلاثة متغيرات بدى أشتق بالنسبة لأحدهم يبقى بعتبر
+
+56
+00:05:39,840 --> 00:05:44,200
+الأثنين الأخرين مقادير ثابتة يعني مشتقة كل واحد
+
+57
+00:05:44,200 --> 00:05:49,180
+فيهم جد إيشبصفر ب zero يعني بعتبر مقدار ثابت و
+
+58
+00:05:49,180 --> 00:06:02,480
+هكذا نعطي أمثلة توضيحية على ذلك مثال الأول
+
+59
+00:06:02,480 --> 00:06:06,580
+find fx
+
+60
+00:06:06,580 --> 00:06:14,860
+and fy for the following
+
+61
+00:06:22,270 --> 00:06:33,290
+F of X Y يساوي Y في تان X تربيع Y تكعين
+
+62
+00:06:39,010 --> 00:06:49,270
+بدها تساوي E أُس XY في صين تكييب X تربيع زائد Y
+
+63
+00:06:49,270 --> 00:07:00,530
+تربيع زائد تلت XY نمرس E F of X وY بديه يساوي
+
+64
+00:07:00,530 --> 00:07:05,970
+integration من X squared plus one ل Y
+
+65
+00:07:31,900 --> 00:07:37,090
+مرة تانيةالمعلومة النظرية اللي أخدناها بالنسبة
+
+66
+00:07:37,090 --> 00:07:41,670
+لمشتقة دلة بالنسبة لأحد المتغيرات نعطي أمثلة
+
+67
+00:07:41,670 --> 00:07:46,450
+توضيحية عليها المثال بيقول لهاتف المشتقة الدلة
+
+68
+00:07:46,450 --> 00:07:51,330
+بالنسبة ل X وكذلك مشتقة الدلة بالنسبة ل Y لكل من
+
+69
+00:07:51,330 --> 00:07:53,530
+الدول التالية
+
+70
+00:08:16,440 --> 00:08:24,240
+بنبدأ بالنقطة الأولىيبدأ يجيب مشتقتها بالنسبة إلى
+
+71
+00:08:24,240 --> 00:08:31,780
+X يبقى يجي إلى FX يعني مشتقة ال F بالنسبة إلى X
+
+72
+00:08:31,780 --> 00:08:36,960
+ونلفهايها يبقى ال Y أشهر اعتبر يا بنات مقدار ثابت
+
+73
+00:08:36,960 --> 00:08:41,400
+بقول يا Y خليك زي ما انت مالكش تعرف وتفضل التان
+
+74
+00:08:42,140 --> 00:08:49,580
+كداش؟ ب 6² الزاوية الزاوية اللي هي من X تربية و Y
+
+75
+00:08:49,580 --> 00:08:53,700
+تكييب طبق اللي تشينره المظروف في مشتقة الزاوية
+
+76
+00:08:53,700 --> 00:08:59,800
+بالنسبة ل X يبقى Y تكييب مقدارا ثابتا مالوش دعوة
+
+77
+00:08:59,800 --> 00:09:07,640
+مشتقة ال X تربية ب2X وال Y تكييب تبقى كما هي واضحة
+
+78
+00:09:07,640 --> 00:09:16,550
+الآن هذي؟ طيبنجيب fy تساوي اللي هو تفاضل ال f
+
+79
+00:09:16,550 --> 00:09:25,210
+بالنسبة إلى y partial f by partial y ايوة هذي y و
+
+80
+00:09:25,210 --> 00:09:30,770
+هذي y يبقى هذي مشتقتها عاصل ضرب دلتين نرجع لك
+
+81
+00:09:30,770 --> 00:09:35,150
+القلص او لثانوية الأولى في مشتقة ثانية زائدة ثانية
+
+82
+00:09:35,150 --> 00:09:40,940
+في مشتقة الأولى يبقى الأولىمشتقة الثانية تفاضل
+
+83
+00:09:40,940 --> 00:09:50,200
+التان بسكت ربيع X ربيع Y تكيب في مشتقة الزاويةليه
+
+84
+00:09:50,200 --> 00:09:55,880
+تلاتة Y تربيع والـ X تربيع مقدارا ثابتا يبقى فيه
+
+85
+00:09:55,880 --> 00:10:01,840
+تلاتة X تربيع وY تربيع هذه الأولى في مشتقة الثانية
+
+86
+00:10:01,840 --> 00:10:06,300
+زائد الدالة الثانية في مشتقة الأولى مشتقة الأولى
+
+87
+00:10:06,300 --> 00:10:13,580
+في قداش؟ بواحد صحيح يبقى زائد تان X تربيع Y تكعيب
+
+88
+00:10:13,580 --> 00:10:15,800
+نمر بيه
+
+89
+00:10:18,840 --> 00:10:23,880
+برضه بنفس الطريقة هذه تعتبر function وتحتوي على ال
+
+90
+00:10:23,880 --> 00:10:28,840
+X و ال Y وهذه function تحتوي على ال X و ال Y يبقى
+
+91
+00:10:28,840 --> 00:10:33,760
+عليك كل الأمرين سواء كان بدنا Fx أو Fy فهي مشتقة
+
+92
+00:10:33,760 --> 00:10:37,860
+حاسوب ضرب ده اللي يتم بجل الدالة الأولى اللي هي
+
+93
+00:10:37,860 --> 00:10:44,800
+Fxy و 7 مشتقة الأولى بجداش يا بنات ال X بوننشل زي
+
+94
+00:10:44,800 --> 00:10:54,450
+مهيضرب مشتقة الأس بالنسبة ل X اللي هو بقداش مشتقة
+
+95
+00:10:54,450 --> 00:11:01,670
+الأس بالنسبة إيه ل X يعني Y ثابت يقداش Y تمام
+
+96
+00:11:01,670 --> 00:11:07,190
+فاهمين هي مشتقة الأولى في الثانية في sign تكيب X
+
+97
+00:11:07,190 --> 00:11:15,050
+تربيع زائد Y تربيع زائد طول XY زائدالدالة الأولى
+
+98
+00:11:15,050 --> 00:11:21,290
+زى ماهى u s x y في تفاضل الدالة التانية يبقى تفاضل
+
+99
+00:11:21,290 --> 00:11:29,550
+التانية التلاتة sin تربيع فى مين فى x تربيع زائد y
+
+100
+00:11:29,550 --> 00:11:36,050
+تربيع زائد تلت x y فى تفاضل ال sin اللى همين
+
+101
+00:11:36,050 --> 00:11:40,590
+بكوسين يبقى كوسين نفس الزاوية
+
+102
+00:11:47,060 --> 00:11:51,940
+لأ ما خلصناش لسه بدك تضرب في تفاضل الزاوية بالنسبة
+
+103
+00:11:51,940 --> 00:11:57,720
+لمين؟ بالنسبة لمين؟ لأكس يبقى هذا بده يضرب يا بنات
+
+104
+00:11:57,720 --> 00:12:04,840
+في مين؟ في تفاضل الزاوية اللي هو اتنين X فقط زائد
+
+105
+00:12:04,840 --> 00:12:14,240
+تلت Y شكل اللعنةيبقى I اشتقنها اشتقاقا كاملا طبعا
+
+106
+00:12:14,240 --> 00:12:20,160
+ممكن يكون عندى اختصار ان التلاتة داخلتها بصير 6X و
+
+107
+00:12:20,160 --> 00:12:26,000
+هنا زائد Y تفرجش مش كتير طيب هذا ال Fx بدنا نروح
+
+108
+00:12:26,000 --> 00:12:32,140
+نجيب ال Fyy ساوى يبقى بنشتق دالة بالنسبة ل Y يبقى
+
+109
+00:12:32,140 --> 00:12:37,740
+ال exponential زي ما هو تتفضل أس بالنسبة إيه ل Y
+
+110
+00:12:37,740 --> 00:12:47,440
+لهو كده ب Xفاهمين؟ في sign تكييب X تربيع زائد Y
+
+111
+00:12:47,440 --> 00:12:54,980
+تربيع زائد طول XY جاي مشتقة الأولى في الثانية زائد
+
+112
+00:12:54,980 --> 00:13:02,160
+الأولى كما هي في مشتقة الثانية sign تكييب لتلاتة
+
+113
+00:13:02,160 --> 00:13:11,480
+sign تربيع الزاوية X تربيعزائد تلت XY في تفاضل
+
+114
+00:13:11,480 --> 00:13:16,940
+الـSin اللي هو الـ Cos X تربيع زائد Y تربيع زائد
+
+115
+00:13:16,940 --> 00:13:25,760
+تلت XY غرب مشتقة الزاوية بالنسبة ل Y اللي هي اتنين
+
+116
+00:13:25,760 --> 00:13:33,440
+Y زائد تلت X هيك اشتقناها اشتقاقا كاملا
+
+117
+00:13:58,800 --> 00:14:07,100
+طيب، نجي لمن؟ للمراسي، المراسي بده مشتقة هذه و هذه
+
+118
+00:14:07,100 --> 00:14:11,080
+عندي تكامل، إذا نروح نكامل الدل و بعدين نشتق،
+
+119
+00:14:11,080 --> 00:14:17,150
+كويس؟لأ بروح اللي ماعنش طبق التكامل ايوة تروح
+
+120
+00:14:17,150 --> 00:14:21,650
+تكامل يبنيك مثلة بتقدريش تتكاملها زي المثلة اللي
+
+121
+00:14:21,650 --> 00:14:26,370
+قدامنا هذا صعب تكاملها very difficult يبقى المقصود
+
+122
+00:14:26,370 --> 00:14:30,030
+مش تروح تكامل انا بقى بتشتق اصدقاء اه اخدنا على
+
+123
+00:14:30,030 --> 00:14:33,550
+ذلك اللي هى مين في كالكولاسيا شو اسم هى النظرية؟
+
+124
+00:14:33,550 --> 00:14:37,930
+fundamental theory of calculus يبقى انا بده اروح
+
+125
+00:14:37,930 --> 00:14:42,560
+اطبق ال fundamentalTheorem of calculus مع مراعاة
+
+126
+00:14:42,560 --> 00:14:48,960
+مين ثابت ومين المتغير يبقى انا بده Fx بده اشتقاد
+
+127
+00:14:48,960 --> 00:14:53,800
+بالنسبة ل X يبقى ال Y ايش تعتبر ثابت اذا هذا يعتبر
+
+128
+00:14:53,800 --> 00:15:01,860
+مقدارا ثابتا يبقى هذا بدي اقول اللي فوق B0 ناقص
+
+129
+00:15:01,860 --> 00:15:09,530
+يبقى هاي ال zero ناقصnotes mean بدي أشيل كل T و
+
+130
+00:15:09,530 --> 00:15:14,190
+أحط مكانها X تربية زائد واحد إذا هذا إيش بتصير
+
+131
+00:15:14,190 --> 00:15:25,210
+sign X تربية زائد واحد fill in بدي أشيل ال T و أحط
+
+132
+00:15:25,210 --> 00:15:32,360
+مكانها X تربيةزائد واحد لكل تربية ناقص واحد ضرب
+
+133
+00:15:32,360 --> 00:15:46,740
+مشتق تمين الدل اللي هو قداش باتنين X طبعا
+
+134
+00:15:46,740 --> 00:15:51,200
+يمكن اختصاره افك هذا وقت مش مشكلة المهم ان اعرف
+
+135
+00:15:51,200 --> 00:15:58,010
+كيف انطبق النظرية طب لو بده fy يا بناتيبقى هذا
+
+136
+00:15:58,010 --> 00:16:03,770
+يعتبر كله كأنه مقدار ثالث يبقى اش باجي بقول بشيل
+
+137
+00:16:03,770 --> 00:16:12,750
+كل T و بحط مكانها Y يبقى اش بصير sign Y تكيب تمام
+
+138
+00:16:12,750 --> 00:16:18,170
+يبقى شيلت ال T و حطيت مكانها اللي هو Y تكيب لن
+
+139
+00:16:30,810 --> 00:16:34,850
+أبقى بنات لو كانت هذه دالة في X وهذه دالة في X
+
+140
+00:16:34,850 --> 00:16:41,870
+وطلبت المشتقة بالنسبة لي Yزيرو ممتاز جدا يبقى لو
+
+141
+00:16:41,870 --> 00:16:45,590
+كانت الدالة اللى فوق بدلالة X ودلالة تحت ال index
+
+142
+00:16:45,590 --> 00:16:50,230
+التابع التكامل بدلالة X وطلبت المشتقة بالنسبة الى
+
+143
+00:16:50,230 --> 00:16:56,070
+Y إذن اوتوماتيك المشتقة تسوى جداش Zero و بالمثل لو
+
+144
+00:16:56,070 --> 00:17:01,870
+كانت الدالة الاثنين متغيرين في Y وطلبت المشتقة
+
+145
+00:17:01,870 --> 00:17:07,610
+بالنسبة ل X النتج يساوي Zero تمام تمامطيب بعد ما
+
+146
+00:17:07,610 --> 00:17:13,590
+انتهينا من هذا المثال بروح ناخد مثال اخر مثال
+
+147
+00:17:13,590 --> 00:17:18,070
+اتنين بيقول
+
+148
+00:17:18,070 --> 00:17:31,270
+find ال fx ال fx و ال fy and ال fz
+
+149
+00:17:49,650 --> 00:18:03,510
+Y و Z تساوي X في E أُس Y زائد Y في E أُس Z زائد Z
+
+150
+00:18:03,510 --> 00:18:15,870
+في E أُس X لمين؟ F of X و Y و Z يساوي 10 Inverse
+
+151
+00:18:15,870 --> 00:18:22,250
+لمين؟ لل X Yزائد YZ
+
+152
+00:18:54,230 --> 00:18:59,470
+الفرق بين المثال رقم اتنين والمثال رقم واحد ان
+
+153
+00:18:59,470 --> 00:19:03,130
+المثال رقم واحد كان function في two variables بس
+
+154
+00:19:03,130 --> 00:19:07,910
+ده function في three variables طلب المشتقة بالنسبة
+
+155
+00:19:07,910 --> 00:19:11,910
+ل X والمشتقة بالنسبة ل Y والمشتقة بالنسبة ل Z إذا
+
+156
+00:19:11,910 --> 00:19:15,450
+بدنا نعمل السؤال بنفس الطريقة اللي عملنا فيها
+
+157
+00:19:15,450 --> 00:19:27,570
+السؤال السابق بدالي للمرة AY و
+
+158
+00:19:27,570 --> 00:19:35,850
+Z ثابت و X هو المتغير يبقى EY كله مقدر ثابت تفضل X
+
+159
+00:19:35,850 --> 00:19:44,650
+جدًا واحد يبقى EY هذا كله Zero هذا Z ثابت ومشتقة
+
+160
+00:19:44,650 --> 00:19:52,620
+EY بالـ EY itselfطبعا طبعا هذا ال f of x بدي ال fy
+
+161
+00:19:52,620 --> 00:20:01,600
+يزاوي ال x ثابت مالكش دعوة مشتقة ال ey بال ey
+
+162
+00:20:01,600 --> 00:20:02,480
+itself
+
+163
+00:20:18,880 --> 00:20:25,300
+مشتقتها صفر هذه ال Y كما هي مشتقة ال E و ال Z بال
+
+164
+00:20:25,300 --> 00:20:32,360
+E و ال Z اتسل مشتقة ال Z بواحد بطارية نمية E أس X
+
+165
+00:20:32,360 --> 00:20:36,900
+طيب و جيبنا المشتقات التلاتة للنقطة الأولى النقطة
+
+166
+00:20:36,900 --> 00:20:43,960
+التانية اللي نمر بيها فنجيب لها F X يساعد حد فيكم
+
+167
+00:20:43,960 --> 00:20:50,100
+الذاكرة كده مشتقتان inverse Xمنتاج واحد على واحد
+
+168
+00:20:50,100 --> 00:20:54,940
+زائد اكثر بما كان ال X أجتني الزاوية اللي هي XY
+
+169
+00:20:54,940 --> 00:21:00,740
+زائد YZ إذن هذه بدأت تصير واحد
+
+170
+00:21:25,370 --> 00:21:32,430
+واحد زائد واحد
+
+171
+00:21:32,430 --> 00:21:33,370
+عالم
+
+172
+00:22:09,630 --> 00:22:16,210
+كل تربيع في مستقلة الزاوية بالنسبة إلى Y كداش بضل
+
+173
+00:22:16,210 --> 00:22:25,090
+هنا X وهنا بضل كداش Z بالمثل بدي أروح أجيب اللي هو
+
+174
+00:22:25,090 --> 00:22:34,790
+ال FZ ال FZ يساوي واحد على واحد زائد اللي هو ال XY
+
+175
+00:22:34,790 --> 00:22:45,630
+زائد Y زائدالكل تربيع في مشتقة هذه بالنسبة لزد
+
+176
+00:22:45,630 --> 00:22:55,270
+اللي هو Y فقط لا غير Y فبطلعي لنا نمر بي له Fx و
+
+177
+00:22:55,270 --> 00:23:00,430
+Fz يختلفوا عن بعض، إذا كان بإمكاني أسيط السؤال
+
+178
+00:23:00,430 --> 00:23:04,250
+صغيرة أخرى و أقول لك show that أن partial F by
+
+179
+00:23:04,250 --> 00:23:09,440
+partial X equal partial F by partial Zطبعا وبدأت
+
+180
+00:23:09,440 --> 00:23:12,900
+الصغير يقول لأ اجيب هذا المشتقه و اجيب هذا المشتقه
+
+181
+00:23:12,900 --> 00:23:16,960
+يتطلعوا اتنين مساوا بعض و يصير كلام انه كلام صحيح
+
+182
+00:23:16,960 --> 00:23:21,440
+طيب احنا في الاشتقاق في كل كلاصية خدنا اشتقاق عادي
+
+183
+00:23:21,440 --> 00:23:27,060
+زي ما بنشتق و خدنا اشتقاطا ضمنيا طبعا اللي هو ال
+
+184
+00:23:27,060 --> 00:23:30,520
+implicit differentiation خلينا ناخد السؤال عن ال
+
+185
+00:23:30,520 --> 00:23:34,660
+implicit و نشوف كيف كمان بدنا نحله يبقى example
+
+186
+00:23:34,660 --> 00:23:35,780
+تلاتة
+
+187
+00:23:37,950 --> 00:23:44,350
+اللي هو implicit differentiation
+
+188
+00:23:44,350 --> 00:23:53,330
+يبقى اشتقاق ضلمي find اللي
+
+189
+00:23:53,330 --> 00:24:01,990
+هو partial z على partial x and partial z على
+
+190
+00:24:01,990 --> 00:24:05,770
+partial y for the function
+
+191
+00:24:08,880 --> 00:24:22,760
+لدالة x تربيع زائد y تربيع في z بده يساوي y تان x
+
+192
+00:24:22,760 --> 00:24:23,580
+y z
+
+193
+00:24:55,210 --> 00:25:04,670
+سؤال مرة تانية يسوي
+
+194
+00:25:04,670 --> 00:25:11,870
+y tan xyz سؤال طلب تفاضل z بالنسبة ل x و تفاضل z
+
+195
+00:25:11,870 --> 00:25:18,370
+بالنسبة لمين؟ y إذا كان هناك متغيرات مستقلة و
+
+196
+00:25:18,370 --> 00:25:24,070
+متغيرات تبع independent variableيعني مين بدي يكون
+
+197
+00:25:24,070 --> 00:25:30,630
+دالة في مين السؤال هو هل ال X دالة في Y و Z و الله
+
+198
+00:25:30,630 --> 00:25:35,490
+ال Y دالة في X و Z و الله ال Z دالة في X و Y Z
+
+199
+00:25:35,490 --> 00:25:40,750
+دالة في X و Y لما طلب تفاضل ال Z بالنسبة ل X و
+
+200
+00:25:40,750 --> 00:25:46,390
+تفاضل ال Z بالنسبة ل M لل Y يبقى هنا بروح نعتبر ان
+
+201
+00:25:46,390 --> 00:25:54,140
+Z is a function ofيبقى باجي بقول هنا ليش ان هاي
+
+202
+00:25:54,140 --> 00:26:02,020
+المطبوق عندنا يبقى we consider بنروح نعتبر ان ال z
+
+203
+00:26:02,020 --> 00:26:12,760
+is a function of x and y هذا يترتب عليه قمر مهم
+
+204
+00:26:12,760 --> 00:26:19,710
+جدا عند الاشتقاء ان لو اشتق x بالنسبة ل yقداش
+
+205
+00:26:19,710 --> 00:26:24,030
+مكون؟ Zero. Zero. ده اشتق واي بالنسبالك. Zero. لكن
+
+206
+00:26:24,030 --> 00:26:29,160
+الباقي لأ؟لأن Z function في كل من X و Y هي
+
+207
+00:26:29,160 --> 00:26:34,760
+المتغيرات المستقلة و Z هو المتغير اتبع Z function
+
+208
+00:26:34,760 --> 00:26:39,300
+في كل من X و Y اضع هذه المعلومة مهمة جدا عند
+
+209
+00:26:39,300 --> 00:26:46,400
+التطبيق اتنين انا مش قاعد اضع Z في شجة و الباقي في
+
+210
+00:26:46,400 --> 00:26:52,130
+شجة تانية يعني لا يمكن فصل المتغيراتبحيث أخلّي
+
+211
+00:26:52,130 --> 00:26:57,150
+الذد في جهة و لا أستطيع تمام إذا هذا الاشتقاق اسمه
+
+212
+00:26:57,150 --> 00:27:03,570
+اشتقاقا ضمنيا تمام يبقى بدي أرجع بذاكرتي إلى
+
+213
+00:27:03,570 --> 00:27:07,970
+الوراء لكالكولاسية للاشتقاق الضمنى و أحط في بالي
+
+214
+00:27:07,970 --> 00:27:14,290
+بدي أفاضل كل شيء في موقعه مع مراعاة قواعد التفاضل
+
+215
+00:27:14,290 --> 00:27:19,210
+التي سبق الدراسة في كالكولاسية فمثلاأنا بدأ أفضل
+
+216
+00:27:19,210 --> 00:27:22,690
+ال N بالنسبة لمين؟ ل X لأنني بدأي partial Z by
+
+217
+00:27:22,690 --> 00:27:30,830
+partial X يبقى كل من Y بيكون ثابت في هذه الحالة و
+
+218
+00:27:30,830 --> 00:27:34,170
+المجاب ال Y هتكون ثابت تفضل X تربعيها بقداش يا
+
+219
+00:27:34,170 --> 00:27:41,490
+مانا؟ 2X ال Y تربعيها مالكش دعوةمختار ثاني تفاضل
+
+220
+00:27:41,490 --> 00:27:47,510
+ال Z اللي احنا بيدناه تفاضل ال Z بالنسبة ل X يبقى
+
+221
+00:27:47,510 --> 00:27:52,250
+الشجة الشمال واضحة الشجة الشمال نجي للشجة اليمين
+
+222
+00:27:52,250 --> 00:27:57,250
+ال Y مختار ثاني لان هو بيبقى بالنسبة ل X وتفاضل
+
+223
+00:27:57,250 --> 00:28:06,640
+تاني بسكتر بيه XYZ في مشتقتي الزاويةمشتقة الزاوية
+
+224
+00:28:06,640 --> 00:28:17,720
+كده مشتقة هذا بالنسبة ل X؟ بYZ تمام زائد هذه كأنها
+
+225
+00:28:17,720 --> 00:28:23,780
+دالة وهذه دالة تانية فبجي بقول مشتقة هذه بواحد وYZ
+
+226
+00:28:23,780 --> 00:28:30,100
+كما هي زائد الدالة الأولى زي ما هي ال Y مقدار ثابت
+
+227
+00:28:30,100 --> 00:28:34,480
+ال Z ل partial Z by partial X
+
+228
+00:28:37,220 --> 00:28:43,080
+واضحات مرة تانية بدأ أقولها هذا الاشتقاق أفعلته
+
+229
+00:28:43,080 --> 00:28:47,660
+اسمه اشتقاق ضمني تمام يبقى بدأ أفضل كل شيء في
+
+230
+00:28:47,660 --> 00:28:51,820
+موقعه مع مراعاة قواعد التفاضل المفتلفة أنا بفضل
+
+231
+00:28:51,820 --> 00:28:55,920
+بالنسبة ل X أولا لإن بدي partial Z by partial X
+
+232
+00:28:55,920 --> 00:29:00,930
+يبقى باجي بقول التفاضل كسبيا باتنين X هذا كلهالـ Y
+
+233
+00:29:00,930 --> 00:29:04,670
+تربية صغيرة مقنعة ثابت تفاضل الـ Z له partial Z by
+
+234
+00:29:04,670 --> 00:29:08,770
+partial X نجي الـ Y مقنعة ثابت مانوش داورة تفاضل
+
+235
+00:29:08,770 --> 00:29:14,180
+التان بسكت تربية ضارب مشتقة الزاويةأعتبر هذه دالة
+
+236
+00:29:14,180 --> 00:29:20,060
+و هذه دالة تانية يبقى مشتقة الأولى بواحد في YZ هاي
+
+237
+00:29:20,060 --> 00:29:25,220
+ال YZ زائد الأولى زي ما هي ال X مشتقة التانية
+
+238
+00:29:25,220 --> 00:29:29,840
+مشتقة ال YZ Y مقدر ثابت مشتقة ال Z اللي هو partial
+
+239
+00:29:29,840 --> 00:29:36,270
+Z by partial Xعاد بعد هيك فكي و طلعيلي partial z
+
+240
+00:29:36,270 --> 00:29:41,450
+by partial x على شجة و ساعمليلي هيك و روحي أخليها
+
+241
+00:29:41,450 --> 00:29:48,430
+باقى الشغل الشغل الروتيني يعني هدف يعني هدفأنا
+
+242
+00:29:48,430 --> 00:29:51,310
+أجيب ال partial z على partial عن بعض و أخد عامل
+
+243
+00:29:51,310 --> 00:29:55,690
+مشترك و أنقل هذا على شكل تاني و أجسم شغل روتيني لا
+
+244
+00:29:55,690 --> 00:30:00,650
+قيمة له و ان غلط فيه بنحاسبك يبقى لا بس فاضليه من
+
+245
+00:30:00,650 --> 00:30:03,490
+الأول للآخر في ال implicit differentiation هذا
+
+246
+00:30:03,490 --> 00:30:07,910
+فاضلي من الأول للآخر صح و روح و خليني تمام؟ مش
+
+247
+00:30:07,910 --> 00:30:11,410
+هنضيع وقت واحنا نقعد نحس فيه لإن احنا اشتقن اشتقطا
+
+248
+00:30:11,410 --> 00:30:17,210
+صحيحاللي هو الاشتقاق بالنسبة إلى X بالذالك ياخد
+
+249
+00:30:17,210 --> 00:30:22,210
+الاشتقاق بالنسبة لمن؟ ل Y بقولك كذلك كذلك مستقل ال
+
+250
+00:30:22,210 --> 00:30:30,470
+X ترمية Zero تمام مستقل تاني نين Y زت
+
+251
+00:30:32,520 --> 00:30:39,600
+خلصت؟ لسه ال Y متغير و ال Z متغير يبقى 2Y في Z
+
+252
+00:30:39,600 --> 00:30:47,480
+زائد Y تربية partial Z by partial Y شوفت كيف
+
+253
+00:30:47,480 --> 00:30:52,120
+اترجعت عن بعض و عن اللي فوق؟ طيب هذا الكلام
+
+254
+00:30:52,120 --> 00:30:57,420
+بالتسابق بنا نشتقت ده لاني بالنسبة لمين؟ ل Y يبقى
+
+255
+00:30:57,420 --> 00:31:05,110
+مشتقة الأولى واحدوظلتان X Y Z زائد Y في تفاضلي
+
+256
+00:31:05,110 --> 00:31:11,530
+التان بسكتر بيها الزاوية ضرب مشتقة الزاوية بالنسبة
+
+257
+00:31:11,530 --> 00:31:17,370
+لمن؟ بالنسبة إلى Y يبقى ال X ايش يُعتبر البلاد؟
+
+258
+00:31:17,370 --> 00:31:25,150
+المقدار ثابت ومشتقة ال Y زد بالنسبة ل Y؟ بزد لأن
+
+259
+00:31:25,150 --> 00:31:26,990
+مشتقة ال Y تاب واحد
+
+260
+00:31:41,490 --> 00:31:45,130
+مرة تانية بقول المشتقة الأخيرة لأن هو اللي ممكن
+
+261
+00:31:45,130 --> 00:31:51,110
+تلخبط فيها طلعيلي كويس هذه دالة وهذه كلها تعتبر
+
+262
+00:31:51,110 --> 00:31:56,100
+دالة تانية يبقى مشتقة الأولى بواحد في تان هذهزي دي
+
+263
+00:31:56,100 --> 00:32:00,220
+دالة الأولى ليه Y مشتقة التان بصيك تربيع في مشتقة
+
+264
+00:32:00,220 --> 00:32:05,060
+الزاوية ال X و ال Y ثوابت لكن احنا بنشتق ليه Y
+
+265
+00:32:05,060 --> 00:32:10,560
+يبقى X فقط هو ثابت و Y و Z هو المتغير يبقى باجي
+
+266
+00:32:10,560 --> 00:32:15,080
+بقول يبقى الأولى X في Z لإنه مشتقة ال Y بواحد
+
+267
+00:32:15,080 --> 00:32:21,440
+بعدين X في Y مشتقة ال Zلو partial z by partial y
+
+268
+00:32:21,440 --> 00:32:26,040
+هك اشتقنا اشتقاقا كاملا وماحدش اللي اعتراض عندنا
+
+269
+00:32:26,040 --> 00:32:31,560
+تمام طيب على اي حال بدنا نيجي هذا بالنسبة لمهم
+
+270
+00:32:31,560 --> 00:32:39,200
+للمشتقة الاولى بدأس السؤال الان احنا في calculus A
+
+271
+00:32:39,200 --> 00:32:42,860
+فبناخد المشتقة الاولى و التانية و التالتة و
+
+272
+00:32:42,860 --> 00:32:47,930
+الرابعة و المشتقة النونية مظبوطهل يوجد عندنا في ال
+
+273
+00:32:47,930 --> 00:32:52,370
+partial derivatives مشتقات أولى و تانية و تالتة و
+
+274
+00:32:52,370 --> 00:32:59,390
+رابعة انونية الإجابة نعم كف كالتالية يبقى بداجي
+
+275
+00:32:59,390 --> 00:33:05,530
+لحاجة اسمها second second
+
+276
+00:33:05,530 --> 00:33:13,530
+and higher order
+
+277
+00:33:17,830 --> 00:33:27,510
+فارشيل دريفتر يعني
+
+278
+00:33:27,510 --> 00:33:31,430
+المشتقة الثانية أو الأعلى، المشتقة التالتة،
+
+279
+00:33:31,430 --> 00:33:33,130
+الرابعة، الاخرية، سبع سنة
+
+280
+00:33:43,970 --> 00:33:48,590
+يبقى دي تعتبر مشتق مين؟ يعني بتشتق مرتين بالنسبة
+
+281
+00:33:48,590 --> 00:33:55,230
+لمين؟ بالنسبة ال X أو معناها partial by partial X
+
+282
+00:33:55,230 --> 00:34:03,170
+ل partial F by partial X الشكل هذا يعني بتشتقوا
+
+283
+00:34:03,170 --> 00:34:06,570
+بالنسبة ال F أولا بالنسبة ال X و اللي هو انت
+
+284
+00:34:06,570 --> 00:34:12,850
+بتشتقه كمان مرة و من جهة الرموز مكتوبة F XX
+
+285
+00:34:16,140 --> 00:34:25,180
+similarly بنفس الطريقة f yy يعني partial square f
+
+286
+00:34:25,180 --> 00:34:33,740
+by partial y squared يعني partial على partial y ل
+
+287
+00:34:33,740 --> 00:34:40,280
+partial f by partial y هذا
+
+288
+00:34:40,280 --> 00:34:47,510
+النقطة الأولى النقطة الثانيةطب لو عندي partial x
+
+289
+00:34:47,510 --> 00:34:53,670
+partial y مش كله زي بعضه مختلفين يعني عندي partial
+
+290
+00:34:53,670 --> 00:35:01,010
+square f على partial x partial y إيش معناها هذه؟
+
+291
+00:35:01,010 --> 00:35:08,470
+معناها إنه partial على partial x ل partial f by
+
+292
+00:35:08,470 --> 00:35:13,660
+partial yيعني إيش معناها يا بنات؟ بدي أشتق أولا
+
+293
+00:35:13,660 --> 00:35:21,660
+بالنسبة ل Y و لا بالنسبة ل X؟ ل Y أولا ثم ل X يعني
+
+294
+00:35:21,660 --> 00:35:29,220
+هذه كيانها إيش؟ كيانها partial على partial X لل FY
+
+295
+00:35:29,220 --> 00:35:32,520
+تمام؟
+
+296
+00:35:32,520 --> 00:35:37,480
+يعني أشتق ل Y أولا ثم بالنسبة ل X أو إن شئتم
+
+297
+00:35:37,480 --> 00:35:38,500
+فقولوا
+
+298
+00:35:46,220 --> 00:36:03,160
+يبقى partial by partial
+
+299
+00:36:03,160 --> 00:36:09,060
+y ل Fx يبقى Fxy
+
+300
+00:36:13,090 --> 00:36:20,730
+قبل ما أكمل جاي في بالي سؤال هل ال Fxy هي نفس ال
+
+301
+00:36:20,730 --> 00:36:29,830
+Fyx؟ زي بعض؟ لأ ليس بالضرورة ممكن يحصل تمام؟ لكن
+
+302
+00:36:29,830 --> 00:36:31,790
+in general لأ
+
+303
+00:36:34,810 --> 00:36:39,690
+ممكن افقول ممكن وقتهش هذا ما سنعرفه في نهاية هذا
+
+304
+00:36:39,690 --> 00:36:45,570
+ال section بنظرية إذا الدلدلة متصلة ومشتقتها دوال
+
+305
+00:36:45,570 --> 00:36:51,590
+متاصلة بالنسبة ل X وكذلك بالنسبة إلى Y وهذه كلها
+
+306
+00:36:51,590 --> 00:36:58,370
+معرفة بيحصل التساوي اللي احنا بنسأل عليه طيب افترض
+
+307
+00:36:58,370 --> 00:36:59,090
+يا بنات
+
+308
+00:37:17,050 --> 00:37:24,730
+فارشال تربيع F على فارشال external يعني هذه كأنها
+
+309
+00:37:24,730 --> 00:37:37,450
+partial على partial Y فال F XX يبقى ال F XXY لو
+
+310
+00:37:37,450 --> 00:37:38,150
+عندك
+
+311
+00:37:50,280 --> 00:37:57,540
+يعني هذه partial تربيع على partial X تربيع ل
+
+312
+00:37:57,540 --> 00:38:04,960
+partial تربيع F على partial Y تربيع يعني هذه
+
+313
+00:38:04,960 --> 00:38:11,420
+partial تربيع على partial X تربيع لمين؟ فالـ FYY
+
+314
+00:38:11,420 --> 00:38:14,340
+يعني هاني هان
+
+315
+00:38:20,010 --> 00:38:25,950
+بتعرف في أول رقم أو أول متغير جريب على الـ F أول
+
+316
+00:38:25,950 --> 00:38:30,110
+اشتقاق بالنسباله و بعدين بروحنا لبعد و لبعد و هكذا
+
+317
+00:38:30,110 --> 00:38:43,170
+طيب نبدأ ناخد بعض الأمثلة التوضيحية طيب
+
+318
+00:38:43,170 --> 00:38:47,790
+قبل التمثلة التوضيحية بقولك لو كانت تلت متغيرات
+
+319
+00:38:47,790 --> 00:38:49,130
+على سبيل المثال
+
+320
+00:39:10,090 --> 00:39:16,610
+يبقى هذه تساوي partial على partial X لمن؟ لpartial
+
+321
+00:39:16,610 --> 00:39:22,830
+على partial Y لpartial F على partial Z يعني بنت
+
+322
+00:39:22,830 --> 00:39:30,010
+هذه تساوي من؟ FZ في الأول وبعدها تفضل بالنسبة ل Y
+
+323
+00:39:30,010 --> 00:39:34,830
+وبعدها تفضل بالنسبة ل X و هكذا
+
+324
+00:39:43,220 --> 00:39:55,060
+سؤال الأول يقول لي let f of x, y و z بدها تساوي x
+
+325
+00:39:55,060 --> 00:40:04,740
+أص خمسة زائد x أص أربعة و y أص أربعة زت كبير زائد
+
+326
+00:40:04,740 --> 00:40:23,180
+y زت تربية fine أوشدوناFXY FYX
+
+327
+00:40:23,180 --> 00:40:28,860
+FXYY
+
+328
+00:40:28,860 --> 00:40:35,300
+FZXY
+
+329
+00:41:23,620 --> 00:41:39,240
+يبقى Fxy يبقى فيه ثلاثة متغيرات يبقى
+
+330
+00:41:39,240 --> 00:41:44,340
+Fxy يبقى فيه ثلاثة متغيرات
+
+331
+00:42:06,030 --> 00:42:13,390
+يجب ان نجيب fxy يبقى بالفضل هو الاسم لمن؟ لل one
+
+332
+00:42:13,390 --> 00:42:19,870
+يبقى هذا؟ Zero مع السلامة يبقى هذا Zero وهذا أربع
+
+333
+00:42:19,870 --> 00:42:29,150
+X تكيب مالاش داوة وهذه أربع Y تكيب وهنا في Z تكيب
+
+334
+00:42:29,150 --> 00:42:32,930
+والباقي ب Zero يبقى النتيجة سارة تقدر
+
+335
+00:42:40,620 --> 00:42:51,100
+بتركيب نمر بيه نمر بيه يبقى في الأول بالاسم الأمين
+
+336
+00:42:51,100 --> 00:42:57,160
+لل FY يبقى بالذاتي لل FY و7 يبقى بالذاتي ال
+
+337
+00:42:57,160 --> 00:43:00,820
+function اللي عندنا يبقى ال X أص خمسة بالدرجة ب
+
+338
+00:43:00,820 --> 00:43:09,680
+Zero يبقى هذه أربعة X أص أربعة زي ما هو Y تركيبفزي
+
+339
+00:43:09,680 --> 00:43:15,760
+التكييب بقى المشتقة بالنسبة ل Y زائد زي التربية
+
+340
+00:43:15,760 --> 00:43:22,020
+بيروح اشتقها بالنسبة لمن؟ ل X يبقى هذا بدي يعطيكي
+
+341
+00:43:22,020 --> 00:43:29,360
+انه FYX يساوي اشتق بالنسبة ل X يبقى ايش مصير عندك؟
+
+342
+00:43:29,360 --> 00:43:46,240
+16 X تكييب Y تكييب Z تكييبزائد Zero بقدر
+
+343
+00:43:46,240 --> 00:43:51,320
+الله تمام هذا يتفق مع نظري اللي قلتلكوا بعد قليل
+
+344
+00:43:51,320 --> 00:43:56,660
+الدالة هذه كثيرة حدود إلى ان هي دالة متصلة مشتقتها
+
+345
+00:43:56,660 --> 00:43:59,520
+بالنسبة لك كثيرة حدود دالة متصلة
+
+346
+00:44:01,930 --> 00:44:07,070
+دالة متصلة ال X Y كثيرة تحوظ المتصلة وهذه متصلة من
+
+347
+00:44:07,070 --> 00:44:11,990
+هنا جاء من جاء هذا التساوي اللي احنا تسألنا عليه
+
+348
+00:44:11,990 --> 00:44:19,230
+قبل قليل يبقى هذا بيه بدأي لنمري ال C نمري ال C
+
+349
+00:44:19,230 --> 00:44:29,730
+قال لي بدي F X Y Y يعني F X Y Y F X Y جاهزة عادي
+
+350
+00:44:34,200 --> 00:44:40,580
+بدي اشتقها كمان مرة بالنسبة لمين بالنسبة ل Y يعني
+
+351
+00:44:40,580 --> 00:44:49,340
+هذه كأنها partial على partial Y ل 16 X تكيب و Y
+
+352
+00:44:49,340 --> 00:44:56,020
+تكيبيبقى Z تكييب نشتق بنسبة ينا Y يبقى يدى تلاتة
+
+353
+00:44:56,020 --> 00:45:02,200
+فى ستاشر تمانية و أربعين X تكييب زى ما دى و هدى Y
+
+354
+00:45:02,200 --> 00:45:12,820
+تربية و هدى Z تكييب نمرى دى نمرى دى بده F Z X Y
+
+355
+00:45:12,820 --> 00:45:16,480
+اللى هو الخطوة تفضل بالنسبة لزى
+
+356
+00:45:23,450 --> 00:45:31,390
+هذه خالية من Z بـ Zero هذه مصير تلاتة X أُس أربعة
+
+357
+00:45:31,390 --> 00:45:42,570
+Y أُس أربعة Z ربيع زائد اتنين Y زائد اتنين Y زائد
+
+358
+00:45:42,570 --> 00:45:49,010
+اتنين Y زائد اتنين Y زائد اتنين
+
+359
+00:45:49,010 --> 00:45:49,530
+Y زائد اتنين Y زائد اتنين Y زائد اتنين Y زائد
+
+360
+00:45:49,530 --> 00:45:50,170
+اتنين Y زائد اتنين Y زائد اتنين Y زائد اتنين Y
+
+361
+00:45:50,170 --> 00:45:50,190
+Y زائد اتنين Y زائد اتنين Y زائد اتنين Y زائد
+
+362
+00:45:50,190 --> 00:45:51,170
+اتنين Y زائد اتنين Y زائد اتنين Y زائد اتنين Y
+
+363
+00:45:51,170 --> 00:46:00,740
+زائد افز اكس تشتغل اسم ال X يبقى اتناشة X تكيب Y
+
+364
+00:46:00,740 --> 00:46:06,400
+قصة اربعة زت تربيه وهذا بالاسم ال X مع السلامة ب
+
+365
+00:46:06,400 --> 00:46:16,360
+Zero الله سعال عليه اللي بعدها بدي F Z X Y هشتغل
+
+366
+00:46:16,360 --> 00:46:20,720
+نتيجة اللي حصلت عليها بالاسم الأمين ال Y اربعة في
+
+367
+00:46:20,720 --> 00:46:21,380
+اتناشة
+
+368
+00:46:29,480 --> 00:46:36,180
+تبقى عرفنا كيف تتم عملية الاشتقاق طيب هذا المثال
+
+369
+00:46:36,180 --> 00:46:41,340
+الأول مثال الثاني show
+
+370
+00:46:41,340 --> 00:46:48,540
+that they function show that they function
+
+371
+00:46:51,310 --> 00:47:05,750
+F of X و Y و Z و 7 E از تلاتة X زائد أربعة Y فساعد
+
+372
+00:47:05,750 --> 00:47:10,490
+خمسة Z satisfies
+
+373
+00:47:21,920 --> 00:47:27,600
+وهذا اللي اتلاف لازم اللي partial تربيع F by
+
+374
+00:47:27,600 --> 00:47:32,880
+partial X تربيع partial تربيع F by partial Y تربيع
+
+375
+00:47:32,880 --> 00:47:39,460
+partial تربيع F by partial Z تربيع
+
+376
+00:48:03,890 --> 00:48:04,830
+ساعدني كثير
+
+377
+00:48:20,070 --> 00:48:25,170
+سؤال مرة تانية نعطيني function في ثلاثة متغيرات
+
+378
+00:48:25,170 --> 00:48:30,170
+exponential أس ثلاثة X زي درب ع Y في Cos خمسة Z
+
+379
+00:48:30,170 --> 00:48:34,310
+وقال لي أثبت لي أن هذه المعادلة بحقها معادلة
+
+380
+00:48:34,310 --> 00:48:39,290
+Laplace يروي بركة بنات معادلة Laplace في متغيرين
+
+381
+00:48:39,290 --> 00:48:44,130
+يكون هذا مش موجود يبقى المشتقة الثانية بالنسبة ل X
+
+382
+00:48:44,130 --> 00:48:47,250
+والمشتقة الثانية بالنسبة ل Y تستوى Zero إذا تلت
+
+383
+00:48:47,250 --> 00:48:51,950
+متغيراتبنضيف المشتقة تانية متغيرة تانية اربعة
+
+384
+00:48:51,950 --> 00:48:56,110
+متغيرات خمس متغيرات ان من المتغيرات كله بنفس
+
+385
+00:48:56,110 --> 00:48:56,710
+الطريقة
+
+386
+00:49:02,440 --> 00:49:07,380
+و مرتين بالنسبة ل Y و مرتين بالنسبة ل Z و نجمع بدل
+
+387
+00:49:07,380 --> 00:49:12,080
+النتج يكون جداش Zero ان حدث ذلك بقول فعلا هذه
+
+388
+00:49:12,080 --> 00:49:17,000
+الدلة تحقق معادلة Laplace equation ل M و جمعنا
+
+389
+00:49:17,000 --> 00:49:24,480
+عليه بضروحه جيد اللي هو partial F by partial Xهذه
+
+390
+00:49:24,480 --> 00:49:30,240
+فيهاش X يبقى X بس فيه الأربعة Y كله مقدار ثابت
+
+391
+00:49:30,240 --> 00:49:34,620
+يبقى ال X مو ننشي نفسها بس مضروبة في جدير في ثلاثة
+
+392
+00:49:34,620 --> 00:49:41,520
+يبقى هاي تلاتة E أس تلاتة X زائد أربعة Y
+
+393
+00:49:45,720 --> 00:49:54,340
+Fx X يعني مشتقة ثانية كمان مرة تصير تسعة يقص تلاتة
+
+394
+00:49:54,340 --> 00:50:02,100
+X زائد اربعة Y كوصين خمسة زائد بالمثل بدي اروح
+
+395
+00:50:02,100 --> 00:50:07,660
+اجيب له من F Y اذا اشتق مرتين بالنسبة ل Y يبقى
+
+396
+00:50:07,660 --> 00:50:13,950
+تلاتة X يعتبر مقداراثابتاً وشقة E وصة 4Y نفسها
+
+397
+00:50:13,950 --> 00:50:24,790
+مضروبة في قداش في 4 يبقى 4 E وصة 3X زائد 4Y E وصة
+
+398
+00:50:24,790 --> 00:50:36,690
+5Z هذا بده يعطيكي ان ال FYY كمان مرة 4X4X16 E وصة
+
+399
+00:50:36,690 --> 00:50:44,950
+3Xزائد اربعة Y كوساين خمسة Z بعدين اذا انا احنا
+
+400
+00:50:44,950 --> 00:50:50,530
+احنا احنا احنا احنا احنا احنا احنا احنا احنا احنا
+
+401
+00:50:50,530 --> 00:50:50,690
+احنا احنا احنا احنا احنا احنا احنا احنا احنا احنا
+
+402
+00:50:50,690 --> 00:50:50,990
+احنا احنا احنا احنا احنا احنا احنا احنا احنا احنا
+
+403
+00:50:50,990 --> 00:50:56,750
+احنا احنا احنا احنا
+
+404
+00:50:56,750 --> 00:51:05,650
+احنا احنا
+
+405
+00:51:05,650 --> 00:51:15,650
+افى sin 5z ثبتنا ال exponential تفاضل cosine بسالب
+
+406
+00:51:15,650 --> 00:51:20,930
+sin الزاوية ضرب تفاضل الزاوية اللى بقدرش خمسة بدنا
+
+407
+00:51:20,930 --> 00:51:25,130
+ال fzz مش
+
+408
+00:51:25,130 --> 00:51:30,410
+تبقى فاهم ان اسمه z هذا كله مقدار ثاني وتفاضل ال
+
+409
+00:51:30,410 --> 00:51:33,850
+sin بcos ضرب خمسة دى بقدرش بصينة
+
+410
+00:51:36,430 --> 00:51:44,310
+يبقى إيش إيه في E مستلات X زائد أربعة Y E Cos خمسة
+
+411
+00:51:44,310 --> 00:51:51,090
+Z نجبع لأنا منها اللي هو partial تربيع ال F على
+
+412
+00:51:51,090 --> 00:51:56,210
+partial X تربيع partial تربيع ال F partial Y تربيع
+
+413
+00:51:56,210 --> 00:52:00,330
+partial تربيع ال F على partial Z تربيع يساوي
+
+414
+00:52:00,330 --> 00:52:10,870
+الأولان يلف XX اللي هي تسعةE أس ثلاثة X زائد أربعة
+
+415
+00:52:10,870 --> 00:52:20,230
+Y في Cos خمسة Z زائد ستة عشر E أس تلاتة X زائد
+
+416
+00:52:20,230 --> 00:52:30,410
+أربعة Yخمسة زد ناقص خمسة وعشرين E واس تلاتة X زائد
+
+417
+00:52:30,410 --> 00:52:37,990
+اربعة Y في Cos خمسة زد كده الناتج خمسة وعشرين ناقص
+
+418
+00:52:37,990 --> 00:52:42,450
+خمسة وعشرين X من فى Cos ب Zero يبقى هنا
+
+419
+00:53:03,730 --> 00:53:09,290
+يجي لنظرية اللي وعدناكوا فيها قبل قليل
+
+420
+00:53:16,680 --> 00:53:34,560
+AIM F F of X Y و ال F X و ال F Y F X و ال F Y و ال
+
+421
+00:53:34,560 --> 00:53:41,760
+F XY and ال FYX
+
+422
+00:53:42,890 --> 00:53:55,730
+are defined are defined كانت محرفة to throw out
+
+423
+00:53:55,730 --> 00:54:06,130
+خلال an open region throw out an open region
+
+424
+00:54:06,130 --> 00:54:09,570
+contiguous
+
+425
+00:54:09,570 --> 00:54:10,370
+point
+
+426
+00:54:12,960 --> 00:54:23,000
+continuing a point a
+
+427
+00:54:23,000 --> 00:54:33,280
+و b and are continuous and a زيادة على ذلك كانوا
+
+428
+00:54:33,280 --> 00:54:40,340
+كذلك دوال متصدا continuous عند النقطة
+
+429
+00:54:42,910 --> 00:54:48,510
+A وB ثم Fxy
+
+430
+00:54:48,510 --> 00:54:58,770
+عند النقطة A وB بسوى FYX عند النقطة A وB كمان
+
+431
+00:54:58,770 --> 00:55:07,490
+نظرياً اخيراً F A
+
+432
+00:55:07,490 --> 00:55:08,210
+function
+
+433
+00:55:12,830 --> 00:55:23,150
+فى الـ function f of x و y is differentiable قابلة
+
+434
+00:55:23,150 --> 00:55:31,810
+للاشتقاء f x naught y naught then ال f
+
+435
+00:56:15,350 --> 00:56:20,390
+بنرجع للنظرية الأولى السؤال طرحناه قبل شوية و
+
+436
+00:56:20,390 --> 00:56:24,130
+جوابنا عليه و الأن بنحطه في سيرة النظرية التالية
+
+437
+00:56:24,130 --> 00:56:28,350
+بيقول لو كانت دوال F of X Y مشتقة بالاسم X مشتقة
+
+438
+00:56:28,350 --> 00:56:33,690
+بالاسم Y مشتقة بالاسم X Y مشتقة بالاسم Y X كله
+
+439
+00:56:33,690 --> 00:56:36,810
+كانت دوال معبفة على open region و هذه ال open
+
+440
+00:56:36,810 --> 00:56:41,810
+region تحت ايه يعني تحتوي على النقطة A و Bوكانوا
+
+441
+00:56:41,810 --> 00:56:46,770
+كذلك كل المشتقات دي دوال متصلة عند نفس النقطة، إن
+
+442
+00:56:46,770 --> 00:56:51,890
+حدث ذلك يبقى المشتقتين هدول معاهم يدهم Yes Sir
+
+443
+00:56:51,890 --> 00:56:57,730
+النظرية هذه تدافق الوصيلة والدالة قابلة الاشتقاق
+
+444
+00:56:57,730 --> 00:57:02,490
+إذا ان هي دالة متصلة هي نفس القصة بالضبط طبعا، لكن
+
+445
+00:57:02,490 --> 00:57:03,550
+هل العكس صحيح؟
+
+446
+00:57:19,820 --> 00:57:25,160
+بالتالي دالة متصلة صحية لكنها دالة غير قابلة
+
+447
+00:57:25,160 --> 00:57:25,940
+للاشتغال
+
+448
+00:57:31,850 --> 00:57:35,930
+أو Vertical Tangent أو الدلة نفسها ماتكونش معظمة
+
+449
+00:57:35,930 --> 00:57:40,270
+عندها مظبوط تبقى هذه الأربع مواقع اللي تدلة فيها
+
+450
+00:57:40,270 --> 00:57:45,810
+تبقى غير قابلة لسه فبنعطي مثال على ذلك example
+
+451
+00:57:45,810 --> 00:57:54,930
+بيقول
+
+452
+00:57:54,930 --> 00:58:06,880
+الات ال F of X هو Y يساويX في صين الـ Y زائد Y في
+
+453
+00:58:06,880 --> 00:58:19,980
+صين الـ X زائد XY شهودان بيجيلي ان ال Fxy بده
+
+454
+00:58:19,980 --> 00:58:26,590
+يساوي ال Fyxيبقى الـ x و الـ y بالاستثناء مش عنده
+
+455
+00:58:26,590 --> 00:58:32,170
+نقطة واحدة و بس وإنما لجميع النقاط تعاتل plain أو
+
+456
+00:58:32,170 --> 00:58:35,950
+النقاط المعرفة عليها الدالة فدول الكميتين
+
+457
+00:58:35,950 --> 00:58:43,010
+متساويتين يبقى الحل solution بدي أروح أجيب له
+
+458
+00:58:43,010 --> 00:58:54,110
+ميلاد fx أولا يبقى fx بمين؟ صين ال yي كوصين ال X
+
+459
+00:58:54,110 --> 00:59:04,110
+زائد Y بدي أجيب له من Fxy Fxy بدي أشتقها دي
+
+460
+00:59:04,110 --> 00:59:14,530
+بالنسبة لمن إلى Y كوصين ال Y زائد كوصين ال X زائد
+
+461
+00:59:14,530 --> 00:59:18,050
+1 بدي أروح أجيب من
+
+462
+00:59:24,250 --> 00:59:36,130
+x لـcos y زائد sin x زائد x بعد ذلك نشتغل بالنسبة
+
+463
+00:59:36,130 --> 00:59:44,550
+إلى x fy x بدل سنة بالنسبة إلى x لcos y بالنسبة
+
+464
+00:59:44,550 --> 00:59:50,970
+إلى x لcos x بالنسبة إلى x اللي هو واحد صلّعيه إلى
+
+465
+00:59:50,970 --> 00:59:57,690
+واحد واتنينfrom واحد
+
+466
+00:59:57,690 --> 01:00:04,850
+and اتنين we have ان
+
+467
+01:00:04,850 --> 01:00:13,510
+ال Fxy بسوء ال Fyx لكل ال X و Y بلا استئناف طب ما
+
+468
+01:00:13,510 --> 01:00:19,750
+هو السبب يا مالاه؟طالعي ليه دالة هذه دالة متصلة
+
+469
+01:00:19,750 --> 01:00:24,070
+ولا لا؟ في نقطة واحدة بتقدر فيه تجيبولي نقطة دالة
+
+470
+01:00:24,070 --> 01:00:29,850
+غير متصلة؟ لأ هذه polynomial هذه sin هذه cos
+
+471
+01:00:29,850 --> 01:00:33,850
+polynomial في sin و polynomial في cos يبقى هذه
+
+472
+01:00:33,850 --> 01:00:40,790
+متصلة على طول الخط مشتقلون Fx نفس القصة متصلة Fxy
+
+473
+01:00:40,790 --> 01:00:48,710
+متصلة Fy متصلةمتاصلة fyx متاصلة وكذلك كلهم معرفات
+
+474
+01:00:48,710 --> 01:00:54,470
+إذا انطبقت كل شروط النظرية مدام انطبقت إذا غصب عن
+
+475
+01:00:54,470 --> 01:00:59,950
+اللي مايرضى بتطلع المقدارين هدول معاهم متساوية لحد
+
+476
+01:00:59,950 --> 01:01:06,270
+هنا انتهى هذا ال section وإليكن أقام المسائل ال
+
+477
+01:01:06,270 --> 01:01:11,350
+exercises أربع تاشر تلاتة المسائل
+
+478
+01:01:13,300 --> 01:01:21,540
+من واحد لتمانية و تلاتين القدر و سؤال خمسة و ستين
+
+479
+01:01:21,540 --> 01:01:28,960
+و ستة و ستين لأ عفوا لأ عفوا لسه جابلهم جابلهم من
+
+480
+01:01:28,960 --> 01:01:33,760
+واحد لتمانية و تلاتين القدر و من واحد و أربعين
+
+481
+01:01:33,760 --> 01:01:42,360
+لغاية أربعة و خمسين كذلك القدروكذلك من اللي هو
+
+482
+01:01:42,360 --> 01:01:52,540
+خمسة وستين او كذلك خمسة وستين وستة
+
+483
+01:01:52,540 --> 01:02:01,220
+وستين وكذلك من تلاتة وسبعين لغاية تمانين القدر
+
+484
+01:02:01,220 --> 01:02:01,840
+كذلك
+
+485
+01:02:11,920 --> 01:02:15,660
+بنتقل هنا يا بنات الى ال section اللي يليه وهو
+
+486
+01:02:15,660 --> 01:02:19,820
+that share rule اللي هي قاعدة السلسلة بنروح ناخد
+
+487
+01:02:19,820 --> 01:02:23,920
+قاعدة السلسلة في ال functions of several variables
+
+488
+01:02:23,920 --> 01:02:27,500
+زي ما درسناها في one variable في calculus A في
+
+489
+01:02:27,500 --> 01:02:30,980
+calculus C بناخدها في functions of several
+
+490
+01:02:30,980 --> 01:02:35,760
+variables وسنتدرج فيها من متغيرين إلى ثلاثة
+
+491
+01:02:35,760 --> 01:02:40,740
+متغيرات إلى أربع إلى نحو ذلك يبقى بدي أبدأ بنظرية
+
+492
+01:02:40,740 --> 01:02:41,420
+U M
+
+493
+01:03:02,230 --> 01:03:11,550
+continuous partial derivatives
+
+494
+01:03:11,550 --> 01:03:19,390
+Fx
+
+495
+01:03:19,390 --> 01:03:36,330
+and Fy and Fالـ X كانت هي X of T والـ Y هي
+
+496
+01:03:36,330 --> 01:03:43,350
+function of T كذلك وكله مدى المالهم are
+
+497
+01:03:43,350 --> 01:03:48,910
+differentiable functions are differentiable
+
+498
+01:03:48,910 --> 01:03:57,230
+functions of متغير رقم اسمه T of T
+
+499
+01:03:59,960 --> 01:04:13,240
+و متساوي f of x of t و y of t as a differentiable
+
+500
+01:04:13,240 --> 01:04:17,980
+function مدالة
+
+501
+01:04:17,980 --> 01:04:31,090
+قابلة للاشتقاء of t and dw by dt متساويpartial w
+
+502
+01:04:31,090 --> 01:04:40,030
+by partial x دي اكس على دي تين زي partial w by
+
+503
+01:04:40,030 --> 01:04:48,690
+partial y دي واي by دي تين. انا النظرية التانية
+
+504
+01:04:48,690 --> 01:04:58,960
+وسارجع للنظرية التانية. يقول ال F ال Wfunction في
+
+505
+01:04:58,960 --> 01:05:12,980
+x, y و z is is
+
+506
+01:05:12,980 --> 01:05:20,220
+differentiable and x,
+
+507
+01:05:20,700 --> 01:05:32,110
+y and zDifferentiable functions are differentiable
+
+508
+01:05:32,110 --> 01:05:40,150
+functions of T then
+
+509
+01:05:40,150 --> 01:05:52,530
+W is a differentiable function of
+
+510
+01:05:52,530 --> 01:05:55,170
+T and
+
+511
+01:05:58,030 --> 01:06:10,830
+DW by DT سوى partial W by partial X DX على DT زائد
+
+512
+01:06:10,830 --> 01:06:19,930
+partial W by partial Y DY على DT زائد partial W by
+
+513
+01:06:19,930 --> 01:06:20,950
+partial Z
+
+514
+01:07:25,020 --> 01:07:29,980
+طيب نرجع لنظرتين اللي كتبناه مرة تانية نظرية
+
+515
+01:07:29,980 --> 01:07:36,880
+الأولى بتقول لو W function في متغيرين X وY واخدنا
+
+516
+01:07:36,880 --> 01:07:42,160
+المشتق الأولى بالنسبة ل X والمشتق الأولى بالنسبة ل
+
+517
+01:07:42,160 --> 01:07:48,760
+Y وكانوا دوال متاصلة وكانت كل من X وY كل واحدة
+
+518
+01:07:48,760 --> 01:07:55,330
+فيهم دالة في متغير آخر يعني W دالة في مين؟كل واحد
+
+519
+01:07:55,330 --> 01:07:58,710
+من المتغيرين دالة في متغير آخر
+
+520
+01:08:07,390 --> 01:08:17,010
+يعني كان و هو function في T فقط دي
+
+521
+01:08:17,010 --> 01:08:22,410
+و بي دي تي شو بده تساوي بقول partial w by partial
+
+522
+01:08:22,410 --> 01:08:29,130
+x ليش قلت partial و لا بقول تفاضل كله لإن و ده فيه
+
+523
+01:08:29,130 --> 01:08:37,000
+متغيرين لكن عند دي x على دي t قلت تفاضل كلهليش ان
+
+524
+01:08:37,000 --> 01:08:41,960
+x بس function في متغيرين واحد يبقى في حالة
+
+525
+01:08:41,960 --> 01:08:46,360
+المتغيرين او تلاتة بقول partial في حالة متغير واحد
+
+526
+01:08:46,360 --> 01:08:52,360
+بقول تفاضل عادي dx by dt زائد طب partial w by
+
+527
+01:08:52,360 --> 01:08:55,460
+partial y في dy على dt
+
+528
+01:09:01,850 --> 01:09:07,330
+كل واحد من المتغيرات التلاتة دالة في متغير جديد
+
+529
+01:09:07,330 --> 01:09:11,210
+اللي هو المتغير T ما شكل ال derivative في هذه
+
+530
+01:09:11,210 --> 01:09:15,290
+الحالة او ما شكل ال general بقول دي دابليو باي دي
+
+531
+01:09:15,290 --> 01:09:24,910
+دي دي دي دي دي دي دي دي دي دي دي دي
+
+532
+01:09:24,910 --> 01:09:29,590
+دي
+
+533
+01:09:31,840 --> 01:09:37,640
+الكلام من خلال الأمثلة دي بقى نيجي لبعض الأمثلة
+
+534
+01:09:37,640 --> 01:09:44,660
+أول
+
+535
+01:09:44,660 --> 01:09:54,100
+مثال بقول لي ان امرأة express عبرلي
+
+536
+01:09:54,100 --> 01:09:59,200
+عن ال dw by dt
+
+537
+01:10:04,320 --> 01:10:11,360
+function of T by two
+
+538
+01:10:11,360 --> 01:10:16,280
+methods بطريقة
+
+539
+01:10:16,280 --> 01:10:20,200
+تانية طريقة
+
+540
+01:10:20,200 --> 01:10:28,280
+الأولى I by using chain
+
+541
+01:10:28,280 --> 01:10:29,800
+rule
+
+542
+01:10:38,360 --> 01:10:47,080
+تانية by expressing .. by expressing
+
+543
+01:10:47,080 --> 01:10:52,060
+w
+
+544
+01:10:52,060 --> 01:11:00,480
+as a function of t directly
+
+545
+01:11:08,830 --> 01:11:15,870
+دورة B W احسب
+
+546
+01:11:15,870 --> 01:11:26,730
+DW by DT at the given value
+
+547
+01:11:26,730 --> 01:11:35,550
+of T السؤال
+
+548
+01:11:35,550 --> 01:11:50,760
+الأوليقول الـ W تساوي X تربيه زائد Y تربيه والـ
+
+549
+01:11:50,760 --> 01:12:04,100
+X تساوي Cos T زائد Sin T والـ Y تساوي Cos T نقص
+
+550
+01:12:04,100 --> 01:12:07,960
+Sin Tو T تساوي زي
+
+551
+01:12:31,760 --> 01:12:37,520
+قبل أن نبدأ المثال حابب أحط هذا اللي أخدناه على
+
+552
+01:12:37,520 --> 01:12:43,180
+أرض الواقع عمليا من خلال رسم بمعنى أنه ممكن تنسي
+
+553
+01:12:43,180 --> 01:12:47,960
+ممكن تسي ممكن الاخري لكن الرسم دائما يخليك
+
+554
+01:12:47,960 --> 01:12:52,820
+معلوماتك دقيقة مائة بالمئة فبالدرجة لل derivative
+
+555
+01:12:52,820 --> 01:12:57,120
+الأول بدي أكتبه على شكل رسم و بعدين أكمل و أحصل
+
+556
+01:12:57,120 --> 01:13:02,300
+على سؤالهذا الجبهة لنبدأ عملية الحل هذا بدأ احاول
+
+557
+01:13:02,300 --> 01:13:07,760
+ارسم كله من النقطة النقطة الأولى الان بدأت اقنع ال
+
+558
+01:13:07,760 --> 01:13:12,760
+W في ما هو function في مين؟ في متغيرين، هذا بقى دي
+
+559
+01:13:12,760 --> 01:13:18,080
+بقول هي النقطة اللي عندها دي بقول W تساوي function
+
+560
+01:13:18,080 --> 01:13:23,520
+في X و Y إذا هنا بدأ أحط خط وهنا خط، بدأ أحط هنا X
+
+561
+01:13:23,520 --> 01:13:34,720
+وهنا Y بعد هيككل من X و Y في متغير واحد يبقى
+
+562
+01:13:34,720 --> 01:13:43,420
+هذا T بعد ذلك بالنسبة ل X و W فيها متغيرين إذا
+
+563
+01:13:43,420 --> 01:13:49,120
+الإشتقاق هذا يكون إشتقاق جزءي partial W by partial
+
+564
+01:13:49,120 --> 01:13:53,880
+X بنفس الطريقة هذا إشتقاق جزءي partial W by
+
+565
+01:13:53,880 --> 01:14:00,550
+partial Yلكن من X الى T ده لم يتغير واحد يبقى في
+
+566
+01:14:00,550 --> 01:14:09,190
+DX على DT وهذا DY على DT طالع عيش اللي سونا اضغط
+
+567
+01:14:09,190 --> 01:14:18,150
+في هذا في هذا زائد هذا في هذا مش بيعطيك ايه الان
+
+568
+01:14:18,150 --> 01:14:19,590
+هذا بالضبط صحيح ولا لا
+
+569
+01:14:27,350 --> 01:14:31,070
+طيب هذا الأمين بالنسبة للحالة اللي وطب الحالة
+
+570
+01:14:31,070 --> 01:14:35,550
+التانية لو كان تلت متغيرات بدي أعملها بنفس الطريقة
+
+571
+01:14:35,550 --> 01:14:42,050
+يبقى بدي أقول w تسوي ال function في x و y و z إذا
+
+572
+01:14:42,050 --> 01:14:48,700
+بدي أكون عندي تلت متغيراتهذا ال X وهذا ال Y وهذا
+
+573
+01:14:48,700 --> 01:14:55,760
+ال Z كل واحد فيهم دالة في نفس المتغير اللي هو T
+
+574
+01:15:00,160 --> 01:15:06,300
+هذه الدلة في تلت متغيرة XYZ يبقى هذا اشتقاقا جزئيا
+
+575
+01:15:06,300 --> 01:15:11,220
+وهذا partial W by partial Y وهذا partial W by
+
+576
+01:15:11,220 --> 01:15:21,960
+partial Z الباقي اشتقاق كله يبقى DX على DTY على DZ
+
+577
+01:15:21,960 --> 01:15:30,460
+على DZ نضربهم في بعضهذول في بعض هذول في بعض و نجمة
+
+578
+01:15:30,460 --> 01:15:35,920
+بتقنمين القاعدة التانية تانية تمام؟ يعني لو أنا
+
+579
+01:15:35,920 --> 01:15:41,080
+ناسي مش عارف كيف احفظهم او حفظ التونسيين من خلال
+
+580
+01:15:41,080 --> 01:15:44,800
+ال diagram اللي قدامنا هذا او الشكل الهندسي اللي
+
+581
+01:15:44,800 --> 01:15:52,920
+قدامنا بقدر اجيب المستقبل حتى لو كنت نسيهاطيب نيجي
+
+582
+01:15:52,920 --> 01:15:56,900
+أحط هالمعلومة هذه علشان جا عندنا ضياء وبدنا نيجي
+
+583
+01:15:56,900 --> 01:16:07,600
+لل solution تبع السؤال تبعه ماتيني w function في x
+
+584
+01:16:07,600 --> 01:16:13,080
+و y و ال x function في t و ال y function في t و
+
+585
+01:16:13,080 --> 01:16:17,640
+قال لي أحسر كلام أنا التي تساوي zero إيش بدي أحسر؟
+
+586
+01:16:18,290 --> 01:16:25,830
+قال لي عبّر عن dw by dt بدلالة T بطريقة تانية
+
+587
+01:16:25,830 --> 01:16:30,070
+الطريقة الأولى باستخدام share rule يعني زي ما احنا
+
+588
+01:16:30,070 --> 01:16:38,410
+كاتبينه إذا باجي بقوله ال dw by dt هي partial w by
+
+589
+01:16:38,410 --> 01:16:46,990
+partial x dx by by dt زي partial w by partial y dy
+
+590
+01:17:03,230 --> 01:17:12,770
+تفاضل الـ W بالنسبة لـ X يبقى الـ Y ثابتة في تفاضل
+
+591
+01:17:12,770 --> 01:17:24,970
+X بالنسبة إلى Tجزاف سالب صيني T زائد Cos T خلاصنا
+
+592
+01:17:24,970 --> 01:17:33,110
+من الشطر الأول DX على DT اللي بعديها زائد تفاضل W
+
+593
+01:17:33,110 --> 01:17:41,030
+بالنسبة ل Y بتنين Y تفاضل Y بالنسبة ل T جزاف سالب
+
+594
+01:17:41,030 --> 01:17:49,530
+صيني T زائد Cos Tماذا قال؟ قال انه يريد هذا الكلام
+
+595
+01:17:49,530 --> 01:17:55,130
+كدالة في T يبقى لا يريد X وY ان يكونوا في المثلة
+
+596
+01:17:55,130 --> 01:17:59,510
+بالمرة يريد المثلة كلها تحولها بدلالة من T طب ماهي
+
+597
+01:17:59,510 --> 01:18:03,970
+مشكلة ماهي الشيء عندك يبقى هذا يساوي اتنين ال X
+
+598
+01:18:03,970 --> 01:18:13,140
+جاء زايا فوق اللي هي مين؟ اللي هي cos T زائدSin T
+
+599
+01:18:13,140 --> 01:18:24,000
+و هذا جاهز Cos T ناقص Sin T زاد اتنين و I هي فوق
+
+600
+01:18:24,000 --> 01:18:38,060
+Cos T زاد Y ناقص Sin T فى
+
+601
+01:18:38,470 --> 01:18:44,150
+مش صح فشو رايح؟ سالب مع سالب نطلعها برا بصير اللي
+
+602
+01:18:44,150 --> 01:18:50,030
+برا هاد ايه؟ سالب و بصير عندنا مين؟ بصير عندنا
+
+603
+01:18:50,030 --> 01:18:58,750
+cosine T زائد sine 50 اذا
+
+604
+01:18:58,750 --> 01:19:05,530
+حابة تفكي بتفكي بالظغريهملكن بمجرد النظر هذا هو
+
+605
+01:19:05,530 --> 01:19:14,210
+هذا صح ولا لا يبغى هذا المشتفى تساويهذا الفرق بين
+
+606
+01:19:14,210 --> 01:19:21,530
+المربعين مربع الأولى ناقص مربع التانية مربع
+
+607
+01:19:21,530 --> 01:19:24,690
+الأولى ناقص مربع التانية مربع الأولى ناقص مربع
+
+608
+01:19:24,690 --> 01:19:30,910
+التانية مربع الأولى ناقص مربع التانية مربع الأولى
+
+609
+01:19:30,910 --> 01:19:32,370
+ناقص مربع التانية
+
+610
+01:19:35,440 --> 01:19:41,740
+حسب تشيره جللها من البداية إذا كتعفرلي علي ال W
+
+611
+01:19:41,740 --> 01:19:45,400
+كfunction في T و تثبت ان ال derivative هذا بده
+
+612
+01:19:45,400 --> 01:19:50,980
+يساوي جداري، بده يساوي جره، جره بسيطة، وجبجيله
+
+613
+01:19:50,980 --> 01:19:55,750
+النقطة الثانيةيجب ان انا اقول الو يجب ان انا اقول
+
+614
+01:19:55,750 --> 01:20:00,410
+الو يجب ان انا اقول الو يجب
+
+615
+01:20:00,410 --> 01:20:07,830
+ان انا اقول الو يجب
+
+616
+01:20:07,830 --> 01:20:11,090
+ان
+
+617
+01:20:11,090 --> 01:20:12,830
+انا اقول الو
+
+618
+01:20:19,960 --> 01:20:31,540
+2sin t cos t زائد sin تربيع t زائد cos تربيع t
+
+619
+01:21:06,440 --> 01:21:13,600
+هذه بالموجة وهذه بالسلف عند ال cos تربيع وcos
+
+620
+01:21:13,600 --> 01:21:15,620
+تربيع
+
+621
+01:21:25,430 --> 01:21:30,830
+يبقى ال cos تربيه T زائد sin تربيه او كمان sin
+
+622
+01:21:30,830 --> 01:21:38,470
+تربيه اتنين sin تربيه 80 لو أخدنا اتنين عامل مشترك
+
+623
+01:21:38,470 --> 01:21:42,630
+بيظل ال cos تربيه زائد sin تربيه يسوى جدير واحد
+
+624
+01:21:42,630 --> 01:21:50,410
+اشتقى يبقى هذا بيضايقيكي DW على DT بيسوى Zero لأن
+
+625
+01:21:50,410 --> 01:21:54,940
+هذا يعتبر مختارا ثالثاإذا القيمة اللى حصلنا عليها
+
+626
+01:21:54,940 --> 01:22:00,340
+بواسطة D تشيلون هي نفس القيمة اللى حصلنا عليها لو
+
+627
+01:22:00,340 --> 01:22:06,140
+كتبنا الدالة بدلالة D وروحنا اشتقناها بعد هيك هذا
+
+628
+01:22:06,140 --> 01:22:10,900
+اللى هو المطلوب الأول نمرى نمرى B قال لي احسب
+
+629
+01:22:10,900 --> 01:22:18,340
+المشتقة وين عند Zero وين المشتقة مشتقة ب Zero عند
+
+630
+01:22:18,340 --> 01:22:26,370
+T تساوي Zero إذا نف Zeroيبقى نمرة B بد ال DW على
+
+631
+01:22:26,370 --> 01:22:32,530
+DT لما ال D تساوي Zero يبقى ب Zero زي مهين لم
+
+632
+01:22:32,530 --> 01:22:41,430
+يتغير شيء طيب
+
+633
+01:22:41,430 --> 01:22:42,790
+خد المثال رقمي
+
+634
+01:22:53,870 --> 01:23:08,010
+و X Y و X تساوي T و Y تساوي Lim T و Z يساوي E أس T
+
+635
+01:23:08,010 --> 01:23:11,970
+ناقص واحد و T تساوي واحد
+
+636
+01:23:22,090 --> 01:23:29,830
+نفس المطالب التلاتة بدنا ياخدوا لسؤال رقم اتنين
+
+637
+01:23:55,590 --> 01:24:01,050
+بعدين بطلع بالأجه ال w function في ثلاثة متغيرات
+
+638
+01:24:01,050 --> 01:24:06,510
+ال x و ال y و كذلك من ال z يبقى هذا مثل السؤال
+
+639
+01:24:06,510 --> 01:24:11,670
+اللي جابله فيه متغيرين هذا فيه ثلاثة يبقى انا ها
+
+640
+01:24:11,670 --> 01:24:17,310
+بدي اجيب له ال dw by dt اللي هي الطريقة الأولى
+
+641
+01:24:39,490 --> 01:24:47,060
+طيبتفاضل يتدلّى
+
+642
+01:24:47,060 --> 01:24:52,120
+بالنسبة لـ X تفاضل يتدلّى بالنسبة لـ Y تفاضل
+
+643
+01:24:52,120 --> 01:24:54,020
+يتدلّى بالنسبة لـ X تفاضل يتدلّى بالنسبة لـ Y
+
+644
+01:24:54,020 --> 01:24:56,500
+تفاضل يتدلّى بالنسبة ل X تفاضل يتدلّى بالنسبة ل Y
+
+645
+01:24:56,500 --> 01:24:59,940
+تفاضل يتدلّى بالنسبة ل X تفاضل يتدلّى بالنسبة ل Y
+
+646
+01:24:59,940 --> 01:25:01,600
+تفاضل يتدلّى بالنسبة ل X تفاضل يتدلّى بالنسبة ل Y
+
+647
+01:25:01,600 --> 01:25:04,440
+تفاضل يتدلّى بالنسبة ل X تفاضل يتدلّى بالنسبة ل Y
+
+648
+01:25:04,440 --> 01:25:11,590
+تفاضل يتدلّى بالنسبة ل X تفاضل يتدلّى بالنتفاضل Z
+
+649
+01:25:11,590 --> 01:25:17,790
+بـ 0 بالنسبة لـ X تفاضل الـ Psi بكوساين بتفاضل
+
+650
+01:25:17,790 --> 01:25:22,910
+الزاوية بالنسبة ل X بالقدر Y وهي السالف زي ماني في
+
+651
+01:25:22,910 --> 01:25:28,330
+DX على DT التفاضل هذا اللي هي بقدرش واحد صحيح اللي
+
+652
+01:25:28,330 --> 01:25:33,850
+بعد زاوية تفاضل ال W بالنسبة ل Y برضه هذا بزيرة
+
+653
+01:25:33,850 --> 01:25:37,030
+ناقص
+
+654
+01:25:37,030 --> 01:25:39,750
+X في كوساين
+
+655
+01:25:45,560 --> 01:25:55,580
+تفاضل ال y بالنسبة ل t هو 1 على t التفاضل
+
+656
+01:25:55,580 --> 01:26:02,180
+ال w بالنسبة ل z هذا كله في zero مشتقة
+
+657
+01:26:02,180 --> 01:26:06,500
+ال z بالنسبة ل t مشتقة ال exponential بال
+
+658
+01:26:06,500 --> 01:26:10,860
+exponential كما هي في مشتقة الوصلة وجدال
+
+659
+01:26:27,300 --> 01:26:37,220
+يبقى هذا ناقص و Y ممكن تقشف ناقص لأن T هو sign من
+
+660
+01:26:37,220 --> 01:26:38,540
+الذي يقول
+
+661
+01:26:56,500 --> 01:27:08,160
+ناقص واحد طيب نختصر يبقى ناقص لنت في cosine ت ت
+
+662
+01:27:08,160 --> 01:27:09,040
+لنت
+
+663
+01:27:43,580 --> 01:27:48,500
+من هذه المشتركة
+
+664
+01:27:57,840 --> 01:28:03,380
+مطلوب التاني قال لأ من الأول فتخلي الدالة بدلالي T
+
+665
+01:28:03,380 --> 01:28:08,800
+و بعدها تشتغل فبقى أجيب و أقوله النقطة الثانية
+
+666
+01:28:08,800 --> 01:28:17,580
+الـW يُسطى بدي أشيل الـZ و أحط بدلها منين E أس T
+
+667
+01:28:17,580 --> 01:28:24,880
+ناقص واحد ناقص sign XYT
+
+668
+01:28:25,630 --> 01:28:31,530
+Limit T يبقى بطلة تصير الدالة هذه مانها Function
+
+669
+01:28:31,530 --> 01:28:38,310
+في X وY وإنما صارت دالة في مين؟ في متغير واحد اللي
+
+670
+01:28:38,310 --> 01:28:43,870
+هو T، يبقى مجتق مباشرة إذا لو جاءت اشتقها دي برضه،
+
+671
+01:28:43,870 --> 01:28:51,890
+إيش سيحصل؟ DW by DT بده يساوي ال exponential زي ما
+
+672
+01:28:51,890 --> 01:28:54,270
+هي ضرب مشتقة الأس
+
+673
+01:28:59,890 --> 01:29:12,070
+ب cos T لن T ضرب مشتقل الزاوية T في واحد على T
+
+674
+01:29:12,070 --> 01:29:22,150
+زائد لن الـ T نختصر يبقى هذه E أس T ناقص واحد ناقص
+
+675
+01:29:22,150 --> 01:29:30,880
+cos T لن T في واحد زائد لن Tهل اختلفوا الإجابتين
+
+676
+01:29:30,880 --> 01:29:35,040
+على البعض هنا ؟ طلع الإجابة اللي مبروزة والإجابة
+
+677
+01:29:35,040 --> 01:29:39,600
+اللي قدامها دنتين نفس الشيء لذلك على كل الأمرين
+
+678
+01:29:39,600 --> 01:29:46,660
+كله بيعطينا نفس النتيجة طيب نقرأ فيه قال لي بدي
+
+679
+01:29:46,660 --> 01:29:53,720
+تحسبلي DW على DT عند T تسوية درجة واحد فبعدين
+
+680
+01:29:53,720 --> 01:30:01,850
+بقوله DW على DTعندك ايه تساوي واحد فهذا بيصير ايه
+
+681
+01:30:01,850 --> 01:30:11,230
+و لكنه كما ناقص ناقص cosine واحد لن الواحد مصبوط
+
+682
+01:30:11,230 --> 01:30:20,550
+هيك لن الواحد وعندك هنا في واحد زائد لن الواحد
+
+683
+01:30:20,550 --> 01:30:24,730
+فهذا بيقدرش واحد لن الواحد
+
+684
+01:30:30,390 --> 01:30:37,750
+لأن هذا بزير النتيجة يساوي واحد ناقص كده يبقى
+
+685
+01:30:37,750 --> 01:30:44,530
+الجواب كمان يساوي زير إذا عند T تساوي واحد قيمة
+
+686
+01:30:44,530 --> 01:30:51,250
+هذه المشتقة تساوي صفر لحد هنا stop و بنكمل ان شاء
+
+687
+01:30:51,250 --> 01:30:56,660
+الله المرة القادمةلسه بننتقل الان بدل ال X و ال Y
+
+688
+01:30:56,660 --> 01:31:03,160
+بدل ما يكون متغير واحد بنخليها في main يعني W دلّ
+
+689
+01:31:03,160 --> 01:31:11,020
+في X و Y و Z وكل من X و Y و Z دلّ في متغيرين و
+
+690
+01:31:11,020 --> 01:31:16,000
+بعدين ناخد special cases كمان يعني لسه لنا شغل في
+
+691
+01:31:16,000 --> 01:31:21,240
+هذا ال section سنكمله ان شاء الله في المرة القادمة
+
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/481Vfp-Apr4_raw.srt b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/481Vfp-Apr4_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..582dd4da30e0338f5145d1b496a195c0ca6f25e6
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/481Vfp-Apr4_raw.srt
@@ -0,0 +1,2780 @@
+1
+00:00:00,000 --> 00:00:02,680
+موسيقى
+
+2
+00:00:15,840 --> 00:00:20,180
+بسم الله الرحمن الرحيم ابتدنا في شبطر اربعة عشر
+
+3
+00:00:20,180 --> 00:00:24,540
+واخدنا فيه two sections ال two sections بتحدث عن
+
+4
+00:00:24,540 --> 00:00:29,560
+ال functions of several variables أخدنا كيف بنجيب
+
+5
+00:00:29,560 --> 00:00:32,880
+ال domain و ال range لهذه ال functions و اتعرفنا
+
+6
+00:00:32,880 --> 00:00:37,460
+كذلك على level curves و level surfaces للمنحنيات
+
+7
+00:00:37,460 --> 00:00:44,780
+او الصطوحبعد ذلك ننتقل إلى جد ال limit و ال
+
+8
+00:00:44,780 --> 00:00:49,760
+continuity للدالة of several variables الان في
+
+9
+00:00:49,760 --> 00:00:55,260
+section 14-3 سنذهب إلى derivatives of functions of
+
+10
+00:00:55,260 --> 00:00:59,660
+several variablesبنبدأ بمتغيرين ثم نذهب لثلاث
+
+11
+00:00:59,660 --> 00:01:05,440
+متغيرات أو أكتر لنتدرج في فهم الموضوع فعندي
+
+12
+00:01:05,440 --> 00:01:10,980
+partially derivatives يعني المشتقات الجزئية في
+
+13
+00:01:10,980 --> 00:01:15,440
+مشتقة كلية و في مشتقة جزئية الإجابة نعم متى تكون
+
+14
+00:01:15,440 --> 00:01:20,860
+المشتقة الكلية و متى تكون المشتقة الجزئيةبتكون
+
+15
+00:01:20,860 --> 00:01:24,900
+المشتقة الكلية إذا عندي function في one variable
+
+16
+00:01:24,900 --> 00:01:29,220
+يبقى بقول هذا اسم اشتقاق كلي total differentiation
+
+17
+00:01:29,220 --> 00:01:34,580
+يبقى بقول dy على dx سوى f prime of x عندي تبقى
+
+18
+00:01:34,580 --> 00:01:38,880
+الدالة y في متغير واحد أما إذا كانت الدالة في
+
+19
+00:01:38,880 --> 00:01:43,180
+متغيرين أو ثلاثة أو أربعة ففي هذه الحالة الاشتقاق
+
+20
+00:01:43,180 --> 00:01:47,600
+بيكون اشتقاق جزءياللي هو الموضوع لليوم فبقى دي
+
+21
+00:01:47,600 --> 00:01:51,800
+بقول في partial derivative المشتقة الجزئية للدالة
+
+22
+00:01:51,800 --> 00:01:57,420
+f of x و y بالنسبة للمتغير x عند النقطة x node و y
+
+23
+00:01:57,420 --> 00:02:02,940
+node as هديها الرمز f و حكم تحتها اللي هو ال index
+
+24
+00:02:02,940 --> 00:02:08,340
+x اللي هو الدليل x يعني ايش معناها؟ معناها المشتقة
+
+25
+00:02:08,340 --> 00:02:12,440
+بالنسبة ل x و بكتبها على الصورة partial f على
+
+26
+00:02:12,440 --> 00:02:15,700
+partial x هدى كمان اللي بقيت اكتب دي عادية
+
+27
+00:02:19,890 --> 00:02:24,450
+يبقى و تقرأ partial F على partial X و يُفهَم منها
+
+28
+00:02:24,450 --> 00:02:29,550
+أننا نريد أن نشتغل الدالة بالنسبة إلى X طب إذا
+
+29
+00:02:29,550 --> 00:02:34,850
+جئنا لنشتغل X ما أخبار ال Y يبقى ال Y بنعتبرها
+
+30
+00:02:34,850 --> 00:02:40,890
+مقدارا ثابتا تمام اتطلع الكلام اللي أنا بقوله
+
+31
+00:02:40,890 --> 00:02:46,910
+هيحطنا عليها على التعريفهذا هو الـ Limit عندما الـ
+
+32
+00:02:46,910 --> 00:02:53,730
+H تذهب إلى الـ 0 لـ F of X0 زائد H وY0 يبقى ثبتنا
+
+33
+00:02:53,730 --> 00:02:59,430
+الـ Y0 وعملنا تغيير في الـ X لأننا نقص F of X0 وY0
+
+34
+00:02:59,430 --> 00:03:05,330
+على H هل شكل التعريف اختلف فيه مضمونه عن التعريف
+
+35
+00:03:05,330 --> 00:03:08,950
+تبع الـ function of one variable؟مش هو نفس التعريف
+
+36
+00:03:08,950 --> 00:03:12,770
+الـ derivative العادى؟ طيب هذا لو كان الاشتقاق
+
+37
+00:03:12,770 --> 00:03:17,510
+بالنسبة ل X طب لو كان الاشتقاق بالنسبة ل Y يبقى
+
+38
+00:03:17,510 --> 00:03:22,310
+نفسي المفهوم اذا اقول FY أو partial F على partial
+
+39
+00:03:22,310 --> 00:03:29,210
+Y عند النقطة X node وY node هو limitبثبت ال X node
+
+40
+00:03:29,210 --> 00:03:33,370
+كإنه مقدار ثابت و بروح باخد التغيير اللي بيحصل في
+
+41
+00:03:33,370 --> 00:03:38,490
+مهم في ال Y فبقول Y node زي ال H نقص of X node و Y
+
+42
+00:03:38,490 --> 00:03:43,750
+node على مين على H بشرط إن ال limit في كلتل حالتين
+
+43
+00:03:43,750 --> 00:03:49,670
+exist يعني ال derivative هذا بيحصل إذا كان عندى
+
+44
+00:03:49,670 --> 00:03:56,220
+إذا كان ال limit هذه مالها existالروح نحط هذا على
+
+45
+00:03:56,220 --> 00:04:08,180
+أرض الواقع فباجي بقول ف f w مثلا تساوي f of x و y
+
+46
+00:04:08,180 --> 00:04:18,520
+و ذهب يبقى باجي بقول to find لإيجاب نمر راحة
+
+47
+00:04:28,130 --> 00:04:38,030
+Y and Z are constants يبقى
+
+48
+00:04:38,030 --> 00:04:44,410
+دول بنعتبرهم ثوابت طيب نمر اتنين لو بدي partial F
+
+49
+00:04:44,410 --> 00:04:49,030
+على partial Y يبقى هنا باجي بقول
+
+50
+00:04:59,080 --> 00:05:05,380
+لو بدنا ال partial F على partial Z و ي consider
+
+51
+00:05:05,380 --> 00:05:15,900
+بنروح نعتبر ان ال X and ال Y are constants و هكذا
+
+52
+00:05:18,560 --> 00:05:23,940
+بدا من الأن فصعدنا بنات لو كانت الدالة في متغيرين
+
+53
+00:05:23,940 --> 00:05:29,960
+و بدى مشتقة بالنسبة لأحد المتغيرين فبعتبر المتغير
+
+54
+00:05:29,960 --> 00:05:34,720
+الثاني ماله ثابت عند الاشتقاء إذا و الله الدالة في
+
+55
+00:05:34,720 --> 00:05:39,840
+ثلاثة متغيرات بدى أشتق بالنسبة لأحدهم يبقى بعتبر
+
+56
+00:05:39,840 --> 00:05:44,200
+الأثنين الأخرين مقادير ثابتة يعني مشتقة كل واحد
+
+57
+00:05:44,200 --> 00:05:49,180
+فيهم جد إيشبصفر ب zero يعني بعتبر مقدار ثابت و
+
+58
+00:05:49,180 --> 00:06:02,480
+هكذا نعطي أمثلة توضيحية على ذلك مثال الأول
+
+59
+00:06:02,480 --> 00:06:06,580
+find fx
+
+60
+00:06:06,580 --> 00:06:14,860
+and fy for the following
+
+61
+00:06:22,270 --> 00:06:33,290
+F of X Y يساوي Y في تان X تربيع Y تكعين
+
+62
+00:06:39,010 --> 00:06:49,270
+بدها تساوي E أُس XY في صين تكييب X تربيع زائد Y
+
+63
+00:06:49,270 --> 00:07:00,530
+تربيع زائد تلت XY نمرس E F of X وY بديه يساوي
+
+64
+00:07:00,530 --> 00:07:05,970
+integration من X squared plus one ل Y
+
+65
+00:07:31,900 --> 00:07:37,090
+مرة تانيةالمعلومة النظرية اللي أخدناها بالنسبة
+
+66
+00:07:37,090 --> 00:07:41,670
+لمشتقة دلة بالنسبة لأحد المتغيرات نعطي أمثلة
+
+67
+00:07:41,670 --> 00:07:46,450
+توضيحية عليها المثال بيقول لهاتف المشتقة الدلة
+
+68
+00:07:46,450 --> 00:07:51,330
+بالنسبة ل X وكذلك مشتقة الدلة بالنسبة ل Y لكل من
+
+69
+00:07:51,330 --> 00:07:53,530
+الدول التالية
+
+70
+00:08:16,440 --> 00:08:24,240
+بنبدأ بالنقطة الأولىيبدأ يجيب مشتقتها بالنسبة إلى
+
+71
+00:08:24,240 --> 00:08:31,780
+X يبقى يجي إلى FX يعني مشتقة ال F بالنسبة إلى X
+
+72
+00:08:31,780 --> 00:08:36,960
+ونلفهايها يبقى ال Y أشهر اعتبر يا بنات مقدار ثابت
+
+73
+00:08:36,960 --> 00:08:41,400
+بقول يا Y خليك زي ما انت مالكش تعرف وتفضل التان
+
+74
+00:08:42,140 --> 00:08:49,580
+كداش؟ ب 6² الزاوية الزاوية اللي هي من X تربية و Y
+
+75
+00:08:49,580 --> 00:08:53,700
+تكييب طبق اللي تشينره المظروف في مشتقة الزاوية
+
+76
+00:08:53,700 --> 00:08:59,800
+بالنسبة ل X يبقى Y تكييب مقدارا ثابتا مالوش دعوة
+
+77
+00:08:59,800 --> 00:09:07,640
+مشتقة ال X تربية ب2X وال Y تكييب تبقى كما هي واضحة
+
+78
+00:09:07,640 --> 00:09:16,550
+الآن هذي؟ طيبنجيب fy تساوي اللي هو تفاضل ال f
+
+79
+00:09:16,550 --> 00:09:25,210
+بالنسبة إلى y partial f by partial y ايوة هذي y و
+
+80
+00:09:25,210 --> 00:09:30,770
+هذي y يبقى هذي مشتقتها عاصل ضرب دلتين نرجع لك
+
+81
+00:09:30,770 --> 00:09:35,150
+القلص او لثانوية الأولى في مشتقة ثانية زائدة ثانية
+
+82
+00:09:35,150 --> 00:09:40,940
+في مشتقة الأولى يبقى الأولىمشتقة الثانية تفاضل
+
+83
+00:09:40,940 --> 00:09:50,200
+التان بسكت ربيع X ربيع Y تكيب في مشتقة الزاويةليه
+
+84
+00:09:50,200 --> 00:09:55,880
+تلاتة Y تربيع والـ X تربيع مقدارا ثابتا يبقى فيه
+
+85
+00:09:55,880 --> 00:10:01,840
+تلاتة X تربيع وY تربيع هذه الأولى في مشتقة الثانية
+
+86
+00:10:01,840 --> 00:10:06,300
+زائد الدالة الثانية في مشتقة الأولى مشتقة الأولى
+
+87
+00:10:06,300 --> 00:10:13,580
+في قداش؟ بواحد صحيح يبقى زائد تان X تربيع Y تكعيب
+
+88
+00:10:13,580 --> 00:10:15,800
+نمر بيه
+
+89
+00:10:18,840 --> 00:10:23,880
+برضه بنفس الطريقة هذه تعتبر function وتحتوي على ال
+
+90
+00:10:23,880 --> 00:10:28,840
+X و ال Y وهذه function تحتوي على ال X و ال Y يبقى
+
+91
+00:10:28,840 --> 00:10:33,760
+عليك كل الأمرين سواء كان بدنا Fx أو Fy فهي مشتقة
+
+92
+00:10:33,760 --> 00:10:37,860
+حاسوب ضرب ده اللي يتم بجل الدالة الأولى اللي هي
+
+93
+00:10:37,860 --> 00:10:44,800
+Fxy و 7 مشتقة الأولى بجداش يا بنات ال X بوننشل زي
+
+94
+00:10:44,800 --> 00:10:54,450
+مهيضرب مشتقة الأس بالنسبة ل X اللي هو بقداش مشتقة
+
+95
+00:10:54,450 --> 00:11:01,670
+الأس بالنسبة إيه ل X يعني Y ثابت يقداش Y تمام
+
+96
+00:11:01,670 --> 00:11:07,190
+فاهمين هي مشتقة الأولى في الثانية في sign تكيب X
+
+97
+00:11:07,190 --> 00:11:15,050
+تربيع زائد Y تربيع زائد طول XY زائدالدالة الأولى
+
+98
+00:11:15,050 --> 00:11:21,290
+زى ماهى u s x y في تفاضل الدالة التانية يبقى تفاضل
+
+99
+00:11:21,290 --> 00:11:29,550
+التانية التلاتة sin تربيع فى مين فى x تربيع زائد y
+
+100
+00:11:29,550 --> 00:11:36,050
+تربيع زائد تلت x y فى تفاضل ال sin اللى همين
+
+101
+00:11:36,050 --> 00:11:40,590
+بكوسين يبقى كوسين نفس الزاوية
+
+102
+00:11:47,060 --> 00:11:51,940
+لأ ما خلصناش لسه بدك تضرب في تفاضل الزاوية بالنسبة
+
+103
+00:11:51,940 --> 00:11:57,720
+لمين؟ بالنسبة لمين؟ لأكس يبقى هذا بده يضرب يا بنات
+
+104
+00:11:57,720 --> 00:12:04,840
+في مين؟ في تفاضل الزاوية اللي هو اتنين X فقط زائد
+
+105
+00:12:04,840 --> 00:12:14,240
+تلت Y شكل اللعنةيبقى I اشتقنها اشتقاقا كاملا طبعا
+
+106
+00:12:14,240 --> 00:12:20,160
+ممكن يكون عندى اختصار ان التلاتة داخلتها بصير 6X و
+
+107
+00:12:20,160 --> 00:12:26,000
+هنا زائد Y تفرجش مش كتير طيب هذا ال Fx بدنا نروح
+
+108
+00:12:26,000 --> 00:12:32,140
+نجيب ال Fyy ساوى يبقى بنشتق دالة بالنسبة ل Y يبقى
+
+109
+00:12:32,140 --> 00:12:37,740
+ال exponential زي ما هو تتفضل أس بالنسبة إيه ل Y
+
+110
+00:12:37,740 --> 00:12:47,440
+لهو كده ب Xفاهمين؟ في sign تكييب X تربيع زائد Y
+
+111
+00:12:47,440 --> 00:12:54,980
+تربيع زائد طول XY جاي مشتقة الأولى في الثانية زائد
+
+112
+00:12:54,980 --> 00:13:02,160
+الأولى كما هي في مشتقة الثانية sign تكييب لتلاتة
+
+113
+00:13:02,160 --> 00:13:11,480
+sign تربيع الزاوية X تربيعزائد تلت XY في تفاضل
+
+114
+00:13:11,480 --> 00:13:16,940
+الـSin اللي هو الـ Cos X تربيع زائد Y تربيع زائد
+
+115
+00:13:16,940 --> 00:13:25,760
+تلت XY غرب مشتقة الزاوية بالنسبة ل Y اللي هي اتنين
+
+116
+00:13:25,760 --> 00:13:33,440
+Y زائد تلت X هيك اشتقناها اشتقاقا كاملا
+
+117
+00:13:58,800 --> 00:14:07,100
+طيب، نجي لمن؟ للمراسي، المراسي بده مشتقة هذه و هذه
+
+118
+00:14:07,100 --> 00:14:11,080
+عندي تكامل، إذا نروح نكامل الدل و بعدين نشتق،
+
+119
+00:14:11,080 --> 00:14:17,150
+كويس؟لأ بروح اللي ماعنش طبق التكامل ايوة تروح
+
+120
+00:14:17,150 --> 00:14:21,650
+تكامل يبنيك مثلة بتقدريش تتكاملها زي المثلة اللي
+
+121
+00:14:21,650 --> 00:14:26,370
+قدامنا هذا صعب تكاملها very difficult يبقى المقصود
+
+122
+00:14:26,370 --> 00:14:30,030
+مش تروح تكامل انا بقى بتشتق اصدقاء اه اخدنا على
+
+123
+00:14:30,030 --> 00:14:33,550
+ذلك اللي هى مين في كالكولاسيا شو اسم هى النظرية؟
+
+124
+00:14:33,550 --> 00:14:37,930
+fundamental theory of calculus يبقى انا بده اروح
+
+125
+00:14:37,930 --> 00:14:42,560
+اطبق ال fundamentalTheorem of calculus مع مراعاة
+
+126
+00:14:42,560 --> 00:14:48,960
+مين ثابت ومين المتغير يبقى انا بده Fx بده اشتقاد
+
+127
+00:14:48,960 --> 00:14:53,800
+بالنسبة ل X يبقى ال Y ايش تعتبر ثابت اذا هذا يعتبر
+
+128
+00:14:53,800 --> 00:15:01,860
+مقدارا ثابتا يبقى هذا بدي اقول اللي فوق B0 ناقص
+
+129
+00:15:01,860 --> 00:15:09,530
+يبقى هاي ال zero ناقصnotes mean بدي أشيل كل T و
+
+130
+00:15:09,530 --> 00:15:14,190
+أحط مكانها X تربية زائد واحد إذا هذا إيش بتصير
+
+131
+00:15:14,190 --> 00:15:25,210
+sign X تربية زائد واحد fill in بدي أشيل ال T و أحط
+
+132
+00:15:25,210 --> 00:15:32,360
+مكانها X تربيةزائد واحد لكل تربية ناقص واحد ضرب
+
+133
+00:15:32,360 --> 00:15:46,740
+مشتق تمين الدل اللي هو قداش باتنين X طبعا
+
+134
+00:15:46,740 --> 00:15:51,200
+يمكن اختصاره افك هذا وقت مش مشكلة المهم ان اعرف
+
+135
+00:15:51,200 --> 00:15:58,010
+كيف انطبق النظرية طب لو بده fy يا بناتيبقى هذا
+
+136
+00:15:58,010 --> 00:16:03,770
+يعتبر كله كأنه مقدار ثالث يبقى اش باجي بقول بشيل
+
+137
+00:16:03,770 --> 00:16:12,750
+كل T و بحط مكانها Y يبقى اش بصير sign Y تكيب تمام
+
+138
+00:16:12,750 --> 00:16:18,170
+يبقى شيلت ال T و حطيت مكانها اللي هو Y تكيب لن
+
+139
+00:16:30,810 --> 00:16:34,850
+أبقى بنات لو كانت هذه دالة في X وهذه دالة في X
+
+140
+00:16:34,850 --> 00:16:41,870
+وطلبت المشتقة بالنسبة لي Yزيرو ممتاز جدا يبقى لو
+
+141
+00:16:41,870 --> 00:16:45,590
+كانت الدالة اللى فوق بدلالة X ودلالة تحت ال index
+
+142
+00:16:45,590 --> 00:16:50,230
+التابع التكامل بدلالة X وطلبت المشتقة بالنسبة الى
+
+143
+00:16:50,230 --> 00:16:56,070
+Y إذن اوتوماتيك المشتقة تسوى جداش Zero و بالمثل لو
+
+144
+00:16:56,070 --> 00:17:01,870
+كانت الدالة الاثنين متغيرين في Y وطلبت المشتقة
+
+145
+00:17:01,870 --> 00:17:07,610
+بالنسبة ل X النتج يساوي Zero تمام تمامطيب بعد ما
+
+146
+00:17:07,610 --> 00:17:13,590
+انتهينا من هذا المثال بروح ناخد مثال اخر مثال
+
+147
+00:17:13,590 --> 00:17:18,070
+اتنين بيقول
+
+148
+00:17:18,070 --> 00:17:31,270
+find ال fx ال fx و ال fy and ال fz
+
+149
+00:17:49,650 --> 00:18:03,510
+Y و Z تساوي X في E أُس Y زائد Y في E أُس Z زائد Z
+
+150
+00:18:03,510 --> 00:18:15,870
+في E أُس X لمين؟ F of X و Y و Z يساوي 10 Inverse
+
+151
+00:18:15,870 --> 00:18:22,250
+لمين؟ لل X Yزائد YZ
+
+152
+00:18:54,230 --> 00:18:59,470
+الفرق بين المثال رقم اتنين والمثال رقم واحد ان
+
+153
+00:18:59,470 --> 00:19:03,130
+المثال رقم واحد كان function في two variables بس
+
+154
+00:19:03,130 --> 00:19:07,910
+ده function في three variables طلب المشتقة بالنسبة
+
+155
+00:19:07,910 --> 00:19:11,910
+ل X والمشتقة بالنسبة ل Y والمشتقة بالنسبة ل Z إذا
+
+156
+00:19:11,910 --> 00:19:15,450
+بدنا نعمل السؤال بنفس الطريقة اللي عملنا فيها
+
+157
+00:19:15,450 --> 00:19:27,570
+السؤال السابق بدالي للمرة AY و
+
+158
+00:19:27,570 --> 00:19:35,850
+Z ثابت و X هو المتغير يبقى EY كله مقدر ثابت تفضل X
+
+159
+00:19:35,850 --> 00:19:44,650
+جدًا واحد يبقى EY هذا كله Zero هذا Z ثابت ومشتقة
+
+160
+00:19:44,650 --> 00:19:52,620
+EY بالـ EY itselfطبعا طبعا هذا ال f of x بدي ال fy
+
+161
+00:19:52,620 --> 00:20:01,600
+يزاوي ال x ثابت مالكش دعوة مشتقة ال ey بال ey
+
+162
+00:20:01,600 --> 00:20:02,480
+itself
+
+163
+00:20:18,880 --> 00:20:25,300
+مشتقتها صفر هذه ال Y كما هي مشتقة ال E و ال Z بال
+
+164
+00:20:25,300 --> 00:20:32,360
+E و ال Z اتسل مشتقة ال Z بواحد بطارية نمية E أس X
+
+165
+00:20:32,360 --> 00:20:36,900
+طيب و جيبنا المشتقات التلاتة للنقطة الأولى النقطة
+
+166
+00:20:36,900 --> 00:20:43,960
+التانية اللي نمر بيها فنجيب لها F X يساعد حد فيكم
+
+167
+00:20:43,960 --> 00:20:50,100
+الذاكرة كده مشتقتان inverse Xمنتاج واحد على واحد
+
+168
+00:20:50,100 --> 00:20:54,940
+زائد اكثر بما كان ال X أجتني الزاوية اللي هي XY
+
+169
+00:20:54,940 --> 00:21:00,740
+زائد YZ إذن هذه بدأت تصير واحد
+
+170
+00:21:25,370 --> 00:21:32,430
+واحد زائد واحد
+
+171
+00:21:32,430 --> 00:21:33,370
+عالم
+
+172
+00:22:09,630 --> 00:22:16,210
+كل تربيع في مستقلة الزاوية بالنسبة إلى Y كداش بضل
+
+173
+00:22:16,210 --> 00:22:25,090
+هنا X وهنا بضل كداش Z بالمثل بدي أروح أجيب اللي هو
+
+174
+00:22:25,090 --> 00:22:34,790
+ال FZ ال FZ يساوي واحد على واحد زائد اللي هو ال XY
+
+175
+00:22:34,790 --> 00:22:45,630
+زائد Y زائدالكل تربيع في مشتقة هذه بالنسبة لزد
+
+176
+00:22:45,630 --> 00:22:55,270
+اللي هو Y فقط لا غير Y فبطلعي لنا نمر بي له Fx و
+
+177
+00:22:55,270 --> 00:23:00,430
+Fz يختلفوا عن بعض، إذا كان بإمكاني أسيط السؤال
+
+178
+00:23:00,430 --> 00:23:04,250
+صغيرة أخرى و أقول لك show that أن partial F by
+
+179
+00:23:04,250 --> 00:23:09,440
+partial X equal partial F by partial Zطبعا وبدأت
+
+180
+00:23:09,440 --> 00:23:12,900
+الصغير يقول لأ اجيب هذا المشتقه و اجيب هذا المشتقه
+
+181
+00:23:12,900 --> 00:23:16,960
+يتطلعوا اتنين مساوا بعض و يصير كلام انه كلام صحيح
+
+182
+00:23:16,960 --> 00:23:21,440
+طيب احنا في الاشتقاق في كل كلاصية خدنا اشتقاق عادي
+
+183
+00:23:21,440 --> 00:23:27,060
+زي ما بنشتق و خدنا اشتقاطا ضمنيا طبعا اللي هو ال
+
+184
+00:23:27,060 --> 00:23:30,520
+implicit differentiation خلينا ناخد السؤال عن ال
+
+185
+00:23:30,520 --> 00:23:34,660
+implicit و نشوف كيف كمان بدنا نحله يبقى example
+
+186
+00:23:34,660 --> 00:23:35,780
+تلاتة
+
+187
+00:23:37,950 --> 00:23:44,350
+اللي هو implicit differentiation
+
+188
+00:23:44,350 --> 00:23:53,330
+يبقى اشتقاق ضلمي find اللي
+
+189
+00:23:53,330 --> 00:24:01,990
+هو partial z على partial x and partial z على
+
+190
+00:24:01,990 --> 00:24:05,770
+partial y for the function
+
+191
+00:24:08,880 --> 00:24:22,760
+لدالة x تربيع زائد y تربيع في z بده يساوي y تان x
+
+192
+00:24:22,760 --> 00:24:23,580
+y z
+
+193
+00:24:55,210 --> 00:25:04,670
+سؤال مرة تانية يسوي
+
+194
+00:25:04,670 --> 00:25:11,870
+y tan xyz سؤال طلب تفاضل z بالنسبة ل x و تفاضل z
+
+195
+00:25:11,870 --> 00:25:18,370
+بالنسبة لمين؟ y إذا كان هناك متغيرات مستقلة و
+
+196
+00:25:18,370 --> 00:25:24,070
+متغيرات تبع independent variableيعني مين بدي يكون
+
+197
+00:25:24,070 --> 00:25:30,630
+دالة في مين السؤال هو هل ال X دالة في Y و Z و الله
+
+198
+00:25:30,630 --> 00:25:35,490
+ال Y دالة في X و Z و الله ال Z دالة في X و Y Z
+
+199
+00:25:35,490 --> 00:25:40,750
+دالة في X و Y لما طلب تفاضل ال Z بالنسبة ل X و
+
+200
+00:25:40,750 --> 00:25:46,390
+تفاضل ال Z بالنسبة ل M لل Y يبقى هنا بروح نعتبر ان
+
+201
+00:25:46,390 --> 00:25:54,140
+Z is a function ofيبقى باجي بقول هنا ليش ان هاي
+
+202
+00:25:54,140 --> 00:26:02,020
+المطبوق عندنا يبقى we consider بنروح نعتبر ان ال z
+
+203
+00:26:02,020 --> 00:26:12,760
+is a function of x and y هذا يترتب عليه قمر مهم
+
+204
+00:26:12,760 --> 00:26:19,710
+جدا عند الاشتقاء ان لو اشتق x بالنسبة ل yقداش
+
+205
+00:26:19,710 --> 00:26:24,030
+مكون؟ Zero. Zero. ده اشتق واي بالنسبالك. Zero. لكن
+
+206
+00:26:24,030 --> 00:26:29,160
+الباقي لأ؟لأن Z function في كل من X و Y هي
+
+207
+00:26:29,160 --> 00:26:34,760
+المتغيرات المستقلة و Z هو المتغير اتبع Z function
+
+208
+00:26:34,760 --> 00:26:39,300
+في كل من X و Y اضع هذه المعلومة مهمة جدا عند
+
+209
+00:26:39,300 --> 00:26:46,400
+التطبيق اتنين انا مش قاعد اضع Z في شجة و الباقي في
+
+210
+00:26:46,400 --> 00:26:52,130
+شجة تانية يعني لا يمكن فصل المتغيراتبحيث أخلّي
+
+211
+00:26:52,130 --> 00:26:57,150
+الذد في جهة و لا أستطيع تمام إذا هذا الاشتقاق اسمه
+
+212
+00:26:57,150 --> 00:27:03,570
+اشتقاقا ضمنيا تمام يبقى بدي أرجع بذاكرتي إلى
+
+213
+00:27:03,570 --> 00:27:07,970
+الوراء لكالكولاسية للاشتقاق الضمنى و أحط في بالي
+
+214
+00:27:07,970 --> 00:27:14,290
+بدي أفاضل كل شيء في موقعه مع مراعاة قواعد التفاضل
+
+215
+00:27:14,290 --> 00:27:19,210
+التي سبق الدراسة في كالكولاسية فمثلاأنا بدأ أفضل
+
+216
+00:27:19,210 --> 00:27:22,690
+ال N بالنسبة لمين؟ ل X لأنني بدأي partial Z by
+
+217
+00:27:22,690 --> 00:27:30,830
+partial X يبقى كل من Y بيكون ثابت في هذه الحالة و
+
+218
+00:27:30,830 --> 00:27:34,170
+المجاب ال Y هتكون ثابت تفضل X تربعيها بقداش يا
+
+219
+00:27:34,170 --> 00:27:41,490
+مانا؟ 2X ال Y تربعيها مالكش دعوةمختار ثاني تفاضل
+
+220
+00:27:41,490 --> 00:27:47,510
+ال Z اللي احنا بيدناه تفاضل ال Z بالنسبة ل X يبقى
+
+221
+00:27:47,510 --> 00:27:52,250
+الشجة الشمال واضحة الشجة الشمال نجي للشجة اليمين
+
+222
+00:27:52,250 --> 00:27:57,250
+ال Y مختار ثاني لان هو بيبقى بالنسبة ل X وتفاضل
+
+223
+00:27:57,250 --> 00:28:06,640
+تاني بسكتر بيه XYZ في مشتقتي الزاويةمشتقة الزاوية
+
+224
+00:28:06,640 --> 00:28:17,720
+كده مشتقة هذا بالنسبة ل X؟ بYZ تمام زائد هذه كأنها
+
+225
+00:28:17,720 --> 00:28:23,780
+دالة وهذه دالة تانية فبجي بقول مشتقة هذه بواحد وYZ
+
+226
+00:28:23,780 --> 00:28:30,100
+كما هي زائد الدالة الأولى زي ما هي ال Y مقدار ثابت
+
+227
+00:28:30,100 --> 00:28:34,480
+ال Z ل partial Z by partial X
+
+228
+00:28:37,220 --> 00:28:43,080
+واضحات مرة تانية بدأ أقولها هذا الاشتقاق أفعلته
+
+229
+00:28:43,080 --> 00:28:47,660
+اسمه اشتقاق ضمني تمام يبقى بدأ أفضل كل شيء في
+
+230
+00:28:47,660 --> 00:28:51,820
+موقعه مع مراعاة قواعد التفاضل المفتلفة أنا بفضل
+
+231
+00:28:51,820 --> 00:28:55,920
+بالنسبة ل X أولا لإن بدي partial Z by partial X
+
+232
+00:28:55,920 --> 00:29:00,930
+يبقى باجي بقول التفاضل كسبيا باتنين X هذا كلهالـ Y
+
+233
+00:29:00,930 --> 00:29:04,670
+تربية صغيرة مقنعة ثابت تفاضل الـ Z له partial Z by
+
+234
+00:29:04,670 --> 00:29:08,770
+partial X نجي الـ Y مقنعة ثابت مانوش داورة تفاضل
+
+235
+00:29:08,770 --> 00:29:14,180
+التان بسكت تربية ضارب مشتقة الزاويةأعتبر هذه دالة
+
+236
+00:29:14,180 --> 00:29:20,060
+و هذه دالة تانية يبقى مشتقة الأولى بواحد في YZ هاي
+
+237
+00:29:20,060 --> 00:29:25,220
+ال YZ زائد الأولى زي ما هي ال X مشتقة التانية
+
+238
+00:29:25,220 --> 00:29:29,840
+مشتقة ال YZ Y مقدر ثابت مشتقة ال Z اللي هو partial
+
+239
+00:29:29,840 --> 00:29:36,270
+Z by partial Xعاد بعد هيك فكي و طلعيلي partial z
+
+240
+00:29:36,270 --> 00:29:41,450
+by partial x على شجة و ساعمليلي هيك و روحي أخليها
+
+241
+00:29:41,450 --> 00:29:48,430
+باقى الشغل الشغل الروتيني يعني هدف يعني هدفأنا
+
+242
+00:29:48,430 --> 00:29:51,310
+أجيب ال partial z على partial عن بعض و أخد عامل
+
+243
+00:29:51,310 --> 00:29:55,690
+مشترك و أنقل هذا على شكل تاني و أجسم شغل روتيني لا
+
+244
+00:29:55,690 --> 00:30:00,650
+قيمة له و ان غلط فيه بنحاسبك يبقى لا بس فاضليه من
+
+245
+00:30:00,650 --> 00:30:03,490
+الأول للآخر في ال implicit differentiation هذا
+
+246
+00:30:03,490 --> 00:30:07,910
+فاضلي من الأول للآخر صح و روح و خليني تمام؟ مش
+
+247
+00:30:07,910 --> 00:30:11,410
+هنضيع وقت واحنا نقعد نحس فيه لإن احنا اشتقن اشتقطا
+
+248
+00:30:11,410 --> 00:30:17,210
+صحيحاللي هو الاشتقاق بالنسبة إلى X بالذالك ياخد
+
+249
+00:30:17,210 --> 00:30:22,210
+الاشتقاق بالنسبة لمن؟ ل Y بقولك كذلك كذلك مستقل ال
+
+250
+00:30:22,210 --> 00:30:30,470
+X ترمية Zero تمام مستقل تاني نين Y زت
+
+251
+00:30:32,520 --> 00:30:39,600
+خلصت؟ لسه ال Y متغير و ال Z متغير يبقى 2Y في Z
+
+252
+00:30:39,600 --> 00:30:47,480
+زائد Y تربية partial Z by partial Y شوفت كيف
+
+253
+00:30:47,480 --> 00:30:52,120
+اترجعت عن بعض و عن اللي فوق؟ طيب هذا الكلام
+
+254
+00:30:52,120 --> 00:30:57,420
+بالتسابق بنا نشتقت ده لاني بالنسبة لمين؟ ل Y يبقى
+
+255
+00:30:57,420 --> 00:31:05,110
+مشتقة الأولى واحدوظلتان X Y Z زائد Y في تفاضلي
+
+256
+00:31:05,110 --> 00:31:11,530
+التان بسكتر بيها الزاوية ضرب مشتقة الزاوية بالنسبة
+
+257
+00:31:11,530 --> 00:31:17,370
+لمن؟ بالنسبة إلى Y يبقى ال X ايش يُعتبر البلاد؟
+
+258
+00:31:17,370 --> 00:31:25,150
+المقدار ثابت ومشتقة ال Y زد بالنسبة ل Y؟ بزد لأن
+
+259
+00:31:25,150 --> 00:31:26,990
+مشتقة ال Y تاب واحد
+
+260
+00:31:41,490 --> 00:31:45,130
+مرة تانية بقول المشتقة الأخيرة لأن هو اللي ممكن
+
+261
+00:31:45,130 --> 00:31:51,110
+تلخبط فيها طلعيلي كويس هذه دالة وهذه كلها تعتبر
+
+262
+00:31:51,110 --> 00:31:56,100
+دالة تانية يبقى مشتقة الأولى بواحد في تان هذهزي دي
+
+263
+00:31:56,100 --> 00:32:00,220
+دالة الأولى ليه Y مشتقة التان بصيك تربيع في مشتقة
+
+264
+00:32:00,220 --> 00:32:05,060
+الزاوية ال X و ال Y ثوابت لكن احنا بنشتق ليه Y
+
+265
+00:32:05,060 --> 00:32:10,560
+يبقى X فقط هو ثابت و Y و Z هو المتغير يبقى باجي
+
+266
+00:32:10,560 --> 00:32:15,080
+بقول يبقى الأولى X في Z لإنه مشتقة ال Y بواحد
+
+267
+00:32:15,080 --> 00:32:21,440
+بعدين X في Y مشتقة ال Zلو partial z by partial y
+
+268
+00:32:21,440 --> 00:32:26,040
+هك اشتقنا اشتقاقا كاملا وماحدش اللي اعتراض عندنا
+
+269
+00:32:26,040 --> 00:32:31,560
+تمام طيب على اي حال بدنا نيجي هذا بالنسبة لمهم
+
+270
+00:32:31,560 --> 00:32:39,200
+للمشتقة الاولى بدأس السؤال الان احنا في calculus A
+
+271
+00:32:39,200 --> 00:32:42,860
+فبناخد المشتقة الاولى و التانية و التالتة و
+
+272
+00:32:42,860 --> 00:32:47,930
+الرابعة و المشتقة النونية مظبوطهل يوجد عندنا في ال
+
+273
+00:32:47,930 --> 00:32:52,370
+partial derivatives مشتقات أولى و تانية و تالتة و
+
+274
+00:32:52,370 --> 00:32:59,390
+رابعة انونية الإجابة نعم كف كالتالية يبقى بداجي
+
+275
+00:32:59,390 --> 00:33:05,530
+لحاجة اسمها second second
+
+276
+00:33:05,530 --> 00:33:13,530
+and higher order
+
+277
+00:33:17,830 --> 00:33:27,510
+فارشيل دريفتر يعني
+
+278
+00:33:27,510 --> 00:33:31,430
+المشتقة الثانية أو الأعلى، المشتقة التالتة،
+
+279
+00:33:31,430 --> 00:33:33,130
+الرابعة، الاخرية، سبع سنة
+
+280
+00:33:43,970 --> 00:33:48,590
+يبقى دي تعتبر مشتق مين؟ يعني بتشتق مرتين بالنسبة
+
+281
+00:33:48,590 --> 00:33:55,230
+لمين؟ بالنسبة ال X أو معناها partial by partial X
+
+282
+00:33:55,230 --> 00:34:03,170
+ل partial F by partial X الشكل هذا يعني بتشتقوا
+
+283
+00:34:03,170 --> 00:34:06,570
+بالنسبة ال F أولا بالنسبة ال X و اللي هو انت
+
+284
+00:34:06,570 --> 00:34:12,850
+بتشتقه كمان مرة و من جهة الرموز مكتوبة F XX
+
+285
+00:34:16,140 --> 00:34:25,180
+similarly بنفس الطريقة f yy يعني partial square f
+
+286
+00:34:25,180 --> 00:34:33,740
+by partial y squared يعني partial على partial y ل
+
+287
+00:34:33,740 --> 00:34:40,280
+partial f by partial y هذا
+
+288
+00:34:40,280 --> 00:34:47,510
+النقطة الأولى النقطة الثانيةطب لو عندي partial x
+
+289
+00:34:47,510 --> 00:34:53,670
+partial y مش كله زي بعضه مختلفين يعني عندي partial
+
+290
+00:34:53,670 --> 00:35:01,010
+square f على partial x partial y إيش معناها هذه؟
+
+291
+00:35:01,010 --> 00:35:08,470
+معناها إنه partial على partial x ل partial f by
+
+292
+00:35:08,470 --> 00:35:13,660
+partial yيعني إيش معناها يا بنات؟ بدي أشتق أولا
+
+293
+00:35:13,660 --> 00:35:21,660
+بالنسبة ل Y و لا بالنسبة ل X؟ ل Y أولا ثم ل X يعني
+
+294
+00:35:21,660 --> 00:35:29,220
+هذه كيانها إيش؟ كيانها partial على partial X لل FY
+
+295
+00:35:29,220 --> 00:35:32,520
+تمام؟
+
+296
+00:35:32,520 --> 00:35:37,480
+يعني أشتق ل Y أولا ثم بالنسبة ل X أو إن شئتم
+
+297
+00:35:37,480 --> 00:35:38,500
+فقولوا
+
+298
+00:35:46,220 --> 00:36:03,160
+يبقى partial by partial
+
+299
+00:36:03,160 --> 00:36:09,060
+y ل Fx يبقى Fxy
+
+300
+00:36:13,090 --> 00:36:20,730
+قبل ما أكمل جاي في بالي سؤال هل ال Fxy هي نفس ال
+
+301
+00:36:20,730 --> 00:36:29,830
+Fyx؟ زي بعض؟ لأ ليس بالضرورة ممكن يحصل تمام؟ لكن
+
+302
+00:36:29,830 --> 00:36:31,790
+in general لأ
+
+303
+00:36:34,810 --> 00:36:39,690
+ممكن افقول ممكن وقتهش هذا ما سنعرفه في نهاية هذا
+
+304
+00:36:39,690 --> 00:36:45,570
+ال section بنظرية إذا الدلدلة متصلة ومشتقتها دوال
+
+305
+00:36:45,570 --> 00:36:51,590
+متاصلة بالنسبة ل X وكذلك بالنسبة إلى Y وهذه كلها
+
+306
+00:36:51,590 --> 00:36:58,370
+معرفة بيحصل التساوي اللي احنا بنسأل عليه طيب افترض
+
+307
+00:36:58,370 --> 00:36:59,090
+يا بنات
+
+308
+00:37:17,050 --> 00:37:24,730
+فارشال تربيع F على فارشال external يعني هذه كأنها
+
+309
+00:37:24,730 --> 00:37:37,450
+partial على partial Y فال F XX يبقى ال F XXY لو
+
+310
+00:37:37,450 --> 00:37:38,150
+عندك
+
+311
+00:37:50,280 --> 00:37:57,540
+يعني هذه partial تربيع على partial X تربيع ل
+
+312
+00:37:57,540 --> 00:38:04,960
+partial تربيع F على partial Y تربيع يعني هذه
+
+313
+00:38:04,960 --> 00:38:11,420
+partial تربيع على partial X تربيع لمين؟ فالـ FYY
+
+314
+00:38:11,420 --> 00:38:14,340
+يعني هاني هان
+
+315
+00:38:20,010 --> 00:38:25,950
+بتعرف في أول رقم أو أول متغير جريب على الـ F أول
+
+316
+00:38:25,950 --> 00:38:30,110
+اشتقاق بالنسباله و بعدين بروحنا لبعد و لبعد و هكذا
+
+317
+00:38:30,110 --> 00:38:43,170
+طيب نبدأ ناخد بعض الأمثلة التوضيحية طيب
+
+318
+00:38:43,170 --> 00:38:47,790
+قبل التمثلة التوضيحية بقولك لو كانت تلت متغيرات
+
+319
+00:38:47,790 --> 00:38:49,130
+على سبيل المثال
+
+320
+00:39:10,090 --> 00:39:16,610
+يبقى هذه تساوي partial على partial X لمن؟ لpartial
+
+321
+00:39:16,610 --> 00:39:22,830
+على partial Y لpartial F على partial Z يعني بنت
+
+322
+00:39:22,830 --> 00:39:30,010
+هذه تساوي من؟ FZ في الأول وبعدها تفضل بالنسبة ل Y
+
+323
+00:39:30,010 --> 00:39:34,830
+وبعدها تفضل بالنسبة ل X و هكذا
+
+324
+00:39:43,220 --> 00:39:55,060
+سؤال الأول يقول لي let f of x, y و z بدها تساوي x
+
+325
+00:39:55,060 --> 00:40:04,740
+أص خمسة زائد x أص أربعة و y أص أربعة زت كبير زائد
+
+326
+00:40:04,740 --> 00:40:23,180
+y زت تربية fine أوشدوناFXY FYX
+
+327
+00:40:23,180 --> 00:40:28,860
+FXYY
+
+328
+00:40:28,860 --> 00:40:35,300
+FZXY
+
+329
+00:41:23,620 --> 00:41:39,240
+يبقى Fxy يبقى فيه ثلاثة متغيرات يبقى
+
+330
+00:41:39,240 --> 00:41:44,340
+Fxy يبقى فيه ثلاثة متغيرات
+
+331
+00:42:06,030 --> 00:42:13,390
+يجب ان نجيب fxy يبقى بالفضل هو الاسم لمن؟ لل one
+
+332
+00:42:13,390 --> 00:42:19,870
+يبقى هذا؟ Zero مع السلامة يبقى هذا Zero وهذا أربع
+
+333
+00:42:19,870 --> 00:42:29,150
+X تكيب مالاش داوة وهذه أربع Y تكيب وهنا في Z تكيب
+
+334
+00:42:29,150 --> 00:42:32,930
+والباقي ب Zero يبقى النتيجة سارة تقدر
+
+335
+00:42:40,620 --> 00:42:51,100
+بتركيب نمر بيه نمر بيه يبقى في الأول بالاسم الأمين
+
+336
+00:42:51,100 --> 00:42:57,160
+لل FY يبقى بالذاتي لل FY و7 يبقى بالذاتي ال
+
+337
+00:42:57,160 --> 00:43:00,820
+function اللي عندنا يبقى ال X أص خمسة بالدرجة ب
+
+338
+00:43:00,820 --> 00:43:09,680
+Zero يبقى هذه أربعة X أص أربعة زي ما هو Y تركيبفزي
+
+339
+00:43:09,680 --> 00:43:15,760
+التكييب بقى المشتقة بالنسبة ل Y زائد زي التربية
+
+340
+00:43:15,760 --> 00:43:22,020
+بيروح اشتقها بالنسبة لمن؟ ل X يبقى هذا بدي يعطيكي
+
+341
+00:43:22,020 --> 00:43:29,360
+انه FYX يساوي اشتق بالنسبة ل X يبقى ايش مصير عندك؟
+
+342
+00:43:29,360 --> 00:43:46,240
+16 X تكييب Y تكييب Z تكييبزائد Zero بقدر
+
+343
+00:43:46,240 --> 00:43:51,320
+الله تمام هذا يتفق مع نظري اللي قلتلكوا بعد قليل
+
+344
+00:43:51,320 --> 00:43:56,660
+الدالة هذه كثيرة حدود إلى ان هي دالة متصلة مشتقتها
+
+345
+00:43:56,660 --> 00:43:59,520
+بالنسبة لك كثيرة حدود دالة متصلة
+
+346
+00:44:01,930 --> 00:44:07,070
+دالة متصلة ال X Y كثيرة تحوظ المتصلة وهذه متصلة من
+
+347
+00:44:07,070 --> 00:44:11,990
+هنا جاء من جاء هذا التساوي اللي احنا تسألنا عليه
+
+348
+00:44:11,990 --> 00:44:19,230
+قبل قليل يبقى هذا بيه بدأي لنمري ال C نمري ال C
+
+349
+00:44:19,230 --> 00:44:29,730
+قال لي بدي F X Y Y يعني F X Y Y F X Y جاهزة عادي
+
+350
+00:44:34,200 --> 00:44:40,580
+بدي اشتقها كمان مرة بالنسبة لمين بالنسبة ل Y يعني
+
+351
+00:44:40,580 --> 00:44:49,340
+هذه كأنها partial على partial Y ل 16 X تكيب و Y
+
+352
+00:44:49,340 --> 00:44:56,020
+تكيبيبقى Z تكييب نشتق بنسبة ينا Y يبقى يدى تلاتة
+
+353
+00:44:56,020 --> 00:45:02,200
+فى ستاشر تمانية و أربعين X تكييب زى ما دى و هدى Y
+
+354
+00:45:02,200 --> 00:45:12,820
+تربية و هدى Z تكييب نمرى دى نمرى دى بده F Z X Y
+
+355
+00:45:12,820 --> 00:45:16,480
+اللى هو الخطوة تفضل بالنسبة لزى
+
+356
+00:45:23,450 --> 00:45:31,390
+هذه خالية من Z بـ Zero هذه مصير تلاتة X أُس أربعة
+
+357
+00:45:31,390 --> 00:45:42,570
+Y أُس أربعة Z ربيع زائد اتنين Y زائد اتنين Y زائد
+
+358
+00:45:42,570 --> 00:45:49,010
+اتنين Y زائد اتنين Y زائد اتنين
+
+359
+00:45:49,010 --> 00:45:49,530
+Y زائد اتنين Y زائد اتنين Y زائد اتنين Y زائد
+
+360
+00:45:49,530 --> 00:45:50,170
+اتنين Y زائد اتنين Y زائد اتنين Y زائد اتنين Y
+
+361
+00:45:50,170 --> 00:45:50,170
+زائد اتنين Y زائد اتنين Y زائد اتنين Y زائد اتنين
+
+362
+00:45:50,170 --> 00:45:50,190
+Y زائد اتنين Y زائد اتنين Y زائد اتنين Y زائد
+
+363
+00:45:50,190 --> 00:45:51,170
+اتنين Y زائد اتنين Y زائد اتنين Y زائد اتنين Y
+
+364
+00:45:51,170 --> 00:46:00,740
+زائد افز اكس تشتغل اسم ال X يبقى اتناشة X تكيب Y
+
+365
+00:46:00,740 --> 00:46:06,400
+قصة اربعة زت تربيه وهذا بالاسم ال X مع السلامة ب
+
+366
+00:46:06,400 --> 00:46:16,360
+Zero الله سعال عليه اللي بعدها بدي F Z X Y هشتغل
+
+367
+00:46:16,360 --> 00:46:20,720
+نتيجة اللي حصلت عليها بالاسم الأمين ال Y اربعة في
+
+368
+00:46:20,720 --> 00:46:21,380
+اتناشة
+
+369
+00:46:29,480 --> 00:46:36,180
+تبقى عرفنا كيف تتم عملية الاشتقاق طيب هذا المثال
+
+370
+00:46:36,180 --> 00:46:41,340
+الأول مثال الثاني show
+
+371
+00:46:41,340 --> 00:46:48,540
+that they function show that they function
+
+372
+00:46:51,310 --> 00:47:05,750
+F of X و Y و Z و 7 E از تلاتة X زائد أربعة Y فساعد
+
+373
+00:47:05,750 --> 00:47:10,490
+خمسة Z satisfies
+
+374
+00:47:21,920 --> 00:47:27,600
+وهذا اللي اتلاف لازم اللي partial تربيع F by
+
+375
+00:47:27,600 --> 00:47:32,880
+partial X تربيع partial تربيع F by partial Y تربيع
+
+376
+00:47:32,880 --> 00:47:39,460
+partial تربيع F by partial Z تربيع
+
+377
+00:48:03,890 --> 00:48:04,830
+ساعدني كثير
+
+378
+00:48:20,070 --> 00:48:25,170
+سؤال مرة تانية نعطيني function في ثلاثة متغيرات
+
+379
+00:48:25,170 --> 00:48:30,170
+exponential أس ثلاثة X زي درب ع Y في Cos خمسة Z
+
+380
+00:48:30,170 --> 00:48:34,310
+وقال لي أثبت لي أن هذه المعادلة بحقها معادلة
+
+381
+00:48:34,310 --> 00:48:39,290
+Laplace يروي بركة بنات معادلة Laplace في متغيرين
+
+382
+00:48:39,290 --> 00:48:44,130
+يكون هذا مش موجود يبقى المشتقة الثانية بالنسبة ل X
+
+383
+00:48:44,130 --> 00:48:47,250
+والمشتقة الثانية بالنسبة ل Y تستوى Zero إذا تلت
+
+384
+00:48:47,250 --> 00:48:51,950
+متغيراتبنضيف المشتقة تانية متغيرة تانية اربعة
+
+385
+00:48:51,950 --> 00:48:56,110
+متغيرات خمس متغيرات ان من المتغيرات كله بنفس
+
+386
+00:48:56,110 --> 00:48:56,710
+الطريقة
+
+387
+00:49:02,440 --> 00:49:07,380
+و مرتين بالنسبة ل Y و مرتين بالنسبة ل Z و نجمع بدل
+
+388
+00:49:07,380 --> 00:49:12,080
+النتج يكون جداش Zero ان حدث ذلك بقول فعلا هذه
+
+389
+00:49:12,080 --> 00:49:17,000
+الدلة تحقق معادلة Laplace equation ل M و جمعنا
+
+390
+00:49:17,000 --> 00:49:24,480
+عليه بضروحه جيد اللي هو partial F by partial Xهذه
+
+391
+00:49:24,480 --> 00:49:30,240
+فيهاش X يبقى X بس فيه الأربعة Y كله مقدار ثابت
+
+392
+00:49:30,240 --> 00:49:34,620
+يبقى ال X مو ننشي نفسها بس مضروبة في جدير في ثلاثة
+
+393
+00:49:34,620 --> 00:49:41,520
+يبقى هاي تلاتة E أس تلاتة X زائد أربعة Y
+
+394
+00:49:45,720 --> 00:49:54,340
+Fx X يعني مشتقة ثانية كمان مرة تصير تسعة يقص تلاتة
+
+395
+00:49:54,340 --> 00:50:02,100
+X زائد اربعة Y كوصين خمسة زائد بالمثل بدي اروح
+
+396
+00:50:02,100 --> 00:50:07,660
+اجيب له من F Y اذا اشتق مرتين بالنسبة ل Y يبقى
+
+397
+00:50:07,660 --> 00:50:13,950
+تلاتة X يعتبر مقداراثابتاً وشقة E وصة 4Y نفسها
+
+398
+00:50:13,950 --> 00:50:24,790
+مضروبة في قداش في 4 يبقى 4 E وصة 3X زائد 4Y E وصة
+
+399
+00:50:24,790 --> 00:50:36,690
+5Z هذا بده يعطيكي ان ال FYY كمان مرة 4X4X16 E وصة
+
+400
+00:50:36,690 --> 00:50:44,950
+3Xزائد اربعة Y كوساين خمسة Z بعدين اذا انا احنا
+
+401
+00:50:44,950 --> 00:50:50,530
+احنا احنا احنا احنا احنا احنا احنا احنا احنا احنا
+
+402
+00:50:50,530 --> 00:50:50,530
+احنا احنا احنا احنا احنا احنا احنا احنا احنا احنا
+
+403
+00:50:50,530 --> 00:50:50,690
+احنا احنا احنا احنا احنا احنا احنا احنا احنا احنا
+
+404
+00:50:50,690 --> 00:50:50,690
+احنا احنا احنا احنا احنا احنا احنا احنا احنا احنا
+
+405
+00:50:50,690 --> 00:50:50,990
+احنا احنا احنا احنا احنا احنا احنا احنا احنا احنا
+
+406
+00:50:50,990 --> 00:50:50,990
+احنا احنا احنا احنا احنا احنا احنا احنا احنا احنا
+
+407
+00:50:50,990 --> 00:50:56,750
+احنا احنا احنا احنا
+
+408
+00:50:56,750 --> 00:51:05,650
+احنا احنا
+
+409
+00:51:05,650 --> 00:51:15,650
+افى sin 5z ثبتنا ال exponential تفاضل cosine بسالب
+
+410
+00:51:15,650 --> 00:51:20,930
+sin الزاوية ضرب تفاضل الزاوية اللى بقدرش خمسة بدنا
+
+411
+00:51:20,930 --> 00:51:25,130
+ال fzz مش
+
+412
+00:51:25,130 --> 00:51:30,410
+تبقى فاهم ان اسمه z هذا كله مقدار ثاني وتفاضل ال
+
+413
+00:51:30,410 --> 00:51:33,850
+sin بcos ضرب خمسة دى بقدرش بصينة
+
+414
+00:51:36,430 --> 00:51:44,310
+يبقى إيش إيه في E مستلات X زائد أربعة Y E Cos خمسة
+
+415
+00:51:44,310 --> 00:51:51,090
+Z نجبع لأنا منها اللي هو partial تربيع ال F على
+
+416
+00:51:51,090 --> 00:51:56,210
+partial X تربيع partial تربيع ال F partial Y تربيع
+
+417
+00:51:56,210 --> 00:52:00,330
+partial تربيع ال F على partial Z تربيع يساوي
+
+418
+00:52:00,330 --> 00:52:10,870
+الأولان يلف XX اللي هي تسعةE أس ثلاثة X زائد أربعة
+
+419
+00:52:10,870 --> 00:52:20,230
+Y في Cos خمسة Z زائد ستة عشر E أس تلاتة X زائد
+
+420
+00:52:20,230 --> 00:52:30,410
+أربعة Yخمسة زد ناقص خمسة وعشرين E واس تلاتة X زائد
+
+421
+00:52:30,410 --> 00:52:37,990
+اربعة Y في Cos خمسة زد كده الناتج خمسة وعشرين ناقص
+
+422
+00:52:37,990 --> 00:52:42,450
+خمسة وعشرين X من فى Cos ب Zero يبقى هنا
+
+423
+00:53:03,730 --> 00:53:09,290
+يجي لنظرية اللي وعدناكوا فيها قبل قليل
+
+424
+00:53:16,680 --> 00:53:34,560
+AIM F F of X Y و ال F X و ال F Y F X و ال F Y و ال
+
+425
+00:53:34,560 --> 00:53:41,760
+F XY and ال FYX
+
+426
+00:53:42,890 --> 00:53:55,730
+are defined are defined كانت محرفة to throw out
+
+427
+00:53:55,730 --> 00:54:06,130
+خلال an open region throw out an open region
+
+428
+00:54:06,130 --> 00:54:09,570
+contiguous
+
+429
+00:54:09,570 --> 00:54:10,370
+point
+
+430
+00:54:12,960 --> 00:54:23,000
+continuing a point a
+
+431
+00:54:23,000 --> 00:54:33,280
+و b and are continuous and a زيادة على ذلك كانوا
+
+432
+00:54:33,280 --> 00:54:40,340
+كذلك دوال متصدا continuous عند النقطة
+
+433
+00:54:42,910 --> 00:54:48,510
+A وB ثم Fxy
+
+434
+00:54:48,510 --> 00:54:58,770
+عند النقطة A وB بسوى FYX عند النقطة A وB كمان
+
+435
+00:54:58,770 --> 00:55:07,490
+نظرياً اخيراً F A
+
+436
+00:55:07,490 --> 00:55:08,210
+function
+
+437
+00:55:12,830 --> 00:55:23,150
+فى الـ function f of x و y is differentiable قابلة
+
+438
+00:55:23,150 --> 00:55:31,810
+للاشتقاء f x naught y naught then ال f
+
+439
+00:56:15,350 --> 00:56:20,390
+بنرجع للنظرية الأولى السؤال طرحناه قبل شوية و
+
+440
+00:56:20,390 --> 00:56:24,130
+جوابنا عليه و الأن بنحطه في سيرة النظرية التالية
+
+441
+00:56:24,130 --> 00:56:28,350
+بيقول لو كانت دوال F of X Y مشتقة بالاسم X مشتقة
+
+442
+00:56:28,350 --> 00:56:33,690
+بالاسم Y مشتقة بالاسم X Y مشتقة بالاسم Y X كله
+
+443
+00:56:33,690 --> 00:56:36,810
+كانت دوال معبفة على open region و هذه ال open
+
+444
+00:56:36,810 --> 00:56:41,810
+region تحت ايه يعني تحتوي على النقطة A و Bوكانوا
+
+445
+00:56:41,810 --> 00:56:46,770
+كذلك كل المشتقات دي دوال متصلة عند نفس النقطة، إن
+
+446
+00:56:46,770 --> 00:56:51,890
+حدث ذلك يبقى المشتقتين هدول معاهم يدهم Yes Sir
+
+447
+00:56:51,890 --> 00:56:57,730
+النظرية هذه تدافق الوصيلة والدالة قابلة الاشتقاق
+
+448
+00:56:57,730 --> 00:57:02,490
+إذا ان هي دالة متصلة هي نفس القصة بالضبط طبعا، لكن
+
+449
+00:57:02,490 --> 00:57:03,550
+هل العكس صحيح؟
+
+450
+00:57:19,820 --> 00:57:25,160
+بالتالي دالة متصلة صحية لكنها دالة غير قابلة
+
+451
+00:57:25,160 --> 00:57:25,940
+للاشتغال
+
+452
+00:57:31,850 --> 00:57:35,930
+أو Vertical Tangent أو الدلة نفسها ماتكونش معظمة
+
+453
+00:57:35,930 --> 00:57:40,270
+عندها مظبوط تبقى هذه الأربع مواقع اللي تدلة فيها
+
+454
+00:57:40,270 --> 00:57:45,810
+تبقى غير قابلة لسه فبنعطي مثال على ذلك example
+
+455
+00:57:45,810 --> 00:57:54,930
+بيقول
+
+456
+00:57:54,930 --> 00:58:06,880
+الات ال F of X هو Y يساويX في صين الـ Y زائد Y في
+
+457
+00:58:06,880 --> 00:58:19,980
+صين الـ X زائد XY شهودان بيجيلي ان ال Fxy بده
+
+458
+00:58:19,980 --> 00:58:26,590
+يساوي ال Fyxيبقى الـ x و الـ y بالاستثناء مش عنده
+
+459
+00:58:26,590 --> 00:58:32,170
+نقطة واحدة و بس وإنما لجميع النقاط تعاتل plain أو
+
+460
+00:58:32,170 --> 00:58:35,950
+النقاط المعرفة عليها الدالة فدول الكميتين
+
+461
+00:58:35,950 --> 00:58:43,010
+متساويتين يبقى الحل solution بدي أروح أجيب له
+
+462
+00:58:43,010 --> 00:58:54,110
+ميلاد fx أولا يبقى fx بمين؟ صين ال yي كوصين ال X
+
+463
+00:58:54,110 --> 00:59:04,110
+زائد Y بدي أجيب له من Fxy Fxy بدي أشتقها دي
+
+464
+00:59:04,110 --> 00:59:14,530
+بالنسبة لمن إلى Y كوصين ال Y زائد كوصين ال X زائد
+
+465
+00:59:14,530 --> 00:59:18,050
+1 بدي أروح أجيب من
+
+466
+00:59:24,250 --> 00:59:36,130
+x لـcos y زائد sin x زائد x بعد ذلك نشتغل بالنسبة
+
+467
+00:59:36,130 --> 00:59:44,550
+إلى x fy x بدل سنة بالنسبة إلى x لcos y بالنسبة
+
+468
+00:59:44,550 --> 00:59:50,970
+إلى x لcos x بالنسبة إلى x اللي هو واحد صلّعيه إلى
+
+469
+00:59:50,970 --> 00:59:57,690
+واحد واتنينfrom واحد
+
+470
+00:59:57,690 --> 01:00:04,850
+and اتنين we have ان
+
+471
+01:00:04,850 --> 01:00:13,510
+ال Fxy بسوء ال Fyx لكل ال X و Y بلا استئناف طب ما
+
+472
+01:00:13,510 --> 01:00:19,750
+هو السبب يا مالاه؟طالعي ليه دالة هذه دالة متصلة
+
+473
+01:00:19,750 --> 01:00:24,070
+ولا لا؟ في نقطة واحدة بتقدر فيه تجيبولي نقطة دالة
+
+474
+01:00:24,070 --> 01:00:29,850
+غير متصلة؟ لأ هذه polynomial هذه sin هذه cos
+
+475
+01:00:29,850 --> 01:00:33,850
+polynomial في sin و polynomial في cos يبقى هذه
+
+476
+01:00:33,850 --> 01:00:40,790
+متصلة على طول الخط مشتقلون Fx نفس القصة متصلة Fxy
+
+477
+01:00:40,790 --> 01:00:48,710
+متصلة Fy متصلةمتاصلة fyx متاصلة وكذلك كلهم معرفات
+
+478
+01:00:48,710 --> 01:00:54,470
+إذا انطبقت كل شروط النظرية مدام انطبقت إذا غصب عن
+
+479
+01:00:54,470 --> 01:00:59,950
+اللي مايرضى بتطلع المقدارين هدول معاهم متساوية لحد
+
+480
+01:00:59,950 --> 01:01:06,270
+هنا انتهى هذا ال section وإليكن أقام المسائل ال
+
+481
+01:01:06,270 --> 01:01:11,350
+exercises أربع تاشر تلاتة المسائل
+
+482
+01:01:13,300 --> 01:01:21,540
+من واحد لتمانية و تلاتين القدر و سؤال خمسة و ستين
+
+483
+01:01:21,540 --> 01:01:28,960
+و ستة و ستين لأ عفوا لأ عفوا لسه جابلهم جابلهم من
+
+484
+01:01:28,960 --> 01:01:33,760
+واحد لتمانية و تلاتين القدر و من واحد و أربعين
+
+485
+01:01:33,760 --> 01:01:42,360
+لغاية أربعة و خمسين كذلك القدروكذلك من اللي هو
+
+486
+01:01:42,360 --> 01:01:52,540
+خمسة وستين او كذلك خمسة وستين وستة
+
+487
+01:01:52,540 --> 01:02:01,220
+وستين وكذلك من تلاتة وسبعين لغاية تمانين القدر
+
+488
+01:02:01,220 --> 01:02:01,840
+كذلك
+
+489
+01:02:11,920 --> 01:02:15,660
+بنتقل هنا يا بنات الى ال section اللي يليه وهو
+
+490
+01:02:15,660 --> 01:02:19,820
+that share rule اللي هي قاعدة السلسلة بنروح ناخد
+
+491
+01:02:19,820 --> 01:02:23,920
+قاعدة السلسلة في ال functions of several variables
+
+492
+01:02:23,920 --> 01:02:27,500
+زي ما درسناها في one variable في calculus A في
+
+493
+01:02:27,500 --> 01:02:30,980
+calculus C بناخدها في functions of several
+
+494
+01:02:30,980 --> 01:02:35,760
+variables وسنتدرج فيها من متغيرين إلى ثلاثة
+
+495
+01:02:35,760 --> 01:02:40,740
+متغيرات إلى أربع إلى نحو ذلك يبقى بدي أبدأ بنظرية
+
+496
+01:02:40,740 --> 01:02:41,420
+U M
+
+497
+01:03:02,230 --> 01:03:11,550
+continuous partial derivatives
+
+498
+01:03:11,550 --> 01:03:19,390
+Fx
+
+499
+01:03:19,390 --> 01:03:36,330
+and Fy and Fالـ X كانت هي X of T والـ Y هي
+
+500
+01:03:36,330 --> 01:03:43,350
+function of T كذلك وكله مدى المالهم are
+
+501
+01:03:43,350 --> 01:03:48,910
+differentiable functions are differentiable
+
+502
+01:03:48,910 --> 01:03:57,230
+functions of متغير رقم اسمه T of T
+
+503
+01:03:59,960 --> 01:04:13,240
+و متساوي f of x of t و y of t as a differentiable
+
+504
+01:04:13,240 --> 01:04:17,980
+function مدالة
+
+505
+01:04:17,980 --> 01:04:31,090
+قابلة للاشتقاء of t and dw by dt متساويpartial w
+
+506
+01:04:31,090 --> 01:04:40,030
+by partial x دي اكس على دي تين زي partial w by
+
+507
+01:04:40,030 --> 01:04:48,690
+partial y دي واي by دي تين. انا النظرية التانية
+
+508
+01:04:48,690 --> 01:04:58,960
+وسارجع للنظرية التانية. يقول ال F ال Wfunction في
+
+509
+01:04:58,960 --> 01:05:12,980
+x, y و z is is
+
+510
+01:05:12,980 --> 01:05:20,220
+differentiable and x,
+
+511
+01:05:20,700 --> 01:05:32,110
+y and zDifferentiable functions are differentiable
+
+512
+01:05:32,110 --> 01:05:40,150
+functions of T then
+
+513
+01:05:40,150 --> 01:05:52,530
+W is a differentiable function of
+
+514
+01:05:52,530 --> 01:05:55,170
+T and
+
+515
+01:05:58,030 --> 01:06:10,830
+DW by DT سوى partial W by partial X DX على DT زائد
+
+516
+01:06:10,830 --> 01:06:19,930
+partial W by partial Y DY على DT زائد partial W by
+
+517
+01:06:19,930 --> 01:06:20,950
+partial Z
+
+518
+01:07:25,020 --> 01:07:29,980
+طيب نرجع لنظرتين اللي كتبناه مرة تانية نظرية
+
+519
+01:07:29,980 --> 01:07:36,880
+الأولى بتقول لو W function في متغيرين X وY واخدنا
+
+520
+01:07:36,880 --> 01:07:42,160
+المشتق الأولى بالنسبة ل X والمشتق الأولى بالنسبة ل
+
+521
+01:07:42,160 --> 01:07:48,760
+Y وكانوا دوال متاصلة وكانت كل من X وY كل واحدة
+
+522
+01:07:48,760 --> 01:07:55,330
+فيهم دالة في متغير آخر يعني W دالة في مين؟كل واحد
+
+523
+01:07:55,330 --> 01:07:58,710
+من المتغيرين دالة في متغير آخر
+
+524
+01:08:07,390 --> 01:08:17,010
+يعني كان و هو function في T فقط دي
+
+525
+01:08:17,010 --> 01:08:22,410
+و بي دي تي شو بده تساوي بقول partial w by partial
+
+526
+01:08:22,410 --> 01:08:29,130
+x ليش قلت partial و لا بقول تفاضل كله لإن و ده فيه
+
+527
+01:08:29,130 --> 01:08:37,000
+متغيرين لكن عند دي x على دي t قلت تفاضل كلهليش ان
+
+528
+01:08:37,000 --> 01:08:41,960
+x بس function في متغيرين واحد يبقى في حالة
+
+529
+01:08:41,960 --> 01:08:46,360
+المتغيرين او تلاتة بقول partial في حالة متغير واحد
+
+530
+01:08:46,360 --> 01:08:52,360
+بقول تفاضل عادي dx by dt زائد طب partial w by
+
+531
+01:08:52,360 --> 01:08:55,460
+partial y في dy على dt
+
+532
+01:09:01,850 --> 01:09:07,330
+كل واحد من المتغيرات التلاتة دالة في متغير جديد
+
+533
+01:09:07,330 --> 01:09:11,210
+اللي هو المتغير T ما شكل ال derivative في هذه
+
+534
+01:09:11,210 --> 01:09:15,290
+الحالة او ما شكل ال general بقول دي دابليو باي دي
+
+535
+01:09:15,290 --> 01:09:24,910
+دي دي دي دي دي دي دي دي دي دي دي دي
+
+536
+01:09:24,910 --> 01:09:29,590
+دي
+
+537
+01:09:31,840 --> 01:09:37,640
+الكلام من خلال الأمثلة دي بقى نيجي لبعض الأمثلة
+
+538
+01:09:37,640 --> 01:09:44,660
+أول
+
+539
+01:09:44,660 --> 01:09:54,100
+مثال بقول لي ان امرأة express عبرلي
+
+540
+01:09:54,100 --> 01:09:59,200
+عن ال dw by dt
+
+541
+01:10:04,320 --> 01:10:11,360
+function of T by two
+
+542
+01:10:11,360 --> 01:10:16,280
+methods بطريقة
+
+543
+01:10:16,280 --> 01:10:20,200
+تانية طريقة
+
+544
+01:10:20,200 --> 01:10:28,280
+الأولى I by using chain
+
+545
+01:10:28,280 --> 01:10:29,800
+rule
+
+546
+01:10:38,360 --> 01:10:47,080
+تانية by expressing .. by expressing
+
+547
+01:10:47,080 --> 01:10:52,060
+w
+
+548
+01:10:52,060 --> 01:11:00,480
+as a function of t directly
+
+549
+01:11:08,830 --> 01:11:15,870
+دورة B W احسب
+
+550
+01:11:15,870 --> 01:11:26,730
+DW by DT at the given value
+
+551
+01:11:26,730 --> 01:11:35,550
+of T السؤال
+
+552
+01:11:35,550 --> 01:11:50,760
+الأوليقول الـ W تساوي X تربيه زائد Y تربيه والـ
+
+553
+01:11:50,760 --> 01:12:04,100
+X تساوي Cos T زائد Sin T والـ Y تساوي Cos T نقص
+
+554
+01:12:04,100 --> 01:12:07,960
+Sin Tو T تساوي زي
+
+555
+01:12:31,760 --> 01:12:37,520
+قبل أن نبدأ المثال حابب أحط هذا اللي أخدناه على
+
+556
+01:12:37,520 --> 01:12:43,180
+أرض الواقع عمليا من خلال رسم بمعنى أنه ممكن تنسي
+
+557
+01:12:43,180 --> 01:12:47,960
+ممكن تسي ممكن الاخري لكن الرسم دائما يخليك
+
+558
+01:12:47,960 --> 01:12:52,820
+معلوماتك دقيقة مائة بالمئة فبالدرجة لل derivative
+
+559
+01:12:52,820 --> 01:12:57,120
+الأول بدي أكتبه على شكل رسم و بعدين أكمل و أحصل
+
+560
+01:12:57,120 --> 01:13:02,300
+على سؤالهذا الجبهة لنبدأ عملية الحل هذا بدأ احاول
+
+561
+01:13:02,300 --> 01:13:07,760
+ارسم كله من النقطة النقطة الأولى الان بدأت اقنع ال
+
+562
+01:13:07,760 --> 01:13:12,760
+W في ما هو function في مين؟ في متغيرين، هذا بقى دي
+
+563
+01:13:12,760 --> 01:13:18,080
+بقول هي النقطة اللي عندها دي بقول W تساوي function
+
+564
+01:13:18,080 --> 01:13:23,520
+في X و Y إذا هنا بدأ أحط خط وهنا خط، بدأ أحط هنا X
+
+565
+01:13:23,520 --> 01:13:34,720
+وهنا Y بعد هيككل من X و Y في متغير واحد يبقى
+
+566
+01:13:34,720 --> 01:13:43,420
+هذا T بعد ذلك بالنسبة ل X و W فيها متغيرين إذا
+
+567
+01:13:43,420 --> 01:13:49,120
+الإشتقاق هذا يكون إشتقاق جزءي partial W by partial
+
+568
+01:13:49,120 --> 01:13:53,880
+X بنفس الطريقة هذا إشتقاق جزءي partial W by
+
+569
+01:13:53,880 --> 01:14:00,550
+partial Yلكن من X الى T ده لم يتغير واحد يبقى في
+
+570
+01:14:00,550 --> 01:14:09,190
+DX على DT وهذا DY على DT طالع عيش اللي سونا اضغط
+
+571
+01:14:09,190 --> 01:14:18,150
+في هذا في هذا زائد هذا في هذا مش بيعطيك ايه الان
+
+572
+01:14:18,150 --> 01:14:19,590
+هذا بالضبط صحيح ولا لا
+
+573
+01:14:27,350 --> 01:14:31,070
+طيب هذا الأمين بالنسبة للحالة اللي وطب الحالة
+
+574
+01:14:31,070 --> 01:14:35,550
+التانية لو كان تلت متغيرات بدي أعملها بنفس الطريقة
+
+575
+01:14:35,550 --> 01:14:42,050
+يبقى بدي أقول w تسوي ال function في x و y و z إذا
+
+576
+01:14:42,050 --> 01:14:48,700
+بدي أكون عندي تلت متغيراتهذا ال X وهذا ال Y وهذا
+
+577
+01:14:48,700 --> 01:14:55,760
+ال Z كل واحد فيهم دالة في نفس المتغير اللي هو T
+
+578
+01:15:00,160 --> 01:15:06,300
+هذه الدلة في تلت متغيرة XYZ يبقى هذا اشتقاقا جزئيا
+
+579
+01:15:06,300 --> 01:15:11,220
+وهذا partial W by partial Y وهذا partial W by
+
+580
+01:15:11,220 --> 01:15:21,960
+partial Z الباقي اشتقاق كله يبقى DX على DTY على DZ
+
+581
+01:15:21,960 --> 01:15:30,460
+على DZ نضربهم في بعضهذول في بعض هذول في بعض و نجمة
+
+582
+01:15:30,460 --> 01:15:35,920
+بتقنمين القاعدة التانية تانية تمام؟ يعني لو أنا
+
+583
+01:15:35,920 --> 01:15:41,080
+ناسي مش عارف كيف احفظهم او حفظ التونسيين من خلال
+
+584
+01:15:41,080 --> 01:15:44,800
+ال diagram اللي قدامنا هذا او الشكل الهندسي اللي
+
+585
+01:15:44,800 --> 01:15:52,920
+قدامنا بقدر اجيب المستقبل حتى لو كنت نسيهاطيب نيجي
+
+586
+01:15:52,920 --> 01:15:56,900
+أحط هالمعلومة هذه علشان جا عندنا ضياء وبدنا نيجي
+
+587
+01:15:56,900 --> 01:16:07,600
+لل solution تبع السؤال تبعه ماتيني w function في x
+
+588
+01:16:07,600 --> 01:16:13,080
+و y و ال x function في t و ال y function في t و
+
+589
+01:16:13,080 --> 01:16:17,640
+قال لي أحسر كلام أنا التي تساوي zero إيش بدي أحسر؟
+
+590
+01:16:18,290 --> 01:16:25,830
+قال لي عبّر عن dw by dt بدلالة T بطريقة تانية
+
+591
+01:16:25,830 --> 01:16:30,070
+الطريقة الأولى باستخدام share rule يعني زي ما احنا
+
+592
+01:16:30,070 --> 01:16:38,410
+كاتبينه إذا باجي بقوله ال dw by dt هي partial w by
+
+593
+01:16:38,410 --> 01:16:46,990
+partial x dx by by dt زي partial w by partial y dy
+
+594
+01:17:03,230 --> 01:17:12,770
+تفاضل الـ W بالنسبة لـ X يبقى الـ Y ثابتة في تفاضل
+
+595
+01:17:12,770 --> 01:17:24,970
+X بالنسبة إلى Tجزاف سالب صيني T زائد Cos T خلاصنا
+
+596
+01:17:24,970 --> 01:17:33,110
+من الشطر الأول DX على DT اللي بعديها زائد تفاضل W
+
+597
+01:17:33,110 --> 01:17:41,030
+بالنسبة ل Y بتنين Y تفاضل Y بالنسبة ل T جزاف سالب
+
+598
+01:17:41,030 --> 01:17:49,530
+صيني T زائد Cos Tماذا قال؟ قال انه يريد هذا الكلام
+
+599
+01:17:49,530 --> 01:17:55,130
+كدالة في T يبقى لا يريد X وY ان يكونوا في المثلة
+
+600
+01:17:55,130 --> 01:17:59,510
+بالمرة يريد المثلة كلها تحولها بدلالة من T طب ماهي
+
+601
+01:17:59,510 --> 01:18:03,970
+مشكلة ماهي الشيء عندك يبقى هذا يساوي اتنين ال X
+
+602
+01:18:03,970 --> 01:18:13,140
+جاء زايا فوق اللي هي مين؟ اللي هي cos T زائدSin T
+
+603
+01:18:13,140 --> 01:18:24,000
+و هذا جاهز Cos T ناقص Sin T زاد اتنين و I هي فوق
+
+604
+01:18:24,000 --> 01:18:38,060
+Cos T زاد Y ناقص Sin T فى
+
+605
+01:18:38,470 --> 01:18:44,150
+مش صح فشو رايح؟ سالب مع سالب نطلعها برا بصير اللي
+
+606
+01:18:44,150 --> 01:18:50,030
+برا هاد ايه؟ سالب و بصير عندنا مين؟ بصير عندنا
+
+607
+01:18:50,030 --> 01:18:58,750
+cosine T زائد sine 50 اذا
+
+608
+01:18:58,750 --> 01:19:05,530
+حابة تفكي بتفكي بالظغريهملكن بمجرد النظر هذا هو
+
+609
+01:19:05,530 --> 01:19:14,210
+هذا صح ولا لا يبغى هذا المشتفى تساويهذا الفرق بين
+
+610
+01:19:14,210 --> 01:19:21,530
+المربعين مربع الأولى ناقص مربع التانية مربع
+
+611
+01:19:21,530 --> 01:19:24,690
+الأولى ناقص مربع التانية مربع الأولى ناقص مربع
+
+612
+01:19:24,690 --> 01:19:30,910
+التانية مربع الأولى ناقص مربع التانية مربع الأولى
+
+613
+01:19:30,910 --> 01:19:32,370
+ناقص مربع التانية
+
+614
+01:19:35,440 --> 01:19:41,740
+حسب تشيره جللها من البداية إذا كتعفرلي علي ال W
+
+615
+01:19:41,740 --> 01:19:45,400
+كfunction في T و تثبت ان ال derivative هذا بده
+
+616
+01:19:45,400 --> 01:19:50,980
+يساوي جداري، بده يساوي جره، جره بسيطة، وجبجيله
+
+617
+01:19:50,980 --> 01:19:55,750
+النقطة الثانيةيجب ان انا اقول الو يجب ان انا اقول
+
+618
+01:19:55,750 --> 01:20:00,410
+الو يجب ان انا اقول الو يجب
+
+619
+01:20:00,410 --> 01:20:07,830
+ان انا اقول الو يجب
+
+620
+01:20:07,830 --> 01:20:11,090
+ان
+
+621
+01:20:11,090 --> 01:20:12,830
+انا اقول الو
+
+622
+01:20:19,960 --> 01:20:31,540
+2sin t cos t زائد sin تربيع t زائد cos تربيع t
+
+623
+01:21:06,440 --> 01:21:13,600
+هذه بالموجة وهذه بالسلف عند ال cos تربيع وcos
+
+624
+01:21:13,600 --> 01:21:15,620
+تربيع
+
+625
+01:21:25,430 --> 01:21:30,830
+يبقى ال cos تربيه T زائد sin تربيه او كمان sin
+
+626
+01:21:30,830 --> 01:21:38,470
+تربيه اتنين sin تربيه 80 لو أخدنا اتنين عامل مشترك
+
+627
+01:21:38,470 --> 01:21:42,630
+بيظل ال cos تربيه زائد sin تربيه يسوى جدير واحد
+
+628
+01:21:42,630 --> 01:21:50,410
+اشتقى يبقى هذا بيضايقيكي DW على DT بيسوى Zero لأن
+
+629
+01:21:50,410 --> 01:21:54,940
+هذا يعتبر مختارا ثالثاإذا القيمة اللى حصلنا عليها
+
+630
+01:21:54,940 --> 01:22:00,340
+بواسطة D تشيلون هي نفس القيمة اللى حصلنا عليها لو
+
+631
+01:22:00,340 --> 01:22:06,140
+كتبنا الدالة بدلالة D وروحنا اشتقناها بعد هيك هذا
+
+632
+01:22:06,140 --> 01:22:10,900
+اللى هو المطلوب الأول نمرى نمرى B قال لي احسب
+
+633
+01:22:10,900 --> 01:22:18,340
+المشتقة وين عند Zero وين المشتقة مشتقة ب Zero عند
+
+634
+01:22:18,340 --> 01:22:26,370
+T تساوي Zero إذا نف Zeroيبقى نمرة B بد ال DW على
+
+635
+01:22:26,370 --> 01:22:32,530
+DT لما ال D تساوي Zero يبقى ب Zero زي مهين لم
+
+636
+01:22:32,530 --> 01:22:41,430
+يتغير شيء طيب
+
+637
+01:22:41,430 --> 01:22:42,790
+خد المثال رقمي
+
+638
+01:22:53,870 --> 01:23:08,010
+و X Y و X تساوي T و Y تساوي Lim T و Z يساوي E أس T
+
+639
+01:23:08,010 --> 01:23:11,970
+ناقص واحد و T تساوي واحد
+
+640
+01:23:22,090 --> 01:23:29,830
+نفس المطالب التلاتة بدنا ياخدوا لسؤال رقم اتنين
+
+641
+01:23:55,590 --> 01:24:01,050
+بعدين بطلع بالأجه ال w function في ثلاثة متغيرات
+
+642
+01:24:01,050 --> 01:24:06,510
+ال x و ال y و كذلك من ال z يبقى هذا مثل السؤال
+
+643
+01:24:06,510 --> 01:24:11,670
+اللي جابله فيه متغيرين هذا فيه ثلاثة يبقى انا ها
+
+644
+01:24:11,670 --> 01:24:17,310
+بدي اجيب له ال dw by dt اللي هي الطريقة الأولى
+
+645
+01:24:39,490 --> 01:24:47,060
+طيبتفاضل يتدلّى
+
+646
+01:24:47,060 --> 01:24:52,120
+بالنسبة لـ X تفاضل يتدلّى بالنسبة لـ Y تفاضل
+
+647
+01:24:52,120 --> 01:24:54,020
+يتدلّى بالنسبة لـ X تفاضل يتدلّى بالنسبة لـ Y
+
+648
+01:24:54,020 --> 01:24:56,500
+تفاضل يتدلّى بالنسبة ل X تفاضل يتدلّى بالنسبة ل Y
+
+649
+01:24:56,500 --> 01:24:59,940
+تفاضل يتدلّى بالنسبة ل X تفاضل يتدلّى بالنسبة ل Y
+
+650
+01:24:59,940 --> 01:25:01,600
+تفاضل يتدلّى بالنسبة ل X تفاضل يتدلّى بالنسبة ل Y
+
+651
+01:25:01,600 --> 01:25:04,440
+تفاضل يتدلّى بالنسبة ل X تفاضل يتدلّى بالنسبة ل Y
+
+652
+01:25:04,440 --> 01:25:11,590
+تفاضل يتدلّى بالنسبة ل X تفاضل يتدلّى بالنتفاضل Z
+
+653
+01:25:11,590 --> 01:25:17,790
+بـ 0 بالنسبة لـ X تفاضل الـ Psi بكوساين بتفاضل
+
+654
+01:25:17,790 --> 01:25:22,910
+الزاوية بالنسبة ل X بالقدر Y وهي السالف زي ماني في
+
+655
+01:25:22,910 --> 01:25:28,330
+DX على DT التفاضل هذا اللي هي بقدرش واحد صحيح اللي
+
+656
+01:25:28,330 --> 01:25:33,850
+بعد زاوية تفاضل ال W بالنسبة ل Y برضه هذا بزيرة
+
+657
+01:25:33,850 --> 01:25:37,030
+ناقص
+
+658
+01:25:37,030 --> 01:25:39,750
+X في كوساين
+
+659
+01:25:45,560 --> 01:25:55,580
+تفاضل ال y بالنسبة ل t هو 1 على t التفاضل
+
+660
+01:25:55,580 --> 01:26:02,180
+ال w بالنسبة ل z هذا كله في zero مشتقة
+
+661
+01:26:02,180 --> 01:26:06,500
+ال z بالنسبة ل t مشتقة ال exponential بال
+
+662
+01:26:06,500 --> 01:26:10,860
+exponential كما هي في مشتقة الوصلة وجدال
+
+663
+01:26:27,300 --> 01:26:37,220
+يبقى هذا ناقص و Y ممكن تقشف ناقص لأن T هو sign من
+
+664
+01:26:37,220 --> 01:26:38,540
+الذي يقول
+
+665
+01:26:56,500 --> 01:27:08,160
+ناقص واحد طيب نختصر يبقى ناقص لنت في cosine ت ت
+
+666
+01:27:08,160 --> 01:27:09,040
+لنت
+
+667
+01:27:43,580 --> 01:27:48,500
+من هذه المشتركة
+
+668
+01:27:57,840 --> 01:28:03,380
+مطلوب التاني قال لأ من الأول فتخلي الدالة بدلالي T
+
+669
+01:28:03,380 --> 01:28:08,800
+و بعدها تشتغل فبقى أجيب و أقوله النقطة الثانية
+
+670
+01:28:08,800 --> 01:28:17,580
+الـW يُسطى بدي أشيل الـZ و أحط بدلها منين E أس T
+
+671
+01:28:17,580 --> 01:28:24,880
+ناقص واحد ناقص sign XYT
+
+672
+01:28:25,630 --> 01:28:31,530
+Limit T يبقى بطلة تصير الدالة هذه مانها Function
+
+673
+01:28:31,530 --> 01:28:38,310
+في X وY وإنما صارت دالة في مين؟ في متغير واحد اللي
+
+674
+01:28:38,310 --> 01:28:43,870
+هو T، يبقى مجتق مباشرة إذا لو جاءت اشتقها دي برضه،
+
+675
+01:28:43,870 --> 01:28:51,890
+إيش سيحصل؟ DW by DT بده يساوي ال exponential زي ما
+
+676
+01:28:51,890 --> 01:28:54,270
+هي ضرب مشتقة الأس
+
+677
+01:28:59,890 --> 01:29:12,070
+ب cos T لن T ضرب مشتقل الزاوية T في واحد على T
+
+678
+01:29:12,070 --> 01:29:22,150
+زائد لن الـ T نختصر يبقى هذه E أس T ناقص واحد ناقص
+
+679
+01:29:22,150 --> 01:29:30,880
+cos T لن T في واحد زائد لن Tهل اختلفوا الإجابتين
+
+680
+01:29:30,880 --> 01:29:35,040
+على البعض هنا ؟ طلع الإجابة اللي مبروزة والإجابة
+
+681
+01:29:35,040 --> 01:29:39,600
+اللي قدامها دنتين نفس الشيء لذلك على كل الأمرين
+
+682
+01:29:39,600 --> 01:29:46,660
+كله بيعطينا نفس النتيجة طيب نقرأ فيه قال لي بدي
+
+683
+01:29:46,660 --> 01:29:53,720
+تحسبلي DW على DT عند T تسوية درجة واحد فبعدين
+
+684
+01:29:53,720 --> 01:30:01,850
+بقوله DW على DTعندك ايه تساوي واحد فهذا بيصير ايه
+
+685
+01:30:01,850 --> 01:30:11,230
+و لكنه كما ناقص ناقص cosine واحد لن الواحد مصبوط
+
+686
+01:30:11,230 --> 01:30:20,550
+هيك لن الواحد وعندك هنا في واحد زائد لن الواحد
+
+687
+01:30:20,550 --> 01:30:24,730
+فهذا بيقدرش واحد لن الواحد
+
+688
+01:30:30,390 --> 01:30:37,750
+لأن هذا بزير النتيجة يساوي واحد ناقص كده يبقى
+
+689
+01:30:37,750 --> 01:30:44,530
+الجواب كمان يساوي زير إذا عند T تساوي واحد قيمة
+
+690
+01:30:44,530 --> 01:30:51,250
+هذه المشتقة تساوي صفر لحد هنا stop و بنكمل ان شاء
+
+691
+01:30:51,250 --> 01:30:56,660
+الله المرة القادمةلسه بننتقل الان بدل ال X و ال Y
+
+692
+01:30:56,660 --> 01:31:03,160
+بدل ما يكون متغير واحد بنخليها في main يعني W دلّ
+
+693
+01:31:03,160 --> 01:31:11,020
+في X و Y و Z وكل من X و Y و Z دلّ في متغيرين و
+
+694
+01:31:11,020 --> 01:31:16,000
+بعدين ناخد special cases كمان يعني لسه لنا شغل في
+
+695
+01:31:16,000 --> 01:31:21,240
+هذا ال section سنكمله ان شاء الله في المرة القادمة
+
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/BfHmF68iUco.srt b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/BfHmF68iUco.srt
new file mode 100644
index 0000000000000000000000000000000000000000..aa872b98014e02792b1bd64b3d57fa78c86a0ee5
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/BfHmF68iUco.srt
@@ -0,0 +1,2819 @@
+1
+00:00:19,020 --> 00:00:25,010
+بسم الله الرحمن الرحيم. نرجع الآن إلى chapter خمسة عشر
+
+2
+00:00:25,010 --> 00:00:29,030
+الذي ابتدأناه المرة الماضية، وأول section اللي هو
+
+3
+00:00:29,030 --> 00:00:33,250
+الـ double integrals على منطقة مستطيلة over
+
+4
+00:00:33,250 --> 00:00:38,190
+rectangular region. على منطقة على شكل مستطيل، أخذناها
+
+5
+00:00:38,190 --> 00:00:41,810
+المرة اللي فاتت. مثلاً واحدة، ومن الآن بنكمل الأمثلة
+
+6
+00:00:41,810 --> 00:00:45,770
+على نفس الموضوع. يبقى كالمرة اللي فاتت، مثال رقم a
+
+7
+00:00:45,770 --> 00:00:54,210
+بدنا نجيء مثلاً رقم b. السؤال الأول، مثال رقم B بيقول
+
+8
+00:00:54,210 --> 00:01:03,470
+بدي تكامل مزدوج على المنطقة A لـ X في Y في E أس X
+
+9
+00:01:07,410 --> 00:01:18,050
+معطينا المنطقة R هي أن X تتغير من 0 لغاية 2، و Y
+
+10
+00:01:18,050 --> 00:01:23,250
+تتغير من 0 لغاية 1
+
+11
+00:01:34,720 --> 00:01:38,480
+المرة اللي فاتت كان كتبنا حدود التكامل على التكامل
+
+12
+00:01:38,480 --> 00:01:43,340
+نفسه، تمام؟ المرة هذه، إن شاء الله تعالى، احنا بدنا
+
+13
+00:01:43,340 --> 00:01:47,640
+نكتب حدود التكامل. طب قلنا الكلام اللي هو إيه؟ جايب
+
+14
+00:01:48,230 --> 00:01:53,930
+يبقى في عندي تكاملين على المنطقة المستطيلة A، هي
+
+15
+00:01:53,930 --> 00:02:00,870
+لـ XY في الـ E أس XY تربيع. يبقى أنا بروح بقول له
+
+16
+00:02:00,870 --> 00:02:08,250
+هذا عبارة عن تكاملين لـ XY في الـ E أس XY تربيع
+
+17
+00:02:08,250 --> 00:02:13,330
+والآن، الشغل يديح. حبيت أكمل بالنسبة لـ X في الأول،
+
+18
+00:02:13,330 --> 00:02:16,850
+بمشي الحال. حبيت أكمل بالنسبة لـ Y في الأول، بمشي
+
+19
+00:02:16,850 --> 00:02:21,090
+الحال، لأن الحدود عندي أرقام، حدود مستطيل،
+
+20
+00:02:21,090 --> 00:02:24,830
+وبالتالي ما عنديش مشكلة في هذه الحالة، لكن بجيب
+
+21
+00:02:24,830 --> 00:02:29,750
+أطلع على الذلة، إيه هو أسهل أكمل للأول؟ هل بالنسبة
+
+22
+00:02:29,750 --> 00:02:34,840
+لـ X ولا بالنسبة لـ Y؟ بالنسبة لـ X بدها integration
+
+23
+00:02:34,840 --> 00:02:39,940
+by parts، صح؟ لكن بالنسبة لـ Y بدها بالتعويض، by
+
+24
+00:02:39,940 --> 00:02:43,500
+substitution. يبقى substitution أسرع ليه من حكاية
+
+25
+00:02:43,500 --> 00:02:44,800
+integration by parts
+
+26
+00:03:02,720 --> 00:03:08,140
+بعد هيك، يبقى كامل بالنسبة الأولى لـ Y، بحط حدود Y
+
+27
+00:03:08,140 --> 00:03:15,040
+يبقى من Zero لغاية One، وهنا من Zero لغاية Two. بعد
+
+28
+00:03:15,040 --> 00:03:20,680
+هيك، بدي كامل هذا الأصل Y تربيع. إذا أنا ممكن أشيل
+
+29
+00:03:20,680 --> 00:03:25,700
+الـ Y تربيع، وأحطه بمتغير جديد. إذا لو راح في
+
+30
+00:03:25,700 --> 00:03:31,320
+الامتحان، حطيتي T تساوي Y تربيع، يعني يبقى dT
+
+31
+00:03:31,320 --> 00:03:38,560
+بتساوي 2Y dY. يبقى بناء عليه، لو شيلت الـ Y اللي
+
+32
+00:03:38,560 --> 00:03:43,560
+عندها دي مع الـ dY، الاثنين هدول مع بعض، تحط بدلهم
+
+33
+00:03:43,560 --> 00:03:48,440
+نص dT. يبقى اتخلصت من الـ variable Y اللي برا
+
+34
+00:03:48,440 --> 00:03:54,020
+وصرت مسألة سهلة الآن. يبقى وصير هذا عبارة عن
+
+35
+00:03:54,020 --> 00:04:03,600
+تكاملين، وعندك هنا X، وهنا E أس X في T. يبقى شيلت
+
+36
+00:04:03,600 --> 00:04:07,830
+الـ X، خليتها زي ما هي. شيلت الـ Y dY، وبدي
+
+37
+00:04:07,830 --> 00:04:12,510
+أكتب بدلها النص dT. النص هذا كونه Standard، بقدر
+
+38
+00:04:12,510 --> 00:04:19,770
+أقوله خليك برا، وبصير عندي هنا dT، وهنا dX. الـ X
+
+39
+00:04:19,770 --> 00:04:22,910
+مالهاش علاقة في الموضوع كده، كونه صدق ما لهاش خبرة
+
+40
+00:04:22,910 --> 00:04:28,910
+يبقى بظل حدود الـ X كما هي، من Zero لمين؟ لغاية 2
+
+41
+00:04:29,440 --> 00:04:34,400
+لكن نظرنا، لو عملنا تعويضة. إذا بدي أشوف ما هي القيم
+
+42
+00:04:34,400 --> 00:04:41,200
+المناظرة لقيم Y بالنسبة للمتغير T. إذا بدي أجيء هنا
+
+43
+00:04:41,200 --> 00:04:45,960
+وأجيء وأقول: آه هذه الواحد والزيرو، هذول حدود مين؟
+
+44
+00:04:45,960 --> 00:04:52,320
+للـ Y. إذا لو كانت الـ Y بواحد، فـ T بواحد تربيع، تعني
+
+45
+00:04:52,320 --> 00:04:58,920
+واحد. ولو كانت الـ Y بـ Zero تربيع، يبقى بـ Zero. يظل من
+
+46
+00:04:58,920 --> 00:05:05,540
+Zero لغاية واحد. إذا ما عندنا مشكلة في هذه الحالة. إذا
+
+47
+00:05:05,540 --> 00:05:13,360
+صار بدي أكامل بالنسبة لـ T في الأول. يبقى الـ X يساوي
+
+48
+00:05:13,360 --> 00:05:20,660
+النص، وهي تكامل من صفر لغاية واحد. وتكامل
+
+49
+00:05:20,660 --> 00:05:25,920
+الـ exponential بالـ exponential itself مقسومة على
+
+50
+00:05:25,920 --> 00:05:31,200
+تفاضل الأس، إن كان من الدرجة الأولى. يبقى الـ X يعتبر
+
+51
+00:05:31,200 --> 00:05:37,860
+مقدار. يبقى ثابت، وتفاضله يبقى ده بواحد. يبقى على X، و
+
+52
+00:05:37,860 --> 00:05:42,940
+الحكي هذا كله من عنده Zero لغاية واحد. وهذه mainly
+
+53
+00:05:42,940 --> 00:05:50,660
+دي X اللي عندك. طيب الآن نختصر الـ X مع الـ X مع
+
+54
+00:05:50,660 --> 00:05:56,460
+السلامة. يبقى آلة المسألة إلى نص تكامل من Zero
+
+55
+00:05:56,460 --> 00:06:01,040
+لغاية 2. وبالتالي، أعوض بالقيمة اللي فوق ناقص اللي تحت، يعني
+
+56
+00:06:01,040 --> 00:06:05,820
+كده، شيل كل T وحط مكانها واحد، وشيل T وحط مكانها
+
+57
+00:06:05,820 --> 00:06:11,600
+Zero. ينفعش. بصير عندي يا بنات هنا E of X وT بواحد
+
+58
+00:06:11,600 --> 00:06:19,250
+ناقص E of Zero اللي هو بواحد. كل هذا الكلام بالنسبة
+
+59
+00:06:19,250 --> 00:06:24,970
+لمين؟ لـ X. يبقى صارت مسألة بسيطة جداً، أقصر مما
+
+60
+00:06:24,970 --> 00:06:30,490
+نتصور. يبقى هذا الكلام بده يساوي نص، فيه بده كامل
+
+61
+00:06:30,490 --> 00:06:36,160
+هذه تكامل الـ exponential، والـ exponential يتكامل بنفسه، ناقص X
+
+62
+00:06:36,160 --> 00:06:41,600
+والحقيقة كلها من Zero لغاية 2. هذا
+
+63
+00:06:41,600 --> 00:06:48,260
+الكلام بده يساوي نص E تربيع ناقص 2. هيعوضنا
+
+64
+00:06:48,260 --> 00:06:53,220
+بالقيمة اللي فوق ناقص اللي تحت. E of Zero اللي هو
+
+65
+00:06:53,220 --> 00:06:59,480
+واحد. وناقص مع ناقص بصير زائد Zero. انتهينا. يبقى
+
+66
+00:06:59,480 --> 00:07:06,770
+المسألة تساوي نصف E تربيع ناقص 2. هذه هي الإجابة. تمام؟ كيف
+
+67
+00:07:06,770 --> 00:07:12,410
+ناقص آه، ناقص 3 ناقص 1 ناقص 2، هي بناقص
+
+68
+00:07:17,530 --> 00:07:23,790
+3. نجيء الآن للمثال الثاني من الأمثلة. المثال
+
+69
+00:07:25,770 --> 00:07:30,890
+بيقول لي: بدي تكاملين على المنطقة المربع أو
+
+70
+00:07:30,890 --> 00:07:40,330
+المستطيلة R للـ X وY تكعيب على X تربيع زائد 1، dA
+
+71
+00:07:40,330 --> 00:07:47,750
+والمنطقة R هي عبارة عن الـ X أكبر من أو تساوي Zero
+
+72
+00:07:47,750 --> 00:07:52,810
+أقل من أو تساوي 1، والـ Y أكبر من أو تساوي Zero
+
+73
+00:07:52,810 --> 00:08:05,120
+أقل من أو تساوي مين؟ تساوي 2. إذا
+
+74
+00:08:05,120 --> 00:08:10,680
+بدنا نجيء للتكامل تبعنا هذا، ونرجع من الأول للجديد
+
+75
+00:08:10,680 --> 00:08:17,260
+ونروح نحط حدود التكامل اللي عندنا. يبقى تكاملين لـ
+
+76
+00:08:17,260 --> 00:08:26,690
+X Y تكعيب على الـ X تربيع زائد 1. أسهل اللي
+
+77
+00:08:26,690 --> 00:08:31,310
+أكمل في الأول بالنسبة لـ Y ولا لـ X؟ ليش لـ X؟ لـ Y
+
+78
+00:08:31,310 --> 00:08:35,770
+ما فيش غيرها أصلاً. بس هذه لسة بدها بص مقام، وأحل الـ
+
+79
+00:08:35,770 --> 00:08:40,110
+بص، وأفاضل المقام، يعني بدها شغلة بسيطة بس. هذه لأ
+
+80
+00:08:40,110 --> 00:08:44,130
+مباشرة. لابد نشتغلها. Y تكعيب لحالة. يبقى الأفضل اللي
+
+81
+00:08:44,130 --> 00:08:48,930
+أكمل بالنسبة لمين؟ لـ Y في الأول. فبروح بقوله: يبقى
+
+82
+00:08:48,930 --> 00:08:57,460
+هنا dY dX. هذه Y تكعيب. يبقى كأنه مين؟ كأنه كل المقدار
+
+83
+00:08:57,460 --> 00:09:01,760
+هذا يعتبر كل ثابت بالنسبة لمين؟ بالنسبة لـ Y
+
+84
+00:09:01,760 --> 00:09:05,720
+يبقى نفسه ده كامل Y تكعيب. إذا نبدأ إلى حدود الـ Y
+
+85
+00:09:05,720 --> 00:09:13,220
+الـ Y من أين لأين؟ من 0 لغاية 2، والـ X من 0 لغاية 1
+
+86
+00:09:13,870 --> 00:09:19,450
+يبقى النتيجة تساوي integration من Zero إلى واحد X
+
+87
+00:09:19,450 --> 00:09:24,650
+على X تربيع زائد 1. ما لوش دعوة. الـ Y تكعيب اللي هو
+
+88
+00:09:24,650 --> 00:09:30,070
+هو Y أس أربعة على 4، والكلام هذا من Zero لغاية
+
+89
+00:09:30,070 --> 00:09:33,730
+2، وهذا dX اللي عندنا
+
+90
+00:09:36,010 --> 00:09:40,610
+الآن نجيء نعوض. يبقى هذا الكلام تكامل من Zero لـ 1
+
+91
+00:09:40,610 --> 00:09:45,810
+لـ X على X تربيع زائد 1. فيه، بضعوض بالقيم اللي
+
+92
+00:09:45,810 --> 00:09:52,730
+فوق، 2 أس 4 على 4، بضل عندي 4 ناقص
+
+93
+00:09:52,730 --> 00:09:54,750
+Y أس 0
+
+94
+00:09:59,140 --> 00:10:03,560
+يبقى Zero أس 4، اللي هي بـ Zero. على كونها، تمام؟
+
+95
+00:10:03,560 --> 00:10:08,740
+وكل هذا مقسوم على 4. هذا جاهز، واحنا قسمنا
+
+96
+00:10:08,740 --> 00:10:14,660
+على 4. يبقى في مين؟ في dX، تماماً. يبقى يا بنات
+
+97
+00:10:14,660 --> 00:10:20,760
+هذا كله يعتبر رقم. الآن بدي أكامل X على X تربيع زي
+
+98
+00:10:20,760 --> 00:10:24,560
+واحد. إيه بدي أكاملها؟ X على X تربيع زي واحد
+
+99
+00:10:37,170 --> 00:10:41,590
+ممتاز. يبقى هي اللي فوق مش تقريباً المقام، بس بدها 2
+
+100
+00:10:41,590 --> 00:10:45,110
+يبقى بسيطة، 2 الحمد لله ربنا ما يسرها. هي 4
+
+101
+00:10:45,110 --> 00:10:52,090
+عندي. يبقى الـ 4، بقول للـ 2 خليك برا، وهي تكامل من
+
+102
+00:10:52,090 --> 00:10:58,370
+صفر لواحد، لـ 2X على X تربيع زائد 1، في dX
+
+103
+00:10:59,680 --> 00:11:04,540
+هكذا تماماً. الـ 4 خلت 2 في 2. يبقى بنقول عليه
+
+104
+00:11:04,540 --> 00:11:11,140
+صار هذا هو البسط، فاضل المقام. يبقى يساوي 2 لـ
+
+105
+00:11:11,140 --> 00:11:16,520
+absolute value للمقام. ولما كان المقام كمية مربعة
+
+106
+00:11:16,520 --> 00:11:21,040
+أو كمية موجبة دائماً وأبداً، يبقى لا داعي للـ
+
+107
+00:11:21,040 --> 00:11:25,960
+absolute value. وبروح بقول الكلام آدم إن هو من
+
+108
+00:11:25,960 --> 00:11:31,990
+Zero لغاية واحد. يبقى هذا الكلام بده يساوي 2 في
+
+109
+00:11:31,990 --> 00:11:37,250
+لن، بتشيل X وتحط مكانها واحد، تربيعه واحد زائد واحد،
+
+110
+00:11:37,250 --> 00:11:43,210
+بـ 2. يبقى لن 2، ناقص لن، من 2 لـ  0، بضل
+
+111
+00:11:43,210 --> 00:11:48,210
+لأن.  لن الواحد، طب لن الواحد ما بدنا إياه، يبقى
+
+112
+00:11:48,210 --> 00:11:51,450
+بضل الجواب 2 لن 2
+
+113
+00:11:53,960 --> 00:11:56,980
+يبقى زي ما شايفين، هذا النوع من المسائل اللي هو
+
+114
+00:11:56,980 --> 00:12:01,500
+مسائل مباشرة. المهم بدي اختار من اللي أسهل لحق
+
+115
+00:12:01,500 --> 00:12:06,180
+حدوده في الأول، والحدود اللي هي قيم عددية، وليست
+
+116
+00:12:06,180 --> 00:12:10,780
+quantity. ننتقل إلى نقطة ثانية من هذا الـ section
+
+117
+00:12:10,780 --> 00:12:20,540
+النقطة رقم 2، اللي هو double integrals، double
+
+118
+00:12:20,540 --> 00:12:28,340
+integrals as volume. يعني ممكن إيه؟ ممكن اللي هو
+
+119
+00:12:28,340 --> 00:12:35,200
+بواسطة تكامل المزدوج نحسب الحجم. أما درسنا في
+
+120
+00:12:35,200 --> 00:12:40,420
+calculus إيه؟ بالتكامل الفردي، مش التكامل المتعدد،
+
+121
+00:12:40,420 --> 00:12:45,080
+فجينا نحسب مين؟ نحسب الحجوم والمساحات والسطوح
+
+122
+00:12:45,080 --> 00:12:49,950
+الدورانية وما إلى ذلك. وهنا بواسطة double integral
+
+123
+00:12:49,950 --> 00:12:55,150
+أو triple integral، هنحصل على الحجوم، وهنقول لك كيف
+
+124
+00:12:55,150 --> 00:12:59,170
+بنحصل على الحجوم. لذلك التفاضل والتكامل كتير
+
+125
+00:12:59,170 --> 00:13:03,430
+بيتشاجروا مع بعض. أنا أفضل منك، أنت أفضل مني، كذا
+
+126
+00:13:03,430 --> 00:13:08,610
+إلى أخرى، فمرة وهم بيحكوا مع بعض، يعني، بيناضروا مع
+
+127
+00:13:08,610 --> 00:13:15,250
+بعض. قال التفاضل: شامتاً أنا، لا تكامل معبر. أنا فاضل
+
+128
+00:13:15,250 --> 00:13:23,430
+متفاضل، أنا متكامل، أكبر. انظر إلى علامتك التي ذيلي، طولوا
+
+129
+00:13:23,430 --> 00:13:29,670
+ويقصروا. زي التكامل. هبقى التكامل هائج، أسكت أنا
+
+130
+00:13:29,670 --> 00:13:37,670
+متحرر. أنا لست لك تابعاً، لا. ولست منك و سطراً أنا
+
+131
+00:13:37,670 --> 00:13:44,850
+للمساحة، حاسب، حتى الحجوم أصورها. يعني بحسب المساحات، و
+
+132
+00:13:44,850 --> 00:13:50,200
+بحسب الحجوم، وأطول المنحنيات، وما إلى ذلك. يبقى أحلى
+
+133
+00:13:50,200 --> 00:13:55,000
+موضوعنا اليوم موضوع استخدام التكامل في حساب الحجوم
+
+134
+00:13:55,000 --> 00:14:00,080
+أو التكامل الثلاثي في حساب الحجوم. بيقول: الـ F الـ
+
+135
+00:14:00,080 --> 00:14:10,180
+F of X وY is positive function. بتأخذ قيم موجبة
+
+136
+00:14:10,180 --> 00:14:14,120
+دائماً وأبداً، وinterpret
+
+137
+00:14:20,560 --> 00:14:34,480
+وI interpret the double integral of
+
+138
+00:14:34,480 --> 00:14:44,900
+F over a region R، على
+
+139
+00:14:44,900 --> 00:14:48,500
+المنطقة R، as the volume
+
+140
+00:14:55,690 --> 00:15:02,670
+of the solid bounded
+
+141
+00:15:02,670 --> 00:15:10,050
+below، محدود
+
+142
+00:15:10,050 --> 00:15:20,450
+من أسفل by region R، ومن
+
+143
+00:15:20,450 --> 00:15:22,750
+أعلى by
+
+144
+00:15:24,610 --> 00:15:29,350
+الـ surface، بالسطح
+
+145
+00:15:29,350 --> 00:15:48,330
+Z يساوي function X وY. that is، أي أن الـ volume V
+
+146
+00:15:48,330 --> 00:15:57,490
+يساوي تكاملين على A للـ F of X وY dA. واللي
+
+147
+00:15:57,490 --> 00:16:03,930
+هو بده يساوي تكاملين على A لـ Z dA
+
+148
+00:16:35,860 --> 00:16:40,040
+نرجع للكلام اللي إحنا كاتبينه هذا مرة ثانية. double
+
+149
+00:16:40,040 --> 00:16:45,400
+integral as volume. بدنا نستخدم التكامل الثنائي في
+
+150
+00:16:45,400 --> 00:16:51,140
+حساب حجوم بعض المجسمات. أقول: لو كانت دالة F of X و
+
+151
+00:16:51,140 --> 00:16:56,780
+Y تأخذ دائماً وأبداً قيماً موجبة، و أنت refraction
+
+152
+00:16:56,780 --> 00:17:05,130
+أنت رتبناها بالعربي، إيش معناها؟ يبقى نفسر
+
+153
+00:17:05,130 --> 00:17:11,700
+دي double integral interpretation of dreams، تفسير
+
+154
+00:17:11,700 --> 00:17:16,620
+الأحلام. يبقى interpret تفسير. يبقى نروح ونفسر الـ
+
+155
+00:17:16,620 --> 00:17:22,560
+double integral على المنطقة R as a volume، كحجم
+
+156
+00:17:22,560 --> 00:17:28,540
+لمجسم، of solid bounded. يبقى هذا المجسم محدود من
+
+157
+00:17:28,540 --> 00:17:33,520
+أعلى بشيء، ومحدود من أسفل بمين؟ بشيء. الآن below
+
+158
+00:17:33,520 --> 00:17:38,520
+by region R. يعني كأن الـ domain تبع، main تبع الـ
+
+159
+00:17:38,520 --> 00:17:42,380
+surface اللي فوق. يبقى محدود من تحت بالـ domain R، أو
+
+160
+00:17:42,380 --> 00:17:46,980
+بالـ region R، and above، ومن أعلى بالـ surface نفسه
+
+161
+00:17:46,980 --> 00:17:51,500
+يبقى الـ surface اللي عندي فوق، هيكون له على المستوى
+
+162
+00:17:51,500 --> 00:17:56,880
+XY اللي هو المجال تبعه. كل المنطقة اللي بين المجال و
+
+163
+00:17:56,880 --> 00:18:00,600
+ما بين الـ surface اللي فوق. يبقى هذا بقدر أجيب
+
+164
+00:18:00,600 --> 00:18:06,140
+حجمها بواسطة من التكامل المزدوج. curve بقولها: ها
+
+165
+00:18:06,140 --> 00:18:10,660
+الـ surface أعطيته المعادلة Z تساوي F of X Y، اللي
+
+166
+00:18:10,660 --> 00:18:15,020
+قلنا عليها. يبقى إحنا يا بنات أعلى مستوى X Y، و
+
+167
+00:18:15,020 --> 00:18:17,700
+أسفل مستوى X Y، والله بنقطعه
+
+168
+00:18:20,270 --> 00:18:24,810
+أعلن أن Z موجب. يعني الـ Z دائماً هو بتأخذ قيم موجبة
+
+169
+00:18:24,810 --> 
+
+223
+00:23:05,820 --> 00:23:11,420
+المستطيلات هو منشور جميع أوجهه الستة مستطيلات
+
+224
+00:23:11,420 --> 00:23:14,940
+الغرفة اللي إحنا فيها، أي مستطيل هناك مستطيل
+
+225
+00:23:14,940 --> 00:23:18,520
+مستطيل، ومستطيل السقف، الأرض كلها مستطيلة، تمام
+
+226
+00:23:18,520 --> 00:23:24,980
+المكعب جميع وجهه الستة مربعات وكلها مربعات متطابقة
+
+227
+00:23:24,980 --> 00:23:29,900
+تمام، يبقى المكعب حالة خاصة من متوازي المستطيلات
+
+228
+00:23:29,900 --> 00:23:33,700
+متوازي المستطيلات حالة خاصة من متوازي السطوح
+
+229
+00:23:33,700 --> 00:23:41,240
+حالة خاصة من المنشور وهكذا، تمام؟ طيب، يمكننا أن نرجع
+
+230
+00:23:41,240 --> 00:23:46,180
+لسؤالنا، يمكننا أن نروح نكامل الدالة اللي عندنا
+
+231
+00:23:46,180 --> 00:23:51,970
+هذه تعطينا الحجم، الدالة هذه اللي هو تكاملها
+
+232
+00:23:51,970 --> 00:24:00,090
+على R لـ 16 ناقص X تربيع ناقص Y تربيع
+
+233
+00:24:12,040 --> 00:24:16,080
+بنكامل  المثلث اللي قدامي بالكامل بالنسبة لـ X و
+
+234
+00:24:16,080 --> 00:24:18,280
+بالنسبة لـ Y، اتنين نفس الشيء، يبقى ما معانا
+
+235
+00:24:18,280 --> 00:24:24,180
+مشكلة، يبقى بدنا نروح نقول مثلاً dx dy، برجع الـ X من
+
+236
+00:24:24,180 --> 00:24:30,460
+صفر لاتنين، والـ Y كذلك من صفر لغاية اتنين، يعني إحنا
+
+237
+00:24:30,460 --> 00:24:33,840
+بنكامل على منطقة مربعة الشكل، الـ domain تبع الـ
+
+238
+00:24:33,840 --> 00:24:38,800
+surface هي منطقة مربعة الشكل، هذا الكلام بده يساوي
+
+239
+00:24:38,800 --> 00:24:41,860
+تكامل من zero لغاية اتنين
+
+240
+00:24:53,580 --> 00:25:02,180
+يبقى كل هذا الكلام من صفر لغاية اتنين  d y، يبقى
+
+241
+00:25:02,180 --> 00:25:06,820
+يساوي integration من صفر لغاية اتنين، نعوض بالقيمة
+
+242
+00:25:06,820 --> 00:25:19,180
+اللي فوق، يبقى ناقص
+
+243
+00:25:19,180 --> 00:25:29,420
+ثمانية على ثلاثة، بعدها ناقص اتنين Y تربيع ناقص صفر
+
+244
+00:25:29,420 --> 00:25:35,060
+زائد صفر زائد صفر، كله بيروح، يعني هذه النتيجة
+
+245
+00:25:35,060 --> 00:25:40,760
+مباشرة، كله بالنسبة لمين؟  d y، طيب بدنا نجمع
+
+246
+00:25:40,760 --> 00:25:45,900
+هذول، ثمانية في ثمانية 64 زائد 32  96
+
+247
+00:25:45,900 --> 00:25:51,410
+ناقص ثمانية، ضل 88، يبقى إحنا بدنا نكامل
+
+248
+00:25:51,410 --> 00:25:58,070
+من zero للاتنين لـ 88 على ثلاثة ناقص
+
+249
+00:25:58,070 --> 00:26:05,630
+اتنين Y تربيع، كله بالنسبة لمين؟ لـ d Y، يبقى هذا
+
+250
+00:26:05,630 --> 00:26:07,010
+الكلام بده يساوي
+
+251
+00:26:16,210 --> 00:26:24,010
+و تكامل، والحقيقة كمان من zero لغاية اتنين نضربهم
+
+252
+00:26:24,010 --> 00:26:28,570
+في الاثنين، اتنين في ثمانية 16، اتنين في ثمانية
+
+253
+00:26:28,570 --> 00:26:37,350
+17 على ثلاثة ناقص  واي تكعيب على اتنين تكعيب
+
+254
+00:26:37,350 --> 00:26:45,180
+ثمانية في اتنين على ثلاثة ناقص صفر زائد صفر
+
+255
+00:26:45,180 --> 00:26:52,620
+بقيّمهما بالسلامة، يبقى 176 نطرح منهم 16 بيصير 160
+
+256
+00:26:52,620 --> 00:26:57,840
+على ثلاثة، حجم المنطقة المحصورة بين الـ surface اللي
+
+257
+00:26:57,840 --> 00:27:05,400
+عندنا هذا وما بين مين؟ المربع هذا، بنات الـ section
+
+258
+00:27:05,400 --> 00:27:11,090
+هو أبسط section موجود في الشطر هذا كله، مش محتاج لا
+
+259
+00:27:11,090 --> 00:27:16,190
+لف ولا دوران زي ما أنتم شايفين، وكلها أمثلة وأسئلة
+
+260
+00:27:16,190 --> 00:27:21,030
+بسيطة، يبقى انتهينا من هذا الـ section وإلى اللقاء
+
+261
+00:27:21,030 --> 00:27:28,670
+في مسائل، يبقى exercises، خمسة عشر واحد، مسائل من
+
+262
+00:27:28,670 --> 00:27:38,630
+واحد لغاية 28، القسم خمسة عشر
+
+263
+00:27:38,630 --> 00:27:46,130
+اتنين، يبقى section خمسة عشر اتنين بتحدث برضه عن الـ
+
+264
+00:27:46,130 --> 00:27:51,270
+double integrals، بس ما بنقول على منطقة مربعة
+
+265
+00:27:51,270 --> 00:27:55,710
+على منطقة  أي منطقة كانت تكون، وهذا بتصير أسهل شوية
+
+266
+00:27:55,710 --> 00:28:00,990
+وحدود التكامل ليس بضرورة أن تكون كلها قيم عددية
+
+267
+00:28:00,990 --> 00:28:05,930
+هنلاحظ بعض الحدود بتصير functions، يعني متغيرات، وهذا
+
+268
+00:28:05,930 --> 00:28:14,310
+ما سنراه بعد قليل، يبقى بجي بقول double integrals
+
+269
+00:28:14,310 --> 00:28:22,410
+over
+
+270
+00:28:22,410 --> 00:28:27,830
+general
+
+271
+00:28:27,830 --> 00:28:30,830
+regions
+
+272
+00:28:39,900 --> 00:28:45,660
+حاجة اسمها، إذا عدت نقاط، النقطة الأولى يجب أن تأخذ
+
+273
+00:28:45,660 --> 00:29:00,340
+double integrals، تكاملات مزدوجة over bounded non
+
+274
+00:29:00,340 --> 00:29:01,640
+rectangular region
+
+275
+00:29:20,030 --> 00:29:23,730
+يعني يا بنات، إحنا الـ section اللي فات كنا بناخد
+
+276
+00:29:23,730 --> 00:29:29,310
+التكامل على منطقة مستطيلة، تمام، الآن بدل منطقة
+
+277
+00:29:29,310 --> 00:29:33,730
+مستطيلة أو منطقة مربعة، بدنا نروح لـ general region
+
+278
+00:29:33,730 --> 00:29:38,310
+منطقة عامة، يمكن تكون مثلث، يمكن تكون متوازية
+
+279
+00:29:38,310 --> 00:29:42,870
+أضلاع، يمكن تكون دائرة، يمكن... يمكن... يمكن شكل
+
+280
+00:29:42,870 --> 00:29:46,750
+إحنا ما إحنا عارفينه، يمكن شبه منحرف، الله أعلم، أيش
+
+281
+00:29:46,750 --> 00:29:50,660
+شكلها تكون، تمام؟ يبقى نقول double integrals over
+
+282
+00:29:50,660 --> 00:29:55,340
+general regions، اللي هي منطقة عامة،  أجي أقول double
+
+283
+00:29:55,340 --> 00:29:59,280
+integrals over bounded non rectangular regions
+
+284
+00:29:59,280 --> 00:30:03,760
+يبقى إحنا بطلنا المستطيلة، يبقى non rectangular
+
+285
+00:30:03,760 --> 00:30:07,800
+region، منطقة غير مستطيلة، أي ما كانت تكون المنطقة
+
+286
+00:30:07,800 --> 00:30:13,480
+هذه، هنعطي نظرية، بناء عليه نستخدم هذه النظرية في حل
+
+287
+00:30:13,480 --> 00:30:24,830
+المثال، النظرية بتقول ما يأتي: theorem let f of x,y
+
+288
+00:30:24,830 --> 00:30:37,090
+be continuous، دالة متصلة on a region R على
+
+289
+00:30:37,090 --> 00:30:43,710
+المنطقة R، دي من واحد if
+
+290
+00:30:43,710 --> 00:30:58,020
+الـ R is defined by،  معظمها التالي، الـ X أكبر من أو
+
+291
+00:30:58,020 --> 00:31:04,000
+تساوي A وأقل من أو تساوي B، والـ G واحد as a
+
+292
+00:31:04,000 --> 00:31:10,360
+function of X، أقل من أو تساوي Y أقل من أو تساوي G2
+
+293
+00:31:10,360 --> 00:31:27,480
+of X، with G واحد and G2 are continuous، كانت
+
+294
+00:31:27,480 --> 00:31:39,720
+دوال متصلة على الفترة المغلقة A وB، then تكاملين
+
+295
+00:31:39,720 --> 00:31:46,840
+على منطقة R للـ F of XY dA
+
+296
+00:31:48,020 --> 00:31:53,820
+بتساوي التكامل الأول من a إلى b، التكامل الثاني من
+
+297
+00:31:53,820 --> 00:32:09,240
+g1 of x إلى g2 of x للـ F of x y dy dx، نقطة
+
+298
+00:32:09,240 --> 00:32:17,440
+ثانية، F، الـ R is defined
+
+299
+00:32:21,670 --> 00:32:31,630
+H1 of Y، أقل من أو يساوي X أقل من أو يساوي H2 of
+
+300
+00:32:31,630 --> 00:32:35,950
+Y، أقل من أو يساوي Y أقل من أو يساوي
+
+301
+00:32:53,380 --> 00:33:02,180
+كانت دوال متصلة على الفترة المغلقة C وD، ثم
+
+302
+00:33:02,180 --> 00:33:12,920
+تكامل على A للـ F of XY dA، بده يعطيني تكامل الأول
+
+303
+00:33:12,920 --> 00:33:18,400
+من C إلى D، والثاني من H1 of Y
+
+304
+00:33:21,830 --> 00:33:30,770
+لـ H2 of Y للـ F of X of Y dx dy
+
+305
+00:34:08,910 --> 00:34:12,530
+نرجع الكلام اللي كتبناه مرة ثانية، نقرأ ثاني و
+
+306
+00:34:12,530 --> 00:34:16,910
+نحاول نفهم، قال: يفترض أن  F of X و Y of  B
+
+307
+00:34:16,910 --> 00:34:22,230
+continuous على region R، مين هي الـ region R؟  حالة
+
+308
+00:34:22,230 --> 00:34:27,590
+الأولى، الـ R is defined by، X تتغير من A إلى B، والـ
+
+309
+00:34:27,590 --> 00:34:32,790
+Y تتغير من G1 of X إلى G2 of X، والـ G1 والـ G2
+
+310
+00:34:32,790 --> 00:34:37,710
+continuous على نفس الفترة، كيف يعني؟ تعالوا نشوف، تلقى
+
+311
+00:34:37,710 --> 00:34:46,170
+مجالها، هذه محور X، وهذه محور Y، وهذا نقطة الأصل، على
+
+312
+00:34:46,170 --> 00:34:53,050
+ سبيل المثال، رحت أخدت الفترة اللي قال لي عنها أولًا،
+
+313
+00:34:53,050 --> 00:35:01,610
+A وB، A وB تعتبر للمتغير X، يبقى على محور X بدي
+
+314
+00:35:01,610 --> 00:35:06,390
+أعمل تغيير من نقطة A لنقطة B
+
+315
+00:35:09,500 --> 00:35:15,060
+Y تتغير من G1 of X إلى G2 of X
+
+316
+00:35:24,800 --> 00:35:31,780
+يعني مين؟ يعني Y تساوي G1 of X، Y هي function في X
+
+317
+00:35:31,780 --> 00:35:37,160
+رسمت المنحنى، ثاني فكان المنحنى الثاني مثلاً بالشكل
+
+318
+00:35:37,160 --> 00:35:45,890
+اللي عندنا هذا، يبقى هذا الـ Y تساوي G2 of X، الآن في
+
+319
+00:35:45,890 --> 00:35:51,590
+منطقة محصورة بين المنحنيين A وB، بين المنحنيين
+
+320
+00:35:51,590 --> 00:35:57,850
+الأول والثاني على الفترة من A إلى B، جت من هنا طالعة
+
+321
+00:35:57,850 --> 00:36:01,910
+هيك الشكل اللي عندنا هذا، ومن هنا جت طالعة بالشكل
+
+322
+00:36:01,910 --> 00:36:08,010
+هذا، وكل G واحد و G اتنين دوال متصلة، إذا ما بين
+
+323
+00:36:08,010 --> 00:36:14,370
+المنحنيين هذول انحصرت المنطقة اللي عندنا هذه، تمام؟
+
+324
+00:36:15,200 --> 00:36:19,600
+بدنا نكامل الـ function اللي عندنا هذه على هذه
+
+325
+00:36:19,600 --> 00:36:26,160
+المنطقة، يبقى لاحظي أن G واحد of x أقل من G اتنين
+
+326
+00:36:26,160 --> 00:36:31,420
+of x، و Y محصورة ما بين الاثنين، تمام، هذه واحدة
+
+327
+00:36:31,420 --> 00:36:36,360
+الثانية، الـ X ستتغير من وين لوين؟ من A إلى B
+
+328
+00:36:36,360 --> 00:36:41,720
+بوصولها من هذه المنطقة المظللة لهذه، تمام؟ يبقى بيكون
+
+329
+00:36:41,720 --> 00:36:48,540
+التكامل، الـ function يساوي تكامل الـ function dy dx، حطيت
+
+330
+00:36:48,540 --> 00:36:54,000
+المتغير في الأول Y، هي G1 of x و Y واحد و Y اتنين
+
+331
+00:36:54,000 --> 00:36:59,860
+هي G2 of x، يبقى بدأت التكامل هذا، دول دوال في x
+
+332
+00:36:59,860 --> 00:37:03,620
+على عكس، مكان ما فيه في الـ section السابق، كانوا
+
+333
+00:37:03,620 --> 00:37:10,140
+أرقام، هذه  بتعطيني متغيرات نفس المتغيرات بس
+
+334
+00:37:10,140 --> 00:37:15,660
+بيطلع بدلالة من X، بكامل Y بيطلع الجواب بدلالة X، في
+
+335
+00:37:15,660 --> 00:37:18,780
+عندي مشكلة، ما في عندي مشكلة، لأن باقي الدالة اللي
+
+336
+00:37:18,780 --> 00:37:24,240
+ضايلة بتصير بدلالة من X، لكن X تتغير من رقم إلى رقم
+
+337
+00:37:24,240 --> 00:37:30,180
+إذا بيطلع في الجواب رقم واحد، طبعاً يبقى هذا يعني، لكن
+
+338
+00:37:30,180 --> 00:37:35,960
+لو حطيت، لو كانت المسألة حطيت المتغيرات في الآخر و
+
+339
+00:37:35,960 --> 00:37:40,740
+الأعداد في الأول، عمرك ما حتحصل نتيجة، طبعاً يبقى في
+
+340
+00:37:40,740 --> 00:37:44,480
+هذه الحالة بكون أنا مجبر أن أكامل بالنسبة لـ Y في
+
+341
+00:37:44,480 --> 00:37:49,060
+الأول، ثم أروح أكامل بالنسبة لمين؟ لـ X، هذه الحالة
+
+342
+00:37:49,060 --> 00:37:51,080
+الأولى، نيجي للحالة الثانية
+
+343
+00:37:56,810 --> 00:38:01,950
+لكن الـ X محصورة بين two functions، وكل function
+
+344
+00:38:01,950 --> 00:38:07,830
+دالة في Y، بـ X as a function of Y، with each one of
+
+345
+00:38:07,830 --> 00:38:11,370
+its two continuous functions، على الفترة اللي هي C
+
+346
+00:38:11,370 --> 00:38:16,930
+و D، كيف يكونوا دالة؟  طلع لي كويس هاي المحاور، هذا
+
+347
+00:38:16,930 --> 00:38:23,420
+محور X، هذا محور Y، وهذه نقطة الأصل اللي عندك، افترضي
+
+348
+00:38:23,420 --> 00:38:28,660
+رسمت المنحنى، فكان المنحنى الأول بالشكل اللي عندنا
+
+349
+00:38:28,660 --> 00:38:38,420
+هذا، يبقى هذا الـ X تساوي H1 of Y، جينا رسمنا المنحنى
+
+350
+00:38:38,420 --> 00:38:43,060
+الثاني، فطلع بقدر الله طلع المنحنى الثاني بالشكل
+
+351
+00:38:43,060 --> 00:38:51,830
+اللي عندك هذا، يبقى هذا الـ X يساوي H2، روحنا على
+
+352
+00:38:51,830 --> 00:38:57,270
+محور Y، قال لي تتغير الـ Y بين C وD، قلنا هي النقطة
+
+353
+00:38:57,270 --> 00:39:01,870
+كانت نقطة C، وهي النقطة الثانية اللي هي نقطة D
+
+354
+00:39:01,870 --> 00:39:09,500
+رسمت موازي لمحور X، قطع المنحنيين  لاثنين هذول، إذا
+
+355
+00:39:09,500 --> 00:39:14,020
+المنحنيين مع الخطين الأفقيين حصروا المنطقة
+
+356
+00:39:14,020 --> 00:39:18,900
+المظللة اللي عندنا هذه، المنطقة الزرقاء زي ما أنتم
+
+357
+00:39:18,900 --> 00:39:23,680
+شايفين، إذا إحنا بنكامل الـ function اللي عندنا على
+
+358
+00:39:23,680 --> 00:39:28,820
+المنطقة المظللة اللي عندنا هذه، فبيصير أيش؟ تكامل الـ
+
+359
+00:39:28,820 --> 00:39:33,520
+function على dA، بدي أحط الدالة اللي بتغير في الأول
+
+360
+00:39:33,520 --> 00:39:38,600
+يمكن بدي أكامل أولاً بالنسبة لمين؟ للـ X، لأن X هي
+
+361
+00:39:38,600 --> 00:39:43,100
+الدالة في Y، هدول أرقام، فبيصير integration من H1
+
+362
+00:39:43,100 --> 00:39:48,360
+of Y لـ H2 of Y، لما أكامل وأعوض مكان الـ X،  اللي
+
+363
+00:39:48,360 --> 00:39:53,290
+بدلالة Y، بيصير المثل كله بدلالة Y، بيصير سهل أكاملة
+
+364
+00:39:53,290 --> 00:39:57,090
+بالنسبة لي، بعد ذلك وأعوض حدود التكامل، وبيطلع لنا
+
+365
+00:39:57,090 --> 00:40:04,190
+نتيجة رقم محدد، طيب يا بنات، هذه أنا بمزاجي يعني
+
+366
+00:40:04,190 --> 00:40:08,690
+ممكن أعملها، والله هو بيكون كاتبهالي، وخلاص أقول
+
+367
+00:40:08,690 --> 00:40:14,130
+والله إحنا بنتطلع، إذا قال لي كامل و second أنا بدي
+
+368
+00:40:14,130 --> 00:40:20,020
+أختار، أن أُحدد أكامل بالنسبة لمين؟ لـ X أولاً أو الـ Y
+
+369
+00:40:20,020 --> 00:40:25,160
+في الأول، يبقى حسب طبيعة المسألة، ممكن هو يعطيني
+
+370
+00:40:25,160 --> 00:40:30,960
+تكاملين، واحد متغير ويحطه لي جوا جوا بالنسبة للمتغير
+
+371
+00:40:30,960 --> 00:40:37,290
+أو العكس، ممكن ما أقدر أقول له، ما أقدر أعمله، بعمل
+
+372
+00:40:37,290 --> 00:40:42,150
+عملية change أو reverse، بقلب حدود التكامل، كيف؟ أنا
+
+373
+00:40:42,150 --> 00:40:47,410
+عند  المنطقة، مثلاً أعطيتها حدود بدلالة X، بروح بحوضها
+
+374
+00:40:47,410 --> 00:40:52,850
+بدلالة Y، فبرووح برسم المنطقة،  أتكامل، ومن خلال هذه
+
+375
+00:40:52,850 --> 00:40:56,770
+المنطقة، بدل ما كانت الحدود بالنسبة لـ X بيخليه يميل
+
+376
+00:40:56,770 --> 00:41:01,770
+بالنسبة لـ Y، بقلب حدود التكامل، وسيلة التكامل s يعني
+
+377
+00:41:01,770 --> 00:41:06,830
+أحياناً ممكن يجبرني إجباراً على ذلك ويطلبه و
+
+378
+00:41:06,830 --> 00:41:10,390
+أحياناً أقول له لأ، أنا برسم بيطلع لي، وبالتالي أنا
+
+379
+00:41:10,390 --> 00:41:13,850
+باختار بالنسبة لـ X أو بالنسبة لـ Y، سواء كان
+
+380
+00:41:13,850 --> 00:41:17,310
+ثاني ولا ثاني،  هأشوف الصنفين، هأعطيك أمثلة على
+
+381
+00:41:17,310 --> 00:41:22,330
+الصنفين بحيث أن نغطيه، وبدل المثال هأعطيك ثمانية بحيث
+
+382
+00:41:22,330 --> 00:41:27,510
+إنه فعلاً نغطي المادة أو نغطي الموضوع تغطية كاملة
+
+383
+00:41:27,510 --> 00:41:33,650
+نبدأ، قبل أن أخش الأمثلة، هل حاضر أن تسألني سؤال؟ هذا
+
+384
+00:41:33,650 --> 00:41:37,510
+كل جزء نظري في الـ sketch، بس بدنا نبدأ نشتغل
+
+385
+00:41:37,510 --> 00:41:49,170
+عليه، نيجي للـ example الأول
+
+386
+00:41:49,170 --> 00:41:53,990
+مثال، الـ sketch is a region of integration، sketch
+
+387
+00:41:53,990 --> 00:42:00,170
+is a region of
+
+388
+00:42:03,500 --> 00:42:13,480
+integration، ارسم لي منطقة التكامل، And evaluate، وروح
+
+389
+00:42:13,480 --> 00:42:21,960
+أحسب لي، evaluate the integral، أحسب لي
+
+390
+00:42:21,960 --> 00:42:30,080
+التكامل، نمرة أيه؟ أريد تكامل من واحد إلى أربعة، تكامل
+
+391
+00:42:30,080 --> 00:42:31,220
+من صفر
+
+445
+00:47:44,220 --> 00:47:45,560
+موجود عندنا
+
+446
+00:48:18,030 --> 00:48:25,370
+نمر بيه من السؤال بيقول
+
+447
+00:48:25,370 --> 00:48:33,150
+بدي تكامل من Zero لغاية ثلاثة على اثنين تكامل آخر
+
+448
+00:48:33,150 --> 00:48:44,890
+من واحد لغاية أربعة ناقص اثنين U لمن؟ للأربعة ناقص
+
+449
+00:48:44,890 --> 00:49:03,030
+اثنين U على V تربيع كل هذا الكلام دي V دي U طبعا
+
+450
+00:49:03,030 --> 00:49:06,350
+واضح أنه سهل أبدأ بالنسبة للـ V بالأول لأن الأربعة
+
+451
+00:49:06,350 --> 00:49:09,910
+ناقص اثنين U وهذا كله يعتبر constant إذا قورن
+
+452
+00:49:09,910 --> 00:49:15,970
+بالـ V إذا بتروح أرسم له منطقة التكامل في الأول بقول له
+
+453
+00:49:15,970 --> 00:49:21,150
+كويس، يجي أنا بدل المحاور X Y بنرسم، صار عندي صار
+
+454
+00:49:21,150 --> 00:49:29,970
+المحور الأول U والمحور الثاني V، قال لي كويس، V هي
+
+455
+00:49:29,970 --> 00:49:35,830
+ممكن تساوي واحد، يبقى في عندي خط أفقي هيك، هذه V
+
+456
+00:49:35,830 --> 00:49:43,990
+تساوي واحد. ثاني V تساوي أربعة ناقص اثنين U، يبقى لما
+
+457
+00:49:43,990 --> 00:49:49,610
+أقول V تساوي أربعة ناقص اثنين U معادلة أيش؟
+
+458
+00:49:49,610 --> 00:49:53,410
+اللي هنا خط مستقيم،  خط المستقيم مش هان ارسمه
+
+459
+00:49:53,410 --> 00:49:59,730
+بكافيني نقطتين عليه، بقول له ماشي لو كانت الـ U بـ Zero
+
+460
+00:49:59,730 --> 00:50:05,710
+إذا V بقت أربعة، يبقى باجي عند الـ Zero هي و باجي طالع
+
+461
+00:50:05,710 --> 00:50:11,970
+أربعة كويس، يبقى هذا V هيو هنا و خليها لمين اللي هي
+
+462
+00:50:11,970 --> 00:50:16,810
+أربعة، يبقى هذا النقطة Zero أربعة تقع على وين؟ على
+
+463
+00:50:16,810 --> 00:50:23,570
+الخط المستقيم، لو كانت الـ U مثلا، هذه لو كانت الـ U بـ
+
+464
+00:50:23,570 --> 00:50:30,790
+Zero، طب لو كانت الـ U باثنين، باثنين بتطلع الـ V بـ Zero
+
+465
+00:50:30,790 --> 00:50:35,150
+يبقى هذا اللي بدي أقطع الخط عند النقطة هنا جديدة
+
+466
+00:50:35,150 --> 00:50:41,670
+اللي هي هذه، اللي هي اثنين و Zero، بجي بمسك هذه
+
+467
+00:50:41,670 --> 00:50:48,510
+المسطرة وبوصل بين النقطتين وبرسم الخط على استقامة
+
+468
+00:50:48,510 --> 00:50:55,070
+بهذا الشكل، طبعا كويس، نجي بعد هيك، الـ U تتغير من
+
+469
+00:50:55,070 --> 00:50:58,890
+عندي الـ Zero لغاية ثلاثة على اثنين، ثلاثة على
+
+470
+00:50:58,890 --> 00:51:03,310
+اثنين يعني كده؟ واحد و نصف، ثلاثة على اثنين يبقى في
+
+471
+00:51:03,310 --> 00:51:11,830
+جيلك هنا واحد و نصف، ثلاثة على اثنين، طيب باجي بقول
+
+472
+00:51:11,830 --> 00:51:18,600
+طب لو كانت U ثلاثة على اثنين، لو كانت الـ U بثلاثة
+
+473
+00:51:18,600 --> 00:51:24,320
+على اثنين، بصير U ناقص ثلاثة، اليوم واحد يبقى هذه
+
+474
+00:51:24,320 --> 00:51:29,080
+بتيجي هنا بالضبط و بتتقابل وين؟ عند النقطة هذه
+
+475
+00:51:29,080 --> 00:51:39,480
+تمامًا، يبقى إحنا كأنه عندنا المثلث المظلل هذا فقط
+
+476
+00:51:39,480 --> 00:51:46,840
+ما بيهمني، يبقى من هنا الـ U تساوي Zero لغاية الـ U تساوي
+
+477
+00:51:46,840 --> 00:51:51,980
+اللي هو ثلاثة على اثنين، المنطقة من هنا لغايتنا
+
+478
+00:51:51,980 --> 00:51:55,680
+طالعنا قابلنا مع الخطين اللي إثنين هدول، صارت
+
+479
+00:51:55,680 --> 00:51:59,740
+المنطقة المظللة بالزرق اللي قدامنا هذه، يبقى هذه من
+
+480
+00:51:59,740 --> 00:52:04,170
+منطقة التكامل اللي موجودة عندنا. طيب، بدنا نروح
+
+481
+00:52:04,170 --> 00:52:13,010
+للتكامل الآن، ببدأ التكامل بالنسبة لـ .. كيف؟ هعكس لك
+
+482
+00:52:13,010 --> 00:52:16,530
+المحاور، بس اصبر شوية، مش هالحين، بعد قليل، بعد ما
+
+483
+00:52:16,530 --> 00:52:20,250
+نخلص المثال هذا، هخليك بدل السؤال ثلاثة تعكس
+
+484
+00:52:20,250 --> 00:52:26,870
+المحاور غصب عنك، مش بخاطرك، تمام؟ طيب، لو عكستي،
+
+485
+00:52:26,870 --> 00:52:31,170
+هيتغيروا الحدود، كل الأربعة حدود ممكن يتغيروا كلهم
+
+486
+00:52:31,170 --> 00:52:37,230
+ولا واحد يظل زي الثاني، بس لو عكست بصير سهل أكامل
+
+487
+00:52:37,230 --> 00:52:41,370
+بالنسبة لـ U كذلك، زي ما قلت سهل أكامل بالنسبة للـ V،
+
+488
+00:52:41,370 --> 00:52:46,490
+يبقى كأنه ببدأ التكامل مين؟ بالنسبة للـ V، ببدأ التكامل مين؟
+
+489
+00:52:46,490 --> 00:52:50,210
+واحد على V تربيع، لأن أربعة ناقص اثنين U يعتبر
+
+490
+00:52:50,210 --> 00:52:56,990
+ثابت، وتكامل واحد على V تربيع بقد ايش؟ -1 على V، إذا
+
+491
+00:52:56,990 --> 00:53:02,290
+هذه لو جاءت تكامل بدي يصير تكامل من Zero لتلاتة على
+
+492
+00:53:02,290 --> 00:53:07,670
+اثنين وهنا أربعة ناقص اثنين U مالكش دعوة، وهذه
+
+493
+00:53:07,670 --> 00:53:14,610
+تكاملها بـ -1 على V، وبيجي أقول من هنا من واحد لأربعة
+
+494
+00:53:14,610 --> 00:53:17,690
+ناقص اثنين U في النهاية
+
+495
+00:53:20,650 --> 00:53:25,070
+يبقى هذا الكلام بيساوي تكامل من 0 إلى 3 على 2
+
+496
+00:53:25,070 --> 00:53:30,950
+لـ أربعة ناقص 2U، فيه بعوض بالقيمة اللي فوق ناقص
+
+497
+00:53:30,950 --> 00:53:37,190
+اللي تحت، يبقى ناقص واحد على أربعة ناقص اثنين U
+
+498
+00:53:37,190 --> 00:53:42,290
+ناقص مع ناقص بصير زائد واحد على واحد، اللي يبقى
+
+499
+00:53:42,290 --> 00:53:50,520
+واحد يبقى عوضنا بالقيمة اللي فوق ناقص القيمة
+
+500
+00:53:50,520 --> 00:53:55,980
+اللي تحت بالشكل هذه، وكل هذا بالنسبة لمن؟ للـ dU
+
+501
+00:53:55,980 --> 00:54:01,100
+يساوي integration من زيرو لغاية ثلاثة على ثلاثة
+
+502
+00:54:01,100 --> 00:54:06,880
+ببدأ أفك هذا الكلام بنات، وشوفوا جداش عندي هنا ناقص واحد
+
+503
+00:54:06,880 --> 00:54:15,200
+وهنا زائد أربعة ناقص اثنين U، كله بالنسبة للـ dU، يبقى
+
+504
+00:54:15,200 --> 00:54:19,660
+هذا بيصير تكامل من Zero لغاية ثلاثة على اثنين
+
+505
+00:54:19,660 --> 00:54:26,960
+لمين؟ لثلاثة ناقص اثنين U، هذه لو روحت
+
+506
+00:54:26,960 --> 00:54:33,690
+كاملتها بتعطيني ما يأتي، يساوي اللي هو مين؟ ثلاثة U
+
+507
+00:54:33,690 --> 00:54:39,530
+ناقص U تربيع على اثنين بتروح مع الاثنين، وانحكي هذا
+
+508
+00:54:39,530 --> 00:54:45,390
+كله بالتعويض من Zero لغاية ثلاثة على اثنين، وU ساوي
+
+509
+00:54:45,390 --> 00:54:51,750
+ثلاثة على اثنين بيصير كده؟ تسعة على اثنين ناقص
+
+510
+00:54:51,750 --> 00:54:57,320
+ثلاثة على اثنين تربيع بتسعة على أربعة، ناقص تسعة على
+
+511
+00:54:57,320 --> 00:55:04,640
+أربعة ناقص Zero زائد Zero، يبقى تسعة على اثنين ناقص
+
+512
+00:55:04,640 --> 00:55:09,680
+تسعة على أربعة، يبقى تسعة على أربعة
+
+513
+00:55:39,360 --> 00:55:47,900
+ناخذ كمان مثال، مثال اثنين بيقول sketch the region
+
+514
+00:55:47,900 --> 00:55:56,700
+of integration, sketch that region of
+
+515
+00:55:56,700 --> 00:56:02,160
+integration of
+
+516
+00:56:02,160 --> 00:56:08,060
+some من منطقة التكامل عن الـ right
+
+517
+00:56:13,420 --> 00:56:20,200
+فاصلة right right
+
+518
+00:56:20,200 --> 00:56:31,140
+and evaluate the
+
+519
+00:56:31,140 --> 00:56:38,580
+equivalent double
+
+520
+00:56:38,580 --> 00:56:39,160
+integral
+
+521
+00:56:48,010 --> 00:56:53,190
+with the order of with
+
+522
+00:56:53,190 --> 00:56:58,970
+the order of
+
+523
+00:56:58,970 --> 00:57:05,250
+integration reversed
+
+524
+00:57:05,250 --> 00:57:11,550
+أمر
+
+525
+00:57:11,550 --> 00:57:20,800
+أعطيتك تكامل من Zero لغاية اثنين تكامل من سالب الجذر
+
+526
+00:57:20,800 --> 00:57:25,740
+التربيعي لأربعة ناقص x تربيع إلى الجذر التربيعي لأربعة ناقص
+
+527
+00:57:25,740 --> 00:57:32,560
+x تربيع  لستة x dy dx
+
+528
+00:58:07,780 --> 00:58:13,540
+سؤال عبارة عن ثلاثة مطالب: ارسم منطقة التكامل، 2
+
+529
+00:58:13,540 --> 00:58:18,800
+اكتب لي واحسب لي equivalent double integrals with
+
+530
+00:58:18,800 --> 00:58:22,220
+order of integration reversed، يعني إيش؟ يعني بدي
+
+531
+00:58:22,220 --> 00:58:27,340
+أغير حدود التكامل اللي عندنا هذه زي السؤال اللي
+
+532
+00:58:27,340 --> 00:58:32,060
+سألته قبل قليل، ومن ثم بعد ما أغير حدود التكامل بدي
+
+533
+00:58:32,060 --> 00:58:37,050
+أروح أحسب التكامل. تعالوا هنشوف كيف بدنا نرسم
+
+534
+00:58:37,050 --> 00:58:41,550
+الرسمة وكيف نغير حدود التكامل، وبعدين التكامل يصبح
+
+535
+00:58:41,550 --> 00:58:45,330
+روتينيًا زي ما حسبنا قبل شوية بنحسب هذا التكامل
+
+536
+00:58:45,330 --> 00:58:51,370
+أبقى بروح بأخذ المحاور اللي عندنا بهذا الشكل، برسم
+
+537
+00:58:51,370 --> 00:58:56,650
+بقول هذا محور X، هذا محور Y، هذا نحو الأصل اللي هي
+
+538
+00:58:56,650 --> 00:59:02,830
+Zero، هذه المناطقة، لما أجي لأول متغير عندي Y يبقى Y
+
+539
+00:59:02,830 --> 00:59:10,750
+تساوي هذا الجذر، يبقى لو جربنا الحل كالتالي: الـ Y تساوي
+
+540
+00:59:10,750 --> 00:59:14,790
+الجذر التربيعي لأربعة ناقص X تربيع، بدي أرفع
+
+541
+00:59:14,790 --> 00:59:22,150
+المعادلة، لو ربعت الطرفين مش بصير بنات بصير Y تربيع
+
+542
+00:59:22,150 --> 00:59:28,760
+زائد X تربيع تساوي أربعة، معادلة أيش؟ هاي دائرة
+
+543
+00:59:28,760 --> 00:59:33,200
+ممتاز، لكن هل هي دائرة كاملة ولا نص دائرة ولا
+
+544
+00:59:33,200 --> 00:59:37,080
+ربع دائرة ولا ثلاثة أرباع دائرة؟ هذا اللي إحنا مش عارفينه
+
+545
+00:59:37,080 --> 00:59:41,820
+كويس، اللي بيحدده مين؟ قيم X، طب القيم اللي فوق
+
+546
+00:59:41,820 --> 00:59:46,420
+هي نفس القيم اللي تحت، بس بالموجب، بالسالب،  إحنا عندنا
+
+547
+00:59:46,420 --> 00:59:51,420
+Y الموجبة و Y السالبة، طب Y الموجبة و Y السالبة قد
+
+548
+00:59:51,420 --> 00:59:55,380
+يكون على اليمين وقد يكون على الشمال وقد يكون
+
+549
+00:59:55,380 --> 01:00:01,300
+كليهما، اللي بده يحدده مين؟ حدود التكامل تبعت الـ X، الـ X
+
+550
+01:00:01,300 --> 01:00:05,960
+هتتغير من Zero لغاية اثنين، يعني مين؟ هي الدائرة
+
+551
+01:00:05,960 --> 01:00:11,700
+الموجبة للنصف اللي على اليمين فقط، يبقى هذه
+
+552
+01:00:11,700 --> 01:00:13,660
+دائرة بهذا الشكل
+
+553
+01:00:18,830 --> 01:00:24,230
+الشكل اللي على الشمال هذا مش موجود، فالرسمة بتكون
+
+554
+01:00:24,230 --> 01:00:31,210
+هيكون منقط بهذا الشكل، تمام؟
+
+555
+01:00:31,210 --> 01:00:37,170
+يبقى هذا، يبقى هذه المنطقة اللي عندنا، هذه المنطقة
+
+556
+01:00:37,170 --> 01:00:41,920
+اللي إحنا بنكامل عليها، يبقى أنا لسه عملت المطلوب
+
+557
+01:00:41,920 --> 01:00:46,980
+الأول، رسمت منطقة التكامل، جبتها من وين؟ جبتها من
+
+558
+01:00:46,980 --> 01:00:52,400
+الحدود اللي موجودة عندي، بعد هيك قال لي بدك تكتب
+
+559
+01:00:52,400 --> 01:00:57,020
+التكامل بعد ما تقلب حدود التكامل، إيش أقلب حدود
+
+560
+01:00:57,020 --> 01:01:01,420
+التكامل؟ أحط الـ X الأول والـ Y الآخر؟ أو ماضي ما
+
+561
+01:01:01,420 --> 01:01:06,360
+هنجيب نتيجة، لا إيش نسوي؟ لأ، بدل ما كنت بتكامل
+
+562
+01:01:06,360 --> 01:01:11,360
+بالنسبة لـ Y وبعدين بالنسبة لـ X، في الأول وبعدين
+
+563
+01:01:11,360 --> 01:01:19,280
+بالنسبة لـ Y، يبقى هذا التكامل بيصير تكامل 6X
+
+564
+01:01:19,280 --> 01:01:27,060
+dx dy، إذا بدي أشوف X بدي تتغير من وين لوين؟ باجي
+
+565
+01:01:27,060 --> 01:01:33,420
+باجي برسم خط يوازي محور X ويقطع منطقة التكامل هذه
+
+566
+01:01:33,420 --> 01:01:40,400
+خط، زي ما شايفينه، يبقى هنا X بقد ايش؟ عند هذه
+
+567
+01:01:40,400 --> 01:01:45,700
+النقطة، قد ايش قيمة X؟ Zero، يبقى هنا Zero، تمام،
+
+568
+01:01:45,700 --> 01:01:52,490
+هذه مين؟ هذه الدائرة X تربيع زائد Y تربيع يساوي أربعة
+
+569
+01:01:52,490 --> 01:01:52,910
+تربيع
+
+570
+01:02:04,140 --> 01:02:11,420
+أو X يساوي الجذر التربيعي لأربعة ناقص Y تربيع
+
+571
+01:02:11,420 --> 01:02:17,060
+وأخذ X الموجبة فقط لأنه ما عنديش X سالبة، يبقى من
+
+572
+01:02:17,060 --> 01:02:23,200
+الجذر التربيعي لأربعة ناقص Y تربيع
+
+573
+01:02:25,940 --> 01:02:31,020
+قد ايش أقل قيمة بده تاخدها Y وأكبر قيمة بده تاخدها
+
+574
+01:02:31,020 --> 01:02:36,340
+Y، يبقى
+
+575
+01:02:36,340 --> 01:02:41,600
+هذا هنا سالب اثنين وهذا هنا اثنين، أو نشوف من
+
+576
+01:02:41,600 --> 01:02:45,820
+أحداثيات النقطة هذه،  إحداثياتها Zero اثنين، وهذه إحداثياتها
+
+577
+01:02:45,820 --> 01:02:52,280
+Zero سالب اثنين، إذا من سالب اثنين لاثنين
+
+578
+01:02:54,310 --> 01:02:57,850
+يبقى شايفين كيف بغير حدود التكامل؟ بغير حدود
+
+579
+01:02:57,850 --> 01:03:02,790
+التكامل من المنطقة تبعت التكامل، مش بمزاجي، بدل
+
+580
+01:03:02,790 --> 01:03:05,990
+هذا مكان هذا وهذا مكان هذا وأمشي، لأ، الآن
+
+581
+01:03:05,990 --> 01:03:11,690
+المنطقة أو حدود التكامل على الدالة هذه تعتمد تمامًا
+
+582
+01:03:11,690 --> 01:03:16,190
+لو حسبناها بـ ... بـساوي نفس القيمة اللي عندنا فورًا،
+
+583
+01:03:16,190 --> 01:03:17,350
+اللي مساحة المظلل
+
+584
+01:03:25,440 --> 01:03:30,260
+بنكامل بالنسبة لـ X بالنسبة لـ Y
+
+585
+01:03:36,230 --> 01:03:42,030
+والحكي هذا من Zero لغاية الجذر التربيعي للأربعة
+
+586
+01:03:42,030 --> 01:03:49,070
+ناقص Y تربيع، وهي الـ dy، وهي التكامل من صفر من
+
+587
+01:03:49,070 --> 01:03:57,890
+سالب اثنين لغاية اثنين، طيب بصير المسألة تساوي ستة
+
+588
+01:03:57,890 --> 01:04:03,540
+على اثنين بتلاتة خليها برا، تكامل من سالب اثنين
+
+589
+01:04:03,540 --> 01:04:09,800
+لاثنين، وضل عندي هنا جذر أربعة ناقص Y تربيع، لما أعوض بطير
+
+590
+01:04:09,800 --> 01:04:17,840
+الجذر وبظل قد ايش؟ بس أربعة ناقص Y تربيع ناقص Zero
+
+591
+01:04:17,840 --> 01:04:21,880
+يبقى مع السلامة، عوض بالقيمة Zero بتروح، بالشكل اللي
+
+592
+01:04:21,880 --> 01:04:30,300
+عندنا هذا، بصير بس هيك بـ Y، أسأل السؤال، الدالة
+
+593
+01:04:30,300 --> 01:04:36,100
+اللي بدي أكاملها قد ايش؟  والله even، هذه even
+
+594
+01:04:36,100 --> 01:04:39,480
+يبقى أطلع على الرقم اللي هنا والرقم اللي هنا
+
+595
+01:04:39,480 --> 01:04:47,280
+اثنين نفس الشيء، يبقى اثنين، التكامل على نصف المنطقة، يبقى
+
+596
+01:04:47,280 --> 01:04:50,780
+هذا الكلام
+
+597
+01:04:50,780 --> 01:04:54,120
+بيساوي هي الثلاثة اللي برا وهي
+
+598
+01:04:54,120 --> 01:04:58,680
+ضربناها كمان باثنين، وتكامل صار من صفر لاثنين بدل
+
+599
+01:04:58,680 --> 01:05:04,240
+من سالب اثنين لاثنين، لمين؟ لأربعة ناقص Y تربيع
+
+600
+01:05:04,240 --> 01:05:15,350
+أعوض بـ Y، يبقى النتيجة ستة في أربعة Y ناقص Y تكعيب على ثلاثة، كل
+
+601
+01:05:15,350 --> 01:05:24,210
+هذا الحكي من Zero لغاية، قد ايش؟ لغاية اثنين، يساوي ستة
+
+602
+01:05:24,210 --> 01:05:31,160
+أيضا برا، تمام؟ وهذا هنا بصير عندنا اثنين في أربعة
+
+603
+01:05:31,160 --> 01:05:39,080
+في ثمانية، وهنا ناقص اللي هو ثمانية على ثلاثة، وهذه
+
+604
+01:05:39,080 --> 01:05:43,720
+Zero، Zero بتروح كلها مع السلامة، يبقى هذا الكلام
+
+605
+01:05:43,720 --> 01:05:49,560
+بتساوي ستة في ثلاثة في ثمانية، أربعة وعشرين، ونزل
+
+606
+01:05:49,560 --> 01:05:55,400
+منها ثمانية على ثلاثة، ثلاثة مع ستة، اثنين، اثنين في ستة عشر، ثمانية وثلاثين، يبقى هذا
+
+607
+01:05:55,400 --> 01:06:00,700
+مقدار اللي هو التكامل اللي عندي، طيب هذا نمر أيش من
+
+608
+01:06:00,700 --> 01:06:06,940
+المثال؟ نمر  بيه، نريد تكامل من واحد لغاية الـ e
+
+609
+01:06:16,340 --> 01:06:22,360
+ومن الـ Zero لغاية لن الـ X للـ x y
+
+610
+01:06:27,700 --> 01:06:30,720
+طبعًا يا بنات إن أنا بقدر أكامل دغري بدون مجلبة لكن
+
+611
+01:06:30,720 --> 01:06:36,120
+هو أمرني، أمر، طلب مني، قال روح اجلب حدود التكامل و
+
+612
+01:06:36,120 --> 01:06:40,300
+بعد هيك بتروح تحسب لي هذا التكامل، إذا بروح ارسم له
+
+613
+01:06:40,300 --> 01:06:45,580
+مين؟ منطقتي التكامل، فبأبدأ ب
+
+667
+01:12:16,150 --> 01:12:22,950
+Y وهنا E أس اتنين Y لو فضلناها كده شو يطلع هنا
+
+668
+01:12:22,950 --> 01:12:28,510
+منها؟ واحد لو كملتها بصير E أس اتنين Y على اتنين
+
+669
+01:12:28,510 --> 01:12:33,270
+لو فضلت كمان مرة بـ Zero لو كملتها كمان مرة بصير E
+
+670
+01:12:33,270 --> 01:12:38,650
+أس اتنين Y على مين؟ على أربعة. هدف إشارة موجب
+
+671
+01:12:41,910 --> 01:12:55,050
+يبقى هنا ناقص نص وهي نتيجة التكامل. ناقص إي أس
+
+672
+01:12:55,050 --> 01:13:05,350
+اتنين Y ناقص رابع إي أس اتنين Y وكل هذا كله من
+
+673
+01:13:05,350 --> 01:13:11,650
+زيرو لغاية كم؟ لغاية واحد. يبقى هنا الكلام الرابع
+
+674
+01:13:11,650 --> 01:13:18,970
+إي تربيع. حط واحد تطلع قيمة. حط زيرو بيطير يبقى رابع
+
+675
+01:13:18,970 --> 01:13:25,170
+إي تربيع اللي هو التكامل الأول. نيجي للتكامل
+
+676
+01:13:25,170 --> 01:13:34,650
+الثاني. يبقى ناقص رابع. وهنا الـ Y بواحد وهنا إي
+
+677
+01:13:34,650 --> 01:13:35,490
+تربيع
+
+678
+01:13:38,390 --> 01:13:46,910
+ناقص في ناقص بـ زائد. نص في ربع بتساوي ثمن. تمام وهنا ثمن
+
+679
+01:13:46,910 --> 01:13:55,150
+الربيع. بعدها زيرو. آه هذه اللي بعدها هي زيرو
+
+680
+01:13:55,150 --> 01:14:06,970
+يبقى هنا ناقص مع ناقص بصير زائد. زيرو زائد زيرو هذه و
+
+681
+01:14:06,970 --> 01:14:11,090
+هذه بتجيب لك الناقص مع ناقص بيصير زائد وناقص بتجيب لك
+
+682
+01:14:11,090 --> 01:14:17,490
+كمان بيصير ناقص الرابع. وهنا بيجيب لك الثمن لإنه في
+
+683
+01:14:17,490 --> 01:14:22,390
+نص برا وهنا إيه والـ Zero اللي هو بقد إيه؟ بـ ثمن
+
+684
+01:14:22,390 --> 01:14:27,890
+الرابع مع رابع بالسالب. الله سهّل عليه يبقى طالع
+
+685
+01:14:27,890 --> 01:14:35,740
+أنا كده شبّنات بتساوي الثمن في إيه؟ تربيع ناقص واحد،
+
+686
+01:14:35,740 --> 01:14:39,740
+هذا قيمة مين؟ قيمة هذا التكامل
+
+687
+01:15:00,630 --> 01:15:04,770
+يلا ورقة و اكتب اسمك ورقمك الجامعي ومرّيها عليهم
+
+688
+01:15:04,770 --> 01:15:16,010
+طيب أروح لنمرة C من المثال. نرجع لنمرة C، نمرة C
+
+689
+01:15:16,010 --> 01:15:23,190
+بيقول تكامل من صفر لغاية 2، تكامل من صفر لغاية 4
+
+690
+01:15:23,190 --> 01:15:34,510
+ناقص X تربيع لـ مين؟ للـ X بـ E أس 2Y على 4 نفس Y dy
+
+691
+01:15:34,510 --> 01:15:43,050
+dx المطلوب
+
+692
+01:15:43,050 --> 01:15:48,350
+الأول اللي بده إيه؟ أرسم له منطقة التكامل بقول له
+
+693
+01:15:48,350 --> 01:15:57,920
+بسيطة هي المحاور. على محور X هذا اللي عندنا. محور Y
+
+694
+01:15:57,920 --> 01:16:04,000
+وهذه نقطة الأصل اللي هي من الـ Zero. الآن تكامل أول
+
+695
+01:16:04,000 --> 01:16:09,700
+بالنسبة لـ Y يبقى Y تساوي Zero. يبقى هذا اللي هو Y
+
+696
+01:16:09,700 --> 01:16:16,690
+تساوي Zero. اللي بعدين Y تساوي أربعة ناقص X تربيع. Y
+
+697
+01:16:16,690 --> 01:16:25,430
+تساوي أربعة ناقص X تربيع.  إلى أعلى. Y تساوي X تربيع إلى أعلى. Y تساوي X
+
+698
+01:16:25,430 --> 01:16:27,690
+تربيع إلى أعلى. Y تساوي X تربيع إلى أعلى. Y تساوي X
+
+699
+01:16:27,690 --> 01:16:33,610
+تربيع إلى أعلى. Y تساوي X تربيع إلى أعلى. Y تساوي
+
+700
+01:16:33,610 --> 01:16:35,910
+X تربيع إلى أعلى
+
+701
+01:16:37,910 --> 01:16:40,530
+بس أنا مش عارف شكل الـ parabola. والله نقصها دي
+
+702
+01:16:40,530 --> 01:16:44,690
+لبالك. لسه إحنا مش عارفين. يبقى بنجي لمين؟ لحدود
+
+703
+01:16:44,690 --> 01:16:50,550
+التكامل. الـ X هتتغير من عند Zero لغاية اتنين. طيب آه
+
+704
+01:16:50,550 --> 01:16:54,810
+لو جت لي الـ parabola هذه على هذا الخط Y تساوي Zero
+
+705
+01:16:54,810 --> 01:17:01,530
+إذًا الـ X بيصير هنا. هذا Y تساوي Zero وهنا الـ X
+
+706
+01:17:01,530 --> 01:17:07,660
+يساوي اتنين. وهنا اليمين. ناقص اتنين. إحنا عندنا من
+
+707
+01:17:07,660 --> 01:17:12,940
+Zero لغاية اتنين. يبقى بيناتنا عليا المنطقة هذه كلها
+
+708
+01:17:12,940 --> 01:17:19,880
+مالها مش موجودة. تمام. يبقى عندنا فقط المنطقة
+
+709
+01:17:19,880 --> 01:17:26,880
+المظللة اللي عندنا هي اللي بنكامل عليها. ما بين Y = 2
+
+710
+01:17:26,880 --> 01:17:32,060
+سواء Zero ومحور المنحنى. وما بين X = Zero و X =
+
+711
+01:17:32,060 --> 01:17:32,820
+اتنين
+
+712
+01:17:38,930 --> 01:17:45,170
+خليني أسأل سؤال. حد فيكم يقدر يكامل هذه أولا
+
+713
+01:17:45,170 --> 01:17:50,780
+بالنسبة إلى Y؟ لو ما قلت لكش أجب  و أعطيتك السؤال
+
+714
+01:17:50,780 --> 01:17:55,300
+زي هي. حد فيكوا بتقدروا تكاملوا هذه بالنسبة لـ Y ولا زي
+
+715
+01:17:55,300 --> 01:18:00,680
+إيه؟ ما أقدرش أكامل بالنسبة لـ Y تمام؟ إجباري حتى لو
+
+716
+01:18:00,680 --> 01:18:04,220
+ما قلت لكش. وما أقدرش أكامل دي. أجب هذه إجباري وأروح
+
+717
+01:18:04,220 --> 01:18:12,000
+أكامل بالنسبة لمين؟ بالنسبة إلى X. يبقى هذه هيك كلها
+
+718
+01:18:12,000 --> 01:18:18,480
+ماليش علاقة فيها دي. ما أقدرش أكاملها بالنسبة لمين؟ Y
+
+719
+01:18:18,480 --> 01:18:23,240
+إذًا إجباري. حجم المثلث بالنسبة لـ X. يبقى هذه بدها
+
+720
+01:18:23,240 --> 01:18:31,860
+تساوي تكاملين لمين؟ لـ X. الـ E أس اتنين Y على أربعة
+
+721
+01:18:31,860 --> 01:18:39,500
+ناقص Y. DX DY. بدي أرجع على رأس الـ T ومن خلالها أحدد
+
+722
+01:18:39,500 --> 01:18:47,000
+حدود التكامل. بنشوف X تتغير من أين لأين. برسم خط
+
+723
+01:18:47,000 --> 01:18:49,860
+موازي لمحور X وبشوف
+
+724
+01:18:58,460 --> 01:19:05,420
+هذه المنحنى Y تساوي أربعة ناقص X تربيع
+
+725
+01:19:14,380 --> 01:19:20,940
+خد الجذر. يبقى X يساوي الجذر التربيعي لـ 4 - Y. وبأخذ
+
+726
+01:19:20,940 --> 01:19:25,420
+القيمة الموجبة. لإن السالبة مش عندي مش موجودة. السالبة
+
+727
+01:19:25,420 --> 01:19:29,700
+الشجرة هذه. لكن إحنا على المنطقة المظللة. يبقى لغاية
+
+728
+01:19:29,700 --> 01:19:33,560
+الجذر التربيعي لـ 4 - Y
+
+729
+01:19:40,250 --> 01:19:46,970
+أربعة معروفة. يبقى من Zero لغاية أربعة. شايفة الحدود
+
+730
+01:19:46,970 --> 01:19:49,970
+اللي فوق واللي كيف واللي تحت تختلف عن
+
+731
+01:19:49,970 --> 01:19:54,370
+بعض تمامًا. يبقى بنروح نكامل بالنسبة لـ X. يبقى هذا
+
+732
+01:19:54,370 --> 01:20:00,280
+يعتبر كله متماثل. إذًا هذا الكلام بده يساوي تكامل من
+
+733
+01:20:00,280 --> 01:20:06,320
+Zero إلى أربعة.  لـ X تربيع على اتنين. والكلام هذا من
+
+734
+01:20:06,320 --> 01:20:13,820
+Zero لأربعة ناقص Y تحت الجذر. في مين؟ بالـ E أس
+
+735
+01:20:13,820 --> 01:20:23,000
+الـ Y على أربعة ناقص Y. Dy. لأن DX خلصنا منها تبقى Dy. طيب
+
+736
+01:20:23,000 --> 01:20:27,940
+هذا الكلام يساوي أظن النص. لو خليته برا مافيش مشكلة
+
+737
+01:20:27,940 --> 01:20:32,140
+هو هي تكامل من Zero إلى أربعة. بتعود بالقيمة اللي
+
+738
+01:20:32,140 --> 01:20:38,940
+فوق لما نربعها بيطير الجذر. يبقى بيصير أربعة ناقص Y
+
+739
+01:20:40,280 --> 01:20:45,560
+والتحت Zero. مع السلامة سهّل عليها. هذا كله مضروب
+
+740
+01:20:45,560 --> 01:20:52,380
+في مين؟ في الـ E أس اتنين Y على الأربعة ناقص Y. كله
+
+741
+01:20:52,380 --> 01:20:57,380
+بالنسبة لـ Dy. أظن بيختصر الجذر اللي فوق مع الجذر
+
+742
+01:20:57,380 --> 01:20:59,960
+اللي تحت وبصير المسألة
+
+743
+01:21:06,670 --> 01:21:10,850
+بتبسط المسألة اللي كانت معقدة في الأول. لأ يمكن
+
+744
+01:21:10,850 --> 01:21:17,490
+صارت مسألة بسيطة جدًا. يبدأ هذا نص وهذا E أس اتنين Y
+
+745
+01:21:17,490 --> 01:21:24,690
+على اتنين. وهذا من Zero. يبقى هذا الكلام بيساوي
+
+746
+01:21:24,690 --> 01:21:32,590
+الرابع في الـ E أس ثمانية ناقص E أس Zero. لو  قد إيه؟ واحد
+
+747
+01:21:32,590 --> 01:21:37,150
+يبقى رابع في E أس ثمانية ناقص
+
+748
+01:21:43,770 --> 01:21:48,930
+يبقى هذا النوع من المسائل أجبرنا إجبارًا على أن
+
+749
+01:21:48,930 --> 01:21:54,230
+نروح إحنا نغيّر حدود التكامل. مش زي المجموعة الأولى
+
+750
+01:21:54,230 --> 01:21:59,450
+من المسائل. يبقى هذا بيختلف شوية عن المجموعة الأولى
+
+751
+01:21:59,450 --> 01:22:05,150
+لأن إحنا غيّرنا حدود التكامل. وبالتالي حسبنا اللي هو
+
+752
+01:22:05,150 --> 01:22:11,600
+حدود التكامل اللي عندنا. الآن نجي للمجموعة الثانية
+
+753
+01:22:11,600 --> 01:22:17,040
+من المسائل. مثلًا two مثلًا
+
+754
+01:22:17,040 --> 01:22:25,160
+أو لنقطة ثانية من هذا الـ section اللي هو finding
+
+755
+01:22:25,160 --> 01:22:29,540
+limits
+
+756
+01:22:29,540 --> 01:22:32,960
+of integration
+
+757
+01:22:40,530 --> 01:22:45,850
+إحنا بدنا نجيب حدود التكامل، مش يعطيها اللي هو
+
+758
+01:22:45,850 --> 01:22:52,110
+ورسم المنطقة، لأ، أنت بدك تحدد حدود التكامل. نعطي
+
+759
+01:22:52,110 --> 01:22:52,670
+مثال
+
+760
+01:22:59,860 --> 01:23:06,600
+واللي find the volume of the solid. find the volume
+
+761
+01:23:06,600 --> 01:23:19,820
+of the solid. بده كده حجم المجسم. that is bounded و
+
+762
+01:23:19,820 --> 01:23:25,960
+اللي بيكون محدود. above by
+
+763
+01:23:31,930 --> 01:23:45,790
+الأسطوانة. بالأسطوانة Z تساوي X تربيع. ومن أسفل
+
+764
+01:23:45,790 --> 01:23:53,410
+بالمنطقة
+
+765
+01:23:53,410 --> 01:23:55,050
+enclosed
+
+766
+01:24:00,110 --> 01:24:07,430
+by the parabola. بالقطع
+
+767
+01:24:07,430 --> 01:24:16,790
+المكافئ Y تساوي اتنين ناقص X تربيع. and the line
+
+768
+01:24:16,790 --> 01:24:20,870
+الخط
+
+769
+01:24:20,870 --> 01:24:30,040
+Y تساوي X. and the X-axis
+
+770
+01:25:04,750 --> 01:25:09,870
+الخمسة أمثلة السابقة كانت تعطينا حدود التكامل،
+
+771
+01:25:09,870 --> 01:25:14,930
+لكنها لم تعطينا أي شيء، أنت بدأت تجيب حدود التكامل
+
+772
+01:25:14,930 --> 01:25:19,330
+من خلال الوصف اللي أعطاه لك لمين؟ للمسألة. يبقى
+
+773
+01:25:19,330 --> 01:25:23,810
+الخمسة أمثلة الأولى اللي هم فكرة شكل، وهذول
+
+774
+01:25:23,810 --> 01:25:27,510
+الأمثلة هذا واللي جاي بعده كمان اللي هم فكرة
+
+775
+01:25:27,510 --> 01:25:33,380
+شكل. يبقى أنا لو رحت رسمت منطقة التكامل بكون
+
+776
+01:25:33,380 --> 01:25:37,680
+حليت العمود الفقري تبع المثال. يفضل التكامل هذا شغل
+
+777
+01:25:37,680 --> 01:25:44,100
+روتيني. طيب جالي هنا الـ الـ الجملة الجميلة دي
+
+778
+01:25:44,100 --> 01:25:47,400
+solid bounded by the cylinder. طب لو ما جاليش
+
+779
+01:25:47,400 --> 01:25:51,440
+cylinder. هو جالي by the surface Z تساوي X تربيع
+
+780
+01:25:51,440 --> 01:25:55,380
+لحالها. بدك تعرف إن هذا الـ cylinder. لأن أنا عندي
+
+781
+01:25:55,380 --> 01:25:59,580
+متغيرين موجودين والثالث غايب. يبقى هذا معادلة
+
+782
+01:25:59,580 --> 01:26:04,260
+cylinder دائماً. وأفدنا ما علينا مش مشكلة. من أسفل
+
+783
+01:26:04,260 --> 01:26:08,680
+يعني الـ domain تبعها. enclosed by this parabola والـ
+
+784
+01:26:08,680 --> 01:26:12,800
+line اللي عندنا. يبقى يا بنات أنا فقط برسم بأساس الـ
+
+785
+01:26:12,800 --> 01:26:17,100
+domain اللي هو منطقتي التكامل. ماليش علاقة بالمجسم
+
+786
+01:26:17,100 --> 01:26:22,120
+المجسم. بدي أكامله. بدي أكامل هذا. بقول له كويس. إذا بدي
+
+787
+01:26:22,120 --> 01:26:27,440
+أروح وأرسم اللي هو اللي عندنا المنطقة. يعني هذا X
+
+788
+01:26:27,440 --> 01:26:34,310
+وهذا Y وهذه نقطة الأصل. الـ parabola اللي عندنا Y
+
+789
+01:26:34,310 --> 01:26:39,250
+تساوي سالب X تربيع وشيفت لفوق بمقدار قد إيه؟
+
+790
+01:26:39,250 --> 01:26:46,030
+بمقدار 2. يبقى النقطة هذه Zero و2. وبنروح نرسم الـ
+
+791
+01:26:46,030 --> 01:26:50,150
+parabola بالشكل اللي عندنا. تمام. يبقى هذه الـ
+
+792
+01:26:50,150 --> 01:26:55,750
+parabola اللي عندنا. بعد هيك بيقول في الخط Y تساوي X
+
+793
+01:26:55,750 --> 01:27:02,030
+يبقى معادلة الخط Y تساوي X. الشكل اللي عندنا هذا وبمده
+
+794
+01:27:02,030 --> 01:27:07,690
+على استقامته مباشرة. بنصير هذه النقطة اللي عندنا
+
+795
+01:27:07,690 --> 01:27:12,470
+هذا والنقطة اللي عندنا هي. يبقى المنطقة اللي إحنا
+
+796
+01:27:12,470 --> 01:27:18,850
+فيها دنياها هي المنطقة المظللة. ما بين الخط المستقيم
+
+797
+01:27:18,850 --> 01:27:24,350
+وما بين الـ parabola. يبقى هذه منطقة الـ main منطقة
+
+798
+01:27:24,350 --> 01:27:32,490
+التكامل. automatically بقول له volume V بتساوي تكاملين على
+
+799
+01:27:32,490 --> 01:27:39,710
+R للـ surface اللي فوق اللي هو Z تساوي قد إيه؟ X تربيع
+
+800
+01:27:39,710 --> 01:27:45,630
+طبعًا؟  ضال عندي بدي أقول له دي إيه؟ لأن أنا مش عارف
+
+801
+01:27:45,630 --> 01:27:50,930
+مين الـ X ومين الـ Y وكذا طبعًا؟ يبقى بقدر أقول هذه
+
+802
+01:27:50,930 --> 01:27:56,570
+التكامل الأول. وهي التكامل الثاني لـ X تربيع
+
+803
+01:28:04,590 --> 01:28:10,550
+هل بقدر أجيب الحدود تبقى سهلة ولا لأ؟ إن قدرت ماشية
+
+804
+01:28:10,550 --> 01:28:14,930
+اللحظة. ما قدرت فبجيبها. الآن بروح وبغيّر مين؟ الحدود
+
+805
+01:28:14,930 --> 01:28:19,930
+بقول بسيطة جدًا. الآن مدام دي ودي DX بدي أشوف Y
+
+806
+01:28:19,930 --> 01:28:25,990
+بتبدأ تتغير من وين لوين؟ بقول له آه بدي برسم خط موازي
+
+807
+01:28:25,990 --> 01:28:33,110
+لمحور Y ويقطع منطقة التكامل. يبقى هنا Y بقد إيه يا
+
+808
+01:28:33,110 --> 01:28:39,990
+بنات؟ Y بقد إيه؟ الخط هذا هو معادلة Y = قد إيه؟ X. طبعًا
+
+809
+01:28:39,990 --> 01:28:48,170
+يبقى قيمة Y هنا بقد إيه؟ بـ X. وقيمة Y هنا بقد إيه؟ بـ
+
+810
+01:28:48,170 --> 01:28:55,630
+2 ناقص X تربيع. يبقى 2 ناقص X تربيع. لإن المنحنى هنا
+
+811
+01:28:55,630 --> 01:29:03,670
+Y يساوي 2 ناقص X تربيع. ضال X بدها تتغير من أقل
+
+812
+01:29:03,670 --> 01:29:10,930
+قيمة هنا لغاية أكبر قيمة اللي عندنا. عشان هيك بدي
+
+813
+01:29:10,930 --> 01:29:17,810
+أحدد ما بين الاثنين. ممتاز جدًا. يبقى أنا عندي Y
+
+814
+01:29:17,810 --> 01:29:22,990
+تساوي X وعندي Y يساوي اتنين ناقص X تربيع. يعني اللي
+
+815
+01:29:22,990 --> 01:29:27,810
+بدي أحل المعادلتين مع بعض. بصير X يساوي اتنين ناقص X
+
+816
+01:29:27,810 --> 01:29:35,780
+تربيع. لو عملناها معادلة صفرية بصير X تربيع زائد X
+
+817
+01:29:35,780 --> 01:29:41,860
+ناقص اتنين يساوي Zero. يبقى هاي قوسين بده يساوي Zero
+
+818
+01:29:41,860 --> 01:29:49,140
+هنا X وهنا X وهنا واحد وهنا اتنين. هذه بالزائد وهذه
+
+819
+01:29:49,140 --> 01:29:54,840
+بالناقص. يبقى يا بنات الـ X بدها تساوي واحد والـ X بده
+
+820
+01:29:54,840 --> 01:30:00,390
+يساوي سالب اتنين. إذًا هذه سالب اتنين وهذه كده. شو هذه؟
+
+821
+01:30:00,390 --> 01:30:07,250
+دي واحد. تمام. إذًا الـ X هتتغير من سالب اتنين لغاية
+
+822
+01:30:07,250 --> 01:30:14,020
+واحد. باقي الشغل صار روتيني خالص. هذا هو العمود
+
+823
+01:30:14,020 --> 01:30:18,320
+الفقري تبع المثال. إني أحدد حدود التكامل من خلال
+
+824
+01:30:18,320 --> 01:30:21,300
+الوصف اللي أعطاه لي. بعدين بصير الشغل روتيني زي
+
+825
+01:30:21,300 --> 01:30:25,860
+اللي فات. يبقى هذا الكلام بده يساوي كده. بده يساوي
+
+826
+01:30:25,860 --> 01:30:31,140
+اللي هو التكامل من سالب اتنين لغاية واحد. وهذه X
+
+827
+01:30:31,140 --> 01:30:38,040
+تربيع على ثلاثة. عفواً. إن X تربيع  كلها كله
+
+828
+01:30:38,040 --> 01:30:44,070
+أسها ما لهاش علاقة في الموضوع. بظل علينا من الـ dy
+
+829
+01:30:44,070 --> 01:30:51,410
+يبقى تكاملها بـ Y من عند الـ X لإتنين ناقص X تربيع
+
+830
+01:30:51,410 --> 01:30:56,170
+كله DX يبقى
+
+831
+01:30:56,170 --> 01:31:00,610
+هذا الكلام بده يساوي تكامل من سالب إتنين لغاية
+
+832
+01:31:00,610 --> 01:31:06,210
+الواحد. X تربيع. من قيمة اللي فوق 
+
+889
+01:38:03,920 --> 01:38:07,640
+يبقى هذا الكلام يبدو يساوي integration من zero
+
+890
+01:38:07,640 --> 01:38:23,560
+لغاية 10 يبقى 16-4X  طبعا هذا ناقص 16-4X³-4X³
+
+891
+01:38:23,560 --> 01:38:30,940
+-4X³-4X³
+
+892
+01:38:30,940 --> 01:38:35,440
+-5X³
+
+893
+01:38:35,440 --> 01:38:41,800
+-8X³
+
+894
+01:38:41,800 --> 01:38:46,260
+-8X³-8X³
+
+895
+01:38:46,800 --> 01:38:52,640
+زي الـ x أُس أربعة كل هذا الكلام بالنسبة إلى dx
+
+896
+01:38:52,640 --> 01:38:59,060
+يساوي التكامل من صفر للإثنين عندك هنا ستة عشر و هنا
+
+897
+01:38:59,060 --> 01:39:05,070
+ناقص ثمانية x تربيع و هنا زي الـ x أُس أربعة و هنا
+
+898
+01:39:05,070 --> 01:39:11,850
+ناقص ثمانية و هنا ناقص فَـناقص ثمانية X تربيع
+
+899
+01:39:11,850 --> 01:39:20,310
+و هنا ناقص نصف X أُس أربعة كله في DX و يساوي تكامل
+
+900
+01:39:20,310 --> 01:39:23,750
+من الصفر للإثنين عندك هنا ستة عشر و هنا ناقص
+
+901
+01:39:23,750 --> 01:39:28,850
+ثمانية  عندك ناقص ثمانية X تربيع و
+
+902
+01:39:28,850 --> 01:39:36,240
+زائد ثمانية X تربيع  أجر الفاتحة على روحك زائد أربعة
+
+903
+01:39:36,240 --> 01:39:38,240
+زائد أربعة زائد أربعة زائد أربعة زائد
+
+904
+01:39:38,240 --> 01:39:41,380
+أربعة زائد أربعة زائد أربعة زائد أربعة زائد أربعة
+
+905
+01:39:41,380 --> 01:39:43,360
+زائد أربعة زائد أربعة زائد أربعة زائد أربعة زائد
+
+906
+01:39:43,360 --> 01:39:45,980
+أربعة زائد أربعة زائد أربعة زائد أربعة زائد أربعة
+
+907
+01:39:45,980 --> 01:39:50,060
+زائد أربعة زائد أربعة زائد أربعة زائد أربعة زائد
+
+908
+01:39:50,060 --> 01:39:52,060
+أربعة زائد أربعة زائد أربعة زائد أربعة زائد أربعة
+
+909
+01:39:52,060 --> 01:39:55,680
+زائد أربعة زائد أربعة زائد أربعة زائد أربعة زائد
+
+910
+01:39:55,680 --> 01:40:03,780
+أربعة زائد أربعة زائد أربعة زائد أربعة زائد أربعة
+
+911
+01:40:03,780 --> 01:40:14,610
+زائد ناقص أربعة أُس ثلاثة X تكعيب وزائد عشرة X أُس خمسة
+
+912
+01:40:14,610 --> 01:40:21,350
+والحكي هذا كله من عند الـ zero لغاية الإثنين يبقى
+
+913
+01:40:21,350 --> 01:40:26,930
+بيصير عندك ستة عشر ناقص ثمانية في أربعة بثلاثة
+
+914
+01:40:26,930 --> 01:40:34,470
+وثلاثين على ثلاثة زائد اثنين وثلاثين هذه تكعيب 8×4
+
+915
+01:40:34,470 --> 01:40:40,250
+هو 32 وهذه تكعيب 8×4 هي 32 على 10 والباقي كله
+
+916
+01:40:40,250 --> 01:40:46,070
+مناقشة 0 والجواب النهائي 128 على 15 يبقى هذا كله
+
+917
+01:40:46,070 --> 01:40:52,250
+متساوي مئة وثمانية وعشرين على خمسة عشر اللي هو
+
+918
+01:40:52,250 --> 01:40:58,850
+مقدار الحجب لا يزال عندنا كمان مثال وبعض الخواص
+
+919
+01:40:58,850 --> 01:41:03,730
+للمرة القادمة إن شاء الله تعالى  حتى ما كتبتش اسم
+
+920
+01:41:03,730 --> 01:41:06,990
+هنا يا بنات قولوا كتب اسم هنا
+
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/BfHmF68iUco_postprocess.srt b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/BfHmF68iUco_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..133d37d8dfe826cb13e9f3859db5379c4b01b920
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/BfHmF68iUco_postprocess.srt
@@ -0,0 +1,3680 @@
+1
+00:00:19,020 --> 00:00:25,010
+بسم الله الرحمن الرحيمنرجع الان ل chapter خمسة عشر
+
+2
+00:00:25,010 --> 00:00:29,030
+اللي ابتدناه المرة الماضية و اول section اللي هو
+
+3
+00:00:29,030 --> 00:00:33,250
+ال double integrals على منطقة مستطيلة over
+
+4
+00:00:33,250 --> 00:00:38,190
+rectangular region على منطقة على شكل مستطيل اخدها
+
+5
+00:00:38,190 --> 00:00:41,810
+المرة اللي فاتت مثلا واحدة و من الان بنكمل الأمثلة
+
+6
+00:00:41,810 --> 00:00:45,770
+على نفس الموضوع يبقى كالمرة اللي فات مثال رقم a
+
+7
+00:00:45,770 --> 00:00:54,210
+بدنا نجيه مثلا رقم bالسؤال الأول مثال رقم B بيقول
+
+8
+00:00:54,210 --> 00:01:03,470
+بدي تاكر أولين على المنطقة A ل X في Y في E أُس X
+
+9
+00:01:07,410 --> 00:01:18,050
+معطينا المنطقة R هي ان X تتغير من 0 لغاية 2 و Y
+
+10
+00:01:18,050 --> 00:01:23,250
+تتغير من 0 لغاية 1
+
+11
+00:01:34,720 --> 00:01:38,480
+المرة اللى فاتت كان كتبلى حدود التكامل على التكامل
+
+12
+00:01:38,480 --> 00:01:43,340
+نفسه، تمام؟ المرة هذه ان شاء الله تعالى احنا بدنا
+
+13
+00:01:43,340 --> 00:01:47,640
+نكتب حدود التكامل طب قلنا الكلام اللى هو ايه جايب
+
+14
+00:01:48,230 --> 00:01:53,930
+يبقى في عندي تكاملين على المنطقة المستطيلة A هي
+
+15
+00:01:53,930 --> 00:02:00,870
+لدلة XY لل E أُس XY تربيع يبقى أنا بروح بقول له
+
+16
+00:02:00,870 --> 00:02:08,250
+هذا عبارة عن تكاملين لل XY في ال E أُس XY تربيع
+
+17
+00:02:08,250 --> 00:02:13,330
+والآن الشغل فيديحبيت أكمل بالنسبة ل X في الأول،
+
+18
+00:02:13,330 --> 00:02:16,850
+بمشي الحال، حبيت أكمل بالنسبة ل Y في الأول، بمشي
+
+19
+00:02:16,850 --> 00:02:21,090
+الحال، لأن الحدود عندي أرقام، حدود مستطيل،
+
+20
+00:02:21,090 --> 00:02:24,830
+وبالتالي ماعنديش مشكلة في هذه الحالة، لكن بجيب
+
+21
+00:02:24,830 --> 00:02:29,750
+أطلع على الذلة، أيه هو أسهل أكمل للأول؟ هل بالنسبة
+
+22
+00:02:29,750 --> 00:02:34,840
+ل X ولا بالنسبة ل Y؟بالنسبة ل X بدها integration
+
+23
+00:02:34,840 --> 00:02:39,940
+by parts صح لكن بالنسبة ل Y بدها بالتعويض by
+
+24
+00:02:39,940 --> 00:02:43,500
+substitution يبقى substitution أسرع ليه من حكاية
+
+25
+00:02:43,500 --> 00:02:44,800
+integration by parts
+
+26
+00:03:02,720 --> 00:03:08,140
+بعد هيك يبقى كامل بالنسبة الأولى ل Y بحط حدود Y
+
+27
+00:03:08,140 --> 00:03:15,040
+يبقى من Zero لغاية One وهنا من Zero لغاية Two بعد
+
+28
+00:03:15,040 --> 00:03:20,680
+هيكمداجة كامل هذا الاصل y تربية اذا انا ممكن اشيل
+
+29
+00:03:20,680 --> 00:03:25,700
+ال y تربية و احطه بمتغير جديد اذا لو راك في
+
+30
+00:03:25,700 --> 00:03:31,320
+الامشيك حطيتي ت تساوي y تربية يعني يبقى دي ت
+
+31
+00:03:31,320 --> 00:03:38,560
+بتساوي اتنين y dyيبقى بناء عليه لو شيلت ال Y اللي
+
+32
+00:03:38,560 --> 00:03:43,560
+عندها دي مع ال D Y الاتنين هدول مع بعض تحط بدلهم
+
+33
+00:03:43,560 --> 00:03:48,440
+Main مُص D T يبقى اتخلصت من ال variable Y اللي برا
+
+34
+00:03:48,440 --> 00:03:54,020
+وصرت مسألة سهلة الأن يبقى وصير هذا عبارة عن
+
+35
+00:03:54,020 --> 00:04:03,600
+تكاملين وعندك هنا X وهنا E أُس X في T يبقى شيلت
+
+36
+00:04:03,600 --> 00:04:07,830
+Mainالـ X خلّيتها زي ما هي شيلت ال Y دي Y و بدى
+
+37
+00:04:07,830 --> 00:04:12,510
+أكتب بدلها النص DT النص هدا كونه Standard بقدر
+
+38
+00:04:12,510 --> 00:04:19,770
+أقوله خلّيك برا و بصير عندي هنا DT و هنا DX ال X
+
+39
+00:04:19,770 --> 00:04:22,910
+مالهاش علاقة في الموضوع كده كونه صدق ماهاش خبر
+
+40
+00:04:22,910 --> 00:04:28,910
+يبقى بظل حدود ال X كما هي من Zero لمين لغاية اتنين
+
+41
+00:04:29,440 --> 00:04:34,400
+لكن نظرنا لو عملنا تعويضة إذا بدي أشوف ما هي القيم
+
+42
+00:04:34,400 --> 00:04:41,200
+المناظرة لقيم Y بالنسبة للمتغير T إذا بدي أجي هنا
+
+43
+00:04:41,200 --> 00:04:45,960
+و أجي و أقول آه هذه الواحد والزيرو هذول حدود دمين
+
+44
+00:04:45,960 --> 00:04:52,320
+لل Y إذا لو كانت ال Y بواحد فT بواحد تربية تعني
+
+45
+00:04:52,320 --> 00:04:58,920
+واحد و لو كانت ال Y ب Zero تربية يبقى ب Zero يظلمن
+
+46
+00:04:58,920 --> 00:05:05,540
+zero لغاية واحد إذا ما عندنا مشكلة في هذه الحقإذا
+
+47
+00:05:05,540 --> 00:05:13,360
+صار بدكامل بالنسبة ل T في الأول يبقى ال X يساوي
+
+48
+00:05:13,360 --> 00:05:20,660
+النص وهي تكامل من صفر لغاية ادنان وتكامل
+
+49
+00:05:20,660 --> 00:05:25,920
+ال exponential بال exponential itself مقسومة على
+
+50
+00:05:25,920 --> 00:05:31,200
+تفاضل الأس إن كان من الدرجة الأولى يبقى ال X يعتبر
+
+51
+00:05:31,200 --> 00:05:37,860
+مقداريبقى ثابت و تفضل يبقى دهش بواحد يبقى على X و
+
+52
+00:05:37,860 --> 00:05:42,940
+الحكي هذا كله من عنده Zero لغاية واحد و هذه mainly
+
+53
+00:05:42,940 --> 00:05:50,660
+دي X اللي عندك طيب الان تختصر ال X مع ال X مع
+
+54
+00:05:50,660 --> 00:05:56,460
+السلامة يبقى آلة المسألة إلى نص تكامل من Zero
+
+55
+00:05:56,460 --> 00:06:01,040
+لغاية اتنينبالتالي اعوض بالقيمة اللي فوق نقصي يعني
+
+56
+00:06:01,040 --> 00:06:05,820
+كده شيل كل T وحط مكانها واحد وشيل T وحط مكانها
+
+57
+00:06:05,820 --> 00:06:11,600
+Zero ينفعش مصير عندي يا بنات هنا E of X وT بواحد
+
+58
+00:06:11,600 --> 00:06:19,250
+ناقص E of Zero اللي هو بواحدكل هذا الكلام بالنسبة
+
+59
+00:06:19,250 --> 00:06:24,970
+لمين؟ لدى x يبقى صارت مسألة بسيطة جدا أقصر مما
+
+60
+00:06:24,970 --> 00:06:30,490
+نتصور يبقى هذا الكلام بده يساوي نص فيه بده كامل
+
+61
+00:06:30,490 --> 00:06:36,160
+هذه تكامل ال exponential وال exponential يتصلنقص X
+
+62
+00:06:36,160 --> 00:06:41,600
+والحقيقة كلها من Zero لغاية كده اش اتنين هذا
+
+63
+00:06:41,600 --> 00:06:48,260
+الكلام بده يساوي نص E ترابيع نقص اتنين هيعوضنا
+
+64
+00:06:48,260 --> 00:06:53,220
+بالقيمة اللي فوق نقص اللي تحت E از Zero اللي هو
+
+65
+00:06:53,220 --> 00:06:59,480
+واحد ونقص مع ناقص بصير زائد Zero انتهينا يبقى
+
+66
+00:06:59,480 --> 00:07:06,770
+المسألة تساوي نصفي اي تربيع ناقص اتنين هذه هي بين
+
+67
+00:07:06,770 --> 00:07:12,410
+الإجابة المهام كيف
+
+68
+00:07:12,410 --> 00:07:17,530
+ناقص اه ناقص تلاتة ناقص واحد نقص اتنين هي بناقص
+
+69
+00:07:17,530 --> 00:07:23,790
+تلاتة نجي الان لنمرسي من المثلة نمرسي
+
+70
+00:07:25,770 --> 00:07:30,890
+بيقول لي بدي تكاملين على المنطقة المربع أو
+
+71
+00:07:30,890 --> 00:07:40,330
+المستطيلة R لل X وY تكيب على X تربيع زائد واحد DA
+
+72
+00:07:40,330 --> 00:07:47,750
+والمنطقة R هي عبارة عن ال X أكبر من أو تساوي Zero
+
+73
+00:07:47,750 --> 00:07:52,810
+أقل من أو تساوي واحد وال I أكبر من أو تساوي Zero
+
+74
+00:07:52,810 --> 00:08:05,120
+أقل من أو تساوي مينتساوي اتنين إذا
+
+75
+00:08:05,120 --> 00:08:10,680
+بدنا نجي للتكامل تبعنا هذا و نقص من الأول و الجديد
+
+76
+00:08:10,680 --> 00:08:17,260
+و نروح نحط حدود التكامل اللي علنا يبقى تكاملين لل
+
+77
+00:08:17,260 --> 00:08:26,690
+X Y تكييف عالمين على ال X تربيع زائد واحدأسهل اللي
+
+78
+00:08:26,690 --> 00:08:31,310
+أكمل في الأول بالنسبة ل Y و لا ل X؟ ليش ل X؟ ل Y
+
+79
+00:08:31,310 --> 00:08:35,770
+مافيش غيرها أصلا بس هذه لسه بدها بص مقام و أخل ال
+
+80
+00:08:35,770 --> 00:08:40,110
+بص و أتفاضل المقام يعني بدها شغلة بسيطة بس هذه لأ
+
+81
+00:08:40,110 --> 00:08:44,130
+مباشرة لابد نشتغلها Y تكيب لحالة يبقى الأفضل اللي
+
+82
+00:08:44,130 --> 00:08:48,930
+أكمل بالنسبة لمن؟ ل Y في الأول فبروح بقوله يبقى
+
+83
+00:08:48,930 --> 00:08:57,460
+هنا DY DX هذي Y تكيبيبقى كأنه مين؟ كأنه كل المقدار
+
+84
+00:08:57,460 --> 00:09:01,760
+هذا يعتبر كل أسطن بالنسبة لمن؟ بالنسبة لي ال Y
+
+85
+00:09:01,760 --> 00:09:05,720
+يبقى نفسي ده كامل Y تاكين اذا نبدأ إلى حدود ال Y
+
+86
+00:09:05,720 --> 00:09:13,220
+ال Y من أين لأين؟ من 0 لغاية 2 وال X من 0 لغاية 1
+
+87
+00:09:13,870 --> 00:09:19,450
+يبقى النتيجة تساوي integration من zero إلى واحد X
+
+88
+00:09:19,450 --> 00:09:24,650
+على X تربية زائد واحد مالوش دعوة ال Y تكييب اللي
+
+89
+00:09:24,650 --> 00:09:30,070
+هو Y أقصى أربع على أربع والكلام هذا من zero لغاية
+
+90
+00:09:30,070 --> 00:09:33,730
+اتنين وهذا DX اللي عندنا
+
+91
+00:09:36,010 --> 00:09:40,610
+الان نجي نعوض يبقى هذا الكلام تجامل من Zero ل واحد
+
+92
+00:09:40,610 --> 00:09:45,810
+ل X على X تربية زائد واحد فيه بضعوض بالقيم اللي
+
+93
+00:09:45,810 --> 00:09:52,730
+فوق اتنين اقص اربعة على اربعة بضل عندي اربعة ناقص
+
+94
+00:09:52,730 --> 00:09:54,750
+Y اقص Zero
+
+95
+00:09:59,140 --> 00:10:03,560
+يبزيرو أسعة أربعة اللي هي بزيرو على كون القط تمام
+
+96
+00:10:03,560 --> 00:10:08,740
+و كل هذا مقسم له على جداش هذا جاهز و احنا قسمنا
+
+97
+00:10:08,740 --> 00:10:14,660
+على كون القط يبقى في مين في DX تماماما يبقى بنات
+
+98
+00:10:14,660 --> 00:10:20,760
+هذا كله يعتبر رقم الان بدي اكمل X على X تربيه زي
+
+99
+00:10:20,760 --> 00:10:24,560
+واحد ايه بدي اكملها؟ X على X تربيه زي واحد
+
+100
+00:10:37,170 --> 00:10:41,590
+ممتاز يبقى هي اللي فوق مش تقة المقام بس بدها اتنين
+
+101
+00:10:41,590 --> 00:10:45,110
+يبقى بسيطة اتنين الحمد لله ربنا ما يسرها هي اربعة
+
+102
+00:10:45,110 --> 00:10:52,090
+عندى يبقى الأربعة بقول لتنين خليك برا وهي تكمل من
+
+103
+00:10:52,090 --> 00:10:58,370
+صفر لواحد دالي اتنين x على x square plus one في dx
+
+104
+00:10:59,680 --> 00:11:04,540
+هك تماما الاربعة خلت اتنين في اتنين يبقى بنقل عليه
+
+105
+00:11:04,540 --> 00:11:11,140
+صار هذا هو البسطة فاضل المقام يبقى يساوي اتنين لل
+
+106
+00:11:11,140 --> 00:11:16,520
+absolute value المقام و لما كان المقام كمية مربعة
+
+107
+00:11:16,520 --> 00:11:21,040
+او كمية موجبة دائما و ابدا يبقى لا داعي لل
+
+108
+00:11:21,040 --> 00:11:25,960
+absolute value و بروح بقول الكلام ادم ان هو من
+
+109
+00:11:25,960 --> 00:11:31,990
+zero لغاية واحديبقى هذا الكلام بده يساوي اتنين في
+
+110
+00:11:31,990 --> 00:11:37,250
+لن بتشيل اكس وخط مكان واحد تربية واحد زي واحد
+
+111
+00:11:37,250 --> 00:11:43,210
+باتنين يبقى لن اتنين نقص اتنين من اتاح ال zero بضل
+
+112
+00:11:43,210 --> 00:11:48,210
+اني جداش لن الواحد طب لن الواحد مابديش بنام يبقى
+
+113
+00:11:48,210 --> 00:11:51,450
+بضل الجواب اتنين لن اتنين
+
+114
+00:11:53,960 --> 00:11:56,980
+يبقى زي ما تشايفين هذا النوع من المسائل اللي هو
+
+115
+00:11:56,980 --> 00:12:01,500
+مسائل مباشرة المهم بدي اختار من اللي أسهل لحق
+
+116
+00:12:01,500 --> 00:12:06,180
+حدوده في الأول و الحدود اللي هي قيم عددية و ليس
+
+117
+00:12:06,180 --> 00:12:10,780
+quantity ننتقل إلى نقطة ثانية من هذا الsection
+
+118
+00:12:10,780 --> 00:12:20,540
+النقطة رقم اتنين اللي هو double integrals double
+
+119
+00:12:20,540 --> 00:12:28,340
+integrals as volumeيعني ممكن ايه؟ ممكن اللي هو
+
+120
+00:12:28,340 --> 00:12:35,200
+بواسطة طابق الانتجار نحسب الحجم اما حدرسنا في
+
+121
+00:12:35,200 --> 00:12:40,420
+calculus ايه؟ بالتكامل الفردي مش التكامل المتعدد،
+
+122
+00:12:40,420 --> 00:12:45,080
+فجينا نحسب مين؟ نحسب الحجوم والمساحات والسطوح
+
+123
+00:12:45,080 --> 00:12:49,950
+الدورانية وما إلى ذلكو هنا بواسطة double integral
+
+124
+00:12:49,950 --> 00:12:55,150
+او triple integral هنحصل من الحجوم و هنقولك كيف
+
+125
+00:12:55,150 --> 00:12:59,170
+بنحصل من الحجوم، لذلك التفاضل والتكامل كتير
+
+126
+00:12:59,170 --> 00:13:03,430
+بتطوشوا مع بعض، انا افضل منك، انت افضل مني، كذا
+
+127
+00:13:03,430 --> 00:13:08,610
+الى اخرى، فمرة و هم بيحكوا مع بعض يعني، بيناضوا مع
+
+128
+00:13:08,610 --> 00:13:15,250
+بعضقال التفاضل شامتا أنا لاتكامل معبره أنا فاضل
+
+129
+00:13:15,250 --> 00:13:23,430
+متفاضل أنا يتكامل أكبر انظر علامتك التي ذيليطولوا
+
+130
+00:13:23,430 --> 00:13:29,670
+ويقصروا زي التكامل هبقى التكامل هائجا أسكت أنا
+
+131
+00:13:29,670 --> 00:13:37,670
+متحرر أنا لم أعد لك تابعا لا و لست منك و سطروا أنا
+
+132
+00:13:37,670 --> 00:13:44,850
+للمساحة حاسب حتى الحجوم أصوره يعني بحسب المساحات و
+
+133
+00:13:44,850 --> 00:13:50,200
+بحسب الحجوم و أطول المنحنيات و ما إلى ذلكيبقى أحلى
+
+134
+00:13:50,200 --> 00:13:55,000
+موضوعنا اليوم موضوع استخدام التكامل في حساب الحجوم
+
+135
+00:13:55,000 --> 00:14:00,080
+او التكامل اللي تلاقي في حساب الحجوم بيقول ال F ال
+
+136
+00:14:00,080 --> 00:14:10,180
+F of X و Y is positive function بتاخد قيم موجبة
+
+137
+00:14:10,180 --> 00:14:14,120
+دائما أبدا و interpret
+
+138
+00:14:20,560 --> 00:14:34,480
+و I interpret the double integral of
+
+139
+00:14:34,480 --> 00:14:44,900
+F over a region R على
+
+140
+00:14:44,900 --> 00:14:48,500
+المنطقة R as the volume
+
+141
+00:14:55,690 --> 00:15:02,670
+of the solid bounded
+
+142
+00:15:02,670 --> 00:15:10,050
+below محدود
+
+143
+00:15:10,050 --> 00:15:20,450
+من أسفل by R region R and above ومن
+
+144
+00:15:20,450 --> 00:15:22,750
+أعلى by
+
+145
+00:15:24,610 --> 00:15:29,350
+الـ surface بالسطح
+
+146
+00:15:29,350 --> 00:15:48,330
+z بساوي function x و y that is أي أن ال volume v
+
+147
+00:15:48,330 --> 00:15:57,490
+بيساوي تكاملين على aللـ f of x و y دي ايه و اللي
+
+148
+00:15:57,490 --> 00:16:03,930
+هو بده يساوي تكاملين على a ل z بدي ايه
+
+149
+00:16:35,860 --> 00:16:40,040
+نرجع الكلام اللي احنا كاتبينه هذا مرة ثانية double
+
+150
+00:16:40,040 --> 00:16:45,400
+integral as volume بدنا نستخدم التكامل إثنائي في
+
+151
+00:16:45,400 --> 00:16:51,140
+حساب حجوم بعض المجسمات اقول لو كانت دالة f of x و
+
+152
+00:16:51,140 --> 00:16:56,780
+y تأخذ دائما و أبدا قيما موجبة و انت refraction
+
+153
+00:16:56,780 --> 00:17:05,130
+انت برتبناها العربي ايش معناها؟يبقى نفسر
+
+154
+00:17:05,130 --> 00:17:11,700
+دي double integralinterpretation of dreams تفسير
+
+155
+00:17:11,700 --> 00:17:16,620
+الأحلام يبقى interpret تفسير يبقى نروح و نفسر ال
+
+156
+00:17:16,620 --> 00:17:22,560
+double integral على المنطقة R as a volume كحجم
+
+157
+00:17:22,560 --> 00:17:28,540
+لمجسم of solid bounded يبقى هذا المجسم محدود من
+
+158
+00:17:28,540 --> 00:17:33,520
+أعلى بشيء و محدود من أسفل من مين بشيء الان below
+
+159
+00:17:33,520 --> 00:17:38,520
+by region Rيعني كأن ال domain تبع main تبع ال
+
+160
+00:17:38,520 --> 00:17:42,380
+surface اللي فوق يبقى محدود من تحت بال domain R أو
+
+161
+00:17:42,380 --> 00:17:46,980
+بال region R and above ومن أعلى بال surface نفسه
+
+162
+00:17:46,980 --> 00:17:51,500
+يبقى ال surface اللي عندي فوق هيكون له على المستوى
+
+163
+00:17:51,500 --> 00:17:56,880
+XY اللي هو المجال تبعهكل المنطقة اللي بين المجال و
+
+164
+00:17:56,880 --> 00:18:00,600
+مابين السطح ال surface اللي فوق يبقى هذا بقدر أجيب
+
+165
+00:18:00,600 --> 00:18:06,140
+حجمها بواسطة من التكامل و ثانوية curve بقولها ها
+
+166
+00:18:06,140 --> 00:18:10,660
+ال surface أعطيته المعادلة z تساوي f of x y اللي
+
+167
+00:18:10,660 --> 00:18:15,020
+قولنا عليها يبقى احنا يا بنات أعلى المستوى x y و
+
+168
+00:18:15,020 --> 00:18:17,700
+أسفى المستوى x y و الله بنقطعه
+
+169
+00:18:20,270 --> 00:18:24,810
+أعلن نجلي موجب يعني ال z دائما هو بتاخد قيام موجبة
+
+170
+00:18:24,810 --> 00:18:28,410
+يعني احنا من مستوى الأرض و طالعين وان وطالعين لفوق
+
+171
+00:18:28,410 --> 00:18:34,090
+من ما نزلش تحت لإن ال z دائما هو بتاخد قياما موجبة
+
+172
+00:18:34,090 --> 00:18:37,930
+يبقى المنطقة اللي محصورة بين ال surface و ما بين
+
+173
+00:18:37,930 --> 00:18:41,670
+ال domain تبعها على المستوى x y او على المستوى z
+
+174
+00:18:41,670 --> 00:18:47,240
+تساوي zero بيكون ايش هو الحجم تبعنااللي هو عبارة
+
+175
+00:18:47,240 --> 00:18:51,160
+عن مين؟ عبارة عن تكامل لـ function f of x و y على
+
+176
+00:18:51,160 --> 00:18:56,720
+المنطقة R أو الـ f of x و y هي z أو تكامل على z
+
+177
+00:18:56,720 --> 00:19:00,260
+لمين او .. إذا لو قال لي هاتلي سؤال و قال لي هاتلي
+
+178
+00:19:00,260 --> 00:19:04,600
+ال volume بشيله z و بحقم انت بدلالة x و y و بروح
+
+179
+00:19:04,600 --> 00:19:07,740
+بكامل حدود التكامل اللي بدي أجيبها من وين؟ من ال
+
+180
+00:19:07,740 --> 00:19:13,180
+domain او من المجال تبع هذه ال function كيف؟ ليش z
+
+181
+00:19:13,180 --> 00:19:18,410
+تكامل من وين؟ما هو التكامل يا ستي هذا لما يكون
+
+182
+00:19:18,410 --> 00:19:23,130
+أعلى ال exactness من calculus ايه تطلع بقيمة موجبة
+
+183
+00:19:23,130 --> 00:19:27,710
+وإذا نزلتي تحت بصير ايه يا عزيزي قيمة سالبة لما لو
+
+184
+00:19:27,710 --> 00:19:30,510
+كان ايش شوية فوق و شوية تحت يمكن ينطلع عندك
+
+185
+00:19:30,510 --> 00:19:33,850
+التكامل ب zero إذا المنطقة اللي فوق ضد المنطقة
+
+186
+00:19:33,850 --> 00:19:38,260
+اللي تحت بتقول معقول مساحة تطلع zeroالسؤال الثاني
+
+187
+00:19:38,260 --> 00:19:43,520
+يمكن لو كانت كلها أسفل لمحور X يبقى بتطلع كلها
+
+188
+00:19:43,520 --> 00:19:46,380
+سالبة، بتقول المعقول ان مساحات تطلع سالبة؟ مافيش
+
+189
+00:19:46,380 --> 00:19:50,160
+مساحة في الدنيا سالبة، إذا في شغل غلط بتقوله، يبقى
+
+190
+00:19:50,160 --> 00:19:54,540
+احنا ضمننا هيك أنه لا يطلع ال zero ولا إشارة
+
+191
+00:19:54,540 --> 00:19:58,040
+سالبة، أنا بحكي على ذلك في one variable، لما ننتقل
+
+192
+00:19:58,040 --> 00:20:03,500
+إلى ال two variables يبقى أنا بصيرأسفل الـ X Y
+
+193
+00:20:03,500 --> 00:20:07,220
+Plane و أعلى الـ X Y Plane يبقى تبقى منطقة موجبة
+
+194
+00:20:07,220 --> 00:20:10,240
+ومنطقة سلبة ربما يلغوا بعض بيطلع التكمل اندي بـ
+
+195
+00:20:10,240 --> 00:20:16,880
+Zero والمعقول حجم يطلع Zeroزي ما أقول يبقى اشتراك
+
+196
+00:20:16,880 --> 00:20:21,660
+موجبة لكن لو كانت اشي فوق و اشي تحت بجسمها إلى
+
+197
+00:20:21,660 --> 00:20:25,520
+جسمين و بروح بحسب المنطقة اللي فوق و المنطقة اللي
+
+198
+00:20:25,520 --> 00:20:29,880
+تحت و باخد ال absolute value و بجمعها بعضيا نجداش
+
+199
+00:20:29,880 --> 00:20:33,760
+اللي هو القيم الحقيقية سؤال وجهي لسؤالته يعني هي
+
+200
+00:20:33,760 --> 00:20:37,240
+دراسته في Calculusية و احنا ذكرناه باللي درسته في
+
+201
+00:20:37,240 --> 00:20:42,460
+Calculusية و سحبنا عليه Calculusطيب نرجع لماين
+
+202
+00:20:42,460 --> 00:20:46,260
+لكلام اللي عندنا هذا حدا فيكوا إلا أي تساؤل حول
+
+203
+00:20:46,260 --> 00:20:50,100
+الكلمتين اللي عندنا هدول في عندكوا في الكتاب حوالي
+
+204
+00:20:50,100 --> 00:21:01,680
+خمس مسائل تقريبا هذا أحدهم example find
+
+205
+00:21:01,680 --> 00:21:11,210
+the volume of the region find the volume ofthe
+
+206
+00:21:11,210 --> 00:21:18,630
+region متقدش حجم المنطقة bounded above bounded
+
+207
+00:21:18,630 --> 00:21:23,210
+above
+
+208
+00:21:23,210 --> 00:21:30,530
+والمحصولة من أعلى أو المحدودة من أعلى by the
+
+209
+00:21:30,530 --> 00:21:34,790
+surface بالسطح
+
+210
+00:21:35,580 --> 00:21:47,500
+z تساوي 16 ناقص x تربيع ناقص y تربيع and below ومن
+
+211
+00:21:47,500 --> 00:22:01,620
+أسفل by the square بالمربع r اللي هو عبارة عن ال x
+
+212
+00:22:01,620 --> 00:22:08,400
+تتغير من zero لغاية اتنينو ال Y بتتغير من Zero
+
+213
+00:22:08,400 --> 00:22:10,880
+لغاية 2 كذا
+
+214
+00:22:13,730 --> 00:22:18,870
+يبقى يا بنت هذه منطقة مربع وليست مستطيلة لأن
+
+215
+00:22:18,870 --> 00:22:25,550
+المربع هو حالة خاصة من مين؟ من المستطيل زي ايش؟ زي
+
+216
+00:22:25,550 --> 00:22:30,730
+متوازي المستطيلات حالة خاصة من متوازي السطوح
+
+217
+00:22:30,730 --> 00:22:40,110
+المكعب حالة خاصة من متوازي المستطيلات حيث نيجي
+
+218
+00:22:40,110 --> 00:22:41,470
+للحل solution
+
+219
+00:22:46,130 --> 00:22:50,250
+سمعتوا متوازي السطوح ولا لا يا بنات؟ خلال كل كلصي
+
+220
+00:22:50,250 --> 00:22:56,970
+تبعنا او ال pipe ايش سمناها؟ parallel pipe مظبوط
+
+221
+00:22:56,970 --> 00:23:01,050
+له متوازي السطوح متوازي السطوح هو عبارة عن منشور
+
+222
+00:23:01,050 --> 00:23:05,820
+رباعي جميع أوجهه الست متوازية الأطباقمتوازي
+
+223
+00:23:05,820 --> 00:23:11,420
+المستطيلات هو منشور جميع أوجهه الستة مستطيلات زي
+
+224
+00:23:11,420 --> 00:23:14,940
+الغرفة اللي احنا فيها أي مستطيل هناك مستطيل التاني
+
+225
+00:23:14,940 --> 00:23:18,520
+مستطيل ومستطيل الساقف الأرض كلها مستطيلة تمام
+
+226
+00:23:18,520 --> 00:23:24,980
+المكعةجميع وجهه الستة مربعات وكلها مربعات متطابقة
+
+227
+00:23:24,980 --> 00:23:29,900
+تمام يبقى المكعب على قصة متوازد المستطيلات متوازد
+
+228
+00:23:29,900 --> 00:23:33,700
+المستطيلات على قصة متوازد السطوح متوازد السطوح على
+
+229
+00:23:33,700 --> 00:23:41,240
+قصة من المنشور وهكذا تمام؟ طيب يمكننا نعيش لمين
+
+230
+00:23:41,240 --> 00:23:46,180
+لسؤال تبعنا يمكننا نروح أكامل الدالة اللي عندنا
+
+231
+00:23:46,180 --> 00:23:51,970
+هذه تعطين ال volumeمين الدالة هذه اللي هو تكاملين
+
+232
+00:23:51,970 --> 00:24:00,090
+على R لمين لستة عشر ناقص X تربيع ناقص Y تربيع
+
+233
+00:24:12,040 --> 00:24:16,080
+بنطلع في المثل اللي قدامي بالكامل بالنسبة ل X و
+
+234
+00:24:16,080 --> 00:24:18,280
+الله بالنسبة له اتنين نفس الشيء يبقى ما معانا
+
+235
+00:24:18,280 --> 00:24:24,180
+مشكلة يبقى بده اروح اقول مثلا DXDY برجع ال X من
+
+236
+00:24:24,180 --> 00:24:30,460
+صفر لاتنينوالـ y كذلك من صفر لغاية اتنين يعني احنا
+
+237
+00:24:30,460 --> 00:24:33,840
+بنكمل على منطقة مربعة الشكل ال domain تبع ال
+
+238
+00:24:33,840 --> 00:24:38,800
+service هي منطقة مربعة الشكل هذا الكلام بدل يساوي
+
+239
+00:24:38,800 --> 00:24:41,860
+تكامل من zero لغاية اتنين
+
+240
+00:24:53,580 --> 00:25:02,180
+يبقى كل هذا الكلام من صفر لغاية اتنين لدي واي يبقى
+
+241
+00:25:02,180 --> 00:25:06,820
+يساوي integration من صفر لغاية اتنين نعوض بالقيمة
+
+242
+00:25:06,820 --> 00:25:19,180
+اللي فوق يبقى ناقص
+
+243
+00:25:19,180 --> 00:25:29,420
+تمانية على تلاتةبعدها ناقص اتنين Y تربيع ناقص Zero
+
+244
+00:25:29,420 --> 00:25:35,060
+زائد Zero زائد Zero كله بروح يعني بهذه النتيجة
+
+245
+00:25:35,060 --> 00:25:40,760
+مباشرة كله بالنسبة لمين ده دي واعي طيب بدنا نجمع
+
+246
+00:25:40,760 --> 00:25:45,900
+هذول ابنات تلاتة في اتنين و تلاتين ستة و تسعين
+
+247
+00:25:45,900 --> 00:25:51,410
+شيلي تمانية وضل تمانية و تمانينيبقى احنا بدنا نكمل
+
+248
+00:25:51,410 --> 00:25:58,070
+من zero للاتنين لتمانية وتمانين على تلاتة ناقص
+
+249
+00:25:58,070 --> 00:26:05,630
+اتنين Y تربيع كله بالنسبة لمين لدي Y يبقى هذا
+
+250
+00:26:05,630 --> 00:26:07,010
+الكلام بده يساوي
+
+251
+00:26:16,210 --> 00:26:24,010
+و تكيب و الحقيقة كمان من zero لغاية اتنين نجلعهم
+
+252
+00:26:24,010 --> 00:26:28,570
+في الاتنين اتنين في تمانية ستة عشر اتنين في تمانية
+
+253
+00:26:28,570 --> 00:26:37,350
+سبعة عشر على تلاتة ناقص و اي تكيب عن اتنين تكيب
+
+254
+00:26:37,350 --> 00:26:45,180
+تمانية في اتنينعلى تلاتة ناقص Zero زائد Zero
+
+255
+00:26:45,180 --> 00:26:52,620
+بقيرمها السلامة يبقى 176 نطرح منهم 16 بيبقى 160
+
+256
+00:26:52,620 --> 00:26:57,840
+على تلاتة حجم المنطقة المحصورة بين ال surface اللي
+
+257
+00:26:57,840 --> 00:27:05,400
+عندنا هذا وما بين مين المربع هذا بنات ال section
+
+258
+00:27:05,400 --> 00:27:11,090
+هو أبسط section موجود في الشطر هذا كلهومش محتاج لا
+
+259
+00:27:11,090 --> 00:27:16,190
+لف ولا دوران زي ما انت شايفين وكلها أمثلة واسئلة
+
+260
+00:27:16,190 --> 00:27:21,030
+بسيطة يبقى انتهينا من هذا ال section وإلى يكون
+
+261
+00:27:21,030 --> 00:27:28,670
+أقام المسائل يبقى exercises خمس تاشر واحد مسائل من
+
+262
+00:27:28,670 --> 00:27:38,630
+واحد لغاية تمانية وعشرين القادة section خمس تاشر
+
+263
+00:27:38,630 --> 00:27:46,130
+اتنينيبقى section خمستاشر اتنين بتحدث برضه عن ال
+
+264
+00:27:46,130 --> 00:27:51,270
+double integrals بس بطلنا ايش نقول على منطقة مربعة
+
+265
+00:27:51,270 --> 00:27:55,710
+على منطقة مينما كانت تكون وهذا بتبقى أتجل شوية
+
+266
+00:27:55,710 --> 00:28:00,990
+وحدود التكامل ليس بضرورة أن تكون كلها قيم عددية
+
+267
+00:28:00,990 --> 00:28:05,930
+هلاحظ بعض الحدود تصير functions يعني متغيرات وهذا
+
+268
+00:28:05,930 --> 00:28:14,310
+ما سنراه بعد قليليبقى بجي بقول double integrals
+
+269
+00:28:14,310 --> 00:28:22,410
+over
+
+270
+00:28:22,410 --> 00:28:27,830
+general
+
+271
+00:28:27,830 --> 00:28:30,830
+regions
+
+272
+00:28:39,900 --> 00:28:45,660
+حاجة اسمها إذا عدت نقاط النقطة الأولى يجب أن يأخذ
+
+273
+00:28:45,660 --> 00:29:00,340
+double integrals تكاملات مثلائية over bounded non
+
+274
+00:29:00,340 --> 00:29:01,640
+rectangular region
+
+275
+00:29:20,030 --> 00:29:23,730
+يعني يا بناتي احنا ال section اللي فات كنا بناخد
+
+276
+00:29:23,730 --> 00:29:29,310
+التكامل على منطقة مستطيلة تمام الان بدل منطقة
+
+277
+00:29:29,310 --> 00:29:33,730
+مستطيلة او منطقة مربعة بدنا نروح ل general region
+
+278
+00:29:33,730 --> 00:29:38,310
+منطقة عامة يمكن تكون مثلة، يمكن تكون متوازية
+
+279
+00:29:38,310 --> 00:29:42,870
+اطلاع، يمكن تكون دائرة، يمكن .. يمكن .. يمكن شكل
+
+280
+00:29:42,870 --> 00:29:46,750
+احنا ماحناش عارفينه، يمكن شبه من الله أعلم، ايش
+
+281
+00:29:46,750 --> 00:29:50,660
+مكانة تكون، تمام؟يبقى يقول double integrals over
+
+282
+00:29:50,660 --> 00:29:55,340
+general regions اللي هي منطقة عامة اجي يقول double
+
+283
+00:29:55,340 --> 00:29:59,280
+integrals over bounded non rectangular regions
+
+284
+00:29:59,280 --> 00:30:03,760
+يبقى احنا بطلاش المستطيلة يبقى non rectangular
+
+285
+00:30:03,760 --> 00:30:07,800
+region منطقة غير مستطيلة اش ما كانت تكون المنطقة
+
+286
+00:30:07,800 --> 00:30:13,480
+هذه هنعطي نظرية بناء عليه نستخدم هذه النظرية في حل
+
+287
+00:30:13,480 --> 00:30:24,830
+المثال النظرية بتقول ما يأتيtheorem let f of x,y
+
+288
+00:30:24,830 --> 00:30:37,090
+be continuous دالة مبتصلة on a region R على
+
+289
+00:30:37,090 --> 00:30:43,710
+المنطقة R دي من واحد if
+
+290
+00:30:43,710 --> 00:30:58,020
+ال Ris defined by معظمك التالي ال X أكبر من أو
+
+291
+00:30:58,020 --> 00:31:04,000
+تساوي A وأقل من أو تساوي B وال G واحد as a
+
+292
+00:31:04,000 --> 00:31:10,360
+function of X أقل من أو تساوي Y أقل من أو تساوي G2
+
+293
+00:31:10,360 --> 00:31:27,480
+of X with G واحدand G2 are continuous كانوا
+
+294
+00:31:27,480 --> 00:31:39,720
+دوال متصلة على الفترة المغلقة A وB then تكاملين
+
+295
+00:31:39,720 --> 00:31:46,840
+على منطقة R لل F of XYDA
+
+296
+00:31:48,020 --> 00:31:53,820
+بتساوي التكامل الأول من a إلى b التكامل التاني من
+
+297
+00:31:53,820 --> 00:32:09,240
+g1 of x إلى g2 of x لل F of x y dy dx نقطة
+
+298
+00:32:09,240 --> 00:32:17,440
+ثانية F ال R is defined
+
+299
+00:32:21,670 --> 00:32:31,630
+H1 of Y أقل من أو يساوي Y أقل من أو يساوي D H2 of
+
+300
+00:32:31,630 --> 00:32:35,950
+Y أقل من أو يساوي X أقل من أو يساوي
+
+301
+00:32:53,380 --> 00:33:02,180
+كانوا دوال متصلة على الفترة المغلقة C وD ثم
+
+302
+00:33:02,180 --> 00:33:12,920
+تكاملت على A لل F of XYDA بدي يعطيني تكاملت الأول
+
+303
+00:33:12,920 --> 00:33:18,400
+من C إلى D والتاني من H1 of Y
+
+304
+00:33:21,830 --> 00:33:30,770
+لل H2 of Y لل F of X of Y DX D1
+
+305
+00:34:08,910 --> 00:34:12,530
+نرجع الكلام اللي كتبناه مرة تانية نقرأ ثاني و
+
+306
+00:34:12,530 --> 00:34:16,910
+نحاول نفهم قال يفترض ان انا لك F of X و Y of B
+
+307
+00:34:16,910 --> 00:34:22,230
+continuous على region R مين هي ال region R حالة
+
+308
+00:34:22,230 --> 00:34:27,590
+الأولى ال R is defined by X تتغير من A إلى B و ال
+
+309
+00:34:27,590 --> 00:34:32,790
+Y تتغير من G1 of X إلى G2 of X و ال G1 و ال G2
+
+310
+00:34:32,790 --> 00:34:37,710
+continuous على نفس الفترة كيف يعني تعالى نشوف تلقى
+
+311
+00:34:37,710 --> 00:34:46,170
+مجاناةهذه محور X وهذه محور Y وهذا نقطة الأصل على
+
+312
+00:34:46,170 --> 00:34:53,050
+سبيل المثال رحت أخد الفترة اللي قاللي عنها الأولي
+
+313
+00:34:53,050 --> 00:35:01,610
+A وB A وB تعتبر للمتغير من X يبقى على محور X بدي
+
+314
+00:35:01,610 --> 00:35:06,390
+أعمل تغيير من نقطة A لنقطة B
+
+315
+00:35:09,500 --> 00:35:15,060
+Y تتغير من G1 of X إلى G2 of X
+
+316
+00:35:24,800 --> 00:35:31,780
+يعني مين يعني Y تساوي G1 of X Y هي function في X
+
+317
+00:35:31,780 --> 00:35:37,160
+رسمت المنحنى ثاني فكان المنحنى التاني مثلا بالشكل
+
+318
+00:35:37,160 --> 00:35:45,890
+اللي عندنا هذا يبقى هذا ال Y تساوي G2 of Xالان في
+
+319
+00:35:45,890 --> 00:35:51,590
+منطقة محصورة بين المنحنيين A وB بين المنحنيين
+
+320
+00:35:51,590 --> 00:35:57,850
+الأول والثاني على الفترة من A إلى B جت من هنا طالع
+
+321
+00:35:57,850 --> 00:36:01,910
+هك الشكل اللي عندنا هذا و من هنا جت طالع بالشكل
+
+322
+00:36:01,910 --> 00:36:08,010
+هذا و كل جي واحد و جي اتنين دوال متاصلة اذا ما بين
+
+323
+00:36:08,010 --> 00:36:14,370
+المنحنيين هدول انحصرت المنطقة اللي عندنا هذا تمام؟
+
+324
+00:36:15,200 --> 00:36:19,600
+بتنا الكامل الـ function اللي عندنا هذه على هذه
+
+325
+00:36:19,600 --> 00:36:26,160
+المنطقة يبقى لاحظي ان جي واحد of x أقل من جي اتنين
+
+326
+00:36:26,160 --> 00:36:31,420
+of x و y محصورة ما بين الاتنين تمام هذه واحدة
+
+327
+00:36:31,420 --> 00:36:36,360
+التانية ال X ستتغير من ايه إلى وين من A إلى B
+
+328
+00:36:36,360 --> 00:36:41,720
+بوصولة من هذه المنطقة المظلة لهذه تماميبقى بيكون
+
+329
+00:36:41,720 --> 00:36:48,540
+التكامل الفنكشن يسوي التكامل الفنكشن dy dx حطيت
+
+330
+00:36:48,540 --> 00:36:54,000
+المتغير في الأول y هي g1 of x و y واحد و y اتنين
+
+331
+00:36:54,000 --> 00:36:59,860
+هي g2 of x يبقى بدأت لما الأكامل هاد دول دوال في x
+
+332
+00:36:59,860 --> 00:37:03,620
+على عكس مكان ما فيه في ال section السابق كانوا
+
+333
+00:37:03,620 --> 00:37:10,140
+أرقامهذه لأ بيعطيني متغيرات نفس من المتغيرات بس
+
+334
+00:37:10,140 --> 00:37:15,660
+بيطلع بدلالة من X بكمل Y بطلع الجواب بدلالة X في
+
+335
+00:37:15,660 --> 00:37:18,780
+عندي مشكلة مافي عندي مشكلة لإن باقي الدالة اللي
+
+336
+00:37:18,780 --> 00:37:24,240
+ضايلة بصير بدلالة من X لكن X تتغير من رقم إلى رقم
+
+337
+00:37:24,240 --> 00:37:30,180
+إذا بطلع في الجواب رقم واحدطبعا يبقى هذا يعني لكن
+
+338
+00:37:30,180 --> 00:37:35,960
+لو حطيت لو كانت السؤال حطيت المتغيرات في الآخر و
+
+339
+00:37:35,960 --> 00:37:40,740
+الاعداد في الأول عمرك ماحجيب نتيجة طبعا يبقى في
+
+340
+00:37:40,740 --> 00:37:44,480
+هذه الحالة بكون انا مجبر ان اكمل بالنسبة لواي في
+
+341
+00:37:44,480 --> 00:37:49,060
+الأول ثم اروح اكمل بالنسبة لمين الاكس هذه الحالة
+
+342
+00:37:49,060 --> 00:37:51,080
+الأولى نجي الحالة التانية
+
+343
+00:37:56,810 --> 00:38:01,950
+لكن ال X محصورة بين two functions وكل function
+
+344
+00:38:01,950 --> 00:38:07,830
+دالة في Y ب X as a function of Y with each one of
+
+345
+00:38:07,830 --> 00:38:11,370
+its two continuous functions على الفترة اللي هو C
+
+346
+00:38:11,370 --> 00:38:16,930
+وD كيف يكونوا دالة؟ طلعيلي كويس هاي المحاور هذا
+
+347
+00:38:16,930 --> 00:38:23,420
+محور Xهذا محور Y وهذه نقطة الاصد اللي عندك افترضي
+
+348
+00:38:23,420 --> 00:38:28,660
+رسمت المنحنى فكان المنحنى الأول بالشكل اللي عندنا
+
+349
+00:38:28,660 --> 00:38:38,420
+هذا يبقى هذا ال X تساوي H1 of Y جينا رسمنا المنحنى
+
+350
+00:38:38,420 --> 00:38:43,060
+التاني فطلع بقدر الله طلع المنحنى التاني بالشكل
+
+351
+00:38:43,060 --> 00:38:51,830
+اللي عندك هذايبقى هذا ال X يساوي H2O روحنا على
+
+352
+00:38:51,830 --> 00:38:57,270
+محور Y قال لي تتغير ال Y بين C وD قلنا هي النقطة
+
+353
+00:38:57,270 --> 00:39:01,870
+كانت نقطة C و هي النقطة التانية اللي هي نقطة D
+
+354
+00:39:01,870 --> 00:39:09,500
+رسمت موازي لمحور Xقطع المنحنايين لاتنين هذول إذا
+
+355
+00:39:09,500 --> 00:39:14,020
+المنحنايين مع الخطين الوفوقيين حصروا المنطقة
+
+356
+00:39:14,020 --> 00:39:18,900
+المظللة اللي عندناها، المنطقة الزرقى زي ما انتوا
+
+357
+00:39:18,900 --> 00:39:23,680
+شايفينإذا احنا بنكمل ال function اللي عندنا على
+
+358
+00:39:23,680 --> 00:39:28,820
+المنطقة المضللة اللي عندنا هذه فبصير ايش تكمل ال
+
+359
+00:39:28,820 --> 00:39:33,520
+function على dA بدي احط الدلة اللي بتغير في الأول
+
+360
+00:39:33,520 --> 00:39:38,600
+يمكن بدي أكمل أولا بالنسبة لمين لل X لأن X هي
+
+361
+00:39:38,600 --> 00:39:43,100
+الدلة في Y هدلت أرقام فبصير ان integration من H1
+
+362
+00:39:43,100 --> 00:39:48,360
+of Y لH2 of Y لما نكمل و أعوض مكان ال X ده اللي
+
+363
+00:39:48,360 --> 00:39:53,290
+بدلة Y بصير المثل كلهبدلالة Y بصير سهل أكمله
+
+364
+00:39:53,290 --> 00:39:57,090
+بالنسبة لي بعد ذلك و أعوض بحوز التكامل و بيطلع لنا
+
+365
+00:39:57,090 --> 00:40:04,190
+نتيجة رقما محددة طيب يا بنات هذه انا بمزاجي يعني
+
+366
+00:40:04,190 --> 00:40:08,690
+ممكن اعملها و الله هو بيكون كتبهالي و خالص اقول
+
+367
+00:40:08,690 --> 00:40:14,130
+والله احنا بنتطلع اذا قال لي كامل و second انا بدي
+
+368
+00:40:14,130 --> 00:40:20,020
+اختاره ان احدد كامل بالنسبة لمن لل Xأول أو الواي
+
+369
+00:40:20,020 --> 00:40:25,160
+في الأول يبقى حسب طبيعة المثل ممكن هو يعطيني
+
+370
+00:40:25,160 --> 00:40:30,960
+تكاملين واحد متغير ويحطه لجوا لجوا بالنسبة للمتغير
+
+371
+00:40:30,960 --> 00:40:37,290
+أو المردوشة كامة مابقاش أقوله مش قادر أقوله لابعمل
+
+372
+00:40:37,290 --> 00:40:42,150
+عملية change او reverse بقلب حدود التكامل كيف انا
+
+373
+00:40:42,150 --> 00:40:47,410
+عند المنطقة مثلا اعطيها حدود بدلالة X بتروح احوضها
+
+374
+00:40:47,410 --> 00:40:52,850
+بدلالة Y فبروح برص المنطقة تتكامل و من خلال هذه
+
+375
+00:40:52,850 --> 00:40:56,770
+المنطقة بدل ما كانت الحدود بالنسبة ل X بيخليه نميل
+
+376
+00:40:56,770 --> 00:41:01,770
+بالنسبة ل Y بقلب حدود التكامل وسيل التكامل Sيعني
+
+377
+00:41:01,770 --> 00:41:06,830
+أحيانًا ممكن يجبرني إجبارًا على ذلك ويطلبه و
+
+378
+00:41:06,830 --> 00:41:10,390
+أحيانًا أقول لأ أنا برسوم بطلع لي و بالتالي أنا
+
+379
+00:41:10,390 --> 00:41:13,850
+باختار بالنسبة للإكس أو بالنسبة للواحد سواء كان
+
+380
+00:41:13,850 --> 00:41:17,310
+تاني و لا تاني هشوف الصنفين هاطلس هعطيك قامتلة على
+
+381
+00:41:17,310 --> 00:41:22,330
+الصنفين بحيث انغطيه و بدل المثال هعطيك تمانية بحيث
+
+382
+00:41:22,330 --> 00:41:27,510
+انه فعلا انغطي المادة او نغطي الموضوع تغطية كاملة
+
+383
+00:41:27,510 --> 00:41:33,650
+نبدأ قبل أن أخش القامتلة هل حاضر ان تسألني سؤالهذا
+
+384
+00:41:33,650 --> 00:41:37,510
+كل جزء نظري في ال sketch بس بدنا ايه نبدأ نشتغل
+
+385
+00:41:37,510 --> 00:41:49,170
+عليه نجلمين لل exactly أول
+
+386
+00:41:49,170 --> 00:41:53,990
+مثال ال sketch is a region of integration sketch
+
+387
+00:41:53,990 --> 00:42:00,170
+is a region of
+
+388
+00:42:03,500 --> 00:42:13,480
+Integration أرسلني منطقتي تكامل And evaluate وروح
+
+389
+00:42:13,480 --> 00:42:21,960
+أحسبلي evaluate the integral أحسبلي
+
+390
+00:42:21,960 --> 00:42:30,080
+تكامل نمرأ أيه؟ أريد تكامل من واحد إلى أربعة تكامل
+
+391
+00:42:30,080 --> 00:42:31,220
+من Zero
+
+392
+00:42:52,160 --> 00:42:58,220
+يبقى هذا المثالعطانى تكاملين وقال لي احسن واجبرني
+
+393
+00:42:58,220 --> 00:43:03,380
+انه اكمل بالنسبة لواي في الأول هو كتب هالي وجهها
+
+394
+00:43:03,380 --> 00:43:07,720
+زي هيك تمام وماقالليش قاللي ارسم المنطقة و بعدين
+
+395
+00:43:07,720 --> 00:43:12,260
+كامل بقوله ارسم المنطقة و بعدين بروح بكامل كيف
+
+396
+00:43:12,260 --> 00:43:16,420
+ارسم المنطقة طيب ماعطانيش منطقة هو ماكتبليش R من
+
+397
+00:43:16,420 --> 00:43:21,460
+كذا لكذا X و Y من كذا لكذا بجيب المنطقة من حدود
+
+398
+00:43:21,460 --> 00:43:27,590
+التكامل اذا بروح بقولههذه المحاور اللي عندنا هذا
+
+399
+00:43:27,590 --> 00:43:31,310
+محور X وهذا محور Y وهذا نقطة الأصل
+
+400
+00:43:34,440 --> 00:43:41,380
+لما يقول هنا هذا جذر X يبقى
+
+401
+00:43:41,380 --> 00:43:47,720
+Y تساوي جذر X يبقى
+
+402
+00:43:47,720 --> 00:43:52,900
+Y تساوي جذر X يبقى
+
+403
+00:43:52,900 --> 00:44:02,280
+هذا Y تساوي جذر X ال index اللي تحت Y تساوي من
+
+404
+00:44:02,280 --> 00:44:10,330
+رمينمحور X يبقى هذا له Y تساوي Z يبقى هذه حدات
+
+405
+00:44:10,330 --> 00:44:16,250
+الشغلات بتتغير بالنسبة لمين ل Y بالنسبة لل X كان X
+
+406
+00:44:16,250 --> 00:44:21,350
+تساوي أربعة و X تساوي واحد X تساوي واحد يعني هذا
+
+407
+00:44:21,350 --> 00:44:28,330
+الخط X يساوي واحد وهذا الخط التاني X تساوي أربعة
+
+408
+00:44:29,030 --> 00:44:34,970
+إذا المنطقة المظللة اللى عايزناها دى هي منطقة مين؟
+
+409
+00:44:34,970 --> 00:44:41,850
+منطقة التكامل تمام؟ قال ال sketch رسمناله منطقة
+
+410
+00:44:41,850 --> 00:44:46,430
+التكامل قال يحسبلي هذا التكامل يبقى ضمن عملية حساب
+
+411
+00:44:46,430 --> 00:44:48,730
+التكامل بقولك بيس هذا
+
+412
+00:44:52,540 --> 00:44:56,380
+بتكمل اول شغلة بالنسبة لـ Y يبقى 1 على جدر ال X
+
+413
+00:44:56,380 --> 00:45:00,920
+يعتبر مقدارا يبقى سهل جدا هذا مش في اي اشكالية
+
+414
+00:45:00,920 --> 00:45:06,140
+تلاتة على اتنين مرة التكامل يبقى هاي تلاتة على
+
+415
+00:45:06,140 --> 00:45:11,700
+اتنين لانه مقدار ثابت تكمل من واحد الى اربع تكمل
+
+416
+00:45:11,700 --> 00:45:18,660
+ال X ponential بال X ponential اتسلمبسومة على
+
+417
+00:45:18,660 --> 00:45:23,620
+تفاضل الأوس إذا كانت تفاضل الأوس من الدرجة الأولى
+
+418
+00:45:23,620 --> 00:45:28,120
+طبعا كل أسطن في Y إذا من الدرجة الأولى يبقى مبسومة
+
+419
+00:45:28,120 --> 00:45:35,120
+عداش يا بناه واحد على جدر ال X هذا الحكي كله بدية
+
+420
+00:45:35,120 --> 00:45:44,500
+من Zero لغاية جدر ال X وهذا DX اللي عندناطيب يبقى
+
+421
+00:45:44,500 --> 00:45:49,120
+بيصير المثلة تلاتة على اتنين تكمن واحد إلى أربع
+
+422
+00:45:49,120 --> 00:45:55,280
+هذه جدر ال X بتنجل و بتطلع وين؟ بتطلع فوق فالحين
+
+423
+00:45:55,280 --> 00:45:59,860
+هذي بيدي أشيل كل Y و أحط مكانها جدر X و أشيل كل Y
+
+424
+00:45:59,860 --> 00:46:04,660
+و أحط مكانها Zero يبقى Good لما أشيل Y و أحط
+
+425
+00:46:04,660 --> 00:46:13,460
+مكانها جدر X يبقى E أس يبقى E فاس NowE والزيرو على
+
+426
+00:46:13,460 --> 00:46:17,480
+جدر X بزيرو E والزيرو بواحد
+
+427
+00:46:19,610 --> 00:46:25,550
+يبقى ال E ناقص واحد صارت مقدار ثابت مظبوط يبقى كأن
+
+428
+00:46:25,550 --> 00:46:31,250
+المسألة أصبح تاندي تلاتة على اتنين اللي برا في E
+
+429
+00:46:31,250 --> 00:46:36,790
+ناقص واحد كله مقدار ثابت مانيش دعوة وهي تكامل من
+
+430
+00:46:36,790 --> 00:46:41,230
+واحد لبايت الأربعة لل X أص نص DX
+
+431
+00:46:43,760 --> 00:46:53,500
+يبقى السؤال عندي تلاتة على اتنين تلاتة
+
+432
+00:46:53,500 --> 00:46:58,300
+على اتنين تلاتة على اتنين تلاتة على اتنين تلاتة
+
+433
+00:46:58,300 --> 00:47:03,220
+على اتنين تلاتة على اتنين تلاتة على اتنين تلاتة
+
+434
+00:47:03,220 --> 00:47:03,600
+على اتنين تلاتة على اتنين تلاتة على اتنين تلاتة
+
+435
+00:47:03,600 --> 00:47:03,620
+على اتنين تلاتة على اتنين تلاتة على اتنين تلاتة
+
+436
+00:47:03,620 --> 00:47:04,220
+على اتنين تلاتة على اتنين تلاتة على اتنين تلاتة
+
+437
+00:47:04,220 --> 00:47:05,920
+على اتنين تلاتة على اتنين تلاتة على اتنين تلاتة
+
+438
+00:47:05,920 --> 00:47:08,400
+على اتنين تلاتة على اتنين تلاتة على اتنين تلاتة
+
+439
+00:47:08,400 --> 00:47:11,620
+على اتنين تلاتة على اتن
+
+440
+00:47:14,630 --> 00:47:21,570
+أربعة تكييب تحت الجدر التربيعي أربعة تكييب أربعة
+
+441
+00:47:21,570 --> 00:47:24,070
+وستين أربعة في أربعة في ستاشر في أربعة في أربعة
+
+442
+00:47:24,070 --> 00:47:29,510
+وستين تحت الجدر التربيعي بتمانية يبقى هذه في
+
+443
+00:47:29,510 --> 00:47:36,930
+تمانية ناقص واحد أسر بكيانه بواحد يبقى الجواب
+
+444
+00:47:36,930 --> 00:47:44,220
+النهائي سبعة في ناقص واحدهذه قيمة التكامل اللي
+
+445
+00:47:44,220 --> 00:47:45,560
+موجود عندنا
+
+446
+00:48:18,030 --> 00:48:25,370
+نمر بيه من السؤال بيقول
+
+447
+00:48:25,370 --> 00:48:33,150
+بدي تكامل من Zero لغاية تلاتة على اتنين تكامل اخر
+
+448
+00:48:33,150 --> 00:48:44,890
+من واحد لغاية اربعة ناقص اتنين U لمن؟ للاربعة ناقص
+
+449
+00:48:44,890 --> 00:49:03,030
+اتنين U علىV تربيع كل هذا الكلام دي V دي U طبعا
+
+450
+00:49:03,030 --> 00:49:06,350
+واضح أنه سهل أكون بالنسبة ل V بالأول لأن الأربع
+
+451
+00:49:06,350 --> 00:49:09,910
+ناقص اتنين U وهذا كله يعتبر constant إذا قُرِن
+
+452
+00:49:09,910 --> 00:49:15,970
+بالـV إذا بتروح أرسمله منطقة التكامل في الأولبقوله
+
+453
+00:49:15,970 --> 00:49:21,150
+كويس يجي انا بدل المحاور X Y بنتش صار عندي صار
+
+454
+00:49:21,150 --> 00:49:29,970
+المحور الأول U والمحور التاني V قال لي كويس V هي
+
+455
+00:49:29,970 --> 00:49:35,830
+ممكن تداشي بواحد يبقى في عندي خط أفقي هيك هذه V
+
+456
+00:49:35,830 --> 00:49:43,990
+تساوي واحدتانى V تساوي اربعة نقص اتنين U يبقى لما
+
+457
+00:49:43,990 --> 00:49:49,610
+اقول V تساوي اربعة نقص اتنين U معادلة ايه شهية
+
+458
+00:49:49,610 --> 00:49:53,410
+اللي هنا خط مستقيم خط المستقيم مش هان ارسمه
+
+459
+00:49:53,410 --> 00:49:59,730
+بكافيني نقطتين عليه بقوله ماشي لو كانت ال U ب zero
+
+460
+00:49:59,730 --> 00:50:05,710
+إذا V بقى ده يبقى باجي عند ال zero هي و باجي طالع
+
+461
+00:50:05,710 --> 00:50:11,970
+اربعة كويسيبقى هدا V هيو هنا و خليها لمين اللي هي
+
+462
+00:50:11,970 --> 00:50:16,810
+أربعة يبقى هدا النقطة Zero أربعة تقع على وين؟ على
+
+463
+00:50:16,810 --> 00:50:23,570
+الخط المستقيم لو كانت ال U مثلا هذه لو كانت ال U ب
+
+464
+00:50:23,570 --> 00:50:30,790
+Zero طب لو كانت ال U باتنينبتنين بتطلع ال V بزيرو
+
+465
+00:50:30,790 --> 00:50:35,150
+يبقى هذا اللي بدي أقطع الخط عند النقطة هنا جديد
+
+466
+00:50:35,150 --> 00:50:41,670
+اللي هي هذه اللي هي اتنين وزيرو بجي بمسك هذه
+
+467
+00:50:41,670 --> 00:50:48,510
+المصطرة و بوصل بين النقطتين و ببد الخط على استقالة
+
+468
+00:50:48,510 --> 00:50:55,070
+بهذا الشكل طبعا كويس نجي بعد هيكالـ U تتغير من
+
+469
+00:50:55,070 --> 00:50:58,890
+عندي الـ Zero لغاية تلاتة على اتنين تلاتة على
+
+470
+00:50:58,890 --> 00:51:03,310
+اتنين يعني كده؟ واحد و نص تلاتة على اتنين يبقى في
+
+471
+00:51:03,310 --> 00:51:11,830
+جيلك هنا واحد و نص تلاتة على اتنين طيب باجي بقول
+
+472
+00:51:11,830 --> 00:51:18,600
+طب لو كانت U تلاتة على اتنينلو كانت ال U بتلاتة
+
+473
+00:51:18,600 --> 00:51:24,320
+على اتنين بصير U ناقص تلاتة اليوم واحد يبقى هذه
+
+474
+00:51:24,320 --> 00:51:29,080
+بتيجي هنا بالضبط و بتتقابل وين عند النقطة هذه
+
+475
+00:51:29,080 --> 00:51:39,480
+تماما يبقى احنا كأنه عند المثلث المظلل هذا فقط
+
+476
+00:51:39,480 --> 00:51:46,840
+مابيهيبقى من هنا ال U تساوي Zero لغاية ال U تساوي
+
+477
+00:51:46,840 --> 00:51:51,980
+اللي هو تلاتة على اتنين المنطقة من هنا لغايتنا
+
+478
+00:51:51,980 --> 00:51:55,680
+طالعنا قابلنا مع الخطين اللي اتنين هدول صارت
+
+479
+00:51:55,680 --> 00:51:59,740
+المنطقة المضلة للزرق اللي قدامنا هذه يبقى هذه من
+
+480
+00:51:59,740 --> 00:52:04,170
+منطقة التكامل اللي موجودة عندناطيب، بدنا نروح
+
+481
+00:52:04,170 --> 00:52:13,010
+الكامل الآن، بدا الكامل بالنسبة .. كيف؟ هعكسلك
+
+482
+00:52:13,010 --> 00:52:16,530
+المحاور، بس اصبر شوية مش هالحين، بعد قليل، بعد ما
+
+483
+00:52:16,530 --> 00:52:20,250
+نخلص المثال هذا، هخليك بدل السؤال تلاتة تعكس
+
+484
+00:52:20,250 --> 00:52:26,870
+المحاور غصب عنك، مش بخاطرك، تمام؟ طيب، لو عكستي،
+
+485
+00:52:26,870 --> 00:52:31,170
+هيتغيروا الحدود، كل الأربع حدود ممكن يتغيروا كلهم
+
+486
+00:52:31,170 --> 00:52:37,230
+ولا واحد يظل زي التانيبس لو عكس بصير سهل أكمل
+
+487
+00:52:37,230 --> 00:52:41,370
+بالنسبة ل U كذلك، زي ما قاله سهل أكمل بالنسبة ل V،
+
+488
+00:52:41,370 --> 00:52:46,490
+يبجد كأنه بدا كامل مين؟ بالنسبة ل V بدا كامل مين؟
+
+489
+00:52:46,490 --> 00:52:50,210
+واحد على V تربية، لأن أربعة نقص اتنين U يعتبر
+
+490
+00:52:50,210 --> 00:52:56,990
+كنصة، وتكامل واحد على V تربية بقداش؟- 1 على V إذا
+
+491
+00:52:56,990 --> 00:53:02,290
+هذي لو جاءت كملة بدى يصير تكمل من Zero لتلاتة على
+
+492
+00:53:02,290 --> 00:53:07,670
+اتنين وهنا اربعة نقص اتنين U مالكش دعوة وهذه
+
+493
+00:53:07,670 --> 00:53:14,610
+تكملها ب- 1 على V وبيجي اقول من هنا من واحد لاربعة
+
+494
+00:53:14,610 --> 00:53:17,690
+نقص اتنين U في الديل
+
+495
+00:53:20,650 --> 00:53:25,070
+يبقى هذا الكلام بيساوي تكامل من 0 إلى 3 على 2
+
+496
+00:53:25,070 --> 00:53:30,950
+للاربعة ناقص 2U فيه فتعود بالقيمة اللي فوق ناقص
+
+497
+00:53:30,950 --> 00:53:37,190
+اللي تحت يبقى ناقص واحد على اربعة ناقص اتنين U
+
+498
+00:53:37,190 --> 00:53:42,290
+ناقص مع ناقص بصير زائد واحد على واحد اللي يبقى
+
+499
+00:53:42,290 --> 00:53:50,520
+درجة واحد يبقى عوضنا بالقيمة اللي فوقنقص القيمة
+
+500
+00:53:50,520 --> 00:53:55,980
+اللي تحصل بالشكل هذه وكل هذا بالنسبة لمن؟ لل DU
+
+501
+00:53:55,980 --> 00:54:01,100
+يساوي integration من زيرو لغاية تلاتة على تالتة
+
+502
+00:54:01,100 --> 00:54:06,880
+بدا افك الجثة ده بنات وشير جداش عندي هنا ناقص واحد
+
+503
+00:54:06,880 --> 00:54:15,200
+وهنا زائد اربع ناقص اتنين U كله بالنسبة ل DUيبقى
+
+504
+00:54:15,200 --> 00:54:19,660
+هذا بيصير تكامل من zero لغاية تلاتة على اتنين
+
+505
+00:54:19,660 --> 00:54:26,960
+لمين؟ ليه تلاتة نقص اتنين يهودي؟ هذه لو روحت
+
+506
+00:54:26,960 --> 00:54:33,690
+كاملتها تعطيلي ما يأتي يساوياللي هو مين؟ تلاتة U
+
+507
+00:54:33,690 --> 00:54:39,530
+ناقص U تربيع على اتنين بتروح مع الاتنين وانحكي هذا
+
+508
+00:54:39,530 --> 00:54:45,390
+كله بالهند ال zero لغاية تلاتة على اتنين و U ساوي
+
+509
+00:54:45,390 --> 00:54:51,750
+تلاتة على اتنين بيصير كده؟ تسعة على اتنين ناقص
+
+510
+00:54:51,750 --> 00:54:57,320
+تلاتة على اتنين تربيع بتسعة على اربعةنقص تسعة على
+
+511
+00:54:57,320 --> 00:55:04,640
+أربعة نقص زيرو زائد زيرو يبقى تسعة على اتنين نقص
+
+512
+00:55:04,640 --> 00:55:09,680
+تسعة على أربعة يبقى تسعة على أربعة
+
+513
+00:55:39,360 --> 00:55:47,900
+ناخد كمان مثال مثال اتنين بيقول sketch the region
+
+514
+00:55:47,900 --> 00:55:56,700
+of integration sketch that region of
+
+515
+00:55:56,700 --> 00:56:02,160
+integration of
+
+516
+00:56:02,160 --> 00:56:08,060
+some من منطقة التكامل عن ال right
+
+517
+00:56:13,420 --> 00:56:20,200
+فاصلة right right
+
+518
+00:56:20,200 --> 00:56:31,140
+and evaluate the
+
+519
+00:56:31,140 --> 00:56:38,580
+equivalent double
+
+520
+00:56:38,580 --> 00:56:39,160
+integral
+
+521
+00:56:48,010 --> 00:56:53,190
+with the order of with
+
+522
+00:56:53,190 --> 00:56:58,970
+the order of
+
+523
+00:56:58,970 --> 00:57:05,250
+integration reversed
+
+524
+00:57:05,250 --> 00:57:11,550
+أمر
+
+525
+00:57:11,550 --> 00:57:20,800
+a يتكاول من zero لغاية اتنينتكامل من سالب الجدرى
+
+526
+00:57:20,800 --> 00:57:25,740
+التربيع إلى أربعة ناقص x تربية للجدرى التربيع إلى
+
+527
+00:57:25,740 --> 00:57:32,560
+أربعة ناقص x تربية إلى ستة x dy dx
+
+528
+00:58:07,780 --> 00:58:13,540
+سؤال عبارة عن ثلاث مطاليب ارسم منطقة التكامل 2
+
+529
+00:58:13,540 --> 00:58:18,800
+اكتب لي واحسب لي equivalent double integrals with
+
+530
+00:58:18,800 --> 00:58:22,220
+order of integration reversed يعني ايش؟ يعني بدي
+
+531
+00:58:22,220 --> 00:58:27,340
+اغير حدود التكامل اللي عندنا هذه زي السؤال اللي
+
+532
+00:58:27,340 --> 00:58:32,060
+سألته قبل قليل ومن ثم بعد ما اغير حدود التكامل بدي
+
+533
+00:58:32,060 --> 00:58:37,050
+اروح احسب من التكاملتعالوا هنشوف كيف بدنا نرسم
+
+534
+00:58:37,050 --> 00:58:41,550
+الرسمة وكيف نتغير حدود التكامل وبعدين التكامل يصبح
+
+535
+00:58:41,550 --> 00:58:45,330
+روتينيا زي ما حسبنا قبل شوية بنحسب هذا التكامل
+
+536
+00:58:45,330 --> 00:58:51,370
+ابقى بروح باخد المحاور اللي عندنا بهذا الشكل بقش
+
+537
+00:58:51,370 --> 00:58:56,650
+بقول هذا محور X هذا محور Y هذا نحو الأصل اللي هي
+
+538
+00:58:56,650 --> 00:59:02,830
+Zero هذه المناط لما أجي لأول متغير عندي Y يبقى Y
+
+539
+00:59:02,830 --> 00:59:10,750
+تساوي هذا الجدر يبقى لو جربه الحل كتالي ال Y تساوي
+
+540
+00:59:10,750 --> 00:59:14,790
+الجدر التربيع إلى أربعة نقص X تربيع بدي أرفع
+
+541
+00:59:14,790 --> 00:59:22,150
+معادلتيش لو ربعت الطرفين مش بصير بنات بصير Y تربيع
+
+542
+00:59:22,150 --> 00:59:28,760
+زائد X تربيع تساوي أربعةمعادلة ايه؟ هاي دائرة
+
+543
+00:59:28,760 --> 00:59:33,200
+ممتاز لكن هل هي دائرة كاملة ولا نص دائرة ولا
+
+544
+00:59:33,200 --> 00:59:37,080
+مدائرة ولا ثلاث تربع دائرة هذا اللي احنا مش عارفين
+
+545
+00:59:37,080 --> 00:59:41,820
+كويس اللي بيحددوا مين قيم واحد طب القيم اللي فوق
+
+546
+00:59:41,820 --> 00:59:46,420
+هي نفس القيم اللي تحت بس بالمئة بشرة سلمإحنا عندنا
+
+547
+00:59:46,420 --> 00:59:51,420
+Y الموجبة و Y السالبة طب Y الموجبة و Y السالبة قد
+
+548
+00:59:51,420 --> 00:59:55,380
+يكون على اليمين و قد يكون على الشمال و قد يكون
+
+549
+00:59:55,380 --> 01:00:01,300
+كليهما اللي بده يحدد مين حدود التكمل تبع ال X ال X
+
+550
+01:00:01,300 --> 01:00:05,960
+هتتغير من Zero لغاية اتنين يعني مين؟ هي الدائرة
+
+551
+01:00:05,960 --> 01:00:11,700
+المصبوخة للدرجة النصف اللي على اليمين فقط يبقى هذه
+
+552
+01:00:11,700 --> 01:00:13,660
+دائرة بهذا الشكل
+
+553
+01:00:18,830 --> 01:00:24,230
+الشكل اللي على الشمال هذا مش موجود فالرسم تهلك
+
+554
+01:00:24,230 --> 01:00:31,210
+هيوم بيكون منقط بهذا الشكل تمام؟
+
+555
+01:00:31,210 --> 01:00:37,170
+يبقى هذا يبقى هاي المنطقة اللي عندنا هاي المنطقة
+
+556
+01:00:37,170 --> 01:00:41,920
+اللي احنا بنكامل عليهايبقى أنا لسه عملت المطلوب
+
+557
+01:00:41,920 --> 01:00:46,980
+الأول رسمت منطقة التكامل جبتها من وين؟ جبتها من
+
+558
+01:00:46,980 --> 01:00:52,400
+الحدود اللي موجودة عندى، بعد هيك قال لي بدك تكتب
+
+559
+01:00:52,400 --> 01:00:57,020
+التكامل بعد ما تقلب حدود التكامل، ايش اقلب حدود
+
+560
+01:00:57,020 --> 01:01:01,420
+التكامل؟ احط هدف الأول و هدف الآخر؟أو مارضي ما
+
+561
+01:01:01,420 --> 01:01:06,360
+هنجيب نتيجة، هايش نسوي لأ بدل ما كنت بتكامل
+
+562
+01:01:06,360 --> 01:01:11,360
+بالنسبة ل Y وبعدين بالنسبة ل X في الأول وبعدين
+
+563
+01:01:11,360 --> 01:01:19,280
+بالنسبة إلى Y يبقى هذا التكامل بيصير تكاملية ل 6X
+
+564
+01:01:19,280 --> 01:01:27,060
+DX DY إذا بدي أشوف X بدي تتغير من وين ل وينباجى
+
+565
+01:01:27,060 --> 01:01:33,420
+بنات برسم خط يوازي محور X ويقطع منطقة التكامل هاي
+
+566
+01:01:33,420 --> 01:01:40,400
+خاط زي ما تشايفينه يبقى هنا X بقداش؟ عند هذه
+
+567
+01:01:40,400 --> 01:01:45,700
+النقطة، قداش قيمة X؟ Zero، يبقى هنا Zero، تمام،
+
+568
+01:01:45,700 --> 01:01:52,490
+هذي مين؟هذه الدائرة X تربيه زائد Y تربيه يسوى من R
+
+569
+01:01:52,490 --> 01:01:52,910
+تربيه
+
+570
+01:02:04,140 --> 01:02:11,420
+أو X يساوي الجذري التربيعي للاربع ناقص من Y تربيعي
+
+571
+01:02:11,420 --> 01:02:17,060
+واخد X الموجبة فقط لأنه ماعنديش X سالبة يبقى مصير
+
+572
+01:02:17,060 --> 01:02:23,200
+من الجذري التربيعي للاربع ناقص Y تربيعي
+
+573
+01:02:25,940 --> 01:02:31,020
+كداش أقل قيمة بده تاخدها Y و أكبر قيمة بده تاخدها
+
+574
+01:02:31,020 --> 01:02:36,340
+Y يبقى
+
+575
+01:02:36,340 --> 01:02:41,600
+هذا هنا سالب اتنين وهذا هنا من اتنين او نشوف من
+
+576
+01:02:41,600 --> 01:02:45,820
+فاقله النقطة هذه احدثية Zero اتنين وهذه احدثية
+
+577
+01:02:45,820 --> 01:02:52,280
+Zero سالب اتنين إذا من سالب اتنين للاتنين
+
+578
+01:02:54,310 --> 01:02:57,850
+يبقى شايفين كيف بغير حدود التكامل؟ بغير حدود
+
+579
+01:02:57,850 --> 01:03:02,790
+التكامل من المنطقة تبعتي التكامل، مش بمزاجي، بدل
+
+580
+01:03:02,790 --> 01:03:05,990
+هذا مكان هذا و هذا مكان هذا و امشي، لأ، الان
+
+581
+01:03:05,990 --> 01:03:11,690
+المنطقة او حدود التكامل على الدالة هذه اضطرت تماما
+
+582
+01:03:11,690 --> 01:03:16,190
+لو حسبناها بزا ساوي نفس القيمة اللي عندنا فور،
+
+583
+01:03:16,190 --> 01:03:17,350
+اللي مساحة تمغط
+
+584
+01:03:25,440 --> 01:03:30,260
+بنكمل بالنسبة ل X بالنسبة ل Y
+
+585
+01:03:36,230 --> 01:03:42,030
+والحكي هذا من Zero لغاية الجدر التربيعي للأربعة
+
+586
+01:03:42,030 --> 01:03:49,070
+ناقص Y تربيعي وهي ال DIY وهي التكامل من صفر من
+
+587
+01:03:49,070 --> 01:03:57,890
+سالق اتنين لغاية اتنين طيب بصير المسألة ساوية ستة
+
+588
+01:03:57,890 --> 01:04:03,540
+على اتنين بتلاتة خليها براوتكابل من سالي باتنين
+
+589
+01:04:03,540 --> 01:04:09,800
+للاتنين وضل عندي هنا ماين X تربية لما اعوض بطير
+
+590
+01:04:09,800 --> 01:04:17,840
+الجدر و بظل قداشر بس ارفع ناقص Y تربية ناقص Zero
+
+591
+01:04:17,840 --> 01:04:21,880
+يبقى مع السلامة عوض بالقناة Zero بتروح بالشكل اللي
+
+592
+01:04:21,880 --> 01:04:30,300
+عندنا هذا بصير بس هيك بYأسأل السؤال التالف الدالة
+
+593
+01:04:30,300 --> 01:04:36,100
+اللي بدي أكملها قد و الله even هذه even
+
+594
+01:04:36,100 --> 01:04:39,480
+يبقى اطلع على الرقم اللي هنا و الرقم اللي هنا
+
+595
+01:04:39,480 --> 01:04:47,280
+اتنين نفس الشيءيبقى اتنين التكامل على نصف المنطقة
+
+596
+01:04:47,280 --> 01:04:50,780
+يبقى
+
+597
+01:04:50,780 --> 01:04:54,120
+هذا الكلام يبدو يساوي هي التلاتة اللي برا وهي
+
+598
+01:04:54,120 --> 01:04:58,680
+جيبنا لها كمان اتنين وتكامل صار من صفر لاتنين بدل
+
+599
+01:04:58,680 --> 01:05:04,240
+من سالب اتنين للاتنين لمين للاربع ناقص Y تربيه
+
+600
+01:05:04,240 --> 01:05:15,350
+اعضى Yيبقى النتيجة 6 في 4Y ناقص Y تكيب على 3 كل
+
+601
+01:05:15,350 --> 01:05:24,210
+هذا الحكي من Zero لغاية كده اش لغاية اتنين يسام 6
+
+602
+01:05:24,210 --> 01:05:31,160
+ايها براتمام؟ وهذا هنا بنصير عندنا اتنين في اربعة
+
+603
+01:05:31,160 --> 01:05:39,080
+في تمانية وهنا ناقص اللي هو تمانية على تلاتة وهذه
+
+604
+01:05:39,080 --> 01:05:43,720
+زيرو زيرو بتروح كلها مع السلامة يبقى هذا الكلام
+
+605
+01:05:43,720 --> 01:05:49,560
+بتساوي ستة في تلاتة في تمانيةأربعة و عشرين و نزل
+
+606
+01:05:49,560 --> 01:05:55,400
+منها تمانية درجة داشر ستة عشر على تلاتة تلاتة مع
+
+607
+01:05:55,400 --> 01:06:00,700
+ستة مولتين في ستة عشر باتنين و تلاتين يبقى هذا
+
+608
+01:06:00,700 --> 01:06:06,940
+مقدار اللي هو التكامل اللي عندي طب هذا نمرأ ايه من
+
+609
+01:06:06,940 --> 01:06:15,540
+المثل نمرأ بيه؟ نريد تكامل ايه؟ من واحد لغاية ال E
+
+610
+01:06:16,340 --> 01:06:22,360
+ومن الـ zero لغاية لإن ال X لل X Y
+
+611
+01:06:27,700 --> 01:06:30,720
+طبعا يا بنات ان انا بقدر اكمل دغري بدون مجلب لكن
+
+612
+01:06:30,720 --> 01:06:36,120
+هو امرني امر طلب مني قال روح اجلب حدود التكامل و
+
+613
+01:06:36,120 --> 01:06:40,300
+بعد هيك بتروح تحسبلي هذا التكامل اذا بروح ارسمله
+
+614
+01:06:40,300 --> 01:06:45,580
+مين؟ منطقتي التكامل فباشي بقوله هذه المحاول اللي
+
+615
+01:06:45,580 --> 01:06:53,220
+عندنا هذا محور X هذا محور Y هذه نقطة الاصلأنا بدأ
+
+616
+01:06:53,220 --> 01:06:57,540
+أكبر بالنسبة نوائي الجهادي Y تساوي Zero Y تساوي
+
+617
+01:06:57,540 --> 01:07:04,580
+Zeroهذا y تساوي zero اللي بعد هو y تساوي لن ال x
+
+618
+01:07:04,580 --> 01:07:09,540
+سابق و درسنا في calculus A و أفرضنا له section
+
+619
+01:07:09,540 --> 01:07:14,080
+كامل أول ما دخلتي على calculus B كان هذا هو
+
+620
+01:07:14,080 --> 01:07:18,180
+section رقم اتنين أخدت هو section معكوس الدالة ثم
+
+621
+01:07:18,180 --> 01:07:23,140
+ال natural لغة رتب يبقى المنحنة كان بهذا الشكل
+
+622
+01:07:27,420 --> 01:07:34,140
+يبقى هذا النقطة اليمين واحد وزير وهذا ال Y تساوي
+
+623
+01:07:34,140 --> 01:07:39,800
+لل Xيبقى رسمنا هذا هو رسمنا هذا بالنسبالي Y نجي ال
+
+624
+01:07:39,800 --> 01:07:46,520
+X جالي X تساوي واحد و X تساوي E و اين ال X تساوي
+
+625
+01:07:46,520 --> 01:07:52,960
+واحد يبقى هذا القط الموازي لمحور Y و اللي بدي ييجي
+
+626
+01:07:52,960 --> 01:07:58,320
+على نفس النقطة لان هذه واحد يبقى هذا X يساوي واحد
+
+627
+01:08:06,090 --> 01:08:12,430
+يبقى بده يجينا الشكل هذا يبقى هذا X يساوي E إذا
+
+628
+01:08:12,430 --> 01:08:17,130
+المنطقة اللي محصورة بينهم وين هي المنطقة المضللة
+
+629
+01:08:17,130 --> 01:08:24,330
+اللي عندها يبقى هذه منطقة التكامل بقوله كويس هذا
+
+630
+01:08:24,330 --> 01:08:30,550
+التكامل بده يساوي يعني تكامل ايه؟ XY زي ما هم بس
+
+631
+01:08:30,550 --> 01:08:31,430
+بدي أقلب
+
+632
+01:08:38,190 --> 01:08:46,130
+بارسم خط موازن لمحور X ويقطع منطقة التكامل الشكل
+
+633
+01:08:46,130 --> 01:08:52,750
+اللي علناه هذا يبقى قطع منطقة التكامل في النقطتين
+
+634
+01:08:52,750 --> 01:08:58,590
+بدي اعرف كم هو X هنا وكم هو X هنا
+
+635
+01:09:01,240 --> 01:09:07,440
+هذا التقى على المنحنى y تساوي لن ال x يبقى احنا
+
+636
+01:09:07,440 --> 01:09:14,780
+عندنا هنا y تساوي لن ال x إذا نقدر نجيب x من هذه
+
+637
+01:09:14,780 --> 01:09:22,580
+المعادلة ارفع تلك أُس للعدد E بصير E أُس Y يساوي
+
+638
+01:09:22,580 --> 01:09:31,660
+كده؟ X يبقى هناهه بدفع أقل قيمة ل X ليه جداش E أُس
+
+639
+01:09:31,660 --> 01:09:39,520
+Y و أكبر قيمة جداش اما نادر E يبقى من E أُس Y إلى
+
+640
+01:09:39,520 --> 01:09:49,800
+E طيب نجي لل Y جداش أقل قيمة عندنا هنا أقل قيمة ل
+
+641
+01:09:49,800 --> 01:09:50,900
+Y Zero
+
+642
+01:09:54,130 --> 01:10:00,430
+لغاية أكبر قيمة عند ال human هنا هنا نقطة مشتركة
+
+643
+01:10:00,430 --> 01:10:04,650
+ما بين الخط وهنا يبقى هشيل ال X وحط مكانها E بس
+
+644
+01:10:04,650 --> 01:10:08,610
+اللي ان ال E بيبقى ده ال واحد يبقى بصير هذي من
+
+645
+01:10:08,610 --> 01:10:13,210
+Zero لغاية واحد اتطلع في الحدود اللي قبله اتطلع في
+
+646
+01:10:13,210 --> 01:10:18,170
+الحدود هذيولا واحد ان شغل بقى ticket غير شكل مظبوط
+
+647
+01:10:18,170 --> 01:10:24,510
+يبقى لكن هذه تطابق أو تكافئ تماما الحدود الأولى
+
+648
+01:10:24,510 --> 01:10:29,250
+يبقى ماضالش عندي إلا ماين إلا عملية التكامل يبقى
+
+649
+01:10:29,250 --> 01:10:33,990
+هذا الكلام بتساوي تكامل من صفر لغاية واحد وانت يا
+
+650
+01:10:33,990 --> 01:10:38,550
+واي مالكش دعوة يبقى صف على شجة وتكامل ال X ب X
+
+651
+01:10:38,550 --> 01:10:44,840
+تربيع على اتنينوالكلام هذا من E قص Y لغاية E وهذا
+
+652
+01:10:44,840 --> 01:10:51,970
+الـ D Yهذا الكلام بدل سوية نص و آيتها كامل من صفر
+
+653
+01:10:51,970 --> 01:10:57,010
+لواحد وهي ال Y و بدعوض القيمة اللي فوق ناقص القيمة
+
+654
+01:10:57,010 --> 01:11:01,050
+اللي تحت لإن بدي أشيل ال X و أضع مكانها E يصير
+
+655
+01:11:01,050 --> 01:11:07,770
+عندي E تربيع ناقص القيمة اللي تحت E أس Y لكل تربيع
+
+656
+01:11:07,770 --> 01:11:16,480
+يعني E أس اتنين Y كله بالنسبة لمن؟ لدي Yيبقى كأن
+
+657
+01:11:16,480 --> 01:11:21,220
+المسألة النُص اللي برا و هي تكمل من صفر لواحد، بدي
+
+658
+01:11:21,220 --> 01:11:28,660
+أفكر جوز هنا بنات يمشي بصير E تربيع Y Dy وهنا ناقص
+
+659
+01:11:28,660 --> 01:11:37,100
+نُص تكمل من صفر لغاية واحد لل Y في E أُس 2Y في Dy
+
+660
+01:11:39,850 --> 01:11:45,250
+طبعا هذا بسيط جدا يبقى هذا نص مالكش دعم و ال E
+
+661
+01:11:45,250 --> 01:11:52,490
+تربيع مقدار ثابت زيه و تكامل ال Y بY تربيع على 2
+
+662
+01:11:52,490 --> 01:11:57,290
+من صفر لغاية واحد طب و ايش رأيكوا في هذه
+
+663
+01:11:57,290 --> 01:12:01,610
+integration
+
+664
+01:12:01,610 --> 01:12:06,190
+by parts يبقى باجي بقوله ان انا بدي اخد
+
+665
+01:12:06,190 --> 01:12:06,950
+derivatives
+
+666
+01:12:10,490 --> 01:12:16,150
+وداخل هنا integrals هنا
+
+667
+01:12:16,150 --> 01:12:22,950
+Y وهنا E أس اتنين Y لو فضلناها كده شو يطلع هنا
+
+668
+01:12:22,950 --> 01:12:28,510
+منها؟ واحد لو كملتها بصير E أس اتنين Y على اتنين
+
+669
+01:12:28,510 --> 01:12:33,270
+لو فضلت كمان مرة ب Zero لو كملتها كمان مرة بصير E
+
+670
+01:12:33,270 --> 01:12:38,650
+أس اتنين Y على مين؟ على أربع هدف هدف إشارة موجب
+
+671
+01:12:41,910 --> 01:12:55,050
+يبقى هنا ناقص نص وهي نتيجة التكامل نقص ي إي أس
+
+672
+01:12:55,050 --> 01:13:05,350
+اتنين ي ناقص رابع ي إي أس اتنين ي وكل هذا كله من
+
+673
+01:13:05,350 --> 01:13:11,650
+زيرو لغاية كم؟ لغاية واحدةيبقى هنا الكلام الرابع
+
+674
+01:13:11,650 --> 01:13:18,970
+اي تربيع حط واحد تطلع بعض حط zero بالطير يبقى رابع
+
+675
+01:13:18,970 --> 01:13:25,170
+اي تربيع اللي همان التكامل الأول نجل التكامل
+
+676
+01:13:25,170 --> 01:13:34,650
+الثاني يبقى ناقص رابع وهنا ال Y بواحد وهنا اي
+
+677
+01:13:34,650 --> 01:13:35,490
+تربيع
+
+678
+01:13:38,390 --> 01:13:46,910
+نقص في نقص بزايد نص في ربع بالتمون تمام و هنا تمون
+
+679
+01:13:46,910 --> 01:13:55,150
+ات الربيع بعدها زيرو اه هذه اللي بعدها هي زيرو
+
+680
+01:13:55,150 --> 01:14:06,970
+يبقى هنا نقص مع نقص بسيط زائد زيروزائد زيرو هذه و
+
+681
+01:14:06,970 --> 01:14:11,090
+هذه بتجيكي الناقص مع ناقص بيصير زائد و ناقص بتجيكي
+
+682
+01:14:11,090 --> 01:14:17,490
+كمان بيصير ناقص الرابع و هنا بيجيكي التمن لإنه في
+
+683
+01:14:17,490 --> 01:14:22,390
+نص برا و هنا ايه و ال zero اللي هو بقداش ابواع
+
+684
+01:14:22,390 --> 01:14:27,890
+الرابع مع رابع بالسالف الله ساهل عليه يبقى طالع
+
+685
+01:14:27,890 --> 01:14:35,740
+انا كده شبنات يساوي التمن في ايه؟تربية ماخص واحد،
+
+686
+01:14:35,740 --> 01:14:39,740
+هذا قيمة مين؟ قيمة هذا التكابن
+
+687
+01:15:00,630 --> 01:15:04,770
+يلا وورقة وكتب اسمك ورقمك الجامعي ومرريها عليهم
+
+688
+01:15:04,770 --> 01:15:16,010
+طيب أروح لنمرة C من المثلة نرجع لمرة C نمرة C
+
+689
+01:15:16,010 --> 01:15:23,190
+بيقول تكامل من سفر لغاية 2 تكامل من سفر لغاية 4
+
+690
+01:15:23,190 --> 01:15:34,510
+ناقص X تربيةلمن؟ لل X بـ E كسي 2Y على 4 نفس Y dy
+
+691
+01:15:34,510 --> 01:15:43,050
+dx المطموب
+
+692
+01:15:43,050 --> 01:15:48,350
+الأول اللي بدها ايه؟ ارسمله منطقة التكامل بقوله
+
+693
+01:15:48,350 --> 01:15:57,920
+بسيطة هي المحاور على محور Xهذا اللي عندنا محور Y
+
+694
+01:15:57,920 --> 01:16:04,000
+وهذه نقطة الأصل اللي هي من الـ Zero الآن تكمل أول
+
+695
+01:16:04,000 --> 01:16:09,700
+بالاسم ل Y يبقى Y تساوي Zero يبقى هذا اللي هو Y
+
+696
+01:16:09,700 --> 01:16:16,690
+تساوي Zero اللي بعدين Y تساوي أربعة ناقص X ترميةY
+
+697
+01:16:16,690 --> 01:16:25,430
+تساوي أربع ناقص X تربيعك إلى أعلى Y تساوي X تربيعك
+
+698
+01:16:25,430 --> 01:16:27,690
+إلى أعلى Y تساوي X تربيعك إلى أعلى Y تساوي X
+
+699
+01:16:27,690 --> 01:16:33,610
+تربيعك إلى أعلى Y تساوي X تربيعك إلى أعلى Y تساوي
+
+700
+01:16:33,610 --> 01:16:35,910
+X تربيعك إلى أعلى
+
+701
+01:16:37,910 --> 01:16:40,530
+بس أنا مش عارف هيكل ال parabola و الله نقصها دي
+
+702
+01:16:40,530 --> 01:16:44,690
+لبالك لسه احنا مش عارفين يبقى بنجي لمين لحدود
+
+703
+01:16:44,690 --> 01:16:50,550
+التكمل ال X هتتغير من عند Zero لغاية اتنين طيب اه
+
+704
+01:16:50,550 --> 01:16:54,810
+لو جتلى ال parabola هذه على هذا الخط Y تساوي Zero
+
+705
+01:16:54,810 --> 01:17:01,530
+إذا ال X بيصير هنا هذا Y تساوي Zero وهنا ال X
+
+706
+01:17:01,530 --> 01:17:07,660
+يساوي اتنين وهنا اليمينفنقص اتنين احنا عندنا من
+
+707
+01:17:07,660 --> 01:17:12,940
+Zero لغاية اتنين يبقى بيننا عليا المنطقة هذه كلها
+
+708
+01:17:12,940 --> 01:17:19,880
+مالها مش موجودة تمام يبقى عندنا فقط المنطقة
+
+709
+01:17:19,880 --> 01:17:26,880
+المضللة اللي عندنا هي اللي بنكمل عليها ما بين Y2
+
+710
+01:17:26,880 --> 01:17:32,060
+سواء Zero ومجان المنحنة و ما بين X في Zero و X بي
+
+711
+01:17:32,060 --> 01:17:32,820
+اتنين
+
+712
+01:17:38,930 --> 01:17:45,170
+خلّيني أسأل سؤال حد فيكم تقدر تكامل هالي أولا
+
+713
+01:17:45,170 --> 01:17:50,780
+بالنسبة إلى why؟لو ما قلليش اجلب و اعطيتك السؤال
+
+714
+01:17:50,780 --> 01:17:55,300
+زي هي حد فيكوا بتقدروا تكمل هذه بالنسبة ل Y ولا زي
+
+715
+01:17:55,300 --> 01:18:00,680
+ايه؟ ماقدرش اكمل بالنسبة ل Y تمام؟ اجباري حتى لو
+
+716
+01:18:00,680 --> 01:18:04,220
+ماقليش و ماقدرش اكمل دي اجلب هذه اجباري و اروح
+
+717
+01:18:04,220 --> 01:18:12,000
+انكمل بالنسبة لمن؟ بالنسبة إلى X يبقى هذه هيك كلها
+
+718
+01:18:12,000 --> 01:18:18,480
+ماليش علاقة فيها دي ماقدرش اكملها بالنسبة لمن؟Y
+
+719
+01:18:18,480 --> 01:18:23,240
+إذا إجباري حجم المثلة بالنسبة ل X يبقى هذه بدها
+
+720
+01:18:23,240 --> 01:18:31,860
+تساوي تكاملين لمين؟ ل X ال E أس اتنين Y على أربع
+
+721
+01:18:31,860 --> 01:18:39,500
+نقص Y DX DY بدي أرجع على رأس ال T ومن خلالها أحدد
+
+722
+01:18:39,500 --> 01:18:47,000
+حدود التكاملبنشوف X تتغير من أين لأين برسم خط
+
+723
+01:18:47,000 --> 01:18:49,860
+موازي لمحور X وبشوف
+
+724
+01:18:58,460 --> 01:19:05,420
+هذه المنحنة Y تساوي أربع ناقص X تربيع
+
+725
+01:19:14,380 --> 01:19:20,940
+خد الجدر يبقى x يساوي الجدر التربيه ل 4-y وباخد
+
+726
+01:19:20,940 --> 01:19:25,420
+القيمة الموجبة لإن السلبة مش عندى مش موجودة السلبة
+
+727
+01:19:25,420 --> 01:19:29,700
+الشجة هذه لكن احنا على المنطقة المضللة يبقى لغاية
+
+728
+01:19:29,700 --> 01:19:33,560
+الجدر التربيه ل 4-y
+
+729
+01:19:40,250 --> 01:19:46,970
+أربعة معروفة يبقى من Zero لغاية أربعة شايفة الخدود
+
+730
+01:19:46,970 --> 01:19:49,970
+اللي فوق و اللي كيف و اللي تحت يجدوا مختلفات عن
+
+731
+01:19:49,970 --> 01:19:54,370
+بعض تماما يبقى بنروحها كامل بالنسبة ل X يبقى هذا
+
+732
+01:19:54,370 --> 01:20:00,280
+يعتبر كله مرتاراإذاً هذا الكلام بدل سوى تكامل من
+
+733
+01:20:00,280 --> 01:20:06,320
+Zero إلى أربعة لل X تربيع على اتنين والكلام هذا من
+
+734
+01:20:06,320 --> 01:20:13,820
+Zero للأربعة ناقص Y تحت الجدر في مين بال E أسطل ال
+
+735
+01:20:13,820 --> 01:20:23,000
+Y على أربعة ناقص Y Dy لأن DX خلصنا منها تبقى Dyطيب
+
+736
+01:20:23,000 --> 01:20:27,940
+هذا الكلام يساوي أظن النص لو خلّيته برا مافي مشكلة
+
+737
+01:20:27,940 --> 01:20:32,140
+هو هي تكامل من zero إلى أربعة بتعود بالقيمة اللي
+
+738
+01:20:32,140 --> 01:20:38,940
+فوق لما ركّعها بطيير الجدر يبقى بيصير أربعة ناقص Y
+
+739
+01:20:40,280 --> 01:20:45,560
+والتحت Zero مع السلام الله سهل عليها هذا كله مضروب
+
+740
+01:20:45,560 --> 01:20:52,380
+في مين؟ في ال E أسنين Y على الأربع ناقص Y كله
+
+741
+01:20:52,380 --> 01:20:57,380
+بالنسبة الى Dy أظن يختصر الجوس اللي فوق مع الجوس
+
+742
+01:20:57,380 --> 01:20:59,960
+اللي تحت وبصير المسألة
+
+743
+01:21:06,670 --> 01:21:10,850
+بتبسط المسألة اللي كانت معقدة في الأول لأ يمكن
+
+744
+01:21:10,850 --> 01:21:17,490
+صارت مسألة بسيطة جدا يبدأ هذا نص وهذا E أس اتنين Y
+
+745
+01:21:17,490 --> 01:21:24,690
+على اتنين وهذا من Zeroيبقى هذا الكلام بيساوي
+
+746
+01:21:24,690 --> 01:21:32,590
+الرابع في ال E أس تمانية ناقص E أس Zero لو قداشر
+
+747
+01:21:32,590 --> 01:21:37,150
+الواحد يبقى رابع في E أس تمانية ناقص
+
+748
+01:21:43,770 --> 01:21:48,930
+يبقى هذا النوع من المسائل أجبرنا إجبارا على إن
+
+749
+01:21:48,930 --> 01:21:54,230
+الروح احنا نغير حدود التكامل مش زي المجموعة الأولى
+
+750
+01:21:54,230 --> 01:21:59,450
+من المسائل يبقى هذا بيختلف شوية عن المجموعة الأولى
+
+751
+01:21:59,450 --> 01:22:05,150
+لإن احنا غيرنا حدود التكامل وبالتالي حسبنا اللى هو
+
+752
+01:22:05,150 --> 01:22:11,600
+حدود التكامل اللى عندناالان نجي للمجموعة الثانية
+
+753
+01:22:11,600 --> 01:22:17,040
+من المسالي مثلا two مثلا
+
+754
+01:22:17,040 --> 01:22:25,160
+او لنقطة تانية من هذا ال section اللي هو finding
+
+755
+01:22:25,160 --> 01:22:29,540
+limits
+
+756
+01:22:29,540 --> 01:22:32,960
+of integration
+
+757
+01:22:40,530 --> 01:22:45,850
+إحنا بدنا نجيب حدود التكامل، مش يعطيها اللي هو
+
+758
+01:22:45,850 --> 01:22:52,110
+ورسم المنطقة، لا، انت بدك تحدد حدود التكامل نعطي
+
+759
+01:22:52,110 --> 01:22:52,670
+مثال
+
+760
+01:22:59,860 --> 01:23:06,600
+واللي find the volume of the solid find the volume
+
+761
+01:23:06,600 --> 01:23:19,820
+of the solid بده كدهش حجم المجسم that is bounded و
+
+762
+01:23:19,820 --> 01:23:25,960
+اللي بيكون محدود above by
+
+763
+01:23:31,930 --> 01:23:45,790
+السيلندر بالأسطوانة Z تساوي X تربيع ومن أسفل
+
+764
+01:23:45,790 --> 01:23:53,410
+بالمنطقة
+
+765
+01:23:53,410 --> 01:23:55,050
+enclosed
+
+766
+01:24:00,110 --> 01:24:07,430
+by the parabola بالقطع
+
+767
+01:24:07,430 --> 01:24:16,790
+المكافئ y تساوي اتنين ناقص x ترابيع and the line
+
+768
+01:24:16,790 --> 01:24:20,870
+الخط
+
+769
+01:24:20,870 --> 01:24:30,040
+y تساوي x and the xwhy play
+
+770
+01:25:04,750 --> 01:25:09,870
+الخمسة أمثلة السابقة كانت تعطينا حدود التكامل،
+
+771
+01:25:09,870 --> 01:25:14,930
+لكنها لم تعطينا أي شيء، انت بدأت تجلب حدود التكامل
+
+772
+01:25:14,930 --> 01:25:19,330
+من خلال الوصف اللي أعطاه لك لمن؟ للمسألة، يبقى
+
+773
+01:25:19,330 --> 01:25:23,810
+الخمسة الأمثلة الأولى اللي هم فكرة شكل، وهدول
+
+774
+01:25:23,810 --> 01:25:27,510
+الأمثلة هذا و اللي جاين بعده كمان اللي هم فكرة
+
+775
+01:25:27,510 --> 01:25:33,380
+شكل،يبقى انا لو روحت رسمت من منطقة التكامل بكون
+
+776
+01:25:33,380 --> 01:25:37,680
+حلية العمودي الفقري تبع المثل يفضل التكامل هذا شغل
+
+777
+01:25:37,680 --> 01:25:44,100
+روتينيطيب جالي هنا ال .. ال .. الجلهات الغلمة ده
+
+778
+01:25:44,100 --> 01:25:47,400
+solid bounded by the cylinder طب لو ماجاليش
+
+779
+01:25:47,400 --> 01:25:51,440
+cylinder هو جالي by the surface Z تساوي X تربيع
+
+780
+01:25:51,440 --> 01:25:55,380
+لحالك بدك تعرف ان هاد ال cylinder لإن انا عندي
+
+781
+01:25:55,380 --> 01:25:59,580
+متغيرين موجودين و التالت غايب يبقى هاد معادلة
+
+782
+01:25:59,580 --> 01:26:04,260
+cylinder دائما و أفدا ما علينا مش مشكلة من أسفل
+
+783
+01:26:04,260 --> 01:26:08,680
+يعني ال domain تبعهاInclosed by this parabola و ال
+
+784
+01:26:08,680 --> 01:26:12,800
+line اللي عندنا يبقى يا بنات انا فقط برسم باسي ال
+
+785
+01:26:12,800 --> 01:26:17,100
+domain اللي هو منطقتي التكامل ماليش علاقة بالمجسم
+
+786
+01:26:17,100 --> 01:26:22,120
+المجسم بدي اكامله بدي اكامل هذا بقوله كويس اذا بدى
+
+787
+01:26:22,120 --> 01:26:27,440
+اروح و ارسم اللي هو اللي عندنا المنطق يعني هذا X
+
+788
+01:26:27,440 --> 01:26:34,310
+وهذا Y وهذه نقطة الاصل ال parabola اللي عندناY
+
+789
+01:26:34,310 --> 01:26:39,250
+تساوي سالب X تساوي سالب U و Shift لفوق بمقدار كده؟
+
+790
+01:26:39,250 --> 01:26:46,030
+بمقدار 2 يبقى النقطة هذه Zero و 2 و بنروح نرسم ال
+
+791
+01:26:46,030 --> 01:26:50,150
+Parabola بالشكل اللي عندنا تمام يبقى هذه ال
+
+792
+01:26:50,150 --> 01:26:55,750
+Parabola اللي عندنا بعد هيك يقول في الخط Y تساوي X
+
+793
+01:26:55,750 --> 01:27:02,030
+يبقى مدى الخط Y تساوي Xالشكل اللي عندنا هذا و بمده
+
+794
+01:27:02,030 --> 01:27:07,690
+على استقامته مباشرة فنصير هذه التقاطة اللي عندنا
+
+795
+01:27:07,690 --> 01:27:12,470
+هذا و التقاطة اللي عندنا هي يبقى المنطقة اللي احنا
+
+796
+01:27:12,470 --> 01:27:18,850
+فيه دنياها هي المنطقة المظللة ما بين الخط المستقيم
+
+797
+01:27:18,850 --> 01:27:24,350
+و ما بين البرابلات يبقى هذه منطقة main منطقة
+
+798
+01:27:24,350 --> 01:27:32,490
+التكامل automatic بقوله volume Bبتساوي تكاملين على
+
+799
+01:27:32,490 --> 01:27:39,710
+R لل surface اللي فوق اللي هو Z تساوي كده؟ X تربيع
+
+800
+01:27:39,710 --> 01:27:45,630
+طبعا؟ ضال عندي بدي أقوله دي إيه لإن أنا مش عارف
+
+801
+01:27:45,630 --> 01:27:50,930
+مين ال X ومين ال Y وكذا طبعا؟ يبقى بقدر أقول هذه
+
+802
+01:27:50,930 --> 01:27:56,570
+التكامل الأول وهي التكامل الثاني لل X تربيع
+
+803
+01:28:04,590 --> 01:28:10,550
+هل بقدر اجيب الحدود تبقى سهلة ولا لأ ان قدرت ماشية
+
+804
+01:28:10,550 --> 01:28:14,930
+اللحظة ماقدرت فاجلبهاالان بروح و بغير مين الحدود
+
+805
+01:28:14,930 --> 01:28:19,930
+بقول بسيطة جدا الان مدام دي و ي دي اكس بدي اشوف وي
+
+806
+01:28:19,930 --> 01:28:25,990
+بدأ تتغير من ويل لويل بقوله اه بدي برسم خط موازن
+
+807
+01:28:25,990 --> 01:28:33,110
+لمحور وي و يقطع منطقة التكامن يبقى هنا وي بقداش يا
+
+808
+01:28:33,110 --> 01:28:39,990
+بنات وي بقداش الخط هذا هو معادلة وي بقداش اكسطبعا
+
+809
+01:28:39,990 --> 01:28:48,170
+يبقى قيمة Y تقبع هنا فجداش ب X وقيمة Y هنا فجداش ب
+
+810
+01:28:48,170 --> 01:28:55,630
+2 ناقص X تربيع يبقى 2 ناقص X تربيع لإن المنحنة هنا
+
+811
+01:28:55,630 --> 01:29:03,670
+Y يسوى 2 ناقص X تربيع ضالة X بدها تتغير من أن أقل
+
+812
+01:29:03,670 --> 01:29:10,930
+قيمة هنا لغاية أكبر قيمة اللي عندنامشان هيك بدي
+
+813
+01:29:10,930 --> 01:29:17,810
+احد يدق ما بين الاتنين ممتاز جدا يبقى انا عندي y
+
+814
+01:29:17,810 --> 01:29:22,990
+تساوي x وعندي y يساوي اتنين نقص x تربية يعني اللي
+
+815
+01:29:22,990 --> 01:29:27,810
+بدي احل المعادلة مع بعض بصير x يساوي اتنين نقص x
+
+816
+01:29:27,810 --> 01:29:35,780
+تربية لو عملناها معادلة صفرية بصير x تربيةزائد X
+
+817
+01:29:35,780 --> 01:29:41,860
+نقص اتنين يساوي Zero يبقى هاي قوسين بده يساوي Zero
+
+818
+01:29:41,860 --> 01:29:49,140
+هنا X وهنا X وهنا واحد وهنا اتنين هذه بالزائد وهذه
+
+819
+01:29:49,140 --> 01:29:54,840
+بالنقص يبقى بنات ال X بدها تساوي واحد وال X بده
+
+820
+01:29:54,840 --> 01:30:00,390
+يساوي سالب اتنين اذا هذه سالب اتنين وهذه كدهشوها
+
+821
+01:30:00,390 --> 01:30:07,250
+دي واحد تمام إذا ال X ستتغير من سالب اتنين لغاية
+
+822
+01:30:07,250 --> 01:30:14,020
+واحد باقى الشغل صار روتيني خلاصهذا هو العمول
+
+823
+01:30:14,020 --> 01:30:18,320
+الفقري تبع المثال اني احدد حدود التكامل من خلال
+
+824
+01:30:18,320 --> 01:30:21,300
+الوصفة اللي اعطاه لي بعدين بصير الشغل روتيني زي
+
+825
+01:30:21,300 --> 01:30:25,860
+اللي جابت يبقى هذا الكلام بده يساوي كده بده يساوي
+
+826
+01:30:25,860 --> 01:30:31,140
+اللي هو التكامل من سلبي اتنين لغاية واحد وهذه X
+
+827
+01:30:31,140 --> 01:30:38,040
+تكيبة على تلاتة عفوا ان X تربية تتبرة كلها كله
+
+828
+01:30:38,040 --> 01:30:44,070
+أسطن مالهاش علاقة في الموضوعبظل عيبنا من الـ dy
+
+829
+01:30:44,070 --> 01:30:51,410
+يبقى تكاملها بY من عند ال X لإتنين ناقص X تربيع
+
+830
+01:30:51,410 --> 01:30:56,170
+كله DX يبقى
+
+831
+01:30:56,170 --> 01:31:00,610
+هذا الكلام بده يساوي تكامل من سالب إتنين لغاية
+
+832
+01:31:00,610 --> 01:31:06,210
+الواحد X تربيعمن قيمة اللي فوق اتنين ناقص X تربية
+
+833
+01:31:06,210 --> 01:31:14,250
+ناقص X كله DX يبقى صارت المسألة تكامل من سالب
+
+834
+01:31:14,250 --> 01:31:23,910
+اتنين لغاية واحد لمن دال اتنين X تربية ناقص X تكيب
+
+835
+01:31:23,910 --> 01:31:32,370
+و هنا ناقص X أُس أربعة وهنا ناقص X تكيب
+
+836
+01:31:38,750 --> 01:31:47,510
+النتيجة تولتين x تكييف ناقص pumps x أُس خمسة وهنا
+
+837
+01:31:47,510 --> 01:31:55,090
+ناقص ربع x أُس أربعة كل هذا الكلام من سالب اتنين
+
+838
+01:31:55,090 --> 01:32:00,590
+لغاية الواحد وإليك الإجابة مش هنضيع وجد فيهاماذا
+
+839
+01:32:00,590 --> 01:32:05,330
+بيظل عليك تحسبيها؟ بتلاقيها مية تمانية وعشرين
+
+840
+01:32:05,330 --> 01:32:12,150
+عالمين على خمستاشر عفوا اللي هي مية .. اللي هي
+
+841
+01:32:12,150 --> 01:32:23,710
+تلاتة وستين على عشرين تلاتة وستين على عشرين ناخد
+
+842
+01:32:23,710 --> 01:32:26,150
+كمان مثال تالتين
+
+843
+01:32:30,930 --> 01:32:40,330
+the volume of the solid كده حجم المجسم cut it from
+
+844
+01:32:40,330 --> 01:32:52,390
+the first octant cut from the first octant
+
+845
+01:32:52,390 --> 01:32:55,930
+الثمني
+
+846
+01:32:55,930 --> 01:33:08,250
+الأول by the surfaceby the surface بالسطح z تساوي
+
+847
+01:33:08,250 --> 01:33:22,410
+أربع ناقص x ترمية ناقص one هذه
+
+848
+01:33:22,410 --> 01:33:29,390
+حجم المجسم اللي مقطوع في ال face في الثمن الأول
+
+849
+01:33:29,810 --> 01:33:34,310
+بواسطة ال service يبقى انا عندي service في الفراغ
+
+850
+01:33:34,310 --> 01:33:38,230
+ايش في الثمن الاول ايش في التاني ايش في التالد ايش
+
+851
+01:33:38,230 --> 01:33:41,550
+في الرابع والسادس والسبعة انا مديش ارتباط الثمن
+
+852
+01:33:41,550 --> 01:33:46,210
+الاول بقوله بسيطة في الثمن الاول زد يا بنات مجدد
+
+853
+01:33:46,210 --> 01:33:51,290
+Zero اذا بقدر احدد شو المنحنة اللي موجودة عندى
+
+854
+01:33:51,290 --> 01:33:52,590
+يبقى هنا
+
+855
+01:33:59,390 --> 01:34:04,050
+هي تحدد منطقة تتكبلي منطقة تقعطها على ال surface
+
+856
+01:34:04,050 --> 01:34:09,830
+مع من؟ مع ال XY plane يعني بدي أحط Z بقداش؟ Zero
+
+857
+01:34:09,830 --> 01:34:17,250
+يبقى put اعطيلي Z تسوى Zeroهذا يعني أن أربعة ناقص
+
+858
+01:34:17,250 --> 01:34:23,430
+X تربية ناقص Y سواء Zero هذا يعني أن Y سواء Main
+
+859
+01:34:23,430 --> 01:34:30,150
+أربعة ناقص X تربية لو روحت أرسم المنطقة هذه بقول
+
+860
+01:34:30,150 --> 01:34:35,860
+هذا محور Xهذا محور Y وهذا المنطقه Zero Y تساوي X
+
+861
+01:34:35,860 --> 01:34:39,720
+تربيع ناقص أربعة يبقى حيجيني بالشكل اللي عندنا هذا
+
+862
+01:34:39,720 --> 01:34:44,920
+لكن هل كله ولا نصه الله أعلم مش عارفين احنا نقول
+
+863
+01:34:44,920 --> 01:34:49,060
+هي رسمنا المنطقة اللي عندنا هذا يبقى هذا المنحدر
+
+864
+01:34:49,060 --> 01:34:57,920
+يبقى Y تساوي أربعة ناقص X تربيع طب
+
+865
+01:34:57,920 --> 01:35:06,130
+كويس الان بدنا نيجي نحددباقي الحدود لمين للمجسم
+
+866
+01:35:06,130 --> 01:35:10,910
+اللى عندنا هنا طيب هذا لما نقطع مع محور X لإن أنا
+
+867
+01:35:10,910 --> 01:35:15,570
+بدي الثمن الأول يعني مديش أفوض ل Y لا بس بتكتفي
+
+868
+01:35:15,570 --> 01:35:26,280
+لحد هنا يفجأة تفجأة Y عندى جداشيجب أن ننزل
+
+869
+01:35:26,280 --> 01:35:30,340
+الارتباط أكتر من
+
+870
+01:35:30,340 --> 01:35:35,780
+الارتباط
+
+871
+01:35:35,900 --> 01:35:41,340
+هذه الاتنين هلقيل في السلم اتنين هذه؟ لأ لأنه جالس
+
+872
+01:35:41,340 --> 01:35:45,800
+في الثمن الأول مالكش دعوة إلك بس في الشجة هذه يبقى
+
+873
+01:35:45,800 --> 01:35:50,720
+منطقة التكامل سارة بس المنطقة المضللة للي عندنا
+
+874
+01:35:50,720 --> 01:35:57,840
+هذا لأنه جالس في الثمن الأول فقط لغيره إذا بناء
+
+875
+01:35:57,840 --> 01:36:02,340
+على الفكرة أحدد له اللي هو اللي بديه يبقى ال
+
+876
+01:36:02,340 --> 01:36:09,740
+volume Vبتسوى تكاملين تكاملين على الذات لازد جداش
+
+877
+01:36:09,740 --> 01:36:17,020
+الذات لاربع ناقص x تربيه ناقص y ان كمال بالنسبة ل
+
+878
+01:36:17,020 --> 01:36:20,920
+x في الأول ماشي كمال بالنسبة ل y في الأول ماشي
+
+879
+01:36:20,920 --> 01:36:25,760
+سيان هذه او تلك كله ماعناش مشكلة بالنسبة له لو
+
+880
+01:36:25,760 --> 01:36:31,940
+حبيت اكمل بالنسبة إلى xيبقى او بالنسبة الى Y سيئا
+
+881
+01:36:31,940 --> 01:36:37,980
+لو نقبل بالنسبة الى Y برسم خط يوازي محول Y ويقطع
+
+882
+01:36:37,980 --> 01:36:46,160
+منطقة التكامل بصير Y بتتغير من Zero لغاية أربعة
+
+883
+01:36:46,160 --> 01:36:51,430
+ناقص X تربيعبتبقى ال X تتغير من اولى اين؟ من Zero
+
+884
+01:36:51,430 --> 01:36:56,770
+لاتنين يبقى من Zero لاتنين خلصنا العمود الفقري في
+
+885
+01:36:56,770 --> 01:37:03,570
+المثلة يبقى DY DX بقى الشغل الروتيني يبقى هذا
+
+886
+01:37:03,570 --> 01:37:06,830
+الكلام تكامل من الصفر لاتنين وهي
+
+887
+01:37:19,340 --> 01:37:23,800
+يبقى هذا الكلام بده يساوي تكامل من صفر لليل
+
+888
+01:37:41,240 --> 01:37:45,480
+وهنا بالنسبة لمن ال ADX
+
+889
+01:38:03,920 --> 01:38:07,640
+يبقى هذا الكلام يبدو يساوي integration من zero
+
+890
+01:38:07,640 --> 01:38:23,560
+لغاية 10 يبقى 16-4X ربيع طبعا هذا ناقص16-4X³-4X³
+
+891
+01:38:23,560 --> 01:38:30,940
+-4X³-4X³
+
+892
+01:38:30,940 --> 01:38:35,440
+-5X³
+
+893
+01:38:35,440 --> 01:38:41,800
+-8X³
+
+894
+01:38:41,800 --> 01:38:46,260
+-8X³-8X³
+
+895
+01:38:46,800 --> 01:38:52,640
+زي الـ x أُص أربعة كل هذا الكلام بالنسبة إلى dx
+
+896
+01:38:52,640 --> 01:38:59,060
+يساوي التكامل من صفر للإتنين عندك هنا ستاشر و هنا
+
+897
+01:38:59,060 --> 01:39:05,070
+ناقص تمانية x تربيع و هنا زي الـ x أُص أربعةو هنا
+
+898
+01:39:05,070 --> 01:39:11,850
+ناقص تمانية و هنا ناقص فناقص بزاية تمانية X تربية
+
+899
+01:39:11,850 --> 01:39:20,310
+و هنا ناقص نص X أُس أربعة كله في DX و يساوي تكاول
+
+900
+01:39:20,310 --> 01:39:23,750
+من الصفر للإتنين عندك هنا ستة عشر و هنا ناقص
+
+901
+01:39:23,750 --> 01:39:28,850
+تمانية بدون جداش تمانية عندك ناقص تمانية X تربية و
+
+902
+01:39:28,850 --> 01:39:36,240
+زائد تمانية X تربية أجر الفاتحة على روحكزائد أربعة
+
+903
+01:39:36,240 --> 01:39:38,240
+زائد أربعة زائد أربعة زائد أربعة زائد أربعة زائد
+
+904
+01:39:38,240 --> 01:39:41,380
+أربعة زائد أربعة زائد أربعة زائد أربعة زائد أربعة
+
+905
+01:39:41,380 --> 01:39:43,360
+زائد أربعة زائد أربعة زائد أربعة زائد أربعة زائد
+
+906
+01:39:43,360 --> 01:39:45,980
+أربعة زائد أربعة زائد أربعة زائد أربعة زائد أربعة
+
+907
+01:39:45,980 --> 01:39:50,060
+زائد أربعة زائد أربعة زائد أربعة زائد أربعة زائد
+
+908
+01:39:50,060 --> 01:39:52,060
+أربعة زائد أربعة زائد أربعة زائد أربعة زائد أربعة
+
+909
+01:39:52,060 --> 01:39:55,680
+زائد أربعة زائد أربعة زائد أربعة زائد أربعة زائد
+
+910
+01:39:55,680 --> 01:40:03,780
+أربعة زائد أربعة زائد أربعة زائد أربعة زائد أربعة
+
+911
+01:40:03,780 --> 01:40:14,610
+زائناقص أربع أتلات X تكييب وزائد عشر X أُس خمسة
+
+912
+01:40:14,610 --> 01:40:21,350
+والحكي هذا كله من عند الـ zero لغاية الإتنين يبقى
+
+913
+01:40:21,350 --> 01:40:26,930
+بصير عندك ستة عشر ناقص تمانية في أربعة باتنين
+
+914
+01:40:26,930 --> 01:40:34,470
+وتلاتين على تلاتة زائد اتنين وتلاتينهذه تكريف 8×4
+
+915
+01:40:34,470 --> 01:40:40,250
+هو 32 وهذه تكريف 8×4 هي 32 على 10 والباقي كله
+
+916
+01:40:40,250 --> 01:40:46,070
+مناقش 0 والجواب النهائي 128 على 15يبقى هذا كله
+
+917
+01:40:46,070 --> 01:40:52,250
+متساوي مية و تمانية و عشرين على خمستاش اللي هو مين
+
+918
+01:40:52,250 --> 01:40:58,850
+مقدار الحجب لا يزال عندنا كمان مثال و بعض الخواص
+
+919
+01:40:58,850 --> 01:41:03,730
+للمرة القادمة اللي شاء الله تعالى حد ما كتبتش اسم
+
+920
+01:41:03,730 --> 01:41:06,990
+هنا يا بنات قوله كتب اسم هنا
+
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/BfHmF68iUco_raw.json b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/BfHmF68iUco_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..0022125e5b72f055ac397d13f3d6787e47a86fe9
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/BfHmF68iUco_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 2120, "start": 19.02, "end": 21.2, "text": "بسم الله الرحمن الرحيم", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640], "avg_logprob": -0.03303222544491291, "compression_ratio": 1.0789473684210527, "no_speech_prob": 0.0, "words": [{"start": 19.02, "end": 19.98, "word": "بسم", "probability": 0.923095703125}, {"start": 19.98, "end": 20.24, "word": " الله", "probability": 0.982421875}, {"start": 20.24, "end": 20.7, "word": " الرحمن", "probability": 0.9658203125}, {"start": 20.7, "end": 21.2, "word": " الرحيم", "probability": 0.9925130208333334}], "temperature": 1.0}, {"id": 2, "seek": 4809, "start": 22.37, "end": 48.09, "text": "نرجع الان ل chapter خمسة عشر اللي ابتدناه المرة الماضية و اول section اللي هو ال double integrals على منطقة مستطيلة over rectangular region على منطقة على شكل مستطيل اخدها المرة اللي فاتت مثلا واحدة و من الان بنكمل الأمثلة على نفس الموضوع يبقى كالمرة اللي فات مثال رقم a بدنا نجيه مثلا رقم b", "tokens": [1863, 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{"id": 35, "seek": 80191, "start": 789.33, "end": 801.91, "text": "قال التفاضل شامتا أنا لاتكامل معبره أنا فاضل متفاضل أنا يتكامل أكبر انظر علامتك التي ذيل", "tokens": [4587, 6027, 16712, 5172, 46958, 1211, 13412, 10943, 2655, 995, 41850, 5296, 9307, 4117, 10943, 1211, 20449, 26890, 3224, 41850, 6156, 46958, 1211, 44650, 5172, 46958, 1211, 41850, 7251, 2655, 4117, 10943, 1211, 5551, 4117, 26890, 16472, 19913, 2288, 11203, 10943, 2655, 4117, 38392, 29910, 26895], "avg_logprob": -0.16497672174839265, "compression_ratio": 1.6428571428571428, "no_speech_prob": 0.0, "words": [{"start": 789.33, "end": 789.71, "word": "قال", "probability": 0.982666015625}, {"start": 789.71, "end": 790.47, "word": " التفاضل", "probability": 0.8509521484375}, {"start": 790.47, "end": 791.47, "word": " شامتا", "probability": 0.9267578125}, {"start": 791.47, "end": 792.01, "word": " أنا", "probability": 0.505859375}, {"start": 792.01, "end": 793.05, "word": " لاتكامل", "probability": 0.80771484375}, {"start": 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التكامل هبقى التكامل هائجا أسكت أنا متحرر أنا لم أعد لك تابعا لا و لست منك و سطروا أنا للمساحة حاسب حتى الحجوم أصوره يعني بحسب المساحات و بحسب الحجوم و أطول المنحنيات و ما إلى ذلك", "tokens": [1829, 9566, 12610, 14407, 4032, 1829, 4587, 9381, 2288, 14407, 30767, 1829, 16712, 4117, 10943, 1211, 8032, 3555, 4587, 7578, 16712, 4117, 10943, 1211, 8032, 16373, 7435, 995, 5551, 3794, 4117, 2655, 41850, 44650, 5016, 2288, 2288, 41850, 32767, 5551, 22488, 5296, 4117, 6055, 16758, 3615, 995, 20193, 4032, 5296, 14851, 9154, 4117, 4032, 8608, 9566, 2288, 14407, 41850, 5296, 19528, 3794, 39319, 3660, 11331, 32277, 3555, 11331, 49975, 21542, 7435, 20498, 5551, 9381, 13063, 3224, 37495, 22653, 4724, 5016, 35457, 9673, 3794, 39319, 9307, 4032, 4724, 5016, 35457, 21542, 7435, 20498, 4032, 5551, 9566, 12610, 9673, 1863, 5016, 22653, 9307, 4032, 19446, 30731, 29910, 23275], "avg_logprob": -0.13259346407150555, "compression_ratio": 1.9398907103825136, "no_speech_prob": 5.364418029785156e-07, "words": 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{"id": 39, "seek": 92275, "start": 895.69, "end": 922.75, "text": "of the solid bounded below محدود من أسفل by R region R and above ومن أعلى by", "tokens": [2670, 264, 5100, 37498, 2507, 3714, 24401, 23328, 9154, 5551, 3794, 5172, 1211, 538, 497, 4458, 497, 293, 3673, 4032, 27842, 5551, 3615, 23942, 538], "avg_logprob": -0.15790264766949874, "compression_ratio": 1.010752688172043, "no_speech_prob": 0.0, "words": [{"start": 895.69, "end": 895.99, "word": "of", "probability": 0.41650390625}, {"start": 895.99, "end": 896.27, "word": " the", "probability": 0.86376953125}, {"start": 896.27, "end": 896.85, "word": " solid", "probability": 0.90234375}, {"start": 896.85, "end": 902.67, "word": " bounded", "probability": 0.94970703125}, {"start": 902.67, "end": 903.75, "word": " below", "probability": 0.93115234375}, {"start": 903.75, "end": 910.05, "word": " محدود", "probability": 0.8899739583333334}, {"start": 910.05, "end": 910.25, "word": " من", "probability": 0.98486328125}, {"start": 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"end": 6045.57, "word": "يبقى", "probability": 0.7974853515625}, {"start": 6045.57, "end": 6045.77, "word": " هذا", "probability": 0.76806640625}, {"start": 6045.77, "end": 6046.07, "word": " كله", "probability": 0.624755859375}, {"start": 6046.07, "end": 6046.77, "word": " متساوي", "probability": 0.861328125}, {"start": 6046.77, "end": 6047.39, "word": " مية", "probability": 0.80517578125}, {"start": 6047.39, "end": 6047.93, "word": " و", "probability": 0.75927734375}, {"start": 6047.93, "end": 6048.45, "word": " تمانية", "probability": 0.9588216145833334}, {"start": 6048.45, "end": 6048.57, "word": " و", "probability": 0.96533203125}, {"start": 6048.57, "end": 6049.29, "word": " عشرين", "probability": 0.9285481770833334}, {"start": 6049.29, "end": 6050.05, "word": " على", "probability": 0.65234375}, {"start": 6050.05, "end": 6051.15, "word": " خمستاش", "probability": 0.8502197265625}, {"start": 6051.15, "end": 6051.73, "word": " اللي", "probability": 0.81201171875}, {"start": 6051.73, "end": 6051.91, "word": " هو", "probability": 0.9794921875}, {"start": 6051.91, "end": 6052.25, "word": " مين", "probability": 0.595947265625}, {"start": 6052.25, "end": 6053.15, "word": " مقدار", "probability": 0.9638671875}, {"start": 6053.15, "end": 6053.79, "word": " الحجب", "probability": 0.9427083333333334}, {"start": 6053.79, "end": 6054.47, "word": " لا", "probability": 0.5537109375}, {"start": 6054.47, "end": 6054.99, "word": " يزال", "probability": 0.9777018229166666}, {"start": 6054.99, "end": 6055.53, "word": " عندنا", "probability": 0.992919921875}, {"start": 6055.53, "end": 6056.25, "word": " كمان", "probability": 0.9923502604166666}, {"start": 6056.25, "end": 6057.65, "word": " مثال", "probability": 0.99462890625}, {"start": 6057.65, "end": 6057.83, "word": " و", "probability": 0.7548828125}, {"start": 6057.83, "end": 6058.21, "word": " بعض", "probability": 0.969970703125}, {"start": 6058.21, "end": 6058.85, "word": " الخواص", "probability": 0.826171875}, {"start": 6058.85, "end": 6059.83, "word": " للمرة", "probability": 0.9475911458333334}, {"start": 6059.83, "end": 6060.67, "word": " القادمة", "probability": 0.9939778645833334}, {"start": 6060.67, "end": 6061.09, "word": " اللي", "probability": 0.931396484375}, {"start": 6061.09, "end": 6061.39, "word": " شاء", "probability": 0.991943359375}, {"start": 6061.39, "end": 6061.63, "word": " الله", "probability": 0.94091796875}, {"start": 6061.63, "end": 6062.17, "word": " تعالى", "probability": 0.9560546875}, {"start": 6062.17, "end": 6062.83, "word": " حد", "probability": 0.732177734375}, {"start": 6062.83, "end": 6062.97, "word": " ما", "probability": 0.84228515625}, {"start": 6062.97, "end": 6063.49, "word": " كتبتش", "probability": 0.93740234375}, {"start": 6063.49, "end": 6063.73, "word": " اسم", "probability": 0.951171875}, {"start": 6063.73, "end": 6063.95, "word": " هنا", "probability": 0.97021484375}, {"start": 6063.95, "end": 6064.13, "word": " يا", "probability": 0.849609375}, 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/BfHmF68iUco_raw.srt b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/BfHmF68iUco_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..133d37d8dfe826cb13e9f3859db5379c4b01b920
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/BfHmF68iUco_raw.srt
@@ -0,0 +1,3680 @@
+1
+00:00:19,020 --> 00:00:25,010
+بسم الله الرحمن الرحيمنرجع الان ل chapter خمسة عشر
+
+2
+00:00:25,010 --> 00:00:29,030
+اللي ابتدناه المرة الماضية و اول section اللي هو
+
+3
+00:00:29,030 --> 00:00:33,250
+ال double integrals على منطقة مستطيلة over
+
+4
+00:00:33,250 --> 00:00:38,190
+rectangular region على منطقة على شكل مستطيل اخدها
+
+5
+00:00:38,190 --> 00:00:41,810
+المرة اللي فاتت مثلا واحدة و من الان بنكمل الأمثلة
+
+6
+00:00:41,810 --> 00:00:45,770
+على نفس الموضوع يبقى كالمرة اللي فات مثال رقم a
+
+7
+00:00:45,770 --> 00:00:54,210
+بدنا نجيه مثلا رقم bالسؤال الأول مثال رقم B بيقول
+
+8
+00:00:54,210 --> 00:01:03,470
+بدي تاكر أولين على المنطقة A ل X في Y في E أُس X
+
+9
+00:01:07,410 --> 00:01:18,050
+معطينا المنطقة R هي ان X تتغير من 0 لغاية 2 و Y
+
+10
+00:01:18,050 --> 00:01:23,250
+تتغير من 0 لغاية 1
+
+11
+00:01:34,720 --> 00:01:38,480
+المرة اللى فاتت كان كتبلى حدود التكامل على التكامل
+
+12
+00:01:38,480 --> 00:01:43,340
+نفسه، تمام؟ المرة هذه ان شاء الله تعالى احنا بدنا
+
+13
+00:01:43,340 --> 00:01:47,640
+نكتب حدود التكامل طب قلنا الكلام اللى هو ايه جايب
+
+14
+00:01:48,230 --> 00:01:53,930
+يبقى في عندي تكاملين على المنطقة المستطيلة A هي
+
+15
+00:01:53,930 --> 00:02:00,870
+لدلة XY لل E أُس XY تربيع يبقى أنا بروح بقول له
+
+16
+00:02:00,870 --> 00:02:08,250
+هذا عبارة عن تكاملين لل XY في ال E أُس XY تربيع
+
+17
+00:02:08,250 --> 00:02:13,330
+والآن الشغل فيديحبيت أكمل بالنسبة ل X في الأول،
+
+18
+00:02:13,330 --> 00:02:16,850
+بمشي الحال، حبيت أكمل بالنسبة ل Y في الأول، بمشي
+
+19
+00:02:16,850 --> 00:02:21,090
+الحال، لأن الحدود عندي أرقام، حدود مستطيل،
+
+20
+00:02:21,090 --> 00:02:24,830
+وبالتالي ماعنديش مشكلة في هذه الحالة، لكن بجيب
+
+21
+00:02:24,830 --> 00:02:29,750
+أطلع على الذلة، أيه هو أسهل أكمل للأول؟ هل بالنسبة
+
+22
+00:02:29,750 --> 00:02:34,840
+ل X ولا بالنسبة ل Y؟بالنسبة ل X بدها integration
+
+23
+00:02:34,840 --> 00:02:39,940
+by parts صح لكن بالنسبة ل Y بدها بالتعويض by
+
+24
+00:02:39,940 --> 00:02:43,500
+substitution يبقى substitution أسرع ليه من حكاية
+
+25
+00:02:43,500 --> 00:02:44,800
+integration by parts
+
+26
+00:03:02,720 --> 00:03:08,140
+بعد هيك يبقى كامل بالنسبة الأولى ل Y بحط حدود Y
+
+27
+00:03:08,140 --> 00:03:15,040
+يبقى من Zero لغاية One وهنا من Zero لغاية Two بعد
+
+28
+00:03:15,040 --> 00:03:20,680
+هيكمداجة كامل هذا الاصل y تربية اذا انا ممكن اشيل
+
+29
+00:03:20,680 --> 00:03:25,700
+ال y تربية و احطه بمتغير جديد اذا لو راك في
+
+30
+00:03:25,700 --> 00:03:31,320
+الامشيك حطيتي ت تساوي y تربية يعني يبقى دي ت
+
+31
+00:03:31,320 --> 00:03:38,560
+بتساوي اتنين y dyيبقى بناء عليه لو شيلت ال Y اللي
+
+32
+00:03:38,560 --> 00:03:43,560
+عندها دي مع ال D Y الاتنين هدول مع بعض تحط بدلهم
+
+33
+00:03:43,560 --> 00:03:48,440
+Main مُص D T يبقى اتخلصت من ال variable Y اللي برا
+
+34
+00:03:48,440 --> 00:03:54,020
+وصرت مسألة سهلة الأن يبقى وصير هذا عبارة عن
+
+35
+00:03:54,020 --> 00:04:03,600
+تكاملين وعندك هنا X وهنا E أُس X في T يبقى شيلت
+
+36
+00:04:03,600 --> 00:04:07,830
+Mainالـ X خلّيتها زي ما هي شيلت ال Y دي Y و بدى
+
+37
+00:04:07,830 --> 00:04:12,510
+أكتب بدلها النص DT النص هدا كونه Standard بقدر
+
+38
+00:04:12,510 --> 00:04:19,770
+أقوله خلّيك برا و بصير عندي هنا DT و هنا DX ال X
+
+39
+00:04:19,770 --> 00:04:22,910
+مالهاش علاقة في الموضوع كده كونه صدق ماهاش خبر
+
+40
+00:04:22,910 --> 00:04:28,910
+يبقى بظل حدود ال X كما هي من Zero لمين لغاية اتنين
+
+41
+00:04:29,440 --> 00:04:34,400
+لكن نظرنا لو عملنا تعويضة إذا بدي أشوف ما هي القيم
+
+42
+00:04:34,400 --> 00:04:41,200
+المناظرة لقيم Y بالنسبة للمتغير T إذا بدي أجي هنا
+
+43
+00:04:41,200 --> 00:04:45,960
+و أجي و أقول آه هذه الواحد والزيرو هذول حدود دمين
+
+44
+00:04:45,960 --> 00:04:52,320
+لل Y إذا لو كانت ال Y بواحد فT بواحد تربية تعني
+
+45
+00:04:52,320 --> 00:04:58,920
+واحد و لو كانت ال Y ب Zero تربية يبقى ب Zero يظلمن
+
+46
+00:04:58,920 --> 00:05:05,540
+zero لغاية واحد إذا ما عندنا مشكلة في هذه الحقإذا
+
+47
+00:05:05,540 --> 00:05:13,360
+صار بدكامل بالنسبة ل T في الأول يبقى ال X يساوي
+
+48
+00:05:13,360 --> 00:05:20,660
+النص وهي تكامل من صفر لغاية ادنان وتكامل
+
+49
+00:05:20,660 --> 00:05:25,920
+ال exponential بال exponential itself مقسومة على
+
+50
+00:05:25,920 --> 00:05:31,200
+تفاضل الأس إن كان من الدرجة الأولى يبقى ال X يعتبر
+
+51
+00:05:31,200 --> 00:05:37,860
+مقداريبقى ثابت و تفضل يبقى دهش بواحد يبقى على X و
+
+52
+00:05:37,860 --> 00:05:42,940
+الحكي هذا كله من عنده Zero لغاية واحد و هذه mainly
+
+53
+00:05:42,940 --> 00:05:50,660
+دي X اللي عندك طيب الان تختصر ال X مع ال X مع
+
+54
+00:05:50,660 --> 00:05:56,460
+السلامة يبقى آلة المسألة إلى نص تكامل من Zero
+
+55
+00:05:56,460 --> 00:06:01,040
+لغاية اتنينبالتالي اعوض بالقيمة اللي فوق نقصي يعني
+
+56
+00:06:01,040 --> 00:06:05,820
+كده شيل كل T وحط مكانها واحد وشيل T وحط مكانها
+
+57
+00:06:05,820 --> 00:06:11,600
+Zero ينفعش مصير عندي يا بنات هنا E of X وT بواحد
+
+58
+00:06:11,600 --> 00:06:19,250
+ناقص E of Zero اللي هو بواحدكل هذا الكلام بالنسبة
+
+59
+00:06:19,250 --> 00:06:24,970
+لمين؟ لدى x يبقى صارت مسألة بسيطة جدا أقصر مما
+
+60
+00:06:24,970 --> 00:06:30,490
+نتصور يبقى هذا الكلام بده يساوي نص فيه بده كامل
+
+61
+00:06:30,490 --> 00:06:36,160
+هذه تكامل ال exponential وال exponential يتصلنقص X
+
+62
+00:06:36,160 --> 00:06:41,600
+والحقيقة كلها من Zero لغاية كده اش اتنين هذا
+
+63
+00:06:41,600 --> 00:06:48,260
+الكلام بده يساوي نص E ترابيع نقص اتنين هيعوضنا
+
+64
+00:06:48,260 --> 00:06:53,220
+بالقيمة اللي فوق نقص اللي تحت E از Zero اللي هو
+
+65
+00:06:53,220 --> 00:06:59,480
+واحد ونقص مع ناقص بصير زائد Zero انتهينا يبقى
+
+66
+00:06:59,480 --> 00:07:06,770
+المسألة تساوي نصفي اي تربيع ناقص اتنين هذه هي بين
+
+67
+00:07:06,770 --> 00:07:12,410
+الإجابة المهام كيف
+
+68
+00:07:12,410 --> 00:07:17,530
+ناقص اه ناقص تلاتة ناقص واحد نقص اتنين هي بناقص
+
+69
+00:07:17,530 --> 00:07:23,790
+تلاتة نجي الان لنمرسي من المثلة نمرسي
+
+70
+00:07:25,770 --> 00:07:30,890
+بيقول لي بدي تكاملين على المنطقة المربع أو
+
+71
+00:07:30,890 --> 00:07:40,330
+المستطيلة R لل X وY تكيب على X تربيع زائد واحد DA
+
+72
+00:07:40,330 --> 00:07:47,750
+والمنطقة R هي عبارة عن ال X أكبر من أو تساوي Zero
+
+73
+00:07:47,750 --> 00:07:52,810
+أقل من أو تساوي واحد وال I أكبر من أو تساوي Zero
+
+74
+00:07:52,810 --> 00:08:05,120
+أقل من أو تساوي مينتساوي اتنين إذا
+
+75
+00:08:05,120 --> 00:08:10,680
+بدنا نجي للتكامل تبعنا هذا و نقص من الأول و الجديد
+
+76
+00:08:10,680 --> 00:08:17,260
+و نروح نحط حدود التكامل اللي علنا يبقى تكاملين لل
+
+77
+00:08:17,260 --> 00:08:26,690
+X Y تكييف عالمين على ال X تربيع زائد واحدأسهل اللي
+
+78
+00:08:26,690 --> 00:08:31,310
+أكمل في الأول بالنسبة ل Y و لا ل X؟ ليش ل X؟ ل Y
+
+79
+00:08:31,310 --> 00:08:35,770
+مافيش غيرها أصلا بس هذه لسه بدها بص مقام و أخل ال
+
+80
+00:08:35,770 --> 00:08:40,110
+بص و أتفاضل المقام يعني بدها شغلة بسيطة بس هذه لأ
+
+81
+00:08:40,110 --> 00:08:44,130
+مباشرة لابد نشتغلها Y تكيب لحالة يبقى الأفضل اللي
+
+82
+00:08:44,130 --> 00:08:48,930
+أكمل بالنسبة لمن؟ ل Y في الأول فبروح بقوله يبقى
+
+83
+00:08:48,930 --> 00:08:57,460
+هنا DY DX هذي Y تكيبيبقى كأنه مين؟ كأنه كل المقدار
+
+84
+00:08:57,460 --> 00:09:01,760
+هذا يعتبر كل أسطن بالنسبة لمن؟ بالنسبة لي ال Y
+
+85
+00:09:01,760 --> 00:09:05,720
+يبقى نفسي ده كامل Y تاكين اذا نبدأ إلى حدود ال Y
+
+86
+00:09:05,720 --> 00:09:13,220
+ال Y من أين لأين؟ من 0 لغاية 2 وال X من 0 لغاية 1
+
+87
+00:09:13,870 --> 00:09:19,450
+يبقى النتيجة تساوي integration من zero إلى واحد X
+
+88
+00:09:19,450 --> 00:09:24,650
+على X تربية زائد واحد مالوش دعوة ال Y تكييب اللي
+
+89
+00:09:24,650 --> 00:09:30,070
+هو Y أقصى أربع على أربع والكلام هذا من zero لغاية
+
+90
+00:09:30,070 --> 00:09:33,730
+اتنين وهذا DX اللي عندنا
+
+91
+00:09:36,010 --> 00:09:40,610
+الان نجي نعوض يبقى هذا الكلام تجامل من Zero ل واحد
+
+92
+00:09:40,610 --> 00:09:45,810
+ل X على X تربية زائد واحد فيه بضعوض بالقيم اللي
+
+93
+00:09:45,810 --> 00:09:52,730
+فوق اتنين اقص اربعة على اربعة بضل عندي اربعة ناقص
+
+94
+00:09:52,730 --> 00:09:54,750
+Y اقص Zero
+
+95
+00:09:59,140 --> 00:10:03,560
+يبزيرو أسعة أربعة اللي هي بزيرو على كون القط تمام
+
+96
+00:10:03,560 --> 00:10:08,740
+و كل هذا مقسم له على جداش هذا جاهز و احنا قسمنا
+
+97
+00:10:08,740 --> 00:10:14,660
+على كون القط يبقى في مين في DX تماماما يبقى بنات
+
+98
+00:10:14,660 --> 00:10:20,760
+هذا كله يعتبر رقم الان بدي اكمل X على X تربيه زي
+
+99
+00:10:20,760 --> 00:10:24,560
+واحد ايه بدي اكملها؟ X على X تربيه زي واحد
+
+100
+00:10:37,170 --> 00:10:41,590
+ممتاز يبقى هي اللي فوق مش تقة المقام بس بدها اتنين
+
+101
+00:10:41,590 --> 00:10:45,110
+يبقى بسيطة اتنين الحمد لله ربنا ما يسرها هي اربعة
+
+102
+00:10:45,110 --> 00:10:52,090
+عندى يبقى الأربعة بقول لتنين خليك برا وهي تكمل من
+
+103
+00:10:52,090 --> 00:10:58,370
+صفر لواحد دالي اتنين x على x square plus one في dx
+
+104
+00:10:59,680 --> 00:11:04,540
+هك تماما الاربعة خلت اتنين في اتنين يبقى بنقل عليه
+
+105
+00:11:04,540 --> 00:11:11,140
+صار هذا هو البسطة فاضل المقام يبقى يساوي اتنين لل
+
+106
+00:11:11,140 --> 00:11:16,520
+absolute value المقام و لما كان المقام كمية مربعة
+
+107
+00:11:16,520 --> 00:11:21,040
+او كمية موجبة دائما و ابدا يبقى لا داعي لل
+
+108
+00:11:21,040 --> 00:11:25,960
+absolute value و بروح بقول الكلام ادم ان هو من
+
+109
+00:11:25,960 --> 00:11:31,990
+zero لغاية واحديبقى هذا الكلام بده يساوي اتنين في
+
+110
+00:11:31,990 --> 00:11:37,250
+لن بتشيل اكس وخط مكان واحد تربية واحد زي واحد
+
+111
+00:11:37,250 --> 00:11:43,210
+باتنين يبقى لن اتنين نقص اتنين من اتاح ال zero بضل
+
+112
+00:11:43,210 --> 00:11:48,210
+اني جداش لن الواحد طب لن الواحد مابديش بنام يبقى
+
+113
+00:11:48,210 --> 00:11:51,450
+بضل الجواب اتنين لن اتنين
+
+114
+00:11:53,960 --> 00:11:56,980
+يبقى زي ما تشايفين هذا النوع من المسائل اللي هو
+
+115
+00:11:56,980 --> 00:12:01,500
+مسائل مباشرة المهم بدي اختار من اللي أسهل لحق
+
+116
+00:12:01,500 --> 00:12:06,180
+حدوده في الأول و الحدود اللي هي قيم عددية و ليس
+
+117
+00:12:06,180 --> 00:12:10,780
+quantity ننتقل إلى نقطة ثانية من هذا الsection
+
+118
+00:12:10,780 --> 00:12:20,540
+النقطة رقم اتنين اللي هو double integrals double
+
+119
+00:12:20,540 --> 00:12:28,340
+integrals as volumeيعني ممكن ايه؟ ممكن اللي هو
+
+120
+00:12:28,340 --> 00:12:35,200
+بواسطة طابق الانتجار نحسب الحجم اما حدرسنا في
+
+121
+00:12:35,200 --> 00:12:40,420
+calculus ايه؟ بالتكامل الفردي مش التكامل المتعدد،
+
+122
+00:12:40,420 --> 00:12:45,080
+فجينا نحسب مين؟ نحسب الحجوم والمساحات والسطوح
+
+123
+00:12:45,080 --> 00:12:49,950
+الدورانية وما إلى ذلكو هنا بواسطة double integral
+
+124
+00:12:49,950 --> 00:12:55,150
+او triple integral هنحصل من الحجوم و هنقولك كيف
+
+125
+00:12:55,150 --> 00:12:59,170
+بنحصل من الحجوم، لذلك التفاضل والتكامل كتير
+
+126
+00:12:59,170 --> 00:13:03,430
+بتطوشوا مع بعض، انا افضل منك، انت افضل مني، كذا
+
+127
+00:13:03,430 --> 00:13:08,610
+الى اخرى، فمرة و هم بيحكوا مع بعض يعني، بيناضوا مع
+
+128
+00:13:08,610 --> 00:13:15,250
+بعضقال التفاضل شامتا أنا لاتكامل معبره أنا فاضل
+
+129
+00:13:15,250 --> 00:13:23,430
+متفاضل أنا يتكامل أكبر انظر علامتك التي ذيليطولوا
+
+130
+00:13:23,430 --> 00:13:29,670
+ويقصروا زي التكامل هبقى التكامل هائجا أسكت أنا
+
+131
+00:13:29,670 --> 00:13:37,670
+متحرر أنا لم أعد لك تابعا لا و لست منك و سطروا أنا
+
+132
+00:13:37,670 --> 00:13:44,850
+للمساحة حاسب حتى الحجوم أصوره يعني بحسب المساحات و
+
+133
+00:13:44,850 --> 00:13:50,200
+بحسب الحجوم و أطول المنحنيات و ما إلى ذلكيبقى أحلى
+
+134
+00:13:50,200 --> 00:13:55,000
+موضوعنا اليوم موضوع استخدام التكامل في حساب الحجوم
+
+135
+00:13:55,000 --> 00:14:00,080
+او التكامل اللي تلاقي في حساب الحجوم بيقول ال F ال
+
+136
+00:14:00,080 --> 00:14:10,180
+F of X و Y is positive function بتاخد قيم موجبة
+
+137
+00:14:10,180 --> 00:14:14,120
+دائما أبدا و interpret
+
+138
+00:14:20,560 --> 00:14:34,480
+و I interpret the double integral of
+
+139
+00:14:34,480 --> 00:14:44,900
+F over a region R على
+
+140
+00:14:44,900 --> 00:14:48,500
+المنطقة R as the volume
+
+141
+00:14:55,690 --> 00:15:02,670
+of the solid bounded
+
+142
+00:15:02,670 --> 00:15:10,050
+below محدود
+
+143
+00:15:10,050 --> 00:15:20,450
+من أسفل by R region R and above ومن
+
+144
+00:15:20,450 --> 00:15:22,750
+أعلى by
+
+145
+00:15:24,610 --> 00:15:29,350
+الـ surface بالسطح
+
+146
+00:15:29,350 --> 00:15:48,330
+z بساوي function x و y that is أي أن ال volume v
+
+147
+00:15:48,330 --> 00:15:57,490
+بيساوي تكاملين على aللـ f of x و y دي ايه و اللي
+
+148
+00:15:57,490 --> 00:16:03,930
+هو بده يساوي تكاملين على a ل z بدي ايه
+
+149
+00:16:35,860 --> 00:16:40,040
+نرجع الكلام اللي احنا كاتبينه هذا مرة ثانية double
+
+150
+00:16:40,040 --> 00:16:45,400
+integral as volume بدنا نستخدم التكامل إثنائي في
+
+151
+00:16:45,400 --> 00:16:51,140
+حساب حجوم بعض المجسمات اقول لو كانت دالة f of x و
+
+152
+00:16:51,140 --> 00:16:56,780
+y تأخذ دائما و أبدا قيما موجبة و انت refraction
+
+153
+00:16:56,780 --> 00:17:05,130
+انت برتبناها العربي ايش معناها؟يبقى نفسر
+
+154
+00:17:05,130 --> 00:17:11,700
+دي double integralinterpretation of dreams تفسير
+
+155
+00:17:11,700 --> 00:17:16,620
+الأحلام يبقى interpret تفسير يبقى نروح و نفسر ال
+
+156
+00:17:16,620 --> 00:17:22,560
+double integral على المنطقة R as a volume كحجم
+
+157
+00:17:22,560 --> 00:17:28,540
+لمجسم of solid bounded يبقى هذا المجسم محدود من
+
+158
+00:17:28,540 --> 00:17:33,520
+أعلى بشيء و محدود من أسفل من مين بشيء الان below
+
+159
+00:17:33,520 --> 00:17:38,520
+by region Rيعني كأن ال domain تبع main تبع ال
+
+160
+00:17:38,520 --> 00:17:42,380
+surface اللي فوق يبقى محدود من تحت بال domain R أو
+
+161
+00:17:42,380 --> 00:17:46,980
+بال region R and above ومن أعلى بال surface نفسه
+
+162
+00:17:46,980 --> 00:17:51,500
+يبقى ال surface اللي عندي فوق هيكون له على المستوى
+
+163
+00:17:51,500 --> 00:17:56,880
+XY اللي هو المجال تبعهكل المنطقة اللي بين المجال و
+
+164
+00:17:56,880 --> 00:18:00,600
+مابين السطح ال surface اللي فوق يبقى هذا بقدر أجيب
+
+165
+00:18:00,600 --> 00:18:06,140
+حجمها بواسطة من التكامل و ثانوية curve بقولها ها
+
+166
+00:18:06,140 --> 00:18:10,660
+ال surface أعطيته المعادلة z تساوي f of x y اللي
+
+167
+00:18:10,660 --> 00:18:15,020
+قولنا عليها يبقى احنا يا بنات أعلى المستوى x y و
+
+168
+00:18:15,020 --> 00:18:17,700
+أسفى المستوى x y و الله بنقطعه
+
+169
+00:18:20,270 --> 00:18:24,810
+أعلن نجلي موجب يعني ال z دائما هو بتاخد قيام موجبة
+
+170
+00:18:24,810 --> 00:18:28,410
+يعني احنا من مستوى الأرض و طالعين وان وطالعين لفوق
+
+171
+00:18:28,410 --> 00:18:34,090
+من ما نزلش تحت لإن ال z دائما هو بتاخد قياما موجبة
+
+172
+00:18:34,090 --> 00:18:37,930
+يبقى المنطقة اللي محصورة بين ال surface و ما بين
+
+173
+00:18:37,930 --> 00:18:41,670
+ال domain تبعها على المستوى x y او على المستوى z
+
+174
+00:18:41,670 --> 00:18:47,240
+تساوي zero بيكون ايش هو الحجم تبعنااللي هو عبارة
+
+175
+00:18:47,240 --> 00:18:51,160
+عن مين؟ عبارة عن تكامل لـ function f of x و y على
+
+176
+00:18:51,160 --> 00:18:56,720
+المنطقة R أو الـ f of x و y هي z أو تكامل على z
+
+177
+00:18:56,720 --> 00:19:00,260
+لمين او .. إذا لو قال لي هاتلي سؤال و قال لي هاتلي
+
+178
+00:19:00,260 --> 00:19:04,600
+ال volume بشيله z و بحقم انت بدلالة x و y و بروح
+
+179
+00:19:04,600 --> 00:19:07,740
+بكامل حدود التكامل اللي بدي أجيبها من وين؟ من ال
+
+180
+00:19:07,740 --> 00:19:13,180
+domain او من المجال تبع هذه ال function كيف؟ ليش z
+
+181
+00:19:13,180 --> 00:19:18,410
+تكامل من وين؟ما هو التكامل يا ستي هذا لما يكون
+
+182
+00:19:18,410 --> 00:19:23,130
+أعلى ال exactness من calculus ايه تطلع بقيمة موجبة
+
+183
+00:19:23,130 --> 00:19:27,710
+وإذا نزلتي تحت بصير ايه يا عزيزي قيمة سالبة لما لو
+
+184
+00:19:27,710 --> 00:19:30,510
+كان ايش شوية فوق و شوية تحت يمكن ينطلع عندك
+
+185
+00:19:30,510 --> 00:19:33,850
+التكامل ب zero إذا المنطقة اللي فوق ضد المنطقة
+
+186
+00:19:33,850 --> 00:19:38,260
+اللي تحت بتقول معقول مساحة تطلع zeroالسؤال الثاني
+
+187
+00:19:38,260 --> 00:19:43,520
+يمكن لو كانت كلها أسفل لمحور X يبقى بتطلع كلها
+
+188
+00:19:43,520 --> 00:19:46,380
+سالبة، بتقول المعقول ان مساحات تطلع سالبة؟ مافيش
+
+189
+00:19:46,380 --> 00:19:50,160
+مساحة في الدنيا سالبة، إذا في شغل غلط بتقوله، يبقى
+
+190
+00:19:50,160 --> 00:19:54,540
+احنا ضمننا هيك أنه لا يطلع ال zero ولا إشارة
+
+191
+00:19:54,540 --> 00:19:58,040
+سالبة، أنا بحكي على ذلك في one variable، لما ننتقل
+
+192
+00:19:58,040 --> 00:20:03,500
+إلى ال two variables يبقى أنا بصيرأسفل الـ X Y
+
+193
+00:20:03,500 --> 00:20:07,220
+Plane و أعلى الـ X Y Plane يبقى تبقى منطقة موجبة
+
+194
+00:20:07,220 --> 00:20:10,240
+ومنطقة سلبة ربما يلغوا بعض بيطلع التكمل اندي بـ
+
+195
+00:20:10,240 --> 00:20:16,880
+Zero والمعقول حجم يطلع Zeroزي ما أقول يبقى اشتراك
+
+196
+00:20:16,880 --> 00:20:21,660
+موجبة لكن لو كانت اشي فوق و اشي تحت بجسمها إلى
+
+197
+00:20:21,660 --> 00:20:25,520
+جسمين و بروح بحسب المنطقة اللي فوق و المنطقة اللي
+
+198
+00:20:25,520 --> 00:20:29,880
+تحت و باخد ال absolute value و بجمعها بعضيا نجداش
+
+199
+00:20:29,880 --> 00:20:33,760
+اللي هو القيم الحقيقية سؤال وجهي لسؤالته يعني هي
+
+200
+00:20:33,760 --> 00:20:37,240
+دراسته في Calculusية و احنا ذكرناه باللي درسته في
+
+201
+00:20:37,240 --> 00:20:42,460
+Calculusية و سحبنا عليه Calculusطيب نرجع لماين
+
+202
+00:20:42,460 --> 00:20:46,260
+لكلام اللي عندنا هذا حدا فيكوا إلا أي تساؤل حول
+
+203
+00:20:46,260 --> 00:20:50,100
+الكلمتين اللي عندنا هدول في عندكوا في الكتاب حوالي
+
+204
+00:20:50,100 --> 00:21:01,680
+خمس مسائل تقريبا هذا أحدهم example find
+
+205
+00:21:01,680 --> 00:21:11,210
+the volume of the region find the volume ofthe
+
+206
+00:21:11,210 --> 00:21:18,630
+region متقدش حجم المنطقة bounded above bounded
+
+207
+00:21:18,630 --> 00:21:23,210
+above
+
+208
+00:21:23,210 --> 00:21:30,530
+والمحصولة من أعلى أو المحدودة من أعلى by the
+
+209
+00:21:30,530 --> 00:21:34,790
+surface بالسطح
+
+210
+00:21:35,580 --> 00:21:47,500
+z تساوي 16 ناقص x تربيع ناقص y تربيع and below ومن
+
+211
+00:21:47,500 --> 00:22:01,620
+أسفل by the square بالمربع r اللي هو عبارة عن ال x
+
+212
+00:22:01,620 --> 00:22:08,400
+تتغير من zero لغاية اتنينو ال Y بتتغير من Zero
+
+213
+00:22:08,400 --> 00:22:10,880
+لغاية 2 كذا
+
+214
+00:22:13,730 --> 00:22:18,870
+يبقى يا بنت هذه منطقة مربع وليست مستطيلة لأن
+
+215
+00:22:18,870 --> 00:22:25,550
+المربع هو حالة خاصة من مين؟ من المستطيل زي ايش؟ زي
+
+216
+00:22:25,550 --> 00:22:30,730
+متوازي المستطيلات حالة خاصة من متوازي السطوح
+
+217
+00:22:30,730 --> 00:22:40,110
+المكعب حالة خاصة من متوازي المستطيلات حيث نيجي
+
+218
+00:22:40,110 --> 00:22:41,470
+للحل solution
+
+219
+00:22:46,130 --> 00:22:50,250
+سمعتوا متوازي السطوح ولا لا يا بنات؟ خلال كل كلصي
+
+220
+00:22:50,250 --> 00:22:56,970
+تبعنا او ال pipe ايش سمناها؟ parallel pipe مظبوط
+
+221
+00:22:56,970 --> 00:23:01,050
+له متوازي السطوح متوازي السطوح هو عبارة عن منشور
+
+222
+00:23:01,050 --> 00:23:05,820
+رباعي جميع أوجهه الست متوازية الأطباقمتوازي
+
+223
+00:23:05,820 --> 00:23:11,420
+المستطيلات هو منشور جميع أوجهه الستة مستطيلات زي
+
+224
+00:23:11,420 --> 00:23:14,940
+الغرفة اللي احنا فيها أي مستطيل هناك مستطيل التاني
+
+225
+00:23:14,940 --> 00:23:18,520
+مستطيل ومستطيل الساقف الأرض كلها مستطيلة تمام
+
+226
+00:23:18,520 --> 00:23:24,980
+المكعةجميع وجهه الستة مربعات وكلها مربعات متطابقة
+
+227
+00:23:24,980 --> 00:23:29,900
+تمام يبقى المكعب على قصة متوازد المستطيلات متوازد
+
+228
+00:23:29,900 --> 00:23:33,700
+المستطيلات على قصة متوازد السطوح متوازد السطوح على
+
+229
+00:23:33,700 --> 00:23:41,240
+قصة من المنشور وهكذا تمام؟ طيب يمكننا نعيش لمين
+
+230
+00:23:41,240 --> 00:23:46,180
+لسؤال تبعنا يمكننا نروح أكامل الدالة اللي عندنا
+
+231
+00:23:46,180 --> 00:23:51,970
+هذه تعطين ال volumeمين الدالة هذه اللي هو تكاملين
+
+232
+00:23:51,970 --> 00:24:00,090
+على R لمين لستة عشر ناقص X تربيع ناقص Y تربيع
+
+233
+00:24:12,040 --> 00:24:16,080
+بنطلع في المثل اللي قدامي بالكامل بالنسبة ل X و
+
+234
+00:24:16,080 --> 00:24:18,280
+الله بالنسبة له اتنين نفس الشيء يبقى ما معانا
+
+235
+00:24:18,280 --> 00:24:24,180
+مشكلة يبقى بده اروح اقول مثلا DXDY برجع ال X من
+
+236
+00:24:24,180 --> 00:24:30,460
+صفر لاتنينوالـ y كذلك من صفر لغاية اتنين يعني احنا
+
+237
+00:24:30,460 --> 00:24:33,840
+بنكمل على منطقة مربعة الشكل ال domain تبع ال
+
+238
+00:24:33,840 --> 00:24:38,800
+service هي منطقة مربعة الشكل هذا الكلام بدل يساوي
+
+239
+00:24:38,800 --> 00:24:41,860
+تكامل من zero لغاية اتنين
+
+240
+00:24:53,580 --> 00:25:02,180
+يبقى كل هذا الكلام من صفر لغاية اتنين لدي واي يبقى
+
+241
+00:25:02,180 --> 00:25:06,820
+يساوي integration من صفر لغاية اتنين نعوض بالقيمة
+
+242
+00:25:06,820 --> 00:25:19,180
+اللي فوق يبقى ناقص
+
+243
+00:25:19,180 --> 00:25:29,420
+تمانية على تلاتةبعدها ناقص اتنين Y تربيع ناقص Zero
+
+244
+00:25:29,420 --> 00:25:35,060
+زائد Zero زائد Zero كله بروح يعني بهذه النتيجة
+
+245
+00:25:35,060 --> 00:25:40,760
+مباشرة كله بالنسبة لمين ده دي واعي طيب بدنا نجمع
+
+246
+00:25:40,760 --> 00:25:45,900
+هذول ابنات تلاتة في اتنين و تلاتين ستة و تسعين
+
+247
+00:25:45,900 --> 00:25:51,410
+شيلي تمانية وضل تمانية و تمانينيبقى احنا بدنا نكمل
+
+248
+00:25:51,410 --> 00:25:58,070
+من zero للاتنين لتمانية وتمانين على تلاتة ناقص
+
+249
+00:25:58,070 --> 00:26:05,630
+اتنين Y تربيع كله بالنسبة لمين لدي Y يبقى هذا
+
+250
+00:26:05,630 --> 00:26:07,010
+الكلام بده يساوي
+
+251
+00:26:16,210 --> 00:26:24,010
+و تكيب و الحقيقة كمان من zero لغاية اتنين نجلعهم
+
+252
+00:26:24,010 --> 00:26:28,570
+في الاتنين اتنين في تمانية ستة عشر اتنين في تمانية
+
+253
+00:26:28,570 --> 00:26:37,350
+سبعة عشر على تلاتة ناقص و اي تكيب عن اتنين تكيب
+
+254
+00:26:37,350 --> 00:26:45,180
+تمانية في اتنينعلى تلاتة ناقص Zero زائد Zero
+
+255
+00:26:45,180 --> 00:26:52,620
+بقيرمها السلامة يبقى 176 نطرح منهم 16 بيبقى 160
+
+256
+00:26:52,620 --> 00:26:57,840
+على تلاتة حجم المنطقة المحصورة بين ال surface اللي
+
+257
+00:26:57,840 --> 00:27:05,400
+عندنا هذا وما بين مين المربع هذا بنات ال section
+
+258
+00:27:05,400 --> 00:27:11,090
+هو أبسط section موجود في الشطر هذا كلهومش محتاج لا
+
+259
+00:27:11,090 --> 00:27:16,190
+لف ولا دوران زي ما انت شايفين وكلها أمثلة واسئلة
+
+260
+00:27:16,190 --> 00:27:21,030
+بسيطة يبقى انتهينا من هذا ال section وإلى يكون
+
+261
+00:27:21,030 --> 00:27:28,670
+أقام المسائل يبقى exercises خمس تاشر واحد مسائل من
+
+262
+00:27:28,670 --> 00:27:38,630
+واحد لغاية تمانية وعشرين القادة section خمس تاشر
+
+263
+00:27:38,630 --> 00:27:46,130
+اتنينيبقى section خمستاشر اتنين بتحدث برضه عن ال
+
+264
+00:27:46,130 --> 00:27:51,270
+double integrals بس بطلنا ايش نقول على منطقة مربعة
+
+265
+00:27:51,270 --> 00:27:55,710
+على منطقة مينما كانت تكون وهذا بتبقى أتجل شوية
+
+266
+00:27:55,710 --> 00:28:00,990
+وحدود التكامل ليس بضرورة أن تكون كلها قيم عددية
+
+267
+00:28:00,990 --> 00:28:05,930
+هلاحظ بعض الحدود تصير functions يعني متغيرات وهذا
+
+268
+00:28:05,930 --> 00:28:14,310
+ما سنراه بعد قليليبقى بجي بقول double integrals
+
+269
+00:28:14,310 --> 00:28:22,410
+over
+
+270
+00:28:22,410 --> 00:28:27,830
+general
+
+271
+00:28:27,830 --> 00:28:30,830
+regions
+
+272
+00:28:39,900 --> 00:28:45,660
+حاجة اسمها إذا عدت نقاط النقطة الأولى يجب أن يأخذ
+
+273
+00:28:45,660 --> 00:29:00,340
+double integrals تكاملات مثلائية over bounded non
+
+274
+00:29:00,340 --> 00:29:01,640
+rectangular region
+
+275
+00:29:20,030 --> 00:29:23,730
+يعني يا بناتي احنا ال section اللي فات كنا بناخد
+
+276
+00:29:23,730 --> 00:29:29,310
+التكامل على منطقة مستطيلة تمام الان بدل منطقة
+
+277
+00:29:29,310 --> 00:29:33,730
+مستطيلة او منطقة مربعة بدنا نروح ل general region
+
+278
+00:29:33,730 --> 00:29:38,310
+منطقة عامة يمكن تكون مثلة، يمكن تكون متوازية
+
+279
+00:29:38,310 --> 00:29:42,870
+اطلاع، يمكن تكون دائرة، يمكن .. يمكن .. يمكن شكل
+
+280
+00:29:42,870 --> 00:29:46,750
+احنا ماحناش عارفينه، يمكن شبه من الله أعلم، ايش
+
+281
+00:29:46,750 --> 00:29:50,660
+مكانة تكون، تمام؟يبقى يقول double integrals over
+
+282
+00:29:50,660 --> 00:29:55,340
+general regions اللي هي منطقة عامة اجي يقول double
+
+283
+00:29:55,340 --> 00:29:59,280
+integrals over bounded non rectangular regions
+
+284
+00:29:59,280 --> 00:30:03,760
+يبقى احنا بطلاش المستطيلة يبقى non rectangular
+
+285
+00:30:03,760 --> 00:30:07,800
+region منطقة غير مستطيلة اش ما كانت تكون المنطقة
+
+286
+00:30:07,800 --> 00:30:13,480
+هذه هنعطي نظرية بناء عليه نستخدم هذه النظرية في حل
+
+287
+00:30:13,480 --> 00:30:24,830
+المثال النظرية بتقول ما يأتيtheorem let f of x,y
+
+288
+00:30:24,830 --> 00:30:37,090
+be continuous دالة مبتصلة on a region R على
+
+289
+00:30:37,090 --> 00:30:43,710
+المنطقة R دي من واحد if
+
+290
+00:30:43,710 --> 00:30:58,020
+ال Ris defined by معظمك التالي ال X أكبر من أو
+
+291
+00:30:58,020 --> 00:31:04,000
+تساوي A وأقل من أو تساوي B وال G واحد as a
+
+292
+00:31:04,000 --> 00:31:10,360
+function of X أقل من أو تساوي Y أقل من أو تساوي G2
+
+293
+00:31:10,360 --> 00:31:27,480
+of X with G واحدand G2 are continuous كانوا
+
+294
+00:31:27,480 --> 00:31:39,720
+دوال متصلة على الفترة المغلقة A وB then تكاملين
+
+295
+00:31:39,720 --> 00:31:46,840
+على منطقة R لل F of XYDA
+
+296
+00:31:48,020 --> 00:31:53,820
+بتساوي التكامل الأول من a إلى b التكامل التاني من
+
+297
+00:31:53,820 --> 00:32:09,240
+g1 of x إلى g2 of x لل F of x y dy dx نقطة
+
+298
+00:32:09,240 --> 00:32:17,440
+ثانية F ال R is defined
+
+299
+00:32:21,670 --> 00:32:31,630
+H1 of Y أقل من أو يساوي Y أقل من أو يساوي D H2 of
+
+300
+00:32:31,630 --> 00:32:35,950
+Y أقل من أو يساوي X أقل من أو يساوي
+
+301
+00:32:53,380 --> 00:33:02,180
+كانوا دوال متصلة على الفترة المغلقة C وD ثم
+
+302
+00:33:02,180 --> 00:33:12,920
+تكاملت على A لل F of XYDA بدي يعطيني تكاملت الأول
+
+303
+00:33:12,920 --> 00:33:18,400
+من C إلى D والتاني من H1 of Y
+
+304
+00:33:21,830 --> 00:33:30,770
+لل H2 of Y لل F of X of Y DX D1
+
+305
+00:34:08,910 --> 00:34:12,530
+نرجع الكلام اللي كتبناه مرة تانية نقرأ ثاني و
+
+306
+00:34:12,530 --> 00:34:16,910
+نحاول نفهم قال يفترض ان انا لك F of X و Y of B
+
+307
+00:34:16,910 --> 00:34:22,230
+continuous على region R مين هي ال region R حالة
+
+308
+00:34:22,230 --> 00:34:27,590
+الأولى ال R is defined by X تتغير من A إلى B و ال
+
+309
+00:34:27,590 --> 00:34:32,790
+Y تتغير من G1 of X إلى G2 of X و ال G1 و ال G2
+
+310
+00:34:32,790 --> 00:34:37,710
+continuous على نفس الفترة كيف يعني تعالى نشوف تلقى
+
+311
+00:34:37,710 --> 00:34:46,170
+مجاناةهذه محور X وهذه محور Y وهذا نقطة الأصل على
+
+312
+00:34:46,170 --> 00:34:53,050
+سبيل المثال رحت أخد الفترة اللي قاللي عنها الأولي
+
+313
+00:34:53,050 --> 00:35:01,610
+A وB A وB تعتبر للمتغير من X يبقى على محور X بدي
+
+314
+00:35:01,610 --> 00:35:06,390
+أعمل تغيير من نقطة A لنقطة B
+
+315
+00:35:09,500 --> 00:35:15,060
+Y تتغير من G1 of X إلى G2 of X
+
+316
+00:35:24,800 --> 00:35:31,780
+يعني مين يعني Y تساوي G1 of X Y هي function في X
+
+317
+00:35:31,780 --> 00:35:37,160
+رسمت المنحنى ثاني فكان المنحنى التاني مثلا بالشكل
+
+318
+00:35:37,160 --> 00:35:45,890
+اللي عندنا هذا يبقى هذا ال Y تساوي G2 of Xالان في
+
+319
+00:35:45,890 --> 00:35:51,590
+منطقة محصورة بين المنحنيين A وB بين المنحنيين
+
+320
+00:35:51,590 --> 00:35:57,850
+الأول والثاني على الفترة من A إلى B جت من هنا طالع
+
+321
+00:35:57,850 --> 00:36:01,910
+هك الشكل اللي عندنا هذا و من هنا جت طالع بالشكل
+
+322
+00:36:01,910 --> 00:36:08,010
+هذا و كل جي واحد و جي اتنين دوال متاصلة اذا ما بين
+
+323
+00:36:08,010 --> 00:36:14,370
+المنحنيين هدول انحصرت المنطقة اللي عندنا هذا تمام؟
+
+324
+00:36:15,200 --> 00:36:19,600
+بتنا الكامل الـ function اللي عندنا هذه على هذه
+
+325
+00:36:19,600 --> 00:36:26,160
+المنطقة يبقى لاحظي ان جي واحد of x أقل من جي اتنين
+
+326
+00:36:26,160 --> 00:36:31,420
+of x و y محصورة ما بين الاتنين تمام هذه واحدة
+
+327
+00:36:31,420 --> 00:36:36,360
+التانية ال X ستتغير من ايه إلى وين من A إلى B
+
+328
+00:36:36,360 --> 00:36:41,720
+بوصولة من هذه المنطقة المظلة لهذه تماميبقى بيكون
+
+329
+00:36:41,720 --> 00:36:48,540
+التكامل الفنكشن يسوي التكامل الفنكشن dy dx حطيت
+
+330
+00:36:48,540 --> 00:36:54,000
+المتغير في الأول y هي g1 of x و y واحد و y اتنين
+
+331
+00:36:54,000 --> 00:36:59,860
+هي g2 of x يبقى بدأت لما الأكامل هاد دول دوال في x
+
+332
+00:36:59,860 --> 00:37:03,620
+على عكس مكان ما فيه في ال section السابق كانوا
+
+333
+00:37:03,620 --> 00:37:10,140
+أرقامهذه لأ بيعطيني متغيرات نفس من المتغيرات بس
+
+334
+00:37:10,140 --> 00:37:15,660
+بيطلع بدلالة من X بكمل Y بطلع الجواب بدلالة X في
+
+335
+00:37:15,660 --> 00:37:18,780
+عندي مشكلة مافي عندي مشكلة لإن باقي الدالة اللي
+
+336
+00:37:18,780 --> 00:37:24,240
+ضايلة بصير بدلالة من X لكن X تتغير من رقم إلى رقم
+
+337
+00:37:24,240 --> 00:37:30,180
+إذا بطلع في الجواب رقم واحدطبعا يبقى هذا يعني لكن
+
+338
+00:37:30,180 --> 00:37:35,960
+لو حطيت لو كانت السؤال حطيت المتغيرات في الآخر و
+
+339
+00:37:35,960 --> 00:37:40,740
+الاعداد في الأول عمرك ماحجيب نتيجة طبعا يبقى في
+
+340
+00:37:40,740 --> 00:37:44,480
+هذه الحالة بكون انا مجبر ان اكمل بالنسبة لواي في
+
+341
+00:37:44,480 --> 00:37:49,060
+الأول ثم اروح اكمل بالنسبة لمين الاكس هذه الحالة
+
+342
+00:37:49,060 --> 00:37:51,080
+الأولى نجي الحالة التانية
+
+343
+00:37:56,810 --> 00:38:01,950
+لكن ال X محصورة بين two functions وكل function
+
+344
+00:38:01,950 --> 00:38:07,830
+دالة في Y ب X as a function of Y with each one of
+
+345
+00:38:07,830 --> 00:38:11,370
+its two continuous functions على الفترة اللي هو C
+
+346
+00:38:11,370 --> 00:38:16,930
+وD كيف يكونوا دالة؟ طلعيلي كويس هاي المحاور هذا
+
+347
+00:38:16,930 --> 00:38:23,420
+محور Xهذا محور Y وهذه نقطة الاصد اللي عندك افترضي
+
+348
+00:38:23,420 --> 00:38:28,660
+رسمت المنحنى فكان المنحنى الأول بالشكل اللي عندنا
+
+349
+00:38:28,660 --> 00:38:38,420
+هذا يبقى هذا ال X تساوي H1 of Y جينا رسمنا المنحنى
+
+350
+00:38:38,420 --> 00:38:43,060
+التاني فطلع بقدر الله طلع المنحنى التاني بالشكل
+
+351
+00:38:43,060 --> 00:38:51,830
+اللي عندك هذايبقى هذا ال X يساوي H2O روحنا على
+
+352
+00:38:51,830 --> 00:38:57,270
+محور Y قال لي تتغير ال Y بين C وD قلنا هي النقطة
+
+353
+00:38:57,270 --> 00:39:01,870
+كانت نقطة C و هي النقطة التانية اللي هي نقطة D
+
+354
+00:39:01,870 --> 00:39:09,500
+رسمت موازي لمحور Xقطع المنحنايين لاتنين هذول إذا
+
+355
+00:39:09,500 --> 00:39:14,020
+المنحنايين مع الخطين الوفوقيين حصروا المنطقة
+
+356
+00:39:14,020 --> 00:39:18,900
+المظللة اللي عندناها، المنطقة الزرقى زي ما انتوا
+
+357
+00:39:18,900 --> 00:39:23,680
+شايفينإذا احنا بنكمل ال function اللي عندنا على
+
+358
+00:39:23,680 --> 00:39:28,820
+المنطقة المضللة اللي عندنا هذه فبصير ايش تكمل ال
+
+359
+00:39:28,820 --> 00:39:33,520
+function على dA بدي احط الدلة اللي بتغير في الأول
+
+360
+00:39:33,520 --> 00:39:38,600
+يمكن بدي أكمل أولا بالنسبة لمين لل X لأن X هي
+
+361
+00:39:38,600 --> 00:39:43,100
+الدلة في Y هدلت أرقام فبصير ان integration من H1
+
+362
+00:39:43,100 --> 00:39:48,360
+of Y لH2 of Y لما نكمل و أعوض مكان ال X ده اللي
+
+363
+00:39:48,360 --> 00:39:53,290
+بدلة Y بصير المثل كلهبدلالة Y بصير سهل أكمله
+
+364
+00:39:53,290 --> 00:39:57,090
+بالنسبة لي بعد ذلك و أعوض بحوز التكامل و بيطلع لنا
+
+365
+00:39:57,090 --> 00:40:04,190
+نتيجة رقما محددة طيب يا بنات هذه انا بمزاجي يعني
+
+366
+00:40:04,190 --> 00:40:08,690
+ممكن اعملها و الله هو بيكون كتبهالي و خالص اقول
+
+367
+00:40:08,690 --> 00:40:14,130
+والله احنا بنتطلع اذا قال لي كامل و second انا بدي
+
+368
+00:40:14,130 --> 00:40:20,020
+اختاره ان احدد كامل بالنسبة لمن لل Xأول أو الواي
+
+369
+00:40:20,020 --> 00:40:25,160
+في الأول يبقى حسب طبيعة المثل ممكن هو يعطيني
+
+370
+00:40:25,160 --> 00:40:30,960
+تكاملين واحد متغير ويحطه لجوا لجوا بالنسبة للمتغير
+
+371
+00:40:30,960 --> 00:40:37,290
+أو المردوشة كامة مابقاش أقوله مش قادر أقوله لابعمل
+
+372
+00:40:37,290 --> 00:40:42,150
+عملية change او reverse بقلب حدود التكامل كيف انا
+
+373
+00:40:42,150 --> 00:40:47,410
+عند المنطقة مثلا اعطيها حدود بدلالة X بتروح احوضها
+
+374
+00:40:47,410 --> 00:40:52,850
+بدلالة Y فبروح برص المنطقة تتكامل و من خلال هذه
+
+375
+00:40:52,850 --> 00:40:56,770
+المنطقة بدل ما كانت الحدود بالنسبة ل X بيخليه نميل
+
+376
+00:40:56,770 --> 00:41:01,770
+بالنسبة ل Y بقلب حدود التكامل وسيل التكامل Sيعني
+
+377
+00:41:01,770 --> 00:41:06,830
+أحيانًا ممكن يجبرني إجبارًا على ذلك ويطلبه و
+
+378
+00:41:06,830 --> 00:41:10,390
+أحيانًا أقول لأ أنا برسوم بطلع لي و بالتالي أنا
+
+379
+00:41:10,390 --> 00:41:13,850
+باختار بالنسبة للإكس أو بالنسبة للواحد سواء كان
+
+380
+00:41:13,850 --> 00:41:17,310
+تاني و لا تاني هشوف الصنفين هاطلس هعطيك قامتلة على
+
+381
+00:41:17,310 --> 00:41:22,330
+الصنفين بحيث انغطيه و بدل المثال هعطيك تمانية بحيث
+
+382
+00:41:22,330 --> 00:41:27,510
+انه فعلا انغطي المادة او نغطي الموضوع تغطية كاملة
+
+383
+00:41:27,510 --> 00:41:33,650
+نبدأ قبل أن أخش القامتلة هل حاضر ان تسألني سؤالهذا
+
+384
+00:41:33,650 --> 00:41:37,510
+كل جزء نظري في ال sketch بس بدنا ايه نبدأ نشتغل
+
+385
+00:41:37,510 --> 00:41:49,170
+عليه نجلمين لل exactly أول
+
+386
+00:41:49,170 --> 00:41:53,990
+مثال ال sketch is a region of integration sketch
+
+387
+00:41:53,990 --> 00:42:00,170
+is a region of
+
+388
+00:42:03,500 --> 00:42:13,480
+Integration أرسلني منطقتي تكامل And evaluate وروح
+
+389
+00:42:13,480 --> 00:42:21,960
+أحسبلي evaluate the integral أحسبلي
+
+390
+00:42:21,960 --> 00:42:30,080
+تكامل نمرأ أيه؟ أريد تكامل من واحد إلى أربعة تكامل
+
+391
+00:42:30,080 --> 00:42:31,220
+من Zero
+
+392
+00:42:52,160 --> 00:42:58,220
+يبقى هذا المثالعطانى تكاملين وقال لي احسن واجبرني
+
+393
+00:42:58,220 --> 00:43:03,380
+انه اكمل بالنسبة لواي في الأول هو كتب هالي وجهها
+
+394
+00:43:03,380 --> 00:43:07,720
+زي هيك تمام وماقالليش قاللي ارسم المنطقة و بعدين
+
+395
+00:43:07,720 --> 00:43:12,260
+كامل بقوله ارسم المنطقة و بعدين بروح بكامل كيف
+
+396
+00:43:12,260 --> 00:43:16,420
+ارسم المنطقة طيب ماعطانيش منطقة هو ماكتبليش R من
+
+397
+00:43:16,420 --> 00:43:21,460
+كذا لكذا X و Y من كذا لكذا بجيب المنطقة من حدود
+
+398
+00:43:21,460 --> 00:43:27,590
+التكامل اذا بروح بقولههذه المحاور اللي عندنا هذا
+
+399
+00:43:27,590 --> 00:43:31,310
+محور X وهذا محور Y وهذا نقطة الأصل
+
+400
+00:43:34,440 --> 00:43:41,380
+لما يقول هنا هذا جذر X يبقى
+
+401
+00:43:41,380 --> 00:43:47,720
+Y تساوي جذر X يبقى
+
+402
+00:43:47,720 --> 00:43:52,900
+Y تساوي جذر X يبقى
+
+403
+00:43:52,900 --> 00:44:02,280
+هذا Y تساوي جذر X ال index اللي تحت Y تساوي من
+
+404
+00:44:02,280 --> 00:44:10,330
+رمينمحور X يبقى هذا له Y تساوي Z يبقى هذه حدات
+
+405
+00:44:10,330 --> 00:44:16,250
+الشغلات بتتغير بالنسبة لمين ل Y بالنسبة لل X كان X
+
+406
+00:44:16,250 --> 00:44:21,350
+تساوي أربعة و X تساوي واحد X تساوي واحد يعني هذا
+
+407
+00:44:21,350 --> 00:44:28,330
+الخط X يساوي واحد وهذا الخط التاني X تساوي أربعة
+
+408
+00:44:29,030 --> 00:44:34,970
+إذا المنطقة المظللة اللى عايزناها دى هي منطقة مين؟
+
+409
+00:44:34,970 --> 00:44:41,850
+منطقة التكامل تمام؟ قال ال sketch رسمناله منطقة
+
+410
+00:44:41,850 --> 00:44:46,430
+التكامل قال يحسبلي هذا التكامل يبقى ضمن عملية حساب
+
+411
+00:44:46,430 --> 00:44:48,730
+التكامل بقولك بيس هذا
+
+412
+00:44:52,540 --> 00:44:56,380
+بتكمل اول شغلة بالنسبة لـ Y يبقى 1 على جدر ال X
+
+413
+00:44:56,380 --> 00:45:00,920
+يعتبر مقدارا يبقى سهل جدا هذا مش في اي اشكالية
+
+414
+00:45:00,920 --> 00:45:06,140
+تلاتة على اتنين مرة التكامل يبقى هاي تلاتة على
+
+415
+00:45:06,140 --> 00:45:11,700
+اتنين لانه مقدار ثابت تكمل من واحد الى اربع تكمل
+
+416
+00:45:11,700 --> 00:45:18,660
+ال X ponential بال X ponential اتسلمبسومة على
+
+417
+00:45:18,660 --> 00:45:23,620
+تفاضل الأوس إذا كانت تفاضل الأوس من الدرجة الأولى
+
+418
+00:45:23,620 --> 00:45:28,120
+طبعا كل أسطن في Y إذا من الدرجة الأولى يبقى مبسومة
+
+419
+00:45:28,120 --> 00:45:35,120
+عداش يا بناه واحد على جدر ال X هذا الحكي كله بدية
+
+420
+00:45:35,120 --> 00:45:44,500
+من Zero لغاية جدر ال X وهذا DX اللي عندناطيب يبقى
+
+421
+00:45:44,500 --> 00:45:49,120
+بيصير المثلة تلاتة على اتنين تكمن واحد إلى أربع
+
+422
+00:45:49,120 --> 00:45:55,280
+هذه جدر ال X بتنجل و بتطلع وين؟ بتطلع فوق فالحين
+
+423
+00:45:55,280 --> 00:45:59,860
+هذي بيدي أشيل كل Y و أحط مكانها جدر X و أشيل كل Y
+
+424
+00:45:59,860 --> 00:46:04,660
+و أحط مكانها Zero يبقى Good لما أشيل Y و أحط
+
+425
+00:46:04,660 --> 00:46:13,460
+مكانها جدر X يبقى E أس يبقى E فاس NowE والزيرو على
+
+426
+00:46:13,460 --> 00:46:17,480
+جدر X بزيرو E والزيرو بواحد
+
+427
+00:46:19,610 --> 00:46:25,550
+يبقى ال E ناقص واحد صارت مقدار ثابت مظبوط يبقى كأن
+
+428
+00:46:25,550 --> 00:46:31,250
+المسألة أصبح تاندي تلاتة على اتنين اللي برا في E
+
+429
+00:46:31,250 --> 00:46:36,790
+ناقص واحد كله مقدار ثابت مانيش دعوة وهي تكامل من
+
+430
+00:46:36,790 --> 00:46:41,230
+واحد لبايت الأربعة لل X أص نص DX
+
+431
+00:46:43,760 --> 00:46:53,500
+يبقى السؤال عندي تلاتة على اتنين تلاتة
+
+432
+00:46:53,500 --> 00:46:58,300
+على اتنين تلاتة على اتنين تلاتة على اتنين تلاتة
+
+433
+00:46:58,300 --> 00:47:03,220
+على اتنين تلاتة على اتنين تلاتة على اتنين تلاتة
+
+434
+00:47:03,220 --> 00:47:03,600
+على اتنين تلاتة على اتنين تلاتة على اتنين تلاتة
+
+435
+00:47:03,600 --> 00:47:03,620
+على اتنين تلاتة على اتنين تلاتة على اتنين تلاتة
+
+436
+00:47:03,620 --> 00:47:04,220
+على اتنين تلاتة على اتنين تلاتة على اتنين تلاتة
+
+437
+00:47:04,220 --> 00:47:05,920
+على اتنين تلاتة على اتنين تلاتة على اتنين تلاتة
+
+438
+00:47:05,920 --> 00:47:08,400
+على اتنين تلاتة على اتنين تلاتة على اتنين تلاتة
+
+439
+00:47:08,400 --> 00:47:11,620
+على اتنين تلاتة على اتن
+
+440
+00:47:14,630 --> 00:47:21,570
+أربعة تكييب تحت الجدر التربيعي أربعة تكييب أربعة
+
+441
+00:47:21,570 --> 00:47:24,070
+وستين أربعة في أربعة في ستاشر في أربعة في أربعة
+
+442
+00:47:24,070 --> 00:47:29,510
+وستين تحت الجدر التربيعي بتمانية يبقى هذه في
+
+443
+00:47:29,510 --> 00:47:36,930
+تمانية ناقص واحد أسر بكيانه بواحد يبقى الجواب
+
+444
+00:47:36,930 --> 00:47:44,220
+النهائي سبعة في ناقص واحدهذه قيمة التكامل اللي
+
+445
+00:47:44,220 --> 00:47:45,560
+موجود عندنا
+
+446
+00:48:18,030 --> 00:48:25,370
+نمر بيه من السؤال بيقول
+
+447
+00:48:25,370 --> 00:48:33,150
+بدي تكامل من Zero لغاية تلاتة على اتنين تكامل اخر
+
+448
+00:48:33,150 --> 00:48:44,890
+من واحد لغاية اربعة ناقص اتنين U لمن؟ للاربعة ناقص
+
+449
+00:48:44,890 --> 00:49:03,030
+اتنين U علىV تربيع كل هذا الكلام دي V دي U طبعا
+
+450
+00:49:03,030 --> 00:49:06,350
+واضح أنه سهل أكون بالنسبة ل V بالأول لأن الأربع
+
+451
+00:49:06,350 --> 00:49:09,910
+ناقص اتنين U وهذا كله يعتبر constant إذا قُرِن
+
+452
+00:49:09,910 --> 00:49:15,970
+بالـV إذا بتروح أرسمله منطقة التكامل في الأولبقوله
+
+453
+00:49:15,970 --> 00:49:21,150
+كويس يجي انا بدل المحاور X Y بنتش صار عندي صار
+
+454
+00:49:21,150 --> 00:49:29,970
+المحور الأول U والمحور التاني V قال لي كويس V هي
+
+455
+00:49:29,970 --> 00:49:35,830
+ممكن تداشي بواحد يبقى في عندي خط أفقي هيك هذه V
+
+456
+00:49:35,830 --> 00:49:43,990
+تساوي واحدتانى V تساوي اربعة نقص اتنين U يبقى لما
+
+457
+00:49:43,990 --> 00:49:49,610
+اقول V تساوي اربعة نقص اتنين U معادلة ايه شهية
+
+458
+00:49:49,610 --> 00:49:53,410
+اللي هنا خط مستقيم خط المستقيم مش هان ارسمه
+
+459
+00:49:53,410 --> 00:49:59,730
+بكافيني نقطتين عليه بقوله ماشي لو كانت ال U ب zero
+
+460
+00:49:59,730 --> 00:50:05,710
+إذا V بقى ده يبقى باجي عند ال zero هي و باجي طالع
+
+461
+00:50:05,710 --> 00:50:11,970
+اربعة كويسيبقى هدا V هيو هنا و خليها لمين اللي هي
+
+462
+00:50:11,970 --> 00:50:16,810
+أربعة يبقى هدا النقطة Zero أربعة تقع على وين؟ على
+
+463
+00:50:16,810 --> 00:50:23,570
+الخط المستقيم لو كانت ال U مثلا هذه لو كانت ال U ب
+
+464
+00:50:23,570 --> 00:50:30,790
+Zero طب لو كانت ال U باتنينبتنين بتطلع ال V بزيرو
+
+465
+00:50:30,790 --> 00:50:35,150
+يبقى هذا اللي بدي أقطع الخط عند النقطة هنا جديد
+
+466
+00:50:35,150 --> 00:50:41,670
+اللي هي هذه اللي هي اتنين وزيرو بجي بمسك هذه
+
+467
+00:50:41,670 --> 00:50:48,510
+المصطرة و بوصل بين النقطتين و ببد الخط على استقالة
+
+468
+00:50:48,510 --> 00:50:55,070
+بهذا الشكل طبعا كويس نجي بعد هيكالـ U تتغير من
+
+469
+00:50:55,070 --> 00:50:58,890
+عندي الـ Zero لغاية تلاتة على اتنين تلاتة على
+
+470
+00:50:58,890 --> 00:51:03,310
+اتنين يعني كده؟ واحد و نص تلاتة على اتنين يبقى في
+
+471
+00:51:03,310 --> 00:51:11,830
+جيلك هنا واحد و نص تلاتة على اتنين طيب باجي بقول
+
+472
+00:51:11,830 --> 00:51:18,600
+طب لو كانت U تلاتة على اتنينلو كانت ال U بتلاتة
+
+473
+00:51:18,600 --> 00:51:24,320
+على اتنين بصير U ناقص تلاتة اليوم واحد يبقى هذه
+
+474
+00:51:24,320 --> 00:51:29,080
+بتيجي هنا بالضبط و بتتقابل وين عند النقطة هذه
+
+475
+00:51:29,080 --> 00:51:39,480
+تماما يبقى احنا كأنه عند المثلث المظلل هذا فقط
+
+476
+00:51:39,480 --> 00:51:46,840
+مابيهيبقى من هنا ال U تساوي Zero لغاية ال U تساوي
+
+477
+00:51:46,840 --> 00:51:51,980
+اللي هو تلاتة على اتنين المنطقة من هنا لغايتنا
+
+478
+00:51:51,980 --> 00:51:55,680
+طالعنا قابلنا مع الخطين اللي اتنين هدول صارت
+
+479
+00:51:55,680 --> 00:51:59,740
+المنطقة المضلة للزرق اللي قدامنا هذه يبقى هذه من
+
+480
+00:51:59,740 --> 00:52:04,170
+منطقة التكامل اللي موجودة عندناطيب، بدنا نروح
+
+481
+00:52:04,170 --> 00:52:13,010
+الكامل الآن، بدا الكامل بالنسبة .. كيف؟ هعكسلك
+
+482
+00:52:13,010 --> 00:52:16,530
+المحاور، بس اصبر شوية مش هالحين، بعد قليل، بعد ما
+
+483
+00:52:16,530 --> 00:52:20,250
+نخلص المثال هذا، هخليك بدل السؤال تلاتة تعكس
+
+484
+00:52:20,250 --> 00:52:26,870
+المحاور غصب عنك، مش بخاطرك، تمام؟ طيب، لو عكستي،
+
+485
+00:52:26,870 --> 00:52:31,170
+هيتغيروا الحدود، كل الأربع حدود ممكن يتغيروا كلهم
+
+486
+00:52:31,170 --> 00:52:37,230
+ولا واحد يظل زي التانيبس لو عكس بصير سهل أكمل
+
+487
+00:52:37,230 --> 00:52:41,370
+بالنسبة ل U كذلك، زي ما قاله سهل أكمل بالنسبة ل V،
+
+488
+00:52:41,370 --> 00:52:46,490
+يبجد كأنه بدا كامل مين؟ بالنسبة ل V بدا كامل مين؟
+
+489
+00:52:46,490 --> 00:52:50,210
+واحد على V تربية، لأن أربعة نقص اتنين U يعتبر
+
+490
+00:52:50,210 --> 00:52:56,990
+كنصة، وتكامل واحد على V تربية بقداش؟- 1 على V إذا
+
+491
+00:52:56,990 --> 00:53:02,290
+هذي لو جاءت كملة بدى يصير تكمل من Zero لتلاتة على
+
+492
+00:53:02,290 --> 00:53:07,670
+اتنين وهنا اربعة نقص اتنين U مالكش دعوة وهذه
+
+493
+00:53:07,670 --> 00:53:14,610
+تكملها ب- 1 على V وبيجي اقول من هنا من واحد لاربعة
+
+494
+00:53:14,610 --> 00:53:17,690
+نقص اتنين U في الديل
+
+495
+00:53:20,650 --> 00:53:25,070
+يبقى هذا الكلام بيساوي تكامل من 0 إلى 3 على 2
+
+496
+00:53:25,070 --> 00:53:30,950
+للاربعة ناقص 2U فيه فتعود بالقيمة اللي فوق ناقص
+
+497
+00:53:30,950 --> 00:53:37,190
+اللي تحت يبقى ناقص واحد على اربعة ناقص اتنين U
+
+498
+00:53:37,190 --> 00:53:42,290
+ناقص مع ناقص بصير زائد واحد على واحد اللي يبقى
+
+499
+00:53:42,290 --> 00:53:50,520
+درجة واحد يبقى عوضنا بالقيمة اللي فوقنقص القيمة
+
+500
+00:53:50,520 --> 00:53:55,980
+اللي تحصل بالشكل هذه وكل هذا بالنسبة لمن؟ لل DU
+
+501
+00:53:55,980 --> 00:54:01,100
+يساوي integration من زيرو لغاية تلاتة على تالتة
+
+502
+00:54:01,100 --> 00:54:06,880
+بدا افك الجثة ده بنات وشير جداش عندي هنا ناقص واحد
+
+503
+00:54:06,880 --> 00:54:15,200
+وهنا زائد اربع ناقص اتنين U كله بالنسبة ل DUيبقى
+
+504
+00:54:15,200 --> 00:54:19,660
+هذا بيصير تكامل من zero لغاية تلاتة على اتنين
+
+505
+00:54:19,660 --> 00:54:26,960
+لمين؟ ليه تلاتة نقص اتنين يهودي؟ هذه لو روحت
+
+506
+00:54:26,960 --> 00:54:33,690
+كاملتها تعطيلي ما يأتي يساوياللي هو مين؟ تلاتة U
+
+507
+00:54:33,690 --> 00:54:39,530
+ناقص U تربيع على اتنين بتروح مع الاتنين وانحكي هذا
+
+508
+00:54:39,530 --> 00:54:45,390
+كله بالهند ال zero لغاية تلاتة على اتنين و U ساوي
+
+509
+00:54:45,390 --> 00:54:51,750
+تلاتة على اتنين بيصير كده؟ تسعة على اتنين ناقص
+
+510
+00:54:51,750 --> 00:54:57,320
+تلاتة على اتنين تربيع بتسعة على اربعةنقص تسعة على
+
+511
+00:54:57,320 --> 00:55:04,640
+أربعة نقص زيرو زائد زيرو يبقى تسعة على اتنين نقص
+
+512
+00:55:04,640 --> 00:55:09,680
+تسعة على أربعة يبقى تسعة على أربعة
+
+513
+00:55:39,360 --> 00:55:47,900
+ناخد كمان مثال مثال اتنين بيقول sketch the region
+
+514
+00:55:47,900 --> 00:55:56,700
+of integration sketch that region of
+
+515
+00:55:56,700 --> 00:56:02,160
+integration of
+
+516
+00:56:02,160 --> 00:56:08,060
+some من منطقة التكامل عن ال right
+
+517
+00:56:13,420 --> 00:56:20,200
+فاصلة right right
+
+518
+00:56:20,200 --> 00:56:31,140
+and evaluate the
+
+519
+00:56:31,140 --> 00:56:38,580
+equivalent double
+
+520
+00:56:38,580 --> 00:56:39,160
+integral
+
+521
+00:56:48,010 --> 00:56:53,190
+with the order of with
+
+522
+00:56:53,190 --> 00:56:58,970
+the order of
+
+523
+00:56:58,970 --> 00:57:05,250
+integration reversed
+
+524
+00:57:05,250 --> 00:57:11,550
+أمر
+
+525
+00:57:11,550 --> 00:57:20,800
+a يتكاول من zero لغاية اتنينتكامل من سالب الجدرى
+
+526
+00:57:20,800 --> 00:57:25,740
+التربيع إلى أربعة ناقص x تربية للجدرى التربيع إلى
+
+527
+00:57:25,740 --> 00:57:32,560
+أربعة ناقص x تربية إلى ستة x dy dx
+
+528
+00:58:07,780 --> 00:58:13,540
+سؤال عبارة عن ثلاث مطاليب ارسم منطقة التكامل 2
+
+529
+00:58:13,540 --> 00:58:18,800
+اكتب لي واحسب لي equivalent double integrals with
+
+530
+00:58:18,800 --> 00:58:22,220
+order of integration reversed يعني ايش؟ يعني بدي
+
+531
+00:58:22,220 --> 00:58:27,340
+اغير حدود التكامل اللي عندنا هذه زي السؤال اللي
+
+532
+00:58:27,340 --> 00:58:32,060
+سألته قبل قليل ومن ثم بعد ما اغير حدود التكامل بدي
+
+533
+00:58:32,060 --> 00:58:37,050
+اروح احسب من التكاملتعالوا هنشوف كيف بدنا نرسم
+
+534
+00:58:37,050 --> 00:58:41,550
+الرسمة وكيف نتغير حدود التكامل وبعدين التكامل يصبح
+
+535
+00:58:41,550 --> 00:58:45,330
+روتينيا زي ما حسبنا قبل شوية بنحسب هذا التكامل
+
+536
+00:58:45,330 --> 00:58:51,370
+ابقى بروح باخد المحاور اللي عندنا بهذا الشكل بقش
+
+537
+00:58:51,370 --> 00:58:56,650
+بقول هذا محور X هذا محور Y هذا نحو الأصل اللي هي
+
+538
+00:58:56,650 --> 00:59:02,830
+Zero هذه المناط لما أجي لأول متغير عندي Y يبقى Y
+
+539
+00:59:02,830 --> 00:59:10,750
+تساوي هذا الجدر يبقى لو جربه الحل كتالي ال Y تساوي
+
+540
+00:59:10,750 --> 00:59:14,790
+الجدر التربيع إلى أربعة نقص X تربيع بدي أرفع
+
+541
+00:59:14,790 --> 00:59:22,150
+معادلتيش لو ربعت الطرفين مش بصير بنات بصير Y تربيع
+
+542
+00:59:22,150 --> 00:59:28,760
+زائد X تربيع تساوي أربعةمعادلة ايه؟ هاي دائرة
+
+543
+00:59:28,760 --> 00:59:33,200
+ممتاز لكن هل هي دائرة كاملة ولا نص دائرة ولا
+
+544
+00:59:33,200 --> 00:59:37,080
+مدائرة ولا ثلاث تربع دائرة هذا اللي احنا مش عارفين
+
+545
+00:59:37,080 --> 00:59:41,820
+كويس اللي بيحددوا مين قيم واحد طب القيم اللي فوق
+
+546
+00:59:41,820 --> 00:59:46,420
+هي نفس القيم اللي تحت بس بالمئة بشرة سلمإحنا عندنا
+
+547
+00:59:46,420 --> 00:59:51,420
+Y الموجبة و Y السالبة طب Y الموجبة و Y السالبة قد
+
+548
+00:59:51,420 --> 00:59:55,380
+يكون على اليمين و قد يكون على الشمال و قد يكون
+
+549
+00:59:55,380 --> 01:00:01,300
+كليهما اللي بده يحدد مين حدود التكمل تبع ال X ال X
+
+550
+01:00:01,300 --> 01:00:05,960
+هتتغير من Zero لغاية اتنين يعني مين؟ هي الدائرة
+
+551
+01:00:05,960 --> 01:00:11,700
+المصبوخة للدرجة النصف اللي على اليمين فقط يبقى هذه
+
+552
+01:00:11,700 --> 01:00:13,660
+دائرة بهذا الشكل
+
+553
+01:00:18,830 --> 01:00:24,230
+الشكل اللي على الشمال هذا مش موجود فالرسم تهلك
+
+554
+01:00:24,230 --> 01:00:31,210
+هيوم بيكون منقط بهذا الشكل تمام؟
+
+555
+01:00:31,210 --> 01:00:37,170
+يبقى هذا يبقى هاي المنطقة اللي عندنا هاي المنطقة
+
+556
+01:00:37,170 --> 01:00:41,920
+اللي احنا بنكامل عليهايبقى أنا لسه عملت المطلوب
+
+557
+01:00:41,920 --> 01:00:46,980
+الأول رسمت منطقة التكامل جبتها من وين؟ جبتها من
+
+558
+01:00:46,980 --> 01:00:52,400
+الحدود اللي موجودة عندى، بعد هيك قال لي بدك تكتب
+
+559
+01:00:52,400 --> 01:00:57,020
+التكامل بعد ما تقلب حدود التكامل، ايش اقلب حدود
+
+560
+01:00:57,020 --> 01:01:01,420
+التكامل؟ احط هدف الأول و هدف الآخر؟أو مارضي ما
+
+561
+01:01:01,420 --> 01:01:06,360
+هنجيب نتيجة، هايش نسوي لأ بدل ما كنت بتكامل
+
+562
+01:01:06,360 --> 01:01:11,360
+بالنسبة ل Y وبعدين بالنسبة ل X في الأول وبعدين
+
+563
+01:01:11,360 --> 01:01:19,280
+بالنسبة إلى Y يبقى هذا التكامل بيصير تكاملية ل 6X
+
+564
+01:01:19,280 --> 01:01:27,060
+DX DY إذا بدي أشوف X بدي تتغير من وين ل وينباجى
+
+565
+01:01:27,060 --> 01:01:33,420
+بنات برسم خط يوازي محور X ويقطع منطقة التكامل هاي
+
+566
+01:01:33,420 --> 01:01:40,400
+خاط زي ما تشايفينه يبقى هنا X بقداش؟ عند هذه
+
+567
+01:01:40,400 --> 01:01:45,700
+النقطة، قداش قيمة X؟ Zero، يبقى هنا Zero، تمام،
+
+568
+01:01:45,700 --> 01:01:52,490
+هذي مين؟هذه الدائرة X تربيه زائد Y تربيه يسوى من R
+
+569
+01:01:52,490 --> 01:01:52,910
+تربيه
+
+570
+01:02:04,140 --> 01:02:11,420
+أو X يساوي الجذري التربيعي للاربع ناقص من Y تربيعي
+
+571
+01:02:11,420 --> 01:02:17,060
+واخد X الموجبة فقط لأنه ماعنديش X سالبة يبقى مصير
+
+572
+01:02:17,060 --> 01:02:23,200
+من الجذري التربيعي للاربع ناقص Y تربيعي
+
+573
+01:02:25,940 --> 01:02:31,020
+كداش أقل قيمة بده تاخدها Y و أكبر قيمة بده تاخدها
+
+574
+01:02:31,020 --> 01:02:36,340
+Y يبقى
+
+575
+01:02:36,340 --> 01:02:41,600
+هذا هنا سالب اتنين وهذا هنا من اتنين او نشوف من
+
+576
+01:02:41,600 --> 01:02:45,820
+فاقله النقطة هذه احدثية Zero اتنين وهذه احدثية
+
+577
+01:02:45,820 --> 01:02:52,280
+Zero سالب اتنين إذا من سالب اتنين للاتنين
+
+578
+01:02:54,310 --> 01:02:57,850
+يبقى شايفين كيف بغير حدود التكامل؟ بغير حدود
+
+579
+01:02:57,850 --> 01:03:02,790
+التكامل من المنطقة تبعتي التكامل، مش بمزاجي، بدل
+
+580
+01:03:02,790 --> 01:03:05,990
+هذا مكان هذا و هذا مكان هذا و امشي، لأ، الان
+
+581
+01:03:05,990 --> 01:03:11,690
+المنطقة او حدود التكامل على الدالة هذه اضطرت تماما
+
+582
+01:03:11,690 --> 01:03:16,190
+لو حسبناها بزا ساوي نفس القيمة اللي عندنا فور،
+
+583
+01:03:16,190 --> 01:03:17,350
+اللي مساحة تمغط
+
+584
+01:03:25,440 --> 01:03:30,260
+بنكمل بالنسبة ل X بالنسبة ل Y
+
+585
+01:03:36,230 --> 01:03:42,030
+والحكي هذا من Zero لغاية الجدر التربيعي للأربعة
+
+586
+01:03:42,030 --> 01:03:49,070
+ناقص Y تربيعي وهي ال DIY وهي التكامل من صفر من
+
+587
+01:03:49,070 --> 01:03:57,890
+سالق اتنين لغاية اتنين طيب بصير المسألة ساوية ستة
+
+588
+01:03:57,890 --> 01:04:03,540
+على اتنين بتلاتة خليها براوتكابل من سالي باتنين
+
+589
+01:04:03,540 --> 01:04:09,800
+للاتنين وضل عندي هنا ماين X تربية لما اعوض بطير
+
+590
+01:04:09,800 --> 01:04:17,840
+الجدر و بظل قداشر بس ارفع ناقص Y تربية ناقص Zero
+
+591
+01:04:17,840 --> 01:04:21,880
+يبقى مع السلامة عوض بالقناة Zero بتروح بالشكل اللي
+
+592
+01:04:21,880 --> 01:04:30,300
+عندنا هذا بصير بس هيك بYأسأل السؤال التالف الدالة
+
+593
+01:04:30,300 --> 01:04:36,100
+اللي بدي أكملها قد و الله even هذه even
+
+594
+01:04:36,100 --> 01:04:39,480
+يبقى اطلع على الرقم اللي هنا و الرقم اللي هنا
+
+595
+01:04:39,480 --> 01:04:47,280
+اتنين نفس الشيءيبقى اتنين التكامل على نصف المنطقة
+
+596
+01:04:47,280 --> 01:04:50,780
+يبقى
+
+597
+01:04:50,780 --> 01:04:54,120
+هذا الكلام يبدو يساوي هي التلاتة اللي برا وهي
+
+598
+01:04:54,120 --> 01:04:58,680
+جيبنا لها كمان اتنين وتكامل صار من صفر لاتنين بدل
+
+599
+01:04:58,680 --> 01:05:04,240
+من سالب اتنين للاتنين لمين للاربع ناقص Y تربيه
+
+600
+01:05:04,240 --> 01:05:15,350
+اعضى Yيبقى النتيجة 6 في 4Y ناقص Y تكيب على 3 كل
+
+601
+01:05:15,350 --> 01:05:24,210
+هذا الحكي من Zero لغاية كده اش لغاية اتنين يسام 6
+
+602
+01:05:24,210 --> 01:05:31,160
+ايها براتمام؟ وهذا هنا بنصير عندنا اتنين في اربعة
+
+603
+01:05:31,160 --> 01:05:39,080
+في تمانية وهنا ناقص اللي هو تمانية على تلاتة وهذه
+
+604
+01:05:39,080 --> 01:05:43,720
+زيرو زيرو بتروح كلها مع السلامة يبقى هذا الكلام
+
+605
+01:05:43,720 --> 01:05:49,560
+بتساوي ستة في تلاتة في تمانيةأربعة و عشرين و نزل
+
+606
+01:05:49,560 --> 01:05:55,400
+منها تمانية درجة داشر ستة عشر على تلاتة تلاتة مع
+
+607
+01:05:55,400 --> 01:06:00,700
+ستة مولتين في ستة عشر باتنين و تلاتين يبقى هذا
+
+608
+01:06:00,700 --> 01:06:06,940
+مقدار اللي هو التكامل اللي عندي طب هذا نمرأ ايه من
+
+609
+01:06:06,940 --> 01:06:15,540
+المثل نمرأ بيه؟ نريد تكامل ايه؟ من واحد لغاية ال E
+
+610
+01:06:16,340 --> 01:06:22,360
+ومن الـ zero لغاية لإن ال X لل X Y
+
+611
+01:06:27,700 --> 01:06:30,720
+طبعا يا بنات ان انا بقدر اكمل دغري بدون مجلب لكن
+
+612
+01:06:30,720 --> 01:06:36,120
+هو امرني امر طلب مني قال روح اجلب حدود التكامل و
+
+613
+01:06:36,120 --> 01:06:40,300
+بعد هيك بتروح تحسبلي هذا التكامل اذا بروح ارسمله
+
+614
+01:06:40,300 --> 01:06:45,580
+مين؟ منطقتي التكامل فباشي بقوله هذه المحاول اللي
+
+615
+01:06:45,580 --> 01:06:53,220
+عندنا هذا محور X هذا محور Y هذه نقطة الاصلأنا بدأ
+
+616
+01:06:53,220 --> 01:06:57,540
+أكبر بالنسبة نوائي الجهادي Y تساوي Zero Y تساوي
+
+617
+01:06:57,540 --> 01:07:04,580
+Zeroهذا y تساوي zero اللي بعد هو y تساوي لن ال x
+
+618
+01:07:04,580 --> 01:07:09,540
+سابق و درسنا في calculus A و أفرضنا له section
+
+619
+01:07:09,540 --> 01:07:14,080
+كامل أول ما دخلتي على calculus B كان هذا هو
+
+620
+01:07:14,080 --> 01:07:18,180
+section رقم اتنين أخدت هو section معكوس الدالة ثم
+
+621
+01:07:18,180 --> 01:07:23,140
+ال natural لغة رتب يبقى المنحنة كان بهذا الشكل
+
+622
+01:07:27,420 --> 01:07:34,140
+يبقى هذا النقطة اليمين واحد وزير وهذا ال Y تساوي
+
+623
+01:07:34,140 --> 01:07:39,800
+لل Xيبقى رسمنا هذا هو رسمنا هذا بالنسبالي Y نجي ال
+
+624
+01:07:39,800 --> 01:07:46,520
+X جالي X تساوي واحد و X تساوي E و اين ال X تساوي
+
+625
+01:07:46,520 --> 01:07:52,960
+واحد يبقى هذا القط الموازي لمحور Y و اللي بدي ييجي
+
+626
+01:07:52,960 --> 01:07:58,320
+على نفس النقطة لان هذه واحد يبقى هذا X يساوي واحد
+
+627
+01:08:06,090 --> 01:08:12,430
+يبقى بده يجينا الشكل هذا يبقى هذا X يساوي E إذا
+
+628
+01:08:12,430 --> 01:08:17,130
+المنطقة اللي محصورة بينهم وين هي المنطقة المضللة
+
+629
+01:08:17,130 --> 01:08:24,330
+اللي عندها يبقى هذه منطقة التكامل بقوله كويس هذا
+
+630
+01:08:24,330 --> 01:08:30,550
+التكامل بده يساوي يعني تكامل ايه؟ XY زي ما هم بس
+
+631
+01:08:30,550 --> 01:08:31,430
+بدي أقلب
+
+632
+01:08:38,190 --> 01:08:46,130
+بارسم خط موازن لمحور X ويقطع منطقة التكامل الشكل
+
+633
+01:08:46,130 --> 01:08:52,750
+اللي علناه هذا يبقى قطع منطقة التكامل في النقطتين
+
+634
+01:08:52,750 --> 01:08:58,590
+بدي اعرف كم هو X هنا وكم هو X هنا
+
+635
+01:09:01,240 --> 01:09:07,440
+هذا التقى على المنحنى y تساوي لن ال x يبقى احنا
+
+636
+01:09:07,440 --> 01:09:14,780
+عندنا هنا y تساوي لن ال x إذا نقدر نجيب x من هذه
+
+637
+01:09:14,780 --> 01:09:22,580
+المعادلة ارفع تلك أُس للعدد E بصير E أُس Y يساوي
+
+638
+01:09:22,580 --> 01:09:31,660
+كده؟ X يبقى هناهه بدفع أقل قيمة ل X ليه جداش E أُس
+
+639
+01:09:31,660 --> 01:09:39,520
+Y و أكبر قيمة جداش اما نادر E يبقى من E أُس Y إلى
+
+640
+01:09:39,520 --> 01:09:49,800
+E طيب نجي لل Y جداش أقل قيمة عندنا هنا أقل قيمة ل
+
+641
+01:09:49,800 --> 01:09:50,900
+Y Zero
+
+642
+01:09:54,130 --> 01:10:00,430
+لغاية أكبر قيمة عند ال human هنا هنا نقطة مشتركة
+
+643
+01:10:00,430 --> 01:10:04,650
+ما بين الخط وهنا يبقى هشيل ال X وحط مكانها E بس
+
+644
+01:10:04,650 --> 01:10:08,610
+اللي ان ال E بيبقى ده ال واحد يبقى بصير هذي من
+
+645
+01:10:08,610 --> 01:10:13,210
+Zero لغاية واحد اتطلع في الحدود اللي قبله اتطلع في
+
+646
+01:10:13,210 --> 01:10:18,170
+الحدود هذيولا واحد ان شغل بقى ticket غير شكل مظبوط
+
+647
+01:10:18,170 --> 01:10:24,510
+يبقى لكن هذه تطابق أو تكافئ تماما الحدود الأولى
+
+648
+01:10:24,510 --> 01:10:29,250
+يبقى ماضالش عندي إلا ماين إلا عملية التكامل يبقى
+
+649
+01:10:29,250 --> 01:10:33,990
+هذا الكلام بتساوي تكامل من صفر لغاية واحد وانت يا
+
+650
+01:10:33,990 --> 01:10:38,550
+واي مالكش دعوة يبقى صف على شجة وتكامل ال X ب X
+
+651
+01:10:38,550 --> 01:10:44,840
+تربيع على اتنينوالكلام هذا من E قص Y لغاية E وهذا
+
+652
+01:10:44,840 --> 01:10:51,970
+الـ D Yهذا الكلام بدل سوية نص و آيتها كامل من صفر
+
+653
+01:10:51,970 --> 01:10:57,010
+لواحد وهي ال Y و بدعوض القيمة اللي فوق ناقص القيمة
+
+654
+01:10:57,010 --> 01:11:01,050
+اللي تحت لإن بدي أشيل ال X و أضع مكانها E يصير
+
+655
+01:11:01,050 --> 01:11:07,770
+عندي E تربيع ناقص القيمة اللي تحت E أس Y لكل تربيع
+
+656
+01:11:07,770 --> 01:11:16,480
+يعني E أس اتنين Y كله بالنسبة لمن؟ لدي Yيبقى كأن
+
+657
+01:11:16,480 --> 01:11:21,220
+المسألة النُص اللي برا و هي تكمل من صفر لواحد، بدي
+
+658
+01:11:21,220 --> 01:11:28,660
+أفكر جوز هنا بنات يمشي بصير E تربيع Y Dy وهنا ناقص
+
+659
+01:11:28,660 --> 01:11:37,100
+نُص تكمل من صفر لغاية واحد لل Y في E أُس 2Y في Dy
+
+660
+01:11:39,850 --> 01:11:45,250
+طبعا هذا بسيط جدا يبقى هذا نص مالكش دعم و ال E
+
+661
+01:11:45,250 --> 01:11:52,490
+تربيع مقدار ثابت زيه و تكامل ال Y بY تربيع على 2
+
+662
+01:11:52,490 --> 01:11:57,290
+من صفر لغاية واحد طب و ايش رأيكوا في هذه
+
+663
+01:11:57,290 --> 01:12:01,610
+integration
+
+664
+01:12:01,610 --> 01:12:06,190
+by parts يبقى باجي بقوله ان انا بدي اخد
+
+665
+01:12:06,190 --> 01:12:06,950
+derivatives
+
+666
+01:12:10,490 --> 01:12:16,150
+وداخل هنا integrals هنا
+
+667
+01:12:16,150 --> 01:12:22,950
+Y وهنا E أس اتنين Y لو فضلناها كده شو يطلع هنا
+
+668
+01:12:22,950 --> 01:12:28,510
+منها؟ واحد لو كملتها بصير E أس اتنين Y على اتنين
+
+669
+01:12:28,510 --> 01:12:33,270
+لو فضلت كمان مرة ب Zero لو كملتها كمان مرة بصير E
+
+670
+01:12:33,270 --> 01:12:38,650
+أس اتنين Y على مين؟ على أربع هدف هدف إشارة موجب
+
+671
+01:12:41,910 --> 01:12:55,050
+يبقى هنا ناقص نص وهي نتيجة التكامل نقص ي إي أس
+
+672
+01:12:55,050 --> 01:13:05,350
+اتنين ي ناقص رابع ي إي أس اتنين ي وكل هذا كله من
+
+673
+01:13:05,350 --> 01:13:11,650
+زيرو لغاية كم؟ لغاية واحدةيبقى هنا الكلام الرابع
+
+674
+01:13:11,650 --> 01:13:18,970
+اي تربيع حط واحد تطلع بعض حط zero بالطير يبقى رابع
+
+675
+01:13:18,970 --> 01:13:25,170
+اي تربيع اللي همان التكامل الأول نجل التكامل
+
+676
+01:13:25,170 --> 01:13:34,650
+الثاني يبقى ناقص رابع وهنا ال Y بواحد وهنا اي
+
+677
+01:13:34,650 --> 01:13:35,490
+تربيع
+
+678
+01:13:38,390 --> 01:13:46,910
+نقص في نقص بزايد نص في ربع بالتمون تمام و هنا تمون
+
+679
+01:13:46,910 --> 01:13:55,150
+ات الربيع بعدها زيرو اه هذه اللي بعدها هي زيرو
+
+680
+01:13:55,150 --> 01:14:06,970
+يبقى هنا نقص مع نقص بسيط زائد زيروزائد زيرو هذه و
+
+681
+01:14:06,970 --> 01:14:11,090
+هذه بتجيكي الناقص مع ناقص بيصير زائد و ناقص بتجيكي
+
+682
+01:14:11,090 --> 01:14:17,490
+كمان بيصير ناقص الرابع و هنا بيجيكي التمن لإنه في
+
+683
+01:14:17,490 --> 01:14:22,390
+نص برا و هنا ايه و ال zero اللي هو بقداش ابواع
+
+684
+01:14:22,390 --> 01:14:27,890
+الرابع مع رابع بالسالف الله ساهل عليه يبقى طالع
+
+685
+01:14:27,890 --> 01:14:35,740
+انا كده شبنات يساوي التمن في ايه؟تربية ماخص واحد،
+
+686
+01:14:35,740 --> 01:14:39,740
+هذا قيمة مين؟ قيمة هذا التكابن
+
+687
+01:15:00,630 --> 01:15:04,770
+يلا وورقة وكتب اسمك ورقمك الجامعي ومرريها عليهم
+
+688
+01:15:04,770 --> 01:15:16,010
+طيب أروح لنمرة C من المثلة نرجع لمرة C نمرة C
+
+689
+01:15:16,010 --> 01:15:23,190
+بيقول تكامل من سفر لغاية 2 تكامل من سفر لغاية 4
+
+690
+01:15:23,190 --> 01:15:34,510
+ناقص X تربيةلمن؟ لل X بـ E كسي 2Y على 4 نفس Y dy
+
+691
+01:15:34,510 --> 01:15:43,050
+dx المطموب
+
+692
+01:15:43,050 --> 01:15:48,350
+الأول اللي بدها ايه؟ ارسمله منطقة التكامل بقوله
+
+693
+01:15:48,350 --> 01:15:57,920
+بسيطة هي المحاور على محور Xهذا اللي عندنا محور Y
+
+694
+01:15:57,920 --> 01:16:04,000
+وهذه نقطة الأصل اللي هي من الـ Zero الآن تكمل أول
+
+695
+01:16:04,000 --> 01:16:09,700
+بالاسم ل Y يبقى Y تساوي Zero يبقى هذا اللي هو Y
+
+696
+01:16:09,700 --> 01:16:16,690
+تساوي Zero اللي بعدين Y تساوي أربعة ناقص X ترميةY
+
+697
+01:16:16,690 --> 01:16:25,430
+تساوي أربع ناقص X تربيعك إلى أعلى Y تساوي X تربيعك
+
+698
+01:16:25,430 --> 01:16:27,690
+إلى أعلى Y تساوي X تربيعك إلى أعلى Y تساوي X
+
+699
+01:16:27,690 --> 01:16:33,610
+تربيعك إلى أعلى Y تساوي X تربيعك إلى أعلى Y تساوي
+
+700
+01:16:33,610 --> 01:16:35,910
+X تربيعك إلى أعلى
+
+701
+01:16:37,910 --> 01:16:40,530
+بس أنا مش عارف هيكل ال parabola و الله نقصها دي
+
+702
+01:16:40,530 --> 01:16:44,690
+لبالك لسه احنا مش عارفين يبقى بنجي لمين لحدود
+
+703
+01:16:44,690 --> 01:16:50,550
+التكمل ال X هتتغير من عند Zero لغاية اتنين طيب اه
+
+704
+01:16:50,550 --> 01:16:54,810
+لو جتلى ال parabola هذه على هذا الخط Y تساوي Zero
+
+705
+01:16:54,810 --> 01:17:01,530
+إذا ال X بيصير هنا هذا Y تساوي Zero وهنا ال X
+
+706
+01:17:01,530 --> 01:17:07,660
+يساوي اتنين وهنا اليمينفنقص اتنين احنا عندنا من
+
+707
+01:17:07,660 --> 01:17:12,940
+Zero لغاية اتنين يبقى بيننا عليا المنطقة هذه كلها
+
+708
+01:17:12,940 --> 01:17:19,880
+مالها مش موجودة تمام يبقى عندنا فقط المنطقة
+
+709
+01:17:19,880 --> 01:17:26,880
+المضللة اللي عندنا هي اللي بنكمل عليها ما بين Y2
+
+710
+01:17:26,880 --> 01:17:32,060
+سواء Zero ومجان المنحنة و ما بين X في Zero و X بي
+
+711
+01:17:32,060 --> 01:17:32,820
+اتنين
+
+712
+01:17:38,930 --> 01:17:45,170
+خلّيني أسأل سؤال حد فيكم تقدر تكامل هالي أولا
+
+713
+01:17:45,170 --> 01:17:50,780
+بالنسبة إلى why؟لو ما قلليش اجلب و اعطيتك السؤال
+
+714
+01:17:50,780 --> 01:17:55,300
+زي هي حد فيكوا بتقدروا تكمل هذه بالنسبة ل Y ولا زي
+
+715
+01:17:55,300 --> 01:18:00,680
+ايه؟ ماقدرش اكمل بالنسبة ل Y تمام؟ اجباري حتى لو
+
+716
+01:18:00,680 --> 01:18:04,220
+ماقليش و ماقدرش اكمل دي اجلب هذه اجباري و اروح
+
+717
+01:18:04,220 --> 01:18:12,000
+انكمل بالنسبة لمن؟ بالنسبة إلى X يبقى هذه هيك كلها
+
+718
+01:18:12,000 --> 01:18:18,480
+ماليش علاقة فيها دي ماقدرش اكملها بالنسبة لمن؟Y
+
+719
+01:18:18,480 --> 01:18:23,240
+إذا إجباري حجم المثلة بالنسبة ل X يبقى هذه بدها
+
+720
+01:18:23,240 --> 01:18:31,860
+تساوي تكاملين لمين؟ ل X ال E أس اتنين Y على أربع
+
+721
+01:18:31,860 --> 01:18:39,500
+نقص Y DX DY بدي أرجع على رأس ال T ومن خلالها أحدد
+
+722
+01:18:39,500 --> 01:18:47,000
+حدود التكاملبنشوف X تتغير من أين لأين برسم خط
+
+723
+01:18:47,000 --> 01:18:49,860
+موازي لمحور X وبشوف
+
+724
+01:18:58,460 --> 01:19:05,420
+هذه المنحنة Y تساوي أربع ناقص X تربيع
+
+725
+01:19:14,380 --> 01:19:20,940
+خد الجدر يبقى x يساوي الجدر التربيه ل 4-y وباخد
+
+726
+01:19:20,940 --> 01:19:25,420
+القيمة الموجبة لإن السلبة مش عندى مش موجودة السلبة
+
+727
+01:19:25,420 --> 01:19:29,700
+الشجة هذه لكن احنا على المنطقة المضللة يبقى لغاية
+
+728
+01:19:29,700 --> 01:19:33,560
+الجدر التربيه ل 4-y
+
+729
+01:19:40,250 --> 01:19:46,970
+أربعة معروفة يبقى من Zero لغاية أربعة شايفة الخدود
+
+730
+01:19:46,970 --> 01:19:49,970
+اللي فوق و اللي كيف و اللي تحت يجدوا مختلفات عن
+
+731
+01:19:49,970 --> 01:19:54,370
+بعض تماما يبقى بنروحها كامل بالنسبة ل X يبقى هذا
+
+732
+01:19:54,370 --> 01:20:00,280
+يعتبر كله مرتاراإذاً هذا الكلام بدل سوى تكامل من
+
+733
+01:20:00,280 --> 01:20:06,320
+Zero إلى أربعة لل X تربيع على اتنين والكلام هذا من
+
+734
+01:20:06,320 --> 01:20:13,820
+Zero للأربعة ناقص Y تحت الجدر في مين بال E أسطل ال
+
+735
+01:20:13,820 --> 01:20:23,000
+Y على أربعة ناقص Y Dy لأن DX خلصنا منها تبقى Dyطيب
+
+736
+01:20:23,000 --> 01:20:27,940
+هذا الكلام يساوي أظن النص لو خلّيته برا مافي مشكلة
+
+737
+01:20:27,940 --> 01:20:32,140
+هو هي تكامل من zero إلى أربعة بتعود بالقيمة اللي
+
+738
+01:20:32,140 --> 01:20:38,940
+فوق لما ركّعها بطيير الجدر يبقى بيصير أربعة ناقص Y
+
+739
+01:20:40,280 --> 01:20:45,560
+والتحت Zero مع السلام الله سهل عليها هذا كله مضروب
+
+740
+01:20:45,560 --> 01:20:52,380
+في مين؟ في ال E أسنين Y على الأربع ناقص Y كله
+
+741
+01:20:52,380 --> 01:20:57,380
+بالنسبة الى Dy أظن يختصر الجوس اللي فوق مع الجوس
+
+742
+01:20:57,380 --> 01:20:59,960
+اللي تحت وبصير المسألة
+
+743
+01:21:06,670 --> 01:21:10,850
+بتبسط المسألة اللي كانت معقدة في الأول لأ يمكن
+
+744
+01:21:10,850 --> 01:21:17,490
+صارت مسألة بسيطة جدا يبدأ هذا نص وهذا E أس اتنين Y
+
+745
+01:21:17,490 --> 01:21:24,690
+على اتنين وهذا من Zeroيبقى هذا الكلام بيساوي
+
+746
+01:21:24,690 --> 01:21:32,590
+الرابع في ال E أس تمانية ناقص E أس Zero لو قداشر
+
+747
+01:21:32,590 --> 01:21:37,150
+الواحد يبقى رابع في E أس تمانية ناقص
+
+748
+01:21:43,770 --> 01:21:48,930
+يبقى هذا النوع من المسائل أجبرنا إجبارا على إن
+
+749
+01:21:48,930 --> 01:21:54,230
+الروح احنا نغير حدود التكامل مش زي المجموعة الأولى
+
+750
+01:21:54,230 --> 01:21:59,450
+من المسائل يبقى هذا بيختلف شوية عن المجموعة الأولى
+
+751
+01:21:59,450 --> 01:22:05,150
+لإن احنا غيرنا حدود التكامل وبالتالي حسبنا اللى هو
+
+752
+01:22:05,150 --> 01:22:11,600
+حدود التكامل اللى عندناالان نجي للمجموعة الثانية
+
+753
+01:22:11,600 --> 01:22:17,040
+من المسالي مثلا two مثلا
+
+754
+01:22:17,040 --> 01:22:25,160
+او لنقطة تانية من هذا ال section اللي هو finding
+
+755
+01:22:25,160 --> 01:22:29,540
+limits
+
+756
+01:22:29,540 --> 01:22:32,960
+of integration
+
+757
+01:22:40,530 --> 01:22:45,850
+إحنا بدنا نجيب حدود التكامل، مش يعطيها اللي هو
+
+758
+01:22:45,850 --> 01:22:52,110
+ورسم المنطقة، لا، انت بدك تحدد حدود التكامل نعطي
+
+759
+01:22:52,110 --> 01:22:52,670
+مثال
+
+760
+01:22:59,860 --> 01:23:06,600
+واللي find the volume of the solid find the volume
+
+761
+01:23:06,600 --> 01:23:19,820
+of the solid بده كدهش حجم المجسم that is bounded و
+
+762
+01:23:19,820 --> 01:23:25,960
+اللي بيكون محدود above by
+
+763
+01:23:31,930 --> 01:23:45,790
+السيلندر بالأسطوانة Z تساوي X تربيع ومن أسفل
+
+764
+01:23:45,790 --> 01:23:53,410
+بالمنطقة
+
+765
+01:23:53,410 --> 01:23:55,050
+enclosed
+
+766
+01:24:00,110 --> 01:24:07,430
+by the parabola بالقطع
+
+767
+01:24:07,430 --> 01:24:16,790
+المكافئ y تساوي اتنين ناقص x ترابيع and the line
+
+768
+01:24:16,790 --> 01:24:20,870
+الخط
+
+769
+01:24:20,870 --> 01:24:30,040
+y تساوي x and the xwhy play
+
+770
+01:25:04,750 --> 01:25:09,870
+الخمسة أمثلة السابقة كانت تعطينا حدود التكامل،
+
+771
+01:25:09,870 --> 01:25:14,930
+لكنها لم تعطينا أي شيء، انت بدأت تجلب حدود التكامل
+
+772
+01:25:14,930 --> 01:25:19,330
+من خلال الوصف اللي أعطاه لك لمن؟ للمسألة، يبقى
+
+773
+01:25:19,330 --> 01:25:23,810
+الخمسة الأمثلة الأولى اللي هم فكرة شكل، وهدول
+
+774
+01:25:23,810 --> 01:25:27,510
+الأمثلة هذا و اللي جاين بعده كمان اللي هم فكرة
+
+775
+01:25:27,510 --> 01:25:33,380
+شكل،يبقى انا لو روحت رسمت من منطقة التكامل بكون
+
+776
+01:25:33,380 --> 01:25:37,680
+حلية العمودي الفقري تبع المثل يفضل التكامل هذا شغل
+
+777
+01:25:37,680 --> 01:25:44,100
+روتينيطيب جالي هنا ال .. ال .. الجلهات الغلمة ده
+
+778
+01:25:44,100 --> 01:25:47,400
+solid bounded by the cylinder طب لو ماجاليش
+
+779
+01:25:47,400 --> 01:25:51,440
+cylinder هو جالي by the surface Z تساوي X تربيع
+
+780
+01:25:51,440 --> 01:25:55,380
+لحالك بدك تعرف ان هاد ال cylinder لإن انا عندي
+
+781
+01:25:55,380 --> 01:25:59,580
+متغيرين موجودين و التالت غايب يبقى هاد معادلة
+
+782
+01:25:59,580 --> 01:26:04,260
+cylinder دائما و أفدا ما علينا مش مشكلة من أسفل
+
+783
+01:26:04,260 --> 01:26:08,680
+يعني ال domain تبعهاInclosed by this parabola و ال
+
+784
+01:26:08,680 --> 01:26:12,800
+line اللي عندنا يبقى يا بنات انا فقط برسم باسي ال
+
+785
+01:26:12,800 --> 01:26:17,100
+domain اللي هو منطقتي التكامل ماليش علاقة بالمجسم
+
+786
+01:26:17,100 --> 01:26:22,120
+المجسم بدي اكامله بدي اكامل هذا بقوله كويس اذا بدى
+
+787
+01:26:22,120 --> 01:26:27,440
+اروح و ارسم اللي هو اللي عندنا المنطق يعني هذا X
+
+788
+01:26:27,440 --> 01:26:34,310
+وهذا Y وهذه نقطة الاصل ال parabola اللي عندناY
+
+789
+01:26:34,310 --> 01:26:39,250
+تساوي سالب X تساوي سالب U و Shift لفوق بمقدار كده؟
+
+790
+01:26:39,250 --> 01:26:46,030
+بمقدار 2 يبقى النقطة هذه Zero و 2 و بنروح نرسم ال
+
+791
+01:26:46,030 --> 01:26:50,150
+Parabola بالشكل اللي عندنا تمام يبقى هذه ال
+
+792
+01:26:50,150 --> 01:26:55,750
+Parabola اللي عندنا بعد هيك يقول في الخط Y تساوي X
+
+793
+01:26:55,750 --> 01:27:02,030
+يبقى مدى الخط Y تساوي Xالشكل اللي عندنا هذا و بمده
+
+794
+01:27:02,030 --> 01:27:07,690
+على استقامته مباشرة فنصير هذه التقاطة اللي عندنا
+
+795
+01:27:07,690 --> 01:27:12,470
+هذا و التقاطة اللي عندنا هي يبقى المنطقة اللي احنا
+
+796
+01:27:12,470 --> 01:27:18,850
+فيه دنياها هي المنطقة المظللة ما بين الخط المستقيم
+
+797
+01:27:18,850 --> 01:27:24,350
+و ما بين البرابلات يبقى هذه منطقة main منطقة
+
+798
+01:27:24,350 --> 01:27:32,490
+التكامل automatic بقوله volume Bبتساوي تكاملين على
+
+799
+01:27:32,490 --> 01:27:39,710
+R لل surface اللي فوق اللي هو Z تساوي كده؟ X تربيع
+
+800
+01:27:39,710 --> 01:27:45,630
+طبعا؟ ضال عندي بدي أقوله دي إيه لإن أنا مش عارف
+
+801
+01:27:45,630 --> 01:27:50,930
+مين ال X ومين ال Y وكذا طبعا؟ يبقى بقدر أقول هذه
+
+802
+01:27:50,930 --> 01:27:56,570
+التكامل الأول وهي التكامل الثاني لل X تربيع
+
+803
+01:28:04,590 --> 01:28:10,550
+هل بقدر اجيب الحدود تبقى سهلة ولا لأ ان قدرت ماشية
+
+804
+01:28:10,550 --> 01:28:14,930
+اللحظة ماقدرت فاجلبهاالان بروح و بغير مين الحدود
+
+805
+01:28:14,930 --> 01:28:19,930
+بقول بسيطة جدا الان مدام دي و ي دي اكس بدي اشوف وي
+
+806
+01:28:19,930 --> 01:28:25,990
+بدأ تتغير من ويل لويل بقوله اه بدي برسم خط موازن
+
+807
+01:28:25,990 --> 01:28:33,110
+لمحور وي و يقطع منطقة التكامن يبقى هنا وي بقداش يا
+
+808
+01:28:33,110 --> 01:28:39,990
+بنات وي بقداش الخط هذا هو معادلة وي بقداش اكسطبعا
+
+809
+01:28:39,990 --> 01:28:48,170
+يبقى قيمة Y تقبع هنا فجداش ب X وقيمة Y هنا فجداش ب
+
+810
+01:28:48,170 --> 01:28:55,630
+2 ناقص X تربيع يبقى 2 ناقص X تربيع لإن المنحنة هنا
+
+811
+01:28:55,630 --> 01:29:03,670
+Y يسوى 2 ناقص X تربيع ضالة X بدها تتغير من أن أقل
+
+812
+01:29:03,670 --> 01:29:10,930
+قيمة هنا لغاية أكبر قيمة اللي عندنامشان هيك بدي
+
+813
+01:29:10,930 --> 01:29:17,810
+احد يدق ما بين الاتنين ممتاز جدا يبقى انا عندي y
+
+814
+01:29:17,810 --> 01:29:22,990
+تساوي x وعندي y يساوي اتنين نقص x تربية يعني اللي
+
+815
+01:29:22,990 --> 01:29:27,810
+بدي احل المعادلة مع بعض بصير x يساوي اتنين نقص x
+
+816
+01:29:27,810 --> 01:29:35,780
+تربية لو عملناها معادلة صفرية بصير x تربيةزائد X
+
+817
+01:29:35,780 --> 01:29:41,860
+نقص اتنين يساوي Zero يبقى هاي قوسين بده يساوي Zero
+
+818
+01:29:41,860 --> 01:29:49,140
+هنا X وهنا X وهنا واحد وهنا اتنين هذه بالزائد وهذه
+
+819
+01:29:49,140 --> 01:29:54,840
+بالنقص يبقى بنات ال X بدها تساوي واحد وال X بده
+
+820
+01:29:54,840 --> 01:30:00,390
+يساوي سالب اتنين اذا هذه سالب اتنين وهذه كدهشوها
+
+821
+01:30:00,390 --> 01:30:07,250
+دي واحد تمام إذا ال X ستتغير من سالب اتنين لغاية
+
+822
+01:30:07,250 --> 01:30:14,020
+واحد باقى الشغل صار روتيني خلاصهذا هو العمول
+
+823
+01:30:14,020 --> 01:30:18,320
+الفقري تبع المثال اني احدد حدود التكامل من خلال
+
+824
+01:30:18,320 --> 01:30:21,300
+الوصفة اللي اعطاه لي بعدين بصير الشغل روتيني زي
+
+825
+01:30:21,300 --> 01:30:25,860
+اللي جابت يبقى هذا الكلام بده يساوي كده بده يساوي
+
+826
+01:30:25,860 --> 01:30:31,140
+اللي هو التكامل من سلبي اتنين لغاية واحد وهذه X
+
+827
+01:30:31,140 --> 01:30:38,040
+تكيبة على تلاتة عفوا ان X تربية تتبرة كلها كله
+
+828
+01:30:38,040 --> 01:30:44,070
+أسطن مالهاش علاقة في الموضوعبظل عيبنا من الـ dy
+
+829
+01:30:44,070 --> 01:30:51,410
+يبقى تكاملها بY من عند ال X لإتنين ناقص X تربيع
+
+830
+01:30:51,410 --> 01:30:56,170
+كله DX يبقى
+
+831
+01:30:56,170 --> 01:31:00,610
+هذا الكلام بده يساوي تكامل من سالب إتنين لغاية
+
+832
+01:31:00,610 --> 01:31:06,210
+الواحد X تربيعمن قيمة اللي فوق اتنين ناقص X تربية
+
+833
+01:31:06,210 --> 01:31:14,250
+ناقص X كله DX يبقى صارت المسألة تكامل من سالب
+
+834
+01:31:14,250 --> 01:31:23,910
+اتنين لغاية واحد لمن دال اتنين X تربية ناقص X تكيب
+
+835
+01:31:23,910 --> 01:31:32,370
+و هنا ناقص X أُس أربعة وهنا ناقص X تكيب
+
+836
+01:31:38,750 --> 01:31:47,510
+النتيجة تولتين x تكييف ناقص pumps x أُس خمسة وهنا
+
+837
+01:31:47,510 --> 01:31:55,090
+ناقص ربع x أُس أربعة كل هذا الكلام من سالب اتنين
+
+838
+01:31:55,090 --> 01:32:00,590
+لغاية الواحد وإليك الإجابة مش هنضيع وجد فيهاماذا
+
+839
+01:32:00,590 --> 01:32:05,330
+بيظل عليك تحسبيها؟ بتلاقيها مية تمانية وعشرين
+
+840
+01:32:05,330 --> 01:32:12,150
+عالمين على خمستاشر عفوا اللي هي مية .. اللي هي
+
+841
+01:32:12,150 --> 01:32:23,710
+تلاتة وستين على عشرين تلاتة وستين على عشرين ناخد
+
+842
+01:32:23,710 --> 01:32:26,150
+كمان مثال تالتين
+
+843
+01:32:30,930 --> 01:32:40,330
+the volume of the solid كده حجم المجسم cut it from
+
+844
+01:32:40,330 --> 01:32:52,390
+the first octant cut from the first octant
+
+845
+01:32:52,390 --> 01:32:55,930
+الثمني
+
+846
+01:32:55,930 --> 01:33:08,250
+الأول by the surfaceby the surface بالسطح z تساوي
+
+847
+01:33:08,250 --> 01:33:22,410
+أربع ناقص x ترمية ناقص one هذه
+
+848
+01:33:22,410 --> 01:33:29,390
+حجم المجسم اللي مقطوع في ال face في الثمن الأول
+
+849
+01:33:29,810 --> 01:33:34,310
+بواسطة ال service يبقى انا عندي service في الفراغ
+
+850
+01:33:34,310 --> 01:33:38,230
+ايش في الثمن الاول ايش في التاني ايش في التالد ايش
+
+851
+01:33:38,230 --> 01:33:41,550
+في الرابع والسادس والسبعة انا مديش ارتباط الثمن
+
+852
+01:33:41,550 --> 01:33:46,210
+الاول بقوله بسيطة في الثمن الاول زد يا بنات مجدد
+
+853
+01:33:46,210 --> 01:33:51,290
+Zero اذا بقدر احدد شو المنحنة اللي موجودة عندى
+
+854
+01:33:51,290 --> 01:33:52,590
+يبقى هنا
+
+855
+01:33:59,390 --> 01:34:04,050
+هي تحدد منطقة تتكبلي منطقة تقعطها على ال surface
+
+856
+01:34:04,050 --> 01:34:09,830
+مع من؟ مع ال XY plane يعني بدي أحط Z بقداش؟ Zero
+
+857
+01:34:09,830 --> 01:34:17,250
+يبقى put اعطيلي Z تسوى Zeroهذا يعني أن أربعة ناقص
+
+858
+01:34:17,250 --> 01:34:23,430
+X تربية ناقص Y سواء Zero هذا يعني أن Y سواء Main
+
+859
+01:34:23,430 --> 01:34:30,150
+أربعة ناقص X تربية لو روحت أرسم المنطقة هذه بقول
+
+860
+01:34:30,150 --> 01:34:35,860
+هذا محور Xهذا محور Y وهذا المنطقه Zero Y تساوي X
+
+861
+01:34:35,860 --> 01:34:39,720
+تربيع ناقص أربعة يبقى حيجيني بالشكل اللي عندنا هذا
+
+862
+01:34:39,720 --> 01:34:44,920
+لكن هل كله ولا نصه الله أعلم مش عارفين احنا نقول
+
+863
+01:34:44,920 --> 01:34:49,060
+هي رسمنا المنطقة اللي عندنا هذا يبقى هذا المنحدر
+
+864
+01:34:49,060 --> 01:34:57,920
+يبقى Y تساوي أربعة ناقص X تربيع طب
+
+865
+01:34:57,920 --> 01:35:06,130
+كويس الان بدنا نيجي نحددباقي الحدود لمين للمجسم
+
+866
+01:35:06,130 --> 01:35:10,910
+اللى عندنا هنا طيب هذا لما نقطع مع محور X لإن أنا
+
+867
+01:35:10,910 --> 01:35:15,570
+بدي الثمن الأول يعني مديش أفوض ل Y لا بس بتكتفي
+
+868
+01:35:15,570 --> 01:35:26,280
+لحد هنا يفجأة تفجأة Y عندى جداشيجب أن ننزل
+
+869
+01:35:26,280 --> 01:35:30,340
+الارتباط أكتر من
+
+870
+01:35:30,340 --> 01:35:35,780
+الارتباط
+
+871
+01:35:35,900 --> 01:35:41,340
+هذه الاتنين هلقيل في السلم اتنين هذه؟ لأ لأنه جالس
+
+872
+01:35:41,340 --> 01:35:45,800
+في الثمن الأول مالكش دعوة إلك بس في الشجة هذه يبقى
+
+873
+01:35:45,800 --> 01:35:50,720
+منطقة التكامل سارة بس المنطقة المضللة للي عندنا
+
+874
+01:35:50,720 --> 01:35:57,840
+هذا لأنه جالس في الثمن الأول فقط لغيره إذا بناء
+
+875
+01:35:57,840 --> 01:36:02,340
+على الفكرة أحدد له اللي هو اللي بديه يبقى ال
+
+876
+01:36:02,340 --> 01:36:09,740
+volume Vبتسوى تكاملين تكاملين على الذات لازد جداش
+
+877
+01:36:09,740 --> 01:36:17,020
+الذات لاربع ناقص x تربيه ناقص y ان كمال بالنسبة ل
+
+878
+01:36:17,020 --> 01:36:20,920
+x في الأول ماشي كمال بالنسبة ل y في الأول ماشي
+
+879
+01:36:20,920 --> 01:36:25,760
+سيان هذه او تلك كله ماعناش مشكلة بالنسبة له لو
+
+880
+01:36:25,760 --> 01:36:31,940
+حبيت اكمل بالنسبة إلى xيبقى او بالنسبة الى Y سيئا
+
+881
+01:36:31,940 --> 01:36:37,980
+لو نقبل بالنسبة الى Y برسم خط يوازي محول Y ويقطع
+
+882
+01:36:37,980 --> 01:36:46,160
+منطقة التكامل بصير Y بتتغير من Zero لغاية أربعة
+
+883
+01:36:46,160 --> 01:36:51,430
+ناقص X تربيعبتبقى ال X تتغير من اولى اين؟ من Zero
+
+884
+01:36:51,430 --> 01:36:56,770
+لاتنين يبقى من Zero لاتنين خلصنا العمود الفقري في
+
+885
+01:36:56,770 --> 01:37:03,570
+المثلة يبقى DY DX بقى الشغل الروتيني يبقى هذا
+
+886
+01:37:03,570 --> 01:37:06,830
+الكلام تكامل من الصفر لاتنين وهي
+
+887
+01:37:19,340 --> 01:37:23,800
+يبقى هذا الكلام بده يساوي تكامل من صفر لليل
+
+888
+01:37:41,240 --> 01:37:45,480
+وهنا بالنسبة لمن ال ADX
+
+889
+01:38:03,920 --> 01:38:07,640
+يبقى هذا الكلام يبدو يساوي integration من zero
+
+890
+01:38:07,640 --> 01:38:23,560
+لغاية 10 يبقى 16-4X ربيع طبعا هذا ناقص16-4X³-4X³
+
+891
+01:38:23,560 --> 01:38:30,940
+-4X³-4X³
+
+892
+01:38:30,940 --> 01:38:35,440
+-5X³
+
+893
+01:38:35,440 --> 01:38:41,800
+-8X³
+
+894
+01:38:41,800 --> 01:38:46,260
+-8X³-8X³
+
+895
+01:38:46,800 --> 01:38:52,640
+زي الـ x أُص أربعة كل هذا الكلام بالنسبة إلى dx
+
+896
+01:38:52,640 --> 01:38:59,060
+يساوي التكامل من صفر للإتنين عندك هنا ستاشر و هنا
+
+897
+01:38:59,060 --> 01:39:05,070
+ناقص تمانية x تربيع و هنا زي الـ x أُص أربعةو هنا
+
+898
+01:39:05,070 --> 01:39:11,850
+ناقص تمانية و هنا ناقص فناقص بزاية تمانية X تربية
+
+899
+01:39:11,850 --> 01:39:20,310
+و هنا ناقص نص X أُس أربعة كله في DX و يساوي تكاول
+
+900
+01:39:20,310 --> 01:39:23,750
+من الصفر للإتنين عندك هنا ستة عشر و هنا ناقص
+
+901
+01:39:23,750 --> 01:39:28,850
+تمانية بدون جداش تمانية عندك ناقص تمانية X تربية و
+
+902
+01:39:28,850 --> 01:39:36,240
+زائد تمانية X تربية أجر الفاتحة على روحكزائد أربعة
+
+903
+01:39:36,240 --> 01:39:38,240
+زائد أربعة زائد أربعة زائد أربعة زائد أربعة زائد
+
+904
+01:39:38,240 --> 01:39:41,380
+أربعة زائد أربعة زائد أربعة زائد أربعة زائد أربعة
+
+905
+01:39:41,380 --> 01:39:43,360
+زائد أربعة زائد أربعة زائد أربعة زائد أربعة زائد
+
+906
+01:39:43,360 --> 01:39:45,980
+أربعة زائد أربعة زائد أربعة زائد أربعة زائد أربعة
+
+907
+01:39:45,980 --> 01:39:50,060
+زائد أربعة زائد أربعة زائد أربعة زائد أربعة زائد
+
+908
+01:39:50,060 --> 01:39:52,060
+أربعة زائد أربعة زائد أربعة زائد أربعة زائد أربعة
+
+909
+01:39:52,060 --> 01:39:55,680
+زائد أربعة زائد أربعة زائد أربعة زائد أربعة زائد
+
+910
+01:39:55,680 --> 01:40:03,780
+أربعة زائد أربعة زائد أربعة زائد أربعة زائد أربعة
+
+911
+01:40:03,780 --> 01:40:14,610
+زائناقص أربع أتلات X تكييب وزائد عشر X أُس خمسة
+
+912
+01:40:14,610 --> 01:40:21,350
+والحكي هذا كله من عند الـ zero لغاية الإتنين يبقى
+
+913
+01:40:21,350 --> 01:40:26,930
+بصير عندك ستة عشر ناقص تمانية في أربعة باتنين
+
+914
+01:40:26,930 --> 01:40:34,470
+وتلاتين على تلاتة زائد اتنين وتلاتينهذه تكريف 8×4
+
+915
+01:40:34,470 --> 01:40:40,250
+هو 32 وهذه تكريف 8×4 هي 32 على 10 والباقي كله
+
+916
+01:40:40,250 --> 01:40:46,070
+مناقش 0 والجواب النهائي 128 على 15يبقى هذا كله
+
+917
+01:40:46,070 --> 01:40:52,250
+متساوي مية و تمانية و عشرين على خمستاش اللي هو مين
+
+918
+01:40:52,250 --> 01:40:58,850
+مقدار الحجب لا يزال عندنا كمان مثال و بعض الخواص
+
+919
+01:40:58,850 --> 01:41:03,730
+للمرة القادمة اللي شاء الله تعالى حد ما كتبتش اسم
+
+920
+01:41:03,730 --> 01:41:06,990
+هنا يا بنات قوله كتب اسم هنا
+
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/Ct7ethd1brI_raw.json b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/Ct7ethd1brI_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..d4dfc6a246215f08f480f147b5dded01b1ebb17b
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/Ct7ethd1brI_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 270, "start": 0.0, "end": 2.7, "text": "موسيقى", "tokens": [2304, 41779, 1829, 4587, 7578], "avg_logprob": -0.4117838541666667, "compression_ratio": 0.5714285714285714, "no_speech_prob": 0.0029277801513671875, "words": [{"start": 0.0, "end": 2.7, "word": "موسيقى", "probability": 0.72119140625}], "temperature": 1.0}, {"id": 2, "seek": 3464, "start": 8.66, "end": 34.64, "text": "أحنا المرة الماضية بدأنا بال cross product و أعطينا ال definition تبع ال cross product ثم أعطينا على ذلك مثالين بنذكر تذكير فقط بالتعريف تبع ال cross product لإنه لازمنا بعد قليل ثم نذهب إلى خواص ال cross product المرة اللي فيها دي كلها لو عدنا two vectors U and ال V عرفنا ال U cross ال V بالطريقة", "tokens": [10721, 5016, 8315, 9673, 25720, 9673, 46958, 10632, 47525, 10721, 8315, 20666, 3278, 1674, 4032, 5551, 3615, 9566, 1829, 8315, 2423, 7123, 6055, 3555, 3615, 2423, 3278, 1674, 38637, 2304, 5551, 3615, 9566, 1829, 8315, 15844, 29910, 23275, 50113, 6027, 9957, 44945, 8848, 37983, 6055, 8848, 4117, 13546, 6156, 47432, 20666, 2655, 3615, 16572, 5172, 6055, 3555, 3615, 2423, 3278, 1674, 5296, 28814, 1863, 3224, 5296, 31377, 2304, 8315, 39182, 12174, 20292, 1211, 38637, 2304, 8717, 24192, 3555, 30731, 16490, 2407, 33546, 2423, 3278, 1674, 9673, 25720, 13672, 1829, 8978, 11296, 11778, 1829, 28242, 11296, 45164, 6225, 3215, 8315, 732, 18875, 624, 293, 2423, 691, 6225, 28480, 8315, 2423, 624, 3278, 2423, 691, 20666, 9566, 16572, 28671], "avg_logprob": -0.19769597849098303, "compression_ratio": 1.9083333333333334, "no_speech_prob": 5.066394805908203e-06, "words": [{"start": 8.66, "end": 9.3, "word": "أحنا", "probability": 0.6870930989583334}, {"start": 9.3, "end": 9.56, "word": " المرة", "probability": 0.90966796875}, {"start": 9.56, "end": 10.1, "word": " الماضية", "probability": 0.9892578125}, {"start": 10.1, "end": 10.54, "word": " بدأنا", "probability": 0.7996419270833334}, {"start": 10.54, "end": 10.7, "word": " بال", "probability": 0.95166015625}, {"start": 10.7, "end": 11.1, "word": " cross", "probability": 0.5498046875}, {"start": 11.1, "end": 11.7, "word": " product", "probability": 0.9599609375}, {"start": 11.7, "end": 12.42, "word": " و", "probability": 0.7021484375}, {"start": 12.42, "end": 12.86, "word": " أعطينا", "probability": 0.822509765625}, {"start": 12.86, "end": 12.98, "word": " ال", "probability": 0.64013671875}, {"start": 12.98, "end": 13.48, "word": " definition", "probability": 0.88232421875}, {"start": 13.48, "end": 13.98, "word": " تبع", "probability": 0.9270833333333334}, {"start": 13.98, "end": 14.14, "word": " ال", "probability": 0.79150390625}, {"start": 14.14, "end": 14.48, "word": " cross", "probability": 0.9619140625}, {"start": 14.48, "end": 14.98, "word": " product", "probability": 0.97509765625}, {"start": 14.98, "end": 15.3, "word": " ثم", "probability": 0.96240234375}, {"start": 15.3, "end": 15.88, "word": " أعطينا", "probability": 0.905078125}, {"start": 15.88, "end": 16.06, "word": " على", "probability": 0.90283203125}, {"start": 16.06, "end": 16.52, "word": " ذلك", "probability": 0.9775390625}, {"start": 16.52, "end": 17.5, "word": " مثالين", "probability": 0.95458984375}, {"start": 17.5, "end": 18.6, "word": " بنذكر", "probability": 0.7646484375}, {"start": 18.6, "end": 19.16, "word": " تذكير", "probability": 0.735107421875}, {"start": 19.16, "end": 19.64, "word": " فقط", "probability": 0.97607421875}, {"start": 19.64, "end": 20.22, "word": " بالتعريف", "probability": 0.965625}, {"start": 20.22, "end": 20.48, "word": " تبع", "probability": 0.9280598958333334}, {"start": 20.48, "end": 20.6, "word": " ال", "probability": 0.5966796875}, {"start": 20.6, "end": 20.88, "word": " cross", "probability": 0.9482421875}, {"start": 20.88, "end": 21.42, "word": " product", "probability": 0.97021484375}, {"start": 21.42, "end": 21.94, "word": " لإنه", "probability": 0.6954345703125}, {"start": 21.94, "end": 22.52, "word": " لازمنا", "probability": 0.9351806640625}, {"start": 22.52, "end": 23.28, "word": " بعد", "probability": 0.9521484375}, {"start": 23.28, "end": 23.84, "word": " قليل", "probability": 0.9952799479166666}, {"start": 23.84, "end": 24.1, "word": " ثم", "probability": 0.994140625}, {"start": 24.1, "end": 24.76, "word": " نذهب", "probability": 0.97998046875}, {"start": 24.76, "end": 25.16, "word": " إلى", "probability": 0.85546875}, {"start": 25.16, "end": 25.72, "word": " خواص", "probability": 0.8556315104166666}, {"start": 25.72, "end": 25.92, "word": " ال", "probability": 0.7763671875}, {"start": 25.92, "end": 26.24, "word": " cross", "probability": 0.96337890625}, {"start": 26.24, "end": 26.82, "word": " product", "probability": 0.97314453125}, {"start": 26.82, "end": 27.8, "word": " المرة", "probability": 0.937255859375}, {"start": 27.8, "end": 27.92, "word": " اللي", "probability": 0.70654296875}, {"start": 27.92, "end": 28.08, "word": " فيها", "probability": 0.58984375}, {"start": 28.08, "end": 28.18, "word": " دي", "probability": 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{"start": 69.39, "end": 70.49, "word": " خارج", "probability": 0.9866536458333334}, {"start": 70.49, "end": 70.95, "word": " فك", "probability": 0.901611328125}, {"start": 70.95, "end": 71.91, "word": " المحدد", "probability": 0.9778645833333334}, {"start": 71.91, "end": 72.97, "word": " الثلاثي", "probability": 0.9462890625}, {"start": 72.97, "end": 73.41, "word": " اللي", "probability": 0.841064453125}, {"start": 73.41, "end": 74.03, "word": " قدامنا", "probability": 0.9765625}, {"start": 74.03, "end": 74.29, "word": " هذا", "probability": 0.84912109375}, {"start": 74.29, "end": 74.55, "word": " هو", "probability": 0.93603515625}, {"start": 74.55, "end": 75.03, "word": " تعريف", "probability": 0.9796549479166666}, {"start": 75.03, "end": 75.39, "word": " مهين", "probability": 0.5467936197916666}, {"start": 75.39, "end": 75.55, "word": " ل", "probability": 0.81689453125}, {"start": 75.55, "end": 75.85, "word": " cross", "probability": 0.56103515625}, {"start": 75.85, "end": 76.35, 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"text": "يبقى الـ scalar بيقول اللي مش عارفونا برا فبصير عندي R في S مضروبات بعض برا وفضل عندي ال cross product ما بين ال vectors U وV", "tokens": [1829, 3555, 4587, 7578, 2423, 39184, 39684, 4724, 1829, 39648, 13672, 1829, 37893, 6225, 9640, 5172, 2407, 8315, 4724, 23557, 6156, 3555, 9381, 13546, 18871, 16254, 497, 8978, 318, 3714, 11242, 32887, 3555, 9307, 45030, 11242, 4724, 23557, 4032, 5172, 11242, 1211, 18871, 16254, 2423, 3278, 1674, 19446, 49374, 2423, 18875, 624, 4032, 53], "avg_logprob": -0.3880681937391108, "compression_ratio": 1.3636363636363635, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 158.67, "end": 159.67, "word": "يبقى", "probability": 0.6037445068359375}, {"start": 159.67, "end": 159.81, "word": " الـ", "probability": 0.2069854736328125}, {"start": 159.81, "end": 160.09, "word": " scalar", "probability": 0.479736328125}, {"start": 160.09, "end": 160.51, "word": " بيقول", "probability": 0.5799967447916666}, {"start": 160.51, "end": 160.65, "word": " 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"word": " إبدالية", "probability": 0.929443359375}, {"start": 323.45, "end": 324.15, "word": " يبقى", "probability": 0.8975830078125}, {"start": 324.15, "end": 324.51, "word": " هالي", "probability": 0.7057291666666666}, {"start": 324.51, "end": 325.01, "word": " معناها", "probability": 0.81201171875}, {"start": 325.01, "end": 325.67, "word": " بينجو", "probability": 0.5125732421875}, {"start": 325.67, "end": 326.05, "word": " سيم", "probability": 0.753662109375}, {"start": 326.05, "end": 326.69, "word": " بقول", "probability": 0.89990234375}, {"start": 326.69, "end": 327.45, "word": " not", "probability": 0.95166015625}, {"start": 327.45, "end": 328.97, "word": " commutative", "probability": 0.9807942708333334}], "temperature": 1.0}, {"id": 14, "seek": 34282, "start": 333.08, "end": 342.82, "text": "ليست ابدالي طيب هذه الخاصية رائعة روحنا الخاصية الخامسة الخاصية الخامسة بيقول لي ان", "tokens": [20292, 14851, 1975, 44510, 6027, 1829, 23032, 1829, 3555, 29538, 33962, 33546, 10632, 12602, 16373, 27884, 12602, 2407, 5016, 8315, 33962, 33546, 10632, 33962, 10943, 3794, 3660, 33962, 33546, 10632, 33962, 10943, 3794, 3660, 4724, 1829, 39648, 32239, 16472], "avg_logprob": -0.24960936829447747, "compression_ratio": 1.7, "no_speech_prob": 0.0014352798461914062, "words": [{"start": 333.08, "end": 333.68, "word": "ليست", "probability": 0.637939453125}, {"start": 333.68, "end": 334.44, "word": " ابدالي", "probability": 0.722900390625}, {"start": 334.44, "end": 335.3, "word": " طيب", "probability": 0.8006184895833334}, {"start": 335.3, "end": 335.54, "word": " هذه", "probability": 0.439208984375}, {"start": 335.54, "end": 336.2, "word": " الخاصية", "probability": 0.9436848958333334}, {"start": 336.2, "end": 336.68, "word": " رائعة", "probability": 0.7692057291666666}, {"start": 336.68, "end": 337.16, "word": " روحنا", "probability": 0.682861328125}, {"start": 337.16, "end": 338.06, "word": " الخاصية", "probability": 0.89404296875}, {"start": 338.06, "end": 339.38, "word": " الخامسة", "probability": 0.973388671875}, {"start": 339.38, "end": 340.62, "word": " الخاصية", "probability": 0.94970703125}, {"start": 340.62, "end": 341.22, "word": " الخامسة", "probability": 0.9864501953125}, {"start": 341.22, "end": 341.68, "word": " بيقول", "probability": 0.9012044270833334}, {"start": 341.68, "end": 341.92, "word": " لي", "probability": 0.467529296875}, {"start": 341.92, "end": 342.82, "word": " ان", "probability": 0.66748046875}], "temperature": 1.0}, {"id": 15, "seek": 36824, "start": 349.92, "end": 368.24, "text": "و Victor ممتاز جدا هذا بده يخليني أتساءل تساؤل يعني طبيعي أني أسأله لما أقول المتجه لو ضربت في نفسه أو في متجه موازي الهو كروس بتبقى الزاوية بينهم كده؟", "tokens": [2407, 15777, 3714, 2304, 2655, 31377, 10874, 28259, 23758, 47525, 3224, 7251, 9778, 1211, 9957, 1829, 5551, 2655, 3794, 16606, 1211, 6055, 3794, 5718, 97, 1211, 37495, 22653, 23032, 21292, 3615, 1829, 14739, 1829, 5551, 3794, 10721, 43761, 5296, 15042, 5551, 39648, 9673, 2655, 7435, 3224, 45164, 48812, 25513, 2655, 8978, 8717, 36178, 3224, 34051, 8978, 44650, 7435, 3224, 3714, 2407, 31377, 1829, 2423, 3224, 2407, 9122, 32887, 3794, 39894, 3555, 4587, 7578, 6024, 110, 995, 2407, 10632, 49374, 16095, 9122, 3215, 3224, 22807], "avg_logprob": -0.257352931359235, "compression_ratio": 1.5433526011560694, "no_speech_prob": 1.1146068572998047e-05, "words": [{"start": 349.92, "end": 350.0, "word": "و", "probability": 0.22216796875}, {"start": 350.0, "end": 350.56, "word": " Victor", "probability": 0.21435546875}, {"start": 350.56, "end": 351.54, "word": " ممتاز", "probability": 0.87158203125}, {"start": 351.54, "end": 351.94, "word": " جدا", "probability": 0.99169921875}, {"start": 351.94, "end": 352.92, "word": " هذا", "probability": 0.55615234375}, {"start": 352.92, "end": 353.2, "word": " بده", "probability": 0.613037109375}, {"start": 353.2, "end": 353.9, "word": " يخليني", "probability": 0.771484375}, {"start": 353.9, "end": 354.68, "word": " أتساءل", "probability": 0.8228515625}, {"start": 354.68, "end": 356.02, "word": " تساؤل", "probability": 0.88740234375}, {"start": 356.02, "end": 357.1, "word": " يعني", "probability": 0.633544921875}, {"start": 357.1, "end": 357.64, "word": " طبيعي", "probability": 0.9605712890625}, {"start": 357.64, "end": 357.98, "word": " أني", "probability": 0.773681640625}, {"start": 357.98, "end": 358.48, "word": " أسأله", "probability": 0.9261474609375}, {"start": 358.48, "end": 359.3, "word": " لما", "probability": 0.90966796875}, {"start": 359.3, "end": 359.72, "word": " أقول", "probability": 0.865234375}, {"start": 359.72, "end": 360.94, "word": " المتجه", "probability": 0.9747314453125}, {"start": 360.94, "end": 361.26, "word": " لو", "probability": 0.9736328125}, {"start": 361.26, "end": 361.9, "word": " ضربت", "probability": 0.8792317708333334}, {"start": 361.9, "end": 362.1, "word": " في", "probability": 0.97802734375}, {"start": 362.1, "end": 362.86, "word": " نفسه", "probability": 0.9905598958333334}, {"start": 362.86, "end": 363.42, "word": " أو", "probability": 0.7890625}, {"start": 363.42, "end": 363.72, "word": " في", "probability": 0.93017578125}, {"start": 363.72, "end": 364.46, "word": " متجه", "probability": 0.9659830729166666}, {"start": 364.46, "end": 365.16, "word": " موازي", "probability": 0.925537109375}, {"start": 365.16, "end": 365.5, "word": " الهو", "probability": 0.4766438802083333}, {"start": 365.5, "end": 366.04, "word": " كروس", "probability": 0.580810546875}, {"start": 366.04, "end": 366.84, "word": " بتبقى", "probability": 0.7264404296875}, {"start": 366.84, "end": 367.24, "word": " الزاوية", "probability": 0.88564453125}, {"start": 367.24, "end": 367.56, "word": " بينهم", "probability": 0.954833984375}, {"start": 367.56, "end": 368.24, "word": " كده؟", "probability": 0.74505615234375}], "temperature": 1.0}, {"id": 16, "seek": 39525, "start": 380.03, "end": 395.25, "text": "معنى هذا الكلام أن الـ zero will you are parallel vectors يبقى من الآن فساعدني الـ zero عبارة عن vector parallel to any other vector", "tokens": [2304, 3615, 1863, 7578, 23758, 2423, 28820, 10943, 14739, 2423, 39184, 4018, 486, 291, 366, 8952, 18875, 7251, 3555, 4587, 7578, 9154, 6024, 48506, 6156, 3794, 995, 22488, 22653, 2423, 39184, 4018, 6225, 3555, 9640, 3660, 18871, 8062, 8952, 281, 604, 661, 8062], "avg_logprob": -0.3549360849640586, "compression_ratio": 1.3208955223880596, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 380.03, "end": 381.03, "word": "معنى", "probability": 0.645965576171875}, {"start": 381.03, "end": 381.31, "word": " هذا", "probability": 0.798828125}, {"start": 381.31, "end": 381.91, "word": " الكلام", "probability": 0.9108072916666666}, {"start": 381.91, "end": 382.37, "word": " أن", "probability": 0.35302734375}, {"start": 382.37, "end": 382.67, "word": " الـ", "probability": 0.382080078125}, {"start": 382.67, "end": 383.05, "word": " zero", "probability": 0.373291015625}, {"start": 383.05, "end": 383.55, "word": " will", "probability": 0.53076171875}, {"start": 383.55, "end": 383.99, "word": " you", "probability": 0.625}, {"start": 383.99, "end": 384.69, "word": " are", "probability": 0.88818359375}, {"start": 384.69, "end": 385.69, "word": " parallel", "probability": 0.78271484375}, {"start": 385.69, "end": 386.81, "word": " vectors", "probability": 0.9521484375}, {"start": 386.81, "end": 388.25, "word": " يبقى", "probability": 0.8140869140625}, {"start": 388.25, "end": 388.41, "word": " من", "probability": 0.84130859375}, {"start": 388.41, "end": 388.93, "word": " الآن", "probability": 0.667236328125}, {"start": 388.93, "end": 389.87, "word": " فساعدني", "probability": 0.7033203125}, {"start": 389.87, "end": 390.21, "word": " الـ", "probability": 0.612548828125}, {"start": 390.21, "end": 390.67, "word": " zero", "probability": 0.8291015625}, {"start": 390.67, "end": 391.87, "word": " عبارة", "probability": 0.9920654296875}, {"start": 391.87, "end": 392.13, "word": " عن", "probability": 0.994140625}, {"start": 392.13, "end": 392.49, "word": " vector", "probability": 0.8349609375}, {"start": 392.49, "end": 393.27, "word": " parallel", "probability": 0.89208984375}, {"start": 393.27, "end": 393.77, "word": " to", "probability": 0.9814453125}, {"start": 393.77, "end": 394.21, "word": " any", "probability": 0.90966796875}, {"start": 394.21, "end": 394.73, "word": " other", "probability": 0.8974609375}, {"start": 394.73, "end": 395.25, "word": " vector", "probability": 0.9599609375}], "temperature": 1.0}, {"id": 17, "seek": 41516, "start": 395.78, "end": 415.16, "text": "يبقى هذا معناه إيش؟ فهذا معناه إن الـ zero vector is parallel to any vector طيب لو رجعنا بالذاكرة إلى الوراق لل dot product", "tokens": [1829, 3555, 4587, 7578, 23758, 20449, 8315, 3224, 11933, 1829, 8592, 22807, 6156, 3224, 15730, 20449, 8315, 3224, 36145, 2423, 39184, 4018, 8062, 307, 8952, 281, 604, 8062, 23032, 1829, 3555, 45164, 12602, 7435, 3615, 8315, 20666, 15730, 4117, 25720, 30731, 2423, 13063, 995, 4587, 24976, 5893, 1674], "avg_logprob": -0.19818240282486896, "compression_ratio": 1.3093525179856116, "no_speech_prob": 0.0, "words": [{"start": 395.78, "end": 396.3, "word": "يبقى", "probability": 0.91357421875}, {"start": 396.3, "end": 396.54, "word": " هذا", "probability": 0.689453125}, {"start": 396.54, "end": 397.1, "word": " معناه", "probability": 0.8536783854166666}, {"start": 397.1, "end": 397.76, "word": " إيش؟", "probability": 0.7591552734375}, {"start": 397.76, "end": 398.22, "word": " فهذا", "probability": 0.8240559895833334}, {"start": 398.22, "end": 399.2, "word": " معناه", "probability": 0.97900390625}, {"start": 399.2, "end": 399.78, "word": " إن", "probability": 0.56103515625}, {"start": 399.78, "end": 400.36, "word": " الـ", "probability": 0.4141845703125}, {"start": 400.36, "end": 400.58, "word": " zero", "probability": 0.498046875}, {"start": 400.58, "end": 401.32, "word": " vector", "probability": 0.951171875}, {"start": 401.32, "end": 402.2, "word": " is", "probability": 0.9228515625}, {"start": 402.2, "end": 403.58, "word": " parallel", "probability": 0.90625}, {"start": 403.58, "end": 406.12, "word": " to", "probability": 0.966796875}, {"start": 406.12, "end": 407.44, "word": " any", "probability": 0.91064453125}, {"start": 407.44, "end": 409.14, "word": " vector", "probability": 0.97314453125}, {"start": 409.14, "end": 411.22, "word": " طيب", "probability": 0.9508463541666666}, {"start": 411.22, "end": 411.48, "word": " لو", "probability": 0.876953125}, {"start": 411.48, "end": 412.02, "word": " رجعنا", "probability": 0.945556640625}, {"start": 412.02, "end": 412.78, "word": " بالذاكرة", "probability": 0.9481201171875}, {"start": 412.78, "end": 413.1, "word": " إلى", "probability": 0.8642578125}, {"start": 413.1, "end": 413.92, "word": " الوراق", "probability": 0.8048095703125}, {"start": 413.92, "end": 414.3, "word": " لل", "probability": 0.48095703125}, {"start": 414.3, "end": 414.58, "word": " dot", "probability": 0.64892578125}, {"start": 414.58, "end": 415.16, "word": " product", "probability": 0.9853515625}], "temperature": 1.0}, {"id": 18, "seek": 43156, "start": 415.98, "end": 431.56, "text": "أثبتنا كمان أن الـ dot أن الـ zero هو الـ dot أن أي vector بدي أعطينا مين الـ zero وبالتالي قلنا أن الـ zero is orthogonal to أي vector إذا الـ zero هو ال vector الوحيد", "tokens": [10721, 12984, 3555, 2655, 8315, 9122, 2304, 7649, 14739, 2423, 39184, 5893, 14739, 2423, 39184, 4018, 31439, 2423, 39184, 5893, 14739, 36632, 8062, 4724, 16254, 5551, 3615, 9566, 1829, 8315, 3714, 9957, 2423, 39184, 4018, 46599, 6027, 2655, 6027, 1829, 12174, 1211, 8315, 14739, 2423, 39184, 4018, 307, 41488, 281, 36632, 8062, 11933, 15730, 2423, 39184, 4018, 31439, 2423, 8062, 2423, 2407, 5016, 25708], "avg_logprob": -0.5144230769230769, "compression_ratio": 1.776978417266187, "no_speech_prob": 0.0, "words": [{"start": 415.97999999999996, "end": 416.7, "word": "أثبتنا", "probability": 0.886328125}, {"start": 416.7, "end": 417.18, "word": " كمان", "probability": 0.7540690104166666}, {"start": 417.18, "end": 417.52, "word": " أن", "probability": 0.5107421875}, {"start": 417.52, "end": 417.7, "word": " الـ", "probability": 0.445556640625}, {"start": 417.7, "end": 418.22, "word": " dot", "probability": 0.4345703125}, {"start": 418.22, "end": 418.58, "word": " أن", "probability": 0.234130859375}, {"start": 418.58, "end": 418.9, "word": " الـ", "probability": 0.5281982421875}, {"start": 418.9, "end": 419.1, "word": " zero", "probability": 0.65283203125}, {"start": 419.1, "end": 419.42, "word": " هو", "probability": 0.278076171875}, {"start": 419.42, "end": 419.46, "word": " الـ", "probability": 0.44384765625}, {"start": 419.46, "end": 419.78, "word": " dot", "probability": 0.662109375}, {"start": 419.78, "end": 420.16, "word": " أن", "probability": 0.1761474609375}, {"start": 420.16, "end": 420.32, "word": " أي", "probability": 0.56640625}, {"start": 420.32, "end": 420.64, "word": " vector", "probability": 0.56298828125}, {"start": 420.64, "end": 420.94, "word": " بدي", "probability": 0.455047607421875}, {"start": 420.94, "end": 421.3, "word": " أعطينا", "probability": 0.69208984375}, {"start": 421.3, "end": 421.74, "word": " مين", "probability": 0.508544921875}, {"start": 421.74, "end": 422.48, "word": " الـ", "probability": 0.346343994140625}, {"start": 422.48, "end": 422.6, "word": " zero", "probability": 0.77685546875}, {"start": 422.6, "end": 423.34, "word": " وبالتالي", "probability": 0.8560546875}, {"start": 423.34, "end": 423.8, "word": " قلنا", "probability": 0.73583984375}, {"start": 423.8, "end": 424.16, "word": " أن", "probability": 0.55224609375}, {"start": 424.16, "end": 424.54, "word": " الـ", "probability": 0.748046875}, {"start": 424.54, "end": 424.78, "word": " zero", "probability": 0.880859375}, {"start": 424.78, "end": 425.38, "word": " is", "probability": 0.26220703125}, {"start": 425.38, "end": 426.3, "word": " orthogonal", "probability": 0.904296875}, {"start": 426.3, "end": 427.24, "word": " to", "probability": 0.7802734375}, {"start": 427.24, "end": 427.5, "word": " أي", "probability": 0.56201171875}, {"start": 427.5, "end": 427.94, "word": " vector", "probability": 0.93603515625}, {"start": 427.94, "end": 428.76, "word": " إذا", "probability": 0.574462890625}, {"start": 428.76, "end": 429.1, "word": " الـ", "probability": 0.45947265625}, {"start": 429.1, "end": 429.34, "word": " zero", "probability": 0.88623046875}, {"start": 429.34, "end": 429.68, "word": " هو", "probability": 0.98828125}, {"start": 429.68, "end": 429.92, "word": " ال", "probability": 0.84521484375}, {"start": 429.92, "end": 430.4, "word": " vector", "probability": 0.86328125}, {"start": 430.4, "end": 431.56, "word": " الوحيد", "probability": 0.9703369140625}], "temperature": 1.0}, {"id": 19, "seek": 46034, "start": 431.88, "end": 460.34, "text": "الذي يكون عمودي على أي vector وفي نفس الوقت parallel to any vector يعني بالنسبة لل vector الواحد ال zero بقدر اقول orthogonal لهذا ال vector وفي نفس الوقت parallel لهذا ال vector لأن ال zero vector الطول تبعه يسوى الصفر وممكن تاخده في أي اتجاه بدكي على كذا زي ما بدكي تمام؟ يبقى هذه الخاصية رقم خمسة نجد الخاصية رقم ستة", "tokens": [6027, 8848, 1829, 7251, 30544, 6225, 2304, 2407, 16254, 15844, 36632, 8062, 4032, 41185, 8717, 36178, 2423, 30543, 2655, 8952, 281, 604, 8062, 37495, 22653, 20666, 1863, 35457, 3660, 24976, 8062, 2423, 14407, 24401, 2423, 4018, 4724, 28543, 2288, 1975, 39648, 41488, 46740, 15730, 2423, 8062, 4032, 41185, 8717, 36178, 2423, 30543, 2655, 8952, 46740, 15730, 2423, 8062, 5296, 33456, 2423, 4018, 8062, 41950, 12610, 6055, 3555, 3615, 3224, 7251, 3794, 2407, 7578, 31767, 5172, 2288, 4032, 2304, 43020, 6055, 47283, 3215, 3224, 8978, 36632, 1975, 2655, 7435, 40294, 47525, 4117, 1829, 15844, 9122, 15730, 30767, 1829, 19446, 47525, 4117, 1829, 46811, 10943, 22807, 7251, 3555, 4587, 7578, 29538, 33962, 33546, 10632, 12602, 4587, 2304, 16490, 2304, 3794, 3660, 8717, 7435, 3215, 33962, 33546, 10632, 12602, 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{"start": 447.0, "end": 447.28, "word": " zero", "probability": 0.8115234375}, {"start": 447.28, "end": 447.84, "word": " vector", "probability": 0.97607421875}, {"start": 447.84, "end": 448.84, "word": " الطول", "probability": 0.912841796875}, {"start": 448.84, "end": 449.28, "word": " تبعه", "probability": 0.753875732421875}, {"start": 449.28, "end": 449.68, "word": " يسوى", "probability": 0.79296875}, {"start": 449.68, "end": 450.04, "word": " الصفر", "probability": 0.8272298177083334}, {"start": 450.04, "end": 450.46, "word": " وممكن", "probability": 0.8505859375}, {"start": 450.46, "end": 451.16, "word": " تاخده", "probability": 0.832275390625}, {"start": 451.16, "end": 451.4, "word": " في", "probability": 0.97900390625}, {"start": 451.4, "end": 451.8, "word": " أي", "probability": 0.68701171875}, {"start": 451.8, "end": 452.56, "word": " اتجاه", "probability": 0.9893798828125}, {"start": 452.56, "end": 453.26, "word": " بدكي", "probability": 0.70263671875}, {"start": 453.26, "end": 453.56, "word": " على", "probability": 0.57958984375}, {"start": 453.56, "end": 453.98, "word": " كذا", "probability": 0.6986083984375}, {"start": 453.98, "end": 454.24, "word": " زي", "probability": 0.649658203125}, {"start": 454.24, "end": 454.34, "word": " ما", "probability": 0.923828125}, {"start": 454.34, "end": 455.06, "word": " بدكي", "probability": 0.7369791666666666}, {"start": 455.06, "end": 455.96, "word": " تمام؟", "probability": 0.6432291666666666}, {"start": 455.96, "end": 456.34, "word": " يبقى", "probability": 0.9422607421875}, {"start": 456.34, "end": 456.56, "word": " هذه", "probability": 0.8115234375}, {"start": 456.56, "end": 457.14, "word": " الخاصية", "probability": 0.9736328125}, {"start": 457.14, "end": 457.66, "word": " رقم", "probability": 0.9905598958333334}, {"start": 457.66, "end": 458.14, "word": " خمسة", "probability": 0.9161376953125}, {"start": 458.14, "end": 458.46, "word": " نجد", "probability": 0.7757161458333334}, {"start": 458.46, "end": 459.14, "word": " الخاصية", "probability": 0.9850260416666666}, {"start": 459.14, "end": 459.7, "word": " رقم", "probability": 0.9900716145833334}, {"start": 459.7, "end": 460.34, "word": " ستة", "probability": 0.96826171875}], "temperature": 1.0}, {"id": 20, "seek": 49206, "start": 462.44, "end": 492.06, "text": "لو قلت لك I cross الـ J هدول two vector بدي أجيب ال cross فيما بينهما، شو بدي يعطيني؟ متجه عمودي على الاتنين، مين المتجه عمودي؟ اللي هو K، يبقى بدي يعطيني K، أليس هذا هو سالب J cross ال I؟ يبقى هذا بدي يعطيك كمان، بدي يعطيك K، هكتب لك باقي ال vector، بس إلي خاطر", "tokens": [1211, 2407, 12174, 1211, 2655, 5296, 4117, 286, 3278, 2423, 39184, 508, 8032, 3215, 12610, 732, 8062, 4724, 16254, 5551, 7435, 1829, 3555, 2423, 3278, 8978, 15042, 49374, 3224, 15042, 12399, 13412, 2407, 4724, 16254, 37495, 9566, 1829, 22653, 22807, 44650, 7435, 3224, 6225, 2304, 2407, 16254, 15844, 2423, 9307, 1863, 9957, 12399, 3714, 9957, 9673, 2655, 7435, 3224, 6225, 2304, 2407, 16254, 22807, 13672, 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{"start": 478.84, "end": 479.34, "word": " بدي", "probability": 0.59906005859375}, {"start": 479.34, "end": 480.06, "word": " يعطيني", "probability": 0.8458251953125}, {"start": 480.06, "end": 480.34, "word": " K،", "probability": 0.6357421875}, {"start": 480.34, "end": 480.96, "word": " أليس", "probability": 0.9117838541666666}, {"start": 480.96, "end": 481.44, "word": " هذا", "probability": 0.89306640625}, {"start": 481.44, "end": 481.82, "word": " هو", "probability": 0.9921875}, {"start": 481.82, "end": 482.6, "word": " سالب", "probability": 0.6407877604166666}, {"start": 482.6, "end": 482.92, "word": " J", "probability": 0.7919921875}, {"start": 482.92, "end": 483.48, "word": " cross", "probability": 0.9375}, {"start": 483.48, "end": 483.78, "word": " ال", "probability": 0.50146484375}, {"start": 483.78, "end": 485.0, "word": " I؟", "probability": 0.75}, {"start": 485.0, "end": 485.48, "word": " يبقى", "probability": 0.978271484375}, {"start": 485.48, "end": 485.8, "word": " هذا", "probability": 0.9462890625}, {"start": 485.8, "end": 486.14, "word": " بدي", "probability": 0.904541015625}, {"start": 486.14, "end": 486.68, "word": " يعطيك", "probability": 0.9952392578125}, {"start": 486.68, "end": 487.34, "word": " كمان،", "probability": 0.659423828125}, {"start": 487.34, "end": 487.74, "word": " بدي", "probability": 0.961181640625}, {"start": 487.74, "end": 488.34, "word": " يعطيك", "probability": 0.9964599609375}, {"start": 488.34, "end": 489.14, "word": " K،", "probability": 0.728271484375}, {"start": 489.14, "end": 489.64, "word": " هكتب", "probability": 0.919921875}, {"start": 489.64, "end": 489.86, "word": " لك", "probability": 0.91748046875}, {"start": 489.86, "end": 490.12, "word": " باقي", "probability": 0.4334309895833333}, {"start": 490.12, "end": 490.26, "word": " ال", "probability": 0.98681640625}, {"start": 490.26, "end": 490.78, "word": " vector،", "probability": 0.74462890625}, {"start": 490.78, "end": 491.1, "word": " بس", "probability": 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"probability": 0.9345703125}, {"start": 498.17, "end": 498.33, "word": " إن", "probability": 0.408447265625}, {"start": 498.33, "end": 498.85, "word": " جاءت", "probability": 0.5303955078125}, {"start": 498.85, "end": 499.65, "word": " وخيلت", "probability": 0.7047119140625}, {"start": 499.65, "end": 500.75, "word": " دائرة", "probability": 0.7652180989583334}, {"start": 500.75, "end": 501.23, "word": " بهذا", "probability": 0.576171875}, {"start": 501.23, "end": 501.93, "word": " الشكل،", "probability": 0.7754720052083334}, {"start": 501.93, "end": 503.41, "word": " ودائرة", "probability": 0.753173828125}, {"start": 503.41, "end": 503.89, "word": " هذه", "probability": 0.71826171875}, {"start": 503.89, "end": 504.83, "word": " أخذت", "probability": 0.7266845703125}, {"start": 504.83, "end": 505.13, "word": " هنا", "probability": 0.6904296875}, {"start": 505.13, "end": 505.45, "word": " الـ", "probability": 0.56640625}, {"start": 505.45, "end": 505.77, "word": " vector", "probability": 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{"start": 625.12, "end": 625.9, "word": " عملية", "probability": 0.9817708333333334}, {"start": 625.9, "end": 626.36, "word": " ضرب", "probability": 0.986572265625}, {"start": 626.36, "end": 627.72, "word": " المتجهات", "probability": 0.9888671875}, {"start": 627.72, "end": 628.98, "word": " اتجاهيا", "probability": 0.9314453125}], "temperature": 1.0}, {"id": 26, "seek": 65757, "start": 629.33, "end": 657.57, "text": "is not associative ليست تجميعية أو ليست إدماجية معقول هذا الكلام أثبتلك هذا الكلام for example كمثال على ذلك لو جيت قولتلك I across ال J across ال J على سبيل المثال بدي أشوف كده إيش تساوي", "tokens": [271, 406, 4180, 1166, 32239, 14851, 6055, 7435, 2304, 40228, 10632, 34051, 32239, 14851, 11933, 40448, 26108, 10632, 20449, 39648, 23758, 2423, 28820, 10943, 5551, 12984, 3555, 2655, 23275, 23758, 2423, 28820, 10943, 337, 1365, 9122, 2304, 12984, 6027, 15844, 29910, 23275, 45164, 10874, 36081, 12174, 12610, 2655, 23275, 286, 2108, 2423, 508, 2108, 2423, 508, 15844, 8608, 21292, 1211, 9673, 12984, 6027, 4724, 16254, 5551, 8592, 38688, 9122, 3215, 3224, 11933, 1829, 8592, 6055, 3794, 995, 45865], "avg_logprob": -0.17681961798969703, "compression_ratio": 1.5797872340425532, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 629.33, "end": 629.67, "word": "is", "probability": 0.498779296875}, {"start": 629.67, "end": 630.15, "word": " not", "probability": 0.94580078125}, {"start": 630.15, "end": 631.43, "word": " associative", "probability": 0.93701171875}, {"start": 631.43, "end": 632.37, "word": " ليست", "probability": 0.865966796875}, {"start": 632.37, "end": 633.45, "word": " تجميعية", "probability": 0.95205078125}, {"start": 633.45, "end": 633.77, "word": " أو", "probability": 0.82861328125}, {"start": 633.77, "end": 634.41, "word": " ليست", "probability": 0.809814453125}, {"start": 634.41, "end": 635.87, "word": " إدماجية", "probability": 0.9036865234375}, {"start": 635.87, "end": 636.93, "word": " معقول", "probability": 0.66796875}, {"start": 636.93, "end": 637.17, "word": " هذا", "probability": 0.9658203125}, {"start": 637.17, "end": 637.73, "word": " الكلام", "probability": 0.96875}, {"start": 637.73, "end": 638.95, "word": " أثبتلك", "probability": 0.8017578125}, {"start": 638.95, "end": 639.27, "word": " هذا", "probability": 0.97021484375}, {"start": 639.27, "end": 639.87, "word": " الكلام", "probability": 0.98291015625}, {"start": 639.87, "end": 640.55, "word": " for", "probability": 0.58837890625}, {"start": 640.55, "end": 641.47, "word": " example", "probability": 0.966796875}, {"start": 641.47, "end": 644.01, "word": " كمثال", "probability": 0.9727783203125}, {"start": 644.01, "end": 644.31, "word": " على", "probability": 0.91943359375}, {"start": 644.31, "end": 645.09, "word": " ذلك", "probability": 0.967041015625}, {"start": 645.09, "end": 645.97, "word": " لو", "probability": 0.84326171875}, {"start": 645.97, "end": 646.33, "word": " جيت", "probability": 0.8818359375}, {"start": 646.33, "end": 647.11, "word": " قولتلك", "probability": 0.81817626953125}, {"start": 647.11, "end": 647.73, "word": " I", "probability": 0.84033203125}, {"start": 647.73, "end": 649.01, "word": " across", "probability": 0.6318359375}, {"start": 649.01, "end": 649.89, "word": " ال", "probability": 0.53515625}, {"start": 649.89, "end": 650.53, "word": " J", "probability": 0.6181640625}, {"start": 650.53, "end": 651.47, "word": " across", "probability": 0.76025390625}, {"start": 651.47, "end": 652.11, "word": " ال", "probability": 0.6962890625}, {"start": 652.11, "end": 652.49, "word": " J", "probability": 0.54345703125}, {"start": 652.49, "end": 654.41, "word": " على", "probability": 0.88916015625}, {"start": 654.41, "end": 654.85, "word": " سبيل", "probability": 0.9847005208333334}, {"start": 654.85, "end": 655.33, "word": " المثال", "probability": 0.9908854166666666}, {"start": 655.33, "end": 656.29, "word": " بدي", "probability": 0.57373046875}, {"start": 656.29, "end": 656.55, "word": " أشوف", "probability": 0.9319661458333334}, {"start": 656.55, "end": 656.85, "word": " كده", "probability": 0.8126627604166666}, {"start": 656.85, "end": 656.97, "word": " إيش", "probability": 0.79296875}, {"start": 656.97, "end": 657.57, "word": " تساوي", "probability": 0.97265625}], "temperature": 1.0}, {"id": 27, "seek": 67955, "start": 657.99, "end": 679.55, "text": "يبقى هذي I cross الجيه كده شباب الات K يبقى K cross الجيه K cross الجيه تعطي كده سالب I يبقى هذه سالب I فات ولكن ال I cross الجيه cross الجيه", "tokens": [1829, 3555, 4587, 7578, 8032, 8848, 1829, 286, 3278, 25724, 1829, 3224, 9122, 3215, 3224, 13412, 3555, 16758, 2423, 9307, 591, 7251, 3555, 4587, 7578, 591, 3278, 25724, 1829, 3224, 591, 3278, 25724, 1829, 3224, 6055, 3615, 9566, 1829, 9122, 3215, 3224, 8608, 6027, 3555, 286, 7251, 3555, 4587, 7578, 29538, 8608, 6027, 3555, 286, 6156, 9307, 35525, 19452, 2423, 286, 3278, 25724, 1829, 3224, 3278, 25724, 1829, 3224], "avg_logprob": -0.32388393580913544, "compression_ratio": 1.990909090909091, "no_speech_prob": 0.0, "words": [{"start": 657.99, "end": 658.59, "word": "يبقى", "probability": 0.8983154296875}, {"start": 658.59, "end": 658.95, "word": " هذي", "probability": 0.4580281575520833}, {"start": 658.95, "end": 659.25, "word": " I", "probability": 0.578125}, {"start": 659.25, "end": 659.75, "word": " cross", "probability": 0.40869140625}, {"start": 659.75, "end": 660.15, "word": " الجيه", "probability": 0.6451822916666666}, {"start": 660.15, "end": 660.39, "word": " كده", "probability": 0.7566731770833334}, {"start": 660.39, "end": 660.81, "word": " شباب", "probability": 0.3182576497395833}, {"start": 660.81, "end": 661.21, "word": " الات", "probability": 0.3092041015625}, {"start": 661.21, "end": 661.57, "word": " K", "probability": 0.58740234375}, {"start": 661.57, "end": 662.73, "word": " يبقى", "probability": 0.8641357421875}, {"start": 662.73, "end": 663.11, "word": " K", "probability": 0.73779296875}, {"start": 663.11, "end": 663.99, "word": " cross", "probability": 0.8173828125}, {"start": 663.99, "end": 664.97, "word": " الجيه", "probability": 0.9615885416666666}, {"start": 664.97, "end": 665.57, "word": " K", "probability": 0.61572265625}, {"start": 665.57, "end": 666.29, "word": " cross", "probability": 0.92822265625}, {"start": 666.29, "end": 667.31, "word": " الجيه", "probability": 0.9798177083333334}, {"start": 667.31, "end": 667.95, "word": " تعطي", "probability": 0.7054443359375}, {"start": 667.95, "end": 668.29, "word": " كده", "probability": 0.8533528645833334}, {"start": 668.29, "end": 669.03, "word": " سالب", "probability": 0.7894694010416666}, {"start": 669.03, "end": 669.69, "word": " I", "probability": 0.99365234375}, {"start": 669.69, "end": 670.81, "word": " يبقى", "probability": 0.9447021484375}, {"start": 670.81, "end": 671.23, "word": " هذه", "probability": 0.6337890625}, {"start": 671.23, "end": 672.37, "word": " سالب", "probability": 0.9697265625}, {"start": 672.37, "end": 672.91, "word": " I", "probability": 0.98828125}, {"start": 672.91, "end": 673.65, "word": " فات", "probability": 0.63916015625}, {"start": 673.65, "end": 675.07, "word": " ولكن", "probability": 0.812744140625}, {"start": 675.07, "end": 675.97, "word": " ال", "probability": 0.5849609375}, {"start": 675.97, "end": 676.45, "word": " I", "probability": 0.94970703125}, {"start": 676.45, "end": 677.21, "word": " cross", "probability": 0.94189453125}, {"start": 677.21, "end": 678.17, "word": " الجيه", "probability": 0.9606119791666666}, {"start": 678.17, "end": 678.67, "word": " cross", "probability": 0.7421875}, {"start": 678.67, "end": 679.55, "word": " الجيه", "probability": 0.9820963541666666}], "temperature": 1.0}, {"id": 28, "seek": 70370, "start": 680.18, "end": 703.7, "text": "لازم يبدأ المخطط ضرب هذا يدخل ضرب هذا للتامة هذول مع بعض يبقى j cross الجيب قداش if I cross ال zero اللي هو قداش ال zero هل ال zero يسوي ناقص I طبعا لأ إذا من الأن فصاعدا عملية cross product is not associated", "tokens": [1211, 31377, 2304, 7251, 44510, 10721, 9673, 9778, 9566, 9566, 48812, 25513, 23758, 7251, 3215, 9778, 1211, 48812, 25513, 23758, 24976, 2655, 10943, 3660, 8032, 8848, 12610, 20449, 45030, 11242, 7251, 3555, 4587, 7578, 361, 3278, 25724, 1829, 3555, 12174, 3215, 33599, 498, 286, 3278, 2423, 4018, 13672, 1829, 31439, 12174, 3215, 33599, 2423, 4018, 8032, 1211, 2423, 4018, 7251, 3794, 45865, 8717, 995, 4587, 9381, 286, 23032, 3555, 3615, 995, 5296, 10721, 11933, 15730, 9154, 16247, 1863, 6156, 9381, 995, 22488, 995, 6225, 42213, 10632, 3278, 1674, 307, 406, 6615], "avg_logprob": -0.3459578736320786, "compression_ratio": 1.5979899497487438, "no_speech_prob": 0.0, "words": [{"start": 680.18, "end": 680.74, "word": "لازم", "probability": 0.5573527018229166}, {"start": 680.74, "end": 681.04, "word": " يبدأ", "probability": 0.7000325520833334}, {"start": 681.04, "end": 681.68, "word": " المخطط", "probability": 0.652099609375}, {"start": 681.68, "end": 681.92, "word": " ضرب", "probability": 0.76611328125}, {"start": 681.92, "end": 682.06, "word": " هذا", "probability": 0.56884765625}, {"start": 682.06, "end": 682.56, "word": " يدخل", "probability": 0.56536865234375}, {"start": 682.56, "end": 682.84, "word": " ضرب", "probability": 0.982421875}, {"start": 682.84, "end": 683.04, "word": " هذا", "probability": 0.74609375}, {"start": 683.04, "end": 683.62, "word": " للتامة", "probability": 0.50408935546875}, {"start": 683.62, "end": 684.02, "word": " هذول", "probability": 0.69873046875}, {"start": 684.02, "end": 684.2, "word": " مع", "probability": 0.98828125}, {"start": 684.2, "end": 684.58, "word": " بعض", "probability": 0.99560546875}, {"start": 684.58, "end": 685.48, "word": " يبقى", "probability": 0.76483154296875}, {"start": 685.48, "end": 685.48, "word": " j", "probability": 0.214599609375}, {"start": 685.48, "end": 685.94, "word": " cross", "probability": 0.6484375}, {"start": 685.94, "end": 686.46, "word": " الجيب", "probability": 0.482666015625}, {"start": 686.46, "end": 687.2, "word": " قداش", "probability": 0.8489583333333334}, {"start": 687.2, "end": 688.04, "word": " if", "probability": 0.451904296875}, {"start": 688.04, "end": 688.48, "word": " I", "probability": 0.464111328125}, {"start": 688.48, "end": 689.08, "word": " cross", "probability": 0.890625}, {"start": 689.08, "end": 689.38, "word": " ال", "probability": 0.796875}, {"start": 689.38, "end": 689.72, "word": " zero", "probability": 0.6162109375}, {"start": 689.72, "end": 689.88, "word": " اللي", "probability": 0.6641845703125}, {"start": 689.88, "end": 690.0, "word": " هو", "probability": 0.96533203125}, {"start": 690.0, "end": 690.68, "word": " قداش", "probability": 0.9822591145833334}, {"start": 690.68, "end": 690.94, "word": " ال", "probability": 0.41552734375}, {"start": 690.94, "end": 691.34, "word": " zero", "probability": 0.81787109375}, {"start": 691.34, "end": 692.12, "word": " هل", "probability": 0.9384765625}, {"start": 692.12, "end": 692.32, "word": " ال", "probability": 0.95703125}, {"start": 692.32, "end": 692.9, "word": " zero", "probability": 0.884765625}, {"start": 692.9, "end": 693.72, "word": " يسوي", "probability": 0.8299153645833334}, {"start": 693.72, "end": 694.42, "word": " ناقص", "probability": 0.9671630859375}, {"start": 694.42, "end": 694.82, "word": " I", "probability": 0.94677734375}, {"start": 694.82, "end": 695.98, "word": " طبعا", "probability": 0.919189453125}, {"start": 695.98, "end": 696.24, "word": " لأ", "probability": 0.8046875}, {"start": 696.24, "end": 696.62, "word": " إذا", "probability": 0.7666015625}, {"start": 696.62, "end": 696.96, "word": " من", "probability": 0.9638671875}, {"start": 696.96, "end": 697.64, "word": " الأن", "probability": 0.706787109375}, {"start": 697.64, "end": 698.68, "word": " فصاعدا", "probability": 0.89189453125}, {"start": 698.68, "end": 699.8, "word": " عملية", "probability": 0.9763997395833334}, {"start": 699.8, "end": 700.3, "word": " cross", "probability": 0.459228515625}, {"start": 700.3, "end": 701.22, "word": " product", "probability": 0.94384765625}, {"start": 701.22, "end": 701.84, "word": " is", "probability": 0.9423828125}, {"start": 701.84, "end": 702.72, "word": " not", "probability": 0.95703125}, {"start": 702.72, "end": 703.7, "word": " associated", "probability": 0.6455078125}], "temperature": 1.0}, {"id": 29, "seek": 73105, "start": 704.11, "end": 731.05, "text": "عملية زي التجميعية أو ليست إدماجية يبقى هذا باختصار بنقول العملية هذه not associative يبقى ليست تجميعية ندل الخاصية التامة يبقى الخاصية التامة لو بدي أجيب طول ال U cross ال B", "tokens": [25957, 1211, 10632, 30767, 1829, 16712, 7435, 2304, 40228, 10632, 34051, 32239, 14851, 11933, 40448, 26108, 10632, 7251, 3555, 4587, 7578, 23758, 4724, 47283, 2655, 9381, 9640, 44945, 39648, 18863, 42213, 10632, 29538, 406, 4180, 1166, 7251, 3555, 4587, 7578, 32239, 14851, 6055, 7435, 2304, 40228, 10632, 8717, 3215, 1211, 33962, 33546, 10632, 16712, 10943, 3660, 7251, 3555, 4587, 7578, 33962, 33546, 10632, 16712, 10943, 3660, 45164, 4724, 16254, 5551, 7435, 1829, 3555, 23032, 12610, 2423, 624, 3278, 2423, 363], "avg_logprob": -0.17611883304737233, "compression_ratio": 1.7309941520467835, "no_speech_prob": 0.0, "words": [{"start": 704.11, "end": 704.83, "word": "عملية", "probability": 0.8859049479166666}, {"start": 704.83, "end": 705.11, "word": " زي", "probability": 0.8349609375}, {"start": 705.11, "end": 706.19, "word": " التجميعية", "probability": 0.767333984375}, {"start": 706.19, "end": 706.49, "word": " أو", "probability": 0.75}, {"start": 706.49, "end": 707.15, "word": " ليست", "probability": 0.9052734375}, {"start": 707.15, "end": 708.85, "word": " إدماجية", "probability": 0.88671875}, {"start": 708.85, "end": 709.85, "word": " يبقى", "probability": 0.90478515625}, {"start": 709.85, "end": 710.19, "word": " هذا", "probability": 0.84814453125}, {"start": 710.19, "end": 711.07, "word": " باختصار", "probability": 0.9404296875}, {"start": 711.07, "end": 711.59, "word": " بنقول", "probability": 0.868896484375}, {"start": 711.59, "end": 712.33, "word": " العملية", "probability": 0.96533203125}, {"start": 712.33, "end": 712.77, "word": " هذه", "probability": 0.95166015625}, {"start": 712.77, "end": 714.07, "word": " not", "probability": 0.266845703125}, {"start": 714.07, "end": 716.57, "word": " associative", "probability": 0.947998046875}, {"start": 716.57, "end": 719.81, "word": " يبقى", "probability": 0.8919677734375}, {"start": 719.81, "end": 720.45, "word": " ليست", "probability": 0.938720703125}, {"start": 720.45, "end": 721.41, "word": " تجميعية", "probability": 0.9427734375}, {"start": 721.41, "end": 721.97, "word": " ندل", "probability": 0.55029296875}, {"start": 721.97, "end": 722.85, "word": " الخاصية", "probability": 0.8400065104166666}, {"start": 722.85, "end": 724.33, "word": " التامة", "probability": 0.9482421875}, {"start": 724.33, "end": 725.11, "word": " يبقى", "probability": 0.9210205078125}, {"start": 725.11, "end": 725.77, "word": " 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ال U في طول ال V في sine الزاوية ثيتا في طول متجه الوحدة N", "tokens": [45340, 2655, 7435, 3224, 23758, 4724, 16254, 5551, 3615, 28480, 12174, 3215, 11933, 1829, 8592, 23032, 12610, 3224, 7251, 3555, 4587, 7578, 23758, 2423, 28820, 10943, 47525, 3224, 7251, 3794, 995, 45865, 23032, 12610, 2423, 624, 8978, 23032, 12610, 2423, 691, 8978, 18609, 6024, 110, 995, 2407, 10632, 38637, 36081, 995, 8978, 23032, 12610, 44650, 7435, 3224, 2423, 2407, 24401, 3660, 426], "avg_logprob": -0.24950397960723392, "compression_ratio": 1.537313432835821, "no_speech_prob": 5.364418029785156e-07, "words": [{"start": 732.19, "end": 733.03, "word": "المتجه", "probability": 0.8231201171875}, {"start": 733.03, "end": 733.27, "word": " هذا", "probability": 0.51171875}, {"start": 733.27, "end": 733.55, "word": " بدي", "probability": 0.542724609375}, {"start": 733.55, "end": 733.93, "word": " أعرف", "probability": 0.84423828125}, {"start": 733.93, "end": 734.23, "word": " قد", "probability": 0.771240234375}, 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{"start": 915.29, "end": 915.95, "word": " تبعته", "probability": 0.7781982421875}, {"start": 915.95, "end": 916.21, "word": " ال", "probability": 0.415283203125}, {"start": 916.21, "end": 916.55, "word": " vectors", "probability": 0.370361328125}, {"start": 916.55, "end": 916.95, "word": " U", "probability": 0.921875}, {"start": 916.95, "end": 917.33, "word": " و", "probability": 0.64306640625}, {"start": 917.33, "end": 917.67, "word": " V", "probability": 0.66552734375}, {"start": 917.67, "end": 918.75, "word": " يبقى", "probability": 0.9366455078125}, {"start": 918.75, "end": 919.03, "word": " هذا", "probability": 0.958984375}, {"start": 919.03, "end": 919.63, "word": " الكلام", "probability": 0.9637044270833334}, {"start": 919.63, "end": 920.15, "word": " بده", "probability": 0.366455078125}, {"start": 920.15, "end": 920.99, "word": " يساوي", "probability": 0.9495849609375}, {"start": 920.99, "end": 922.05, "word": " the", "probability": 0.2276611328125}, {"start": 922.05, "end": 923.97, "word": " area", "probability": 0.84619140625}, {"start": 923.97, "end": 925.17, "word": " of", "probability": 0.96337890625}, {"start": 925.17, "end": 926.31, "word": " the", "probability": 0.69921875}, {"start": 926.31, "end": 927.71, "word": " parallel", "probability": 0.85546875}], "temperature": 1.0}, {"id": 37, "seek": 95249, "start": 930.83, "end": 952.49, "text": "Parallelogram يعني متوازن أطلاع determined والمحدد by the by the vectors U and L", "tokens": [46087, 336, 338, 12820, 37495, 22653, 44650, 2407, 31377, 1863, 5551, 9566, 15040, 3615, 9540, 16070, 2304, 24401, 3215, 538, 264, 538, 264, 18875, 624, 293, 441], "avg_logprob": -0.26799664965697695, "compression_ratio": 1.0, "no_speech_prob": 0.0, "words": [{"start": 930.83, "end": 932.23, "word": "Parallelogram", "probability": 0.867919921875}, {"start": 932.23, "end": 933.63, "word": " يعني", "probability": 0.75341796875}, {"start": 933.63, "end": 934.45, "word": " متوازن", "probability": 0.9554443359375}, 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متوازن أطباع اللي ضلعيه المتجاورين اللي هم ال vector u و ال vector v طيب نهج الآن لكتابة ال cross productive ثلاثي بطريقة جديدة يعني بدي أحاول أرغب الآن ما بين ال cross productive", "tokens": [1829, 3555, 4587, 7578, 6225, 2304, 20292, 995, 14111, 23758, 20449, 8315, 3224, 47524, 39319, 3660, 44650, 2407, 31377, 1863, 5551, 9566, 3555, 45761, 13672, 1829, 48812, 1211, 3615, 1829, 3224, 9673, 2655, 7435, 995, 13063, 9957, 13672, 1829, 8032, 2304, 2423, 8062, 344, 4032, 2423, 8062, 371, 23032, 1829, 3555, 8717, 3224, 7435, 6024, 48506, 5296, 4117, 2655, 16758, 3660, 2423, 3278, 13304, 38637, 1211, 5718, 104, 1829, 4724, 9566, 16572, 28671, 10874, 16254, 41891, 37495, 22653, 4724, 16254, 5551, 5016, 995, 12610, 5551, 2288, 17082, 3555, 6024, 48506, 19446, 49374, 2423, 3278, 13304], "avg_logprob": -0.23128254571929574, "compression_ratio": 1.6354679802955665, "no_speech_prob": 1.0132789611816406e-06, "words": [{"start": 954.23, "end": 954.71, "word": "يبقى", "probability": 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"end": 971.21, "word": " productive", "probability": 0.359375}, {"start": 971.21, "end": 972.63, "word": " ثلاثي", "probability": 0.92646484375}, {"start": 972.63, "end": 973.75, "word": " بطريقة", "probability": 0.9869384765625}, {"start": 973.75, "end": 975.33, "word": " جديدة", "probability": 0.9879557291666666}, {"start": 975.33, "end": 978.83, "word": " يعني", "probability": 0.93701171875}, {"start": 978.83, "end": 979.11, "word": " بدي", "probability": 0.58819580078125}, {"start": 979.11, "end": 979.59, "word": " أحاول", "probability": 0.9359130859375}, {"start": 979.59, "end": 980.29, "word": " أرغب", "probability": 0.6585693359375}, {"start": 980.29, "end": 981.19, "word": " الآن", "probability": 0.60797119140625}, {"start": 981.19, "end": 981.37, "word": " ما", "probability": 0.92529296875}, {"start": 981.37, "end": 981.53, "word": " بين", "probability": 0.9951171875}, {"start": 981.53, "end": 981.71, "word": " ال", "probability": 0.8662109375}, {"start": 981.71, "end": 982.03, "word": " cross", "probability": 0.9111328125}, {"start": 982.03, "end": 982.27, "word": " productive", "probability": 0.6904296875}], "temperature": 1.0}, {"id": 39, "seek": 99337, "start": 986.95, "end": 993.37, "text": "يبقى بداخله خاصية رقم تسعة، خاصية رقم تسعة بتقول ما ياتي", "tokens": [1829, 3555, 4587, 7578, 47525, 47283, 43761, 16490, 33546, 10632, 12602, 4587, 2304, 6055, 3794, 27884, 12399, 16490, 33546, 10632, 12602, 4587, 2304, 6055, 3794, 27884, 39894, 39648, 19446, 7251, 9307, 1829], "avg_logprob": -0.20383522727272727, "compression_ratio": 1.36, "no_speech_prob": 0.0, "words": [{"start": 986.95, "end": 987.39, "word": "يبقى", "probability": 0.927734375}, {"start": 987.39, "end": 987.87, "word": " بداخله", "probability": 0.6202799479166666}, {"start": 987.87, "end": 988.61, "word": " خاصية", "probability": 0.8453776041666666}, {"start": 988.61, "end": 989.17, "word": " رقم", "probability": 0.9928385416666666}, {"start": 989.17, "end": 989.83, "word": " تسعة،", "probability": 0.7105712890625}, {"start": 989.83, "end": 990.85, "word": " خاصية", "probability": 0.9765625}, {"start": 990.85, "end": 991.33, "word": " رقم", "probability": 0.9920247395833334}, {"start": 991.33, "end": 991.87, "word": " تسعة", "probability": 0.9905598958333334}, {"start": 991.87, "end": 992.41, "word": " بتقول", "probability": 0.6158447265625}, {"start": 992.41, "end": 992.85, "word": " ما", "probability": 0.53857421875}, {"start": 992.85, "end": 993.37, "word": " ياتي", "probability": 0.8250325520833334}], "temperature": 1.0}, {"id": 40, "seek": 104633, "start": 1036.72, "end": 1046.34, "text": "يبقى هذه وسيلة كيف احسب الضرب الثلاثي باستخدام الضرب القياسي", "tokens": [1829, 3555, 4587, 7578, 29538, 46952, 26895, 3660, 9122, 33911, 1975, 5016, 35457, 6024, 114, 25513, 6024, 104, 1211, 5718, 104, 1829, 4724, 995, 14851, 9778, 3215, 10943, 6024, 114, 25513, 25062, 25528, 3794, 1829], "avg_logprob": -0.11794704633454482, "compression_ratio": 1.353658536585366, "no_speech_prob": 4.76837158203125e-07, "words": [{"start": 1036.7199999999998, "end": 1038.12, "word": "يبقى", "probability": 0.795166015625}, {"start": 1038.12, "end": 1038.4, "word": " هذه", "probability": 0.87451171875}, {"start": 1038.4, "end": 1039.24, "word": " وسيلة", "probability": 0.9615885416666666}, {"start": 1039.24, "end": 1039.92, "word": " كيف", "probability": 0.922119140625}, {"start": 1039.92, "end": 1040.62, "word": " احسب", "probability": 0.8440755208333334}, {"start": 1040.62, "end": 1041.56, "word": " الضرب", "probability": 0.8019205729166666}, {"start": 1041.56, "end": 1042.52, "word": " الثلاثي", "probability": 0.93017578125}, {"start": 1042.52, "end": 1043.66, "word": " باستخدام", "probability": 0.977783203125}, {"start": 1043.66, "end": 1044.62, "word": " الضرب", "probability": 0.9488932291666666}, {"start": 1044.62, "end": 1046.34, "word": " القياسي", "probability": 0.912109375}], "temperature": 1.0}, {"id": 41, "seek": 107477, "start": 1046.79, "end": 1074.77, "text": "طيب سؤال انت قال هنا dot و dot هذا حاصل ضرب اتجاهي بطلعليه متجه ولا بطلعليه كمية قياسية؟ حاصل ضرب اتجاه بطلعليه متجه هذا متجه ولا لا؟ متجه لأن هذا رقم مضروب في متجه وهذا رقم مضروب في متجه هو طرح الاتنين من بعض يبقى طرح two vectors بيعطينا مام vector جديد", "tokens": [9566, 1829, 3555, 8608, 33604, 6027, 16472, 2655, 50239, 34105, 5893, 4032, 5893, 23758, 11331, 33546, 1211, 48812, 25513, 1975, 2655, 7435, 40294, 1829, 4724, 9566, 1211, 3615, 20292, 3224, 44650, 7435, 3224, 49429, 4724, 9566, 1211, 3615, 20292, 3224, 9122, 2304, 10632, 12174, 25528, 3794, 10632, 22807, 11331, 33546, 1211, 48812, 25513, 1975, 2655, 7435, 40294, 4724, 9566, 1211, 3615, 20292, 3224, 44650, 7435, 3224, 23758, 44650, 7435, 3224, 49429, 20193, 22807, 44650, 7435, 3224, 5296, 33456, 23758, 12602, 4587, 2304, 3714, 11242, 32887, 3555, 8978, 44650, 7435, 3224, 37037, 15730, 12602, 4587, 2304, 3714, 11242, 32887, 3555, 8978, 44650, 7435, 3224, 31439, 23032, 2288, 5016, 2423, 9307, 1863, 9957, 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1498.34, "word": " U", "probability": 0.95263671875}, {"start": 1498.34, "end": 1499.04, "word": " cross", "probability": 0.890625}, {"start": 1499.04, "end": 1499.4, "word": " ال", "probability": 0.73681640625}, {"start": 1499.4, "end": 1499.62, "word": " V", "probability": 0.96875}], "temperature": 1.0}, {"id": 57, "seek": 152355, "start": 1501.99, "end": 1523.55, "text": "يبقى هذا عمودي على كل من V وعمودي على U لكن مع W راح عمل زاوية مقدرها كم؟ مقدرها ثيتا تمام هذا خط في المستوى اللي فوق مدته", "tokens": [1829, 3555, 4587, 7578, 23758, 6225, 2304, 2407, 16254, 15844, 28242, 9154, 691, 4032, 3615, 2304, 2407, 16254, 15844, 624, 44381, 20449, 343, 12602, 39319, 6225, 42213, 30767, 995, 2407, 10632, 3714, 28543, 2288, 11296, 9122, 2304, 22807, 3714, 28543, 2288, 11296, 38637, 36081, 995, 46811, 10943, 23758, 16490, 9566, 8978, 9673, 14851, 2407, 7578, 13672, 1829, 6156, 30543, 3714, 3215, 47395], "avg_logprob": -0.21651786329254272, "compression_ratio": 1.5970149253731343, "no_speech_prob": 0.0, "words": [{"start": 1501.99, "end": 1502.55, "word": "يبقى", "probability": 0.8765869140625}, {"start": 1502.55, "end": 1502.93, "word": " هذا", "probability": 0.89208984375}, {"start": 1502.93, "end": 1503.61, "word": " عمودي", "probability": 0.965576171875}, {"start": 1503.61, "end": 1503.95, "word": " على", "probability": 0.7958984375}, {"start": 1503.95, "end": 1504.59, "word": " كل", "probability": 0.9287109375}, {"start": 1504.59, "end": 1505.25, "word": " من", "probability": 0.79248046875}, {"start": 1505.25, "end": 1506.01, "word": " V", "probability": 0.62353515625}, {"start": 1506.01, "end": 1507.03, "word": " وعمودي", "probability": 0.839306640625}, {"start": 1507.03, "end": 1507.51, "word": " على", "probability": 0.91748046875}, {"start": 1507.51, "end": 1508.03, "word": " U", "probability": 0.96142578125}, {"start": 1508.03, "end": 1508.85, "word": " لكن", "probability": 0.830078125}, {"start": 1508.85, "end": 1509.19, "word": " مع", "probability": 0.95947265625}, {"start": 1509.19, "end": 1509.85, "word": " W", "probability": 0.78125}, {"start": 1509.85, "end": 1510.45, "word": " راح", "probability": 0.7083740234375}, {"start": 1510.45, "end": 1510.91, "word": " عمل", "probability": 0.835205078125}, {"start": 1510.91, "end": 1511.67, "word": " زاوية", "probability": 0.8017578125}, {"start": 1511.67, "end": 1512.39, "word": " مقدرها", "probability": 0.9029541015625}, {"start": 1512.39, "end": 1513.53, "word": " كم؟", "probability": 0.5506184895833334}, {"start": 1513.53, "end": 1514.55, "word": " مقدرها", "probability": 0.9696044921875}, {"start": 1514.55, "end": 1516.19, "word": " ثيتا", "probability": 0.6471354166666666}, {"start": 1516.19, "end": 1517.83, "word": " تمام", "probability": 0.830078125}, {"start": 1517.83, "end": 1518.97, "word": " هذا", "probability": 0.77490234375}, {"start": 1518.97, "end": 1519.53, "word": " خط", "probability": 0.76611328125}, {"start": 1519.53, "end": 1519.73, "word": " في", "probability": 0.814453125}, {"start": 1519.73, "end": 1520.43, "word": " المستوى", "probability": 0.97607421875}, {"start": 1520.43, "end": 1520.65, "word": " اللي", "probability": 0.737060546875}, {"start": 1520.65, "end": 1521.19, "word": " فوق", "probability": 0.98291015625}, {"start": 1521.19, "end": 1523.55, "word": " مدته", "probability": 0.6240234375}], "temperature": 1.0}, {"id": 58, "seek": 154543, "start": 1526.75, "end": 1545.43, "text": "لأن هذا عمودي على القاعدة اللي تحت، إذا عمودي على القاعدة اللي فوق الموازية لها، كويس، كدهش هذا من هنا إلى هنا بدات الأرتفاع، أليس هو طول الـW في Cos الزاوية ثانية؟ صح؟", "tokens": [1211, 33456, 23758, 6225, 2304, 2407, 16254, 15844, 25062, 995, 22488, 3660, 13672, 1829, 6055, 33753, 12399, 11933, 15730, 6225, 2304, 2407, 16254, 15844, 25062, 995, 22488, 3660, 13672, 1829, 6156, 30543, 9673, 2407, 31377, 10632, 5296, 11296, 12399, 9122, 45865, 3794, 12399, 9122, 3215, 3224, 8592, 23758, 9154, 34105, 30731, 34105, 47525, 9307, 16247, 43500, 5172, 45761, 12399, 5551, 20292, 3794, 31439, 23032, 12610, 2423, 39184, 54, 8978, 15855, 6024, 110, 995, 2407, 10632, 38637, 7649, 10632, 22807, 20328, 5016, 22807], "avg_logprob": -0.29028614745082626, "compression_ratio": 1.7857142857142858, "no_speech_prob": 0.0, "words": [{"start": 1526.75, "end": 1527.07, "word": "لأن", "probability": 0.5511474609375}, {"start": 1527.07, "end": 1527.31, "word": " هذا", "probability": 0.6767578125}, {"start": 1527.31, "end": 1527.77, "word": " عمودي", "probability": 0.9647216796875}, {"start": 1527.77, "end": 1527.99, "word": " على", "probability": 0.8515625}, {"start": 1527.99, "end": 1528.51, "word": " القاعدة", "probability": 0.9466552734375}, {"start": 1528.51, "end": 1528.63, "word": " اللي", "probability": 0.4952392578125}, {"start": 1528.63, "end": 1528.97, "word": " تحت،", "probability": 0.6994222005208334}, {"start": 1528.97, "end": 1529.17, "word": " إذا", "probability": 0.74072265625}, {"start": 1529.17, "end": 1529.87, "word": " عمودي", "probability": 0.942138671875}, {"start": 1529.87, "end": 1530.33, "word": " على", "probability": 0.8447265625}, {"start": 1530.33, "end": 1531.39, "word": " القاعدة", "probability": 0.9761962890625}, {"start": 1531.39, "end": 1531.55, "word": " اللي", "probability": 0.913818359375}, {"start": 1531.55, "end": 1531.83, "word": " فوق", "probability": 0.97998046875}, {"start": 1531.83, "end": 1532.69, "word": " الموازية", "probability": 0.833740234375}, {"start": 1532.69, "end": 1533.57, "word": " لها،", "probability": 0.7666015625}, {"start": 1533.57, "end": 1534.69, "word": " كويس،", "probability": 0.70501708984375}, {"start": 1534.69, "end": 1535.43, "word": " كدهش", "probability": 0.642578125}, {"start": 1535.43, "end": 1535.73, "word": " هذا", "probability": 0.8076171875}, {"start": 1535.73, "end": 1535.97, "word": " من", "probability": 0.966796875}, {"start": 1535.97, "end": 1536.33, "word": " هنا", "probability": 0.9931640625}, {"start": 1536.33, "end": 1536.53, "word": " إلى", "probability": 0.216796875}, {"start": 1536.53, "end": 1536.71, "word": " هنا", "probability": 0.91650390625}, {"start": 1536.71, "end": 1537.25, "word": " بدات", "probability": 0.627685546875}, {"start": 1537.25, "end": 1538.89, "word": " الأرتفاع،", "probability": 0.85712890625}, {"start": 1538.89, "end": 1539.49, "word": " أليس", "probability": 0.9541015625}, {"start": 1539.49, "end": 1539.91, "word": " هو", "probability": 0.994140625}, {"start": 1539.91, "end": 1540.55, "word": " طول", "probability": 0.9912109375}, {"start": 1540.55, "end": 1541.49, "word": " الـW", "probability": 0.5367838541666666}, {"start": 1541.49, "end": 1541.93, "word": " في", "probability": 0.97607421875}, {"start": 1541.93, "end": 1542.37, "word": " Cos", "probability": 0.301025390625}, {"start": 1542.37, "end": 1543.19, "word": " الزاوية", "probability": 0.8263671875}, {"start": 1543.19, "end": 1543.99, "word": " ثانية؟", "probability": 0.563995361328125}, {"start": 1543.99, "end": 1545.43, "word": " صح؟", "probability": 0.9461263020833334}], "temperature": 1.0}, {"id": 59, "seek": 157419, "start": 1546.05, "end": 1574.19, "text": "يبقى هذا هو طول ال W في ال cosine الزاوية تتاعي، إذا أنا لو جيت الآن بدي أجيب حصل الضرب اللي عندي ال volume يبقى ال volume اللي أنا بقول عنه بدي يسوي مساحة القاعدة آه لكروسكرودك كده قبل قليل كنت لما أضرب الكروسكرودك إلى ال two vectors بيعطيني مساحة من المتوازن أضغط", "tokens": [1829, 3555, 4587, 7578, 23758, 31439, 23032, 12610, 2423, 343, 8978, 2423, 23565, 6024, 110, 995, 2407, 10632, 6055, 2655, 45761, 1829, 12399, 11933, 15730, 41850, 45164, 10874, 36081, 6024, 48506, 4724, 16254, 5551, 7435, 1829, 3555, 11331, 9381, 1211, 6024, 114, 25513, 13672, 1829, 18871, 16254, 2423, 5523, 7251, 3555, 4587, 7578, 2423, 5523, 13672, 1829, 41850, 4724, 39648, 18871, 3224, 4724, 16254, 7251, 3794, 45865, 47524, 39319, 3660, 25062, 995, 22488, 3660, 19753, 3224, 5296, 4117, 32887, 3794, 4117, 32887, 3215, 4117, 9122, 3215, 3224, 12174, 36150, 12174, 20292, 1211, 9122, 29399, 5296, 15042, 5551, 11242, 25513, 33251, 32887, 3794, 4117, 32887, 3215, 4117, 30731, 2423, 732, 18875, 4724, 40228, 9566, 9957, 1829, 47524, 39319, 3660, 9154, 9673, 2655, 2407, 31377, 1863, 5551, 11242, 17082, 9566], "avg_logprob": -0.2921511627906977, "compression_ratio": 1.8178137651821862, "no_speech_prob": 0.0, "words": [{"start": 1546.05, "end": 1546.55, "word": "يبقى", "probability": 0.81390380859375}, {"start": 1546.55, "end": 1546.85, "word": " هذا", "probability": 0.830078125}, {"start": 1546.85, "end": 1547.09, "word": " هو", "probability": 0.95263671875}, {"start": 1547.09, "end": 1547.39, "word": " طول", "probability": 0.993408203125}, {"start": 1547.39, "end": 1547.55, "word": " ال", "probability": 0.78955078125}, {"start": 1547.55, "end": 1547.89, "word": " W", "probability": 0.325439453125}, {"start": 1547.89, "end": 1548.11, "word": " في", "probability": 0.875}, {"start": 1548.11, "end": 1548.23, "word": " ال", "probability": 0.475830078125}, {"start": 1548.23, "end": 1548.57, "word": " cosine", "probability": 0.25146484375}, {"start": 1548.57, "end": 1549.17, "word": " الزاوية", "probability": 0.845947265625}, {"start": 1549.17, "end": 1549.65, "word": " تتاعي،", "probability": 0.4656005859375}, {"start": 1549.65, "end": 1549.97, "word": " إذا", "probability": 0.6514892578125}, {"start": 1549.97, "end": 1551.09, "word": " أنا", "probability": 0.63671875}, {"start": 1551.09, "end": 1551.33, "word": " لو", "probability": 0.97412109375}, {"start": 1551.33, "end": 1551.63, "word": " جيت", "probability": 0.94287109375}, {"start": 1551.63, "end": 1552.21, "word": " الآن", "probability": 0.6956787109375}, {"start": 1552.21, "end": 1552.87, "word": " بدي", "probability": 0.583740234375}, {"start": 1552.87, "end": 1553.85, "word": " أجيب", "probability": 0.97119140625}, {"start": 1553.85, "end": 1554.63, "word": " حصل", "probability": 0.6937662760416666}, {"start": 1554.63, "end": 1555.11, "word": " الضرب", "probability": 0.8645833333333334}, {"start": 1555.11, "end": 1555.39, "word": " اللي", "probability": 0.96240234375}, {"start": 1555.39, "end": 1555.83, "word": " عندي", "probability": 0.80712890625}, {"start": 1555.83, "end": 1556.07, "word": " ال", "probability": 0.82763671875}, {"start": 1556.07, "end": 1556.71, "word": " volume", "probability": 0.9404296875}, {"start": 1556.71, "end": 1557.79, "word": " يبقى", "probability": 0.9090576171875}, {"start": 1557.79, "end": 1557.95, "word": " ال", "probability": 0.9658203125}, {"start": 1557.95, "end": 1558.39, "word": " volume", "probability": 0.9873046875}, {"start": 1558.39, "end": 1558.77, "word": " اللي", "probability": 0.990478515625}, {"start": 1558.77, "end": 1559.09, "word": " أنا", "probability": 0.85009765625}, {"start": 1559.09, "end": 1559.67, "word": " بقول", "probability": 0.97802734375}, {"start": 1559.67, "end": 1560.49, "word": " عنه", "probability": 0.990966796875}, {"start": 1560.49, "end": 1561.35, "word": " بدي", "probability": 0.739990234375}, {"start": 1561.35, "end": 1561.83, "word": " يسوي", "probability": 0.8092447916666666}, {"start": 1561.83, "end": 1562.69, "word": " مساحة", "probability": 0.96044921875}, {"start": 1562.69, "end": 1564.35, "word": " القاعدة", "probability": 0.9910888671875}, {"start": 1564.35, "end": 1565.25, "word": " آه", "probability": 0.5716552734375}, {"start": 1565.25, "end": 1566.47, "word": " لكروسكرودك", "probability": 0.66925048828125}, {"start": 1566.47, "end": 1566.79, "word": " كده", "probability": 0.7229817708333334}, {"start": 1566.79, "end": 1567.35, "word": " قبل", "probability": 0.984619140625}, {"start": 1567.35, "end": 1568.37, "word": " قليل", "probability": 0.9962565104166666}, {"start": 1568.37, "end": 1568.91, "word": " كنت", "probability": 0.2572021484375}, {"start": 1568.91, "end": 1569.17, "word": " لما", "probability": 0.956787109375}, {"start": 1569.17, "end": 1569.65, "word": " أضرب", "probability": 0.91552734375}, {"start": 1569.65, "end": 1570.67, "word": " الكروسكرودك", "probability": 0.8604910714285714}, {"start": 1570.67, "end": 1570.85, "word": " إلى", "probability": 0.345947265625}, {"start": 1570.85, "end": 1571.05, "word": " ال", "probability": 0.54833984375}, {"start": 1571.05, "end": 1571.21, "word": " two", "probability": 0.49365234375}, {"start": 1571.21, "end": 1571.65, "word": " vectors", "probability": 0.68310546875}, {"start": 1571.65, "end": 1572.27, "word": " بيعطيني", "probability": 0.82841796875}, {"start": 1572.27, "end": 1572.83, "word": " مساحة", "probability": 0.9664713541666666}, {"start": 1572.83, "end": 1573.05, "word": " من", "probability": 0.60986328125}, {"start": 1573.05, "end": 1573.81, "word": " المتوازن", "probability": 0.88271484375}, {"start": 1573.81, "end": 1574.19, "word": " أضغط", "probability": 0.662017822265625}], "temperature": 1.0}, {"id": 60, "seek": 160440, "start": 1574.84, "end": 1604.4, "text": "إذا مساحة متوازن أضلع هو عبارة عن طول ل cross product U cross V هذه مساحة القاعدة الارتفاع البعد هذا اللي هو طول W في cosine الزاوية تتا يبقى طول المتجه الأول في طول المتجه التاني في cosine الزاوية تتا هذا يا بنات الارتفاع", "tokens": [28814, 15730, 47524, 39319, 3660, 44650, 2407, 31377, 1863, 5551, 11242, 1211, 3615, 31439, 6225, 3555, 9640, 3660, 18871, 23032, 12610, 5296, 3278, 1674, 624, 3278, 691, 29538, 47524, 39319, 3660, 25062, 995, 22488, 3660, 2423, 9640, 2655, 5172, 45761, 29739, 22488, 23758, 13672, 1829, 31439, 23032, 12610, 343, 8978, 23565, 6024, 110, 995, 2407, 10632, 6055, 2655, 995, 7251, 3555, 4587, 7578, 23032, 12610, 9673, 2655, 7435, 3224, 16247, 12610, 8978, 23032, 12610, 9673, 2655, 7435, 3224, 16712, 7649, 1829, 8978, 23565, 6024, 110, 995, 2407, 10632, 6055, 2655, 995, 23758, 35186, 4724, 8315, 2655, 2423, 9640, 2655, 5172, 45761], "avg_logprob": -0.20052082982717775, "compression_ratio": 1.9119170984455958, "no_speech_prob": 0.0, "words": [{"start": 1574.84, "end": 1575.16, "word": "إذا", "probability": 0.776611328125}, {"start": 1575.16, 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نقاط بجيب أقوله كويس إذا النقطة الأولى لو قلت هذه النقطة هي P اللي لحداتي تبعها واحد سالب واحد واثنين", "tokens": [1863, 7435, 1211, 3794, 8608, 33604, 6027, 8315, 16712, 6027, 1829, 8717, 3615, 9566, 1829, 3224, 6055, 1211, 2655, 8717, 4587, 41193, 8978, 27188, 2288, 9640, 4032, 4587, 6027, 8032, 9307, 20292, 44650, 7435, 3224, 36764, 24401, 3660, 6225, 2304, 2407, 16254, 15844, 9673, 14851, 2407, 7578, 13672, 8848, 1829, 7251, 33753, 45865, 15844, 29538, 16712, 1211, 9307, 8717, 4587, 41193, 4724, 7435, 1829, 3555, 5551, 39648, 3224, 9122, 45865, 3794, 11933, 15730, 28239, 47432, 3660, 16247, 12610, 7578, 45164, 12174, 1211, 2655, 29538, 28239, 47432, 3660, 39896, 430, 13672, 1829, 5296, 24401, 9307, 1829, 6055, 3555, 3615, 11296, 36764, 24401, 8608, 6027, 3555, 36764, 24401, 4032, 5718, 104, 1863, 9957], "avg_logprob": -0.31668527477553915, "compression_ratio": 1.8916256157635467, "no_speech_prob": 8.940696716308594e-07, "words": [{"start": 2498.86, "end": 2500.0, "word": "نجلس", 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"probability": 0.9814453125}, {"start": 3826.72, "end": 3827.56, "word": " a؟", "probability": 0.6759033203125}, {"start": 3827.56, "end": 3827.94, "word": " كان", "probability": 0.96728515625}, {"start": 3827.94, "end": 3828.26, "word": " ال", "probability": 0.99365234375}, {"start": 3828.26, "end": 3828.64, "word": " u", "probability": 0.92431640625}, {"start": 3828.64, "end": 3829.46, "word": " cross", "probability": 0.92822265625}, {"start": 3829.46, "end": 3829.88, "word": " ال", "probability": 0.978515625}, {"start": 3829.88, "end": 3830.3, "word": " v", "probability": 0.59326171875}, {"start": 3830.3, "end": 3831.32, "word": " نقص", "probability": 0.9586588541666666}, {"start": 3831.32, "end": 3831.52, "word": " ال", "probability": 0.99365234375}, {"start": 3831.52, "end": 3831.96, "word": " w", "probability": 0.8369140625}, {"start": 3831.96, "end": 3832.46, "word": " تساوي", "probability": 0.9512939453125}, {"start": 3832.46, "end": 3833.1, "word": " كم؟", "probability": 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"end": 3847.71, "word": " الـW", "probability": 0.9666341145833334}, {"start": 3847.71, "end": 3848.73, "word": " بتساوي", "probability": 0.8538818359375}, {"start": 3848.73, "end": 3849.51, "word": " كده؟", "probability": 0.645477294921875}, {"start": 3849.51, "end": 3850.43, "word": " Zero", "probability": 0.75537109375}, {"start": 3850.43, "end": 3851.05, "word": " scalar", "probability": 0.8662109375}, {"start": 3851.05, "end": 3851.95, "word": " أو", "probability": 0.8759765625}, {"start": 3851.95, "end": 3852.49, "word": " بمعنى", "probability": 0.97890625}, {"start": 3852.49, "end": 3853.15, "word": " آخر", "probability": 0.88427734375}, {"start": 3853.15, "end": 3854.07, "word": " طول", "probability": 0.852294921875}, {"start": 3854.07, "end": 3854.71, "word": " الـU", "probability": 0.9607747395833334}, {"start": 3854.71, "end": 3855.55, "word": " في", "probability": 0.77490234375}, {"start": 3855.55, "end": 3855.91, "word": " طول", "probability": 0.996337890625}, {"start": 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0.8681640625}], "temperature": 1.0}, {"id": 139, "seek": 388586, "start": 3868.84, "end": 3885.86, "text": "أو بمعنى أخر لو ربعت الطرفين بصير طول ال U تربيع طول ال V ضاقص ال W تربيع في صين تربيع ثيتا يساوي Zero واعتبر المعادلة هذه رقم واحد", "tokens": [10721, 2407, 4724, 2304, 3615, 1863, 7578, 5551, 34740, 45164, 12602, 3555, 34268, 41950, 28480, 9957, 4724, 9381, 13546, 23032, 12610, 2423, 624, 6055, 2288, 21292, 3615, 23032, 12610, 2423, 691, 48812, 995, 4587, 9381, 2423, 343, 6055, 2288, 21292, 3615, 8978, 20328, 9957, 6055, 2288, 21292, 3615, 38637, 36081, 995, 7251, 3794, 995, 45865, 17182, 36764, 34268, 26890, 9673, 3615, 18513, 37977, 29538, 12602, 4587, 2304, 36764, 24401], "avg_logprob": -0.3323660692998341, "compression_ratio": 1.5442176870748299, "no_speech_prob": 4.172325134277344e-07, "words": [{"start": 3868.84, "end": 3869.96, "word": "أو", "probability": 0.50323486328125}, {"start": 3869.96, "end": 3871.08, "word": " بمعنى", "probability": 0.842236328125}, {"start": 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"end": 3878.14, "word": " ضاقص", "probability": 0.6353759765625}, {"start": 3878.14, "end": 3878.3, "word": " ال", "probability": 0.95556640625}, {"start": 3878.3, "end": 3878.7, "word": " W", "probability": 0.943359375}, {"start": 3878.7, "end": 3879.64, "word": " تربيع", "probability": 0.9317626953125}, {"start": 3879.64, "end": 3880.02, "word": " في", "probability": 0.72021484375}, {"start": 3880.02, "end": 3880.66, "word": " صين", "probability": 0.53265380859375}, {"start": 3880.66, "end": 3881.44, "word": " تربيع", "probability": 0.63006591796875}, {"start": 3881.44, "end": 3882.08, "word": " ثيتا", "probability": 0.7383626302083334}, {"start": 3882.08, "end": 3882.96, "word": " يساوي", "probability": 0.9053955078125}, {"start": 3882.96, "end": 3883.34, "word": " Zero", "probability": 0.4462890625}, {"start": 3883.34, "end": 3884.24, "word": " واعتبر", "probability": 0.80859375}, {"start": 3884.24, "end": 3884.8, "word": " المعادلة", "probability": 0.8067626953125}, {"start": 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فباجي", "probability": 0.7203369140625}, {"start": 3892.96, "end": 3893.4, "word": " بقول", "probability": 0.931640625}, {"start": 3893.4, "end": 3893.78, "word": " أنا", "probability": 0.64892578125}, {"start": 3893.78, "end": 3894.22, "word": " عند", "probability": 0.468505859375}, {"start": 3894.22, "end": 3895.32, "word": " با", "probability": 0.61083984375}, {"start": 3895.32, "end": 3896.82, "word": " ولكن", "probability": 0.797119140625}, {"start": 3896.82, "end": 3897.62, "word": " u", "probability": 0.38427734375}, {"start": 3897.62, "end": 3898.12, "word": " dot", "probability": 0.65185546875}, {"start": 3898.12, "end": 3898.6, "word": " v", "probability": 0.95458984375}, {"start": 3898.6, "end": 3899.36, "word": " بدي", "probability": 0.56591796875}, {"start": 3899.36, "end": 3899.88, "word": " سوى", "probability": 0.8082682291666666}, {"start": 3899.88, "end": 3900.16, "word": " u", "probability": 0.8681640625}, {"start": 3900.16, "end": 3900.58, "word": " dot", 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الطرفين يبقى طول ال U تربيع في طول ال V ناقص ال W تربيع في Cos تربية ثيتا يساوي 0 وهذا المعادلة اتنين", "tokens": [40228, 22653, 1975, 1829, 8592, 20449, 1863, 7578, 23758, 2423, 28820, 10943, 16472, 23032, 12610, 2423, 624, 8978, 23032, 12610, 2423, 691, 8717, 995, 4587, 9381, 2423, 343, 8978, 15855, 30767, 995, 2407, 10632, 38637, 36081, 995, 7251, 3794, 995, 45865, 1958, 1975, 2407, 45164, 12602, 3555, 34268, 41950, 28480, 9957, 7251, 3555, 4587, 7578, 23032, 12610, 2423, 624, 6055, 2288, 21292, 3615, 8978, 23032, 12610, 2423, 691, 8717, 995, 4587, 9381, 2423, 343, 6055, 2288, 21292, 3615, 8978, 15855, 6055, 2288, 21292, 3660, 38637, 36081, 995, 7251, 3794, 995, 45865, 1958, 37037, 15730, 9673, 3615, 18513, 37977, 1975, 2655, 1863, 9957], "avg_logprob": -0.2087378663924134, "compression_ratio": 1.9940119760479043, "no_speech_prob": 0.0, "words": [{"start": 3920.74, "end": 3921.14, "word": "يعني", "probability": 0.898681640625}, {"start": 3921.14, "end": 3921.5, "word": " ايش", 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0.78692626953125}, {"start": 3928.46, "end": 3928.7, "word": " ال", "probability": 0.90283203125}, {"start": 3928.7, "end": 3929.22, "word": " W", "probability": 0.931640625}, {"start": 3929.22, "end": 3930.06, "word": " في", "probability": 0.85986328125}, {"start": 3930.06, "end": 3930.6, "word": " Cos", "probability": 0.5859375}, {"start": 3930.6, "end": 3931.62, "word": " زاوية", "probability": 0.638885498046875}, {"start": 3931.62, "end": 3932.32, "word": " ثيتا", "probability": 0.7332356770833334}, {"start": 3932.32, "end": 3933.42, "word": " يساوي", "probability": 0.609466552734375}, {"start": 3933.42, "end": 3933.84, "word": " 0", "probability": 0.324951171875}, {"start": 3933.84, "end": 3935.02, "word": " او", "probability": 0.87939453125}, {"start": 3935.02, "end": 3935.24, "word": " لو", "probability": 0.90966796875}, {"start": 3935.24, "end": 3935.74, "word": " ربعت", "probability": 0.9285481770833334}, {"start": 3935.74, "end": 3936.66, "word": " الطرفين", "probability": 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3942.0, "end": 3942.76, "word": " تربيع", "probability": 0.952392578125}, {"start": 3942.76, "end": 3943.28, "word": " في", "probability": 0.93798828125}, {"start": 3943.28, "end": 3943.94, "word": " Cos", "probability": 0.87109375}, {"start": 3943.94, "end": 3944.72, "word": " تربية", "probability": 0.8095703125}, {"start": 3944.72, "end": 3945.44, "word": " ثيتا", "probability": 0.9261067708333334}, {"start": 3945.44, "end": 3946.3, "word": " يساوي", "probability": 0.968505859375}, {"start": 3946.3, "end": 3946.84, "word": " 0", "probability": 0.8505859375}, {"start": 3946.84, "end": 3947.78, "word": " وهذا", "probability": 0.570068359375}, {"start": 3947.78, "end": 3948.64, "word": " المعادلة", "probability": 0.8922119140625}, {"start": 3948.64, "end": 3949.44, "word": " اتنين", "probability": 0.7877197265625}], "temperature": 1.0}, {"id": 142, "seek": 395338, "start": 3951.28, "end": 3953.38, "text": "الأن بدي أجمع المعادلة", "tokens": [6027, 33456, 4724, 16254, 5551, 7435, 2304, 3615, 9673, 3615, 18513, 37977], "avg_logprob": -0.27058292352236235, "compression_ratio": 0.8723404255319149, "no_speech_prob": 0.0, "words": [{"start": 3951.28, "end": 3951.72, "word": "الأن", "probability": 0.5570068359375}, {"start": 3951.72, "end": 3952.08, "word": " بدي", "probability": 0.678955078125}, {"start": 3952.08, "end": 3952.56, "word": " أجمع", "probability": 0.9207763671875}, {"start": 3952.56, "end": 3953.38, "word": " المعادلة", "probability": 0.8687744140625}], "temperature": 1.0}, {"id": 143, "seek": 399095, "start": 3968.29, "end": 3990.95, "text": "يبقى لو أخدت عامل مشترك بصير طول ال U تربيع فطول ال V نقص ال W تربيع بضل عندي sin تربيع ثيتا زائد cosine تربيع ثيتا يسوى قداش Zero المقدار بين القوسين واحد صحيح يبقى هذا معناه ايه؟", "tokens": [1829, 3555, 4587, 7578, 45164, 5551, 9778, 3215, 2655, 6225, 10943, 1211, 37893, 2655, 31747, 4724, 9381, 13546, 23032, 12610, 2423, 624, 6055, 2288, 21292, 3615, 6156, 9566, 12610, 2423, 691, 8717, 4587, 9381, 2423, 343, 6055, 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الـAutomatic التاني بيساوي قدرية Zero هذا معناته أن طول الـB ناقص الـD", "tokens": [1863, 4587, 9381, 2423, 39184, 54, 6055, 25513, 10632, 4724, 1829, 3794, 995, 45865, 17182, 8608, 33604, 6027, 3714, 25720, 6055, 7649, 10632, 3714, 3615, 9566, 9957, 1829, 8978, 9673, 3615, 9566, 1829, 9307, 14739, 23032, 12610, 2423, 39184, 52, 20193, 7251, 3794, 995, 45865, 17182, 11933, 15730, 23032, 12610, 2423, 39184, 52, 16712, 25513, 10632, 20193, 7251, 43020, 14739, 7251, 3794, 995, 45865, 17182, 11331, 33546, 1211, 48812, 25513, 23032, 12610, 11296, 7251, 3794, 995, 45865, 20328, 5172, 2288, 36764, 24401, 9154, 16095, 19446, 7251, 3794, 995, 45865, 31767, 5172, 2288, 11933, 15730, 2423, 39184, 49769, 13143, 16712, 7649, 1829, 4724, 1829, 3794, 995, 45865, 12174, 3215, 2288, 10632, 17182, 23758, 20449, 8315, 47395, 14739, 23032, 12610, 2423, 39184, 33, 8717, 995, 4587, 9381, 2423, 39184, 35], "avg_logprob": -0.2599321705426357, "compression_ratio": 2.0, "no_speech_prob": 2.6226043701171875e-06, 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18513, 46007, 4032, 12602, 3555, 15042, 6055, 8592, 17082, 1211, 28242, 9673, 5016, 46958, 25720, 25062, 18513, 46007, 9673, 19913, 37977, 16247, 16095, 10632], "avg_logprob": -0.28110397419082783, "compression_ratio": 2.037433155080214, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 6041.84, "end": 6042.26, "word": "يبقى", "probability": 0.756744384765625}, {"start": 6042.26, "end": 6042.4, "word": " ال", "probability": 0.6875}, {"start": 6042.4, "end": 6042.58, "word": " X", "probability": 0.333251953125}, {"start": 6042.58, "end": 6043.04, "word": " يساوي", "probability": 0.68212890625}, {"start": 6043.04, "end": 6043.8, "word": " تلاتة", "probability": 0.85443115234375}, {"start": 6043.8, "end": 6044.66, "word": " و", "probability": 0.80810546875}, {"start": 6044.66, "end": 6045.12, "word": " Zero", "probability": 0.70654296875}, {"start": 6045.12, "end": 6045.74, "word": " او", "probability": 0.6820068359375}, {"start": 6045.74, "end": 6046.24, "word": " أربعة", "probability": 0.79736328125}, {"start": 6046.24, "end": 6047.38, "word": " لحد", "probability": 0.858154296875}, {"start": 6047.38, "end": 6047.86, "word": " هنا", "probability": 0.98876953125}, {"start": 6047.86, "end": 6049.1, "word": " انتهى", "probability": 0.9319661458333334}, {"start": 6049.1, "end": 6049.9, "word": " حل", "probability": 0.97314453125}, {"start": 6049.9, "end": 6050.6, "word": " هذا", "probability": 0.97900390625}, {"start": 6050.6, "end": 6051.52, "word": " المثال", "probability": 0.9737955729166666}, {"start": 6051.52, "end": 6052.12, "word": " و", "probability": 0.363525390625}, {"start": 6052.12, "end": 6052.66, "word": " بانتهاء", "probability": 0.7510986328125}, {"start": 6052.66, "end": 6053.08, "word": " حل", "probability": 0.96728515625}, {"start": 6053.08, "end": 6053.34, "word": " هذا", "probability": 0.98876953125}, {"start": 6053.34, "end": 6053.96, "word": " المثال", "probability": 0.9847005208333334}, {"start": 6053.96, "end": 6054.86, "word": " تنتهي", "probability": 0.8558349609375}, {"start": 6054.86, "end": 6055.52, "word": " محاضرة", "probability": 0.9298095703125}, {"start": 6055.52, "end": 6056.22, "word": " اليوم", "probability": 0.9130859375}, {"start": 6056.22, "end": 6056.84, "word": " و", "probability": 0.23388671875}, {"start": 6056.84, "end": 6057.32, "word": " بقيت", "probability": 0.5772298177083334}, {"start": 6057.32, "end": 6057.74, "word": " الأربعة", "probability": 0.9593098958333334}, {"start": 6057.74, "end": 6057.98, "word": " اللي", "probability": 0.555908203125}, {"start": 6057.98, "end": 6058.2, "word": " تبقى", "probability": 0.617340087890625}, {"start": 6058.2, "end": 6058.38, "word": " اللي", "probability": 0.647705078125}, {"start": 6058.38, "end": 6058.76, "word": " مالك", "probability": 0.5443522135416666}, {"start": 6058.76, "end": 6059.58, "word": " شغلها", "probability": 0.68408203125}, {"start": 6059.58, "end": 6061.42, "word": " للمحاضرة", "probability": 0.9302734375}, {"start": 6061.42, "end": 6062.48, "word": " القادمة", "probability": 0.9147135416666666}, {"start": 6062.48, "end": 6062.8, "word": " و", "probability": 0.9716796875}, {"start": 6062.8, "end": 6063.58, "word": " ربما", "probability": 0.9630533854166666}, {"start": 6063.58, "end": 6064.58, "word": " تشغل", "probability": 0.991943359375}, {"start": 6064.58, "end": 6065.14, "word": " كل", "probability": 0.994140625}, {"start": 6065.14, "end": 6066.0, "word": " المحاضرة", "probability": 0.9224853515625}, {"start": 6066.0, "end": 6066.74, "word": " القادمة", "probability": 0.97802734375}, {"start": 6066.74, "end": 6067.66, "word": " المظلة", "probability": 0.4677734375}, {"start": 6067.66, "end": 6068.52, "word": " الأهمية", "probability": 0.8128255208333334}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 6090.292, "duration_after_vad": 4886.82971875002}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/Ilto5AXE7dw.srt b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/Ilto5AXE7dw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..55dabe01ea6f98ec81c9a23715c6f1bc435d353c
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/Ilto5AXE7dw.srt
@@ -0,0 +1,2011 @@
+1
+00:00:12,380 --> 00:00:17,540
+الأخر section في هذا ال chapter هو substitution in
+
+2
+00:00:17,540 --> 00:00:24,540
+trigonometric or in multiple integrals يبقى التعويض
+
+3
+00:00:24,540 --> 00:00:30,580
+في التكاملات المتعددة هناخد أول حاجة التعويض في
+
+4
+00:00:30,580 --> 00:00:34,700
+التكامل ب two integrals وبعدها نروح لمين؟ ل three
+
+5
+00:00:34,700 --> 00:00:41,710
+integrals يبقى substitution in double integrals لو
+
+6
+00:00:41,710 --> 00:00:45,750
+أن هذا ال F و X و Y و بقى عندي تكامل عليه على
+
+7
+00:00:45,750 --> 00:00:51,770
+المنطقة R يمكن نُحوّل هذا التكامل إلى تكامل مكافئ له
+
+8
+00:00:51,770 --> 00:00:56,230
+على منطقة أخرى بدي أسميها مين؟ ال G هذا الكلام
+
+9
+00:00:56,230 --> 00:01:01,810
+بيحصل، عندي function g و h كل واحدة فيهم one to
+
+10
+00:01:01,810 --> 00:01:08,870
+one، بمعنى أن x تساوي f of g و y تساوي f of g و y
+
+11
+00:01:08,870 --> 00:01:10,990
+تساوي f of g و y تساوي h of u و v، هدول ال two
+
+12
+00:01:10,990 --> 00:01:15,820
+functions are one to one functions لأن كل نقطة في
+
+13
+00:01:15,820 --> 00:01:19,820
+المساحة الأولى ستوديها الأمين إلى نظيرتها في
+
+14
+00:01:19,820 --> 00:01:24,060
+المساحة الثانية، وبالتالي هذه المساحة من ناحية
+
+15
+00:01:24,060 --> 00:01:29,100
+القيمة، جدّ المساحة الثانية لكن شكلهم مختلف، ليس بضرورة
+
+16
+00:01:29,100 --> 00:01:34,050
+يكونوا مثل بعض، لكن من ناحية المساحة جدّ بعض، طيب
+
+17
+00:01:34,050 --> 00:01:38,630
+مضروب في مين؟ في ال absolute value ل J of U و V
+
+18
+00:01:38,630 --> 00:01:43,090
+هذا J زي معامل البنات، زي ما نقول معامل التمدد
+
+19
+00:01:43,090 --> 00:01:46,390
+الحاجة، معامل التمدد الطولي، يبقى هنا احنا بنقول هنا
+
+20
+00:01:46,390 --> 00:01:51,690
+هذا هو الجاكوبيان، مين الجاكوبيان هذا؟ شو قصته هذه؟
+
+21
+00:01:51,690 --> 00:01:56,380
+بقول لك where ال J of U و V هو عبارة عن تفضل X
+
+22
+00:01:56,380 --> 00:02:00,800
+بالنسبة للمتغير الأول، و تفضل X بالنسبة للمتغير
+
+23
+00:02:00,800 --> 00:02:04,160
+الثاني اللي عملناه للمتغير X، هفروح نعمله لمين؟ للمتغير
+
+24
+00:02:04,160 --> 00:02:10,880
+للمتغير Y، نفك المحدد هذا هيعطيني قيمة محددة، هذه
+
+25
+00:02:10,880 --> 00:02:14,900
+القيمة هي اللي بتبقى بال Jacob، يعني إذا موجبة بقى
+
+26
+00:02:14,900 --> 00:02:18,260
+خلاص مافيش absolute value، لكن إذا سالبة بتاخد لها
+
+27
+00:02:18,260 --> 00:02:23,540
+مين؟ ال absolute value، يبقى هذا هو الـ Jacobin of
+
+28
+00:02:23,540 --> 00:02:27,100
+the coordinates transformations، يبقى هذا المعامل
+
+29
+00:02:27,100 --> 00:02:31,860
+تبع مين؟ تبع التحويل، الآن بدنا نحسب اللي هو معامل
+
+30
+00:02:31,860 --> 00:02:36,440
+التحويل لدوال مختلفة، بدنا نبدأ ناخد أمثلة على ذلك
+
+31
+00:02:36,680 --> 00:02:42,420
+ولو أحصل على الجاكوبيان لتغيير الإحداثيات من وضع
+
+32
+00:02:42,420 --> 00:02:43,440
+إحداثيات إحداثيات إحداثيات إحداثيات إحداثيات إحداثيات
+
+33
+00:02:43,440 --> 00:02:46,580
+إحداثيات
+
+34
+00:02:46,580 --> 00:02:56,780
+إحداثيات إحداثيات
+
+35
+00:02:56,780 --> 00:03:00,400
+إحداثيات
+
+36
+00:03:01,210 --> 00:03:04,990
+القطبية، وفيه شغلة بدنا نضرب فيها، طبعاً استخدمناها
+
+37
+00:03:04,990 --> 00:03:09,770
+قبلها هيك، وقلنا هي عبارة عن إيش؟ عبارة عن R، قلنا
+
+38
+00:03:09,770 --> 00:03:15,950
+dx dy في الكارتيزي، وقابله r dr dθ، من أين لك r
+
+39
+00:03:15,950 --> 00:03:19,050
+و وعدناكم يوم، وقلنا لكم إن شاء الله في نهاية هذا ال
+
+40
+00:03:19,050 --> 00:03:25,160
+chapter بنوريكم كيف جبنا هذه ال r، طيب، بنجي نحسب
+
+41
+00:03:25,160 --> 00:03:28,780
+مقدار الجاكوبيان لهذا اللي إحنا بنقول هو r، بنجي
+
+42
+00:03:28,780 --> 00:03:33,260
+نقول اه، ال x في الإحداثيات الكارتيزية هي عبارة عن
+
+43
+00:03:33,260 --> 00:03:38,560
+r cos θ في الإحداثيات القطبية، وكذلك ال y في
+
+44
+00:03:38,560 --> 00:03:43,380
+الإحداثيات الكارتيزية هي r sin θ في الإحداثيات
+
+45
+00:03:43,380 --> 00:03:50,740
+القطبية، يبقى بنات u في مين؟ جاء مكانها هنا r و θ
+
+46
+00:03:58,240 --> 00:04:04,420
+تفضل x بالنسبة ل r، تفضل x بالنسبة ل θ، اللي
+
+47
+00:04:04,420 --> 00:04:09,100
+عملناه بالنسبة ل x، أروح نعمله بالنسبة ل y يبقى
+
+48
+00:04:09,100 --> 00:04:14,840
+∂y/∂r، ∂y/∂θ
+
+49
+00:04:16,300 --> 00:04:21,540
+يساوي، هي الديترمينانت، نيجي تفاضل ال x بالنسبة
+
+50
+00:04:21,540 --> 00:04:27,720
+إلى مين؟ كوساين θ، يبقى هي كوساين θ، تفاضل ال
+
+51
+00:04:27,720 --> 00:04:29,780
+x بالنسبة ل θ
+
+52
+00:04:32,870 --> 00:04:40,410
+-r sin θ، تفضل ال y بالنسبة إلى r، بساين θ
+
+53
+00:04:40,410 --> 00:04:47,050
+تفضل ال y بالنسبة ل θ، ب r كوساين θ
+
+54
+00:04:47,050 --> 00:04:52,710
+هذا المحدد يساوي حاصل ضرب عناصر القطر الرئيسي
+
+55
+00:04:52,710 --> 00:04:58,910
+اللي هو r كوساين تربيع θ ناقص حاصل ضرب عناصر
+
+56
+00:04:58,910 --> 00:05:04,270
+القطر الثانوي، مع ناقص بصير زائد r ساين تربيع
+
+57
+00:05:04,270 --> 00:05:09,950
+θ، إذا ناخد r عامل مشترك، بيظل كوساين تربيع θ
+
+58
+00:05:09,950 --> 00:05:15,000
+زائد ساين تربيع θ، ليه؟ لأنه بيساوي واحد، يبقى النتيجة قداش؟
+
+59
+00:05:15,000 --> 00:05:20,240
+يبقى عرفنا أن إحنا جبنا ال polar، من أين جاءت هذه؟ يبقى
+
+60
+00:05:20,240 --> 00:05:24,700
+هذه هي قيمة الجاكوبيان في التحويل من الإحداثيات
+
+61
+00:05:24,700 --> 00:05:29,140
+الكارتيزية إلى الإحداثيات القطبية، وبعد قليل
+
+62
+00:05:29,140 --> 00:05:33,860
+إن شاء الله، هروح لجاكوبيان تبع التحويل من
+
+63
+00:05:33,860 --> 00:05:36,380
+الكارتيزية للأسفيرية
+
+64
+00:05:56,970 --> 00:06:05,010
+المثال الثاني بيقول: لي
+
+65
+00:06:05,010 --> 00:06:14,410
+جيب هذه region defined، جي ب the region defined by
+
+66
+00:06:14,410 --> 00:06:19,010
+والمعرفة
+
+67
+00:06:19,010 --> 00:06:24,830
+بيه: ال u أكبر من أو يساوي واحد، وأقل من أو يساوي
+
+68
+00:06:24,830 --> 00:06:29,950
+اثنين، وال u في ال v كمان أكبر من أو يساوي واحد
+
+69
+00:06:29,950 --> 00:06:38,070
+وأقل من أو يساوي اثنين in the UV plane and the UV
+
+70
+00:06:38,070 --> 00:06:50,010
+plane where ال x بدها تساوي ال u، وال y بدها تساوي
+
+71
+00:06:50,010 --> 00:06:58,390
+ال u في ال v، السؤال بيقول لي: transform حول
+
+72
+00:06:58,390 --> 00:07:08,370
+the integral، قولي التكامل اللي هو مين؟ تكامل من
+
+73
+00:07:08,370 --> 00:07:15,930
+واحد للاثنين، تكامل كذلك من واحد للاثنين، لل y على x
+
+74
+00:07:15,930 --> 00:07:25,890
+dy dx into an integral over g، into an integral
+
+75
+00:07:25,890 --> 00:07:34,890
+over g and evaluate، and evaluate
+
+76
+00:07:36,840 --> 00:07:42,060
+و احسب لي كذلك the uv integral
+
+77
+00:08:06,340 --> 00:08:12,360
+سؤال مرة ثانية، بيعطيني المنطقة G، u محصورة بين واحد
+
+78
+00:08:12,360 --> 00:08:18,060
+و اثنين، وحاصل ضرب u في v محصورة بين واحد و اثنين، هذا
+
+79
+00:08:18,060 --> 00:08:22,820
+على ال uv plane، وعطاني علاقة بتربط بين x و y وكذا
+
+80
+00:08:22,820 --> 00:08:29,500
+كالمتغيرات الجديدة u و v، x يساوي u، و y يساوي u في v
+
+81
+00:08:29,500 --> 00:08:34,280
+بيقول لي: transform the integral، حول التكامل اللي
+
+82
+00:08:34,280 --> 00:08:40,010
+عندنا هذا، into an integral over G، لتكامل على G
+
+83
+00:08:40,010 --> 00:08:44,990
+واحسب لي هذا التكامل الجديد، زي و لتشيبير بالضبط
+
+84
+00:08:44,990 --> 00:08:49,070
+بالتقريب، لما كنا بنحول من كارتيزي ال integral إلى
+
+85
+00:08:49,070 --> 00:08:54,350
+polar integral، و بنروح نحسب، قدرنا قيمة ال polar
+
+86
+00:08:54,350 --> 00:08:58,950
+integral، يبقى هنا نفس القصة بالضبط، تماماً، يعني بدي
+
+87
+00:08:58,950 --> 00:09:04,630
+أشوف المثل لا x ولا y، بدي أحولها كلها بدلالة من r
+
+88
+00:09:04,630 --> 00:09:10,170
+و z، بقول له كويس، يبقى هي التكاملات الاثنين اللي عندنا
+
+89
+00:09:10,170 --> 00:09:17,510
+ال y بقدرها u في v، ال x ب u، أيوة، ضل بدنا ال
+
+90
+00:09:17,510 --> 00:09:24,730
+Jacobian، كويس، فاهمين؟ في ال Jacobian تبع ال u و ال v
+
+91
+00:09:24,730 --> 00:09:33,940
+absolute value، دي v، دي u، أو دي u، دي v، طب نيجي الآن
+
+92
+00:09:33,940 --> 00:09:40,400
+بدنا نحسب الجاكوبيان، و بدنا نحسب حدود التكامل، طب
+
+93
+00:09:40,400 --> 00:09:44,460
+تعالي نحسب الجاكوبيان في الأول، يبقى يا بنات أنا بدي
+
+94
+00:09:44,460 --> 00:09:49,640
+∂x/∂u، و ∂x/∂v
+
+95
+00:09:49,640 --> 00:09:52,600
+بدي ∂y/∂u
+
+96
+00:09:57,550 --> 00:10:04,130
+تفاضل x بالنسبة إلى u، بواحد، تفاضل x بالنسبة إلى v
+
+97
+00:10:06,490 --> 00:10:12,890
+يبقى هنا صفر، بعد ذلك تفاضل ال y بالنسبة إلى u، v
+
+98
+00:10:12,890 --> 00:10:19,410
+تفاضل y بالنسبة إلى v، ب u، حاصل ضرب الرئيسي ناقص
+
+99
+00:10:19,410 --> 00:10:23,770
+الثانوية، يبقى كده إيش؟ يبقى مقدار الجاكوبيان بده
+
+100
+00:10:23,770 --> 00:10:30,050
+يساوي كم؟ بده يساوي u، طيب، إذا هذا، هذا كله على
+
+101
+00:10:30,050 --> 00:10:35,770
+المنطقة اللي هي G، يبقى هذا الكلام بدل يساوي تكاملين
+
+102
+00:10:35,770 --> 00:10:42,550
+لمين؟ ال u، مع ال u بتروح هذه مع هذه، بيظل v، ومقدار
+
+103
+00:10:42,550 --> 00:10:51,050
+الجاكوبيان ب u dv du، طب نرجع لمين يا بنات؟
+
+104
+00:10:51,050 --> 00:10:58,370
+للمعطيات هذه، بقدر أقول له: لو قسمت الطرفين على v إذا
+
+105
+00:10:58,370 --> 00:11:03,110
+الواحد أقل من أو يساوي u و v أقل من أو يساوي اثنين
+
+106
+00:11:03,110 --> 00:11:08,690
+implied أن ال v محصورة بين واحد على u و ما بين
+
+107
+00:11:08,690 --> 00:11:13,530
+اثنين على u، إذا أنا أخدت التكامل في الأول بالنسبة
+
+108
+00:11:13,530 --> 00:11:19,870
+إلى v، يبقى هنا واحد على u، وهنا اثنين على u، ال u
+
+109
+00:11:19,870 --> 00:11:24,990
+تتغير من أين إلى أين؟ يبقى جاهزة من واحد إلى اثنين،
+
+110
+00:11:24,990 --> 00:11:29,330
+الآن بنقدر نكمل التكامل هذا، ليش؟ لأن هدول فعلاً
+
+111
+00:11:29,330 --> 00:11:35,150
+متغيرات بدلالة u، لكن u بأرقام، وبالتالي بقدر أطلع
+
+112
+00:11:35,150 --> 00:11:40,230
+قداش القيمة الحقيقية لهذا التكامل، يبقى هذا الكلام
+
+113
+00:11:40,230 --> 00:11:46,370
+يساوي تكامل من واحد للاثنين، يبقى u مقدار ثابت، يبقى
+
+114
+00:11:46,370 --> 00:11:54,070
+بدي أكامل ال v بس، اللي هي v تربيع على اثنين من واحد
+
+115
+00:11:54,070 --> 00:11:59,110
+على u ل اثنين على u، في ال u، في ال du
+
+116
+00:12:02,420 --> 00:12:08,200
+يبقى هذا الكلام بده يساوي، هي النص برا، وهي تكامل من
+
+117
+00:12:08,200 --> 00:12:14,800
+واحد للاثنين، بظل v تربيع، يبقى اللي هي أربعة على u
+
+118
+00:12:14,800 --> 00:12:23,280
+تربيع ناقص واحد على u تربيع، كله في ال du، والله في
+
+119
+00:12:23,280 --> 00:12:29,180
+ال u du، في عندي u لسه أضعه إلى برا، يبقى في ال u du
+
+120
+00:12:42,970 --> 00:12:53,110
+يبقى ثلاثة على
+
+121
+00:12:53,110 --> 00:12:56,430
+u du، يبقى الجواب ثلاثة على u du، يبقى الجواب
+
+122
+00:12:56,430 --> 00:12:57,280
+ثلاثة على u du، يبقى الجواب ثلاثة على u du، ثلاثة
+
+123
+00:12:57,280 --> 00:13:03,340
+على اثنين، لأن absolute value ل u، من عند الواحد
+
+124
+00:13:03,340 --> 00:13:10,280
+لغاية اثنين، يبقى ثلاثة على اثنين لأن اثنين ناقص
+
+125
+00:13:10,280 --> 00:13:16,300
+لأن الواحد، طبعاً لأن الواحد ما بيبقى، ضلّ عندنا
+
+126
+00:13:16,300 --> 00:13:21,460
+عندنا بس ثلاثة على اثنين لأن اثنين هذا قيمة
+
+127
+00:13:21,460 --> 00:13:24,500
+التكامل اللي موجود عندنا
+
+128
+00:13:41,880 --> 00:13:46,860
+بنروح مثال رقم اثنين ولا ثلاثة؟ الحين مثال رقم
+
+129
+00:13:46,860 --> 00:13:50,340
+ثلاثة
+
+130
+00:13:50,340 --> 00:13:53,640
+بيقول
+
+131
+00:13:53,640 --> 00:13:59,640
+use the transformation، use the trans
+
+132
+00:14:07,380 --> 00:14:17,100
+اللي هو ال x بدي أساويه u زائد نصف v، وال y بدي أساويه
+
+133
+00:14:17,100 --> 00:14:25,580
+v، to evaluate the integral، to evaluate the
+
+134
+00:14:25,580 --> 00:14:35,060
+integral، مش هنتحسب التكامل اللي هو تكامل من صفر
+
+135
+00:14:35,060 --> 00:14:44,020
+للاثنين، تكامل من y على اثنين إلى y زائد أربعة، كله على
+
+136
+00:14:44,020 --> 00:14:52,720
+اثنين، لمين؟ لل y تكعيب، في 2x ناقص y، في ال
+
+137
+00:14:52,720 --> 00:15:00,920
+exponential، لل 2x ناقص y، الكل تربيع، لل dx
+
+138
+00:15:04,380 --> 00:15:12,660
+by writing it، يعني
+
+139
+00:15:12,660 --> 00:15:22,580
+بكتابة هذا التكامل، as an integral over
+
+140
+00:15:22,580 --> 00:15:50,960
+a region G، a region G in the UV plane، نمسح
+
+141
+00:15:50,960 --> 00:15:52,160
+الشجرة دي كلها، بنات
+
+142
+00:16:16,520 --> 00:16:21,220
+نرجع لسؤال، مرة ثانية، قال: استخدم التحويل x يساوي u
+
+143
+00:16:21,220 --> 00:16:27,000
+زائد نصف v، وال y تساوي v، عشان نحول التكامل اللي هو
+
+144
+00:16:27,000 --> 00:16:33,040
+الحمد لله شكله، وشكلها أيضاً، by writing it، بكتابتي ك
+
+145
+00:16:33,040 --> 00:16:38,580
+integral over region G، تمين في ال uv plane، نقوله
+
+146
+00:16:38,580 --> 00:16:43,580
+كويس، إذا إحنا، خلّيني نحسب الجاكوبيان، ونحسب
+
+147
+00:16:43,580 --> 00:16:47,950
+حدود التكامل، ونخلص من مشكلتنا هذه، كيف كانت التاليّة؟
+
+148
+00:16:47,950 --> 00:16:52,290
+يبقى ال x جاهزة، وال y جاهزة، يبقى على طول الخُطَب
+
+149
+00:16:52,290 --> 00:16:56,150
+نروح نحسب ال Jacobian، يبقى بده يجي جاهز ال Jacobian
+
+150
+00:16:56,150 --> 00:17:02,710
+تبع ال u و ال v، بده يساوي: تفاضل ال x بالنسبة إلى u،
+
+151
+00:17:02,710 --> 00:17:08,670
+تفاضل ال x بالنسبة إلى v، تفاضل ال y بالنسبة إلى u،
+
+152
+00:17:08,670 --> 00:17:15,160
+تفاضل ال y بالنسبة إلى v، بعطيني المحدد، تفاضل x
+
+153
+00:17:15,160 --> 00:17:20,000
+بالنسبة ل u، بقداش؟ بواحد، والباقي صفر، تفاضل
+
+154
+00:17:20,000 --> 00:17:28,340
+x بالنسبة ل v، بكام؟ بنصف، تفاضل y بالنسبة ل u، صفر
+
+155
+00:17:28,340 --> 00:17:34,920
+تفاضل y بالنسبة ل v، بواحد، يبقى المحدد كده بيساوي واحد
+
+156
+00:17:34,920 --> 00:17:41,850
+ممتاز جداً، يبقى ضل عندي حدود التكامل، بدي أعرف حدود
+
+157
+00:17:41,850 --> 00:17:47,390
+التكامل هذه، من وين لوين؟ بقول له: بسيطة، إحنا بدنا نكامل
+
+158
+00:17:47,390 --> 00:17:55,470
+أول شيء بالنسبة لمين؟ يبقى أنا عندي x هنا تساوي y
+
+159
+00:17:55,470 --> 00:18:04,770
+زائد أربعة على اثنين، هذا الكلام بدي أعطيه ال x
+
+160
+00:18:04,770 --> 00:18:14,000
+عندي بقداش؟ u زائد نصف v، يبقى هذا u زائد v على اثنين
+
+161
+00:18:14,000 --> 00:18:21,800
+بده يساوي ال y، عندي بقداش؟ v، يبقى هذه v على اثنين
+
+162
+00:18:21,800 --> 00:18:26,600
+زائد اثنين، أربعة على اثنين باثنين، وشيلت ال y وحطّيت
+
+163
+00:18:26,600 --> 00:18:31,140
+مكانها v، أظلّ لو جبت ال v، عند ال v بتروح، الله يسهّل
+
+164
+00:18:31,140 --> 00:18:33,700
+عليها، بيعطيني قداش هنا وهنا
+
+165
+00:18:36,630 --> 00:18:43,770
+يبقى ال u تساوي قداش؟ اثنين، إذا اثنين هذه بدّها تكون كافة
+
+166
+00:18:43,770 --> 00:18:49,290
+مين؟ بدّها كافة y زائد أربعة على اثنين، باجي بقول له:
+
+167
+00:18:49,290 --> 00:18:56,870
+بتاخد x الثانية، x تساوي y على اثنين، ال u زائد v
+
+168
+00:18:56,870 --> 00:19:03,590
+على اثنين تساوي ال y، هذه v على اثنين، يبقى هذا بدي
+
+169
+00:19:03,590 --> 00:19:09,450
+أعطيك أن u تساوي قداش؟ صفر، يبقى هذا بدي أعطينا أن
+
+170
+00:19:09,450 --> 00:19:14,730
+u تساوي صفر، يبقى هذه جبت حدود التكامل تبع، تمام
+
+171
+00:19:15,160 --> 00:19:21,380
+تبع ال u، بدي
+
+223
+00:25:34,610 --> 00:25:36,850
+X زائد واحد
+
+224
+00:26:08,460 --> 00:26:13,000
+نرجع لسؤالنا هذا مرة ثانية، بقول استخدام الـ
+
+225
+00:26:13,000 --> 00:26:18,300
+Transformation، يتحويل إلى U تساوي X ناقص Y، و V
+
+226
+00:26:18,300 --> 00:26:23,500
+يساوي 2X زائد Y، لكي تحسب التكامل، لأن هذا على
+
+227
+00:26:23,500 --> 00:26:28,060
+المنطقة R في الربع الأول، وهذه المنطقة محدودة
+
+228
+00:26:28,060 --> 00:26:35,080
+بالمستقيمات الأربع. الأعلى هو البسيط. تعالَ نشوف هذا
+
+229
+00:26:35,080 --> 00:26:39,940
+السؤال يختلف عن ثلاثة أسئلة السابقة، ما أعطانيش حدود
+
+230
+00:26:39,940 --> 00:26:45,680
+التكامل، أنا بدي أطلع حدود التكامل لحالي، تمام؟ يعني
+
+231
+00:26:45,680 --> 00:26:49,720
+أي واحدة. بس قبل كان بيقول من كذا لكذا، يبقى فجأة
+
+232
+00:26:49,720 --> 00:26:54,300
+بيعطيني حدود التكامل، وبالتالي المشكلة هنا أصعب شوية.
+
+233
+00:26:54,300 --> 00:27:02,200
+طيب، شغلة ثانية، ما أعطانيش أن x بدلالة u وv، لأ
+
+234
+00:27:02,200 --> 00:27:07,760
+أعطاني u بدلالة x وy، وأعطاني v بدلالة x وy، يبقى
+
+235
+00:27:07,760 --> 00:27:13,240
+الخطوة الأولى عندي، بدي أجيب الـ x والـ y بدلالة u
+
+236
+00:27:13,240 --> 00:27:16,700
+و v، حتى أقدر أحسب الـ Jacobian، وأنا ما جِبتوش، ما أقدرش
+
+237
+00:27:16,700 --> 00:27:22,090
+أحسب الـ Jacobian. بقول له كويس، طيب، تعالَ، بدنا نجيب من
+
+238
+00:27:22,090 --> 00:27:31,260
+المعادلتين هدول X و Y بدلالة... تمام، تمام. يبقى أصلاً
+
+239
+00:27:31,260 --> 00:27:35,580
+لو جمعناهم، بيطير الـ Y، بيجيب الـ X دغري، مش هيك؟ يبقى بسيطة.
+
+240
+00:27:35,580 --> 00:27:42,880
+باجي بقول أنا عندي الـ U تساوي X ناقص الـ Y، وعندي V
+
+241
+00:27:42,880 --> 00:27:50,520
+يساوي 2X زائد الـ Y. لو جمعت مباشرة، بيطلع عندي إيش؟
+
+242
+00:27:50,520 --> 00:27:58,620
+بيطلع عندي أن ثلاثة X بده يساوي U زائد V، أو إن شئتَ
+
+243
+00:27:59,080 --> 00:28:06,500
+فبقول أن الـ X بيساوي U زائد V كله على ثلاثة، أو U
+
+244
+00:28:06,500 --> 00:28:13,660
+على ثلاثة زائد V على ثلاثة. جبنا الـ X. إذا ما بنقدر
+
+245
+00:28:13,660 --> 00:28:19,720
+نجيب الـ Y، فبجيب آخذ المعادلة اللي عندي دي
+
+246
+00:28:19,720 --> 00:28:28,120
+فمنها بقول أن الـ Y تساوي X ناقص الـ U. جبنا هذا هنا
+
+247
+00:28:28,120 --> 00:28:33,780
+وهذا هنا، يبقى هذا الكلام بيكون يساوي، X عندي اللي
+
+248
+00:28:33,780 --> 00:28:39,160
+حصلنا عليها، V على ثلاثة، أو U زائد V على ثلاثة، يبقى
+
+249
+00:28:39,160 --> 00:28:46,620
+هذه U زائد V على ثلاثة ناقص الـ U، يبقى ببساطة
+
+250
+00:28:46,620 --> 00:28:52,680
+هذا بدي يعطينا أن Y تساوي، كله على ثلاثة، بيصير U
+
+251
+00:28:53,040 --> 00:29:02,180
+زائد V ناقص ثلاثة U، إذا V ناقص اثنين U على ثلاثة.
+
+252
+00:29:02,180 --> 00:29:12,380
+يبقى هذه قيمة X، وهذه قيمة Y، أو يساوي V على ثلاثة
+
+253
+00:29:12,380 --> 00:29:18,650
+ناقص اثنين U على ثلاثة. سواء كان هذه أو هذه، يبقى
+
+254
+00:29:18,650 --> 00:29:27,110
+حصلت على قيمتي X و Y بدلالة، بدلالة U و V. نحسب
+
+255
+00:29:27,110 --> 00:29:33,650
+الـ Jacobian. بالمرة نحسب الـ Jacobian تبع الـ U والـ V.
+
+256
+00:29:33,650 --> 00:29:40,150
+تساوي المحدد: تفاضل الـ X بالنسبة إلى U، تفاضل الـ X
+
+257
+00:29:40,150 --> 00:29:46,670
+بالنسبة إلى V، تفاضل الـ Y بالنسبة إلى U، تفاضل Y
+
+258
+00:29:46,670 --> 00:29:55,730
+بالنسبة إلى V. يساوي: تفاضل X بالنسبة إلى U، ثلث.
+
+259
+00:29:55,730 --> 00:29:59,030
+تفاضل
+
+260
+00:29:59,030 --> 00:30:07,650
+X بالنسبة إلى V، ثلث. تفاضل Y بالنسبة إلى U، سالب
+
+261
+00:30:07,650 --> 00:30:11,590
+ثلثين. يبقى سالب ثلثين.
+
+262
+00:30:14,800 --> 00:30:25,840
+ثلث، ويساوي: نفك المحدد، يبقى تسعة زائد تسعة على ثلاث
+
+263
+00:30:25,840 --> 00:30:33,280
+على تسعة، يعني ثلث، يساوي ثلث. إذا المقدار الـ Jacobian
+
+264
+00:30:33,280 --> 00:30:42,430
+يساوي ثلث. حسبنا الـ Jacobian. سهل أشيل X و Y وأحط قيمهم
+
+265
+00:30:42,430 --> 00:30:47,650
+من هنا. شو ضايل عندي؟ ضايل حدود التكامل، وما أدري
+
+266
+00:30:47,650 --> 00:30:51,530
+شرح حدود التكامل. طب كيف بدنا نحصل على حدود
+
+267
+00:30:51,530 --> 00:30:55,310
+التكامل؟
+
+268
+00:30:55,310 --> 00:30:59,390
+وين القاطعة، التقاطع؟ يعني بدنا ندور عن قاطع
+
+269
+00:30:59,390 --> 00:31:04,790
+التقاطع، صح؟ أنا عندي رأي آخر، أنا عندي أربعة
+
+270
+00:31:04,790 --> 00:31:10,060
+مستقيمات، حتى الآن ما استخدمتهمش، بظبط؟ طب إذا بدي
+
+271
+00:31:10,060 --> 00:31:16,100
+أروح أحول المستقيمات هذه من الـ X والـ Y إلى مين؟
+
+272
+00:31:16,100 --> 00:31:19,100
+إلى U و V.  إذا لو جيت
+
+273
+00:31:19,100 --> 00:31:28,600
+للمستقيم الأول اللي هو Y تساوي ناقص 2X زائد 4. Y
+
+274
+00:31:28,600 --> 00:31:34,900
+جاهزة. علمًا أن هذه هي V على ثلاثة ناقص 2U على ثلاثة.
+
+275
+00:31:34,900 --> 00:31:47,860
+يبقى V على ثلاثة ناقص اثنين U على ثلاثة تساوي... تساوي
+
+276
+00:31:47,860 --> 00:31:52,900
+الـ X كمان جاهزة عندنا هاي. يبقى بالتعويض هيدا شبه ما
+
+277
+00:31:52,900 --> 00:31:57,720
+أنا أقول في السالب اثنين، يبقى السالب اثنين U على
+
+278
+00:31:57,720 --> 00:32:11,080
+ثلاثة. سالب اثنين U على ثلاثة، وسالب اثنين
+
+279
+00:32:11,080 --> 00:32:20,480
+V على ثلاثة. سالب اثنين V على ثلاثة زائد أربعة. أطلع
+
+280
+00:32:20,480 --> 00:32:26,620
+هذه وهذه، وروحوا مع بعض. تمام. بنجيب الـ V. عند هذه
+
+281
+00:32:26,620 --> 00:32:34,080
+بيصير كده عندي... بيصير ثلاثة، يعني V. هذه لو جت عند هذه
+
+282
+00:32:34,080 --> 00:32:39,320
+بيصير ثلث وثلثين، تبقى واحد صحيح. هذا بدي يعطيك V
+
+283
+00:32:39,320 --> 00:32:46,080
+تساوي أربعة. والله كويس، هذا يعني شغل كويس. طب لو جيت
+
+284
+00:32:46,080 --> 00:32:49,640
+قلت وكتبت اثنين
+
+285
+00:33:00,940 --> 00:33:08,560
+يبقى الـ V على ثلاثة ناقص اثنين U على ثلاثة يساوي
+
+286
+00:33:08,560 --> 00:33:14,580
+ناقص اثنين U على ثلاثة ناقص اثنين V على ثلاثة زائد
+
+287
+00:33:14,580 --> 00:33:18,260
+سبعة. يبقى V تساوي سبعة.
+
+288
+00:33:22,570 --> 00:33:28,410
+يبقى لدينا مستقيمين. يبقى Y تساوي X ناقص
+
+289
+00:33:28,410 --> 00:33:38,530
+اثنين. Y تساوي X ناقص اثنين. Y ما تغيرتش. يبقى V على
+
+290
+00:33:38,530 --> 00:33:44,090
+ثلاثة ناقص اثنين U على ثلاثة. و X ما تغيرتش، بس مش
+
+291
+00:33:44,090 --> 00:33:48,270
+مضروبة ولا في حاجة، إلا يبقى أحطها زي ما هي. U على
+
+292
+00:33:48,270 --> 00:33:56,190
+ثلاثة زائد V على ثلاثة ناقص اثنين أظن V على ثلاثة.
+
+293
+00:33:56,190 --> 00:34:01,130
+لو راح تنضرب ثلاثة مع السلامة. هذه لو اجت تصير
+
+294
+00:34:01,130 --> 00:34:09,030
+عندها ناقص U، ناقص U بده يساوي ناقص اثنين، يبقى U
+
+295
+00:34:09,030 --> 00:34:16,570
+تساوي كده اثنين. بالمثل، Y تساوي X زائد واحد، أظن X
+
+296
+00:34:16,570 --> 00:34:23,360
+زائد واحد، imply أن V على ثلاثة ناقص اثنين U على ثلاثة
+
+297
+00:34:23,360 --> 00:34:30,020
+بدها تساوي U على ثلاثة زائد V على ثلاثة زائد واحد. V على
+
+298
+00:34:30,020 --> 00:34:35,840
+ثلاثة مع V على ثلاثة. هذه هنا، بصير عندك U تساوي واحد.
+
+299
+00:34:36,110 --> 00:34:41,250
+يبقى الـ U من واحد لاثنين، والـ V من أربعة
+
+300
+00:34:41,250 --> 00:34:46,150
+إلى سبعة. إذا حددنا حدود التكامل، يبقى مش ضايل إلا
+
+301
+00:34:46,150 --> 00:34:53,610
+نعوض في المسألة تبعتنا فقط لا غير. كم؟
+
+302
+00:34:53,610 --> 00:35:02,090
+U باثنين هذه. طيب، استني شوية، جيب الـ U هذه بس. آه، سهل
+
+303
+00:35:02,090 --> 00:35:02,330
+يا بابا.
+
+304
+00:35:05,420 --> 00:35:10,740
+طيب، يبقى لم يبقى لنا إلا نعوض في التكامل مباشرة.
+
+305
+00:35:10,740 --> 00:35:16,560
+يبقى التكامل تبعنا يصير بالشكل اللي عرفناه الآن. بدنا
+
+306
+00:35:16,560 --> 00:35:24,260
+نجيب  لأن 2 X تربيع، يبقى 2 في، جوا الـ X تربيع يبقى
+
+307
+00:35:24,260 --> 00:35:29,540
+هاي هاي الـ X تربيع اللي همّينا، أو هادي سهلة، يبقى
+
+308
+00:35:29,540 --> 00:35:36,840
+بقدر أقول له U على 3، U على ثلاثة. والله خليها إيش
+
+309
+00:35:36,840 --> 00:35:43,800
+رأيك؟ U زائد V كلها على ثلاثة، مرة واحدة الكل تربيع.
+
+310
+00:35:43,800 --> 00:35:53,120
+بعديها ناقص X، اللي هو U زائد V على ثلاثة، تمام. في الـ Y، الـ
+
+311
+00:35:53,120 --> 00:35:58,060
+Y اللي هو V على ثلاثة ناقص اثنين U على ثلاثة. V على
+
+312
+00:35:58,060 --> 00:36:06,360
+ثلاثة ناقص اثنين U على ثلاثة. ناقص Y تربيع، V على
+
+313
+00:36:06,360 --> 00:36:13,320
+ثلاثة ناقص اثنين U على ثلاثة، الكل تربيع. يبقى إيه؟
+
+314
+00:36:13,320 --> 00:36:18,880
+الدوال العالمية. ضايل عندنا الـ Jacobian، الـ Jacobian
+
+315
+00:36:18,880 --> 00:36:26,480
+حسبناه وجبناه. طول. بقول يا بنات، هنا سهلة بالنسبة ليوم
+
+316
+00:36:26,480 --> 00:36:30,020
+في الأول، وبالنسبة لي ميلي اثنين أردّهم، لأنهم
+
+317
+00:36:30,020 --> 00:36:37,700
+أعداد وتأثيرية زي تأثيري فيه. إذا لو راحت قلت لك DVD
+
+318
+00:36:37,700 --> 00:36:44,600
+بقى حدود التكامل فيه بتتغير من عند الأربعة لغاية
+
+319
+00:36:44,600 --> 00:36:49,160
+السبعة، والـ U بتتغير من واحد لغاية اثنين.
+
+320
+00:36:49,880 --> 00:36:55,020
+تمام؟ يبقى ضايل علينا نضرب هذه المسألة، تبقى حلها
+
+321
+00:36:55,020 --> 00:37:00,460
+المشكلة هنا هي الثلث برا. تكامل من سالب واحد لاثنين،
+
+322
+00:37:00,460 --> 00:37:05,760
+تكامل من أربعة لسبعة. بدنا نفك هذا يا بنات، يبقى هذا
+
+323
+00:37:05,760 --> 00:37:13,940
+إيش بصير؟ تسعة في U تربيع زائد اثنين UV زائد
+
+324
+00:37:13,940 --> 00:37:17,980
+V تربيع. مربع الثلث بتسعة، وعندي اثنين برا، يبقى
+
+325
+00:37:17,980 --> 00:37:25,300
+تسعة واثنين. فكتنا بعض هذه، ثلث في ثلث بيطلع برا في
+
+326
+00:37:25,300 --> 00:37:35,160
+كده تسع، تمام. نضرب هدول في بعض، يبقى هذه U في V
+
+327
+00:37:35,160 --> 00:37:47,340
+U في V، هذه الناقص اثنين U تربيع، وهنا زائد V تربيع
+
+328
+00:37:47,340 --> 00:37:54,020
+ناقص اثنين U في الـ V. والثلاثة مع الثلاثة مع الثلاثة
+
+329
+00:37:54,020 --> 00:37:55,400
+طلعت برا بالمرة.
+
+330
+00:38:01,460 --> 00:38:06,160
+ما رأيك آخذ التسعة برا بالمرة؟ يلا، سهّل لي الشغل، هاي
+
+331
+00:38:06,160 --> 00:38:12,460
+التسعة برا، بيضل عندنا مين؟ بيضل عندنا هنا V تربيع
+
+332
+00:38:12,460 --> 00:38:21,960
+ناقص أربعة U في الـ V زائد أربعة U تربيع، بظبط هيك؟
+
+333
+00:38:21,960 --> 00:38:29,180
+خلصنا منها. طيب، بدي أمسح بس القرن هذا، مش هنكمل
+
+334
+00:38:29,180 --> 00:38:37,520
+مسألتنا. لحد هنا قفلنا، وهذا الـ DVD، طيب.
+
+335
+00:38:37,520 --> 00:38:43,300
+إيش رأيك؟ تسعة مع تسعة مع تسعة نطلع برا، وعندي هنا
+
+336
+00:38:43,300 --> 00:38:45,520
+طول بيصير واحد على سبعة، وإيش؟
+
+337
+00:38:54,250 --> 00:38:59,570
+هي تكامل من أربعة لسبعة، وهيتكامل من أربعة لـ
+
+338
+00:38:59,570 --> 00:39:01,090
+اثنين.
+
+339
+00:39:02,970 --> 00:39:09,510
+زائد أربعة U في V زائد اثنين V تربيع. فكّيت الجُزء
+
+340
+00:39:09,510 --> 00:39:14,430
+الأول. بدنا ندخل إشارة السالب على الجُزء الثاني، يبقى
+
+341
+00:39:14,430 --> 00:39:22,110
+ناقص U في V زائد اثنين U تربيع ناقص V تربيع زائد
+
+342
+00:39:22,110 --> 00:39:28,790
+اثنين U في V. اللي بعده، ندخل إشارة ناقص، يبقى ناقص V
+
+343
+00:39:28,790 --> 00:39:36,670
+تربيع زائد أربعة U في V ناقص أربعة U تربيع. قفلنا الجُزء.
+
+344
+00:39:36,670 --> 00:39:43,150
+وهذا كله مين؟ كله DVD.
+
+345
+00:39:46,240 --> 00:39:52,020
+فهذا كلام مدهش. واحد على سبعة وعشرين، تكامل من سالب
+
+346
+00:39:52,020 --> 00:39:57,020
+واحد لاثنين، تكامل من أربعة لسبعة. طلع يا بنات،
+
+347
+00:39:57,020 --> 00:40:03,400
+اثنين U تربيع واثنين U تربيع، أربعة U تربيع، وسالب
+
+348
+00:40:03,400 --> 00:40:09,820
+أربعة U تربيع، غير مأسوف عليهم، مع السلامة. ندّى نشوف
+
+349
+00:40:09,820 --> 00:40:20,180
+الـ U في الـ V، أربعة U في V واثنين U في V، ستة U في
+
+350
+00:40:20,180 --> 00:40:27,360
+V. شيل منهم واحد ويظل خمسة U في V. وأربعة، تسعة U
+
+351
+00:40:27,360 --> 00:40:36,630
+في V. يبقى تسعة U في الـ V. الـ V تربيع، يبقى هذا اثنين
+
+352
+00:40:36,630 --> 00:40:43,110
+V تربيع، وسالب واحد V تربيع، وسالب واحد V تربيع.
+
+353
+00:40:43,110 --> 00:40:49,350
+برضه غير مأسوف عليهم. يبقى مع السلامة. شو ضايل
+
+354
+00:40:49,350 --> 00:40:54,910
+عندي؟ مش ضايل إلا دي V dU. وضايل كويس، يعني هذا
+
+355
+00:40:54,910 --> 00:40:59,570
+اختصار ممتاز جداً. طب ما هو رأيك، تسعة مع تسعة كمان
+
+356
+00:40:59,570 --> 00:41:05,500
+يطيروا؟ مع السلامة. يبقى هذا الكلام بده يساوي طول
+
+357
+00:41:05,500 --> 00:41:11,460
+وهي تكامل من سالب واحد لغاية اثنين، تكامل من أربعة
+
+358
+00:41:11,460 --> 00:41:20,920
+لغاية سبعة. dU dV dU. نمسح اللي فوق، هذا اللي
+
+359
+00:41:20,920 --> 00:41:21,900
+ما له شخصيات.
+
+360
+00:41:36,130 --> 00:41:42,630
+طيب، هذا الكلام يساوي... قلت ما لكش دعوة. وتكامل من سالب
+
+361
+00:41:42,630 --> 00:41:48,590
+واحد لغاية اثنين، ونجي نكامل بالنسبة الى V، يبقى V
+
+362
+00:41:48,590 --> 00:41:55,310
+تربيع على اثنين، V تربيع على اثنين من عند الأربعة
+
+363
+00:41:55,310 --> 00:42:02,860
+لغاية السبعة. وبظل عندنا U في الدّيم. تمام، مش رأيك
+
+364
+00:42:02,860 --> 00:42:09,340
+نطلع النص برا مع الثلث، بصير كده؟ بصير سُدس تكامل من
+
+365
+00:42:09,340 --> 00:42:15,880
+سالب واحد إلى اثنين. وسبعة في سبعة، تسعة وأربعين
+
+366
+00:42:15,880 --> 00:42:24,900
+ناقص أربعة في أربعة اللي هو ستة عشر. كله خلّصنا منه في
+
+367
+00:42:24,900 --> 00:42:32,800
+الـ dU. أظن ستة من تسعة بيظل ثلاثة وثلاثين، يبقى هذا
+
+368
+00:42:32,800 --> 00:42:39,480
+هنا بيصير ثلاثة وثلاثين على ستة، تكامل من سالب واحد
+
+369
+00:42:39,480 --> 00:42:45,640
+لاثنين لـ dU. هذا الكلام بده يساوي ثلاثة و
+
+370
+00:42:45,640 --> 00:42:51,160
+ثلاثين على ستة، في اختصار على ثلاثة، بيظل أحد عشر على
+
+371
+00:42:51,160 --> 00:42:59,510
+اثنين. وهذه 6 تربيع على الاثنين من سالب واحد لغاية
+
+372
+00:42:59,510 --> 00:43:09,390
+اثنين. يبقى هذا الكلام 11 على اثنين فيه هنا أربعة، ناقص
+
+373
+00:43:09,390 --> 00:43:14,970
+ناقص واحد تربيع اللي هو واحد. بيضل ثلاثة في أحد عشر،
+
+374
+00:43:14,970 --> 00:43:22,550
+ثلاثة وثلاثين على أربعة. قيمة هذا التكامل. حاضرة فيك
+
+375
+00:43:22,550 --> 00:43:28,390
+ما بتحب تسأل أي سؤال هنا؟ خلاص؟
+
+376
+00:43:28,840 --> 00:43:33,060
+طيب، أخذنا الآن بدل المثال، أربعة على الـ double
+
+377
+00:43:33,060 --> 00:43:41,960
+integral. ننتقل الآن للـ triple integral، لأن إذا
+
+378
+00:43:41,960 --> 00:43:45,380
+انتقلنا للـ triple integral، للنقطة الثانية من هذا
+
+379
+00:43:45,380 --> 00:43:50,140
+الـ section، نحتاج أن نذهب نحسن الـ Jacobian الأول
+
+380
+00:43:50,140 --> 00:43:54,420
+لأنه سيصبح عندي بدل المتغيرين كمان، يعني لأن عندي
+
+381
+00:43:54,420 --> 00:44:03,310
+X وY وZ، الجبال هيكون U و V و W، بدل ما كنا نشتغل
+
+382
+00:44:03,310 --> 00:44:08,390
+فيه في الليل، بدنا نشتغل في الـ space، الفراغ.
+
+383
+00:44:08,390 --> 00:44:16,190
+كويس؟ يا فجأة؟ فن
+
+445
+00:51:59,290 --> 00:52:06,730
+تربية في ساين تربيع ثيتا قفل للجوز زائد زيرو في
+
+446
+00:52:06,730 --> 00:52:11,590
+محدد و بزير يبقى سرنجل يكوبي
+
+447
+00:52:14,580 --> 00:52:20,900
+وثيتا بده يسار على الأقل هناك واضح أن عندي رو
+
+448
+00:52:20,900 --> 00:52:28,240
+تربيع ساين فاي كوساين فاي عامل مشترك وعندي كوساين برا
+
+449
+00:52:28,240 --> 00:52:36,440
+فبصير رو تربيع ساين فاي كوساين تربيع فاي يبقى هاي رو
+
+450
+00:52:36,440 --> 00:52:44,640
+تربيع كوساين تربيع فاي في ساين فاي  يأخدنا رو تربيع
+
+451
+00:52:44,640 --> 00:52:50,540
+فاي كوساين فاي برا كده  بيبقى لدي هنا بنات كوساين
+
+452
+00:52:50,540 --> 00:52:55,560
+تربيع ثيتا طيب أخدنا رو تربيع برا وأخدنا كوساين
+
+453
+00:52:55,560 --> 00:53:01,960
+كوساين تربيع ثيتا بيبقى زائد مين؟ زائد ساين تربيع ثيتا هذا
+
+454
+00:53:01,960 --> 00:53:07,900
+الترم الأول نجي للترم الثاني عندك هنا رو ساين
+
+455
+00:53:07,900 --> 00:53:21,230
+تربيع فاي عامل مشترك وعندك رو ساين فاي برا يبقى
+
+456
+00:53:21,230 --> 00:53:33,410
+زائد رو ساين أو رو تربيع ساين تكعيب فاي برا هذا يعني
+
+457
+00:53:33,410 --> 00:53:36,810
+كوساين تربيع ثيتا زائد كوساين تربيع ثيتا
+
+458
+00:53:40,640 --> 00:53:47,220
+زائد ساين تربيع ثيتا طبعا هذه كدهش وهذه كدهش واحد
+
+459
+00:53:47,220 --> 00:53:52,500
+راحة يبقى هذا الكلام بالدوسام شو رايك؟ عندي رو
+
+460
+00:53:52,500 --> 00:53:59,780
+تربيع موجودة في الإثنين وعندي ساين فاي موجودة في
+
+461
+00:53:59,780 --> 00:54:05,600
+الإثنين يبقى بضال عندي هنا قداش و ساين تربيع فيه و
+
+462
+00:54:05,600 --> 00:54:10,960
+هنا بضال قداش عندي ساين تربيع فيه لأنه خد ساين برا
+
+463
+00:54:10,960 --> 00:54:17,080
+اللي بين قوسين قداش يبقى هذا كمان بواحد يبقى بضال
+
+464
+00:54:17,080 --> 00:54:23,860
+قداش رو تربيع ساين فيه وهذا ما وعدناكم به في
+
+465
+00:54:23,860 --> 00:54:30,380
+المحاضرة الماضية لما انحولنا من DX DY DZ إلى D ρ D
+
+466
+00:54:30,380 --> 00:54:35,600
+فاي D ثيتا ضربنا في رو تربيع ساين فاي ويومها كان
+
+467
+00:54:35,600 --> 00:54:39,240
+السؤال من أين لك هذا فقلنا لكم إن شاء الله في ال
+
+468
+00:54:39,240 --> 00:54:42,140
+section القادم اللي هو ال section اللي بين أيدينا
+
+469
+00:54:42,140 --> 00:54:48,360
+اليوم وها نحن نفي بوعدنا طيب حد إلى أي تساؤل هذا
+
+470
+00:54:48,360 --> 00:54:50,300
+قبل أن أذهب إلى المثال الثاني
+
+471
+00:54:55,430 --> 00:55:04,670
+ثالث نسمة بيقول let D be the region let D be the
+
+472
+00:55:04,670 --> 00:55:19,350
+region عبارة عن المنطقة  in X Y Z space defined
+
+473
+00:55:19,350 --> 00:55:22,810
+by the inequalities defined
+
+474
+00:55:23,950 --> 00:55:34,450
+by the inequalities المتباينات
+
+475
+00:55:34,450 --> 00:55:40,450
+الـ X أكبر من أو يساوي واحد وأقل من أو يساوي اثنين
+
+476
+00:55:40,450 --> 00:55:46,970
+والـ X في Y أكبر من أو يساوي صفر وأقل من أو يساوي
+
+477
+00:55:46,970 --> 00:55:52,630
+اثنين والـ Z أكبر من أو يساوي صفر وأقل من أو يساوي
+
+478
+00:55:52,630 --> 00:55:52,990
+واحد
+
+479
+00:55:59,070 --> 00:56:04,010
+خلّي أحسب ال Value
+
+480
+00:56:04,010 --> 00:56:16,850
+للتكاملات الثلاثية على D لمين؟ للـ X تربيع Y زائد ثلاثة XYZ
+
+481
+00:56:16,850 --> 00:56:26,490
+كل هذا DX DY DZ By applying
+
+482
+00:56:30,360 --> 00:56:41,800
+applying the transformation the transformation
+
+483
+00:56:41,800 --> 00:56:45,800
+الـ
+
+484
+00:56:45,800 --> 00:56:56,080
+U بده يساوي الـ X والـ V بده يساوي الـ XY والـ W بده
+
+485
+00:56:56,080 --> 00:57:07,420
+يساوي ثلاثة Z and integrate over
+
+486
+00:57:07,420 --> 00:57:20,480
+an appropriate region
+
+487
+00:57:20,480 --> 00:57:26,300
+D in
+
+488
+00:57:26,300 --> 00:57:28,100
+the
+
+489
+00:57:31,390 --> 00:57:37,210
+U V W Space الـ U V W Space
+
+490
+00:58:15,770 --> 00:58:20,850
+بنرجع لسؤالنا مرة ثانية، بيقول افترض D هي المنطقة
+
+491
+00:58:20,850 --> 00:58:26,150
+اللي في الـ X,Y,Z space والمعرفة بالمتباينات X
+
+492
+00:58:26,150 --> 00:58:33,090
+محصورة بين 1 و 2، X في الـ Y محصورة بين 0 و 2، Z
+
+493
+00:58:33,090 --> 00:58:39,850
+محصورة بين 0 و 1 بيقول احسب لي التكامل اللي قدامنا هذا
+
+494
+00:58:39,850 --> 00:58:44,210
+كيف؟ By applying that transformation يبقى أعطاني
+
+495
+00:58:44,210 --> 00:58:51,150
+تحويل الـ U تساوي الـ X، الـ V تساوي الـ X في Y، الـ W
+
+496
+00:58:51,150 --> 00:58:57,080
+يساوي ثلاثة Z الأصل أنه يعطيني الـ Z بدلالة
+
+497
+00:58:57,080 --> 00:59:01,600
+المتغيرات الثلاثة هنا لكن هنا يا شقلبق بمين الموضوع
+
+498
+00:59:01,600 --> 00:59:08,560
+إذا شغلتنا نحسب كله من X و Y و Z بدلالة الـ U والـ
+
+499
+00:59:08,560 --> 00:59:12,040
+V والـ W وبعد هيك نشوف كيف يصير
+
+500
+00:59:17,890 --> 00:59:22,410
+أفضل لما أقول لي الـ U تساوي الـ X يبقى الـ X بتساوي
+
+501
+00:59:22,410 --> 00:59:32,350
+الـ U تمام؟ أنا بدي الـ Y، V على X، والـ X بقدرش بـ U
+
+502
+00:59:32,350 --> 00:59:40,770
+يبقى هذا بدي أعطيك إن Y تساوي V على U وهذه الـ Z
+
+503
+00:59:40,770 --> 00:59:48,350
+بتساوي ثلث W أو W على 3 يبقى بناء عليه اروح نكتب
+
+504
+00:59:48,350 --> 00:59:54,050
+المتغيرات اللي عندي بدلالة من المتغيرات الجديدة
+
+505
+00:59:54,050 --> 00:59:59,290
+اللي هو U و V و W لذا نخليه نحسب ال Jacobian بالمرة
+
+506
+00:59:59,290 --> 01:00:08,890
+ال Jacobian تبع الـ U والـ V والـ W في هذه المحددة
+
+507
+01:00:08,890 --> 01:00:14,630
+بنجي هنا partial X على partial U، partial X على
+
+508
+01:00:14,630 --> 01:00:20,250
+partial V، partial X على partial W، partial Y على
+
+509
+01:00:20,250 --> 01:00:25,390
+partial U، partial Y على partial V، partial Y على
+
+510
+01:00:25,390 --> 01:00:30,810
+partial W، partial Z على partial U، partial Z على
+
+511
+01:00:30,810 --> 01:00:35,370
+partial V، partial Z على partial W
+
+512
+01:00:38,600 --> 01:00:44,800
+يبقى هذا هو المحدد تمام تفاضل الـ X بالنسبة إلى U
+
+513
+01:00:44,800 --> 01:00:50,280
+بواحد تفاضل الـ X بالنسبة لـ V و بالنسبة لـ W بصفر
+
+514
+01:00:50,280 --> 01:00:57,580
+ماعنديش يبقى هاي صفر وهاي صفر تفاضل الـ Y بالنسبة
+
+515
+01:00:57,580 --> 01:00:58,500
+إلى U
+
+516
+01:01:10,600 --> 01:01:14,740
+طيب صبر شو بس بس بس بس بس بس بس بس بس بس بس بس
+
+517
+01:01:14,740 --> 01:01:14,920
+بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس
+
+518
+01:01:14,920 --> 01:01:20,000
+بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس
+
+519
+01:01:20,000 --> 01:01:22,660
+بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس
+
+520
+01:01:22,660 --> 01:01:22,800
+بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس
+
+521
+01:01:22,800 --> 01:01:22,880
+بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس
+
+522
+01:01:22,880 --> 01:01:31,840
+بس بس بس بس بس بس بس بس بس
+
+523
+01:01:31,840 --> 01:01:40,630
+بماشي يبقى هو الـ V مالوش دعوة والواحد على U سالب
+
+524
+01:01:40,630 --> 01:01:46,590
+واحد على U تربيع يبقى سالب V على U تربيع يبقى سالب V
+
+525
+01:01:46,590 --> 01:01:53,150
+على U تربيع طب بدنا تفاضلها بالنسبة لـ V واحد على U
+
+526
+01:01:53,150 --> 01:02:00,050
+يبقى واحد على U يبقى تفاضلها بالنسبة لمين؟ لـ W بصفر
+
+527
+01:02:00,050 --> 01:02:10,010
+طب بدنا لـ Z بالنسبة لـ U صفر وصفر هنا طول يالله يا
+
+528
+01:02:10,010 --> 01:02:17,170
+بنات قداش؟ يعني
+
+529
+01:02:17,170 --> 01:02:23,590
+قداش الجواب؟ دي هي اللي هيك. أليس محدد لمصفوفة مثلثة
+
+530
+01:02:23,590 --> 01:02:29,010
+سفلية يبقى حاصل ضرب عناصر القطر الرئيسي فقط. ده يغير
+
+531
+01:02:29,010 --> 01:02:33,950
+لأنه يطلع هي القطر الرئيسي وفوق كلها أصفار. محدد
+
+532
+01:02:33,950 --> 01:02:37,630
+المصفوفة المثلثة العليا أو المصفوفة المثلثة السفلى
+
+533
+01:02:38,800 --> 01:02:42,420
+حاصل ضرب عناصر القطر الرئيسي أو الـ scalar matrix
+
+534
+01:02:42,420 --> 01:02:47,060
+يبقى بس بنضرب حاصل ضرب عناصر القطر الرئيسي ينفذ
+
+535
+01:02:47,060 --> 01:02:52,320
+بيطلع واحد على ثلاثة U مش مصدقة تعالى نفك
+
+536
+01:02:52,320 --> 01:02:57,240
+باستخدام عناصر الصف الأول وشطّ بصفه عمود كل واحد
+
+537
+01:02:57,240 --> 01:03:02,110
+على U في ثلث، بواحد، ثلث U، صفر، بواحد، ثلث U، بواحد
+
+538
+01:03:02,110 --> 01:03:05,910
+بواحد، ثلث U. إذا حاصل ضرب عناصر القطر الرئيسي
+
+539
+01:03:05,910 --> 01:03:11,050
+مباشرة. هذا مين؟ هذا ال Jacobian تبع الـ U والـ V والـ
+
+540
+01:03:11,050 --> 01:03:17,670
+W. طيب احنا ضايل عندنا حدود التكامل. بدي أعرف U
+
+541
+01:03:17,670 --> 01:03:25,530
+بدها تتغير من وين لوين؟ أظن قصتنا بسيطة، ما فيش مشكلة
+
+542
+01:03:25,530 --> 01:03:30,830
+الـ U من واحد لاثنين. طيب تعالى نشوف نشيل الـ X ونحط
+
+543
+01:03:30,830 --> 01:03:36,470
+الـ U بيصير محصورة بين مين؟ وواحد واثنين. طيب تعالى
+
+544
+01:03:36,470 --> 01:03:41,850
+لثانية يعني الثانية عندك لو قسمت على X بيصير Y
+
+545
+01:03:41,850 --> 01:03:48,830
+محصورة بين صفر واثنين على X يبقى هنا أها باجي
+
+546
+01:03:48,830 --> 01:03:56,090
+بقول صفر أقل من أو يساوي XY أقل من أو يساوي
+
+547
+01:03:56,090 --> 01:04:00,030
+Y أقل
+
+548
+01:04:00,030 --> 01:04:06,310
+من أو يساوي Y أقل من أو يساوي Y أقل من أو يساوي
+
+549
+01:04:06,310 --> 01:04:06,570
+الـ Y أقل من أو يساوي Y أقل من أو يساوي Y أقل
+
+550
+01:04:06,570 --> 01:04:06,830
+من أو يساوي Y أقل من أو يساوي Y أقل من أو يساوي
+
+551
+01:04:06,830 --> 01:04:07,530
+الـ Y أقل من أو يساوي Y أقل من أو يساوي Y أقل
+
+552
+01:04:07,530 --> 01:04:12,150
+الـ Y أقل من أو يساوي Y أقل من أو يساوي Y أقل
+
+553
+01:04:12,150 --> 01:04:18,970
+من أو يساوي Y أقل من أو أكبر من أو تساوي صفر
+
+554
+01:04:18,970 --> 01:04:26,430
+أقل من أو يساوي اثنين على U طيب ممتاز من خلال
+
+555
+01:04:26,430 --> 01:04:35,450
+نتيجة U زائد ثلث W يبقى بقى إني بقوله ثلث
+
+556
+01:04:35,450 --> 01:04:38,830
+ثلث W على ثلاثة
+
+557
+01:04:49,700 --> 01:04:55,020
+يبقى الـ W محصورة بين الصفر وبين الواحد وبين
+
+558
+01:04:55,020 --> 01:05:07,180
+الثلاثة إذا مشكلتي أصبحت مالها؟ أصبحت محلولة الـ
+
+559
+01:05:07,180 --> 01:05:09,180
+Y محصورة بين الصفر والاثنين
+
+560
+01:05:13,130 --> 01:05:19,010
+أه أه فهمت عليك أه هذه أمانات على طول الخط هذا بدي
+
+561
+01:05:19,010 --> 01:05:24,110
+أعطيك إنه صفر أقل من أو يساوي الـ Y اللي عندنا من
+
+562
+01:05:24,110 --> 01:05:36,370
+وراها V على U يبقى هذه V على U أقل من أو يساوي اثنين
+
+563
+01:05:36,370 --> 01:05:42,900
+على U أضرب بكله في U بصير إن دجاج بصير الصفر أقل
+
+564
+01:05:42,900 --> 01:05:47,900
+من أو يساوي V أقل من أو يساوي قداش؟ اثنين يبقى
+
+565
+01:05:47,900 --> 01:05:54,380
+حددت حدود التكامل تحديدا سليما وجبت الجاكوبيان
+
+566
+01:05:54,380 --> 01:06:01,600
+يبقى إلا عملية التكامل يبقى بروح بقول ثلاثة تكاملات
+
+567
+01:06:01,600 --> 01:06:06,480
+وبأبدأ لحد قداش؟ للـ X تربيع وين الـ X؟
+
+568
+01:06:13,570 --> 01:06:25,270
+والـ Y بـ V على U يبقى هذه V على U اللي بعدها زائد
+
+569
+01:06:25,270 --> 01:06:37,950
+ثلاثة U لأن X بـ U والـ Y بـ V على U وهذه V على U و
+
+570
+01:06:37,950 --> 01:06:42,650
+الـ Z اللي هي W على ثلاثة، الـ W
+
+571
+01:06:45,250 --> 01:06:50,390
+الـ Jacobian، الـ Jacobian واحد على ثلاثة U يبقى
+
+572
+01:06:50,390 --> 01:07:00,970
+واحد على ثلاثة U وهنا D V D و الله إيش D W D W و
+
+573
+01:07:00,970 --> 01:07:07,610
+الله خليها D U في الأول مش مشكلة أي حاجة D W D V D
+
+574
+01:07:07,610 --> 01:07:12,990
+U طبعا واضح ما فيهاش شغلات صعبة كتيرة لكن لو خلتها
+
+575
+01:07:12,990 --> 01:07:13,610
+لآخر
+
+576
+01:07:17,020 --> 01:07:22,580
+يبقى بداخل الحدود كون كتبت الـ W يبقى الـ W تتغير
+
+577
+01:07:22,580 --> 01:07:29,620
+من أين لأين؟ من صفر لغاية ثلاثة الـ V ستتغير من
+
+578
+01:07:29,620 --> 01:07:36,320
+صفر لغاية اثنين الـ U تتغير من أين لأين؟ من واحد
+
+579
+01:07:36,320 --> 01:07:42,200
+لغاية اثنين الشكل عندنا طيب نبسط المثال تكامل من
+
+580
+01:07:42,200 --> 01:07:47,120
+واحد للاثنين تكامل من صفر للاثنين تكامل من صفر لثلاثة هذا يا بنات بيظل عندي U في V وهذه زائد
+
+581
+01:07:47,120 --> 01:07:54,120
+ثلاثة مع ثلاثة والـ U مع الـ U بيظل بس VW يبقى زائد
+
+582
+01:07:54,120 --> 01:08:02,920
+VW في واحد على ثلاثة U DW DV DU
+
+583
+01:08:02,920 --> 01:08:12,400
+طيب هذا الكلام بده يساوي شو رايك؟ الثلث برا وهي
+
+584
+01:08:14,450 --> 01:08:19,190
+تكامل من واحد لاثنين وهي تكامل من صفر لغاية
+
+585
+01:08:19,190 --> 01:08:25,050
+الثلاثة بده يدخل الـ U جوا قالي قداش V زائد VW على U
+
+586
+01:08:25,050 --> 01:08:33,710
+في مين؟ في الـ DW DV DU كيف؟
+
+587
+01:08:42,680 --> 01:08:51,660
+من صفر لاثنين تكامل هنا من صفر لاثنين يبقى الآن
+
+588
+01:08:51,660 --> 01:08:56,640
+أنا بأبدأ أكامل بالنسبة لمين؟ للـ DW يبقى هذا الكلام بده
+
+589
+01:08:56,640 --> 01:09:02,940
+يساوي هاي الثلث برا وهي تكاملين من صفر للاثنين ومن
+
+590
+01:09:02,940 --> 01:09:07,460
+واحد لغاية اثنين للـ VW
+
+591
+01:09:09,920 --> 01:09:18,680
+اللي هو VW تربيع على اثنين U والـ W تتغير من الصفر
+
+592
+01:09:18,680 --> 01:09:25,320
+لغاية الثلاثة لـ DV DU يساوي
+
+593
+01:09:25,320 --> 01:09:31,060
+أي الثلث برا وهي تكاملين من صفر لواحد ومن الصفر
+
+594
+01:09:31,060 --> 01:09:35,860
+للاثنين يجب أن أشيل الـ W وأضع بدلها ثلاثة
+
+595
+01:09:35,860 --> 01:09:39,180
+ثلاثة
+
+596
+01:09:39,180 --> 01:09:49,550
+V وهنا زائد الـ W تربيع بصير تسعة على تسعة V على
+
+597
+01:09:49,550 --> 01:09:57,930
+اثنين U، تسعة V على اثنين U تمام؟ ناقص صفر، صفر مع
+
+598
+01:09:57,930 --> 01:10:04,970
+السلامة كل هذا في DV DU شو رأيك يا بنات؟
+
+599
+01:10:07,810 --> 01:10:14,470
+برا معامل غير مصوف عليك يبقى هذا الكلام تكامل من
+
+600
+01:10:14,470 --> 01:10:21,870
+صفر لواحد تكامل من صفر للاثنين للـ V زائد ثلاثة
+
+601
+01:10:21,870 --> 01:10:33,210
+V على اثنين U DV DU يبقى هذا الكلام بالدوسام تكامل
+
+602
+01:10:33,210 --> 01:10:34,650
+من صفر لواحد
+
+603
+01:10:44,940 --> 01:10:51,440
+والحكي هذا كله من صفر للاثنين لدي يوم. يبقى هذا
+
+604
+01:10:51,440 --> 01:10:55,620
+الكلام يصير تكامل من صفر لواحد.
+
+605
+01:10:59,000 --> 01:11:06,020
+سبحان الله يبقى هذا من واحد للاثنين وهذا من واحد
+
+606
+01:11:06,020 --> 01:11:16,280
+للاثنين وهذا من الواحد للاثنين وهذا من واحد لغاية
+
+607
+01:11:16,280 --> 01:11:23,100
+اثنين وما أنسانية إلا الشيطان القرعي. هذه فنيات
+
+608
+01:11:23,100 --> 01:11:26,860
+صورة بنات. الكافية
+
+609
+01:11:29,370 --> 01:11:35,050
+طبعا وبدها في كافهم كده؟ ثلاثة سنين وزائد وتسعة عمره حد بيظل نايم ثلاثمية وتسعة وتسعون ولا
+
+610
+01:11:35,050 --> 01:11:39,770
+ثلاثمية وتسعة سنين؟ غريب يعني لكن ما غريب للشيطان
+
+611
+01:11:39,770 --> 01:11:46,630
+أن الله على كل شيء قادر. طيب العوض إذا دي أربعة
+
+612
+01:11:46,630 --> 01:11:57,570
+على اثنين بيظل كده؟ بيظل اثنين زائد هنا كمان أربعة
+
+613
+01:11:57,570 --> 01:12:03,930
+بتروح مع الأربعة بضع قداش؟ ثلاثة عليهم زائد ثلاثة
+
+614
+01:12:03,930 --> 01:12:07,630
+عليهم كله في الديام
+
+615
+01:12:10,040 --> 01:12:17,480
+يبقى هذا الكلام بده يسا
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/Ilto5AXE7dw_postprocess.srt b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/Ilto5AXE7dw_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..6c396546a9f6b48e555a29aff937231f25ca59f6
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/Ilto5AXE7dw_postprocess.srt
@@ -0,0 +1,2588 @@
+1
+00:00:12,380 --> 00:00:17,540
+الاخر section في هذا ال chapter هو substitution in
+
+2
+00:00:17,540 --> 00:00:24,540
+trigonometric or in multiple integralيبقى التعويض
+
+3
+00:00:24,540 --> 00:00:30,580
+في التكامل المتعددة هناخد أول حاجة التعويض في
+
+4
+00:00:30,580 --> 00:00:34,700
+التكامل ب two integrals و بعدها نروح لمين ل three
+
+5
+00:00:34,700 --> 00:00:41,710
+integrals يبقى substitution in double integralsلو
+
+6
+00:00:41,710 --> 00:00:45,750
+ان ده ال F و X و Y و بقى عندي تكامل عليه على
+
+7
+00:00:45,750 --> 00:00:51,770
+المنطقة R يمكن نخل هذا التكامل إلى تكامل مكافئ له
+
+8
+00:00:51,770 --> 00:00:56,230
+على منطقة أخرى بدي أسميها مين ال G هذا الكلام
+
+9
+00:00:56,230 --> 00:01:01,810
+بيحصللو عندى function g وh كل واحدة فيهم one to
+
+10
+00:01:01,810 --> 00:01:08,870
+one بمعنى ان x تساوي f of g وy تساوي f of g وy
+
+11
+00:01:08,870 --> 00:01:10,990
+تساوي f of g وy تساوي h of u وv هدول ال two
+
+12
+00:01:10,990 --> 00:01:15,820
+functions are one to one functionsلأن كل نقطة في
+
+13
+00:01:15,820 --> 00:01:19,820
+المساحة الأولى ستوديها الامين إلى نظيرتها في
+
+14
+00:01:19,820 --> 00:01:24,060
+المساحة الثانية وبالتالي هذه المساحة من ناحية
+
+15
+00:01:24,060 --> 00:01:29,100
+القيمة جد المساحة تانية لكن شكلهم مختلف ليس بضرورة
+
+16
+00:01:29,100 --> 00:01:34,050
+يكونوا مثل بعض لكن من ناحية المساحة جد بعضطيب
+
+17
+00:01:34,050 --> 00:01:38,630
+مضروف في مين؟ في ال absolute value ل J of U و V
+
+18
+00:01:38,630 --> 00:01:43,090
+هذا J زي معامل البنات زي ما نقول معامل التمدد
+
+19
+00:01:43,090 --> 00:01:46,390
+الحاجو معامل التمدد الطولي يبقى هنا احنا بقول هنا
+
+20
+00:01:46,390 --> 00:01:51,690
+هذا هو الجاكوبين مين الجاكوبين هذا؟ شو قصته هذه؟
+
+21
+00:01:51,690 --> 00:01:56,380
+بقولك where ال J of U و Vهو عبارة عن تفضل X
+
+22
+00:01:56,380 --> 00:02:00,800
+بالنسبة للمتغير الأول والتفضل X بالنسبة للمتغير
+
+23
+00:02:00,800 --> 00:02:04,160
+الثاني اللي عملناه للمتغير X هفروح نعمله لمهم
+
+24
+00:02:04,160 --> 00:02:10,880
+للمتغير Y نفك المحدد هذا هيعطيني قيمة محددة هذه
+
+25
+00:02:10,880 --> 00:02:14,900
+القيمة هي اللي بتبقى بال Jacob يعني إذا موجة بقى
+
+26
+00:02:14,900 --> 00:02:18,260
+خلاص مافيش absolute value لكن إذا سالبة بتاخدلها
+
+27
+00:02:18,260 --> 00:02:23,540
+مهم ال absolute valueيبقى هذا هو الـ Jacobin of
+
+28
+00:02:23,540 --> 00:02:27,100
+the coordinates transformations يبقى هذا المعامل
+
+29
+00:02:27,100 --> 00:02:31,860
+تبع من تبع التحويل الآن بدنا نحسب اللي هو معاملة
+
+30
+00:02:31,860 --> 00:02:36,440
+التحويل لدول مختلفة بدنا نبدأ ناخد أمثلة على ذلك
+
+31
+00:02:36,680 --> 00:02:42,420
+ولو أحصل على الكوبيان لتغيير الوضع الكوردنسي لوضع
+
+32
+00:02:42,420 --> 00:02:43,440
+كوردنسي كوردنسي كوردنسي كوردنسي كوردنسي كوردنسي
+
+33
+00:02:43,440 --> 00:02:46,580
+كوردنسي
+
+34
+00:02:46,580 --> 00:02:56,780
+كوردنسي كوردنسي
+
+35
+00:02:56,780 --> 00:03:00,400
+كوردنسي
+
+36
+00:03:01,210 --> 00:03:04,990
+القطبية وفيه شغلة بدنا نضرب فيها طبعا استخدمناها
+
+37
+00:03:04,990 --> 00:03:09,770
+قبلنا هيك وقلنا هي عبارة عن إيش؟ عبارة عن R فقلنا
+
+38
+00:03:09,770 --> 00:03:15,950
+DX DY في الكرتزيني وقابله RERD من أين لك R
+
+39
+00:03:15,950 --> 00:03:19,050
+وعدناكوا يوم وقلناكم ان شاء الله في نهاية هذا ال
+
+40
+00:03:19,050 --> 00:03:25,160
+chapter بنوريكوا كيف جبنا هذه ال R طيببنجي نحسن
+
+41
+00:03:25,160 --> 00:03:28,780
+مقدار الجاكوبيا لهذا اللي احنا بنقول هو R بنجي
+
+42
+00:03:28,780 --> 00:03:33,260
+نقول اه ال X في الأحداثيات الكارتيزية هي عبارة عن
+
+43
+00:03:33,260 --> 00:03:38,560
+R cos θ في الأحداثيات القطبية وكذلك ال Y في
+
+44
+00:03:38,560 --> 00:03:43,380
+الأحداثيات الكارتيزية هي R sin θ في الأحداثيات
+
+45
+00:03:43,380 --> 00:03:50,740
+القطبية يبقى بنات U في مين أجى مكانها هنا R و θ
+
+46
+00:03:58,240 --> 00:04:04,420
+تفضل X بالنسبة الى R تفضل X بالنسبة الى θية اللى
+
+47
+00:04:04,420 --> 00:04:09,100
+عملناه بالنسبة ل X اروح نعمله بالنسبة ل Y يبقى
+
+48
+00:04:09,100 --> 00:04:14,840
+partial Y على partial R partial Y على partial θية
+
+49
+00:04:16,300 --> 00:04:21,540
+يساوي هي الـ determinant نيجي تفاضل ال X بالنسبة
+
+50
+00:04:21,540 --> 00:04:27,720
+إلى أرمين cosine ثيتا يبقى هي cosine ثيتا تفاضل ال
+
+51
+00:04:27,720 --> 00:04:29,780
+X بالنسبة لثيتا
+
+52
+00:04:32,870 --> 00:04:40,410
+R في صين الزاوية تيتا تفضل ال Y بالنسبة إلى R بصين
+
+53
+00:04:40,410 --> 00:04:47,050
+تيتا تفضل ال Y بالنسبة لتيتا بR في كوصين الزاوية
+
+54
+00:04:47,050 --> 00:04:52,710
+تيتا هذا المحدد يسارحاصل ضرب عناصر القطر الرئيسي
+
+55
+00:04:52,710 --> 00:04:58,910
+اللي هو R في Cos تربيه ثيته ناقص حاصل ضرب عناصر
+
+56
+00:04:58,910 --> 00:05:04,270
+القطر الثانوي مع ناقص بصير زائد R في Sin تربيه
+
+57
+00:05:04,270 --> 00:05:09,950
+ثيته إذا ناخد R عام المشترك بيظل Cos تربيه ثيته
+
+58
+00:05:09,950 --> 00:05:15,000
+زائد Sin تربيه ثيته ليه بقدرش؟يبقى النتيجة قداش
+
+59
+00:05:15,000 --> 00:05:20,240
+يبقى عرف ان انا ارتعت ال polar من اين اجت هذه يبقى
+
+60
+00:05:20,240 --> 00:05:24,700
+هذه هي قيمة الجاكوبيان في التحويل من الاحداثيات
+
+61
+00:05:24,700 --> 00:05:29,140
+الكارتيزية الامام الى الاحداثيات القطبية وبعد قليل
+
+62
+00:05:29,140 --> 00:05:33,860
+ان شاء الله هروح زي الجاكوبيان تبع التحويل من
+
+63
+00:05:33,860 --> 00:05:36,380
+الكارتيزيا لالاسفريكا
+
+64
+00:05:56,970 --> 00:06:05,010
+المثال الثاني بيقول لت
+
+65
+00:06:05,010 --> 00:06:14,410
+جيب دي region definedجي بـ the region defined by
+
+66
+00:06:14,410 --> 00:06:19,010
+والمعرفة
+
+67
+00:06:19,010 --> 00:06:24,830
+بيه ال U أكبر من أو يساوي واحد وأقل من أو يساوي
+
+68
+00:06:24,830 --> 00:06:29,950
+اتنين و ال U في ال V كمان أكبر من أو يساوي واحد
+
+69
+00:06:29,950 --> 00:06:38,070
+وأقل من أو يساوي اتنين in the UV plane and theU V
+
+70
+00:06:38,070 --> 00:06:50,010
+لين وير حيث ال X بدها تساوي ال U و ال Y بدها تساوي
+
+71
+00:06:50,010 --> 00:06:58,390
+ال U في ال V السؤال بيقول لي transform حول
+
+72
+00:06:58,390 --> 00:07:08,370
+the integral قول لي التكاملاللي هو مين؟ تكامل من
+
+73
+00:07:08,370 --> 00:07:15,930
+واحد للإتنين تكامل كذلك من واحد للإتنين لل y على x
+
+74
+00:07:15,930 --> 00:07:25,890
+dy dx into an integral over g into an integral
+
+75
+00:07:25,890 --> 00:07:34,890
+over g and evaluate and evaluate
+
+76
+00:07:36,840 --> 00:07:42,060
+و احسبلي كذلك the uv integral
+
+77
+00:08:06,340 --> 00:08:12,360
+سؤال مرة تانية بيعطيني المنطقة G U محصورة بين واحد
+
+78
+00:08:12,360 --> 00:08:18,060
+واتنين وحصل ضرب U في V محصورة بين واحد واتنين هذا
+
+79
+00:08:18,060 --> 00:08:22,820
+على ال U V plane وعطاني علاقة بتربط بين X وY وكذا
+
+80
+00:08:22,820 --> 00:08:29,500
+كالمتغيرات الجديدة U وV X يساوي U وY يساوي U في V
+
+81
+00:08:29,500 --> 00:08:34,280
+بيقولي transform the integral حول التكامل اللي
+
+82
+00:08:34,280 --> 00:08:40,010
+عندنا هذاInto an integral over G لتكامل على G
+
+83
+00:08:40,010 --> 00:08:44,990
+واحسب لهذا التكامل الجديد زي و لتشيبير بالضبط
+
+84
+00:08:44,990 --> 00:08:49,070
+بقناع لما كنا بنحول من كارتيزيا ال integral إلى
+
+85
+00:08:49,070 --> 00:08:54,350
+polar integral و بنروح نحسببقدرش قيمة ال polar
+
+86
+00:08:54,350 --> 00:08:58,950
+integral يبقى هنا نفس القصة بالضغط تماما يعني بديش
+
+87
+00:08:58,950 --> 00:09:04,630
+اشوف المثل لا X ولا Y بدي احولها كلها بدلالة من R
+
+88
+00:09:04,630 --> 00:09:10,170
+و Z بقوله كويس يبقى هي التكملات اتنين اللي عندنا
+
+89
+00:09:10,170 --> 00:09:17,510
+ال Y بقدرش U في V ال X ب U ايوة ضل بدنا ال
+
+90
+00:09:17,510 --> 00:09:24,730
+Jacobian كويس فاهمين في ال Jacobianتبع ال U وال V
+
+91
+00:09:24,730 --> 00:09:33,940
+absolute value دي V دي U او دي U دي Vطب نيجي الآن
+
+92
+00:09:33,940 --> 00:09:40,400
+بدنا نحسب الجاكوبين و بدنا نحسب حدود التكامل طب
+
+93
+00:09:40,400 --> 00:09:44,460
+تعالى نحسب الجاكوبين في الأول يبقى يا بنات انا بدي
+
+94
+00:09:44,460 --> 00:09:49,640
+partial x by partial u و partial x by partial v
+
+95
+00:09:49,640 --> 00:09:52,600
+بدي partial y by partial u
+
+96
+00:09:57,550 --> 00:10:04,130
+تفاضل X بالنسبة إلى U بقدرش تفاضل X بالنسبة إلى V
+
+97
+00:10:06,490 --> 00:10:12,890
+يبقى هنا zero بعد ذلك التفاضل ال Y بالنسبة الى U V
+
+98
+00:10:12,890 --> 00:10:19,410
+تفاضل Y بالنسبة الى V ب U حصر ضرب الرئيس ينقص
+
+99
+00:10:19,410 --> 00:10:23,770
+الثانوية يبقى كده ايش؟ يبقى مقدار الجاكوبيا بده
+
+100
+00:10:23,770 --> 00:10:30,050
+يساوي من؟ بده يساوي LU طيب إذا هذا هذا كله على
+
+101
+00:10:30,050 --> 00:10:35,770
+المنطقة اللي هي Gيبقى هذا الكلام بدل يسوي تكاملين
+
+102
+00:10:35,770 --> 00:10:42,550
+لمين ال U مع ال U بتروح هذه مع هذه بيظل V ومقدار
+
+103
+00:10:42,550 --> 00:10:51,050
+الجاكوبيا بي U دي V دي U طب نرجع لمين يا بنات
+
+104
+00:10:51,050 --> 00:10:58,370
+للمعطينيها هذهبقدر أقوله لو قسمت الطرفين على V إذا
+
+105
+00:10:58,370 --> 00:11:03,110
+الواحد أقل من أو يساوي U و V أقل من أو يساوي اتنين
+
+106
+00:11:03,110 --> 00:11:08,690
+implied ان ال V محصورة بين واحد على U و ما بين
+
+107
+00:11:08,690 --> 00:11:13,530
+اتنين على U إذا أنا أخدت التكامل في الأول بالنسبة
+
+108
+00:11:13,530 --> 00:11:19,870
+إلى V يبقى هنا واحد على U و هنا اتنين على U ال U
+
+109
+00:11:19,870 --> 00:11:24,990
+تتغير من أين إلى أين؟يبقى جاهزة من واحد إلى اتنين،
+
+110
+00:11:24,990 --> 00:11:29,330
+الآن بنقدر نكمل التكامل هذا، ليش؟ لأن هدول فعلا
+
+111
+00:11:29,330 --> 00:11:35,150
+متغيرات بدلالة U، لكن U بأرقاموبالتالي بقدر اطلع
+
+112
+00:11:35,150 --> 00:11:40,230
+جداش القيمة الحقيقية لهذا التكامل يبقى هذا الكلام
+
+113
+00:11:40,230 --> 00:11:46,370
+يساوي تكامل من واحد لاتنين يبقى U مقدر ثابت يبقى
+
+114
+00:11:46,370 --> 00:11:54,070
+بدي اكمل ال V بس اللي هي V تربيع على اتنين من واحد
+
+115
+00:11:54,070 --> 00:11:59,110
+على U لاتنين على U في ال U في ال DU
+
+116
+00:12:02,420 --> 00:12:08,200
+يبقى هذا الكلام بده يسافر هي النص برا و هي تكمل من
+
+117
+00:12:08,200 --> 00:12:14,800
+واحد للاثنين بظل V تربيع يبقى اللي هي اربعة على U
+
+118
+00:12:14,800 --> 00:12:23,280
+تربيع ناقص واحد على U تربيع كله في ال DU والله في
+
+119
+00:12:23,280 --> 00:12:29,180
+ال U DU في عندي U لسه اضعه الى برا يبقى في ال U DU
+
+120
+00:12:42,970 --> 00:12:53,110
+يبقى تلاتة على
+
+121
+00:12:53,110 --> 00:12:56,430
+U دي U يبقى الجواب تلاتة على U دي U يبقى الجواب
+
+122
+00:12:56,430 --> 00:12:57,280
+تلاتة على U دي U يبقى الجواب تلاتة على U دي Uتلاتة
+
+123
+00:12:57,280 --> 00:13:03,340
+على اتنين لان absolute value ل U من عند الواحد
+
+124
+00:13:03,340 --> 00:13:10,280
+لغاية اتنين يبقى تلاتة على اتنين لان اتنين ناقص
+
+125
+00:13:10,280 --> 00:13:16,300
+لان الواحد طبعا لان الواحد مايبقى داشر بزيرو بظل
+
+126
+00:13:16,300 --> 00:13:21,460
+عندنا بس تلاتة على اتنين لان اتنين هذا قيمة
+
+127
+00:13:21,460 --> 00:13:24,500
+التكامل اللي موجود عندنا
+
+128
+00:13:41,880 --> 00:13:46,860
+بنروح مثال رقم اتنين ولا تلاتة الحين مثال رقم
+
+129
+00:13:46,860 --> 00:13:50,340
+تلاتة
+
+130
+00:13:50,340 --> 00:13:53,640
+بيقول
+
+131
+00:13:53,640 --> 00:13:59,640
+use the transformation use the trans
+
+132
+00:14:07,380 --> 00:14:17,100
+اللي هو ال X بدي ساوي U زائد نص V و ال Y بدي ساوي
+
+133
+00:14:17,100 --> 00:14:25,580
+V to evaluate the integral to evaluate the
+
+134
+00:14:25,580 --> 00:14:35,060
+integral مش هنتحسب التكامل اللي هو تكامل من Zero
+
+135
+00:14:35,060 --> 00:14:44,020
+للإتنينتكامل من y على 2 إلى y زائد أربعة كله على
+
+136
+00:14:44,020 --> 00:14:52,720
+اتنين لمن؟ لل y تكيب في 2x ناقص y في ال
+
+137
+00:14:52,720 --> 00:15:00,920
+exponential لل 2x ناقص y لكل ربيع لل dx
+
+138
+00:15:04,380 --> 00:15:12,660
+by writing it يعني
+
+139
+00:15:12,660 --> 00:15:22,580
+بكتابة هذا التكامل as an integral over
+
+140
+00:15:22,580 --> 00:15:50,960
+a region G a region G in theUV Play نمسح
+
+141
+00:15:50,960 --> 00:15:52,160
+الشجرة دي كلها بنات
+
+142
+00:16:16,520 --> 00:16:21,220
+نرجع لسؤال مرة تانية قال استخدم التحويل x يساوي u
+
+143
+00:16:21,220 --> 00:16:27,000
+زائد نص V وال Y تساوي V عشان نحوّل التكامل ان هو
+
+144
+00:16:27,000 --> 00:16:33,040
+الحمد لله شكله وشكلها ايضا By writing it بكتابتي ك
+
+145
+00:16:33,040 --> 00:16:38,580
+Integral over region G تمين في ال U V Plane نقوله
+
+146
+00:16:38,580 --> 00:16:43,580
+كويس اذا احنا خلّيني نحسب التكائل جاكوبيا ونحسب
+
+147
+00:16:43,580 --> 00:16:47,950
+حدود التكامل ونقلصها من مشكلتنا هذهكيف كانت تالية
+
+148
+00:16:47,950 --> 00:16:52,290
+يبقى ال X جاهزة و ال Y جاهزة يبقى على طول الخطب
+
+149
+00:16:52,290 --> 00:16:56,150
+نروح أسيبه ال Jacobian يبقى بدا جاهزه ال Jacobian
+
+150
+00:16:56,150 --> 00:17:02,710
+تبع ال U و ال V بده يساوي تفاضل ال X بالنسبة إلى U
+
+151
+00:17:02,710 --> 00:17:08,670
+تفاضل ال X بالنسبة إلى V تفاضل ال Y بالنسبة إلى U
+
+152
+00:17:08,670 --> 00:17:15,160
+تفاضل ال Y بالنسبة إلى Vباعطيني المحدد تفاضل X
+
+153
+00:17:15,160 --> 00:17:20,000
+بالنسبة ل U بقداشي بنامي واحد والباقية Zero تفاضل
+
+154
+00:17:20,000 --> 00:17:28,340
+X بالنسبة ل V كدهش نصف تفاضل Y بالنسبة ل U Zero
+
+155
+00:17:28,340 --> 00:17:34,920
+تفاضل Y بالنسبة ل V يبقى المحدد كدهش بساوي واحد
+
+156
+00:17:34,920 --> 00:17:41,850
+ممتاز جدا يبقى ضالة عندي حدود التكاملبدي اعرف حدود
+
+157
+00:17:41,850 --> 00:17:47,390
+التكمل هذه من ويل لويل بقوله بسيطة احنا بدنا نكمل
+
+158
+00:17:47,390 --> 00:17:55,470
+اول شئ بالنسبة لمين يبقى انا عندي x هنا تساوي y
+
+159
+00:17:55,470 --> 00:18:04,770
+زائد اربعة على اتنين هذا الكلام بدري اعطينا ال x
+
+160
+00:18:04,770 --> 00:18:14,000
+عندي بقداشU زي نص V يبقى هذا U زائد V على اتنين
+
+161
+00:18:14,000 --> 00:18:21,800
+بده يساوي ال Y عندى بقداش V يبقى هذه V على اتنين
+
+162
+00:18:21,800 --> 00:18:26,600
+زائد اتنين اربع على اتنين باتنين وشيلت ال Y وحطت
+
+163
+00:18:26,600 --> 00:18:31,140
+مكانها V اظل لو جبت ال V عند ال V بتروح الله يسهل
+
+164
+00:18:31,140 --> 00:18:33,700
+عليها بيعطينى جداش هنا و هنا
+
+165
+00:18:36,630 --> 00:18:43,770
+يبقى ال U تساوي قدراش اتنين اذا اتنين هذي بدت كافة
+
+166
+00:18:43,770 --> 00:18:49,290
+مين؟ بدت كافة Y زائد اربع على اتنين باجي بقوله
+
+167
+00:18:49,290 --> 00:18:56,870
+بتاخد X التانية X تساوي Y على اتنين ال U زائد V
+
+168
+00:18:56,870 --> 00:19:03,590
+على اتنين تساوي ال Y هادف Vعلى اتنين يبقى هذا بدي
+
+169
+00:19:03,590 --> 00:19:09,450
+اعطيك ان U تساوي كده؟ Zero يبقى هذا بدي اعطينا ان
+
+170
+00:19:09,450 --> 00:19:14,730
+U تساوي Zero يبقى هاي جيبت حدود التكامل تبع تمام
+
+171
+00:19:15,160 --> 00:19:21,380
+تبعت ال U بدي أجيب حدود التكمل تبعت ال V هذه Y لها
+
+172
+00:19:21,380 --> 00:19:26,220
+الحدود لإتنين اللي عندنا يبقى لما أقول Y تساوي
+
+173
+00:19:26,220 --> 00:19:32,080
+اتنين معناته ان V قداش تساوي اتنين لأن Y تساوي V
+
+174
+00:19:32,080 --> 00:19:38,300
+لما أقول Y تساوي Zero معناته V قداش تساوي Zero إذا
+
+175
+00:19:38,300 --> 00:19:43,270
+جبت حدود التكمل تبعت ال U و Vبضلّف عليه بس شغل
+
+176
+00:19:43,270 --> 00:19:50,170
+واحدة أحسبله قداش اتنين X ناقص Y كلها بدلالة U وP
+
+177
+00:19:50,170 --> 00:19:58,690
+بقوله بسيطة يبقى بدالي أخد اتنين X ناقص Y يبقى هاي
+
+178
+00:19:58,690 --> 00:20:05,270
+اتنين فيه ال X اللي عندي اللي هو U زائد V عليها
+
+179
+00:20:09,310 --> 00:20:16,490
+نقص وي يعني مجداش ناقص في افك الجوز هذا يبقى اتنين
+
+180
+00:20:16,490 --> 00:20:23,030
+يوم زائد في ناقص في ويسر مجداش يبقى الحين صارت قصة
+
+181
+00:20:23,030 --> 00:20:28,590
+بسيطة وسهلة طبعا ففاجي بقوله بدي أصير عندي التكامل
+
+182
+00:20:28,590 --> 00:20:34,670
+هذا على الشكل التالي ال وي تكيب يعني مين
+
+183
+00:20:39,020 --> 00:20:50,600
+و2x-y يعني 2u خلاصنا منها وهذه E أسعى 2U لكل تربيع
+
+184
+00:20:50,600 --> 00:20:56,540
+أيهم أسهل كامل بالنسبة الأول V of U فهذا البجي
+
+185
+00:20:56,540 --> 00:21:03,780
+بقوله DV DUوالحمد لله فاتوش لأن الاتنين كله من صفر
+
+186
+00:21:03,780 --> 00:21:08,660
+للاتنين يبقى هنا من zero لغاية اتنين ومن هنا من
+
+187
+00:21:08,660 --> 00:21:14,740
+zero لغاية اتنين هذا الكلام يساوي تكامل من صفر
+
+188
+00:21:14,740 --> 00:21:22,900
+للاتنين هذه عبارة عن V أس 4 على 4 من وين لوين من
+
+189
+00:21:22,900 --> 00:21:29,780
+zero لغاية اتنين ويبقى لعيني اتنين يومبمين في ال E
+
+190
+00:21:29,780 --> 00:21:37,440
+قوس 2U كل تربيع دي تمام
+
+191
+00:21:37,440 --> 00:21:47,200
+بدي أعود بالقيمة اللي فوق 16 على 4 4 في 2 8 يبقى
+
+192
+00:21:47,200 --> 00:21:56,370
+يصير من أن تكامل من 0 إلى 2 إلى 8Uفي E أس اتنين U
+
+193
+00:21:56,370 --> 00:22:00,570
+لكل تربية و الله ياش رأيك افكها بالمرة التانية دي
+
+194
+00:22:00,570 --> 00:22:05,510
+خلونا نخلص من هذه الشرقة هذه عبارة عن أربعة U
+
+195
+00:22:05,510 --> 00:22:07,010
+تربية D
+
+196
+00:22:10,640 --> 00:22:15,000
+يبقى صار سؤالي بسيط بعد بكلم كل كاهي غير شكل صار
+
+197
+00:22:15,000 --> 00:22:20,020
+بقى سؤالي بسيط جدا يعني ما علي اللي حط مال تعويضة
+
+198
+00:22:20,020 --> 00:22:23,900
+و بيكون خلصنا من هذه الشغله يعني كأنها بناتها دي
+
+199
+00:22:23,900 --> 00:22:33,890
+ايه كأنها تكاملللـ E أس T DT حيث الـ T تساوي أربعة
+
+200
+00:22:33,890 --> 00:22:41,450
+U تربيع لإن لو فضلت الـ DT بقى يقول تمانية U D U
+
+201
+00:22:41,450 --> 00:22:48,070
+هي التمانية U وهي الـ D U باقية حدود التكامل لما
+
+202
+00:22:48,070 --> 00:22:56,740
+تبقى U باتنين فصير T بقداش سبتاش16 و لما تبقى ال U
+
+203
+00:22:56,740 --> 00:23:01,720
+ب Zero بظل هذي ب Zero تكامل ال exponential بال
+
+204
+00:23:01,720 --> 00:23:09,000
+exponential itself من Zero لغاية 16 يبقى E أُس 16
+
+205
+00:23:09,000 --> 00:23:17,100
+ناقص E أُس Zero يعني E أُس 16 ناقص كده ناقص واحد
+
+206
+00:23:17,100 --> 00:23:23,940
+هذا قيمة ميم قيمة التكامل اللي موجود عندناطبعا
+
+207
+00:23:23,940 --> 00:23:30,100
+بإمكاني ارسم منطقة تكامل بس لمجرد اتعرف عليها لكن
+
+208
+00:23:30,100 --> 00:23:35,880
+ليس بالضرورة نرسمها بلاش
+
+209
+00:23:35,880 --> 00:23:42,220
+ريحتوني نجي ناخد المثال الرابع يبقى بغرف الأربع
+
+210
+00:23:42,220 --> 00:23:46,680
+use
+
+211
+00:23:46,680 --> 00:23:47,560
+the transformation
+
+212
+00:23:54,630 --> 00:24:02,270
+transformations استخدم التحويلات U تساوي X ناقص
+
+213
+00:24:02,270 --> 00:24:13,170
+الـY و V يساوي 2X زائد الـY تقول بالـU انتجرال
+
+214
+00:24:13,170 --> 00:24:17,910
+عشان
+
+215
+00:24:17,910 --> 00:24:19,830
+نحسب التكامل
+
+216
+00:24:23,280 --> 00:24:31,480
+w is the integral تكاملين على r للإتنين x تربيع
+
+217
+00:24:31,480 --> 00:24:43,580
+ناقص x y ناقص y تربيع كله dx dy for the region R
+
+218
+00:24:43,580 --> 00:24:52,620
+for the region R for the region R in the first
+
+219
+00:24:56,150 --> 00:25:02,030
+equadrant في الرابع الأول equadrant
+
+220
+00:25:02,030 --> 00:25:15,010
+bounded by the lines بالخطوط
+
+221
+00:25:15,010 --> 00:25:23,690
+المستقيمة y تساوي نقص اتنين x زائد اربعةY تساوي
+
+222
+00:25:23,690 --> 00:25:34,610
+نقص اتنين X زائد سبعة Y تساوي X نقص اتنين Y تساوي
+
+223
+00:25:34,610 --> 00:25:36,850
+X زائد واحد
+
+224
+00:26:08,460 --> 00:26:13,000
+نرجع لسؤالنا هذا مرة ثانية بقول استخدام الـ
+
+225
+00:26:13,000 --> 00:26:18,300
+Transformation يتحويل إلى U تساوي X ناقص Y و V
+
+226
+00:26:18,300 --> 00:26:23,500
+يساوي 2X زائد Y لكي تحسب ان التكمل لأن هذا على
+
+227
+00:26:23,500 --> 00:26:28,060
+المنطقة R في الربع الأول وهذه المنطقة محدودة
+
+228
+00:26:28,060 --> 00:26:35,080
+بالمستقيمات الأربع الأعلى هو البسيطة تعالى نشوفهذا
+
+229
+00:26:35,080 --> 00:26:39,940
+السؤال يختلف عن ثلاثة أسئلة السابقة ماطنيش حدود
+
+230
+00:26:39,940 --> 00:26:45,680
+التكامل انا بده اطلع حدود التكامل لحالي تمام يعني
+
+231
+00:26:45,680 --> 00:26:49,720
+اي واحدة بس قبل كان بيقول من كذا لكذا يبقى فجأة
+
+232
+00:26:49,720 --> 00:26:54,300
+بيعطيني حدود التكامل وبالتالي مشكلة هنا أصعب شوية
+
+233
+00:26:54,300 --> 00:27:02,200
+طيبوشغلة تانية ما اعطانيش انه x بدلالة u وv لأ
+
+234
+00:27:02,200 --> 00:27:07,760
+اعطاني u بدلالة x وy و اعطاني v بدلالة x وy يبقى
+
+235
+00:27:07,760 --> 00:27:13,240
+الخطوة الأولى عندي بدى اجيب ال x و ال y بدلالة u
+
+236
+00:27:13,240 --> 00:27:16,700
+وv حتى اقدر احسب ال jacobian وانا ماجبتوش ماقدرش
+
+237
+00:27:16,700 --> 00:27:22,090
+احسب ال jacobianبقوله كويس طيب تعالى بدنا نجيب من
+
+238
+00:27:22,090 --> 00:27:31,260
+المعادلاتين هدول X و Y بدلالة تمام تمام يبقىأصلا
+
+239
+00:27:31,260 --> 00:27:35,580
+لو جمعناهم يطير ال Y يجيب X دغري مش هيك يبقى بسيطة
+
+240
+00:27:35,580 --> 00:27:42,880
+باجي بقول انا عند ال U تساوي X نقص ال Y وعندي V
+
+241
+00:27:42,880 --> 00:27:50,520
+يساوي 2X زائد ال Y لو جمعت مباشرة بطلع عند ايش
+
+242
+00:27:50,520 --> 00:27:58,620
+بطلع عند انه تلاتة X بده يساوي U زائد V او ان شئته
+
+243
+00:27:59,080 --> 00:28:06,500
+فقولوا ان ال X بيساوي U زائد V كله على تلاتة أو U
+
+244
+00:28:06,500 --> 00:28:13,660
+على تلاتة زائد V على تلاتة جيبنا ال X إذا ما بنقدر
+
+245
+00:28:13,660 --> 00:28:19,720
+نجيب من ال Y فبجيب اخد المعادلة اللي عندها دي
+
+246
+00:28:19,720 --> 00:28:28,120
+فمنها بقول ان ال Y تساوي X ماقص ال Uجبنا هذا هنا
+
+247
+00:28:28,120 --> 00:28:33,780
+وهذا هنا يبقى هذا الكلام بيكون ساوي X عندي اللي
+
+248
+00:28:33,780 --> 00:28:39,160
+حصلنا عليها V على تلاتة او U زائد V على تلاتة يبقى
+
+249
+00:28:39,160 --> 00:28:46,620
+هذه U زائد V على تلاتة ناقص ال U يبقى بلاء عليه
+
+250
+00:28:46,620 --> 00:28:52,680
+هذا بدي يعطينا ان Y تساوي كله على تلاتة بيصير U
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+251
+00:28:53,040 --> 00:29:02,180
+زائد V ناقص تلاتة U إذا V ناقص اتنين U على تلاتة
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+252
+00:29:02,180 --> 00:29:12,380
+يبقى هذه قيمة X وهذه قيمة Y أو يساوي V على تلاتة
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+253
+00:29:12,380 --> 00:29:18,650
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+254
+00:29:18,650 --> 00:29:27,110
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+255
+00:29:27,110 --> 00:29:33,650
+الجيكوريا البالمرة نحسب الجيكوريا تبع ال U وال V
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+256
+00:29:33,650 --> 00:29:40,150
+تسوى المحدد تفاضل ال X بالنسبة إلى U تفاضل ال X
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+257
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+258
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+بالنسبة إلى V يساوي تفاضل X بالنسبة إلى U تلت
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+259
+00:29:55,730 --> 00:29:59,030
+تفاضل
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+260
+00:29:59,030 --> 00:30:07,650
+X بالنسبة إلى V تلت تفاضل Y بالنسبة إلى U سالب
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+261
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+تلتين يبقى سالب تلتين
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+262
+00:30:14,800 --> 00:30:25,840
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+265
+00:30:42,430 --> 00:30:47,650
+من هنا، شو ضال عندي؟ ضالت حدود التكامل وما أدرى
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+266
+00:30:47,650 --> 00:30:51,530
+كما حدود التكامل. طب كيف بدنا نحصل على حدود
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+267
+00:30:51,530 --> 00:30:55,310
+التكامل؟
+
+268
+00:30:55,310 --> 00:30:59,390
+وين القاطة التقاطة؟ يعني بدنا ندور عن قاطة
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+269
+00:30:59,390 --> 00:31:04,790
+التقاطة، صح؟ أنا عند رأي آخر، أنا عندي أربعة
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+270
+00:31:04,790 --> 00:31:10,060
+مستخدمات حتى الآن مستخدمتهمش،بظبط ؟ طب إذا بدي
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+271
+00:31:10,060 --> 00:31:16,100
+أروح أحوّل المستقيمات هذه من ال X و ال Y إلى مين؟
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+00:31:16,100 --> 00:31:19,100
+إلى ال Y و ال B و ال E و الشباطين إذا لو جيت
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+273
+00:31:19,100 --> 00:31:28,600
+للمستقيم الأول اللي هو Y تساوي ناقص 2X زات 4 Y
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+274
+00:31:28,600 --> 00:31:34,900
+جاهزة علم هذا هي V على تلاتة ناقص 2U على تلاتة
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+275
+00:31:34,900 --> 00:31:47,860
+يبقى Vعلى تلاتة ناقص اتنين U على تلاتة تساوي تساوي
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+276
+00:31:47,860 --> 00:31:52,900
+ال X كمان جاهزة عندنا هاي يبقى بالظروف هيدا شبه ما
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+277
+00:31:52,900 --> 00:31:57,720
+انا اقول فالسالب اتنين يبقى السالب اتنين U على
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+278
+00:31:57,720 --> 00:32:11,080
+تلاتة سالب اتنينU على تلاتة و سالب اتنين
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+279
+00:32:11,080 --> 00:32:20,480
+V على تلاتة سالب اتنين V على تلاتة زائد اربع اطلع
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+280
+00:32:20,480 --> 00:32:26,620
+هذه وهذه وروحوا مع بعض تمام بنجيب ال V عند هذه
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+281
+00:32:26,620 --> 00:32:34,080
+بيصير كده عندهبصير تلاتي يعني V هذي لو جت عند هذي
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+282
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+بصير تلت و تلتين تبقى واحد صحيح هذا بدي أعطيك V
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+283
+00:32:39,320 --> 00:32:46,080
+تساوي أربع والله كويس هذا يعني شغل كويس طب لو جت
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+284
+00:32:46,080 --> 00:32:49,640
+قلت واكتس اتنين
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+285
+00:33:00,940 --> 00:33:08,560
+يبقى ال V على تلاتة نقص اتنين U على تلاتة يساوي
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+286
+00:33:08,560 --> 00:33:14,580
+نقص اتنين U على تلاتة نقص اتنين V على تلاتة زائد
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+287
+00:33:14,580 --> 00:33:18,260
+سبعة يبقى V تساوي سبعة
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+288
+00:33:22,570 --> 00:33:28,410
+يبقى لدينا مستقيمات اتنين يبقى Y تساوي X ناقص
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+289
+00:33:28,410 --> 00:33:38,530
+اتنين Y تساوي X ناقص اتنين Y ماتغيرتش يبقى B على
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+290
+00:33:38,530 --> 00:33:44,090
+تلاتة ناقص اتنين U على تلاتة و X ماتغيرتش بس مش
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+291
+00:33:44,090 --> 00:33:48,270
+مضروبة ولا في حاجة إلا يبقى بحطها زي ما هي U على
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+292
+00:33:48,270 --> 00:33:56,190
+تلاتةزائد V على تلاتة ناقص اتنين اظن V على تلاتة
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+293
+00:33:56,190 --> 00:34:01,130
+لو راح تنبيها تلاتة مع السلامة هذه لو اجت تصيير
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+294
+00:34:01,130 --> 00:34:09,030
+عندها ناقص U ناقص U بده يسوي ناقص اتنين يبقى U
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+00:34:09,030 --> 00:34:16,570
+تسوي كده اتنين بالمثل Y تسوي X زايد واحد اظن X
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+296
+00:34:16,570 --> 00:34:23,360
+زايد واحدimply ان v ع تلاتة نقص اتنين و على تلاتة
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+297
+00:34:23,360 --> 00:34:30,020
+بدها تساوي u ع تلاتة زائد v ع تلاتة زائد واحد v ع
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+298
+00:34:30,020 --> 00:34:35,840
+تلاتة مع v ع تلاتة هذه هنا بصير عندك u تساوي جدار
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+299
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+الواحد يبقى ال U من واحدة لإتنين وال V من أربعة
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+300
+00:34:41,250 --> 00:34:46,150
+إلى سبعة إذا نحددنا حدود التكامل يبقى مش ضايل إلا
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+301
+00:34:46,150 --> 00:34:53,610
+انعوض في المسألة تبعتنا فقط لا غير كم؟
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+302
+00:34:53,610 --> 00:35:02,090
+U باتنين هذي طيب استني شوية جيب ال U هذي بس أه سهل
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+303
+00:35:02,090 --> 00:35:02,330
+يا بابا
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+304
+00:35:05,420 --> 00:35:10,740
+طيب يبقى لم يبقى لنا إلا نعوض في التكمل مباشرة
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+305
+00:35:10,740 --> 00:35:16,560
+يبقى التكمل تبعنا يصير بالشكل اللي عناه الآن بدنا
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+306
+00:35:16,560 --> 00:35:24,260
+نجلد لانه 2 X تربيع يبقى 2 فيه جل ال X تربيع يبقى
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+307
+00:35:24,260 --> 00:35:29,540
+هاي هاي ال X تربيع اللي همين او هادي سيئة يبقى
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+308
+00:35:29,540 --> 00:35:36,840
+بقدر اقول له U على 3 Uعلى تلاتة و الله خلّيها إيش
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+309
+00:35:36,840 --> 00:35:43,800
+رأيك U زائد V كلها على تلاتة مرة واحدة الكل تربية
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+310
+00:35:43,800 --> 00:35:53,120
+بعديها ناقص X له U زائد V على تلاتة تمينفي ال Y ال
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+311
+00:35:53,120 --> 00:35:58,060
+Y اللي هو V على تلاتة نقص اتنين U على تلاتة V على
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+312
+00:35:58,060 --> 00:36:06,360
+تلاتة نقص اتنين U على تلاتة نقص Y ترابيع V على
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+313
+00:36:06,360 --> 00:36:13,320
+تلاتة نقص اتنين U على تلاتة الكل ترابيع يبقى ايه
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+314
+00:36:13,320 --> 00:36:18,880
+الدول العالمين ضايل عندنا الجاكوبين الجاكوبين
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+315
+00:36:18,880 --> 00:36:26,480
+حسبنا وجيناه طولأقول يا بنات هنا سهلة بالنسبة ليوم
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+316
+00:36:26,480 --> 00:36:30,020
+في الأول و بالنسبة لي ميلي اتنين اردسهم لأنهم
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+317
+00:36:30,020 --> 00:36:37,700
+اعداد و تأثيريه زي تأثيري بيه اذا لو راحت قلتل DVD
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+318
+00:36:37,700 --> 00:36:44,600
+بقى الحدود التكامل بيه بتتغير من عند الأربعة لغاية
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+319
+00:36:44,600 --> 00:36:49,160
+السابعة و اليوم بتتغير من سنة واحدة لغاية اتنين
+
+320
+00:36:49,880 --> 00:36:55,020
+تمام؟ يبقى ضال علينا بصر بصر هالمثلة تبقى حلة
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+321
+00:36:55,020 --> 00:37:00,460
+المشكلة هنا هي التلت برا تكامل من سالب واحد لإتنين
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+322
+00:37:00,460 --> 00:37:05,760
+تكامل من أربعة لسبعة بدا أفك هذا يا بنات يبقى هذا
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+323
+00:37:05,760 --> 00:37:13,940
+ايش مصير؟ تسعين في ال U تربية زائد اتنين U V زائد
+
+324
+00:37:13,940 --> 00:37:17,980
+B تربية مربع التلتة بتسعى وعندي اتنين برا يبقى
+
+325
+00:37:17,980 --> 00:37:25,300
+تسعين وI فكتنجي لبعض هذه تلت في تلت بطلع برا في
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+326
+00:37:25,300 --> 00:37:35,160
+كده اش ابتسع تمام نضرب هدول في بعض يبقى هذه U في V
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+327
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+U في V هذه الناقص اتنين U تربيعوهنا زائد V تربيع
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+328
+00:37:47,340 --> 00:37:54,020
+نقص اتنين U في ال V والتلاتة مع التلاتة مع التلاتة
+
+329
+00:37:54,020 --> 00:37:55,400
+طلعت برا بالمرة
+
+330
+00:38:01,460 --> 00:38:06,160
+ما رايك اخد التسعة برا بالمرة يالا سهللي الشغل هاي
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+331
+00:38:06,160 --> 00:38:12,460
+التسعة برا بيضل عندنا مين؟ بيضل عندنا هنا V تربيع
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+332
+00:38:12,460 --> 00:38:21,960
+ناقص اربعة U في ال V زائد اربعة U تربيع بظبط هيك؟
+
+333
+00:38:21,960 --> 00:38:29,180
+خلصنا منها طيب بدي امسح بس القرن هذيمش هنكمل
+
+334
+00:38:29,180 --> 00:38:37,520
+مسألتنا، لحد هنا قفلنا و هذا ال DVD طيب،
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+335
+00:38:37,520 --> 00:38:43,300
+إيش رايك؟ تسعة مع تسعة مع تسعة نطلع ورا، وعندي هنا
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+336
+00:38:43,300 --> 00:38:45,520
+طول بصير واحد على سبعة وإيش؟
+
+337
+00:38:54,250 --> 00:38:59,570
+هي تكمل من اربع الى سبعة و هيتكمل من اربع الى
+
+338
+00:38:59,570 --> 00:39:01,090
+اتنين
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+339
+00:39:02,970 --> 00:39:09,510
+زائد أربعة U في V زائد اتنين V تربيع فكّيت الجثث
+
+340
+00:39:09,510 --> 00:39:14,430
+الأول بدا أدخل إشارة السلف على الجثث الثاني يبقى
+
+341
+00:39:14,430 --> 00:39:22,110
+ناقص U في V زائد اتنين U تربيع ناقص V تربيع زائد
+
+342
+00:39:22,110 --> 00:39:28,790
+اتنين U في Vاللي بعده هدخل إشارة ناقص يبقى ناقص V
+
+343
+00:39:28,790 --> 00:39:36,670
+تربيع زائد أربع U في V ناقص أربع U تربيع قفل الجوز
+
+344
+00:39:36,670 --> 00:39:43,150
+وهذا كله مين؟ كله DVD
+
+345
+00:39:46,240 --> 00:39:52,020
+فهذا كلام مدهسان واحد على سبعة وعشرين تكمل من سالب
+
+346
+00:39:52,020 --> 00:39:57,020
+واحد للاتنين تكمل من اربعة الى سبعة طلع يا بنات
+
+347
+00:39:57,020 --> 00:40:03,400
+اتنين U تربيع و اتنين U تربيع اربعة U تربيع و سالب
+
+348
+00:40:03,400 --> 00:40:09,820
+اربعة U تربيع غير مأسوف عليهم مع السلامة ندى نشوف
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+00:40:09,820 --> 00:40:20,180
+ال U في ال V اربعة U في Vو اتنين U في V بستة U في
+
+350
+00:40:20,180 --> 00:40:27,360
+V شيل منهم واحد و يظل خمسة U في V و اربعة تسعة U
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+351
+00:40:27,360 --> 00:40:36,630
+في V يبقى تسعة U في ال V ال V تربيعيبقى هذا اتنين
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+352
+00:40:36,630 --> 00:40:43,110
+في تربيع و سالب واحد في تربيع و سالب واحد في تربيع
+
+353
+00:40:43,110 --> 00:40:49,350
+برضه غير مأسوف على شبابهم يبقى مع السلام شو ضايق
+
+354
+00:40:49,350 --> 00:40:54,910
+عندي؟ مش ضايق الا دي VDU وضعيق كويس يعني هذا
+
+355
+00:40:54,910 --> 00:40:59,570
+اختصار ممتاز جدا طب ماهيش رأيك تسعة مع تسعة كمان
+
+356
+00:40:59,570 --> 00:41:05,500
+الطير؟مع الصلامة يبقى هذا الكلام بده يساوي الطول
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+357
+00:41:05,500 --> 00:41:11,460
+وهي تكامل من سالب واحد دليل اتنين تكامل من اربعة
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+00:41:11,460 --> 00:41:20,920
+لغاية سبعة لل U V D V D U نمسح اللي فوق هذا اللي
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+359
+00:41:20,920 --> 00:41:21,900
+مالك شخصيات
+
+360
+00:41:36,130 --> 00:41:42,630
+طيب هذا الكلام يساوي قلت مالكش دعوة وتكامل من سالب
+
+361
+00:41:42,630 --> 00:41:48,590
+واحد لغاية اتنين ونجي نكامل بالنسبة الى V يبقى V
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+00:41:48,590 --> 00:41:55,310
+تربيع على اتنين V تربيع على اتنين من عند الأربعة
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+363
+00:41:55,310 --> 00:42:02,860
+لغاية السبعة وبظل عندنا U في الديم تماممش رايك
+
+364
+00:42:02,860 --> 00:42:09,340
+نطلع النص برا مع تلس فصير كده؟ فصير سُدس تكامل من
+
+365
+00:42:09,340 --> 00:42:15,880
+سالب واحد إلى اتنين و سبعة في سبعة في تسعة واربعين
+
+366
+00:42:15,880 --> 00:42:24,900
+ناقص اربع في اربع اللي هو ست عشر كله خلصنا منه في
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+367
+00:42:24,900 --> 00:42:32,800
+ال UDأظن ستة من تسعة بيظل تلاتة و تلاتين يبقى هذا
+
+368
+00:42:32,800 --> 00:42:39,480
+هنا بصير تلاتة و تلاتين على ستة تكامل من سالب واحد
+
+369
+00:42:39,480 --> 00:42:45,640
+لليتنين لليوديو هذا الكلام بده يساوي تلاتة و
+
+370
+00:42:45,640 --> 00:42:51,160
+تلاتين على ستة في اختصار على تلاتة بيظل احداشر على
+
+371
+00:42:51,160 --> 00:42:59,510
+اتنينوهذه 6 يتربي على الاتنين من سالب واحد لغاية
+
+372
+00:42:59,510 --> 00:43:09,390
+اتنين يبقى هذا الكلام 11 على 4 فيه هنا أربع ناقص
+
+373
+00:43:09,390 --> 00:43:14,970
+ناقص واحد تربيه لهو قدر بواحد بضل تلاتة في احداشر
+
+374
+00:43:14,970 --> 00:43:22,550
+تلاتة و تلاتين على أربع قيمة هذا التكاملحاضرة فيك
+
+375
+00:43:22,550 --> 00:43:28,390
+ما بتحب تسأل أي سؤال هنا؟ خلاص؟
+
+376
+00:43:28,840 --> 00:43:33,060
+طيب أخدنا الأن بدل المثال أربع على ال double
+
+377
+00:43:33,060 --> 00:43:41,960
+integral ننتقل الأن لل triple integral لأن إذا
+
+378
+00:43:41,960 --> 00:43:45,380
+انتقلنا لل triple integral للنقطة الثانية من هذا
+
+379
+00:43:45,380 --> 00:43:50,140
+ال section نحتاج أن نذهب نحسن ال Jacobian الأول
+
+380
+00:43:50,140 --> 00:43:54,420
+لأنه سيصبح عندي بدل المتغير جدا كمان يعني لأن عندي
+
+381
+00:43:54,420 --> 00:44:03,310
+X وY وZالجبال هم هيكون U و V و W بدل ما كنا نشتغل
+
+382
+00:44:03,310 --> 00:44:08,390
+فيه في الليل، بدنا نشتغل في ال space، الفراغ،
+
+383
+00:44:08,390 --> 00:44:16,190
+كويس؟ يا فجأة؟ فنمسح هذا و ننتقل الأن إلى الشغل في
+
+384
+00:44:16,190 --> 00:44:16,870
+ال space
+
+385
+00:44:41,810 --> 00:44:54,650
+نمسح هذه خلاص يبقى
+
+386
+00:44:54,650 --> 00:44:59,270
+ننتقل إلى النقطة الثانية من هذا ال section وهي
+
+387
+00:44:59,270 --> 00:45:05,490
+substitution substitution
+
+388
+00:45:05,490 --> 00:45:09,270
+and
+
+389
+00:45:09,270 --> 00:45:10,730
+triple
+
+390
+00:45:21,060 --> 00:45:24,160
+نفس المعلومات لذلك بدنا نقوم باستخدام جاكوبيا ان
+
+391
+00:45:24,160 --> 00:45:30,780
+دوري نقوم باستخدام جاكوبيا ان دوري
+
+392
+00:45:33,330 --> 00:45:38,370
+سيكون محدد ثلاثي أو من الدرجة التالتة وليس من
+
+393
+00:45:38,370 --> 00:45:43,810
+الدرجة الثالثة يبقى بقول هنا partial x على partial
+
+394
+00:45:43,810 --> 00:45:47,870
+u partial x على partial y هذه كانت في المحدد
+
+395
+00:45:47,870 --> 00:45:53,970
+الثلاثي باضيف عليها partial x على partial main w
+
+396
+00:45:53,970 --> 00:45:59,390
+اللي عملنا لل x بدنا نروح نعمله ل main لل y يبقى
+
+397
+00:45:59,390 --> 00:46:05,390
+partial yعلى partial W.اللي عملناه دروايب نروح
+
+398
+00:46:05,390 --> 00:46:10,130
+نعمله للـ Z على partial U و partial Z على partial
+
+399
+00:46:10,130 --> 00:46:19,650
+V و partial Z على partial W. هذا المحدد بالله.طيب
+
+400
+00:46:19,650 --> 00:46:25,250
+بدنا نبدأ نعطي أمثلة على ذلك وسأبدأ ان شاء الله
+
+401
+00:46:25,250 --> 00:46:35,500
+بما وعدناكوا به قبل ذلك.يبقى examples بدنا
+
+402
+00:46:35,500 --> 00:46:46,700
+نبدأ بأول detail بيقول ان spherical coordinates
+
+403
+00:46:46,700 --> 00:46:51,360
+find
+
+404
+00:46:51,360 --> 00:46:55,420
+الجقابل
+
+405
+00:46:55,420 --> 00:46:58,640
+تبع الروة وفاى وثيتا
+
+406
+00:47:08,590 --> 00:47:14,130
+طب اذا عارفين الإجابة كداش الإجابة؟ Rotary بي
+
+407
+00:47:14,130 --> 00:47:19,250
+assign في إذا بدي أوصل لهذه الإجابة بتروح اكتب X
+
+408
+00:47:19,250 --> 00:47:25,570
+بدلالة رو و في و ثيتا Y بدلالة رو و في و ثيتا Z
+
+409
+00:47:25,570 --> 00:47:32,970
+بدلالة رو و في و ثيتا طيب نجي الآن ال X كداش ال X
+
+410
+00:47:32,970 --> 00:47:34,790
+يا بنات اخدها المرة الماضية
+
+411
+00:47:39,520 --> 00:47:51,100
+cos θ الان ال y كانت ره صين فاي صين ثيتا إذا كانت
+
+412
+00:47:51,100 --> 00:47:59,000
+كده ره قصين فاي أبصر كده في تيتا ولا فيش تيتا بلاش
+
+413
+00:47:59,000 --> 00:48:07,040
+يبقى بنا نروح ناخد جاكوبيا تبع ره وفاي وثيتا وغير
+
+414
+00:48:07,040 --> 00:48:13,190
+المحدديبقى بالنا تفاضل ال X بالنسبة لأول متغير،
+
+415
+00:48:13,190 --> 00:48:18,070
+مين أول متغير؟ اللي هو ال raw يبقى partial X على
+
+416
+00:48:18,070 --> 00:48:24,630
+partial raw اللي هو مين بيطلع عندنا؟ Psi Phi Cos
+
+417
+00:48:24,630 --> 00:48:31,350
+Phi partial X على partial Phi اللي هو مين؟
+
+418
+00:48:36,000 --> 00:48:41,440
+ثيتا والرو مانهم مش علاقة بعدك بتفضل X بالنسبة
+
+419
+00:48:41,440 --> 00:48:45,100
+لثيتا الرو ساين الفاي مانهم مش علاقة ال cosine
+
+420
+00:48:45,100 --> 00:48:56,000
+بسالب ساين يبقى سالب رو ساين فاي ساين ثتر خلاص من
+
+421
+00:48:56,000 --> 00:48:59,700
+الصف الأول في المحدد نجي للصف الثاني اللي عملنا ال
+
+422
+00:48:59,700 --> 00:49:01,980
+X بنروح نعمله لمين ل Y
+
+423
+00:49:07,130 --> 00:49:13,810
+تفاضلها بالنسبة ل رو تفاضلها بالنسبة لفاي يبقى رو
+
+424
+00:49:13,810 --> 00:49:24,250
+كوساين فاي ساين ثيتا تفاضلها بالنسبة لثيتا يبقى رو
+
+425
+00:49:24,250 --> 00:49:29,610
+ساين فاي مالكش دعوة وتفاضلوا الـSin بكساين ثيتا
+
+426
+00:49:29,610 --> 00:49:35,450
+نيجي للصف التالت نفضل الـZ بالنسبة إلى رو
+
+427
+00:49:37,910 --> 00:49:45,210
+بنفضلها بالنسبة لفاي يبقى ماقصره في صين الفاي
+
+428
+00:49:45,210 --> 00:49:54,070
+بنفضلها بالنسبة لثيتا يبقى بزيرو نفك هذا المحدد
+
+429
+00:49:54,070 --> 00:50:02,550
+باستخدام عناصر الصفرالعمود الأخضر صف التالت أو
+
+430
+00:50:02,550 --> 00:50:09,530
+العمود التالت لإن فيه Zero يختصر لي طول القيمة
+
+431
+00:50:09,530 --> 00:50:14,130
+يفجأ باجي بقول له هذا المحدد بالدرسية هو cosine
+
+432
+00:50:14,130 --> 00:50:20,410
+فايفين هو شو طويل صفه هو عموده فماشي بيبقى اللي
+
+433
+00:50:20,410 --> 00:50:27,090
+عندنا قاعد البلد عشان ما تقلشاحنا هنا يبقى ر تربيع
+
+434
+00:50:27,090 --> 00:50:36,030
+صين فاي كوسين فاي كسين تربيع تتر يبقى هاي ر تربيع
+
+435
+00:50:36,030 --> 00:50:43,190
+ر تربيع ر
+
+436
+00:50:43,190 --> 00:50:54,880
+تربيع كسين ولا صينفاي كوساين فاي كوساين تربيع ثيتا
+
+437
+00:50:54,880 --> 00:51:01,180
+ناقص الثانوي فى عندى إشارة ناقص بصير زرق قراءة
+
+438
+00:51:01,180 --> 00:51:10,920
+تربيع صين فاي كوساين فاي صين تربيع ثيتا قفلنا
+
+439
+00:51:10,920 --> 00:51:15,590
+القصربعد ذلك وصلنا لهذه حسب قاعدة الشباط اللي
+
+440
+00:51:15,590 --> 00:51:21,630
+شباطها بعيد كان ناقص مع ناقص بيصير زائد يبقى زائد
+
+441
+00:51:21,630 --> 00:51:32,850
+رو في صين فاي فايها برا نجي اشطق صفه و عموده اش
+
+442
+00:51:32,850 --> 00:51:39,750
+بيصير عندنا رو صين تربيع فاي و صين تربيع تتا
+
+443
+00:51:47,650 --> 00:51:54,250
+الرئيسي ناقص مع ناقص بيصير زائد وهذه الرقم بضلال
+
+444
+00:51:54,250 --> 00:51:59,290
+نمين يبقى ساين تربية في ساين تربية ثيتا يبقى ساين
+
+445
+00:51:59,290 --> 00:52:06,730
+تربية في ساين تربية ثيتا قفل للجوز زائد زيرو في
+
+446
+00:52:06,730 --> 00:52:11,590
+محدد و بزير يبقى سرنجل يكوبي
+
+447
+00:52:14,580 --> 00:52:20,900
+وثيتا بده يسار على الاقل هناك واضح ان عندي رو
+
+448
+00:52:20,900 --> 00:52:28,240
+تربيع صين فاي كوسين فاي عامل مشترك وعندي كوسين برا
+
+449
+00:52:28,240 --> 00:52:36,440
+فبصير رو تربيع صين فاي كوسين تربيع فاي يبقى هاي رو
+
+450
+00:52:36,440 --> 00:52:44,640
+تربيع كوسين تربيع في في صين الفايأخدنا رو تربيع
+
+451
+00:52:44,640 --> 00:52:50,540
+فاي كوساين فاي برا كدهش بيبقى لدي هنا بنات كوساين
+
+452
+00:52:50,540 --> 00:52:55,560
+تربيع ثيتا طيب أخدنا رو تربيع برا و أخدنا كوساين
+
+453
+00:52:55,560 --> 00:53:01,960
+كوساين بيبقى زائد مين؟ زائد ساين تربيع ثيتا هذا
+
+454
+00:53:01,960 --> 00:53:07,900
+الترم الأول نجي للترم التاني عندك هنا رو ساين
+
+455
+00:53:07,900 --> 00:53:21,230
+تربيع فاي عامل مشتركوعندك رو صين فاي برا يبقى
+
+456
+00:53:21,230 --> 00:53:33,410
+زائد رو صين او رو تربيع صين تكيب فاي برا هذا يعني
+
+457
+00:53:33,410 --> 00:53:36,810
+كوصين تربيع تيتا زائد كوصين تربيع تيتا
+
+458
+00:53:40,640 --> 00:53:47,220
+زائد صين تربية تسعة طبعا هذه كدهش و هذه كدهش واحد
+
+459
+00:53:47,220 --> 00:53:52,500
+راحة يبقى هذا الكلام بالدوسام شو رايك؟ عندي رو
+
+460
+00:53:52,500 --> 00:53:59,780
+تربية موجودة في الإتنين وعندي صين في موجودة في
+
+461
+00:53:59,780 --> 00:54:05,600
+الإتنينيبقى بضال عندي هنا قداش و sign تربية فيه و
+
+462
+00:54:05,600 --> 00:54:10,960
+هنا بضال قداش عندي sign تربية فيه لانه خد sign برا
+
+463
+00:54:10,960 --> 00:54:17,080
+اللي بين قسين قداش يبقى هذا كمان بواحد يبقى بضال
+
+464
+00:54:17,080 --> 00:54:23,860
+قداش ر تربية sign فيهوهذا ما وعدناكم به في
+
+465
+00:54:23,860 --> 00:54:30,380
+المحاضرة الماضية لما انحولنا من DX DY DZ إلى D ρو
+
+466
+00:54:30,380 --> 00:54:35,600
+D فاي D ثيتا ضربنا في روتر بيه sign فاي ويومها كان
+
+467
+00:54:35,600 --> 00:54:39,240
+السؤال من أين لك هذا فقلنا لكم ان شاء الله في ال
+
+468
+00:54:39,240 --> 00:54:42,140
+section القادم اللي هو ال section اللي بين ايدينا
+
+469
+00:54:42,140 --> 00:54:48,360
+اليوم وها نحن نفي بوعدنا طيب حد إلى أي تساؤل هذا
+
+470
+00:54:48,360 --> 00:54:50,300
+قبل أن أذهب إلى المثال الثاني
+
+471
+00:54:55,430 --> 00:55:04,670
+تالث نسمة بيقول let D be the region let D be the
+
+472
+00:55:04,670 --> 00:55:19,350
+region عبارة عن المنطقة N X Y Z space defined
+
+473
+00:55:19,350 --> 00:55:22,810
+by the inequalities defined
+
+474
+00:55:23,950 --> 00:55:34,450
+by the inequalities المتباينات
+
+475
+00:55:34,450 --> 00:55:40,450
+ال X أكبر من أو يساوي واحد وأقل من أو يساوي اتنين
+
+476
+00:55:40,450 --> 00:55:46,970
+وال X في Y أكبر من أو يساوي Zero أقل من أو يساوي
+
+477
+00:55:46,970 --> 00:55:52,630
+اتنين وال Z أكبر من أو يساوي Zero أقل من أو يساوي
+
+478
+00:55:52,630 --> 00:55:52,990
+واحد
+
+479
+00:55:59,070 --> 00:56:04,010
+خلّي أحسب Value
+
+480
+00:56:04,010 --> 00:56:16,850
+تلت تكمنات على D لمين لل X تربيع Y زائد تلاتة XYZ
+
+481
+00:56:16,850 --> 00:56:26,490
+كل هذا DX DY DZ By applying
+
+482
+00:56:30,360 --> 00:56:41,800
+applying the transformation the transformation
+
+483
+00:56:41,800 --> 00:56:45,800
+ال
+
+484
+00:56:45,800 --> 00:56:56,080
+U بده يساوي ال X و ال V بده يساوي ال XY و ال W بده
+
+485
+00:56:56,080 --> 00:57:07,420
+يساوي تلاتة Zand integrate over
+
+486
+00:57:07,420 --> 00:57:20,480
+an appropriate region
+
+487
+00:57:20,480 --> 00:57:26,300
+D in
+
+488
+00:57:26,300 --> 00:57:28,100
+the
+
+489
+00:57:31,390 --> 00:57:37,210
+W Space الـ U V W Space
+
+490
+00:58:15,770 --> 00:58:20,850
+بنرجع لسؤالنا مرة ثانية، بيقول افترض D هي المنطقة
+
+491
+00:58:20,850 --> 00:58:26,150
+اللي في ال X,Y,Z space والمعرفة بالمتباينات X
+
+492
+00:58:26,150 --> 00:58:33,090
+محصورة بين 1 و 2، X في ال Y محصورة بين 0 و 2، Z
+
+493
+00:58:33,090 --> 00:58:39,850
+محصورة بين Z و 1يقول احسبلي التكمل اللى قدامنا هذى
+
+494
+00:58:39,850 --> 00:58:44,210
+كيف By applying that transformation يبقى اعطانى
+
+495
+00:58:44,210 --> 00:58:51,150
+تحويلة ال U تسوى ال X ال V تسوى ال X في Y ال W
+
+496
+00:58:51,150 --> 00:58:57,080
+يسوى تلاتة Zالأصل أنه يعطيني الـ z بدلالة
+
+497
+00:58:57,080 --> 00:59:01,600
+المتغيرات التلاتة هنا لكن هنا ياشقال بمين الموضوع
+
+498
+00:59:01,600 --> 00:59:08,560
+إذا شغلتنا أحسب كله من x و y و z بدلالة ال u و ال
+
+499
+00:59:08,560 --> 00:59:12,040
+v و ال w وبعد هيك نشوف كيف يصير
+
+500
+00:59:17,890 --> 00:59:22,410
+أفضل لما أقول لي ال U تساوي ال X يبقى ال X بتساوي
+
+501
+00:59:22,410 --> 00:59:32,350
+ال U تمام؟ انا بدي ال Y V على X و ال X بقدرش ب U
+
+502
+00:59:32,350 --> 00:59:40,770
+يبقى هذا بدي أعطيك ان Y تساوي V على U و هذه ال Z
+
+503
+00:59:40,770 --> 00:59:48,350
+بتساوي طول W أو W على 3يبقى بناء ان علي اروح نكتب
+
+504
+00:59:48,350 --> 00:59:54,050
+المتغيرات اللى عندى بدلالة من المتغيرات الجديدة
+
+505
+00:59:54,050 --> 00:59:59,290
+اللى هو U وV وW لذا نخليه نحسب ال Jacobian بالمرة
+
+506
+00:59:59,290 --> 01:00:08,890
+ال Jacobian تبع ال U و ال V و ال W في هذه المحددة
+
+507
+01:00:08,890 --> 01:00:14,630
+بنجي هنا partial X على partial U partial Xعلى
+
+508
+01:00:14,630 --> 01:00:20,250
+partial v partial x على partial w partial y على
+
+509
+01:00:20,250 --> 01:00:25,390
+partial u partial y على partial v partial y على
+
+510
+01:00:25,390 --> 01:00:30,810
+partial w partial z على partial u partial z على
+
+511
+01:00:30,810 --> 01:00:35,370
+partial v partial z على partial w
+
+512
+01:00:38,600 --> 01:00:44,800
+يبقى هذا هو المحدد تمام تفاض ال X بالنسبة إلى U
+
+513
+01:00:44,800 --> 01:00:50,280
+بواحد تفاض ال X بالنسبة ل V و بالنسبة ل W ب Zero
+
+514
+01:00:50,280 --> 01:00:57,580
+ماعنديش يبقى هاي Zero وهاي Zeroتفاضل ال Y بالنسبة
+
+515
+01:00:57,580 --> 01:00:58,500
+إلى U
+
+516
+01:01:10,600 --> 01:01:14,740
+طيب صبر شو بس بس بس بس بس بس بس بس بس بس بس بس بس
+
+517
+01:01:14,740 --> 01:01:14,920
+بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس
+
+518
+01:01:14,920 --> 01:01:20,000
+بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس
+
+519
+01:01:20,000 --> 01:01:22,660
+بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس
+
+520
+01:01:22,660 --> 01:01:22,800
+بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس
+
+521
+01:01:22,800 --> 01:01:22,880
+بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس
+
+522
+01:01:22,880 --> 01:01:31,840
+بس بس بس بس بس بس بس بس بس
+
+523
+01:01:31,840 --> 01:01:40,630
+بس بماشي يبقى هو ال V مالوش دعوة و ال 1 علي U سالب
+
+524
+01:01:40,630 --> 01:01:46,590
+1 علي U تربية يبقى سالب V علي U تربية يبقى سالب V
+
+525
+01:01:46,590 --> 01:01:53,150
+علي U تربية طب بدنا تفاضلها بالنسبة ل V 1 علي U
+
+526
+01:01:53,150 --> 01:02:00,050
+يبقى 1 علي U يبقى تفاضلها بالنسبة ل مين ل W بزيرو
+
+527
+01:02:00,050 --> 01:02:10,010
+طب بدنا ل Z بالنسبة ل Uزيرو وزيرو هنا طول يالله يا
+
+528
+01:02:10,010 --> 01:02:17,170
+بنات قداش؟ يعني
+
+529
+01:02:17,170 --> 01:02:23,590
+قداش الجواب دي هو اللي هيكأليس محدد لمصوفة مثلثة
+
+530
+01:02:23,590 --> 01:02:29,010
+سفلة يبقى حاصل ضرب عناصر القطر الرئيسي فقط ده يغير
+
+531
+01:02:29,010 --> 01:02:33,950
+لإنه يطلع هي القطر الرئيسي ولفوق كل أسفار محدد
+
+532
+01:02:33,950 --> 01:02:37,630
+المصوفة المثلثة العليا أو المصوفة المثلثة السفلة
+
+533
+01:02:38,800 --> 01:02:42,420
+حاصل ضرب عناصر القطر الرئيسي أو الـ scalar matrix
+
+534
+01:02:42,420 --> 01:02:47,060
+يبقى بس بنضرب حاصل ضرب عناصر القطر الرئيسي ينفذش
+
+535
+01:02:47,060 --> 01:02:52,320
+بيطلع واحد على تلاتة U مش مصدقة تعالى انفك
+
+536
+01:02:52,320 --> 01:02:57,240
+باستخدام عناصر الصف الأول وشط بصفه عموده كل واحد
+
+537
+01:02:57,240 --> 01:03:02,110
+على Uفي تلت بواعة تلت U نقص Zero بواعة تلت U بواعة
+
+538
+01:03:02,110 --> 01:03:05,910
+بواعة تلت U. إذا حصل ضرب عناصر القطر الرئيسي
+
+539
+01:03:05,910 --> 01:03:11,050
+مباشرة. هذا مين؟ هذا ال Jacobian تبع ال U و ال V و
+
+540
+01:03:11,050 --> 01:03:17,670
+ال W. طيب احنا ضايل عندنا حدود التكامل. بدي أعرف U
+
+541
+01:03:17,670 --> 01:03:25,530
+بدي تتغير من وين لوين. أظن قصتنا بسيطة.مافيش مشكلة
+
+542
+01:03:25,530 --> 01:03:30,830
+ال U من واحد للاثنين.طيب تعالى نشوف نشيل ال X ونحط
+
+543
+01:03:30,830 --> 01:03:36,470
+ال U بيصير محصولة بين واحد ومين والاتنين طب تعالى
+
+544
+01:03:36,470 --> 01:03:41,850
+للتانية يعني التانية عندك لو قسمت على X بيصير Y
+
+545
+01:03:41,850 --> 01:03:48,830
+محصولة بين Zero واتنين على X يبقى هنا اها باجي
+
+546
+01:03:48,830 --> 01:03:56,090
+بقول A Zeroاقل من او يسوى ال X Y اقل من او يسوى ال
+
+547
+01:03:56,090 --> 01:04:00,030
+Y اقل
+
+548
+01:04:00,030 --> 01:04:06,310
+من او يسوى ال Y اقل من او يسوى ال Y اقل من او يسوى
+
+549
+01:04:06,310 --> 01:04:06,570
+ال Y اقل من او يسوى ال Y اقل من او يسوى ال Y اقل
+
+550
+01:04:06,570 --> 01:04:06,830
+من او يسوى ال Y اقل من او يسوى ال Y اقل من او يسوى
+
+551
+01:04:06,830 --> 01:04:07,530
+ال Y اقل من او يسوى ال Y اقل من او يسوى ال Y اقل
+
+552
+01:04:07,530 --> 01:04:12,150
+ال Y اقل من او يسوى ال Y اقل من او يسوى ال Y اقل
+
+553
+01:04:12,150 --> 01:04:18,970
+من او يسوى ال Y اقل من او يأكبر من أو تسوى Zero
+
+554
+01:04:18,970 --> 01:04:26,430
+أقل من أو يسوى اتنين على U طيب ممتاز من خلال
+
+555
+01:04:26,430 --> 01:04:35,450
+انتيجة U ازد و على تلاتة يبقى بقى اني بقوله ازد
+
+556
+01:04:35,450 --> 01:04:38,830
+تسوى W على تلاتة
+
+557
+01:04:49,700 --> 01:04:55,020
+يبقى الـ W محصورة بين الصفر و بين الواحد و بين
+
+558
+01:04:55,020 --> 01:05:07,180
+التلاتة اذا مشكلتي أصبحت مالها أصبحت محلولة ال
+
+559
+01:05:07,180 --> 01:05:09,180
+Y محصورة بين الصفر و الاتنين
+
+560
+01:05:13,130 --> 01:05:19,010
+اه اه فهمت عليك اه هذه امانات على طول الخط هذا بدي
+
+561
+01:05:19,010 --> 01:05:24,110
+اعطيلك انه zero اقل من او يساوي ال Y اللي عندنا من
+
+562
+01:05:24,110 --> 01:05:36,370
+وراها V على U يبقى هذه V على U اقل من او يساوي 2
+
+563
+01:05:36,370 --> 01:05:42,900
+على Uأُضر بكله في U بصير أن دجاج بصير ال zero أقل
+
+564
+01:05:42,900 --> 01:05:47,900
+من أو يساوي بيه أقل من أو يساوي جداش اتنين يبقى
+
+565
+01:05:47,900 --> 01:05:54,380
+حددت حدود التكامل تحديدا سليما وجبت الجاكوبيا لم
+
+566
+01:05:54,380 --> 01:06:01,600
+يبقى إلا عملية التكامل يبقى بروح بقول ثلاث تكاملات
+
+567
+01:06:01,600 --> 01:06:06,480
+وبداجي لجداش لل X تربيع وين ال X؟
+
+568
+01:06:13,570 --> 01:06:25,270
+و ال Y ب V على U يبقى هذه V على U اللي بعدها زائد
+
+569
+01:06:25,270 --> 01:06:37,950
+تلاتة U لأن X ب U و ال Y ب V على U وهذه V على U و
+
+570
+01:06:37,950 --> 01:06:42,650
+ال Z اللي هي W على تلاتة ال W
+
+571
+01:06:45,250 --> 01:06:50,390
+الـ Jacobian الـ Jacobian واحد على تلاتة U يبقى
+
+572
+01:06:50,390 --> 01:07:00,970
+واحد على تلاتة U وهنا D V D و الله ايش D W D W و
+
+573
+01:07:00,970 --> 01:07:07,610
+الله خليها D U في الأول مش مشكلة اي حاجة D W D V D
+
+574
+01:07:07,610 --> 01:07:12,990
+U طبعا واضح فيش فيها شغلات صعبة كتيرة لكن لو خلتها
+
+575
+01:07:12,990 --> 01:07:13,610
+للاخر
+
+576
+01:07:17,020 --> 01:07:22,580
+يبقى بداخل الحدود كوني كتبت ال W يبقى ال W تتغير
+
+577
+01:07:22,580 --> 01:07:29,620
+من أين لأين من Zero لغاية تلاتة ال V ستتغير من
+
+578
+01:07:29,620 --> 01:07:36,320
+Zero لغاية اتنين ال U تتغير من أين لأين من واحد
+
+579
+01:07:36,320 --> 01:07:42,200
+لغاية اتنين الشكل عندنا طيب نبسط المثال تكامل من
+
+580
+01:07:42,200 --> 01:07:47,120
+واحد للاتنين تكامل من صفر للاتنينتكوّن مصطفى الـD
+
+581
+01:07:47,120 --> 01:07:54,120
+تلاتة هذي يا بنات بيظل عندي U في الـV وهذه زائد
+
+582
+01:07:54,120 --> 01:08:02,920
+تلاتة مع تلاتة و الـU مع الـU بيظل بس VW يبقى زائد
+
+583
+01:08:02,920 --> 01:08:12,400
+VW في 101 على تلاتة U DW DVDU
+
+584
+01:08:14,450 --> 01:08:19,190
+طيب هذا الكلام بده يساوي شو رايك التلت برا وهي
+
+585
+01:08:19,190 --> 01:08:25,050
+تكامل من واحد لإتنين وهي تكامل من Zero لغاية
+
+586
+01:08:25,050 --> 01:08:33,710
+التلتة بده يدخل ال U جوا غالي قداش V زائد VW على U
+
+587
+01:08:33,710 --> 01:08:41,790
+في مين؟ في ال DW DVB كيف؟
+
+588
+01:08:42,680 --> 01:08:51,660
+من Zero لإتنين تكامل هنا من Zero لإتنين يبقى الان
+
+589
+01:08:51,660 --> 01:08:56,640
+انا بدأ اكمل بالاسم لمن؟ لل DW يبقى هذا الكلام بده
+
+590
+01:08:56,640 --> 01:09:02,940
+يسوي هاي الطول برا وهي تكاملين من Zero لإتنين ومن
+
+591
+01:09:02,940 --> 01:09:07,460
+واحد لغاية اتنين لل VW
+
+592
+01:09:09,920 --> 01:09:18,680
+اللي هو V W تربيع على 2U و الـ W تتغير من الـ Zero
+
+593
+01:09:18,680 --> 01:09:25,320
+لغاية التلاتة لـ DVD يساوى
+
+594
+01:09:25,320 --> 01:09:31,060
+أي التلت برا و هي تكاملين من صفر لواحد و من الصفر
+
+595
+01:09:31,060 --> 01:09:35,860
+لإتنين يجب أن أشيل الـ W و أضع بدلها من تلاتة
+
+596
+01:09:35,860 --> 01:09:39,180
+تلاتة
+
+597
+01:09:39,180 --> 01:09:49,550
+Vوهنا زائد ال W تربيع بصير تسعة على تسعة V على
+
+598
+01:09:49,550 --> 01:09:57,930
+اتنين U تسعة V على اتنين U تمام؟ ناقص Zero Zero مع
+
+599
+01:09:57,930 --> 01:10:04,970
+السلامة كل هذا في DVD شو رأيك يا بنات؟
+
+600
+01:10:07,810 --> 01:10:14,470
+برا معاكل غير مصوف عليك يبقى هذا الكلام تكامل من
+
+601
+01:10:14,470 --> 01:10:21,870
+zero ل واحد تكامل من zero للإتنين لل V زائد تلاتة
+
+602
+01:10:21,870 --> 01:10:33,210
+V على اتنين U DV DU يبقى هذا الكلام بالدرسام تكامل
+
+603
+01:10:33,210 --> 01:10:34,650
+من zero لواحد
+
+604
+01:10:44,940 --> 01:10:51,440
+والحكي هذا كله من Zero للإتنين لديه يوم. يبقى هذا
+
+605
+01:10:51,440 --> 01:10:55,620
+الكلام يصير تكامل من Zero لواحد.
+
+606
+01:10:59,000 --> 01:11:06,020
+سبحان الله يبقى هذا من واحد للإتنين وهذا من واحد
+
+607
+01:11:06,020 --> 01:11:16,280
+للإتنين وهذا من الواحد للإتنينوهذا من واحد لغاية
+
+608
+01:11:16,280 --> 01:11:23,100
+اتنين وما أنسانيه إلا الشيطان القرعى . هذه فنيات
+
+609
+01:11:23,100 --> 01:11:26,860
+صورة بنات . الكافة
+
+610
+01:11:29,370 --> 01:11:35,050
+طبعا ولبدوا في كافهم كده؟ تلاتة سنين و أزداد و
+
+611
+01:11:35,050 --> 01:11:39,770
+تسعة عمره حد بيظل نايم تلاتمية وتسعة وتسعين و لا
+
+612
+01:11:39,770 --> 01:11:46,630
+تلاتمية وتسعة سنين؟ غريب يعني لكن ما غريب للشيطان
+
+613
+01:11:46,630 --> 01:11:50,430
+أن الله على كل شيء قادر. طيب العوض اذا دي أربعة
+
+614
+01:11:50,430 --> 01:11:57,570
+علي اتنين بيظل كده؟ بيظل اتنينزائد هنا كمان أربع
+
+615
+01:11:57,570 --> 01:12:03,930
+بتروح مع الأربع بضع قداش تلاتة عليهم زائد تلاتة
+
+616
+01:12:03,930 --> 01:12:07,630
+عليهم كله في الديام
+
+617
+01:12:10,040 --> 01:12:17,480
+يبقى هذا الكلام بده يساوي اللي هو اتنين U و هنا
+
+618
+01:12:17,480 --> 01:12:28,460
+زائد تلاتة كده لم absolute value ل U وهذا كله
+
+619
+01:12:28,460 --> 01:12:34,890
+تلاتة لين أبسط تلاتة ليوم الواحدلغاية اتنين يساوي
+
+620
+01:12:34,890 --> 01:12:42,870
+اها اتنين في اتنين اربعة زائد تلاتة لان اتنين ناقص
+
+621
+01:12:42,870 --> 01:12:51,410
+اتنين او هنا ناقص Zero لان الواحد هو Zero تمام
+
+622
+01:12:51,410 --> 01:12:57,750
+مباشرة يبقى هذا الكلام يساوي اتنين زائد تلاتة
+
+623
+01:13:03,230 --> 01:13:10,090
+زائد لن تمانية، من فعلا؟ لن اتنين تقعي بالأمهات
+
+624
+01:13:10,090 --> 01:13:15,770
+بلن تمانية ماعرفنا حد يانا الصبح يعطيكوا الأعافية،
+
+625
+01:13:15,770 --> 01:13:20,950
+يعطيكوا أرقام، مسائل، اتجربوا فيها، ومبناش نكتر
+
+626
+01:13:20,950 --> 01:13:28,130
+عليكم يعنيخاصة دنيا رمضان ووصلنا الى العشر الأواخر
+
+627
+01:13:28,130 --> 01:13:36,610
+فعنا exercises خمسة أشهر تمانية المسائل التالية
+
+628
+01:13:36,610 --> 01:13:47,650
+خمسة وسبعة وتسعة وتلتاش وخمستاش وتلاتة وعشرين
+
+629
+01:13:55,120 --> 01:14:02,860
+طيب اليوم هذا كده في رمضان 17 رمضان و كده في أغسطس
+
+630
+01:14:02,860 --> 01:14:09,400
+17 لتوافق الرقمات وبفضل الله انه يتوافق مع شيء
+
+631
+01:14:09,400 --> 01:14:16,920
+ثانيلا مثل كهذا. إيش حصل في 17 رمضان؟ God was with
+
+632
+01:14:16,920 --> 01:14:21,780
+them وكان النصر حليف منين؟ يبقى احنا بيناية هذا
+
+633
+01:14:21,780 --> 01:14:26,740
+الشرفر من هذا المقارنة كما أن الرسول صلى الله عليه
+
+634
+01:14:26,740 --> 01:14:32,480
+وسلم وضع المشرك إلى يوم مبدأ. تمام؟ يبدأ إن شاء
+
+635
+01:14:32,480 --> 01:14:37,950
+الله يقولمن الناجحين كما انتصر رسوله عليه الصلاة
+
+636
+01:14:37,950 --> 01:14:41,930
+والسلام ونجحة في معركة إيه وانتوا ان شاء الله
+
+637
+01:14:41,930 --> 01:14:46,790
+بتنجحوا يوم الخميس مش القادم هذا اللي غُكرة اللي
+
+638
+01:14:46,790 --> 01:14:51,550
+يقعدوا وكل امتعان يوم خمسة وعشرين ان شاء الله
+
+639
+01:14:51,550 --> 01:14:59,880
+تعالى الساعة عشرة واثقة و الله يلقاها من عالممش
+
+640
+01:14:59,880 --> 01:15:04,680
+مكتوبة؟ على اي حاجة بصفة على وجهة الرئيس بس اللي
+
+641
+01:15:04,680 --> 01:15:08,720
+بيعطيكوا الjawاب مباشرة ايه نعم بس وين القاعة مش
+
+642
+01:15:08,720 --> 01:15:13,460
+عارف يعني انا قرأت على ال net بس الان نسيت الحقيقة
+
+643
+01:15:13,460 --> 01:15:19,500
+ايه نعم ماشي طيب لم يبقى بنات الا انه سامحوا بعضنا
+
+644
+01:15:19,500 --> 01:15:24,580
+بعضا انا بالنسبالي مسامح انه قد يكون انسان استغاب
+
+645
+01:15:24,580 --> 01:15:29,690
+انسان اتكلم في حقه الاخروأنتوا وأنا باطلوا منكم
+
+646
+01:15:29,690 --> 01:15:34,550
+اتسامحوني وبارك الله فيكم السلام عليكم ورحمة الله
+
+647
+01:15:34,550 --> 01:15:35,550
+وبركاته
+
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/Ilto5AXE7dw_raw.srt b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/Ilto5AXE7dw_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f65d5a65133a39f21158884684767147abad1dac
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/Ilto5AXE7dw_raw.srt
@@ -0,0 +1,2592 @@
+1
+00:00:12,380 --> 00:00:17,540
+الاخر section في هذا ال chapter هو substitution in
+
+2
+00:00:17,540 --> 00:00:24,540
+trigonometric or in multiple integralيبقى التعويض
+
+3
+00:00:24,540 --> 00:00:30,580
+في التكامل المتعددة هناخد أول حاجة التعويض في
+
+4
+00:00:30,580 --> 00:00:34,700
+التكامل ب two integrals و بعدها نروح لمين ل three
+
+5
+00:00:34,700 --> 00:00:41,710
+integrals يبقى substitution in double integralsلو
+
+6
+00:00:41,710 --> 00:00:45,750
+ان ده ال F و X و Y و بقى عندي تكامل عليه على
+
+7
+00:00:45,750 --> 00:00:51,770
+المنطقة R يمكن نخل هذا التكامل إلى تكامل مكافئ له
+
+8
+00:00:51,770 --> 00:00:56,230
+على منطقة أخرى بدي أسميها مين ال G هذا الكلام
+
+9
+00:00:56,230 --> 00:01:01,810
+بيحصللو عندى function g وh كل واحدة فيهم one to
+
+10
+00:01:01,810 --> 00:01:08,870
+one بمعنى ان x تساوي f of g وy تساوي f of g وy
+
+11
+00:01:08,870 --> 00:01:10,990
+تساوي f of g وy تساوي h of u وv هدول ال two
+
+12
+00:01:10,990 --> 00:01:15,820
+functions are one to one functionsلأن كل نقطة في
+
+13
+00:01:15,820 --> 00:01:19,820
+المساحة الأولى ستوديها الامين إلى نظيرتها في
+
+14
+00:01:19,820 --> 00:01:24,060
+المساحة الثانية وبالتالي هذه المساحة من ناحية
+
+15
+00:01:24,060 --> 00:01:29,100
+القيمة جد المساحة تانية لكن شكلهم مختلف ليس بضرورة
+
+16
+00:01:29,100 --> 00:01:34,050
+يكونوا مثل بعض لكن من ناحية المساحة جد بعضطيب
+
+17
+00:01:34,050 --> 00:01:38,630
+مضروف في مين؟ في ال absolute value ل J of U و V
+
+18
+00:01:38,630 --> 00:01:43,090
+هذا J زي معامل البنات زي ما نقول معامل التمدد
+
+19
+00:01:43,090 --> 00:01:46,390
+الحاجو معامل التمدد الطولي يبقى هنا احنا بقول هنا
+
+20
+00:01:46,390 --> 00:01:51,690
+هذا هو الجاكوبين مين الجاكوبين هذا؟ شو قصته هذه؟
+
+21
+00:01:51,690 --> 00:01:56,380
+بقولك where ال J of U و Vهو عبارة عن تفضل X
+
+22
+00:01:56,380 --> 00:02:00,800
+بالنسبة للمتغير الأول والتفضل X بالنسبة للمتغير
+
+23
+00:02:00,800 --> 00:02:04,160
+الثاني اللي عملناه للمتغير X هفروح نعمله لمهم
+
+24
+00:02:04,160 --> 00:02:10,880
+للمتغير Y نفك المحدد هذا هيعطيني قيمة محددة هذه
+
+25
+00:02:10,880 --> 00:02:14,900
+القيمة هي اللي بتبقى بال Jacob يعني إذا موجة بقى
+
+26
+00:02:14,900 --> 00:02:18,260
+خلاص مافيش absolute value لكن إذا سالبة بتاخدلها
+
+27
+00:02:18,260 --> 00:02:23,540
+مهم ال absolute valueيبقى هذا هو الـ Jacobin of
+
+28
+00:02:23,540 --> 00:02:27,100
+the coordinates transformations يبقى هذا المعامل
+
+29
+00:02:27,100 --> 00:02:31,860
+تبع من تبع التحويل الآن بدنا نحسب اللي هو معاملة
+
+30
+00:02:31,860 --> 00:02:36,440
+التحويل لدول مختلفة بدنا نبدأ ناخد أمثلة على ذلك
+
+31
+00:02:36,680 --> 00:02:42,420
+ولو أحصل على الكوبيان لتغيير الوضع الكوردنسي لوضع
+
+32
+00:02:42,420 --> 00:02:43,440
+كوردنسي كوردنسي كوردنسي كوردنسي كوردنسي كوردنسي
+
+33
+00:02:43,440 --> 00:02:46,580
+كوردنسي
+
+34
+00:02:46,580 --> 00:02:56,780
+كوردنسي كوردنسي
+
+35
+00:02:56,780 --> 00:03:00,400
+كوردنسي
+
+36
+00:03:01,210 --> 00:03:04,990
+القطبية وفيه شغلة بدنا نضرب فيها طبعا استخدمناها
+
+37
+00:03:04,990 --> 00:03:09,770
+قبلنا هيك وقلنا هي عبارة عن إيش؟ عبارة عن R فقلنا
+
+38
+00:03:09,770 --> 00:03:15,950
+DX DY في الكرتزيني وقابله RERD من أين لك R
+
+39
+00:03:15,950 --> 00:03:19,050
+وعدناكوا يوم وقلناكم ان شاء الله في نهاية هذا ال
+
+40
+00:03:19,050 --> 00:03:25,160
+chapter بنوريكوا كيف جبنا هذه ال R طيببنجي نحسن
+
+41
+00:03:25,160 --> 00:03:28,780
+مقدار الجاكوبيا لهذا اللي احنا بنقول هو R بنجي
+
+42
+00:03:28,780 --> 00:03:33,260
+نقول اه ال X في الأحداثيات الكارتيزية هي عبارة عن
+
+43
+00:03:33,260 --> 00:03:38,560
+R cos θ في الأحداثيات القطبية وكذلك ال Y في
+
+44
+00:03:38,560 --> 00:03:43,380
+الأحداثيات الكارتيزية هي R sin θ في الأحداثيات
+
+45
+00:03:43,380 --> 00:03:50,740
+القطبية يبقى بنات U في مين أجى مكانها هنا R و θ
+
+46
+00:03:58,240 --> 00:04:04,420
+تفضل X بالنسبة الى R تفضل X بالنسبة الى θية اللى
+
+47
+00:04:04,420 --> 00:04:09,100
+عملناه بالنسبة ل X اروح نعمله بالنسبة ل Y يبقى
+
+48
+00:04:09,100 --> 00:04:14,840
+partial Y على partial R partial Y على partial θية
+
+49
+00:04:16,300 --> 00:04:21,540
+يساوي هي الـ determinant نيجي تفاضل ال X بالنسبة
+
+50
+00:04:21,540 --> 00:04:27,720
+إلى أرمين cosine ثيتا يبقى هي cosine ثيتا تفاضل ال
+
+51
+00:04:27,720 --> 00:04:29,780
+X بالنسبة لثيتا
+
+52
+00:04:32,870 --> 00:04:40,410
+R في صين الزاوية تيتا تفضل ال Y بالنسبة إلى R بصين
+
+53
+00:04:40,410 --> 00:04:47,050
+تيتا تفضل ال Y بالنسبة لتيتا بR في كوصين الزاوية
+
+54
+00:04:47,050 --> 00:04:52,710
+تيتا هذا المحدد يسارحاصل ضرب عناصر القطر الرئيسي
+
+55
+00:04:52,710 --> 00:04:58,910
+اللي هو R في Cos تربيه ثيته ناقص حاصل ضرب عناصر
+
+56
+00:04:58,910 --> 00:05:04,270
+القطر الثانوي مع ناقص بصير زائد R في Sin تربيه
+
+57
+00:05:04,270 --> 00:05:09,950
+ثيته إذا ناخد R عام المشترك بيظل Cos تربيه ثيته
+
+58
+00:05:09,950 --> 00:05:15,000
+زائد Sin تربيه ثيته ليه بقدرش؟يبقى النتيجة قداش
+
+59
+00:05:15,000 --> 00:05:20,240
+يبقى عرف ان انا ارتعت ال polar من اين اجت هذه يبقى
+
+60
+00:05:20,240 --> 00:05:24,700
+هذه هي قيمة الجاكوبيان في التحويل من الاحداثيات
+
+61
+00:05:24,700 --> 00:05:29,140
+الكارتيزية الامام الى الاحداثيات القطبية وبعد قليل
+
+62
+00:05:29,140 --> 00:05:33,860
+ان شاء الله هروح زي الجاكوبيان تبع التحويل من
+
+63
+00:05:33,860 --> 00:05:36,380
+الكارتيزيا لالاسفريكا
+
+64
+00:05:56,970 --> 00:06:05,010
+المثال الثاني بيقول لت
+
+65
+00:06:05,010 --> 00:06:14,410
+جيب دي region definedجي بـ the region defined by
+
+66
+00:06:14,410 --> 00:06:19,010
+والمعرفة
+
+67
+00:06:19,010 --> 00:06:24,830
+بيه ال U أكبر من أو يساوي واحد وأقل من أو يساوي
+
+68
+00:06:24,830 --> 00:06:29,950
+اتنين و ال U في ال V كمان أكبر من أو يساوي واحد
+
+69
+00:06:29,950 --> 00:06:38,070
+وأقل من أو يساوي اتنين in the UV plane and theU V
+
+70
+00:06:38,070 --> 00:06:50,010
+لين وير حيث ال X بدها تساوي ال U و ال Y بدها تساوي
+
+71
+00:06:50,010 --> 00:06:58,390
+ال U في ال V السؤال بيقول لي transform حول
+
+72
+00:06:58,390 --> 00:07:08,370
+the integral قول لي التكاملاللي هو مين؟ تكامل من
+
+73
+00:07:08,370 --> 00:07:15,930
+واحد للإتنين تكامل كذلك من واحد للإتنين لل y على x
+
+74
+00:07:15,930 --> 00:07:25,890
+dy dx into an integral over g into an integral
+
+75
+00:07:25,890 --> 00:07:34,890
+over g and evaluate and evaluate
+
+76
+00:07:36,840 --> 00:07:42,060
+و احسبلي كذلك the uv integral
+
+77
+00:08:06,340 --> 00:08:12,360
+سؤال مرة تانية بيعطيني المنطقة G U محصورة بين واحد
+
+78
+00:08:12,360 --> 00:08:18,060
+واتنين وحصل ضرب U في V محصورة بين واحد واتنين هذا
+
+79
+00:08:18,060 --> 00:08:22,820
+على ال U V plane وعطاني علاقة بتربط بين X وY وكذا
+
+80
+00:08:22,820 --> 00:08:29,500
+كالمتغيرات الجديدة U وV X يساوي U وY يساوي U في V
+
+81
+00:08:29,500 --> 00:08:34,280
+بيقولي transform the integral حول التكامل اللي
+
+82
+00:08:34,280 --> 00:08:40,010
+عندنا هذاInto an integral over G لتكامل على G
+
+83
+00:08:40,010 --> 00:08:44,990
+واحسب لهذا التكامل الجديد زي و لتشيبير بالضبط
+
+84
+00:08:44,990 --> 00:08:49,070
+بقناع لما كنا بنحول من كارتيزيا ال integral إلى
+
+85
+00:08:49,070 --> 00:08:54,350
+polar integral و بنروح نحسببقدرش قيمة ال polar
+
+86
+00:08:54,350 --> 00:08:58,950
+integral يبقى هنا نفس القصة بالضغط تماما يعني بديش
+
+87
+00:08:58,950 --> 00:09:04,630
+اشوف المثل لا X ولا Y بدي احولها كلها بدلالة من R
+
+88
+00:09:04,630 --> 00:09:10,170
+و Z بقوله كويس يبقى هي التكملات اتنين اللي عندنا
+
+89
+00:09:10,170 --> 00:09:17,510
+ال Y بقدرش U في V ال X ب U ايوة ضل بدنا ال
+
+90
+00:09:17,510 --> 00:09:24,730
+Jacobian كويس فاهمين في ال Jacobianتبع ال U وال V
+
+91
+00:09:24,730 --> 00:09:33,940
+absolute value دي V دي U او دي U دي Vطب نيجي الآن
+
+92
+00:09:33,940 --> 00:09:40,400
+بدنا نحسب الجاكوبين و بدنا نحسب حدود التكامل طب
+
+93
+00:09:40,400 --> 00:09:44,460
+تعالى نحسب الجاكوبين في الأول يبقى يا بنات انا بدي
+
+94
+00:09:44,460 --> 00:09:49,640
+partial x by partial u و partial x by partial v
+
+95
+00:09:49,640 --> 00:09:52,600
+بدي partial y by partial u
+
+96
+00:09:57,550 --> 00:10:04,130
+تفاضل X بالنسبة إلى U بقدرش تفاضل X بالنسبة إلى V
+
+97
+00:10:06,490 --> 00:10:12,890
+يبقى هنا zero بعد ذلك التفاضل ال Y بالنسبة الى U V
+
+98
+00:10:12,890 --> 00:10:19,410
+تفاضل Y بالنسبة الى V ب U حصر ضرب الرئيس ينقص
+
+99
+00:10:19,410 --> 00:10:23,770
+الثانوية يبقى كده ايش؟ يبقى مقدار الجاكوبيا بده
+
+100
+00:10:23,770 --> 00:10:30,050
+يساوي من؟ بده يساوي LU طيب إذا هذا هذا كله على
+
+101
+00:10:30,050 --> 00:10:35,770
+المنطقة اللي هي Gيبقى هذا الكلام بدل يسوي تكاملين
+
+102
+00:10:35,770 --> 00:10:42,550
+لمين ال U مع ال U بتروح هذه مع هذه بيظل V ومقدار
+
+103
+00:10:42,550 --> 00:10:51,050
+الجاكوبيا بي U دي V دي U طب نرجع لمين يا بنات
+
+104
+00:10:51,050 --> 00:10:58,370
+للمعطينيها هذهبقدر أقوله لو قسمت الطرفين على V إذا
+
+105
+00:10:58,370 --> 00:11:03,110
+الواحد أقل من أو يساوي U و V أقل من أو يساوي اتنين
+
+106
+00:11:03,110 --> 00:11:08,690
+implied ان ال V محصورة بين واحد على U و ما بين
+
+107
+00:11:08,690 --> 00:11:13,530
+اتنين على U إذا أنا أخدت التكامل في الأول بالنسبة
+
+108
+00:11:13,530 --> 00:11:19,870
+إلى V يبقى هنا واحد على U و هنا اتنين على U ال U
+
+109
+00:11:19,870 --> 00:11:24,990
+تتغير من أين إلى أين؟يبقى جاهزة من واحد إلى اتنين،
+
+110
+00:11:24,990 --> 00:11:29,330
+الآن بنقدر نكمل التكامل هذا، ليش؟ لأن هدول فعلا
+
+111
+00:11:29,330 --> 00:11:35,150
+متغيرات بدلالة U، لكن U بأرقاموبالتالي بقدر اطلع
+
+112
+00:11:35,150 --> 00:11:40,230
+جداش القيمة الحقيقية لهذا التكامل يبقى هذا الكلام
+
+113
+00:11:40,230 --> 00:11:46,370
+يساوي تكامل من واحد لاتنين يبقى U مقدر ثابت يبقى
+
+114
+00:11:46,370 --> 00:11:54,070
+بدي اكمل ال V بس اللي هي V تربيع على اتنين من واحد
+
+115
+00:11:54,070 --> 00:11:59,110
+على U لاتنين على U في ال U في ال DU
+
+116
+00:12:02,420 --> 00:12:08,200
+يبقى هذا الكلام بده يسافر هي النص برا و هي تكمل من
+
+117
+00:12:08,200 --> 00:12:14,800
+واحد للاثنين بظل V تربيع يبقى اللي هي اربعة على U
+
+118
+00:12:14,800 --> 00:12:23,280
+تربيع ناقص واحد على U تربيع كله في ال DU والله في
+
+119
+00:12:23,280 --> 00:12:29,180
+ال U DU في عندي U لسه اضعه الى برا يبقى في ال U DU
+
+120
+00:12:42,970 --> 00:12:53,110
+يبقى تلاتة على
+
+121
+00:12:53,110 --> 00:12:56,430
+U دي U يبقى الجواب تلاتة على U دي U يبقى الجواب
+
+122
+00:12:56,430 --> 00:12:57,280
+تلاتة على U دي U يبقى الجواب تلاتة على U دي Uتلاتة
+
+123
+00:12:57,280 --> 00:13:03,340
+على اتنين لان absolute value ل U من عند الواحد
+
+124
+00:13:03,340 --> 00:13:10,280
+لغاية اتنين يبقى تلاتة على اتنين لان اتنين ناقص
+
+125
+00:13:10,280 --> 00:13:16,300
+لان الواحد طبعا لان الواحد مايبقى داشر بزيرو بظل
+
+126
+00:13:16,300 --> 00:13:21,460
+عندنا بس تلاتة على اتنين لان اتنين هذا قيمة
+
+127
+00:13:21,460 --> 00:13:24,500
+التكامل اللي موجود عندنا
+
+128
+00:13:41,880 --> 00:13:46,860
+بنروح مثال رقم اتنين ولا تلاتة الحين مثال رقم
+
+129
+00:13:46,860 --> 00:13:50,340
+تلاتة
+
+130
+00:13:50,340 --> 00:13:53,640
+بيقول
+
+131
+00:13:53,640 --> 00:13:59,640
+use the transformation use the trans
+
+132
+00:14:07,380 --> 00:14:17,100
+اللي هو ال X بدي ساوي U زائد نص V و ال Y بدي ساوي
+
+133
+00:14:17,100 --> 00:14:25,580
+V to evaluate the integral to evaluate the
+
+134
+00:14:25,580 --> 00:14:35,060
+integral مش هنتحسب التكامل اللي هو تكامل من Zero
+
+135
+00:14:35,060 --> 00:14:44,020
+للإتنينتكامل من y على 2 إلى y زائد أربعة كله على
+
+136
+00:14:44,020 --> 00:14:52,720
+اتنين لمن؟ لل y تكيب في 2x ناقص y في ال
+
+137
+00:14:52,720 --> 00:15:00,920
+exponential لل 2x ناقص y لكل ربيع لل dx
+
+138
+00:15:04,380 --> 00:15:12,660
+by writing it يعني
+
+139
+00:15:12,660 --> 00:15:22,580
+بكتابة هذا التكامل as an integral over
+
+140
+00:15:22,580 --> 00:15:50,960
+a region G a region G in theUV Play نمسح
+
+141
+00:15:50,960 --> 00:15:52,160
+الشجرة دي كلها بنات
+
+142
+00:16:16,520 --> 00:16:21,220
+نرجع لسؤال مرة تانية قال استخدم التحويل x يساوي u
+
+143
+00:16:21,220 --> 00:16:27,000
+زائد نص V وال Y تساوي V عشان نحوّل التكامل ان هو
+
+144
+00:16:27,000 --> 00:16:33,040
+الحمد لله شكله وشكلها ايضا By writing it بكتابتي ك
+
+145
+00:16:33,040 --> 00:16:38,580
+Integral over region G تمين في ال U V Plane نقوله
+
+146
+00:16:38,580 --> 00:16:43,580
+كويس اذا احنا خلّيني نحسب التكائل جاكوبيا ونحسب
+
+147
+00:16:43,580 --> 00:16:47,950
+حدود التكامل ونقلصها من مشكلتنا هذهكيف كانت تالية
+
+148
+00:16:47,950 --> 00:16:52,290
+يبقى ال X جاهزة و ال Y جاهزة يبقى على طول الخطب
+
+149
+00:16:52,290 --> 00:16:56,150
+نروح أسيبه ال Jacobian يبقى بدا جاهزه ال Jacobian
+
+150
+00:16:56,150 --> 00:17:02,710
+تبع ال U و ال V بده يساوي تفاضل ال X بالنسبة إلى U
+
+151
+00:17:02,710 --> 00:17:08,670
+تفاضل ال X بالنسبة إلى V تفاضل ال Y بالنسبة إلى U
+
+152
+00:17:08,670 --> 00:17:15,160
+تفاضل ال Y بالنسبة إلى Vباعطيني المحدد تفاضل X
+
+153
+00:17:15,160 --> 00:17:20,000
+بالنسبة ل U بقداشي بنامي واحد والباقية Zero تفاضل
+
+154
+00:17:20,000 --> 00:17:28,340
+X بالنسبة ل V كدهش نصف تفاضل Y بالنسبة ل U Zero
+
+155
+00:17:28,340 --> 00:17:34,920
+تفاضل Y بالنسبة ل V يبقى المحدد كدهش بساوي واحد
+
+156
+00:17:34,920 --> 00:17:41,850
+ممتاز جدا يبقى ضالة عندي حدود التكاملبدي اعرف حدود
+
+157
+00:17:41,850 --> 00:17:47,390
+التكمل هذه من ويل لويل بقوله بسيطة احنا بدنا نكمل
+
+158
+00:17:47,390 --> 00:17:55,470
+اول شئ بالنسبة لمين يبقى انا عندي x هنا تساوي y
+
+159
+00:17:55,470 --> 00:18:04,770
+زائد اربعة على اتنين هذا الكلام بدري اعطينا ال x
+
+160
+00:18:04,770 --> 00:18:14,000
+عندي بقداشU زي نص V يبقى هذا U زائد V على اتنين
+
+161
+00:18:14,000 --> 00:18:21,800
+بده يساوي ال Y عندى بقداش V يبقى هذه V على اتنين
+
+162
+00:18:21,800 --> 00:18:26,600
+زائد اتنين اربع على اتنين باتنين وشيلت ال Y وحطت
+
+163
+00:18:26,600 --> 00:18:31,140
+مكانها V اظل لو جبت ال V عند ال V بتروح الله يسهل
+
+164
+00:18:31,140 --> 00:18:33,700
+عليها بيعطينى جداش هنا و هنا
+
+165
+00:18:36,630 --> 00:18:43,770
+يبقى ال U تساوي قدراش اتنين اذا اتنين هذي بدت كافة
+
+166
+00:18:43,770 --> 00:18:49,290
+مين؟ بدت كافة Y زائد اربع على اتنين باجي بقوله
+
+167
+00:18:49,290 --> 00:18:56,870
+بتاخد X التانية X تساوي Y على اتنين ال U زائد V
+
+168
+00:18:56,870 --> 00:19:03,590
+على اتنين تساوي ال Y هادف Vعلى اتنين يبقى هذا بدي
+
+169
+00:19:03,590 --> 00:19:09,450
+اعطيك ان U تساوي كده؟ Zero يبقى هذا بدي اعطينا ان
+
+170
+00:19:09,450 --> 00:19:14,730
+U تساوي Zero يبقى هاي جيبت حدود التكامل تبع تمام
+
+171
+00:19:15,160 --> 00:19:21,380
+تبعت ال U بدي أجيب حدود التكمل تبعت ال V هذه Y لها
+
+172
+00:19:21,380 --> 00:19:26,220
+الحدود لإتنين اللي عندنا يبقى لما أقول Y تساوي
+
+173
+00:19:26,220 --> 00:19:32,080
+اتنين معناته ان V قداش تساوي اتنين لأن Y تساوي V
+
+174
+00:19:32,080 --> 00:19:38,300
+لما أقول Y تساوي Zero معناته V قداش تساوي Zero إذا
+
+175
+00:19:38,300 --> 00:19:43,270
+جبت حدود التكمل تبعت ال U و Vبضلّف عليه بس شغل
+
+176
+00:19:43,270 --> 00:19:50,170
+واحدة أحسبله قداش اتنين X ناقص Y كلها بدلالة U وP
+
+177
+00:19:50,170 --> 00:19:58,690
+بقوله بسيطة يبقى بدالي أخد اتنين X ناقص Y يبقى هاي
+
+178
+00:19:58,690 --> 00:20:05,270
+اتنين فيه ال X اللي عندي اللي هو U زائد V عليها
+
+179
+00:20:09,310 --> 00:20:16,490
+نقص وي يعني مجداش ناقص في افك الجوز هذا يبقى اتنين
+
+180
+00:20:16,490 --> 00:20:23,030
+يوم زائد في ناقص في ويسر مجداش يبقى الحين صارت قصة
+
+181
+00:20:23,030 --> 00:20:28,590
+بسيطة وسهلة طبعا ففاجي بقوله بدي أصير عندي التكامل
+
+182
+00:20:28,590 --> 00:20:34,670
+هذا على الشكل التالي ال وي تكيب يعني مين
+
+183
+00:20:39,020 --> 00:20:50,600
+و2x-y يعني 2u خلاصنا منها وهذه E أسعى 2U لكل تربيع
+
+184
+00:20:50,600 --> 00:20:56,540
+أيهم أسهل كامل بالنسبة الأول V of U فهذا البجي
+
+185
+00:20:56,540 --> 00:21:03,780
+بقوله DV DUوالحمد لله فاتوش لأن الاتنين كله من صفر
+
+186
+00:21:03,780 --> 00:21:08,660
+للاتنين يبقى هنا من zero لغاية اتنين ومن هنا من
+
+187
+00:21:08,660 --> 00:21:14,740
+zero لغاية اتنين هذا الكلام يساوي تكامل من صفر
+
+188
+00:21:14,740 --> 00:21:22,900
+للاتنين هذه عبارة عن V أس 4 على 4 من وين لوين من
+
+189
+00:21:22,900 --> 00:21:29,780
+zero لغاية اتنين ويبقى لعيني اتنين يومبمين في ال E
+
+190
+00:21:29,780 --> 00:21:37,440
+قوس 2U كل تربيع دي تمام
+
+191
+00:21:37,440 --> 00:21:47,200
+بدي أعود بالقيمة اللي فوق 16 على 4 4 في 2 8 يبقى
+
+192
+00:21:47,200 --> 00:21:56,370
+يصير من أن تكامل من 0 إلى 2 إلى 8Uفي E أس اتنين U
+
+193
+00:21:56,370 --> 00:22:00,570
+لكل تربية و الله ياش رأيك افكها بالمرة التانية دي
+
+194
+00:22:00,570 --> 00:22:05,510
+خلونا نخلص من هذه الشرقة هذه عبارة عن أربعة U
+
+195
+00:22:05,510 --> 00:22:07,010
+تربية D
+
+196
+00:22:10,640 --> 00:22:15,000
+يبقى صار سؤالي بسيط بعد بكلم كل كاهي غير شكل صار
+
+197
+00:22:15,000 --> 00:22:20,020
+بقى سؤالي بسيط جدا يعني ما علي اللي حط مال تعويضة
+
+198
+00:22:20,020 --> 00:22:23,900
+و بيكون خلصنا من هذه الشغله يعني كأنها بناتها دي
+
+199
+00:22:23,900 --> 00:22:33,890
+ايه كأنها تكاملللـ E أس T DT حيث الـ T تساوي أربعة
+
+200
+00:22:33,890 --> 00:22:41,450
+U تربيع لإن لو فضلت الـ DT بقى يقول تمانية U D U
+
+201
+00:22:41,450 --> 00:22:48,070
+هي التمانية U وهي الـ D U باقية حدود التكامل لما
+
+202
+00:22:48,070 --> 00:22:56,740
+تبقى U باتنين فصير T بقداش سبتاش16 و لما تبقى ال U
+
+203
+00:22:56,740 --> 00:23:01,720
+ب Zero بظل هذي ب Zero تكامل ال exponential بال
+
+204
+00:23:01,720 --> 00:23:09,000
+exponential itself من Zero لغاية 16 يبقى E أُس 16
+
+205
+00:23:09,000 --> 00:23:17,100
+ناقص E أُس Zero يعني E أُس 16 ناقص كده ناقص واحد
+
+206
+00:23:17,100 --> 00:23:23,940
+هذا قيمة ميم قيمة التكامل اللي موجود عندناطبعا
+
+207
+00:23:23,940 --> 00:23:30,100
+بإمكاني ارسم منطقة تكامل بس لمجرد اتعرف عليها لكن
+
+208
+00:23:30,100 --> 00:23:35,880
+ليس بالضرورة نرسمها بلاش
+
+209
+00:23:35,880 --> 00:23:42,220
+ريحتوني نجي ناخد المثال الرابع يبقى بغرف الأربع
+
+210
+00:23:42,220 --> 00:23:46,680
+use
+
+211
+00:23:46,680 --> 00:23:47,560
+the transformation
+
+212
+00:23:54,630 --> 00:24:02,270
+transformations استخدم التحويلات U تساوي X ناقص
+
+213
+00:24:02,270 --> 00:24:13,170
+الـY و V يساوي 2X زائد الـY تقول بالـU انتجرال
+
+214
+00:24:13,170 --> 00:24:17,910
+عشان
+
+215
+00:24:17,910 --> 00:24:19,830
+نحسب التكامل
+
+216
+00:24:23,280 --> 00:24:31,480
+w is the integral تكاملين على r للإتنين x تربيع
+
+217
+00:24:31,480 --> 00:24:43,580
+ناقص x y ناقص y تربيع كله dx dy for the region R
+
+218
+00:24:43,580 --> 00:24:52,620
+for the region R for the region R in the first
+
+219
+00:24:56,150 --> 00:25:02,030
+equadrant في الرابع الأول equadrant
+
+220
+00:25:02,030 --> 00:25:15,010
+bounded by the lines بالخطوط
+
+221
+00:25:15,010 --> 00:25:23,690
+المستقيمة y تساوي نقص اتنين x زائد اربعةY تساوي
+
+222
+00:25:23,690 --> 00:25:34,610
+نقص اتنين X زائد سبعة Y تساوي X نقص اتنين Y تساوي
+
+223
+00:25:34,610 --> 00:25:36,850
+X زائد واحد
+
+224
+00:26:08,460 --> 00:26:13,000
+نرجع لسؤالنا هذا مرة ثانية بقول استخدام الـ
+
+225
+00:26:13,000 --> 00:26:18,300
+Transformation يتحويل إلى U تساوي X ناقص Y و V
+
+226
+00:26:18,300 --> 00:26:23,500
+يساوي 2X زائد Y لكي تحسب ان التكمل لأن هذا على
+
+227
+00:26:23,500 --> 00:26:28,060
+المنطقة R في الربع الأول وهذه المنطقة محدودة
+
+228
+00:26:28,060 --> 00:26:35,080
+بالمستقيمات الأربع الأعلى هو البسيطة تعالى نشوفهذا
+
+229
+00:26:35,080 --> 00:26:39,940
+السؤال يختلف عن ثلاثة أسئلة السابقة ماطنيش حدود
+
+230
+00:26:39,940 --> 00:26:45,680
+التكامل انا بده اطلع حدود التكامل لحالي تمام يعني
+
+231
+00:26:45,680 --> 00:26:49,720
+اي واحدة بس قبل كان بيقول من كذا لكذا يبقى فجأة
+
+232
+00:26:49,720 --> 00:26:54,300
+بيعطيني حدود التكامل وبالتالي مشكلة هنا أصعب شوية
+
+233
+00:26:54,300 --> 00:27:02,200
+طيبوشغلة تانية ما اعطانيش انه x بدلالة u وv لأ
+
+234
+00:27:02,200 --> 00:27:07,760
+اعطاني u بدلالة x وy و اعطاني v بدلالة x وy يبقى
+
+235
+00:27:07,760 --> 00:27:13,240
+الخطوة الأولى عندي بدى اجيب ال x و ال y بدلالة u
+
+236
+00:27:13,240 --> 00:27:16,700
+وv حتى اقدر احسب ال jacobian وانا ماجبتوش ماقدرش
+
+237
+00:27:16,700 --> 00:27:22,090
+احسب ال jacobianبقوله كويس طيب تعالى بدنا نجيب من
+
+238
+00:27:22,090 --> 00:27:31,260
+المعادلاتين هدول X و Y بدلالة تمام تمام يبقىأصلا
+
+239
+00:27:31,260 --> 00:27:35,580
+لو جمعناهم يطير ال Y يجيب X دغري مش هيك يبقى بسيطة
+
+240
+00:27:35,580 --> 00:27:42,880
+باجي بقول انا عند ال U تساوي X نقص ال Y وعندي V
+
+241
+00:27:42,880 --> 00:27:50,520
+يساوي 2X زائد ال Y لو جمعت مباشرة بطلع عند ايش
+
+242
+00:27:50,520 --> 00:27:58,620
+بطلع عند انه تلاتة X بده يساوي U زائد V او ان شئته
+
+243
+00:27:59,080 --> 00:28:06,500
+فقولوا ان ال X بيساوي U زائد V كله على تلاتة أو U
+
+244
+00:28:06,500 --> 00:28:13,660
+على تلاتة زائد V على تلاتة جيبنا ال X إذا ما بنقدر
+
+245
+00:28:13,660 --> 00:28:19,720
+نجيب من ال Y فبجيب اخد المعادلة اللي عندها دي
+
+246
+00:28:19,720 --> 00:28:28,120
+فمنها بقول ان ال Y تساوي X ماقص ال Uجبنا هذا هنا
+
+247
+00:28:28,120 --> 00:28:33,780
+وهذا هنا يبقى هذا الكلام بيكون ساوي X عندي اللي
+
+248
+00:28:33,780 --> 00:28:39,160
+حصلنا عليها V على تلاتة او U زائد V على تلاتة يبقى
+
+249
+00:28:39,160 --> 00:28:46,620
+هذه U زائد V على تلاتة ناقص ال U يبقى بلاء عليه
+
+250
+00:28:46,620 --> 00:28:52,680
+هذا بدي يعطينا ان Y تساوي كله على تلاتة بيصير U
+
+251
+00:28:53,040 --> 00:29:02,180
+زائد V ناقص تلاتة U إذا V ناقص اتنين U على تلاتة
+
+252
+00:29:02,180 --> 00:29:12,380
+يبقى هذه قيمة X وهذه قيمة Y أو يساوي V على تلاتة
+
+253
+00:29:12,380 --> 00:29:18,650
+ناقص اتنين U على تلاتةسواء كان هذى و الله هذى يبقى
+
+254
+00:29:18,650 --> 00:29:27,110
+حصلت على قيمتي X وY بدلالة main بدلالة U وV نحسب
+
+255
+00:29:27,110 --> 00:29:33,650
+الجيكوريا البالمرة نحسب الجيكوريا تبع ال U وال V
+
+256
+00:29:33,650 --> 00:29:40,150
+تسوى المحدد تفاضل ال X بالنسبة إلى U تفاضل ال X
+
+257
+00:29:40,150 --> 00:29:46,670
+بالنسبة إلى V تفاضل ال Y بالنسبة إلى Uتفاضل Y
+
+258
+00:29:46,670 --> 00:29:55,730
+بالنسبة إلى V يساوي تفاضل X بالنسبة إلى U تلت
+
+259
+00:29:55,730 --> 00:29:59,030
+تفاضل
+
+260
+00:29:59,030 --> 00:30:07,650
+X بالنسبة إلى V تلت تفاضل Y بالنسبة إلى U سالب
+
+261
+00:30:07,650 --> 00:30:11,590
+تلتين يبقى سالب تلتين
+
+262
+00:30:14,800 --> 00:30:25,840
+بتل و يساوي نفك المحدد يبقى تسع زائد تسعين تلت
+
+263
+00:30:25,840 --> 00:30:33,280
+أتساع تعني تلت يساوي تلت إذا المقدار الجاكوبين
+
+264
+00:30:33,280 --> 00:30:42,430
+يساوي تلت حسبنا الجاكوبينسهل أشيل X وY و أحط قيمهم
+
+265
+00:30:42,430 --> 00:30:47,650
+من هنا، شو ضال عندي؟ ضالت حدود التكامل وما أدرى
+
+266
+00:30:47,650 --> 00:30:51,530
+كما حدود التكامل. طب كيف بدنا نحصل على حدود
+
+267
+00:30:51,530 --> 00:30:55,310
+التكامل؟
+
+268
+00:30:55,310 --> 00:30:59,390
+وين القاطة التقاطة؟ يعني بدنا ندور عن قاطة
+
+269
+00:30:59,390 --> 00:31:04,790
+التقاطة، صح؟ أنا عند رأي آخر، أنا عندي أربعة
+
+270
+00:31:04,790 --> 00:31:10,060
+مستخدمات حتى الآن مستخدمتهمش،بظبط ؟ طب إذا بدي
+
+271
+00:31:10,060 --> 00:31:16,100
+أروح أحوّل المستقيمات هذه من ال X و ال Y إلى مين؟
+
+272
+00:31:16,100 --> 00:31:19,100
+إلى ال Y و ال B و ال E و الشباطين إذا لو جيت
+
+273
+00:31:19,100 --> 00:31:28,600
+للمستقيم الأول اللي هو Y تساوي ناقص 2X زات 4 Y
+
+274
+00:31:28,600 --> 00:31:34,900
+جاهزة علم هذا هي V على تلاتة ناقص 2U على تلاتة
+
+275
+00:31:34,900 --> 00:31:47,860
+يبقى Vعلى تلاتة ناقص اتنين U على تلاتة تساوي تساوي
+
+276
+00:31:47,860 --> 00:31:52,900
+ال X كمان جاهزة عندنا هاي يبقى بالظروف هيدا شبه ما
+
+277
+00:31:52,900 --> 00:31:57,720
+انا اقول فالسالب اتنين يبقى السالب اتنين U على
+
+278
+00:31:57,720 --> 00:32:11,080
+تلاتة سالب اتنينU على تلاتة و سالب اتنين
+
+279
+00:32:11,080 --> 00:32:20,480
+V على تلاتة سالب اتنين V على تلاتة زائد اربع اطلع
+
+280
+00:32:20,480 --> 00:32:26,620
+هذه وهذه وروحوا مع بعض تمام بنجيب ال V عند هذه
+
+281
+00:32:26,620 --> 00:32:34,080
+بيصير كده عندهبصير تلاتي يعني V هذي لو جت عند هذي
+
+282
+00:32:34,080 --> 00:32:39,320
+بصير تلت و تلتين تبقى واحد صحيح هذا بدي أعطيك V
+
+283
+00:32:39,320 --> 00:32:46,080
+تساوي أربع والله كويس هذا يعني شغل كويس طب لو جت
+
+284
+00:32:46,080 --> 00:32:49,640
+قلت واكتس اتنين
+
+285
+00:33:00,940 --> 00:33:08,560
+يبقى ال V على تلاتة نقص اتنين U على تلاتة يساوي
+
+286
+00:33:08,560 --> 00:33:14,580
+نقص اتنين U على تلاتة نقص اتنين V على تلاتة زائد
+
+287
+00:33:14,580 --> 00:33:18,260
+سبعة يبقى V تساوي سبعة
+
+288
+00:33:22,570 --> 00:33:28,410
+يبقى لدينا مستقيمات اتنين يبقى Y تساوي X ناقص
+
+289
+00:33:28,410 --> 00:33:38,530
+اتنين Y تساوي X ناقص اتنين Y ماتغيرتش يبقى B على
+
+290
+00:33:38,530 --> 00:33:44,090
+تلاتة ناقص اتنين U على تلاتة و X ماتغيرتش بس مش
+
+291
+00:33:44,090 --> 00:33:48,270
+مضروبة ولا في حاجة إلا يبقى بحطها زي ما هي U على
+
+292
+00:33:48,270 --> 00:33:56,190
+تلاتةزائد V على تلاتة ناقص اتنين اظن V على تلاتة
+
+293
+00:33:56,190 --> 00:34:01,130
+لو راح تنبيها تلاتة مع السلامة هذه لو اجت تصيير
+
+294
+00:34:01,130 --> 00:34:09,030
+عندها ناقص U ناقص U بده يسوي ناقص اتنين يبقى U
+
+295
+00:34:09,030 --> 00:34:16,570
+تسوي كده اتنين بالمثل Y تسوي X زايد واحد اظن X
+
+296
+00:34:16,570 --> 00:34:23,360
+زايد واحدimply ان v ع تلاتة نقص اتنين و على تلاتة
+
+297
+00:34:23,360 --> 00:34:30,020
+بدها تساوي u ع تلاتة زائد v ع تلاتة زائد واحد v ع
+
+298
+00:34:30,020 --> 00:34:35,840
+تلاتة مع v ع تلاتة هذه هنا بصير عندك u تساوي جدار
+
+299
+00:34:36,110 --> 00:34:41,250
+الواحد يبقى ال U من واحدة لإتنين وال V من أربعة
+
+300
+00:34:41,250 --> 00:34:46,150
+إلى سبعة إذا نحددنا حدود التكامل يبقى مش ضايل إلا
+
+301
+00:34:46,150 --> 00:34:53,610
+انعوض في المسألة تبعتنا فقط لا غير كم؟
+
+302
+00:34:53,610 --> 00:35:02,090
+U باتنين هذي طيب استني شوية جيب ال U هذي بس أه سهل
+
+303
+00:35:02,090 --> 00:35:02,330
+يا بابا
+
+304
+00:35:05,420 --> 00:35:10,740
+طيب يبقى لم يبقى لنا إلا نعوض في التكمل مباشرة
+
+305
+00:35:10,740 --> 00:35:16,560
+يبقى التكمل تبعنا يصير بالشكل اللي عناه الآن بدنا
+
+306
+00:35:16,560 --> 00:35:24,260
+نجلد لانه 2 X تربيع يبقى 2 فيه جل ال X تربيع يبقى
+
+307
+00:35:24,260 --> 00:35:29,540
+هاي هاي ال X تربيع اللي همين او هادي سيئة يبقى
+
+308
+00:35:29,540 --> 00:35:36,840
+بقدر اقول له U على 3 Uعلى تلاتة و الله خلّيها إيش
+
+309
+00:35:36,840 --> 00:35:43,800
+رأيك U زائد V كلها على تلاتة مرة واحدة الكل تربية
+
+310
+00:35:43,800 --> 00:35:53,120
+بعديها ناقص X له U زائد V على تلاتة تمينفي ال Y ال
+
+311
+00:35:53,120 --> 00:35:58,060
+Y اللي هو V على تلاتة نقص اتنين U على تلاتة V على
+
+312
+00:35:58,060 --> 00:36:06,360
+تلاتة نقص اتنين U على تلاتة نقص Y ترابيع V على
+
+313
+00:36:06,360 --> 00:36:13,320
+تلاتة نقص اتنين U على تلاتة الكل ترابيع يبقى ايه
+
+314
+00:36:13,320 --> 00:36:18,880
+الدول العالمين ضايل عندنا الجاكوبين الجاكوبين
+
+315
+00:36:18,880 --> 00:36:26,480
+حسبنا وجيناه طولأقول يا بنات هنا سهلة بالنسبة ليوم
+
+316
+00:36:26,480 --> 00:36:30,020
+في الأول و بالنسبة لي ميلي اتنين اردسهم لأنهم
+
+317
+00:36:30,020 --> 00:36:37,700
+اعداد و تأثيريه زي تأثيري بيه اذا لو راحت قلتل DVD
+
+318
+00:36:37,700 --> 00:36:44,600
+بقى الحدود التكامل بيه بتتغير من عند الأربعة لغاية
+
+319
+00:36:44,600 --> 00:36:49,160
+السابعة و اليوم بتتغير من سنة واحدة لغاية اتنين
+
+320
+00:36:49,880 --> 00:36:55,020
+تمام؟ يبقى ضال علينا بصر بصر هالمثلة تبقى حلة
+
+321
+00:36:55,020 --> 00:37:00,460
+المشكلة هنا هي التلت برا تكامل من سالب واحد لإتنين
+
+322
+00:37:00,460 --> 00:37:05,760
+تكامل من أربعة لسبعة بدا أفك هذا يا بنات يبقى هذا
+
+323
+00:37:05,760 --> 00:37:13,940
+ايش مصير؟ تسعين في ال U تربية زائد اتنين U V زائد
+
+324
+00:37:13,940 --> 00:37:17,980
+B تربية مربع التلتة بتسعى وعندي اتنين برا يبقى
+
+325
+00:37:17,980 --> 00:37:25,300
+تسعين وI فكتنجي لبعض هذه تلت في تلت بطلع برا في
+
+326
+00:37:25,300 --> 00:37:35,160
+كده اش ابتسع تمام نضرب هدول في بعض يبقى هذه U في V
+
+327
+00:37:35,160 --> 00:37:47,340
+U في V هذه الناقص اتنين U تربيعوهنا زائد V تربيع
+
+328
+00:37:47,340 --> 00:37:54,020
+نقص اتنين U في ال V والتلاتة مع التلاتة مع التلاتة
+
+329
+00:37:54,020 --> 00:37:55,400
+طلعت برا بالمرة
+
+330
+00:38:01,460 --> 00:38:06,160
+ما رايك اخد التسعة برا بالمرة يالا سهللي الشغل هاي
+
+331
+00:38:06,160 --> 00:38:12,460
+التسعة برا بيضل عندنا مين؟ بيضل عندنا هنا V تربيع
+
+332
+00:38:12,460 --> 00:38:21,960
+ناقص اربعة U في ال V زائد اربعة U تربيع بظبط هيك؟
+
+333
+00:38:21,960 --> 00:38:29,180
+خلصنا منها طيب بدي امسح بس القرن هذيمش هنكمل
+
+334
+00:38:29,180 --> 00:38:37,520
+مسألتنا، لحد هنا قفلنا و هذا ال DVD طيب،
+
+335
+00:38:37,520 --> 00:38:43,300
+إيش رايك؟ تسعة مع تسعة مع تسعة نطلع ورا، وعندي هنا
+
+336
+00:38:43,300 --> 00:38:45,520
+طول بصير واحد على سبعة وإيش؟
+
+337
+00:38:54,250 --> 00:38:59,570
+هي تكمل من اربع الى سبعة و هيتكمل من اربع الى
+
+338
+00:38:59,570 --> 00:39:01,090
+اتنين
+
+339
+00:39:02,970 --> 00:39:09,510
+زائد أربعة U في V زائد اتنين V تربيع فكّيت الجثث
+
+340
+00:39:09,510 --> 00:39:14,430
+الأول بدا أدخل إشارة السلف على الجثث الثاني يبقى
+
+341
+00:39:14,430 --> 00:39:22,110
+ناقص U في V زائد اتنين U تربيع ناقص V تربيع زائد
+
+342
+00:39:22,110 --> 00:39:28,790
+اتنين U في Vاللي بعده هدخل إشارة ناقص يبقى ناقص V
+
+343
+00:39:28,790 --> 00:39:36,670
+تربيع زائد أربع U في V ناقص أربع U تربيع قفل الجوز
+
+344
+00:39:36,670 --> 00:39:43,150
+وهذا كله مين؟ كله DVD
+
+345
+00:39:46,240 --> 00:39:52,020
+فهذا كلام مدهسان واحد على سبعة وعشرين تكمل من سالب
+
+346
+00:39:52,020 --> 00:39:57,020
+واحد للاتنين تكمل من اربعة الى سبعة طلع يا بنات
+
+347
+00:39:57,020 --> 00:40:03,400
+اتنين U تربيع و اتنين U تربيع اربعة U تربيع و سالب
+
+348
+00:40:03,400 --> 00:40:09,820
+اربعة U تربيع غير مأسوف عليهم مع السلامة ندى نشوف
+
+349
+00:40:09,820 --> 00:40:20,180
+ال U في ال V اربعة U في Vو اتنين U في V بستة U في
+
+350
+00:40:20,180 --> 00:40:27,360
+V شيل منهم واحد و يظل خمسة U في V و اربعة تسعة U
+
+351
+00:40:27,360 --> 00:40:36,630
+في V يبقى تسعة U في ال V ال V تربيعيبقى هذا اتنين
+
+352
+00:40:36,630 --> 00:40:43,110
+في تربيع و سالب واحد في تربيع و سالب واحد في تربيع
+
+353
+00:40:43,110 --> 00:40:49,350
+برضه غير مأسوف على شبابهم يبقى مع السلام شو ضايق
+
+354
+00:40:49,350 --> 00:40:54,910
+عندي؟ مش ضايق الا دي VDU وضعيق كويس يعني هذا
+
+355
+00:40:54,910 --> 00:40:59,570
+اختصار ممتاز جدا طب ماهيش رأيك تسعة مع تسعة كمان
+
+356
+00:40:59,570 --> 00:41:05,500
+الطير؟مع الصلامة يبقى هذا الكلام بده يساوي الطول
+
+357
+00:41:05,500 --> 00:41:11,460
+وهي تكامل من سالب واحد دليل اتنين تكامل من اربعة
+
+358
+00:41:11,460 --> 00:41:20,920
+لغاية سبعة لل U V D V D U نمسح اللي فوق هذا اللي
+
+359
+00:41:20,920 --> 00:41:21,900
+مالك شخصيات
+
+360
+00:41:36,130 --> 00:41:42,630
+طيب هذا الكلام يساوي قلت مالكش دعوة وتكامل من سالب
+
+361
+00:41:42,630 --> 00:41:48,590
+واحد لغاية اتنين ونجي نكامل بالنسبة الى V يبقى V
+
+362
+00:41:48,590 --> 00:41:55,310
+تربيع على اتنين V تربيع على اتنين من عند الأربعة
+
+363
+00:41:55,310 --> 00:42:02,860
+لغاية السبعة وبظل عندنا U في الديم تماممش رايك
+
+364
+00:42:02,860 --> 00:42:09,340
+نطلع النص برا مع تلس فصير كده؟ فصير سُدس تكامل من
+
+365
+00:42:09,340 --> 00:42:15,880
+سالب واحد إلى اتنين و سبعة في سبعة في تسعة واربعين
+
+366
+00:42:15,880 --> 00:42:24,900
+ناقص اربع في اربع اللي هو ست عشر كله خلصنا منه في
+
+367
+00:42:24,900 --> 00:42:32,800
+ال UDأظن ستة من تسعة بيظل تلاتة و تلاتين يبقى هذا
+
+368
+00:42:32,800 --> 00:42:39,480
+هنا بصير تلاتة و تلاتين على ستة تكامل من سالب واحد
+
+369
+00:42:39,480 --> 00:42:45,640
+لليتنين لليوديو هذا الكلام بده يساوي تلاتة و
+
+370
+00:42:45,640 --> 00:42:51,160
+تلاتين على ستة في اختصار على تلاتة بيظل احداشر على
+
+371
+00:42:51,160 --> 00:42:59,510
+اتنينوهذه 6 يتربي على الاتنين من سالب واحد لغاية
+
+372
+00:42:59,510 --> 00:43:09,390
+اتنين يبقى هذا الكلام 11 على 4 فيه هنا أربع ناقص
+
+373
+00:43:09,390 --> 00:43:14,970
+ناقص واحد تربيه لهو قدر بواحد بضل تلاتة في احداشر
+
+374
+00:43:14,970 --> 00:43:22,550
+تلاتة و تلاتين على أربع قيمة هذا التكاملحاضرة فيك
+
+375
+00:43:22,550 --> 00:43:28,390
+ما بتحب تسأل أي سؤال هنا؟ خلاص؟
+
+376
+00:43:28,840 --> 00:43:33,060
+طيب أخدنا الأن بدل المثال أربع على ال double
+
+377
+00:43:33,060 --> 00:43:41,960
+integral ننتقل الأن لل triple integral لأن إذا
+
+378
+00:43:41,960 --> 00:43:45,380
+انتقلنا لل triple integral للنقطة الثانية من هذا
+
+379
+00:43:45,380 --> 00:43:50,140
+ال section نحتاج أن نذهب نحسن ال Jacobian الأول
+
+380
+00:43:50,140 --> 00:43:54,420
+لأنه سيصبح عندي بدل المتغير جدا كمان يعني لأن عندي
+
+381
+00:43:54,420 --> 00:44:03,310
+X وY وZالجبال هم هيكون U و V و W بدل ما كنا نشتغل
+
+382
+00:44:03,310 --> 00:44:08,390
+فيه في الليل، بدنا نشتغل في ال space، الفراغ،
+
+383
+00:44:08,390 --> 00:44:16,190
+كويس؟ يا فجأة؟ فنمسح هذا و ننتقل الأن إلى الشغل في
+
+384
+00:44:16,190 --> 00:44:16,870
+ال space
+
+385
+00:44:41,810 --> 00:44:54,650
+نمسح هذه خلاص يبقى
+
+386
+00:44:54,650 --> 00:44:59,270
+ننتقل إلى النقطة الثانية من هذا ال section وهي
+
+387
+00:44:59,270 --> 00:45:05,490
+substitution substitution
+
+388
+00:45:05,490 --> 00:45:09,270
+and
+
+389
+00:45:09,270 --> 00:45:10,730
+triple
+
+390
+00:45:21,060 --> 00:45:24,160
+نفس المعلومات لذلك بدنا نقوم باستخدام جاكوبيا ان
+
+391
+00:45:24,160 --> 00:45:30,780
+دوري نقوم باستخدام جاكوبيا ان دوري
+
+392
+00:45:33,330 --> 00:45:38,370
+سيكون محدد ثلاثي أو من الدرجة التالتة وليس من
+
+393
+00:45:38,370 --> 00:45:43,810
+الدرجة الثالثة يبقى بقول هنا partial x على partial
+
+394
+00:45:43,810 --> 00:45:47,870
+u partial x على partial y هذه كانت في المحدد
+
+395
+00:45:47,870 --> 00:45:53,970
+الثلاثي باضيف عليها partial x على partial main w
+
+396
+00:45:53,970 --> 00:45:59,390
+اللي عملنا لل x بدنا نروح نعمله ل main لل y يبقى
+
+397
+00:45:59,390 --> 00:46:05,390
+partial yعلى partial W.اللي عملناه دروايب نروح
+
+398
+00:46:05,390 --> 00:46:10,130
+نعمله للـ Z على partial U و partial Z على partial
+
+399
+00:46:10,130 --> 00:46:19,650
+V و partial Z على partial W. هذا المحدد بالله.طيب
+
+400
+00:46:19,650 --> 00:46:25,250
+بدنا نبدأ نعطي أمثلة على ذلك وسأبدأ ان شاء الله
+
+401
+00:46:25,250 --> 00:46:35,500
+بما وعدناكوا به قبل ذلك.يبقى examples بدنا
+
+402
+00:46:35,500 --> 00:46:46,700
+نبدأ بأول detail بيقول ان spherical coordinates
+
+403
+00:46:46,700 --> 00:46:51,360
+find
+
+404
+00:46:51,360 --> 00:46:55,420
+الجقابل
+
+405
+00:46:55,420 --> 00:46:58,640
+تبع الروة وفاى وثيتا
+
+406
+00:47:08,590 --> 00:47:14,130
+طب اذا عارفين الإجابة كداش الإجابة؟ Rotary بي
+
+407
+00:47:14,130 --> 00:47:19,250
+assign في إذا بدي أوصل لهذه الإجابة بتروح اكتب X
+
+408
+00:47:19,250 --> 00:47:25,570
+بدلالة رو و في و ثيتا Y بدلالة رو و في و ثيتا Z
+
+409
+00:47:25,570 --> 00:47:32,970
+بدلالة رو و في و ثيتا طيب نجي الآن ال X كداش ال X
+
+410
+00:47:32,970 --> 00:47:34,790
+يا بنات اخدها المرة الماضية
+
+411
+00:47:39,520 --> 00:47:51,100
+cos θ الان ال y كانت ره صين فاي صين ثيتا إذا كانت
+
+412
+00:47:51,100 --> 00:47:59,000
+كده ره قصين فاي أبصر كده في تيتا ولا فيش تيتا بلاش
+
+413
+00:47:59,000 --> 00:48:07,040
+يبقى بنا نروح ناخد جاكوبيا تبع ره وفاي وثيتا وغير
+
+414
+00:48:07,040 --> 00:48:13,190
+المحدديبقى بالنا تفاضل ال X بالنسبة لأول متغير،
+
+415
+00:48:13,190 --> 00:48:18,070
+مين أول متغير؟ اللي هو ال raw يبقى partial X على
+
+416
+00:48:18,070 --> 00:48:24,630
+partial raw اللي هو مين بيطلع عندنا؟ Psi Phi Cos
+
+417
+00:48:24,630 --> 00:48:31,350
+Phi partial X على partial Phi اللي هو مين؟
+
+418
+00:48:36,000 --> 00:48:41,440
+ثيتا والرو مانهم مش علاقة بعدك بتفضل X بالنسبة
+
+419
+00:48:41,440 --> 00:48:45,100
+لثيتا الرو ساين الفاي مانهم مش علاقة ال cosine
+
+420
+00:48:45,100 --> 00:48:56,000
+بسالب ساين يبقى سالب رو ساين فاي ساين ثتر خلاص من
+
+421
+00:48:56,000 --> 00:48:59,700
+الصف الأول في المحدد نجي للصف الثاني اللي عملنا ال
+
+422
+00:48:59,700 --> 00:49:01,980
+X بنروح نعمله لمين ل Y
+
+423
+00:49:07,130 --> 00:49:13,810
+تفاضلها بالنسبة ل رو تفاضلها بالنسبة لفاي يبقى رو
+
+424
+00:49:13,810 --> 00:49:24,250
+كوساين فاي ساين ثيتا تفاضلها بالنسبة لثيتا يبقى رو
+
+425
+00:49:24,250 --> 00:49:29,610
+ساين فاي مالكش دعوة وتفاضلوا الـSin بكساين ثيتا
+
+426
+00:49:29,610 --> 00:49:35,450
+نيجي للصف التالت نفضل الـZ بالنسبة إلى رو
+
+427
+00:49:37,910 --> 00:49:45,210
+بنفضلها بالنسبة لفاي يبقى ماقصره في صين الفاي
+
+428
+00:49:45,210 --> 00:49:54,070
+بنفضلها بالنسبة لثيتا يبقى بزيرو نفك هذا المحدد
+
+429
+00:49:54,070 --> 00:50:02,550
+باستخدام عناصر الصفرالعمود الأخضر صف التالت أو
+
+430
+00:50:02,550 --> 00:50:09,530
+العمود التالت لإن فيه Zero يختصر لي طول القيمة
+
+431
+00:50:09,530 --> 00:50:14,130
+يفجأ باجي بقول له هذا المحدد بالدرسية هو cosine
+
+432
+00:50:14,130 --> 00:50:20,410
+فايفين هو شو طويل صفه هو عموده فماشي بيبقى اللي
+
+433
+00:50:20,410 --> 00:50:27,090
+عندنا قاعد البلد عشان ما تقلشاحنا هنا يبقى ر تربيع
+
+434
+00:50:27,090 --> 00:50:36,030
+صين فاي كوسين فاي كسين تربيع تتر يبقى هاي ر تربيع
+
+435
+00:50:36,030 --> 00:50:43,190
+ر تربيع ر
+
+436
+00:50:43,190 --> 00:50:54,880
+تربيع كسين ولا صينفاي كوساين فاي كوساين تربيع ثيتا
+
+437
+00:50:54,880 --> 00:51:01,180
+ناقص الثانوي فى عندى إشارة ناقص بصير زرق قراءة
+
+438
+00:51:01,180 --> 00:51:10,920
+تربيع صين فاي كوساين فاي صين تربيع ثيتا قفلنا
+
+439
+00:51:10,920 --> 00:51:15,590
+القصربعد ذلك وصلنا لهذه حسب قاعدة الشباط اللي
+
+440
+00:51:15,590 --> 00:51:21,630
+شباطها بعيد كان ناقص مع ناقص بيصير زائد يبقى زائد
+
+441
+00:51:21,630 --> 00:51:32,850
+رو في صين فاي فايها برا نجي اشطق صفه و عموده اش
+
+442
+00:51:32,850 --> 00:51:39,750
+بيصير عندنا رو صين تربيع فاي و صين تربيع تتا
+
+443
+00:51:47,650 --> 00:51:54,250
+الرئيسي ناقص مع ناقص بيصير زائد وهذه الرقم بضلال
+
+444
+00:51:54,250 --> 00:51:59,290
+نمين يبقى ساين تربية في ساين تربية ثيتا يبقى ساين
+
+445
+00:51:59,290 --> 00:52:06,730
+تربية في ساين تربية ثيتا قفل للجوز زائد زيرو في
+
+446
+00:52:06,730 --> 00:52:11,590
+محدد و بزير يبقى سرنجل يكوبي
+
+447
+00:52:14,580 --> 00:52:20,900
+وثيتا بده يسار على الاقل هناك واضح ان عندي رو
+
+448
+00:52:20,900 --> 00:52:28,240
+تربيع صين فاي كوسين فاي عامل مشترك وعندي كوسين برا
+
+449
+00:52:28,240 --> 00:52:36,440
+فبصير رو تربيع صين فاي كوسين تربيع فاي يبقى هاي رو
+
+450
+00:52:36,440 --> 00:52:44,640
+تربيع كوسين تربيع في في صين الفايأخدنا رو تربيع
+
+451
+00:52:44,640 --> 00:52:50,540
+فاي كوساين فاي برا كدهش بيبقى لدي هنا بنات كوساين
+
+452
+00:52:50,540 --> 00:52:55,560
+تربيع ثيتا طيب أخدنا رو تربيع برا و أخدنا كوساين
+
+453
+00:52:55,560 --> 00:53:01,960
+كوساين بيبقى زائد مين؟ زائد ساين تربيع ثيتا هذا
+
+454
+00:53:01,960 --> 00:53:07,900
+الترم الأول نجي للترم التاني عندك هنا رو ساين
+
+455
+00:53:07,900 --> 00:53:21,230
+تربيع فاي عامل مشتركوعندك رو صين فاي برا يبقى
+
+456
+00:53:21,230 --> 00:53:33,410
+زائد رو صين او رو تربيع صين تكيب فاي برا هذا يعني
+
+457
+00:53:33,410 --> 00:53:36,810
+كوصين تربيع تيتا زائد كوصين تربيع تيتا
+
+458
+00:53:40,640 --> 00:53:47,220
+زائد صين تربية تسعة طبعا هذه كدهش و هذه كدهش واحد
+
+459
+00:53:47,220 --> 00:53:52,500
+راحة يبقى هذا الكلام بالدوسام شو رايك؟ عندي رو
+
+460
+00:53:52,500 --> 00:53:59,780
+تربية موجودة في الإتنين وعندي صين في موجودة في
+
+461
+00:53:59,780 --> 00:54:05,600
+الإتنينيبقى بضال عندي هنا قداش و sign تربية فيه و
+
+462
+00:54:05,600 --> 00:54:10,960
+هنا بضال قداش عندي sign تربية فيه لانه خد sign برا
+
+463
+00:54:10,960 --> 00:54:17,080
+اللي بين قسين قداش يبقى هذا كمان بواحد يبقى بضال
+
+464
+00:54:17,080 --> 00:54:23,860
+قداش ر تربية sign فيهوهذا ما وعدناكم به في
+
+465
+00:54:23,860 --> 00:54:30,380
+المحاضرة الماضية لما انحولنا من DX DY DZ إلى D ρو
+
+466
+00:54:30,380 --> 00:54:35,600
+D فاي D ثيتا ضربنا في روتر بيه sign فاي ويومها كان
+
+467
+00:54:35,600 --> 00:54:39,240
+السؤال من أين لك هذا فقلنا لكم ان شاء الله في ال
+
+468
+00:54:39,240 --> 00:54:42,140
+section القادم اللي هو ال section اللي بين ايدينا
+
+469
+00:54:42,140 --> 00:54:48,360
+اليوم وها نحن نفي بوعدنا طيب حد إلى أي تساؤل هذا
+
+470
+00:54:48,360 --> 00:54:50,300
+قبل أن أذهب إلى المثال الثاني
+
+471
+00:54:55,430 --> 00:55:04,670
+تالث نسمة بيقول let D be the region let D be the
+
+472
+00:55:04,670 --> 00:55:19,350
+region عبارة عن المنطقة N X Y Z space defined
+
+473
+00:55:19,350 --> 00:55:22,810
+by the inequalities defined
+
+474
+00:55:23,950 --> 00:55:34,450
+by the inequalities المتباينات
+
+475
+00:55:34,450 --> 00:55:40,450
+ال X أكبر من أو يساوي واحد وأقل من أو يساوي اتنين
+
+476
+00:55:40,450 --> 00:55:46,970
+وال X في Y أكبر من أو يساوي Zero أقل من أو يساوي
+
+477
+00:55:46,970 --> 00:55:52,630
+اتنين وال Z أكبر من أو يساوي Zero أقل من أو يساوي
+
+478
+00:55:52,630 --> 00:55:52,990
+واحد
+
+479
+00:55:59,070 --> 00:56:04,010
+خلّي أحسب Value
+
+480
+00:56:04,010 --> 00:56:16,850
+تلت تكمنات على D لمين لل X تربيع Y زائد تلاتة XYZ
+
+481
+00:56:16,850 --> 00:56:26,490
+كل هذا DX DY DZ By applying
+
+482
+00:56:30,360 --> 00:56:41,800
+applying the transformation the transformation
+
+483
+00:56:41,800 --> 00:56:45,800
+ال
+
+484
+00:56:45,800 --> 00:56:56,080
+U بده يساوي ال X و ال V بده يساوي ال XY و ال W بده
+
+485
+00:56:56,080 --> 00:57:07,420
+يساوي تلاتة Zand integrate over
+
+486
+00:57:07,420 --> 00:57:20,480
+an appropriate region
+
+487
+00:57:20,480 --> 00:57:26,300
+D in
+
+488
+00:57:26,300 --> 00:57:28,100
+the
+
+489
+00:57:31,390 --> 00:57:37,210
+W Space الـ U V W Space
+
+490
+00:58:15,770 --> 00:58:20,850
+بنرجع لسؤالنا مرة ثانية، بيقول افترض D هي المنطقة
+
+491
+00:58:20,850 --> 00:58:26,150
+اللي في ال X,Y,Z space والمعرفة بالمتباينات X
+
+492
+00:58:26,150 --> 00:58:33,090
+محصورة بين 1 و 2، X في ال Y محصورة بين 0 و 2، Z
+
+493
+00:58:33,090 --> 00:58:39,850
+محصورة بين Z و 1يقول احسبلي التكمل اللى قدامنا هذى
+
+494
+00:58:39,850 --> 00:58:44,210
+كيف By applying that transformation يبقى اعطانى
+
+495
+00:58:44,210 --> 00:58:51,150
+تحويلة ال U تسوى ال X ال V تسوى ال X في Y ال W
+
+496
+00:58:51,150 --> 00:58:57,080
+يسوى تلاتة Zالأصل أنه يعطيني الـ z بدلالة
+
+497
+00:58:57,080 --> 00:59:01,600
+المتغيرات التلاتة هنا لكن هنا ياشقال بمين الموضوع
+
+498
+00:59:01,600 --> 00:59:08,560
+إذا شغلتنا أحسب كله من x و y و z بدلالة ال u و ال
+
+499
+00:59:08,560 --> 00:59:12,040
+v و ال w وبعد هيك نشوف كيف يصير
+
+500
+00:59:17,890 --> 00:59:22,410
+أفضل لما أقول لي ال U تساوي ال X يبقى ال X بتساوي
+
+501
+00:59:22,410 --> 00:59:32,350
+ال U تمام؟ انا بدي ال Y V على X و ال X بقدرش ب U
+
+502
+00:59:32,350 --> 00:59:40,770
+يبقى هذا بدي أعطيك ان Y تساوي V على U و هذه ال Z
+
+503
+00:59:40,770 --> 00:59:48,350
+بتساوي طول W أو W على 3يبقى بناء ان علي اروح نكتب
+
+504
+00:59:48,350 --> 00:59:54,050
+المتغيرات اللى عندى بدلالة من المتغيرات الجديدة
+
+505
+00:59:54,050 --> 00:59:59,290
+اللى هو U وV وW لذا نخليه نحسب ال Jacobian بالمرة
+
+506
+00:59:59,290 --> 01:00:08,890
+ال Jacobian تبع ال U و ال V و ال W في هذه المحددة
+
+507
+01:00:08,890 --> 01:00:14,630
+بنجي هنا partial X على partial U partial Xعلى
+
+508
+01:00:14,630 --> 01:00:20,250
+partial v partial x على partial w partial y على
+
+509
+01:00:20,250 --> 01:00:25,390
+partial u partial y على partial v partial y على
+
+510
+01:00:25,390 --> 01:00:30,810
+partial w partial z على partial u partial z على
+
+511
+01:00:30,810 --> 01:00:35,370
+partial v partial z على partial w
+
+512
+01:00:38,600 --> 01:00:44,800
+يبقى هذا هو المحدد تمام تفاض ال X بالنسبة إلى U
+
+513
+01:00:44,800 --> 01:00:50,280
+بواحد تفاض ال X بالنسبة ل V و بالنسبة ل W ب Zero
+
+514
+01:00:50,280 --> 01:00:57,580
+ماعنديش يبقى هاي Zero وهاي Zeroتفاضل ال Y بالنسبة
+
+515
+01:00:57,580 --> 01:00:58,500
+إلى U
+
+516
+01:01:10,600 --> 01:01:14,740
+طيب صبر شو بس بس بس بس بس بس بس بس بس بس بس بس بس
+
+517
+01:01:14,740 --> 01:01:14,920
+بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس
+
+518
+01:01:14,920 --> 01:01:20,000
+بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس
+
+519
+01:01:20,000 --> 01:01:22,660
+بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس
+
+520
+01:01:22,660 --> 01:01:22,800
+بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس
+
+521
+01:01:22,800 --> 01:01:22,880
+بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس بس
+
+522
+01:01:22,880 --> 01:01:31,840
+بس بس بس بس بس بس بس بس بس
+
+523
+01:01:31,840 --> 01:01:40,630
+بس بماشي يبقى هو ال V مالوش دعوة و ال 1 علي U سالب
+
+524
+01:01:40,630 --> 01:01:46,590
+1 علي U تربية يبقى سالب V علي U تربية يبقى سالب V
+
+525
+01:01:46,590 --> 01:01:53,150
+علي U تربية طب بدنا تفاضلها بالنسبة ل V 1 علي U
+
+526
+01:01:53,150 --> 01:02:00,050
+يبقى 1 علي U يبقى تفاضلها بالنسبة ل مين ل W بزيرو
+
+527
+01:02:00,050 --> 01:02:10,010
+طب بدنا ل Z بالنسبة ل Uزيرو وزيرو هنا طول يالله يا
+
+528
+01:02:10,010 --> 01:02:17,170
+بنات قداش؟ يعني
+
+529
+01:02:17,170 --> 01:02:23,590
+قداش الجواب دي هو اللي هيكأليس محدد لمصوفة مثلثة
+
+530
+01:02:23,590 --> 01:02:29,010
+سفلة يبقى حاصل ضرب عناصر القطر الرئيسي فقط ده يغير
+
+531
+01:02:29,010 --> 01:02:33,950
+لإنه يطلع هي القطر الرئيسي ولفوق كل أسفار محدد
+
+532
+01:02:33,950 --> 01:02:37,630
+المصوفة المثلثة العليا أو المصوفة المثلثة السفلة
+
+533
+01:02:38,800 --> 01:02:42,420
+حاصل ضرب عناصر القطر الرئيسي أو الـ scalar matrix
+
+534
+01:02:42,420 --> 01:02:47,060
+يبقى بس بنضرب حاصل ضرب عناصر القطر الرئيسي ينفذش
+
+535
+01:02:47,060 --> 01:02:52,320
+بيطلع واحد على تلاتة U مش مصدقة تعالى انفك
+
+536
+01:02:52,320 --> 01:02:57,240
+باستخدام عناصر الصف الأول وشط بصفه عموده كل واحد
+
+537
+01:02:57,240 --> 01:03:02,110
+على Uفي تلت بواعة تلت U نقص Zero بواعة تلت U بواعة
+
+538
+01:03:02,110 --> 01:03:05,910
+بواعة تلت U. إذا حصل ضرب عناصر القطر الرئيسي
+
+539
+01:03:05,910 --> 01:03:11,050
+مباشرة. هذا مين؟ هذا ال Jacobian تبع ال U و ال V و
+
+540
+01:03:11,050 --> 01:03:17,670
+ال W. طيب احنا ضايل عندنا حدود التكامل. بدي أعرف U
+
+541
+01:03:17,670 --> 01:03:25,530
+بدي تتغير من وين لوين. أظن قصتنا بسيطة.مافيش مشكلة
+
+542
+01:03:25,530 --> 01:03:30,830
+ال U من واحد للاثنين.طيب تعالى نشوف نشيل ال X ونحط
+
+543
+01:03:30,830 --> 01:03:36,470
+ال U بيصير محصولة بين واحد ومين والاتنين طب تعالى
+
+544
+01:03:36,470 --> 01:03:41,850
+للتانية يعني التانية عندك لو قسمت على X بيصير Y
+
+545
+01:03:41,850 --> 01:03:48,830
+محصولة بين Zero واتنين على X يبقى هنا اها باجي
+
+546
+01:03:48,830 --> 01:03:56,090
+بقول A Zeroاقل من او يسوى ال X Y اقل من او يسوى ال
+
+547
+01:03:56,090 --> 01:04:00,030
+Y اقل
+
+548
+01:04:00,030 --> 01:04:06,310
+من او يسوى ال Y اقل من او يسوى ال Y اقل من او يسوى
+
+549
+01:04:06,310 --> 01:04:06,570
+ال Y اقل من او يسوى ال Y اقل من او يسوى ال Y اقل
+
+550
+01:04:06,570 --> 01:04:06,830
+من او يسوى ال Y اقل من او يسوى ال Y اقل من او يسوى
+
+551
+01:04:06,830 --> 01:04:07,530
+ال Y اقل من او يسوى ال Y اقل من او يسوى ال Y اقل
+
+552
+01:04:07,530 --> 01:04:07,530
+من او يسوى ال Y اقل من او يسوى ال Y اقل من او يسوى
+
+553
+01:04:07,530 --> 01:04:12,150
+ال Y اقل من او يسوى ال Y اقل من او يسوى ال Y اقل
+
+554
+01:04:12,150 --> 01:04:18,970
+من او يسوى ال Y اقل من او يأكبر من أو تسوى Zero
+
+555
+01:04:18,970 --> 01:04:26,430
+أقل من أو يسوى اتنين على U طيب ممتاز من خلال
+
+556
+01:04:26,430 --> 01:04:35,450
+انتيجة U ازد و على تلاتة يبقى بقى اني بقوله ازد
+
+557
+01:04:35,450 --> 01:04:38,830
+تسوى W على تلاتة
+
+558
+01:04:49,700 --> 01:04:55,020
+يبقى الـ W محصورة بين الصفر و بين الواحد و بين
+
+559
+01:04:55,020 --> 01:05:07,180
+التلاتة اذا مشكلتي أصبحت مالها أصبحت محلولة ال
+
+560
+01:05:07,180 --> 01:05:09,180
+Y محصورة بين الصفر و الاتنين
+
+561
+01:05:13,130 --> 01:05:19,010
+اه اه فهمت عليك اه هذه امانات على طول الخط هذا بدي
+
+562
+01:05:19,010 --> 01:05:24,110
+اعطيلك انه zero اقل من او يساوي ال Y اللي عندنا من
+
+563
+01:05:24,110 --> 01:05:36,370
+وراها V على U يبقى هذه V على U اقل من او يساوي 2
+
+564
+01:05:36,370 --> 01:05:42,900
+على Uأُضر بكله في U بصير أن دجاج بصير ال zero أقل
+
+565
+01:05:42,900 --> 01:05:47,900
+من أو يساوي بيه أقل من أو يساوي جداش اتنين يبقى
+
+566
+01:05:47,900 --> 01:05:54,380
+حددت حدود التكامل تحديدا سليما وجبت الجاكوبيا لم
+
+567
+01:05:54,380 --> 01:06:01,600
+يبقى إلا عملية التكامل يبقى بروح بقول ثلاث تكاملات
+
+568
+01:06:01,600 --> 01:06:06,480
+وبداجي لجداش لل X تربيع وين ال X؟
+
+569
+01:06:13,570 --> 01:06:25,270
+و ال Y ب V على U يبقى هذه V على U اللي بعدها زائد
+
+570
+01:06:25,270 --> 01:06:37,950
+تلاتة U لأن X ب U و ال Y ب V على U وهذه V على U و
+
+571
+01:06:37,950 --> 01:06:42,650
+ال Z اللي هي W على تلاتة ال W
+
+572
+01:06:45,250 --> 01:06:50,390
+الـ Jacobian الـ Jacobian واحد على تلاتة U يبقى
+
+573
+01:06:50,390 --> 01:07:00,970
+واحد على تلاتة U وهنا D V D و الله ايش D W D W و
+
+574
+01:07:00,970 --> 01:07:07,610
+الله خليها D U في الأول مش مشكلة اي حاجة D W D V D
+
+575
+01:07:07,610 --> 01:07:12,990
+U طبعا واضح فيش فيها شغلات صعبة كتيرة لكن لو خلتها
+
+576
+01:07:12,990 --> 01:07:13,610
+للاخر
+
+577
+01:07:17,020 --> 01:07:22,580
+يبقى بداخل الحدود كوني كتبت ال W يبقى ال W تتغير
+
+578
+01:07:22,580 --> 01:07:29,620
+من أين لأين من Zero لغاية تلاتة ال V ستتغير من
+
+579
+01:07:29,620 --> 01:07:36,320
+Zero لغاية اتنين ال U تتغير من أين لأين من واحد
+
+580
+01:07:36,320 --> 01:07:42,200
+لغاية اتنين الشكل عندنا طيب نبسط المثال تكامل من
+
+581
+01:07:42,200 --> 01:07:47,120
+واحد للاتنين تكامل من صفر للاتنينتكوّن مصطفى الـD
+
+582
+01:07:47,120 --> 01:07:54,120
+تلاتة هذي يا بنات بيظل عندي U في الـV وهذه زائد
+
+583
+01:07:54,120 --> 01:08:02,920
+تلاتة مع تلاتة و الـU مع الـU بيظل بس VW يبقى زائد
+
+584
+01:08:02,920 --> 01:08:12,400
+VW في 101 على تلاتة U DW DVDU
+
+585
+01:08:14,450 --> 01:08:19,190
+طيب هذا الكلام بده يساوي شو رايك التلت برا وهي
+
+586
+01:08:19,190 --> 01:08:25,050
+تكامل من واحد لإتنين وهي تكامل من Zero لغاية
+
+587
+01:08:25,050 --> 01:08:33,710
+التلتة بده يدخل ال U جوا غالي قداش V زائد VW على U
+
+588
+01:08:33,710 --> 01:08:41,790
+في مين؟ في ال DW DVB كيف؟
+
+589
+01:08:42,680 --> 01:08:51,660
+من Zero لإتنين تكامل هنا من Zero لإتنين يبقى الان
+
+590
+01:08:51,660 --> 01:08:56,640
+انا بدأ اكمل بالاسم لمن؟ لل DW يبقى هذا الكلام بده
+
+591
+01:08:56,640 --> 01:09:02,940
+يسوي هاي الطول برا وهي تكاملين من Zero لإتنين ومن
+
+592
+01:09:02,940 --> 01:09:07,460
+واحد لغاية اتنين لل VW
+
+593
+01:09:09,920 --> 01:09:18,680
+اللي هو V W تربيع على 2U و الـ W تتغير من الـ Zero
+
+594
+01:09:18,680 --> 01:09:25,320
+لغاية التلاتة لـ DVD يساوى
+
+595
+01:09:25,320 --> 01:09:31,060
+أي التلت برا و هي تكاملين من صفر لواحد و من الصفر
+
+596
+01:09:31,060 --> 01:09:35,860
+لإتنين يجب أن أشيل الـ W و أضع بدلها من تلاتة
+
+597
+01:09:35,860 --> 01:09:39,180
+تلاتة
+
+598
+01:09:39,180 --> 01:09:49,550
+Vوهنا زائد ال W تربيع بصير تسعة على تسعة V على
+
+599
+01:09:49,550 --> 01:09:57,930
+اتنين U تسعة V على اتنين U تمام؟ ناقص Zero Zero مع
+
+600
+01:09:57,930 --> 01:10:04,970
+السلامة كل هذا في DVD شو رأيك يا بنات؟
+
+601
+01:10:07,810 --> 01:10:14,470
+برا معاكل غير مصوف عليك يبقى هذا الكلام تكامل من
+
+602
+01:10:14,470 --> 01:10:21,870
+zero ل واحد تكامل من zero للإتنين لل V زائد تلاتة
+
+603
+01:10:21,870 --> 01:10:33,210
+V على اتنين U DV DU يبقى هذا الكلام بالدرسام تكامل
+
+604
+01:10:33,210 --> 01:10:34,650
+من zero لواحد
+
+605
+01:10:44,940 --> 01:10:51,440
+والحكي هذا كله من Zero للإتنين لديه يوم. يبقى هذا
+
+606
+01:10:51,440 --> 01:10:55,620
+الكلام يصير تكامل من Zero لواحد.
+
+607
+01:10:59,000 --> 01:11:06,020
+سبحان الله يبقى هذا من واحد للإتنين وهذا من واحد
+
+608
+01:11:06,020 --> 01:11:16,280
+للإتنين وهذا من الواحد للإتنينوهذا من واحد لغاية
+
+609
+01:11:16,280 --> 01:11:23,100
+اتنين وما أنسانيه إلا الشيطان القرعى . هذه فنيات
+
+610
+01:11:23,100 --> 01:11:26,860
+صورة بنات . الكافة
+
+611
+01:11:29,370 --> 01:11:35,050
+طبعا ولبدوا في كافهم كده؟ تلاتة سنين و أزداد و
+
+612
+01:11:35,050 --> 01:11:39,770
+تسعة عمره حد بيظل نايم تلاتمية وتسعة وتسعين و لا
+
+613
+01:11:39,770 --> 01:11:46,630
+تلاتمية وتسعة سنين؟ غريب يعني لكن ما غريب للشيطان
+
+614
+01:11:46,630 --> 01:11:50,430
+أن الله على كل شيء قادر. طيب العوض اذا دي أربعة
+
+615
+01:11:50,430 --> 01:11:57,570
+علي اتنين بيظل كده؟ بيظل اتنينزائد هنا كمان أربع
+
+616
+01:11:57,570 --> 01:12:03,930
+بتروح مع الأربع بضع قداش تلاتة عليهم زائد تلاتة
+
+617
+01:12:03,930 --> 01:12:07,630
+عليهم كله في الديام
+
+618
+01:12:10,040 --> 01:12:17,480
+يبقى هذا الكلام بده يساوي اللي هو اتنين U و هنا
+
+619
+01:12:17,480 --> 01:12:28,460
+زائد تلاتة كده لم absolute value ل U وهذا كله
+
+620
+01:12:28,460 --> 01:12:34,890
+تلاتة لين أبسط تلاتة ليوم الواحدلغاية اتنين يساوي
+
+621
+01:12:34,890 --> 01:12:42,870
+اها اتنين في اتنين اربعة زائد تلاتة لان اتنين ناقص
+
+622
+01:12:42,870 --> 01:12:51,410
+اتنين او هنا ناقص Zero لان الواحد هو Zero تمام
+
+623
+01:12:51,410 --> 01:12:57,750
+مباشرة يبقى هذا الكلام يساوي اتنين زائد تلاتة
+
+624
+01:13:03,230 --> 01:13:10,090
+زائد لن تمانية، من فعلا؟ لن اتنين تقعي بالأمهات
+
+625
+01:13:10,090 --> 01:13:15,770
+بلن تمانية ماعرفنا حد يانا الصبح يعطيكوا الأعافية،
+
+626
+01:13:15,770 --> 01:13:20,950
+يعطيكوا أرقام، مسائل، اتجربوا فيها، ومبناش نكتر
+
+627
+01:13:20,950 --> 01:13:28,130
+عليكم يعنيخاصة دنيا رمضان ووصلنا الى العشر الأواخر
+
+628
+01:13:28,130 --> 01:13:36,610
+فعنا exercises خمسة أشهر تمانية المسائل التالية
+
+629
+01:13:36,610 --> 01:13:47,650
+خمسة وسبعة وتسعة وتلتاش وخمستاش وتلاتة وعشرين
+
+630
+01:13:55,120 --> 01:14:02,860
+طيب اليوم هذا كده في رمضان 17 رمضان و كده في أغسطس
+
+631
+01:14:02,860 --> 01:14:09,400
+17 لتوافق الرقمات وبفضل الله انه يتوافق مع شيء
+
+632
+01:14:09,400 --> 01:14:16,920
+ثانيلا مثل كهذا. إيش حصل في 17 رمضان؟ God was with
+
+633
+01:14:16,920 --> 01:14:21,780
+them وكان النصر حليف منين؟ يبقى احنا بيناية هذا
+
+634
+01:14:21,780 --> 01:14:26,740
+الشرفر من هذا المقارنة كما أن الرسول صلى الله عليه
+
+635
+01:14:26,740 --> 01:14:32,480
+وسلم وضع المشرك إلى يوم مبدأ. تمام؟ يبدأ إن شاء
+
+636
+01:14:32,480 --> 01:14:37,950
+الله يقولمن الناجحين كما انتصر رسوله عليه الصلاة
+
+637
+01:14:37,950 --> 01:14:41,930
+والسلام ونجحة في معركة إيه وانتوا ان شاء الله
+
+638
+01:14:41,930 --> 01:14:46,790
+بتنجحوا يوم الخميس مش القادم هذا اللي غُكرة اللي
+
+639
+01:14:46,790 --> 01:14:51,550
+يقعدوا وكل امتعان يوم خمسة وعشرين ان شاء الله
+
+640
+01:14:51,550 --> 01:14:59,880
+تعالى الساعة عشرة واثقة و الله يلقاها من عالممش
+
+641
+01:14:59,880 --> 01:15:04,680
+مكتوبة؟ على اي حاجة بصفة على وجهة الرئيس بس اللي
+
+642
+01:15:04,680 --> 01:15:08,720
+بيعطيكوا الjawاب مباشرة ايه نعم بس وين القاعة مش
+
+643
+01:15:08,720 --> 01:15:13,460
+عارف يعني انا قرأت على ال net بس الان نسيت الحقيقة
+
+644
+01:15:13,460 --> 01:15:19,500
+ايه نعم ماشي طيب لم يبقى بنات الا انه سامحوا بعضنا
+
+645
+01:15:19,500 --> 01:15:24,580
+بعضا انا بالنسبالي مسامح انه قد يكون انسان استغاب
+
+646
+01:15:24,580 --> 01:15:29,690
+انسان اتكلم في حقه الاخروأنتوا وأنا باطلوا منكم
+
+647
+01:15:29,690 --> 01:15:34,550
+اتسامحوني وبارك الله فيكم السلام عليكم ورحمة الله
+
+648
+01:15:34,550 --> 01:15:35,550
+وبركاته
+
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/RFjaGoXcZxE_postprocess.srt b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/RFjaGoXcZxE_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..fe6154bdf45da2c87ec218b69a304af3f0ad4b7f
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/RFjaGoXcZxE_postprocess.srt
@@ -0,0 +1,2848 @@
+1
+00:00:12,960 --> 00:00:17,880
+بسم الله الرحمن الرحيم عود على build المرة اللي
+
+2
+00:00:17,880 --> 00:00:23,220
+فاتت ابتدأنا في section 14 او 14 و8 share role فعل
+
+3
+00:00:23,220 --> 00:00:27,080
+السلسلة واخدنا الحالة الأولى لو كانت ال function
+
+4
+00:00:27,080 --> 00:00:32,650
+مالا في موضة ليه rideوكل متغير من المتغيرين
+
+5
+00:00:32,650 --> 00:00:37,810
+function T متغير الاخر ثم بعد ذلك أخذنا لو كانت
+
+6
+00:00:37,810 --> 00:00:43,930
+دالة function T ثلاثة متغيرات وكل متغير دالة في
+
+7
+00:00:43,930 --> 00:00:48,830
+متغير الأخر الآن ننتقل إلى النقطة الثانية وهي
+
+8
+00:00:48,830 --> 00:00:55,450
+function T متغيرين أو ثلاثة متغيرات وكل من هذه
+
+9
+00:00:55,450 --> 00:01:00,480
+المتغيرات functionفى two variables وليس فى
+
+10
+00:01:00,480 --> 00:01:05,320
+variable واحد تمام وبالتالي مش هيكون عندنا اشتغال
+
+11
+00:01:05,320 --> 00:01:10,100
+كل زى ما كنا بقوله دي و باي دي تي يبقى بتصير
+
+12
+00:01:10,100 --> 00:01:15,820
+partial و باي partial المتغير اللى عندنا هذا لذلك
+
+13
+00:01:15,820 --> 00:01:21,940
+هنحط هذا الكلام فى الصيغة التالية بجب اقول theorem
+
+14
+00:01:21,940 --> 00:01:25,640
+suppose ذات ال w
+
+15
+00:01:31,010 --> 00:01:39,790
+الـ W تساوي الـ function في X of Y of Z والـ X
+
+16
+00:01:39,790 --> 00:01:48,190
+function في R و S ده اللي فيه متغيرين والـ Y تساوي
+
+17
+00:01:48,190 --> 00:01:53,350
+H of R و S والـ Z كذلك
+
+18
+00:02:11,490 --> 00:02:18,770
+إذا كانت الدول الأربع هذه are differentiable
+
+19
+00:02:18,770 --> 00:02:19,890
+functions
+
+20
+00:02:21,920 --> 00:02:31,660
+دوال قابلة للاشتقاء then w is differentiable
+
+21
+00:02:31,660 --> 00:02:45,920
+function of a and s and نمرا
+
+22
+00:02:45,920 --> 00:02:52,020
+واحدpartial w by partial r سبب partial w by
+
+23
+00:02:52,020 --> 00:02:58,660
+partial x في partial x by partial r زائد partial w
+
+24
+00:02:58,660 --> 00:03:04,920
+by partial y في partial y by partial r زائد
+
+25
+00:03:04,920 --> 00:03:11,220
+partial w by partial z في partial z by partial r
+
+26
+00:03:12,040 --> 00:03:17,740
+نمر اتنين يساوي
+
+27
+00:03:17,740 --> 00:03:23,640
+partial w by partial x في partial x by partial s
+
+28
+00:03:23,640 --> 00:03:29,220
+زائد partial w by partial y partial y by partial s
+
+29
+00:03:29,220 --> 00:03:35,100
+زائد partial w by partial z partial z by partial s
+
+30
+00:03:57,130 --> 00:04:02,670
+مرة تانية بقول المرة هذه عندنا ال w function في
+
+31
+00:04:02,670 --> 00:04:08,830
+ثلاثة متغيرات x و y و z وكل من المتغيرات التلاتة x
+
+32
+00:04:08,830 --> 00:04:13,410
+و y و z ده اللي فيه متغيرين لكن المرة اللي فاتت
+
+33
+00:04:13,410 --> 00:04:19,020
+كانتفي متغير واحد ومن هنا مش قادرين نقول هنا
+
+34
+00:04:19,020 --> 00:04:24,260
+اشتقاقا كليا وانما بيكون اشتقاق جزئي يبقى
+
+35
+00:04:24,260 --> 00:04:27,720
+partially derivative يبقى بالدرجة دلوقتي partial W
+
+36
+00:04:27,720 --> 00:04:29,360
+by partial R
+
+37
+00:04:32,440 --> 00:04:35,920
+مضافا اليها partial w by partial x في partial x by
+
+38
+00:04:35,920 --> 00:04:39,820
+partial r مضافا اليها partial w by partial y
+
+39
+00:04:39,820 --> 00:04:44,440
+partial y by partial r مضافا اليها partial w by
+
+40
+00:04:44,440 --> 00:04:48,450
+partial z في partial z by partial rأحنا جيبنا
+
+41
+00:04:48,450 --> 00:04:54,050
+مشتقة بالنسبة لأحدى المتغيرين اللي هو R يبقى مثل
+
+42
+00:04:54,050 --> 00:04:57,990
+ما جيبنا ال R بنروح نجيب لمين إلى S اللي هو
+
+43
+00:04:57,990 --> 00:05:02,230
+المتغير الأخر فبروح أخد partial W by partial S
+
+44
+00:05:02,230 --> 00:05:07,130
+بنفس الطريقة اللي فوق بس بشيل كل R و بحط مكانها
+
+45
+00:05:07,130 --> 00:05:13,890
+مين بحط مكانها S طب لو حبينا نرسم الشكل هذا خوفا
+
+46
+00:05:13,890 --> 00:05:20,950
+من النسيان على شكل هندسيفبجي بقول هي عندي w تساوي
+
+47
+00:05:20,950 --> 00:05:30,190
+function x و y و z إذا بده يتفرع منها ثلاثة أفرق x
+
+48
+00:05:30,190 --> 00:05:36,710
+و y و z الآن هذا بيكون كله اشتقاق بالنسبة لمن؟
+
+49
+00:05:36,710 --> 00:05:44,340
+بالنسبة إلى R إذاهتجينا المستقى هنا نظرا لأن
+
+50
+00:05:44,340 --> 00:05:48,720
+الدالة في أكتر من متغير فبتقول partial w by
+
+51
+00:05:48,720 --> 00:05:53,580
+partial x وهنا partial w by partial y وهنا partial
+
+52
+00:05:53,580 --> 00:05:59,290
+w by partial zلأن كلهم من X وY وZ دالة في أكتر من
+
+53
+00:05:59,290 --> 00:06:04,390
+متغير فيه متغيرين إذا سيكون الاشتقاق اشتقاقا جزئيا
+
+54
+00:06:04,390 --> 00:06:09,470
+يبقى partial X by partial R partial Y by partial R
+
+55
+00:06:09,470 --> 00:06:15,250
+partial Z by partial A اللي عملنا بالنسبة لR بدنا
+
+56
+00:06:15,250 --> 00:06:20,470
+نروح نعمله كذلك بالنسبة إلى S يبقى بقى اجي بقول له
+
+57
+00:06:20,470 --> 00:06:28,030
+ايه W ليه ال functionفي X و Y و Z وهذا عنده X وهنا
+
+58
+00:06:28,030 --> 00:06:37,950
+Y وهنا Z وهنا S شكلها
+
+59
+00:06:37,950 --> 00:06:44,970
+نادرإذا تفضل ال W بالنسبة لX استقاقا جزئيا يبقى
+
+60
+00:06:44,970 --> 00:06:49,430
+partial W by partial X partial W by partial Y
+
+61
+00:06:49,430 --> 00:06:55,490
+partial W by partial Z هنا كذلك ال X دالة في
+
+62
+00:06:55,490 --> 00:07:00,090
+متغيرين و ال Y دالة في متغيرينإذا هو هكذا إذا بدي
+
+63
+00:07:00,090 --> 00:07:06,150
+يصير partial X by partial S partial Y by partial S
+
+64
+00:07:06,150 --> 00:07:14,130
+partial Z by partial Sإذا لو روحنا الصيغة اللي فوق
+
+65
+00:07:14,130 --> 00:07:19,330
+بسيطة جدا يبقى بضرب هذا في هذا زاد هذا في هذا زاد
+
+66
+00:07:19,330 --> 00:07:24,150
+هذا في هذا بكون حصلت عالميا على تفاضل ال W بالنسبة
+
+67
+00:07:24,150 --> 00:07:30,330
+لR بالمثل تفاضل ال W بالنسبة إلى S يبقى بضرب اتنين
+
+68
+00:07:30,330 --> 00:07:32,910
+الدول في بعض زاد اتنين الدول في بعض زاد اتنين
+
+69
+00:07:32,910 --> 00:07:38,050
+الدول في بعضيبقى سواء كانت بالرسم أو بالجزء النظر
+
+70
+00:07:38,050 --> 00:07:42,430
+الأول كله الأثنين نفس النتيجة يبقى الرسمة فقط
+
+71
+00:07:42,430 --> 00:07:53,790
+لتثبيت المعلومة نعطي مثال example بقول
+
+72
+00:07:53,790 --> 00:08:03,770
+let ال W بدأت ساوي لن X تربيع لن X تربيع زائد Y
+
+73
+00:08:07,520 --> 00:08:19,660
+تربية وال X بدها تساوي U في E أس V في Cos U وال Y
+
+74
+00:08:19,660 --> 00:08:29,940
+بدها تساوي U في E أس V في Cos U وال Z بدها تساوي U
+
+75
+00:08:29,940 --> 00:08:33,600
+في E أس V Find
+
+76
+00:08:35,410 --> 00:08:45,530
+المطلوب الأول نمرا a partial w by partial u by its
+
+77
+00:08:45,530 --> 00:08:54,450
+chain rule يبقى بواصل قاعدة السلسلة نمرا b partial
+
+78
+00:08:54,450 --> 00:09:04,450
+w by partial u directly مباشرة
+
+79
+00:09:05,920 --> 00:09:12,960
+after expressing are tab expressing
+
+80
+00:09:12,960 --> 00:09:20,340
+w
+
+81
+00:09:20,340 --> 00:09:29,020
+in terms of u and v
+
+82
+00:09:44,280 --> 00:09:48,940
+سؤال مرة تانية، ماعطيني w function في ثلاثة
+
+83
+00:09:48,940 --> 00:09:54,820
+متغيرات، لإن x تربية زي y تربية زي z تربية وكل من
+
+84
+00:09:54,820 --> 00:10:02,480
+x و y و z دالة في متغيرين، اللي همين u و vوطلب
+
+85
+00:10:02,480 --> 00:10:08,100
+مشتقة ال W بالنسبة لمن؟ بالنسبة إلى U يبقى كأنه
+
+86
+00:10:08,100 --> 00:10:11,640
+احنا عند الحالة الأولى اللى عندناها دى بس بدل R
+
+87
+00:10:11,640 --> 00:10:16,260
+حطينا مكانها مين؟ حطينا مكانها U قال ليه؟ بدي
+
+88
+00:10:16,260 --> 00:10:21,820
+اشتغل هذا بصرفين يبقى بدي اجيب له partial W by
+
+89
+00:10:21,820 --> 00:10:27,600
+partial U الان W فيه ثلاثة متغيرات يبقى بقوله
+
+90
+00:10:27,600 --> 00:10:33,680
+partial Wبارشيل X بارشيل X بارشيل U بارشيل W
+
+91
+00:10:33,680 --> 00:10:39,560
+بارشيل Y بارشيل Y بارشيل U زائد بارشيل W بارشيل Z
+
+92
+00:10:39,560 --> 00:10:45,980
+بارشيل Z بارشيل U يبقى بناء عليه أصبح بارشيل W
+
+93
+00:10:45,980 --> 00:10:52,290
+بارشيل U بنفسهفإذا نشتقت W بالنسبة لX اللي فوق
+
+94
+00:10:52,290 --> 00:10:57,810
+يبقى مشتقتها واحد على اللي داخل الـLin في مشتقة ما
+
+95
+00:10:57,810 --> 00:11:02,910
+داخل الـLin بالنسبة إلى X يبقى الـY تربيع وZ تربيع
+
+96
+00:11:02,910 --> 00:11:09,290
+وطبعا constant يبقى هذه ب2X على X تربيع زائد Y
+
+97
+00:11:09,290 --> 00:11:09,390
+تربيع
+
+98
+00:11:12,620 --> 00:11:17,680
+هذا فقط لو partial w by partial x بدي اضرب في
+
+99
+00:11:17,680 --> 00:11:22,620
+تفاضل ال x بالنسبة الى u يجب ان يكون ال E Os V
+
+100
+00:11:22,620 --> 00:11:29,700
+يعتبر constant وهذا يعتبر مشتق بالحاصل ضاربةدالتين
+
+101
+00:11:29,700 --> 00:11:34,000
+لأنها مفضلة نسبة لمن؟ بالنسبة إلى U لكن لو كان
+
+102
+00:11:34,000 --> 00:11:38,980
+الشقاق بالنسبة إلى V لكان أسهل كتير جدا يعني
+
+103
+00:11:38,980 --> 00:11:43,480
+الشقاق بالنسبة ل V very easy لكن بالنسبة ل U في
+
+104
+00:11:43,480 --> 00:11:49,200
+صعوبة شوية يبقى هذا كله مضروب في مشتق تحصل ضرب
+
+105
+00:11:49,200 --> 00:12:00,440
+دالتين يبقى النتيجة E Os V في Sine U زائدU E Os V
+
+106
+00:12:00,440 --> 00:12:08,040
+في Cos U يبقى هذا جزء الأول بالمثل نعود للجزء
+
+107
+00:12:08,040 --> 00:12:13,860
+الثاني أفعل ال W بالنسبة إلى Y زي ال X مع الفارق
+
+108
+00:12:13,860 --> 00:12:21,350
+المصمم ل Y يبقى 2Yعلى X تربية زائد Y تربية زائد Z
+
+109
+00:12:21,350 --> 00:12:27,970
+تربية في تفاضل ال Y بالنسبة إلى U كذلك مستخدم حاصل
+
+110
+00:12:27,970 --> 00:12:37,010
+ضرب دالتين يبدأ E Os V في Cos U زائد U E Os V
+
+111
+00:12:37,010 --> 00:12:43,790
+وتفاضل Cos بقدر؟ بسالف Sine U هاي خلصنا الجزء من
+
+112
+00:12:43,790 --> 00:12:47,110
+الجزء الثاني بنجي لجزء التاني
+
+113
+00:12:50,680 --> 00:12:59,680
+تفاضل ال Z بالنسبة إلى U يبقى
+
+114
+00:12:59,680 --> 00:13:07,640
+بنفس الطريقة 2Z على X تربيع زائد Y تربيع زائد Z
+
+115
+00:13:07,640 --> 00:13:12,220
+تربيع مضروب تفاضل ال Z بالنسبة إلى U
+
+116
+00:13:18,430 --> 00:13:23,450
+طيب هذا طبعا الإجابة عندنا مزوج الحمد لله ال X
+
+117
+00:13:23,450 --> 00:13:28,430
+موجودة و ال Y و ال Z و ال U و ال V كله لكن احنا
+
+118
+00:13:28,430 --> 00:13:31,930
+بدنا ايها بدلالة main ال U و ال V اللي يعتبر
+
+119
+00:13:31,930 --> 00:13:37,570
+المتغيرات اذا بدروح احول كل ال X و ال Y و ال Z
+
+120
+00:13:37,570 --> 00:13:42,650
+بدلالة ال U و ال V و نشوف كده بده يساوي طب لو جيت
+
+121
+00:13:42,650 --> 00:13:49,320
+للقيم هدولمعناته مربع الاربع التلاتة هادول ونشوف
+
+122
+00:13:49,320 --> 00:13:53,200
+كده شو بده يساوي طب لو جيت في الهام شمال تكس تربية
+
+123
+00:13:53,200 --> 00:13:59,120
+زائد Y تربية زائد Z تربية شو بده يعطيني بده يعطيني
+
+124
+00:13:59,120 --> 00:14:08,580
+U تربية E أس اتنين V Cos تربية U زائد U تربية Sin
+
+125
+00:14:08,580 --> 00:14:09,400
+تربية U
+
+126
+00:14:15,110 --> 00:14:22,790
+زائد اللي هو U تربيع E أس اتنين V Cos تربيع ال V
+
+127
+00:14:22,790 --> 00:14:30,250
+زائد U تربيع E أس اتنين V إيش بتلاحظ يا بنات في
+
+128
+00:14:30,250 --> 00:14:36,580
+عامل مشترك اللي هو U تربيع E أس اتنين Vيبقى هنا
+
+129
+00:14:36,580 --> 00:14:41,720
+صين تربيع زائد زائد صين تربيع زائد كوسين تربيع ال
+
+130
+00:14:41,720 --> 00:14:49,160
+U يبقى هنا بصير صين تربيع ال U زائد كوسين تربيع ال
+
+131
+00:14:49,160 --> 00:14:56,800
+U زائد كده؟ زائد واحد طب هذه كده؟ واحد كذلك يبقى
+
+132
+00:14:56,800 --> 00:15:03,070
+اتنين U تربيع إيقوس اتنين بيه هذا هو المجموعيبقى
+
+133
+00:15:03,070 --> 00:15:07,750
+بلاءً عليه بصير عندي partial w by partial u بده
+
+134
+00:15:07,750 --> 00:15:12,050
+يساوي هي اتنين اللي عندنا وبده اشيل ال X واخد
+
+135
+00:15:12,050 --> 00:15:20,650
+قمتها اللي هو U في E أس V في صين ال U على مين؟ على
+
+136
+00:15:20,650 --> 00:15:30,170
+ال X البيضة اللي هو اتنين U تربيع E أس اتنين Vكل
+
+137
+00:15:30,170 --> 00:15:38,050
+هذا مضروب في مين؟ في E أس V في Sine U زائد U E أس
+
+138
+00:15:38,050 --> 00:15:50,810
+V في Cos U زائد اتنين ال Y هي U في E أس V في Cos U
+
+139
+00:15:50,810 --> 00:15:58,990
+على اتنين U تربيع E أس اتنين V في مين؟ في E أس V
+
+140
+00:15:59,460 --> 00:16:12,920
+cos U-U E Os V Cos U زي اتنين زد عندنا اتنين U E
+
+141
+00:16:12,920 --> 00:16:21,460
+Os V في E Os V يبقى E Os 2 V على مين؟ على اتنين U
+
+142
+00:16:21,460 --> 00:16:28,920
+تربيع اتنين U تربيع E Os 2 V
+
+143
+00:16:31,270 --> 00:16:38,550
+يسار اتنين مع اتنين و ال U مع التربيع و ال E Os V
+
+144
+00:16:38,550 --> 00:16:44,610
+مع ال E Os V و بظل عندنا من الصين طيب يا بنات هذه
+
+145
+00:16:44,610 --> 00:16:53,230
+E Os V لو طلعت فبرا مع E Os V مع E Os 2V بتروح بظل
+
+146
+00:16:53,230 --> 00:17:02,140
+عندي قداش هنا واحد عليه فقط في الصين ال Uزائد U في
+
+147
+00:17:02,140 --> 00:17:12,420
+Cos U وعندي هنا sign U اللي برا يبقى هنا في sign U
+
+148
+00:17:12,420 --> 00:17:19,780
+هذا الجزء الأول الجزء الثاني برضه اذا طلع USB مع
+
+149
+00:17:19,780 --> 00:17:27,540
+USB مع USB بصير E أس اتنين V مع E أس اتنين Vو
+
+150
+00:17:27,540 --> 00:17:34,280
+اتنين مع اتنين والتربيع مع ال U بيظل كوصين ال U
+
+151
+00:17:34,280 --> 00:17:44,160
+علي U في كوصين ال U ناقص U صين ال U الجزء الأخير
+
+152
+00:17:44,160 --> 00:17:54,380
+بيظل عندي زائد يعني بس واحد علي U كمان؟ مافيش رأيك
+
+153
+00:17:54,380 --> 00:17:56,860
+يا بنات هذا الكلام بده يساوي
+
+154
+00:18:01,150 --> 00:18:06,190
+عندك هنا واحد على يوم وعندك هنا واحد على يوم وعندك
+
+155
+00:18:06,190 --> 00:18:08,370
+هنا واحد على يوم وعندك هنا واحد على يوم وعندك هنا
+
+156
+00:18:08,370 --> 00:18:08,930
+وعندك هنا واحد على يوم وعندك هنا واحد على يوم
+
+157
+00:18:08,930 --> 00:18:13,610
+وعندك هنا واحد على يوم وعندك هنا واحد على يوم
+
+158
+00:18:13,610 --> 00:18:21,550
+وعندك هنا واحد على
+
+159
+00:18:21,550 --> 00:18:33,210
+يوم وعندك هنامقص ال U, Sine U, Cos U، تلقين القرص،
+
+160
+00:18:33,210 --> 00:18:35,850
+تلقين القرص، تلقين القرص، تلقين القرص، تلقين
+
+161
+00:18:35,850 --> 00:18:37,130
+القرص، تلقين القرص، تلقين القرص، تلقين القرص،
+
+162
+00:18:37,130 --> 00:18:37,950
+تلقين القرص، تلقين القرص، تلقين القرص، تلقين
+
+163
+00:18:37,950 --> 00:18:39,850
+القرص، تلقين القرص، تلقين القرص، تلقين القرص،
+
+164
+00:18:39,850 --> 00:18:40,570
+تلقين القرص، تلقين القرص، تلقين القرص، تلقين
+
+165
+00:18:40,570 --> 00:18:41,090
+القرص، تلقين القرص، تلقين القرص، تلقين القرص،
+
+166
+00:18:41,090 --> 00:18:45,090
+تلقين القرص، تلقين القرص، تلقين القرص، تلقين
+
+167
+00:18:45,090 --> 00:18:46,750
+القرص، تلق
+
+168
+00:18:53,830 --> 00:18:57,930
+إذاً هذا المشتقة اللي مكلك عليه كبيرة صفت عليه جزء
+
+169
+00:18:57,930 --> 00:19:09,490
+بسيط اللي هو عبارة عن اتنين عليه فقط لا غير إذا
+
+170
+00:19:09,490 --> 00:19:14,450
+انتهينا من المطقوب الأول في المسألة و بدنا نروح
+
+171
+00:19:14,450 --> 00:19:20,170
+للمطقوب التاني وهو نمرى بيه نمرى بيه قال لي بدي
+
+172
+00:19:20,170 --> 00:19:26,750
+هالمشتقة هذه ههdirectly مباشرة بعد ما اتعبر عن ال
+
+173
+00:19:26,750 --> 00:19:32,770
+W بدلالة ال U و ال V يفجأة انا بالداخل هقول له هاي
+
+174
+00:19:32,770 --> 00:19:40,130
+ال W تساعد لإن ال X تربيع زي Y تربيع زي Z تربيع
+
+175
+00:19:40,130 --> 00:19:47,350
+حسبناها هاي اتنين U تربيع E أس اتنين V اتنين U
+
+176
+00:19:47,350 --> 00:19:57,620
+تربيع E أس اتنين Vبالنسبة لمن؟ بالنسبة الي U و بدي
+
+177
+00:19:57,620 --> 00:20:01,300
+اثبت ان النتيجة قدش تساوي 2 على U
+
+178
+00:20:22,150 --> 00:20:28,050
+طيب اقتصدي يوس اتنين V مع يوس اتنين V اتنين مع
+
+179
+00:20:28,050 --> 00:20:34,370
+اتنين U مع التربية تبقى كمان اتنين على U نفس
+
+180
+00:20:34,370 --> 00:20:39,910
+النتيجة اللي حصلنا عليها هناك بالضبط تماماgood
+
+181
+00:20:39,910 --> 00:20:49,070
+exercise لك exercise find partial w by partial v
+
+182
+00:20:49,070 --> 00:20:58,810
+اللي هي أسهل من مين انتبهت اليوم بدنا
+
+183
+00:20:58,810 --> 00:21:03,530
+نجي ناخد أبنات من القاعدة اللي تو special cases
+
+184
+00:21:03,530 --> 00:21:14,150
+حالات خاصة الحالة الأولىلو كانت ال w function x و
+
+185
+00:21:14,150 --> 00:21:24,450
+y و ال x function في ال r و ال s and ال y function
+
+186
+00:21:24,450 --> 00:21:35,250
+كذلك في ال r و ال s يبقى
+
+187
+00:21:35,250 --> 00:21:42,200
+هذه دالة في مين؟في متغيرين وليس في ثلاثة وكل من
+
+188
+00:21:42,200 --> 00:21:49,960
+المتغيرين دال في متغيرين آخرينيبقى هي نفس النتيجة
+
+189
+00:21:49,960 --> 00:21:54,000
+اللي فاتت بس اخر سنة تبعها ستتشيلوا لإن هو مش
+
+190
+00:21:54,000 --> 00:21:59,280
+موجود عندي إذا بناء أنا عليه بصير عندي partial w
+
+191
+00:21:59,280 --> 00:22:06,040
+by partial r بدي أسوي partial w by partial x by
+
+192
+00:22:06,040 --> 00:22:11,640
+partial x by partial r زايد partial w by partial y
+
+193
+00:22:11,640 --> 00:22:16,700
+by partial y by partial r and
+
+194
+00:22:19,470 --> 00:22:24,490
+بدي partial w by partial s يبقى partial w by
+
+195
+00:22:24,490 --> 00:22:32,070
+partial x في partial x by partial s زائد partial w
+
+196
+00:22:32,070 --> 00:22:42,610
+by partial y في partial y by partial s ممكن
+
+197
+00:22:42,610 --> 00:22:50,050
+نرسم رسمة أوضحية كذلك لهذه الشكلينفاجي بقول انا
+
+198
+00:22:50,050 --> 00:22:57,650
+عندي w تساوي function x y، اذا بطلع عندي خطين او
+
+199
+00:22:57,650 --> 00:23:05,210
+فرعين و ليس ثلاثة، بقول هنا x وهنا y وكل واحد منهم
+
+200
+00:23:05,210 --> 00:23:10,470
+function تمين في R، اذا المستقال تكون على الشكل
+
+201
+00:23:10,470 --> 00:23:15,540
+التاليتفاضل الـ W بالنسبة إلى X تفاضل الـ W
+
+202
+00:23:15,540 --> 00:23:21,320
+بالنسبة إلى Y تفاضل الـ X بالنسبة إلى R تفاضل الـ
+
+203
+00:23:21,320 --> 00:23:26,780
+Y بالنسبة إلى R اضرب اتنين في بعض اتنين اضرب بعض و
+
+204
+00:23:26,780 --> 00:23:34,400
+اجمع تظهر الحالة الأولى نأتي للحالة الثانية الـ W
+
+205
+00:23:34,400 --> 00:23:41,380
+كذلك function في X و Y وهنا لدينا الـ Xوهنا ال y
+
+206
+00:23:41,380 --> 00:23:47,320
+وكل واحد فيهم function في مين في S يبقى هنا تفاضل
+
+207
+00:23:47,320 --> 00:23:56,000
+ال W بالنسبة إلى X في تفاضل ال X بالنسبة إلى S هنا
+
+208
+00:23:56,000 --> 00:24:01,840
+تفاضل ال W بالنسبة إلى Y هنا تفاضل ال Y بالنسبة
+
+209
+00:24:01,840 --> 00:24:11,340
+إلى S هذه الحالة الأولة الحالة الثانيةهذه الأولى
+
+210
+00:24:11,340 --> 00:24:22,940
+التاني f w يسوى function of x and ال x function
+
+211
+00:24:22,940 --> 00:24:26,580
+فيه متغيرين r وs
+
+212
+00:24:34,890 --> 00:24:43,470
+دي partial w by partial r تساوي الهن يا بنات w
+
+213
+00:24:43,470 --> 00:24:48,290
+function في مين؟ في متغير واحد اللي هو x إذا
+
+214
+00:24:48,290 --> 00:24:51,310
+ماقدرش أقول إشتقاء قد يظهر إيه وانما بيكون إشتقاء
+
+215
+00:24:51,310 --> 00:25:00,380
+كله يبقى باجي بقول دي w by دي xلكن الـ x function
+
+216
+00:25:00,380 --> 00:25:06,420
+في مين؟ في المتغيرين، إذا بقوله في partial ده في
+
+217
+00:25:06,420 --> 00:25:16,560
+partial x by partial r أكتر من هيك ماعنديش and لو
+
+218
+00:25:16,560 --> 00:25:23,700
+بدي partial w by partial s يبقى dw على dx في
+
+219
+00:25:23,700 --> 00:25:32,610
+partial x by partial sلو حبنا نتعرف على شكل الرسمة
+
+220
+00:25:32,610 --> 00:25:39,530
+للاتنين هدول فماجي بقول احنا عندنا w function of x
+
+221
+00:25:39,530 --> 00:25:46,350
+هيقول هيطلع خط واحد لان ماعنديش إلا ومتغير واحد هو
+
+222
+00:25:46,350 --> 00:25:56,430
+مين؟ هو x إذا بصير عند هنا dw علىDX اشتقاق عادي
+
+223
+00:25:56,430 --> 00:26:02,330
+لكن ال X ده في مين؟ في المتغيرين يبقى باجي بقول
+
+224
+00:26:02,330 --> 00:26:08,710
+هنا R وبالتالي بصير partial X على partial R وهنا
+
+225
+00:26:08,710 --> 00:26:16,310
+هيجي KS ويكون partial X على partial S يبقى هذا
+
+226
+00:26:16,310 --> 00:26:20,890
+بتجيبلي الحالة الأولى وهذا بتجيبلي من؟ الحالة
+
+227
+00:26:20,890 --> 00:26:22,890
+الثانية وهكذا
+
+228
+00:26:51,810 --> 00:27:09,670
+نعطي مثال على ذلك أو أكثر من مثال مثال أول
+
+229
+00:27:09,670 --> 00:27:21,290
+مثال يقول find partial z على partial u andpartial
+
+230
+00:27:21,290 --> 00:27:38,480
+z على partial v as functions of u and vF z تساوي
+
+231
+00:27:38,480 --> 00:27:49,000
+tan inverse لمين ل x على y و ال x بدها تساوي u في
+
+232
+00:27:49,000 --> 00:28:01,300
+cos v و ال y بدها تساوي u في sin v
+
+233
+00:28:15,020 --> 00:28:20,460
+عليه بالك هنا بجي بتطلع بلقى Z ده اللي في مين في
+
+234
+00:28:20,460 --> 00:28:28,960
+متغيرين XY وكل من المتغيرين XY ده اللي في متغيرين
+
+235
+00:28:28,960 --> 00:28:35,080
+الآخرين في U وB إذا احنا مع من؟ مع الحالة الأولى
+
+236
+00:28:35,080 --> 00:28:41,800
+وليست الحالة الثالثة طب كويس يبقى هنا بجي بتقول لو
+
+237
+00:28:41,800 --> 00:28:44,080
+بدي أجيب الجزء الأول
+
+238
+00:28:47,780 --> 00:28:54,200
+بارشيل Z على بارشيل X بارشيل X على بارشيل U زائد
+
+239
+00:28:54,200 --> 00:29:00,840
+بارشيل Z على بارشيل Y بارشيل Y على بارشيل U هذا
+
+240
+00:29:00,840 --> 00:29:07,580
+الجزر L أول يجي نعوض يبقى بارشيل Z على بارشيل U
+
+241
+00:29:07,580 --> 00:29:16,050
+يسبب تفاضل Z بالنسبة إلى Xتفاضل التالين بس واحد
+
+242
+00:29:16,050 --> 00:29:22,590
+على واحد زي ال X تربية على Y تربية في مشتقة
+
+243
+00:29:22,590 --> 00:29:30,890
+الزاوية بالنسبة لمن؟ لجداش واحد على Y وليس واحد
+
+244
+00:29:30,890 --> 00:29:37,630
+عليه تفاضل X بواحد لجداش واحد على Y فهذا الكلام
+
+245
+00:29:37,630 --> 00:29:42,670
+كله مضروف في تفاضل ال Xتفاضل Z بالنسبة الى U لما
+
+246
+00:29:42,670 --> 00:29:54,810
+تفاضلها
+
+247
+00:29:54,810 --> 00:30:02,450
+بالنسبة ل Y هل تقدر تقولي كده نتيجة تفاضل
+
+248
+00:30:02,450 --> 00:30:03,730
+Y بالنسبة ل Y كده
+
+249
+00:30:09,440 --> 00:30:16,920
+Y تربيع X على Y تربيع يبقى سالب X على Y تربيع في
+
+250
+00:30:16,920 --> 00:30:22,980
+تفاضل Y بالنسبة إلى U الهمين ساين الفيه طب في
+
+251
+00:30:22,980 --> 00:30:27,980
+الهقم الشيخ اذا قلتك بالله يقداش X تربيع زاد Y
+
+252
+00:30:27,980 --> 00:30:34,020
+تربيع تسابع ايش مصير عندك U تربيع كساين تربيع زاد
+
+253
+00:30:34,020 --> 00:30:41,830
+U تربيع ساين تربيع يبقى ب U تربيع فقططيب هذا
+
+254
+00:30:41,830 --> 00:30:47,710
+الكلام partial z by partial u تساوي شو رايكوا ده
+
+255
+00:30:47,710 --> 00:30:54,890
+واحد المقامات إذا بتطلع y تربيع 4 هنا y تربيع زاد
+
+256
+00:30:54,890 --> 00:31:04,770
+x تربيع واحد على y في cosine ال b زاد y تربيع y
+
+257
+00:31:04,770 --> 00:31:14,940
+تربيع زاد x تربيع ناقص xعلى Y تربيع في صين ال V
+
+258
+00:31:14,940 --> 00:31:24,020
+طيب هذا كله مستحيل طلعيني Y مع Y تربيع بيظل كدهش
+
+259
+00:31:24,020 --> 00:31:34,980
+بيظل بس Y كدهش ال Y يو يو يو في صين ال V كله
+
+260
+00:31:34,980 --> 00:31:41,430
+مقصومة لعالمين X تربيع زي ال Y تربيع له 100U تربيع
+
+261
+00:31:41,430 --> 00:31:51,510
+و هنا عندي Cos V هذه تربيع
+
+262
+00:31:51,510 --> 00:31:59,690
+مع تربيع الله يسالي عليها ال X هو U Cos V U Cos V
+
+263
+00:31:59,690 --> 00:32:02,490
+في مين؟ في Sin V
+
+264
+00:32:16,520 --> 00:32:19,900
+يبقى الناتج كله يساوي زيه
+
+265
+00:32:23,880 --> 00:32:28,860
+و sin cos على u و هنا sin cos على u يبقى كله ب
+
+266
+00:32:28,860 --> 00:32:33,100
+zero و الحمد لله يبقى هذا تفاضل ال z بالنسبة الى u
+
+267
+00:32:33,100 --> 00:32:37,700
+قاللي هاتي تفاضل ال z بالنسبة الى v يبقى يقدروا
+
+268
+00:32:37,700 --> 00:32:42,720
+ايقله partial z by partial v اللي هو عبارة عن
+
+269
+00:32:42,720 --> 00:32:49,960
+partial z على partial x partial x على partial v زي
+
+270
+00:32:49,960 --> 00:32:55,370
+partial z على partial yيبقى partial y على partial
+
+271
+00:32:55,370 --> 00:33:04,030
+v إذا partial z على partial b بده يسار تفضل ال z
+
+272
+00:33:04,030 --> 00:33:11,530
+بالنسبة إلى x طب الله اللي جابنا هي اللي فوق قداش
+
+273
+00:33:11,530 --> 00:33:18,330
+طلعت اللي هي هذه صح؟ يبقى حطها على طول و y على x
+
+274
+00:33:18,330 --> 00:33:24,860
+تربية زي ال y تربية يبقى هذه yعلى X تربيع زائد Y
+
+275
+00:33:24,860 --> 00:33:31,100
+تربيع تمين في تفاضل ال X بالنسبة إلى B تفاضل ال X
+
+276
+00:33:31,100 --> 00:33:37,740
+بالنسبة إلى B لو سالب U سين ال V في سالب U في سين
+
+277
+00:33:37,740 --> 00:33:44,440
+ال V زائد partial Z على partial Y partial Z على
+
+278
+00:33:44,440 --> 00:33:48,800
+partial Y هي من فوق برضه يبقى أدب
+
+279
+00:33:57,100 --> 00:34:07,240
+Y تربيع في تفامل Y بالنسبة الى V U E Cos V وهذا
+
+280
+00:34:07,240 --> 00:34:13,480
+الكلام from above يبقى
+
+281
+00:34:13,480 --> 00:34:18,620
+هذا اختصرته Objective of the form Yزا يجب ان اشيل
+
+282
+00:34:18,620 --> 00:34:30,690
+Y و اتقدمها ل U Sin V U Sin V فيسالب U Cos V كل
+
+283
+00:34:30,690 --> 00:34:43,590
+هذا الكلام على U تربيه وهنا ناقص نجي لل X ال X
+
+284
+00:34:43,590 --> 00:34:53,890
+اللي هو U Cos V يبقى U Cos V في U Cos V على U
+
+285
+00:34:53,890 --> 00:34:54,610
+تربيه
+
+286
+00:34:57,860 --> 00:35:05,020
+Partial X على Partial V نقص Sine V Partial X على
+
+287
+00:35:05,020 --> 00:35:05,420
+Partial V نقص Sine V Partial X على Partial V نقص
+
+288
+00:35:05,420 --> 00:35:05,440
+Sine V Partial X على Partial V نقص Sine V Partial
+
+289
+00:35:05,440 --> 00:35:05,960
+X على Partial V نقص Sine V Partial X على Partial V
+
+290
+00:35:05,960 --> 00:35:06,200
+نقص Sine V Partial X على Partial V نقص Sine V
+
+291
+00:35:06,200 --> 00:35:06,220
+Partial X على Partial V نقص Sine V Partial X على
+
+292
+00:35:06,220 --> 00:35:07,180
+نقص Sine V Partial X على Partial V نقص Sine V
+
+293
+00:35:07,180 --> 00:35:08,260
+Partial X على Partial V نقص Sine V Partial X على
+
+294
+00:35:08,260 --> 00:35:13,600
+Partial V نقص
+
+295
+00:35:13,600 --> 00:35:24,460
+Sine V Partial X على Partial V نقص Sine V Partial
+
+296
+00:35:24,460 --> 00:35:32,410
+Xهاخد ناقص U تربيع عامل مشترك يبقى ناقص U تربيع
+
+297
+00:35:32,410 --> 00:35:40,330
+عامل مشترك و هنا على U تربيع بصير عندي sin تربيع V
+
+298
+00:35:40,330 --> 00:35:43,950
+زائد cosine تربيع V
+
+299
+00:36:18,810 --> 00:36:27,210
+بناخد تمام مثال مثال اتنين نقول
+
+300
+00:36:27,210 --> 00:36:31,270
+define partial
+
+301
+00:36:31,270 --> 00:36:42,830
+z على partial u and partial z على partial v at u
+
+302
+00:36:42,830 --> 00:36:44,710
+وv بدأت
+
+303
+00:36:49,120 --> 00:37:01,120
+فإذا كان الـ Z يساوي لن لـQ و لـQ تساوي ال square
+
+304
+00:37:01,120 --> 00:37:08,880
+root ل V زائد تلاتة في تان inverse U
+
+305
+00:37:48,540 --> 00:37:55,080
+طيب نرجع لسؤالنا هذا مرة تانية بنلاحظ ان زد دالة
+
+306
+00:37:55,080 --> 00:37:59,980
+في مين تغير واحد والمتغير دالة في مين في متغيرين
+
+307
+00:37:59,980 --> 00:38:04,600
+اللي هي الحالة التانية تمام التمام بقوله كويس يبقى
+
+308
+00:38:04,600 --> 00:38:10,360
+احنا بدنا نجيبله partial z على partial u يبقى بعدي
+
+309
+00:38:10,360 --> 00:38:16,350
+بقوله اه اهاليو موجودة عندك يبقى حسب الحالة اني
+
+310
+00:38:16,350 --> 00:38:24,470
+ايش بدي اقول ايش ابنها يبقى DZ على مين؟ على DQ في
+
+311
+00:38:24,470 --> 00:38:34,010
+مين؟ في partial EQ على partial U فيه كمان؟فى ايه؟
+
+312
+00:38:34,010 --> 00:38:38,830
+لأ لأشهر دالة فى متغير واحد والمتغير دالة فى مين؟
+
+313
+00:38:38,830 --> 00:38:44,630
+فى متغيرين بقوله بسيطة if I'm partial z على
+
+314
+00:38:44,630 --> 00:38:50,930
+partial u يساوي تفاضل ال z بالنسبة ل q يبقى واحد
+
+315
+00:38:50,930 --> 00:38:57,390
+على ال q فتفاضل ال q بالنسبة لمين إلى uفى الجدرى
+
+316
+00:38:57,390 --> 00:39:02,350
+التربية لـ V زائد ثلاثة ملاكش دعوة يعتبر مقدرا
+
+317
+00:39:02,350 --> 00:39:09,670
+ثابتا وتان Inversio له واحد على واحد زائد U تربية
+
+318
+00:39:09,670 --> 00:39:12,850
+طيب
+
+319
+00:39:12,850 --> 00:39:17,190
+اذا اكتب ابدا لأتي ال U و ال V يبقى هذا الكلام
+
+320
+00:39:17,190 --> 00:39:25,190
+يساوي جدرى التربية ل V زائد تلاتة على واحد زائد U
+
+321
+00:39:25,190 --> 00:39:34,840
+تربيةفي ال Q ال جدر التربيعي ال V زائد تلاتة في
+
+322
+00:39:34,840 --> 00:39:41,800
+تان Inverse U الجدر مع الجدر يبقى آلة المسألة في
+
+323
+00:39:41,800 --> 00:39:48,870
+ال واحد زائد U تربية في تان Inverse Uقال يحسبني
+
+324
+00:39:48,870 --> 00:39:53,670
+هذا المقدار عند الواحد والسالب اتنين اذا بدي اجيب
+
+325
+00:39:53,670 --> 00:39:59,090
+له partial z على partial u عند النقطة واحد وسالب
+
+326
+00:39:59,090 --> 00:40:08,030
+اتنين هو يساوي واحد على واحد زائد واحد في تان
+
+327
+00:40:08,030 --> 00:40:13,490
+inverse one يبقى نص كده اش بقول الله يا بنات تان
+
+328
+00:40:13,490 --> 00:40:23,300
+inverse oneيبقى الجواب كله نين على بار نروح أجيب
+
+329
+00:40:23,300 --> 00:40:32,540
+له partial z by partial v يبقى دي ديزل by دي كيو
+
+330
+00:40:32,540 --> 00:40:39,630
+في partial k by partial vيبقى هذا الكلام بالديسافر
+
+331
+00:40:39,630 --> 00:40:44,690
+تفاضل ال Z بالنسبة ل ال EQ بواحد على ال EQ تفاضل
+
+332
+00:40:44,690 --> 00:40:50,270
+ال EQ بالنسبة إلى V يبقى tan inverse مقدار ثابت
+
+333
+00:40:50,270 --> 00:40:58,930
+واحد على اتنين الجذر التربيعي ل V زائد تلاتة في
+
+334
+00:40:58,930 --> 00:41:05,390
+مين في tan inverse U طيب
+
+335
+00:41:05,390 --> 00:41:14,420
+نبسطهاهذا الكلام تان انفرس يو كله مبسوما على ال EQ
+
+336
+00:41:14,420 --> 00:41:23,740
+الجدر التربيعي ل V زائد تلاتة في تان انفرس يو هذا
+
+337
+00:41:23,740 --> 00:41:30,750
+ال EQ في اتنين الجدر في اتنين الجدر التربيعيV زائد
+
+338
+00:41:30,750 --> 00:41:36,090
+تلاتة تان انفرست مع تان انفرست يبقى هتقول المسألة
+
+339
+00:41:36,090 --> 00:41:43,810
+الى واحد على اتنين في V زائد تلاتة اذا بقدر احسب
+
+340
+00:41:43,810 --> 00:41:50,710
+لمين ففاضل ال Z بالنسبة الى V عند النقطة واحد ونقص
+
+341
+00:41:50,710 --> 00:41:56,470
+اتنين تساوي واحد على اتنين في نقص اتنين
+
+342
+00:42:07,250 --> 00:42:15,310
+هذا اسم كله اشتقاق مباشر سواء كان اشتقاق كله او
+
+343
+00:42:15,310 --> 00:42:21,290
+اشتقاق ضمنه لكن قد يكون اشتقاق اشتقاق ضمنه يعني
+
+344
+00:42:21,290 --> 00:42:26,510
+اذا بدأ نيجي لحاجة اسمها implicit differentiation
+
+345
+00:42:40,120 --> 00:42:45,580
+التفاضل الضمني بقول
+
+346
+00:42:45,580 --> 00:42:50,580
+suppose that طلب
+
+347
+00:42:50,580 --> 00:43:02,140
+انه capital F of XY is a differentiable function
+
+348
+00:43:02,140 --> 00:43:08,080
+ذالك قابل للاشتقام and that
+
+349
+00:43:10,700 --> 00:43:22,900
+Equation f of x, y تساوي 0 defines بتعرفي
+
+350
+00:43:22,900 --> 00:43:37,360
+y as a differentiable function of x then at any
+
+351
+00:43:37,360 --> 00:43:46,140
+pointعند أي نقطة where الـ
+
+352
+00:43:46,140 --> 00:43:56,720
+fy لا تساوي zero we have ال
+
+353
+00:43:56,720 --> 00:44:04,080
+dy على dx بدي ساوي سالب fx
+
+354
+00:44:16,760 --> 00:44:24,280
+أقصد ذلك الـ
+
+355
+00:44:24,280 --> 00:44:28,480
+equation X
+
+356
+00:44:28,480 --> 00:44:42,240
+الـ E أُس Y زائد Sine XY زائد Y ناقص لإن اتنين يجب
+
+357
+00:44:42,240 --> 00:44:45,200
+أن نسميه Zero Define
+
+358
+00:44:47,530 --> 00:45:01,330
+يتعرف لي y as a differentiable function of x قاعد
+
+359
+00:45:01,330 --> 00:45:16,170
+هو اشتغلنا dy by dx at القاعد عند النقطة zero ولن
+
+360
+00:46:04,880 --> 00:46:08,540
+النقطة اللي بين إيدينا الألملات التي هي ال
+
+361
+00:46:08,540 --> 00:46:14,180
+differentiation التفاضل الضمني فده يقول افترض ان
+
+362
+00:46:14,180 --> 00:46:20,400
+عندي دالة F of X وY دالة قابلة للاشتقاء وفي نفس
+
+363
+00:46:20,400 --> 00:46:26,380
+الوقت F of X وY يساوي انه بتعرفي Y كدالة في X يبقى
+
+364
+00:46:26,380 --> 00:46:32,060
+هذه بهذا الشكل هذا علاقة تربط بين X وY يبقى لكنها
+
+365
+00:46:32,060 --> 00:46:34,240
+مشتركة مع بعض مش كده
+
+366
+00:46:43,570 --> 00:46:49,190
+بيقول لي عند أي نقطة بحيث المشتقة ال F بالنسبة ال
+
+367
+00:46:49,190 --> 00:46:54,610
+Y لا يمكن أن تساوي Zero بعرف المشتقة DY على DX
+
+368
+00:46:54,610 --> 00:47:00,430
+بأنها سالب مشتقة F بالنسبة لX مقسم على مشتقة F
+
+369
+00:47:00,430 --> 00:47:04,950
+بالنسبة ال Y طبعا إذا برهان صغير مش عايزين برهانه
+
+370
+00:47:04,950 --> 00:47:08,250
+تجريه في الكتاب كله ساطر و نص مش أكتر
+
+371
+00:47:13,980 --> 00:47:18,480
+بتعرف لي Y كدالة في X هاتلي دي Y علي دي X عن نقطة
+
+372
+00:47:18,480 --> 00:47:23,900
+Zero و لين اتنين بقول لكوا ايش طب وين F of X و Y
+
+373
+00:47:23,900 --> 00:47:28,480
+هتروح اشتقها موجودة
+
+374
+00:47:28,480 --> 00:47:33,200
+عندى F of X و Y؟ موجودة هذه لازم تساوي Zero اللي
+
+375
+00:47:33,200 --> 00:47:33,760
+هي هذه
+
+376
+00:47:37,240 --> 00:47:42,220
+يبقى ال F of X و Y هي الدالة دي بدون Zero يبقى بجي
+
+377
+00:47:42,220 --> 00:47:51,880
+بقوله F of X و Y هي عبارة عن مين؟ X UY زائد Sine
+
+378
+00:47:51,880 --> 00:48:01,240
+XY زائد Y نقص لانتنين بقدر أجيب له لانف X
+
+379
+00:48:09,690 --> 00:48:15,070
+في Y في مشتقة الزاوية بالنسبة لـ X اللي بيقدر Y
+
+380
+00:48:15,070 --> 00:48:24,350
+والباقي كله بـ 0. بدنا نجيب له FY يساوي X مشتقة
+
+381
+00:48:24,350 --> 00:48:31,610
+الـ EOS Y بالـ EOS Y itself. أمام ذات اللي هو
+
+382
+00:48:31,610 --> 00:48:37,610
+تفاضل الـ Sine. P Cos XY مشتقتها بالنسبة لـ X.
+
+383
+00:48:38,060 --> 00:48:45,960
+المشتقة الواحدة في الجداج، يا أبو واحد، تمام؟ خير
+
+384
+00:48:45,960 --> 00:48:54,120
+ان شاء الله، كده ساعتك العيد؟ احنا أبدا، يعني ضالة
+
+385
+00:48:54,120 --> 00:48:59,840
+لوقت العزة بس، اما محاضرتنا خلصت تقريبا، ساعتنا،
+
+386
+00:48:59,840 --> 00:49:03,520
+الا خمس دقايق،
+
+387
+00:49:03,520 --> 00:49:27,360
+طيبيبقى Fx يبقى Fx يبقى Fx يبقى Fx
+
+388
+00:49:27,360 --> 00:49:33,080
+يبقى Fx يبقى Fx يبقى Fx يبقى Fx يبقى Fx يبقى Fx
+
+389
+00:49:33,080 --> 00:49:33,300
+يبقى Fx يبقى Fx يبقى Fx يبقى Fx يبقى Fx يبقى Fx
+
+390
+00:49:33,300 --> 00:49:35,480
+يبقى Fx يبقى Fx يبقى Fx يبقى Fx يبقى Fxزائد Y Cos
+
+391
+00:49:35,480 --> 00:49:46,360
+XY على مين على اي شرط السلك برنامج على FYX UY زائد
+
+392
+00:49:46,360 --> 00:49:57,460
+X Cos XY زائد Y قال يحسبلي هذه ال D Y على DX عند
+
+393
+00:49:57,460 --> 00:50:00,000
+النقطة مين عند النقطة
+
+394
+00:50:09,980 --> 00:50:22,040
+يبقى ناقص E أس لن اتنين زائد لن اتنين في cos صفر
+
+395
+00:50:22,040 --> 00:50:26,700
+عشرين
+
+396
+00:50:27,810 --> 00:50:33,830
+يبدأ يحط مكانها لن اتنين تمام يبقى بيصير لن اتنين
+
+397
+00:50:33,830 --> 00:50:40,130
+فيه cosine صفر في لن اتنين اللي هو صفر على المقام
+
+398
+00:50:40,130 --> 00:50:45,790
+x بزيرو يبقى طاري ال term اللي عندك هذا كله و x
+
+399
+00:50:45,790 --> 00:50:51,210
+بزيرو طاري ال term هذا كله بيظل كده؟ بيظل واحد
+
+400
+00:50:51,210 --> 00:51:03,210
+يبقى هذه بيظل و يساوي ناقص اتنين زائدلن اتنين ناقص
+
+401
+00:51:03,210 --> 00:51:10,590
+للكل مش هيك ناقص لن اتنين يبقى بنات هذه حطوها بين
+
+402
+00:51:10,590 --> 00:51:16,290
+قسير بالشكل هذا حتى يصير كلامنا دقيق مائة بالمائة
+
+403
+00:51:16,290 --> 00:51:23,890
+خدها الملاحظة بالمرة يبقى ناشطة
+
+404
+00:51:33,140 --> 00:51:38,980
+لا يساوي زيرو بتعرف
+
+405
+00:51:38,980 --> 00:51:57,500
+لي z as a function of x and y and if وإذا كان if z
+
+406
+00:51:57,500 --> 00:51:59,760
+لا يساوي زيرو
+
+407
+00:52:03,390 --> 00:52:11,470
+partial z على partial x بده يساوي ناقص fx على fz
+
+408
+00:52:11,470 --> 00:52:21,270
+and partial z على partial y بده يساوي ناقص fy على
+
+409
+00:52:21,270 --> 00:52:31,730
+fz انقارن
+
+410
+00:52:32,250 --> 00:52:36,850
+الملاحظة مع الكلام اللي كتبناه في الحالة الأولى
+
+411
+00:52:36,850 --> 00:52:41,070
+يابانات احنا قولنا هذا بيعرف ل Y ك function في X
+
+412
+00:52:41,070 --> 00:52:45,470
+إذا صارت دالة في متغير واحد إذا روحنا و قولنا هنا
+
+413
+00:52:45,470 --> 00:52:52,450
+إيشأشتقاق كلي لكن قال لي هنا بعرف للـ z as a
+
+414
+00:52:52,450 --> 00:52:59,170
+function في مين في متغيرين إذا بصير اشتقاق جزءي
+
+415
+00:52:59,170 --> 00:53:04,010
+وليس اشتقاقا كليا إذا بقول partial z على partial x
+
+416
+00:53:04,010 --> 00:53:10,460
+و partial z على partial yهنا X هنا Fx و المقام Fz
+
+417
+00:53:10,460 --> 00:53:17,700
+هنا Y هنا Fy و المقام Fz خد مثال توضيحي على دنيا
+
+418
+00:53:17,700 --> 00:53:23,280
+for example let
+
+419
+00:53:23,280 --> 00:53:38,290
+Z تكيب ناقص XY ناقص YZنقص x y زائد y z زائد y تكيب
+
+420
+00:53:38,290 --> 00:53:47,670
+نقص اتنين تساوي زيرو fine عسبونا partial z by
+
+421
+00:53:47,670 --> 00:53:55,650
+partial x and partial z by partial y at النقطة
+
+422
+00:53:55,650 --> 00:53:58,070
+واحد هو واحد هو واحد
+
+423
+00:54:12,420 --> 00:54:21,680
+بدا بنات نحسب اللي هو الدالة f of x و y of z كلها
+
+424
+00:54:21,680 --> 00:54:27,140
+يبقى هذه اللي قالت تساوي قداش zero لو أخدت الآن z
+
+425
+00:54:27,140 --> 00:54:31,880
+function في x و y يبقى بصير f of x و y و z هي
+
+426
+00:54:31,880 --> 00:54:39,880
+عبارة عن z تكيب نقص x y زائد y z زائد y تكيب نقص
+
+427
+00:54:39,880 --> 00:54:48,480
+اتنينبقدر احسب له fx يبقى سالب y فيه كمان؟ ولا
+
+428
+00:54:48,480 --> 00:54:55,340
+حاجة بقدر احسب له fy نقص
+
+429
+00:54:55,340 --> 00:55:06,580
+x زائد z زائد 3I تربية نقدر احسب له كمان fz كل
+
+430
+00:55:06,580 --> 00:55:14,780
+هذا بروحوضلت لا تزد تربيع وهنا زائد Y وزي ما انت
+
+431
+00:55:14,780 --> 00:55:22,080
+شايفه لا تساوي Zero يبقى هذه لا تساوي Zero قال لي
+
+432
+00:55:22,080 --> 00:55:26,980
+والله إذا Fz مش Zero إذا بتقدر تجيب هذه بتقدر تجيب
+
+433
+00:55:26,980 --> 00:55:31,900
+اللي عندك هذه بقوله كويس إذا أنا بدي أروح أجيب له
+
+434
+00:55:31,900 --> 00:55:35,360
+ال partial F
+
+435
+00:55:43,410 --> 00:55:51,570
+يبقى هذا الكلام بدي اسمه هاي الناقص برا فاجي بقوله
+
+436
+00:55:51,570 --> 00:55:59,450
+Fx على Fz هاي الناقص برا Fx اللي يبقى داجة ناقص Y
+
+437
+00:55:59,450 --> 00:56:09,600
+Fz اللي هو تلاتة Z تربيع زائد Yطيب ناقص مع ناقص F
+
+438
+00:56:09,600 --> 00:56:16,500
+زائد ال Y عندى مقدشة فانا F واحد على تلاتة زائد
+
+439
+00:56:16,500 --> 00:56:22,880
+واحد ويسوى كده؟ رابع عند النقطة اللى بديها بدي
+
+440
+00:56:22,880 --> 00:56:31,560
+partial Z by partial Y يبقى ناقص FY على FZ يبقى هى
+
+441
+00:56:31,560 --> 00:56:34,400
+الناقص برا وبدهش ال FY
+
+442
+00:56:39,700 --> 00:56:46,100
+تلاتة وY تربيع على مين على FZ اللي هو تلاتة Z
+
+443
+00:56:46,100 --> 00:56:53,760
+تربيع زائد Y ويساوي هي الناقص برا هنا ناقص واحد
+
+444
+00:56:53,760 --> 00:57:03,660
+زائد واحد زائد تلاتة على تلاتة زائد واحد أطلع سالب
+
+445
+00:57:03,660 --> 00:57:07,880
+تلات تربع يبقى هنا سالب تلات تربع
+
+446
+00:57:35,100 --> 00:57:39,340
+عليك بيكون وصلنا الى نهاية هذا ال section وإلى
+
+447
+00:57:39,340 --> 00:57:49,520
+يكون أرقام المسائل التالية يبقى exercises يبقى
+
+448
+00:57:49,520 --> 00:57:56,540
+exercises أربعة عشر أربعة المسائل تلاتة خمسة سبعة
+
+449
+00:57:56,540 --> 00:57:59,580
+تسعة تلاتة خمسة سبعة
+
+450
+00:58:02,570 --> 00:58:09,250
+تسع تاش واحد وعشرين تسع تاش واحد وعشرين تلاتة
+
+451
+00:58:09,250 --> 00:58:11,950
+وعشرين تلاتين اتنين
+
+452
+00:58:15,350 --> 00:58:22,830
+تلاتة وتلاتين خمسة وتلاتين سبعة وتلاتين وسبعة
+
+453
+00:58:22,830 --> 00:58:28,010
+وتلاتين وتسعة وتلاتين وخمسة واربعين وتمانية
+
+454
+00:58:28,010 --> 00:58:39,270
+واربعين وخمسة واربعين وتمانية واربعين الان
+
+455
+00:58:39,270 --> 00:58:42,930
+هنتفل الى ال section اللذي يليهي
+
+456
+00:58:46,590 --> 00:58:53,410
+بقى سيكشن أربعة أشهر كام سا اللي هو directional
+
+457
+00:58:53,410 --> 00:58:57,270
+derivatives
+
+458
+00:58:57,270 --> 00:59:02,930
+directional
+
+459
+00:59:02,930 --> 00:59:10,910
+derivatives يعني المشتقاد المتجه and the gradient
+
+460
+00:59:23,000 --> 00:59:27,720
+بنواصل الآن يا بناد للمحاضرة طبيعتنا وننتقل إلى ال
+
+461
+00:59:27,720 --> 00:59:31,940
+section 14-5 اللي بتكلم عن ال directional
+
+462
+00:59:31,940 --> 00:59:38,620
+derivatives يعني المشتقات المتجهة يعني مشتقة في
+
+463
+00:59:38,620 --> 00:59:45,400
+اتجاه الماء and gradient vectors والمتجهات اللي
+
+464
+00:59:45,400 --> 00:59:50,840
+بتبقى على شكل grade Fأو دل F أو نقلة F هذا مثلًا
+
+465
+00:59:50,840 --> 00:59:57,080
+رأيكم بعد قليل هنقلت تعريفين و بعد التعريفين هنروح
+
+466
+00:59:57,080 --> 01:00:02,260
+لبعض الأمثلة أطبعيًا أول تعريف يقول the gradient
+
+467
+01:00:02,260 --> 01:00:08,460
+vector of a function f of x و y عند النقصة P node
+
+468
+01:00:08,460 --> 01:00:12,220
+of x node و y node is the vector يبقى فيه أن ال
+
+469
+01:00:12,220 --> 01:00:19,500
+gradient vector هذا يبقى متجهلمين؟ للدلة F شو
+
+470
+01:00:19,500 --> 01:00:27,280
+برمزله؟ بالرمز المثلث لرأسه لأسفل ويقرأ grade F أو
+
+471
+01:00:27,280 --> 01:00:33,780
+gradient F يختصر إلى grade F أو دل F أو نقلة F
+
+472
+01:00:33,780 --> 01:00:44,800
+يبقى هذا الرمز يا بروح بقول grade F يا إما بقول دل
+
+473
+01:00:44,800 --> 01:00:55,620
+Fيا أما بقول نطلع F كل واحد فيهم هذول أي واحد من
+
+474
+01:00:55,620 --> 01:01:01,120
+التلاتة هذول الرمز هذا كله هو عبارة عن مين اللي هو
+
+475
+01:01:01,120 --> 01:01:02,700
+grade F
+
+476
+01:01:05,110 --> 01:01:09,730
+هذا من ناحية التسمي لكن بدا نجي لمفهومه as a
+
+477
+01:01:09,730 --> 01:01:14,730
+vector يبقى مفهومه as a vector ومستقل يتبلف
+
+478
+01:01:14,730 --> 01:01:21,150
+بالنسبة لX عند النقطة P0 في اتجاه I المستقل يتبلف
+
+479
+01:01:21,150 --> 01:01:25,270
+بالنسبة له عند P0 في اتجاه الجي يعني معناه كل ما
+
+480
+01:01:25,270 --> 01:01:28,390
+بدي أجيب له partial F على partial X و أعوض
+
+481
+01:01:28,390 --> 01:01:31,750
+بإحداثية النقطة الرقم اللي بيطلع بيقول هذا في
+
+482
+01:01:31,750 --> 01:01:38,360
+اتجاه Iزاد مشتقة ال F بالنسبة إلى Y وعوض بحداثية
+
+483
+01:01:38,360 --> 01:01:42,720
+النقطة هيطلع عندي رقم بقول هذا في اتجاه الجي اتنين
+
+484
+01:01:42,720 --> 01:01:48,440
+مع بعض بيكونوني اللي هو ما يسمى graph F يبقى F X
+
+485
+01:01:48,440 --> 01:01:52,180
+عند X node وY node في اتجاه I زاد F Y عند X node
+
+486
+01:01:52,180 --> 01:01:58,730
+وY node في اتجاه الجي طب لو كانتلت متجهات يعني في
+
+487
+01:01:58,730 --> 01:02:03,910
+تلت محاور يبقى بضفلهم كمان مين FZ وهذا ما سنرجع
+
+488
+01:02:03,910 --> 01:02:09,410
+عليه خلال هذا ال section تمام تعريف التاني تعريف
+
+489
+01:02:09,410 --> 01:02:12,770
+التاني هو نصف الأول من العنوان اللي احنا رافقيله
+
+490
+01:02:12,770 --> 01:02:15,870
+اللي هو ال directional derivatives المشتقات
+
+491
+01:02:15,870 --> 01:02:22,430
+المتجهة فبعرف المشتقة تبع التدريب عند النقطة في
+
+492
+01:02:22,430 --> 01:02:25,610
+اتجاه المتجه لأن هذا is
+
+493
+01:02:28,930 --> 01:02:35,490
+هيبقى اشتق جزئيا سواء كان بالنسبة ل X أو بالنسبة ل
+
+494
+01:02:35,490 --> 01:02:39,830
+Y بتعوض بيه احداثيات النقطة اللي عيلنا هذه يبقى
+
+495
+01:02:39,830 --> 01:02:46,150
+جيبنا مين جيبنا grade F اه اتجاه unit vector U
+
+496
+01:02:46,150 --> 01:02:50,250
+يبقى بتفهم ان U هذا معناه مش vector عادي وانما
+
+497
+01:02:50,250 --> 01:02:55,620
+متجهوحدة حطيته مركبتين يو واحد في اتجاه ال I زي دي
+
+498
+01:02:55,620 --> 01:03:02,340
+و اتنين في اتجاه ال J as V U F عند ال P نوت الرمز
+
+499
+01:03:02,340 --> 01:03:07,600
+يدل على ال directional derivative طب هذا الرمز يا
+
+500
+01:03:07,600 --> 01:03:12,660
+بكتبه بشكل هذا يا بكتبه قرية F عند نقطة P نوت ضد
+
+501
+01:03:12,660 --> 01:03:18,340
+متجه الواحدة U يجب ان اشيل هذا و اكتبه زي ما عرفت
+
+502
+01:03:18,340 --> 01:03:24,100
+فيهم وهذازي ما عرفته هنا بالشكل اعناعي اعمل ضمة
+
+503
+01:03:24,100 --> 01:03:28,920
+product فيما بينهما بصيارة ال domain f x في u1 زي
+
+504
+01:03:28,920 --> 01:03:35,380
+f y في u2 بناء عليه الناتج كمية قياسية او كمية
+
+505
+01:03:35,380 --> 01:03:43,220
+اتجاهيةIowascalar يبقى مقدار المشتقة المتجهة عند
+
+506
+01:03:43,220 --> 01:03:49,020
+نقطة هي المقصود فيه منه هو grad F عند تلك النقطة
+
+507
+01:03:49,020 --> 01:03:55,140
+ضد متجه الوحدة U عند تلك النقطة يبقى هذا تعريف ال
+
+508
+01:03:55,140 --> 01:03:59,520
+directional derivative نعطي بعض الأمثل عليه نجي
+
+509
+01:03:59,520 --> 01:04:02,240
+ناخد أول مثال examples
+
+510
+01:04:08,710 --> 01:04:13,330
+بقول find the derivative of the function find the
+
+511
+01:04:13,330 --> 01:04:29,150
+derivative of the function لذالة f of x y f of x y
+
+512
+01:04:29,150 --> 01:04:43,010
+بساوي x ناقص ال y على x y زائد اتنينعند النقطة P
+
+513
+01:04:43,010 --> 01:04:56,170
+naught of واحد مسالب واحد in the direction of
+
+514
+01:04:56,170 --> 01:05:07,760
+the vector اتجاه المتجد اللي هوذى بدى يساوي ماعشر
+
+515
+01:05:07,760 --> 01:05:24,480
+I زائد خمسة J إذا
+
+516
+01:05:24,480 --> 01:05:26,160
+مشينا لإيجاد طريقة
+
+517
+01:05:37,780 --> 01:05:45,140
+النقطة المعطنية هي المعطنية المعطنية المعطنية
+
+518
+01:05:45,140 --> 01:05:52,220
+المعطنية المعطنية المعطنية المعطنية المعطنية
+
+519
+01:05:52,220 --> 01:05:59,180
+المعطنية المعطنية
+
+520
+01:06:04,560 --> 01:06:12,460
+عند من؟ عند .. عند .. بالنسبة للمتغير X، F، X ها
+
+521
+01:06:12,460 --> 01:06:18,000
+يا ابنها البص بدلرة X والمقام بدلرة X إذا مشتقت
+
+522
+01:06:18,000 --> 01:06:26,260
+خارج قسمة دالتين يبقى المقام لمشتقة البص بالنسبة
+
+523
+01:06:26,260 --> 01:06:28,860
+لX اللي هو كده ايش؟ واحد
+
+524
+01:06:34,460 --> 01:06:42,100
+في مشتقة المقام بالنسبة لـ X أو Y كل هذا الكلام
+
+525
+01:06:42,100 --> 01:06:49,600
+على مربع المقام الأصلي هذا يبدو سواء يا بناه X Y
+
+526
+01:06:49,600 --> 01:07:00,140
+زائد 2 ناقص XY زائد Y ترابيع كله على XY زائد 2 لكل
+
+527
+01:07:00,140 --> 01:07:07,520
+ترابيعهذه تذهب مع هذه يبقى اتنين زائد Y تربية على
+
+528
+01:07:07,520 --> 01:07:13,260
+XY زائد اتنين كل تربية شو رايكوا بالمرة نحسبها عند
+
+529
+01:07:13,260 --> 01:07:19,800
+النقطة يبقى بالتاجة اخد له F X عند واحد و سالب
+
+530
+01:07:19,800 --> 01:07:24,420
+واحد لان هشيل كل X و احط مكانها واحد و اشيل Y و
+
+531
+01:07:24,420 --> 01:07:33,370
+احط مكانها واحدزائد سالب واحد تربيع على واحد سالب
+
+532
+01:07:33,370 --> 01:07:42,650
+واحد زائد اتنين لكل تربيع يمجي هنا تلاتة وهنا واحد
+
+533
+01:07:42,650 --> 01:07:49,530
+هو يسوي قداش تلاتة انا اروح اجيب له ال FY يمجي FY
+
+534
+01:07:49,530 --> 01:07:52,310
+بنفس الطريقة المقام
+
+535
+01:07:54,790 --> 01:08:01,690
+بمشتقة ال bus بالنسبة ل y سالب واحد ناقص ال bus
+
+536
+01:08:01,690 --> 01:08:08,730
+بمشتقة المقام بالنسبة إيه ل y لو قداش x على مربع
+
+537
+01:08:08,730 --> 01:08:15,610
+المقام الأصلي xy زي دي اتنين لكل تربية y و 7
+
+538
+01:08:45,380 --> 01:08:51,340
+بنحسب fy نقطة واحدة وسالك واحدة
+
+539
+01:08:59,170 --> 01:09:04,630
+زائد اتنين الكل تربيع ناقص تلاتة على واحد اللي هو
+
+540
+01:09:04,630 --> 01:09:10,550
+ناقص تلاتة تعالوا نطلع نجيب جراد F عند النقطة
+
+541
+01:09:10,550 --> 01:09:21,890
+يابانا هاي يبقى بروح بقوله جراد F عند النقطة P0 أو
+
+542
+01:09:21,890 --> 01:09:25,250
+عند النقطة اللي هي واحد
+
+543
+01:09:29,340 --> 01:09:35,960
+بدا تساوي ال Fx طلعناها بتلاتة يبقى تلاتة I وناقص
+
+544
+01:09:35,960 --> 01:09:44,360
+تلاتة G I بدنا ال vector هذا نخليه زي ما هو ال
+
+545
+01:09:44,360 --> 01:09:47,700
+unit vector إذا بدنا نجيب متجة الواحدة بالنسبة
+
+546
+01:09:47,700 --> 01:09:55,600
+لمين لهذا المتجة إذن ال U بدو يساوي ال V على طول
+
+547
+01:09:55,600 --> 01:09:58,960
+ال V ال V اللي هو اتناشر I
+
+548
+01:10:01,590 --> 01:10:11,610
+على الجدر التربيعي لـ 144 زائد 25 يساوي 12 على 13
+
+549
+01:10:11,610 --> 01:10:22,490
+I خمسة على تلتاشر اذا بدى اجيبله الـ D U F عند
+
+550
+01:10:22,490 --> 01:10:30,930
+النقطة واحد وسالب واحد يساوي تلاتة I ناقص تلاتة J
+
+551
+01:10:31,620 --> 01:10:39,680
+بوت المتجه عندنا اتناشر عالى تلتاشر I خمسة عالى
+
+552
+01:10:39,680 --> 01:10:46,800
+تلتاشر J و يسابر اتناشر في تلاتة بستة و تلاتين
+
+553
+01:10:46,800 --> 01:10:59,260
+عالى تلتاشر ناقص خمستاشر عالى تلتاشر و يسابر واحد
+
+554
+01:10:59,260 --> 01:11:04,490
+و عشرينعلى تلتاشة أي قيمة الـ Directional
+
+555
+01:11:04,490 --> 01:11:11,610
+Derivative عن مين عند النقطة المُعطَرة في روايكم
+
+556
+01:11:11,610 --> 01:11:17,910
+هذا ال section لا يخلو أي امتحان من سؤال عليه
+
+557
+01:11:17,910 --> 01:11:21,590
+مظارا
+
+558
+01:11:21,590 --> 01:11:27,510
+لأهميته ناخد كمان مثال اتنين
+
+559
+01:11:35,630 --> 01:11:48,010
+بالعكس فالـ F of X وY بدها تساوي X تربيع ناقص XY
+
+560
+01:11:48,010 --> 01:11:58,510
+زائد Y تربيع ناقص Y Find the directions
+
+561
+01:12:01,690 --> 01:12:11,370
+find the directions U for which يحيث
+
+562
+01:12:11,370 --> 01:12:24,510
+ان for which اللي هو D U F عند النقطة اللي هي من
+
+563
+01:12:24,510 --> 01:12:27,230
+واحد و سالب واحد
+
+564
+01:12:45,460 --> 01:12:52,580
+هذا سؤال زي سابقني بس حوّرنا الفكرة شغالة لأقنى
+
+565
+01:12:52,580 --> 01:12:59,320
+مستقل المتجه ماعطيه تبتدى جدرى سالب ثلاثة ومتجه
+
+566
+01:12:59,320 --> 01:13:04,040
+يوم ماعطانى شريعة وعطانى الدالة مبلهات المتجه
+
+567
+01:13:04,040 --> 01:13:10,420
+اليوم يعني بدي أجيب لمتجه الوحدة للمتجه عند النقطة
+
+568
+01:13:10,420 --> 01:13:16,580
+الموضعة في اتجاهه بدأ سوى من سالب تلاتةخليني امشي
+
+569
+01:13:16,580 --> 01:13:22,500
+ماشي طبيعي و احط كل شيء في مكانه هوصل بالاخر لمن؟
+
+570
+01:13:22,500 --> 01:13:27,280
+لنتيجة او لنتيجة اللي هو بدوها يبقى فيها ده سؤال
+
+571
+01:13:27,280 --> 01:13:32,600
+عايزني ليه التيجة تبع متجه الواحدة يوم؟ يعني كأنه
+
+572
+01:13:32,600 --> 01:13:36,520
+بده متجه الواحدة يوم شو شكله اللي خلّى المستقل
+
+573
+01:13:36,520 --> 01:13:42,320
+متجها تساوي سالت تلتة اذا انا بده اروح اجيبله من؟
+
+574
+01:13:43,370 --> 01:13:47,630
+ممتاز زي ما بدأنا بالظبط تماما يبقى بدأ أروح أجيب
+
+575
+01:13:47,630 --> 01:13:59,090
+له F X Y ساعة تنين X نقصها نحسبها بالمرة يبقى F X
+
+576
+01:13:59,090 --> 01:14:03,010
+يبقى
+
+577
+01:14:03,010 --> 01:14:12,310
+ال F X عند النقطة واحد وسالب واحد ساعة تلاتةنقص
+
+578
+01:14:12,310 --> 01:14:21,290
+نقص واحد هو تساوي تلاتة كذا بدي fy يبقى ناقص x
+
+579
+01:14:21,290 --> 01:14:31,390
+زائد اتنين y ناقص واحد وهذا الكلام الfy ان النقطة
+
+580
+01:14:31,390 --> 01:14:39,730
+واحدة سالك واحد بدي سالك واحدزائد اتنين في سالب
+
+581
+01:14:39,730 --> 01:14:48,270
+واحد هنا سالب واحد حصل سالب اربعة يبقى صار اندجريد
+
+582
+01:14:48,270 --> 01:14:56,110
+F عند النقطة واحد وسالب واحد يبقى يساوي تلاتة I
+
+583
+01:14:56,110 --> 01:14:58,650
+ناقص اربعة G
+
+584
+01:15:01,760 --> 01:15:10,960
+أنا عندي بدأ افترض عندي متجر واحدة U أسيوم طردت أن
+
+585
+01:15:10,960 --> 01:15:18,780
+U يتساوي واحد في اتجاه I و U اتنين في اتجاه J إذا
+
+586
+01:15:18,780 --> 01:15:26,120
+بدأ أجيب له Directionary Derivative DuF عند النقطة
+
+587
+01:15:26,120 --> 01:15:26,740
+واحدة
+
+588
+01:15:30,250 --> 01:15:39,590
+implies اقرأة الـ F هي تلاتة I ناقص أربعة G ضد U
+
+589
+01:15:39,590 --> 01:15:45,090
+واحد اتجاه الـ I U اتنين اتجاه الـ G تساوي سالب
+
+590
+01:15:45,090 --> 01:15:54,230
+تلاتة إذا تلاتة U واحد ناقص أربعة U اتنين تساوي
+
+591
+01:15:54,230 --> 01:15:56,810
+قدرت سالب تلاتة
+
+592
+01:16:00,330 --> 01:16:08,090
+U1 يتساوي 4U2
+
+593
+01:16:08,090 --> 01:16:14,070
+-3 يتساوي 4U2-3 يتساوي
+
+594
+01:16:14,070 --> 01:16:17,810
+4U2-3 يتساوي
+
+595
+01:16:17,810 --> 01:16:21,370
+4U2-3 يتساوى 4U2-3 يتساوى 4U2-3 يتساوى 4U2-3
+
+596
+01:16:21,370 --> 01:16:21,410
+يتساوى 4U2-3 يتساوى 4U2-3 يتساوى 4U2-3 يتساوى 4U2
+
+597
+01:16:21,410 --> 01:16:21,610
+-3 يتساوى 4U2-3 يتساوى 4U2-3 يتساوى 4U2-3 يتساوى
+
+598
+01:16:21,610 --> 01:16:22,030
+4U2-3 يتساوى 4U2-3 يتساوى 4U2-3 يتساوى 4U2-3
+
+599
+01:16:22,030 --> 01:16:27,640
+يتساوى 4U2-3 يتساوى 4U2-3 يتساوىحذفتي يا رجل من
+
+600
+01:16:27,640 --> 01:16:37,840
+أين إذا جيب الأولاق الأخرى؟ وجدها قدامك علمها طلعي
+
+601
+01:16:37,840 --> 01:16:45,560
+في التعريف تبع ال directional derivative وين
+
+602
+01:16:45,560 --> 01:16:52,360
+التعريف؟ مسحناه؟ مسحناه، طيب الـU هذا إيه الشكل يا
+
+603
+01:16:52,360 --> 01:17:00,530
+بنت؟قلتك إيه؟ قلتك يا واخر يعني قدش طولك قلتها
+
+604
+01:17:00,530 --> 01:17:07,490
+جيبه هاله علاقة تانية نرجع هنا بقوله بقى ولكن جدري
+
+605
+01:17:07,490 --> 01:17:12,990
+التربية يوحى التربية زادي و اتنين تربية تساوي
+
+606
+01:17:12,990 --> 01:17:20,150
+واحدة لو ربعنا هذا معناه يوحى التربية زادي و اتنين
+
+607
+01:17:20,150 --> 01:17:33,480
+تربية تساوي واحدة هذا معناهY1 تربيع زائد هذا معناه
+
+608
+01:17:33,480 --> 01:17:38,120
+يبقى
+
+609
+01:17:38,120 --> 01:17:47,600
+توسع في 4Y2 ناقص تلاتة لكل تربيع زائد Y2 تربيع
+
+610
+01:17:47,600 --> 01:17:52,680
+وزائد Y1 زي
+
+611
+01:17:52,680 --> 01:18:00,200
+ما تشوفون يا بناتهذه عبارة عن معادلة في مجهول واحد
+
+612
+01:18:00,200 --> 01:18:04,240
+إذا كنت مستطيع أن أحسب هذا المجهول لذلك يجب أن أفك
+
+613
+01:18:04,240 --> 01:18:07,160
+هذا التربيه يجب أن أفك هذا التربيه يجب أن أفك هذا
+
+614
+01:18:07,160 --> 01:18:07,280
+التربيه يجب أن أفك هذا التربيه يجب أن أفك هذا
+
+615
+01:18:07,280 --> 01:18:07,800
+التربيه يجب أن أفك هذا التربيه يجب أن أفك هذا
+
+616
+01:18:07,800 --> 01:18:10,780
+التربيه يجب أن أفك هذا التربيه يجب أن أفك هذا
+
+617
+01:18:10,780 --> 01:18:12,740
+التربيه يجب أن أفك هذا التربيه يجب أن أفك هذا
+
+618
+01:18:12,740 --> 01:18:15,880
+التربيه يجب أن أفك هذا التربيه يجب أن أفك هذا
+
+619
+01:18:15,880 --> 01:18:19,420
+التربيه يجب أن أفك
+
+620
+01:18:24,660 --> 01:18:33,820
+يوت نين تربيع تساوي واحد تكيلي هذه قصيرة ستة عشر
+
+621
+01:18:33,820 --> 01:18:41,400
+على تسعة يوت نين تربيع ناقص اربع وعشرين على تسعة
+
+622
+01:18:41,400 --> 01:18:50,500
+يوت نين زائد واحد زائد يوت نين تربيع
+
+623
+01:18:53,790 --> 01:18:59,370
+أحنا يا بنات باعتباره كم؟ تسعة على تسعة، بيقصر كم؟
+
+624
+01:18:59,370 --> 01:19:06,030
+خمسة وعشرين على تسعة، يبقى خمسة وعشرين على تسعة
+
+625
+01:19:06,030 --> 01:19:18,400
+يوت نين اربعين، تمام؟25 على 9 U2 تربية وهذا ناقص
+
+626
+01:19:18,400 --> 01:19:26,640
+24 على 9 U عشان بدي أسوي صفات؟ ممكن طيب بدي أخد ال
+
+627
+01:19:26,640 --> 01:19:34,000
+U عامل مشترك مش بصير عندي U2 طبعا U2 أبدا أبدا خير
+
+628
+01:19:34,000 --> 01:19:40,520
+بصير 25 على 9 U2
+
+629
+01:19:46,360 --> 01:19:59,340
+الـ U2 بدها تساوي 0 او الـ U2 بدها تساوي 24 على 25
+
+630
+01:20:05,780 --> 01:20:11,360
+إتنين لذلك قد ما طلعنا نقول له five direction zero
+
+631
+01:20:11,360 --> 01:20:15,860
+يعني المتجهات الوحدة التي تحقق
+
+632
+01:20:37,240 --> 01:20:47,280
+لو كانت U2 تساوي 0، فلا يهاتش بنصيرها بنات، هذه ال
+
+633
+01:20:47,280 --> 01:20:52,340
+start، يعني نجح نعوض المعادلة start، لو كانت U2
+
+634
+01:20:52,340 --> 01:20:56,880
+تساوي 0، يبلغ U1 مقدار سالب واحد
+
+635
+01:21:02,480 --> 01:21:09,720
+يساوي سالف واحد هذا بدي اعطيكي ان ال U يساوي سالف
+
+636
+01:21:09,720 --> 01:21:16,340
+A متجهة واحدة ولا لا متجهة واحدة الحالة التانية F
+
+637
+01:21:16,340 --> 01:21:24,280
+U2 يساوي اربع على خمسة وعشرين اربع عشر على خمسة
+
+638
+01:21:24,280 --> 01:21:35,690
+وعشرين then U واحد يساوي طول Fأربعة أربعة في أربعة
+
+639
+01:21:35,690 --> 01:21:45,610
+وعشرين بستة وتسعين على خمسة وعشرين ماقص تلت مظبوط
+
+640
+01:21:45,610 --> 01:21:52,330
+هيك تلتة في خمسة وعشرين بخمسة وسبعين من ستة وتسعين
+
+641
+01:21:52,330 --> 01:22:00,800
+بكم بطلع كذا شبنات واحد وعشرين على خمسة وعشرينيعني
+
+642
+01:22:00,800 --> 01:22:15,760
+قدير 7 على 25 إذا ال U يسار ال U1 اللي طلعناها و
+
+643
+01:22:15,760 --> 01:22:25,320
+ال U2 ال U1 هذه اللي طلعناها هو 7 على 25 في اتجاه
+
+644
+01:22:25,320 --> 01:22:32,770
+الأعلىو U2 اللي هو زائد أربعة و عشرين على خمسة و
+
+645
+01:22:32,770 --> 01:22:41,910
+عشرين في اتجاه M في اتجاه الـ J طبعا
+
+646
+01:22:41,910 --> 01:22:46,790
+يبقى هذا متجه الوحدة الثاني اللي بيضمنها هذا
+
+647
+01:22:46,790 --> 01:22:52,950
+المتجه الأول اللي أطلبه وهذا هو متجه الوحدة الثاني
+
+648
+01:22:52,950 --> 01:22:54,090
+اللي هو طلبه
+
+649
+01:23:00,370 --> 01:23:05,610
+طيب نجي لخواص directionally driven نجي ل ال
+
+650
+01:23:21,530 --> 01:23:31,630
+بطل U وهي بدأت تساوي لهوليجراد F في Cos الزاوية
+
+651
+01:23:31,630 --> 01:23:35,830
+أول
+
+652
+01:23:35,830 --> 01:23:47,930
+خاصية من هذه القوات الـ Function F increases most
+
+653
+01:23:47,930 --> 01:23:49,370
+rapidly
+
+654
+01:23:53,680 --> 01:24:03,520
+most rapidly when
+
+655
+01:24:03,520 --> 01:24:22,200
+theta تساوي zero that is in when اليوم and they
+
+656
+01:24:23,480 --> 01:24:31,120
+Same Direction
+
+657
+01:24:31,120 --> 01:24:43,360
+قام اجراد ال F هذا بدي أعطيكم ان ال DUF بدي ساوي
+
+658
+01:24:43,360 --> 01:24:47,540
+طول اجراد ال F فقط لغة
+
+659
+01:24:51,740 --> 01:25:03,380
+again this case في هذه الحالة الـ DUF as its as
+
+660
+01:25:03,380 --> 01:25:10,000
+its largest as
+
+661
+01:25:10,000 --> 01:25:16,500
+its largest positive value
+
+662
+01:25:16,500 --> 01:25:19,040
+when
+
+663
+01:25:21,190 --> 01:25:33,010
+فيتا يساوي ساعة. دمرة اتنين، similar to function.
+
+664
+01:26:13,490 --> 01:26:24,890
+الـ F لـ U and a graded F in
+
+665
+01:26:24,890 --> 01:26:39,990
+the opposite directions that
+
+666
+01:26:39,990 --> 01:26:40,350
+is
+
+667
+01:26:52,700 --> 01:27:02,380
+صار الـ D والـ F بدأت تساوي كل جراد الـ F في Cos
+
+668
+01:27:02,380 --> 01:27:07,860
+بقعة و يساوي سالب absolute value
+
+669
+01:27:38,870 --> 01:27:39,850
+العزيزي .
+
+670
+01:28:20,280 --> 01:28:27,300
+أو يمكن أن تكون positive أو negative او positive
+
+671
+01:28:27,300 --> 01:28:28,240
+او negative او positive او positive او positive او
+
+672
+01:28:28,240 --> 01:28:30,240
+positive او positive او positive او positive او
+
+673
+01:28:30,240 --> 01:28:32,440
+positive او positive او positive او positive او
+
+674
+01:28:32,440 --> 01:28:32,540
+positive او positive او positive او positive او
+
+675
+01:28:32,540 --> 01:28:32,580
+positive او positive او positive او positive او
+
+676
+01:28:32,580 --> 01:28:32,980
+positive او positive او positive او positive او
+
+677
+01:28:32,980 --> 01:28:33,620
+positive او positive او positive او positive او
+
+678
+01:28:33,620 --> 01:28:33,660
+positive او positive او positive او positive او
+
+679
+01:28:33,660 --> 01:28:35,220
+positive او positive ا
+
+680
+01:28:38,340 --> 01:28:41,800
+اللي بقول أنا الخواص طبعا ال direction أنا دريبه
+
+681
+01:28:41,800 --> 01:28:47,580
+فبقى اجي بقول ال D U F يبقى ايه اجراد ال F ضد ال U
+
+682
+01:28:47,580 --> 01:28:52,810
+يبقى طوللغراد ال F في طول ال U في Cos الزاوية
+
+683
+01:28:52,810 --> 01:28:58,270
+تيتا، كده طول ال U يبقى بطير، بظل طول غراد ال F في
+
+684
+01:28:58,270 --> 01:29:03,050
+Cos الزاوية تيتا، ليش؟ لأن ال U هو متجه الواحدة،
+
+685
+01:29:03,050 --> 01:29:06,630
+فطوله يسوي كده شخص صحيح، لذا هذا يسوي طول غراد ال
+
+686
+01:29:06,630 --> 01:29:11,280
+F في Cos الزاوية تيتااللي انا بدى اشوف القيمة دي
+
+687
+01:29:11,280 --> 01:29:15,860
+وقتش بتكون اكبر ما يمكن وقتش اقل ما يمكن وقتش
+
+688
+01:29:15,860 --> 01:29:20,360
+بتبقى zero بقول الدالة if increases most rapidly
+
+689
+01:29:20,360 --> 01:29:28,720
+تتزايد بسرعة فائقة most rapidly بسرعة when θ تبقى
+
+690
+01:29:28,720 --> 01:29:33,780
+zeroماذا يعني هذا الكلام؟ يعني يجب أن يكون U و F
+
+691
+01:29:33,780 --> 01:29:38,780
+اتنين مالهم في نفس الاتجاه لأن الزوابن هم Zero
+
+692
+01:29:38,780 --> 01:29:45,260
+That is when ال U in the same direction of F اتنين
+
+693
+01:29:45,260 --> 01:29:50,140
+في نفس الاتجاه تبقى بصير عندك كوسين صفر بجدير واحد
+
+694
+01:29:50,140 --> 01:29:55,320
+أكبر قيمة بياخدها الكوسين جدير إذا هذه بتاخد أقصى
+
+695
+01:29:55,320 --> 01:29:59,700
+قيمة لهاعند θ تساوي zero عندما u و grade ال F
+
+696
+01:29:59,700 --> 01:30:06,360
+يكونوا في نفس الاتجاه كده مقدارها؟ مقدارها طول
+
+697
+01:30:06,360 --> 01:30:10,520
+grade ال F لأن ال direction derivative طول grade
+
+698
+01:30:10,520 --> 01:30:15,080
+ال F كسين زوية تيتا كسين تيتا بواحد يبقى بظهر أكبر
+
+699
+01:30:15,080 --> 01:30:21,160
+قيمة لطول grade ال F طب كده شقة القيمة؟يقول لو
+
+700
+01:30:21,160 --> 01:30:25,380
+كانوا اثنين ماشيين في اتجاهين متعدين ليش ان قصة
+
+701
+01:30:25,380 --> 01:30:29,660
+مية و تمانين بسالب واحد وهي اقل قيمة بياخدها ال
+
+702
+01:30:29,660 --> 01:30:30,000
+cosine
+
+703
+01:30:50,590 --> 01:30:55,470
+إتنين في اتجاهين متضادين في اتجاهين متضادين يقزق
+
+704
+01:30:55,470 --> 01:31:03,250
+بينهم كم؟ 180 درجة الهنكو ساي 180 سالب واحد يبقى
+
+705
+01:31:03,250 --> 01:31:07,510
+بصير قيمة ال direction derivative هي سالب grade ال
+
+706
+01:31:07,510 --> 01:31:11,330
+F يعني انا في الحالتين الاتنين هدول إذا جبت grade
+
+707
+01:31:11,330 --> 01:31:17,290
+ال F بكون خلاص جبت main أكبر قيمة و أقل قيمة سالب
+
+708
+01:31:17,290 --> 01:31:23,850
+طول grade ال Fبعطي أفضل قيمة للدراكشين
+
+709
+01:31:23,850 --> 01:31:33,650
+دريفاتيب اذا اتنين او اتنين او اتنين او اتنين او
+
+710
+01:31:33,650 --> 01:31:41,050
+اتنين او اتنين او اتنينمتعمدة، الآن عندنا أمثل
+
+711
+01:31:41,050 --> 01:31:44,990
+عليهم، لكن أنا بقولك تفي بهذا القدر اليوم لإنه
+
+712
+01:31:44,990 --> 01:31:50,270
+بدنا نوزع أوراق لامتحان ان شاء الله تعالى
+
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/RFjaGoXcZxE_raw.json b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/RFjaGoXcZxE_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..b13bbb9f4007e24b84a2c2f23cb171df717fb262
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/RFjaGoXcZxE_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 2932, "start": 12.96, "end": 29.32, "text": "بسم الله الرحمن الرحيم عود على build المرة اللي فاتت ابتدأنا في section 14 او 14 و8 share role فعل السلسلة واخدنا الحالة الأولى لو كانت ال function مالا في موضة ليه ride", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 6225, 23328, 15844, 1322, 9673, 25720, 13672, 1829, 6156, 9307, 2655, 48127, 2655, 3215, 10721, 8315, 8978, 3541, 3499, 1975, 2407, 3499, 4032, 23, 2073, 3090, 6156, 30241, 21136, 1211, 3794, 37977, 4032, 47283, 3215, 8315, 21542, 6027, 3660, 16247, 12610, 7578, 45164, 25961, 2655, 2423, 2445, 3714, 6027, 995, 8978, 3714, 2407, 11242, 3660, 32239, 3224, 5077], "avg_logprob": -0.42463236565099044, "compression_ratio": 1.4972067039106145, "no_speech_prob": 4.172325134277344e-06, "words": [{"start": 12.960000000000006, "end": 13.88, "word": "بسم", "probability": 0.782470703125}, {"start": 13.88, "end": 14.06, "word": " الله", "probability": 0.96923828125}, {"start": 14.06, "end": 14.48, "word": " الرحمن", "probability": 0.97265625}, {"start": 14.48, "end": 15.02, "word": " الرحيم", "probability": 0.98828125}, {"start": 15.02, "end": 16.2, "word": " عود", "probability": 0.92431640625}, {"start": 16.2, "end": 16.64, "word": " على", "probability": 0.79052734375}, {"start": 16.64, "end": 17.06, "word": " build", "probability": 0.225830078125}, {"start": 17.06, "end": 17.72, "word": " المرة", "probability": 0.6357421875}, {"start": 17.72, "end": 17.88, "word": " اللي", "probability": 0.731689453125}, {"start": 17.88, "end": 18.44, "word": " فاتت", "probability": 0.8297526041666666}, {"start": 18.44, "end": 19.6, "word": " ابتدأنا", "probability": 0.9}, {"start": 19.6, "end": 19.76, "word": " في", "probability": 0.4140625}, {"start": 19.76, "end": 20.06, "word": " section", "probability": 0.69189453125}, {"start": 20.06, "end": 20.62, "word": " 14", "probability": 0.8515625}, {"start": 20.62, "end": 20.84, "word": " او", "probability": 0.183990478515625}, {"start": 20.84, "end": 21.16, "word": " 14", "probability": 0.85546875}, {"start": 21.16, "end": 21.54, "word": " و8", "probability": 0.44329833984375}, {"start": 21.54, "end": 22.12, "word": " share", "probability": 0.77880859375}, {"start": 22.12, "end": 22.72, "word": " role", "probability": 0.611328125}, {"start": 22.72, "end": 23.22, "word": " فعل", "probability": 0.4443359375}, {"start": 23.22, "end": 23.98, "word": " السلسلة", "probability": 0.664520263671875}, {"start": 23.98, "end": 25.14, "word": " واخدنا", "probability": 0.94384765625}, {"start": 25.14, "end": 25.6, "word": " الحالة", "probability": 0.9757486979166666}, {"start": 25.6, "end": 26.06, "word": " الأولى", "probability": 0.8763020833333334}, {"start": 26.06, "end": 26.28, "word": " لو", "probability": 0.89453125}, {"start": 26.28, "end": 26.64, "word": " كانت", "probability": 0.94970703125}, {"start": 26.64, "end": 26.72, "word": " ال", "probability": 0.8974609375}, {"start": 26.72, "end": 27.08, "word": " function", "probability": 0.92431640625}, {"start": 27.08, "end": 27.56, "word": " مالا", "probability": 0.3234049479166667}, {"start": 27.56, "end": 27.82, "word": " في", "probability": 0.93115234375}, {"start": 27.82, "end": 28.42, "word": " موضة", "probability": 0.5220947265625}, {"start": 28.42, "end": 28.96, "word": " ليه", "probability": 0.6064453125}, {"start": 28.96, "end": 29.32, "word": " ride", "probability": 0.2020263671875}], "temperature": 1.0}, {"id": 2, "seek": 5703, "start": 29.73, "end": 57.03, "text": "وكل متغير من المتغيرين function T متغير الاخر ثم بعد ذلك أخذنا لو كانت دالة function T ثلاثة متغيرات وكل متغير دالة في متغير الأخر الآن ننتقل إلى النقطة الثانية وهي function T متغيرين أو ثلاثة متغيرات وكل من هذه المتغيرات function", "tokens": [2407, 28820, 44650, 17082, 13546, 9154, 9673, 2655, 17082, 13546, 9957, 2445, 314, 44650, 17082, 13546, 2423, 47283, 2288, 38637, 2304, 39182, 29910, 23275, 5551, 9778, 8848, 8315, 45164, 25961, 2655, 11778, 6027, 3660, 2445, 314, 38637, 1211, 5718, 104, 3660, 44650, 17082, 13546, 9307, 4032, 28820, 44650, 17082, 13546, 11778, 6027, 3660, 8978, 44650, 17082, 13546, 16247, 34740, 6024, 48506, 8717, 29399, 4587, 1211, 30731, 28239, 47432, 3660, 6024, 104, 7649, 10632, 37037, 1829, 2445, 314, 44650, 17082, 13546, 9957, 34051, 38637, 1211, 5718, 104, 3660, 44650, 17082, 13546, 9307, 4032, 28820, 9154, 29538, 9673, 2655, 17082, 13546, 9307, 2445], "avg_logprob": -0.1924019550868109, "compression_ratio": 2.1215469613259668, "no_speech_prob": 4.172325134277344e-07, "words": [{"start": 29.73, "end": 30.51, "word": "وكل", "probability": 0.7568359375}, {"start": 30.51, "end": 31.37, "word": " متغير", "probability": 0.9762369791666666}, {"start": 31.37, "end": 31.61, "word": " من", "probability": 0.94287109375}, {"start": 31.61, "end": 32.65, "word": " المتغيرين", "probability": 0.95673828125}, {"start": 32.65, "end": 33.25, "word": " function", "probability": 0.224365234375}, {"start": 33.25, "end": 33.59, "word": " T", "probability": 0.113037109375}, {"start": 33.59, "end": 34.35, "word": " متغير", "probability": 0.7932942708333334}, {"start": 34.35, "end": 35.45, "word": " الاخر", "probability": 0.7099609375}, {"start": 35.45, "end": 35.87, "word": " ثم", "probability": 0.940185546875}, {"start": 35.87, "end": 36.15, "word": " بعد", "probability": 0.71923828125}, {"start": 36.15, "end": 36.67, "word": " ذلك", "probability": 0.98681640625}, {"start": 36.67, "end": 37.17, "word": " أخذنا", "probability": 0.65386962890625}, {"start": 37.17, "end": 37.43, "word": " لو", "probability": 0.85107421875}, {"start": 37.43, "end": 37.81, "word": " كانت", "probability": 0.89892578125}, {"start": 37.81, "end": 38.19, "word": " دالة", "probability": 0.7008463541666666}, {"start": 38.19, "end": 38.61, "word": " function", "probability": 0.81982421875}, {"start": 38.61, "end": 39.05, "word": " T", "probability": 0.70068359375}, {"start": 39.05, "end": 39.81, "word": " ثلاثة", "probability": 0.88671875}, {"start": 39.81, "end": 41.03, "word": " متغيرات", "probability": 0.8828125}, {"start": 41.03, "end": 41.97, "word": " وكل", "probability": 0.909912109375}, {"start": 41.97, "end": 42.89, "word": " متغير", "probability": 0.9900716145833334}, {"start": 42.89, "end": 43.77, "word": " دالة", "probability": 0.9637044270833334}, {"start": 43.77, "end": 43.93, "word": " في", "probability": 0.849609375}, {"start": 43.93, "end": 44.61, "word": " متغير", "probability": 0.9817708333333334}, {"start": 44.61, "end": 45.45, "word": " الأخر", "probability": 0.5999755859375}, {"start": 45.45, "end": 46.29, "word": " الآن", "probability": 0.755859375}, {"start": 46.29, "end": 46.85, "word": " ننتقل", "probability": 0.7540283203125}, {"start": 46.85, "end": 47.03, "word": " إلى", "probability": 0.83203125}, {"start": 47.03, "end": 47.53, "word": " النقطة", "probability": 0.95361328125}, {"start": 47.53, "end": 48.13, "word": " الثانية", "probability": 0.918701171875}, {"start": 48.13, "end": 48.83, "word": " وهي", "probability": 0.83251953125}, {"start": 48.83, "end": 49.27, "word": " function", "probability": 0.85302734375}, {"start": 49.27, "end": 49.89, "word": " T", "probability": 0.93994140625}, {"start": 49.89, "end": 51.05, "word": " متغيرين", "probability": 0.9713134765625}, {"start": 51.05, "end": 51.35, "word": " أو", "probability": 0.77099609375}, {"start": 51.35, "end": 52.13, "word": " ثلاثة", "probability": 0.93759765625}, {"start": 52.13, "end": 53.57, "word": " متغيرات", "probability": 0.9144287109375}, {"start": 53.57, "end": 54.67, "word": " وكل", "probability": 0.948486328125}, {"start": 54.67, "end": 55.03, "word": " من", "probability": 0.97265625}, {"start": 55.03, "end": 55.45, "word": " هذه", "probability": 0.9638671875}, {"start": 55.45, "end": 56.57, "word": " المتغيرات", "probability": 0.9859375}, {"start": 56.57, "end": 57.03, "word": " function", "probability": 0.9033203125}], "temperature": 1.0}, {"id": 3, "seek": 8564, "start": 58.28, "end": 85.64, "text": "فى two variables وليس فى variable واحد تمام وبالتالي مش هيكون عندنا اشتغال كل زى ما كنا بقوله دي و باي دي تي يبقى بتصير partial و باي partial المتغير اللى عندنا هذا لذلك هنحط هذا الكلام فى الصيغة التالية بجب اقول theorem suppose ذات ال w", "tokens": [5172, 7578, 732, 9102, 4032, 20292, 3794, 6156, 7578, 7006, 36764, 24401, 46811, 10943, 46599, 6027, 2655, 6027, 1829, 37893, 39896, 30544, 43242, 8315, 1975, 8592, 2655, 17082, 6027, 28242, 30767, 7578, 19446, 9122, 8315, 4724, 39648, 3224, 11778, 1829, 4032, 4724, 47302, 11778, 1829, 6055, 1829, 7251, 3555, 4587, 7578, 39894, 9381, 13546, 14641, 4032, 4724, 47302, 14641, 9673, 2655, 17082, 13546, 13672, 7578, 43242, 8315, 23758, 5296, 8848, 23275, 8032, 1863, 5016, 9566, 23758, 2423, 28820, 10943, 6156, 7578, 31767, 1829, 17082, 3660, 16712, 6027, 10632, 4724, 7435, 3555, 1975, 39648, 20904, 7297, 29910, 9307, 2423, 261], "avg_logprob": -0.3690624922513962, "compression_ratio": 1.7227272727272727, "no_speech_prob": 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64.8, "end": 65.32, "word": " اشتغال", "probability": 0.77060546875}, {"start": 65.32, "end": 65.7, "word": " كل", "probability": 0.54150390625}, {"start": 65.7, "end": 66.04, "word": " زى", "probability": 0.6103515625}, {"start": 66.04, "end": 66.14, "word": " ما", "probability": 0.90283203125}, {"start": 66.14, "end": 66.38, "word": " كنا", "probability": 0.861572265625}, {"start": 66.38, "end": 66.7, "word": " بقوله", "probability": 0.6394856770833334}, {"start": 66.7, "end": 67.72, "word": " دي", "probability": 0.42425537109375}, {"start": 67.72, "end": 67.72, "word": " و", "probability": 0.114990234375}, {"start": 67.72, "end": 68.08, "word": " باي", "probability": 0.4356689453125}, {"start": 68.08, "end": 68.34, "word": " دي", "probability": 0.80029296875}, {"start": 68.34, "end": 69.14, "word": " تي", "probability": 0.735107421875}, {"start": 69.14, "end": 69.52, "word": " يبقى", "probability": 0.723236083984375}, {"start": 69.52, "end": 70.1, "word": " بتصير", "probability": 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"end": 77.4, "word": " فى", "probability": 0.81005859375}, {"start": 77.4, "end": 78.26, "word": " الصيغة", "probability": 0.9600830078125}, {"start": 78.26, "end": 79.82, "word": " التالية", "probability": 0.9869791666666666}, {"start": 79.82, "end": 80.76, "word": " بجب", "probability": 0.5385335286458334}, {"start": 80.76, "end": 81.14, "word": " اقول", "probability": 0.823486328125}, {"start": 81.14, "end": 81.94, "word": " theorem", "probability": 0.83837890625}, {"start": 81.94, "end": 84.64, "word": " suppose", "probability": 0.484619140625}, {"start": 84.64, "end": 84.98, "word": " ذات", "probability": 0.822265625}, {"start": 84.98, "end": 85.12, "word": " ال", "probability": 0.86767578125}, {"start": 85.12, "end": 85.64, "word": " w", "probability": 0.33349609375}], "temperature": 1.0}, {"id": 4, "seek": 11335, "start": 91.01, "end": 113.35, "text": "الـ W تساوي الـ function في X of Y of Z والـ X function في R و S ده اللي فيه متغيرين والـ Y تساوي H of R و S والـ Z كذلك", "tokens": [6027, 39184, 343, 6055, 3794, 995, 45865, 2423, 39184, 2445, 8978, 1783, 295, 398, 295, 1176, 16070, 39184, 1783, 2445, 8978, 497, 4032, 318, 11778, 3224, 13672, 1829, 8978, 3224, 44650, 17082, 13546, 9957, 16070, 39184, 398, 6055, 3794, 995, 45865, 389, 295, 497, 4032, 318, 16070, 39184, 1176, 9122, 8848, 23275], "avg_logprob": -0.19590211701842974, "compression_ratio": 1.5263157894736843, "no_speech_prob": 0.0, "words": [{"start": 91.01, "end": 91.45, "word": "الـ", "probability": 0.666748046875}, {"start": 91.45, "end": 92.01, "word": " W", "probability": 0.63232421875}, {"start": 92.01, "end": 93.69, "word": " تساوي", "probability": 0.9290771484375}, {"start": 93.69, "end": 94.03, "word": " الـ", "probability": 0.749755859375}, {"start": 94.03, "end": 94.65, "word": " function", "probability": 0.8134765625}, {"start": 94.65, "end": 95.27, "word": " في", "probability": 0.93896484375}, {"start": 95.27, "end": 95.71, "word": " X", "probability": 0.91748046875}, {"start": 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{"start": 104.01, "end": 104.37, "word": " فيه", "probability": 0.9658203125}, {"start": 104.37, "end": 105.37, "word": " متغيرين", "probability": 0.95361328125}, {"start": 105.37, "end": 106.87, "word": " والـ", "probability": 0.8447265625}, {"start": 106.87, "end": 107.27, "word": " Y", "probability": 0.92578125}, {"start": 107.27, "end": 108.19, "word": " تساوي", "probability": 0.9794921875}, {"start": 108.19, "end": 108.85, "word": " H", "probability": 0.94970703125}, {"start": 108.85, "end": 109.37, "word": " of", "probability": 0.9619140625}, {"start": 109.37, "end": 110.11, "word": " R", "probability": 0.99658203125}, {"start": 110.11, "end": 110.37, "word": " و", "probability": 0.91357421875}, {"start": 110.37, "end": 110.73, "word": " S", "probability": 0.60693359375}, {"start": 110.73, "end": 111.91, "word": " والـ", "probability": 0.7421875}, {"start": 111.91, "end": 112.25, "word": " Z", "probability": 0.95703125}, {"start": 112.25, "end": 113.35, "word": " كذلك", 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وال Z بدها تساوي U في E أس V Find", "tokens": [2655, 2288, 21292, 3660, 16070, 1783, 47525, 11296, 6055, 3794, 995, 45865, 624, 8978, 462, 5551, 3794, 691, 8978, 15855, 624, 16070, 398, 47525, 11296, 6055, 3794, 995, 45865, 624, 8978, 462, 5551, 3794, 691, 8978, 15855, 624, 16070, 1176, 47525, 11296, 6055, 3794, 995, 45865, 624, 8978, 462, 5551, 3794, 691, 11809], "avg_logprob": -0.21368633652174915, "compression_ratio": 2.072289156626506, "no_speech_prob": 6.556510925292969e-07, "words": [{"start": 487.52000000000004, "end": 488.72, "word": "تربية", "probability": 0.4871826171875}, {"start": 488.72, "end": 489.92, "word": " وال", "probability": 0.4658203125}, {"start": 489.92, "end": 490.52, "word": " X", "probability": 0.457275390625}, {"start": 490.52, "end": 491.82, "word": " بدها", "probability": 0.76806640625}, {"start": 491.82, "end": 492.46, "word": " تساوي", "probability": 0.9022216796875}, {"start": 492.46, "end": 493.84, "word": " U", "probability": 0.82958984375}, {"start": 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"end": 516.85, "word": " الأول", "probability": 0.911376953125}, {"start": 516.85, "end": 517.71, "word": " نمرا", "probability": 0.3335367838541667}, {"start": 517.71, "end": 518.13, "word": " a", "probability": 0.339599609375}, {"start": 518.13, "end": 519.43, "word": " partial", "probability": 0.41748046875}, {"start": 519.43, "end": 520.33, "word": " w", "probability": 0.88134765625}, {"start": 520.33, "end": 521.17, "word": " by", "probability": 0.87060546875}, {"start": 521.17, "end": 522.19, "word": " partial", "probability": 0.94970703125}, {"start": 522.19, "end": 523.27, "word": " u", "probability": 0.958984375}, {"start": 523.27, "end": 524.49, "word": " by", "probability": 0.88232421875}, {"start": 524.49, "end": 525.53, "word": " its", "probability": 0.82958984375}, {"start": 525.53, "end": 526.51, "word": " chain", "probability": 0.56103515625}, {"start": 526.51, "end": 527.51, "word": " rule", "probability": 0.859375}, {"start": 527.51, "end": 529.77, "word": " يبقى", "probability": 0.712890625}, {"start": 529.77, "end": 530.31, "word": " بواصل", "probability": 0.76373291015625}, {"start": 530.31, "end": 530.89, "word": " قاعدة", "probability": 0.8465576171875}, {"start": 530.89, "end": 531.55, "word": " السلسلة", "probability": 0.9873046875}, {"start": 531.55, "end": 532.65, "word": " نمرا", "probability": 0.89501953125}, {"start": 532.65, "end": 533.05, "word": " b", "probability": 0.6689453125}, {"start": 533.05, "end": 534.45, "word": " partial", "probability": 0.2119140625}, {"start": 534.45, "end": 535.39, "word": " w", "probability": 0.9755859375}, {"start": 535.39, "end": 536.17, "word": " by", "probability": 0.9453125}, {"start": 536.17, "end": 536.79, "word": " partial", "probability": 0.95263671875}, {"start": 536.79, "end": 537.57, "word": " u", "probability": 0.97802734375}, {"start": 537.57, "end": 539.57, "word": " directly", "probability": 0.88134765625}, {"start": 539.57, "end": 544.45, "word": " مباشرة", "probability": 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371], "avg_logprob": -0.2180989519175556, "compression_ratio": 1.5379310344827586, "no_speech_prob": 0.0, "words": [{"start": 584.28, "end": 584.74, "word": "سؤال", "probability": 0.83544921875}, {"start": 584.74, "end": 585.04, "word": " مرة", "probability": 0.9501953125}, {"start": 585.04, "end": 586.46, "word": " تانية،", "probability": 0.813232421875}, {"start": 586.46, "end": 587.04, "word": " ماعطيني", "probability": 0.7821533203125}, {"start": 587.04, "end": 587.38, "word": " w", "probability": 0.32373046875}, {"start": 587.38, "end": 587.96, "word": " function", "probability": 0.77978515625}, {"start": 587.96, "end": 588.24, "word": " في", "probability": 0.9150390625}, {"start": 588.24, "end": 588.94, "word": " ثلاثة", "probability": 0.921484375}, {"start": 588.94, "end": 590.44, "word": " متغيرات،", "probability": 0.877978515625}, {"start": 590.44, "end": 590.98, "word": " لإن", "probability": 0.760498046875}, {"start": 590.98, "end": 591.22, "word": " x", "probability": 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"probability": 0.6689453125}, {"start": 3606.52, "end": 3607.3, "word": " عند", "probability": 0.958984375}, {"start": 3607.3, "end": 3607.96, "word": " النقصة", "probability": 0.73828125}, {"start": 3607.96, "end": 3608.14, "word": " P", "probability": 0.82373046875}, {"start": 3608.14, "end": 3608.46, "word": " node", "probability": 0.492919921875}, {"start": 3608.46, "end": 3608.64, "word": " of", "probability": 0.91064453125}, {"start": 3608.64, "end": 3608.9, "word": " x", "probability": 0.76513671875}, {"start": 3608.9, "end": 3609.24, "word": " node", "probability": 0.489013671875}, {"start": 3609.24, "end": 3609.38, "word": " و", "probability": 0.65380859375}, {"start": 3609.38, "end": 3609.54, "word": " y", "probability": 0.4677734375}, {"start": 3609.54, "end": 3609.82, "word": " node", "probability": 0.556640625}, {"start": 3609.82, "end": 3610.16, "word": " is", "probability": 0.57861328125}, {"start": 3610.16, "end": 3610.38, "word": " the", "probability": 0.8623046875}, {"start": 3610.38, "end": 3610.72, "word": " vector", "probability": 0.966796875}, {"start": 3610.72, "end": 3611.7, "word": " يبقى", "probability": 0.69549560546875}, {"start": 3611.7, "end": 3611.92, "word": " فيه", "probability": 0.67626953125}, {"start": 3611.92, "end": 3612.08, "word": " أن", "probability": 0.257080078125}, {"start": 3612.08, "end": 3612.22, "word": " ال", "probability": 0.7294921875}, {"start": 3612.22, "end": 3612.7, "word": " gradient", "probability": 0.79248046875}, {"start": 3612.7, "end": 3613.3, "word": " vector", "probability": 0.98779296875}, {"start": 3613.3, "end": 3613.58, "word": " هذا", "probability": 0.65625}, {"start": 3613.58, "end": 3613.76, "word": " يبقى", "probability": 0.7755126953125}, {"start": 3613.76, "end": 3615.38, "word": " متجه", "probability": 0.7259114583333334}], "temperature": 1.0}, {"id": 128, "seek": 364594, "start": 3616.68, "end": 3645.94, "text": "لمين؟ للدلة F شو برمزله؟ بالرمز المثلث لرأسه لأسفل ويقرأ grade F أو gradient F يختصر إلى grade F أو دل F أو نقلة F يبقى هذا الرمز يا بروح بقول grade F يا إما بقول دل F", "tokens": [19528, 9957, 22807, 24976, 3215, 37977, 479, 13412, 2407, 4724, 2288, 2304, 11622, 43761, 22807, 20666, 2288, 2304, 11622, 9673, 12984, 1211, 12984, 5296, 2288, 10721, 3794, 3224, 5296, 10721, 3794, 5172, 1211, 4032, 1829, 4587, 2288, 10721, 7204, 479, 34051, 16235, 479, 7251, 46456, 9381, 2288, 30731, 7204, 479, 34051, 11778, 1211, 479, 34051, 8717, 4587, 37977, 479, 7251, 3555, 4587, 7578, 23758, 34892, 2304, 11622, 35186, 4724, 32887, 5016, 4724, 39648, 7204, 479, 35186, 11933, 15042, 4724, 39648, 11778, 1211, 479], "avg_logprob": -0.17931548009316126, "compression_ratio": 1.6729559748427674, "no_speech_prob": 2.980232238769531e-07, "words": [{"start": 3616.68, "end": 3617.78, "word": "لمين؟", "probability": 0.59619140625}, {"start": 3617.78, "end": 3618.48, "word": " للدلة", "probability": 0.6193033854166666}, {"start": 3618.48, "end": 3618.84, "word": " F", "probability": 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F كل واحد فيهم هذول أي واحد من التلاتة هذول الرمز هذا كله هو عبارة عن مين اللي هو grade F", "tokens": [25528, 5551, 15042, 4724, 39648, 8717, 9566, 1211, 3615, 479, 28242, 36764, 24401, 8978, 16095, 8032, 8848, 12610, 36632, 36764, 24401, 9154, 16712, 1211, 9307, 3660, 8032, 8848, 12610, 34892, 2304, 11622, 23758, 28242, 3224, 31439, 6225, 3555, 9640, 3660, 18871, 3714, 9957, 13672, 1829, 31439, 7204, 479], "avg_logprob": -0.3396045918367347, "compression_ratio": 1.4251968503937007, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 3646.94, "end": 3647.2, "word": "يا", "probability": 0.0892333984375}, {"start": 3647.2, "end": 3647.5, "word": " أما", "probability": 0.54296875}, {"start": 3647.5, "end": 3648.14, "word": " بقول", "probability": 0.669189453125}, {"start": 3648.14, "end": 3650.16, "word": " نطلع", "probability": 0.8348388671875}, {"start": 3650.16, "end": 3650.82, "word": " F", "probability": 0.417236328125}, {"start": 3650.82, "end": 3652.74, "word": " كل", 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بتكون", "probability": 0.893310546875}, {"start": 5352.1, "end": 5352.7, "word": " اكبر", "probability": 0.8860677083333334}, {"start": 5352.7, "end": 5352.86, "word": " ما", "probability": 0.7236328125}, {"start": 5352.86, "end": 5353.32, "word": " يمكن", "probability": 0.851318359375}, {"start": 5353.32, "end": 5354.14, "word": " وقتش", "probability": 0.8391927083333334}, {"start": 5354.14, "end": 5354.5, "word": " اقل", "probability": 0.875}, {"start": 5354.5, "end": 5354.68, "word": " ما", "probability": 0.98046875}, {"start": 5354.68, "end": 5355.14, "word": " يمكن", "probability": 0.946533203125}, {"start": 5355.14, "end": 5355.86, "word": " وقتش", "probability": 0.9563802083333334}, {"start": 5355.86, "end": 5356.52, "word": " بتبقى", "probability": 0.8680419921875}, {"start": 5356.52, "end": 5357.12, "word": " zero", "probability": 0.4365234375}, {"start": 5357.12, "end": 5358.12, "word": " بقول", "probability": 0.6990966796875}, {"start": 5358.12, "end": 5358.62, "word": " 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θ", "probability": 0.3994140625}, {"start": 5368.1, "end": 5368.72, "word": " تبقى", "probability": 0.973388671875}, {"start": 5368.72, "end": 5369.1, "word": " zero", "probability": 0.8037109375}], "temperature": 1.0}, {"id": 189, "seek": 539624, "start": 5369.42, "end": 5396.24, "text": "ماذا يعني هذا الكلام؟ يعني يجب أن يكون U و F اتنين مالهم في نفس الاتجاه لأن الزوابن هم Zero That is when ال U in the same direction of F اتنين في نفس الاتجاه تبقى بصير عندك كوسين صفر بجدير واحد أكبر قيمة بياخدها الكوسين جدير إذا هذه بتاخد أقصى قيمة لها", "tokens": [2304, 45636, 995, 37495, 22653, 23758, 2423, 28820, 10943, 22807, 37495, 22653, 7251, 7435, 3555, 14739, 7251, 30544, 624, 4032, 479, 1975, 2655, 1863, 9957, 3714, 6027, 16095, 8978, 8717, 36178, 2423, 9307, 7435, 40294, 5296, 33456, 6024, 110, 14407, 3555, 1863, 8032, 2304, 17182, 663, 307, 562, 2423, 624, 294, 264, 912, 3513, 295, 479, 1975, 2655, 1863, 9957, 8978, 8717, 36178, 2423, 9307, 7435, 40294, 6055, 3555, 4587, 7578, 4724, 9381, 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5390.72, "end": 5391.04, "word": " قيمة", "probability": 0.9884440104166666}, {"start": 5391.04, "end": 5391.44, "word": " بياخدها", "probability": 0.90302734375}, {"start": 5391.44, "end": 5391.84, "word": " الكوسين", "probability": 0.7648111979166666}, {"start": 5391.84, "end": 5392.4, "word": " جدير", "probability": 0.9560546875}, {"start": 5392.4, "end": 5393.24, "word": " إذا", "probability": 0.62841796875}, {"start": 5393.24, "end": 5393.62, "word": " هذه", "probability": 0.59375}, {"start": 5393.62, "end": 5394.18, "word": " بتاخد", "probability": 0.9031575520833334}, {"start": 5394.18, "end": 5395.32, "word": " أقصى", "probability": 0.97119140625}, {"start": 5395.32, "end": 5395.92, "word": " قيمة", "probability": 0.9930013020833334}, {"start": 5395.92, "end": 5396.24, "word": " لها", "probability": 0.978271484375}], "temperature": 1.0}, {"id": 190, "seek": 542026, "start": 5396.52, "end": 5420.26, "text": "عند θ تساوي zero عندما u و grade ال F يكونوا في نفس الاتجاه كده 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index 0000000000000000000000000000000000000000..93a20bcda3429b7e4f0959ec7612ca324dfa3228
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+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/RFjaGoXcZxE_raw.srt
@@ -0,0 +1,2924 @@
+1
+00:00:12,960 --> 00:00:17,880
+بسم الله الرحمن الرحيم عود على build المرة اللي
+
+2
+00:00:17,880 --> 00:00:23,220
+فاتت ابتدأنا في section 14 او 14 و8 share role فعل
+
+3
+00:00:23,220 --> 00:00:27,080
+السلسلة واخدنا الحالة الأولى لو كانت ال function
+
+4
+00:00:27,080 --> 00:00:32,650
+مالا في موضة ليه rideوكل متغير من المتغيرين
+
+5
+00:00:32,650 --> 00:00:37,810
+function T متغير الاخر ثم بعد ذلك أخذنا لو كانت
+
+6
+00:00:37,810 --> 00:00:43,930
+دالة function T ثلاثة متغيرات وكل متغير دالة في
+
+7
+00:00:43,930 --> 00:00:48,830
+متغير الأخر الآن ننتقل إلى النقطة الثانية وهي
+
+8
+00:00:48,830 --> 00:00:55,450
+function T متغيرين أو ثلاثة متغيرات وكل من هذه
+
+9
+00:00:55,450 --> 00:01:00,480
+المتغيرات functionفى two variables وليس فى
+
+10
+00:01:00,480 --> 00:01:05,320
+variable واحد تمام وبالتالي مش هيكون عندنا اشتغال
+
+11
+00:01:05,320 --> 00:01:10,100
+كل زى ما كنا بقوله دي و باي دي تي يبقى بتصير
+
+12
+00:01:10,100 --> 00:01:15,820
+partial و باي partial المتغير اللى عندنا هذا لذلك
+
+13
+00:01:15,820 --> 00:01:21,940
+هنحط هذا الكلام فى الصيغة التالية بجب اقول theorem
+
+14
+00:01:21,940 --> 00:01:25,640
+suppose ذات ال w
+
+15
+00:01:31,010 --> 00:01:39,790
+الـ W تساوي الـ function في X of Y of Z والـ X
+
+16
+00:01:39,790 --> 00:01:48,190
+function في R و S ده اللي فيه متغيرين والـ Y تساوي
+
+17
+00:01:48,190 --> 00:01:53,350
+H of R و S والـ Z كذلك
+
+18
+00:02:11,490 --> 00:02:18,770
+إذا كانت الدول الأربع هذه are differentiable
+
+19
+00:02:18,770 --> 00:02:19,890
+functions
+
+20
+00:02:21,920 --> 00:02:31,660
+دوال قابلة للاشتقاء then w is differentiable
+
+21
+00:02:31,660 --> 00:02:45,920
+function of a and s and نمرا
+
+22
+00:02:45,920 --> 00:02:52,020
+واحدpartial w by partial r سبب partial w by
+
+23
+00:02:52,020 --> 00:02:58,660
+partial x في partial x by partial r زائد partial w
+
+24
+00:02:58,660 --> 00:03:04,920
+by partial y في partial y by partial r زائد
+
+25
+00:03:04,920 --> 00:03:11,220
+partial w by partial z في partial z by partial r
+
+26
+00:03:12,040 --> 00:03:17,740
+نمر اتنين يساوي
+
+27
+00:03:17,740 --> 00:03:23,640
+partial w by partial x في partial x by partial s
+
+28
+00:03:23,640 --> 00:03:29,220
+زائد partial w by partial y partial y by partial s
+
+29
+00:03:29,220 --> 00:03:35,100
+زائد partial w by partial z partial z by partial s
+
+30
+00:03:57,130 --> 00:04:02,670
+مرة تانية بقول المرة هذه عندنا ال w function في
+
+31
+00:04:02,670 --> 00:04:08,830
+ثلاثة متغيرات x و y و z وكل من المتغيرات التلاتة x
+
+32
+00:04:08,830 --> 00:04:13,410
+و y و z ده اللي فيه متغيرين لكن المرة اللي فاتت
+
+33
+00:04:13,410 --> 00:04:19,020
+كانتفي متغير واحد ومن هنا مش قادرين نقول هنا
+
+34
+00:04:19,020 --> 00:04:24,260
+اشتقاقا كليا وانما بيكون اشتقاق جزئي يبقى
+
+35
+00:04:24,260 --> 00:04:27,720
+partially derivative يبقى بالدرجة دلوقتي partial W
+
+36
+00:04:27,720 --> 00:04:29,360
+by partial R
+
+37
+00:04:32,440 --> 00:04:35,920
+مضافا اليها partial w by partial x في partial x by
+
+38
+00:04:35,920 --> 00:04:39,820
+partial r مضافا اليها partial w by partial y
+
+39
+00:04:39,820 --> 00:04:44,440
+partial y by partial r مضافا اليها partial w by
+
+40
+00:04:44,440 --> 00:04:48,450
+partial z في partial z by partial rأحنا جيبنا
+
+41
+00:04:48,450 --> 00:04:54,050
+مشتقة بالنسبة لأحدى المتغيرين اللي هو R يبقى مثل
+
+42
+00:04:54,050 --> 00:04:57,990
+ما جيبنا ال R بنروح نجيب لمين إلى S اللي هو
+
+43
+00:04:57,990 --> 00:05:02,230
+المتغير الأخر فبروح أخد partial W by partial S
+
+44
+00:05:02,230 --> 00:05:07,130
+بنفس الطريقة اللي فوق بس بشيل كل R و بحط مكانها
+
+45
+00:05:07,130 --> 00:05:13,890
+مين بحط مكانها S طب لو حبينا نرسم الشكل هذا خوفا
+
+46
+00:05:13,890 --> 00:05:20,950
+من النسيان على شكل هندسيفبجي بقول هي عندي w تساوي
+
+47
+00:05:20,950 --> 00:05:30,190
+function x و y و z إذا بده يتفرع منها ثلاثة أفرق x
+
+48
+00:05:30,190 --> 00:05:36,710
+و y و z الآن هذا بيكون كله اشتقاق بالنسبة لمن؟
+
+49
+00:05:36,710 --> 00:05:44,340
+بالنسبة إلى R إذاهتجينا المستقى هنا نظرا لأن
+
+50
+00:05:44,340 --> 00:05:48,720
+الدالة في أكتر من متغير فبتقول partial w by
+
+51
+00:05:48,720 --> 00:05:53,580
+partial x وهنا partial w by partial y وهنا partial
+
+52
+00:05:53,580 --> 00:05:59,290
+w by partial zلأن كلهم من X وY وZ دالة في أكتر من
+
+53
+00:05:59,290 --> 00:06:04,390
+متغير فيه متغيرين إذا سيكون الاشتقاق اشتقاقا جزئيا
+
+54
+00:06:04,390 --> 00:06:09,470
+يبقى partial X by partial R partial Y by partial R
+
+55
+00:06:09,470 --> 00:06:15,250
+partial Z by partial A اللي عملنا بالنسبة لR بدنا
+
+56
+00:06:15,250 --> 00:06:20,470
+نروح نعمله كذلك بالنسبة إلى S يبقى بقى اجي بقول له
+
+57
+00:06:20,470 --> 00:06:28,030
+ايه W ليه ال functionفي X و Y و Z وهذا عنده X وهنا
+
+58
+00:06:28,030 --> 00:06:37,950
+Y وهنا Z وهنا S شكلها
+
+59
+00:06:37,950 --> 00:06:44,970
+نادرإذا تفضل ال W بالنسبة لX استقاقا جزئيا يبقى
+
+60
+00:06:44,970 --> 00:06:49,430
+partial W by partial X partial W by partial Y
+
+61
+00:06:49,430 --> 00:06:55,490
+partial W by partial Z هنا كذلك ال X دالة في
+
+62
+00:06:55,490 --> 00:07:00,090
+متغيرين و ال Y دالة في متغيرينإذا هو هكذا إذا بدي
+
+63
+00:07:00,090 --> 00:07:06,150
+يصير partial X by partial S partial Y by partial S
+
+64
+00:07:06,150 --> 00:07:14,130
+partial Z by partial Sإذا لو روحنا الصيغة اللي فوق
+
+65
+00:07:14,130 --> 00:07:19,330
+بسيطة جدا يبقى بضرب هذا في هذا زاد هذا في هذا زاد
+
+66
+00:07:19,330 --> 00:07:24,150
+هذا في هذا بكون حصلت عالميا على تفاضل ال W بالنسبة
+
+67
+00:07:24,150 --> 00:07:30,330
+لR بالمثل تفاضل ال W بالنسبة إلى S يبقى بضرب اتنين
+
+68
+00:07:30,330 --> 00:07:32,910
+الدول في بعض زاد اتنين الدول في بعض زاد اتنين
+
+69
+00:07:32,910 --> 00:07:38,050
+الدول في بعضيبقى سواء كانت بالرسم أو بالجزء النظر
+
+70
+00:07:38,050 --> 00:07:42,430
+الأول كله الأثنين نفس النتيجة يبقى الرسمة فقط
+
+71
+00:07:42,430 --> 00:07:53,790
+لتثبيت المعلومة نعطي مثال example بقول
+
+72
+00:07:53,790 --> 00:08:03,770
+let ال W بدأت ساوي لن X تربيع لن X تربيع زائد Y
+
+73
+00:08:07,520 --> 00:08:19,660
+تربية وال X بدها تساوي U في E أس V في Cos U وال Y
+
+74
+00:08:19,660 --> 00:08:29,940
+بدها تساوي U في E أس V في Cos U وال Z بدها تساوي U
+
+75
+00:08:29,940 --> 00:08:33,600
+في E أس V Find
+
+76
+00:08:35,410 --> 00:08:45,530
+المطلوب الأول نمرا a partial w by partial u by its
+
+77
+00:08:45,530 --> 00:08:54,450
+chain rule يبقى بواصل قاعدة السلسلة نمرا b partial
+
+78
+00:08:54,450 --> 00:09:04,450
+w by partial u directly مباشرة
+
+79
+00:09:05,920 --> 00:09:12,960
+after expressing are tab expressing
+
+80
+00:09:12,960 --> 00:09:20,340
+w
+
+81
+00:09:20,340 --> 00:09:29,020
+in terms of u and v
+
+82
+00:09:44,280 --> 00:09:48,940
+سؤال مرة تانية، ماعطيني w function في ثلاثة
+
+83
+00:09:48,940 --> 00:09:54,820
+متغيرات، لإن x تربية زي y تربية زي z تربية وكل من
+
+84
+00:09:54,820 --> 00:10:02,480
+x و y و z دالة في متغيرين، اللي همين u و vوطلب
+
+85
+00:10:02,480 --> 00:10:08,100
+مشتقة ال W بالنسبة لمن؟ بالنسبة إلى U يبقى كأنه
+
+86
+00:10:08,100 --> 00:10:11,640
+احنا عند الحالة الأولى اللى عندناها دى بس بدل R
+
+87
+00:10:11,640 --> 00:10:16,260
+حطينا مكانها مين؟ حطينا مكانها U قال ليه؟ بدي
+
+88
+00:10:16,260 --> 00:10:21,820
+اشتغل هذا بصرفين يبقى بدي اجيب له partial W by
+
+89
+00:10:21,820 --> 00:10:27,600
+partial U الان W فيه ثلاثة متغيرات يبقى بقوله
+
+90
+00:10:27,600 --> 00:10:33,680
+partial Wبارشيل X بارشيل X بارشيل U بارشيل W
+
+91
+00:10:33,680 --> 00:10:39,560
+بارشيل Y بارشيل Y بارشيل U زائد بارشيل W بارشيل Z
+
+92
+00:10:39,560 --> 00:10:45,980
+بارشيل Z بارشيل U يبقى بناء عليه أصبح بارشيل W
+
+93
+00:10:45,980 --> 00:10:52,290
+بارشيل U بنفسهفإذا نشتقت W بالنسبة لX اللي فوق
+
+94
+00:10:52,290 --> 00:10:57,810
+يبقى مشتقتها واحد على اللي داخل الـLin في مشتقة ما
+
+95
+00:10:57,810 --> 00:11:02,910
+داخل الـLin بالنسبة إلى X يبقى الـY تربيع وZ تربيع
+
+96
+00:11:02,910 --> 00:11:09,290
+وطبعا constant يبقى هذه ب2X على X تربيع زائد Y
+
+97
+00:11:09,290 --> 00:11:09,390
+تربيع
+
+98
+00:11:12,620 --> 00:11:17,680
+هذا فقط لو partial w by partial x بدي اضرب في
+
+99
+00:11:17,680 --> 00:11:22,620
+تفاضل ال x بالنسبة الى u يجب ان يكون ال E Os V
+
+100
+00:11:22,620 --> 00:11:29,700
+يعتبر constant وهذا يعتبر مشتق بالحاصل ضاربةدالتين
+
+101
+00:11:29,700 --> 00:11:34,000
+لأنها مفضلة نسبة لمن؟ بالنسبة إلى U لكن لو كان
+
+102
+00:11:34,000 --> 00:11:38,980
+الشقاق بالنسبة إلى V لكان أسهل كتير جدا يعني
+
+103
+00:11:38,980 --> 00:11:43,480
+الشقاق بالنسبة ل V very easy لكن بالنسبة ل U في
+
+104
+00:11:43,480 --> 00:11:49,200
+صعوبة شوية يبقى هذا كله مضروب في مشتق تحصل ضرب
+
+105
+00:11:49,200 --> 00:12:00,440
+دالتين يبقى النتيجة E Os V في Sine U زائدU E Os V
+
+106
+00:12:00,440 --> 00:12:08,040
+في Cos U يبقى هذا جزء الأول بالمثل نعود للجزء
+
+107
+00:12:08,040 --> 00:12:13,860
+الثاني أفعل ال W بالنسبة إلى Y زي ال X مع الفارق
+
+108
+00:12:13,860 --> 00:12:21,350
+المصمم ل Y يبقى 2Yعلى X تربية زائد Y تربية زائد Z
+
+109
+00:12:21,350 --> 00:12:27,970
+تربية في تفاضل ال Y بالنسبة إلى U كذلك مستخدم حاصل
+
+110
+00:12:27,970 --> 00:12:37,010
+ضرب دالتين يبدأ E Os V في Cos U زائد U E Os V
+
+111
+00:12:37,010 --> 00:12:43,790
+وتفاضل Cos بقدر؟ بسالف Sine U هاي خلصنا الجزء من
+
+112
+00:12:43,790 --> 00:12:47,110
+الجزء الثاني بنجي لجزء التاني
+
+113
+00:12:50,680 --> 00:12:59,680
+تفاضل ال Z بالنسبة إلى U يبقى
+
+114
+00:12:59,680 --> 00:13:07,640
+بنفس الطريقة 2Z على X تربيع زائد Y تربيع زائد Z
+
+115
+00:13:07,640 --> 00:13:12,220
+تربيع مضروب تفاضل ال Z بالنسبة إلى U
+
+116
+00:13:18,430 --> 00:13:23,450
+طيب هذا طبعا الإجابة عندنا مزوج الحمد لله ال X
+
+117
+00:13:23,450 --> 00:13:28,430
+موجودة و ال Y و ال Z و ال U و ال V كله لكن احنا
+
+118
+00:13:28,430 --> 00:13:31,930
+بدنا ايها بدلالة main ال U و ال V اللي يعتبر
+
+119
+00:13:31,930 --> 00:13:37,570
+المتغيرات اذا بدروح احول كل ال X و ال Y و ال Z
+
+120
+00:13:37,570 --> 00:13:42,650
+بدلالة ال U و ال V و نشوف كده بده يساوي طب لو جيت
+
+121
+00:13:42,650 --> 00:13:49,320
+للقيم هدولمعناته مربع الاربع التلاتة هادول ونشوف
+
+122
+00:13:49,320 --> 00:13:53,200
+كده شو بده يساوي طب لو جيت في الهام شمال تكس تربية
+
+123
+00:13:53,200 --> 00:13:59,120
+زائد Y تربية زائد Z تربية شو بده يعطيني بده يعطيني
+
+124
+00:13:59,120 --> 00:14:08,580
+U تربية E أس اتنين V Cos تربية U زائد U تربية Sin
+
+125
+00:14:08,580 --> 00:14:09,400
+تربية U
+
+126
+00:14:15,110 --> 00:14:22,790
+زائد اللي هو U تربيع E أس اتنين V Cos تربيع ال V
+
+127
+00:14:22,790 --> 00:14:30,250
+زائد U تربيع E أس اتنين V إيش بتلاحظ يا بنات في
+
+128
+00:14:30,250 --> 00:14:36,580
+عامل مشترك اللي هو U تربيع E أس اتنين Vيبقى هنا
+
+129
+00:14:36,580 --> 00:14:41,720
+صين تربيع زائد زائد صين تربيع زائد كوسين تربيع ال
+
+130
+00:14:41,720 --> 00:14:49,160
+U يبقى هنا بصير صين تربيع ال U زائد كوسين تربيع ال
+
+131
+00:14:49,160 --> 00:14:56,800
+U زائد كده؟ زائد واحد طب هذه كده؟ واحد كذلك يبقى
+
+132
+00:14:56,800 --> 00:15:03,070
+اتنين U تربيع إيقوس اتنين بيه هذا هو المجموعيبقى
+
+133
+00:15:03,070 --> 00:15:07,750
+بلاءً عليه بصير عندي partial w by partial u بده
+
+134
+00:15:07,750 --> 00:15:12,050
+يساوي هي اتنين اللي عندنا وبده اشيل ال X واخد
+
+135
+00:15:12,050 --> 00:15:20,650
+قمتها اللي هو U في E أس V في صين ال U على مين؟ على
+
+136
+00:15:20,650 --> 00:15:30,170
+ال X البيضة اللي هو اتنين U تربيع E أس اتنين Vكل
+
+137
+00:15:30,170 --> 00:15:38,050
+هذا مضروب في مين؟ في E أس V في Sine U زائد U E أس
+
+138
+00:15:38,050 --> 00:15:50,810
+V في Cos U زائد اتنين ال Y هي U في E أس V في Cos U
+
+139
+00:15:50,810 --> 00:15:58,990
+على اتنين U تربيع E أس اتنين V في مين؟ في E أس V
+
+140
+00:15:59,460 --> 00:16:12,920
+cos U-U E Os V Cos U زي اتنين زد عندنا اتنين U E
+
+141
+00:16:12,920 --> 00:16:21,460
+Os V في E Os V يبقى E Os 2 V على مين؟ على اتنين U
+
+142
+00:16:21,460 --> 00:16:28,920
+تربيع اتنين U تربيع E Os 2 V
+
+143
+00:16:31,270 --> 00:16:38,550
+يسار اتنين مع اتنين و ال U مع التربيع و ال E Os V
+
+144
+00:16:38,550 --> 00:16:44,610
+مع ال E Os V و بظل عندنا من الصين طيب يا بنات هذه
+
+145
+00:16:44,610 --> 00:16:53,230
+E Os V لو طلعت فبرا مع E Os V مع E Os 2V بتروح بظل
+
+146
+00:16:53,230 --> 00:17:02,140
+عندي قداش هنا واحد عليه فقط في الصين ال Uزائد U في
+
+147
+00:17:02,140 --> 00:17:12,420
+Cos U وعندي هنا sign U اللي برا يبقى هنا في sign U
+
+148
+00:17:12,420 --> 00:17:19,780
+هذا الجزء الأول الجزء الثاني برضه اذا طلع USB مع
+
+149
+00:17:19,780 --> 00:17:27,540
+USB مع USB بصير E أس اتنين V مع E أس اتنين Vو
+
+150
+00:17:27,540 --> 00:17:34,280
+اتنين مع اتنين والتربيع مع ال U بيظل كوصين ال U
+
+151
+00:17:34,280 --> 00:17:44,160
+علي U في كوصين ال U ناقص U صين ال U الجزء الأخير
+
+152
+00:17:44,160 --> 00:17:54,380
+بيظل عندي زائد يعني بس واحد علي U كمان؟ مافيش رأيك
+
+153
+00:17:54,380 --> 00:17:56,860
+يا بنات هذا الكلام بده يساوي
+
+154
+00:18:01,150 --> 00:18:06,190
+عندك هنا واحد على يوم وعندك هنا واحد على يوم وعندك
+
+155
+00:18:06,190 --> 00:18:08,370
+هنا واحد على يوم وعندك هنا واحد على يوم وعندك هنا
+
+156
+00:18:08,370 --> 00:18:08,370
+واحد على يوم وعندك هنا واحد على يوم وعندك هنا واحد
+
+157
+00:18:08,370 --> 00:18:08,370
+على يوم وعندك هنا واحد على يوم وعندك هنا واحد على
+
+158
+00:18:08,370 --> 00:18:08,370
+يوم وعندك هنا واحد على يوم وعندك هنا واحد على يوم
+
+159
+00:18:08,370 --> 00:18:08,930
+وعندك هنا واحد على يوم وعندك هنا واحد على يوم
+
+160
+00:18:08,930 --> 00:18:08,930
+وعندك هنا واحد على يوم وعندك هنا واحد على يوم
+
+161
+00:18:08,930 --> 00:18:08,930
+وعندك هنا واحد على يوم وعندك هنا واحد على يوم
+
+162
+00:18:08,930 --> 00:18:08,930
+وعندك هنا واحد على يوم وعندك هنا واحد على يوم
+
+163
+00:18:08,930 --> 00:18:13,610
+وعندك هنا واحد على يوم وعندك هنا واحد على يوم
+
+164
+00:18:13,610 --> 00:18:21,550
+وعندك هنا واحد على
+
+165
+00:18:21,550 --> 00:18:33,210
+يوم وعندك هنامقص ال U, Sine U, Cos U، تلقين القرص،
+
+166
+00:18:33,210 --> 00:18:35,850
+تلقين القرص، تلقين القرص، تلقين القرص، تلقين
+
+167
+00:18:35,850 --> 00:18:37,130
+القرص، تلقين القرص، تلقين القرص، تلقين القرص،
+
+168
+00:18:37,130 --> 00:18:37,950
+تلقين القرص، تلقين القرص، تلقين القرص، تلقين
+
+169
+00:18:37,950 --> 00:18:39,850
+القرص، تلقين القرص، تلقين القرص، تلقين القرص،
+
+170
+00:18:39,850 --> 00:18:40,570
+تلقين القرص، تلقين القرص، تلقين القرص، تلقين
+
+171
+00:18:40,570 --> 00:18:41,090
+القرص، تلقين القرص، تلقين القرص، تلقين القرص،
+
+172
+00:18:41,090 --> 00:18:45,090
+تلقين القرص، تلقين القرص، تلقين القرص، تلقين
+
+173
+00:18:45,090 --> 00:18:46,750
+القرص، تلق
+
+174
+00:18:53,830 --> 00:18:57,930
+إذاً هذا المشتقة اللي مكلك عليه كبيرة صفت عليه جزء
+
+175
+00:18:57,930 --> 00:19:09,490
+بسيط اللي هو عبارة عن اتنين عليه فقط لا غير إذا
+
+176
+00:19:09,490 --> 00:19:14,450
+انتهينا من المطقوب الأول في المسألة و بدنا نروح
+
+177
+00:19:14,450 --> 00:19:20,170
+للمطقوب التاني وهو نمرى بيه نمرى بيه قال لي بدي
+
+178
+00:19:20,170 --> 00:19:26,750
+هالمشتقة هذه ههdirectly مباشرة بعد ما اتعبر عن ال
+
+179
+00:19:26,750 --> 00:19:32,770
+W بدلالة ال U و ال V يفجأة انا بالداخل هقول له هاي
+
+180
+00:19:32,770 --> 00:19:40,130
+ال W تساعد لإن ال X تربيع زي Y تربيع زي Z تربيع
+
+181
+00:19:40,130 --> 00:19:47,350
+حسبناها هاي اتنين U تربيع E أس اتنين V اتنين U
+
+182
+00:19:47,350 --> 00:19:57,620
+تربيع E أس اتنين Vبالنسبة لمن؟ بالنسبة الي U و بدي
+
+183
+00:19:57,620 --> 00:20:01,300
+اثبت ان النتيجة قدش تساوي 2 على U
+
+184
+00:20:22,150 --> 00:20:28,050
+طيب اقتصدي يوس اتنين V مع يوس اتنين V اتنين مع
+
+185
+00:20:28,050 --> 00:20:34,370
+اتنين U مع التربية تبقى كمان اتنين على U نفس
+
+186
+00:20:34,370 --> 00:20:39,910
+النتيجة اللي حصلنا عليها هناك بالضبط تماماgood
+
+187
+00:20:39,910 --> 00:20:49,070
+exercise لك exercise find partial w by partial v
+
+188
+00:20:49,070 --> 00:20:58,810
+اللي هي أسهل من مين انتبهت اليوم بدنا
+
+189
+00:20:58,810 --> 00:21:03,530
+نجي ناخد أبنات من القاعدة اللي تو special cases
+
+190
+00:21:03,530 --> 00:21:14,150
+حالات خاصة الحالة الأولىلو كانت ال w function x و
+
+191
+00:21:14,150 --> 00:21:24,450
+y و ال x function في ال r و ال s and ال y function
+
+192
+00:21:24,450 --> 00:21:35,250
+كذلك في ال r و ال s يبقى
+
+193
+00:21:35,250 --> 00:21:42,200
+هذه دالة في مين؟في متغيرين وليس في ثلاثة وكل من
+
+194
+00:21:42,200 --> 00:21:49,960
+المتغيرين دال في متغيرين آخرينيبقى هي نفس النتيجة
+
+195
+00:21:49,960 --> 00:21:54,000
+اللي فاتت بس اخر سنة تبعها ستتشيلوا لإن هو مش
+
+196
+00:21:54,000 --> 00:21:59,280
+موجود عندي إذا بناء أنا عليه بصير عندي partial w
+
+197
+00:21:59,280 --> 00:22:06,040
+by partial r بدي أسوي partial w by partial x by
+
+198
+00:22:06,040 --> 00:22:11,640
+partial x by partial r زايد partial w by partial y
+
+199
+00:22:11,640 --> 00:22:16,700
+by partial y by partial r and
+
+200
+00:22:19,470 --> 00:22:24,490
+بدي partial w by partial s يبقى partial w by
+
+201
+00:22:24,490 --> 00:22:32,070
+partial x في partial x by partial s زائد partial w
+
+202
+00:22:32,070 --> 00:22:42,610
+by partial y في partial y by partial s ممكن
+
+203
+00:22:42,610 --> 00:22:50,050
+نرسم رسمة أوضحية كذلك لهذه الشكلينفاجي بقول انا
+
+204
+00:22:50,050 --> 00:22:57,650
+عندي w تساوي function x y، اذا بطلع عندي خطين او
+
+205
+00:22:57,650 --> 00:23:05,210
+فرعين و ليس ثلاثة، بقول هنا x وهنا y وكل واحد منهم
+
+206
+00:23:05,210 --> 00:23:10,470
+function تمين في R، اذا المستقال تكون على الشكل
+
+207
+00:23:10,470 --> 00:23:15,540
+التاليتفاضل الـ W بالنسبة إلى X تفاضل الـ W
+
+208
+00:23:15,540 --> 00:23:21,320
+بالنسبة إلى Y تفاضل الـ X بالنسبة إلى R تفاضل الـ
+
+209
+00:23:21,320 --> 00:23:26,780
+Y بالنسبة إلى R اضرب اتنين في بعض اتنين اضرب بعض و
+
+210
+00:23:26,780 --> 00:23:34,400
+اجمع تظهر الحالة الأولى نأتي للحالة الثانية الـ W
+
+211
+00:23:34,400 --> 00:23:41,380
+كذلك function في X و Y وهنا لدينا الـ Xوهنا ال y
+
+212
+00:23:41,380 --> 00:23:47,320
+وكل واحد فيهم function في مين في S يبقى هنا تفاضل
+
+213
+00:23:47,320 --> 00:23:56,000
+ال W بالنسبة إلى X في تفاضل ال X بالنسبة إلى S هنا
+
+214
+00:23:56,000 --> 00:24:01,840
+تفاضل ال W بالنسبة إلى Y هنا تفاضل ال Y بالنسبة
+
+215
+00:24:01,840 --> 00:24:11,340
+إلى S هذه الحالة الأولة الحالة الثانيةهذه الأولى
+
+216
+00:24:11,340 --> 00:24:22,940
+التاني f w يسوى function of x and ال x function
+
+217
+00:24:22,940 --> 00:24:26,580
+فيه متغيرين r وs
+
+218
+00:24:34,890 --> 00:24:43,470
+دي partial w by partial r تساوي الهن يا بنات w
+
+219
+00:24:43,470 --> 00:24:48,290
+function في مين؟ في متغير واحد اللي هو x إذا
+
+220
+00:24:48,290 --> 00:24:51,310
+ماقدرش أقول إشتقاء قد يظهر إيه وانما بيكون إشتقاء
+
+221
+00:24:51,310 --> 00:25:00,380
+كله يبقى باجي بقول دي w by دي xلكن الـ x function
+
+222
+00:25:00,380 --> 00:25:06,420
+في مين؟ في المتغيرين، إذا بقوله في partial ده في
+
+223
+00:25:06,420 --> 00:25:16,560
+partial x by partial r أكتر من هيك ماعنديش and لو
+
+224
+00:25:16,560 --> 00:25:23,700
+بدي partial w by partial s يبقى dw على dx في
+
+225
+00:25:23,700 --> 00:25:32,610
+partial x by partial sلو حبنا نتعرف على شكل الرسمة
+
+226
+00:25:32,610 --> 00:25:39,530
+للاتنين هدول فماجي بقول احنا عندنا w function of x
+
+227
+00:25:39,530 --> 00:25:46,350
+هيقول هيطلع خط واحد لان ماعنديش إلا ومتغير واحد هو
+
+228
+00:25:46,350 --> 00:25:56,430
+مين؟ هو x إذا بصير عند هنا dw علىDX اشتقاق عادي
+
+229
+00:25:56,430 --> 00:26:02,330
+لكن ال X ده في مين؟ في المتغيرين يبقى باجي بقول
+
+230
+00:26:02,330 --> 00:26:08,710
+هنا R وبالتالي بصير partial X على partial R وهنا
+
+231
+00:26:08,710 --> 00:26:16,310
+هيجي KS ويكون partial X على partial S يبقى هذا
+
+232
+00:26:16,310 --> 00:26:20,890
+بتجيبلي الحالة الأولى وهذا بتجيبلي من؟ الحالة
+
+233
+00:26:20,890 --> 00:26:22,890
+الثانية وهكذا
+
+234
+00:26:51,810 --> 00:27:09,670
+نعطي مثال على ذلك أو أكثر من مثال مثال أول
+
+235
+00:27:09,670 --> 00:27:21,290
+مثال يقول find partial z على partial u andpartial
+
+236
+00:27:21,290 --> 00:27:38,480
+z على partial v as functions of u and vF z تساوي
+
+237
+00:27:38,480 --> 00:27:49,000
+tan inverse لمين ل x على y و ال x بدها تساوي u في
+
+238
+00:27:49,000 --> 00:28:01,300
+cos v و ال y بدها تساوي u في sin v
+
+239
+00:28:15,020 --> 00:28:20,460
+عليه بالك هنا بجي بتطلع بلقى Z ده اللي في مين في
+
+240
+00:28:20,460 --> 00:28:28,960
+متغيرين XY وكل من المتغيرين XY ده اللي في متغيرين
+
+241
+00:28:28,960 --> 00:28:35,080
+الآخرين في U وB إذا احنا مع من؟ مع الحالة الأولى
+
+242
+00:28:35,080 --> 00:28:41,800
+وليست الحالة الثالثة طب كويس يبقى هنا بجي بتقول لو
+
+243
+00:28:41,800 --> 00:28:44,080
+بدي أجيب الجزء الأول
+
+244
+00:28:47,780 --> 00:28:54,200
+بارشيل Z على بارشيل X بارشيل X على بارشيل U زائد
+
+245
+00:28:54,200 --> 00:29:00,840
+بارشيل Z على بارشيل Y بارشيل Y على بارشيل U هذا
+
+246
+00:29:00,840 --> 00:29:07,580
+الجزر L أول يجي نعوض يبقى بارشيل Z على بارشيل U
+
+247
+00:29:07,580 --> 00:29:16,050
+يسبب تفاضل Z بالنسبة إلى Xتفاضل التالين بس واحد
+
+248
+00:29:16,050 --> 00:29:22,590
+على واحد زي ال X تربية على Y تربية في مشتقة
+
+249
+00:29:22,590 --> 00:29:30,890
+الزاوية بالنسبة لمن؟ لجداش واحد على Y وليس واحد
+
+250
+00:29:30,890 --> 00:29:37,630
+عليه تفاضل X بواحد لجداش واحد على Y فهذا الكلام
+
+251
+00:29:37,630 --> 00:29:42,670
+كله مضروف في تفاضل ال Xتفاضل Z بالنسبة الى U لما
+
+252
+00:29:42,670 --> 00:29:54,810
+تفاضلها
+
+253
+00:29:54,810 --> 00:30:02,450
+بالنسبة ل Y هل تقدر تقولي كده نتيجة تفاضل
+
+254
+00:30:02,450 --> 00:30:03,730
+Y بالنسبة ل Y كده
+
+255
+00:30:09,440 --> 00:30:16,920
+Y تربيع X على Y تربيع يبقى سالب X على Y تربيع في
+
+256
+00:30:16,920 --> 00:30:22,980
+تفاضل Y بالنسبة إلى U الهمين ساين الفيه طب في
+
+257
+00:30:22,980 --> 00:30:27,980
+الهقم الشيخ اذا قلتك بالله يقداش X تربيع زاد Y
+
+258
+00:30:27,980 --> 00:30:34,020
+تربيع تسابع ايش مصير عندك U تربيع كساين تربيع زاد
+
+259
+00:30:34,020 --> 00:30:41,830
+U تربيع ساين تربيع يبقى ب U تربيع فقططيب هذا
+
+260
+00:30:41,830 --> 00:30:47,710
+الكلام partial z by partial u تساوي شو رايكوا ده
+
+261
+00:30:47,710 --> 00:30:54,890
+واحد المقامات إذا بتطلع y تربيع 4 هنا y تربيع زاد
+
+262
+00:30:54,890 --> 00:31:04,770
+x تربيع واحد على y في cosine ال b زاد y تربيع y
+
+263
+00:31:04,770 --> 00:31:14,940
+تربيع زاد x تربيع ناقص xعلى Y تربيع في صين ال V
+
+264
+00:31:14,940 --> 00:31:24,020
+طيب هذا كله مستحيل طلعيني Y مع Y تربيع بيظل كدهش
+
+265
+00:31:24,020 --> 00:31:34,980
+بيظل بس Y كدهش ال Y يو يو يو في صين ال V كله
+
+266
+00:31:34,980 --> 00:31:41,430
+مقصومة لعالمين X تربيع زي ال Y تربيع له 100U تربيع
+
+267
+00:31:41,430 --> 00:31:51,510
+و هنا عندي Cos V هذه تربيع
+
+268
+00:31:51,510 --> 00:31:59,690
+مع تربيع الله يسالي عليها ال X هو U Cos V U Cos V
+
+269
+00:31:59,690 --> 00:32:02,490
+في مين؟ في Sin V
+
+270
+00:32:16,520 --> 00:32:19,900
+يبقى الناتج كله يساوي زيه
+
+271
+00:32:23,880 --> 00:32:28,860
+و sin cos على u و هنا sin cos على u يبقى كله ب
+
+272
+00:32:28,860 --> 00:32:33,100
+zero و الحمد لله يبقى هذا تفاضل ال z بالنسبة الى u
+
+273
+00:32:33,100 --> 00:32:37,700
+قاللي هاتي تفاضل ال z بالنسبة الى v يبقى يقدروا
+
+274
+00:32:37,700 --> 00:32:42,720
+ايقله partial z by partial v اللي هو عبارة عن
+
+275
+00:32:42,720 --> 00:32:49,960
+partial z على partial x partial x على partial v زي
+
+276
+00:32:49,960 --> 00:32:55,370
+partial z على partial yيبقى partial y على partial
+
+277
+00:32:55,370 --> 00:33:04,030
+v إذا partial z على partial b بده يسار تفضل ال z
+
+278
+00:33:04,030 --> 00:33:11,530
+بالنسبة إلى x طب الله اللي جابنا هي اللي فوق قداش
+
+279
+00:33:11,530 --> 00:33:18,330
+طلعت اللي هي هذه صح؟ يبقى حطها على طول و y على x
+
+280
+00:33:18,330 --> 00:33:24,860
+تربية زي ال y تربية يبقى هذه yعلى X تربيع زائد Y
+
+281
+00:33:24,860 --> 00:33:31,100
+تربيع تمين في تفاضل ال X بالنسبة إلى B تفاضل ال X
+
+282
+00:33:31,100 --> 00:33:37,740
+بالنسبة إلى B لو سالب U سين ال V في سالب U في سين
+
+283
+00:33:37,740 --> 00:33:44,440
+ال V زائد partial Z على partial Y partial Z على
+
+284
+00:33:44,440 --> 00:33:48,800
+partial Y هي من فوق برضه يبقى أدب
+
+285
+00:33:57,100 --> 00:34:07,240
+Y تربيع في تفامل Y بالنسبة الى V U E Cos V وهذا
+
+286
+00:34:07,240 --> 00:34:13,480
+الكلام from above يبقى
+
+287
+00:34:13,480 --> 00:34:18,620
+هذا اختصرته Objective of the form Yزا يجب ان اشيل
+
+288
+00:34:18,620 --> 00:34:30,690
+Y و اتقدمها ل U Sin V U Sin V فيسالب U Cos V كل
+
+289
+00:34:30,690 --> 00:34:43,590
+هذا الكلام على U تربيه وهنا ناقص نجي لل X ال X
+
+290
+00:34:43,590 --> 00:34:53,890
+اللي هو U Cos V يبقى U Cos V في U Cos V على U
+
+291
+00:34:53,890 --> 00:34:54,610
+تربيه
+
+292
+00:34:57,860 --> 00:35:05,020
+Partial X على Partial V نقص Sine V Partial X على
+
+293
+00:35:05,020 --> 00:35:05,420
+Partial V نقص Sine V Partial X على Partial V نقص
+
+294
+00:35:05,420 --> 00:35:05,440
+Sine V Partial X على Partial V نقص Sine V Partial
+
+295
+00:35:05,440 --> 00:35:05,960
+X على Partial V نقص Sine V Partial X على Partial V
+
+296
+00:35:05,960 --> 00:35:06,200
+نقص Sine V Partial X على Partial V نقص Sine V
+
+297
+00:35:06,200 --> 00:35:06,220
+Partial X على Partial V نقص Sine V Partial X على
+
+298
+00:35:06,220 --> 00:35:06,220
+Partial V نقص Sine V Partial X على Partial V نقص
+
+299
+00:35:06,220 --> 00:35:06,220
+Sine V Partial X على Partial V نقص Sine V Partial
+
+300
+00:35:06,220 --> 00:35:06,220
+X على Partial V نقص Sine V Partial X على Partial V
+
+301
+00:35:06,220 --> 00:35:07,180
+نقص Sine V Partial X على Partial V نقص Sine V
+
+302
+00:35:07,180 --> 00:35:08,260
+Partial X على Partial V نقص Sine V Partial X على
+
+303
+00:35:08,260 --> 00:35:13,600
+Partial V نقص
+
+304
+00:35:13,600 --> 00:35:24,460
+Sine V Partial X على Partial V نقص Sine V Partial
+
+305
+00:35:24,460 --> 00:35:32,410
+Xهاخد ناقص U تربيع عامل مشترك يبقى ناقص U تربيع
+
+306
+00:35:32,410 --> 00:35:40,330
+عامل مشترك و هنا على U تربيع بصير عندي sin تربيع V
+
+307
+00:35:40,330 --> 00:35:43,950
+زائد cosine تربيع V
+
+308
+00:36:18,810 --> 00:36:27,210
+بناخد تمام مثال مثال اتنين نقول
+
+309
+00:36:27,210 --> 00:36:31,270
+define partial
+
+310
+00:36:31,270 --> 00:36:42,830
+z على partial u and partial z على partial v at u
+
+311
+00:36:42,830 --> 00:36:44,710
+وv بدأت
+
+312
+00:36:49,120 --> 00:37:01,120
+فإذا كان الـ Z يساوي لن لـQ و لـQ تساوي ال square
+
+313
+00:37:01,120 --> 00:37:08,880
+root ل V زائد تلاتة في تان inverse U
+
+314
+00:37:48,540 --> 00:37:55,080
+طيب نرجع لسؤالنا هذا مرة تانية بنلاحظ ان زد دالة
+
+315
+00:37:55,080 --> 00:37:59,980
+في مين تغير واحد والمتغير دالة في مين في متغيرين
+
+316
+00:37:59,980 --> 00:38:04,600
+اللي هي الحالة التانية تمام التمام بقوله كويس يبقى
+
+317
+00:38:04,600 --> 00:38:10,360
+احنا بدنا نجيبله partial z على partial u يبقى بعدي
+
+318
+00:38:10,360 --> 00:38:16,350
+بقوله اه اهاليو موجودة عندك يبقى حسب الحالة اني
+
+319
+00:38:16,350 --> 00:38:24,470
+ايش بدي اقول ايش ابنها يبقى DZ على مين؟ على DQ في
+
+320
+00:38:24,470 --> 00:38:34,010
+مين؟ في partial EQ على partial U فيه كمان؟فى ايه؟
+
+321
+00:38:34,010 --> 00:38:38,830
+لأ لأشهر دالة فى متغير واحد والمتغير دالة فى مين؟
+
+322
+00:38:38,830 --> 00:38:44,630
+فى متغيرين بقوله بسيطة if I'm partial z على
+
+323
+00:38:44,630 --> 00:38:50,930
+partial u يساوي تفاضل ال z بالنسبة ل q يبقى واحد
+
+324
+00:38:50,930 --> 00:38:57,390
+على ال q فتفاضل ال q بالنسبة لمين إلى uفى الجدرى
+
+325
+00:38:57,390 --> 00:39:02,350
+التربية لـ V زائد ثلاثة ملاكش دعوة يعتبر مقدرا
+
+326
+00:39:02,350 --> 00:39:09,670
+ثابتا وتان Inversio له واحد على واحد زائد U تربية
+
+327
+00:39:09,670 --> 00:39:12,850
+طيب
+
+328
+00:39:12,850 --> 00:39:17,190
+اذا اكتب ابدا لأتي ال U و ال V يبقى هذا الكلام
+
+329
+00:39:17,190 --> 00:39:25,190
+يساوي جدرى التربية ل V زائد تلاتة على واحد زائد U
+
+330
+00:39:25,190 --> 00:39:34,840
+تربيةفي ال Q ال جدر التربيعي ال V زائد تلاتة في
+
+331
+00:39:34,840 --> 00:39:41,800
+تان Inverse U الجدر مع الجدر يبقى آلة المسألة في
+
+332
+00:39:41,800 --> 00:39:48,870
+ال واحد زائد U تربية في تان Inverse Uقال يحسبني
+
+333
+00:39:48,870 --> 00:39:53,670
+هذا المقدار عند الواحد والسالب اتنين اذا بدي اجيب
+
+334
+00:39:53,670 --> 00:39:59,090
+له partial z على partial u عند النقطة واحد وسالب
+
+335
+00:39:59,090 --> 00:40:08,030
+اتنين هو يساوي واحد على واحد زائد واحد في تان
+
+336
+00:40:08,030 --> 00:40:13,490
+inverse one يبقى نص كده اش بقول الله يا بنات تان
+
+337
+00:40:13,490 --> 00:40:23,300
+inverse oneيبقى الجواب كله نين على بار نروح أجيب
+
+338
+00:40:23,300 --> 00:40:32,540
+له partial z by partial v يبقى دي ديزل by دي كيو
+
+339
+00:40:32,540 --> 00:40:39,630
+في partial k by partial vيبقى هذا الكلام بالديسافر
+
+340
+00:40:39,630 --> 00:40:44,690
+تفاضل ال Z بالنسبة ل ال EQ بواحد على ال EQ تفاضل
+
+341
+00:40:44,690 --> 00:40:50,270
+ال EQ بالنسبة إلى V يبقى tan inverse مقدار ثابت
+
+342
+00:40:50,270 --> 00:40:58,930
+واحد على اتنين الجذر التربيعي ل V زائد تلاتة في
+
+343
+00:40:58,930 --> 00:41:05,390
+مين في tan inverse U طيب
+
+344
+00:41:05,390 --> 00:41:14,420
+نبسطهاهذا الكلام تان انفرس يو كله مبسوما على ال EQ
+
+345
+00:41:14,420 --> 00:41:23,740
+الجدر التربيعي ل V زائد تلاتة في تان انفرس يو هذا
+
+346
+00:41:23,740 --> 00:41:30,750
+ال EQ في اتنين الجدر في اتنين الجدر التربيعيV زائد
+
+347
+00:41:30,750 --> 00:41:36,090
+تلاتة تان انفرست مع تان انفرست يبقى هتقول المسألة
+
+348
+00:41:36,090 --> 00:41:43,810
+الى واحد على اتنين في V زائد تلاتة اذا بقدر احسب
+
+349
+00:41:43,810 --> 00:41:50,710
+لمين ففاضل ال Z بالنسبة الى V عند النقطة واحد ونقص
+
+350
+00:41:50,710 --> 00:41:56,470
+اتنين تساوي واحد على اتنين في نقص اتنين
+
+351
+00:42:07,250 --> 00:42:15,310
+هذا اسم كله اشتقاق مباشر سواء كان اشتقاق كله او
+
+352
+00:42:15,310 --> 00:42:21,290
+اشتقاق ضمنه لكن قد يكون اشتقاق اشتقاق ضمنه يعني
+
+353
+00:42:21,290 --> 00:42:26,510
+اذا بدأ نيجي لحاجة اسمها implicit differentiation
+
+354
+00:42:40,120 --> 00:42:45,580
+التفاضل الضمني بقول
+
+355
+00:42:45,580 --> 00:42:50,580
+suppose that طلب
+
+356
+00:42:50,580 --> 00:43:02,140
+انه capital F of XY is a differentiable function
+
+357
+00:43:02,140 --> 00:43:08,080
+ذالك قابل للاشتقام and that
+
+358
+00:43:10,700 --> 00:43:22,900
+Equation f of x, y تساوي 0 defines بتعرفي
+
+359
+00:43:22,900 --> 00:43:37,360
+y as a differentiable function of x then at any
+
+360
+00:43:37,360 --> 00:43:46,140
+pointعند أي نقطة where الـ
+
+361
+00:43:46,140 --> 00:43:56,720
+fy لا تساوي zero we have ال
+
+362
+00:43:56,720 --> 00:44:04,080
+dy على dx بدي ساوي سالب fx
+
+363
+00:44:16,760 --> 00:44:24,280
+أقصد ذلك الـ
+
+364
+00:44:24,280 --> 00:44:28,480
+equation X
+
+365
+00:44:28,480 --> 00:44:42,240
+الـ E أُس Y زائد Sine XY زائد Y ناقص لإن اتنين يجب
+
+366
+00:44:42,240 --> 00:44:45,200
+أن نسميه Zero Define
+
+367
+00:44:47,530 --> 00:45:01,330
+يتعرف لي y as a differentiable function of x قاعد
+
+368
+00:45:01,330 --> 00:45:16,170
+هو اشتغلنا dy by dx at القاعد عند النقطة zero ولن
+
+369
+00:46:04,880 --> 00:46:08,540
+النقطة اللي بين إيدينا الألملات التي هي ال
+
+370
+00:46:08,540 --> 00:46:14,180
+differentiation التفاضل الضمني فده يقول افترض ان
+
+371
+00:46:14,180 --> 00:46:20,400
+عندي دالة F of X وY دالة قابلة للاشتقاء وفي نفس
+
+372
+00:46:20,400 --> 00:46:26,380
+الوقت F of X وY يساوي انه بتعرفي Y كدالة في X يبقى
+
+373
+00:46:26,380 --> 00:46:32,060
+هذه بهذا الشكل هذا علاقة تربط بين X وY يبقى لكنها
+
+374
+00:46:32,060 --> 00:46:34,240
+مشتركة مع بعض مش كده
+
+375
+00:46:43,570 --> 00:46:49,190
+بيقول لي عند أي نقطة بحيث المشتقة ال F بالنسبة ال
+
+376
+00:46:49,190 --> 00:46:54,610
+Y لا يمكن أن تساوي Zero بعرف المشتقة DY على DX
+
+377
+00:46:54,610 --> 00:47:00,430
+بأنها سالب مشتقة F بالنسبة لX مقسم على مشتقة F
+
+378
+00:47:00,430 --> 00:47:04,950
+بالنسبة ال Y طبعا إذا برهان صغير مش عايزين برهانه
+
+379
+00:47:04,950 --> 00:47:08,250
+تجريه في الكتاب كله ساطر و نص مش أكتر
+
+380
+00:47:13,980 --> 00:47:18,480
+بتعرف لي Y كدالة في X هاتلي دي Y علي دي X عن نقطة
+
+381
+00:47:18,480 --> 00:47:23,900
+Zero و لين اتنين بقول لكوا ايش طب وين F of X و Y
+
+382
+00:47:23,900 --> 00:47:28,480
+هتروح اشتقها موجودة
+
+383
+00:47:28,480 --> 00:47:33,200
+عندى F of X و Y؟ موجودة هذه لازم تساوي Zero اللي
+
+384
+00:47:33,200 --> 00:47:33,760
+هي هذه
+
+385
+00:47:37,240 --> 00:47:42,220
+يبقى ال F of X و Y هي الدالة دي بدون Zero يبقى بجي
+
+386
+00:47:42,220 --> 00:47:51,880
+بقوله F of X و Y هي عبارة عن مين؟ X UY زائد Sine
+
+387
+00:47:51,880 --> 00:48:01,240
+XY زائد Y نقص لانتنين بقدر أجيب له لانف X
+
+388
+00:48:09,690 --> 00:48:15,070
+في Y في مشتقة الزاوية بالنسبة لـ X اللي بيقدر Y
+
+389
+00:48:15,070 --> 00:48:24,350
+والباقي كله بـ 0. بدنا نجيب له FY يساوي X مشتقة
+
+390
+00:48:24,350 --> 00:48:31,610
+الـ EOS Y بالـ EOS Y itself. أمام ذات اللي هو
+
+391
+00:48:31,610 --> 00:48:37,610
+تفاضل الـ Sine. P Cos XY مشتقتها بالنسبة لـ X.
+
+392
+00:48:38,060 --> 00:48:45,960
+المشتقة الواحدة في الجداج، يا أبو واحد، تمام؟ خير
+
+393
+00:48:45,960 --> 00:48:54,120
+ان شاء الله، كده ساعتك العيد؟ احنا أبدا، يعني ضالة
+
+394
+00:48:54,120 --> 00:48:59,840
+لوقت العزة بس، اما محاضرتنا خلصت تقريبا، ساعتنا،
+
+395
+00:48:59,840 --> 00:49:03,520
+الا خمس دقايق،
+
+396
+00:49:03,520 --> 00:49:27,360
+طيبيبقى Fx يبقى Fx يبقى Fx يبقى Fx
+
+397
+00:49:27,360 --> 00:49:33,080
+يبقى Fx يبقى Fx يبقى Fx يبقى Fx يبقى Fx يبقى Fx
+
+398
+00:49:33,080 --> 00:49:33,300
+يبقى Fx يبقى Fx يبقى Fx يبقى Fx يبقى Fx يبقى Fx
+
+399
+00:49:33,300 --> 00:49:35,480
+يبقى Fx يبقى Fx يبقى Fx يبقى Fx يبقى Fxزائد Y Cos
+
+400
+00:49:35,480 --> 00:49:46,360
+XY على مين على اي شرط السلك برنامج على FYX UY زائد
+
+401
+00:49:46,360 --> 00:49:57,460
+X Cos XY زائد Y قال يحسبلي هذه ال D Y على DX عند
+
+402
+00:49:57,460 --> 00:50:00,000
+النقطة مين عند النقطة
+
+403
+00:50:09,980 --> 00:50:22,040
+يبقى ناقص E أس لن اتنين زائد لن اتنين في cos صفر
+
+404
+00:50:22,040 --> 00:50:26,700
+عشرين
+
+405
+00:50:27,810 --> 00:50:33,830
+يبدأ يحط مكانها لن اتنين تمام يبقى بيصير لن اتنين
+
+406
+00:50:33,830 --> 00:50:40,130
+فيه cosine صفر في لن اتنين اللي هو صفر على المقام
+
+407
+00:50:40,130 --> 00:50:45,790
+x بزيرو يبقى طاري ال term اللي عندك هذا كله و x
+
+408
+00:50:45,790 --> 00:50:51,210
+بزيرو طاري ال term هذا كله بيظل كده؟ بيظل واحد
+
+409
+00:50:51,210 --> 00:51:03,210
+يبقى هذه بيظل و يساوي ناقص اتنين زائدلن اتنين ناقص
+
+410
+00:51:03,210 --> 00:51:10,590
+للكل مش هيك ناقص لن اتنين يبقى بنات هذه حطوها بين
+
+411
+00:51:10,590 --> 00:51:16,290
+قسير بالشكل هذا حتى يصير كلامنا دقيق مائة بالمائة
+
+412
+00:51:16,290 --> 00:51:23,890
+خدها الملاحظة بالمرة يبقى ناشطة
+
+413
+00:51:33,140 --> 00:51:38,980
+لا يساوي زيرو بتعرف
+
+414
+00:51:38,980 --> 00:51:57,500
+لي z as a function of x and y and if وإذا كان if z
+
+415
+00:51:57,500 --> 00:51:59,760
+لا يساوي زيرو
+
+416
+00:52:03,390 --> 00:52:11,470
+partial z على partial x بده يساوي ناقص fx على fz
+
+417
+00:52:11,470 --> 00:52:21,270
+and partial z على partial y بده يساوي ناقص fy على
+
+418
+00:52:21,270 --> 00:52:31,730
+fz انقارن
+
+419
+00:52:32,250 --> 00:52:36,850
+الملاحظة مع الكلام اللي كتبناه في الحالة الأولى
+
+420
+00:52:36,850 --> 00:52:41,070
+يابانات احنا قولنا هذا بيعرف ل Y ك function في X
+
+421
+00:52:41,070 --> 00:52:45,470
+إذا صارت دالة في متغير واحد إذا روحنا و قولنا هنا
+
+422
+00:52:45,470 --> 00:52:52,450
+إيشأشتقاق كلي لكن قال لي هنا بعرف للـ z as a
+
+423
+00:52:52,450 --> 00:52:59,170
+function في مين في متغيرين إذا بصير اشتقاق جزءي
+
+424
+00:52:59,170 --> 00:53:04,010
+وليس اشتقاقا كليا إذا بقول partial z على partial x
+
+425
+00:53:04,010 --> 00:53:10,460
+و partial z على partial yهنا X هنا Fx و المقام Fz
+
+426
+00:53:10,460 --> 00:53:17,700
+هنا Y هنا Fy و المقام Fz خد مثال توضيحي على دنيا
+
+427
+00:53:17,700 --> 00:53:23,280
+for example let
+
+428
+00:53:23,280 --> 00:53:38,290
+Z تكيب ناقص XY ناقص YZنقص x y زائد y z زائد y تكيب
+
+429
+00:53:38,290 --> 00:53:47,670
+نقص اتنين تساوي زيرو fine عسبونا partial z by
+
+430
+00:53:47,670 --> 00:53:55,650
+partial x and partial z by partial y at النقطة
+
+431
+00:53:55,650 --> 00:53:58,070
+واحد هو واحد هو واحد
+
+432
+00:54:12,420 --> 00:54:21,680
+بدا بنات نحسب اللي هو الدالة f of x و y of z كلها
+
+433
+00:54:21,680 --> 00:54:27,140
+يبقى هذه اللي قالت تساوي قداش zero لو أخدت الآن z
+
+434
+00:54:27,140 --> 00:54:31,880
+function في x و y يبقى بصير f of x و y و z هي
+
+435
+00:54:31,880 --> 00:54:39,880
+عبارة عن z تكيب نقص x y زائد y z زائد y تكيب نقص
+
+436
+00:54:39,880 --> 00:54:48,480
+اتنينبقدر احسب له fx يبقى سالب y فيه كمان؟ ولا
+
+437
+00:54:48,480 --> 00:54:55,340
+حاجة بقدر احسب له fy نقص
+
+438
+00:54:55,340 --> 00:55:06,580
+x زائد z زائد 3I تربية نقدر احسب له كمان fz كل
+
+439
+00:55:06,580 --> 00:55:14,780
+هذا بروحوضلت لا تزد تربيع وهنا زائد Y وزي ما انت
+
+440
+00:55:14,780 --> 00:55:22,080
+شايفه لا تساوي Zero يبقى هذه لا تساوي Zero قال لي
+
+441
+00:55:22,080 --> 00:55:26,980
+والله إذا Fz مش Zero إذا بتقدر تجيب هذه بتقدر تجيب
+
+442
+00:55:26,980 --> 00:55:31,900
+اللي عندك هذه بقوله كويس إذا أنا بدي أروح أجيب له
+
+443
+00:55:31,900 --> 00:55:35,360
+ال partial F
+
+444
+00:55:43,410 --> 00:55:51,570
+يبقى هذا الكلام بدي اسمه هاي الناقص برا فاجي بقوله
+
+445
+00:55:51,570 --> 00:55:59,450
+Fx على Fz هاي الناقص برا Fx اللي يبقى داجة ناقص Y
+
+446
+00:55:59,450 --> 00:56:09,600
+Fz اللي هو تلاتة Z تربيع زائد Yطيب ناقص مع ناقص F
+
+447
+00:56:09,600 --> 00:56:16,500
+زائد ال Y عندى مقدشة فانا F واحد على تلاتة زائد
+
+448
+00:56:16,500 --> 00:56:22,880
+واحد ويسوى كده؟ رابع عند النقطة اللى بديها بدي
+
+449
+00:56:22,880 --> 00:56:31,560
+partial Z by partial Y يبقى ناقص FY على FZ يبقى هى
+
+450
+00:56:31,560 --> 00:56:34,400
+الناقص برا وبدهش ال FY
+
+451
+00:56:39,700 --> 00:56:46,100
+تلاتة وY تربيع على مين على FZ اللي هو تلاتة Z
+
+452
+00:56:46,100 --> 00:56:53,760
+تربيع زائد Y ويساوي هي الناقص برا هنا ناقص واحد
+
+453
+00:56:53,760 --> 00:57:03,660
+زائد واحد زائد تلاتة على تلاتة زائد واحد أطلع سالب
+
+454
+00:57:03,660 --> 00:57:07,880
+تلات تربع يبقى هنا سالب تلات تربع
+
+455
+00:57:35,100 --> 00:57:39,340
+عليك بيكون وصلنا الى نهاية هذا ال section وإلى
+
+456
+00:57:39,340 --> 00:57:49,520
+يكون أرقام المسائل التالية يبقى exercises يبقى
+
+457
+00:57:49,520 --> 00:57:56,540
+exercises أربعة عشر أربعة المسائل تلاتة خمسة سبعة
+
+458
+00:57:56,540 --> 00:57:59,580
+تسعة تلاتة خمسة سبعة
+
+459
+00:58:02,570 --> 00:58:09,250
+تسع تاش واحد وعشرين تسع تاش واحد وعشرين تلاتة
+
+460
+00:58:09,250 --> 00:58:11,950
+وعشرين تلاتين اتنين
+
+461
+00:58:15,350 --> 00:58:22,830
+تلاتة وتلاتين خمسة وتلاتين سبعة وتلاتين وسبعة
+
+462
+00:58:22,830 --> 00:58:28,010
+وتلاتين وتسعة وتلاتين وخمسة واربعين وتمانية
+
+463
+00:58:28,010 --> 00:58:39,270
+واربعين وخمسة واربعين وتمانية واربعين الان
+
+464
+00:58:39,270 --> 00:58:42,930
+هنتفل الى ال section اللذي يليهي
+
+465
+00:58:46,590 --> 00:58:53,410
+بقى سيكشن أربعة أشهر كام سا اللي هو directional
+
+466
+00:58:53,410 --> 00:58:57,270
+derivatives
+
+467
+00:58:57,270 --> 00:59:02,930
+directional
+
+468
+00:59:02,930 --> 00:59:10,910
+derivatives يعني المشتقاد المتجه and the gradient
+
+469
+00:59:23,000 --> 00:59:27,720
+بنواصل الآن يا بناد للمحاضرة طبيعتنا وننتقل إلى ال
+
+470
+00:59:27,720 --> 00:59:31,940
+section 14-5 اللي بتكلم عن ال directional
+
+471
+00:59:31,940 --> 00:59:38,620
+derivatives يعني المشتقات المتجهة يعني مشتقة في
+
+472
+00:59:38,620 --> 00:59:45,400
+اتجاه الماء and gradient vectors والمتجهات اللي
+
+473
+00:59:45,400 --> 00:59:50,840
+بتبقى على شكل grade Fأو دل F أو نقلة F هذا مثلًا
+
+474
+00:59:50,840 --> 00:59:57,080
+رأيكم بعد قليل هنقلت تعريفين و بعد التعريفين هنروح
+
+475
+00:59:57,080 --> 01:00:02,260
+لبعض الأمثلة أطبعيًا أول تعريف يقول the gradient
+
+476
+01:00:02,260 --> 01:00:08,460
+vector of a function f of x و y عند النقصة P node
+
+477
+01:00:08,460 --> 01:00:12,220
+of x node و y node is the vector يبقى فيه أن ال
+
+478
+01:00:12,220 --> 01:00:19,500
+gradient vector هذا يبقى متجهلمين؟ للدلة F شو
+
+479
+01:00:19,500 --> 01:00:27,280
+برمزله؟ بالرمز المثلث لرأسه لأسفل ويقرأ grade F أو
+
+480
+01:00:27,280 --> 01:00:33,780
+gradient F يختصر إلى grade F أو دل F أو نقلة F
+
+481
+01:00:33,780 --> 01:00:44,800
+يبقى هذا الرمز يا بروح بقول grade F يا إما بقول دل
+
+482
+01:00:44,800 --> 01:00:55,620
+Fيا أما بقول نطلع F كل واحد فيهم هذول أي واحد من
+
+483
+01:00:55,620 --> 01:01:01,120
+التلاتة هذول الرمز هذا كله هو عبارة عن مين اللي هو
+
+484
+01:01:01,120 --> 01:01:02,700
+grade F
+
+485
+01:01:05,110 --> 01:01:09,730
+هذا من ناحية التسمي لكن بدا نجي لمفهومه as a
+
+486
+01:01:09,730 --> 01:01:14,730
+vector يبقى مفهومه as a vector ومستقل يتبلف
+
+487
+01:01:14,730 --> 01:01:21,150
+بالنسبة لX عند النقطة P0 في اتجاه I المستقل يتبلف
+
+488
+01:01:21,150 --> 01:01:25,270
+بالنسبة له عند P0 في اتجاه الجي يعني معناه كل ما
+
+489
+01:01:25,270 --> 01:01:28,390
+بدي أجيب له partial F على partial X و أعوض
+
+490
+01:01:28,390 --> 01:01:31,750
+بإحداثية النقطة الرقم اللي بيطلع بيقول هذا في
+
+491
+01:01:31,750 --> 01:01:38,360
+اتجاه Iزاد مشتقة ال F بالنسبة إلى Y وعوض بحداثية
+
+492
+01:01:38,360 --> 01:01:42,720
+النقطة هيطلع عندي رقم بقول هذا في اتجاه الجي اتنين
+
+493
+01:01:42,720 --> 01:01:48,440
+مع بعض بيكونوني اللي هو ما يسمى graph F يبقى F X
+
+494
+01:01:48,440 --> 01:01:52,180
+عند X node وY node في اتجاه I زاد F Y عند X node
+
+495
+01:01:52,180 --> 01:01:58,730
+وY node في اتجاه الجي طب لو كانتلت متجهات يعني في
+
+496
+01:01:58,730 --> 01:02:03,910
+تلت محاور يبقى بضفلهم كمان مين FZ وهذا ما سنرجع
+
+497
+01:02:03,910 --> 01:02:09,410
+عليه خلال هذا ال section تمام تعريف التاني تعريف
+
+498
+01:02:09,410 --> 01:02:12,770
+التاني هو نصف الأول من العنوان اللي احنا رافقيله
+
+499
+01:02:12,770 --> 01:02:15,870
+اللي هو ال directional derivatives المشتقات
+
+500
+01:02:15,870 --> 01:02:22,430
+المتجهة فبعرف المشتقة تبع التدريب عند النقطة في
+
+501
+01:02:22,430 --> 01:02:25,610
+اتجاه المتجه لأن هذا is
+
+502
+01:02:28,930 --> 01:02:35,490
+هيبقى اشتق جزئيا سواء كان بالنسبة ل X أو بالنسبة ل
+
+503
+01:02:35,490 --> 01:02:39,830
+Y بتعوض بيه احداثيات النقطة اللي عيلنا هذه يبقى
+
+504
+01:02:39,830 --> 01:02:46,150
+جيبنا مين جيبنا grade F اه اتجاه unit vector U
+
+505
+01:02:46,150 --> 01:02:50,250
+يبقى بتفهم ان U هذا معناه مش vector عادي وانما
+
+506
+01:02:50,250 --> 01:02:55,620
+متجهوحدة حطيته مركبتين يو واحد في اتجاه ال I زي دي
+
+507
+01:02:55,620 --> 01:03:02,340
+و اتنين في اتجاه ال J as V U F عند ال P نوت الرمز
+
+508
+01:03:02,340 --> 01:03:07,600
+يدل على ال directional derivative طب هذا الرمز يا
+
+509
+01:03:07,600 --> 01:03:12,660
+بكتبه بشكل هذا يا بكتبه قرية F عند نقطة P نوت ضد
+
+510
+01:03:12,660 --> 01:03:18,340
+متجه الواحدة U يجب ان اشيل هذا و اكتبه زي ما عرفت
+
+511
+01:03:18,340 --> 01:03:24,100
+فيهم وهذازي ما عرفته هنا بالشكل اعناعي اعمل ضمة
+
+512
+01:03:24,100 --> 01:03:28,920
+product فيما بينهما بصيارة ال domain f x في u1 زي
+
+513
+01:03:28,920 --> 01:03:35,380
+f y في u2 بناء عليه الناتج كمية قياسية او كمية
+
+514
+01:03:35,380 --> 01:03:43,220
+اتجاهيةIowascalar يبقى مقدار المشتقة المتجهة عند
+
+515
+01:03:43,220 --> 01:03:49,020
+نقطة هي المقصود فيه منه هو grad F عند تلك النقطة
+
+516
+01:03:49,020 --> 01:03:55,140
+ضد متجه الوحدة U عند تلك النقطة يبقى هذا تعريف ال
+
+517
+01:03:55,140 --> 01:03:59,520
+directional derivative نعطي بعض الأمثل عليه نجي
+
+518
+01:03:59,520 --> 01:04:02,240
+ناخد أول مثال examples
+
+519
+01:04:08,710 --> 01:04:13,330
+بقول find the derivative of the function find the
+
+520
+01:04:13,330 --> 01:04:29,150
+derivative of the function لذالة f of x y f of x y
+
+521
+01:04:29,150 --> 01:04:43,010
+بساوي x ناقص ال y على x y زائد اتنينعند النقطة P
+
+522
+01:04:43,010 --> 01:04:56,170
+naught of واحد مسالب واحد in the direction of
+
+523
+01:04:56,170 --> 01:05:07,760
+the vector اتجاه المتجد اللي هوذى بدى يساوي ماعشر
+
+524
+01:05:07,760 --> 01:05:24,480
+I زائد خمسة J إذا
+
+525
+01:05:24,480 --> 01:05:26,160
+مشينا لإيجاد طريقة
+
+526
+01:05:37,780 --> 01:05:45,140
+النقطة المعطنية هي المعطنية المعطنية المعطنية
+
+527
+01:05:45,140 --> 01:05:52,220
+المعطنية المعطنية المعطنية المعطنية المعطنية
+
+528
+01:05:52,220 --> 01:05:59,180
+المعطنية المعطنية
+
+529
+01:06:04,560 --> 01:06:12,460
+عند من؟ عند .. عند .. بالنسبة للمتغير X، F، X ها
+
+530
+01:06:12,460 --> 01:06:18,000
+يا ابنها البص بدلرة X والمقام بدلرة X إذا مشتقت
+
+531
+01:06:18,000 --> 01:06:26,260
+خارج قسمة دالتين يبقى المقام لمشتقة البص بالنسبة
+
+532
+01:06:26,260 --> 01:06:28,860
+لX اللي هو كده ايش؟ واحد
+
+533
+01:06:34,460 --> 01:06:42,100
+في مشتقة المقام بالنسبة لـ X أو Y كل هذا الكلام
+
+534
+01:06:42,100 --> 01:06:49,600
+على مربع المقام الأصلي هذا يبدو سواء يا بناه X Y
+
+535
+01:06:49,600 --> 01:07:00,140
+زائد 2 ناقص XY زائد Y ترابيع كله على XY زائد 2 لكل
+
+536
+01:07:00,140 --> 01:07:07,520
+ترابيعهذه تذهب مع هذه يبقى اتنين زائد Y تربية على
+
+537
+01:07:07,520 --> 01:07:13,260
+XY زائد اتنين كل تربية شو رايكوا بالمرة نحسبها عند
+
+538
+01:07:13,260 --> 01:07:19,800
+النقطة يبقى بالتاجة اخد له F X عند واحد و سالب
+
+539
+01:07:19,800 --> 01:07:24,420
+واحد لان هشيل كل X و احط مكانها واحد و اشيل Y و
+
+540
+01:07:24,420 --> 01:07:33,370
+احط مكانها واحدزائد سالب واحد تربيع على واحد سالب
+
+541
+01:07:33,370 --> 01:07:42,650
+واحد زائد اتنين لكل تربيع يمجي هنا تلاتة وهنا واحد
+
+542
+01:07:42,650 --> 01:07:49,530
+هو يسوي قداش تلاتة انا اروح اجيب له ال FY يمجي FY
+
+543
+01:07:49,530 --> 01:07:52,310
+بنفس الطريقة المقام
+
+544
+01:07:54,790 --> 01:08:01,690
+بمشتقة ال bus بالنسبة ل y سالب واحد ناقص ال bus
+
+545
+01:08:01,690 --> 01:08:08,730
+بمشتقة المقام بالنسبة إيه ل y لو قداش x على مربع
+
+546
+01:08:08,730 --> 01:08:15,610
+المقام الأصلي xy زي دي اتنين لكل تربية y و 7
+
+547
+01:08:45,380 --> 01:08:51,340
+بنحسب fy نقطة واحدة وسالك واحدة
+
+548
+01:08:59,170 --> 01:09:04,630
+زائد اتنين الكل تربيع ناقص تلاتة على واحد اللي هو
+
+549
+01:09:04,630 --> 01:09:10,550
+ناقص تلاتة تعالوا نطلع نجيب جراد F عند النقطة
+
+550
+01:09:10,550 --> 01:09:21,890
+يابانا هاي يبقى بروح بقوله جراد F عند النقطة P0 أو
+
+551
+01:09:21,890 --> 01:09:25,250
+عند النقطة اللي هي واحد
+
+552
+01:09:29,340 --> 01:09:35,960
+بدا تساوي ال Fx طلعناها بتلاتة يبقى تلاتة I وناقص
+
+553
+01:09:35,960 --> 01:09:44,360
+تلاتة G I بدنا ال vector هذا نخليه زي ما هو ال
+
+554
+01:09:44,360 --> 01:09:47,700
+unit vector إذا بدنا نجيب متجة الواحدة بالنسبة
+
+555
+01:09:47,700 --> 01:09:55,600
+لمين لهذا المتجة إذن ال U بدو يساوي ال V على طول
+
+556
+01:09:55,600 --> 01:09:58,960
+ال V ال V اللي هو اتناشر I
+
+557
+01:10:01,590 --> 01:10:11,610
+على الجدر التربيعي لـ 144 زائد 25 يساوي 12 على 13
+
+558
+01:10:11,610 --> 01:10:22,490
+I خمسة على تلتاشر اذا بدى اجيبله الـ D U F عند
+
+559
+01:10:22,490 --> 01:10:30,930
+النقطة واحد وسالب واحد يساوي تلاتة I ناقص تلاتة J
+
+560
+01:10:31,620 --> 01:10:39,680
+بوت المتجه عندنا اتناشر عالى تلتاشر I خمسة عالى
+
+561
+01:10:39,680 --> 01:10:46,800
+تلتاشر J و يسابر اتناشر في تلاتة بستة و تلاتين
+
+562
+01:10:46,800 --> 01:10:59,260
+عالى تلتاشر ناقص خمستاشر عالى تلتاشر و يسابر واحد
+
+563
+01:10:59,260 --> 01:11:04,490
+و عشرينعلى تلتاشة أي قيمة الـ Directional
+
+564
+01:11:04,490 --> 01:11:11,610
+Derivative عن مين عند النقطة المُعطَرة في روايكم
+
+565
+01:11:11,610 --> 01:11:17,910
+هذا ال section لا يخلو أي امتحان من سؤال عليه
+
+566
+01:11:17,910 --> 01:11:21,590
+مظارا
+
+567
+01:11:21,590 --> 01:11:27,510
+لأهميته ناخد كمان مثال اتنين
+
+568
+01:11:35,630 --> 01:11:48,010
+بالعكس فالـ F of X وY بدها تساوي X تربيع ناقص XY
+
+569
+01:11:48,010 --> 01:11:58,510
+زائد Y تربيع ناقص Y Find the directions
+
+570
+01:12:01,690 --> 01:12:11,370
+find the directions U for which يحيث
+
+571
+01:12:11,370 --> 01:12:24,510
+ان for which اللي هو D U F عند النقطة اللي هي من
+
+572
+01:12:24,510 --> 01:12:27,230
+واحد و سالب واحد
+
+573
+01:12:45,460 --> 01:12:52,580
+هذا سؤال زي سابقني بس حوّرنا الفكرة شغالة لأقنى
+
+574
+01:12:52,580 --> 01:12:59,320
+مستقل المتجه ماعطيه تبتدى جدرى سالب ثلاثة ومتجه
+
+575
+01:12:59,320 --> 01:13:04,040
+يوم ماعطانى شريعة وعطانى الدالة مبلهات المتجه
+
+576
+01:13:04,040 --> 01:13:10,420
+اليوم يعني بدي أجيب لمتجه الوحدة للمتجه عند النقطة
+
+577
+01:13:10,420 --> 01:13:16,580
+الموضعة في اتجاهه بدأ سوى من سالب تلاتةخليني امشي
+
+578
+01:13:16,580 --> 01:13:22,500
+ماشي طبيعي و احط كل شيء في مكانه هوصل بالاخر لمن؟
+
+579
+01:13:22,500 --> 01:13:27,280
+لنتيجة او لنتيجة اللي هو بدوها يبقى فيها ده سؤال
+
+580
+01:13:27,280 --> 01:13:32,600
+عايزني ليه التيجة تبع متجه الواحدة يوم؟ يعني كأنه
+
+581
+01:13:32,600 --> 01:13:36,520
+بده متجه الواحدة يوم شو شكله اللي خلّى المستقل
+
+582
+01:13:36,520 --> 01:13:42,320
+متجها تساوي سالت تلتة اذا انا بده اروح اجيبله من؟
+
+583
+01:13:43,370 --> 01:13:47,630
+ممتاز زي ما بدأنا بالظبط تماما يبقى بدأ أروح أجيب
+
+584
+01:13:47,630 --> 01:13:59,090
+له F X Y ساعة تنين X نقصها نحسبها بالمرة يبقى F X
+
+585
+01:13:59,090 --> 01:14:03,010
+يبقى
+
+586
+01:14:03,010 --> 01:14:12,310
+ال F X عند النقطة واحد وسالب واحد ساعة تلاتةنقص
+
+587
+01:14:12,310 --> 01:14:21,290
+نقص واحد هو تساوي تلاتة كذا بدي fy يبقى ناقص x
+
+588
+01:14:21,290 --> 01:14:31,390
+زائد اتنين y ناقص واحد وهذا الكلام الfy ان النقطة
+
+589
+01:14:31,390 --> 01:14:39,730
+واحدة سالك واحد بدي سالك واحدزائد اتنين في سالب
+
+590
+01:14:39,730 --> 01:14:48,270
+واحد هنا سالب واحد حصل سالب اربعة يبقى صار اندجريد
+
+591
+01:14:48,270 --> 01:14:56,110
+F عند النقطة واحد وسالب واحد يبقى يساوي تلاتة I
+
+592
+01:14:56,110 --> 01:14:58,650
+ناقص اربعة G
+
+593
+01:15:01,760 --> 01:15:10,960
+أنا عندي بدأ افترض عندي متجر واحدة U أسيوم طردت أن
+
+594
+01:15:10,960 --> 01:15:18,780
+U يتساوي واحد في اتجاه I و U اتنين في اتجاه J إذا
+
+595
+01:15:18,780 --> 01:15:26,120
+بدأ أجيب له Directionary Derivative DuF عند النقطة
+
+596
+01:15:26,120 --> 01:15:26,740
+واحدة
+
+597
+01:15:30,250 --> 01:15:39,590
+implies اقرأة الـ F هي تلاتة I ناقص أربعة G ضد U
+
+598
+01:15:39,590 --> 01:15:45,090
+واحد اتجاه الـ I U اتنين اتجاه الـ G تساوي سالب
+
+599
+01:15:45,090 --> 01:15:54,230
+تلاتة إذا تلاتة U واحد ناقص أربعة U اتنين تساوي
+
+600
+01:15:54,230 --> 01:15:56,810
+قدرت سالب تلاتة
+
+601
+01:16:00,330 --> 01:16:08,090
+U1 يتساوي 4U2
+
+602
+01:16:08,090 --> 01:16:14,070
+-3 يتساوي 4U2-3 يتساوي
+
+603
+01:16:14,070 --> 01:16:17,810
+4U2-3 يتساوي
+
+604
+01:16:17,810 --> 01:16:21,370
+4U2-3 يتساوى 4U2-3 يتساوى 4U2-3 يتساوى 4U2-3
+
+605
+01:16:21,370 --> 01:16:21,410
+يتساوى 4U2-3 يتساوى 4U2-3 يتساوى 4U2-3 يتساوى 4U2
+
+606
+01:16:21,410 --> 01:16:21,610
+-3 يتساوى 4U2-3 يتساوى 4U2-3 يتساوى 4U2-3 يتساوى
+
+607
+01:16:21,610 --> 01:16:22,030
+4U2-3 يتساوى 4U2-3 يتساوى 4U2-3 يتساوى 4U2-3
+
+608
+01:16:22,030 --> 01:16:27,640
+يتساوى 4U2-3 يتساوى 4U2-3 يتساوىحذفتي يا رجل من
+
+609
+01:16:27,640 --> 01:16:37,840
+أين إذا جيب الأولاق الأخرى؟ وجدها قدامك علمها طلعي
+
+610
+01:16:37,840 --> 01:16:45,560
+في التعريف تبع ال directional derivative وين
+
+611
+01:16:45,560 --> 01:16:52,360
+التعريف؟ مسحناه؟ مسحناه، طيب الـU هذا إيه الشكل يا
+
+612
+01:16:52,360 --> 01:17:00,530
+بنت؟قلتك إيه؟ قلتك يا واخر يعني قدش طولك قلتها
+
+613
+01:17:00,530 --> 01:17:07,490
+جيبه هاله علاقة تانية نرجع هنا بقوله بقى ولكن جدري
+
+614
+01:17:07,490 --> 01:17:12,990
+التربية يوحى التربية زادي و اتنين تربية تساوي
+
+615
+01:17:12,990 --> 01:17:20,150
+واحدة لو ربعنا هذا معناه يوحى التربية زادي و اتنين
+
+616
+01:17:20,150 --> 01:17:33,480
+تربية تساوي واحدة هذا معناهY1 تربيع زائد هذا معناه
+
+617
+01:17:33,480 --> 01:17:38,120
+يبقى
+
+618
+01:17:38,120 --> 01:17:47,600
+توسع في 4Y2 ناقص تلاتة لكل تربيع زائد Y2 تربيع
+
+619
+01:17:47,600 --> 01:17:52,680
+وزائد Y1 زي
+
+620
+01:17:52,680 --> 01:18:00,200
+ما تشوفون يا بناتهذه عبارة عن معادلة في مجهول واحد
+
+621
+01:18:00,200 --> 01:18:04,240
+إذا كنت مستطيع أن أحسب هذا المجهول لذلك يجب أن أفك
+
+622
+01:18:04,240 --> 01:18:07,160
+هذا التربيه يجب أن أفك هذا التربيه يجب أن أفك هذا
+
+623
+01:18:07,160 --> 01:18:07,160
+التربيه يجب أن أفك هذا التربيه يجب أن أفك هذا
+
+624
+01:18:07,160 --> 01:18:07,280
+التربيه يجب أن أفك هذا التربيه يجب أن أفك هذا
+
+625
+01:18:07,280 --> 01:18:07,800
+التربيه يجب أن أفك هذا التربيه يجب أن أفك هذا
+
+626
+01:18:07,800 --> 01:18:10,780
+التربيه يجب أن أفك هذا التربيه يجب أن أفك هذا
+
+627
+01:18:10,780 --> 01:18:12,740
+التربيه يجب أن أفك هذا التربيه يجب أن أفك هذا
+
+628
+01:18:12,740 --> 01:18:15,880
+التربيه يجب أن أفك هذا التربيه يجب أن أفك هذا
+
+629
+01:18:15,880 --> 01:18:19,420
+التربيه يجب أن أفك
+
+630
+01:18:24,660 --> 01:18:33,820
+يوت نين تربيع تساوي واحد تكيلي هذه قصيرة ستة عشر
+
+631
+01:18:33,820 --> 01:18:41,400
+على تسعة يوت نين تربيع ناقص اربع وعشرين على تسعة
+
+632
+01:18:41,400 --> 01:18:50,500
+يوت نين زائد واحد زائد يوت نين تربيع
+
+633
+01:18:53,790 --> 01:18:59,370
+أحنا يا بنات باعتباره كم؟ تسعة على تسعة، بيقصر كم؟
+
+634
+01:18:59,370 --> 01:19:06,030
+خمسة وعشرين على تسعة، يبقى خمسة وعشرين على تسعة
+
+635
+01:19:06,030 --> 01:19:18,400
+يوت نين اربعين، تمام؟25 على 9 U2 تربية وهذا ناقص
+
+636
+01:19:18,400 --> 01:19:26,640
+24 على 9 U عشان بدي أسوي صفات؟ ممكن طيب بدي أخد ال
+
+637
+01:19:26,640 --> 01:19:34,000
+U عامل مشترك مش بصير عندي U2 طبعا U2 أبدا أبدا خير
+
+638
+01:19:34,000 --> 01:19:40,520
+بصير 25 على 9 U2
+
+639
+01:19:46,360 --> 01:19:59,340
+الـ U2 بدها تساوي 0 او الـ U2 بدها تساوي 24 على 25
+
+640
+01:20:05,780 --> 01:20:11,360
+إتنين لذلك قد ما طلعنا نقول له five direction zero
+
+641
+01:20:11,360 --> 01:20:15,860
+يعني المتجهات الوحدة التي تحقق
+
+642
+01:20:37,240 --> 01:20:47,280
+لو كانت U2 تساوي 0، فلا يهاتش بنصيرها بنات، هذه ال
+
+643
+01:20:47,280 --> 01:20:52,340
+start، يعني نجح نعوض المعادلة start، لو كانت U2
+
+644
+01:20:52,340 --> 01:20:56,880
+تساوي 0، يبلغ U1 مقدار سالب واحد
+
+645
+01:21:02,480 --> 01:21:09,720
+يساوي سالف واحد هذا بدي اعطيكي ان ال U يساوي سالف
+
+646
+01:21:09,720 --> 01:21:16,340
+A متجهة واحدة ولا لا متجهة واحدة الحالة التانية F
+
+647
+01:21:16,340 --> 01:21:24,280
+U2 يساوي اربع على خمسة وعشرين اربع عشر على خمسة
+
+648
+01:21:24,280 --> 01:21:35,690
+وعشرين then U واحد يساوي طول Fأربعة أربعة في أربعة
+
+649
+01:21:35,690 --> 01:21:45,610
+وعشرين بستة وتسعين على خمسة وعشرين ماقص تلت مظبوط
+
+650
+01:21:45,610 --> 01:21:52,330
+هيك تلتة في خمسة وعشرين بخمسة وسبعين من ستة وتسعين
+
+651
+01:21:52,330 --> 01:22:00,800
+بكم بطلع كذا شبنات واحد وعشرين على خمسة وعشرينيعني
+
+652
+01:22:00,800 --> 01:22:15,760
+قدير 7 على 25 إذا ال U يسار ال U1 اللي طلعناها و
+
+653
+01:22:15,760 --> 01:22:25,320
+ال U2 ال U1 هذه اللي طلعناها هو 7 على 25 في اتجاه
+
+654
+01:22:25,320 --> 01:22:32,770
+الأعلىو U2 اللي هو زائد أربعة و عشرين على خمسة و
+
+655
+01:22:32,770 --> 01:22:41,910
+عشرين في اتجاه M في اتجاه الـ J طبعا
+
+656
+01:22:41,910 --> 01:22:46,790
+يبقى هذا متجه الوحدة الثاني اللي بيضمنها هذا
+
+657
+01:22:46,790 --> 01:22:52,950
+المتجه الأول اللي أطلبه وهذا هو متجه الوحدة الثاني
+
+658
+01:22:52,950 --> 01:22:54,090
+اللي هو طلبه
+
+659
+01:23:00,370 --> 01:23:05,610
+طيب نجي لخواص directionally driven نجي ل ال
+
+660
+01:23:21,530 --> 01:23:31,630
+بطل U وهي بدأت تساوي لهوليجراد F في Cos الزاوية
+
+661
+01:23:31,630 --> 01:23:35,830
+أول
+
+662
+01:23:35,830 --> 01:23:47,930
+خاصية من هذه القوات الـ Function F increases most
+
+663
+01:23:47,930 --> 01:23:49,370
+rapidly
+
+664
+01:23:53,680 --> 01:24:03,520
+most rapidly when
+
+665
+01:24:03,520 --> 01:24:22,200
+theta تساوي zero that is in when اليوم and they
+
+666
+01:24:23,480 --> 01:24:31,120
+Same Direction
+
+667
+01:24:31,120 --> 01:24:43,360
+قام اجراد ال F هذا بدي أعطيكم ان ال DUF بدي ساوي
+
+668
+01:24:43,360 --> 01:24:47,540
+طول اجراد ال F فقط لغة
+
+669
+01:24:51,740 --> 01:25:03,380
+again this case في هذه الحالة الـ DUF as its as
+
+670
+01:25:03,380 --> 01:25:10,000
+its largest as
+
+671
+01:25:10,000 --> 01:25:16,500
+its largest positive value
+
+672
+01:25:16,500 --> 01:25:19,040
+when
+
+673
+01:25:21,190 --> 01:25:33,010
+فيتا يساوي ساعة. دمرة اتنين، similar to function.
+
+674
+01:26:13,490 --> 01:26:24,890
+الـ F لـ U and a graded F in
+
+675
+01:26:24,890 --> 01:26:39,990
+the opposite directions that
+
+676
+01:26:39,990 --> 01:26:40,350
+is
+
+677
+01:26:52,700 --> 01:27:02,380
+صار الـ D والـ F بدأت تساوي كل جراد الـ F في Cos
+
+678
+01:27:02,380 --> 01:27:07,860
+بقعة و يساوي سالب absolute value
+
+679
+01:27:38,870 --> 01:27:39,850
+العزيزي .
+
+680
+01:28:20,280 --> 01:28:27,300
+أو يمكن أن تكون positive أو negative او positive
+
+681
+01:28:27,300 --> 01:28:28,240
+او negative او positive او positive او positive او
+
+682
+01:28:28,240 --> 01:28:30,240
+positive او positive او positive او positive او
+
+683
+01:28:30,240 --> 01:28:32,440
+positive او positive او positive او positive او
+
+684
+01:28:32,440 --> 01:28:32,540
+positive او positive او positive او positive او
+
+685
+01:28:32,540 --> 01:28:32,580
+positive او positive او positive او positive او
+
+686
+01:28:32,580 --> 01:28:32,580
+positive او positive او positive او positive او
+
+687
+01:28:32,580 --> 01:28:32,580
+positive او positive او positive او positive او
+
+688
+01:28:32,580 --> 01:28:32,580
+positive او positive او positive او positive او
+
+689
+01:28:32,580 --> 01:28:32,980
+positive او positive او positive او positive او
+
+690
+01:28:32,980 --> 01:28:33,620
+positive او positive او positive او positive او
+
+691
+01:28:33,620 --> 01:28:33,620
+positive او positive او positive او positive او
+
+692
+01:28:33,620 --> 01:28:33,620
+positive او positive او positive او positive او
+
+693
+01:28:33,620 --> 01:28:33,620
+positive او positive او positive او positive او
+
+694
+01:28:33,620 --> 01:28:33,620
+positive او positive او positive او positive او
+
+695
+01:28:33,620 --> 01:28:33,620
+positive او positive او positive او positive او
+
+696
+01:28:33,620 --> 01:28:33,620
+positive او positive او positive او positive او
+
+697
+01:28:33,620 --> 01:28:33,660
+positive او positive او positive او positive او
+
+698
+01:28:33,660 --> 01:28:35,220
+positive او positive ا
+
+699
+01:28:38,340 --> 01:28:41,800
+اللي بقول أنا الخواص طبعا ال direction أنا دريبه
+
+700
+01:28:41,800 --> 01:28:47,580
+فبقى اجي بقول ال D U F يبقى ايه اجراد ال F ضد ال U
+
+701
+01:28:47,580 --> 01:28:52,810
+يبقى طوللغراد ال F في طول ال U في Cos الزاوية
+
+702
+01:28:52,810 --> 01:28:58,270
+تيتا، كده طول ال U يبقى بطير، بظل طول غراد ال F في
+
+703
+01:28:58,270 --> 01:29:03,050
+Cos الزاوية تيتا، ليش؟ لأن ال U هو متجه الواحدة،
+
+704
+01:29:03,050 --> 01:29:06,630
+فطوله يسوي كده شخص صحيح، لذا هذا يسوي طول غراد ال
+
+705
+01:29:06,630 --> 01:29:11,280
+F في Cos الزاوية تيتااللي انا بدى اشوف القيمة دي
+
+706
+01:29:11,280 --> 01:29:15,860
+وقتش بتكون اكبر ما يمكن وقتش اقل ما يمكن وقتش
+
+707
+01:29:15,860 --> 01:29:20,360
+بتبقى zero بقول الدالة if increases most rapidly
+
+708
+01:29:20,360 --> 01:29:28,720
+تتزايد بسرعة فائقة most rapidly بسرعة when θ تبقى
+
+709
+01:29:28,720 --> 01:29:33,780
+zeroماذا يعني هذا الكلام؟ يعني يجب أن يكون U و F
+
+710
+01:29:33,780 --> 01:29:38,780
+اتنين مالهم في نفس الاتجاه لأن الزوابن هم Zero
+
+711
+01:29:38,780 --> 01:29:45,260
+That is when ال U in the same direction of F اتنين
+
+712
+01:29:45,260 --> 01:29:50,140
+في نفس الاتجاه تبقى بصير عندك كوسين صفر بجدير واحد
+
+713
+01:29:50,140 --> 01:29:55,320
+أكبر قيمة بياخدها الكوسين جدير إذا هذه بتاخد أقصى
+
+714
+01:29:55,320 --> 01:29:59,700
+قيمة لهاعند θ تساوي zero عندما u و grade ال F
+
+715
+01:29:59,700 --> 01:30:06,360
+يكونوا في نفس الاتجاه كده مقدارها؟ مقدارها طول
+
+716
+01:30:06,360 --> 01:30:10,520
+grade ال F لأن ال direction derivative طول grade
+
+717
+01:30:10,520 --> 01:30:15,080
+ال F كسين زوية تيتا كسين تيتا بواحد يبقى بظهر أكبر
+
+718
+01:30:15,080 --> 01:30:21,160
+قيمة لطول grade ال F طب كده شقة القيمة؟يقول لو
+
+719
+01:30:21,160 --> 01:30:25,380
+كانوا اثنين ماشيين في اتجاهين متعدين ليش ان قصة
+
+720
+01:30:25,380 --> 01:30:29,660
+مية و تمانين بسالب واحد وهي اقل قيمة بياخدها ال
+
+721
+01:30:29,660 --> 01:30:30,000
+cosine
+
+722
+01:30:50,590 --> 01:30:55,470
+إتنين في اتجاهين متضادين في اتجاهين متضادين يقزق
+
+723
+01:30:55,470 --> 01:31:03,250
+بينهم كم؟ 180 درجة الهنكو ساي 180 سالب واحد يبقى
+
+724
+01:31:03,250 --> 01:31:07,510
+بصير قيمة ال direction derivative هي سالب grade ال
+
+725
+01:31:07,510 --> 01:31:11,330
+F يعني انا في الحالتين الاتنين هدول إذا جبت grade
+
+726
+01:31:11,330 --> 01:31:17,290
+ال F بكون خلاص جبت main أكبر قيمة و أقل قيمة سالب
+
+727
+01:31:17,290 --> 01:31:23,850
+طول grade ال Fبعطي أفضل قيمة للدراكشين
+
+728
+01:31:23,850 --> 01:31:33,650
+دريفاتيب اذا اتنين او اتنين او اتنين او اتنين او
+
+729
+01:31:33,650 --> 01:31:41,050
+اتنين او اتنين او اتنينمتعمدة، الآن عندنا أمثل
+
+730
+01:31:41,050 --> 01:31:44,990
+عليهم، لكن أنا بقولك تفي بهذا القدر اليوم لإنه
+
+731
+01:31:44,990 --> 01:31:50,270
+بدنا نوزع أوراق لامتحان ان شاء الله تعالى
+
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/SmdhLcwuMIw.srt b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/SmdhLcwuMIw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..679ddce1f498d1e6453ad7c05fd98e09095a666e
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/SmdhLcwuMIw.srt
@@ -0,0 +1,2129 @@
+1
+00:00:00,000 --> 00:00:02,680
+موسيقى
+
+2
+00:00:13,140 --> 00:00:18,180
+بسم الله الرحمن الرحيم، المرة اللي فاتت آخر حاجة
+
+3
+00:00:18,180 --> 00:00:22,640
+أخرناها اللي هو الـ unit tangent vector T اللي كانت
+
+4
+00:00:22,640 --> 00:00:27,740
+DR عالية باسم نواصل وسنرجع مرة ثانية للـ unit
+
+5
+00:00:27,740 --> 00:00:31,040
+tangent vector اللي إحنا لزمنا خلال هذا الـ section
+
+6
+00:00:31,040 --> 00:00:34,760
+والـ section اللي بعده كمان، يبقى هذا الشيء أساسي
+
+7
+00:00:34,760 --> 00:00:37,880
+هنيجي للـ section اللي هو curvature and
+
+8
+00:00:37,880 --> 00:00:42,740
+normal vectors of curvature، يعني بالعربي يا بنات
+
+9
+00:00:42,740 --> 00:00:48,900
+اللي هو التقوس أو الانحناء لمنحنى، نحسب مقدار
+
+10
+00:00:48,900 --> 00:00:53,780
+التقوس لمنحنى أو مقدار الانحناء لهذا المنحنى،
+
+11
+00:00:53,780 --> 00:01:00,860
+normal vector، المتجه العمودي على المنحنى، وسنعرف أن
+
+12
+00:01:00,860 --> 00:01:05,760
+المتجه العمودي على المنحنى هو المتجه العمودي على
+
+13
+00:01:05,760 --> 00:01:11,330
+المماس لهذا المنحنى، هذا سنعرفه بعد قليل إن شاء الله.
+
+14
+00:01:11,330 --> 00:01:15,650
+تعالوا، يبقى المتجه العمودي على المنحنى هو المتجه
+
+15
+00:01:15,650 --> 00:01:21,450
+العمودي على المماس لهذا المنحنى عند نقطة تقع على هذا
+
+16
+00:01:21,450 --> 00:01:28,890
+المنحنى. سنقسم هذا الـ section إلى نقطتين، النقطة
+
+17
+00:01:28,890 --> 00:01:34,370
+الأولى بناخد curvature of a plane curve، يعني بنحسب
+
+18
+00:01:34,370 --> 00:01:40,590
+الكيرفتشر لمين؟ لمنحنى موجود في مستوى، وبعد ما
+
+19
+00:01:40,590 --> 00:01:46,350
+نخلص بنروح للـ curvature لمين؟ لمنحنى موجود في الـ space
+
+20
+00:01:46,350 --> 00:01:51,390
+اللي هو في الفراغ، يبقى هيكون شغلنا في الحالة
+
+21
+00:01:51,390 --> 00:01:56,020
+الأولى الـ vector اللي بناخده بدلالة i و j فقط، في
+
+22
+00:01:56,020 --> 00:02:00,380
+الحالة الثانية بيكون دلوقتي الـ i والـ j والـ k إن
+
+23
+00:02:00,380 --> 00:02:04,640
+شاء الله تعالى. بدنا نعطي definition للـ curvature و
+
+24
+00:02:04,640 --> 00:02:08,400
+نشوف كيف نستخدم اللي هو الـ curvature في الحالات
+
+25
+00:02:08,400 --> 00:02:15,680
+المختلفة. يبقى بجي بقول: If T is the unit tangent
+
+26
+00:02:15,680 --> 00:02:23,380
+vector, is the unit tangent vector
+
+27
+00:02:26,220 --> 00:02:36,740
+of a smooth curve, of a smooth curve، لمنحنى
+
+28
+00:02:36,740 --> 00:02:47,200
+أملس. The curvature function, the curvature function
+
+29
+00:02:47,200 --> 00:02:55,520
+دالة التقوس أو دالة الانحناء، of the curve of a plane
+
+30
+00:02:58,680 --> 00:03:04,660
+curvature
+
+31
+00:03:04,660 --> 00:03:17,120
+curvature curvature curvature curvature curvature curvature curvature
+
+32
+00:03:17,120 --> 00:03:17,920
+curvature curvature curvature curvature curvature curvature curvature
+
+33
+00:03:32,790 --> 00:03:43,230
+R of T is given in terms of parameter T.
+
+34
+00:03:58,750 --> 00:04:06,470
+parameter اللي هو T, rather
+
+35
+00:04:06,470 --> 00:04:13,270
+than, rather
+
+36
+00:04:13,270 --> 00:04:26,250
+than بدلًا من the arc length S, the arc length اللي
+
+37
+00:04:26,250 --> 00:04:32,990
+هو الـ S. Then the curvature
+
+38
+00:04:32,990 --> 00:04:38,210
+curvature
+
+39
+00:04:38,210 --> 00:04:46,290
+K, curvature
+
+40
+00:04:46,290 --> 00:04:46,390
+curvature K curvature K curvature K curvature K
+
+41
+00:04:46,390 --> 00:04:49,070
+curvature K curvature K curvature K curvature K
+
+42
+00:04:49,070 --> 00:04:56,250
+curvature
+
+43
+00:04:56,250 --> 00:05:11,470
+K، بقدر أقول الـ dT على dS، وهنا dS على dT، هذا
+
+44
+00:05:11,470 --> 00:05:24,230
+الكلام بده يساوي الـ dT على dT، dT على dT، الطول تبعه
+
+45
+00:05:24,230 --> 00:05:32,650
+على مين؟ على طول الـ V، و
+
+46
+00:05:32,650 --> 00:05:39,790
+لحظة بسيطة قبل أن نرجع إلى هذا التعريف.  Since T
+
+47
+00:05:39,790 --> 00:05:45,050
+has a constant
+
+48
+00:05:47,850 --> 00:05:55,190
+لأن طول T يساوي مقدارًا ثابتًا اللي هو واحد صحيح،
+
+49
+00:05:55,190 --> 00:06:06,950
+we have، هيكون هنا اللي هو dT على dS ⋅ T  بيساوي
+
+50
+00:06:06,950 --> 00:06:10,130
+zero, that is
+
+51
+00:06:12,530 --> 00:06:21,890
+الـ dT على dS and T are orthogonal.
+
+52
+00:06:47,900 --> 00:06:52,040
+اللي إحنا كاتبينها مرة ثانية، نقرأ التعريف قراءة جيدة،
+
+53
+00:06:52,040 --> 00:06:57,880
+ونحاول نفهم كل لقطة موجودة فيه. إذا إحنا الآن بنتكلم
+
+54
+00:06:57,880 --> 00:07:02,380
+عن الـ curvature في الـ plane curve، يبقى المنحنى
+
+55
+00:07:02,380 --> 00:07:07,360
+اللي موجود في مستوى. التعريف بيقول: ما لو كان الـ T
+
+56
+00:07:07,360 --> 00:07:11,740
+هو الـ unit tangent vector لـ smooth curve، يبقى الـ
+
+57
+00:07:11,740 --> 00:07:15,280
+curvature تبع الـ plane curve في هذه الحالة، كابا
+
+58
+00:07:15,910 --> 00:07:24,050
+تنطق كالتالي يا بنات: كابا، اللي هي كابا، تنطق
+
+59
+00:07:24,050 --> 00:07:28,910
+بهذا الشكل. يبقى كابا، رمزها كاف اللي عندنا، هذه
+
+60
+00:07:29,230 --> 00:07:33,850
+تساوي طول الـ dT على dS، يعني إيش اللي بدي أحصل؟ بدي
+
+61
+00:07:33,850 --> 00:07:36,930
+أشتقه
+
+62
+00:07:36,930 --> 00:07:42,130
+بالنسبة لـ arc parameter S، وآخد الطول تبعه، بيعطينا
+
+63
+00:07:42,130 --> 00:07:47,290
+الـ curvature اللي هي كابا، يبقى بناء عليه الـ
+
+64
+00:07:47,290 --> 00:07:50,190
+curvature كابا، هذا سكلار ولا فيكتور؟
+
+65
+00:07:52,840 --> 00:07:59,420
+أو dT على dS هو فيكتور، لكن لما ناخد طوله، بيصبح سكلار، إذا هذه كمية قياسية وليست كمية
+
+66
+00:07:59,420 --> 00:08:04,500
+اتجاهية، وقد تكون رقم واحد، قد تكون دالة في متغير
+
+67
+00:08:04,500 --> 00:08:10,640
+مثل T مثلًا. طيب، بقول: لو small curve R of T is
+
+68
+00:08:15,380 --> 00:08:19,140
+given in terms of parameter T
+
+69
+00:08:23,700 --> 00:08:28,840
+لو كانت في الـ parameter T بدلًا من الـ arc length
+
+70
+00:08:28,840 --> 00:08:34,200
+S، يبقى في هذه الحالة الكيرفتشر كابا ستأخذ شكلًا
+
+71
+00:08:34,200 --> 00:08:38,100
+جديدًا، إيش هو هذا الشكل؟ بقول: dT على dS زي ما هي،
+
+72
+00:08:38,100 --> 00:08:43,860
+معرفة الآن S function في T، والـ T كمان function في T،
+
+73
+00:08:43,860 --> 00:08:48,000
+إذا بقدر أقول dT على dS فيها dT على dT
+
+74
+00:08:43,860 --> 00:08:48,000
+إذا بقدر أقول dT/dS × dS/dT
+
+75
+00:08:53,280 --> 00:09:00,740
+بقدر أقول هذه vector ولا scalar؟ dT على dS، dT
+
+76
+00:09:00,740 --> 00:09:07,500
+على dS، dS  vector ولا scalar؟ هذه
+
+77
+00:09:07,500 --> 00:09:11,630
+scalar، هذه ما خلتها vector، هذه الـ vector، يبقى دي
+
+78
+00:09:11,630 --> 00:09:14,510
+تي كتر، هذا الـ unit، تانية بس هذا الـ parameter، وهذا
+
+79
+00:09:14,510 --> 00:09:18,490
+الـ parameter، يبقى هذا ما هو vector، إذا لو عرفنا
+
+80
+00:09:18,490 --> 00:09:22,370
+لو كان هذا vector ما أقدرش أكتب هذه إلا إذا كانت كله
+
+81
+00:09:22,370 --> 00:09:26,610
+ماشي، أبقى قادرة أكتبها، لكن هذه الآن scalar، وهذه هي
+
+82
+00:09:26,610 --> 00:09:30,850
+من هذه الـ vector، إذا dT على dS لو نزلتها
+
+83
+00:09:30,850 --> 00:09:35,810
+كلها ما عاد يصير dS على dT، وببقى اللي فوق اللي
+
+84
+00:09:35,810 --> 00:09:42,420
+هو dT، يعني هذه كأنه طول dT على dT في الـ
+
+85
+00:09:42,420 --> 00:09:48,840
+absolute value، dT على dS يبقى هذا طول وهذا
+
+86
+00:09:48,840 --> 00:09:50,180
+absolute value
+
+87
+00:09:53,810 --> 00:10:00,130
+لأ، هذا طول المتجه dT على dT وهذا هو الـ
+
+88
+00:10:00,130 --> 00:10:05,890
+absolute value، القيمة المطلقة لـ dS على dT، طيب
+
+89
+00:10:05,890 --> 00:10:10,890
+ممتاز، الـ dS على dT أليس هذا طول الـ Velocity V؟
+
+90
+00:10:10,890 --> 00:10:15,770
+يبقى بحط بدل طول الـ Velocity V، إذا من الآن
+
+91
+00:10:15,770 --> 00:10:21,400
+فصاعدًا، من أحد ما يعطي الـ R of T as a function of T،
+
+92
+00:10:21,400 --> 00:10:27,660
+لو فضل مرة بجيب السرعة، آخد المشتقة بيجيب
+
+93
+00:10:27,660 --> 00:10:34,720
+مقدار السرعة اللي هو الـ speed، بقسم السرعة على الـ
+
+94
+00:10:34,720 --> 00:10:39,080
+speed بيعطينا الـ unit tangent vector، لو
+
+95
+00:10:39,080 --> 00:10:45,540
+اشتقته بالنسبة إلى T بيصير الـ dT على dT،
+
+96
+00:10:47,900 --> 00:10:51,660
+أجيب له الطول، وأقسمه على مقدار السرعة، بيعطيني
+
+97
+00:10:51,660 --> 00:10:56,900
+مقدار الـ curvature، وبالتالي ما لزمنا الـ
+
+98
+00:10:56,900 --> 00:11:01,380
+parameter S، ستعت التخلص منه، واكتفيت بالـ parameter
+
+99
+00:11:01,380 --> 00:11:07,040
+T، وهذا أسهل عمليًا كثيرًا من أن أنا أروح
+
+100
+00:11:07,040 --> 00:11:10,800
+أحسبه، الـ R كله، لأ، وبعدين أروح أشتغل، لأ، لأ، لأ.
+
+101
+00:11:10,800 --> 00:11:16,510
+هنا الدالة في R of T بقسمها، مرة ما جبت الـ V، بجيب
+
+102
+00:11:16,510 --> 00:11:21,650
+الطول تبع الـ V، بشتق الـ T بالنسبة لـ T، بقسم 2 على
+
+103
+00:11:21,650 --> 00:11:28,060
+4، بقول حصلت على مين؟ على الـ K،  الـ K هو لنظرة
+
+104
+00:11:28,060 --> 00:11:32,500
+لأن T لديه كونستانت لين، مش هو not vector، يبقى طوله
+
+105
+00:11:32,500 --> 00:11:39,080
+دائمًا واحد صحيح، يبقى طوله واحد صحيح. نحن لدينا T ⋅ T
+
+106
+00:11:39,080 --> 00:11:43,600
+على dS ⋅ T بيبقى يساوي zero، مرت علينا هذه
+
+107
+00:11:43,600 --> 00:11:49,480
+يا بنات قبل دقيقة ولا لسه جديد؟ لأول مرة نشوفها لو
+
+108
+00:11:49,480 --> 00:11:54,460
+كان عندي vector of constant length واشتقيته وعملته
+
+109
+00:12:03,500 --> 00:12:08,200
+إذا في عندي vector of constant length، واشتقيته dot
+
+110
+00:12:08,200 --> 00:12:13,540
+نفسه يبقى هذا بيعطيني قيمة zero، وأثبتنالكم هذه
+
+111
+00:12:13,540 --> 00:12:18,340
+القاعدة، يبقى بناء عليه، مدام T هو vector of
+
+112
+00:12:18,340 --> 00:12:22,400
+constant length، الطول تبعه يساوي واحد صحيح، إذا
+
+113
+00:12:22,400 --> 00:12:27,530
+مشتقته بالنسبة لـ S، dT بده يساوي مين؟ zero، يبقى
+
+114
+00:12:27,530 --> 00:12:32,070
+dT على dS و T الاثنين orthogonal بيكونوا
+
+115
+00:12:32,070 --> 00:12:36,690
+اثنين متعامدين. نعطي مثال توضيحي على الكلام اللي إحنا
+
+116
+00:12:36,690 --> 00:12:48,010
+بنقوله هذا، show them
+
+117
+00:12:48,010 --> 00:12:48,650
+the curvature
+
+118
+00:12:58,940 --> 00:13:07,240
+curvature of a circle
+
+119
+00:13:07,240 --> 00:13:21,960
+with center at the origin, with center at
+
+120
+00:13:21,960 --> 00:13:38,600
+the origin، المركز هو نقطة الأصل، and radius a، هو واحد
+
+121
+00:13:38,600 --> 00:13:39,680
+على a
+
+122
+00:13:55,260 --> 00:14:00,080
+سؤال مرة ثانية، بقول: لو عندنا دائرة، دائرة مركزها
+
+123
+00:14:00,080 --> 00:14:05,400
+نقطة الأصل ونصف قطرها يساوي a، قول تبعه يساوي a؟
+
+124
+00:14:05,400 --> 00:14:10,220
+بدي أثبت أن الـ curvature لهذه الدائرة يساوي قداش؟
+
+125
+00:14:10,220 --> 00:14:14,760
+واحد على a، يعني الـ curvature عند أي نقطة على
+
+126
+00:14:14,760 --> 00:14:19,720
+محيط الدائرة بدها تكون قيمة ثابتة وهو واحد على
+
+127
+00:14:19,720 --> 00:14:25,140
+القيمة العددية له واحد على نصف القطر، يبقى بقول إيش؟ إن
+
+128
+00:14:25,140 --> 00:14:29,520
+الـ curvature لدائرة مركزها نقطة الأصل ونصف قطرها
+
+129
+00:14:29,520 --> 00:14:33,380
+يساوي a، هو عبارة عن واحد، يعني بدنا نثبت أنه
+
+130
+00:14:33,380 --> 00:14:37,880
+كابا تساوي مين؟ واحد على a، بقول: كويس، وقال لي
+
+131
+00:14:37,880 --> 00:14:42,300
+أكثر ما عنديش معلومة أكثر من أنه عندي دائرة مركزها
+
+132
+00:14:42,300 --> 00:14:48,320
+نقطة الأصل ونصف قطرها يساوي a، كيف يعني؟ يعني
+
+133
+00:14:48,320 --> 00:14:54,260
+لو جينا وقلنا هي عندنا دائرة، شكلها هذا، ارسموها هي
+
+134
+00:14:54,260 --> 00:14:59,900
+عندنا، ارسموها بالشكل اللي هنا، تمام؟
+
+135
+00:14:59,900 --> 00:15:05,120
+وقلنا هذا محور x وهذا محور y، وهذه نقطة الأصل اللي
+
+136
+00:15:05,120 --> 00:15:11,280
+هو zero.  من نقطة الأصل إلى أي نقطة على المحيط
+
+137
+00:15:11,280 --> 00:15:18,110
+هذا يعتبر من الـ radius a، نصف القطر. لو افترضنا أن هذه
+
+138
+00:15:18,110 --> 00:15:26,830
+النقطة هي P(x,y)، ورح ننزل من هنا عمود على محور
+
+139
+00:15:26,830 --> 00:15:34,270
+x، بيكون هذا الجزء هو x، وهذا الجزء هو y. لو كانت
+
+140
+00:15:34,270 --> 00:15:38,690
+الزاوية اللي عندنا هذه اللي هي الزاوية ثيتا، إذا الـ
+
+141
+00:15:38,690 --> 00:15:43,710
+x كانت، مش متساويّة يا بنات، x يساوي a cos θ، والـ y
+
+142
+00:15:47,110 --> 00:15:59,510
+يبقى يصير عندنا x = a cos θ، و y = a sin θ، طب
+
+143
+00:15:59,510 --> 00:16:05,690
+لو ربعناهم وجمعناهم، بيعطيني معادلة الدائرة، طبعًا
+
+144
+00:16:05,690 --> 00:16:08,030
+المعادلة دي، مركزها نقطة الأصل، نصف قطرها هي
+
+145
+00:16:08,030 --> 00:16:13,570
+يساوي a، x² + y² = a²
+
+146
+00:16:13,570 --> 00:16:18,150
+مظبوط، طب تعالوا نربع هدول، يبقى x² + y²
+
+147
+00:16:18,150 --> 00:16:23,790
+= a² cos²θ + a² sin²θ
+
+148
+00:16:23,790 --> 00:16:25,390
+sin²θ
+
+149
+00:16:31,480 --> 00:16:38,400
+يبقى هدول بسميهم المعادلات البارامترية لمين؟
+
+150
+00:16:38,400 --> 00:16:44,460
+للـ circle، يبقى هدول الاثنين مع بعض، هذه the
+
+151
+00:16:44,460 --> 00:16:54,260
+parametric equations of the circle.
+
+152
+00:16:56,620 --> 00:17:01,360
+طيب، لو بدأنا نكتب هذا الكلام على صورة unit vector
+
+153
+00:17:01,360 --> 00:17:05,440
+بنكتبها على شكل اللي هو vector valued function،
+
+154
+00:17:05,440 --> 00:17:12,380
+يبقى بروح بقول أن الـ R of θ بدها تساوي a cos θ في
+
+155
+00:17:12,380 --> 00:17:19,020
+اتجاه الـ i زائد، أو a R of θ هنا، أو θ، يبقى a cos θ
+
+156
+00:17:19,020 --> 00:17:25,340
+في اتجاه الـ i زائد a sin θ في اتجاه الـ j. يعني إحنا
+
+157
+00:17:25,640 --> 00:17:30,820
+فلِيه؟ عشان نجيب الـ curvature. إذا بروح أجيب من؟
+
+158
+00:17:30,820 --> 00:17:34,160
+الـ unit tangent لأن هي الـ curvature اللي عندي
+
+159
+00:17:34,160 --> 00:17:40,760
+بلزمني الـ unit tangent وأشتقه على طول الـ V، تمام؟
+
+160
+00:17:40,760 --> 00:17:49,140
+بقول: كويس، يبقى الآن أنا بدي أجيب له V of θ اللي
+
+161
+00:17:49,140 --> 00:17:55,420
+عبارة عن dR على dθ اللي هو ناقص a sin θ في
+
+162
+00:17:55,420 --> 00:18:03,930
+اتجاه i زائد a cos θ في اتجاه j، بالذات لمين؟ هنا طول
+
+163
+00:18:03,930 --> 00:18:09,430
+الـ V، إذا بتروح بتجيب له كده طول الـ V، إذا طول الـ V
+
+164
+00:18:09,430 --> 00:18:15,510
+بده يساوي الـ square root لـ a² sin²θ
+
+165
+00:18:15,510 --> 00:18:21,370
+زائد a² cos²θ، يساوي الجذر التربيعي
+
+166
+00:18:21,370 --> 00:18:31,460
+التربيعي لـ a² في مين؟ في sin²θ +
+
+167
+00:18:31,460 --> 00:18:38,700
+cos²θ، بتنزل، ده واحد، في a²، أبقى يبقى
+
+168
+00:18:38,700 --> 00:18:46,880
+هنا a. طبعًا يبقى... جبت اللي هو طول الـ V اللي هو
+
+169
+00:18:46,880 --> 00:18:50,740
+يساوي قد إيش؟... بقول: مش absolute value لإيش؟ لأن طوله
+
+170
+00:18:50,740 --> 00:18:54,400
+عمره ما كان قيمة سالبة، مظبوط؟  والله بنقول: لو
+
+171
+00:18:54,400 --> 00:18:57,820
+قسنا أي واحدة فيه وقلنا والله طولها هذه سالب متر
+
+172
+00:18:57,820 --> 00:19:02,360
+ونص، لأ، متر ونص على طول، يبقى الطول قيمة موجبة،
+
+173
+00:19:02,360 --> 00:19:09,180
+طبعًا؟ الآن بدنا الـ unit tangent T اللي هو الـ V على
+
+174
+00:19:09,180 --> 00:19:13,690
+طول الـ V، اللي أخذناها آخر نقطة أخذناها المحاضرة
+
+175
+00:19:13,690 --> 00:19:17,430
+الماضية، قلنا الـ Unit Tangent Vector T هو الـ
+
+176
+
+223
+00:25:00,770 --> 00:25:04,650
+principle unit normal is undefined ما هو معرّف
+
+224
+00:25:04,650 --> 00:25:09,190
+إذا ضروري الكيرفتشر ما يكون 0 بالـ principle unit
+
+225
+00:25:09,190 --> 00:25:14,240
+normal vector of S. مؤكد كيرفتشر فيه plane هو واحد على
+
+226
+00:25:14,240 --> 00:25:19,780
+كابة في DT على DS يبقى واحد على كابة scalar وهذا
+
+227
+00:25:19,780 --> 00:25:25,940
+vector. إذا هذا vector زي ما احنا بنقول، طيب اتجاهه
+
+228
+00:25:25,940 --> 00:25:31,760
+وين؟ والاتجاه will point toward يبقى اتجاهه بيكون
+
+229
+00:25:31,760 --> 00:25:37,670
+the concave side of the curve فى اتجاه تقعر المنحنى
+
+230
+00:25:37,670 --> 00:25:43,710
+وليس خارج المنحنى، طلعي المنحنى هنا الـ concave way
+
+231
+00:25:43,710 --> 00:25:50,330
+down. إذا الـ N بده يكون بالشكل هذا، عمودي عليه يبقى
+
+232
+00:25:50,330 --> 00:25:55,370
+هذا الـ N بده يكون عمودي على الـ T اللي هو بده يساوي
+
+233
+00:25:55,370 --> 00:26:05,590
+واحد على كابة، واحد على كابة دي تي على دي إس، طيب لو
+
+234
+00:26:05,590 --> 00:26:12,050
+مشينا ثانية ووصلنا لنقطة ثانية مثل النقطة P2 وروحنا
+
+235
+00:26:12,050 --> 00:26:18,450
+رسمنا الـ unit tangent عند هذه النقطة، فكان الـ unit
+
+236
+00:26:18,450 --> 00:26:23,970
+tangent vector اللي هو T يبقى N بده يكون للداخل
+
+237
+00:26:23,970 --> 00:26:29,160
+الشكل اللي عندنا هذا، يبقى هذا N اللي هو بده يساوي
+
+238
+00:26:29,160 --> 00:26:36,980
+واحد على كابة في DT على DS، يبقى دائما اتجاهه
+
+239
+00:26:36,980 --> 00:26:43,420
+وين؟ للداخل، عمودي على الـ curve و عمودي على الـ unit
+
+240
+00:26:43,420 --> 00:26:48,460
+tangent، أن ده نقطة التماس، اتجاهه دائما هو قبل اللي
+
+241
+00:26:48,460 --> 00:26:54,720
+وين؟ للداخل، لاتجاه تقعر مين؟ المنحنى هذا بالنسبة
+
+242
+00:26:54,720 --> 00:27:00,000
+لمين؟ للـ unit normal vector، لكن لاحظوا أن الـ unit
+
+243
+00:27:00,000 --> 00:27:04,690
+normal vector احنا كاتبينه بدلالة ال curvature و
+
+244
+00:27:04,690 --> 00:27:10,430
+كتبناه بدلالة DT على مين؟ DS، توقفني شوية الـ
+
+245
+00:27:10,430 --> 00:27:14,810
+curvature، بطلنا نكتبها بدلالة الـ S، كتبناها كلها
+
+246
+00:27:14,810 --> 00:27:20,210
+بدلالة مين؟ بدلالة الـ T، يبقى الآن بدنا نروح بنفس
+
+247
+00:27:20,210 --> 00:27:25,450
+الطريقة نكتب الـ curvature بدلالة الـ T parameter
+
+248
+00:27:25,450 --> 00:27:31,010
+وليس بدلالة الـ S parameter، تمام؟ يبقى من أروح نكتب
+
+249
+00:27:31,010 --> 00:27:36,370
+هذا الكلام على صورة الـ remark التالية، يبقى remark
+
+250
+00:27:36,370 --> 00:27:58,050
+يبقى
+
+251
+00:27:58,050 --> 00:27:58,310
+remark يبقى remark يبقى remark يبقى remark يبقى
+
+252
+00:27:58,310 --> 00:28:04,740
+remark يبقى remark، يبقى finding بدون ما نوجد الـ
+
+253
+00:28:04,740 --> 00:28:14,740
+curvature kappa and الـ S، طبعا زي ما شايفين الـ
+
+254
+00:28:14,740 --> 00:28:19,100
+normal يعتمد على kappa وعلى الـ S، يبقى أنا
+
+255
+00:28:19,100 --> 00:28:21,720
+بده أجيب الـ principle normal بدون ما أجيب الـ
+
+256
+00:28:21,720 --> 00:28:25,220
+curvature ولا أجيب الـ arc parameter length اللي هو
+
+257
+00:28:25,220 --> 00:28:28,940
+الـ S، كيف؟ كالتالي، as follows
+
+258
+00:28:36,570 --> 00:28:43,110
+بساوي واحد على الـ curvature كابة في الـ DT على DS
+
+259
+00:28:43,110 --> 00:28:48,030
+ويمسك هذا
+
+260
+00:28:48,030 --> 00:28:56,750
+بقدر أقول DT على DS، الكابة اللي هي طول
+
+261
+00:28:56,750 --> 00:29:03,710
+الـ DT على DS، طبعا
+
+262
+00:29:03,710 --> 00:29:05,790
+بقدر أقول هذا الكلام
+
+263
+00:29:09,160 --> 00:29:17,840
+على DT في DT على DS، على طول
+
+264
+00:29:17,840 --> 00:29:25,060
+الـ DT على DT في DT على DS
+
+265
+00:29:53,660 --> 00:29:59,780
+الـ Dt على Ds اتفقنا أنها scalar، طيب المرة الماضية
+
+266
+00:29:59,780 --> 00:30:04,680
+الـ Dt على Ds أقل من الـ Zero ولا أكبر من الـ Zero؟
+
+267
+00:30:04,680 --> 00:30:10,320
+أكبر من الـ Zero، أكبر من الـ Zero، يبقى Ds على Dt
+
+268
+00:30:10,320 --> 00:30:17,520
+هي طول الـ V، وطول موجة مظبوط، يبقى قيمة الموجة بلو
+
+269
+00:30:17,520 --> 00:30:21,360
+قلبتها بسيستراليب، والله بظلها موجة، بقى بظلها موجة
+
+270
+00:30:21,360 --> 00:30:27,890
+بقى ممتاز جدا، إذا أنا لما أجي أقول هذا الكلام دي تي
+
+271
+00:30:27,890 --> 00:30:37,230
+على دي تي في دي تي على دي إس، وهذا طول
+
+272
+00:30:37,230 --> 00:30:46,010
+ال دي تي على دي تي في دي تيعلى DS، إذا نقلت طولته
+
+273
+00:30:46,010 --> 00:30:50,310
+أو الـ absolute value لها، الـ absolute value، والله
+
+274
+00:30:50,310 --> 00:30:55,350
+مش الـ absolute، إثنتين هذول إثنتين موجبتين جات بعض
+
+275
+00:30:55,350 --> 00:31:01,950
+تماما، يبقى بنقدر نختصرهم ونقول المسألة إلى أن الـ
+
+276
+00:31:01,950 --> 00:31:09,690
+principal unit normal N من الآن صاعدا هو Dt على Dt
+
+277
+00:31:09,690 --> 00:31:18,590
+مقسوما على طول Dt على Dt، بالشكل اللي عندنا واضح أن
+
+278
+00:31:18,590 --> 00:31:22,450
+الـ principal unit normal هذه لا فيها curvature ولا
+
+279
+00:31:22,450 --> 00:31:28,330
+فيها S زي ما احنا ادعينا قبل قليل
+
+280
+00:31:30,200 --> 00:31:36,020
+يبقى بناء عليه لا الكيرفتشر ولا الـ principle
+
+281
+00:31:36,020 --> 00:31:40,560
+normal  بكتب بدلالة الـ S، بسيطة، بكتب بدلالة الـ T أسهل
+
+282
+00:31:40,560 --> 00:31:47,000
+زي ما أنتم شايفين، ناخد مثال توضيحي على ذلك، example
+
+283
+00:31:47,000 --> 00:31:52,720
+will
+
+284
+00:31:52,720 --> 00:32:02,330
+find الـ T والـ principle normal vector N and
+
+285
+00:32:02,330 --> 00:32:05,590
+الكيروفتشر كابة
+
+286
+00:32:05,590 --> 00:32:19,390
+for the أبلاين كيرف للمنحنى اللي هو R of T يساوي  
+
+287
+00:32:19,390 --> 00:32:26,350
+سيك T كله في اتجاه الـ I زائد T في اتجاه الـ J
+
+288
+00:32:26,350 --> 00:32:33,450
+والـ T هذه محصورة بين سالب باي على اتنين وبين باي
+
+289
+00:32:33,450 --> 00:32:34,150
+على اتنين
+
+290
+00:32:39,420 --> 00:32:47,940
+مرة ثانية، قال هاتلي unit tangent vector، ثلاثة
+
+291
+00:32:47,940 --> 00:32:52,580
+هاتلي الكيرفتشر كابة للمنحنى اللي عندنا هذا، وحطني
+
+292
+00:32:52,580 --> 00:32:58,060
+على interval من سالب باي على اتنين لغاية باي على اتنين
+
+293
+00:32:58,060 --> 00:33:01,280
+لأن يا بنات عند الـ باي على اتنين والـ سالب باي على اتنين
+
+294
+00:33:01,280 --> 00:33:08,320
+الـ secant is undefined ومن هنا ما حطيناش يساوي، تمام؟
+
+295
+00:33:08,320 --> 00:33:12,100
+من حالة السيكانت اللي أخذته في الكلكلس 2 و
+
+296
+00:33:12,100 --> 00:33:15,840
+section في أول chapter كانت الـ trigonometric
+
+297
+00:33:15,840 --> 00:33:20,260
+functions، تمام؟ لما رسمت السيكانت كانت عند الـ
+
+298
+00:33:20,260 --> 00:33:24,720
+باي على اتنين وسالب باي على اتنين is undefined، يبقى من هنا
+
+299
+00:33:24,720 --> 00:33:29,180
+ما حطيناش يساوي، ما علينا هذه بس معلومة هامشية جانبية
+
+300
+00:33:29,780 --> 00:33:34,860
+يبقى الآن نجيب الـ unit tangent vector T، T هي عبارة
+
+301
+00:33:34,860 --> 00:33:40,480
+عن مين؟ الـ V على طول الـ V، مظبوط، يبقى على هذا
+
+302
+00:33:40,480 --> 00:33:46,840
+الكلام بدي أجيب له مين؟ ك الـ V في الأول، يبقى الـ V
+
+303
+00:33:46,840 --> 00:33:54,820
+اللي هي DR على DT، يساوي تفضل ان تسكب جدا شباب
+
+304
+00:33:55,390 --> 00:34:03,090
+واخد sec T في مشتقة الـ sec اللي هي sec T tan T في
+
+305
+00:34:03,090 --> 00:34:09,810
+اتجاه الـ I زائد مشتقة الـ T بواحد في اتجاه الـ J
+
+306
+00:34:09,810 --> 00:34:18,050
+يبقى أصبحت الـ DR على DT تساوي sec مع sec يبقى tan T في اتجاه
+
+307
+00:34:18,050 --> 00:34:24,640
+الـ I زائد J، يبقى هذا الـ velocity عند أي لحظة أو
+
+308
+00:34:24,640 --> 00:34:30,020
+متجه السرعة، بدي أحسب قد إيش طول متجه السرعة، يبقى هذا
+
+309
+00:34:30,020 --> 00:34:37,450
+بدي يعطينا طول الـ V بده يساوي الجذر التربيعي ل tan
+
+310
+00:34:37,450 --> 00:34:44,670
+تربيع T زائد واحد، اللي هو كده؟ sec تربيع من حساب
+
+311
+00:34:44,670 --> 00:34:52,490
+المثلثات، والـ sec تربيع تطلع من تحت الجذر بـ sec T والله
+
+312
+00:34:52,490 --> 00:34:59,610
+absolute value ل sec T، لا هي بنقول absolute value
+
+313
+00:34:59,610 --> 00:35:05,850
+لسك T، مظبوط؟ يعني كده شهر قيمة المحطة بسؤال لما
+
+314
+00:35:05,850 --> 00:35:08,890
+أقول من سالب باي على اتنين ل باي على اتنين، يعني إيه؟
+
+315
+00:35:08,890 --> 00:35:15,030
+الربع، يبقى نفعليه؟ من سالب باي على اتنين لـ باي
+
+316
+00:35:15,030 --> 00:35:20,070
+على اتنين يبقى إيه؟ الربع الرابع والربع
+
+317
+00:35:20,070 --> 00:35:25,760
+الأول، من سالب باي على اتنين لباي على اتنين، مظبوط؟ يبقى
+
+318
+00:35:25,760 --> 00:35:30,820
+الربع الرابع ثم الربع الأول، طب الـ sec و الـ cosine
+
+319
+00:35:30,820 --> 00:35:35,240
+في الربع الأول والرابع موجبة، موجبة، يبقى حطيت الـ
+
+320
+00:35:35,240 --> 00:35:39,780
+absolute value وأنا شيلتها، كلها بالموجبة يعني
+
+321
+00:35:39,780 --> 00:35:43,880
+زيادة كلك، على ما حطيتها، تمام، السيك موجب في الربع
+
+322
+00:35:43,880 --> 00:35:47,100
+الرابع والأول، وكذلك الـ cosine، يبقى لا
+
+323
+00:35:47,100 --> 00:35:52,490
+داعي لكتابة الـ absolute value، تمام؟ لأن الـ sec
+
+324
+00:35:52,490 --> 00:35:56,830
+موجب في الربع الأول والرابع، طيب حسب domain
+
+325
+00:35:56,830 --> 00:36:02,250
+طول الـ V، إذا بده المطلوب الأول الـ unit tangent V
+
+326
+00:36:02,250 --> 00:36:11,510
+هو V على طول الـ V، وين الـ V؟ هاي الـ V اللي هي tan
+
+327
+00:36:11,510 --> 00:36:23,100
+T في اتجاه الـ I زائد J كله على sec T
+
+328
+00:36:23,100 --> 00:36:28,870
+ويساوي ثانية يا بنات اللي هي عبارة عن مين؟ sin على
+
+329
+00:36:28,870 --> 00:36:35,190
+cos، و sec مقلوب الـ cos، يبقى بضربها ب دي بس قد إيش sin
+
+330
+00:36:35,190 --> 00:36:41,210
+واحدة يبقى بيصير الـ sin T في اتجاه الـ I زائد
+
+331
+00:36:41,210 --> 00:36:50,390
+واحد على sec، cos يبقى هذا cos T في اتجاه الـ J، يبقى
+
+332
+00:36:50,390 --> 00:36:55,470
+أصبح المطلوب الأول الـ unit tangent vector T هو
+
+333
+00:36:55,470 --> 00:37:01,890
+sin T في اتجاه I زائد cos T في اتجاه الـ J، هذا
+
+334
+00:37:01,890 --> 00:37:08,610
+هو الـ unit tangent vector T، نقلب بعدين للبنية الـ
+
+335
+00:37:08,610 --> 00:37:13,990
+principle unit normal، و فوق يبقى بنروح نشتقه
+
+336
+00:37:13,990 --> 00:37:21,120
+بالنسبة إلى T، وأقسم على طوله، يبقى بدي أجي آخد الـ
+
+337
+00:37:21,120 --> 00:37:27,280
+DT على DT، بدي أشتق هذه الدالة بالنسبة إلى T، فبيضل الـ
+
+338
+00:37:27,280 --> 00:37:33,160
+sin ب cos T في اتجاه الـ I ناقص sin T في اتجاه
+
+339
+00:37:33,160 --> 00:37:40,170
+الـ J، بدي أجيب الطول تبعه، يبقى طول تبع الـ Dt على Dt
+
+340
+00:37:40,170 --> 00:37:46,150
+بدي أسوي الـ square root لـ cos تربيع T زائد sin
+
+341
+00:37:46,150 --> 00:37:52,170
+تربيع T، اللي هو بقدرش كمان؟ واحد صحيح، يبقى بناء
+
+342
+00:37:52,170 --> 00:37:58,670
+على ذلك، الـ principle normal N بدي أجي هنا وأقسمه على
+
+343
+00:37:58,670 --> 00:38:03,790
+طوله، يعني بدي أقسمه على قد إيش بتغير؟ لأ، يبقى هذا
+
+344
+00:38:03,790 --> 00:38:09,970
+بيصير cos T في اتجاه الـ I ناقص sin T في اتجاه
+
+345
+00:38:09,970 --> 00:38:16,350
+الـ J، مقسوما على واحد صحيح، بظل هو نفسه، يبقى هذا الـ
+
+346
+00:38:16,350 --> 00:38:21,550
+principle unit normal vector، بعدين قال ليش؟ بدي
+
+347
+00:38:21,550 --> 00:38:29,770
+أجيب للـ curvature كابة، الكيرفتشر قد إيش تساوي؟ طول
+
+348
+00:38:29,770 --> 00:38:37,170
+الـ V، طول الـ V، طول الـ V، طول الـ V، طول الـ V، طول الـ V
+
+349
+00:38:37,170 --> 00:38:39,750
+طول الـ V، طول الـ V، طول الـ V، طول الـ V، طول الـ V، طول
+
+350
+00:38:39,750 --> 00:38:43,010
+الـ V، طول الـ V، طول الـ V، طول الـ V، طول الـ V، طول الـ V
+
+351
+00:38:43,010 --> 00:38:44,890
+طول الـ V، طول الـ V، طول الـ V، طول الـ V، طول الـ V، طول الـ V
+
+352
+00:38:44,890 --> 00:38:45,790
+طول الـ V، طول الـ V، طول الـ V، طول الـ V، طول الـ V، طول الـ V
+
+353
+00:38:45,790 --> 00:38:47,490
+طول الـ V، طول الـ V، طول الـ V، طول الـ V، طول الـ V، طول الـ V
+
+354
+00:38:47,490 --> 00:38:47,550
+طول الـ V، طول الـ V، طول الـ V، طول الـ V، طول الـ V، طول الـ V
+
+355
+00:38:47,550 --> 00:38:54,070
+طول الـ V، طول الـ V، طول، بدي الكيرفتشر كابة اللي هو
+
+356
+00:38:54,070 --> 00:39:00,410
+واحد على طول الـ V بالفعل، يبقى هذه اللي هي قد إيش
+
+357
+00:39:00,410 --> 00:39:06,430
+تساوي اللي هو، أو نكتبها لكم بالتفصيل، وبعدين بنعوض
+
+358
+00:39:06,430 --> 00:39:15,010
+فيها، يبقى الكيرفتشر كابة كانت اللي هو قد إيش؟ طول
+
+359
+00:39:15,010 --> 00:39:18,770
+الـ V في المقام، وفوق... كان إيه يا شباب أنا بتحدثكم
+
+360
+00:39:18,770 --> 00:39:28,350
+كتير؟ DT على DT، طوله تبعه، يبقى DT على DT، الطول تبعه
+
+361
+00:39:28,350 --> 00:39:33,030
+بهذا الشكل، الطول تبعه طلعناه، قد إيش؟ بواحد، يبقى
+
+362
+00:39:33,030 --> 00:39:38,450
+بدي نسبة واحد على طول الـ V، وطول الـ V طلعناه قد إيش؟ sec T
+
+363
+00:39:38,450 --> 00:39:46,190
+يبقى sec T هذا، بدي أعطيكم إنه كيرفتشر كابة
+
+364
+00:40:18,020 --> 00:40:23,040
+بنجي للنقطة الثالثة في هذا الـ section، حاجة اسمها
+
+365
+00:40:23,040 --> 00:40:31,630
+دائرة الانحناء The circle of curvature، أفرض أنا عندي
+
+366
+00:40:31,630 --> 00:40:38,110
+منحنى ما، وعند نقطة ما على هذا المنحنى بدي أحسب
+
+367
+00:40:38,110 --> 00:40:43,070
+the circle of curvature، دائرة التكور أو دائرة
+
+368
+00:40:43,070 --> 00:40:48,990
+الانحناءات، بدي الـ center of curvature، مركز الانحناءات
+
+369
+00:40:48,990 --> 00:40:54,490
+بدي الـ radius of curvature، نصف قطر الانحناءات
+
+370
+00:40:57,500 --> 00:41:05,060
+هذا كله نصف قطر انحناء، مركز الانحناء هو نصف قطر
+
+371
+00:41:05,060 --> 00:41:11,100
+دائرة الانحناء وهي مركز دائرة الانحناء، طب لو
+
+372
+00:41:11,100 --> 00:41:17,460
+رسمناها على منحنى، بتكون جهة الداخل ولا جهة الخارج؟
+
+373
+00:41:17,890 --> 00:41:24,430
+جهة الداخل، بتكون بتمس المنحنى عند النقطة اللي
+
+374
+00:41:24,430 --> 00:41:28,990
+بنحسب عليها الـ circle of curvature، يبقى الـ radius
+
+375
+00:41:28,990 --> 00:41:33,950
+of curvature يا بنات هي دائرة في نفس المستوى تبع
+
+376
+00:41:33,950 --> 00:41:40,210
+المنحنى، بتمسه عند نقطة، يعني الـ unit tangent
+
+377
+00:41:40,210 --> 00:41:45,990
+بيكون هو tangent للدائرة وللمنحنى في نفس الوقت
+
+378
+00:41:46,310 --> 00:41:50,990
+الـ Radius تبعها هو نفس الـ Radius تبع الكيرفتشر
+
+379
+00:41:50,990 --> 00:41:55,350
+الـ Center تبعها هو الـ Center تبع الكيرفتشر
+
+380
+00:41:55,350 --> 00:42:00,530
+التقوس بيكون، أو الدائرة بتكون لوين؟ للداخل، يبقى
+
+381
+00:42:00,530 --> 00:42:05,870
+بدنا نعطي تعريف لها أو نرسمها لأي منحنى موجود
+
+382
+00:42:05,870 --> 00:42:07,970
+عندنا، على سبيل المثال
+
+383
+00:42:16,090 --> 00:42:28,070
+الـ Circle of curvature for a plane curve
+
+384
+00:42:28,070 --> 00:42:36,810
+Definition،
+
+385
+00:42:36,810 --> 00:42:42,550
+أعطيها التعريف التالي، The circle of curvature
+
+386
+00:42:44,010 --> 00:42:53,330
+circle of curvature، بعض الكتب يا بنات بتسميها الـ
+
+387
+00:42:53,330 --> 00:43:03,050
+oscillating circle، oscillating
+
+388
+00:43:03,050 --> 00:43:08,050
+circle أو الـ circle of curvature، الاثنين نفس القصة
+
+389
+00:43:08,050 --> 00:43:22,210
+at a point P on a plane curve، on a plane curve
+
+390
+00:43:22,210 --> 00:43:35,630
+لمنحنى حيث الكيرفتشر لا تساوي صفر، where the curvature is not equal to zero
+
+445
+00:50:29,960 --> 00:50:36,800
+عندنا هذا، هكذا بدي يكون لو رسمت مماس الشكل اللي
+
+446
+00:50:36,800 --> 00:50:42,190
+عندنا هذا، بدي يكون هذا الـ unit tangent vector يبقى
+
+447
+00:50:42,190 --> 00:50:48,510
+ثانياً، الـ vector مماس للمنحنى و للدائرة في نقطة واحدة
+
+448
+00:50:48,510 --> 00:50:52,290
+فهذا معنى النقطة الأولى، النقطة الثانية are the
+
+449
+00:50:52,290 --> 00:50:57,170
+same curvature، لو حسبت الـ curvature للمنحنى والـ
+
+450
+00:50:57,170 --> 00:51:02,910
+curvature للدائرة، الإثنين are the same، طيب بنقدر
+
+451
+00:51:02,910 --> 00:51:09,470
+نعرف قديش الـ curvature للدائرة، يعني قديش عددياً
+
+452
+00:51:11,690 --> 00:51:17,610
+واحد على الـ radius،  تواطنها ميفان الدائرة الـ
+
+453
+00:51:17,610 --> 00:51:21,250
+curvature تبعها يساوي المقابل، نسبة واحد على نصف قطر
+
+454
+00:51:21,250 --> 00:51:30,330
+هذه الدائرة مماس جداً، يبقى لو عرفنا الدائرة وعرفنا نص
+
+455
+00:51:30,330 --> 00:51:35,790
+القطر تبعها، بنعرف قديش الـ curvature للمنحنى
+
+456
+00:51:35,790 --> 00:51:40,130
+بقول واحد على نصف القطر تبع الدائرة، دائرة الانحناءات
+
+457
+00:51:40,510 --> 00:51:46,230
+تمام، تمام، نمرة ثلاثة، تقع في الجزء الداخلي للمنحنى
+
+458
+00:51:46,230 --> 00:51:51,070
+وليس في الجزء الخارجي، لأنه لو رسمناها هنا بتجي برا
+
+459
+00:51:51,070 --> 00:51:56,430
+يبقى هي للداخل، طيب نجي للـ definition الثاني، قال
+
+460
+00:51:56,430 --> 00:52:04,950
+نصف قطر الانحناء للمنحنى عند النقطة B هو نصف قطره
+
+461
+00:52:04,950 --> 00:52:11,610
+يساوي عملياً واحد على الكيرفتشر، نص القطر يبقى هذا
+
+462
+00:52:11,610 --> 00:52:20,410
+نصف القطر هذا اللي هو نصف القطر يبقى
+
+463
+00:52:20,410 --> 00:52:33,430
+بنات هذا اسمه الـ radius of curvature، وهذه اسمها الـ
+
+464
+00:52:33,430 --> 00:52:42,130
+circle of curvature، هاي أبو هذا، مركز الدائرة الـ
+
+465
+00:52:42,130 --> 00:52:53,190
+center of curvature، يبقى هذا اسمه الـ center of
+
+466
+00:52:53,190 --> 00:52:55,250
+curvature
+
+467
+00:53:01,320 --> 00:53:07,580
+طلعت نصف قطر الانحناء، ونصف قطر دائرة الانحناء، و
+
+468
+00:53:07,580 --> 00:53:13,100
+يساوي عملياً رو، تساوي واحد على كابا، يبقى هذا الـ
+
+469
+00:53:13,100 --> 00:53:19,640
+radius اللي هو رو، تساوي واحد على كابا اللي هو
+
+470
+00:53:19,640 --> 00:53:27,650
+radius of curvature عند النقطة
+
+471
+00:53:27,650 --> 00:53:33,800
+B، هو الـ center تبع دائرة الكيرفتشر، يبقى الآن
+
+472
+00:53:33,800 --> 00:53:38,900
+فهمنا معنى الـ circle of curvature، عاملية السؤال
+
+473
+00:53:38,900 --> 00:53:44,020
+هو بتقدر تحسب الـ radius of curvature، و الـ center of
+
+474
+00:53:44,020 --> 00:53:48,620
+curvature، و الـ equation تبع الـ circle of curvature
+
+475
+00:53:48,620 --> 00:53:55,760
+أم لا، هذا السؤال الذي سنجيب عليه بمثال عددي، عشان
+
+476
+00:53:55,760 --> 00:53:59,980
+نعرف كيف نشتغل هذا الشغل، نبقى example
+
+477
+00:54:05,960 --> 00:54:13,780
+يقول لي find and graph، يوجد، وارسم، find and graph
+
+478
+00:54:13,780 --> 00:54:25,060
+مين؟ قال لي ده oscillating circle of
+
+479
+00:54:25,060 --> 00:54:28,360
+the
+
+480
+00:54:28,360 --> 00:54:32,320
+curve
+
+481
+00:54:32,320 --> 00:54:42,670
+للمنحنى R of T تساوي T في اتجاه I، زائد Sine T في
+
+482
+00:54:42,670 --> 00:54:49,730
+اتجاه J، في اتجاه G التي تساوي Pi على M
+
+483
+00:55:06,690 --> 00:55:10,410
+المنحنى، لأننا لا نعرف شكله، لماذا لا نعرف شكله؟
+
+484
+00:55:10,410 --> 00:55:14,930
+معطى في الصيغة البارامترية، لكن لو حولته لصيغة
+
+485
+00:55:14,930 --> 00:55:20,410
+كارتيزية، يصبح المنحنى معروف بالنسبة لنا، وربما
+
+486
+00:55:20,410 --> 00:55:26,950
+يكون أسهل مما نتصور، يبقى R of T باعتبار X of T في
+
+487
+00:55:26,950 --> 00:55:33,710
+اتجاه I، زي Y of T في اتجاه J، صح ولا لأ؟ يبقى كأن X
+
+488
+00:55:33,710 --> 00:55:40,370
+هنا في، سوء المين،  الـ y تساوي سين الـ t، هذا بدي
+
+489
+00:55:40,370 --> 00:55:45,950
+أعطيك مين، إن الـ y قد إتش، سببنا سين الـ x، هذا
+
+490
+00:55:45,950 --> 00:55:50,270
+المنحنى معروف ولا لا؟ يبقى المنحنى اللي عندنا منحنى
+
+491
+00:55:50,270 --> 00:55:56,130
+الجيب، يبقى كويس، عرفنا على شكل المنحنى اللي بنقدر
+
+492
+00:55:56,130 --> 00:56:03,530
+نرسمه الآن، صار بالنسبة لنا سهل، طيب كويس، بعد ذلك قال
+
+493
+00:56:03,530 --> 00:56:08,570
+لي، فاهم، واقرأ في الـ circulating circle للمنحنى
+
+494
+00:56:08,570 --> 00:56:13,910
+اللي عندنا، بدك ترسمها وتوجدها، كذلك لما يقول لي
+
+495
+00:56:13,910 --> 00:56:19,210
+وجدها، يعني بدك توجد معادلتها، إذا أنا مش هتوجد هذه
+
+496
+00:56:19,210 --> 00:56:22,330
+المعادلة بالزمن، نصف القطر
+
+497
+00:56:26,700 --> 00:56:32,460
+هل المركز هو نقطة الاصل؟ ماهو  نقطة الاصل؟ الأخرى
+
+498
+00:56:32,460 --> 00:56:39,520
+هذا كله كلام، بيقولوا
+
+499
+00:56:39,520 --> 00:56:45,340
+الله، كويس، يبقى أنا بدي إيش؟ بدي معادلة الدائرة، و
+
+500
+00:56:45,340 --> 00:56:50,680
+بدي مركز هذه الدائرة، وإذا عرفت المركز والمعادلة
+
+501
+00:56:50,680 --> 00:56:55,120
+بكون عرفتها، ده جالي fine، وبالتالي بيصير سهل رسمها،
+
+502
+00:56:55,120 --> 00:57:02,900
+مظبوط؟ تمام، تمام، طيب بدنا نروح نحسب كل الشغلات
+
+503
+00:57:02,900 --> 00:57:08,280
+اللي بتلزمني، مشان نعرف هذه المعادلة، أنا عندي R of T
+
+504
+00:57:08,280 --> 00:57:14,600
+لو اشتقيتها، بحصل على مين؟ على V، يبقى باجي بقوله V
+
+505
+00:57:14,600 --> 00:57:22,020
+تساوي DR على DT، اللي هي I، زائد cosine T في اتجاه
+
+506
+00:57:22,020 --> 00:57:29,380
+الـ J، نحسب طول الـ V، اللي هو الجذر التربيعي لواحد
+
+507
+00:57:29,380 --> 00:57:36,880
+زائد cosine تربيع T، بقدر ألعب فيها أكثر من ذلك، ولا
+
+508
+00:57:36,880 --> 00:57:42,520
+حاجة، تمام، يبقى زي ما هو، يبقى هذا طول الـ V، بقدر
+
+509
+00:57:42,520 --> 00:57:48,180
+أجيب الـ unit tangent T، يبقى unit tangent T اللي هو
+
+510
+00:57:48,180 --> 00:57:52,380
+V على طول الـ V، يبقى بيصير واحد
+
+511
+00:57:55,740 --> 00:58:01,840
+زائد cosine تربيع T في اتجاه I، زائد cosine T على
+
+512
+00:58:01,840 --> 00:58:06,720
+الجذر التربيعي لواحد زائد cosine تربيع T في اتجاه
+
+513
+00:58:06,720 --> 00:58:13,260
+J، أو إن شئتم فقولوا T يساوي واحد زائد cosine
+
+514
+00:58:13,260 --> 00:58:22,220
+تربيع T، أس سالب نصف في اتجاه I، زائد cosine T في واحد
+
+515
+00:58:22,220 --> 00:58:29,180
+زائد cosine تربيع T أس سالب نصف في اتجاه مين؟ في
+
+516
+00:58:29,180 --> 00:58:34,540
+اتجاه الـ J، يبقى أنا جبت الـ unit tangent vector
+
+517
+00:58:34,540 --> 00:58:41,160
+اللي عندنا هنا الآن، بقدر أشتقه، وقبل أشتقه، من هنا
+
+518
+00:58:41,160 --> 00:58:47,830
+بنات، لو قال لي V عند Pi على اثنين، يبقى الـ V عند
+
+519
+00:58:47,830 --> 00:58:53,510
+الـ باي على اثنين، الطول تبعها، يبقى بده يساوي الجذر
+
+520
+00:58:53,510 --> 00:59:00,270
+التربيعي لواحد زائد قديش cos باي على اثنين، صفر
+
+521
+00:59:00,270 --> 00:59:10,930
+يبقى الجواب يساوي واحد، صحيح، طيب بدي أجيب له الآن الـ
+
+522
+00:59:10,930 --> 00:59:13,370
+DT على DT
+
+523
+00:59:16,240 --> 00:59:24,240
+يبقى الأس في القوس مرفوع
+
+524
+00:59:24,240 --> 00:59:29,200
+للأس نفسه مطروح منه واحد، في سالب ثلاثة على اثنين
+
+525
+00:59:29,200 --> 00:59:37,500
+في مشتقة مدخل القوس، اللي هو اثنين cosine t في
+
+526
+00:59:37,500 --> 00:59:43,280
+سالب sine t، كل هذا في اتجاه الـ I
+
+527
+00:59:46,260 --> 00:59:51,740
+مرة ثانية، بدي أمسحها وأعيدها ثاني، عشان أخلص سطر
+
+528
+00:59:51,740 --> 01:00:01,900
+ساعة المشتقة كلها، أترك هذا لحد هنا، وبدا أقول DT
+
+529
+01:00:01,900 --> 01:00:10,940
+على DT، يساوي اللي هو سالب نصف في اللي هو واحد زائد
+
+530
+01:00:10,940 --> 01:00:13,060
+cosine تربيع الـ T
+
+531
+01:00:18,670 --> 01:00:24,610
+سالب اثنين cosine T في sine T، كله في اتجاه الـ I
+
+532
+01:00:24,610 --> 01:00:33,630
+اللي بعده زائد هذا، مشتقة حاصل ضرب دالتين، يبقى
+
+533
+01:00:33,630 --> 01:00:40,110
+مشتقة الأولى بسالب sine، يبقى هذا بيصير  مضروب هذا زائد
+
+534
+01:00:40,110 --> 01:00:47,450
+وخليه جوا كله، يبقى هاي سالب sine T في الجذر واحد
+
+535
+01:00:47,680 --> 01:00:55,200
+زائد cosine تربيع T، أس سالب نصف، زائد يبقى مشتقة
+
+536
+01:00:55,200 --> 01:01:00,860
+الأولى في الثانية، اللي بعدها، بده أشتق هذه، مشتقة
+
+537
+01:01:00,860 --> 01:01:10,460
+هذه هي صح، يبقى هذا الكلام بده يصير، سالب نصف في
+
+538
+01:01:10,460 --> 01:01:17,500
+cosine T في واحد زائد cosine تربيع T، أس سالب ثلاثة
+
+539
+01:01:20,060 --> 01:01:29,940
+في سالب اثنين cosine T في sine T، كل هذا في اتجاه مين؟
+
+540
+01:01:29,940 --> 01:01:36,280
+في اتجاه الـ J، مش واضحة، أظن كبرها شوية ونوضحها
+
+541
+01:01:36,280 --> 01:01:39,400
+يبقى
+
+542
+01:01:39,400 --> 01:01:49,820
+هذا كله مضروب في سالب اثنين cosine T في sine T، وهي
+
+543
+01:01:49,820 --> 01:01:57,500
+قفلنا الجذر، هذا كله كبير، في اتجاه من؟ في اتجاه
+
+544
+01:01:57,500 --> 01:02:00,560
+الـ J
+
+545
+01:02:00,560 --> 01:02:06,420
+يبقى إن أجيبنا دي تي على دي تي، بدي احسب له قديش الـ
+
+546
+01:02:06,420 --> 01:02:12,020
+دي تي على دي تي، أسهل، ما بديش أقعد أجمع وأضيع
+
+547
+01:02:12,020 --> 01:02:16,520
+أكثر، اللي أنا بدي أعوض دغري، طلع يا بنات هنا، هذه باي
+
+548
+01:02:16,520 --> 01:02:21,560
+على اثنين، قديش cos باي على اثنين، صفر، بظل واحد لأي أس يبقى واحد
+
+549
+01:02:21,560 --> 01:02:26,840
+في نص، يبقى هذا ناقص نصف، وهذا قديش cos باي على اثنين، صفر، لأنه صار
+
+550
+01:02:26,840 --> 01:02:30,540
+باي على اثنين، وواحد في نصف، يبقى هذا كله صار بصفر
+
+551
+01:02:30,540 --> 01:02:37,850
+في اتجاه الـ I، نجي للي بعدها، هذه باي على اثنين، نرجع
+
+552
+01:02:37,850 --> 01:02:42,690
+لسؤالنا مرة ثانية، لما تبقى الاشتقاقات كبيرة زي
+
+553
+01:02:42,690 --> 01:02:46,090
+هيك مش سواء،  أتجمع فيها وما فيه أتعب، هذه بقي وقت
+
+554
+01:02:46,090 --> 01:02:50,870
+كتير، أنت بتعوض مباشرة، تبحث في القيم، فباجي
+
+555
+01:02:50,870 --> 01:02:55,870
+بقوله هنا، باجي بقوله، بدي أشيل كل تي وأحط مكانها
+
+556
+01:02:55,870 --> 01:02:58,050
+باي على اثنين، لأنه قال لي بدي الكلام هذا عند
+
+557
+01:02:58,050 --> 01:03:02,980
+باي على اثنين، فبعدين بقوله هنا باي على 2 بـ 0، وبظل
+
+558
+01:03:02,980 --> 01:03:07,500
+1، أس أي رقم بواحد، في نصف، يبقى هنا السالب نصف، وهنا
+
+559
+01:03:07,500 --> 01:03:11,540
+صفر، يبقى كله نصف في صفر، يطلع كله بصفر، صفر في
+
+560
+01:03:11,540 --> 01:03:17,180
+اتجاه الـ I، نجي لهنا، هذا بواحد، وهنا اللي هو كله
+
+561
+01:03:17,180 --> 01:03:24,020
+بواحد، تمام، يبقى هنا عندي ناقص واحد، وعندي هنا يبقى
+
+562
+01:03:24,020 --> 01:03:27,740
+هذا ناقص واحد، أشوف الثاني شو بده يجيب لي، هذا الـ
+
+563
+01:03:27,740 --> 01:03:35,560
+صفر كله، يبقى بظل بس قديش؟ ناقص J في الشكل، لأن هذا
+
+564
+01:03:35,560 --> 01:03:41,760
+الكلام اللي هو بيبقى ناقص J، طيب من هذه الحالة
+
+565
+01:03:41,760 --> 01:03:46,600
+بقدر أقول اه، أستنى شوية، تديني بالك إن أصلاً هنا
+
+566
+01:03:46,600 --> 01:03:52,720
+ناقص هنا، ناقص هذه بتروح، وهذه بظل لها، مظبوط، هذه
+
+567
+01:03:52,720 --> 01:03:57,060
+كلها بتروح، وتجيبها، ماشي، يبقى هذا بدي يعطينا طول
+
+568
+01:03:57,060 --> 01:04:03,930
+الـ DT على DT، قولوا بتساوي كذا؟ واحد صحيح، إذا بقدر
+
+569
+01:04:03,930 --> 01:04:10,350
+أحسب الـ curvature ولا لا؟ طيب الـ curvature اللي هو
+
+570
+01:04:10,350 --> 01:04:19,210
+كابا، تساوي طول الـ V عندي، وطول الـ DT على DT عندي، إذا
+
+571
+01:04:19,210 --> 01:04:26,910
+صارت قصتنا سهلة جداً كذا؟
+
+572
+01:04:26,910 --> 01:04:28,330
+كده؟ كده؟ كده؟ كده؟ كده؟ كده؟ كده؟ كده؟ كده؟ كده؟
+
+573
+01:04:39,180 --> 01:04:46,620
+بتساوي مين؟ طول الـ DT على DT برضه عند الـ باي على 2
+
+574
+01:04:46,620 --> 01:04:53,780
+مقسوماً على طول الـ V عند الـ باي على 2،  يساوي واحد
+
+575
+01:04:53,780 --> 01:04:59,040
+على واحد، يساوي واحد، الآن بدي الـ radius of the
+
+576
+01:04:59,040 --> 01:05:05,740
+circle of curvature،  باجي بقول له، the radius of
+
+577
+01:05:06,290 --> 01:05:16,890
+the circle of curvature around، تساوي واحد على كابا
+
+578
+01:05:16,890 --> 01:05:22,530
+كابا بقديش عندنا؟ واحد، يبقى واحد على واحد، هو يساوي
+
+579
+01:05:22,530 --> 01:05:28,870
+كده واحد، يبقى نصف قطر دائرة الانحناء يساوي كده واحد
+
+580
+01:05:28,870 --> 01:05:34,220
+صحيح، ممتاز، شو ضل عندنا؟ المركز، مشان نحسب المركز
+
+581
+01:05:34,220 --> 01:05:38,720
+تعالوا نرسم المنحنى اللي عندنا ونشوف كيف بدنا نجيب
+
+582
+01:05:38,720 --> 01:05:45,080
+المركز منه، لو جينا للمنحنى اللي عندنا بالشكل هذا
+
+583
+01:05:45,080 --> 01:05:54,500
+هذا محور X، هذا محور Y، وجيت تخيل أن هذا الخط الوهمي
+
+584
+01:05:54,500 --> 01:05:55,880
+عندنا واحد
+
+585
+01:06:04,420 --> 01:06:09,840
+تطلع من هنا، على أن المنحنى هو منحنى الجيب، أو الـ
+
+586
+01:06:09,840 --> 01:06:16,460
+sine curve، لو رجعنا إلى Calculus A ورسمنا المنحنى
+
+587
+01:06:16,460 --> 01:06:24,400
+فالمنحنى طبعاً بيجي هكذا، وبيجي نازل هكذا، وهكذا
+
+588
+01:06:38,820 --> 01:06:51,500
+هذه النقطة باي على اثنين، وهذه النقطة باي على
+
+589
+01:06:51,500 --> 01:06:57,280
+اثنين، وهذه النقطة باي على اثنين، وهذه النقطة باي
+
+590
+01:07:08,420 --> 01:07:15,020
+عشان تطلعي هنا، قديش نصف القطر؟ واحد صحيح، قديش
+
+591
+01:07:15,020 --> 01:07:19,940
+المسافة هذه كلها بنات واحد، إذا بدي يجي المركز
+
+592
+01:07:19,940 --> 01:07:26,700
+تبعها هنا، وجهة الكونكية،  بصعيد مش فوق، حتكون هنا،
+
+593
+01:07:26,700 --> 01:07:28,720
+إذا الدائرة حتصير
+
+594
+01:07:49,850 --> 01:07:54,810
+تمام؟ يبقى صارت عندي دائرة بهذا الشكل، السؤال هو، حد
+
+595
+01:07:54,810 --> 01:08:02,590
+فيكم بيقدر يقول لي قديش إحداثيات المركز؟ تمام، باي
+
+596
+01:08:02,590 --> 01:08:08,110
+على اثنين، وصفر، هذا الـ X من هنا لهنا، و باي على اثنين
+
+597
+01:08:08,110 --> 01:08:09,950
+والـ Y مهو بصفر
+
+598
+01:08:33,380 --> 01:08:39,880
+يبقى كويس، يبقى ناقص
+
+599
+01:08:39,880 --> 01:08:47,420
+y ناقص باي على 2 الكل تربيع، يبقى
+
+600
+01:08:47,420 --> 01:08:49,840
+ناقص y ناقص باي على 2 الكل تربيع
+
+601
+01:08:53,120 --> 01:09:04,040
+يبقى هذه الـ equation of the circle of
+
+602
+01:09:04,040 --> 01:09:08,780
+curvature، قال
+
+603
+01:09:08,780 --> 01:09:14,920
+لي، اوجد وارسم، رسمنا، واوجدنا اللي هو الدائرة، و
+
+604
+01:09:14,920 --> 01:09:18,860
+المركز تبعها، والـ center وما إلى ذلك، يبقى ده إيش
+
+605
+01:09:18,860 --> 01:09:25,320
+اسم النقطة ده يا بنات؟ الـ radius of curvature
+
+606
+01:09:25,320 --> 01:09:29,620
+اللي هو الـ radius of the circle of curvature، هذا
+
+607
+01:09:29,620 --> 01:09:34,500
+الـ center of curvature، اللي هو الـ center تبع الـ
+
+608
+01:09:34,500 --> 01:09:39,160
+radius of curvature، هذه الدائرة كلها الـ circle of
+
+609
+01:09:39,160 --> 01:09:44,100
+curvature، يبقى هذه الدائرة، ها اللي هي الـ circle
+
+610
+01:09:53,880 --> 01:09:57,240
+طيب، الشغل اللي اشتغلناه كله هذا الوقت كان على
+
+611
+01:09:57,240 --> 01:10:04,600
+مين؟ على الـ plane، وهو الآن ن
+
+667
+01:17:14,190 --> 01:17:22,070
+مين؟ في .. بدي أربع هذه، بزايد كلها بيصير sin تربيع
+
+668
+01:17:22,070 --> 01:17:33,030
+2 sin T cos T  زي كوساين تربيع T زائد هذه
+
+669
+01:17:33,030 --> 01:17:37,970
+كمان لو ربعتها بيصير مين؟ واحد يبقى بده أخليه برا،
+
+670
+01:17:37,970 --> 01:17:44,370
+هاي الخطأ برا، يبقى بده أجيب تربيع هذه Cos تربيع T
+
+671
+01:17:44,370 --> 01:17:53,230
+ناقص 2 Sine T Cos T زائد Sine تربيع T تمام؟
+
+672
+01:17:55,760 --> 01:18:01,960
+هذه موجبة وهذه سالبة، مع السلامة بيصير 2 sin تربيع
+
+673
+01:18:01,960 --> 01:18:09,780
+تربيع زي 2 sin تربيع يبقى الجذر التربيعي لنصف
+
+674
+01:18:09,780 --> 01:18:13,740
+في 2 في sin تربيعي
+
+675
+01:18:29,440 --> 01:18:40,020
+d T على d T نقصم على قول d T على d T، الـ d T على d T هي
+
+676
+01:18:40,020 --> 01:18:48,840
+على واحد يبقى بظل زي ما هو يبقى هذا الكلام سليم
+
+677
+01:18:48,840 --> 01:18:57,100
+واحد على جذر 2 في الـ sin T زائد cos T كل
+
+678
+01:18:57,100 --> 01:19:03,560
+هذا في اتجاه الـ I، واحد على جذر 2 فيه cos T
+
+679
+01:19:03,560 --> 01:19:10,760
+ناقص sin T كله في اتجاه الجيب، ضال ان الكيربت
+
+680
+01:19:10,760 --> 01:19:18,800
+شارك هذا كم جداش بيساوي طول الـ dT على dT على طول
+
+681
+01:19:18,800 --> 01:19:20,860
+الـ V يبقى
+
+682
+01:19:30,370 --> 01:19:39,330
+طول الـ V، طول الـ V له 2 أو جذر 2 E أسطى
+
+683
+01:19:39,330 --> 01:19:47,390
+يبقى جذر 2 E أسطى يبقى هذا الكلام معناته يعني
+
+684
+01:19:47,390 --> 01:19:55,490
+واحد على جذر 2 أو واحد على جذر 2 في E
+
+685
+01:19:55,490 --> 01:20:00,510
+والسالب فيه يبقى هذا الـ curve شركابة اللي موجودة
+
+686
+01:20:00,510 --> 01:20:08,170
+هنا أو اللي هو بده يعني لحد هنا، stop يا بنات المرة
+
+687
+01:20:08,170 --> 01:20:12,230
+الجاية بجيب لكم إن شاء الله أرقام المسائل تبعت هذا
+
+688
+01:20:12,230 --> 01:20:12,790
+ال section
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/SmdhLcwuMIw_postprocess.srt b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/SmdhLcwuMIw_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..26b63dae3cc87d317f17deba2e0e3a1e5313493e
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/SmdhLcwuMIw_postprocess.srt
@@ -0,0 +1,2752 @@
+1
+00:00:00,000 --> 00:00:02,680
+موسيقى
+
+2
+00:00:13,140 --> 00:00:18,180
+بسم الله الرحمن الرحيم المرة اللى فاتت اخر حاجة
+
+3
+00:00:18,180 --> 00:00:22,640
+اخرناها اللى هو ال unit tangent vector T اللى كانت
+
+4
+00:00:22,640 --> 00:00:27,740
+DR عالية باسم نواصل وسنرجع مرة ثانية ال unit
+
+5
+00:00:27,740 --> 00:00:31,040
+tangent vector اللى نحن لزمنا خلال هذا ال section
+
+6
+00:00:31,040 --> 00:00:34,760
+و ال section اللى بعده كمان يبقى هذا الشيء أساسي
+
+7
+00:00:34,760 --> 00:00:37,880
+هنجي ل section اللى يوم اللي هو care picture and
+
+8
+00:00:37,880 --> 00:00:42,740
+normal vectors of careكرفتشر يعني بالعربي يا بنات
+
+9
+00:00:42,740 --> 00:00:48,900
+اللي هو التقوس أو الإنحناء لمنحنى نحسب مقدار
+
+10
+00:00:48,900 --> 00:00:53,780
+التقوس لمنحنى أو مقدار الإنحناء لهذا المنحنى
+
+11
+00:00:53,780 --> 00:01:00,860
+normal vector المتجه العمودي على المنحنى وسنعرف أن
+
+12
+00:01:00,860 --> 00:01:05,760
+المتجه العمودي على المنحنى هو المتجه العمودي على
+
+13
+00:01:05,760 --> 00:01:11,330
+المماس لهذا المنحنىهذا سنعرفه بعد قليل ان شاء الله
+
+14
+00:01:11,330 --> 00:01:15,650
+تعالى يبقى المتجه العمودي على المنحنة هو المتجه
+
+15
+00:01:15,650 --> 00:01:21,450
+العمودي على المماث لهذا المنحنة عند نقطة تقع لهذا
+
+16
+00:01:21,450 --> 00:01:28,890
+المنحنة سنقسم هذا ال section إلى نقطتينالنقطة
+
+17
+00:01:28,890 --> 00:01:34,370
+الأولى بناخد كيرفتشار of a plane curve يعني بنحسب
+
+18
+00:01:34,370 --> 00:01:40,590
+الكيرفتشار لمين لمنحنا موجود فيه مستوى وبعد ما
+
+19
+00:01:40,590 --> 00:01:46,350
+نخلص بنروح لكيرفتشار لمين لمنحنا موجود في ال space
+
+20
+00:01:46,350 --> 00:01:51,390
+اللي هو في الفرار يبقى هيكون شغلنا في الحالة
+
+21
+00:01:51,390 --> 00:01:56,020
+الأولى ال vector اللي بناخده بدلالة I وG فقطفي
+
+22
+00:01:56,020 --> 00:02:00,380
+الحالة الثانية بيكون دلوقتي الـ I و ال J و ال K ان
+
+23
+00:02:00,380 --> 00:02:04,640
+شاء الله تعالى بدنا نعطي definition لل curvature و
+
+24
+00:02:04,640 --> 00:02:08,400
+نشوف كيف نستخدم اللي هو ال curvature في الحالات
+
+25
+00:02:08,400 --> 00:02:15,680
+المختلفة يبقى بجي بقول F T is the unit tangent
+
+26
+00:02:15,680 --> 00:02:23,380
+vector is the unit tangent vector
+
+27
+00:02:26,220 --> 00:02:36,740
+of a smooth curve of a smooth curve لمنحنى
+
+28
+00:02:36,740 --> 00:02:47,200
+أملس the curvature function the curvature function
+
+29
+00:02:47,200 --> 00:02:55,520
+دالة التقوس أو دالة الحنان of the curve of a plane
+
+30
+00:02:58,680 --> 00:03:04,660
+كيرب از كيرب
+
+31
+00:03:04,660 --> 00:03:17,120
+از كيرب از كيرب از كيرب از كيرب از كيرب از كيرب از
+
+32
+00:03:17,120 --> 00:03:17,920
+كيرب از كيرب از كيرب از كيرب از كيرب از كيرب از
+
+33
+00:03:32,790 --> 00:03:43,230
+R of T is given in terms of parameter T
+
+34
+00:03:58,750 --> 00:04:06,470
+parameter اللي هو T rather
+
+35
+00:04:06,470 --> 00:04:13,270
+than rather
+
+36
+00:04:13,270 --> 00:04:26,250
+than بدلا من the arc length S the arc length اللي
+
+37
+00:04:26,250 --> 00:04:32,990
+هو الـ Sthen الكيربتشار
+
+38
+00:04:32,990 --> 00:04:38,210
+كيربتشار
+
+39
+00:04:38,210 --> 00:04:46,290
+K كيربتشار
+
+40
+00:04:46,290 --> 00:04:46,390
+كيربتشار K كيربتشار K كيربتشار K كيربتشار K
+
+41
+00:04:46,390 --> 00:04:49,070
+كيربتشار K كيربتشار K كيربتشار K كيربتشار K
+
+42
+00:04:49,070 --> 00:04:56,250
+كيربتشار
+
+43
+00:04:56,250 --> 00:05:11,470
+Kبقدر اقول الـ DT على DS و هنا على DS على DT هذا
+
+44
+00:05:11,470 --> 00:05:24,230
+الكلام بده يساوي الـ DTعلى DT DT على DT الطول تبعه
+
+45
+00:05:24,230 --> 00:05:32,650
+على مين؟ على طول ال V و
+
+46
+00:05:32,650 --> 00:05:39,790
+لحظة بسيطة قبل أن نرجع إلى هذا التعريف not since T
+
+47
+00:05:39,790 --> 00:05:45,050
+has a constant
+
+48
+00:05:47,850 --> 00:05:55,190
+لأن تقول تبعه يساوي مقدارا ثابتا اللي هو واحد صحيح
+
+49
+00:05:55,190 --> 00:06:06,950
+we have هيكون هنا اللي هو DT على DS بطة D بتساوي
+
+50
+00:06:06,950 --> 00:06:10,130
+zero that is
+
+51
+00:06:12,530 --> 00:06:21,890
+الـ Dt على Ds and Dt are orthogonal
+
+52
+00:06:47,900 --> 00:06:52,040
+اللي احنا كاتيها مرة تانية نقرأ التعريف قراءة جيدة
+
+53
+00:06:52,040 --> 00:06:57,880
+نحاول نفهم كل لقطة موجودة عنه إذا احنا الآن بنتكلم
+
+54
+00:06:57,880 --> 00:07:02,380
+عن ال curvature في ال plane curve يبقى المنحنة
+
+55
+00:07:02,380 --> 00:07:07,360
+اللي موجود في مستوى التعريف بيقول ما لو كان ال T
+
+56
+00:07:07,360 --> 00:07:11,740
+هو ال unit tangent vector ال smooth curve يبقى ال
+
+57
+00:07:11,740 --> 00:07:15,280
+curvature تبع ال plane curve في هذه الحالة كابة
+
+58
+00:07:15,910 --> 00:07:24,050
+تنطق كالتالي يا بنات كيها اللي هي كابا تنطق
+
+59
+00:07:24,050 --> 00:07:28,910
+بهذا الشكل يبقى كابا لحدها الرمز كي اللي عندنا هذه
+
+60
+00:07:29,230 --> 00:07:33,850
+تساوي طول ال DT على DS يعني ايش اللي بدي احصل؟ بدي
+
+61
+00:07:33,850 --> 00:07:36,930
+اشتقه
+
+62
+00:07:36,930 --> 00:07:42,130
+بالنسبة لل arc parameter S واخد الطول تبعه بيعطينا
+
+63
+00:07:42,130 --> 00:07:47,290
+ال curvature اللي هي كابا يبقى بناء عليه ال
+
+64
+00:07:47,290 --> 00:07:50,190
+curvature كابا هذا scalar ولا vector
+
+65
+00:07:52,840 --> 00:07:59,420
+أو DT DT على DS هو Vector لكن لما ناخد قوة سيارتنا
+
+66
+00:07:59,420 --> 00:08:04,500
+ستصبح Scalar إذا هذه كمية قياسية و ليست كمية
+
+67
+00:08:04,500 --> 00:08:10,640
+اتجاهية و قد تكون رقم واحد قد تكون دالة في متغير
+
+68
+00:08:10,640 --> 00:08:15,380
+مثل T مثلا طيب بقول لو كل small curve R of T is
+
+69
+00:08:15,380 --> 00:08:19,140
+given in terms of parameter ER
+
+70
+00:08:23,700 --> 00:08:28,840
+لو كانت في ال parameter T بدل من من ال arc length
+
+71
+00:08:28,840 --> 00:08:34,200
+S يبقى في هذه الحالة الكربتشار كابة ستأخذ شكلًا
+
+72
+00:08:34,200 --> 00:08:38,100
+جديدًا شهو هذا الشكل بقول دي T على دي S زي ما هي
+
+73
+00:08:38,100 --> 00:08:43,860
+معرفة الان S function في T والT كمان function في T
+
+74
+00:08:43,860 --> 00:08:48,000
+إذا بقدر أقول دي T على دي S فيها دي T على دي S
+
+75
+00:08:53,280 --> 00:09:00,740
+بقدر هدها هدى vector ولا scalar دي ت على دي اس دي
+
+76
+00:09:00,740 --> 00:09:07,500
+ت على دي اس دي small ت vector ولا scalar هدى
+
+77
+00:09:07,500 --> 00:09:11,630
+scalar هدى مش خلّاها vector هدى ال vectorيبقى دي
+
+78
+00:09:11,630 --> 00:09:14,510
+تي كتر هذا ال unit تانية بس هذا ال parameter وهذا
+
+79
+00:09:14,510 --> 00:09:18,490
+ال parameter يبقى هذا ما هواش vector إذا لو عارفة
+
+80
+00:09:18,490 --> 00:09:22,370
+لو كان هذا vector ماقدرش أكتب هذه إلا إذا كانت كله
+
+81
+00:09:22,370 --> 00:09:26,610
+ماشي أبقى قادرة أكتبها لكن هذه الانس كتر وهذه هي
+
+82
+00:09:26,610 --> 00:09:30,850
+من هذه ال vector إذا دي تي على دي اس لو نزلتها
+
+83
+00:09:30,850 --> 00:09:35,810
+كلها ماعش بصير دي اس على دي تي وببقى اللي فوق اللي
+
+84
+00:09:35,810 --> 00:09:42,420
+هو دي يعني هذه كأنهطول دي تي على دي تي في ال
+
+85
+00:09:42,420 --> 00:09:48,840
+absolute value دي تي على دي أسطى يبقى هذا طول وهذا
+
+86
+00:09:48,840 --> 00:09:50,180
+absolute value
+
+87
+00:09:53,810 --> 00:10:00,130
+لأ هذا طول المتجة دي تي على دي تي وهذا هو ال
+
+88
+00:10:00,130 --> 00:10:05,890
+absolute value القيمة المطلقة ل DS على دي تي طيب
+
+89
+00:10:05,890 --> 00:10:10,890
+ممتاز ال DS على دي تي أليس دي طول ال Velocity V
+
+90
+00:10:10,890 --> 00:10:15,770
+يبقى شرطة حاطة بدل طول ال Velocity V إذا من الآن
+
+91
+00:10:15,770 --> 00:10:21,400
+فصاعدامن حد ما يعطي ال R of T as a function of T،
+
+92
+00:10:21,400 --> 00:10:27,660
+لو فضل مرة بجيب السرعة، أخد ال generator بيجيب
+
+93
+00:10:27,660 --> 00:10:34,720
+مقدار السرعة اللي هو ال speedهقسم الصرعة على الـ
+
+94
+00:10:34,720 --> 00:10:39,080
+speed بيعطينا الـ mean الـ unit tangent vector لو
+
+95
+00:10:39,080 --> 00:10:45,540
+اشتقته بالنسبة الى T بصيب الـ DT على DT
+
+96
+00:10:47,900 --> 00:10:51,660
+أجيب له الطول و أقسمه على مقدار السرعة بيعطيني
+
+97
+00:10:51,660 --> 00:10:56,900
+مقدار main الكيربيتش أركبه وبالتالي ما لزمتليش ال
+
+98
+00:10:56,900 --> 00:11:01,380
+parameter S ستعت التخلص منه واكتفيت بال parameter
+
+99
+00:11:01,380 --> 00:11:07,040
+main T وهذا أسهل عمليا كثيرا من ان انا لسه بيدروح
+
+100
+00:11:07,040 --> 00:11:10,800
+أحسبه ال R كله لأ و بعدين بيدروح أشتغل لأ لأ لأ
+
+101
+00:11:10,800 --> 00:11:16,510
+هنا الدالة في R of T بقفلها مرة ما جبت ال Vبجيب
+
+102
+00:11:16,510 --> 00:11:21,650
+الطول تبع ال V، بشتق ال T بالنسبالي T، بكسم 2 على
+
+103
+00:11:21,650 --> 00:11:28,060
+4، بقول حصلت على مين؟ على ال K الواتشة Kهو لنظرة
+
+104
+00:11:28,060 --> 00:11:32,500
+لأن T لديه كونستانت لين مش هو not vector يبقى طوله
+
+105
+00:11:32,500 --> 00:11:39,080
+قدام واحد صحيح يبقى طوله واحد صحيح نحن لدينا T T
+
+106
+00:11:39,080 --> 00:11:43,600
+على DS dot T بيبقى سواء من Zero مرت علينا هذه
+
+107
+00:11:43,600 --> 00:11:49,480
+أبنات قبل دقيقة ولا لسه جديد لأول مرة نشوفها لو
+
+108
+00:11:49,480 --> 00:11:54,460
+كان عندي vector of constant length واشتقيته وعملته
+
+109
+00:12:03,500 --> 00:12:08,200
+اذا في عندي vector of constant length واشتقته dot
+
+110
+00:12:08,200 --> 00:12:13,540
+نفسه يبقى هذا بيعطيني قدرة zero وأثبتنالكوا هذه
+
+111
+00:12:13,540 --> 00:12:18,340
+القاعدة يبقى بناء عليه مدام T هو vector of
+
+112
+00:12:18,340 --> 00:12:22,400
+constant length الطول تبعه يسوى واحد صحيح إذا
+
+113
+00:12:22,400 --> 00:12:27,530
+مشتقته بالنسبة ل Sطب دي تي بده يسوى مين؟ Zero يبقى
+
+114
+00:12:27,530 --> 00:12:32,070
+دي تي على دي اس والتي اتنين ار او orthogonal بيكون
+
+115
+00:12:32,070 --> 00:12:36,690
+اتنين متعمدين نعطي مثال توضيح على الكلام اللي احنا
+
+116
+00:12:36,690 --> 00:12:48,010
+بنقوله هذا show them
+
+117
+00:12:48,010 --> 00:12:48,650
+the curvature
+
+118
+00:12:58,940 --> 00:13:07,240
+curvature of a circle
+
+119
+00:13:07,240 --> 00:13:21,960
+with center at the origin with center at
+
+120
+00:13:21,960 --> 00:13:38,600
+theorigin المركز هو نقطة أصل and radius a هو واحد
+
+121
+00:13:38,600 --> 00:13:39,680
+على a
+
+122
+00:13:55,260 --> 00:14:00,080
+سؤال مرة ثانية بقول لو عندنا دائرة دائرة مركزها
+
+123
+00:14:00,080 --> 00:14:05,400
+نقطة الأصل و نصف قطرة يساوي ايه قول تبعه يساوي ايه
+
+124
+00:14:05,400 --> 00:14:10,220
+بدي اثبت ان ال curvature لهذه الدائرة يساوي قداش
+
+125
+00:14:10,220 --> 00:14:14,760
+واحد على ايه يعني ال curvature عند اي نقطة على
+
+126
+00:14:14,760 --> 00:14:19,720
+محيط الدائرة بدي تكون مقدر ثابت وهو واحد القيمة
+
+127
+00:14:19,720 --> 00:14:25,140
+العددية له واحد على نصف القطر يبقى بقولبيللي ان
+
+128
+00:14:25,140 --> 00:14:29,520
+الكيربتشارلي دائرة مركزها نقطة الأصل و نصف قطرها
+
+129
+00:14:29,520 --> 00:14:33,380
+يساوي ايه؟ هو عبارة عن واحد يعني بدأ تبتله انه
+
+130
+00:14:33,380 --> 00:14:37,880
+كابة تساوي مين واحد على ايه؟ بقوله كويس وقاللي
+
+131
+00:14:37,880 --> 00:14:42,300
+أكتر ماعنديش معلومة أكتر من انه عندي دائرة مركزها
+
+132
+00:14:42,300 --> 00:14:48,320
+نقطة الأصل و نصف قطرها يساوي ايه؟ كيف يعني؟ يعني
+
+133
+00:14:48,320 --> 00:14:54,260
+لو جينا و قولنا هي عنا دائرة شكل عنها هذا اكتروهي
+
+134
+00:14:54,260 --> 00:14:59,900
+عندي محاول بالشكل اللي هنا تمام
+
+135
+00:14:59,900 --> 00:15:05,120
+وقولنا هذا محور X وهذا محور Y وهذا نقطة الأصل اللي
+
+136
+00:15:05,120 --> 00:15:11,280
+هو Zero في أن نقطة الأصل إلى أي نقطة على المحيط
+
+137
+00:15:11,280 --> 00:15:18,110
+هذا يعتبر من ال radius E نصف القطرلو اخترقت ان هذه
+
+138
+00:15:18,110 --> 00:15:26,830
+النقطة هي P of X Y و رح نزلت من هنا عمود على محور
+
+139
+00:15:26,830 --> 00:15:34,270
+X بيكون هذا الجزء هو X و هذا الجزء هو من Y لو كانت
+
+140
+00:15:34,270 --> 00:15:38,690
+الزاوية اللي عندنا هذه اللي هي الزاوية ثيتا إذا ال
+
+141
+00:15:38,690 --> 00:15:43,710
+X كانت مش متساومة بنات X أكو صحيح ثيتا و ال Y
+
+142
+00:15:47,110 --> 00:15:59,510
+يبقى مصير عنا X يساوي A Cos θ و Y يساوي A Sin θ طب
+
+143
+00:15:59,510 --> 00:16:05,690
+لو ربعتهم وجمعت بيعطيني معادلة الدائرةطبعا
+
+144
+00:16:05,690 --> 00:16:08,030
+المعادلة دي على مركزها النقطة الأصول نصف قطرة هي
+
+145
+00:16:08,030 --> 00:16:13,570
+يساوي a يا x تربية زائد y تربية تساوي a تربية
+
+146
+00:16:13,570 --> 00:16:18,150
+مظبوط طب تعالوا نربع هدول يبقى x تربية زائد y
+
+147
+00:16:18,150 --> 00:16:23,790
+تربية يساوي a تربية cosine تربية تيتا زائد a تربية
+
+148
+00:16:23,790 --> 00:16:25,390
+sine تربية تيتا
+
+149
+00:16:31,480 --> 00:16:38,400
+يبقى هدول بسميهم المعادلات ال parameterية لمين
+
+150
+00:16:38,400 --> 00:16:44,460
+للcircle يبقى هدول التنتين مع بعض هذه the
+
+151
+00:16:44,460 --> 00:16:54,260
+parametric equations of the circle
+
+152
+00:16:56,620 --> 00:17:01,360
+طيب لو بدأ اكتب هذا الكلام على صورة unit جرس
+
+153
+00:17:01,360 --> 00:17:05,440
+بتكتبها على شكل اللي هو vector valued function
+
+154
+00:17:05,440 --> 00:17:12,380
+يبقى بروح بقول ان ال R of T بدي يسوى A Cos θ في
+
+155
+00:17:12,380 --> 00:17:19,020
+اتجاه ال I زائد او A R of θ هنا او θ يبقى A Cos θ
+
+156
+00:17:19,020 --> 00:17:25,340
+في اتجاه ال I زائد A Sin θ في اتجاه ال A يعني احنا
+
+157
+00:17:25,640 --> 00:17:30,820
+فليب ليه؟ أعلى بال curvature إذا بضروح أجيبله من؟
+
+158
+00:17:30,820 --> 00:17:34,160
+ال unit tangent لأن هاي ال curvature اللي عندي
+
+159
+00:17:34,160 --> 00:17:40,760
+بلزمني ال unit tangent و أشتقه على طول ال V تمام
+
+160
+00:17:40,760 --> 00:17:49,140
+بقوله كويس يبقى الأن أنا بدي أجيبله V of θاللي
+
+161
+00:17:49,140 --> 00:17:55,420
+عبارة عن dR على dθ اللي هو ناقص A في sin θ في
+
+162
+00:17:55,420 --> 00:18:03,930
+اتجاه I زائد A cos θ في اتجاه Gبالذات لمين هنا طول
+
+163
+00:18:03,930 --> 00:18:09,430
+ال V إذا بتروح ع سيبله كده طول ال V إذا طول ال V
+
+164
+00:18:09,430 --> 00:18:15,510
+بده يساوي ال square root ل A تربيع sine تربيع ثيتا
+
+165
+00:18:15,510 --> 00:18:21,370
+زائد A تربيع cosine تربيع ثيتا يساوي الجذري
+
+166
+00:18:21,370 --> 00:18:31,460
+التربيعي ل A تربيع في مين؟ في sine تربيع ثيتازائد
+
+167
+00:18:31,460 --> 00:18:38,700
+cosine تربيتي تنقل ده واحد في ايه تربية ابقى يبقى
+
+168
+00:18:38,700 --> 00:18:46,880
+هنا ايهطبعا يبقى .. جبت اللي هو طول ال V اللي هو
+
+169
+00:18:46,880 --> 00:18:50,740
+يسوى قداشة .. بقولش absolute value لإيه؟ لأن طوله
+
+170
+00:18:50,740 --> 00:18:54,400
+عمره ما كان قيمة سالبة، مظبوط؟ و الله بنقول لو
+
+171
+00:18:54,400 --> 00:18:57,820
+قسنا اي واحدة فيه و نقول و الله طولها هذه سالب متر
+
+172
+00:18:57,820 --> 00:19:02,360
+و نص، لأ متر و نص على طول، يبقى الطول قيمة موجبة،
+
+173
+00:19:02,360 --> 00:19:09,180
+طبعا؟ الان بدنا ال unit tangent T اللي هو ال V على
+
+174
+00:19:09,180 --> 00:19:13,690
+طول ال Vاللي أخدناها آخر نقطة أخدناها المحاضرة
+
+175
+00:19:13,690 --> 00:19:17,430
+الماضيةقلنا الـ Unit Tangent Vector T هو الـ
+
+176
+00:19:17,430 --> 00:19:21,790
+Velocity على مقدار الـ Velocity ال Velocity وين؟
+
+177
+00:19:21,790 --> 00:19:27,190
+هي اللي موجودة يبقى تساوي الناقص A Sine Theta في
+
+178
+00:19:27,190 --> 00:19:32,490
+اتجاه I زائد A Cosine Theta في اتجاه الجهة كله
+
+179
+00:19:32,490 --> 00:19:38,590
+مقسوم على مين؟ على A اللي هو قد يساوي سالب Sine
+
+180
+00:19:38,590 --> 00:19:42,670
+Theta في اتجاه I زائد
+
+181
+00:19:49,950 --> 00:19:57,190
+يبقى دي تي على دي
+
+182
+00:19:57,190 --> 00:19:57,730
+تيتا
+
+183
+00:20:03,930 --> 00:20:09,850
+نقص sin θ في اتجاه ال I نقص sin θ في اتجاه main
+
+184
+00:20:09,850 --> 00:20:16,270
+الجهة جالي بده الطول تبع هذا المتجر بقوله I الجهة
+
+185
+00:20:16,270 --> 00:20:23,030
+ده بده يعطينا ان طول ال DT على D ثيتا بده يسوى
+
+186
+00:20:23,030 --> 00:20:30,170
+الجدر التربيعي لcos تربيع ثيتا زائد sin تربيع ثيتا
+
+187
+00:20:30,170 --> 00:20:36,760
+لغة درجة واحد صحيحيبقى هذا الطول، الآن طول ال V
+
+188
+00:20:36,760 --> 00:20:43,380
+موجود عندى، مظبوط؟ والان طول او ال DT على Dθ موجود
+
+189
+00:20:43,380 --> 00:20:49,820
+عندى، اذا بقولوا كيرفيتشاركابة اللى مطلبه يساوي ال
+
+190
+00:20:49,820 --> 00:20:58,880
+DT على Dθ، الان هنا على طول ال V ويساوي طوله هذا
+
+191
+00:20:58,880 --> 00:21:06,770
+مقدش بواحد وطوله ايه؟أظن و هو المطلوب إذا من الآن
+
+192
+00:21:06,770 --> 00:21:11,810
+فصادم الدكتورافيلي ان الدائرة اللي مركزها نقطة
+
+193
+00:21:11,810 --> 00:21:16,710
+الأصل و نصف قطرها يساوي ايه؟ لو بدنا نجيب ال
+
+194
+00:21:16,710 --> 00:21:21,870
+curvature لها يبقى يساوي قيمة ثابتة اللي بيساوي
+
+195
+00:21:21,870 --> 00:21:27,010
+واحد على نصف قطر هذه الدائرة
+
+196
+00:21:40,940 --> 00:21:45,240
+طيب هذه أول نقطة اللي أعرفنا فيها الكلبتشر نجي
+
+197
+00:21:45,240 --> 00:21:50,020
+لنقطة ثانية ال principle unit normal النقطة
+
+198
+00:21:50,020 --> 00:21:55,660
+الثانية من هذا ال section اللي هو the principle
+
+199
+00:21:55,660 --> 00:22:07,020
+unit normal vector unit normal vector و اللي احنا
+
+200
+00:22:07,020 --> 00:22:11,360
+كنا كاتبينه في عنوان هذا ال sectionوانا كامل
+
+201
+00:22:11,360 --> 00:22:15,940
+curvature and unit normal vectors of a curve يمنيش
+
+202
+00:22:15,940 --> 00:22:22,220
+لتعريف ال unit normal vector of a curve بقول at a
+
+203
+00:22:22,220 --> 00:22:32,240
+point at a point where حيث ال curvature كامل لدو
+
+204
+00:22:32,240 --> 00:22:36,280
+سوى zero the principal unit normal vector
+
+205
+00:22:39,660 --> 00:22:52,120
+principal unit normal vector of
+
+206
+00:22:52,120 --> 00:23:00,460
+a smooth curve in
+
+207
+00:23:00,460 --> 00:23:05,240
+the plane في
+
+208
+00:23:05,240 --> 00:23:14,430
+مستوى earthهدله الرمز capital N وانه بتساوي واحد
+
+209
+00:23:14,430 --> 00:23:25,610
+على كاره فى دي تي على دي اس دي تي على دي اس that
+
+210
+00:23:25,610 --> 00:23:36,130
+will point that will point toward
+
+211
+00:23:36,130 --> 00:23:37,570
+the concave side
+
+212
+00:23:42,270 --> 00:23:50,150
+the concave side of the cave
+
+213
+00:24:06,880 --> 00:24:13,720
+نفترض أن هذا اللي هو ال smooth curve جينا عندها
+
+214
+00:24:13,720 --> 00:24:19,480
+نقطة زي النقطة اللي عندها دي على سبيل المثال رسمنا
+
+215
+00:24:19,480 --> 00:24:23,700
+ال unit tangent vector فكان ال unit tangent vector
+
+216
+00:24:23,700 --> 00:24:29,190
+T بالشكل هذابدي اعرف وين بدي اكون ال principle
+
+217
+00:24:29,190 --> 00:24:34,150
+normal vector يعني المتجه العمودي على المنحنى عند
+
+218
+00:24:34,150 --> 00:24:39,630
+هذه النقطة يعني المتجه العمودي على ال tangent لهذا
+
+219
+00:24:39,630 --> 00:24:44,430
+المنحنى او ال tangent vector لهذا المنحنى عند هذه
+
+220
+00:24:44,430 --> 00:24:50,770
+النقطة يبقى هذا النقطة لو روحته سميتها P1 على سبيل
+
+221
+00:24:50,770 --> 00:24:56,090
+المثالماذا يقول هنا عند نقطة الكيربتشار كابة فيها
+
+222
+00:24:56,090 --> 00:25:00,770
+لا تساوي 0 طبعا لو كانت كابة تساوي 0 اللي أصبح ال
+
+223
+00:25:00,770 --> 00:25:04,650
+principle unit normal is undefined ما هوش معرّف
+
+224
+00:25:04,650 --> 00:25:09,190
+إذا ضروري الكيربتشار مايكونش 0 بال principle unit
+
+225
+00:25:09,190 --> 00:25:14,240
+normal vector of S مؤكد كيرب فيه planeهو واحد على
+
+226
+00:25:14,240 --> 00:25:19,780
+كابة في DT على DS يبقى واحد على كابة scalar وهذا
+
+227
+00:25:19,780 --> 00:25:25,940
+vector إذا هذا vector زي ما احنا بنقول طيب اتجاهه
+
+228
+00:25:25,940 --> 00:25:31,760
+وين؟ والذات will point toward يبقى اتجاهه بيكون
+
+229
+00:25:31,760 --> 00:25:37,670
+the concave side of the curveفى اتجاه تقعر المنحنى
+
+230
+00:25:37,670 --> 00:25:43,710
+وليس تحد بالمنحنى طلعي المنحنى هنا الـ concave way
+
+231
+00:25:43,710 --> 00:25:50,330
+down إذا ال N بدي يكون بالشكل هذا عمودي عليه يبقى
+
+232
+00:25:50,330 --> 00:25:55,370
+هذا ال N بدي يكون عمودي على T اللي هو بدي يساوي
+
+233
+00:25:55,370 --> 00:26:05,590
+واحد على كابة واحد على كابة دي تي على دي اسمطيب لو
+
+234
+00:26:05,590 --> 00:26:12,050
+مشينا تاني ووصلنا لنقطة تانية مثل النقطة P2 وروحنا
+
+235
+00:26:12,050 --> 00:26:18,450
+رسمنا ال unit tangent عند هذه النقطة فكان ال unit
+
+236
+00:26:18,450 --> 00:26:23,970
+tangent vector اللي هو T يبقى N بده يكون لداخل
+
+237
+00:26:23,970 --> 00:26:29,160
+الشكل اللي عندنا هذايبقى هذا N اللي هو بده يساوي
+
+238
+00:26:29,160 --> 00:26:36,980
+واحد على كظه في DT على DS يبقى دائما وقابله اتجاه
+
+239
+00:26:36,980 --> 00:26:43,420
+وين؟ للداخل عمودي على ال curve و عمودي على ال unit
+
+240
+00:26:43,420 --> 00:26:48,460
+tangent أن ده نقطة التماسواتجاهه دائما هو قبل اللي
+
+241
+00:26:48,460 --> 00:26:54,720
+وين؟ للداخل، لاتجاه تقعر مين؟ المنحنى هذا بالنسبة
+
+242
+00:26:54,720 --> 00:27:00,000
+لمين؟ لل unit normal vector لكن لاحظوا ان ال unit
+
+243
+00:27:00,000 --> 00:27:04,690
+normal vector احنا كاتبينه بدلات ال curvatureو
+
+244
+00:27:04,690 --> 00:27:10,430
+كتبينه بدلالة DT عالمين DS توقفني شويه ال
+
+245
+00:27:10,430 --> 00:27:14,810
+curvature بطلنا نكتبها بدلالة ال S كتبناها كلها
+
+246
+00:27:14,810 --> 00:27:20,210
+بدلالة مين؟ بدلالة ال T يبقى الآن بدنا نروح بنفس
+
+247
+00:27:20,210 --> 00:27:25,450
+الطريقة نكتب ال curvature بدلالة ال T parameter
+
+248
+00:27:25,450 --> 00:27:31,010
+وليس بدلالة ال S parameter تمام؟يبقى من أروح نكتب
+
+249
+00:27:31,010 --> 00:27:36,370
+هذا الكلام على صورة الـ remark التالية يبقى remark
+
+250
+00:27:36,370 --> 00:27:58,050
+يبقى
+
+251
+00:27:58,050 --> 00:27:58,310
+remark يبقى remark يبقى remark يبقى remark يبقى
+
+252
+00:27:58,310 --> 00:28:04,740
+remark يبقى remark يبقfinding بدون ما نوجد ال
+
+253
+00:28:04,740 --> 00:28:14,740
+curvature kappa and ال S طبعا زي ما تشايفين ال
+
+254
+00:28:14,740 --> 00:28:19,100
+normal يعتمد على kappa وعلى main على S يبقى أنا
+
+255
+00:28:19,100 --> 00:28:21,720
+بده أجيب ال principle normal بدون اللي أجيب ال
+
+256
+00:28:21,720 --> 00:28:25,220
+curvature ولا أجيب ال arc parameter length اللي هو
+
+257
+00:28:25,220 --> 00:28:28,940
+main S كيف؟ كالتالي as follows
+
+258
+00:28:36,570 --> 00:28:43,110
+بساوي واحد على الـ curvature كابة في الـ DT على DS
+
+259
+00:28:43,110 --> 00:28:48,030
+و يمسك هذا
+
+260
+00:28:48,030 --> 00:28:56,750
+بقدر اقول DT على DS الكابة اللي و مين اللي هي طول
+
+261
+00:28:56,750 --> 00:29:03,710
+الـ DT على DS طبعا
+
+262
+00:29:03,710 --> 00:29:05,790
+بقدر اقول هذا الكلمة
+
+263
+00:29:09,160 --> 00:29:17,840
+على DT في DT على DS على طول
+
+264
+00:29:17,840 --> 00:29:25,060
+الـ DT على DT في DT على DS
+
+265
+00:29:53,660 --> 00:29:59,780
+الـ Dt على Ds اتفقنا انها scalar طيب مرة الماضية
+
+266
+00:29:59,780 --> 00:30:04,680
+الـ Dt على Ds أقل من الـ Zero ولا أكبر من الـ Zero
+
+267
+00:30:04,680 --> 00:30:10,320
+أكبر من الـ Zero اكبر من الـ Zero يبقى Ds على Dt
+
+268
+00:30:10,320 --> 00:30:17,520
+هي طول ال V وطول موجة مظبوط يبقى قيمة الموجة بلو
+
+269
+00:30:17,520 --> 00:30:21,360
+قلبتها بسيستراليب والله بظلها موجة بقى بظلها موجة
+
+270
+00:30:21,360 --> 00:30:27,890
+بقى ممتاز جداإذا أنا لما أجي أقول هذا الكلام دي تي
+
+271
+00:30:27,890 --> 00:30:37,230
+على ا دي تي على دي تي في دي تي على دي اس وهذا طول
+
+272
+00:30:37,230 --> 00:30:46,010
+ال دي تي على دي تي في دي تيعلى DS اذا نقلت طولته
+
+273
+00:30:46,010 --> 00:30:50,310
+او ال absolute value لها ال absolute value والله
+
+274
+00:30:50,310 --> 00:30:55,350
+مش ال absolute تنتين هذول تنتين موجبتين جات بعض
+
+275
+00:30:55,350 --> 00:31:01,950
+تماما يبقى بنقدر نختصرهم وتقول المسألة الى ان ال
+
+276
+00:31:01,950 --> 00:31:09,690
+principal unit normal N من الانف صاعداهو Dt على Dt
+
+277
+00:31:09,690 --> 00:31:18,590
+مقسوما على طول Dt على Dt بالشكل اللي عندنا واضح ان
+
+278
+00:31:18,590 --> 00:31:22,450
+ال principal unit normal هذه لا فيها curvature ولا
+
+279
+00:31:22,450 --> 00:31:28,330
+فيها S زي ما احنا ادعينا قبل قليل
+
+280
+00:31:30,200 --> 00:31:36,020
+يبقى بناء عليه لا الكيروفيتشار ولا ال principle
+
+281
+00:31:36,020 --> 00:31:40,560
+normal بكتف دلالة ال S بسيطة بكتف دلالة ال T أسهل
+
+282
+00:31:40,560 --> 00:31:47,000
+زي ما انت شايفه ناخد مثال توضيح على ذلك example
+
+283
+00:31:47,000 --> 00:31:52,720
+will
+
+284
+00:31:52,720 --> 00:32:02,330
+find ال Tوالـ principal normal vector N and
+
+285
+00:32:02,330 --> 00:32:05,590
+الكيروفيتشاركابة
+
+286
+00:32:05,590 --> 00:32:19,390
+for theأبلين كيرف للمنحنة اللي هو R of T يساوي لين
+
+287
+00:32:19,390 --> 00:32:26,350
+سيك T كله في اتجاه الـ I زائد T في اتجاه الـ J
+
+288
+00:32:26,350 --> 00:32:33,450
+والـ T هذه محصورة بين سالف باي على اتنين وبين باي
+
+289
+00:32:33,450 --> 00:32:34,150
+على اتنين
+
+290
+00:32:39,420 --> 00:32:47,940
+مرة تانية قال هاتلي unit tangent vector تلاتة
+
+291
+00:32:47,940 --> 00:32:52,580
+هاتلي الكيرفت شركابة للمنحلة اللي عندنا هذا وحطني
+
+292
+00:32:52,580 --> 00:32:58,060
+على interval من by على اتنين لغاية by على اتنين
+
+293
+00:32:58,060 --> 00:33:01,280
+لأن يا بنات عند ال by على اتنين و ال by على اتنين
+
+294
+00:33:01,280 --> 00:33:08,320
+ال stickis undefined ومن هنا ما جليش يساوي تمام؟
+
+295
+00:33:08,320 --> 00:33:12,100
+من حالة سكت اللي أخدته في الكلب و دستين آخر
+
+296
+00:33:12,100 --> 00:33:15,840
+section في أول chapter كانت ال trigonometric
+
+297
+00:33:15,840 --> 00:33:20,260
+functions تمام؟ لما رسمت السكت كانت عند ال
+
+298
+00:33:20,260 --> 00:33:24,720
+بايعتنين و وصلت بايعتنين is undefined يبقى من هنا
+
+299
+00:33:24,720 --> 00:33:29,180
+ماحطناش يساوي ما علينا هذه بس معلومة هامشية جانبية
+
+300
+00:33:29,780 --> 00:33:34,860
+يبقى الان نجيب ال unit tangent vector T T هي عبارة
+
+301
+00:33:34,860 --> 00:33:40,480
+عن مين؟ ال V على طول ال V مظبوط يبقى على هذا
+
+302
+00:33:40,480 --> 00:33:46,840
+الكلام بدي أجيب له مين ك ال V في الأول يبقى ال V
+
+303
+00:33:46,840 --> 00:33:54,820
+اللي هي DR على DD يساوى تفضل ان تسكب جدا شبنانة
+
+304
+00:33:55,390 --> 00:34:03,090
+واخد على سك T في مشتقة السك اللي بسك T تان T في
+
+305
+00:34:03,090 --> 00:34:09,810
+اتجاه ال I زائد مشتقة ال T بواحد في اتجاه ال J
+
+306
+00:34:09,810 --> 00:34:18,050
+يبقى أصبحت ال D تساوي سك مع سك يبقى تان T في اتجاه
+
+307
+00:34:18,050 --> 00:34:24,640
+ال I زائد Jيبقى هذا ال velocity عند اي لحظة او
+
+308
+00:34:24,640 --> 00:34:30,020
+متجه السرعة بدي احسب قداش طول متجه السرعة يبقى هذا
+
+309
+00:34:30,020 --> 00:34:37,450
+بدي يعطينا طول ال V بده ساوي الجدري التربيهيلتان
+
+310
+00:34:37,450 --> 00:34:44,670
+تربية T زائد واحد اللي هو كده؟ سك تربية من حساب
+
+311
+00:34:44,670 --> 00:34:52,490
+المثلثات والسك تربية تطلع من تحت الجذر بسك T والله
+
+312
+00:34:52,490 --> 00:34:59,610
+absolute value لسك T لا هي بنقول absolute value
+
+313
+00:34:59,610 --> 00:35:05,850
+لسك T، مظبوط؟ يعني كده شهر قيمة المحطة بسؤاللما
+
+314
+00:35:05,850 --> 00:35:08,890
+اقول من سالب بايع اتنين لبايع اتنين يعني ايه
+
+315
+00:35:08,890 --> 00:35:15,030
+الاربع يبقى نفعليه؟ من سالب بايع على اتنين لبايع
+
+316
+00:35:15,030 --> 00:35:20,070
+على اتنين يبقى ايه الاربع؟ الرابع الرابع و الرابع
+
+317
+00:35:20,070 --> 00:35:25,760
+الاول من سالب بايع اتنين لبايع اتنينمظبوط يبقى
+
+318
+00:35:25,760 --> 00:35:30,820
+الربع الرابع ثم الربع الأول طب السيك و ال cosine
+
+319
+00:35:30,820 --> 00:35:35,240
+في الربع الأول و الرابع موجبة موجبة يبقى حطيت ال
+
+320
+00:35:35,240 --> 00:35:39,780
+absolute value و انا شيلتها كله بالموجبة يعني
+
+321
+00:35:39,780 --> 00:35:43,880
+زيادة كلك على ما حطيتها تمام السيك موجب في الربع
+
+322
+00:35:43,880 --> 00:35:47,100
+الرابع و الرابع الأول و كذلك ال cosine يبقى لا
+
+323
+00:35:47,100 --> 00:35:52,490
+داعي لكتابة ال absolute valueتمام؟ لأن الـ Sec
+
+324
+00:35:52,490 --> 00:35:56,830
+موجب في الرابع الأول والرابع الرابع طيب حسب domain
+
+325
+00:35:56,830 --> 00:36:02,250
+طول ال V إذا بده المطموب الأول ال unit tangent V
+
+326
+00:36:02,250 --> 00:36:11,510
+هو V على طول ال V وين ال V؟ هاي ال V اللي هي تاني
+
+327
+00:36:11,510 --> 00:36:23,100
+Tزائد I تنتي في اتجاه الـ I زائد J كله على سك T
+
+328
+00:36:23,100 --> 00:36:28,870
+ويساوي تانية يا بنات اللي هي عبارة عن مين؟Sin على
+
+329
+00:36:28,870 --> 00:36:35,190
+Cos وSec مقلوب الـ Cos يبقى بضالة دي بس قداشت Sin
+
+330
+00:36:35,190 --> 00:36:41,210
+واحدة يبقى بيصير الـ Sin تي في اتجاه الـ I زايد
+
+331
+00:36:41,210 --> 00:36:50,390
+واحد على سك Cos يبقى هذا Cos تي في اتجاه الـ Gيبقى
+
+332
+00:36:50,390 --> 00:36:55,470
+أصبح المطلوب الأول ال unit tangent vector T هو
+
+333
+00:36:55,470 --> 00:37:01,890
+sine T في اتجاه I زائد cosine T في اتجاه ال J هذا
+
+334
+00:37:01,890 --> 00:37:08,610
+هو ال unit tangent vector T نقلب بعدين بالنمية ال
+
+335
+00:37:08,610 --> 00:37:13,990
+principle unit normal I و فوق يبقى بنروح أشتقه
+
+336
+00:37:13,990 --> 00:37:21,120
+بالنسبة إلى T و أقسم على طولهيبقى بدي اجي اخد ال
+
+337
+00:37:21,120 --> 00:37:27,280
+DT على DT بدي اشتق هذه الدلة بالنسبة الى T ففضل ال
+
+338
+00:37:27,280 --> 00:37:33,160
+sine ب cosine T في اتجاه ال I ماقص sine T في اتجاه
+
+339
+00:37:33,160 --> 00:37:40,170
+ال J بدي اجيب الطول تبعهيبقى قول تبع ال Dt على Dt
+
+340
+00:37:40,170 --> 00:37:46,150
+بدي أسوأ ال square root لقو صين تربية T زائد صين
+
+341
+00:37:46,150 --> 00:37:52,170
+تربية T اللي هو بقدرش كمان؟ واحد صحيح يبقى بناء
+
+342
+00:37:52,170 --> 00:37:58,670
+على ال principle normal Nبدي اجي هنا و اسمه على
+
+343
+00:37:58,670 --> 00:38:03,790
+طول يعني بدي اسمه على قداش بتغير؟ لأ يبقى هذا
+
+344
+00:38:03,790 --> 00:38:09,970
+بيصير cosine T في اتجاه ال I ماطس sine T في اتجاه
+
+345
+00:38:09,970 --> 00:38:16,350
+ال J مقسوما على واحد صحيح بظل هو نفسه يبقى هذا ال
+
+346
+00:38:16,350 --> 00:38:21,550
+principle unit normal vector بعدين قال ليش؟ بدي
+
+347
+00:38:21,550 --> 00:38:29,770
+تجيب لل curvature كابةكرفيت شركابة جداش تساوي طول
+
+348
+00:38:29,770 --> 00:38:37,170
+ال V طول ال V طول ال V طول ال V طول ال V طول ال V
+
+349
+00:38:37,170 --> 00:38:39,750
+طول ال V طول ال V طول ال V طول ال V طول ال V طول
+
+350
+00:38:39,750 --> 00:38:43,010
+ال V طول ال V طول ال V طول ال V طول ال V طول ال V
+
+351
+00:38:43,010 --> 00:38:44,890
+طول ال V طول ال V طول ال V طول ال V طول ال V طول
+
+352
+00:38:44,890 --> 00:38:45,790
+ال V طول ال V طول ال V طول ال V طول ال V طول ال V
+
+353
+00:38:45,790 --> 00:38:47,490
+طول ال V طول ال V طول ال V طول ال V طول ال V طول
+
+354
+00:38:47,490 --> 00:38:47,550
+طول ال V طول ال V طول ال V طول ال V طول ال V طول
+
+355
+00:38:47,550 --> 00:38:54,070
+طول ال V طول ال V طولبدي الكيروفيتشاركابة اللي هو
+
+356
+00:38:54,070 --> 00:39:00,410
+واحد على طول ال V بالفعل يبقى هذه اللي هي قداش
+
+357
+00:39:00,410 --> 00:39:06,430
+تساوي اللي هو او نكتبها لك بالتفصيل و بعدين بنعوض
+
+358
+00:39:06,430 --> 00:39:15,010
+بيها يبقى الكيروفيتشاركابة كانت اللي هو قداش طول
+
+359
+00:39:15,010 --> 00:39:18,770
+ال V في المقام و فوق .. كان ايه يا شباب انا بتحدثك
+
+360
+00:39:18,770 --> 00:39:28,350
+كتير؟DT على T طول تبعه يبقى DT على DT الطول تبعه
+
+361
+00:39:28,350 --> 00:39:33,030
+بهذا الشكل الطول تبعه طلعناه في جداش بواحد يبقى
+
+362
+00:39:33,030 --> 00:39:38,450
+بدي نسبة واحد على طول ال V وطول ال V طلعناه في
+
+363
+00:39:38,450 --> 00:39:46,190
+جداش سك T يبقى سك T هذا بدي أعطيك انه كربت شركابة
+
+364
+00:40:18,020 --> 00:40:23,040
+بنجي للنقطة التالتة في هذا ال section حاجة اسمها
+
+365
+00:40:23,040 --> 00:40:31,630
+دائرة الإلحن The circle of curvatureأفرض أنا عندي
+
+366
+00:40:31,630 --> 00:40:38,110
+منحنى ماء وعند نقطة ماء على هذا المنحنى بدي أحسب
+
+367
+00:40:38,110 --> 00:40:43,070
+the circle of curvature دائرة التكوّس أو دائرة
+
+368
+00:40:43,070 --> 00:40:48,990
+الإنحنات بدي ال center of curvature مركز الإنحنات
+
+369
+00:40:48,990 --> 00:40:54,490
+بدي ال radius of curvature نصف بطء الإنحنات
+
+370
+00:40:57,500 --> 00:41:05,060
+هذا كله نصف قطر انحناء مركز الانحناء هو نصف قطر
+
+371
+00:41:05,060 --> 00:41:11,100
+دائرة الانحناء وهي مركز دائرة الانحناء طب لو
+
+372
+00:41:11,100 --> 00:41:17,460
+رسمناها على منحلة بتكون جهة الداخل ولا جهة الخارج؟
+
+373
+00:41:17,890 --> 00:41:24,430
+جات الداخل اتنين بتتمسي المنحنة عند النقطة اللي
+
+374
+00:41:24,430 --> 00:41:28,990
+بنحسب عليها ال circle of curvature يبقى ال radius
+
+375
+00:41:28,990 --> 00:41:33,950
+of curvature يا بنات هي دائرة في نفس المستوى تبع
+
+376
+00:41:33,950 --> 00:41:40,210
+المنحنة تمسوا عندها نقطة يعني ال unit tangent
+
+377
+00:41:40,210 --> 00:41:45,990
+بيكون هو tangent لل circle و لل curve في نفس الوقت
+
+378
+00:41:46,310 --> 00:41:50,990
+الـ Radius تبعها هو نفس الـ Radius تبع الكيربتشار
+
+379
+00:41:50,990 --> 00:41:55,350
+الـ Center تبعها هو الـ Center تبع الكيربتشار
+
+380
+00:41:55,350 --> 00:42:00,530
+التقوس بيكون أو الدائرة بيكون لوين؟ للداخل يبقى
+
+381
+00:42:00,530 --> 00:42:05,870
+بدنا نعطي تعريف لها أو نرسمها لأي منحلة موجود
+
+382
+00:42:05,870 --> 00:42:07,970
+عندنا على سبيل المثال
+
+383
+00:42:16,090 --> 00:42:28,070
+الـ Circle of curvature for a plane curve
+
+384
+00:42:28,070 --> 00:42:36,810
+Definition،
+
+385
+00:42:36,810 --> 00:42:42,550
+أعطيها التعريف التالي The circle of curvature
+
+386
+00:42:44,010 --> 00:42:53,330
+circle of curvature بعض الكتب البنات بتسميها ال
+
+387
+00:42:53,330 --> 00:43:03,050
+oscillating circle oscillating
+
+388
+00:43:03,050 --> 00:43:08,050
+circle أو ال circle of curvature لإتنين نفس القصة
+
+389
+00:43:08,050 --> 00:43:22,210
+at a pointP on a plain curve on a plain curve
+
+390
+00:43:22,210 --> 00:43:35,630
+لمنحنا where حيث الكربت شركاها لاتساوي zero if the
+
+391
+00:43:35,630 --> 00:43:42,230
+circle is the circle and
+
+392
+00:43:43,270 --> 00:43:50,610
+the plane عبارة عن دائرة في نفس المستوى of the
+
+393
+00:43:50,610 --> 00:44:04,290
+curve A is tangent to
+
+394
+00:44:04,290 --> 00:44:08,950
+the curve at
+
+395
+00:44:08,950 --> 00:44:09,910
+P
+
+396
+00:44:14,400 --> 00:44:20,600
+نمرا V has the
+
+397
+00:44:20,600 --> 00:44:29,720
+same curvature as
+
+398
+00:44:29,720 --> 00:44:42,060
+the curve at P نمرا C lies toward
+
+399
+00:44:45,810 --> 00:44:51,630
+داكون curve او
+
+400
+00:44:51,630 --> 00:44:59,250
+inner inner side of
+
+401
+00:44:59,250 --> 00:45:08,650
+the curve Definition
+
+402
+00:45:08,650 --> 00:45:16,220
+رقم اتنين The radius of curvatureالراديوس
+
+403
+00:45:16,220 --> 00:45:21,620
+الكيرفيتشا
+
+404
+00:45:21,620 --> 00:45:24,900
+نصف
+
+405
+00:45:24,900 --> 00:45:37,380
+قطرة لمحنة of the curve at P is the radius of the
+
+406
+00:45:37,380 --> 00:45:42,140
+circle is the radius
+
+407
+00:45:44,820 --> 00:45:54,520
+of the circle of curvature of
+
+408
+00:45:54,520 --> 00:45:59,080
+curvature and
+
+409
+00:45:59,080 --> 00:46:08,600
+this radius and this radius is هديله الرمز روغ
+
+410
+00:46:08,600 --> 00:46:15,900
+اللي هو بده يسوى واحد على كترdefinition رقم تلاتة
+
+411
+00:46:15,900 --> 00:46:29,800
+the center of curvature the center of curvature of
+
+412
+00:46:29,800 --> 00:46:35,280
+the curve at
+
+413
+00:46:35,280 --> 00:46:40,280
+النقطة P is the center of the circle of curvature
+
+414
+00:46:40,280 --> 00:46:56,360
+is theسينتا of the circle of curvature
+
+415
+00:47:35,150 --> 00:47:42,630
+نعود الآن لكل تعريف من التعريف الثلاثة ونحاول أن
+
+416
+00:47:42,630 --> 00:47:48,570
+نفهم كل نقطة فيه ثم نعطي رسم توضيحي للكلام اللي
+
+417
+00:47:48,570 --> 00:47:51,750
+قلناه خلال هذا التعريف
+
+418
+00:48:01,240 --> 00:48:06,040
+التقاوس أو دائرة المنحنى لمنحنى موجود في مستوى
+
+419
+00:48:06,040 --> 00:48:10,980
+التعريف الأول the circle of curvature أو الـ
+
+420
+00:48:10,980 --> 00:48:14,040
+oscillating circle with oscillating circle
+
+421
+00:48:14,040 --> 00:48:17,680
+الcircle of curvature الاتنين are the same at a
+
+422
+00:48:17,680 --> 00:48:22,700
+point P على ال plane curve بحيث القابلة تسمي Zero
+
+423
+00:48:22,700 --> 00:48:27,230
+is the circle in the plane of the curve دهيبقى هي
+
+424
+00:48:27,230 --> 00:48:34,270
+الدائرة اللى موجودة في المستوى والتي تحقق ثلاثة
+
+425
+00:48:34,270 --> 00:48:40,970
+شروط الشرط الأول نمرا A is tangent to the curve at
+
+426
+00:48:40,970 --> 00:48:46,770
+P اه يعني احنا لو جينا قولنا على سبيل المثال
+
+427
+00:48:46,770 --> 00:48:52,510
+افترضوا اننا ملحنة بهذا الشكل يبقى هذا ال curve
+
+428
+00:48:52,510 --> 00:48:57,760
+اللى عندنابدي اجي عنده نقطة زي مين زي النقطة اللى
+
+429
+00:48:57,760 --> 00:49:05,860
+عندنا مثلا هذا بدي اقول هذا النقطة فيه الدائرة
+
+430
+00:49:05,860 --> 00:49:10,860
+اللى عندنا هتبقى ممثل للمنحنة عنده فيه بقول اه
+
+431
+00:49:10,860 --> 00:49:16,620
+بقدر ارسمها برا هنا و بقدر ارسمها جوا هنا بقدر
+
+432
+00:49:16,620 --> 00:49:21,180
+ارسم دائرة هنا و هنا تمام السؤال هو مين منهم
+
+433
+00:49:21,180 --> 00:49:27,710
+بالضغط بروح بكملنمرا بى has the same curvature as
+
+434
+00:49:27,710 --> 00:49:32,690
+the curve at P لها نفس التقوس يعني لها نفس قيمة
+
+435
+00:49:32,690 --> 00:49:37,470
+Kappa ما علينا نمرسى that's towards the concave
+
+436
+00:49:37,470 --> 00:49:43,530
+side أو ال inner side inner يعني داخلي يبقى جهة
+
+437
+00:49:43,530 --> 00:49:49,810
+التقوس الداخلي للمنحنة اه يعني لو جيت رسمتها بدت
+
+438
+00:49:49,810 --> 00:49:51,110
+يجين الدائرة هيك
+
+439
+00:49:54,890 --> 00:50:02,330
+في هذا الشكل يبقى الدائرة بتكون وين؟ للداخل زي ما
+
+440
+00:50:02,330 --> 00:50:09,750
+انتوا شايفين بتتمسك المنحنة عند مين؟ عند نقطة P و
+
+441
+00:50:09,750 --> 00:50:14,790
+تكون وين؟ جهة الداخل زي ما انتوا شايفين يبقى مرة
+
+442
+00:50:14,790 --> 00:50:15,310
+تالية
+
+443
+00:50:18,480 --> 00:50:23,220
+تانجنت هذا فيه يبقى المماس عنده فيه بده يمس
+
+444
+00:50:23,220 --> 00:50:29,960
+المنحنة ودائرة يعني الدائرة هذه اللي بالشكل اللي
+
+445
+00:50:29,960 --> 00:50:36,800
+عندنا هذا هيك بدي يكون لو رسمت مماس الشكل اللي
+
+446
+00:50:36,800 --> 00:50:42,190
+عندنا هذا بدي يكون هذا ال unit tangent vectorيبقى
+
+447
+00:50:42,190 --> 00:50:48,510
+تاني ال vector مماس للمنحنة و للدائرة في آلة واحدة
+
+448
+00:50:48,510 --> 00:50:52,290
+فهذا معنى النقطة الأولى النقطة التانية are the
+
+449
+00:50:52,290 --> 00:50:57,170
+same curvature لو حسبت ال curvature للمنحنة وال
+
+450
+00:50:57,170 --> 00:51:02,910
+curvature للدائرة الأتنين are the same طيب بنقدر
+
+451
+00:51:02,910 --> 00:51:09,470
+نعرف قداش ال curvature للدائرة يعني قداش عدديا
+
+452
+00:51:11,690 --> 00:51:17,610
+واحد على ال radius تواطنها ميفان الدائرة ال
+
+453
+00:51:17,610 --> 00:51:21,250
+curvature تبعها يسوى المقار نسبة واحد على نصف قطر
+
+454
+00:51:21,250 --> 00:51:30,330
+هذه الدائرة ممداز جدا يبقى لو عرفي الدائرة وعرف نص
+
+455
+00:51:30,330 --> 00:51:35,790
+القطر تبعها وطرد مني جداش ال curvature للمنحنة
+
+456
+00:51:35,790 --> 00:51:40,130
+بقول واحد على نصف القطر تبع الدائرة دائرة الانحنات
+
+457
+00:51:40,510 --> 00:51:46,230
+تمام تمام نمرة تلاتة تقع في الجزء الداخلي للمنحنة
+
+458
+00:51:46,230 --> 00:51:51,070
+وليس في الجزء الخارج لأنه لو رسمناها هنا بتجي برا
+
+459
+00:51:51,070 --> 00:51:56,430
+يبقى هي للداخل طيب نجي لل definition التاني قال
+
+460
+00:51:56,430 --> 00:52:04,950
+نصف قطر الإنحن للمنحنة عند النقطة B هو نصف قطرو
+
+461
+00:52:04,950 --> 00:52:11,610
+يسوى عمليا واحد على الكيربيتشار نص القطر يبجى هذا
+
+462
+00:52:11,610 --> 00:52:20,410
+نص القطر هذا اللي هو نص القطر يبجى
+
+463
+00:52:20,410 --> 00:52:33,430
+بنات هذا اسمه ال radius of curvature وهذه اسمها ال
+
+464
+00:52:33,430 --> 00:52:42,130
+circleof curvature هاي أبو هذا المركز الدائرة ال
+
+465
+00:52:42,130 --> 00:52:53,190
+center of curvature يبقى هذا اسمه ال center of
+
+466
+00:52:53,190 --> 00:52:55,250
+curvature
+
+467
+00:53:01,320 --> 00:53:07,580
+طلعت نصف قطر الإنحناء و نصف قطر دائرة الإنحناء و
+
+468
+00:53:07,580 --> 00:53:13,100
+يسوى عملياً رو تسوى واحد على كابة يبقى هذا ال
+
+469
+00:53:13,100 --> 00:53:19,640
+radius اللي هو رو تسوى واحد على كابة اللي هو
+
+470
+00:53:19,640 --> 00:53:27,650
+radius of curvatureعند النقطة
+
+471
+00:53:27,650 --> 00:53:33,800
+B هو ال center تبع دائرة الكيروفيتشاريبقى الأن
+
+472
+00:53:33,800 --> 00:53:38,900
+فهمنا معنى الـ circle of curvature عاملية السؤال
+
+473
+00:53:38,900 --> 00:53:44,020
+هو بتقدر تحسب radius of curvature و ال center of
+
+474
+00:53:44,020 --> 00:53:48,620
+curvature و ال equation تبع ال circle of curvature
+
+475
+00:53:48,620 --> 00:53:55,760
+أم لا هذا السؤال الذي سنجوب عليه بمثال عددي عشان
+
+476
+00:53:55,760 --> 00:53:59,980
+نعرف كيف نشتغل هذا الشغل نبقى example
+
+477
+00:54:05,960 --> 00:54:13,780
+يقولي find and graph يوجد and ارسم find and graph
+
+478
+00:54:13,780 --> 00:54:25,060
+مين؟ قاللي ده oscillating circle of
+
+479
+00:54:25,060 --> 00:54:28,360
+the
+
+480
+00:54:28,360 --> 00:54:32,320
+curve
+
+481
+00:54:32,320 --> 00:54:42,670
+للمنحنةR of T تساوي T في اتجاه I زائد Sine T في
+
+482
+00:54:42,670 --> 00:54:49,730
+اتجاه M في اتجاه G التي تساوي Pi على M
+
+483
+00:55:06,690 --> 00:55:10,410
+المنحنى لأننا لا نعرف أنه بنادر لماذا لا نعرف أنه
+
+484
+00:55:10,410 --> 00:55:14,930
+مُعطَى في الصيغة البرامترية لكن لو حولته لصيغة
+
+485
+00:55:14,930 --> 00:55:20,410
+كارتيزية لأصبح المنحنى معروف بالنسبة لنا وربما
+
+486
+00:55:20,410 --> 00:55:26,950
+يكون أسهل مما نتصور يبقى R of T باعتبار X of T في
+
+487
+00:55:26,950 --> 00:55:33,710
+اتجاه I زي Y of T في اتجاه J صح ولا لأ يبقى كأن X
+
+488
+00:55:33,710 --> 00:55:40,370
+هنا في سوء المينو ال y تساوي صين ال t هذا بدي
+
+489
+00:55:40,370 --> 00:55:45,950
+اعطيك مين ان ال y قد اتش سببنا صين ال x هذا
+
+490
+00:55:45,950 --> 00:55:50,270
+المنحنة معروف ولا لا يبقى المنحنة اللي عندنا منحنة
+
+491
+00:55:50,270 --> 00:55:56,130
+الجيب يبقى كويس تعرفنا على شكل المنحنة اللي بنقدر
+
+492
+00:55:56,130 --> 00:56:03,530
+نرسمه الآن صار بالنسبة لنا سهل طيب كويس بعد ذلكقال
+
+493
+00:56:03,530 --> 00:56:08,570
+لي فاهم و اقرا في ال circulating circle للمنحنة
+
+494
+00:56:08,570 --> 00:56:13,910
+اللى عندها بدك ترسمها وتوجدها كذلك لما يقول لي
+
+495
+00:56:13,910 --> 00:56:19,210
+وجدها يعني بدك توجد معادلتها إذا أنا مش هتوجد هذه
+
+496
+00:56:19,210 --> 00:56:22,330
+المعادلة بالزمن نصف القطر
+
+497
+00:56:26,700 --> 00:56:32,460
+هل المركز هو نقطة الاصل؟ ماهواش نقطة الاصل؟ الاخرى
+
+498
+00:56:32,460 --> 00:56:39,520
+هذا كله كلام بيقولوا
+
+499
+00:56:39,520 --> 00:56:45,340
+الله كويسيبقى انا بدي ايش؟ بدي معادلة الدائرة و
+
+500
+00:56:45,340 --> 00:56:50,680
+بدي مركز هذه الدائرة و اذا عرفت المركز و المعادلة
+
+501
+00:56:50,680 --> 00:56:55,120
+بكون عرفته ده جالي fine وبالتالي بصير سهل رسمها،
+
+502
+00:56:55,120 --> 00:57:02,900
+مظبوط؟ تمام تمام طيب بدنا نروح نحسب كل الشغلات
+
+503
+00:57:02,900 --> 00:57:08,280
+اللي بتلزمني مشان نعرف هذه المعادلةأنا عندي R of T
+
+504
+00:57:08,280 --> 00:57:14,600
+لو اشتقيتها بحصل على مين؟ على V يبقى باجي بقوله V
+
+505
+00:57:14,600 --> 00:57:22,020
+تساوي DR على DT اللي هي I زائد cosine T في اتجاه
+
+506
+00:57:22,020 --> 00:57:29,380
+ال G نحسب فول ال V اللي هو الجدري التربيعي لواحد
+
+507
+00:57:29,380 --> 00:57:36,880
+زائد cosine تربيع Tبقدر ألعب فيها أكتر من ذلك ولا
+
+508
+00:57:36,880 --> 00:57:42,520
+حاجة تمام يبقى زي مانيو يبقى هذا قول ال V بقدر
+
+509
+00:57:42,520 --> 00:57:48,180
+أجيب ال unit tangent T يبقى unit tangent T اللي هو
+
+510
+00:57:48,180 --> 00:57:52,380
+V على قول ال V يبقى بصير واحد
+
+511
+00:57:55,740 --> 00:58:01,840
+زائد cosine تربية T في اتجاه I زائد cosine T على
+
+512
+00:58:01,840 --> 00:58:06,720
+الجدر التربية الواحد زائد cosine تربية T في اتجاه
+
+513
+00:58:06,720 --> 00:58:13,260
+J او ان شئتم فاقولوا T يساوي واحد زائد cosine
+
+514
+00:58:13,260 --> 00:58:22,220
+تربية T قص سالب نص في اتجاه Iزائد cosine T في واحد
+
+515
+00:58:22,220 --> 00:58:29,180
+زائد cosine تربيع T أُس سالف نص في اتجاه مين؟ في
+
+516
+00:58:29,180 --> 00:58:34,540
+اتجاه الجيه يبقى أنا جبت ال unit tangent vector
+
+517
+00:58:34,540 --> 00:58:41,160
+اللي عندنا هنا الان بقدر اشتقه و قبل اشتقه من هنا
+
+518
+00:58:41,160 --> 00:58:47,830
+بنات لو قال لي V under Pi على اتنينيبقى ال V عند
+
+519
+00:58:47,830 --> 00:58:53,510
+ال باي على اتنين الطول تبعها يبقى بده يساوي الجدري
+
+520
+00:58:53,510 --> 00:59:00,270
+التربيعي ل واحد زائد جداش مصايب باي على اتنين صفرة
+
+521
+00:59:00,270 --> 00:59:10,930
+يبقى الجواب يساوي واحد صحيح طيب بده اجيبله الان ال
+
+522
+00:59:10,930 --> 00:59:13,370
+Dt على Dt
+
+523
+00:59:16,240 --> 00:59:24,240
+يبقى الأس في القوس مرفوع
+
+524
+00:59:24,240 --> 00:59:29,200
+لنفس الأس مطروح منه واحد في سالب ثلاثة على اتنين
+
+525
+00:59:29,200 --> 00:59:37,500
+في مشتقة مداخل القوس اللي هو اتنين بوصين ات في
+
+526
+00:59:37,500 --> 00:59:43,280
+سالب صين ات كل هذا في اتجاه الأرض
+
+527
+00:59:46,260 --> 00:59:51,740
+مرة تانية بدي أمسحها و أعيدها تاني عشان أخلص سطر
+
+528
+00:59:51,740 --> 01:00:01,900
+ساعة المشتقة كلها أترك هذا لحد هنا و بدا أقول DT
+
+529
+01:00:01,900 --> 01:00:10,940
+على DT يساق اللي هو سالب نص في اللي هو واحد زائد
+
+530
+01:00:10,940 --> 01:00:13,060
+cosine تربيع ال T
+
+531
+01:00:18,670 --> 01:00:24,610
+سالب اتنين وصين ال T في صين ال T كله في اتجاه ال I
+
+532
+01:00:24,610 --> 01:00:33,630
+اللي بعده زاد هذا مشتقت حاصل ضارب دالي تل يبقى
+
+533
+01:00:33,630 --> 01:00:40,110
+مشتقة الأولى بسالب صين يبقى هذا شبصي رملاد هذا زاد
+
+534
+01:00:40,110 --> 01:00:47,450
+وخليه جوز كله يبقى هاي سالب صين ال T في الجوز واحد
+
+535
+01:00:47,680 --> 01:00:55,200
+زائد cosine تربية T قص سالب نص زائد يبقى مشتقة
+
+536
+01:00:55,200 --> 01:01:00,860
+الأولى في الثانية اللى بعدها بده اشتق هذه مشتقة
+
+537
+01:01:00,860 --> 01:01:10,460
+هذه هي صح يبقى هذا الكلام بده يصير ماقص نص في
+
+538
+01:01:10,460 --> 01:01:17,500
+cosine T في واحد زائد cosine تربية T قص سالب تلاتى
+
+539
+01:01:20,060 --> 01:01:29,940
+في سالب اتنين Cos T في Sine T كل هذا في اتجاه مين؟
+
+540
+01:01:29,940 --> 01:01:36,280
+في اتجاه الـG مش واضحة اظن كبّرها شوية ونوضحها
+
+541
+01:01:36,280 --> 01:01:39,400
+يبقى
+
+542
+01:01:39,400 --> 01:01:49,820
+هذا كله مضروب في سالب اتنين Cos T في Sine Tوهي
+
+543
+01:01:49,820 --> 01:01:57,500
+قفلنا الجوس هذا كله لكبير في اتجاه من؟ في اتجاه
+
+544
+01:01:57,500 --> 01:02:00,560
+الجهة
+
+545
+01:02:00,560 --> 01:02:06,420
+يبقى ان اجيبنا دي تي على دي تي بدي احسبله قداش ال
+
+546
+01:02:06,420 --> 01:02:12,020
+دي تي على دي تي اتجمع اكتر بديش اقعد اجمع وضيع
+
+547
+01:02:12,020 --> 01:02:16,520
+اكتر اللي انا بده اعوض دغري طلع يا بنات هناهذه باي
+
+548
+01:02:16,520 --> 01:02:21,560
+على اتنين مقداشي ب zero بظل واحد لأي أس يبقى واحد
+
+549
+01:02:21,560 --> 01:02:26,840
+في نص يبقى هذا ناقص نص وهذا مقداشي ب zero لإنه صار
+
+550
+01:02:26,840 --> 01:02:30,540
+باي على اتنين و واحد في نص يبقى هذا كله صار ب zero
+
+551
+01:02:30,540 --> 01:02:37,850
+في اتجاه الأعلى نجي لبعدهذه باية على اتنين نرجع
+
+552
+01:02:37,850 --> 01:02:42,690
+لسؤالنا مرة ثانية لما تبقى المستقم كالكعة كبيرة زي
+
+553
+01:02:42,690 --> 01:02:46,090
+هيك مش سواء يتجمع فيها و مافيه اتعاوض، هذه بقى وقت
+
+554
+01:02:46,090 --> 01:02:50,870
+كتير، انت بتعاوض مباشرة، تبحث في القيام دوري، فبجي
+
+555
+01:02:50,870 --> 01:02:55,870
+بقوله هنا، بجي بقوله، بدي أشيل كلتي و أحط مكانها
+
+556
+01:02:55,870 --> 01:02:58,050
+باية على اتنين، لإنه قال لي بدي الكلام هذا عند
+
+557
+01:02:58,050 --> 01:03:02,980
+باية على اتنينفبعدين بقوله هنا by على 2 بـ 0 و بظل
+
+558
+01:03:02,980 --> 01:03:07,500
+1 أُس أي رقم بواحد في نص يبقى هنا السلب نص و هنا
+
+559
+01:03:07,500 --> 01:03:11,540
+zero يبقى كله نص في zero اختار كله بـ zero zero في
+
+560
+01:03:11,540 --> 01:03:17,180
+اتجاه العين نجي لهنا هذا بواحد وهنا اللي هو كله
+
+561
+01:03:17,180 --> 01:03:24,020
+بواحد تمام يبقى هنا عندي ناقص واحد وعندي هنا يبقى
+
+562
+01:03:24,020 --> 01:03:27,740
+هذا ناقص واحد هشوف التاني شو بده يجيبلي هذا ال
+
+563
+01:03:27,740 --> 01:03:35,560
+zero كلهيبقى بظل بس قداش ناقص جيه في الشكل لأن هذا
+
+564
+01:03:35,560 --> 01:03:41,760
+الكلام اللي هو بيبقى ناقص جيه طيب من هذه الحالة
+
+565
+01:03:41,760 --> 01:03:46,600
+بقدر اقول اه بستنى شوية تديني بالك ان اصلا هنا
+
+566
+01:03:46,600 --> 01:03:52,720
+ناقص هنا ناقص هذه بتروح وهذه بظل لها مظبوط هذه
+
+567
+01:03:52,720 --> 01:03:57,060
+كلها بتروح و تجيبها ماشي يبقى هذا بدي يعطينا طول
+
+568
+01:03:57,060 --> 01:04:03,930
+ال DTعلى DT قولوا بتساوي كده؟ واحد صحيح إذا بقدر
+
+569
+01:04:03,930 --> 01:04:10,350
+أحسب ال curvature ولا لا؟ طيب ال curvature اللي هو
+
+570
+01:04:10,350 --> 01:04:19,210
+كبه تساوي طول ال V عندي وطول ال DT على DT عندي إذا
+
+571
+01:04:19,210 --> 01:04:26,910
+صارت قصتنا سهل جدا كده؟
+
+572
+01:04:26,910 --> 01:04:28,330
+كده؟ كده؟ كده؟ كده؟ كده؟ كده؟ كده؟ كده؟ كده؟ كده؟
+
+573
+01:04:39,180 --> 01:04:46,620
+بتساومين طول ال DT على DT برضه عند ال Y على 2
+
+574
+01:04:46,620 --> 01:04:53,780
+مبسوما على طول ال V عند ال Y على 2 Y يساوي واحد
+
+575
+01:04:53,780 --> 01:04:59,040
+على واحد يساوي واحد الان بدي ال radius of the
+
+576
+01:04:59,040 --> 01:05:05,740
+circle of curvature الجبالي بقولوا the radius of
+
+577
+01:05:06,290 --> 01:05:16,890
+the circle of curvature around تسوى واحد على كده
+
+578
+01:05:16,890 --> 01:05:22,530
+كده بقداش عندنا واحد يبقى واحد على واحد هو يسوى
+
+579
+01:05:22,530 --> 01:05:28,870
+كده واحد يبقى نصف قطر دائرة الانحلال يسوى كده واحد
+
+580
+01:05:28,870 --> 01:05:34,220
+صحيح ممتاز شو ضال عندنا؟المركز مشان نحسب المركز
+
+581
+01:05:34,220 --> 01:05:38,720
+تعالوا نرسم المنحنى اللى عندنا ونشوف كيف بدنا نجيب
+
+582
+01:05:38,720 --> 01:05:45,080
+المركز منه لو جينا للمنحنى اللى عندنا بالشكل هذا
+
+583
+01:05:45,080 --> 01:05:54,500
+هذا محور X هذا محور Y وجيت تخيل ان هذا الخط الوهمى
+
+584
+01:05:54,500 --> 01:05:55,880
+عندنا واحد
+
+585
+01:06:04,420 --> 01:06:09,840
+تفاجنا من هنا على ان المنحنى هو منحنى الجب أو الـ
+
+586
+01:06:09,840 --> 01:06:16,460
+signكر لو رجعنا الى calculus A و رسمنا المنحنى
+
+587
+01:06:16,460 --> 01:06:24,400
+فالمنحنى طبعا بيجي هك و بيجي نازل هك و هكذا
+
+588
+01:06:38,820 --> 01:06:51,500
+هذه النقطة باية على اتنين وهذه النقطة باية على
+
+589
+01:06:51,500 --> 01:06:57,280
+اتنين وهذه النقطة باية على اتنين وهذه النقطة باية
+
+590
+01:07:08,420 --> 01:07:15,020
+عشان تطلعين هنا، كداش نصف القطر واحد صحيح، كداش
+
+591
+01:07:15,020 --> 01:07:19,940
+المسافة هذه كلها بنات واحد، إذا بدي يجي المركز
+
+592
+01:07:19,940 --> 01:07:26,700
+تبعها هذه، وجهة الكونكية بصعيد مش فوق هتكون ده،
+
+593
+01:07:26,700 --> 01:07:28,720
+إذا الدائرة هصير
+
+594
+01:07:49,850 --> 01:07:54,810
+تمام؟ يبقى صارت عندي دائرة بهذا الشكل السؤال هو حد
+
+595
+01:07:54,810 --> 01:08:02,590
+فيكم بتقدر تقولي جداش إحداه في المركز؟ تمام باي
+
+596
+01:08:02,590 --> 01:08:08,110
+عتنين و زيرو هذا ال X من هنا لهنا و باي على اتنين
+
+597
+01:08:08,110 --> 01:08:09,950
+و ال Y مهي بزيرو
+
+598
+01:08:33,380 --> 01:08:39,880
+يبقى كويس يبقى ناقص
+
+599
+01:08:39,880 --> 01:08:47,420
+y على 2 لكل تربيع يبقى
+
+600
+01:08:47,420 --> 01:08:49,840
+ناقص y على 2 لكل قطار
+
+601
+01:08:53,120 --> 01:09:04,040
+يبقى هذه ال equation of the circle of
+
+602
+01:09:04,040 --> 01:09:08,780
+curvature قال
+
+603
+01:09:08,780 --> 01:09:14,920
+لي اوجد و ارسم رسمنا و اوجدنا اللي هو الدائرة و
+
+604
+01:09:14,920 --> 01:09:18,860
+المركز تبعها و ال center و ما إلى ذلك يبقى ده ايش
+
+605
+01:09:18,860 --> 01:09:25,320
+اسم المنقطة ده يا بنات؟الـ radius of curvature
+
+606
+01:09:25,320 --> 01:09:29,620
+اللي هو ال radius of the circle of curvature هذا
+
+607
+01:09:29,620 --> 01:09:34,500
+ال center of curvature اللي هو ال center تبع ال
+
+608
+01:09:34,500 --> 01:09:39,160
+radius of curvature هذه الدائرة كلها ال circle of
+
+609
+01:09:39,160 --> 01:09:44,100
+curvature يبقى هذه الدائرة ها اللي هي ال circle
+
+610
+01:09:53,880 --> 01:09:57,240
+طيب، الشغل اللي اشتغلناه كله هذا الوقت كان على
+
+611
+01:09:57,240 --> 01:10:04,600
+مين؟ على الـ plane و هو الآن ننتقل إلى الشغل في
+
+612
+01:10:04,600 --> 01:10:09,800
+الفرار الشغل
+
+613
+01:10:09,800 --> 01:10:14,700
+في الفرار لن يختلف عن ال plane ولا حاجة نفس
+
+614
+01:10:14,700 --> 01:10:18,740
+المعلومات اللي أخذناها على ال plane صحيحة على
+
+615
+01:10:18,740 --> 01:10:26,140
+الفراراللهم إلا بشري عندي تلات مركبات بدلا من
+
+616
+01:10:26,140 --> 01:10:31,260
+مركبتين وبعدين بدي أحطها في شبكة remark التالية
+
+617
+01:10:31,260 --> 01:10:36,940
+remark if
+
+618
+01:10:36,940 --> 01:10:45,160
+we have a space curve if we have
+
+619
+01:10:45,160 --> 01:10:48,060
+a space curve
+
+620
+01:11:13,140 --> 01:11:25,830
+نفس النتائجas the case as the case of the plane
+
+621
+01:11:25,830 --> 01:11:34,330
+curve كما في حالة المنحنة في مستوى نعطي مثال for
+
+622
+01:11:34,330 --> 01:11:37,490
+example
+
+623
+01:11:37,490 --> 01:11:47,540
+you will find الـT و الـN and الكيروتشاركاتfor the
+
+624
+01:11:47,540 --> 01:11:58,880
+space curve for the space curve اللي همين R of T
+
+625
+01:11:58,880 --> 01:12:09,120
+بده يساوي E أس T cosine T في اتجاه I زائد E أس T
+
+626
+01:12:09,120 --> 01:12:15,780
+sine T في اتجاه J زائد 2K
+
+627
+01:12:43,260 --> 01:12:48,260
+السؤال مرة ثانية بيقول ان لو انتقلنا من المستوى
+
+628
+01:12:48,260 --> 01:12:51,960
+إلى الفرار هل المعلومات اللي هتتغير و لا تبقى كما
+
+629
+01:12:51,960 --> 01:12:57,760
+هي؟ الإجابة تبقى كما هي نعطي مثال توضيحي بيقول
+
+630
+01:12:57,760 --> 01:13:01,700
+هاتلي ال unit tangent و ال principal normal و ال
+
+631
+01:13:01,700 --> 01:13:06,200
+curvature لل space curve اروكتي بيبقى كذا يبقى
+
+632
+01:13:06,200 --> 01:13:12,900
+باجي بيقول انه solutionبدي اوجد دموعين ال V of T
+
+633
+01:13:12,900 --> 01:13:19,530
+اللي هى TR على Dيبدأ اشتق هذه حوارة حاصل ضرب
+
+634
+01:13:19,530 --> 01:13:27,130
+داليتين يبقى لو اشتقت ال Eost في Eost وSin T ناقص
+
+635
+01:13:27,130 --> 01:13:36,810
+Eost Sin T هذا في اتجاه I زائد Eost Sin T زائد
+
+636
+01:13:36,810 --> 01:13:45,560
+Eost Sin T كله في اتجاه J زائدهذا كل الـ sine كله
+
+637
+01:13:45,560 --> 01:13:52,100
+بـ 0 تمام؟ بدي أجيب وقول أوه بقدر أقول هذه E أُس T
+
+638
+01:13:52,100 --> 01:13:59,580
+في Cos T نقص Sine T في اتجاه I زائد E أُس T في
+
+639
+01:13:59,580 --> 01:14:06,080
+Sine T زائد Cos T كله في اتجاه مين؟ في اتجاه الـ J
+
+640
+01:14:06,080 --> 01:14:14,860
+بدي أجيب له طول الـ V يبقى الجذر الترابي يمينيقص
+
+641
+01:14:14,860 --> 01:14:24,920
+اتنين T في cosine تربية T نقص اتنين sin T cosine T
+
+642
+01:14:24,920 --> 01:14:31,260
+زائد sin تربية T زائدبتاخد هذه وهذه ت برا منهم
+
+643
+01:14:31,260 --> 01:14:36,700
+عاملة مشتركة يبقى بضربها هذه بالمرة يبقى sin تربيه
+
+644
+01:14:36,700 --> 01:14:45,220
+ت زائد اتنين sin t cos t زائد cos تربيه تطبعا هذه
+
+645
+01:14:45,220 --> 01:14:49,200
+بالموجة وهذه بالسالب مع السلامة بس يبقى لديها
+
+646
+01:14:49,200 --> 01:14:55,420
+بناءت اتنين sin تربية و اتنين cosine تربية يبقى
+
+647
+01:14:55,420 --> 01:15:01,560
+هذا الكلام الجذري التربية ل E اص اتنين T في اتنين
+
+648
+01:15:01,560 --> 01:15:08,530
+cosine تربية T زائد cosine تربية P له قدرأو 1
+
+649
+01:15:08,530 --> 01:15:14,490
+الجدرى التربية اللي هي 2E أُس 2E هو يساوي جدرى 2
+
+650
+01:15:14,490 --> 01:15:20,890
+في مين؟ في E أُس Tطب بدأ أجيب له المطلوب الأول ال
+
+651
+01:15:20,890 --> 01:15:27,650
+unit tangent vector T يبقى T بدأ تساوي المتجه V
+
+652
+01:15:27,650 --> 01:15:32,490
+على طول المتجه V يعني بدي أقسم على مين على المقدار
+
+653
+01:15:32,490 --> 01:15:37,630
+اللي عندنا هذا وين ال V هي ال V يبقى بدي أقسم على
+
+654
+01:15:37,630 --> 01:15:42,030
+U of T بالطير هذه و الطير هذه و جيك مين واحد على
+
+655
+01:15:42,030 --> 01:15:49,940
+جدر اتنين يبقى واحد على جدر اتنين في مينبـ cos T
+
+656
+01:15:49,940 --> 01:15:56,300
+نقص sin T في اتجاه الـ I زائد واحد على جدر اتنين
+
+657
+01:15:56,300 --> 01:16:03,200
+بـ sin T زائد cos T في اتجاه من؟ في اتجاه الـ J
+
+658
+01:16:03,200 --> 01:16:10,220
+يبقى جيبناه من المطلوب الأول المطلوب التاني شوف
+
+659
+01:16:10,220 --> 01:16:19,020
+الزمن هنا يبقى أشتق هذا يبقى بداجي أخده DTعلى DT
+
+660
+01:16:19,020 --> 01:16:25,380
+ويسوي 1 على جذر 2 يبقى على الحياد الإيجابي وعدم
+
+661
+01:16:25,380 --> 01:16:32,700
+الانحياز يبقى من الاشتقال ما يصير ماقص sin T وهذا
+
+662
+01:16:32,700 --> 01:16:40,110
+ماقص في sin T كله في اتجاه Iو هذي زائد واحدة على
+
+663
+01:16:40,110 --> 01:16:45,770
+جدر اتنين تقص صين T نقص صين T في اتجاه مين؟ في
+
+664
+01:16:45,770 --> 01:16:51,510
+اتجاه الجهة بدي الطول تبعه يبقى
+
+665
+01:17:01,770 --> 01:17:06,950
+لو أخدت ناقص ما ناقص يطلع برا مربعه بطير الله يسهل
+
+666
+01:17:06,950 --> 01:17:14,190
+عليه وواحد عليه جدر اتنين مربعه بنص يبقى هذا نص في
+
+667
+01:17:14,190 --> 01:17:22,070
+مين؟ في .. بدي أربع هذه بزايد كلها بصير sin تربية
+
+668
+01:17:22,070 --> 01:17:33,030
+T زي دي اتنين sin T cos T زي كسين تربية Tزاد هذه
+
+669
+01:17:33,030 --> 01:17:37,970
+كمان لو ربعتها بيصير مين؟ مُص يبقى بده أخليه برا،
+
+670
+01:17:37,970 --> 01:17:44,370
+هاي الخط برا، يبقى بده أجيب تربيه هذه Cos تربيه T
+
+671
+01:17:44,370 --> 01:17:53,230
+نقص اتنين Sine T Cos T زائد Sine تربيه T تمام؟
+
+672
+01:17:55,760 --> 01:18:01,960
+هذه موجبة وهذه سلبة مع السلامة بيصير اتنين بصين
+
+673
+01:18:01,960 --> 01:18:09,780
+تربية زي اتنين صين تربية يبقى الجذر التربيهي لنص
+
+674
+01:18:09,780 --> 01:18:13,740
+في اتنين في صين تربيهي
+
+675
+01:18:29,440 --> 01:18:40,020
+DT على DT نقصوم على قول DT على DT الـ DT على DT هي
+
+676
+01:18:40,020 --> 01:18:48,840
+على واحد يبقى بظل زي ما هو يبقى هذا الكلام سالم
+
+677
+01:18:48,840 --> 01:18:57,100
+واحد على جدر اثنين في الـ sineت زائد cosine ت كل
+
+678
+01:18:57,100 --> 01:19:03,560
+هذا في اتجاه ال I واحد على جانر اتنين فيه cosine T
+
+679
+01:19:03,560 --> 01:19:10,760
+ناقص sine T كله في اتجاه من الجيب ضال ان الكيربت
+
+680
+01:19:10,760 --> 01:19:18,800
+شارك هذا كم جداش بيساوي طول ال DT على DT على طول
+
+681
+01:19:18,800 --> 01:19:20,860
+ال V يبقى
+
+682
+01:19:30,370 --> 01:19:39,330
+طول ال V طول ال V له اتنين او جدر اتنين E أسطى
+
+683
+01:19:39,330 --> 01:19:47,390
+يبقى جدر اتنين E أسطىيبقى هذا الكلام معناته يعني
+
+684
+01:19:47,390 --> 01:19:55,490
+واحد على جدر اتنين او واحد على جدر اتنين في إيه
+
+685
+01:19:55,490 --> 01:20:00,510
+والسالب فيه يبقى هذا ال curve شركابة اللي موجودة
+
+686
+01:20:00,510 --> 01:20:08,170
+هنا او اللي هو بده يعني لحد هنا stop يا بنات المرة
+
+687
+01:20:08,170 --> 01:20:12,230
+الجاية بجيبكوا ان شاء الله أرقام المسائل تبعت هذا
+
+688
+01:20:12,230 --> 01:20:12,790
+ال section
+
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/SmdhLcwuMIw_raw.json b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/SmdhLcwuMIw_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..1a79985d88dd2346f1037ab8f579b8b24e37d94d
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/SmdhLcwuMIw_raw.json
@@ -0,0 +1 @@
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"end": 1697.78, "word": " على", "probability": 0.78662109375}, {"start": 1697.78, "end": 1698.14, "word": " S", "probability": 0.875}, {"start": 1698.14, "end": 1698.82, "word": " يبقى", "probability": 0.69586181640625}, {"start": 1698.82, "end": 1699.1, "word": " أنا", "probability": 0.484375}, {"start": 1699.1, "end": 1699.42, "word": " بده", "probability": 0.65478515625}, {"start": 1699.42, "end": 1699.8, "word": " أجيب", "probability": 0.906005859375}, {"start": 1699.8, "end": 1699.96, "word": " ال", "probability": 0.76416015625}, {"start": 1699.96, "end": 1700.44, "word": " principle", "probability": 0.607421875}, {"start": 1700.44, "end": 1700.82, "word": " normal", "probability": 0.5439453125}, {"start": 1700.82, "end": 1701.16, "word": " بدون", "probability": 0.9912109375}, {"start": 1701.16, "end": 1701.3, "word": " اللي", "probability": 0.7220458984375}, {"start": 1701.3, "end": 1701.58, "word": " أجيب", "probability": 0.9293212890625}, {"start": 1701.58, "end": 1701.72, "word": " ال", "probability": 0.880859375}, {"start": 1701.72, "end": 1702.16, "word": " curvature", "probability": 0.9404296875}, {"start": 1702.16, "end": 1702.98, "word": " ولا", "probability": 0.3759765625}, {"start": 1702.98, "end": 1703.3, "word": " أجيب", "probability": 0.941650390625}, {"start": 1703.3, "end": 1703.42, "word": " ال", "probability": 0.94775390625}, {"start": 1703.42, "end": 1703.64, "word": " arc", "probability": 0.72900390625}, {"start": 1703.64, "end": 1704.14, "word": " parameter", "probability": 0.9716796875}, {"start": 1704.14, "end": 1704.7, "word": " length", "probability": 0.80517578125}, {"start": 1704.7, "end": 1705.04, "word": " اللي", "probability": 0.962890625}, {"start": 1705.04, "end": 1705.22, "word": " هو", "probability": 0.9306640625}, {"start": 1705.22, "end": 1705.52, "word": " main", "probability": 0.86474609375}, {"start": 1705.52, "end": 1706.32, "word": " S", "probability": 0.80712890625}, {"start": 1706.32, "end": 1707.06, "word": " كيف؟", "probability": 0.87841796875}, {"start": 1707.06, "end": 1707.96, "word": " كالتالي", "probability": 0.87939453125}, {"start": 1707.96, "end": 1708.44, "word": " as", "probability": 0.75927734375}, {"start": 1708.44, "end": 1708.94, "word": " follows", "probability": 0.395263671875}], "temperature": 1.0}, {"id": 69, "seek": 174579, "start": 1716.57, "end": 1745.79, "text": "بساوي واحد على الـ curvature كابة في الـ DT على DS و يمسك هذا بقدر اقول DT على DS الكابة اللي و مين اللي هي طول الـ DT على DS طبعا بقدر اقول هذا الكلمة", "tokens": [3555, 3794, 995, 45865, 36764, 24401, 15844, 2423, 39184, 37638, 9122, 16758, 3660, 8978, 2423, 39184, 413, 51, 15844, 15816, 4032, 7251, 2304, 3794, 4117, 23758, 4724, 28543, 2288, 1975, 39648, 413, 51, 15844, 15816, 33251, 16758, 3660, 13672, 1829, 4032, 3714, 9957, 13672, 1829, 39896, 23032, 12610, 2423, 39184, 413, 51, 15844, 15816, 23032, 3555, 3615, 995, 4724, 28543, 2288, 1975, 39648, 23758, 33251, 19528, 3660], "avg_logprob": 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"probability": 0.92578125}, {"start": 1723.11, "end": 1723.39, "word": " و", "probability": 0.7919921875}, {"start": 1723.39, "end": 1723.91, "word": " يمسك", "probability": 0.626220703125}, {"start": 1723.91, "end": 1728.03, "word": " هذا", "probability": 0.454833984375}, {"start": 1728.03, "end": 1729.07, "word": " بقدر", "probability": 0.7850748697916666}, {"start": 1729.07, "end": 1729.49, "word": " اقول", "probability": 0.7734375}, {"start": 1729.49, "end": 1730.75, "word": " DT", "probability": 0.76611328125}, {"start": 1730.75, "end": 1731.83, "word": " على", "probability": 0.85302734375}, {"start": 1731.83, "end": 1732.69, "word": " DS", "probability": 0.98779296875}, {"start": 1732.69, "end": 1734.13, "word": " الكابة", "probability": 0.9298502604166666}, {"start": 1734.13, "end": 1734.71, "word": " اللي", "probability": 0.802978515625}, {"start": 1734.71, "end": 1734.83, "word": " و", "probability": 0.352783203125}, {"start": 1734.83, "end": 1735.25, "word": " مين", "probability": 0.68212890625}, {"start": 1735.25, "end": 1735.67, "word": " اللي", "probability": 0.881103515625}, {"start": 1735.67, "end": 1735.97, "word": " هي", "probability": 0.513671875}, {"start": 1735.97, "end": 1736.75, "word": " طول", "probability": 0.885986328125}, {"start": 1736.75, "end": 1737.53, "word": " الـ", "probability": 0.5780029296875}, {"start": 1737.53, "end": 1738.65, "word": " DT", "probability": 0.924560546875}, {"start": 1738.65, "end": 1739.47, "word": " على", "probability": 0.88037109375}, {"start": 1739.47, "end": 1740.13, "word": " DS", "probability": 0.98486328125}, {"start": 1740.13, "end": 1743.71, "word": " طبعا", "probability": 0.8370361328125}, {"start": 1743.71, "end": 1744.97, "word": " بقدر", "probability": 0.8546549479166666}, {"start": 1744.97, "end": 1745.25, "word": " اقول", "probability": 0.91845703125}, {"start": 1745.25, "end": 1745.57, "word": " هذا", "probability": 0.93408203125}, {"start": 1745.57, "end": 1745.79, "word": " الكلمة", "probability": 0.671875}], "temperature": 1.0}, {"id": 70, "seek": 176506, "start": 1749.16, "end": 1765.06, "text": "على DT في DT على DS على طول الـ DT على DT في DT على DS", "tokens": [3615, 23942, 413, 51, 8978, 413, 51, 15844, 15816, 15844, 23032, 12610, 2423, 39184, 413, 51, 15844, 413, 51, 8978, 413, 51, 15844, 15816], "avg_logprob": -0.20281249523162842, "compression_ratio": 1.6808510638297873, "no_speech_prob": 0.0, "words": [{"start": 1749.16, "end": 1749.68, "word": "على", "probability": 0.91552734375}, {"start": 1749.68, "end": 1750.42, "word": " DT", "probability": 0.4326171875}, {"start": 1750.42, "end": 1751.02, "word": " في", "probability": 0.7470703125}, {"start": 1751.02, "end": 1752.1, "word": " DT", "probability": 0.908447265625}, {"start": 1752.1, "end": 1752.92, "word": " على", "probability": 0.8974609375}, {"start": 1752.92, "end": 1753.62, "word": " DS", "probability": 0.966796875}, {"start": 1753.62, "end": 1754.68, "word": " على", "probability": 0.73779296875}, {"start": 1754.68, "end": 1757.84, "word": " طول", "probability": 0.74755859375}, {"start": 1757.84, "end": 1758.78, "word": " الـ", "probability": 0.65673828125}, {"start": 1758.78, "end": 1759.4, "word": " DT", "probability": 0.90869140625}, {"start": 1759.4, "end": 1760.32, "word": " على", "probability": 0.87548828125}, {"start": 1760.32, "end": 1761.28, "word": " DT", "probability": 0.9638671875}, {"start": 1761.28, "end": 1761.76, "word": " في", "probability": 0.91162109375}, {"start": 1761.76, "end": 1762.8, "word": " DT", "probability": 0.962890625}, {"start": 1762.8, "end": 1763.94, "word": " على", "probability": 0.923828125}, {"start": 1763.94, "end": 1765.06, "word": " DS", "probability": 0.9755859375}], "temperature": 1.0}, {"id": 71, "seek": 182240, "start": 1793.66, "end": 1822.4, "text": "الـ Dt على Ds اتفقنا انها scalar طيب مرة الماضية الـ Dt على Ds أقل من الـ Zero ولا أكبر من الـ Zero أكبر من الـ Zero اكبر من الـ Zero يبقى Ds على Dt هي طول ال V وطول موجة مظبوط يبقى قيمة الموجة بلو قلبتها بسيستراليب والله بظلها موجة بقى بظلها موجة بقى ممتاز جدا", "tokens": [6027, 39184, 413, 83, 15844, 413, 82, 1975, 2655, 5172, 4587, 8315, 16472, 11296, 39684, 23032, 1829, 3555, 3714, 25720, 9673, 46958, 10632, 2423, 39184, 413, 83, 15844, 413, 82, 5551, 4587, 1211, 9154, 2423, 39184, 17182, 49429, 5551, 4117, 26890, 9154, 2423, 39184, 17182, 5551, 4117, 26890, 9154, 2423, 39184, 17182, 1975, 4117, 26890, 9154, 2423, 39184, 17182, 7251, 3555, 4587, 7578, 413, 82, 15844, 413, 83, 39896, 23032, 12610, 2423, 691, 4032, 9566, 12610, 3714, 29245, 3660, 3714, 19913, 3555, 2407, 9566, 7251, 3555, 4587, 7578, 12174, 32640, 3660, 9673, 29245, 3660, 4724, 1211, 2407, 12174, 46152, 2655, 11296, 4724, 3794, 1829, 14851, 2288, 6027, 1829, 3555, 16070, 43761, 4724, 19913, 1211, 11296, 3714, 29245, 3660, 4724, 4587, 7578, 4724, 19913, 1211, 11296, 3714, 29245, 3660, 4724, 4587, 7578, 3714, 2304, 2655, 31377, 10874, 28259], "avg_logprob": -0.25022646244885266, "compression_ratio": 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"seek": 306947, "start": 3041.57, "end": 3069.47, "text": "يبقى تاني ال vector مماس للمنحنة و للدائرة في آلة واحدة فهذا معنى النقطة الأولى النقطة التانية are the same curvature لو حسبت ال curvature للمنحنة وال curvature للدائرة الأتنين are the same طيب بنقدر نعرف قداش ال curvature للدائرة يعني قداش عدديا", "tokens": [1829, 3555, 4587, 7578, 6055, 7649, 1829, 2423, 8062, 3714, 15042, 3794, 5296, 19528, 1863, 5016, 1863, 3660, 4032, 24976, 3215, 16373, 25720, 8978, 19753, 37977, 36764, 24401, 3660, 6156, 3224, 15730, 20449, 1863, 7578, 28239, 47432, 3660, 16247, 12610, 7578, 28239, 47432, 3660, 16712, 7649, 10632, 366, 264, 912, 37638, 45164, 11331, 35457, 2655, 2423, 37638, 5296, 19528, 1863, 5016, 1863, 3660, 16070, 37638, 24976, 3215, 16373, 25720, 16247, 2655, 1863, 9957, 366, 264, 912, 23032, 1829, 3555, 44945, 28543, 2288, 8717, 3615, 28480, 12174, 3215, 33599, 2423, 37638, 24976, 3215, 16373, 25720, 37495, 22653, 12174, 3215, 33599, 6225, 3215, 16254, 995], "avg_logprob": 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"word": " حسبت", "probability": 0.9412434895833334}, {"start": 3054.79, "end": 3054.89, "word": " ال", "probability": 0.5888671875}, {"start": 3054.89, "end": 3055.49, "word": " curvature", "probability": 0.7294921875}, {"start": 3055.49, "end": 3056.61, "word": " للمنحنة", "probability": 0.9747721354166666}, {"start": 3056.61, "end": 3057.17, "word": " وال", "probability": 0.83154296875}, {"start": 3057.17, "end": 3057.71, "word": " curvature", "probability": 0.3759765625}, {"start": 3057.71, "end": 3058.43, "word": " للدائرة", "probability": 0.94775390625}, {"start": 3058.43, "end": 3059.19, "word": " الأتنين", "probability": 0.7100830078125}, {"start": 3059.19, "end": 3060.01, "word": " are", "probability": 0.8671875}, {"start": 3060.01, "end": 3060.27, "word": " the", "probability": 0.923828125}, {"start": 3060.27, "end": 3060.69, "word": " same", "probability": 0.91259765625}, {"start": 3060.69, "end": 3062.23, "word": " طيب", "probability": 0.9583333333333334}, {"start": 3062.23, 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مني جداش ال curvature للمنحنة بقول واحد على نصف القطر تبع الدائرة دائرة الانحنات", "tokens": [14407, 24401, 15844, 2423, 15845, 33427, 41193, 1863, 11296, 3714, 33911, 7649, 32748, 16373, 25720, 2423, 37638, 6055, 3555, 3615, 11296, 7251, 3794, 2407, 7578, 9673, 4587, 9640, 8717, 35457, 3660, 36764, 24401, 15844, 8717, 9381, 5172, 12174, 9566, 2288, 29538, 32748, 16373, 25720, 3714, 2304, 3215, 31377, 10874, 28259, 7251, 3555, 4587, 7578, 45164, 6225, 28480, 1829, 32748, 16373, 25720, 4032, 3615, 28480, 8717, 9381, 25062, 9566, 2288, 6055, 3555, 3615, 11296, 4032, 9566, 2288, 3215, 9154, 1829, 10874, 3215, 33599, 2423, 37638, 5296, 19528, 1863, 5016, 1863, 3660, 4724, 39648, 36764, 24401, 15844, 8717, 9381, 5172, 25062, 9566, 2288, 6055, 3555, 3615, 32748, 16373, 25720, 11778, 16373, 25720, 2423, 7649, 5016, 8315, 2655], "avg_logprob": -0.1951778076332191, "compression_ratio": 2.0954773869346734, "no_speech_prob": 0.0, "words": [{"start": 3071.69, "end": 3072.31, "word": "واحد", 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"text": "تفاجنا من هنا على ان المنحنى هو منحنى الجب أو الـ signكر لو رجعنا الى calculus A و رسمنا المنحنى فالمنحنى طبعا بيجي هك و بيجي نازل هك و هكذا", "tokens": [2655, 5172, 26108, 8315, 9154, 34105, 15844, 16472, 9673, 1863, 5016, 1863, 7578, 31439, 9154, 5016, 1863, 7578, 25724, 3555, 34051, 2423, 39184, 1465, 37983, 45164, 12602, 7435, 3615, 8315, 2423, 7578, 33400, 316, 4032, 12602, 38251, 8315, 9673, 1863, 5016, 1863, 7578, 6156, 45340, 1863, 5016, 1863, 7578, 23032, 3555, 3615, 995, 4724, 1829, 7435, 1829, 8032, 4117, 4032, 4724, 1829, 7435, 1829, 8717, 31377, 1211, 8032, 4117, 4032, 8032, 4117, 15730], "avg_logprob": -0.38154562260653524, "compression_ratio": 1.63013698630137, "no_speech_prob": 3.2782554626464844e-06, "words": [{"start": 3964.42, "end": 3965.66, "word": "تفاجنا", "probability": 0.317413330078125}, {"start": 3965.66, "end": 3965.84, "word": " من", "probability": 0.76708984375}, {"start": 3965.84, "end": 3966.12, "word": " هنا", "probability": 0.97314453125}, 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من مركبتين وبعدين بدي أحطها في شبكة remark التالية remark if we have a space curve if we have a space curve", "tokens": [6027, 43761, 2304, 11933, 15040, 4724, 8592, 16572, 18871, 16254, 6055, 1211, 9307, 3714, 31747, 3555, 9307, 47525, 15040, 9154, 3714, 31747, 3555, 2655, 9957, 46599, 22488, 9957, 4724, 16254, 5551, 5016, 9566, 11296, 8978, 13412, 3555, 4117, 3660, 7942, 16712, 6027, 10632, 7942, 498, 321, 362, 257, 1901, 7605, 498, 321, 362, 257, 1901, 7605], "avg_logprob": -0.35827849622358354, "compression_ratio": 1.5107913669064748, "no_speech_prob": 0.0, "words": [{"start": 4219.98, "end": 4220.86, "word": "اللهم", "probability": 0.5248616536458334}, {"start": 4220.86, "end": 4221.38, "word": " إلا", "probability": 0.580810546875}, {"start": 4221.38, "end": 4222.28, "word": " بشري", "probability": 0.4710286458333333}, {"start": 4222.28, "end": 4222.82, "word": " عندي", "probability": 0.874755859375}, {"start": 4222.82, "end": 4223.42, "word": " تلات", "probability": 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remark", "probability": 0.328125}, {"start": 4232.82, "end": 4236.94, "word": " if", "probability": 0.7431640625}, {"start": 4236.94, "end": 4237.12, "word": " we", "probability": 0.9462890625}, {"start": 4237.12, "end": 4237.36, "word": " have", "probability": 0.96142578125}, {"start": 4237.36, "end": 4237.56, "word": " a", "probability": 0.49560546875}, {"start": 4237.56, "end": 4237.96, "word": " space", "probability": 0.69384765625}, {"start": 4237.96, "end": 4238.52, "word": " curve", "probability": 0.9716796875}, {"start": 4238.52, "end": 4239.28, "word": " if", "probability": 0.84912109375}, {"start": 4239.28, "end": 4240.48, "word": " we", "probability": 0.9638671875}, {"start": 4240.48, "end": 4245.16, "word": " have", "probability": 0.962890625}, {"start": 4245.16, "end": 4246.88, "word": " a", "probability": 0.97021484375}, {"start": 4246.88, "end": 4247.34, "word": " space", "probability": 0.9111328125}, {"start": 4247.34, "end": 4248.06, "word": " curve", "probability": 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"end": 4596.8, "text": "على DT ويسوي 1 على جذر 2 يبقى على الحياد الإيجابي وعدم الانحياز يبقى من الاشتقال ما يصير ماقص sin T وهذا ماقص في sin T كله في اتجاه I", "tokens": [3615, 23942, 413, 51, 4032, 1829, 3794, 45865, 502, 15844, 10874, 8848, 2288, 568, 7251, 3555, 4587, 7578, 15844, 21542, 1829, 18513, 33688, 1829, 7435, 16758, 1829, 4032, 22488, 2304, 2423, 7649, 5016, 1829, 31377, 7251, 3555, 4587, 7578, 9154, 2423, 33599, 2655, 4587, 6027, 19446, 7251, 9381, 13546, 19446, 4587, 9381, 3343, 314, 4032, 3224, 15730, 19446, 4587, 9381, 8978, 3343, 314, 28242, 3224, 8978, 1975, 2655, 7435, 40294, 286], "avg_logprob": -0.4351128546728028, "compression_ratio": 1.5664335664335665, "no_speech_prob": 1.1324882507324219e-06, "words": [{"start": 4577.44, "end": 4578.14, "word": "على", "probability": 0.508056640625}, {"start": 4578.14, "end": 4579.02, "word": " DT", "probability": 0.29949951171875}, {"start": 4579.02, "end": 4579.74, "word": " ويسوي", "probability": 0.51959228515625}, {"start": 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4805.59, "word": " هنا", "probability": 0.9873046875}, {"start": 4805.59, "end": 4805.93, "word": " stop", "probability": 0.2880859375}, {"start": 4805.93, "end": 4806.13, "word": " يا", "probability": 0.65283203125}, {"start": 4806.13, "end": 4806.61, "word": " بنات", "probability": 0.9055989583333334}, {"start": 4806.61, "end": 4808.17, "word": " المرة", "probability": 0.923828125}, {"start": 4808.17, "end": 4808.49, "word": " الجاية", "probability": 0.6590983072916666}, {"start": 4808.49, "end": 4808.95, "word": " بجيبكوا", "probability": 0.724609375}, {"start": 4808.95, "end": 4809.07, "word": " ان", "probability": 0.8359375}, {"start": 4809.07, "end": 4809.31, "word": " شاء", "probability": 0.953857421875}, {"start": 4809.31, "end": 4809.43, "word": " الله", "probability": 0.95556640625}, {"start": 4809.43, "end": 4810.29, "word": " أرقام", "probability": 0.878173828125}, {"start": 4810.29, "end": 4811.15, "word": " المسائل", "probability": 0.914306640625}, {"start": 4811.15, "end": 4811.71, "word": " تبعت", "probability": 0.680908203125}, {"start": 4811.71, "end": 4812.23, "word": " هذا", "probability": 0.8564453125}, {"start": 4812.23, "end": 4812.47, "word": " ال", "probability": 0.6259765625}, {"start": 4812.47, "end": 4812.79, "word": " section", "probability": 0.8125}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 4813.5895, "duration_after_vad": 4328.442218750017}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/SmdhLcwuMIw_raw.srt b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/SmdhLcwuMIw_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..b8774f5badb2f63702c1107d553b359ac1cb22e3
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/SmdhLcwuMIw_raw.srt
@@ -0,0 +1,2832 @@
+1
+00:00:00,000 --> 00:00:02,680
+موسيقى
+
+2
+00:00:13,140 --> 00:00:18,180
+بسم الله الرحمن الرحيم المرة اللى فاتت اخر حاجة
+
+3
+00:00:18,180 --> 00:00:22,640
+اخرناها اللى هو ال unit tangent vector T اللى كانت
+
+4
+00:00:22,640 --> 00:00:27,740
+DR عالية باسم نواصل وسنرجع مرة ثانية ال unit
+
+5
+00:00:27,740 --> 00:00:31,040
+tangent vector اللى نحن لزمنا خلال هذا ال section
+
+6
+00:00:31,040 --> 00:00:34,760
+و ال section اللى بعده كمان يبقى هذا الشيء أساسي
+
+7
+00:00:34,760 --> 00:00:37,880
+هنجي ل section اللى يوم اللي هو care picture and
+
+8
+00:00:37,880 --> 00:00:42,740
+normal vectors of careكرفتشر يعني بالعربي يا بنات
+
+9
+00:00:42,740 --> 00:00:48,900
+اللي هو التقوس أو الإنحناء لمنحنى نحسب مقدار
+
+10
+00:00:48,900 --> 00:00:53,780
+التقوس لمنحنى أو مقدار الإنحناء لهذا المنحنى
+
+11
+00:00:53,780 --> 00:01:00,860
+normal vector المتجه العمودي على المنحنى وسنعرف أن
+
+12
+00:01:00,860 --> 00:01:05,760
+المتجه العمودي على المنحنى هو المتجه العمودي على
+
+13
+00:01:05,760 --> 00:01:11,330
+المماس لهذا المنحنىهذا سنعرفه بعد قليل ان شاء الله
+
+14
+00:01:11,330 --> 00:01:15,650
+تعالى يبقى المتجه العمودي على المنحنة هو المتجه
+
+15
+00:01:15,650 --> 00:01:21,450
+العمودي على المماث لهذا المنحنة عند نقطة تقع لهذا
+
+16
+00:01:21,450 --> 00:01:28,890
+المنحنة سنقسم هذا ال section إلى نقطتينالنقطة
+
+17
+00:01:28,890 --> 00:01:34,370
+الأولى بناخد كيرفتشار of a plane curve يعني بنحسب
+
+18
+00:01:34,370 --> 00:01:40,590
+الكيرفتشار لمين لمنحنا موجود فيه مستوى وبعد ما
+
+19
+00:01:40,590 --> 00:01:46,350
+نخلص بنروح لكيرفتشار لمين لمنحنا موجود في ال space
+
+20
+00:01:46,350 --> 00:01:51,390
+اللي هو في الفرار يبقى هيكون شغلنا في الحالة
+
+21
+00:01:51,390 --> 00:01:56,020
+الأولى ال vector اللي بناخده بدلالة I وG فقطفي
+
+22
+00:01:56,020 --> 00:02:00,380
+الحالة الثانية بيكون دلوقتي الـ I و ال J و ال K ان
+
+23
+00:02:00,380 --> 00:02:04,640
+شاء الله تعالى بدنا نعطي definition لل curvature و
+
+24
+00:02:04,640 --> 00:02:08,400
+نشوف كيف نستخدم اللي هو ال curvature في الحالات
+
+25
+00:02:08,400 --> 00:02:15,680
+المختلفة يبقى بجي بقول F T is the unit tangent
+
+26
+00:02:15,680 --> 00:02:23,380
+vector is the unit tangent vector
+
+27
+00:02:26,220 --> 00:02:36,740
+of a smooth curve of a smooth curve لمنحنى
+
+28
+00:02:36,740 --> 00:02:47,200
+أملس the curvature function the curvature function
+
+29
+00:02:47,200 --> 00:02:55,520
+دالة التقوس أو دالة الحنان of the curve of a plane
+
+30
+00:02:58,680 --> 00:03:04,660
+كيرب از كيرب
+
+31
+00:03:04,660 --> 00:03:17,120
+از كيرب از كيرب از كيرب از كيرب از كيرب از كيرب از
+
+32
+00:03:17,120 --> 00:03:17,920
+كيرب از كيرب از كيرب از كيرب از كيرب از كيرب از
+
+33
+00:03:17,920 --> 00:03:17,920
+كيرب از كيرب از كيرب از كيرب از كيرب
+
+34
+00:03:32,790 --> 00:03:43,230
+R of T is given in terms of parameter T
+
+35
+00:03:58,750 --> 00:04:06,470
+parameter اللي هو T rather
+
+36
+00:04:06,470 --> 00:04:13,270
+than rather
+
+37
+00:04:13,270 --> 00:04:26,250
+than بدلا من the arc length S the arc length اللي
+
+38
+00:04:26,250 --> 00:04:32,990
+هو الـ Sthen الكيربتشار
+
+39
+00:04:32,990 --> 00:04:38,210
+كيربتشار
+
+40
+00:04:38,210 --> 00:04:46,290
+K كيربتشار
+
+41
+00:04:46,290 --> 00:04:46,290
+K كيربتشار K كيربتشار K كيربتشار K كيربتشار K
+
+42
+00:04:46,290 --> 00:04:46,390
+كيربتشار K كيربتشار K كيربتشار K كيربتشار K
+
+43
+00:04:46,390 --> 00:04:46,390
+كيربتشار K كيربتشار K كيربتشار K كيربتشار K
+
+44
+00:04:46,390 --> 00:04:46,390
+كيربتشار K كيربتشار K كيربتشار K كيربتشار K
+
+45
+00:04:46,390 --> 00:04:46,390
+كيربتشار K كيربتشار K كيربتشار K كيربتشار K
+
+46
+00:04:46,390 --> 00:04:46,390
+كيربتشار K كيربتشار K كيربتشار K كيربتشار K
+
+47
+00:04:46,390 --> 00:04:49,070
+كيربتشار K كيربتشار K كيربتشار K كيربتشار K
+
+48
+00:04:49,070 --> 00:04:56,250
+كيربتشار
+
+49
+00:04:56,250 --> 00:05:11,470
+Kبقدر اقول الـ DT على DS و هنا على DS على DT هذا
+
+50
+00:05:11,470 --> 00:05:24,230
+الكلام بده يساوي الـ DTعلى DT DT على DT الطول تبعه
+
+51
+00:05:24,230 --> 00:05:32,650
+على مين؟ على طول ال V و
+
+52
+00:05:32,650 --> 00:05:39,790
+لحظة بسيطة قبل أن نرجع إلى هذا التعريف not since T
+
+53
+00:05:39,790 --> 00:05:45,050
+has a constant
+
+54
+00:05:47,850 --> 00:05:55,190
+لأن تقول تبعه يساوي مقدارا ثابتا اللي هو واحد صحيح
+
+55
+00:05:55,190 --> 00:06:06,950
+we have هيكون هنا اللي هو DT على DS بطة D بتساوي
+
+56
+00:06:06,950 --> 00:06:10,130
+zero that is
+
+57
+00:06:12,530 --> 00:06:21,890
+الـ Dt على Ds and Dt are orthogonal
+
+58
+00:06:47,900 --> 00:06:52,040
+اللي احنا كاتيها مرة تانية نقرأ التعريف قراءة جيدة
+
+59
+00:06:52,040 --> 00:06:57,880
+نحاول نفهم كل لقطة موجودة عنه إذا احنا الآن بنتكلم
+
+60
+00:06:57,880 --> 00:07:02,380
+عن ال curvature في ال plane curve يبقى المنحنة
+
+61
+00:07:02,380 --> 00:07:07,360
+اللي موجود في مستوى التعريف بيقول ما لو كان ال T
+
+62
+00:07:07,360 --> 00:07:11,740
+هو ال unit tangent vector ال smooth curve يبقى ال
+
+63
+00:07:11,740 --> 00:07:15,280
+curvature تبع ال plane curve في هذه الحالة كابة
+
+64
+00:07:15,910 --> 00:07:24,050
+تنطق كالتالي يا بنات كيها اللي هي كابا تنطق
+
+65
+00:07:24,050 --> 00:07:28,910
+بهذا الشكل يبقى كابا لحدها الرمز كي اللي عندنا هذه
+
+66
+00:07:29,230 --> 00:07:33,850
+تساوي طول ال DT على DS يعني ايش اللي بدي احصل؟ بدي
+
+67
+00:07:33,850 --> 00:07:36,930
+اشتقه
+
+68
+00:07:36,930 --> 00:07:42,130
+بالنسبة لل arc parameter S واخد الطول تبعه بيعطينا
+
+69
+00:07:42,130 --> 00:07:47,290
+ال curvature اللي هي كابا يبقى بناء عليه ال
+
+70
+00:07:47,290 --> 00:07:50,190
+curvature كابا هذا scalar ولا vector
+
+71
+00:07:52,840 --> 00:07:59,420
+أو DT DT على DS هو Vector لكن لما ناخد قوة سيارتنا
+
+72
+00:07:59,420 --> 00:08:04,500
+ستصبح Scalar إذا هذه كمية قياسية و ليست كمية
+
+73
+00:08:04,500 --> 00:08:10,640
+اتجاهية و قد تكون رقم واحد قد تكون دالة في متغير
+
+74
+00:08:10,640 --> 00:08:15,380
+مثل T مثلا طيب بقول لو كل small curve R of T is
+
+75
+00:08:15,380 --> 00:08:19,140
+given in terms of parameter ER
+
+76
+00:08:23,700 --> 00:08:28,840
+لو كانت في ال parameter T بدل من من ال arc length
+
+77
+00:08:28,840 --> 00:08:34,200
+S يبقى في هذه الحالة الكربتشار كابة ستأخذ شكلًا
+
+78
+00:08:34,200 --> 00:08:38,100
+جديدًا شهو هذا الشكل بقول دي T على دي S زي ما هي
+
+79
+00:08:38,100 --> 00:08:43,860
+معرفة الان S function في T والT كمان function في T
+
+80
+00:08:43,860 --> 00:08:48,000
+إذا بقدر أقول دي T على دي S فيها دي T على دي S
+
+81
+00:08:53,280 --> 00:09:00,740
+بقدر هدها هدى vector ولا scalar دي ت على دي اس دي
+
+82
+00:09:00,740 --> 00:09:07,500
+ت على دي اس دي small ت vector ولا scalar هدى
+
+83
+00:09:07,500 --> 00:09:11,630
+scalar هدى مش خلّاها vector هدى ال vectorيبقى دي
+
+84
+00:09:11,630 --> 00:09:14,510
+تي كتر هذا ال unit تانية بس هذا ال parameter وهذا
+
+85
+00:09:14,510 --> 00:09:18,490
+ال parameter يبقى هذا ما هواش vector إذا لو عارفة
+
+86
+00:09:18,490 --> 00:09:22,370
+لو كان هذا vector ماقدرش أكتب هذه إلا إذا كانت كله
+
+87
+00:09:22,370 --> 00:09:26,610
+ماشي أبقى قادرة أكتبها لكن هذه الانس كتر وهذه هي
+
+88
+00:09:26,610 --> 00:09:30,850
+من هذه ال vector إذا دي تي على دي اس لو نزلتها
+
+89
+00:09:30,850 --> 00:09:35,810
+كلها ماعش بصير دي اس على دي تي وببقى اللي فوق اللي
+
+90
+00:09:35,810 --> 00:09:42,420
+هو دي يعني هذه كأنهطول دي تي على دي تي في ال
+
+91
+00:09:42,420 --> 00:09:48,840
+absolute value دي تي على دي أسطى يبقى هذا طول وهذا
+
+92
+00:09:48,840 --> 00:09:50,180
+absolute value
+
+93
+00:09:53,810 --> 00:10:00,130
+لأ هذا طول المتجة دي تي على دي تي وهذا هو ال
+
+94
+00:10:00,130 --> 00:10:05,890
+absolute value القيمة المطلقة ل DS على دي تي طيب
+
+95
+00:10:05,890 --> 00:10:10,890
+ممتاز ال DS على دي تي أليس دي طول ال Velocity V
+
+96
+00:10:10,890 --> 00:10:15,770
+يبقى شرطة حاطة بدل طول ال Velocity V إذا من الآن
+
+97
+00:10:15,770 --> 00:10:21,400
+فصاعدامن حد ما يعطي ال R of T as a function of T،
+
+98
+00:10:21,400 --> 00:10:27,660
+لو فضل مرة بجيب السرعة، أخد ال generator بيجيب
+
+99
+00:10:27,660 --> 00:10:34,720
+مقدار السرعة اللي هو ال speedهقسم الصرعة على الـ
+
+100
+00:10:34,720 --> 00:10:39,080
+speed بيعطينا الـ mean الـ unit tangent vector لو
+
+101
+00:10:39,080 --> 00:10:45,540
+اشتقته بالنسبة الى T بصيب الـ DT على DT
+
+102
+00:10:47,900 --> 00:10:51,660
+أجيب له الطول و أقسمه على مقدار السرعة بيعطيني
+
+103
+00:10:51,660 --> 00:10:56,900
+مقدار main الكيربيتش أركبه وبالتالي ما لزمتليش ال
+
+104
+00:10:56,900 --> 00:11:01,380
+parameter S ستعت التخلص منه واكتفيت بال parameter
+
+105
+00:11:01,380 --> 00:11:07,040
+main T وهذا أسهل عمليا كثيرا من ان انا لسه بيدروح
+
+106
+00:11:07,040 --> 00:11:10,800
+أحسبه ال R كله لأ و بعدين بيدروح أشتغل لأ لأ لأ
+
+107
+00:11:10,800 --> 00:11:16,510
+هنا الدالة في R of T بقفلها مرة ما جبت ال Vبجيب
+
+108
+00:11:16,510 --> 00:11:21,650
+الطول تبع ال V، بشتق ال T بالنسبالي T، بكسم 2 على
+
+109
+00:11:21,650 --> 00:11:28,060
+4، بقول حصلت على مين؟ على ال K الواتشة Kهو لنظرة
+
+110
+00:11:28,060 --> 00:11:32,500
+لأن T لديه كونستانت لين مش هو not vector يبقى طوله
+
+111
+00:11:32,500 --> 00:11:39,080
+قدام واحد صحيح يبقى طوله واحد صحيح نحن لدينا T T
+
+112
+00:11:39,080 --> 00:11:43,600
+على DS dot T بيبقى سواء من Zero مرت علينا هذه
+
+113
+00:11:43,600 --> 00:11:49,480
+أبنات قبل دقيقة ولا لسه جديد لأول مرة نشوفها لو
+
+114
+00:11:49,480 --> 00:11:54,460
+كان عندي vector of constant length واشتقيته وعملته
+
+115
+00:12:03,500 --> 00:12:08,200
+اذا في عندي vector of constant length واشتقته dot
+
+116
+00:12:08,200 --> 00:12:13,540
+نفسه يبقى هذا بيعطيني قدرة zero وأثبتنالكوا هذه
+
+117
+00:12:13,540 --> 00:12:18,340
+القاعدة يبقى بناء عليه مدام T هو vector of
+
+118
+00:12:18,340 --> 00:12:22,400
+constant length الطول تبعه يسوى واحد صحيح إذا
+
+119
+00:12:22,400 --> 00:12:27,530
+مشتقته بالنسبة ل Sطب دي تي بده يسوى مين؟ Zero يبقى
+
+120
+00:12:27,530 --> 00:12:32,070
+دي تي على دي اس والتي اتنين ار او orthogonal بيكون
+
+121
+00:12:32,070 --> 00:12:36,690
+اتنين متعمدين نعطي مثال توضيح على الكلام اللي احنا
+
+122
+00:12:36,690 --> 00:12:48,010
+بنقوله هذا show them
+
+123
+00:12:48,010 --> 00:12:48,650
+the curvature
+
+124
+00:12:58,940 --> 00:13:07,240
+curvature of a circle
+
+125
+00:13:07,240 --> 00:13:21,960
+with center at the origin with center at
+
+126
+00:13:21,960 --> 00:13:38,600
+theorigin المركز هو نقطة أصل and radius a هو واحد
+
+127
+00:13:38,600 --> 00:13:39,680
+على a
+
+128
+00:13:55,260 --> 00:14:00,080
+سؤال مرة ثانية بقول لو عندنا دائرة دائرة مركزها
+
+129
+00:14:00,080 --> 00:14:05,400
+نقطة الأصل و نصف قطرة يساوي ايه قول تبعه يساوي ايه
+
+130
+00:14:05,400 --> 00:14:10,220
+بدي اثبت ان ال curvature لهذه الدائرة يساوي قداش
+
+131
+00:14:10,220 --> 00:14:14,760
+واحد على ايه يعني ال curvature عند اي نقطة على
+
+132
+00:14:14,760 --> 00:14:19,720
+محيط الدائرة بدي تكون مقدر ثابت وهو واحد القيمة
+
+133
+00:14:19,720 --> 00:14:25,140
+العددية له واحد على نصف القطر يبقى بقولبيللي ان
+
+134
+00:14:25,140 --> 00:14:29,520
+الكيربتشارلي دائرة مركزها نقطة الأصل و نصف قطرها
+
+135
+00:14:29,520 --> 00:14:33,380
+يساوي ايه؟ هو عبارة عن واحد يعني بدأ تبتله انه
+
+136
+00:14:33,380 --> 00:14:37,880
+كابة تساوي مين واحد على ايه؟ بقوله كويس وقاللي
+
+137
+00:14:37,880 --> 00:14:42,300
+أكتر ماعنديش معلومة أكتر من انه عندي دائرة مركزها
+
+138
+00:14:42,300 --> 00:14:48,320
+نقطة الأصل و نصف قطرها يساوي ايه؟ كيف يعني؟ يعني
+
+139
+00:14:48,320 --> 00:14:54,260
+لو جينا و قولنا هي عنا دائرة شكل عنها هذا اكتروهي
+
+140
+00:14:54,260 --> 00:14:59,900
+عندي محاول بالشكل اللي هنا تمام
+
+141
+00:14:59,900 --> 00:15:05,120
+وقولنا هذا محور X وهذا محور Y وهذا نقطة الأصل اللي
+
+142
+00:15:05,120 --> 00:15:11,280
+هو Zero في أن نقطة الأصل إلى أي نقطة على المحيط
+
+143
+00:15:11,280 --> 00:15:18,110
+هذا يعتبر من ال radius E نصف القطرلو اخترقت ان هذه
+
+144
+00:15:18,110 --> 00:15:26,830
+النقطة هي P of X Y و رح نزلت من هنا عمود على محور
+
+145
+00:15:26,830 --> 00:15:34,270
+X بيكون هذا الجزء هو X و هذا الجزء هو من Y لو كانت
+
+146
+00:15:34,270 --> 00:15:38,690
+الزاوية اللي عندنا هذه اللي هي الزاوية ثيتا إذا ال
+
+147
+00:15:38,690 --> 00:15:43,710
+X كانت مش متساومة بنات X أكو صحيح ثيتا و ال Y
+
+148
+00:15:47,110 --> 00:15:59,510
+يبقى مصير عنا X يساوي A Cos θ و Y يساوي A Sin θ طب
+
+149
+00:15:59,510 --> 00:16:05,690
+لو ربعتهم وجمعت بيعطيني معادلة الدائرةطبعا
+
+150
+00:16:05,690 --> 00:16:08,030
+المعادلة دي على مركزها النقطة الأصول نصف قطرة هي
+
+151
+00:16:08,030 --> 00:16:13,570
+يساوي a يا x تربية زائد y تربية تساوي a تربية
+
+152
+00:16:13,570 --> 00:16:18,150
+مظبوط طب تعالوا نربع هدول يبقى x تربية زائد y
+
+153
+00:16:18,150 --> 00:16:23,790
+تربية يساوي a تربية cosine تربية تيتا زائد a تربية
+
+154
+00:16:23,790 --> 00:16:25,390
+sine تربية تيتا
+
+155
+00:16:31,480 --> 00:16:38,400
+يبقى هدول بسميهم المعادلات ال parameterية لمين
+
+156
+00:16:38,400 --> 00:16:44,460
+للcircle يبقى هدول التنتين مع بعض هذه the
+
+157
+00:16:44,460 --> 00:16:54,260
+parametric equations of the circle
+
+158
+00:16:56,620 --> 00:17:01,360
+طيب لو بدأ اكتب هذا الكلام على صورة unit جرس
+
+159
+00:17:01,360 --> 00:17:05,440
+بتكتبها على شكل اللي هو vector valued function
+
+160
+00:17:05,440 --> 00:17:12,380
+يبقى بروح بقول ان ال R of T بدي يسوى A Cos θ في
+
+161
+00:17:12,380 --> 00:17:19,020
+اتجاه ال I زائد او A R of θ هنا او θ يبقى A Cos θ
+
+162
+00:17:19,020 --> 00:17:25,340
+في اتجاه ال I زائد A Sin θ في اتجاه ال A يعني احنا
+
+163
+00:17:25,640 --> 00:17:30,820
+فليب ليه؟ أعلى بال curvature إذا بضروح أجيبله من؟
+
+164
+00:17:30,820 --> 00:17:34,160
+ال unit tangent لأن هاي ال curvature اللي عندي
+
+165
+00:17:34,160 --> 00:17:40,760
+بلزمني ال unit tangent و أشتقه على طول ال V تمام
+
+166
+00:17:40,760 --> 00:17:49,140
+بقوله كويس يبقى الأن أنا بدي أجيبله V of θاللي
+
+167
+00:17:49,140 --> 00:17:55,420
+عبارة عن dR على dθ اللي هو ناقص A في sin θ في
+
+168
+00:17:55,420 --> 00:18:03,930
+اتجاه I زائد A cos θ في اتجاه Gبالذات لمين هنا طول
+
+169
+00:18:03,930 --> 00:18:09,430
+ال V إذا بتروح ع سيبله كده طول ال V إذا طول ال V
+
+170
+00:18:09,430 --> 00:18:15,510
+بده يساوي ال square root ل A تربيع sine تربيع ثيتا
+
+171
+00:18:15,510 --> 00:18:21,370
+زائد A تربيع cosine تربيع ثيتا يساوي الجذري
+
+172
+00:18:21,370 --> 00:18:31,460
+التربيعي ل A تربيع في مين؟ في sine تربيع ثيتازائد
+
+173
+00:18:31,460 --> 00:18:38,700
+cosine تربيتي تنقل ده واحد في ايه تربية ابقى يبقى
+
+174
+00:18:38,700 --> 00:18:46,880
+هنا ايهطبعا يبقى .. جبت اللي هو طول ال V اللي هو
+
+175
+00:18:46,880 --> 00:18:50,740
+يسوى قداشة .. بقولش absolute value لإيه؟ لأن طوله
+
+176
+00:18:50,740 --> 00:18:54,400
+عمره ما كان قيمة سالبة، مظبوط؟ و الله بنقول لو
+
+177
+00:18:54,400 --> 00:18:57,820
+قسنا اي واحدة فيه و نقول و الله طولها هذه سالب متر
+
+178
+00:18:57,820 --> 00:19:02,360
+و نص، لأ متر و نص على طول، يبقى الطول قيمة موجبة،
+
+179
+00:19:02,360 --> 00:19:09,180
+طبعا؟ الان بدنا ال unit tangent T اللي هو ال V على
+
+180
+00:19:09,180 --> 00:19:13,690
+طول ال Vاللي أخدناها آخر نقطة أخدناها المحاضرة
+
+181
+00:19:13,690 --> 00:19:17,430
+الماضيةقلنا الـ Unit Tangent Vector T هو الـ
+
+182
+00:19:17,430 --> 00:19:21,790
+Velocity على مقدار الـ Velocity ال Velocity وين؟
+
+183
+00:19:21,790 --> 00:19:27,190
+هي اللي موجودة يبقى تساوي الناقص A Sine Theta في
+
+184
+00:19:27,190 --> 00:19:32,490
+اتجاه I زائد A Cosine Theta في اتجاه الجهة كله
+
+185
+00:19:32,490 --> 00:19:38,590
+مقسوم على مين؟ على A اللي هو قد يساوي سالب Sine
+
+186
+00:19:38,590 --> 00:19:42,670
+Theta في اتجاه I زائد
+
+187
+00:19:49,950 --> 00:19:57,190
+يبقى دي تي على دي
+
+188
+00:19:57,190 --> 00:19:57,730
+تيتا
+
+189
+00:20:03,930 --> 00:20:09,850
+نقص sin θ في اتجاه ال I نقص sin θ في اتجاه main
+
+190
+00:20:09,850 --> 00:20:16,270
+الجهة جالي بده الطول تبع هذا المتجر بقوله I الجهة
+
+191
+00:20:16,270 --> 00:20:23,030
+ده بده يعطينا ان طول ال DT على D ثيتا بده يسوى
+
+192
+00:20:23,030 --> 00:20:30,170
+الجدر التربيعي لcos تربيع ثيتا زائد sin تربيع ثيتا
+
+193
+00:20:30,170 --> 00:20:36,760
+لغة درجة واحد صحيحيبقى هذا الطول، الآن طول ال V
+
+194
+00:20:36,760 --> 00:20:43,380
+موجود عندى، مظبوط؟ والان طول او ال DT على Dθ موجود
+
+195
+00:20:43,380 --> 00:20:49,820
+عندى، اذا بقولوا كيرفيتشاركابة اللى مطلبه يساوي ال
+
+196
+00:20:49,820 --> 00:20:58,880
+DT على Dθ، الان هنا على طول ال V ويساوي طوله هذا
+
+197
+00:20:58,880 --> 00:21:06,770
+مقدش بواحد وطوله ايه؟أظن و هو المطلوب إذا من الآن
+
+198
+00:21:06,770 --> 00:21:11,810
+فصادم الدكتورافيلي ان الدائرة اللي مركزها نقطة
+
+199
+00:21:11,810 --> 00:21:16,710
+الأصل و نصف قطرها يساوي ايه؟ لو بدنا نجيب ال
+
+200
+00:21:16,710 --> 00:21:21,870
+curvature لها يبقى يساوي قيمة ثابتة اللي بيساوي
+
+201
+00:21:21,870 --> 00:21:27,010
+واحد على نصف قطر هذه الدائرة
+
+202
+00:21:40,940 --> 00:21:45,240
+طيب هذه أول نقطة اللي أعرفنا فيها الكلبتشر نجي
+
+203
+00:21:45,240 --> 00:21:50,020
+لنقطة ثانية ال principle unit normal النقطة
+
+204
+00:21:50,020 --> 00:21:55,660
+الثانية من هذا ال section اللي هو the principle
+
+205
+00:21:55,660 --> 00:22:07,020
+unit normal vector unit normal vector و اللي احنا
+
+206
+00:22:07,020 --> 00:22:11,360
+كنا كاتبينه في عنوان هذا ال sectionوانا كامل
+
+207
+00:22:11,360 --> 00:22:15,940
+curvature and unit normal vectors of a curve يمنيش
+
+208
+00:22:15,940 --> 00:22:22,220
+لتعريف ال unit normal vector of a curve بقول at a
+
+209
+00:22:22,220 --> 00:22:32,240
+point at a point where حيث ال curvature كامل لدو
+
+210
+00:22:32,240 --> 00:22:36,280
+سوى zero the principal unit normal vector
+
+211
+00:22:39,660 --> 00:22:52,120
+principal unit normal vector of
+
+212
+00:22:52,120 --> 00:23:00,460
+a smooth curve in
+
+213
+00:23:00,460 --> 00:23:05,240
+the plane في
+
+214
+00:23:05,240 --> 00:23:14,430
+مستوى earthهدله الرمز capital N وانه بتساوي واحد
+
+215
+00:23:14,430 --> 00:23:25,610
+على كاره فى دي تي على دي اس دي تي على دي اس that
+
+216
+00:23:25,610 --> 00:23:36,130
+will point that will point toward
+
+217
+00:23:36,130 --> 00:23:37,570
+the concave side
+
+218
+00:23:42,270 --> 00:23:50,150
+the concave side of the cave
+
+219
+00:24:06,880 --> 00:24:13,720
+نفترض أن هذا اللي هو ال smooth curve جينا عندها
+
+220
+00:24:13,720 --> 00:24:19,480
+نقطة زي النقطة اللي عندها دي على سبيل المثال رسمنا
+
+221
+00:24:19,480 --> 00:24:23,700
+ال unit tangent vector فكان ال unit tangent vector
+
+222
+00:24:23,700 --> 00:24:29,190
+T بالشكل هذابدي اعرف وين بدي اكون ال principle
+
+223
+00:24:29,190 --> 00:24:34,150
+normal vector يعني المتجه العمودي على المنحنى عند
+
+224
+00:24:34,150 --> 00:24:39,630
+هذه النقطة يعني المتجه العمودي على ال tangent لهذا
+
+225
+00:24:39,630 --> 00:24:44,430
+المنحنى او ال tangent vector لهذا المنحنى عند هذه
+
+226
+00:24:44,430 --> 00:24:50,770
+النقطة يبقى هذا النقطة لو روحته سميتها P1 على سبيل
+
+227
+00:24:50,770 --> 00:24:56,090
+المثالماذا يقول هنا عند نقطة الكيربتشار كابة فيها
+
+228
+00:24:56,090 --> 00:25:00,770
+لا تساوي 0 طبعا لو كانت كابة تساوي 0 اللي أصبح ال
+
+229
+00:25:00,770 --> 00:25:04,650
+principle unit normal is undefined ما هوش معرّف
+
+230
+00:25:04,650 --> 00:25:09,190
+إذا ضروري الكيربتشار مايكونش 0 بال principle unit
+
+231
+00:25:09,190 --> 00:25:14,240
+normal vector of S مؤكد كيرب فيه planeهو واحد على
+
+232
+00:25:14,240 --> 00:25:19,780
+كابة في DT على DS يبقى واحد على كابة scalar وهذا
+
+233
+00:25:19,780 --> 00:25:25,940
+vector إذا هذا vector زي ما احنا بنقول طيب اتجاهه
+
+234
+00:25:25,940 --> 00:25:31,760
+وين؟ والذات will point toward يبقى اتجاهه بيكون
+
+235
+00:25:31,760 --> 00:25:37,670
+the concave side of the curveفى اتجاه تقعر المنحنى
+
+236
+00:25:37,670 --> 00:25:43,710
+وليس تحد بالمنحنى طلعي المنحنى هنا الـ concave way
+
+237
+00:25:43,710 --> 00:25:50,330
+down إذا ال N بدي يكون بالشكل هذا عمودي عليه يبقى
+
+238
+00:25:50,330 --> 00:25:55,370
+هذا ال N بدي يكون عمودي على T اللي هو بدي يساوي
+
+239
+00:25:55,370 --> 00:26:05,590
+واحد على كابة واحد على كابة دي تي على دي اسمطيب لو
+
+240
+00:26:05,590 --> 00:26:12,050
+مشينا تاني ووصلنا لنقطة تانية مثل النقطة P2 وروحنا
+
+241
+00:26:12,050 --> 00:26:18,450
+رسمنا ال unit tangent عند هذه النقطة فكان ال unit
+
+242
+00:26:18,450 --> 00:26:23,970
+tangent vector اللي هو T يبقى N بده يكون لداخل
+
+243
+00:26:23,970 --> 00:26:29,160
+الشكل اللي عندنا هذايبقى هذا N اللي هو بده يساوي
+
+244
+00:26:29,160 --> 00:26:36,980
+واحد على كظه في DT على DS يبقى دائما وقابله اتجاه
+
+245
+00:26:36,980 --> 00:26:43,420
+وين؟ للداخل عمودي على ال curve و عمودي على ال unit
+
+246
+00:26:43,420 --> 00:26:48,460
+tangent أن ده نقطة التماسواتجاهه دائما هو قبل اللي
+
+247
+00:26:48,460 --> 00:26:54,720
+وين؟ للداخل، لاتجاه تقعر مين؟ المنحنى هذا بالنسبة
+
+248
+00:26:54,720 --> 00:27:00,000
+لمين؟ لل unit normal vector لكن لاحظوا ان ال unit
+
+249
+00:27:00,000 --> 00:27:04,690
+normal vector احنا كاتبينه بدلات ال curvatureو
+
+250
+00:27:04,690 --> 00:27:10,430
+كتبينه بدلالة DT عالمين DS توقفني شويه ال
+
+251
+00:27:10,430 --> 00:27:14,810
+curvature بطلنا نكتبها بدلالة ال S كتبناها كلها
+
+252
+00:27:14,810 --> 00:27:20,210
+بدلالة مين؟ بدلالة ال T يبقى الآن بدنا نروح بنفس
+
+253
+00:27:20,210 --> 00:27:25,450
+الطريقة نكتب ال curvature بدلالة ال T parameter
+
+254
+00:27:25,450 --> 00:27:31,010
+وليس بدلالة ال S parameter تمام؟يبقى من أروح نكتب
+
+255
+00:27:31,010 --> 00:27:36,370
+هذا الكلام على صورة الـ remark التالية يبقى remark
+
+256
+00:27:36,370 --> 00:27:58,050
+يبقى
+
+257
+00:27:58,050 --> 00:27:58,310
+remark يبقى remark يبقى remark يبقى remark يبقى
+
+258
+00:27:58,310 --> 00:27:58,310
+remark يبقى remark يبقى remark يبقى remark يبقى
+
+259
+00:27:58,310 --> 00:27:58,310
+remark يبقى remark يبقى remark يبقى remark يبقى
+
+260
+00:27:58,310 --> 00:27:58,310
+remark يبقى remark يبقى remark يبقى remark يبقى
+
+261
+00:27:58,310 --> 00:27:58,310
+remark يبقى remark يبقى remark يبقى remark يبقى
+
+262
+00:27:58,310 --> 00:27:58,310
+remark يبقى remark يبقى remark يبقى remark يبقى
+
+263
+00:27:58,310 --> 00:27:58,310
+remark يبقى remark يبقى remark يبقى remark يبقى
+
+264
+00:27:58,310 --> 00:27:58,310
+remark يبقى remark يبقى remark يبقى remark يبقى
+
+265
+00:27:58,310 --> 00:27:58,310
+remark يبقى remark يبقى remark يبقى remark يبقى
+
+266
+00:27:58,310 --> 00:28:04,740
+remark يبقى remark يبقfinding بدون ما نوجد ال
+
+267
+00:28:04,740 --> 00:28:14,740
+curvature kappa and ال S طبعا زي ما تشايفين ال
+
+268
+00:28:14,740 --> 00:28:19,100
+normal يعتمد على kappa وعلى main على S يبقى أنا
+
+269
+00:28:19,100 --> 00:28:21,720
+بده أجيب ال principle normal بدون اللي أجيب ال
+
+270
+00:28:21,720 --> 00:28:25,220
+curvature ولا أجيب ال arc parameter length اللي هو
+
+271
+00:28:25,220 --> 00:28:28,940
+main S كيف؟ كالتالي as follows
+
+272
+00:28:36,570 --> 00:28:43,110
+بساوي واحد على الـ curvature كابة في الـ DT على DS
+
+273
+00:28:43,110 --> 00:28:48,030
+و يمسك هذا
+
+274
+00:28:48,030 --> 00:28:56,750
+بقدر اقول DT على DS الكابة اللي و مين اللي هي طول
+
+275
+00:28:56,750 --> 00:29:03,710
+الـ DT على DS طبعا
+
+276
+00:29:03,710 --> 00:29:05,790
+بقدر اقول هذا الكلمة
+
+277
+00:29:09,160 --> 00:29:17,840
+على DT في DT على DS على طول
+
+278
+00:29:17,840 --> 00:29:25,060
+الـ DT على DT في DT على DS
+
+279
+00:29:53,660 --> 00:29:59,780
+الـ Dt على Ds اتفقنا انها scalar طيب مرة الماضية
+
+280
+00:29:59,780 --> 00:30:04,680
+الـ Dt على Ds أقل من الـ Zero ولا أكبر من الـ Zero
+
+281
+00:30:04,680 --> 00:30:10,320
+أكبر من الـ Zero اكبر من الـ Zero يبقى Ds على Dt
+
+282
+00:30:10,320 --> 00:30:17,520
+هي طول ال V وطول موجة مظبوط يبقى قيمة الموجة بلو
+
+283
+00:30:17,520 --> 00:30:21,360
+قلبتها بسيستراليب والله بظلها موجة بقى بظلها موجة
+
+284
+00:30:21,360 --> 00:30:27,890
+بقى ممتاز جداإذا أنا لما أجي أقول هذا الكلام دي تي
+
+285
+00:30:27,890 --> 00:30:37,230
+على ا دي تي على دي تي في دي تي على دي اس وهذا طول
+
+286
+00:30:37,230 --> 00:30:46,010
+ال دي تي على دي تي في دي تيعلى DS اذا نقلت طولته
+
+287
+00:30:46,010 --> 00:30:50,310
+او ال absolute value لها ال absolute value والله
+
+288
+00:30:50,310 --> 00:30:55,350
+مش ال absolute تنتين هذول تنتين موجبتين جات بعض
+
+289
+00:30:55,350 --> 00:31:01,950
+تماما يبقى بنقدر نختصرهم وتقول المسألة الى ان ال
+
+290
+00:31:01,950 --> 00:31:09,690
+principal unit normal N من الانف صاعداهو Dt على Dt
+
+291
+00:31:09,690 --> 00:31:18,590
+مقسوما على طول Dt على Dt بالشكل اللي عندنا واضح ان
+
+292
+00:31:18,590 --> 00:31:22,450
+ال principal unit normal هذه لا فيها curvature ولا
+
+293
+00:31:22,450 --> 00:31:28,330
+فيها S زي ما احنا ادعينا قبل قليل
+
+294
+00:31:30,200 --> 00:31:36,020
+يبقى بناء عليه لا الكيروفيتشار ولا ال principle
+
+295
+00:31:36,020 --> 00:31:40,560
+normal بكتف دلالة ال S بسيطة بكتف دلالة ال T أسهل
+
+296
+00:31:40,560 --> 00:31:47,000
+زي ما انت شايفه ناخد مثال توضيح على ذلك example
+
+297
+00:31:47,000 --> 00:31:52,720
+will
+
+298
+00:31:52,720 --> 00:32:02,330
+find ال Tوالـ principal normal vector N and
+
+299
+00:32:02,330 --> 00:32:05,590
+الكيروفيتشاركابة
+
+300
+00:32:05,590 --> 00:32:19,390
+for theأبلين كيرف للمنحنة اللي هو R of T يساوي لين
+
+301
+00:32:19,390 --> 00:32:26,350
+سيك T كله في اتجاه الـ I زائد T في اتجاه الـ J
+
+302
+00:32:26,350 --> 00:32:33,450
+والـ T هذه محصورة بين سالف باي على اتنين وبين باي
+
+303
+00:32:33,450 --> 00:32:34,150
+على اتنين
+
+304
+00:32:39,420 --> 00:32:47,940
+مرة تانية قال هاتلي unit tangent vector تلاتة
+
+305
+00:32:47,940 --> 00:32:52,580
+هاتلي الكيرفت شركابة للمنحلة اللي عندنا هذا وحطني
+
+306
+00:32:52,580 --> 00:32:58,060
+على interval من by على اتنين لغاية by على اتنين
+
+307
+00:32:58,060 --> 00:33:01,280
+لأن يا بنات عند ال by على اتنين و ال by على اتنين
+
+308
+00:33:01,280 --> 00:33:08,320
+ال stickis undefined ومن هنا ما جليش يساوي تمام؟
+
+309
+00:33:08,320 --> 00:33:12,100
+من حالة سكت اللي أخدته في الكلب و دستين آخر
+
+310
+00:33:12,100 --> 00:33:15,840
+section في أول chapter كانت ال trigonometric
+
+311
+00:33:15,840 --> 00:33:20,260
+functions تمام؟ لما رسمت السكت كانت عند ال
+
+312
+00:33:20,260 --> 00:33:24,720
+بايعتنين و وصلت بايعتنين is undefined يبقى من هنا
+
+313
+00:33:24,720 --> 00:33:29,180
+ماحطناش يساوي ما علينا هذه بس معلومة هامشية جانبية
+
+314
+00:33:29,780 --> 00:33:34,860
+يبقى الان نجيب ال unit tangent vector T T هي عبارة
+
+315
+00:33:34,860 --> 00:33:40,480
+عن مين؟ ال V على طول ال V مظبوط يبقى على هذا
+
+316
+00:33:40,480 --> 00:33:46,840
+الكلام بدي أجيب له مين ك ال V في الأول يبقى ال V
+
+317
+00:33:46,840 --> 00:33:54,820
+اللي هي DR على DD يساوى تفضل ان تسكب جدا شبنانة
+
+318
+00:33:55,390 --> 00:34:03,090
+واخد على سك T في مشتقة السك اللي بسك T تان T في
+
+319
+00:34:03,090 --> 00:34:09,810
+اتجاه ال I زائد مشتقة ال T بواحد في اتجاه ال J
+
+320
+00:34:09,810 --> 00:34:18,050
+يبقى أصبحت ال D تساوي سك مع سك يبقى تان T في اتجاه
+
+321
+00:34:18,050 --> 00:34:24,640
+ال I زائد Jيبقى هذا ال velocity عند اي لحظة او
+
+322
+00:34:24,640 --> 00:34:30,020
+متجه السرعة بدي احسب قداش طول متجه السرعة يبقى هذا
+
+323
+00:34:30,020 --> 00:34:37,450
+بدي يعطينا طول ال V بده ساوي الجدري التربيهيلتان
+
+324
+00:34:37,450 --> 00:34:44,670
+تربية T زائد واحد اللي هو كده؟ سك تربية من حساب
+
+325
+00:34:44,670 --> 00:34:52,490
+المثلثات والسك تربية تطلع من تحت الجذر بسك T والله
+
+326
+00:34:52,490 --> 00:34:59,610
+absolute value لسك T لا هي بنقول absolute value
+
+327
+00:34:59,610 --> 00:35:05,850
+لسك T، مظبوط؟ يعني كده شهر قيمة المحطة بسؤاللما
+
+328
+00:35:05,850 --> 00:35:08,890
+اقول من سالب بايع اتنين لبايع اتنين يعني ايه
+
+329
+00:35:08,890 --> 00:35:15,030
+الاربع يبقى نفعليه؟ من سالب بايع على اتنين لبايع
+
+330
+00:35:15,030 --> 00:35:20,070
+على اتنين يبقى ايه الاربع؟ الرابع الرابع و الرابع
+
+331
+00:35:20,070 --> 00:35:25,760
+الاول من سالب بايع اتنين لبايع اتنينمظبوط يبقى
+
+332
+00:35:25,760 --> 00:35:30,820
+الربع الرابع ثم الربع الأول طب السيك و ال cosine
+
+333
+00:35:30,820 --> 00:35:35,240
+في الربع الأول و الرابع موجبة موجبة يبقى حطيت ال
+
+334
+00:35:35,240 --> 00:35:39,780
+absolute value و انا شيلتها كله بالموجبة يعني
+
+335
+00:35:39,780 --> 00:35:43,880
+زيادة كلك على ما حطيتها تمام السيك موجب في الربع
+
+336
+00:35:43,880 --> 00:35:47,100
+الرابع و الرابع الأول و كذلك ال cosine يبقى لا
+
+337
+00:35:47,100 --> 00:35:52,490
+داعي لكتابة ال absolute valueتمام؟ لأن الـ Sec
+
+338
+00:35:52,490 --> 00:35:56,830
+موجب في الرابع الأول والرابع الرابع طيب حسب domain
+
+339
+00:35:56,830 --> 00:36:02,250
+طول ال V إذا بده المطموب الأول ال unit tangent V
+
+340
+00:36:02,250 --> 00:36:11,510
+هو V على طول ال V وين ال V؟ هاي ال V اللي هي تاني
+
+341
+00:36:11,510 --> 00:36:23,100
+Tزائد I تنتي في اتجاه الـ I زائد J كله على سك T
+
+342
+00:36:23,100 --> 00:36:28,870
+ويساوي تانية يا بنات اللي هي عبارة عن مين؟Sin على
+
+343
+00:36:28,870 --> 00:36:35,190
+Cos وSec مقلوب الـ Cos يبقى بضالة دي بس قداشت Sin
+
+344
+00:36:35,190 --> 00:36:41,210
+واحدة يبقى بيصير الـ Sin تي في اتجاه الـ I زايد
+
+345
+00:36:41,210 --> 00:36:50,390
+واحد على سك Cos يبقى هذا Cos تي في اتجاه الـ Gيبقى
+
+346
+00:36:50,390 --> 00:36:55,470
+أصبح المطلوب الأول ال unit tangent vector T هو
+
+347
+00:36:55,470 --> 00:37:01,890
+sine T في اتجاه I زائد cosine T في اتجاه ال J هذا
+
+348
+00:37:01,890 --> 00:37:08,610
+هو ال unit tangent vector T نقلب بعدين بالنمية ال
+
+349
+00:37:08,610 --> 00:37:13,990
+principle unit normal I و فوق يبقى بنروح أشتقه
+
+350
+00:37:13,990 --> 00:37:21,120
+بالنسبة إلى T و أقسم على طولهيبقى بدي اجي اخد ال
+
+351
+00:37:21,120 --> 00:37:27,280
+DT على DT بدي اشتق هذه الدلة بالنسبة الى T ففضل ال
+
+352
+00:37:27,280 --> 00:37:33,160
+sine ب cosine T في اتجاه ال I ماقص sine T في اتجاه
+
+353
+00:37:33,160 --> 00:37:40,170
+ال J بدي اجيب الطول تبعهيبقى قول تبع ال Dt على Dt
+
+354
+00:37:40,170 --> 00:37:46,150
+بدي أسوأ ال square root لقو صين تربية T زائد صين
+
+355
+00:37:46,150 --> 00:37:52,170
+تربية T اللي هو بقدرش كمان؟ واحد صحيح يبقى بناء
+
+356
+00:37:52,170 --> 00:37:58,670
+على ال principle normal Nبدي اجي هنا و اسمه على
+
+357
+00:37:58,670 --> 00:38:03,790
+طول يعني بدي اسمه على قداش بتغير؟ لأ يبقى هذا
+
+358
+00:38:03,790 --> 00:38:09,970
+بيصير cosine T في اتجاه ال I ماطس sine T في اتجاه
+
+359
+00:38:09,970 --> 00:38:16,350
+ال J مقسوما على واحد صحيح بظل هو نفسه يبقى هذا ال
+
+360
+00:38:16,350 --> 00:38:21,550
+principle unit normal vector بعدين قال ليش؟ بدي
+
+361
+00:38:21,550 --> 00:38:29,770
+تجيب لل curvature كابةكرفيت شركابة جداش تساوي طول
+
+362
+00:38:29,770 --> 00:38:37,170
+ال V طول ال V طول ال V طول ال V طول ال V طول ال V
+
+363
+00:38:37,170 --> 00:38:39,750
+طول ال V طول ال V طول ال V طول ال V طول ال V طول
+
+364
+00:38:39,750 --> 00:38:43,010
+ال V طول ال V طول ال V طول ال V طول ال V طول ال V
+
+365
+00:38:43,010 --> 00:38:44,890
+طول ال V طول ال V طول ال V طول ال V طول ال V طول
+
+366
+00:38:44,890 --> 00:38:45,790
+ال V طول ال V طول ال V طول ال V طول ال V طول ال V
+
+367
+00:38:45,790 --> 00:38:47,490
+طول ال V طول ال V طول ال V طول ال V طول ال V طول
+
+368
+00:38:47,490 --> 00:38:47,490
+ال V طول ال V طول ال V طول ال V طول ال V طول ال V
+
+369
+00:38:47,490 --> 00:38:47,550
+طول ال V طول ال V طول ال V طول ال V طول ال V طول
+
+370
+00:38:47,550 --> 00:38:47,550
+ال V طول ال V طول ال V طول ال V طول ال V طول ال V
+
+371
+00:38:47,550 --> 00:38:54,070
+طول ال V طول ال V طولبدي الكيروفيتشاركابة اللي هو
+
+372
+00:38:54,070 --> 00:39:00,410
+واحد على طول ال V بالفعل يبقى هذه اللي هي قداش
+
+373
+00:39:00,410 --> 00:39:06,430
+تساوي اللي هو او نكتبها لك بالتفصيل و بعدين بنعوض
+
+374
+00:39:06,430 --> 00:39:15,010
+بيها يبقى الكيروفيتشاركابة كانت اللي هو قداش طول
+
+375
+00:39:15,010 --> 00:39:18,770
+ال V في المقام و فوق .. كان ايه يا شباب انا بتحدثك
+
+376
+00:39:18,770 --> 00:39:28,350
+كتير؟DT على T طول تبعه يبقى DT على DT الطول تبعه
+
+377
+00:39:28,350 --> 00:39:33,030
+بهذا الشكل الطول تبعه طلعناه في جداش بواحد يبقى
+
+378
+00:39:33,030 --> 00:39:38,450
+بدي نسبة واحد على طول ال V وطول ال V طلعناه في
+
+379
+00:39:38,450 --> 00:39:46,190
+جداش سك T يبقى سك T هذا بدي أعطيك انه كربت شركابة
+
+380
+00:40:18,020 --> 00:40:23,040
+بنجي للنقطة التالتة في هذا ال section حاجة اسمها
+
+381
+00:40:23,040 --> 00:40:31,630
+دائرة الإلحن The circle of curvatureأفرض أنا عندي
+
+382
+00:40:31,630 --> 00:40:38,110
+منحنى ماء وعند نقطة ماء على هذا المنحنى بدي أحسب
+
+383
+00:40:38,110 --> 00:40:43,070
+the circle of curvature دائرة التكوّس أو دائرة
+
+384
+00:40:43,070 --> 00:40:48,990
+الإنحنات بدي ال center of curvature مركز الإنحنات
+
+385
+00:40:48,990 --> 00:40:54,490
+بدي ال radius of curvature نصف بطء الإنحنات
+
+386
+00:40:57,500 --> 00:41:05,060
+هذا كله نصف قطر انحناء مركز الانحناء هو نصف قطر
+
+387
+00:41:05,060 --> 00:41:11,100
+دائرة الانحناء وهي مركز دائرة الانحناء طب لو
+
+388
+00:41:11,100 --> 00:41:17,460
+رسمناها على منحلة بتكون جهة الداخل ولا جهة الخارج؟
+
+389
+00:41:17,890 --> 00:41:24,430
+جات الداخل اتنين بتتمسي المنحنة عند النقطة اللي
+
+390
+00:41:24,430 --> 00:41:28,990
+بنحسب عليها ال circle of curvature يبقى ال radius
+
+391
+00:41:28,990 --> 00:41:33,950
+of curvature يا بنات هي دائرة في نفس المستوى تبع
+
+392
+00:41:33,950 --> 00:41:40,210
+المنحنة تمسوا عندها نقطة يعني ال unit tangent
+
+393
+00:41:40,210 --> 00:41:45,990
+بيكون هو tangent لل circle و لل curve في نفس الوقت
+
+394
+00:41:46,310 --> 00:41:50,990
+الـ Radius تبعها هو نفس الـ Radius تبع الكيربتشار
+
+395
+00:41:50,990 --> 00:41:55,350
+الـ Center تبعها هو الـ Center تبع الكيربتشار
+
+396
+00:41:55,350 --> 00:42:00,530
+التقوس بيكون أو الدائرة بيكون لوين؟ للداخل يبقى
+
+397
+00:42:00,530 --> 00:42:05,870
+بدنا نعطي تعريف لها أو نرسمها لأي منحلة موجود
+
+398
+00:42:05,870 --> 00:42:07,970
+عندنا على سبيل المثال
+
+399
+00:42:16,090 --> 00:42:28,070
+الـ Circle of curvature for a plane curve
+
+400
+00:42:28,070 --> 00:42:36,810
+Definition،
+
+401
+00:42:36,810 --> 00:42:42,550
+أعطيها التعريف التالي The circle of curvature
+
+402
+00:42:44,010 --> 00:42:53,330
+circle of curvature بعض الكتب البنات بتسميها ال
+
+403
+00:42:53,330 --> 00:43:03,050
+oscillating circle oscillating
+
+404
+00:43:03,050 --> 00:43:08,050
+circle أو ال circle of curvature لإتنين نفس القصة
+
+405
+00:43:08,050 --> 00:43:22,210
+at a pointP on a plain curve on a plain curve
+
+406
+00:43:22,210 --> 00:43:35,630
+لمنحنا where حيث الكربت شركاها لاتساوي zero if the
+
+407
+00:43:35,630 --> 00:43:42,230
+circle is the circle and
+
+408
+00:43:43,270 --> 00:43:50,610
+the plane عبارة عن دائرة في نفس المستوى of the
+
+409
+00:43:50,610 --> 00:44:04,290
+curve A is tangent to
+
+410
+00:44:04,290 --> 00:44:08,950
+the curve at
+
+411
+00:44:08,950 --> 00:44:09,910
+P
+
+412
+00:44:14,400 --> 00:44:20,600
+نمرا V has the
+
+413
+00:44:20,600 --> 00:44:29,720
+same curvature as
+
+414
+00:44:29,720 --> 00:44:42,060
+the curve at P نمرا C lies toward
+
+415
+00:44:45,810 --> 00:44:51,630
+داكون curve او
+
+416
+00:44:51,630 --> 00:44:59,250
+inner inner side of
+
+417
+00:44:59,250 --> 00:45:08,650
+the curve Definition
+
+418
+00:45:08,650 --> 00:45:16,220
+رقم اتنين The radius of curvatureالراديوس
+
+419
+00:45:16,220 --> 00:45:21,620
+الكيرفيتشا
+
+420
+00:45:21,620 --> 00:45:24,900
+نصف
+
+421
+00:45:24,900 --> 00:45:37,380
+قطرة لمحنة of the curve at P is the radius of the
+
+422
+00:45:37,380 --> 00:45:42,140
+circle is the radius
+
+423
+00:45:44,820 --> 00:45:54,520
+of the circle of curvature of
+
+424
+00:45:54,520 --> 00:45:59,080
+curvature and
+
+425
+00:45:59,080 --> 00:46:08,600
+this radius and this radius is هديله الرمز روغ
+
+426
+00:46:08,600 --> 00:46:15,900
+اللي هو بده يسوى واحد على كترdefinition رقم تلاتة
+
+427
+00:46:15,900 --> 00:46:29,800
+the center of curvature the center of curvature of
+
+428
+00:46:29,800 --> 00:46:35,280
+the curve at
+
+429
+00:46:35,280 --> 00:46:40,280
+النقطة P is the center of the circle of curvature
+
+430
+00:46:40,280 --> 00:46:56,360
+is theسينتا of the circle of curvature
+
+431
+00:47:35,150 --> 00:47:42,630
+نعود الآن لكل تعريف من التعريف الثلاثة ونحاول أن
+
+432
+00:47:42,630 --> 00:47:48,570
+نفهم كل نقطة فيه ثم نعطي رسم توضيحي للكلام اللي
+
+433
+00:47:48,570 --> 00:47:51,750
+قلناه خلال هذا التعريف
+
+434
+00:48:01,240 --> 00:48:06,040
+التقاوس أو دائرة المنحنى لمنحنى موجود في مستوى
+
+435
+00:48:06,040 --> 00:48:10,980
+التعريف الأول the circle of curvature أو الـ
+
+436
+00:48:10,980 --> 00:48:14,040
+oscillating circle with oscillating circle
+
+437
+00:48:14,040 --> 00:48:17,680
+الcircle of curvature الاتنين are the same at a
+
+438
+00:48:17,680 --> 00:48:22,700
+point P على ال plane curve بحيث القابلة تسمي Zero
+
+439
+00:48:22,700 --> 00:48:27,230
+is the circle in the plane of the curve دهيبقى هي
+
+440
+00:48:27,230 --> 00:48:34,270
+الدائرة اللى موجودة في المستوى والتي تحقق ثلاثة
+
+441
+00:48:34,270 --> 00:48:40,970
+شروط الشرط الأول نمرا A is tangent to the curve at
+
+442
+00:48:40,970 --> 00:48:46,770
+P اه يعني احنا لو جينا قولنا على سبيل المثال
+
+443
+00:48:46,770 --> 00:48:52,510
+افترضوا اننا ملحنة بهذا الشكل يبقى هذا ال curve
+
+444
+00:48:52,510 --> 00:48:57,760
+اللى عندنابدي اجي عنده نقطة زي مين زي النقطة اللى
+
+445
+00:48:57,760 --> 00:49:05,860
+عندنا مثلا هذا بدي اقول هذا النقطة فيه الدائرة
+
+446
+00:49:05,860 --> 00:49:10,860
+اللى عندنا هتبقى ممثل للمنحنة عنده فيه بقول اه
+
+447
+00:49:10,860 --> 00:49:16,620
+بقدر ارسمها برا هنا و بقدر ارسمها جوا هنا بقدر
+
+448
+00:49:16,620 --> 00:49:21,180
+ارسم دائرة هنا و هنا تمام السؤال هو مين منهم
+
+449
+00:49:21,180 --> 00:49:27,710
+بالضغط بروح بكملنمرا بى has the same curvature as
+
+450
+00:49:27,710 --> 00:49:32,690
+the curve at P لها نفس التقوس يعني لها نفس قيمة
+
+451
+00:49:32,690 --> 00:49:37,470
+Kappa ما علينا نمرسى that's towards the concave
+
+452
+00:49:37,470 --> 00:49:43,530
+side أو ال inner side inner يعني داخلي يبقى جهة
+
+453
+00:49:43,530 --> 00:49:49,810
+التقوس الداخلي للمنحنة اه يعني لو جيت رسمتها بدت
+
+454
+00:49:49,810 --> 00:49:51,110
+يجين الدائرة هيك
+
+455
+00:49:54,890 --> 00:50:02,330
+في هذا الشكل يبقى الدائرة بتكون وين؟ للداخل زي ما
+
+456
+00:50:02,330 --> 00:50:09,750
+انتوا شايفين بتتمسك المنحنة عند مين؟ عند نقطة P و
+
+457
+00:50:09,750 --> 00:50:14,790
+تكون وين؟ جهة الداخل زي ما انتوا شايفين يبقى مرة
+
+458
+00:50:14,790 --> 00:50:15,310
+تالية
+
+459
+00:50:18,480 --> 00:50:23,220
+تانجنت هذا فيه يبقى المماس عنده فيه بده يمس
+
+460
+00:50:23,220 --> 00:50:29,960
+المنحنة ودائرة يعني الدائرة هذه اللي بالشكل اللي
+
+461
+00:50:29,960 --> 00:50:36,800
+عندنا هذا هيك بدي يكون لو رسمت مماس الشكل اللي
+
+462
+00:50:36,800 --> 00:50:42,190
+عندنا هذا بدي يكون هذا ال unit tangent vectorيبقى
+
+463
+00:50:42,190 --> 00:50:48,510
+تاني ال vector مماس للمنحنة و للدائرة في آلة واحدة
+
+464
+00:50:48,510 --> 00:50:52,290
+فهذا معنى النقطة الأولى النقطة التانية are the
+
+465
+00:50:52,290 --> 00:50:57,170
+same curvature لو حسبت ال curvature للمنحنة وال
+
+466
+00:50:57,170 --> 00:51:02,910
+curvature للدائرة الأتنين are the same طيب بنقدر
+
+467
+00:51:02,910 --> 00:51:09,470
+نعرف قداش ال curvature للدائرة يعني قداش عدديا
+
+468
+00:51:11,690 --> 00:51:17,610
+واحد على ال radius تواطنها ميفان الدائرة ال
+
+469
+00:51:17,610 --> 00:51:21,250
+curvature تبعها يسوى المقار نسبة واحد على نصف قطر
+
+470
+00:51:21,250 --> 00:51:30,330
+هذه الدائرة ممداز جدا يبقى لو عرفي الدائرة وعرف نص
+
+471
+00:51:30,330 --> 00:51:35,790
+القطر تبعها وطرد مني جداش ال curvature للمنحنة
+
+472
+00:51:35,790 --> 00:51:40,130
+بقول واحد على نصف القطر تبع الدائرة دائرة الانحنات
+
+473
+00:51:40,510 --> 00:51:46,230
+تمام تمام نمرة تلاتة تقع في الجزء الداخلي للمنحنة
+
+474
+00:51:46,230 --> 00:51:51,070
+وليس في الجزء الخارج لأنه لو رسمناها هنا بتجي برا
+
+475
+00:51:51,070 --> 00:51:56,430
+يبقى هي للداخل طيب نجي لل definition التاني قال
+
+476
+00:51:56,430 --> 00:52:04,950
+نصف قطر الإنحن للمنحنة عند النقطة B هو نصف قطرو
+
+477
+00:52:04,950 --> 00:52:11,610
+يسوى عمليا واحد على الكيربيتشار نص القطر يبجى هذا
+
+478
+00:52:11,610 --> 00:52:20,410
+نص القطر هذا اللي هو نص القطر يبجى
+
+479
+00:52:20,410 --> 00:52:33,430
+بنات هذا اسمه ال radius of curvature وهذه اسمها ال
+
+480
+00:52:33,430 --> 00:52:42,130
+circleof curvature هاي أبو هذا المركز الدائرة ال
+
+481
+00:52:42,130 --> 00:52:53,190
+center of curvature يبقى هذا اسمه ال center of
+
+482
+00:52:53,190 --> 00:52:55,250
+curvature
+
+483
+00:53:01,320 --> 00:53:07,580
+طلعت نصف قطر الإنحناء و نصف قطر دائرة الإنحناء و
+
+484
+00:53:07,580 --> 00:53:13,100
+يسوى عملياً رو تسوى واحد على كابة يبقى هذا ال
+
+485
+00:53:13,100 --> 00:53:19,640
+radius اللي هو رو تسوى واحد على كابة اللي هو
+
+486
+00:53:19,640 --> 00:53:27,650
+radius of curvatureعند النقطة
+
+487
+00:53:27,650 --> 00:53:33,800
+B هو ال center تبع دائرة الكيروفيتشاريبقى الأن
+
+488
+00:53:33,800 --> 00:53:38,900
+فهمنا معنى الـ circle of curvature عاملية السؤال
+
+489
+00:53:38,900 --> 00:53:44,020
+هو بتقدر تحسب radius of curvature و ال center of
+
+490
+00:53:44,020 --> 00:53:48,620
+curvature و ال equation تبع ال circle of curvature
+
+491
+00:53:48,620 --> 00:53:55,760
+أم لا هذا السؤال الذي سنجوب عليه بمثال عددي عشان
+
+492
+00:53:55,760 --> 00:53:59,980
+نعرف كيف نشتغل هذا الشغل نبقى example
+
+493
+00:54:05,960 --> 00:54:13,780
+يقولي find and graph يوجد and ارسم find and graph
+
+494
+00:54:13,780 --> 00:54:25,060
+مين؟ قاللي ده oscillating circle of
+
+495
+00:54:25,060 --> 00:54:28,360
+the
+
+496
+00:54:28,360 --> 00:54:32,320
+curve
+
+497
+00:54:32,320 --> 00:54:42,670
+للمنحنةR of T تساوي T في اتجاه I زائد Sine T في
+
+498
+00:54:42,670 --> 00:54:49,730
+اتجاه M في اتجاه G التي تساوي Pi على M
+
+499
+00:55:06,690 --> 00:55:10,410
+المنحنى لأننا لا نعرف أنه بنادر لماذا لا نعرف أنه
+
+500
+00:55:10,410 --> 00:55:14,930
+مُعطَى في الصيغة البرامترية لكن لو حولته لصيغة
+
+501
+00:55:14,930 --> 00:55:20,410
+كارتيزية لأصبح المنحنى معروف بالنسبة لنا وربما
+
+502
+00:55:20,410 --> 00:55:26,950
+يكون أسهل مما نتصور يبقى R of T باعتبار X of T في
+
+503
+00:55:26,950 --> 00:55:33,710
+اتجاه I زي Y of T في اتجاه J صح ولا لأ يبقى كأن X
+
+504
+00:55:33,710 --> 00:55:40,370
+هنا في سوء المينو ال y تساوي صين ال t هذا بدي
+
+505
+00:55:40,370 --> 00:55:45,950
+اعطيك مين ان ال y قد اتش سببنا صين ال x هذا
+
+506
+00:55:45,950 --> 00:55:50,270
+المنحنة معروف ولا لا يبقى المنحنة اللي عندنا منحنة
+
+507
+00:55:50,270 --> 00:55:56,130
+الجيب يبقى كويس تعرفنا على شكل المنحنة اللي بنقدر
+
+508
+00:55:56,130 --> 00:56:03,530
+نرسمه الآن صار بالنسبة لنا سهل طيب كويس بعد ذلكقال
+
+509
+00:56:03,530 --> 00:56:08,570
+لي فاهم و اقرا في ال circulating circle للمنحنة
+
+510
+00:56:08,570 --> 00:56:13,910
+اللى عندها بدك ترسمها وتوجدها كذلك لما يقول لي
+
+511
+00:56:13,910 --> 00:56:19,210
+وجدها يعني بدك توجد معادلتها إذا أنا مش هتوجد هذه
+
+512
+00:56:19,210 --> 00:56:22,330
+المعادلة بالزمن نصف القطر
+
+513
+00:56:26,700 --> 00:56:32,460
+هل المركز هو نقطة الاصل؟ ماهواش نقطة الاصل؟ الاخرى
+
+514
+00:56:32,460 --> 00:56:39,520
+هذا كله كلام بيقولوا
+
+515
+00:56:39,520 --> 00:56:45,340
+الله كويسيبقى انا بدي ايش؟ بدي معادلة الدائرة و
+
+516
+00:56:45,340 --> 00:56:50,680
+بدي مركز هذه الدائرة و اذا عرفت المركز و المعادلة
+
+517
+00:56:50,680 --> 00:56:55,120
+بكون عرفته ده جالي fine وبالتالي بصير سهل رسمها،
+
+518
+00:56:55,120 --> 00:57:02,900
+مظبوط؟ تمام تمام طيب بدنا نروح نحسب كل الشغلات
+
+519
+00:57:02,900 --> 00:57:08,280
+اللي بتلزمني مشان نعرف هذه المعادلةأنا عندي R of T
+
+520
+00:57:08,280 --> 00:57:14,600
+لو اشتقيتها بحصل على مين؟ على V يبقى باجي بقوله V
+
+521
+00:57:14,600 --> 00:57:22,020
+تساوي DR على DT اللي هي I زائد cosine T في اتجاه
+
+522
+00:57:22,020 --> 00:57:29,380
+ال G نحسب فول ال V اللي هو الجدري التربيعي لواحد
+
+523
+00:57:29,380 --> 00:57:36,880
+زائد cosine تربيع Tبقدر ألعب فيها أكتر من ذلك ولا
+
+524
+00:57:36,880 --> 00:57:42,520
+حاجة تمام يبقى زي مانيو يبقى هذا قول ال V بقدر
+
+525
+00:57:42,520 --> 00:57:48,180
+أجيب ال unit tangent T يبقى unit tangent T اللي هو
+
+526
+00:57:48,180 --> 00:57:52,380
+V على قول ال V يبقى بصير واحد
+
+527
+00:57:55,740 --> 00:58:01,840
+زائد cosine تربية T في اتجاه I زائد cosine T على
+
+528
+00:58:01,840 --> 00:58:06,720
+الجدر التربية الواحد زائد cosine تربية T في اتجاه
+
+529
+00:58:06,720 --> 00:58:13,260
+J او ان شئتم فاقولوا T يساوي واحد زائد cosine
+
+530
+00:58:13,260 --> 00:58:22,220
+تربية T قص سالب نص في اتجاه Iزائد cosine T في واحد
+
+531
+00:58:22,220 --> 00:58:29,180
+زائد cosine تربيع T أُس سالف نص في اتجاه مين؟ في
+
+532
+00:58:29,180 --> 00:58:34,540
+اتجاه الجيه يبقى أنا جبت ال unit tangent vector
+
+533
+00:58:34,540 --> 00:58:41,160
+اللي عندنا هنا الان بقدر اشتقه و قبل اشتقه من هنا
+
+534
+00:58:41,160 --> 00:58:47,830
+بنات لو قال لي V under Pi على اتنينيبقى ال V عند
+
+535
+00:58:47,830 --> 00:58:53,510
+ال باي على اتنين الطول تبعها يبقى بده يساوي الجدري
+
+536
+00:58:53,510 --> 00:59:00,270
+التربيعي ل واحد زائد جداش مصايب باي على اتنين صفرة
+
+537
+00:59:00,270 --> 00:59:10,930
+يبقى الجواب يساوي واحد صحيح طيب بده اجيبله الان ال
+
+538
+00:59:10,930 --> 00:59:13,370
+Dt على Dt
+
+539
+00:59:16,240 --> 00:59:24,240
+يبقى الأس في القوس مرفوع
+
+540
+00:59:24,240 --> 00:59:29,200
+لنفس الأس مطروح منه واحد في سالب ثلاثة على اتنين
+
+541
+00:59:29,200 --> 00:59:37,500
+في مشتقة مداخل القوس اللي هو اتنين بوصين ات في
+
+542
+00:59:37,500 --> 00:59:43,280
+سالب صين ات كل هذا في اتجاه الأرض
+
+543
+00:59:46,260 --> 00:59:51,740
+مرة تانية بدي أمسحها و أعيدها تاني عشان أخلص سطر
+
+544
+00:59:51,740 --> 01:00:01,900
+ساعة المشتقة كلها أترك هذا لحد هنا و بدا أقول DT
+
+545
+01:00:01,900 --> 01:00:10,940
+على DT يساق اللي هو سالب نص في اللي هو واحد زائد
+
+546
+01:00:10,940 --> 01:00:13,060
+cosine تربيع ال T
+
+547
+01:00:18,670 --> 01:00:24,610
+سالب اتنين وصين ال T في صين ال T كله في اتجاه ال I
+
+548
+01:00:24,610 --> 01:00:33,630
+اللي بعده زاد هذا مشتقت حاصل ضارب دالي تل يبقى
+
+549
+01:00:33,630 --> 01:00:40,110
+مشتقة الأولى بسالب صين يبقى هذا شبصي رملاد هذا زاد
+
+550
+01:00:40,110 --> 01:00:47,450
+وخليه جوز كله يبقى هاي سالب صين ال T في الجوز واحد
+
+551
+01:00:47,680 --> 01:00:55,200
+زائد cosine تربية T قص سالب نص زائد يبقى مشتقة
+
+552
+01:00:55,200 --> 01:01:00,860
+الأولى في الثانية اللى بعدها بده اشتق هذه مشتقة
+
+553
+01:01:00,860 --> 01:01:10,460
+هذه هي صح يبقى هذا الكلام بده يصير ماقص نص في
+
+554
+01:01:10,460 --> 01:01:17,500
+cosine T في واحد زائد cosine تربية T قص سالب تلاتى
+
+555
+01:01:20,060 --> 01:01:29,940
+في سالب اتنين Cos T في Sine T كل هذا في اتجاه مين؟
+
+556
+01:01:29,940 --> 01:01:36,280
+في اتجاه الـG مش واضحة اظن كبّرها شوية ونوضحها
+
+557
+01:01:36,280 --> 01:01:39,400
+يبقى
+
+558
+01:01:39,400 --> 01:01:49,820
+هذا كله مضروب في سالب اتنين Cos T في Sine Tوهي
+
+559
+01:01:49,820 --> 01:01:57,500
+قفلنا الجوس هذا كله لكبير في اتجاه من؟ في اتجاه
+
+560
+01:01:57,500 --> 01:02:00,560
+الجهة
+
+561
+01:02:00,560 --> 01:02:06,420
+يبقى ان اجيبنا دي تي على دي تي بدي احسبله قداش ال
+
+562
+01:02:06,420 --> 01:02:12,020
+دي تي على دي تي اتجمع اكتر بديش اقعد اجمع وضيع
+
+563
+01:02:12,020 --> 01:02:16,520
+اكتر اللي انا بده اعوض دغري طلع يا بنات هناهذه باي
+
+564
+01:02:16,520 --> 01:02:21,560
+على اتنين مقداشي ب zero بظل واحد لأي أس يبقى واحد
+
+565
+01:02:21,560 --> 01:02:26,840
+في نص يبقى هذا ناقص نص وهذا مقداشي ب zero لإنه صار
+
+566
+01:02:26,840 --> 01:02:30,540
+باي على اتنين و واحد في نص يبقى هذا كله صار ب zero
+
+567
+01:02:30,540 --> 01:02:37,850
+في اتجاه الأعلى نجي لبعدهذه باية على اتنين نرجع
+
+568
+01:02:37,850 --> 01:02:42,690
+لسؤالنا مرة ثانية لما تبقى المستقم كالكعة كبيرة زي
+
+569
+01:02:42,690 --> 01:02:46,090
+هيك مش سواء يتجمع فيها و مافيه اتعاوض، هذه بقى وقت
+
+570
+01:02:46,090 --> 01:02:50,870
+كتير، انت بتعاوض مباشرة، تبحث في القيام دوري، فبجي
+
+571
+01:02:50,870 --> 01:02:55,870
+بقوله هنا، بجي بقوله، بدي أشيل كلتي و أحط مكانها
+
+572
+01:02:55,870 --> 01:02:58,050
+باية على اتنين، لإنه قال لي بدي الكلام هذا عند
+
+573
+01:02:58,050 --> 01:03:02,980
+باية على اتنينفبعدين بقوله هنا by على 2 بـ 0 و بظل
+
+574
+01:03:02,980 --> 01:03:07,500
+1 أُس أي رقم بواحد في نص يبقى هنا السلب نص و هنا
+
+575
+01:03:07,500 --> 01:03:11,540
+zero يبقى كله نص في zero اختار كله بـ zero zero في
+
+576
+01:03:11,540 --> 01:03:17,180
+اتجاه العين نجي لهنا هذا بواحد وهنا اللي هو كله
+
+577
+01:03:17,180 --> 01:03:24,020
+بواحد تمام يبقى هنا عندي ناقص واحد وعندي هنا يبقى
+
+578
+01:03:24,020 --> 01:03:27,740
+هذا ناقص واحد هشوف التاني شو بده يجيبلي هذا ال
+
+579
+01:03:27,740 --> 01:03:35,560
+zero كلهيبقى بظل بس قداش ناقص جيه في الشكل لأن هذا
+
+580
+01:03:35,560 --> 01:03:41,760
+الكلام اللي هو بيبقى ناقص جيه طيب من هذه الحالة
+
+581
+01:03:41,760 --> 01:03:46,600
+بقدر اقول اه بستنى شوية تديني بالك ان اصلا هنا
+
+582
+01:03:46,600 --> 01:03:52,720
+ناقص هنا ناقص هذه بتروح وهذه بظل لها مظبوط هذه
+
+583
+01:03:52,720 --> 01:03:57,060
+كلها بتروح و تجيبها ماشي يبقى هذا بدي يعطينا طول
+
+584
+01:03:57,060 --> 01:04:03,930
+ال DTعلى DT قولوا بتساوي كده؟ واحد صحيح إذا بقدر
+
+585
+01:04:03,930 --> 01:04:10,350
+أحسب ال curvature ولا لا؟ طيب ال curvature اللي هو
+
+586
+01:04:10,350 --> 01:04:19,210
+كبه تساوي طول ال V عندي وطول ال DT على DT عندي إذا
+
+587
+01:04:19,210 --> 01:04:26,910
+صارت قصتنا سهل جدا كده؟
+
+588
+01:04:26,910 --> 01:04:28,330
+كده؟ كده؟ كده؟ كده؟ كده؟ كده؟ كده؟ كده؟ كده؟ كده؟
+
+589
+01:04:28,330 --> 01:04:28,330
+كده؟ كده؟ كده؟ كده؟ كده؟ كده؟ كده؟ كده؟ كده؟ كده؟
+
+590
+01:04:28,330 --> 01:04:28,330
+كده؟ كده؟ كده؟ كده؟ كده؟ كده؟ كده؟ كده؟ كده؟ كده؟
+
+591
+01:04:28,330 --> 01:04:28,330
+كده؟ كده؟ كده؟ كده؟ كده؟
+
+592
+01:04:39,180 --> 01:04:46,620
+بتساومين طول ال DT على DT برضه عند ال Y على 2
+
+593
+01:04:46,620 --> 01:04:53,780
+مبسوما على طول ال V عند ال Y على 2 Y يساوي واحد
+
+594
+01:04:53,780 --> 01:04:59,040
+على واحد يساوي واحد الان بدي ال radius of the
+
+595
+01:04:59,040 --> 01:05:05,740
+circle of curvature الجبالي بقولوا the radius of
+
+596
+01:05:06,290 --> 01:05:16,890
+the circle of curvature around تسوى واحد على كده
+
+597
+01:05:16,890 --> 01:05:22,530
+كده بقداش عندنا واحد يبقى واحد على واحد هو يسوى
+
+598
+01:05:22,530 --> 01:05:28,870
+كده واحد يبقى نصف قطر دائرة الانحلال يسوى كده واحد
+
+599
+01:05:28,870 --> 01:05:34,220
+صحيح ممتاز شو ضال عندنا؟المركز مشان نحسب المركز
+
+600
+01:05:34,220 --> 01:05:38,720
+تعالوا نرسم المنحنى اللى عندنا ونشوف كيف بدنا نجيب
+
+601
+01:05:38,720 --> 01:05:45,080
+المركز منه لو جينا للمنحنى اللى عندنا بالشكل هذا
+
+602
+01:05:45,080 --> 01:05:54,500
+هذا محور X هذا محور Y وجيت تخيل ان هذا الخط الوهمى
+
+603
+01:05:54,500 --> 01:05:55,880
+عندنا واحد
+
+604
+01:06:04,420 --> 01:06:09,840
+تفاجنا من هنا على ان المنحنى هو منحنى الجب أو الـ
+
+605
+01:06:09,840 --> 01:06:16,460
+signكر لو رجعنا الى calculus A و رسمنا المنحنى
+
+606
+01:06:16,460 --> 01:06:24,400
+فالمنحنى طبعا بيجي هك و بيجي نازل هك و هكذا
+
+607
+01:06:38,820 --> 01:06:51,500
+هذه النقطة باية على اتنين وهذه النقطة باية على
+
+608
+01:06:51,500 --> 01:06:57,280
+اتنين وهذه النقطة باية على اتنين وهذه النقطة باية
+
+609
+01:06:57,280 --> 01:06:57,280
+على اتنين
+
+610
+01:07:08,420 --> 01:07:15,020
+عشان تطلعين هنا، كداش نصف القطر واحد صحيح، كداش
+
+611
+01:07:15,020 --> 01:07:19,940
+المسافة هذه كلها بنات واحد، إذا بدي يجي المركز
+
+612
+01:07:19,940 --> 01:07:26,700
+تبعها هذه، وجهة الكونكية بصعيد مش فوق هتكون ده،
+
+613
+01:07:26,700 --> 01:07:28,720
+إذا الدائرة هصير
+
+614
+01:07:49,850 --> 01:07:54,810
+تمام؟ يبقى صارت عندي دائرة بهذا الشكل السؤال هو حد
+
+615
+01:07:54,810 --> 01:08:02,590
+فيكم بتقدر تقولي جداش إحداه في المركز؟ تمام باي
+
+616
+01:08:02,590 --> 01:08:08,110
+عتنين و زيرو هذا ال X من هنا لهنا و باي على اتنين
+
+617
+01:08:08,110 --> 01:08:09,950
+و ال Y مهي بزيرو
+
+618
+01:08:33,380 --> 01:08:39,880
+يبقى كويس يبقى ناقص
+
+619
+01:08:39,880 --> 01:08:47,420
+y على 2 لكل تربيع يبقى
+
+620
+01:08:47,420 --> 01:08:49,840
+ناقص y على 2 لكل قطار
+
+621
+01:08:53,120 --> 01:09:04,040
+يبقى هذه ال equation of the circle of
+
+622
+01:09:04,040 --> 01:09:08,780
+curvature قال
+
+623
+01:09:08,780 --> 01:09:14,920
+لي اوجد و ارسم رسمنا و اوجدنا اللي هو الدائرة و
+
+624
+01:09:14,920 --> 01:09:18,860
+المركز تبعها و ال center و ما إلى ذلك يبقى ده ايش
+
+625
+01:09:18,860 --> 01:09:25,320
+اسم المنقطة ده يا بنات؟الـ radius of curvature
+
+626
+01:09:25,320 --> 01:09:29,620
+اللي هو ال radius of the circle of curvature هذا
+
+627
+01:09:29,620 --> 01:09:34,500
+ال center of curvature اللي هو ال center تبع ال
+
+628
+01:09:34,500 --> 01:09:39,160
+radius of curvature هذه الدائرة كلها ال circle of
+
+629
+01:09:39,160 --> 01:09:44,100
+curvature يبقى هذه الدائرة ها اللي هي ال circle
+
+630
+01:09:53,880 --> 01:09:57,240
+طيب، الشغل اللي اشتغلناه كله هذا الوقت كان على
+
+631
+01:09:57,240 --> 01:10:04,600
+مين؟ على الـ plane و هو الآن ننتقل إلى الشغل في
+
+632
+01:10:04,600 --> 01:10:09,800
+الفرار الشغل
+
+633
+01:10:09,800 --> 01:10:14,700
+في الفرار لن يختلف عن ال plane ولا حاجة نفس
+
+634
+01:10:14,700 --> 01:10:18,740
+المعلومات اللي أخذناها على ال plane صحيحة على
+
+635
+01:10:18,740 --> 01:10:26,140
+الفراراللهم إلا بشري عندي تلات مركبات بدلا من
+
+636
+01:10:26,140 --> 01:10:31,260
+مركبتين وبعدين بدي أحطها في شبكة remark التالية
+
+637
+01:10:31,260 --> 01:10:36,940
+remark if
+
+638
+01:10:36,940 --> 01:10:45,160
+we have a space curve if we have
+
+639
+01:10:45,160 --> 01:10:48,060
+a space curve
+
+640
+01:11:13,140 --> 01:11:25,830
+نفس النتائجas the case as the case of the plane
+
+641
+01:11:25,830 --> 01:11:34,330
+curve كما في حالة المنحنة في مستوى نعطي مثال for
+
+642
+01:11:34,330 --> 01:11:37,490
+example
+
+643
+01:11:37,490 --> 01:11:47,540
+you will find الـT و الـN and الكيروتشاركاتfor the
+
+644
+01:11:47,540 --> 01:11:58,880
+space curve for the space curve اللي همين R of T
+
+645
+01:11:58,880 --> 01:12:09,120
+بده يساوي E أس T cosine T في اتجاه I زائد E أس T
+
+646
+01:12:09,120 --> 01:12:15,780
+sine T في اتجاه J زائد 2K
+
+647
+01:12:43,260 --> 01:12:48,260
+السؤال مرة ثانية بيقول ان لو انتقلنا من المستوى
+
+648
+01:12:48,260 --> 01:12:51,960
+إلى الفرار هل المعلومات اللي هتتغير و لا تبقى كما
+
+649
+01:12:51,960 --> 01:12:57,760
+هي؟ الإجابة تبقى كما هي نعطي مثال توضيحي بيقول
+
+650
+01:12:57,760 --> 01:13:01,700
+هاتلي ال unit tangent و ال principal normal و ال
+
+651
+01:13:01,700 --> 01:13:06,200
+curvature لل space curve اروكتي بيبقى كذا يبقى
+
+652
+01:13:06,200 --> 01:13:12,900
+باجي بيقول انه solutionبدي اوجد دموعين ال V of T
+
+653
+01:13:12,900 --> 01:13:19,530
+اللي هى TR على Dيبدأ اشتق هذه حوارة حاصل ضرب
+
+654
+01:13:19,530 --> 01:13:27,130
+داليتين يبقى لو اشتقت ال Eost في Eost وSin T ناقص
+
+655
+01:13:27,130 --> 01:13:36,810
+Eost Sin T هذا في اتجاه I زائد Eost Sin T زائد
+
+656
+01:13:36,810 --> 01:13:45,560
+Eost Sin T كله في اتجاه J زائدهذا كل الـ sine كله
+
+657
+01:13:45,560 --> 01:13:52,100
+بـ 0 تمام؟ بدي أجيب وقول أوه بقدر أقول هذه E أُس T
+
+658
+01:13:52,100 --> 01:13:59,580
+في Cos T نقص Sine T في اتجاه I زائد E أُس T في
+
+659
+01:13:59,580 --> 01:14:06,080
+Sine T زائد Cos T كله في اتجاه مين؟ في اتجاه الـ J
+
+660
+01:14:06,080 --> 01:14:14,860
+بدي أجيب له طول الـ V يبقى الجذر الترابي يمينيقص
+
+661
+01:14:14,860 --> 01:14:24,920
+اتنين T في cosine تربية T نقص اتنين sin T cosine T
+
+662
+01:14:24,920 --> 01:14:31,260
+زائد sin تربية T زائدبتاخد هذه وهذه ت برا منهم
+
+663
+01:14:31,260 --> 01:14:36,700
+عاملة مشتركة يبقى بضربها هذه بالمرة يبقى sin تربيه
+
+664
+01:14:36,700 --> 01:14:45,220
+ت زائد اتنين sin t cos t زائد cos تربيه تطبعا هذه
+
+665
+01:14:45,220 --> 01:14:49,200
+بالموجة وهذه بالسالب مع السلامة بس يبقى لديها
+
+666
+01:14:49,200 --> 01:14:55,420
+بناءت اتنين sin تربية و اتنين cosine تربية يبقى
+
+667
+01:14:55,420 --> 01:15:01,560
+هذا الكلام الجذري التربية ل E اص اتنين T في اتنين
+
+668
+01:15:01,560 --> 01:15:08,530
+cosine تربية T زائد cosine تربية P له قدرأو 1
+
+669
+01:15:08,530 --> 01:15:14,490
+الجدرى التربية اللي هي 2E أُس 2E هو يساوي جدرى 2
+
+670
+01:15:14,490 --> 01:15:20,890
+في مين؟ في E أُس Tطب بدأ أجيب له المطلوب الأول ال
+
+671
+01:15:20,890 --> 01:15:27,650
+unit tangent vector T يبقى T بدأ تساوي المتجه V
+
+672
+01:15:27,650 --> 01:15:32,490
+على طول المتجه V يعني بدي أقسم على مين على المقدار
+
+673
+01:15:32,490 --> 01:15:37,630
+اللي عندنا هذا وين ال V هي ال V يبقى بدي أقسم على
+
+674
+01:15:37,630 --> 01:15:42,030
+U of T بالطير هذه و الطير هذه و جيك مين واحد على
+
+675
+01:15:42,030 --> 01:15:49,940
+جدر اتنين يبقى واحد على جدر اتنين في مينبـ cos T
+
+676
+01:15:49,940 --> 01:15:56,300
+نقص sin T في اتجاه الـ I زائد واحد على جدر اتنين
+
+677
+01:15:56,300 --> 01:16:03,200
+بـ sin T زائد cos T في اتجاه من؟ في اتجاه الـ J
+
+678
+01:16:03,200 --> 01:16:10,220
+يبقى جيبناه من المطلوب الأول المطلوب التاني شوف
+
+679
+01:16:10,220 --> 01:16:19,020
+الزمن هنا يبقى أشتق هذا يبقى بداجي أخده DTعلى DT
+
+680
+01:16:19,020 --> 01:16:25,380
+ويسوي 1 على جذر 2 يبقى على الحياد الإيجابي وعدم
+
+681
+01:16:25,380 --> 01:16:32,700
+الانحياز يبقى من الاشتقال ما يصير ماقص sin T وهذا
+
+682
+01:16:32,700 --> 01:16:40,110
+ماقص في sin T كله في اتجاه Iو هذي زائد واحدة على
+
+683
+01:16:40,110 --> 01:16:45,770
+جدر اتنين تقص صين T نقص صين T في اتجاه مين؟ في
+
+684
+01:16:45,770 --> 01:16:51,510
+اتجاه الجهة بدي الطول تبعه يبقى
+
+685
+01:17:01,770 --> 01:17:06,950
+لو أخدت ناقص ما ناقص يطلع برا مربعه بطير الله يسهل
+
+686
+01:17:06,950 --> 01:17:14,190
+عليه وواحد عليه جدر اتنين مربعه بنص يبقى هذا نص في
+
+687
+01:17:14,190 --> 01:17:22,070
+مين؟ في .. بدي أربع هذه بزايد كلها بصير sin تربية
+
+688
+01:17:22,070 --> 01:17:33,030
+T زي دي اتنين sin T cos T زي كسين تربية Tزاد هذه
+
+689
+01:17:33,030 --> 01:17:37,970
+كمان لو ربعتها بيصير مين؟ مُص يبقى بده أخليه برا،
+
+690
+01:17:37,970 --> 01:17:44,370
+هاي الخط برا، يبقى بده أجيب تربيه هذه Cos تربيه T
+
+691
+01:17:44,370 --> 01:17:53,230
+نقص اتنين Sine T Cos T زائد Sine تربيه T تمام؟
+
+692
+01:17:55,760 --> 01:18:01,960
+هذه موجبة وهذه سلبة مع السلامة بيصير اتنين بصين
+
+693
+01:18:01,960 --> 01:18:09,780
+تربية زي اتنين صين تربية يبقى الجذر التربيهي لنص
+
+694
+01:18:09,780 --> 01:18:13,740
+في اتنين في صين تربيهي
+
+695
+01:18:29,440 --> 01:18:40,020
+DT على DT نقصوم على قول DT على DT الـ DT على DT هي
+
+696
+01:18:40,020 --> 01:18:48,840
+على واحد يبقى بظل زي ما هو يبقى هذا الكلام سالم
+
+697
+01:18:48,840 --> 01:18:57,100
+واحد على جدر اثنين في الـ sineت زائد cosine ت كل
+
+698
+01:18:57,100 --> 01:19:03,560
+هذا في اتجاه ال I واحد على جانر اتنين فيه cosine T
+
+699
+01:19:03,560 --> 01:19:10,760
+ناقص sine T كله في اتجاه من الجيب ضال ان الكيربت
+
+700
+01:19:10,760 --> 01:19:18,800
+شارك هذا كم جداش بيساوي طول ال DT على DT على طول
+
+701
+01:19:18,800 --> 01:19:20,860
+ال V يبقى
+
+702
+01:19:30,370 --> 01:19:39,330
+طول ال V طول ال V له اتنين او جدر اتنين E أسطى
+
+703
+01:19:39,330 --> 01:19:47,390
+يبقى جدر اتنين E أسطىيبقى هذا الكلام معناته يعني
+
+704
+01:19:47,390 --> 01:19:55,490
+واحد على جدر اتنين او واحد على جدر اتنين في إيه
+
+705
+01:19:55,490 --> 01:20:00,510
+والسالب فيه يبقى هذا ال curve شركابة اللي موجودة
+
+706
+01:20:00,510 --> 01:20:08,170
+هنا او اللي هو بده يعني لحد هنا stop يا بنات المرة
+
+707
+01:20:08,170 --> 01:20:12,230
+الجاية بجيبكوا ان شاء الله أرقام المسائل تبعت هذا
+
+708
+01:20:12,230 --> 01:20:12,790
+ال section
+
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/WBeNRZv00d4_postprocess.srt b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/WBeNRZv00d4_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..bdf730951683f7f588a9632b1c68cb59dc1adf20
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/WBeNRZv00d4_postprocess.srt
@@ -0,0 +1,3320 @@
+1
+00:00:00,000 --> 00:00:02,680
+موسيقى
+
+2
+00:00:10,750 --> 00:00:12,090
+رحمان الله رحمان الله رحمان الله رحمان الله رحمان
+
+3
+00:00:12,090 --> 00:00:15,670
+رحمان
+
+4
+00:00:15,670 --> 00:00:15,810
+الله رحمان الله رحمان الله رحمان الله رحمان الله
+
+5
+00:00:15,810 --> 00:00:18,390
+رحمان الله رحمان الله رحمان الله رحمان الله رحمان
+
+6
+00:00:18,390 --> 00:00:32,690
+الله رحمان الله رحمان الله رحمان الله رحمان
+
+7
+00:00:32,690 --> 00:00:38,660
+اللهالنقطة الأولى هو functions of two variables
+
+8
+00:00:38,660 --> 00:00:41,740
+والنقطة الثانية هي functions of
+
+9
+00:00:47,190 --> 00:00:54,290
+النقطة الأولى الدوال في متغيرين والجزء الأخير هو
+
+10
+00:00:54,290 --> 00:01:00,110
+الدوال في ثلاث متغيرات طب كويس بدنا نيجي الآن لل
+
+11
+00:01:00,110 --> 00:01:03,810
+functions of two variables وفي عندى بعض ال
+
+12
+00:01:03,810 --> 00:01:08,890
+definitions الأساسية اللي لازم نعرفها و اللي بدنا
+
+13
+00:01:08,890 --> 00:01:13,220
+نبني دراستنا عليها ان شاء الله تعالىالتعريف الأول
+
+14
+00:01:13,220 --> 00:01:18,280
+بيقول اللي هي point X node و Y node in a region R
+
+15
+00:01:18,280 --> 00:01:24,200
+النقطة الي احداثيها X node و A node في المنطقة R
+
+16
+00:01:24,200 --> 00:01:31,120
+in the XY plane يبقى في المستوى XY is an interior
+
+17
+00:01:31,120 --> 00:01:37,840
+point of R بسميها نقطة داخلية في المنطقة R if it
+
+18
+00:01:37,840 --> 00:01:40,540
+is a center of a disk
+
+19
+00:01:49,480 --> 00:01:58,460
+والذي يقع كليا في المنطقة R يبقى
+
+20
+00:01:58,460 --> 00:02:02,320
+انا لو جيت في المستوى XY يعني في ال plane اللي
+
+21
+00:02:02,320 --> 00:02:06,420
+عندناو روحنا و قولنا هذه المحاور على سبيل المثال
+
+22
+00:02:06,420 --> 00:02:14,980
+هذا محور X هذا محور I وهذه المنطقة التي هي R في
+
+23
+00:02:14,980 --> 00:02:21,820
+عندي نقطة هنا معناها النقطة هذه اللي إحداثيها X
+
+24
+00:02:21,820 --> 00:02:29,990
+node و Y nodeالنقطة دي بسميها interior point إذا
+
+25
+00:02:29,990 --> 00:02:35,270
+لقيتها كانت مركز ل disk وهذا ال disk يقع بأكمله
+
+26
+00:02:35,270 --> 00:02:40,350
+داخل المنطقة R يعني يا بنات لو جينا اتخيلت ال disk
+
+27
+00:02:40,350 --> 00:02:45,950
+بالشكل اللي عندها ده هيك انا رسمته هداني منقط مشان
+
+28
+00:02:45,950 --> 00:02:52,980
+ايه؟ مشان يعرف ان هذا هو ال diskيبقى النقطة X نقطة
+
+29
+00:02:52,980 --> 00:02:58,460
+و Y نقطة بسميها نقطة داخلية إذا جدرت أخليها مركز ل
+
+30
+00:02:58,460 --> 00:03:03,860
+desk و ال desk يقع بأكمله داخل المنطقة بسميها
+
+31
+00:03:03,860 --> 00:03:08,120
+interior point هذا ال first definition نجي لل
+
+32
+00:03:08,120 --> 00:03:11,860
+second definition التعريف الثاني النقطة X نقطة
+
+33
+00:03:11,860 --> 00:03:16,180
+بسميها boundary point of a region
+
+34
+00:03:18,890 --> 00:03:24,190
+حدية يعني نقطة حدية على الحدود الإقليمية يعني ولا
+
+35
+00:03:24,190 --> 00:03:28,250
+تشبيه لو كنا الخط الأخضر ما بيننا و بين اليهود
+
+36
+00:03:28,250 --> 00:03:32,010
+السلك النقطة اللي تقع على السلك هذي بيسميها مين
+
+37
+00:03:32,010 --> 00:03:37,210
+boundary point يبقى باجي بقولك النقطة هذي بسميها
+
+38
+00:03:37,210 --> 00:03:43,070
+boundary point للمنطقة if every disc centered at
+
+39
+00:03:43,560 --> 00:03:50,100
+إذا كان أي disk مركزه كان النقطة هذه ال disk ماله
+
+40
+00:03:50,100 --> 00:03:58,020
+يحتوي على نقاط تقع خارج ال region R as well as
+
+41
+00:03:58,020 --> 00:04:03,520
+points that lies in Rيعني إيش؟ يعني لو عملت disk
+
+42
+00:04:03,520 --> 00:04:08,260
+حوالين هذه النقطة لازم هذا ال disk يحتوي على نقاط
+
+43
+00:04:08,260 --> 00:04:13,360
+تقع داخل المنطقة R و نقاط أخرى تقع وين خارج
+
+44
+00:04:13,360 --> 00:04:17,700
+المنطقة R يعني لو جيت كلت النقطة اللي عندنا هذه
+
+45
+00:04:17,700 --> 00:04:24,920
+على سبيل المثال، كويس؟ لو جيت رسمت حواليها disk،
+
+46
+00:04:24,920 --> 00:04:25,820
+يبقى ال disk
+
+47
+00:04:28,940 --> 00:04:34,700
+Chorus تمام دائرة بس مصممة هذا ال disk احتوى على
+
+48
+00:04:34,700 --> 00:04:39,780
+نقاط داخل المنطقة R اللي همين اللي هي النقاط اللي
+
+49
+00:04:39,780 --> 00:04:45,740
+تقع في المنطقة المظلة لهذه ونقاط أخرى خارج المنطقة
+
+50
+00:04:45,740 --> 00:04:52,540
+R يبقى هذه اسم يا بنات boundary point
+
+51
+00:04:52,540 --> 00:04:55,700
+وهذه
+
+52
+00:04:55,700 --> 00:04:56,820
+النقطة اسمها
+
+53
+00:05:02,520 --> 00:05:17,060
+يبقى هذه النقطة الداخلية يبقى
+
+54
+00:05:17,060 --> 00:05:21,020
+هذه
+
+55
+00:05:21,020 --> 00:05:24,980
+التعريف رقم اتنين
+
+56
+00:05:28,190 --> 00:05:34,430
+النقاط الحدية ليست
+
+57
+00:05:34,430 --> 00:05:42,070
+بالضرورة تكون واقعة داخل المنطقة R ممكن تكون خارج
+
+58
+00:05:42,070 --> 00:05:46,730
+المنطقة R كما سنرى بعد قليل ان شاء الله من خلال
+
+59
+00:05:46,730 --> 00:05:52,620
+الأمثلةيعني هعطيكي مثال ان النقاط الحدي هذه او
+
+60
+00:05:52,620 --> 00:05:57,520
+النقاط اللي على الحدود تقع داخل المنطقة R ومثال
+
+61
+00:05:57,520 --> 00:06:03,960
+اخر نقاط الحدود خارج المنطقة R بعد هيك النقطة
+
+62
+00:06:03,960 --> 00:06:09,100
+التالتة نقول المنطقة R بسميها open منطقة مفتوحة
+
+63
+00:06:09,100 --> 00:06:16,950
+إذا كانت تتكوّل كليا انت يرلي كلياof interior
+
+64
+00:06:16,950 --> 00:06:21,210
+points بالنقاط الداخلية يعني المنطقة بس هي المنطقة
+
+65
+00:06:21,210 --> 00:06:26,750
+مفتوحة إذا كان كل نقطة موجودة في هذه المنطقة هي
+
+66
+00:06:26,750 --> 00:06:35,350
+interior point طيب التعريف اللي بعدبسميها closed
+
+67
+00:06:35,350 --> 00:06:40,710
+إذا احتوت كل ال boundary points إذا احتوت كل ال
+
+68
+00:06:40,710 --> 00:06:44,710
+boundary points تبعتها بسميها a closed region
+
+69
+00:06:44,710 --> 00:06:49,850
+منطقة مغلقة يبقى عرفنا إيش الفرق ما بينهم يبقى ال
+
+70
+00:06:49,850 --> 00:06:55,430
+open region هي المنطقة اللي جميع النقاط تبعتها in
+
+71
+00:06:55,430 --> 00:07:01,880
+terror points لكن ال closed regionهي المنطقة التي
+
+72
+00:07:01,880 --> 00:07:07,020
+تحتوي على كل ال boundary points تبعتها طيب
+
+73
+00:07:07,020 --> 00:07:13,400
+definition أخير هنقسمه إلى نقطتين المنطقة قد تكون
+
+74
+00:07:13,400 --> 00:07:19,680
+bounded يعني محدودة وقد تكون unbounded غير محدودة
+
+75
+00:07:20,180 --> 00:07:24,500
+بجل التعريف الأول بقول ال region R في المستوى is
+
+76
+00:07:24,500 --> 00:07:30,020
+bounded محدودة if it lies inside of a disk of a
+
+77
+00:07:30,020 --> 00:07:34,180
+fixed radius يبقى المنطقة اللي أنا بسميها محدودة
+
+78
+00:07:34,180 --> 00:07:40,940
+لو وقعت بأكملها داخل disk و ال disk نصف قطره معروف
+
+79
+00:07:40,940 --> 00:07:46,870
+ثابت تمام؟ يبقى المنطقة مرة تانيةبقول عنها bounded
+
+80
+00:07:46,870 --> 00:07:52,930
+محدودة إذا جدرت أخلي disk يحتوي عالمين على هذه
+
+81
+00:07:52,930 --> 00:07:59,090
+المنطقة كلها، إذا بسميها إيش؟bounded region طب ايش
+
+82
+00:07:59,090 --> 00:08:04,030
+ال unbounded region اللي ماقدرش احطها داخل ال disk
+
+83
+00:08:04,030 --> 00:08:08,850
+تمام فقاللي ال region are unbounded اذا ماكنتش
+
+84
+00:08:08,850 --> 00:08:12,690
+bounded يعني حطي ال disk اللي جاية تظلة شوية منها
+
+85
+00:08:12,690 --> 00:08:16,590
+و برا كمان disk أكبر من اللي باقي منها و برا و
+
+86
+00:08:16,590 --> 00:08:22,670
+هكذا يبقى ايه لا يمكن اضع المنطقة هذه داخل ال disk
+
+87
+00:08:22,670 --> 00:08:27,800
+الا انتبه عليها الأشكال اللي ممكن تظهرهاهنعطيك بدل
+
+88
+00:08:27,800 --> 00:08:33,680
+الشكل أشكال مُنطَظَمة أو غير مُنطَظَمة، أي شكل من
+
+89
+00:08:33,680 --> 00:08:38,260
+الأشكال سواء كانت هندسية و لا غيرها، لكن شغلنا كله
+
+90
+00:08:38,260 --> 00:08:42,940
+في الـplane، ليس بالضرورة أن يكون شكلا مُنطَظَمة،
+
+91
+00:08:42,940 --> 00:08:50,090
+زي مثلث مختلف الأبضاعهه يبقى هل المثلث المختلف أضع
+
+92
+00:08:50,090 --> 00:08:54,270
+بقدر أجوبه على أي شكل منتظر؟ لأ، لكن بقدر أحط
+
+93
+00:08:54,270 --> 00:08:59,850
+المثلث المختلف أضع داخل this صحيح ولا لا؟ يفجأة
+
+94
+00:08:59,850 --> 00:09:05,570
+بيكون المثلث في هذه الحالة bounded regionمنطقة
+
+95
+00:09:05,570 --> 00:09:10,850
+محدودة و هكذا طيب نعطي أمثلة من الواقع الكلام اللي
+
+96
+00:09:10,850 --> 00:09:15,270
+احنا كاتبينه هذا يبقى هناخد بدل المثال اتنين بدي
+
+97
+00:09:15,270 --> 00:09:30,710
+أوضح الشغل هذه اول مثال يبقى example بيقول
+
+98
+00:09:30,710 --> 00:09:32,170
+لي نمر واحد
+
+99
+00:09:37,360 --> 00:09:45,060
+القطع المستقيم و ال triangles و
+
+100
+00:09:45,060 --> 00:09:49,040
+ال rectangles
+
+101
+00:09:49,040 --> 00:09:54,300
+و
+
+102
+00:09:54,300 --> 00:10:05,920
+ال circles and ال discs كلهم
+
+103
+00:10:05,920 --> 00:10:17,420
+هدولare bounded sets يبقى كلهم مجموعات محدودة in
+
+104
+00:10:17,420 --> 00:10:23,020
+the plane نمر
+
+105
+00:10:23,020 --> 00:10:28,120
+اتنين ال
+
+106
+00:10:28,120 --> 00:10:34,020
+lines خطوط المستقيمة وال coordinate
+
+107
+00:10:37,160 --> 00:10:48,240
+أكسيز محاول الإحداثية والكوادران و
+
+108
+00:10:48,240 --> 00:10:55,440
+ال half a plane و
+
+109
+00:10:55,440 --> 00:11:04,000
+ال half a plane and a planeوالمستويات كلها are
+
+110
+00:11:04,000 --> 00:11:07,920
+unbound
+
+111
+00:11:07,920 --> 00:11:14,680
+sets
+
+112
+00:11:14,680 --> 00:11:17,900
+in
+
+113
+00:11:17,900 --> 00:11:20,100
+the plane
+
+114
+00:11:43,130 --> 00:11:47,350
+مرة تانية المثال
+
+115
+00:11:47,350 --> 00:11:53,290
+بيقول ال line segment يعني القطعة المستقيمة مثل
+
+116
+00:11:53,290 --> 00:11:57,890
+هذا الخط هذا بسميها قطعة مستقيمة هل هي bounded or
+
+117
+00:11:57,890 --> 00:12:02,110
+unbounded بقول بقدر اعمل disk حواليهاإذا هذا إيش؟
+
+118
+00:12:02,110 --> 00:12:05,770
+boundary يبقى هي النقطة الأولى التانية ال
+
+119
+00:12:05,770 --> 00:12:11,150
+triangles المثلثات و أشرنا له لما ستختخلص قبل قليل
+
+120
+00:12:11,150 --> 00:12:17,190
+قلنا لها اه triangles اه ال rectangles المستاطيلات
+
+121
+00:12:17,190 --> 00:12:23,850
+بقدر أعمله داخل disk إذا هذا منطقة محدودة عندك ال
+
+122
+00:12:23,850 --> 00:12:28,670
+circles الدوائر بقدر أعمل disk أكبر منها
+
+123
+00:12:31,530 --> 00:12:36,190
+القرص نفسه بقدر اعمل قرص اكبر منه يبقى هذه كلها
+
+124
+00:12:36,190 --> 00:12:41,350
+مناطق محدودة يبقى هذه bounded sets او bounded
+
+125
+00:12:41,350 --> 00:12:46,970
+regions كله في المستوى طبعا المثال التاني ال lines
+
+126
+00:12:46,970 --> 00:12:52,210
+من وين بيبدأ ال line يا بنات؟ من سنة ب infinity ل
+
+127
+00:12:52,210 --> 00:12:56,870
+infinity طبيعي الشعيعببدأ من عندي ال zero و بضل
+
+128
+00:12:56,870 --> 00:13:03,240
+راشي لوين ل الفرقيبقى هذا ياشي بقدرش أحطه داخل ال
+
+129
+00:13:03,240 --> 00:13:06,740
+disk صحيح ولا لأ ولا الخط المستقيم داخل ال disk
+
+130
+00:13:06,740 --> 00:13:12,560
+كمان ال coordinate axes محاور الإحداثية محور X
+
+131
+00:13:12,560 --> 00:13:18,120
+ومحور Y بمدد لويا لسالب infinity وإلى infinity ال
+
+132
+00:13:18,120 --> 00:13:22,600
+quadrants الأرباع الأربعة صحيح ببدأ من عند ال zero
+
+133
+00:13:22,600 --> 00:13:30,020
+لكن مظل مفتوح إلى ما لا نهايةالـ half plane نص في
+
+134
+00:13:30,020 --> 00:13:34,340
+المستوى كيف نص في المستوى طبعا المستوى برضه ببدأ
+
+135
+00:13:34,340 --> 00:13:38,620
+زي الخطب المستقيم من سلب infinity بنتهي لوين يعني
+
+136
+00:13:38,620 --> 00:13:44,080
+لو عملت plane ما بيقسم الكون اللي احنا عنده اللي
+
+137
+00:13:44,080 --> 00:13:48,160
+احنا فيه إلى نصفين اشي أعلى ال plane و اشي أسفل ال
+
+138
+00:13:48,160 --> 00:13:51,560
+plane او اشي على يمين ال plane و اشي على شمال ال
+
+139
+00:13:51,560 --> 00:13:55,770
+plane يبقى half ال plane نص ال planeومن باب أولى
+
+140
+00:13:55,770 --> 00:14:02,190
+لـ Plain كلهيبقى وماقدرش أحطه داخل disk نهائي و ال
+
+141
+00:14:02,190 --> 00:14:06,870
+plans كلها are unbounded sets يبقى هذه كلها إيش
+
+142
+00:14:06,870 --> 00:14:12,390
+شغلات أو مناطق غير محدودة مفتوحة إلى ما شاء الله
+
+143
+00:14:12,390 --> 00:14:16,150
+وإلى أن يرث الله الأرض ومال عليها لكن احنا كبشر
+
+144
+00:14:16,150 --> 00:14:21,770
+بالنسبة لعلمنا نقول أن هذه unbounded sets يبقى
+
+145
+00:14:21,770 --> 00:14:28,700
+اللي هو مناطق أو مجموعات غير محدودةطيب انت هنا فى
+
+146
+00:14:28,700 --> 00:14:32,100
+الرسم رسمتلنا ال interior point و ال boundary
+
+147
+00:14:32,100 --> 00:14:41,340
+point تمام طيب بتقدر ترسملنا بس نقاط حدية فقط على
+
+148
+00:14:41,340 --> 00:14:45,680
+الرسم يقولك اه بنقدر كيف بنقدر اشتغل فمثلا لو جيت
+
+149
+00:14:45,680 --> 00:14:53,800
+قولتلك هذا المحور هذا محور X وهذا محور Y اعطيتك
+
+150
+00:14:53,800 --> 00:14:59,680
+الآن الصيغة التاليةأنا في عندي علاقة بتقوللي ما
+
+151
+00:14:59,680 --> 00:15:09,550
+يأتي أن ال X تربيع زائد Y تربيع أقل من واحدماذا
+
+152
+00:15:09,550 --> 00:15:17,670
+يعني؟ اذا كانت تساوي واحد فهي دائرة لكن اقل من
+
+153
+00:15:17,670 --> 00:15:23,350
+واحد كل النقاط داخل الدائرة يعني لو جيت رسمت
+
+154
+00:15:23,350 --> 00:15:30,870
+الدائرة اللي مركزها نقطة الأصل و نصف قطرهابسميها
+
+155
+00:15:30,870 --> 00:15:35,790
+بنات unit circle طبعا الرسم تدى مُنَقَض دليل على
+
+156
+00:15:35,790 --> 00:15:42,810
+أن المحيط تبع داره ليس من ضمن المطقع كل النقاط
+
+157
+00:15:42,810 --> 00:15:48,210
+الداخلية اللى عندناهذه سؤال في عندي boundary point
+
+158
+00:15:48,210 --> 00:15:53,030
+هنا مش واضح ان عندي boundary point هو في تمام لكن
+
+159
+00:15:53,030 --> 00:15:59,030
+ايش خارج المنطقة تبعتنا يبقى هذه تمثل كلها ايش
+
+160
+00:15:59,030 --> 00:16:06,470
+interior points يبقى هذه interior points
+
+161
+00:16:07,040 --> 00:16:13,180
+يبقى هذه نقاط داخلية المحيط تبع هذه الداربانات هو
+
+162
+00:16:13,180 --> 00:16:18,320
+ال boundary points لكن هل النقاط هدول من ضمن
+
+163
+00:16:18,320 --> 00:16:23,880
+المنطقة؟ لأ هم حدود اللي صحية لكنهم ليسوا من ضمن
+
+164
+00:16:23,880 --> 00:16:29,940
+المنطقة طب السؤال هو المنطقة المظلة لهذه open
+
+165
+00:16:29,940 --> 00:16:35,090
+region ولا closed region؟طلع فوق، اطلع هنا تحت،
+
+166
+00:16:35,090 --> 00:16:40,270
+يبقى هنا هذه كلها open region يبقى المنطقة اللي
+
+167
+00:16:40,270 --> 00:16:45,930
+عنده هذه كلها open region يبقى المنطقة المظلة لهذه
+
+168
+00:16:45,930 --> 00:16:53,270
+كلها بسميها open region، منطقة مفتوحة، تمام؟ طيب
+
+169
+00:16:53,270 --> 00:16:57,450
+يا بنات، لو قلوا الصيغة الأخرى، انه x تربية
+
+170
+00:17:00,380 --> 00:17:07,600
+أو تساوي واحد كويس يبقى بده صورة أنه ال disk أو
+
+171
+00:17:07,600 --> 00:17:14,100
+الدائرة بالشكل هذا هيك تمام يبقى كل المنطقة
+
+172
+00:17:14,100 --> 00:17:20,940
+المظللة هذه هذا محور X وهذا محور Y كل المنطقة
+
+173
+00:17:20,940 --> 00:17:27,120
+المظللة بما فيها المحيط تمام طيب وين ال boundary
+
+174
+00:17:27,120 --> 00:17:34,070
+point؟اللي هو محيط الدائرة شو يمثلوا؟ يمثلوا X
+
+175
+00:17:34,070 --> 00:17:40,490
+تربية زائد Y تربية تساوي واحد يبقى ال boundary هنا
+
+176
+00:17:40,490 --> 00:17:43,890
+يمثل
+
+177
+00:17:43,890 --> 00:17:50,030
+بالعلاقة X تربية زائد Y تربية يساوي مين؟ واحد اللي
+
+178
+00:17:50,030 --> 00:17:55,670
+هو مين كل ال boundary points طب السؤال هو is it a
+
+179
+00:17:55,670 --> 00:18:02,370
+closed region؟هل هذه منطقة مغلقة؟ نرجع المنطقة
+
+180
+00:18:02,370 --> 00:18:06,530
+المغلقة اللى بتحتوي كل ال boundary points تبعتها
+
+181
+00:18:06,530 --> 00:18:11,470
+احتواتهم للمحيط الدارة كل ال boundary points إذا
+
+182
+00:18:11,470 --> 00:18:17,950
+هذه closed region يبقى هذه النهارد كلها closed
+
+183
+00:18:17,950 --> 00:18:19,110
+region
+
+184
+00:18:21,400 --> 00:18:25,660
+يبقى هذه هي المنطقة المغلقة يبقى المنطقة المغلقة
+
+185
+00:18:25,660 --> 00:18:30,060
+هي المنطقة اللي تحتوي كل ال boundary points تبعتها
+
+186
+00:18:30,060 --> 00:18:36,200
+مفتوحة يبقى اللي بتحتوي عليها كل النقاط الداخلية
+
+187
+00:18:36,200 --> 00:18:41,660
+يبقى هاي الفرق ما بين هذه و هذا طيب نعطي مثال عملي
+
+188
+00:18:41,660 --> 00:18:49,000
+يعني مثال عددي حسابات نحسب الشغلات هذه لسؤال عددي
+
+189
+00:19:14,470 --> 00:19:26,230
+example fine هو الدونا النقطة الأولى the domain
+
+190
+00:19:26,230 --> 00:19:34,370
+of the following functions
+
+191
+00:19:40,020 --> 00:19:47,300
+the interior and
+
+192
+00:19:47,300 --> 00:19:56,100
+the boundary of
+
+193
+00:19:56,100 --> 00:20:03,360
+this domain نقطة
+
+194
+00:20:03,360 --> 00:20:08,320
+تالتة whether
+
+195
+00:20:08,320 --> 00:20:09,160
+the domain
+
+196
+00:20:14,540 --> 00:20:24,940
+هل الدمين مفتوح او مفتوح؟ مفتوح او مفتوح؟ نقطة
+
+197
+00:20:24,940 --> 00:20:32,020
+الرابعة whether the domain is
+
+198
+00:20:32,020 --> 00:20:37,560
+bounded or
+
+199
+00:20:37,560 --> 00:20:42,680
+unbounded or unbounded
+
+200
+00:20:44,210 --> 00:20:51,290
+نبدأ باستخدام
+
+201
+00:20:51,290 --> 00:20:54,930
+جدري التربيهي Fxy
+
+202
+00:21:39,540 --> 00:21:43,360
+بناخد اكثر من ال function كل واحدة من هذه ال
+
+203
+00:21:43,360 --> 00:21:47,280
+functions بدي احسب انها اربعة شغلات المطمئنن الأول
+
+204
+00:21:47,280 --> 00:21:52,480
+بدي احسب ال domain لهذه الدالة اتنين بدي اجيب ال
+
+205
+00:21:52,480 --> 00:21:56,220
+internal و ال boundary لهذا ال domain اللي حصلنا
+
+206
+00:21:56,220 --> 00:22:01,000
+عليه تلاتة بدي اشوف ال domain هل هذا بيكون منطقة
+
+207
+00:22:01,000 --> 00:22:06,320
+مفتوحة ولا منطقة مغلقةبعد هي كده بدي أشوف هل ال
+
+208
+00:22:06,320 --> 00:22:11,160
+domain هذا بيكون bounded ولا unbounded يبقى كله
+
+209
+00:22:11,160 --> 00:22:16,020
+يعتمد على شكل ال domain اللي احنا بدنا نطلعه بجي
+
+210
+00:22:16,020 --> 00:22:22,460
+بقوله بكويس يبقى بجي بقوله domain الـ F منهم كل
+
+211
+00:22:22,460 --> 00:22:30,100
+العناصر X وY بحيث أن القيمة اللي تحت الجدل ناقص 9
+
+212
+00:22:30,100 --> 00:22:36,620
+greater than or equal to 0لأن الجدر مش معرف إلا
+
+213
+00:22:36,620 --> 00:22:43,100
+لقيمة موجبة أو للصفر يبقى هذا الكلام يبدو يساوي كل
+
+214
+00:22:43,100 --> 00:22:48,660
+ال elements x و y such that x تربية زائد y تربية
+
+215
+00:22:48,660 --> 00:22:58,800
+greater than or equal to 9 يعني كل إنقاء اللي لو
+
+216
+00:22:58,800 --> 00:23:05,560
+ربعناه يبدو يتبع المجموع 9 فما هوطب لو حبينا نرسمه
+
+217
+00:23:05,560 --> 00:23:11,100
+معانا الطبيعي نعرف مين هو هذا ال domain هذا محور X
+
+218
+00:23:11,100 --> 00:23:17,420
+هذا محور Y هذه نقطة الأصل اللي هي Zero نروح نقسم
+
+219
+00:23:17,420 --> 00:23:22,780
+الدائرة اللي عندنا هذه يبقى هي الدائرة اللي عندنا
+
+220
+00:23:24,620 --> 00:23:30,240
+طيب كان ال X تربيع زي ال Y تربيع ماله W أكبر من أو
+
+221
+00:23:30,240 --> 00:23:36,780
+يسوء 9 يبقى كل المنطقة اللي خارج الدائرة اللي
+
+222
+00:23:36,780 --> 00:23:44,010
+عندنا هذهبالاضافة إلى رحيط الدائرة بسبب ماذا؟ بسبب
+
+223
+00:23:44,010 --> 00:23:50,450
+وجود اليساوي إذا خلصناه المطلوب الأول يبقى كل
+
+224
+00:23:50,450 --> 00:23:55,810
+المطلوب الأول ال domain كل النقاط outside the
+
+225
+00:23:55,810 --> 00:24:00,450
+circle or on the circle يبقى هذه لو بدي أصيغها
+
+226
+00:24:00,450 --> 00:24:03,170
+بقول all the points
+
+227
+00:24:25,820 --> 00:24:31,600
+كل النقاط اللي على الدائرة هذه أو خارجها هذا ال
+
+228
+00:24:31,600 --> 00:24:34,700
+domain هذا المطموب الأول مطموب التاني
+
+229
+00:24:39,550 --> 00:24:44,410
+الانترال والمقاومة في هذا المجال
+
+230
+00:25:04,350 --> 00:25:08,270
+أقل يعني، يعني داخل الدار، والله صحيح صرنا في
+
+231
+00:25:08,270 --> 00:25:11,750
+الدمان ولا صرنا برا الدمان؟ واش اللي بنايا؟ صح
+
+232
+00:25:11,750 --> 00:25:15,690
+كلامي ولا غلط؟ لإن طول الوقت بدي أكون جوا الدمان،
+
+233
+00:25:15,690 --> 00:25:19,290
+يعني وين؟ يعني في المنطقة المظلة، اللي جوا هذه
+
+234
+00:25:19,290 --> 00:25:23,090
+ماليش داعو فيها، الدمان يا بنات المنطقة المظلة
+
+235
+00:25:23,090 --> 00:25:26,670
+اللي أشرتك عليها بالأزرق هذه، اللي جوا ماليش علاقة
+
+236
+00:25:26,670 --> 00:25:31,980
+فيها، مالك انت جلبت الوضع 180 درجة والله إيهيبقى
+
+237
+00:25:31,980 --> 00:25:35,520
+ال intro كل النقاط اللي موجودة داخل ال domain
+
+238
+00:25:35,520 --> 00:25:41,820
+كتبتلك ال domain كتابة كل النقاط اللي على المحيط و
+
+239
+00:25:41,820 --> 00:25:46,740
+اللي outside الدائرة كامك تخلوه داخل الدائرة هذا
+
+240
+00:25:46,740 --> 00:25:52,400
+كلام غلط مش صحيح يبقى هذا بالنسبة لل domain الآن
+
+241
+00:25:52,400 --> 00:25:58,080
+ال intro تبع من تبع هذا ال domain يبقى باجي بقول
+
+242
+00:25:58,080 --> 00:25:59,060
+ال intro
+
+243
+00:26:03,260 --> 00:26:11,860
+منهم يساوي كل النقاط X وY بحيث ان X تربيها زيد وY
+
+244
+00:26:11,860 --> 00:26:19,240
+تربيها مالها أكبر من تسعة وأقل من ماين من infinity
+
+245
+00:26:19,240 --> 00:26:23,340
+يبقى وانا احنا في المنطقة المضلة اللي هي الزرق
+
+246
+00:26:23,340 --> 00:26:29,260
+اللي برا هذه أكبر من تسعة يبقى برا وضلك ماشي ليه
+
+247
+00:26:29,260 --> 00:26:33,000
+مالها نهايةيبقى هاي ال intro تبع مين؟ تبع ال
+
+248
+00:26:33,000 --> 00:26:36,720
+domain إيش قاللي كمان؟ بد ال boundary تبع ال
+
+249
+00:26:36,720 --> 00:26:40,400
+domain من ال boundary تبع ال domain؟ محمد محمد
+
+250
+00:26:40,400 --> 00:26:42,080
+محمد محمد محمد محمد محمد محمد محمد محمد محمد محمد
+
+251
+00:26:42,080 --> 00:26:42,180
+محمد محمد محمد محمد محمد محمد محمد محمد محمد محمد
+
+252
+00:26:42,180 --> 00:26:46,240
+محمد محمد محمد محمد محمد محمد محمد محمد محمد محمد
+
+253
+00:26:46,240 --> 00:26:46,280
+محمد محمد محمد محمد محمد محمد محمد محمد محمد محمد
+
+254
+00:26:46,280 --> 00:26:52,160
+محمد محمد محمد محمد محمد محمد
+
+255
+00:26:52,160 --> 00:26:58,520
+محمد
+
+256
+00:26:58,520 --> 00:27:05,330
+محميبقى ال boundary تبع ال domain مين هو كل
+
+257
+00:27:05,330 --> 00:27:11,610
+العناصر X وY جهاته ان X تربية وY تربية يساوي 9
+
+258
+00:27:11,610 --> 00:27:16,510
+يبقى
+
+259
+00:27:16,510 --> 00:27:25,250
+كل المحيط تبع من؟ تبع الدائرة يعني لو حبينا نرسمه
+
+260
+00:27:25,250 --> 00:27:30,940
+بنقول هي الدائرة هيكهذا محور X و هذا اللي فوق هو
+
+261
+00:27:30,940 --> 00:27:41,820
+محور Y تمام؟ و الدائرة عندنا هتكون بالشكل هذا يبقى
+
+262
+00:27:41,820 --> 00:27:46,640
+هذه الدائرة اللي عندنا
+
+263
+00:27:46,640 --> 00:27:54,100
+يبقى
+
+264
+00:27:54,100 --> 00:28:00,250
+كل النقاط اللي عندنا هذههي ال boundary point فقط
+
+265
+00:28:00,250 --> 00:28:06,290
+لا غير يبقى هذا هو ال boundary ماليش دعوة النقاط
+
+266
+00:28:06,290 --> 00:28:08,770
+اللي برا الدائرة ولا اللي جوا الدائرة انا على
+
+267
+00:28:08,770 --> 00:28:17,610
+الحدود ايوة علي صوتك شوية خلينا نسمع ال interior
+
+268
+00:28:17,610 --> 00:28:22,330
+points ماشي الحالة بدنا نجيب ال interior points كل
+
+269
+00:28:22,330 --> 00:28:27,040
+النقاط اللتي تقع داخل ال domainحددنا ال domain من
+
+270
+00:28:27,040 --> 00:28:31,320
+أين إلى أين كل
+
+271
+00:28:31,320 --> 00:28:34,900
+النقاط اللي تحقق ال link والتي هذه X تربيها زاد وY
+
+272
+00:28:34,900 --> 00:28:40,080
+تربيها يكون أكبر من أو يسوى التسعة كل المحيط تبع
+
+273
+00:28:40,080 --> 00:28:47,360
+الدائرة اللي عندنا هذه زاد النقاط اللي برا، مظبوط؟
+
+274
+00:28:47,360 --> 00:28:51,860
+مش هذا ال domain؟ طيب، دي النقاط الداخلية لهذا ال
+
+275
+00:28:51,860 --> 00:28:56,810
+domainوليست النقاط الحدية يبقى بدى أستثنى مين
+
+276
+00:28:56,810 --> 00:29:03,310
+المحيط مشان أستثنى المحيط فباجى بقول انتوا رأى كل
+
+277
+00:29:03,310 --> 00:29:07,290
+النقاط اللى عندنا اللى أكبر من تسعة صح ولا لأ
+
+278
+00:29:07,290 --> 00:29:11,130
+لليكسر بيه عزيزي وعزيزي بيكون أكبر من تسعة تسعة
+
+279
+00:29:11,130 --> 00:29:15,210
+بكون احنا على الحدود هنا أكبر من تسعة يبقى برا هنا
+
+280
+00:29:15,210 --> 00:29:17,870
+هذه كلها نقاط داخلية
+
+281
+00:29:22,690 --> 00:29:27,650
+النقاط الحدية طب بيه النقاط الحدية اللي تقع على
+
+282
+00:29:27,650 --> 00:29:33,950
+محيط الدار؟ واضحات ولا لسه؟ مش كتير شايف فبل شو
+
+283
+00:29:33,950 --> 00:29:43,310
+رايك تعالى هنا تعالى بس قومي و ليه الهاجينة تعالى
+
+284
+00:29:43,310 --> 00:29:43,510
+هنا
+
+285
+00:29:51,090 --> 00:29:54,750
+هو قال ليه لعرف مجالك؟ وين ال domain تبعك ده اللي
+
+286
+00:29:54,750 --> 00:29:59,970
+هو ال boundary و ال outside؟ و اللي برا، تمام؟ انا
+
+287
+00:29:59,970 --> 00:30:04,930
+بدي النقاط الداخلية نتقع داخل ال domain، بتقدر
+
+288
+00:30:04,930 --> 00:30:07,770
+تحدديلي وين؟ بيدي، بتقوليلي هنا، بتيجي النقطة
+
+289
+00:30:07,770 --> 00:30:15,110
+الداخلية؟ إذا المجال هو ال boundary و ال outside،
+
+290
+00:30:15,110 --> 00:30:18,970
+from you مافيش داخلية؟ داخل ال domain، ال boundary
+
+291
+00:30:18,970 --> 00:30:27,120
+.. ال control لل domainيبقى داخل الدمين داخل
+
+292
+00:30:27,120 --> 00:30:36,460
+الدمين داخل الدمين داخل الدمين داخل
+
+293
+00:30:36,460 --> 00:30:45,200
+الدمين داخل الدمين داخل الدمين داخل الدمين داخل
+
+294
+00:30:45,200 --> 00:30:51,920
+الدمين داخل الدمين داخل الدمينصحيح ولا لأ يبقى هذه
+
+295
+00:30:51,920 --> 00:31:00,620
+interim point شوفت هناك ماكنتش متأكده تمام دل مصر
+
+296
+00:31:00,620 --> 00:31:05,860
+على داخل ملمون الدائرة هذا كله الأبيض برا الدمين
+
+297
+00:31:05,860 --> 00:31:09,800
+ماليش علاقة فيه داخل
+
+298
+00:31:09,800 --> 00:31:15,000
+الدمين اللي مكتوب عليه داخل الدمين واضحة؟ حد بتسأل
+
+299
+00:31:15,000 --> 00:31:21,180
+تاني؟ انا بتفضلهذا ما اسمه الـ interior points و
+
+300
+00:31:21,180 --> 00:31:23,780
+ال boundary points اللي هو المطلوب رقم اتنين
+
+301
+00:31:23,780 --> 00:31:28,100
+المطلوب رقم تلاتة بيقول whether the domain open or
+
+302
+00:31:28,100 --> 00:31:33,980
+closed هل ال domain هذا open و لا closed تعريف ال
+
+303
+00:31:33,980 --> 00:31:38,740
+closed انه اذا احتوى على كل ال boundary points ال
+
+304
+00:31:38,740 --> 00:31:42,660
+domain هذا احتوى على ال boundary points ولا لا اذا
+
+305
+00:31:42,660 --> 00:31:46,820
+هذا ال domain closed انترى اه closed ريزي يبقى
+
+306
+00:31:46,820 --> 00:31:56,230
+باجي بقوله النقطة التالتةThe domain is
+
+307
+00:31:56,230 --> 00:32:09,850
+an enclosed region is a closed region because
+
+308
+00:32:09,850 --> 00:32:20,190
+it contains all
+
+309
+00:32:23,100 --> 00:32:33,040
+boundary points طيب نقطة الرابعة بيقوللي
+
+310
+00:32:33,040 --> 00:32:37,740
+هل ال domain هذا منطقة محدودة و لا منطقة غير
+
+311
+00:32:37,740 --> 00:32:42,980
+محدودة طبعا ال dialogues اللي بيبقى عليها نقدرش
+
+312
+00:32:42,980 --> 00:32:49,200
+نوصل إليها يبقى هذي إيش بسميها unbounded region
+
+313
+00:32:49,610 --> 00:32:59,590
+يبدأ بالي بقول له that domain is a is an bounded
+
+314
+00:32:59,590 --> 00:33:05,310
+region هذه
+
+315
+00:33:05,310 --> 00:33:12,930
+منطقة مغلقة و الله ايه مغلقة و بس لو محدودة كمان
+
+316
+00:33:12,930 --> 00:33:17,350
+طب هذا نمرى ايه من المثال نمرى ايه لو أخدنا
+
+317
+00:33:17,350 --> 00:33:25,070
+function تانيةالـ function التانية f of x و y يبقى
+
+318
+00:33:25,070 --> 00:33:33,730
+f of x و y تساوي len x ناقص y تربيع على سبيل
+
+319
+00:33:33,730 --> 00:33:38,550
+المثال نجيب
+
+320
+00:33:38,550 --> 00:33:42,770
+الأربع مطالب لهذه الـ function بأول شغلة نجيب main
+
+321
+00:33:42,770 --> 00:33:48,010
+ال domain تبع ال f يبقى النقطة الأولىبدا أخد
+
+322
+00:33:48,010 --> 00:33:55,510
+domain ال F يبقى كل النقاط X وY بحيث أن X ناقص Y
+
+323
+00:33:55,510 --> 00:33:59,670
+تربيع أبصر مالها أكبر من الصفراء أبو ليش أكبر من
+
+324
+00:33:59,670 --> 00:34:05,870
+الصفراء؟ لأن ال لن يا بنات مش معرف إلا لقيمة موجبة
+
+325
+00:34:05,870 --> 00:34:12,010
+و أخدتوا في Calculus B كان منحنا اللن عندكم بالشكل
+
+326
+00:34:12,010 --> 00:34:18,560
+هذا هيك أمام؟يبقى بالشكل اللي عندك هذا هذا محور X
+
+327
+00:34:18,560 --> 00:34:25,440
+هذا محور Y هذا نقطة الأصل وهذا منحنى لين ال X كله
+
+328
+00:34:25,440 --> 00:34:30,760
+بعد Zero وعند Zero بنخسف لوين لسالب Infinity يبقى
+
+329
+00:34:30,760 --> 00:34:35,580
+معنا هذا الكلام بدي هذا المقدار كله يكون ماله أكبر
+
+330
+00:34:35,580 --> 00:34:44,440
+من Zero وإن شرطونا فقولناكل ال X وY such that ال X
+
+331
+00:34:44,440 --> 00:34:52,240
+أكبر من Y تربيع فبدي أسألكوا سؤال و أشوف فهمتوا
+
+332
+00:34:52,240 --> 00:34:56,980
+هذا ولا لا حد فيكم بتقدر يجيب لي نقطة واحدة في ال
+
+333
+00:34:56,980 --> 00:35:01,000
+domain مع الأنه مع الأنه اللي موجود فيه ما لا
+
+334
+00:35:01,000 --> 00:35:06,060
+نهاية من النقاط فتقدروا تجيبوا لي نقطة واحدة داخل
+
+335
+00:35:06,060 --> 00:35:06,860
+هذا ال domain
+
+336
+00:35:11,230 --> 00:35:15,910
+مش هنقدر احدد لما ارسم اعرف وان المنطقة بالضبط بد
+
+337
+00:35:15,910 --> 00:35:21,210
+نقطة داخله تحقق
+
+338
+00:35:21,210 --> 00:35:26,730
+ال inequality واحد و واحد كلام مش صحيح ليه؟ لما
+
+339
+00:35:26,730 --> 00:35:30,970
+احط ال X بواحد يبقى Y بواحد اللي هي اشهر اكبر منها
+
+340
+00:35:30,970 --> 00:35:37,410
+يعني بدك تاخدي قيمتين قيمة X تبقى اكبر من مربع
+
+341
+00:35:37,410 --> 00:35:45,060
+قيمة Y زي مين؟0 و 1 و لا لا و لا واحد واحد و Zero
+
+342
+00:35:45,060 --> 00:35:51,820
+اتنين و واحد يبقى هذه نقطة تالية كلها ب X ب اتنين
+
+343
+00:35:51,820 --> 00:35:55,800
+و Y بواحد لو ربعت Y بطلها واحد و X باتنين يبقى
+
+344
+00:35:55,800 --> 00:36:00,860
+اتنين اكبر من واحد واحد اكبر من Zero و هكذا يبقى
+
+345
+00:36:00,860 --> 00:36:06,720
+طب هذه لو كانت X يساوي Y تربيع X و واحدة لاتيش هذه
+
+346
+00:36:06,720 --> 00:36:11,640
+ترابلة منتاج جدايبقى لو روحت رسمتي ال Parabola
+
+347
+00:36:11,640 --> 00:36:17,600
+تقبل Parabola بهذا الشكل هذا محور X هذا محور Y هذه
+
+348
+00:36:17,600 --> 00:36:24,800
+نقطة الأصل هذا يعني مش Y تساوي X تربيع X تساوي Y
+
+349
+00:36:24,800 --> 00:36:31,220
+تربيع يبقى ال axis هو محور X يبقى لو روحت رسمته
+
+350
+00:36:31,220 --> 00:36:37,060
+ماعنديش مساواة ولذلك حرص مماله منقط بالشكل اللي
+
+351
+00:36:37,060 --> 00:36:43,820
+عندها دايماطيب قال لي X أكبر من أو يساوي Y تربيع
+
+352
+00:36:43,820 --> 00:36:48,940
+أنا مش عارف هي المنطقة اللي داخل البرابله ولا
+
+353
+00:36:48,940 --> 00:36:53,960
+المنطقة اللي خارج البرابلهمظبوط لكن لما اقول دور
+
+354
+00:36:53,960 --> 00:36:59,160
+على نقطة تحقق هذه قالت أخكوا اتنين و واحد و أنا
+
+355
+00:36:59,160 --> 00:37:03,800
+اقترحت واحد و زيرو و ممكن تقترحها مش نقطة ملايين
+
+356
+00:37:03,800 --> 00:37:08,580
+النقاط او مالا نهاية من النقاط لو جينا قولنا نقطة
+
+357
+00:37:08,580 --> 00:37:13,060
+واحد و زيرو اللي أسهل حاجة وين بتيجي ان هي نقطة
+
+358
+00:37:13,060 --> 00:37:17,400
+واحد و زيرو يبقى وين بدها تكون المنطقة اللي وين
+
+359
+00:37:17,400 --> 00:37:21,600
+اللي داخل ال parabola ولا اللي خارجكل المنطقة اللى
+
+360
+00:37:21,600 --> 00:37:30,260
+داخل ال parabola كل المنطقة يعنى طب السؤال هل محيط
+
+361
+00:37:30,260 --> 00:37:36,560
+ال parabola من ضمن ال domain لأ يبقى صار ال domain
+
+362
+00:37:36,560 --> 00:37:45,240
+هذا والله ده area inside the parabola
+
+363
+00:37:47,780 --> 00:37:53,340
+اللي هو main x يساوي y تابع المنطقة اللي داخل
+
+364
+00:37:53,340 --> 00:37:58,040
+البرامولة دي كلها main كلها ال domain طيب نقطة
+
+365
+00:37:58,040 --> 00:38:03,260
+ثانية قال لي مين؟ قال لي بدك تجيبلي ال interior و
+
+366
+00:38:03,260 --> 00:38:07,400
+ال boundary points تبعتي ال domain يبقى ال
+
+367
+00:38:07,400 --> 00:38:15,150
+interior points ها ال interior تبع ال domainيبقى
+
+368
+00:38:15,150 --> 00:38:23,390
+هو كل النقاط x و y بحيث أنها نفس
+
+369
+00:38:23,390 --> 00:38:30,730
+اللي فوق x أكبر من y تربية يعني هذه نقطة داخلية
+
+370
+00:38:30,730 --> 00:38:38,550
+هذه نقطة داخلية مظبوط؟ ليش؟ إن ال disk وقع بأكمله
+
+371
+00:38:38,550 --> 00:38:46,570
+داخل المنطقة وهكذا أي نقطة أخرى تعتبرنقطة داخلية و
+
+372
+00:38:46,570 --> 00:38:53,450
+هكذا طيب هذا ال intro بد ال boundary يبقى بد ال
+
+373
+00:38:53,450 --> 00:38:57,530
+boundary تبع
+
+374
+00:38:57,530 --> 00:39:04,130
+ال domain مين هو ابنها؟ ليه؟ ليها ولا ليها معقول
+
+375
+00:39:04,130 --> 00:39:08,730
+منطقة مايكونش يلها boundary؟ مالهاش حدود؟ فهل تلمس
+
+376
+00:39:08,730 --> 00:39:15,270
+لها مشاعر؟طب اقرب الله لعندك البودري لما انعرفناه
+
+377
+00:39:15,270 --> 00:39:20,470
+و حطينالك عبارة بين قوسين و قولنا لك البودري قد
+
+378
+00:39:20,470 --> 00:39:25,290
+يكون من المنطقة و قد يكون من غير المنطقة صحيح ولا
+
+379
+00:39:25,290 --> 00:39:31,010
+لا؟ في المثال السابق كان البودري اللي عندي مضمن
+
+380
+00:39:31,010 --> 00:39:36,010
+المنطقة لكن البودري هنا ماله؟ من خارج المنطقة على
+
+381
+00:39:36,010 --> 00:39:41,200
+الحدود مباشرةمظبوط ولا لأ؟ هي أعطيتك المثال الأول
+
+382
+00:39:41,200 --> 00:39:45,500
+ال boundary كان من ضمن المنطقة يعني من ضمن ال
+
+383
+00:39:45,500 --> 00:39:49,720
+domain هنا ال boundary ليس من ضمن ال domain يبقى
+
+384
+00:39:49,720 --> 00:39:54,000
+ال boundary the set of all elements x و y such
+
+385
+00:39:54,000 --> 00:39:59,880
+that x يساوي y تربيع اللي هي مين؟ اللي هي المنطقة
+
+386
+00:39:59,880 --> 00:40:07,210
+المنقطة هذه بالضبط يا بنات المنقطة الزرقيةكل هذا
+
+387
+00:40:07,210 --> 00:40:11,350
+اللي هو ال boundary يبقى هذا اللي هو ال boundary
+
+388
+00:40:11,350 --> 00:40:17,610
+لكن ان قطعة ال boundary مش موجودة في ال domain
+
+389
+00:40:17,610 --> 00:40:23,290
+خارج ال domain و كتبتها لك بين قوسين عشان تعرف انه
+
+390
+00:40:23,290 --> 00:40:27,110
+ممكن تكون من ضمن ال domain كما في المثال الأول أو
+
+391
+00:40:27,110 --> 00:40:32,850
+من خارج ال domain كما في المثال الثاني النقطة
+
+392
+00:40:32,850 --> 00:40:37,970
+التالتةقال لي هل ال domain هذا open region و لا
+
+393
+00:40:37,970 --> 00:40:42,410
+closed region قبل أولاني إيش كان في المثال closed
+
+394
+00:40:42,410 --> 00:40:49,090
+يبقى هنا ال domain is
+
+395
+00:40:49,090 --> 00:40:57,390
+an open region قبل إيش open region يبنى؟ لأنه
+
+396
+00:40:57,390 --> 00:41:01,650
+اجتمل كل النقاط الداخلية طيب النقطة الرابعة و
+
+397
+00:41:01,650 --> 00:41:06,660
+الأخيرةو قال لي whether ال domain هذا bounded ولا
+
+398
+00:41:06,660 --> 00:41:14,580
+unbounded انبعض لأنه مفتوح لماء لنهاية بيظل يبقى
+
+399
+00:41:14,580 --> 00:41:24,420
+هنا ال domain is unbound يبقى
+
+400
+00:41:24,420 --> 00:41:28,460
+ماعرف احنا حد بتحب تسأل اي سؤال هنا قبل ما نواصل
+
+401
+00:41:28,460 --> 00:41:31,740
+اي
+
+402
+00:41:31,740 --> 00:41:32,400
+تساؤل
+
+403
+00:42:02,150 --> 00:42:30,310
+مستحالة خلاص هذا مثلا ماكتب عليه لوضعة
+
+404
+00:42:30,310 --> 00:42:37,030
+definition دي لبنانdefinition عن جسمه إلى نقطتين
+
+405
+00:42:37,030 --> 00:42:48,310
+النقطة الأولى the curve المنحلة in a space in
+
+406
+00:42:48,310 --> 00:43:01,430
+which the plane in which the plane z تساوي c cuts
+
+407
+00:43:08,520 --> 00:43:20,320
+السطح z يساوي f of x of y f of x of y is called is
+
+408
+00:43:20,320 --> 00:43:30,340
+called the contour curve contour
+
+409
+00:43:30,340 --> 00:43:31,660
+curve of
+
+410
+00:43:38,120 --> 00:43:48,200
+F of X و Y بدو ساوي C نمرة اتنين The
+
+411
+00:43:48,200 --> 00:43:55,260
+set of points مجموعة
+
+412
+00:43:55,260 --> 00:43:59,300
+النقاط in the domain of F
+
+413
+00:44:07,460 --> 00:44:14,280
+XY Plane XY
+
+414
+00:44:14,280 --> 00:44:19,860
+Plane XY Plane XY Plane XY Plane XY Plane XY Plane
+
+415
+00:44:19,860 --> 00:44:25,540
+XY Plane XY Plane XY Plane XY Plane XY Plane XY
+
+416
+00:44:25,540 --> 00:44:26,240
+Plane XY Plane XY Plane XY Plane XY Plane XY Plane
+
+417
+00:44:26,240 --> 00:44:26,880
+XY Plane XY Plane XY Plane XY Plane XY Plane XY
+
+418
+00:44:26,880 --> 00:44:27,160
+Plane XY Plane XY Plane XY Plane XY Plane XY Plane
+
+419
+00:44:27,160 --> 00:44:27,180
+XY Plane XY Plane XY Plane XY Plane XY Plane XY
+
+420
+00:44:27,180 --> 00:44:27,260
+XY Plane XY Plane XY Plane XY Plane XY Plane XY
+
+421
+00:44:27,260 --> 00:44:36,360
+XY Plane XY Plane XY Plane XY Plane XY
+
+422
+00:44:36,360 --> 00:44:36,820
+Plane
+
+423
+00:44:39,750 --> 00:44:53,350
+level curve of f للظلة f نرجع
+
+424
+00:44:53,350 --> 00:44:58,630
+مرة تانية للكلام اللي احنا كاتبينه ونحاول نفهمه
+
+425
+00:44:58,630 --> 00:45:02,790
+جيدا تعريف
+
+426
+00:45:02,790 --> 00:45:10,860
+الأول هو the curve in spaceالمنحنى في الفرار in
+
+427
+00:45:10,860 --> 00:45:17,460
+which the plane z يساوي c يعني z يساوي مقدار ثابت
+
+428
+00:45:17,460 --> 00:45:22,140
+cuts the surface بيرفع على السطح z يساوي f of x وy
+
+429
+00:45:22,140 --> 00:45:26,500
+is called the contour curve contour curve يعني
+
+430
+00:45:26,500 --> 00:45:31,160
+المنحنى المحيط منحنى المحيط
+
+431
+00:45:35,460 --> 00:45:42,160
+بمعنى اخر لما اجيب المنحنة z يساوي c و اقطع
+
+432
+00:45:42,160 --> 00:45:47,060
+المنحنة بصير المستوى هذا و ال surface اللي عنده
+
+433
+00:45:47,060 --> 00:45:51,910
+اشتراكوا مع بعض في نفس النقارإذا ما بشيل ال f of x
+
+434
+00:45:51,910 --> 00:45:57,490
+و y هذه و بحط بدلها c يعني صار ال z تساوي c أو f
+
+435
+00:45:57,490 --> 00:46:02,110
+of x و y يساوي c بيصارت منطقة مشتركة ما بين
+
+436
+00:46:02,110 --> 00:46:07,270
+المستوى و ال surface هذه المنطقة بيسميها مين ال
+
+437
+00:46:07,270 --> 00:46:14,470
+contourCare تمام كيف هذا الكلام وقولك اه لو جينا
+
+438
+00:46:14,470 --> 00:46:20,650
+تخيلنا ان احنا عندنا المحاور التلاتة هذا محور X
+
+439
+00:46:20,650 --> 00:46:30,870
+هذا محور Y و هذا محور Z تمام و جينا رسمنا اي مجسم
+
+440
+00:46:30,870 --> 00:46:36,050
+any surface في الفرح فكان المجسم على سبيل المثال
+
+441
+00:46:36,050 --> 00:46:37,430
+بهذا الشكل
+
+442
+00:46:42,060 --> 00:46:47,400
+فرضي عندي مجسم بهذا الشكل يبقى هذا مجسم موجود في
+
+443
+00:46:47,400 --> 00:46:52,940
+الفرقات جيت قاطعته بمستوى وين المستوى اللي قاطعته
+
+444
+00:46:52,940 --> 00:46:57,640
+فيه هجعل المستوى بالشكل هذا طبعا من ناحية تانية مش
+
+445
+00:46:57,640 --> 00:47:05,360
+هيظهر و هيجيني هك بالشكل هذا المستوى هذا هو
+
+446
+00:47:05,360 --> 00:47:12,240
+المستوى المظلن الشكل اللي عندناقطع المجسم في curve
+
+447
+00:47:12,240 --> 00:47:16,500
+وين ال curve اللي قطعوا فيه؟ قطعوا في ال curve هذا
+
+448
+00:47:16,500 --> 00:47:23,800
+مثلا المنحنى اللي عندك يبقى هذا الجزء بيكون ظاهر
+
+449
+00:47:23,800 --> 00:47:29,640
+هذا بيكون في الناحية التانية بيضاليش فبيكون منقطع
+
+450
+00:47:29,640 --> 00:47:34,840
+تمام؟ يبقى هذا هو اللي بيسميه ال contour curve
+
+451
+00:47:34,840 --> 00:47:42,750
+يبقى هذا الخطاللي يشفيه الدائرة طبعا ليس بالضرورة
+
+452
+00:47:42,750 --> 00:47:47,190
+أن يكون دائرة حسب شكل المجسم اللي عندي هذا اللي هو
+
+453
+00:47:47,190 --> 00:47:52,310
+بسميه contour curve
+
+454
+00:47:52,310 --> 00:47:57,810
+يعني المنحنة اللي أجى على محيط main ال surface
+
+455
+00:47:57,810 --> 00:48:05,390
+نتيجة لقطعها اللي هو mainالمجسم هذا بالـ plane Z
+
+456
+00:48:05,390 --> 00:48:12,170
+تساوي C وإن Z تساوي C يبقى هذا النقطة يساوي C يبقى
+
+457
+00:48:12,170 --> 00:48:20,610
+هذا الـ plane Z يساوي C طيب هذا التعريف الأول
+
+458
+00:48:20,610 --> 00:48:24,850
+التعريف التاني مش بقول ليه The set of points in
+
+459
+00:48:24,850 --> 00:48:30,370
+the domain of F وين دمية دلنا F يا بنات؟لما أقول z
+
+460
+00:48:30,370 --> 00:48:38,450
+يساوي f of x و y أين يقع ال domain؟ حاجة بتعرف؟
+
+461
+00:48:38,450 --> 00:48:44,750
+بديش شكلها بدي أقول بيها في أي مستوى يعني z تساوي
+
+462
+00:48:44,750 --> 00:48:54,090
+f of x و y surface بدي ال domain تابع في المنطقة
+
+463
+00:48:54,090 --> 00:48:58,450
+اللي مقطوعة فوقأبو ايش رأيك باقي المجسم هذا اللي
+
+464
+00:48:58,450 --> 00:49:04,410
+تحت والمجسم اللي فوق وين مجاله بدي يكون؟ يعني
+
+465
+00:49:04,410 --> 00:49:12,170
+القيم اللتي تاخدها X وY يعني مين بيكون؟
+
+466
+00:49:12,170 --> 00:49:15,870
+بس
+
+467
+00:49:15,870 --> 00:49:21,610
+يعني الدمير بيطلع فوق، في نصه مثلا صحيح هذا
+
+468
+00:49:21,610 --> 00:49:24,810
+الكلام؟ يا بنت الحلال بقولك ايه
+
+469
+00:49:28,040 --> 00:49:33,920
+وين بيجوا X و Y هدول؟ في الـ X Y plane يا أخ سارة
+
+470
+00:49:33,920 --> 00:49:40,580
+يبقى الرسم هذه وين مجالها؟ X و Y و بطلع Z فوق يبقى
+
+471
+00:49:40,580 --> 00:49:45,340
+ال X و Y بيكونوا المجال تبعها هو في الـ X Y plane
+
+472
+00:49:45,340 --> 00:49:50,500
+أيوة، إيش قاللي؟ النقاط اللي موجودة في ال domain
+
+473
+00:49:50,500 --> 00:49:53,440
+تبع الدلة F يعني في المستوى
+
+474
+00:50:00,110 --> 00:50:04,970
+which in which بحيث ان f of x y بدي اسوي constant
+
+475
+00:50:04,970 --> 00:50:10,170
+c is called the level curve of f طب وين ال level
+
+476
+00:50:10,170 --> 00:50:14,330
+curve بالظبط في هذه الحلقة بقول شايف المقطع ال
+
+477
+00:50:14,330 --> 00:50:18,390
+contour يا بنات هذا بدي أسقطه على ال domain يبقى
+
+478
+00:50:18,390 --> 00:50:23,050
+لو جيت أسقطه على ال domain إيش بصير عندي بصير هي
+
+479
+00:50:23,050 --> 00:50:29,660
+من هنا بدي أنزل رأسي هنا و بدي أنزل رأسي هنااللي
+
+480
+00:50:29,660 --> 00:50:41,920
+هو هذا يبقى هذا اسمه level curve طب ايش يعني معناه
+
+481
+00:50:41,920 --> 00:50:52,360
+level curve منحنى المنسوب level curve المناسبة
+
+482
+00:50:52,360 --> 00:51:02,370
+على أي حال؟بعض الكتب أو بعض المؤلفين لا يفرق بين
+
+483
+00:51:02,370 --> 00:51:05,970
+ال control و level care، بعتبره اتنين واحد،
+
+484
+00:51:05,970 --> 00:51:10,390
+الاكتاب المؤلف تبعده Thomas Galler قال هذا بسميه
+
+485
+00:51:10,390 --> 00:51:14,870
+خط ال control و هذا بسميه level care، control بدي
+
+486
+00:51:14,870 --> 00:51:18,310
+اصطفه على ال domain تبع الدالة، يعني على المستوى
+
+487
+00:51:18,310 --> 00:51:22,430
+XY planeالمنحنى اللى بيطلع يبقى هذا هو اللى بيسميه
+
+488
+00:51:22,430 --> 00:51:26,490
+level care السؤال هو طب أحصل عليه كيف؟ بيقولك
+
+489
+00:51:26,490 --> 00:51:31,030
+بسيطة جدا حط F وFx وY يسووا كونستان فبتعرف أيه
+
+490
+00:51:31,030 --> 00:51:37,050
+الشكل ال level care طبعا طيب يبقى هذه المعلومات
+
+491
+00:51:37,050 --> 00:51:42,730
+اللى كتبناها بدنا نحاول ناخدها عمليا او نحسبها
+
+492
+00:51:42,730 --> 00:51:47,490
+عمليا مشان نثبت هذه المعلومة يبقى example
+
+493
+00:51:54,050 --> 00:52:03,910
+find the level curves for the following surfaces
+
+494
+00:52:03,910 --> 00:52:15,010
+for the following surfaces نمر
+
+495
+00:52:15,010 --> 00:52:29,930
+A بد ال F of X و Y بد يساويهو X تربيع زائد تسعة Y
+
+496
+00:52:29,930 --> 00:52:37,410
+تربيع مرة
+
+497
+00:52:37,410 --> 00:52:43,030
+تانية جالي هات لي liver curves لكل من المرحلات
+
+498
+00:52:43,030 --> 00:52:47,170
+التالية وراها طالي اللي هو الملحدة اللي قدامك إذا
+
+499
+00:52:47,170 --> 00:52:48,370
+الحل كان تاني
+
+500
+00:52:52,730 --> 00:52:57,390
+بنجيب له level يبقى automatic بتروح تحط دلق يسوي
+
+501
+00:52:57,390 --> 00:53:05,470
+constant C يبقى ماجي بيقولوا the level curves are
+
+502
+00:53:05,470 --> 00:53:13,490
+in the form بالشكل التالي اللي هم مين X تربيع زي
+
+503
+00:53:13,490 --> 00:53:17,890
+التسعة Y تربيع يسوي constant C
+
+504
+00:53:25,960 --> 00:53:30,840
+مش بيصير واحد صحيح X تربيع علي C تربيع زي تسعة و
+
+505
+00:53:30,840 --> 00:53:35,540
+ات تربيع علي C تربيع يساوي واحد ممتاز جدا يبقى
+
+506
+00:53:35,540 --> 00:53:39,560
+level curve في هذه الحالة أوي level curves بدها
+
+507
+00:53:39,560 --> 00:53:43,520
+أصير ellipses مختلفة طب حبيت نرسم هما دول و نتعرف
+
+508
+00:53:43,520 --> 00:53:46,660
+عليهم يبقى هدول يمثلولي
+
+509
+00:53:49,840 --> 00:53:55,800
+يبقى هذا قطوع ناقصة لو حبيت اعرفها هذه بالضبط فبجي
+
+510
+00:53:55,800 --> 00:54:01,380
+بقول حط C الرقم اللي عجبك و بيطلعك S اللي هو level
+
+511
+00:54:01,380 --> 00:54:08,200
+curve الأول فبجي بقول لو كانت ال C تساوي Zero then
+
+512
+00:54:08,200 --> 00:54:18,800
+that level curveS لو كانت C تساوي Zero يبقى بصير X
+
+513
+00:54:18,800 --> 00:54:23,980
+تربيه زائد تسعة أو تربيه يساوي Zero صح؟ متى يحدث
+
+514
+00:54:23,980 --> 00:54:28,300
+ذلك؟ ال origin يبقى بصير ال level curve هو نقطة
+
+515
+00:54:28,300 --> 00:54:34,360
+الأصل بصير عندنا ال level curve لو قلت هي المحاور
+
+516
+00:54:34,360 --> 00:54:43,260
+هيك بدي يكون هو نقطة الأصل هذا محور Xوهذا محور Y
+
+517
+00:54:43,260 --> 00:54:51,520
+طيب لو أخدت ال C يا بنات في واحد مثلة يبقى F C
+
+518
+00:54:51,520 --> 00:54:57,480
+تساوي واحد the level curve S حط ال C بواحد ايش
+
+519
+00:54:57,480 --> 00:55:07,160
+بصير ال ellipse اللي هو من ال ellipse شو
+
+520
+00:55:07,160 --> 00:55:15,060
+معادلة هذهلي X تربيع زي تسعة Y تربيع يساوي واحد
+
+521
+00:55:15,060 --> 00:55:21,000
+طيب ال major axis او ال focal axis هو محور X ولا
+
+522
+00:55:21,000 --> 00:55:26,040
+محور Y سمعت
+
+523
+00:55:26,040 --> 00:55:31,400
+جبتات سمعت محور X ومحور Y كيف بنحكم ان ال major
+
+524
+00:55:31,400 --> 00:55:36,620
+axis تبع ال ellipseحسب المقام الأولي أكبر يبقى هذا
+
+525
+00:55:36,620 --> 00:55:42,020
+لما أقرأها إيش بيصير X تربيه على واحد زاد Y تربيه
+
+526
+00:55:42,020 --> 00:55:47,880
+على التسعة بده سوى قدرش واحد يبقى مين الأكبر مقام
+
+527
+00:55:47,880 --> 00:55:53,080
+ال X ولا مقام ال Y الواحد صحيح ولا التسعة
+
+528
+00:55:55,560 --> 00:56:01,260
+يبقى ال module axis هو محور X يبقى لو روحت رسمت ال
+
+529
+00:56:01,260 --> 00:56:11,120
+ellipse بدي يكون ال ellipse عندنا بشكل هذا كمان
+
+530
+00:56:11,120 --> 00:56:20,380
+طيب لو جينا قولنا F ال C تسوى تلاتة مثلا يبقى بدي
+
+531
+00:56:20,380 --> 00:56:26,510
+يكون كمان ellipseالمعادلة تبعت X تربية زي تسعة Y
+
+532
+00:56:26,510 --> 00:56:31,650
+تربية تساوي تلاتة او ان شئ تنفقه ل X تربية على
+
+533
+00:56:31,650 --> 00:56:38,030
+تلاتة زي تلاتة Y تربية يسوى قداش واحد يعني X تربية
+
+534
+00:56:38,030 --> 00:56:42,930
+على تلاتة زي ال Y تربية على تولد يسوى برضه اللي هو
+
+535
+00:56:42,930 --> 00:56:48,330
+X يبقى بده يصير اكبر منه بس بالشكل اللي عندنا هذا
+
+536
+00:56:48,330 --> 00:56:58,250
+هيك يبقى يا بناتهذه اللي هو C تساوي Zero وهذه اللي
+
+537
+00:56:58,250 --> 00:57:04,850
+هو C تساوي واحد وهذه اللي هو C تساوي تلتة كلهم
+
+538
+00:57:04,850 --> 00:57:11,730
+هذول level curves عند قيم مختلفة لمين لـC يبقى هذه
+
+539
+00:57:11,730 --> 00:57:20,160
+level curves طيب نمر بيه من السؤالنمر بيه من
+
+540
+00:57:20,160 --> 00:57:30,600
+السؤال لو أخدنا ال F of X و Y F of X و Y تساوي X
+
+541
+00:57:30,600 --> 00:57:36,520
+زائد Y ترميه بدي
+
+542
+00:57:36,520 --> 00:57:44,520
+ال level curves لهذا المنحنة بقوله فضطرنا X زائد Y
+
+543
+00:57:44,520 --> 00:57:52,400
+ترميه بيساوي constant Cأو ال X يساوي سالب Y تربيع
+
+544
+00:57:52,400 --> 00:57:59,400
+زايد كونستان سي برابولة
+
+545
+00:57:59,400 --> 00:58:05,000
+ممتاز جدا أيوة يعني هذا البرابولة لو روحت رسمته
+
+546
+00:58:05,000 --> 00:58:11,820
+بياخد الشكل التالي هذا محور X و هذا محور Yالأصل
+
+547
+00:58:11,820 --> 00:58:17,340
+هذا اللي هو x يساوي y تربيه مفتوح جهة اليمين لكن
+
+548
+00:58:17,340 --> 00:58:23,580
+لما صار صالب y تربيه مفتوح جهة الشمال طيب بدي أجيب
+
+549
+00:58:23,580 --> 00:58:28,240
+ال level curves في هذه الحالة بجي بقوله لو كانت ال
+
+550
+00:58:28,240 --> 00:58:38,370
+c تساوي zero يبقى بجي بقوله هنا that level curveX
+
+551
+00:58:38,370 --> 00:58:48,370
+يساوي سالب Y تربية X يساوي سالب Y تربية X
+
+552
+00:58:48,370 --> 00:58:57,050
+يساوي سالب Y تربية X يساوي سالب Y تربية X يساوي
+
+553
+00:58:57,050 --> 00:59:04,570
+سالب Y تربية X يساوي سالب Y تربية X يساوي سالب Y
+
+554
+00:59:04,570 --> 00:59:12,340
+تربيةزي اكس تساوي السالق وي تربيع زي واحد يبقى شو
+
+555
+00:59:12,340 --> 00:59:18,140
+بده اعمله shift للخلف بمقدار واحد يعني جهة كل يمين
+
+556
+00:59:18,140 --> 00:59:22,320
+بده يجي هنا اللي هو المين واحد يجيك ال parabola
+
+557
+00:59:22,320 --> 00:59:29,140
+بالشكل هذا يبقى هذا حصلنا عليه عند c تساوي zero
+
+558
+00:59:29,140 --> 00:59:35,500
+هذا حصلنا عليه عند c تساوي كداش واحدلو كانت C
+
+559
+00:59:35,500 --> 00:59:39,580
+تساوي تلاتة زي اللي فوق او اتنين او اربع او عشرة
+
+560
+00:59:39,580 --> 00:59:45,020
+او زي ما بده يبقى هنا F C تساوي اتنين
+
+561
+00:59:54,040 --> 00:59:59,940
+شفت للخلف مقدار اتنين يبقى ده حصل عليه لما C تساوي
+
+562
+00:59:59,940 --> 01:00:06,640
+اتنين ومعادلته X تساوي سالب Y تربيع زائد اتنين
+
+563
+01:00:06,640 --> 01:00:15,320
+اللي في المص هذا X تساوي سالب Y تربيع زائد واحدأى
+
+564
+01:00:15,320 --> 01:00:20,120
+رقم قد يكون موجب قد يكون سالب ماعنديش مشكلة اي نعم
+
+565
+01:00:20,120 --> 01:00:24,660
+اى رقم يجى فى بالك يبقى هدول كلهم مارسمتش اني
+
+566
+01:00:24,660 --> 01:00:29,000
+المنحنية تبانات انا رسمت ال level curve وليس
+
+567
+01:00:29,000 --> 01:00:33,580
+الدالة الأصلية هذا مش رسمة الدالة الأصلية هذا مسقط
+
+568
+01:00:33,580 --> 01:00:39,220
+ال contour على ال XY plane لحظة اخد كله XY يبقى
+
+569
+01:00:39,220 --> 01:00:43,480
+هذا مين هذا الرسم اللى تحت السودا فى مسألتنااللي
+
+570
+01:00:43,480 --> 01:00:47,340
+هو مسقط ال control line قد يكون ellipse قد يكون
+
+571
+01:00:47,340 --> 01:00:51,760
+parabola قد يكون hyperabola قد يكون circle قد يكون
+
+572
+01:00:51,760 --> 01:00:55,740
+مربع قد يكون متوازي أطلع حسب نوعية ال surface اللي
+
+573
+01:00:55,740 --> 01:01:01,560
+عندي يبقى حسب المجسم اللي موجود عندك طب هذا حكينا
+
+574
+01:01:01,560 --> 01:01:06,320
+على functions of two variables بدأ نتقل إلى النقطة
+
+575
+01:01:06,320 --> 01:01:09,260
+الأخيرة وهي functions of three variables
+
+576
+01:01:12,860 --> 01:01:16,700
+ننتقل الآن إلى النقطة الأخيرة من هذا الsection وهي
+
+577
+01:01:16,700 --> 01:01:21,300
+الـ functions of three variables أقرب تعريف أخدناه
+
+578
+01:01:21,300 --> 01:01:25,440
+قبل قليل كان الـ Linear Curve فلو دالة فيه ثلاث
+
+579
+01:01:25,440 --> 01:01:29,920
+متغيرات، ماذا بدى يسمي الودالة لو سميتها
+
+580
+01:01:29,920 --> 01:01:34,480
+بـconstant C؟ هذا موضوع الـ definition التالف بكل
+
+581
+01:01:34,480 --> 01:01:40,870
+set of points X وY وZ، مجموعة النقاط في الفرقوالـ
+
+582
+01:01:40,870 --> 01:01:45,590
+F of X وY بدل سوى C يعني سونا الدالة كلها بكونستان
+
+583
+01:01:45,590 --> 01:01:49,390
+C وC ده بالأول مقدار ثابت is called a level
+
+584
+01:01:49,390 --> 01:01:53,930
+surface لدالة F يبقى إذا الدالة في متغيرين و
+
+585
+01:01:53,930 --> 01:01:59,030
+سوناها بكونستان اسمه level curve تطلع منحنى لكن
+
+586
+01:01:59,030 --> 01:02:02,850
+إذا كان في ثلاث متغيرات تطلع عندنا main surface
+
+587
+01:02:02,850 --> 01:02:07,610
+فبالتالي بيسمي main level surface هنوريكي كيف نحسب
+
+588
+01:02:07,610 --> 01:02:17,010
+هذا الكلام عمليامن خلال الأمثلة يبقى example قول
+
+589
+01:02:17,010 --> 01:02:26,590
+find and sketch find and sketch أوجد و أرسم the
+
+590
+01:02:26,590 --> 01:02:35,590
+level surfaces of
+
+591
+01:02:35,590 --> 01:02:48,950
+theFollowing Functions F of
+
+592
+01:02:48,950 --> 01:02:57,710
+X O Y بدأت ساوي لم F تعيقظ X تربيع زاد Y تربيع زاد
+
+593
+01:03:14,840 --> 01:03:20,940
+يبقى نتقل الان الى الدالة فيه ثلاث متغيرات بدنا
+
+594
+01:03:20,940 --> 01:03:24,680
+نحسب ال level surface لهذه الدالة اللى قدامنا يبقى
+
+595
+01:03:24,680 --> 01:03:28,820
+الدالة f of x y و z لإن x تربيه زاد و اتربيه زاد z
+
+596
+01:03:28,820 --> 01:03:33,580
+تربيه يبقى بنسوى الدالة هذا الميان بكون constant c
+
+597
+01:03:33,580 --> 01:03:35,200
+يبقى solution
+
+598
+01:03:39,050 --> 01:03:48,510
+the level surfaces are لن
+
+599
+01:03:48,510 --> 01:03:55,910
+X تربيع زائد Y تربيع زائد Z تربيع كل هذا الكلام
+
+600
+01:03:55,910 --> 01:04:02,790
+يدوي سوية constant C ممكن أن أعيد صياغتها رفعنا كل
+
+601
+01:04:02,790 --> 01:04:05,710
+واحد منه كأس للعدد A
+
+602
+01:04:17,030 --> 01:04:25,630
+EOC يبقى هذا الشكل العام لمن؟ لل level surfaces طب
+
+603
+01:04:25,630 --> 01:04:31,190
+مين تعرف تقولي هذا شو بنسميه ال surface اللي
+
+604
+01:04:31,190 --> 01:04:34,430
+عندنا، شو اسمه هذا؟ من هالمعادلة في المرضى،
+
+605
+01:04:34,430 --> 01:04:41,720
+ellipsoid؟ المقامات زي بعضالانفصايد اذا ال a سواء
+
+606
+01:04:41,720 --> 01:04:47,260
+ال b سواء ال c انفصايد اذا ال a سواء ال b سواء ال
+
+607
+01:04:47,260 --> 01:04:55,200
+c انفصايد اذا ال a سواء ال b سواء ال c انفصايد اذا
+
+608
+01:04:55,200 --> 01:04:56,680
+ال a سواء ال b سواء ال c
+
+609
+01:05:05,210 --> 01:05:10,870
+ليش؟ لأن الـ E أُسها ده رقم عادى جد ما يكون اتنين،
+
+610
+01:05:10,870 --> 01:05:15,230
+تلاتة، عشرة، مية، جد ما يكون طيب، خلّيني أتعالى
+
+611
+01:05:15,230 --> 01:05:23,570
+نحسبها في الحالات المختلفة بني بقول F C تساوي زيوت
+
+612
+01:05:23,570 --> 01:05:28,150
+يبقى ده sphere S
+
+613
+01:05:41,480 --> 01:05:52,980
+Level Surface of the sphere التي هي الكرة X تربية
+
+614
+01:05:52,980 --> 01:05:59,640
+زائد Y تربية زائد Z تربية تساوي E O Zero E O Zero
+
+615
+01:05:59,640 --> 01:06:04,820
+كده؟ اف واحد يبقى هي كرة نصف قطر هي يساوي كده؟
+
+616
+01:06:04,820 --> 01:06:06,200
+واحد الصحيح
+
+617
+01:06:19,380 --> 01:06:23,800
+زيد ويه الترفيه زيد زي الترفيه يسوى اتنين وسبعة من
+
+618
+01:06:23,800 --> 01:06:30,280
+عشر طب لو حبينا نبصمهم على الطبيعة باجي بقول هي
+
+619
+01:06:30,280 --> 01:06:42,480
+المحاور هذا محور X هذا محور Y هذا محور Z أنا عندي
+
+620
+01:06:42,480 --> 01:06:49,000
+كرةمركزها نقطة الأصل و نصف قطر يبقى ساوي كداش واحد
+
+621
+01:06:49,000 --> 01:06:57,620
+صحيح يبقى الكرة هتكون بهذا الشكل لبعد
+
+622
+01:06:57,620 --> 01:07:02,260
+اتنين والسبعة من عشرة يبقى بدها تيجي عندك سفير
+
+623
+01:07:02,260 --> 01:07:14,590
+بهذا الشكل يبقى هنا هذي سي تساوي واحدهذه C تساوي 0
+
+624
+01:07:14,590 --> 01:07:24,030
+يبقى هذا ال levels يعني كأنها كرة داخل كرة طيب
+
+625
+01:07:24,030 --> 01:07:28,850
+هذا النقطة الأولى النقطة الثانية نمرأ بين
+
+626
+01:07:33,930 --> 01:07:43,730
+و Y و Z تساوي Z تربيع ناقص X تربيع ناقص Y تربيع
+
+627
+01:07:43,730 --> 01:07:58,090
+على سبيل المثال طيب
+
+628
+01:07:58,090 --> 01:08:02,250
+بده أجيب ال level surfaces يبقى الشباج بقول
+
+629
+01:08:04,800 --> 01:08:11,420
+زي تربية ناقص X تربية ناقص Y تربية يساوي constant
+
+630
+01:08:11,420 --> 01:08:17,060
+C أو
+
+631
+01:08:17,060 --> 01:08:28,660
+زي تربية يساوي X تربية زي Y تربية زي constant C ده
+
+632
+01:08:28,660 --> 01:08:37,160
+يقول لو كانت الـC تساوي Zero يبقى دهlevel surface
+
+633
+01:08:37,160 --> 01:08:45,960
+is شو بده يصير z تربية بيساوي x تربية زائد y تربية
+
+634
+01:08:45,960 --> 01:08:50,580
+عدم الذاكرة معادلة ايش هذه من المعادلات الستة
+
+635
+01:08:50,580 --> 01:08:56,060
+مخروط بس المقطع تبعه عبارة عن دارة يبقى circular
+
+636
+01:08:56,060 --> 01:09:02,500
+cone يبقى هذا circular cone
+
+637
+01:09:05,000 --> 01:09:11,980
+إذا المخروط دائري المقطع هذا النقطة الحللونة حلال
+
+638
+01:09:11,980 --> 01:09:18,400
+تانية لو كانت C مثلا تساوي واحد يبقى بده يصير عندك
+
+639
+01:09:18,400 --> 01:09:29,400
+مين the level surface is ز
+
+640
+01:09:29,400 --> 01:09:37,640
+تربيع بيساوي X تربيةزائد واي تربيع زائد واحد ها
+
+641
+01:09:37,640 --> 01:09:42,780
+يالا حدا من الذكرة المعادلة؟ مبتده Circular
+
+642
+01:09:42,780 --> 01:09:51,620
+Paraboloid ايوه Circular Paraboloid ممتاز جدا يبقى
+
+643
+01:09:51,620 --> 01:09:58,680
+high paraboloid of two sheets يبقى هذا اسمه high
+
+644
+01:09:58,680 --> 01:10:02,220
+paraboloid
+
+645
+01:10:03,210 --> 01:10:11,390
+up to sheets او
+
+646
+01:10:11,390 --> 01:10:20,370
+لو حبينا نرسم هذا الكلام بقول اه خد المحور هذا
+
+647
+01:10:20,370 --> 01:10:31,210
+محور X هذا محور Y هذا محور Z بتاجي للمخروجبتعرف
+
+648
+01:10:31,210 --> 01:10:36,350
+وين المحور تبع المخروط برجع للمعادلة اللي عندنا
+
+649
+01:10:36,350 --> 01:10:40,710
+يبقى z في ناحية يبقى المحور هو محور z يبقى ال
+
+650
+01:10:40,710 --> 01:10:46,410
+circular يبقى بيكون على شكل ايه دائرة بالشكل هذا
+
+651
+01:10:46,410 --> 01:10:50,730
+يبقى هذا دائرة و ليست ellipse ليش ان احنا في
+
+652
+01:10:50,730 --> 01:10:56,390
+الفرار ارسم يبقى بديجيك الخط هذا بالشكل هذا و
+
+653
+01:10:56,390 --> 01:10:58,950
+بديجيك الخط التاني بالشكل هذا
+
+654
+01:11:04,750 --> 01:11:09,130
+هذا هو المخروط
+
+655
+01:11:09,130 --> 01:11:15,170
+اللي عندنا يبقى هذا هو المخروط اللي معادله Z تربيه
+
+656
+01:11:15,170 --> 01:11:20,310
+تسوى X تربيه زي Y تربيه اللي هو ال level surface
+
+657
+01:11:20,310 --> 01:11:26,910
+الأول طب بدنا نجي لل level surface التاليبرضه
+
+658
+01:11:26,910 --> 01:11:32,170
+المحور تبعه main هو محور z يبقى بده يجيك وين في
+
+659
+01:11:32,170 --> 01:11:42,410
+الداخل عنده بهذا الشكل طبعا
+
+660
+01:11:42,410 --> 01:11:48,130
+انا سافضله بخط الأزرق التاني بده يكون وين زيه بس
+
+661
+01:11:48,130 --> 01:11:58,650
+وين بس لفوق شوية هذا هيكو هذا هيك و هنا هيك و هذا
+
+662
+01:11:58,650 --> 01:12:02,310
+هيك
+
+663
+01:12:02,310 --> 01:12:09,830
+يبقى هذا اللي هو ال high paraboloid of two sheets
+
+664
+01:12:09,830 --> 01:12:19,590
+هذا مع هذا اللي هو ال high paraboloid of two
+
+665
+01:12:19,590 --> 01:12:20,970
+sheets
+
+666
+01:12:59,110 --> 01:13:04,450
+طب ناخد مثال عام على level curve و level surfaces
+
+667
+01:13:04,450 --> 01:13:10,390
+example يقول
+
+668
+01:13:10,390 --> 01:13:18,610
+find an equation find an equation هتلنا معادلة for
+
+669
+01:13:18,610 --> 01:13:27,410
+a level curve أو for the level curve level curve
+
+670
+01:13:27,410 --> 01:13:36,590
+orlevel surface level surface
+
+671
+01:13:36,590 --> 01:13:40,330
+فاصز
+
+672
+01:13:40,330 --> 01:13:49,370
+اثرور فاصز اثرور والذي يمر من خلال the given
+
+673
+01:13:49,370 --> 01:13:57,770
+points النقاط المعطاة for the following functions
+
+674
+01:13:57,770 --> 01:14:07,930
+orthe following functions للدوران التالية نمر A F
+
+675
+01:14:07,930 --> 01:14:17,170
+of X Y F of X Y تساوي اللي هو ستة عشر ناقص X تربيع
+
+676
+01:14:17,170 --> 01:14:24,130
+ناقص Y تربيع نمر B طبعا والنقطة المعطاعة اللي هي
+
+677
+01:14:24,130 --> 01:14:34,200
+النقطة اتنين جدر اتنينوجذر اتنين نمر بإيه؟ الـ G
+
+678
+01:14:34,200 --> 01:14:41,420
+of X أو Y أو Z يسوى الـ summation من N equal zero
+
+679
+01:14:41,420 --> 01:14:47,780
+to infinity لل X زائد Y to the power N على N
+
+680
+01:14:47,780 --> 01:14:58,490
+factorial KZ to the power Mهي لن اتنين ولن اربع
+
+681
+01:15:30,510 --> 01:15:37,110
+عليه بالكم يا اولى بنات نعطيني مثلتين و بيقوللي في
+
+682
+01:15:37,110 --> 01:15:41,210
+كل واحدة فيهم هتلي المناسب اذا كان liver tail او
+
+683
+01:15:41,210 --> 01:15:45,730
+liver cell بيقوللي ماشي بدي اجي للنقطة الاولى نمر
+
+684
+01:15:45,730 --> 01:15:51,870
+ايه؟ بدي احطه f of x و y بدي احطه constant c هذا
+
+685
+01:15:51,870 --> 01:15:54,570
+معناته ايش؟ معناته انه صدر
+
+686
+01:15:57,580 --> 01:16:03,220
+زائد ناقص Y تربيع كله بيديه ساوية منين؟ من وسط
+
+687
+01:16:03,220 --> 01:16:09,680
+الـC أو بتنقل هدول هناك X تربيع زائد Y تربيع
+
+688
+01:16:09,680 --> 01:16:16,160
+بيساوية 16 ناقص C قال المنحنة هذا يا مربو نقطة
+
+689
+01:16:16,160 --> 01:16:20,290
+منين؟إتنين جدر اتنين و جدر اتنين إذا انا هشيل ال X
+
+690
+01:16:20,290 --> 01:16:23,450
+و أحط مكانها اتنين جدر اتنين و اشيل ال Y و أحط
+
+691
+01:16:23,450 --> 01:16:29,390
+مكانها جدر اتنين يبقى اتنين جدر اتنين لكل تربيع
+
+692
+01:16:29,390 --> 01:16:35,690
+زائد جدر اتنين لكل تربيع بسوى ستة عشر ناقصي هذا
+
+693
+01:16:35,690 --> 01:16:42,470
+بدي يعطينا طبعا هذا كده شبنات تمانية زائدإتنين بدر
+
+694
+01:16:42,470 --> 01:16:48,210
+ساوي ستة عشر ناقص C هذا بدي أعطيك انه C to sell
+
+695
+01:16:48,210 --> 01:16:55,470
+هذه عشر تمام جيبي هذه عندها بدر قداش ناقص ستة إذا
+
+696
+01:16:55,470 --> 01:17:02,610
+C تساوي ستة يبقى صار عند هذا level service ولا
+
+697
+01:17:02,610 --> 01:17:09,090
+level care بمناطق لأن ال bus متغيرين وليس تلاتة as
+
+698
+01:17:26,160 --> 01:17:34,040
+يبقى هذا اللي بال curve is a circle طيب نمر بيه
+
+699
+01:17:34,040 --> 01:17:39,500
+بتحط summation من n equal zero to infinity
+
+700
+01:18:06,700 --> 01:18:11,760
+أخدنا مفكوك تايلور و مفكوك ماكلوري ماكلور سيريز و
+
+701
+01:18:11,760 --> 01:18:16,880
+تايلور سيريز تمام؟ و أخدته أول مثال في ماكلور
+
+702
+01:18:16,880 --> 01:18:23,620
+سيريز اللي هو E أُس X قالت إيش؟ اللي X to the
+
+703
+01:18:23,620 --> 01:18:29,560
+power N على N factorialمظبوط؟ إذا تحكم او تذكر او
+
+704
+01:18:29,560 --> 01:18:35,040
+تعلم شغل زي ذلك يبقى لما أجي أطلع X to the power
+
+705
+01:18:35,040 --> 01:18:40,320
+of N على N factorial يبقى هذي كده E أُس X إذا هذي
+
+706
+01:18:40,320 --> 01:18:49,300
+مين؟ E أُس X زائد Y على Z يبقى هذا المنحنى، مظبوط
+
+707
+01:18:49,300 --> 01:18:54,560
+او لا؟ طيب هذا المنحنى فيه ثلاث متغيرات يبقى هذا
+
+708
+01:18:54,560 --> 01:19:05,260
+يريد يعطيناthe level surface is مين هو E أُس X
+
+709
+01:19:05,260 --> 01:19:12,980
+زائد Y على Z يسوى كونستان C عظم الكلكة ع الشغل هيك
+
+710
+01:19:12,980 --> 01:19:19,520
+شوية طب ده نفكر كعتها شو رايح ناخد لله الطرفين إذا
+
+711
+01:19:19,520 --> 01:19:27,230
+لو خدت لله الطرفين تصير X زائد Y على Zبدو يسوى لن
+
+712
+01:19:27,230 --> 01:19:34,010
+C من المعادلة هذه بقدر أجيب قدر C من خلال إحداثيات
+
+713
+01:19:34,010 --> 01:19:42,630
+النقطة تبقى لن 2 زائد لن الأربعة على تلاتة بدو
+
+714
+01:19:42,630 --> 01:19:52,300
+يسوى لن C هذا شو بيعطينا هذا بيبقى 2 لن 2يبقى
+
+715
+01:19:52,300 --> 01:19:58,320
+بيصير تلاتة لن اتنين على تلاتة يسوى لن سي فهذا
+
+716
+01:19:58,320 --> 01:20:04,800
+معناته ان لن اتنين يسوى لن سي يبقى سي تسوى جداش
+
+717
+01:20:04,800 --> 01:20:14,200
+تسوى اتنين يبقى باجي بقوله the level surfaces are
+
+718
+01:20:14,200 --> 01:20:24,860
+in the form في الشكل التاليE أس X زائد Y على C على
+
+719
+01:20:24,860 --> 01:20:35,360
+Z يساوي كده يساوي اتنين او اللي هو X زائد Y على Z
+
+720
+01:20:35,360 --> 01:20:44,480
+يساوي لان اتنين او إذا تحطيها في شكل آخرز يسوى
+
+721
+01:20:44,480 --> 01:20:51,520
+واحد على لن اتنين في ال X زائد ال one يبقى هذا شكل
+
+722
+01:20:51,520 --> 01:20:56,900
+ال level surface في هذه الحالة آخر نقطة عندنا في
+
+723
+01:20:56,900 --> 01:21:02,600
+هذا ال section اللي هو بعض التعريفات some
+
+724
+01:21:02,600 --> 01:21:05,420
+definitions
+
+725
+01:21:18,490 --> 01:21:24,090
+تعريف الأول نعرف التعريفات اللي عرفناهم على
+
+726
+01:21:24,090 --> 01:21:33,510
+الـplane نعرفهم على الـspace يبقى a point بـx
+
+727
+01:21:33,510 --> 01:21:36,110
+نوض و y نوض و z نوض
+
+728
+01:21:39,650 --> 01:21:51,510
+and interior point نقطة داخلية of a region a على
+
+729
+01:21:51,510 --> 01:22:02,330
+منطقة a in a space في الفرق if
+
+730
+01:22:02,330 --> 01:22:06,050
+it
+
+731
+01:22:06,050 --> 01:22:06,530
+is
+
+732
+01:22:11,580 --> 01:22:23,420
+the center of a solid ball كرة مغنقة و كرة مصمة
+
+733
+01:22:23,420 --> 01:22:35,240
+that lies that lies entirely كلياً
+
+734
+01:22:35,240 --> 01:22:47,410
+in اللي هي upنمر اتنين a point x نون و y نون و z
+
+735
+01:22:47,410 --> 01:22:58,430
+نون is a boundary point is a boundary point يبقى
+
+736
+01:22:58,430 --> 01:23:08,090
+هذه نقطة حدية of R if every
+
+737
+01:23:09,820 --> 01:23:28,920
+أسفير F
+
+738
+01:23:28,920 --> 01:23:35,900
+over أسفير مركز على
+
+739
+01:23:35,900 --> 01:23:45,750
+X نوت وY نوتwas it not contains
+
+740
+01:23:45,750 --> 01:23:53,850
+points that
+
+741
+01:23:53,850 --> 01:24:01,430
+lie outside
+
+742
+01:24:01,430 --> 01:24:08,290
+of
+
+743
+01:24:09,290 --> 01:24:17,890
+are as well as
+
+744
+01:24:17,890 --> 01:24:30,390
+points that
+
+745
+01:24:30,390 --> 01:24:33,790
+lie
+
+746
+01:24:33,790 --> 01:24:37,510
+inside
+
+747
+01:25:03,320 --> 01:25:16,360
+أولى ثلاثة The integral of R is
+
+748
+01:25:16,360 --> 01:25:22,260
+the set
+
+749
+01:25:22,260 --> 01:25:28,200
+of all integral points
+
+750
+01:25:40,640 --> 01:25:51,840
+المقاومات المقاومات من R من R هي مجموعة من
+
+751
+01:25:51,840 --> 01:25:53,700
+المقاومات المقاومات
+
+752
+01:26:05,270 --> 01:26:21,290
+of points of a أخر حاجة أربعة a region a region is
+
+753
+01:26:21,290 --> 01:26:33,950
+open منطقة مفتوحة if it is consists if it consists
+
+754
+01:27:00,260 --> 01:27:08,140
+هي مدينة داخلية
+
+755
+01:27:13,840 --> 01:27:20,380
+منطقة مغلقة if it
+
+756
+01:27:20,380 --> 01:27:30,300
+contains its entire
+
+757
+01:27:30,300 --> 01:27:36,320
+boundary
+
+758
+01:27:36,320 --> 01:27:37,180
+points
+
+759
+01:28:04,190 --> 01:28:19,530
+فإن ال demand of f of x, y و z يساوي لن x ناقص
+
+760
+01:28:19,530 --> 01:28:26,570
+اتنين y زائد تلاتة z ناقص ستة
+
+761
+01:28:57,290 --> 01:29:03,030
+النقطة التانية كانت ال control of the boundary
+
+762
+01:29:03,030 --> 01:29:15,850
+while the control كان boundary of
+
+763
+01:29:15,850 --> 01:29:19,570
+the domain
+
+764
+01:29:33,770 --> 01:29:44,890
+مفتح او مغلق مفتوح او
+
+765
+01:29:44,890 --> 01:29:53,590
+مغلق او
+
+766
+01:29:53,590 --> 01:29:55,710
+مفتوح
+
+767
+01:30:19,890 --> 01:30:23,270
+لو رجعت ال definitions هدول هما نفس ال definitions
+
+768
+01:30:31,710 --> 01:30:35,430
+بعد ما كنت أقول desk بدأت أقول هنا سفير بدل ما كنت
+
+769
+01:30:35,430 --> 01:30:41,450
+أقول نقطة بإحداثية بدأت أقول نقطة بثلاث إحداثية
+
+770
+01:30:41,450 --> 01:30:46,450
+بثلاثة إحداثيات فقط لغاية تبقى لما أتي بجديد كل
+
+771
+01:30:46,450 --> 01:30:50,090
+الكلام اللي عتيجي النص عندك بسفيري desk حطي بدل
+
+772
+01:30:50,090 --> 01:30:53,950
+سفير النقطة إحداثية تخلي بالها مكان هاياش تلاتي
+
+773
+01:30:53,950 --> 01:30:59,020
+أبقى لما نأتي نقول باقي كله زي ما هوطيب نحسب هذا
+
+774
+01:30:59,020 --> 01:31:02,900
+الكلام عمليا نعطي دلّه و نقول هاتلي ال domain تبع
+
+775
+01:31:02,900 --> 01:31:09,820
+الدلّه اللي عنها انا باشي بقوله domain الدلّه Fهو
+
+776
+01:31:09,820 --> 01:31:15,020
+مين؟ كل العناصر X وY وZ يعني كل النقاط X وY وZ
+
+777
+01:31:15,020 --> 01:31:21,100
+طبعا الـ Lin مش معرفة إلا لقيمة مجبة بحيث أن X
+
+778
+01:31:21,100 --> 01:31:29,100
+ناقص اتنين Y زائد تلاتة Z ناقص ستة بديها أكبر من
+
+779
+01:31:29,100 --> 01:31:36,720
+مين؟ من Zero أو إن شئتم فقولواx و y و z such that
+
+780
+01:31:36,720 --> 01:31:44,160
+x نقص اتنين y زي التلاتة z اكبر من مين اكبر من
+
+781
+01:31:44,160 --> 01:31:49,460
+zero طب بدأ اعرف من هالمنطقة هذه هذه بنات معادلتاش
+
+782
+01:31:49,460 --> 01:31:55,560
+لو قلت تسوي ستة ليه؟ تمام يعني انا لو روحت جدلا
+
+783
+01:31:55,560 --> 01:31:58,900
+رسمت المحاول بالشكل اللي قدامنا هذا
+
+784
+01:32:07,080 --> 01:32:13,020
+و روحت و قلت ما هي المحاور هذا
+
+785
+01:32:13,020 --> 01:32:20,580
+X وهذا Y وهذا Z و جاءت و قلت المستوى اللي عندنا هو
+
+786
+01:32:20,580 --> 01:32:26,140
+Y و Z و Zero بس هال X بقداش؟ ب6 يبقى لو جيت و قلت
+
+787
+01:32:26,140 --> 01:32:34,430
+النقطة هذي 6 و Zero و Zeroحط X و Z هو Zero بصير Y
+
+788
+01:32:34,430 --> 01:32:40,470
+بسالب تلاتة يعني لو مديتها على استقامته فتصير هذه
+
+789
+01:32:40,470 --> 01:32:47,770
+اللي هو Zero و سالب تلاتة و Zero حط X و Y ب Zero
+
+790
+01:32:47,770 --> 01:32:53,510
+بصير Z باتنين يفجر النقطة اللي عندك هذه Zero و
+
+791
+01:32:53,510 --> 01:32:59,710
+Zero و اتنين الان لو جيت وصلفي مابين النقاط هذه
+
+792
+01:32:59,710 --> 01:33:08,410
+التلاتة بهذا الشكل اكبر
+
+793
+01:33:08,410 --> 01:33:15,230
+من 6 يبقى كل space اللي أعلى من هذا ال plane يعني
+
+794
+01:33:15,230 --> 01:33:21,270
+كل المنطقة اللي عندك هذه كل جزء من الفرار اللي
+
+795
+01:33:21,270 --> 01:33:26,790
+أعلى هذا المثلث يبقى هنا ليه space؟
+
+796
+01:33:29,100 --> 01:33:36,340
+أو الـ half space above
+
+797
+01:33:36,340 --> 01:33:46,840
+the E plane اللي هو من X نقص اتنين Y زائد تلاتة Z
+
+798
+01:33:46,840 --> 01:33:52,480
+يسوى ستة كل الفرق طيب هل ال E plane من ضمن هذه
+
+799
+01:33:52,480 --> 01:33:58,100
+المنطقة؟ لأ مش من ضمنها ماعنديش مساواة خلصنا منه
+
+800
+01:33:58,390 --> 01:34:02,950
+هذه النقطة الأولى اللي هو ال domain طيب النقطة
+
+801
+01:34:02,950 --> 01:34:07,690
+الثانية جالي هذا ال domain ال interior و ال
+
+802
+01:34:07,690 --> 01:34:11,990
+boundary لهذا ال domain ال interior تبع هذا ال
+
+803
+01:34:11,990 --> 01:34:17,350
+domain اللي ويله ويله يا بنات من عند ال plane هذا
+
+804
+01:34:17,350 --> 01:34:25,200
+لغاية ما لنهاية يبقى ال interiorتبع هذا ال domain
+
+805
+01:34:25,200 --> 01:34:33,840
+كل العناصر x و y و z بحيث ان ال x نقص اتنين y زائد
+
+806
+01:34:33,840 --> 01:34:43,640
+تلاتة z بدها تكون اكبر من 100 من 6 يعني كأن ال x
+
+807
+01:34:43,640 --> 01:34:50,640
+نقص اتنين y زائد تلاتة z اكبر من 6 و اقل من 100 من
+
+808
+01:34:50,640 --> 01:34:55,270
+infinityهذا من المطلوب التاني اللي هو الانقرار ال
+
+809
+01:34:55,270 --> 01:35:03,150
+boundary من ال boundary؟ اللي هو ال plane يبقى ال
+
+810
+01:35:03,150 --> 01:35:07,670
+boundary is
+
+811
+01:35:07,670 --> 01:35:16,970
+the plane اللي هو x نقص اتنين y زي التلاتة z يسوي
+
+812
+01:35:16,970 --> 01:35:19,590
+ستة طيب النقطة التالتة
+
+813
+01:35:22,870 --> 01:35:26,950
+قال لي هل ال domain open و لا closed؟ open أنه
+
+814
+01:35:26,950 --> 01:35:34,150
+احتوى كل ال interior points يبقى ال domain of that
+
+815
+01:35:34,150 --> 01:35:42,030
+domain is open ليش؟ أنه احتوى كل ال interior
+
+816
+01:35:42,030 --> 01:35:46,670
+points النقطة الرابعة والاخيرة قال لي هل ال domain
+
+817
+01:35:46,670 --> 01:35:50,740
+bounded or unbounded؟طبعا واضح انه بيظل لوين الى
+
+818
+01:35:50,740 --> 01:36:00,100
+مدى نهاية يبقى unbounded domain الان بدنا منك ال
+
+819
+01:36:00,100 --> 01:36:07,040
+exercises التالي يبقى exercises اربعتاشر واحد
+
+820
+01:36:07,040 --> 01:36:14,560
+المسائل التالية تلاتة خمسة سبعة تسعة احداشر
+
+821
+01:36:14,560 --> 01:36:16,900
+تسعتاشر
+
+822
+01:36:17,690 --> 01:36:24,570
+تلاتة و عشرين، خمسة و عشرين، واحد و تلاتين، انه
+
+823
+01:36:24,570 --> 01:36:31,930
+تلاتين، تلاتة و تلاتين، سبعة و تلاتين، تسعة و
+
+824
+01:36:31,930 --> 01:36:40,150
+تلاتين، واحد و أربعين، تلاتة و أربعين، أربعة و
+
+825
+01:36:40,150 --> 01:36:40,730
+أربعين
+
+826
+01:36:46,040 --> 01:36:49,900
+المرة القادمة ان شاء الله بنروح لل section اللي
+
+827
+01:36:49,900 --> 01:36:58,720
+بعده حد بتحب تسأل اي سؤال هنا ولا هناك؟ اي تساؤل؟
+
+828
+01:36:58,720 --> 01:37:03,560
+حول ال domain ال range ال interior ال boundary ال
+
+829
+01:37:03,560 --> 01:37:09,760
+bounded ال unbounded كل الأمور هذه yes؟ فلأ سيبقى
+
+830
+01:37:09,760 --> 01:37:11,400
+للمرة القادمة ان شاء الله
+
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/WBeNRZv00d4_raw.json b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/WBeNRZv00d4_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..5a5dbb5ba538ec5ec1a9daeaf6fb60e5c869c862
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/WBeNRZv00d4_raw.json
@@ -0,0 +1 @@
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415.75, "end": 416.31, "word": " points", "probability": 0.50732421875}, {"start": 416.31, "end": 417.27, "word": " لكن", "probability": 0.9052734375}, {"start": 417.27, "end": 417.57, "word": " ال", "probability": 0.83251953125}, {"start": 417.57, "end": 418.07, "word": " closed", "probability": 0.94775390625}, {"start": 418.07, "end": 418.69, "word": " region", "probability": 0.947265625}], "temperature": 1.0}, {"id": 19, "seek": 43968, "start": 419.06, "end": 439.68, "text": "هي المنطقة التي تحتوي على كل ال boundary points تبعتها طيب definition أخير هنقسمه إلى نقطتين المنطقة قد تكون bounded يعني محدودة وقد تكون unbounded غير محدودة", "tokens": [3224, 1829, 9673, 1863, 9566, 28671, 38392, 6055, 33753, 45865, 15844, 28242, 2423, 12866, 2793, 6055, 3555, 34268, 11296, 23032, 1829, 3555, 7123, 5551, 9778, 13546, 8032, 1863, 4587, 38251, 3224, 30731, 8717, 47432, 2655, 9957, 9673, 1863, 9566, 28671, 12174, 3215, 6055, 30544, 37498, 37495, 22653, 3714, 24401, 23328, 3660, 4032, 28543, 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0.865234375}, {"start": 425.64, "end": 427.02, "word": " طيب", "probability": 0.86767578125}, {"start": 427.02, "end": 427.66, "word": " definition", "probability": 0.509765625}, {"start": 427.66, "end": 428.6, "word": " أخير", "probability": 0.7154134114583334}, {"start": 428.6, "end": 430.32, "word": " هنقسمه", "probability": 0.77373046875}, {"start": 430.32, "end": 430.48, "word": " إلى", "probability": 0.80419921875}, {"start": 430.48, "end": 431.18, "word": " نقطتين", "probability": 0.960693359375}, {"start": 431.18, "end": 432.44, "word": " المنطقة", "probability": 0.9390869140625}, {"start": 432.44, "end": 432.88, "word": " قد", "probability": 0.993896484375}, {"start": 432.88, "end": 433.4, "word": " تكون", "probability": 0.9921875}, {"start": 433.4, "end": 434.16, "word": " bounded", "probability": 0.9560546875}, {"start": 434.16, "end": 434.8, "word": " يعني", "probability": 0.908935546875}, {"start": 434.8, "end": 435.64, "word": " محدودة", "probability": 0.9893798828125}, {"start": 435.64, "end": 436.3, "word": " وقد", "probability": 0.7340087890625}, {"start": 436.3, "end": 436.86, "word": " تكون", "probability": 0.994873046875}, {"start": 436.86, "end": 438.36, "word": " unbounded", "probability": 0.94189453125}, {"start": 438.36, "end": 438.92, "word": " غير", "probability": 0.988037109375}, {"start": 438.92, "end": 439.68, "word": " محدودة", "probability": 0.990966796875}], "temperature": 1.0}, {"id": 20, "seek": 46468, "start": 440.18, "end": 464.68, "text": "بجل التعريف الأول بقول ال region R في المستوى is bounded محدودة if it lies inside of a disk of a fixed radius يبقى المنطقة اللي أنا بسميها محدودة لو وقعت بأكملها داخل disk و ال disk نصف قطره معروف ثابت تمام؟ يبقى المنطقة مرة تانية", "tokens": [3555, 7435, 1211, 16712, 3615, 16572, 5172, 16247, 12610, 4724, 39648, 2423, 4458, 497, 8978, 9673, 14851, 2407, 7578, 307, 37498, 3714, 24401, 23328, 3660, 498, 309, 9134, 1854, 295, 257, 12355, 295, 257, 6806, 15845, 7251, 3555, 4587, 7578, 9673, 1863, 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0.7509765625}, {"start": 449.56, "end": 449.78, "word": " of", "probability": 0.96044921875}, {"start": 449.78, "end": 450.02, "word": " a", "probability": 0.2423095703125}, {"start": 450.02, "end": 450.3, "word": " fixed", "probability": 0.9169921875}, {"start": 450.3, "end": 450.86, "word": " radius", "probability": 0.87841796875}, {"start": 450.86, "end": 451.78, "word": " يبقى", "probability": 0.934326171875}, {"start": 451.78, "end": 452.22, "word": " المنطقة", "probability": 0.98486328125}, {"start": 452.22, "end": 452.38, "word": " اللي", "probability": 0.90625}, {"start": 452.38, "end": 452.5, "word": " أنا", "probability": 0.6494140625}, {"start": 452.5, "end": 453.16, "word": " بسميها", "probability": 0.98388671875}, {"start": 453.16, "end": 454.18, "word": " محدودة", "probability": 0.98681640625}, {"start": 454.18, "end": 454.74, "word": " لو", "probability": 0.96630859375}, {"start": 454.74, "end": 455.46, "word": " وقعت", "probability": 0.9280598958333334}, {"start": 455.46, "end": 456.82, "word": " بأكملها", "probability": 0.933203125}, {"start": 456.82, "end": 458.18, "word": " داخل", "probability": 0.96630859375}, {"start": 458.18, "end": 458.72, "word": " disk", "probability": 0.80078125}, {"start": 458.72, "end": 459.14, "word": " و", "probability": 0.755859375}, {"start": 459.14, "end": 459.26, "word": " ال", "probability": 0.505859375}, {"start": 459.26, "end": 459.48, "word": " disk", "probability": 0.9794921875}, {"start": 459.48, "end": 460.0, "word": " نصف", "probability": 0.9423828125}, {"start": 460.0, "end": 460.46, "word": " قطره", "probability": 0.8515625}, {"start": 460.46, "end": 460.94, "word": " معروف", "probability": 0.9895833333333334}, {"start": 460.94, "end": 461.74, "word": " ثابت", "probability": 0.9742838541666666}, {"start": 461.74, "end": 462.92, "word": " تمام؟", "probability": 0.6048990885416666}, {"start": 462.92, "end": 463.26, "word": " يبقى", "probability": 0.985107421875}, {"start": 463.26, "end": 463.84, "word": " المنطقة", "probability": 0.9178466796875}, {"start": 463.84, "end": 464.26, "word": " مرة", "probability": 0.856201171875}, {"start": 464.26, "end": 464.68, "word": " تانية", "probability": 0.9599609375}], "temperature": 1.0}, {"id": 21, "seek": 47597, "start": 465.09, "end": 475.97, "text": "بقول عنها bounded محدودة إذا جدرت أخلي disk يحتوي عالمين على هذه المنطقة كلها، إذا بسميها إيش؟", "tokens": [3555, 39648, 18871, 11296, 37498, 3714, 24401, 23328, 3660, 11933, 15730, 10874, 3215, 43500, 5551, 9778, 20292, 12355, 7251, 33753, 45865, 6225, 45340, 9957, 15844, 29538, 9673, 1863, 9566, 28671, 28242, 11296, 12399, 11933, 15730, 4724, 38251, 1829, 11296, 11933, 1829, 8592, 22807], "avg_logprob": -0.14754970981316132, "compression_ratio": 1.2384615384615385, "no_speech_prob": 0.0, "words": [{"start": 465.09, "end": 465.55, "word": "بقول", "probability": 0.92919921875}, {"start": 465.55, "end": 465.89, "word": " عنها", "probability": 0.923583984375}, {"start": 465.89, "end": 466.87, 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"probability": 0.775390625}, {"start": 640.3, "end": 642.58, "word": " والكوادران", "probability": 0.7132161458333334}, {"start": 642.58, "end": 648.24, "word": " و", "probability": 0.1925048828125}, {"start": 648.24, "end": 648.42, "word": " ال", "probability": 0.564453125}, {"start": 648.42, "end": 648.66, "word": " half", "probability": 0.5498046875}, {"start": 648.66, "end": 648.86, "word": " a", "probability": 0.400634765625}, {"start": 648.86, "end": 649.28, "word": " plane", "probability": 0.67822265625}, {"start": 649.28, "end": 655.44, "word": " و", "probability": 0.3798828125}, {"start": 655.44, "end": 655.46, "word": " ال", "probability": 0.60498046875}, {"start": 655.46, "end": 655.7, "word": " half", "probability": 0.673828125}, {"start": 655.7, "end": 655.9, "word": " a", "probability": 0.83349609375}, {"start": 655.9, "end": 656.32, "word": " plane", "probability": 0.8974609375}, {"start": 656.32, "end": 657.54, "word": " and", "probability": 0.425048828125}, {"start": 657.54, "end": 659.08, "word": " a", "probability": 0.336181640625}, {"start": 659.08, "end": 659.6, "word": " plane", "probability": 0.423583984375}], "temperature": 1.0}, {"id": 29, "seek": 68010, "start": 660.82, "end": 680.1, "text": "والمستويات كلها are unbound sets in the plane", "tokens": [2407, 45340, 14851, 45865, 9307, 28242, 11296, 366, 517, 18767, 6352, 294, 264, 5720], "avg_logprob": -0.2885416785875956, "compression_ratio": 0.8676470588235294, "no_speech_prob": 0.0, "words": [{"start": 660.82, "end": 661.96, "word": "والمستويات", "probability": 0.8943359375}, {"start": 661.96, "end": 663.38, "word": " كلها", "probability": 0.9580078125}, {"start": 663.38, "end": 664.0, "word": " are", "probability": 0.89453125}, {"start": 664.0, "end": 667.92, "word": " unbound", "probability": 0.64453125}, {"start": 667.92, "end": 674.68, "word": " sets", "probability": 0.375244140625}, {"start": 674.68, "end": 677.9, "word": " in", "probability": 0.5087890625}, {"start": 677.9, "end": 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"avg_logprob": -0.4952566751411983, "compression_ratio": 1.2842105263157895, "no_speech_prob": 0.0, "words": [{"start": 3114.0499999999997, "end": 3115.45, "word": "find", "probability": 0.074951171875}, {"start": 3115.45, "end": 3116.85, "word": " the", "probability": 0.78173828125}, {"start": 3116.85, "end": 3118.51, "word": " level", "probability": 0.91845703125}, {"start": 3118.51, "end": 3119.89, "word": " curves", "probability": 0.87255859375}, {"start": 3119.89, "end": 3122.49, "word": " for", "probability": 0.61181640625}, {"start": 3122.49, "end": 3122.71, "word": " the", "probability": 0.88916015625}, {"start": 3122.71, "end": 3123.09, "word": " following", "probability": 0.8642578125}, {"start": 3123.09, "end": 3123.91, "word": " surfaces", "probability": 0.95751953125}, {"start": 3123.91, "end": 3124.65, "word": " for", "probability": 0.1253662109375}, {"start": 3124.65, "end": 3126.25, "word": " the", "probability": 0.89013671875}, {"start": 3126.25, "end": 3128.03, "word": " following", "probability": 0.8564453125}, {"start": 3128.03, "end": 3131.01, "word": " surfaces", "probability": 0.96044921875}, {"start": 3131.01, "end": 3135.01, "word": " نمر", "probability": 0.560302734375}, {"start": 3135.01, "end": 3135.51, "word": " A", "probability": 0.1300048828125}, {"start": 3135.51, "end": 3137.11, "word": " بد", "probability": 0.39111328125}, {"start": 3137.11, "end": 3137.35, "word": " ال", "probability": 0.364013671875}, {"start": 3137.35, "end": 3137.79, "word": " F", "probability": 0.84765625}, {"start": 3137.79, "end": 3138.67, "word": " of", "probability": 0.7958984375}, {"start": 3138.67, "end": 3139.23, "word": " X", "probability": 0.9306640625}, {"start": 3139.23, "end": 3140.07, "word": " و", "probability": 0.81201171875}, {"start": 3140.07, "end": 3140.49, "word": " Y", "probability": 0.53662109375}, {"start": 3140.49, "end": 3141.23, "word": " بد", "probability": 0.939453125}, {"start": 3141.23, "end": 3142.01, "word": " يساوي", 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{"start": 3161.75, "end": 3162.15, "word": " لكل", "probability": 0.91357421875}, {"start": 3162.15, "end": 3162.39, "word": " من", "probability": 0.86572265625}, {"start": 3162.39, "end": 3163.03, "word": " المرحلات", "probability": 0.85927734375}, {"start": 3163.03, "end": 3163.73, "word": " التالية", "probability": 0.9864908854166666}, {"start": 3163.73, "end": 3164.59, "word": " وراها", "probability": 0.70947265625}, {"start": 3164.59, "end": 3165.05, "word": " طالي", "probability": 0.7791341145833334}, {"start": 3165.05, "end": 3165.19, "word": " اللي", "probability": 0.75439453125}, {"start": 3165.19, "end": 3165.29, "word": " هو", "probability": 0.82763671875}, {"start": 3165.29, "end": 3165.81, "word": " الملحدة", "probability": 0.7431640625}, {"start": 3165.81, "end": 3165.95, "word": " اللي", "probability": 0.965576171875}, {"start": 3165.95, "end": 3166.57, "word": " قدامك", "probability": 0.8402099609375}, {"start": 3166.57, "end": 3167.17, "word": " إذا", "probability": 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"start": 4379.11, "end": 4408.51, "text": "طب ناخد مثال عام على level curve و level surfaces example يقول find an equation find an equation هتلنا معادلة for a level curve أو for the level curve level curve or", "tokens": [9566, 3555, 8717, 47283, 3215, 50113, 6027, 6225, 10943, 15844, 1496, 7605, 4032, 1496, 16130, 1365, 7251, 39648, 915, 364, 5367, 915, 364, 5367, 8032, 2655, 1211, 8315, 20449, 18513, 37977, 337, 257, 1496, 7605, 34051, 337, 264, 1496, 7605, 1496, 7605, 420], "avg_logprob": -0.3462358076464046, "compression_ratio": 1.4525547445255473, "no_speech_prob": 0.0, "words": [{"start": 4379.11, "end": 4379.33, "word": "طب", "probability": 0.56488037109375}, {"start": 4379.33, "end": 4379.71, "word": " ناخد", "probability": 0.984375}, {"start": 4379.71, "end": 4380.19, "word": " مثال", "probability": 0.966796875}, {"start": 4380.19, "end": 4380.71, "word": " عام", "probability": 0.995361328125}, {"start": 4380.71, "end": 4382.01, "word": " على", "probability": 0.70068359375}, 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0.91943359375}, {"start": 4487.78, "end": 4488.78, "word": " factorial", "probability": 0.8017578125}, {"start": 4488.78, "end": 4489.86, "word": " KZ", "probability": 0.624755859375}, {"start": 4489.86, "end": 4490.28, "word": " to", "probability": 0.96337890625}, {"start": 4490.28, "end": 4490.46, "word": " the", "probability": 0.90673828125}, {"start": 4490.46, "end": 4490.94, "word": " power", "probability": 0.86669921875}, {"start": 4490.94, "end": 4491.3, "word": " M", "probability": 0.71728515625}], "temperature": 1.0}, {"id": 165, "seek": 449849, "start": 4493.67, "end": 4498.49, "text": "هي لن اتنين ولن اربع", "tokens": [3224, 1829, 5296, 1863, 1975, 2655, 1863, 9957, 35525, 1863, 1975, 25513, 3615], "avg_logprob": -0.34933036140033175, "compression_ratio": 0.9473684210526315, "no_speech_prob": 0.00014066696166992188, "words": [{"start": 4493.67, "end": 4495.07, "word": "هي", "probability": 0.4276123046875}, {"start": 4495.07, "end": 4495.73, "word": " لن", "probability": 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"word": "فإن", "probability": 0.4142659505208333}, {"start": 5284.73, "end": 5284.91, "word": " ال", "probability": 0.466552734375}, {"start": 5284.91, "end": 5285.41, "word": " demand", "probability": 0.31201171875}, {"start": 5285.41, "end": 5287.41, "word": " of", "probability": 0.89306640625}, {"start": 5287.41, "end": 5289.99, "word": " f", "probability": 0.61376953125}, {"start": 5289.99, "end": 5290.87, "word": " of", "probability": 0.2626953125}, {"start": 5290.87, "end": 5291.41, "word": " x,", "probability": 0.8935546875}, {"start": 5291.61, "end": 5292.47, "word": " y", "probability": 0.7822265625}, {"start": 5292.47, "end": 5292.75, "word": " و", "probability": 0.505859375}, {"start": 5292.75, "end": 5293.11, "word": " z", "probability": 0.6923828125}, {"start": 5293.11, "end": 5294.99, "word": " يساوي", "probability": 0.913330078125}, {"start": 5294.99, "end": 5296.45, "word": " لن", "probability": 0.4150390625}, {"start": 5296.45, "end": 5298.13, "word": " x", 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"end": 5348.41, "word": " control", "probability": 0.67041015625}, {"start": 5348.41, "end": 5350.15, "word": " كان", "probability": 0.265869140625}, {"start": 5350.15, "end": 5352.45, "word": " boundary", "probability": 0.8505859375}, {"start": 5352.45, "end": 5355.85, "word": " of", "probability": 0.97216796875}, {"start": 5355.85, "end": 5357.93, "word": " the", "probability": 0.80615234375}, {"start": 5357.93, "end": 5359.57, "word": " domain", "probability": 0.98291015625}], "temperature": 1.0}, {"id": 192, "seek": 539571, "start": 5373.77, "end": 5395.71, "text": "مفتح او مغلق مفتوح او مغلق او مفتوح", "tokens": [2304, 5172, 2655, 5016, 1975, 2407, 3714, 17082, 1211, 4587, 3714, 5172, 2655, 2407, 5016, 1975, 2407, 3714, 17082, 1211, 4587, 1975, 2407, 3714, 5172, 2655, 2407, 5016], "avg_logprob": -0.6082974384570944, "compression_ratio": 1.4651162790697674, "no_speech_prob": 0.0, "words": [{"start": 5373.77, "end": 5374.33, "word": "مفتح", "probability": 0.5458221435546875}, 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بسفيري desk حطي بدل سفير النقطة إحداثية تخلي بالها مكان هاياش تلاتي أبقى لما نأتي نقول باقي كله زي ما هو", "tokens": [3555, 22488, 19446, 9122, 29399, 5551, 39648, 10026, 47525, 10721, 2655, 5551, 39648, 34105, 8608, 5172, 13546, 47525, 1211, 19446, 9122, 29399, 5551, 39648, 8717, 47432, 3660, 4724, 28814, 24401, 5718, 104, 10632, 47525, 10721, 2655, 5551, 39648, 8717, 47432, 3660, 4724, 12984, 1211, 5718, 104, 11933, 24401, 5718, 104, 10632, 4724, 12984, 1211, 5718, 104, 3660, 11933, 24401, 5718, 104, 1829, 9307, 6156, 47432, 5296, 17082, 995, 10632, 6055, 3555, 4587, 7578, 5296, 15042, 5551, 31371, 4724, 7435, 16254, 3215, 28242, 2423, 28820, 10943, 13672, 1829, 6225, 31371, 7435, 1829, 28239, 9381, 43242, 4117, 4724, 3794, 5172, 13546, 1829, 10026, 11331, 9566, 1829, 47525, 1211, 8608, 5172, 13546, 28239, 47432, 3660, 11933, 24401, 5718, 104, 10632, 6055, 9778, 20292, 20666, 11296, 3714, 41361, 8032, 47302, 33599, 6055, 1211, 9307, 1829, 5551, 3555, 4587, 7578, 5296, 15042, 8717, 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" منك", "probability": 0.872314453125}, {"start": 5759.98, "end": 5760.1, "word": " ال", "probability": 0.9697265625}, {"start": 5760.1, "end": 5760.82, "word": " exercises", "probability": 0.7841796875}, {"start": 5760.82, "end": 5761.66, "word": " التالي", "probability": 0.8478190104166666}, {"start": 5761.66, "end": 5762.66, "word": " يبقى", "probability": 0.91650390625}, {"start": 5762.66, "end": 5763.86, "word": " exercises", "probability": 0.87890625}, {"start": 5763.86, "end": 5766.08, "word": " اربعتاشر", "probability": 0.7476806640625}, {"start": 5766.08, "end": 5767.04, "word": " واحد", "probability": 0.845947265625}, {"start": 5767.04, "end": 5767.74, "word": " المسائل", "probability": 0.84423828125}, {"start": 5767.74, "end": 5768.42, "word": " التالية", "probability": 0.9348958333333334}, {"start": 5768.42, "end": 5770.4, "word": " تلاتة", "probability": 0.85205078125}, {"start": 5770.4, "end": 5771.34, "word": " خمسة", "probability": 0.8726806640625}, {"start": 5771.34, "end": 5772.12, "word": " سبعة", "probability": 0.9295247395833334}, {"start": 5772.12, "end": 5773.04, "word": " تسعة", "probability": 0.98876953125}, {"start": 5773.04, "end": 5774.56, "word": " احداشر", "probability": 0.8782958984375}, {"start": 5774.56, "end": 5776.9, "word": " تسعتاشر", "probability": 0.876318359375}], "temperature": 1.0}, {"id": 207, "seek": 580073, "start": 5777.69, "end": 5800.73, "text": "تلاتة و عشرين، خمسة و عشرين، واحد و تلاتين، انه تلاتين، تلاتة و تلاتين، سبعة و تلاتين، تسعة و تلاتين، واحد و أربعين، تلاتة و أربعين، أربعة و أربعين", "tokens": [2655, 1211, 9307, 3660, 4032, 6225, 46309, 9957, 12399, 16490, 2304, 3794, 3660, 4032, 6225, 46309, 9957, 12399, 36764, 24401, 4032, 6055, 1211, 9307, 9957, 12399, 16472, 3224, 6055, 1211, 9307, 9957, 12399, 6055, 1211, 9307, 3660, 4032, 6055, 1211, 9307, 9957, 12399, 8608, 3555, 27884, 4032, 6055, 1211, 9307, 9957, 12399, 6055, 3794, 27884, 4032, 6055, 1211, 9307, 9957, 12399, 36764, 24401, 4032, 5551, 25513, 3615, 9957, 12399, 6055, 1211, 9307, 3660, 4032, 5551, 25513, 3615, 9957, 12399, 5551, 25513, 27884, 4032, 5551, 25513, 3615, 9957], "avg_logprob": -0.09374999873001467, "compression_ratio": 2.8, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 5777.69, "end": 5778.37, "word": "تلاتة", "probability": 0.868408203125}, {"start": 5778.37, "end": 5778.47, "word": " و", "probability": 0.9775390625}, {"start": 5778.47, "end": 5779.61, "word": " عشرين،", "probability": 0.64373779296875}, {"start": 5779.61, "end": 5780.39, "word": " خمسة", "probability": 0.9739990234375}, {"start": 5780.39, "end": 5780.59, "word": " و", "probability": 0.99365234375}, {"start": 5780.59, "end": 5782.03, "word": " عشرين،", "probability": 0.9124755859375}, {"start": 5782.03, "end": 5782.75, "word": " واحد", "probability": 0.990966796875}, {"start": 5782.75, "end": 5782.91, "word": " و", "probability": 0.6865234375}, {"start": 5782.91, "end": 5784.25, "word": " تلاتين،", "probability": 0.9630859375}, {"start": 5784.25, "end": 5784.57, "word": " انه", "probability": 0.413330078125}, {"start": 5784.57, "end": 5785.79, "word": " تلاتين،", "probability": 0.94306640625}, {"start": 5785.79, "end": 5786.41, "word": " تلاتة", "probability": 0.960205078125}, {"start": 5786.41, "end": 5786.51, "word": " و", "probability": 0.95654296875}, {"start": 5786.51, "end": 5787.93, "word": " تلاتين،", "probability": 0.986328125}, {"start": 5787.93, "end": 5788.47, "word": " سبعة", "probability": 0.9679361979166666}, {"start": 5788.47, "end": 5788.67, "word": " و", "probability": 0.9951171875}, {"start": 5788.67, "end": 5790.77, "word": " تلاتين،", "probability": 0.98544921875}, {"start": 5790.77, "end": 5791.49, "word": " تسعة", "probability": 0.9930013020833334}, {"start": 5791.49, "end": 5791.93, "word": " و", "probability": 0.99462890625}, {"start": 5791.93, "end": 5794.11, "word": " تلاتين،", "probability": 0.98515625}, {"start": 5794.11, "end": 5794.63, "word": " واحد", "probability": 0.989990234375}, {"start": 5794.63, "end": 5794.77, "word": " و", "probability": 0.9736328125}, {"start": 5794.77, "end": 5796.79, "word": " أربعين،", "probability": 0.90302734375}, {"start": 5796.79, "end": 5797.51, "word": " تلاتة", "probability": 0.9866943359375}, {"start": 5797.51, "end": 5797.63, "word": " و", "probability": 0.99755859375}, {"start": 5797.63, "end": 5798.97, "word": " أربعين،", "probability": 0.96884765625}, {"start": 5798.97, "end": 5799.75, "word": " أربعة", "probability": 0.88037109375}, {"start": 5799.75, "end": 5800.15, "word": " و", "probability": 0.990234375}, {"start": 5800.15, "end": 5800.73, "word": " أربعين", "probability": 0.961181640625}], "temperature": 1.0}, {"id": 208, "seek": 583140, "start": 5806.04, "end": 5831.4, "text": "المرة القادمة ان شاء الله بنروح لل section اللي بعده حد بتحب تسأل اي سؤال هنا ولا هناك؟ اي تساؤل؟ حول ال domain ال range ال interior ال boundary ال bounded ال unbounded كل الأمور هذه yes؟ فلأ سيبقى للمرة القادمة ان شاء الله", 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"probability": 0.9541015625}, {"start": 5814.1, "end": 5814.26, "word": " ولا", "probability": 0.7587890625}, {"start": 5814.26, "end": 5815.78, "word": " هناك؟", "probability": 0.5413004557291666}, {"start": 5815.78, "end": 5816.94, "word": " اي", "probability": 0.81640625}, {"start": 5816.94, "end": 5818.72, "word": " تساؤل؟", "probability": 0.8285319010416666}, {"start": 5818.72, "end": 5819.56, "word": " حول", "probability": 0.966552734375}, {"start": 5819.56, "end": 5819.7, "word": " ال", "probability": 0.96728515625}, {"start": 5819.7, "end": 5820.08, "word": " domain", "probability": 0.99267578125}, {"start": 5820.08, "end": 5820.42, "word": " ال", "probability": 0.5986328125}, {"start": 5820.42, "end": 5820.9, "word": " range", "probability": 0.93896484375}, {"start": 5820.9, "end": 5821.1, "word": " ال", "probability": 0.9384765625}, {"start": 5821.1, "end": 5821.62, "word": " interior", "probability": 0.802734375}, {"start": 5821.62, "end": 5822.04, "word": " ال", 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/WBeNRZv00d4_raw.srt b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/WBeNRZv00d4_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..c101d879d4932dbf12fb6322af11bb108636cbf0
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/WBeNRZv00d4_raw.srt
@@ -0,0 +1,3336 @@
+1
+00:00:00,000 --> 00:00:02,680
+موسيقى
+
+2
+00:00:10,750 --> 00:00:12,090
+رحمان الله رحمان الله رحمان الله رحمان الله رحمان
+
+3
+00:00:12,090 --> 00:00:12,090
+الله رحمان الله رحمان الله رحمان الله رحمان الله
+
+4
+00:00:12,090 --> 00:00:15,670
+رحمان
+
+5
+00:00:15,670 --> 00:00:15,810
+الله رحمان الله رحمان الله رحمان الله رحمان الله
+
+6
+00:00:15,810 --> 00:00:18,390
+رحمان الله رحمان الله رحمان الله رحمان الله رحمان
+
+7
+00:00:18,390 --> 00:00:32,690
+الله رحمان الله رحمان الله رحمان الله رحمان
+
+8
+00:00:32,690 --> 00:00:38,660
+اللهالنقطة الأولى هو functions of two variables
+
+9
+00:00:38,660 --> 00:00:41,740
+والنقطة الثانية هي functions of
+
+10
+00:00:47,190 --> 00:00:54,290
+النقطة الأولى الدوال في متغيرين والجزء الأخير هو
+
+11
+00:00:54,290 --> 00:01:00,110
+الدوال في ثلاث متغيرات طب كويس بدنا نيجي الآن لل
+
+12
+00:01:00,110 --> 00:01:03,810
+functions of two variables وفي عندى بعض ال
+
+13
+00:01:03,810 --> 00:01:08,890
+definitions الأساسية اللي لازم نعرفها و اللي بدنا
+
+14
+00:01:08,890 --> 00:01:13,220
+نبني دراستنا عليها ان شاء الله تعالىالتعريف الأول
+
+15
+00:01:13,220 --> 00:01:18,280
+بيقول اللي هي point X node و Y node in a region R
+
+16
+00:01:18,280 --> 00:01:24,200
+النقطة الي احداثيها X node و A node في المنطقة R
+
+17
+00:01:24,200 --> 00:01:31,120
+in the XY plane يبقى في المستوى XY is an interior
+
+18
+00:01:31,120 --> 00:01:37,840
+point of R بسميها نقطة داخلية في المنطقة R if it
+
+19
+00:01:37,840 --> 00:01:40,540
+is a center of a disk
+
+20
+00:01:49,480 --> 00:01:58,460
+والذي يقع كليا في المنطقة R يبقى
+
+21
+00:01:58,460 --> 00:02:02,320
+انا لو جيت في المستوى XY يعني في ال plane اللي
+
+22
+00:02:02,320 --> 00:02:06,420
+عندناو روحنا و قولنا هذه المحاور على سبيل المثال
+
+23
+00:02:06,420 --> 00:02:14,980
+هذا محور X هذا محور I وهذه المنطقة التي هي R في
+
+24
+00:02:14,980 --> 00:02:21,820
+عندي نقطة هنا معناها النقطة هذه اللي إحداثيها X
+
+25
+00:02:21,820 --> 00:02:29,990
+node و Y nodeالنقطة دي بسميها interior point إذا
+
+26
+00:02:29,990 --> 00:02:35,270
+لقيتها كانت مركز ل disk وهذا ال disk يقع بأكمله
+
+27
+00:02:35,270 --> 00:02:40,350
+داخل المنطقة R يعني يا بنات لو جينا اتخيلت ال disk
+
+28
+00:02:40,350 --> 00:02:45,950
+بالشكل اللي عندها ده هيك انا رسمته هداني منقط مشان
+
+29
+00:02:45,950 --> 00:02:52,980
+ايه؟ مشان يعرف ان هذا هو ال diskيبقى النقطة X نقطة
+
+30
+00:02:52,980 --> 00:02:58,460
+و Y نقطة بسميها نقطة داخلية إذا جدرت أخليها مركز ل
+
+31
+00:02:58,460 --> 00:03:03,860
+desk و ال desk يقع بأكمله داخل المنطقة بسميها
+
+32
+00:03:03,860 --> 00:03:08,120
+interior point هذا ال first definition نجي لل
+
+33
+00:03:08,120 --> 00:03:11,860
+second definition التعريف الثاني النقطة X نقطة
+
+34
+00:03:11,860 --> 00:03:16,180
+بسميها boundary point of a region
+
+35
+00:03:18,890 --> 00:03:24,190
+حدية يعني نقطة حدية على الحدود الإقليمية يعني ولا
+
+36
+00:03:24,190 --> 00:03:28,250
+تشبيه لو كنا الخط الأخضر ما بيننا و بين اليهود
+
+37
+00:03:28,250 --> 00:03:32,010
+السلك النقطة اللي تقع على السلك هذي بيسميها مين
+
+38
+00:03:32,010 --> 00:03:37,210
+boundary point يبقى باجي بقولك النقطة هذي بسميها
+
+39
+00:03:37,210 --> 00:03:43,070
+boundary point للمنطقة if every disc centered at
+
+40
+00:03:43,560 --> 00:03:50,100
+إذا كان أي disk مركزه كان النقطة هذه ال disk ماله
+
+41
+00:03:50,100 --> 00:03:58,020
+يحتوي على نقاط تقع خارج ال region R as well as
+
+42
+00:03:58,020 --> 00:04:03,520
+points that lies in Rيعني إيش؟ يعني لو عملت disk
+
+43
+00:04:03,520 --> 00:04:08,260
+حوالين هذه النقطة لازم هذا ال disk يحتوي على نقاط
+
+44
+00:04:08,260 --> 00:04:13,360
+تقع داخل المنطقة R و نقاط أخرى تقع وين خارج
+
+45
+00:04:13,360 --> 00:04:17,700
+المنطقة R يعني لو جيت كلت النقطة اللي عندنا هذه
+
+46
+00:04:17,700 --> 00:04:24,920
+على سبيل المثال، كويس؟ لو جيت رسمت حواليها disk،
+
+47
+00:04:24,920 --> 00:04:25,820
+يبقى ال disk
+
+48
+00:04:28,940 --> 00:04:34,700
+Chorus تمام دائرة بس مصممة هذا ال disk احتوى على
+
+49
+00:04:34,700 --> 00:04:39,780
+نقاط داخل المنطقة R اللي همين اللي هي النقاط اللي
+
+50
+00:04:39,780 --> 00:04:45,740
+تقع في المنطقة المظلة لهذه ونقاط أخرى خارج المنطقة
+
+51
+00:04:45,740 --> 00:04:52,540
+R يبقى هذه اسم يا بنات boundary point
+
+52
+00:04:52,540 --> 00:04:55,700
+وهذه
+
+53
+00:04:55,700 --> 00:04:56,820
+النقطة اسمها
+
+54
+00:05:02,520 --> 00:05:17,060
+يبقى هذه النقطة الداخلية يبقى
+
+55
+00:05:17,060 --> 00:05:21,020
+هذه
+
+56
+00:05:21,020 --> 00:05:24,980
+التعريف رقم اتنين
+
+57
+00:05:28,190 --> 00:05:34,430
+النقاط الحدية ليست
+
+58
+00:05:34,430 --> 00:05:42,070
+بالضرورة تكون واقعة داخل المنطقة R ممكن تكون خارج
+
+59
+00:05:42,070 --> 00:05:46,730
+المنطقة R كما سنرى بعد قليل ان شاء الله من خلال
+
+60
+00:05:46,730 --> 00:05:52,620
+الأمثلةيعني هعطيكي مثال ان النقاط الحدي هذه او
+
+61
+00:05:52,620 --> 00:05:57,520
+النقاط اللي على الحدود تقع داخل المنطقة R ومثال
+
+62
+00:05:57,520 --> 00:06:03,960
+اخر نقاط الحدود خارج المنطقة R بعد هيك النقطة
+
+63
+00:06:03,960 --> 00:06:09,100
+التالتة نقول المنطقة R بسميها open منطقة مفتوحة
+
+64
+00:06:09,100 --> 00:06:16,950
+إذا كانت تتكوّل كليا انت يرلي كلياof interior
+
+65
+00:06:16,950 --> 00:06:21,210
+points بالنقاط الداخلية يعني المنطقة بس هي المنطقة
+
+66
+00:06:21,210 --> 00:06:26,750
+مفتوحة إذا كان كل نقطة موجودة في هذه المنطقة هي
+
+67
+00:06:26,750 --> 00:06:35,350
+interior point طيب التعريف اللي بعدبسميها closed
+
+68
+00:06:35,350 --> 00:06:40,710
+إذا احتوت كل ال boundary points إذا احتوت كل ال
+
+69
+00:06:40,710 --> 00:06:44,710
+boundary points تبعتها بسميها a closed region
+
+70
+00:06:44,710 --> 00:06:49,850
+منطقة مغلقة يبقى عرفنا إيش الفرق ما بينهم يبقى ال
+
+71
+00:06:49,850 --> 00:06:55,430
+open region هي المنطقة اللي جميع النقاط تبعتها in
+
+72
+00:06:55,430 --> 00:07:01,880
+terror points لكن ال closed regionهي المنطقة التي
+
+73
+00:07:01,880 --> 00:07:07,020
+تحتوي على كل ال boundary points تبعتها طيب
+
+74
+00:07:07,020 --> 00:07:13,400
+definition أخير هنقسمه إلى نقطتين المنطقة قد تكون
+
+75
+00:07:13,400 --> 00:07:19,680
+bounded يعني محدودة وقد تكون unbounded غير محدودة
+
+76
+00:07:20,180 --> 00:07:24,500
+بجل التعريف الأول بقول ال region R في المستوى is
+
+77
+00:07:24,500 --> 00:07:30,020
+bounded محدودة if it lies inside of a disk of a
+
+78
+00:07:30,020 --> 00:07:34,180
+fixed radius يبقى المنطقة اللي أنا بسميها محدودة
+
+79
+00:07:34,180 --> 00:07:40,940
+لو وقعت بأكملها داخل disk و ال disk نصف قطره معروف
+
+80
+00:07:40,940 --> 00:07:46,870
+ثابت تمام؟ يبقى المنطقة مرة تانيةبقول عنها bounded
+
+81
+00:07:46,870 --> 00:07:52,930
+محدودة إذا جدرت أخلي disk يحتوي عالمين على هذه
+
+82
+00:07:52,930 --> 00:07:59,090
+المنطقة كلها، إذا بسميها إيش؟bounded region طب ايش
+
+83
+00:07:59,090 --> 00:08:04,030
+ال unbounded region اللي ماقدرش احطها داخل ال disk
+
+84
+00:08:04,030 --> 00:08:08,850
+تمام فقاللي ال region are unbounded اذا ماكنتش
+
+85
+00:08:08,850 --> 00:08:12,690
+bounded يعني حطي ال disk اللي جاية تظلة شوية منها
+
+86
+00:08:12,690 --> 00:08:16,590
+و برا كمان disk أكبر من اللي باقي منها و برا و
+
+87
+00:08:16,590 --> 00:08:22,670
+هكذا يبقى ايه لا يمكن اضع المنطقة هذه داخل ال disk
+
+88
+00:08:22,670 --> 00:08:27,800
+الا انتبه عليها الأشكال اللي ممكن تظهرهاهنعطيك بدل
+
+89
+00:08:27,800 --> 00:08:33,680
+الشكل أشكال مُنطَظَمة أو غير مُنطَظَمة، أي شكل من
+
+90
+00:08:33,680 --> 00:08:38,260
+الأشكال سواء كانت هندسية و لا غيرها، لكن شغلنا كله
+
+91
+00:08:38,260 --> 00:08:42,940
+في الـplane، ليس بالضرورة أن يكون شكلا مُنطَظَمة،
+
+92
+00:08:42,940 --> 00:08:50,090
+زي مثلث مختلف الأبضاعهه يبقى هل المثلث المختلف أضع
+
+93
+00:08:50,090 --> 00:08:54,270
+بقدر أجوبه على أي شكل منتظر؟ لأ، لكن بقدر أحط
+
+94
+00:08:54,270 --> 00:08:59,850
+المثلث المختلف أضع داخل this صحيح ولا لا؟ يفجأة
+
+95
+00:08:59,850 --> 00:09:05,570
+بيكون المثلث في هذه الحالة bounded regionمنطقة
+
+96
+00:09:05,570 --> 00:09:10,850
+محدودة و هكذا طيب نعطي أمثلة من الواقع الكلام اللي
+
+97
+00:09:10,850 --> 00:09:15,270
+احنا كاتبينه هذا يبقى هناخد بدل المثال اتنين بدي
+
+98
+00:09:15,270 --> 00:09:30,710
+أوضح الشغل هذه اول مثال يبقى example بيقول
+
+99
+00:09:30,710 --> 00:09:32,170
+لي نمر واحد
+
+100
+00:09:37,360 --> 00:09:45,060
+القطع المستقيم و ال triangles و
+
+101
+00:09:45,060 --> 00:09:49,040
+ال rectangles
+
+102
+00:09:49,040 --> 00:09:54,300
+و
+
+103
+00:09:54,300 --> 00:10:05,920
+ال circles and ال discs كلهم
+
+104
+00:10:05,920 --> 00:10:17,420
+هدولare bounded sets يبقى كلهم مجموعات محدودة in
+
+105
+00:10:17,420 --> 00:10:23,020
+the plane نمر
+
+106
+00:10:23,020 --> 00:10:28,120
+اتنين ال
+
+107
+00:10:28,120 --> 00:10:34,020
+lines خطوط المستقيمة وال coordinate
+
+108
+00:10:37,160 --> 00:10:48,240
+أكسيز محاول الإحداثية والكوادران و
+
+109
+00:10:48,240 --> 00:10:55,440
+ال half a plane و
+
+110
+00:10:55,440 --> 00:11:04,000
+ال half a plane and a planeوالمستويات كلها are
+
+111
+00:11:04,000 --> 00:11:07,920
+unbound
+
+112
+00:11:07,920 --> 00:11:14,680
+sets
+
+113
+00:11:14,680 --> 00:11:17,900
+in
+
+114
+00:11:17,900 --> 00:11:20,100
+the plane
+
+115
+00:11:43,130 --> 00:11:47,350
+مرة تانية المثال
+
+116
+00:11:47,350 --> 00:11:53,290
+بيقول ال line segment يعني القطعة المستقيمة مثل
+
+117
+00:11:53,290 --> 00:11:57,890
+هذا الخط هذا بسميها قطعة مستقيمة هل هي bounded or
+
+118
+00:11:57,890 --> 00:12:02,110
+unbounded بقول بقدر اعمل disk حواليهاإذا هذا إيش؟
+
+119
+00:12:02,110 --> 00:12:05,770
+boundary يبقى هي النقطة الأولى التانية ال
+
+120
+00:12:05,770 --> 00:12:11,150
+triangles المثلثات و أشرنا له لما ستختخلص قبل قليل
+
+121
+00:12:11,150 --> 00:12:17,190
+قلنا لها اه triangles اه ال rectangles المستاطيلات
+
+122
+00:12:17,190 --> 00:12:23,850
+بقدر أعمله داخل disk إذا هذا منطقة محدودة عندك ال
+
+123
+00:12:23,850 --> 00:12:28,670
+circles الدوائر بقدر أعمل disk أكبر منها
+
+124
+00:12:31,530 --> 00:12:36,190
+القرص نفسه بقدر اعمل قرص اكبر منه يبقى هذه كلها
+
+125
+00:12:36,190 --> 00:12:41,350
+مناطق محدودة يبقى هذه bounded sets او bounded
+
+126
+00:12:41,350 --> 00:12:46,970
+regions كله في المستوى طبعا المثال التاني ال lines
+
+127
+00:12:46,970 --> 00:12:52,210
+من وين بيبدأ ال line يا بنات؟ من سنة ب infinity ل
+
+128
+00:12:52,210 --> 00:12:56,870
+infinity طبيعي الشعيعببدأ من عندي ال zero و بضل
+
+129
+00:12:56,870 --> 00:13:03,240
+راشي لوين ل الفرقيبقى هذا ياشي بقدرش أحطه داخل ال
+
+130
+00:13:03,240 --> 00:13:06,740
+disk صحيح ولا لأ ولا الخط المستقيم داخل ال disk
+
+131
+00:13:06,740 --> 00:13:12,560
+كمان ال coordinate axes محاور الإحداثية محور X
+
+132
+00:13:12,560 --> 00:13:18,120
+ومحور Y بمدد لويا لسالب infinity وإلى infinity ال
+
+133
+00:13:18,120 --> 00:13:22,600
+quadrants الأرباع الأربعة صحيح ببدأ من عند ال zero
+
+134
+00:13:22,600 --> 00:13:30,020
+لكن مظل مفتوح إلى ما لا نهايةالـ half plane نص في
+
+135
+00:13:30,020 --> 00:13:34,340
+المستوى كيف نص في المستوى طبعا المستوى برضه ببدأ
+
+136
+00:13:34,340 --> 00:13:38,620
+زي الخطب المستقيم من سلب infinity بنتهي لوين يعني
+
+137
+00:13:38,620 --> 00:13:44,080
+لو عملت plane ما بيقسم الكون اللي احنا عنده اللي
+
+138
+00:13:44,080 --> 00:13:48,160
+احنا فيه إلى نصفين اشي أعلى ال plane و اشي أسفل ال
+
+139
+00:13:48,160 --> 00:13:51,560
+plane او اشي على يمين ال plane و اشي على شمال ال
+
+140
+00:13:51,560 --> 00:13:55,770
+plane يبقى half ال plane نص ال planeومن باب أولى
+
+141
+00:13:55,770 --> 00:14:02,190
+لـ Plain كلهيبقى وماقدرش أحطه داخل disk نهائي و ال
+
+142
+00:14:02,190 --> 00:14:06,870
+plans كلها are unbounded sets يبقى هذه كلها إيش
+
+143
+00:14:06,870 --> 00:14:12,390
+شغلات أو مناطق غير محدودة مفتوحة إلى ما شاء الله
+
+144
+00:14:12,390 --> 00:14:16,150
+وإلى أن يرث الله الأرض ومال عليها لكن احنا كبشر
+
+145
+00:14:16,150 --> 00:14:21,770
+بالنسبة لعلمنا نقول أن هذه unbounded sets يبقى
+
+146
+00:14:21,770 --> 00:14:28,700
+اللي هو مناطق أو مجموعات غير محدودةطيب انت هنا فى
+
+147
+00:14:28,700 --> 00:14:32,100
+الرسم رسمتلنا ال interior point و ال boundary
+
+148
+00:14:32,100 --> 00:14:41,340
+point تمام طيب بتقدر ترسملنا بس نقاط حدية فقط على
+
+149
+00:14:41,340 --> 00:14:45,680
+الرسم يقولك اه بنقدر كيف بنقدر اشتغل فمثلا لو جيت
+
+150
+00:14:45,680 --> 00:14:53,800
+قولتلك هذا المحور هذا محور X وهذا محور Y اعطيتك
+
+151
+00:14:53,800 --> 00:14:59,680
+الآن الصيغة التاليةأنا في عندي علاقة بتقوللي ما
+
+152
+00:14:59,680 --> 00:15:09,550
+يأتي أن ال X تربيع زائد Y تربيع أقل من واحدماذا
+
+153
+00:15:09,550 --> 00:15:17,670
+يعني؟ اذا كانت تساوي واحد فهي دائرة لكن اقل من
+
+154
+00:15:17,670 --> 00:15:23,350
+واحد كل النقاط داخل الدائرة يعني لو جيت رسمت
+
+155
+00:15:23,350 --> 00:15:30,870
+الدائرة اللي مركزها نقطة الأصل و نصف قطرهابسميها
+
+156
+00:15:30,870 --> 00:15:35,790
+بنات unit circle طبعا الرسم تدى مُنَقَض دليل على
+
+157
+00:15:35,790 --> 00:15:42,810
+أن المحيط تبع داره ليس من ضمن المطقع كل النقاط
+
+158
+00:15:42,810 --> 00:15:48,210
+الداخلية اللى عندناهذه سؤال في عندي boundary point
+
+159
+00:15:48,210 --> 00:15:53,030
+هنا مش واضح ان عندي boundary point هو في تمام لكن
+
+160
+00:15:53,030 --> 00:15:59,030
+ايش خارج المنطقة تبعتنا يبقى هذه تمثل كلها ايش
+
+161
+00:15:59,030 --> 00:16:06,470
+interior points يبقى هذه interior points
+
+162
+00:16:07,040 --> 00:16:13,180
+يبقى هذه نقاط داخلية المحيط تبع هذه الداربانات هو
+
+163
+00:16:13,180 --> 00:16:18,320
+ال boundary points لكن هل النقاط هدول من ضمن
+
+164
+00:16:18,320 --> 00:16:23,880
+المنطقة؟ لأ هم حدود اللي صحية لكنهم ليسوا من ضمن
+
+165
+00:16:23,880 --> 00:16:29,940
+المنطقة طب السؤال هو المنطقة المظلة لهذه open
+
+166
+00:16:29,940 --> 00:16:35,090
+region ولا closed region؟طلع فوق، اطلع هنا تحت،
+
+167
+00:16:35,090 --> 00:16:40,270
+يبقى هنا هذه كلها open region يبقى المنطقة اللي
+
+168
+00:16:40,270 --> 00:16:45,930
+عنده هذه كلها open region يبقى المنطقة المظلة لهذه
+
+169
+00:16:45,930 --> 00:16:53,270
+كلها بسميها open region، منطقة مفتوحة، تمام؟ طيب
+
+170
+00:16:53,270 --> 00:16:57,450
+يا بنات، لو قلوا الصيغة الأخرى، انه x تربية
+
+171
+00:17:00,380 --> 00:17:07,600
+أو تساوي واحد كويس يبقى بده صورة أنه ال disk أو
+
+172
+00:17:07,600 --> 00:17:14,100
+الدائرة بالشكل هذا هيك تمام يبقى كل المنطقة
+
+173
+00:17:14,100 --> 00:17:20,940
+المظللة هذه هذا محور X وهذا محور Y كل المنطقة
+
+174
+00:17:20,940 --> 00:17:27,120
+المظللة بما فيها المحيط تمام طيب وين ال boundary
+
+175
+00:17:27,120 --> 00:17:34,070
+point؟اللي هو محيط الدائرة شو يمثلوا؟ يمثلوا X
+
+176
+00:17:34,070 --> 00:17:40,490
+تربية زائد Y تربية تساوي واحد يبقى ال boundary هنا
+
+177
+00:17:40,490 --> 00:17:43,890
+يمثل
+
+178
+00:17:43,890 --> 00:17:50,030
+بالعلاقة X تربية زائد Y تربية يساوي مين؟ واحد اللي
+
+179
+00:17:50,030 --> 00:17:55,670
+هو مين كل ال boundary points طب السؤال هو is it a
+
+180
+00:17:55,670 --> 00:18:02,370
+closed region؟هل هذه منطقة مغلقة؟ نرجع المنطقة
+
+181
+00:18:02,370 --> 00:18:06,530
+المغلقة اللى بتحتوي كل ال boundary points تبعتها
+
+182
+00:18:06,530 --> 00:18:11,470
+احتواتهم للمحيط الدارة كل ال boundary points إذا
+
+183
+00:18:11,470 --> 00:18:17,950
+هذه closed region يبقى هذه النهارد كلها closed
+
+184
+00:18:17,950 --> 00:18:19,110
+region
+
+185
+00:18:21,400 --> 00:18:25,660
+يبقى هذه هي المنطقة المغلقة يبقى المنطقة المغلقة
+
+186
+00:18:25,660 --> 00:18:30,060
+هي المنطقة اللي تحتوي كل ال boundary points تبعتها
+
+187
+00:18:30,060 --> 00:18:36,200
+مفتوحة يبقى اللي بتحتوي عليها كل النقاط الداخلية
+
+188
+00:18:36,200 --> 00:18:41,660
+يبقى هاي الفرق ما بين هذه و هذا طيب نعطي مثال عملي
+
+189
+00:18:41,660 --> 00:18:49,000
+يعني مثال عددي حسابات نحسب الشغلات هذه لسؤال عددي
+
+190
+00:19:14,470 --> 00:19:26,230
+example fine هو الدونا النقطة الأولى the domain
+
+191
+00:19:26,230 --> 00:19:34,370
+of the following functions
+
+192
+00:19:40,020 --> 00:19:47,300
+the interior and
+
+193
+00:19:47,300 --> 00:19:56,100
+the boundary of
+
+194
+00:19:56,100 --> 00:20:03,360
+this domain نقطة
+
+195
+00:20:03,360 --> 00:20:08,320
+تالتة whether
+
+196
+00:20:08,320 --> 00:20:09,160
+the domain
+
+197
+00:20:14,540 --> 00:20:24,940
+هل الدمين مفتوح او مفتوح؟ مفتوح او مفتوح؟ نقطة
+
+198
+00:20:24,940 --> 00:20:32,020
+الرابعة whether the domain is
+
+199
+00:20:32,020 --> 00:20:37,560
+bounded or
+
+200
+00:20:37,560 --> 00:20:42,680
+unbounded or unbounded
+
+201
+00:20:44,210 --> 00:20:51,290
+نبدأ باستخدام
+
+202
+00:20:51,290 --> 00:20:54,930
+جدري التربيهي Fxy
+
+203
+00:21:39,540 --> 00:21:43,360
+بناخد اكثر من ال function كل واحدة من هذه ال
+
+204
+00:21:43,360 --> 00:21:47,280
+functions بدي احسب انها اربعة شغلات المطمئنن الأول
+
+205
+00:21:47,280 --> 00:21:52,480
+بدي احسب ال domain لهذه الدالة اتنين بدي اجيب ال
+
+206
+00:21:52,480 --> 00:21:56,220
+internal و ال boundary لهذا ال domain اللي حصلنا
+
+207
+00:21:56,220 --> 00:22:01,000
+عليه تلاتة بدي اشوف ال domain هل هذا بيكون منطقة
+
+208
+00:22:01,000 --> 00:22:06,320
+مفتوحة ولا منطقة مغلقةبعد هي كده بدي أشوف هل ال
+
+209
+00:22:06,320 --> 00:22:11,160
+domain هذا بيكون bounded ولا unbounded يبقى كله
+
+210
+00:22:11,160 --> 00:22:16,020
+يعتمد على شكل ال domain اللي احنا بدنا نطلعه بجي
+
+211
+00:22:16,020 --> 00:22:22,460
+بقوله بكويس يبقى بجي بقوله domain الـ F منهم كل
+
+212
+00:22:22,460 --> 00:22:30,100
+العناصر X وY بحيث أن القيمة اللي تحت الجدل ناقص 9
+
+213
+00:22:30,100 --> 00:22:36,620
+greater than or equal to 0لأن الجدر مش معرف إلا
+
+214
+00:22:36,620 --> 00:22:43,100
+لقيمة موجبة أو للصفر يبقى هذا الكلام يبدو يساوي كل
+
+215
+00:22:43,100 --> 00:22:48,660
+ال elements x و y such that x تربية زائد y تربية
+
+216
+00:22:48,660 --> 00:22:58,800
+greater than or equal to 9 يعني كل إنقاء اللي لو
+
+217
+00:22:58,800 --> 00:23:05,560
+ربعناه يبدو يتبع المجموع 9 فما هوطب لو حبينا نرسمه
+
+218
+00:23:05,560 --> 00:23:11,100
+معانا الطبيعي نعرف مين هو هذا ال domain هذا محور X
+
+219
+00:23:11,100 --> 00:23:17,420
+هذا محور Y هذه نقطة الأصل اللي هي Zero نروح نقسم
+
+220
+00:23:17,420 --> 00:23:22,780
+الدائرة اللي عندنا هذه يبقى هي الدائرة اللي عندنا
+
+221
+00:23:24,620 --> 00:23:30,240
+طيب كان ال X تربيع زي ال Y تربيع ماله W أكبر من أو
+
+222
+00:23:30,240 --> 00:23:36,780
+يسوء 9 يبقى كل المنطقة اللي خارج الدائرة اللي
+
+223
+00:23:36,780 --> 00:23:44,010
+عندنا هذهبالاضافة إلى رحيط الدائرة بسبب ماذا؟ بسبب
+
+224
+00:23:44,010 --> 00:23:50,450
+وجود اليساوي إذا خلصناه المطلوب الأول يبقى كل
+
+225
+00:23:50,450 --> 00:23:55,810
+المطلوب الأول ال domain كل النقاط outside the
+
+226
+00:23:55,810 --> 00:24:00,450
+circle or on the circle يبقى هذه لو بدي أصيغها
+
+227
+00:24:00,450 --> 00:24:03,170
+بقول all the points
+
+228
+00:24:25,820 --> 00:24:31,600
+كل النقاط اللي على الدائرة هذه أو خارجها هذا ال
+
+229
+00:24:31,600 --> 00:24:34,700
+domain هذا المطموب الأول مطموب التاني
+
+230
+00:24:39,550 --> 00:24:44,410
+الانترال والمقاومة في هذا المجال
+
+231
+00:25:04,350 --> 00:25:08,270
+أقل يعني، يعني داخل الدار، والله صحيح صرنا في
+
+232
+00:25:08,270 --> 00:25:11,750
+الدمان ولا صرنا برا الدمان؟ واش اللي بنايا؟ صح
+
+233
+00:25:11,750 --> 00:25:15,690
+كلامي ولا غلط؟ لإن طول الوقت بدي أكون جوا الدمان،
+
+234
+00:25:15,690 --> 00:25:19,290
+يعني وين؟ يعني في المنطقة المظلة، اللي جوا هذه
+
+235
+00:25:19,290 --> 00:25:23,090
+ماليش داعو فيها، الدمان يا بنات المنطقة المظلة
+
+236
+00:25:23,090 --> 00:25:26,670
+اللي أشرتك عليها بالأزرق هذه، اللي جوا ماليش علاقة
+
+237
+00:25:26,670 --> 00:25:31,980
+فيها، مالك انت جلبت الوضع 180 درجة والله إيهيبقى
+
+238
+00:25:31,980 --> 00:25:35,520
+ال intro كل النقاط اللي موجودة داخل ال domain
+
+239
+00:25:35,520 --> 00:25:41,820
+كتبتلك ال domain كتابة كل النقاط اللي على المحيط و
+
+240
+00:25:41,820 --> 00:25:46,740
+اللي outside الدائرة كامك تخلوه داخل الدائرة هذا
+
+241
+00:25:46,740 --> 00:25:52,400
+كلام غلط مش صحيح يبقى هذا بالنسبة لل domain الآن
+
+242
+00:25:52,400 --> 00:25:58,080
+ال intro تبع من تبع هذا ال domain يبقى باجي بقول
+
+243
+00:25:58,080 --> 00:25:59,060
+ال intro
+
+244
+00:26:03,260 --> 00:26:11,860
+منهم يساوي كل النقاط X وY بحيث ان X تربيها زيد وY
+
+245
+00:26:11,860 --> 00:26:19,240
+تربيها مالها أكبر من تسعة وأقل من ماين من infinity
+
+246
+00:26:19,240 --> 00:26:23,340
+يبقى وانا احنا في المنطقة المضلة اللي هي الزرق
+
+247
+00:26:23,340 --> 00:26:29,260
+اللي برا هذه أكبر من تسعة يبقى برا وضلك ماشي ليه
+
+248
+00:26:29,260 --> 00:26:33,000
+مالها نهايةيبقى هاي ال intro تبع مين؟ تبع ال
+
+249
+00:26:33,000 --> 00:26:36,720
+domain إيش قاللي كمان؟ بد ال boundary تبع ال
+
+250
+00:26:36,720 --> 00:26:40,400
+domain من ال boundary تبع ال domain؟ محمد محمد
+
+251
+00:26:40,400 --> 00:26:42,080
+محمد محمد محمد محمد محمد محمد محمد محمد محمد محمد
+
+252
+00:26:42,080 --> 00:26:42,180
+محمد محمد محمد محمد محمد محمد محمد محمد محمد محمد
+
+253
+00:26:42,180 --> 00:26:46,240
+محمد محمد محمد محمد محمد محمد محمد محمد محمد محمد
+
+254
+00:26:46,240 --> 00:26:46,240
+محمد محمد محمد محمد محمد محمد محمد محمد محمد محمد
+
+255
+00:26:46,240 --> 00:26:46,280
+محمد محمد محمد محمد محمد محمد محمد محمد محمد محمد
+
+256
+00:26:46,280 --> 00:26:52,160
+محمد محمد محمد محمد محمد محمد
+
+257
+00:26:52,160 --> 00:26:58,520
+محمد
+
+258
+00:26:58,520 --> 00:27:05,330
+محميبقى ال boundary تبع ال domain مين هو كل
+
+259
+00:27:05,330 --> 00:27:11,610
+العناصر X وY جهاته ان X تربية وY تربية يساوي 9
+
+260
+00:27:11,610 --> 00:27:16,510
+يبقى
+
+261
+00:27:16,510 --> 00:27:25,250
+كل المحيط تبع من؟ تبع الدائرة يعني لو حبينا نرسمه
+
+262
+00:27:25,250 --> 00:27:30,940
+بنقول هي الدائرة هيكهذا محور X و هذا اللي فوق هو
+
+263
+00:27:30,940 --> 00:27:41,820
+محور Y تمام؟ و الدائرة عندنا هتكون بالشكل هذا يبقى
+
+264
+00:27:41,820 --> 00:27:46,640
+هذه الدائرة اللي عندنا
+
+265
+00:27:46,640 --> 00:27:54,100
+يبقى
+
+266
+00:27:54,100 --> 00:28:00,250
+كل النقاط اللي عندنا هذههي ال boundary point فقط
+
+267
+00:28:00,250 --> 00:28:06,290
+لا غير يبقى هذا هو ال boundary ماليش دعوة النقاط
+
+268
+00:28:06,290 --> 00:28:08,770
+اللي برا الدائرة ولا اللي جوا الدائرة انا على
+
+269
+00:28:08,770 --> 00:28:17,610
+الحدود ايوة علي صوتك شوية خلينا نسمع ال interior
+
+270
+00:28:17,610 --> 00:28:22,330
+points ماشي الحالة بدنا نجيب ال interior points كل
+
+271
+00:28:22,330 --> 00:28:27,040
+النقاط اللتي تقع داخل ال domainحددنا ال domain من
+
+272
+00:28:27,040 --> 00:28:31,320
+أين إلى أين كل
+
+273
+00:28:31,320 --> 00:28:34,900
+النقاط اللي تحقق ال link والتي هذه X تربيها زاد وY
+
+274
+00:28:34,900 --> 00:28:40,080
+تربيها يكون أكبر من أو يسوى التسعة كل المحيط تبع
+
+275
+00:28:40,080 --> 00:28:47,360
+الدائرة اللي عندنا هذه زاد النقاط اللي برا، مظبوط؟
+
+276
+00:28:47,360 --> 00:28:51,860
+مش هذا ال domain؟ طيب، دي النقاط الداخلية لهذا ال
+
+277
+00:28:51,860 --> 00:28:56,810
+domainوليست النقاط الحدية يبقى بدى أستثنى مين
+
+278
+00:28:56,810 --> 00:29:03,310
+المحيط مشان أستثنى المحيط فباجى بقول انتوا رأى كل
+
+279
+00:29:03,310 --> 00:29:07,290
+النقاط اللى عندنا اللى أكبر من تسعة صح ولا لأ
+
+280
+00:29:07,290 --> 00:29:11,130
+لليكسر بيه عزيزي وعزيزي بيكون أكبر من تسعة تسعة
+
+281
+00:29:11,130 --> 00:29:15,210
+بكون احنا على الحدود هنا أكبر من تسعة يبقى برا هنا
+
+282
+00:29:15,210 --> 00:29:17,870
+هذه كلها نقاط داخلية
+
+283
+00:29:22,690 --> 00:29:27,650
+النقاط الحدية طب بيه النقاط الحدية اللي تقع على
+
+284
+00:29:27,650 --> 00:29:33,950
+محيط الدار؟ واضحات ولا لسه؟ مش كتير شايف فبل شو
+
+285
+00:29:33,950 --> 00:29:43,310
+رايك تعالى هنا تعالى بس قومي و ليه الهاجينة تعالى
+
+286
+00:29:43,310 --> 00:29:43,510
+هنا
+
+287
+00:29:51,090 --> 00:29:54,750
+هو قال ليه لعرف مجالك؟ وين ال domain تبعك ده اللي
+
+288
+00:29:54,750 --> 00:29:59,970
+هو ال boundary و ال outside؟ و اللي برا، تمام؟ انا
+
+289
+00:29:59,970 --> 00:30:04,930
+بدي النقاط الداخلية نتقع داخل ال domain، بتقدر
+
+290
+00:30:04,930 --> 00:30:07,770
+تحدديلي وين؟ بيدي، بتقوليلي هنا، بتيجي النقطة
+
+291
+00:30:07,770 --> 00:30:15,110
+الداخلية؟ إذا المجال هو ال boundary و ال outside،
+
+292
+00:30:15,110 --> 00:30:18,970
+from you مافيش داخلية؟ داخل ال domain، ال boundary
+
+293
+00:30:18,970 --> 00:30:27,120
+.. ال control لل domainيبقى داخل الدمين داخل
+
+294
+00:30:27,120 --> 00:30:36,460
+الدمين داخل الدمين داخل الدمين داخل
+
+295
+00:30:36,460 --> 00:30:45,200
+الدمين داخل الدمين داخل الدمين داخل الدمين داخل
+
+296
+00:30:45,200 --> 00:30:51,920
+الدمين داخل الدمين داخل الدمينصحيح ولا لأ يبقى هذه
+
+297
+00:30:51,920 --> 00:31:00,620
+interim point شوفت هناك ماكنتش متأكده تمام دل مصر
+
+298
+00:31:00,620 --> 00:31:05,860
+على داخل ملمون الدائرة هذا كله الأبيض برا الدمين
+
+299
+00:31:05,860 --> 00:31:09,800
+ماليش علاقة فيه داخل
+
+300
+00:31:09,800 --> 00:31:15,000
+الدمين اللي مكتوب عليه داخل الدمين واضحة؟ حد بتسأل
+
+301
+00:31:15,000 --> 00:31:21,180
+تاني؟ انا بتفضلهذا ما اسمه الـ interior points و
+
+302
+00:31:21,180 --> 00:31:23,780
+ال boundary points اللي هو المطلوب رقم اتنين
+
+303
+00:31:23,780 --> 00:31:28,100
+المطلوب رقم تلاتة بيقول whether the domain open or
+
+304
+00:31:28,100 --> 00:31:33,980
+closed هل ال domain هذا open و لا closed تعريف ال
+
+305
+00:31:33,980 --> 00:31:38,740
+closed انه اذا احتوى على كل ال boundary points ال
+
+306
+00:31:38,740 --> 00:31:42,660
+domain هذا احتوى على ال boundary points ولا لا اذا
+
+307
+00:31:42,660 --> 00:31:46,820
+هذا ال domain closed انترى اه closed ريزي يبقى
+
+308
+00:31:46,820 --> 00:31:56,230
+باجي بقوله النقطة التالتةThe domain is
+
+309
+00:31:56,230 --> 00:32:09,850
+an enclosed region is a closed region because
+
+310
+00:32:09,850 --> 00:32:20,190
+it contains all
+
+311
+00:32:23,100 --> 00:32:33,040
+boundary points طيب نقطة الرابعة بيقوللي
+
+312
+00:32:33,040 --> 00:32:37,740
+هل ال domain هذا منطقة محدودة و لا منطقة غير
+
+313
+00:32:37,740 --> 00:32:42,980
+محدودة طبعا ال dialogues اللي بيبقى عليها نقدرش
+
+314
+00:32:42,980 --> 00:32:49,200
+نوصل إليها يبقى هذي إيش بسميها unbounded region
+
+315
+00:32:49,610 --> 00:32:59,590
+يبدأ بالي بقول له that domain is a is an bounded
+
+316
+00:32:59,590 --> 00:33:05,310
+region هذه
+
+317
+00:33:05,310 --> 00:33:12,930
+منطقة مغلقة و الله ايه مغلقة و بس لو محدودة كمان
+
+318
+00:33:12,930 --> 00:33:17,350
+طب هذا نمرى ايه من المثال نمرى ايه لو أخدنا
+
+319
+00:33:17,350 --> 00:33:25,070
+function تانيةالـ function التانية f of x و y يبقى
+
+320
+00:33:25,070 --> 00:33:33,730
+f of x و y تساوي len x ناقص y تربيع على سبيل
+
+321
+00:33:33,730 --> 00:33:38,550
+المثال نجيب
+
+322
+00:33:38,550 --> 00:33:42,770
+الأربع مطالب لهذه الـ function بأول شغلة نجيب main
+
+323
+00:33:42,770 --> 00:33:48,010
+ال domain تبع ال f يبقى النقطة الأولىبدا أخد
+
+324
+00:33:48,010 --> 00:33:55,510
+domain ال F يبقى كل النقاط X وY بحيث أن X ناقص Y
+
+325
+00:33:55,510 --> 00:33:59,670
+تربيع أبصر مالها أكبر من الصفراء أبو ليش أكبر من
+
+326
+00:33:59,670 --> 00:34:05,870
+الصفراء؟ لأن ال لن يا بنات مش معرف إلا لقيمة موجبة
+
+327
+00:34:05,870 --> 00:34:12,010
+و أخدتوا في Calculus B كان منحنا اللن عندكم بالشكل
+
+328
+00:34:12,010 --> 00:34:18,560
+هذا هيك أمام؟يبقى بالشكل اللي عندك هذا هذا محور X
+
+329
+00:34:18,560 --> 00:34:25,440
+هذا محور Y هذا نقطة الأصل وهذا منحنى لين ال X كله
+
+330
+00:34:25,440 --> 00:34:30,760
+بعد Zero وعند Zero بنخسف لوين لسالب Infinity يبقى
+
+331
+00:34:30,760 --> 00:34:35,580
+معنا هذا الكلام بدي هذا المقدار كله يكون ماله أكبر
+
+332
+00:34:35,580 --> 00:34:44,440
+من Zero وإن شرطونا فقولناكل ال X وY such that ال X
+
+333
+00:34:44,440 --> 00:34:52,240
+أكبر من Y تربيع فبدي أسألكوا سؤال و أشوف فهمتوا
+
+334
+00:34:52,240 --> 00:34:56,980
+هذا ولا لا حد فيكم بتقدر يجيب لي نقطة واحدة في ال
+
+335
+00:34:56,980 --> 00:35:01,000
+domain مع الأنه مع الأنه اللي موجود فيه ما لا
+
+336
+00:35:01,000 --> 00:35:06,060
+نهاية من النقاط فتقدروا تجيبوا لي نقطة واحدة داخل
+
+337
+00:35:06,060 --> 00:35:06,860
+هذا ال domain
+
+338
+00:35:11,230 --> 00:35:15,910
+مش هنقدر احدد لما ارسم اعرف وان المنطقة بالضبط بد
+
+339
+00:35:15,910 --> 00:35:21,210
+نقطة داخله تحقق
+
+340
+00:35:21,210 --> 00:35:26,730
+ال inequality واحد و واحد كلام مش صحيح ليه؟ لما
+
+341
+00:35:26,730 --> 00:35:30,970
+احط ال X بواحد يبقى Y بواحد اللي هي اشهر اكبر منها
+
+342
+00:35:30,970 --> 00:35:37,410
+يعني بدك تاخدي قيمتين قيمة X تبقى اكبر من مربع
+
+343
+00:35:37,410 --> 00:35:45,060
+قيمة Y زي مين؟0 و 1 و لا لا و لا واحد واحد و Zero
+
+344
+00:35:45,060 --> 00:35:51,820
+اتنين و واحد يبقى هذه نقطة تالية كلها ب X ب اتنين
+
+345
+00:35:51,820 --> 00:35:55,800
+و Y بواحد لو ربعت Y بطلها واحد و X باتنين يبقى
+
+346
+00:35:55,800 --> 00:36:00,860
+اتنين اكبر من واحد واحد اكبر من Zero و هكذا يبقى
+
+347
+00:36:00,860 --> 00:36:06,720
+طب هذه لو كانت X يساوي Y تربيع X و واحدة لاتيش هذه
+
+348
+00:36:06,720 --> 00:36:11,640
+ترابلة منتاج جدايبقى لو روحت رسمتي ال Parabola
+
+349
+00:36:11,640 --> 00:36:17,600
+تقبل Parabola بهذا الشكل هذا محور X هذا محور Y هذه
+
+350
+00:36:17,600 --> 00:36:24,800
+نقطة الأصل هذا يعني مش Y تساوي X تربيع X تساوي Y
+
+351
+00:36:24,800 --> 00:36:31,220
+تربيع يبقى ال axis هو محور X يبقى لو روحت رسمته
+
+352
+00:36:31,220 --> 00:36:37,060
+ماعنديش مساواة ولذلك حرص مماله منقط بالشكل اللي
+
+353
+00:36:37,060 --> 00:36:43,820
+عندها دايماطيب قال لي X أكبر من أو يساوي Y تربيع
+
+354
+00:36:43,820 --> 00:36:48,940
+أنا مش عارف هي المنطقة اللي داخل البرابله ولا
+
+355
+00:36:48,940 --> 00:36:53,960
+المنطقة اللي خارج البرابلهمظبوط لكن لما اقول دور
+
+356
+00:36:53,960 --> 00:36:59,160
+على نقطة تحقق هذه قالت أخكوا اتنين و واحد و أنا
+
+357
+00:36:59,160 --> 00:37:03,800
+اقترحت واحد و زيرو و ممكن تقترحها مش نقطة ملايين
+
+358
+00:37:03,800 --> 00:37:08,580
+النقاط او مالا نهاية من النقاط لو جينا قولنا نقطة
+
+359
+00:37:08,580 --> 00:37:13,060
+واحد و زيرو اللي أسهل حاجة وين بتيجي ان هي نقطة
+
+360
+00:37:13,060 --> 00:37:17,400
+واحد و زيرو يبقى وين بدها تكون المنطقة اللي وين
+
+361
+00:37:17,400 --> 00:37:21,600
+اللي داخل ال parabola ولا اللي خارجكل المنطقة اللى
+
+362
+00:37:21,600 --> 00:37:30,260
+داخل ال parabola كل المنطقة يعنى طب السؤال هل محيط
+
+363
+00:37:30,260 --> 00:37:36,560
+ال parabola من ضمن ال domain لأ يبقى صار ال domain
+
+364
+00:37:36,560 --> 00:37:45,240
+هذا والله ده area inside the parabola
+
+365
+00:37:47,780 --> 00:37:53,340
+اللي هو main x يساوي y تابع المنطقة اللي داخل
+
+366
+00:37:53,340 --> 00:37:58,040
+البرامولة دي كلها main كلها ال domain طيب نقطة
+
+367
+00:37:58,040 --> 00:38:03,260
+ثانية قال لي مين؟ قال لي بدك تجيبلي ال interior و
+
+368
+00:38:03,260 --> 00:38:07,400
+ال boundary points تبعتي ال domain يبقى ال
+
+369
+00:38:07,400 --> 00:38:15,150
+interior points ها ال interior تبع ال domainيبقى
+
+370
+00:38:15,150 --> 00:38:23,390
+هو كل النقاط x و y بحيث أنها نفس
+
+371
+00:38:23,390 --> 00:38:30,730
+اللي فوق x أكبر من y تربية يعني هذه نقطة داخلية
+
+372
+00:38:30,730 --> 00:38:38,550
+هذه نقطة داخلية مظبوط؟ ليش؟ إن ال disk وقع بأكمله
+
+373
+00:38:38,550 --> 00:38:46,570
+داخل المنطقة وهكذا أي نقطة أخرى تعتبرنقطة داخلية و
+
+374
+00:38:46,570 --> 00:38:53,450
+هكذا طيب هذا ال intro بد ال boundary يبقى بد ال
+
+375
+00:38:53,450 --> 00:38:57,530
+boundary تبع
+
+376
+00:38:57,530 --> 00:39:04,130
+ال domain مين هو ابنها؟ ليه؟ ليها ولا ليها معقول
+
+377
+00:39:04,130 --> 00:39:08,730
+منطقة مايكونش يلها boundary؟ مالهاش حدود؟ فهل تلمس
+
+378
+00:39:08,730 --> 00:39:15,270
+لها مشاعر؟طب اقرب الله لعندك البودري لما انعرفناه
+
+379
+00:39:15,270 --> 00:39:20,470
+و حطينالك عبارة بين قوسين و قولنا لك البودري قد
+
+380
+00:39:20,470 --> 00:39:25,290
+يكون من المنطقة و قد يكون من غير المنطقة صحيح ولا
+
+381
+00:39:25,290 --> 00:39:31,010
+لا؟ في المثال السابق كان البودري اللي عندي مضمن
+
+382
+00:39:31,010 --> 00:39:36,010
+المنطقة لكن البودري هنا ماله؟ من خارج المنطقة على
+
+383
+00:39:36,010 --> 00:39:41,200
+الحدود مباشرةمظبوط ولا لأ؟ هي أعطيتك المثال الأول
+
+384
+00:39:41,200 --> 00:39:45,500
+ال boundary كان من ضمن المنطقة يعني من ضمن ال
+
+385
+00:39:45,500 --> 00:39:49,720
+domain هنا ال boundary ليس من ضمن ال domain يبقى
+
+386
+00:39:49,720 --> 00:39:54,000
+ال boundary the set of all elements x و y such
+
+387
+00:39:54,000 --> 00:39:59,880
+that x يساوي y تربيع اللي هي مين؟ اللي هي المنطقة
+
+388
+00:39:59,880 --> 00:40:07,210
+المنقطة هذه بالضبط يا بنات المنقطة الزرقيةكل هذا
+
+389
+00:40:07,210 --> 00:40:11,350
+اللي هو ال boundary يبقى هذا اللي هو ال boundary
+
+390
+00:40:11,350 --> 00:40:17,610
+لكن ان قطعة ال boundary مش موجودة في ال domain
+
+391
+00:40:17,610 --> 00:40:23,290
+خارج ال domain و كتبتها لك بين قوسين عشان تعرف انه
+
+392
+00:40:23,290 --> 00:40:27,110
+ممكن تكون من ضمن ال domain كما في المثال الأول أو
+
+393
+00:40:27,110 --> 00:40:32,850
+من خارج ال domain كما في المثال الثاني النقطة
+
+394
+00:40:32,850 --> 00:40:37,970
+التالتةقال لي هل ال domain هذا open region و لا
+
+395
+00:40:37,970 --> 00:40:42,410
+closed region قبل أولاني إيش كان في المثال closed
+
+396
+00:40:42,410 --> 00:40:49,090
+يبقى هنا ال domain is
+
+397
+00:40:49,090 --> 00:40:57,390
+an open region قبل إيش open region يبنى؟ لأنه
+
+398
+00:40:57,390 --> 00:41:01,650
+اجتمل كل النقاط الداخلية طيب النقطة الرابعة و
+
+399
+00:41:01,650 --> 00:41:06,660
+الأخيرةو قال لي whether ال domain هذا bounded ولا
+
+400
+00:41:06,660 --> 00:41:14,580
+unbounded انبعض لأنه مفتوح لماء لنهاية بيظل يبقى
+
+401
+00:41:14,580 --> 00:41:24,420
+هنا ال domain is unbound يبقى
+
+402
+00:41:24,420 --> 00:41:28,460
+ماعرف احنا حد بتحب تسأل اي سؤال هنا قبل ما نواصل
+
+403
+00:41:28,460 --> 00:41:31,740
+اي
+
+404
+00:41:31,740 --> 00:41:32,400
+تساؤل
+
+405
+00:42:02,150 --> 00:42:30,310
+مستحالة خلاص هذا مثلا ماكتب عليه لوضعة
+
+406
+00:42:30,310 --> 00:42:37,030
+definition دي لبنانdefinition عن جسمه إلى نقطتين
+
+407
+00:42:37,030 --> 00:42:48,310
+النقطة الأولى the curve المنحلة in a space in
+
+408
+00:42:48,310 --> 00:43:01,430
+which the plane in which the plane z تساوي c cuts
+
+409
+00:43:08,520 --> 00:43:20,320
+السطح z يساوي f of x of y f of x of y is called is
+
+410
+00:43:20,320 --> 00:43:30,340
+called the contour curve contour
+
+411
+00:43:30,340 --> 00:43:31,660
+curve of
+
+412
+00:43:38,120 --> 00:43:48,200
+F of X و Y بدو ساوي C نمرة اتنين The
+
+413
+00:43:48,200 --> 00:43:55,260
+set of points مجموعة
+
+414
+00:43:55,260 --> 00:43:59,300
+النقاط in the domain of F
+
+415
+00:44:07,460 --> 00:44:14,280
+XY Plane XY
+
+416
+00:44:14,280 --> 00:44:19,860
+Plane XY Plane XY Plane XY Plane XY Plane XY Plane
+
+417
+00:44:19,860 --> 00:44:25,540
+XY Plane XY Plane XY Plane XY Plane XY Plane XY
+
+418
+00:44:25,540 --> 00:44:26,240
+Plane XY Plane XY Plane XY Plane XY Plane XY Plane
+
+419
+00:44:26,240 --> 00:44:26,880
+XY Plane XY Plane XY Plane XY Plane XY Plane XY
+
+420
+00:44:26,880 --> 00:44:27,160
+Plane XY Plane XY Plane XY Plane XY Plane XY Plane
+
+421
+00:44:27,160 --> 00:44:27,180
+XY Plane XY Plane XY Plane XY Plane XY Plane XY
+
+422
+00:44:27,180 --> 00:44:27,180
+Plane XY Plane XY Plane XY Plane XY Plane XY Plane
+
+423
+00:44:27,180 --> 00:44:27,260
+XY Plane XY Plane XY Plane XY Plane XY Plane XY
+
+424
+00:44:27,260 --> 00:44:27,260
+Plane XY Plane XY Plane XY Plane XY Plane XY Plane
+
+425
+00:44:27,260 --> 00:44:36,360
+XY Plane XY Plane XY Plane XY Plane XY
+
+426
+00:44:36,360 --> 00:44:36,820
+Plane
+
+427
+00:44:39,750 --> 00:44:53,350
+level curve of f للظلة f نرجع
+
+428
+00:44:53,350 --> 00:44:58,630
+مرة تانية للكلام اللي احنا كاتبينه ونحاول نفهمه
+
+429
+00:44:58,630 --> 00:45:02,790
+جيدا تعريف
+
+430
+00:45:02,790 --> 00:45:10,860
+الأول هو the curve in spaceالمنحنى في الفرار in
+
+431
+00:45:10,860 --> 00:45:17,460
+which the plane z يساوي c يعني z يساوي مقدار ثابت
+
+432
+00:45:17,460 --> 00:45:22,140
+cuts the surface بيرفع على السطح z يساوي f of x وy
+
+433
+00:45:22,140 --> 00:45:26,500
+is called the contour curve contour curve يعني
+
+434
+00:45:26,500 --> 00:45:31,160
+المنحنى المحيط منحنى المحيط
+
+435
+00:45:35,460 --> 00:45:42,160
+بمعنى اخر لما اجيب المنحنة z يساوي c و اقطع
+
+436
+00:45:42,160 --> 00:45:47,060
+المنحنة بصير المستوى هذا و ال surface اللي عنده
+
+437
+00:45:47,060 --> 00:45:51,910
+اشتراكوا مع بعض في نفس النقارإذا ما بشيل ال f of x
+
+438
+00:45:51,910 --> 00:45:57,490
+و y هذه و بحط بدلها c يعني صار ال z تساوي c أو f
+
+439
+00:45:57,490 --> 00:46:02,110
+of x و y يساوي c بيصارت منطقة مشتركة ما بين
+
+440
+00:46:02,110 --> 00:46:07,270
+المستوى و ال surface هذه المنطقة بيسميها مين ال
+
+441
+00:46:07,270 --> 00:46:14,470
+contourCare تمام كيف هذا الكلام وقولك اه لو جينا
+
+442
+00:46:14,470 --> 00:46:20,650
+تخيلنا ان احنا عندنا المحاور التلاتة هذا محور X
+
+443
+00:46:20,650 --> 00:46:30,870
+هذا محور Y و هذا محور Z تمام و جينا رسمنا اي مجسم
+
+444
+00:46:30,870 --> 00:46:36,050
+any surface في الفرح فكان المجسم على سبيل المثال
+
+445
+00:46:36,050 --> 00:46:37,430
+بهذا الشكل
+
+446
+00:46:42,060 --> 00:46:47,400
+فرضي عندي مجسم بهذا الشكل يبقى هذا مجسم موجود في
+
+447
+00:46:47,400 --> 00:46:52,940
+الفرقات جيت قاطعته بمستوى وين المستوى اللي قاطعته
+
+448
+00:46:52,940 --> 00:46:57,640
+فيه هجعل المستوى بالشكل هذا طبعا من ناحية تانية مش
+
+449
+00:46:57,640 --> 00:47:05,360
+هيظهر و هيجيني هك بالشكل هذا المستوى هذا هو
+
+450
+00:47:05,360 --> 00:47:12,240
+المستوى المظلن الشكل اللي عندناقطع المجسم في curve
+
+451
+00:47:12,240 --> 00:47:16,500
+وين ال curve اللي قطعوا فيه؟ قطعوا في ال curve هذا
+
+452
+00:47:16,500 --> 00:47:23,800
+مثلا المنحنى اللي عندك يبقى هذا الجزء بيكون ظاهر
+
+453
+00:47:23,800 --> 00:47:29,640
+هذا بيكون في الناحية التانية بيضاليش فبيكون منقطع
+
+454
+00:47:29,640 --> 00:47:34,840
+تمام؟ يبقى هذا هو اللي بيسميه ال contour curve
+
+455
+00:47:34,840 --> 00:47:42,750
+يبقى هذا الخطاللي يشفيه الدائرة طبعا ليس بالضرورة
+
+456
+00:47:42,750 --> 00:47:47,190
+أن يكون دائرة حسب شكل المجسم اللي عندي هذا اللي هو
+
+457
+00:47:47,190 --> 00:47:52,310
+بسميه contour curve
+
+458
+00:47:52,310 --> 00:47:57,810
+يعني المنحنة اللي أجى على محيط main ال surface
+
+459
+00:47:57,810 --> 00:48:05,390
+نتيجة لقطعها اللي هو mainالمجسم هذا بالـ plane Z
+
+460
+00:48:05,390 --> 00:48:12,170
+تساوي C وإن Z تساوي C يبقى هذا النقطة يساوي C يبقى
+
+461
+00:48:12,170 --> 00:48:20,610
+هذا الـ plane Z يساوي C طيب هذا التعريف الأول
+
+462
+00:48:20,610 --> 00:48:24,850
+التعريف التاني مش بقول ليه The set of points in
+
+463
+00:48:24,850 --> 00:48:30,370
+the domain of F وين دمية دلنا F يا بنات؟لما أقول z
+
+464
+00:48:30,370 --> 00:48:38,450
+يساوي f of x و y أين يقع ال domain؟ حاجة بتعرف؟
+
+465
+00:48:38,450 --> 00:48:44,750
+بديش شكلها بدي أقول بيها في أي مستوى يعني z تساوي
+
+466
+00:48:44,750 --> 00:48:54,090
+f of x و y surface بدي ال domain تابع في المنطقة
+
+467
+00:48:54,090 --> 00:48:58,450
+اللي مقطوعة فوقأبو ايش رأيك باقي المجسم هذا اللي
+
+468
+00:48:58,450 --> 00:49:04,410
+تحت والمجسم اللي فوق وين مجاله بدي يكون؟ يعني
+
+469
+00:49:04,410 --> 00:49:12,170
+القيم اللتي تاخدها X وY يعني مين بيكون؟
+
+470
+00:49:12,170 --> 00:49:15,870
+بس
+
+471
+00:49:15,870 --> 00:49:21,610
+يعني الدمير بيطلع فوق، في نصه مثلا صحيح هذا
+
+472
+00:49:21,610 --> 00:49:24,810
+الكلام؟ يا بنت الحلال بقولك ايه
+
+473
+00:49:28,040 --> 00:49:33,920
+وين بيجوا X و Y هدول؟ في الـ X Y plane يا أخ سارة
+
+474
+00:49:33,920 --> 00:49:40,580
+يبقى الرسم هذه وين مجالها؟ X و Y و بطلع Z فوق يبقى
+
+475
+00:49:40,580 --> 00:49:45,340
+ال X و Y بيكونوا المجال تبعها هو في الـ X Y plane
+
+476
+00:49:45,340 --> 00:49:50,500
+أيوة، إيش قاللي؟ النقاط اللي موجودة في ال domain
+
+477
+00:49:50,500 --> 00:49:53,440
+تبع الدلة F يعني في المستوى
+
+478
+00:50:00,110 --> 00:50:04,970
+which in which بحيث ان f of x y بدي اسوي constant
+
+479
+00:50:04,970 --> 00:50:10,170
+c is called the level curve of f طب وين ال level
+
+480
+00:50:10,170 --> 00:50:14,330
+curve بالظبط في هذه الحلقة بقول شايف المقطع ال
+
+481
+00:50:14,330 --> 00:50:18,390
+contour يا بنات هذا بدي أسقطه على ال domain يبقى
+
+482
+00:50:18,390 --> 00:50:23,050
+لو جيت أسقطه على ال domain إيش بصير عندي بصير هي
+
+483
+00:50:23,050 --> 00:50:29,660
+من هنا بدي أنزل رأسي هنا و بدي أنزل رأسي هنااللي
+
+484
+00:50:29,660 --> 00:50:41,920
+هو هذا يبقى هذا اسمه level curve طب ايش يعني معناه
+
+485
+00:50:41,920 --> 00:50:52,360
+level curve منحنى المنسوب level curve المناسبة
+
+486
+00:50:52,360 --> 00:51:02,370
+على أي حال؟بعض الكتب أو بعض المؤلفين لا يفرق بين
+
+487
+00:51:02,370 --> 00:51:05,970
+ال control و level care، بعتبره اتنين واحد،
+
+488
+00:51:05,970 --> 00:51:10,390
+الاكتاب المؤلف تبعده Thomas Galler قال هذا بسميه
+
+489
+00:51:10,390 --> 00:51:14,870
+خط ال control و هذا بسميه level care، control بدي
+
+490
+00:51:14,870 --> 00:51:18,310
+اصطفه على ال domain تبع الدالة، يعني على المستوى
+
+491
+00:51:18,310 --> 00:51:22,430
+XY planeالمنحنى اللى بيطلع يبقى هذا هو اللى بيسميه
+
+492
+00:51:22,430 --> 00:51:26,490
+level care السؤال هو طب أحصل عليه كيف؟ بيقولك
+
+493
+00:51:26,490 --> 00:51:31,030
+بسيطة جدا حط F وFx وY يسووا كونستان فبتعرف أيه
+
+494
+00:51:31,030 --> 00:51:37,050
+الشكل ال level care طبعا طيب يبقى هذه المعلومات
+
+495
+00:51:37,050 --> 00:51:42,730
+اللى كتبناها بدنا نحاول ناخدها عمليا او نحسبها
+
+496
+00:51:42,730 --> 00:51:47,490
+عمليا مشان نثبت هذه المعلومة يبقى example
+
+497
+00:51:54,050 --> 00:52:03,910
+find the level curves for the following surfaces
+
+498
+00:52:03,910 --> 00:52:15,010
+for the following surfaces نمر
+
+499
+00:52:15,010 --> 00:52:29,930
+A بد ال F of X و Y بد يساويهو X تربيع زائد تسعة Y
+
+500
+00:52:29,930 --> 00:52:37,410
+تربيع مرة
+
+501
+00:52:37,410 --> 00:52:43,030
+تانية جالي هات لي liver curves لكل من المرحلات
+
+502
+00:52:43,030 --> 00:52:47,170
+التالية وراها طالي اللي هو الملحدة اللي قدامك إذا
+
+503
+00:52:47,170 --> 00:52:48,370
+الحل كان تاني
+
+504
+00:52:52,730 --> 00:52:57,390
+بنجيب له level يبقى automatic بتروح تحط دلق يسوي
+
+505
+00:52:57,390 --> 00:53:05,470
+constant C يبقى ماجي بيقولوا the level curves are
+
+506
+00:53:05,470 --> 00:53:13,490
+in the form بالشكل التالي اللي هم مين X تربيع زي
+
+507
+00:53:13,490 --> 00:53:17,890
+التسعة Y تربيع يسوي constant C
+
+508
+00:53:25,960 --> 00:53:30,840
+مش بيصير واحد صحيح X تربيع علي C تربيع زي تسعة و
+
+509
+00:53:30,840 --> 00:53:35,540
+ات تربيع علي C تربيع يساوي واحد ممتاز جدا يبقى
+
+510
+00:53:35,540 --> 00:53:39,560
+level curve في هذه الحالة أوي level curves بدها
+
+511
+00:53:39,560 --> 00:53:43,520
+أصير ellipses مختلفة طب حبيت نرسم هما دول و نتعرف
+
+512
+00:53:43,520 --> 00:53:46,660
+عليهم يبقى هدول يمثلولي
+
+513
+00:53:49,840 --> 00:53:55,800
+يبقى هذا قطوع ناقصة لو حبيت اعرفها هذه بالضبط فبجي
+
+514
+00:53:55,800 --> 00:54:01,380
+بقول حط C الرقم اللي عجبك و بيطلعك S اللي هو level
+
+515
+00:54:01,380 --> 00:54:08,200
+curve الأول فبجي بقول لو كانت ال C تساوي Zero then
+
+516
+00:54:08,200 --> 00:54:18,800
+that level curveS لو كانت C تساوي Zero يبقى بصير X
+
+517
+00:54:18,800 --> 00:54:23,980
+تربيه زائد تسعة أو تربيه يساوي Zero صح؟ متى يحدث
+
+518
+00:54:23,980 --> 00:54:28,300
+ذلك؟ ال origin يبقى بصير ال level curve هو نقطة
+
+519
+00:54:28,300 --> 00:54:34,360
+الأصل بصير عندنا ال level curve لو قلت هي المحاور
+
+520
+00:54:34,360 --> 00:54:43,260
+هيك بدي يكون هو نقطة الأصل هذا محور Xوهذا محور Y
+
+521
+00:54:43,260 --> 00:54:51,520
+طيب لو أخدت ال C يا بنات في واحد مثلة يبقى F C
+
+522
+00:54:51,520 --> 00:54:57,480
+تساوي واحد the level curve S حط ال C بواحد ايش
+
+523
+00:54:57,480 --> 00:55:07,160
+بصير ال ellipse اللي هو من ال ellipse شو
+
+524
+00:55:07,160 --> 00:55:15,060
+معادلة هذهلي X تربيع زي تسعة Y تربيع يساوي واحد
+
+525
+00:55:15,060 --> 00:55:21,000
+طيب ال major axis او ال focal axis هو محور X ولا
+
+526
+00:55:21,000 --> 00:55:26,040
+محور Y سمعت
+
+527
+00:55:26,040 --> 00:55:31,400
+جبتات سمعت محور X ومحور Y كيف بنحكم ان ال major
+
+528
+00:55:31,400 --> 00:55:36,620
+axis تبع ال ellipseحسب المقام الأولي أكبر يبقى هذا
+
+529
+00:55:36,620 --> 00:55:42,020
+لما أقرأها إيش بيصير X تربيه على واحد زاد Y تربيه
+
+530
+00:55:42,020 --> 00:55:47,880
+على التسعة بده سوى قدرش واحد يبقى مين الأكبر مقام
+
+531
+00:55:47,880 --> 00:55:53,080
+ال X ولا مقام ال Y الواحد صحيح ولا التسعة
+
+532
+00:55:55,560 --> 00:56:01,260
+يبقى ال module axis هو محور X يبقى لو روحت رسمت ال
+
+533
+00:56:01,260 --> 00:56:11,120
+ellipse بدي يكون ال ellipse عندنا بشكل هذا كمان
+
+534
+00:56:11,120 --> 00:56:20,380
+طيب لو جينا قولنا F ال C تسوى تلاتة مثلا يبقى بدي
+
+535
+00:56:20,380 --> 00:56:26,510
+يكون كمان ellipseالمعادلة تبعت X تربية زي تسعة Y
+
+536
+00:56:26,510 --> 00:56:31,650
+تربية تساوي تلاتة او ان شئ تنفقه ل X تربية على
+
+537
+00:56:31,650 --> 00:56:38,030
+تلاتة زي تلاتة Y تربية يسوى قداش واحد يعني X تربية
+
+538
+00:56:38,030 --> 00:56:42,930
+على تلاتة زي ال Y تربية على تولد يسوى برضه اللي هو
+
+539
+00:56:42,930 --> 00:56:48,330
+X يبقى بده يصير اكبر منه بس بالشكل اللي عندنا هذا
+
+540
+00:56:48,330 --> 00:56:58,250
+هيك يبقى يا بناتهذه اللي هو C تساوي Zero وهذه اللي
+
+541
+00:56:58,250 --> 00:57:04,850
+هو C تساوي واحد وهذه اللي هو C تساوي تلتة كلهم
+
+542
+00:57:04,850 --> 00:57:11,730
+هذول level curves عند قيم مختلفة لمين لـC يبقى هذه
+
+543
+00:57:11,730 --> 00:57:20,160
+level curves طيب نمر بيه من السؤالنمر بيه من
+
+544
+00:57:20,160 --> 00:57:30,600
+السؤال لو أخدنا ال F of X و Y F of X و Y تساوي X
+
+545
+00:57:30,600 --> 00:57:36,520
+زائد Y ترميه بدي
+
+546
+00:57:36,520 --> 00:57:44,520
+ال level curves لهذا المنحنة بقوله فضطرنا X زائد Y
+
+547
+00:57:44,520 --> 00:57:52,400
+ترميه بيساوي constant Cأو ال X يساوي سالب Y تربيع
+
+548
+00:57:52,400 --> 00:57:59,400
+زايد كونستان سي برابولة
+
+549
+00:57:59,400 --> 00:58:05,000
+ممتاز جدا أيوة يعني هذا البرابولة لو روحت رسمته
+
+550
+00:58:05,000 --> 00:58:11,820
+بياخد الشكل التالي هذا محور X و هذا محور Yالأصل
+
+551
+00:58:11,820 --> 00:58:17,340
+هذا اللي هو x يساوي y تربيه مفتوح جهة اليمين لكن
+
+552
+00:58:17,340 --> 00:58:23,580
+لما صار صالب y تربيه مفتوح جهة الشمال طيب بدي أجيب
+
+553
+00:58:23,580 --> 00:58:28,240
+ال level curves في هذه الحالة بجي بقوله لو كانت ال
+
+554
+00:58:28,240 --> 00:58:38,370
+c تساوي zero يبقى بجي بقوله هنا that level curveX
+
+555
+00:58:38,370 --> 00:58:48,370
+يساوي سالب Y تربية X يساوي سالب Y تربية X
+
+556
+00:58:48,370 --> 00:58:57,050
+يساوي سالب Y تربية X يساوي سالب Y تربية X يساوي
+
+557
+00:58:57,050 --> 00:59:04,570
+سالب Y تربية X يساوي سالب Y تربية X يساوي سالب Y
+
+558
+00:59:04,570 --> 00:59:12,340
+تربيةزي اكس تساوي السالق وي تربيع زي واحد يبقى شو
+
+559
+00:59:12,340 --> 00:59:18,140
+بده اعمله shift للخلف بمقدار واحد يعني جهة كل يمين
+
+560
+00:59:18,140 --> 00:59:22,320
+بده يجي هنا اللي هو المين واحد يجيك ال parabola
+
+561
+00:59:22,320 --> 00:59:29,140
+بالشكل هذا يبقى هذا حصلنا عليه عند c تساوي zero
+
+562
+00:59:29,140 --> 00:59:35,500
+هذا حصلنا عليه عند c تساوي كداش واحدلو كانت C
+
+563
+00:59:35,500 --> 00:59:39,580
+تساوي تلاتة زي اللي فوق او اتنين او اربع او عشرة
+
+564
+00:59:39,580 --> 00:59:45,020
+او زي ما بده يبقى هنا F C تساوي اتنين
+
+565
+00:59:54,040 --> 00:59:59,940
+شفت للخلف مقدار اتنين يبقى ده حصل عليه لما C تساوي
+
+566
+00:59:59,940 --> 01:00:06,640
+اتنين ومعادلته X تساوي سالب Y تربيع زائد اتنين
+
+567
+01:00:06,640 --> 01:00:15,320
+اللي في المص هذا X تساوي سالب Y تربيع زائد واحدأى
+
+568
+01:00:15,320 --> 01:00:20,120
+رقم قد يكون موجب قد يكون سالب ماعنديش مشكلة اي نعم
+
+569
+01:00:20,120 --> 01:00:24,660
+اى رقم يجى فى بالك يبقى هدول كلهم مارسمتش اني
+
+570
+01:00:24,660 --> 01:00:29,000
+المنحنية تبانات انا رسمت ال level curve وليس
+
+571
+01:00:29,000 --> 01:00:33,580
+الدالة الأصلية هذا مش رسمة الدالة الأصلية هذا مسقط
+
+572
+01:00:33,580 --> 01:00:39,220
+ال contour على ال XY plane لحظة اخد كله XY يبقى
+
+573
+01:00:39,220 --> 01:00:43,480
+هذا مين هذا الرسم اللى تحت السودا فى مسألتنااللي
+
+574
+01:00:43,480 --> 01:00:47,340
+هو مسقط ال control line قد يكون ellipse قد يكون
+
+575
+01:00:47,340 --> 01:00:51,760
+parabola قد يكون hyperabola قد يكون circle قد يكون
+
+576
+01:00:51,760 --> 01:00:55,740
+مربع قد يكون متوازي أطلع حسب نوعية ال surface اللي
+
+577
+01:00:55,740 --> 01:01:01,560
+عندي يبقى حسب المجسم اللي موجود عندك طب هذا حكينا
+
+578
+01:01:01,560 --> 01:01:06,320
+على functions of two variables بدأ نتقل إلى النقطة
+
+579
+01:01:06,320 --> 01:01:09,260
+الأخيرة وهي functions of three variables
+
+580
+01:01:12,860 --> 01:01:16,700
+ننتقل الآن إلى النقطة الأخيرة من هذا الsection وهي
+
+581
+01:01:16,700 --> 01:01:21,300
+الـ functions of three variables أقرب تعريف أخدناه
+
+582
+01:01:21,300 --> 01:01:25,440
+قبل قليل كان الـ Linear Curve فلو دالة فيه ثلاث
+
+583
+01:01:25,440 --> 01:01:29,920
+متغيرات، ماذا بدى يسمي الودالة لو سميتها
+
+584
+01:01:29,920 --> 01:01:34,480
+بـconstant C؟ هذا موضوع الـ definition التالف بكل
+
+585
+01:01:34,480 --> 01:01:40,870
+set of points X وY وZ، مجموعة النقاط في الفرقوالـ
+
+586
+01:01:40,870 --> 01:01:45,590
+F of X وY بدل سوى C يعني سونا الدالة كلها بكونستان
+
+587
+01:01:45,590 --> 01:01:49,390
+C وC ده بالأول مقدار ثابت is called a level
+
+588
+01:01:49,390 --> 01:01:53,930
+surface لدالة F يبقى إذا الدالة في متغيرين و
+
+589
+01:01:53,930 --> 01:01:59,030
+سوناها بكونستان اسمه level curve تطلع منحنى لكن
+
+590
+01:01:59,030 --> 01:02:02,850
+إذا كان في ثلاث متغيرات تطلع عندنا main surface
+
+591
+01:02:02,850 --> 01:02:07,610
+فبالتالي بيسمي main level surface هنوريكي كيف نحسب
+
+592
+01:02:07,610 --> 01:02:17,010
+هذا الكلام عمليامن خلال الأمثلة يبقى example قول
+
+593
+01:02:17,010 --> 01:02:26,590
+find and sketch find and sketch أوجد و أرسم the
+
+594
+01:02:26,590 --> 01:02:35,590
+level surfaces of
+
+595
+01:02:35,590 --> 01:02:48,950
+theFollowing Functions F of
+
+596
+01:02:48,950 --> 01:02:57,710
+X O Y بدأت ساوي لم F تعيقظ X تربيع زاد Y تربيع زاد
+
+597
+01:03:14,840 --> 01:03:20,940
+يبقى نتقل الان الى الدالة فيه ثلاث متغيرات بدنا
+
+598
+01:03:20,940 --> 01:03:24,680
+نحسب ال level surface لهذه الدالة اللى قدامنا يبقى
+
+599
+01:03:24,680 --> 01:03:28,820
+الدالة f of x y و z لإن x تربيه زاد و اتربيه زاد z
+
+600
+01:03:28,820 --> 01:03:33,580
+تربيه يبقى بنسوى الدالة هذا الميان بكون constant c
+
+601
+01:03:33,580 --> 01:03:35,200
+يبقى solution
+
+602
+01:03:39,050 --> 01:03:48,510
+the level surfaces are لن
+
+603
+01:03:48,510 --> 01:03:55,910
+X تربيع زائد Y تربيع زائد Z تربيع كل هذا الكلام
+
+604
+01:03:55,910 --> 01:04:02,790
+يدوي سوية constant C ممكن أن أعيد صياغتها رفعنا كل
+
+605
+01:04:02,790 --> 01:04:05,710
+واحد منه كأس للعدد A
+
+606
+01:04:17,030 --> 01:04:25,630
+EOC يبقى هذا الشكل العام لمن؟ لل level surfaces طب
+
+607
+01:04:25,630 --> 01:04:31,190
+مين تعرف تقولي هذا شو بنسميه ال surface اللي
+
+608
+01:04:31,190 --> 01:04:34,430
+عندنا، شو اسمه هذا؟ من هالمعادلة في المرضى،
+
+609
+01:04:34,430 --> 01:04:41,720
+ellipsoid؟ المقامات زي بعضالانفصايد اذا ال a سواء
+
+610
+01:04:41,720 --> 01:04:47,260
+ال b سواء ال c انفصايد اذا ال a سواء ال b سواء ال
+
+611
+01:04:47,260 --> 01:04:55,200
+c انفصايد اذا ال a سواء ال b سواء ال c انفصايد اذا
+
+612
+01:04:55,200 --> 01:04:56,680
+ال a سواء ال b سواء ال c
+
+613
+01:05:05,210 --> 01:05:10,870
+ليش؟ لأن الـ E أُسها ده رقم عادى جد ما يكون اتنين،
+
+614
+01:05:10,870 --> 01:05:15,230
+تلاتة، عشرة، مية، جد ما يكون طيب، خلّيني أتعالى
+
+615
+01:05:15,230 --> 01:05:23,570
+نحسبها في الحالات المختلفة بني بقول F C تساوي زيوت
+
+616
+01:05:23,570 --> 01:05:28,150
+يبقى ده sphere S
+
+617
+01:05:41,480 --> 01:05:52,980
+Level Surface of the sphere التي هي الكرة X تربية
+
+618
+01:05:52,980 --> 01:05:59,640
+زائد Y تربية زائد Z تربية تساوي E O Zero E O Zero
+
+619
+01:05:59,640 --> 01:06:04,820
+كده؟ اف واحد يبقى هي كرة نصف قطر هي يساوي كده؟
+
+620
+01:06:04,820 --> 01:06:06,200
+واحد الصحيح
+
+621
+01:06:19,380 --> 01:06:23,800
+زيد ويه الترفيه زيد زي الترفيه يسوى اتنين وسبعة من
+
+622
+01:06:23,800 --> 01:06:30,280
+عشر طب لو حبينا نبصمهم على الطبيعة باجي بقول هي
+
+623
+01:06:30,280 --> 01:06:42,480
+المحاور هذا محور X هذا محور Y هذا محور Z أنا عندي
+
+624
+01:06:42,480 --> 01:06:49,000
+كرةمركزها نقطة الأصل و نصف قطر يبقى ساوي كداش واحد
+
+625
+01:06:49,000 --> 01:06:57,620
+صحيح يبقى الكرة هتكون بهذا الشكل لبعد
+
+626
+01:06:57,620 --> 01:07:02,260
+اتنين والسبعة من عشرة يبقى بدها تيجي عندك سفير
+
+627
+01:07:02,260 --> 01:07:14,590
+بهذا الشكل يبقى هنا هذي سي تساوي واحدهذه C تساوي 0
+
+628
+01:07:14,590 --> 01:07:24,030
+يبقى هذا ال levels يعني كأنها كرة داخل كرة طيب
+
+629
+01:07:24,030 --> 01:07:28,850
+هذا النقطة الأولى النقطة الثانية نمرأ بين
+
+630
+01:07:33,930 --> 01:07:43,730
+و Y و Z تساوي Z تربيع ناقص X تربيع ناقص Y تربيع
+
+631
+01:07:43,730 --> 01:07:58,090
+على سبيل المثال طيب
+
+632
+01:07:58,090 --> 01:08:02,250
+بده أجيب ال level surfaces يبقى الشباج بقول
+
+633
+01:08:04,800 --> 01:08:11,420
+زي تربية ناقص X تربية ناقص Y تربية يساوي constant
+
+634
+01:08:11,420 --> 01:08:17,060
+C أو
+
+635
+01:08:17,060 --> 01:08:28,660
+زي تربية يساوي X تربية زي Y تربية زي constant C ده
+
+636
+01:08:28,660 --> 01:08:37,160
+يقول لو كانت الـC تساوي Zero يبقى دهlevel surface
+
+637
+01:08:37,160 --> 01:08:45,960
+is شو بده يصير z تربية بيساوي x تربية زائد y تربية
+
+638
+01:08:45,960 --> 01:08:50,580
+عدم الذاكرة معادلة ايش هذه من المعادلات الستة
+
+639
+01:08:50,580 --> 01:08:56,060
+مخروط بس المقطع تبعه عبارة عن دارة يبقى circular
+
+640
+01:08:56,060 --> 01:09:02,500
+cone يبقى هذا circular cone
+
+641
+01:09:05,000 --> 01:09:11,980
+إذا المخروط دائري المقطع هذا النقطة الحللونة حلال
+
+642
+01:09:11,980 --> 01:09:18,400
+تانية لو كانت C مثلا تساوي واحد يبقى بده يصير عندك
+
+643
+01:09:18,400 --> 01:09:29,400
+مين the level surface is ز
+
+644
+01:09:29,400 --> 01:09:37,640
+تربيع بيساوي X تربيةزائد واي تربيع زائد واحد ها
+
+645
+01:09:37,640 --> 01:09:42,780
+يالا حدا من الذكرة المعادلة؟ مبتده Circular
+
+646
+01:09:42,780 --> 01:09:51,620
+Paraboloid ايوه Circular Paraboloid ممتاز جدا يبقى
+
+647
+01:09:51,620 --> 01:09:58,680
+high paraboloid of two sheets يبقى هذا اسمه high
+
+648
+01:09:58,680 --> 01:10:02,220
+paraboloid
+
+649
+01:10:03,210 --> 01:10:11,390
+up to sheets او
+
+650
+01:10:11,390 --> 01:10:20,370
+لو حبينا نرسم هذا الكلام بقول اه خد المحور هذا
+
+651
+01:10:20,370 --> 01:10:31,210
+محور X هذا محور Y هذا محور Z بتاجي للمخروجبتعرف
+
+652
+01:10:31,210 --> 01:10:36,350
+وين المحور تبع المخروط برجع للمعادلة اللي عندنا
+
+653
+01:10:36,350 --> 01:10:40,710
+يبقى z في ناحية يبقى المحور هو محور z يبقى ال
+
+654
+01:10:40,710 --> 01:10:46,410
+circular يبقى بيكون على شكل ايه دائرة بالشكل هذا
+
+655
+01:10:46,410 --> 01:10:50,730
+يبقى هذا دائرة و ليست ellipse ليش ان احنا في
+
+656
+01:10:50,730 --> 01:10:56,390
+الفرار ارسم يبقى بديجيك الخط هذا بالشكل هذا و
+
+657
+01:10:56,390 --> 01:10:58,950
+بديجيك الخط التاني بالشكل هذا
+
+658
+01:11:04,750 --> 01:11:09,130
+هذا هو المخروط
+
+659
+01:11:09,130 --> 01:11:15,170
+اللي عندنا يبقى هذا هو المخروط اللي معادله Z تربيه
+
+660
+01:11:15,170 --> 01:11:20,310
+تسوى X تربيه زي Y تربيه اللي هو ال level surface
+
+661
+01:11:20,310 --> 01:11:26,910
+الأول طب بدنا نجي لل level surface التاليبرضه
+
+662
+01:11:26,910 --> 01:11:32,170
+المحور تبعه main هو محور z يبقى بده يجيك وين في
+
+663
+01:11:32,170 --> 01:11:42,410
+الداخل عنده بهذا الشكل طبعا
+
+664
+01:11:42,410 --> 01:11:48,130
+انا سافضله بخط الأزرق التاني بده يكون وين زيه بس
+
+665
+01:11:48,130 --> 01:11:58,650
+وين بس لفوق شوية هذا هيكو هذا هيك و هنا هيك و هذا
+
+666
+01:11:58,650 --> 01:12:02,310
+هيك
+
+667
+01:12:02,310 --> 01:12:09,830
+يبقى هذا اللي هو ال high paraboloid of two sheets
+
+668
+01:12:09,830 --> 01:12:19,590
+هذا مع هذا اللي هو ال high paraboloid of two
+
+669
+01:12:19,590 --> 01:12:20,970
+sheets
+
+670
+01:12:59,110 --> 01:13:04,450
+طب ناخد مثال عام على level curve و level surfaces
+
+671
+01:13:04,450 --> 01:13:10,390
+example يقول
+
+672
+01:13:10,390 --> 01:13:18,610
+find an equation find an equation هتلنا معادلة for
+
+673
+01:13:18,610 --> 01:13:27,410
+a level curve أو for the level curve level curve
+
+674
+01:13:27,410 --> 01:13:36,590
+orlevel surface level surface
+
+675
+01:13:36,590 --> 01:13:40,330
+فاصز
+
+676
+01:13:40,330 --> 01:13:49,370
+اثرور فاصز اثرور والذي يمر من خلال the given
+
+677
+01:13:49,370 --> 01:13:57,770
+points النقاط المعطاة for the following functions
+
+678
+01:13:57,770 --> 01:14:07,930
+orthe following functions للدوران التالية نمر A F
+
+679
+01:14:07,930 --> 01:14:17,170
+of X Y F of X Y تساوي اللي هو ستة عشر ناقص X تربيع
+
+680
+01:14:17,170 --> 01:14:24,130
+ناقص Y تربيع نمر B طبعا والنقطة المعطاعة اللي هي
+
+681
+01:14:24,130 --> 01:14:34,200
+النقطة اتنين جدر اتنينوجذر اتنين نمر بإيه؟ الـ G
+
+682
+01:14:34,200 --> 01:14:41,420
+of X أو Y أو Z يسوى الـ summation من N equal zero
+
+683
+01:14:41,420 --> 01:14:47,780
+to infinity لل X زائد Y to the power N على N
+
+684
+01:14:47,780 --> 01:14:58,490
+factorial KZ to the power Mهي لن اتنين ولن اربع
+
+685
+01:15:30,510 --> 01:15:37,110
+عليه بالكم يا اولى بنات نعطيني مثلتين و بيقوللي في
+
+686
+01:15:37,110 --> 01:15:41,210
+كل واحدة فيهم هتلي المناسب اذا كان liver tail او
+
+687
+01:15:41,210 --> 01:15:45,730
+liver cell بيقوللي ماشي بدي اجي للنقطة الاولى نمر
+
+688
+01:15:45,730 --> 01:15:51,870
+ايه؟ بدي احطه f of x و y بدي احطه constant c هذا
+
+689
+01:15:51,870 --> 01:15:54,570
+معناته ايش؟ معناته انه صدر
+
+690
+01:15:57,580 --> 01:16:03,220
+زائد ناقص Y تربيع كله بيديه ساوية منين؟ من وسط
+
+691
+01:16:03,220 --> 01:16:09,680
+الـC أو بتنقل هدول هناك X تربيع زائد Y تربيع
+
+692
+01:16:09,680 --> 01:16:16,160
+بيساوية 16 ناقص C قال المنحنة هذا يا مربو نقطة
+
+693
+01:16:16,160 --> 01:16:20,290
+منين؟إتنين جدر اتنين و جدر اتنين إذا انا هشيل ال X
+
+694
+01:16:20,290 --> 01:16:23,450
+و أحط مكانها اتنين جدر اتنين و اشيل ال Y و أحط
+
+695
+01:16:23,450 --> 01:16:29,390
+مكانها جدر اتنين يبقى اتنين جدر اتنين لكل تربيع
+
+696
+01:16:29,390 --> 01:16:35,690
+زائد جدر اتنين لكل تربيع بسوى ستة عشر ناقصي هذا
+
+697
+01:16:35,690 --> 01:16:42,470
+بدي يعطينا طبعا هذا كده شبنات تمانية زائدإتنين بدر
+
+698
+01:16:42,470 --> 01:16:48,210
+ساوي ستة عشر ناقص C هذا بدي أعطيك انه C to sell
+
+699
+01:16:48,210 --> 01:16:55,470
+هذه عشر تمام جيبي هذه عندها بدر قداش ناقص ستة إذا
+
+700
+01:16:55,470 --> 01:17:02,610
+C تساوي ستة يبقى صار عند هذا level service ولا
+
+701
+01:17:02,610 --> 01:17:09,090
+level care بمناطق لأن ال bus متغيرين وليس تلاتة as
+
+702
+01:17:26,160 --> 01:17:34,040
+يبقى هذا اللي بال curve is a circle طيب نمر بيه
+
+703
+01:17:34,040 --> 01:17:39,500
+بتحط summation من n equal zero to infinity
+
+704
+01:18:06,700 --> 01:18:11,760
+أخدنا مفكوك تايلور و مفكوك ماكلوري ماكلور سيريز و
+
+705
+01:18:11,760 --> 01:18:16,880
+تايلور سيريز تمام؟ و أخدته أول مثال في ماكلور
+
+706
+01:18:16,880 --> 01:18:23,620
+سيريز اللي هو E أُس X قالت إيش؟ اللي X to the
+
+707
+01:18:23,620 --> 01:18:29,560
+power N على N factorialمظبوط؟ إذا تحكم او تذكر او
+
+708
+01:18:29,560 --> 01:18:35,040
+تعلم شغل زي ذلك يبقى لما أجي أطلع X to the power
+
+709
+01:18:35,040 --> 01:18:40,320
+of N على N factorial يبقى هذي كده E أُس X إذا هذي
+
+710
+01:18:40,320 --> 01:18:49,300
+مين؟ E أُس X زائد Y على Z يبقى هذا المنحنى، مظبوط
+
+711
+01:18:49,300 --> 01:18:54,560
+او لا؟ طيب هذا المنحنى فيه ثلاث متغيرات يبقى هذا
+
+712
+01:18:54,560 --> 01:19:05,260
+يريد يعطيناthe level surface is مين هو E أُس X
+
+713
+01:19:05,260 --> 01:19:12,980
+زائد Y على Z يسوى كونستان C عظم الكلكة ع الشغل هيك
+
+714
+01:19:12,980 --> 01:19:19,520
+شوية طب ده نفكر كعتها شو رايح ناخد لله الطرفين إذا
+
+715
+01:19:19,520 --> 01:19:27,230
+لو خدت لله الطرفين تصير X زائد Y على Zبدو يسوى لن
+
+716
+01:19:27,230 --> 01:19:34,010
+C من المعادلة هذه بقدر أجيب قدر C من خلال إحداثيات
+
+717
+01:19:34,010 --> 01:19:42,630
+النقطة تبقى لن 2 زائد لن الأربعة على تلاتة بدو
+
+718
+01:19:42,630 --> 01:19:52,300
+يسوى لن C هذا شو بيعطينا هذا بيبقى 2 لن 2يبقى
+
+719
+01:19:52,300 --> 01:19:58,320
+بيصير تلاتة لن اتنين على تلاتة يسوى لن سي فهذا
+
+720
+01:19:58,320 --> 01:20:04,800
+معناته ان لن اتنين يسوى لن سي يبقى سي تسوى جداش
+
+721
+01:20:04,800 --> 01:20:14,200
+تسوى اتنين يبقى باجي بقوله the level surfaces are
+
+722
+01:20:14,200 --> 01:20:24,860
+in the form في الشكل التاليE أس X زائد Y على C على
+
+723
+01:20:24,860 --> 01:20:35,360
+Z يساوي كده يساوي اتنين او اللي هو X زائد Y على Z
+
+724
+01:20:35,360 --> 01:20:44,480
+يساوي لان اتنين او إذا تحطيها في شكل آخرز يسوى
+
+725
+01:20:44,480 --> 01:20:51,520
+واحد على لن اتنين في ال X زائد ال one يبقى هذا شكل
+
+726
+01:20:51,520 --> 01:20:56,900
+ال level surface في هذه الحالة آخر نقطة عندنا في
+
+727
+01:20:56,900 --> 01:21:02,600
+هذا ال section اللي هو بعض التعريفات some
+
+728
+01:21:02,600 --> 01:21:05,420
+definitions
+
+729
+01:21:18,490 --> 01:21:24,090
+تعريف الأول نعرف التعريفات اللي عرفناهم على
+
+730
+01:21:24,090 --> 01:21:33,510
+الـplane نعرفهم على الـspace يبقى a point بـx
+
+731
+01:21:33,510 --> 01:21:36,110
+نوض و y نوض و z نوض
+
+732
+01:21:39,650 --> 01:21:51,510
+and interior point نقطة داخلية of a region a على
+
+733
+01:21:51,510 --> 01:22:02,330
+منطقة a in a space في الفرق if
+
+734
+01:22:02,330 --> 01:22:06,050
+it
+
+735
+01:22:06,050 --> 01:22:06,530
+is
+
+736
+01:22:11,580 --> 01:22:23,420
+the center of a solid ball كرة مغنقة و كرة مصمة
+
+737
+01:22:23,420 --> 01:22:35,240
+that lies that lies entirely كلياً
+
+738
+01:22:35,240 --> 01:22:47,410
+in اللي هي upنمر اتنين a point x نون و y نون و z
+
+739
+01:22:47,410 --> 01:22:58,430
+نون is a boundary point is a boundary point يبقى
+
+740
+01:22:58,430 --> 01:23:08,090
+هذه نقطة حدية of R if every
+
+741
+01:23:09,820 --> 01:23:28,920
+أسفير F
+
+742
+01:23:28,920 --> 01:23:35,900
+over أسفير مركز على
+
+743
+01:23:35,900 --> 01:23:45,750
+X نوت وY نوتwas it not contains
+
+744
+01:23:45,750 --> 01:23:53,850
+points that
+
+745
+01:23:53,850 --> 01:24:01,430
+lie outside
+
+746
+01:24:01,430 --> 01:24:08,290
+of
+
+747
+01:24:09,290 --> 01:24:17,890
+are as well as
+
+748
+01:24:17,890 --> 01:24:30,390
+points that
+
+749
+01:24:30,390 --> 01:24:33,790
+lie
+
+750
+01:24:33,790 --> 01:24:37,510
+inside
+
+751
+01:25:03,320 --> 01:25:16,360
+أولى ثلاثة The integral of R is
+
+752
+01:25:16,360 --> 01:25:22,260
+the set
+
+753
+01:25:22,260 --> 01:25:28,200
+of all integral points
+
+754
+01:25:40,640 --> 01:25:51,840
+المقاومات المقاومات من R من R هي مجموعة من
+
+755
+01:25:51,840 --> 01:25:53,700
+المقاومات المقاومات
+
+756
+01:26:05,270 --> 01:26:21,290
+of points of a أخر حاجة أربعة a region a region is
+
+757
+01:26:21,290 --> 01:26:33,950
+open منطقة مفتوحة if it is consists if it consists
+
+758
+01:27:00,260 --> 01:27:08,140
+هي مدينة داخلية
+
+759
+01:27:13,840 --> 01:27:20,380
+منطقة مغلقة if it
+
+760
+01:27:20,380 --> 01:27:30,300
+contains its entire
+
+761
+01:27:30,300 --> 01:27:36,320
+boundary
+
+762
+01:27:36,320 --> 01:27:37,180
+points
+
+763
+01:28:04,190 --> 01:28:19,530
+فإن ال demand of f of x, y و z يساوي لن x ناقص
+
+764
+01:28:19,530 --> 01:28:26,570
+اتنين y زائد تلاتة z ناقص ستة
+
+765
+01:28:57,290 --> 01:29:03,030
+النقطة التانية كانت ال control of the boundary
+
+766
+01:29:03,030 --> 01:29:15,850
+while the control كان boundary of
+
+767
+01:29:15,850 --> 01:29:19,570
+the domain
+
+768
+01:29:33,770 --> 01:29:44,890
+مفتح او مغلق مفتوح او
+
+769
+01:29:44,890 --> 01:29:53,590
+مغلق او
+
+770
+01:29:53,590 --> 01:29:55,710
+مفتوح
+
+771
+01:30:19,890 --> 01:30:23,270
+لو رجعت ال definitions هدول هما نفس ال definitions
+
+772
+01:30:31,710 --> 01:30:35,430
+بعد ما كنت أقول desk بدأت أقول هنا سفير بدل ما كنت
+
+773
+01:30:35,430 --> 01:30:41,450
+أقول نقطة بإحداثية بدأت أقول نقطة بثلاث إحداثية
+
+774
+01:30:41,450 --> 01:30:46,450
+بثلاثة إحداثيات فقط لغاية تبقى لما أتي بجديد كل
+
+775
+01:30:46,450 --> 01:30:50,090
+الكلام اللي عتيجي النص عندك بسفيري desk حطي بدل
+
+776
+01:30:50,090 --> 01:30:53,950
+سفير النقطة إحداثية تخلي بالها مكان هاياش تلاتي
+
+777
+01:30:53,950 --> 01:30:59,020
+أبقى لما نأتي نقول باقي كله زي ما هوطيب نحسب هذا
+
+778
+01:30:59,020 --> 01:31:02,900
+الكلام عمليا نعطي دلّه و نقول هاتلي ال domain تبع
+
+779
+01:31:02,900 --> 01:31:09,820
+الدلّه اللي عنها انا باشي بقوله domain الدلّه Fهو
+
+780
+01:31:09,820 --> 01:31:15,020
+مين؟ كل العناصر X وY وZ يعني كل النقاط X وY وZ
+
+781
+01:31:15,020 --> 01:31:21,100
+طبعا الـ Lin مش معرفة إلا لقيمة مجبة بحيث أن X
+
+782
+01:31:21,100 --> 01:31:29,100
+ناقص اتنين Y زائد تلاتة Z ناقص ستة بديها أكبر من
+
+783
+01:31:29,100 --> 01:31:36,720
+مين؟ من Zero أو إن شئتم فقولواx و y و z such that
+
+784
+01:31:36,720 --> 01:31:44,160
+x نقص اتنين y زي التلاتة z اكبر من مين اكبر من
+
+785
+01:31:44,160 --> 01:31:49,460
+zero طب بدأ اعرف من هالمنطقة هذه هذه بنات معادلتاش
+
+786
+01:31:49,460 --> 01:31:55,560
+لو قلت تسوي ستة ليه؟ تمام يعني انا لو روحت جدلا
+
+787
+01:31:55,560 --> 01:31:58,900
+رسمت المحاول بالشكل اللي قدامنا هذا
+
+788
+01:32:07,080 --> 01:32:13,020
+و روحت و قلت ما هي المحاور هذا
+
+789
+01:32:13,020 --> 01:32:20,580
+X وهذا Y وهذا Z و جاءت و قلت المستوى اللي عندنا هو
+
+790
+01:32:20,580 --> 01:32:26,140
+Y و Z و Zero بس هال X بقداش؟ ب6 يبقى لو جيت و قلت
+
+791
+01:32:26,140 --> 01:32:34,430
+النقطة هذي 6 و Zero و Zeroحط X و Z هو Zero بصير Y
+
+792
+01:32:34,430 --> 01:32:40,470
+بسالب تلاتة يعني لو مديتها على استقامته فتصير هذه
+
+793
+01:32:40,470 --> 01:32:47,770
+اللي هو Zero و سالب تلاتة و Zero حط X و Y ب Zero
+
+794
+01:32:47,770 --> 01:32:53,510
+بصير Z باتنين يفجر النقطة اللي عندك هذه Zero و
+
+795
+01:32:53,510 --> 01:32:59,710
+Zero و اتنين الان لو جيت وصلفي مابين النقاط هذه
+
+796
+01:32:59,710 --> 01:33:08,410
+التلاتة بهذا الشكل اكبر
+
+797
+01:33:08,410 --> 01:33:15,230
+من 6 يبقى كل space اللي أعلى من هذا ال plane يعني
+
+798
+01:33:15,230 --> 01:33:21,270
+كل المنطقة اللي عندك هذه كل جزء من الفرار اللي
+
+799
+01:33:21,270 --> 01:33:26,790
+أعلى هذا المثلث يبقى هنا ليه space؟
+
+800
+01:33:29,100 --> 01:33:36,340
+أو الـ half space above
+
+801
+01:33:36,340 --> 01:33:46,840
+the E plane اللي هو من X نقص اتنين Y زائد تلاتة Z
+
+802
+01:33:46,840 --> 01:33:52,480
+يسوى ستة كل الفرق طيب هل ال E plane من ضمن هذه
+
+803
+01:33:52,480 --> 01:33:58,100
+المنطقة؟ لأ مش من ضمنها ماعنديش مساواة خلصنا منه
+
+804
+01:33:58,390 --> 01:34:02,950
+هذه النقطة الأولى اللي هو ال domain طيب النقطة
+
+805
+01:34:02,950 --> 01:34:07,690
+الثانية جالي هذا ال domain ال interior و ال
+
+806
+01:34:07,690 --> 01:34:11,990
+boundary لهذا ال domain ال interior تبع هذا ال
+
+807
+01:34:11,990 --> 01:34:17,350
+domain اللي ويله ويله يا بنات من عند ال plane هذا
+
+808
+01:34:17,350 --> 01:34:25,200
+لغاية ما لنهاية يبقى ال interiorتبع هذا ال domain
+
+809
+01:34:25,200 --> 01:34:33,840
+كل العناصر x و y و z بحيث ان ال x نقص اتنين y زائد
+
+810
+01:34:33,840 --> 01:34:43,640
+تلاتة z بدها تكون اكبر من 100 من 6 يعني كأن ال x
+
+811
+01:34:43,640 --> 01:34:50,640
+نقص اتنين y زائد تلاتة z اكبر من 6 و اقل من 100 من
+
+812
+01:34:50,640 --> 01:34:55,270
+infinityهذا من المطلوب التاني اللي هو الانقرار ال
+
+813
+01:34:55,270 --> 01:35:03,150
+boundary من ال boundary؟ اللي هو ال plane يبقى ال
+
+814
+01:35:03,150 --> 01:35:07,670
+boundary is
+
+815
+01:35:07,670 --> 01:35:16,970
+the plane اللي هو x نقص اتنين y زي التلاتة z يسوي
+
+816
+01:35:16,970 --> 01:35:19,590
+ستة طيب النقطة التالتة
+
+817
+01:35:22,870 --> 01:35:26,950
+قال لي هل ال domain open و لا closed؟ open أنه
+
+818
+01:35:26,950 --> 01:35:34,150
+احتوى كل ال interior points يبقى ال domain of that
+
+819
+01:35:34,150 --> 01:35:42,030
+domain is open ليش؟ أنه احتوى كل ال interior
+
+820
+01:35:42,030 --> 01:35:46,670
+points النقطة الرابعة والاخيرة قال لي هل ال domain
+
+821
+01:35:46,670 --> 01:35:50,740
+bounded or unbounded؟طبعا واضح انه بيظل لوين الى
+
+822
+01:35:50,740 --> 01:36:00,100
+مدى نهاية يبقى unbounded domain الان بدنا منك ال
+
+823
+01:36:00,100 --> 01:36:07,040
+exercises التالي يبقى exercises اربعتاشر واحد
+
+824
+01:36:07,040 --> 01:36:14,560
+المسائل التالية تلاتة خمسة سبعة تسعة احداشر
+
+825
+01:36:14,560 --> 01:36:16,900
+تسعتاشر
+
+826
+01:36:17,690 --> 01:36:24,570
+تلاتة و عشرين، خمسة و عشرين، واحد و تلاتين، انه
+
+827
+01:36:24,570 --> 01:36:31,930
+تلاتين، تلاتة و تلاتين، سبعة و تلاتين، تسعة و
+
+828
+01:36:31,930 --> 01:36:40,150
+تلاتين، واحد و أربعين، تلاتة و أربعين، أربعة و
+
+829
+01:36:40,150 --> 01:36:40,730
+أربعين
+
+830
+01:36:46,040 --> 01:36:49,900
+المرة القادمة ان شاء الله بنروح لل section اللي
+
+831
+01:36:49,900 --> 01:36:58,720
+بعده حد بتحب تسأل اي سؤال هنا ولا هناك؟ اي تساؤل؟
+
+832
+01:36:58,720 --> 01:37:03,560
+حول ال domain ال range ال interior ال boundary ال
+
+833
+01:37:03,560 --> 01:37:09,760
+bounded ال unbounded كل الأمور هذه yes؟ فلأ سيبقى
+
+834
+01:37:09,760 --> 01:37:11,400
+للمرة القادمة ان شاء الله
+
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/XhdO8919qXw.srt b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/XhdO8919qXw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..bbc84dd3228eb766e7ef97acf4f3ab4a965fc14d
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/XhdO8919qXw.srt
@@ -0,0 +1,2756 @@
+1
+00:00:00,000 --> 00:00:02,680
+موسيقى
+
+2
+00:00:12,980 --> 00:00:17,380
+يبقى يا بنات إحنا كنا بنتكلم في الـ sections
+
+3
+00:00:17,380 --> 00:00:21,940
+الماضية عن الـ double integrals يبقى تكاملين
+
+4
+00:00:21,940 --> 00:00:25,620
+أخذنا التكاملين الاتنين دول في الـ Cartesian
+
+5
+00:00:25,620 --> 00:00:30,760
+coordinates وكذلك في الـ polar coordinates الآن من
+
+6
+00:00:30,760 --> 00:00:36,440
+التكاملين سنتقل إلى ثلاث تكاملات في الإحداثيات
+
+7
+00:00:36,440 --> 00:00:41,760
+الكارتيزية وكذلك سنشير إلى إحداثيات جديدة لم نكن
+
+8
+00:00:41,760 --> 00:00:46,360
+نعرفها من قبل إن شاء الله تعالى لكن هذا الـ section
+
+9
+00:00:46,360 --> 00:00:52,060
+اللي هو 15-5 سيتكلم عن التكاملات الثلاثية في
+
+10
+00:00:52,060 --> 00:00:53,240
+الإحداثيات
+
+11
+00:00:55,540 --> 00:01:00,000
+يبقى triple integrals in rectangular coordinates
+
+12
+00:01:00,000 --> 00:01:06,320
+التكاملات الثلاثية في الإحداثيات الكارتيزية أو في
+
+13
+00:01:06,320 --> 00:01:10,760
+الإحداثيات المستطيلة rectangular  إذن لما
+
+14
+00:01:10,760 --> 00:01:13,740
+أقول إحداثيات مستطيلة أو إحداثيات كارتيزية
+
+15
+00:01:13,740 --> 00:01:20,240
+الاثنين are the same طيب بيقول هنا volume V الحجم
+
+16
+00:01:20,240 --> 00:01:22,700
+V of a closed bounded region
+
+17
+00:01:26,650 --> 00:01:30,190
+عندي حجم باجي بقول the volume of a closed
+
+18
+00:01:30,190 --> 00:01:36,350
+bounded region D in space  V بيساوي triple
+
+19
+00:01:36,350 --> 00:01:41,550
+integrals على المنطقة دي بالنسبة لدي V طبعا دي V
+
+20
+00:01:41,550 --> 00:01:46,670
+هي مناطق دي Dx Dy Dz أو Dz Dy Dx اللي هم التلاتة
+
+21
+00:01:46,900 --> 00:01:51,020
+مضروبات في بعض باختصار بيقول إحنا DV زي ما في
+
+22
+00:01:51,020 --> 00:01:55,200
+حالة الـ double integral بيقول دي إيه لكن دي إيه
+
+23
+00:01:55,200 --> 00:02:00,760
+بفهمنا دي اكس دي واي أو دي واي دي اكس السؤال هو
+
+24
+00:02:00,760 --> 00:02:04,280
+how to evaluate the triple integrals يعني كيف بدنا
+
+25
+00:02:04,280 --> 00:02:10,340
+نعرف نحسب التكاملات الثلاثية بقوله بسيطة ثلاث
+
+26
+00:02:10,340 --> 00:02:13,800
+خطوات لها خطوة الأولى
+
+27
+00:02:41,250 --> 00:02:48,170
+الخطوة الثانية بتقول sketch the projection R of the
+
+28
+00:02:48,170 --> 00:02:53,210
+solid on the XY plane يبقى المجسم اللي عندي فوق ده
+
+29
+00:02:53,210 --> 00:02:57,190
+أسقطه على مين؟ على مستوى الـ X والـ Y يبقى بتظهر رسمة
+
+30
+00:02:57,190 --> 00:03:01,570
+فين؟ في الـ plane  ظهرت إن الرسمة في الـ plane
+
+31
+00:03:01,570 --> 00:03:05,930
+لما أشوف الـ X من وين ل وين متغير والـ Y من وين ل وين
+
+32
+00:03:05,930 --> 00:03:18,230
+وبالتالي حددت حدود التكامل من هنا بتحدد حدود
+
+33
+00:03:18,230 --> 00:03:25,790
+التكامل على المجال A تمام يبقى الخطوة الثانية
+
+34
+00:03:25,790 --> 00:03:34,490
+اتنين حددنا حدود التكامل بالنسبة لكل من X و Y خطوة
+
+35
+00:03:34,490 --> 00:03:39,950
+الثالثة كما كنا بنكامل في الـ sections الماضية
+
+36
+00:03:39,950 --> 00:03:44,770
+integrated as in the previous sections
+
+37
+00:03:51,860 --> 00:03:58,180
+المنطقة دي  للفولوم dx dy dz هي عبارة عن تكاملين
+
+38
+00:03:58,180 --> 00:04:02,440
+على R وأول حاجة بيقول إن أنا بكامل بالنسبة لـ
+
+39
+00:04:02,440 --> 00:04:07,140
+z يبقى بروح بكامل الدالة بالنسبة لـ z وبعوض بحدود
+
+40
+00:04:07,140 --> 00:04:12,920
+التكامل بصير المثل لكل دالة  لـ x و y يعني اتخلصنا
+
+41
+00:04:12,920 --> 00:04:16,540
+من قصة z بالمرة نهائيا وما ظِل عندي إلا تكامل بالنسبة
+
+42
+00:04:16,540 --> 00:04:21,800
+لـ x و y بكامل زي ما كنت بكامل في الـ sections الماضية
+
+43
+00:04:21,800 --> 00:04:25,620
+إذن أفضل بالنسبة لـ x بروح بكامل بالنسبة لـ x إذا مش
+
+44
+00:04:25,620 --> 00:04:29,680
+أفضل بروح بكامل بالنسبة لـ y وهكذا إني أحتاج تغيير
+
+45
+00:04:29,680 --> 00:04:36,400
+بروح بغير وهكذا آخر نقطة نظرية في هذا الـ section
+
+46
+00:04:36,400 --> 00:04:40,320
+بيقول اللي بدك تجيبه هي عن القيمة المتوسطة للدالة
+
+47
+00:04:40,320 --> 00:04:46,180
+the average value أو معدل الدالة f of x و y على
+
+48
+00:04:46,180 --> 00:04:51,980
+منطقة التكامل دي بعرفها إنها واحد على الـ volume
+
+49
+00:04:51,980 --> 00:04:56,880
+بتاع الـ D والتكاملات على الـ D للدالة function
+
+50
+00:04:56,880 --> 00:05:02,280
+اللي عندنا يبقى لما نأتي بجديد تلات تكاملات كما هي اللي
+
+51
+00:05:02,280 --> 00:05:07,600
+هو المنطقة دي بروح أكاملها وهكذا، يبقى هي دي اللي
+
+52
+00:05:07,600 --> 00:05:11,280
+بيحصل عندنا، اللي هو الكلام اللي قلناه بدنا نبدأ
+
+53
+00:05:11,280 --> 00:05:19,470
+نطبقه عاملين نحسب اللي قدامنا هذا تكامل على x لديه z
+
+54
+00:05:19,470 --> 00:05:24,550
+dy dx طبعا الـ z هتتغير من تلاتة لأربعة ناقص x تربيع
+
+55
+00:05:24,550 --> 00:05:29,430
+ناقص y الـ y هتتغير من zero لواحد ناقص x تربيع الـ x
+
+56
+00:05:29,430 --> 00:05:33,450
+هتتغير من وين لوين؟ من zero لغاية واحد
+
+57
+00:05:38,730 --> 00:05:43,370
+مقدار ثابت يبقى هذا الكلام بده يساوي integration
+
+58
+00:05:43,370 --> 00:05:49,030
+من zero لواحد integration من zero لـ ناقص x تربيع الـ
+
+59
+00:05:49,030 --> 00:05:55,650
+x مقدار ثابت ما بنعوضش تكامل dz ب z من عندي تلاتة
+
+60
+00:05:55,650 --> 00:05:59,090
+لغاية أربعة ناقص x تربيع ناقص y
+
+61
+00:06:03,470 --> 00:06:09,810
+يبقى هذا الكلام يساوي تكامله من 0 لـ 1 من 0 لـ 1 ناقص x
+
+62
+00:06:09,810 --> 00:06:14,290
+تربيع x ما لوش دعوة الآن بنعوض بالقيم اللي فوق ناقص
+
+63
+00:06:14,290 --> 00:06:23,050
+اللي تحت يبقى 4 ناقص x تربيع ناقص y ناقص 3 كله dy
+
+64
+00:06:23,360 --> 00:06:28,160
+dx عندي أربعة وناقص ثلاثة بيبقى كده واحد
+
+65
+00:06:28,160 --> 00:06:33,220
+اتجهالة المسألة الى integration من zero لواحد من
+
+66
+00:06:33,220 --> 00:06:40,120
+zero لواحد ناقص x تربيع لواحد ناقص x تربيع ناقص y
+
+67
+00:06:40,120 --> 00:06:46,300
+كله dy dx ويساوي الـ integration من zero لواحد
+
+68
+00:06:46,300 --> 00:06:50,380
+بدي أكامل بالنسبة لـ dy كيف؟
+
+69
+00:06:53,620 --> 00:06:57,000
+يبقى دي مضروبة في x يبقى بدي أفكها على طول الخط
+
+70
+00:06:57,000 --> 00:07:05,200
+يبقى هذا ب x وهذا ب x تكعيب وهذا ب xy ناقص xy
+
+71
+00:07:05,200 --> 00:07:09,020
+بالشكل اللي عندنا هذا dy dx الأهم اللي ده كامل
+
+72
+00:07:09,020 --> 00:07:13,920
+بالنسبة لـ y يبقى كل الـ x باعتبرها constants يبقى
+
+73
+00:07:13,920 --> 00:07:22,060
+integration من 0 لـ 1 للـ xy ناقص x تكعيب y ناقص x
+
+74
+00:07:28,870 --> 00:07:34,630
+ناقص x تربيع هذا الكلام يبدو يساوي يبقى integration
+
+75
+00:07:34,630 --> 00:07:38,570
+من zero لغاية واحد بعوض يا بنات بالقيم اللي فوق
+
+76
+00:07:38,570 --> 00:07:44,370
+ناقص اللي تحت يبقى شبه صغير x في واحد ناقص x
+
+77
+00:07:44,370 --> 00:07:52,630
+تربيع ناقص x تكعيب في واحد ناقص x تربيع ناقص نصف x
+
+78
+00:07:52,630 --> 00:07:58,590
+في واحد ناقص x تربيع الكل تربيع كله بالنسبة لمين؟
+
+79
+00:07:58,590 --> 00:08:03,170
+إلى x يبقى هذا الكلام بيساوي integration من zero
+
+80
+00:08:03,170 --> 00:08:08,170
+لواحد ببدأ أفك الأقواس عشان أجمعهم مع بعض يبقى يصير
+
+81
+00:08:08,170 --> 00:08:17,030
+x ناقص x تكعيب ناقص x تكعيب كذلك وهنا زائد
+
+82
+00:08:20,730 --> 00:08:25,030
+بدي أفك القوس وأضرب يبقى هذا لو فكّيته بِـ لغتي اللي
+
+83
+00:08:25,030 --> 00:08:31,790
+هو واحد ناقص اثنين x تربيع زائد x أس أربعة بدي
+
+84
+00:08:31,790 --> 00:08:37,030
+أضرب في من؟ في نصف x زائد ليه مش يصير عندي هنا
+
+85
+00:08:37,030 --> 00:08:44,670
+ناقص نصف x ناقص في ناقص بزائد نصف في اثنين مع السلامة
+
+86
+00:08:44,670 --> 00:08:53,410
+بيظل عندي  ثلاثة أرباع x تكعيب وبعد ذلك ناقص نصف x أس خمسة
+
+87
+00:08:53,410 --> 00:09:00,850
+كله بالنسبة لمين؟ إلى dx طب تعالي نجمع عندنا هنا x
+
+88
+00:09:00,850 --> 00:09:07,010
+وعندنا هنا نصف x يبقى بالسالب بيظل ثلاثة أرباع  نصف x
+
+89
+00:09:07,010 --> 00:09:14,730
+بالموجب يبقى هذا الكلام تكامل من صفر لواحد لنصف x
+
+90
+00:09:15,520 --> 00:09:20,020
+بعد ذلك أنا عندي هنا x تكعيب سالب و x تكعيب
+
+91
+00:09:20,020 --> 00:09:27,560
+موجب مع السلامة بيظل عندنا كم؟ ناقص x تكعيب بعد
+
+92
+00:09:27,560 --> 00:09:33,780
+ذلك عندي هنا x أس خمسة وناقص نصف x أس خمسة بيظل
+
+93
+00:09:33,780 --> 00:09:41,730
+عندنا نصف x أس خمسة بالموجب يبقى زائد نصف x أس
+
+94
+00:09:41,730 --> 00:09:48,910
+خمسة كله هذا بالنسبة لمين؟ إلى dx هذا الكلام يساوي
+
+95
+00:09:48,910 --> 00:09:57,090
+بدي أكامل الآن يبقى ربع x تربيع وعندك هنا ناقص
+
+96
+00:09:57,090 --> 00:10:06,250
+ربع x أس أربعة وعندك هنا زائد اللي هو مين؟ بنضيف
+
+97
+00:10:06,250 --> 00:10:11,190
+للأس واحد وبنقسم على الأس الجديد يعني واحد على
+
+98
+00:10:11,190 --> 00:10:17,210
+اثنا عشر x أس ستة بدنا
+
+99
+00:10:17,210 --> 00:10:20,630
+نعوض بالقيم اللي فوق ناقص اللي تحت يبقى هذا الكلام
+
+100
+00:10:20,630 --> 00:10:28,490
+بده يساوي الربع ناقص الربع زائد واحد على اثنا عشر
+
+101
+00:10:28,490 --> 00:10:35,100
+ناقص zero الباقي كله zero يبقى الجواب جديد واحد على 12
+
+102
+00:10:35,100 --> 00:10:41,120
+فقط لقيمة هذا التكامل الثلاثي
+
+103
+00:10:59,790 --> 00:11:07,190
+بس بنجيب نجسمه على حجم المنطقة بيطلع لي جدش المتوسط
+
+104
+00:11:07,190 --> 00:11:12,330
+خلال فترة التكامل أذكرك بكلاسيكية برضه بجنبها
+
+105
+00:11:12,330 --> 00:11:16,730
+نحسب الـ average للدالة فقلنا بنكامل الدالة على
+
+106
+00:11:16,730 --> 00:11:21,450
+الـ interval وبنقسم على طول الـ interval بيطلع لي
+
+107
+00:11:21,450 --> 00:11:26,980
+جدش المتوسط هذا إذن بدنا نحسب المتوسط بيحدث عند أي
+
+108
+00:11:26,980 --> 00:11:31,360
+نقطة برضه بنحسب من جيب النقاط الكلاسيكية
+
+109
+00:11:31,360 --> 00:11:35,840
+الكلاسيكية نفس الفكرة بالضبط تماما إذن نحسب التكاملات
+
+110
+00:11:35,840 --> 00:11:40,400
+الثلاثية على الدالة ونحسب التكامل الثلاثي على
+
+111
+00:11:40,400 --> 00:11:45,020
+المنطقة اللي نريد أن نتبعها لأننا نكامل عليه ونقسم
+
+112
+00:11:45,020 --> 00:11:49,520
+الاثنين على بعض واحد على الـ volume بتاع الدي بثلاث
+
+113
+00:11:49,520 --> 00:11:52,120
+تكاملات على الدي للدالة
+
+114
+00:11:57,380 --> 00:12:02,360
+مش إحنا بنكامل على المنطقة دي، بدي أحسب كده حجم
+
+115
+00:12:02,360 --> 00:12:07,460
+المنطقة دي، كويس؟ حسبنا بنحسب التكاملات
+
+116
+00:12:07,460 --> 00:12:13,380
+الثلاثية على الدالة  نحسبها نقسم هذا على هذا واحد
+
+117
+00:12:13,380 --> 00:12:18,160
+على مضروب هذا فوق في البسط وليس في المقام يبقى هذا
+
+118
+00:12:18,160 --> 00:12:21,240
+في البسط وهذا في المقام نقسم الاثنين على بعض بيطلع
+
+119
+00:12:21,240 --> 00:12:28,480
+جدش متوسط الدالة على هذه المنطقة نحسب
+
+120
+00:12:28,480 --> 00:12:33,300
+ثلاث تكاملات دي زد دي واي دي اكس دي حاجة من الأول
+
+121
+00:12:34,060 --> 00:12:39,740
+كمان؟ يبقى جبنا الحجم  بعد هيك بروح
+
+122
+00:12:39,740 --> 00:12:45,740
+بأحسب التكاملات الثلاثية للدالة على هذه المنطقة كويس؟
+
+123
+00:12:45,740 --> 00:12:49,600
+وبيكون جبت كده من حجم المنطقة أو من أربعة نجيب
+
+124
+00:12:49,600 --> 00:12:51,720
+المنطقة أصلًا تجيب المنطقة تجيب المنطقة تجيب
+
+125
+00:12:51,720 --> 00:12:54,240
+المنطقة تجيب المنطقة تجيب المنطقة تجيب
+
+126
+00:12:54,240 --> 00:12:54,400
+تجب المنطقة تجيب المنطقة تجيب المنطقة تجيب
+
+127
+00:12:54,400 --> 00:12:57,080
+المنطقة تجيب المنطقة تجيب المنطقة تجيب المنطقة
+
+128
+00:12:57,080 --> 00:13:02,660
+تجب المنطقة تجيب المنطقة تجيب المنطقة تجيب المنط
+
+129
+00:13:06,170 --> 00:13:13,870
+بتاني رقم اثنين بيقول لك حاجة اسمها a و b  نمرة
+
+130
+00:13:13,870 --> 00:13:21,830
+a بيقول لي evaluate أحسب لي integration من zero لـ
+
+131
+00:13:21,830 --> 00:13:26,750
+one integration من سالب one لـ zero integration من
+
+132
+00:13:26,750 --> 00:13:38,070
+zero لـ y تربيع لـ dz dy dx المطلوب الثاني نمرة b
+
+133
+00:13:38,070 --> 00:13:46,890
+rewrite rewrite قعد كتابة the integral the
+
+134
+00:13:46,890 --> 00:14:00,930
+integral التكامل as an equivalent as
+
+135
+00:14:00,930 --> 00:14:03,450
+an equivalent integral
+
+136
+00:14:07,260 --> 00:14:13,260
+in the order dy
+
+137
+00:14:13,260 --> 00:14:16,440
+dz
+
+138
+00:14:16,440 --> 00:14:22,460
+dx وراح
+
+139
+00:14:22,460 --> 00:14:28,120
+مش هذا أحد أسئلة الكتاب رسم لي الرسمة وقال لي احصل
+
+140
+00:14:28,120 --> 00:14:36,530
+نجي نرسم الرسمة يبقى الرسمة كالتالي هذا محور x، هذا
+
+141
+00:14:36,530 --> 00:14:43,510
+محور y، هذا محور z، خلص معايا بنات، يبقى من هنا
+
+142
+00:14:43,510 --> 00:14:51,090
+مُدَد على استقامة، ومن هنا جرسا موازيا له، وطلع
+
+143
+00:14:51,090 --> 00:14:58,490
+رأسي هيك ومن هنا طلع رأسي هيك ومن هنا رسم موازي
+
+144
+00:14:58,490 --> 00:15:05,010
+لمحور x ومن هنا موازي لمحور x الشكل اللي عندنا
+
+145
+00:15:05,010 --> 00:15:08,590
+هذا تمام؟
+
+146
+00:15:08,590 --> 00:15:13,610
+و
+
+147
+00:15:13,610 --> 00:15:20,290
+الراجل هنا هيك رسم لي قوس الشكل اللي عندنا هذا ومن
+
+148
+00:15:20,290 --> 00:15:22,370
+هنا قوس الشكل اللي عندنا هذا
+
+149
+00:15:26,990 --> 00:15:30,910
+شايفين الخط الأزرق القوسي من هنا اللي فوق يبقى هذا
+
+150
+00:15:30,910 --> 00:15:37,510
+هو السطح العلوي تمام الشكل اللي عندنا هذا الأسود
+
+151
+00:15:37,510 --> 00:15:45,210
+اللي تحت  أرسمه لكم بالشكل الأسود هذا هو المستوى
+
+152
+00:15:45,210 --> 00:15:50,030
+السفلي اللي موجود في مستوى XY plane
+
+153
+00:15:57,330 --> 00:16:02,950
+طيب كل النقاط اللي عندنا هذه حطّ لي إحداثيات كل نقطة
+
+154
+00:16:02,950 --> 00:16:09,570
+من هذه النقاط يبقى واحد وسالب واحد و zero النقطة
+
+155
+00:16:09,570 --> 00:16:14,710
+اللي عندنا هذه لفوق واحد وسالب واحد وواحد والنقطة
+
+156
+00:16:14,710 --> 00:16:20,910
+هذه zero وسالب واحد وواحد أكتر من هيك ما عنديش
+
+157
+00:16:20,910 --> 00:16:26,390
+معلومات وهذه النقطة اللي بين اللي هي نقطة اللي هي
+
+158
+00:16:26,390 --> 00:16:26,590
+zero
+
+159
+00:16:30,660 --> 00:16:33,840
+و أعطاني هذه النقطة اللي هي واحد و zero zero
+
+160
+00:16:33,840 --> 00:16:37,400
+تخيلي
+
+161
+00:16:37,400 --> 00:16:46,600
+إن الشكل الشكل الأزرق اللي فوق هذا هذا كله يُعتبر
+
+162
+00:16:46,600 --> 00:16:52,880
+بنات المستوى العلوي ويُحصر كل اللي منه تحت يبقى هذا
+
+163
+00:16:52,880 --> 00:16:58,020
+يُعتبر السطح العلوي والمخطط بالأسود هذا يُعتبر السطح
+
+164
+00:16:58,020 --> 00:17:03,960
+السفلي أو المستوى السفلي لهذا المجسم والمستوى اللي
+
+165
+00:17:03,960 --> 00:17:09,900
+عندنا هذا زي ما أنتو شايفين هذا موازٍ للـ XZ plane
+
+166
+00:17:09,900 --> 00:17:15,380
+موازٍ له تماما قال لي أحسب لي التكامل اللي فوق وبعد
+
+167
+00:17:15,380 --> 00:17:19,720
+هيك المطلوب الثاني الـ rewrite the integral قعدت
+
+168
+00:17:19,720 --> 00:17:26,040
+كتابة هذا التكامل بِـ مين؟ بتكامل مكافئ له لكن مش
+
+169
+00:17:26,040 --> 00:17:35,520
+بالترتيب dz dy dx وإنما dy dz dx يعني هنا الأخير
+
+170
+00:17:35,520 --> 00:17:42,020
+خلاه زي ما هو وجاب الاثنين دول مكان بعض إذن هنغير
+
+171
+00:17:42,020 --> 00:17:47,890
+نغير حدود التكامل طبقا لذلك والروح نحسب التكامل هذا
+
+172
+00:17:47,890 --> 00:17:53,070
+السؤال هو يا ترى في كل التكاملين بيطلع إن قيمتهم
+
+173
+00:17:53,070 --> 00:17:58,010
+مختلفتين أو نفس القيمة نفس القيمة لأن هذا حاجة
+
+174
+00:17:58,010 --> 00:18:01,890
+ده وأنا أطلّع لغيره يبقى هذا بيطلع إن إيه نفس
+
+175
+00:18:01,890 --> 00:18:04,910
+القيمة يبقى باجي بقى أحله عادي
+
+176
+00:18:07,930 --> 00:18:13,270
+أول تكامل من 0 إلى 1 من سالب واحد إلى zero وهذه
+
+1
+
+223
+00:23:59,020 --> 00:24:05,600
+قيمة لزد، وكم أكبر قيمة لزد؟ من صفر لواحد، من
+
+224
+00:24:05,600 --> 00:24:13,420
+صفر لواحد، كم أقل قيمة ل X وأكبر قيمة ل X؟ من
+
+225
+00:24:13,420 --> 00:24:20,470
+صفر لواحد كذلك، من صفر لواحد. طيب، لو الحجم هذا
+
+226
+00:24:20,470 --> 00:24:26,690
+لم يطلع طول، يبقى شغلي غلط على كل الخط أو بكون غلط
+
+227
+00:24:26,690 --> 00:24:31,970
+في الحسابات، سأراجع معلوماتنا مرة ثانية. طب
+
+228
+00:24:31,970 --> 00:24:35,370
+تعالوا نحسب هذا ونشوف كده شو بده يساوي. يبقى
+
+229
+00:24:35,370 --> 00:24:42,870
+التكامل من صفر لواحد لل Y من عند سالب واحد
+
+230
+00:24:42,870 --> 00:24:48,850
+لغاية سالب جذر ال Z. وهنا DZ DX
+
+231
+00:24:50,740 --> 00:24:58,420
+نستخدم التكامل من 0 إلى 1 ل سالب
+
+232
+00:24:58,420 --> 00:25:05,200
+جذر الـ z زائد واحد. كل هذا ناقص جذر الـ z زائد
+
+233
+00:25:05,200 --> 00:25:05,740
+واحد
+
+234
+00:25:17,210 --> 00:25:20,330
+يبقى هذا الكلام بدل ما يساوي التكامل من صفر
+
+235
+00:25:20,330 --> 00:25:24,930
+لواحد، بدي أكمل الدالة هذه بالنسبة إلى زد، هذه
+
+236
+00:25:24,930 --> 00:25:32,930
+تعتبر زد قُدره؟ طولين
+
+237
+00:25:32,930 --> 00:25:37,890
+زد قُدره ثلاثة على اثنين، بس بشارة سالب، يبقى سالب
+
+238
+00:25:37,890 --> 00:25:39,070
+طولين
+
+239
+00:25:44,340 --> 00:25:50,620
+الحاجة دي كلها بنات من where ل where؟ من صفر لغاية
+
+240
+00:25:50,620 --> 00:25:55,920
+واحد. ولسه باقي علينا دي الـ X. طب نعوض بالقيمة اللي فوق
+
+241
+00:25:55,920 --> 00:26:00,100
+ناقص اللي تحت. يبقى هذا الكلام بده يساوي
+
+242
+00:26:00,100 --> 00:26:07,680
+التكامل من صفر لواحد ل سالب ثلثين زائد واحد
+
+243
+00:26:07,680 --> 00:26:13,840
+ناقص صفر بيروح مع السلامة. كل هذا بالنسبة لمين؟
+
+244
+00:26:13,840 --> 00:26:22,930
+ل دي الـ X. يبقى تكامل من صفر لواحد للطول DX. يبقى طول X
+
+245
+00:26:22,930 --> 00:26:29,110
+من صفر لواحد. يبقى قد ايش ويساوي طول نفس الحجم اللي
+
+246
+00:26:29,110 --> 00:26:34,410
+طلعناها قبل قليل. لو ما طلعش يبقى يا إما الحساب
+
+247
+00:26:34,410 --> 00:26:40,090
+عندنا غلط، يا إما حدود التكامل اللي طلعناها مش
+
+248
+00:26:40,090 --> 00:26:46,790
+دقيقة، لكن الحدود عندنا سليمة مائة بالمائة. طيب نروح
+
+249
+00:26:46,790 --> 00:26:57,550
+لـ example تلاتة بيقول
+
+250
+00:26:57,550 --> 00:26:59,190
+find the volume of the region
+
+251
+00:27:08,520 --> 00:27:20,120
+نجد حجم المنطقة، كانت from the cylinder اللي
+
+252
+00:27:20,120 --> 00:27:27,500
+أُقطعت من الأسطوانة  x تربيع زائد y تربيع يساوي واحد
+
+253
+00:27:28,480 --> 00:27:38,280
+by the planes, by the planes، بالمستويين z يساوي
+
+254
+00:27:38,280 --> 00:27:47,180
+ناقص y، and z يساوي صفر. وكذلك رسم لي المنطقة
+
+255
+00:27:52,130 --> 00:27:58,110
+هذا محور X، هذا محور Y، هذا محور Z
+
+256
+00:28:40,930 --> 00:28:51,130
+X, Y, Z. أكثر من ما أعطانيش معلومة، لكن أعطاني هذا
+
+257
+00:28:51,130 --> 00:28:59,020
+اللي هو الواحد. قال له آخر قال أنا ثلاث سنوات، ثلاث سنوات
+
+258
+00:28:59,020 --> 00:29:05,920
+في خطأ. أرسل، قال مات، مات لحد هنا أنا، وقال في جيله
+
+259
+00:29:05,920 --> 00:29:12,920
+لغايتين، وقال أنا جيلي بالشكل ده، كيف يا بسم الله
+
+260
+00:29:12,920 --> 00:29:19,160
+يحفظ أنا المرحلة. يالي واحد، وأهلي واحد بالشكل ده
+
+261
+00:29:24,270 --> 00:29:29,650
+يبقى زي السفينة اللي أجت من هنا، وهذا أجت من هنا، يتلاقوا
+
+262
+00:29:29,650 --> 00:29:34,530
+مع بعض. يبقى جزء من كل مستوى رأسي يقطعها بمستوى
+
+263
+00:29:34,530 --> 00:29:41,010
+مائل، وهذا المستوى أفضل لأنه Z بيساوي واحد. الآن بدأ
+
+264
+00:29:41,010 --> 00:29:47,270
+نخطط كل مستوى من المستويين عشان نحدد كويس. يبقى هذا
+
+265
+00:29:47,270 --> 00:29:52,650
+مستوى الأرض، يعني مستوى مائل
+
+266
+00:29:56,040 --> 00:30:02,000
+المستوى الأزرق هو مستوى الأرض، ال XY Plane، المستوى
+
+267
+00:30:02,000 --> 00:30:05,080
+المائل هو المستوى من فوق
+
+268
+00:30:17,320 --> 00:30:20,780
+يبقى المخطط بالأزرق اللي هو المستوى الأفقي، Z
+
+269
+00:30:20,780 --> 00:30:26,380
+تساوي صفر، والمخطط بالأسود اللي هو المستوى المائل
+
+270
+00:30:26,380 --> 00:30:31,880
+اللي هو Z يساوي سالب Y. إذا هذين المستويين
+
+271
+00:30:31,880 --> 00:30:40,720
+معادلته Z تساوي سالب Y، والمستوى الأفقي هذا اللي هو
+
+272
+00:30:40,720 --> 00:30:43,940
+Z تساوي كم؟ تساوي صفر
+
+273
+00:30:47,300 --> 00:30:51,620
+جاء هذا، لنجد حجم المنطقة اللي قطعناها من
+
+274
+00:30:51,620 --> 00:30:57,020
+الأسطوانة اللي عندنا دي بين ال two planes. بقوله
+
+275
+00:30:57,020 --> 00:31:02,380
+بسيطة، ال volume V، طبعا مرسومة في الكتاب برضه رسمها
+
+276
+00:31:02,380 --> 00:31:12,080
+لها، ال V هذه بدها تساوي ثلاثة تكاملات ل DZ DY DX
+
+277
+00:31:14,390 --> 00:31:19,590
+المستوى الأفقي هو z يساوي صفر، المستوى المائل z
+
+278
+00:31:19,590 --> 00:31:27,850
+يساوي واحد. يبقى لو جيت رسمت قطع منطقة التكامل من عند
+
+279
+00:31:27,850 --> 00:31:34,230
+المستوى الأفقي، وجيت طالع رأسي موازي لمحور z، قابل
+
+280
+00:31:34,230 --> 00:31:38,330
+المستوى المائل عند النقطة اللي فوق. يبقى النقطة
+
+281
+00:31:38,330 --> 00:31:44,700
+اللي فوق كده يا بنات z يساوي واحد، وهنا z كده. إذًا
+
+282
+00:31:44,700 --> 00:31:53,640
+بدي أقوله من صفر لغاية سالب Y. من ضال عندنا؟ مين
+
+283
+00:31:53,640 --> 00:31:59,060
+ضال عندنا ال X وY.  لمّا تتوضح لكم الصورة بدي أرسم
+
+284
+00:31:59,060 --> 00:32:04,200
+نصف الدائرة اللي عندنا هنا، تمام؟ لمّا أعرف برضه
+
+285
+00:32:04,200 --> 00:32:09,480
+نصف الدائرة. بدي أغير من ويل لويل بعدين. بقوله هذا
+
+286
+00:32:09,480 --> 00:32:17,920
+اللي هو محور X، وهذا محور Y، هذا X، وهذا Y، وهذه نقطة
+
+287
+00:32:17,920 --> 00:32:25,300
+الأصل. Z، X بدأت تتغير من عند السالب واحد لغاية
+
+288
+00:32:25,300 --> 00:32:33,240
+الواحد. يبقى سالب واحد، واحد. هل نحن جهة Y الموجبة
+
+289
+00:32:33,240 --> 00:32:38,020
+ولا جهة Y السالبة؟ جهة Y السالبة. كبيرة الرسمة بدأت
+
+290
+00:32:38,020 --> 00:32:45,360
+تظهر أعلى محور X ولا أسفل محور X؟ أسفل المحور X. يبقى
+
+291
+00:32:45,360 --> 00:32:52,940
+هذا يعتبر
+
+292
+00:32:52,940 --> 00:32:58,480
+هو ال domain تبع الدالة. خطوة ثانية: حدد ال domain
+
+293
+00:32:58,480 --> 00:33:04,460
+أي حددنا ال domain تبع الدالة. إذا بدنا نكمل
+
+294
+00:33:04,460 --> 00:33:11,080
+بالنسبة ل Y في الأول. بنروح وبنرسم خط يقطع منطقة
+
+295
+00:33:11,080 --> 00:33:17,900
+التكامل بالشكل هذا. هذا هو موازي لمحور Y. يبقى هنا Y
+
+296
+00:33:17,900 --> 00:33:26,260
+موجبة، أما هنا صفر. طب هنا Y موجبة. نرجع
+
+297
+00:33:26,260 --> 00:33:31,380
+لمين؟ هذه معادلة الدائرة. الدائرة إيش كانت؟ X تربيع
+
+298
+00:33:31,380 --> 00:33:37,140
+زائد Y تربيع تساوي واحد. أنا بدي Y، يبقى بصير عندي مين؟
+
+299
+00:33:37,140 --> 00:33:43,780
+بصير عندي Y تربيع يساوي واحد ناقص X تربيع. إذا بناءً
+
+300
+00:33:43,780 --> 00:33:50,720
+عليه Y تساوي زائد أو ناقص الجذر التربيعي ل واحد
+
+301
+00:33:50,720 --> 00:33:56,940
+ناقص X تربيع. لكن Y سالبة ولا موجبة؟ سالبة. يبقى بصير
+
+302
+00:33:56,940 --> 00:34:03,780
+سالب الجذر. يبقى معنى هذا الكلام أن Y بدي أحط تحت
+
+303
+00:34:03,780 --> 00:34:10,100
+هنا يا بنات صفر، وفوق سالب الجذر. صفر يبقى هذه صفر
+
+304
+00:34:10,100 --> 00:34:14,940
+تعتبر القيمة الكبرى، وهذه الصغيرة لأنها سالبة. يبقى
+
+305
+00:34:14,940 --> 00:34:20,100
+باجي بقوله من سالب الجذر التربيعي لواحد ناقص X
+
+306
+00:34:20,100 --> 00:34:29,360
+تربيع لغاية صفر. ضالّ الـ X تتغير من سالب واحد إلى
+
+307
+00:34:29,360 --> 00:34:34,850
+واحد. يبقى من سالب واحد إلى واحد. حددنا حدود التكامل
+
+308
+00:34:34,850 --> 00:34:38,630
+صح. بضل بعد ذلك الشغل الروتيني. يبقى... زي ما أنتم
+
+309
+00:34:38,630 --> 00:34:42,910
+شايفيني، بنتدرج في الأسئلة شوية شوية. كل سؤال أدخل
+
+310
+00:34:42,910 --> 00:34:48,030
+في مش التاني حتى نستوعب الموضوع. تفضلي يا عزيزتي، تعالي
+
+311
+00:34:48,030 --> 00:34:53,450
+هنا على اللوحة. شوف، تعالي يلا، كوني مثالًا لغيرك
+
+312
+00:34:53,450 --> 00:34:57,450
+يعني هي تبرعت بنفسها لأنها قالت أنا مش فاهمة كيف
+
+313
+00:34:57,450 --> 00:35:00,960
+جئنا حدود التكامل. يبقى خذوا بالكم كيف بدنا نجيب
+
+314
+00:35:00,960 --> 00:35:07,220
+حدود التكامل. أول حاجة، في مشكلة على ذات؟ بس خليني
+
+315
+00:35:07,220 --> 00:35:10,260
+مع هذا واحد واحد. إذا فهمنا هذا بكون أنا طيب
+
+316
+00:35:10,260 --> 00:35:15,460
+حتقولي دفتر بالله يا بنهاد؟ لا، هذا دفتر، كويس. تعالي
+
+317
+00:35:15,460 --> 00:35:21,300
+الدفتر يعني؟ واحد أفقي وواحد عمودي. يبقى الأفقي هو
+
+318
+00:35:21,300 --> 00:35:27,340
+هذا، والعمودي اللي جاي من وراء هذا. كويس، أنا بدي أجيب
+
+319
+00:35:27,340 --> 00:35:33,020
+من الماء، المستوى المائل وهيك، كويس. يبقى زد
+
+320
+00:35:33,020 --> 00:35:40,620
+هنا بكم؟ صفر. زد هنا معادلة إثنين، والزد يساوي ناقص
+
+321
+00:35:40,620 --> 00:35:46,200
+واحد، صح ولا لا؟ إذًا بصير زد تتغير من صفر. يعني أنا
+
+322
+00:35:46,200 --> 00:35:50,840
+بدأت بالخط الأزرق اللي رسمناه كده من عند ال Z تساوي
+
+323
+00:35:50,840 --> 00:35:54,120
+صفر هنا لغاية Y لغاية ما قابلّت المستوى ده بقى
+
+324
+00:35:54,120 --> 00:35:59,540
+واضحة الصورة يعني؟ طيب خلاص. لما نقصت Z، يبقى Z
+
+325
+00:35:59,540 --> 00:36:04,440
+تغيرت من صفر لواحد ل ناقص Y. وده دفعك لتبقى بقى
+
+326
+00:36:04,440 --> 00:36:12,160
+عندي طيب، المجهول عندي؟ طيب حدود ال Y و ال X، ال Y و
+
+327
+00:36:12,160 --> 00:36:16,590
+ال X هو ال domain تبعي ده. يعني مين؟ يعني نصف
+
+328
+00:36:16,590 --> 00:36:21,570
+الدائرة اللي عندنا، تمام. فجيت رسمت نصف الدائرة
+
+329
+00:36:21,570 --> 00:36:27,770
+قلت: آه، هي محور Y وهي محور X. هذه مش ال Y الموجبة
+
+330
+00:36:27,770 --> 00:36:33,890
+بجهة Y مين؟ إذًا نقول هي Y السالبة. لنجعلها نصف الدائرة
+
+331
+00:36:33,890 --> 00:36:38,770
+السفلية. الآن بدنا نحدد Y. بده تتغير من وين لوين؟ وإيه
+
+332
+00:36:38,770 --> 00:36:42,250
+يعني يا بنات، إحنا الآن بدنا نشتغل زي ما كنا بنشتغل
+
+333
+00:36:42,250 --> 00:36:49,100
+وين؟ في ال sections الماضي. قلنا بنرسم خط يوازي محور
+
+334
+00:36:49,100 --> 00:36:54,880
+Y، وبشوف Y قد ايش تأخذ أقل قيمة لها، وقد ايش أكبر
+
+335
+00:36:54,880 --> 00:36:59,580
+قيمة لها. و Y قد ايش أقل قيمة؟ هي سالب الجذر التربيعي
+
+336
+00:36:59,580 --> 00:37:01,340
+لواحد ناقص X تربيع
+
+337
+00:37:04,780 --> 00:37:11,940
+لأن Y عندنا بالسالب. و لو Y موجبة كانت الرسمة فوق. يبقى
+
+338
+00:37:11,940 --> 00:37:18,160
+هنا أقل قيمة ل Y هي سالب الجذر، وأكبر قيمة كم؟ إذًا
+
+339
+00:37:18,160 --> 00:37:21,860
+Y تغيرت من سالب الجذر لغاية صفر. مين ضايل اللي
+
+340
+00:37:21,860 --> 00:37:26,640
+عندنا؟ من أين لغاية؟ واضحة هي، واضحة؟ بتكتسلي في
+
+341
+00:37:26,640 --> 00:37:28,880
+اللي قبل ما يسأل، يلا، تكتسلي، لا ما أنا كنت بدي أسأل
+
+342
+00:37:28,880 --> 00:37:32,780
+ليش؟ أنا أخطأت، أخذنا من عمودي من هناك، بس أنا لا
+
+343
+00:37:32,780 --> 00:37:36,520
+عرفت شو أعمل. لا ما إحنا في الأول أعطاني إجازة،
+
+344
+00:37:36,520 --> 00:37:39,840
+ما فيهاش مشكلة. هنا لما بدأنا نحدد حدود التكامل،
+
+345
+00:37:39,840 --> 00:37:44,580
+قال لي أول تكامل بتكون بالنسبة لمين؟ بس هنا جد إيش
+
+346
+00:37:44,580 --> 00:37:50,960
+كان؟ وهنا D زد، يبقى هنا ل Y. يبقى رحنا رسمنا خط
+
+347
+00:37:50,960 --> 00:37:57,620
+أفقي موازٍ لمحور Y، وشوفنا Y بتتغير من وين لوين. حد
+
+348
+00:37:57,620 --> 00:38:03,460
+بتسأل ثاني يا بنات؟ حد مش فاهمة؟ ها، لا تخجلي، أنتم
+
+349
+00:38:03,460 --> 00:38:07,040
+ما تخجليش على نفسك، تبخلي بالسؤال، ما تبخلي على حالك،
+
+350
+00:38:07,040 --> 00:38:15,320
+مش علينا. ها، خلاص واضحة، تمام؟ طيب بعد ايه؟ بعد ما
+
+351
+00:38:15,320 --> 00:38:21,100
+حددنا حدود التكامل تحديدًا سليمًا، ما يبقى إلا نروح نكامل
+
+352
+00:38:21,100 --> 00:38:26,040
+كامل. فباجي بقول هذا الكلام بده يساوي التكامل
+
+353
+00:38:26,040 --> 00:38:30,220
+من سالب واحد لواحد، التكامل من سالب الجذر
+
+354
+00:38:30,220 --> 00:38:37,000
+التربيعي لواحد ناقص X تربيعي لزيرو، و تكامل DZ ب Z
+
+355
+00:38:37,000 --> 00:38:41,700
+اللي فوق ناقص اللي تحت، يبقى بس ناقص Y
+
+356
+00:38:46,200 --> 00:38:51,100
+نكامل، يبقى هذا الكلام يساوي التكامل من سالب
+
+357
+00:38:51,100 --> 00:38:57,840
+واحد لواحد. تكامل ناقص Y بناقص Y تربيع على اثنين
+
+358
+00:38:57,840 --> 00:39:03,440
+من سالب الجذر التربيعي لواحد ناقص X تربيع ل صفر
+
+359
+00:39:03,440 --> 00:39:10,280
+ل DX. يبقى هذا الكلام يساوي ناقص، خليك برا، وهي
+
+360
+00:39:10,280 --> 00:39:15,280
+تكامل من سالب واحد إلى واحد. القيمة اللي فوق
+
+361
+00:39:21,420 --> 00:39:29,960
+ناقص الجذر التربيعي لواحد ناقص X تربيع الكل تربيع
+
+362
+00:39:29,960 --> 00:39:33,220
+بالشكل اللي عنده. هذا ماله؟ DX
+
+363
+00:39:35,660 --> 00:39:40,180
+عندما رُبع إشارة السالب. مع السلامة بتظهر إشارة
+
+364
+00:39:40,180 --> 00:39:46,300
+السالب اللي برا، والجذر مع السلامة. السالب اللي برا مع
+
+365
+00:39:46,300 --> 00:39:50,580
+السالب اللي برا، ماذا يصير؟ بالموجب. يبقى بتقول
+
+366
+00:39:50,580 --> 00:39:56,640
+المسألة إلى نص تكامل من سالب واحد إلى واحد لواحد
+
+367
+00:39:56,640 --> 00:40:06,640
+ناقص X تربيع DX فقط، لا غير. طب السؤال هو، اللي جوا
+
+368
+00:40:06,640 --> 00:40:12,560
+هذا يا بنات even function ولا odd function؟ ما هو
+
+369
+00:40:12,560 --> 00:40:14,800
+أنت قلت odd و even، لأنّي أعرف منهم
+
+370
+00:40:25,760 --> 00:40:31,700
+يبقى هذه even function. وحدود
+
+371
+00:40:31,700 --> 00:40:36,960
+التكامل نفسها بس واحدة موجبة بواحدة سالبة. يبقى نص
+
+372
+00:40:36,960 --> 00:40:44,760
+في اثنين، التكامل من صفر لواحد لواحد ناقص X تربيع DX
+
+373
+00:40:44,760 --> 00:40:51,160
+عظم النصف، الاثنين مع السلامة، وبتقول:  X ناقص X
+
+374
+00:40:51,160 --> 00:40:58,140
+تربيع على ثلاثة من عند صفر لغاية الواحد. يبقى
+
+375
+00:40:58,140 --> 00:41:05,280
+الجواب واحد ناقص ثلث ناقص صفر مع السلامة، بيظل
+
+376
+00:41:05,280 --> 00:41:06,480
+ثلثين
+
+377
+00:41:35,050 --> 00:41:38,050
+هذا كان المثال رقم 3
+
+378
+00:41:45,990 --> 00:41:49,650
+مثال رقم أربعة بيقول: find the volume of the region
+
+379
+00:41:49,650 --> 00:42:02,350
+find the volume of the region، كم حجم المنطقة
+
+380
+00:42:02,350 --> 00:42:08,050
+common to
+
+381
+00:42:08,050 --> 00:42:10,470
+the interior
+
+382
+00:42:16,410 --> 00:42:25,110
+إنها  of the cylinders of the
+
+383
+00:42:25,110 --> 00:42:33,710
+cylinders، x تربيع زائد y تربيع يساوي واحد، and x
+
+384
+00:42:33,710 --> 00:42:38,390
+تربيع زائد z تربيع الكل يساوي واحد
+
+385
+00:42:44,460 --> 00:42:50,220
+هذا لازم والله نمشي عليه يا بنات؟ ماشي
+
+386
+00:42:50,220 --> 00:42:56,080
+طيب نرجع لسؤالنا هذا مرة ثانية. بيقول: جدّ حجم
+
+387
+00:42:56,080 --> 00:43:02,020
+المنطقة المشتركة ما بين ال two cylinders الاثنين
+
+388
+00:43:02,020 --> 00:43:06,380
+اللي عندنا دول. يبقى احنا عندنا أسطوانتان
+
+389
+00:43:06,380 --> 00:43:13,420
+أسطوانتان، بينهما تق
+
+445
+00:48:20,450 --> 00:48:26,870
+الخط الأزرق المتواصل اللي أنتم شايفينه هذا تمام؟
+
+446
+00:48:26,870 --> 00:48:33,010
+طيب يعني وين صارت منطقة التقاطع بالضبط؟ طلعيني
+
+447
+00:48:33,010 --> 00:48:41,180
+هخليها كل منطقة زرقاء غامقة هذه هي من هنا وهذا
+
+448
+00:48:41,180 --> 00:48:46,500
+طبعا هذا مش هيظهر لأن هذا بيكون ثاني، هذا بيكون في
+
+449
+00:48:46,500 --> 00:48:51,960
+مستوى الـ X Y  فلذلك مش هيظهر وهذا كمان يا بِنات مش
+
+450
+00:48:51,960 --> 00:48:56,620
+هيظهر لأنه في الناحية الثانية وهذا مش هيظهر يبقى
+
+451
+00:48:56,620 --> 00:49:02,090
+صارت المنطقة هذه كالتالي، هنرسم المستوى اللي فوق
+
+452
+00:49:02,090 --> 00:49:06,250
+والمستوى اللي تحته، اللي فوق طبعا مش مستوى، حيكون
+
+453
+00:49:06,250 --> 00:49:14,690
+على شكل ميل، يبقى اللي فوق هكذا، هذه كل المنطقة
+
+454
+00:49:14,690 --> 00:49:18,970
+اللي فوق، طب وين المنطقة اللي تحت؟ المنطقة في
+
+455
+00:49:18,970 --> 00:49:26,930
+المستوى X Y Plane، دي المنطقة هذه، تمام؟
+
+456
+00:49:27,910 --> 00:49:39,850
+يبقى هذه المنطقة مرة ثانية، هذا خط
+
+457
+00:49:39,850 --> 00:49:44,170
+اللي فوق هو المستوى العلوي واللي تحت، هذا الأسود
+
+458
+00:49:44,170 --> 00:49:50,450
+هو المستوى السفلي يبقى
+
+459
+00:49:50,450 --> 00:49:55,010
+هذه المنطقة المشتركة بين الاثنين، طبعا مش
+
+460
+00:49:55,010 --> 00:49:59,130
+واضحة الرسمة عندكم بالكتاب، الحلقة تبع أحد مسائل
+
+461
+00:49:59,130 --> 00:50:03,330
+الكتاب، مش واضحة الرسمة، فهي وضحت لكم الرسمة تماما
+
+462
+00:50:03,330 --> 00:50:08,370
+طيب، بدي أكمل، أول حاجة بالنسبة لـ Z يبقى، بدي
+
+463
+00:50:08,370 --> 00:50:13,880
+أشوف Z بدأت تتغير منين لوين، يبقى بتروح تقولي بدي
+
+464
+00:50:13,880 --> 00:50:19,880
+أخذ الـ volume V اللي بيقول عنه، يبقى تكامل من اتنين
+
+465
+00:50:19,880 --> 00:50:27,840
+ثلاثة لـ DZ DY DX مثلا أو DX DY DZ، يبقى بده يشوف الـ
+
+466
+00:50:27,840 --> 00:50:33,500
+Z بدها تتغير من وين لوين، هرسمه بخط أسود، هدوء
+
+467
+00:50:33,500 --> 00:50:37,870
+الكلام لسا معين، بأطلع من مستوى الأرض للمستوى الأسود
+
+468
+00:50:37,870 --> 00:50:42,630
+لغاية ما أقابل المستوى الأزرق، مش المستوى المائل
+
+469
+00:50:42,630 --> 00:50:49,010
+اللي جاي من فوق، يبقى بدي أبدأ من هنا ههه وأجي طالعة
+
+470
+00:50:49,010 --> 00:50:53,130
+أرضاً لغاية ما أقابل المائل، أقابل السطح اللي جاييني
+
+471
+00:50:53,130 --> 00:50:59,750
+من فوق هنا، Z يبقى بدي Zero، تفاجئت يبقى من عند
+
+472
+00:50:59,750 --> 00:51:07,190
+Zero بدي أجي لهذاهذه يا ترى جاية على السطح الأفقي
+
+473
+00:51:07,190 --> 00:51:12,970
+ولا على السطح الرأسي؟ آه جاية على السطح الأفقي،
+
+474
+00:51:12,970 --> 00:51:17,710
+منها داخل السطح الرأسي، جوا، مظبوط؟ إذا جاية على
+
+475
+00:51:17,710 --> 00:51:21,990
+وين؟ على السطح الأفقي، طبعا السطح الأفقي مين
+
+476
+00:51:21,990 --> 00:51:29,450
+هنا؟ أيوة، من هذه بتصير Z يساوي الجذر التربيعي لواحد
+
+477
+00:51:29,450 --> 00:51:35,930
+ناقص X تربيع، إذا هنا Z عند هذه النقطة بدأت تساوي
+
+478
+00:51:35,930 --> 00:51:41,210
+الجذر التربيعي لواحد ناقص X تربيع، وزي ما شايفين
+
+479
+00:51:41,210 --> 00:51:46,310
+أخذنا الجذر الموجب وليس السالب لأنها أعلى المستوى
+
+480
+00:51:46,310 --> 00:51:51,070
+XY Plane وليست أسفل المستوى XY Plane
+
+481
+00:52:10,270 --> 00:52:15,850
+يبقى هذا Y وهذا X وهذا X
+
+482
+00:52:18,390 --> 00:52:26,350
+وهذا رأس X وهذا جزء من دائرة أو ربع دائرة يبقى
+
+483
+00:52:26,350 --> 00:52:30,970
+هذه الدائرة اللي عندنا بالشكل هذا، أنا بدي أكمل
+
+484
+00:52:30,970 --> 00:52:37,190
+بالنسبة لـ Y يبقى بدي أرسم خط يوازي محور Y يبقى
+
+485
+00:52:37,190 --> 00:52:42,310
+لو رحت رسمت خط موازي لمحور Y هتيجي النقطة هذه
+
+486
+00:52:42,310 --> 00:52:49,110
+وهذه النقطة الثانية، طب هنا Y يبقى كم؟ Zero لأن هنا
+
+487
+00:52:49,110 --> 00:52:56,130
+نقطة الأصل، يبقى من عند Y تساوي Zero إلى Y أكثر، كم؟
+
+488
+00:52:56,130 --> 00:53:01,250
+آه هذه الدائرة هي الدائرة الأولى تبعت الأسطوانة
+
+489
+00:53:01,250 --> 00:53:05,710
+اللي نازلة من فوق، X تربيع زائد Y تربيع يساوي واحد
+
+490
+00:53:05,710 --> 00:53:12,910
+يبقى هنا Y تساوي الجذر التربيعي لواحد ناقص X تربيع
+
+491
+00:53:13,270 --> 00:53:20,950
+يبقى هنا الجذر التربيعي لواحد ناقص X تربيع، طيب
+
+492
+00:53:20,950 --> 00:53:29,170
+هنا مين الـ X؟ ستتغير من هنا لغاية هنا، ما بتبدأش
+
+493
+00:53:29,170 --> 00:53:35,030
+من النقطة في الـ X؟ Zero وهذه الدائرة نصف قطرها يساوي
+
+494
+00:53:35,030 --> 00:53:38,830
+واحد، يبقى هذه واحد وكذلك هذه
+
+495
+00:53:44,190 --> 00:53:48,550
+جبل، مروحة كاملة، حدّ بيسأل أي سؤال هنا في حدود
+
+496
+00:53:48,550 --> 00:53:57,330
+التكامل أو كيف جبناهم أو... أو... إلى آخره؟
+
+497
+00:53:57,330 --> 00:54:03,990
+حطّ
+
+498
+00:54:03,990 --> 00:54:07,550
+دفترك وتعالى أشوف كيف سؤالك بالضبط، حطّ دفترك و
+
+499
+00:54:07,550 --> 00:54:13,450
+تعالى طيب
+
+500
+00:54:14,440 --> 00:54:18,540
+تحكي عن مستوى Z لما جبناها، بشيء كانت على أفق
+
+501
+00:54:18,540 --> 00:54:22,940
+إيه؟ لأ، على أفق إيه؟ هي Z تساوي Zero، له مستوى الأرض
+
+502
+00:54:22,940 --> 00:54:27,600
+بس هذا سطح جاي من فوق على، يعني آه آه، على هي
+
+503
+00:54:27,600 --> 00:54:31,380
+وهي هذا هو الخط اللي هو جاي على سطح، يعني جبناها
+
+504
+00:54:31,380 --> 00:54:34,760
+من المعادلة تبع الأسطوانة الأفقي، آه بالضبط، صحيح، لو
+
+505
+00:54:34,760 --> 00:54:37,880
+كانت على الـ.. لو كانت نجيبها من المعادلة اللي على
+
+506
+00:54:37,880 --> 00:54:41,780
+الأسطوانة الرأسية، تقدري تجيبيها على الأسطوانة الرأسية
+
+507
+00:54:41,780 --> 00:54:45,840
+أكثر، بقى دلوقتي نفسنا في واحدة، فضل إيه؟ هي عندك أسطوانة
+
+508
+00:54:45,840 --> 00:54:51,640
+رأسية، كويس، هي أسطوانة رأسية وعندك الخط جاي في
+
+509
+00:54:51,640 --> 00:54:56,960
+الوسط، كيف بدك تجيبيها؟ لا يمكن تقاطع موازي إليها،
+
+510
+00:54:56,960 --> 00:55:05,280
+فيش تقاطع أصلاً، هذه
+
+511
+00:55:05,280 --> 00:55:11,020
+ما بنعمل هيك، بنكتب.. نكتب Z بتاع.. وين هي Z؟
+
+512
+00:55:11,020 --> 00:55:16,660
+وين هي Z فيها؟ مش موجودة يبقى تفكيرك من الأول مش صحيح
+
+513
+00:55:16,660 --> 00:55:21,980
+لما
+
+514
+00:55:21,980 --> 00:55:25,280
+نحدد.. لما نقول لبنات Z من كده لكده أو Y من
+
+515
+00:55:25,280 --> 00:55:29,060
+كده لكده، بتكون في تقاطع، مش تقاطع، يبقى مدرّش، ولا هذا
+
+516
+00:55:29,060 --> 00:55:33,300
+يبقى مدرّش، إلاّ لو رسمت الخط اللي.. اللي عندي أسود
+
+517
+00:55:33,300 --> 00:55:37,990
+هذا، بيقطع مع المستوى الأفقي وبيقطع مع المائل،
+
+518
+00:55:37,990 --> 00:55:43,930
+الأسطوانة اللي جاية من فوق، يعني السطح، الأسطوانة الأفقي
+
+519
+00:55:43,930 --> 00:55:51,400
+حدّ بيسأل أي سؤال ثاني كمان؟ طيب يبقى مضلّش في عندنا إلاّ
+
+520
+00:55:51,400 --> 00:55:59,240
+التكامل يبقى هذه تكاملها من 0 لـ 1 ناقص
+
+521
+00:55:59,240 --> 00:56:05,520
+X تربيع، ويتكاملها بـ Z بالقيمة اللي فوق فقط، لـ 1
+
+522
+00:56:05,520 --> 00:56:07,220
+ناقص X تربيع
+
+523
+00:56:21,880 --> 00:56:31,840
+يبقى هذا الكلام
+
+524
+00:56:31,840 --> 00:56:35,180
+تكامل من Zero لواحد، لـ 1 ناقص X تربيع
+
+525
+00:56:45,730 --> 00:56:51,610
+تكامل من صفر لواحد لواحد ناقص X تربيع DX، واللي هو
+
+526
+00:56:51,610 --> 00:56:57,450
+بده يساوي X ناقص X تكعيب على ثلاثة، كله من Zero لواحد
+
+527
+00:56:57,450 --> 00:57:06,850
+ويساوي واحد ناقص ثلث ويساوي ثلثين، خلصت
+
+528
+00:57:06,850 --> 00:57:10,070
+نفس الإجابة، جاب السؤال اللي جابته، بس كل واحد شكل، مش
+
+529
+00:57:10,070 --> 00:57:11,170
+علاقة بالثاني
+
+530
+00:57:37,260 --> 00:57:47,040
+كذا، نسينا الثمانية، ثمانية
+
+531
+00:57:47,040 --> 00:57:51,660
+ثمانية ثمانية ثمانية ثمانية ثمانية ثمانية ثمانية
+
+532
+00:57:51,660 --> 00:57:57,060
+ثمانية ثمانية ثمانية ثمانية
+
+533
+00:58:07,180 --> 00:58:12,560
+السؤال الخامس بيقول
+
+534
+00:58:12,560 --> 00:58:13,820
+يحسب لي التكامل
+
+535
+00:58:21,390 --> 00:58:36,130
+تكامل من 0 لـ 1، تكامل من X تربيع لغاية 1، لـ 12 X Z e
+
+536
+00:58:36,130 --> 00:58:43,750
+أس Z Y تربيع DY DX
+
+537
+00:58:54,060 --> 00:58:59,200
+أول حاجة، بدي أكمل بالنسبة لـ Z، يبقى هدول كلهم
+
+538
+00:58:59,200 --> 00:59:05,440
+ما لهم أهمية، ثوابت، والـ Z ثابت يبقى أنا بدي أكمل X
+
+539
+00:59:05,440 --> 00:59:06,720
+و Y تربيع
+
+540
+00:59:15,600 --> 00:59:24,260
+إذا كتبناها على شكل Power Series، سنستطيع أن نضعها
+
+541
+00:59:24,260 --> 00:59:29,380
+هناك لما يقارب هذا المعقد هذا، تمام؟ يبقى في هذه
+
+542
+00:59:29,380 --> 00:59:34,300
+الحالة، يصير، ما عندناش إمكانية لهذه الشغلة، يبقى
+
+543
+00:59:34,300 --> 00:59:39,280
+بناءً عليه، إجباري هغير الـ order of integration، بدي
+
+544
+00:59:39,280 --> 00:59:44,780
+أغير ترتيب وضع التكامل، يبقى بالشكل هذا، مش حاجة
+
+545
+00:59:44,780 --> 00:59:51,060
+صعبة، طيب لو غيرت وضع التكامل يبقى بدي أخليها DX DY
+
+546
+00:59:51,060 --> 00:59:55,500
+بيصير هذا كله مقدار ثابت وهذا ثابت.. بيصير هذه
+
+547
+00:59:55,500 --> 01:00:01,110
+تكامل X فقط، لغاية.. يصبح معناها العملية سهلة جداً، إذا
+
+548
+01:00:01,110 --> 01:00:06,430
+بأجي بقوله هذا Y يساوي التكامل من صفر لواحد
+
+549
+01:00:06,430 --> 01:00:10,930
+اللي بنحلها فيه، هذول تكاملين، وبنشوف كيف بدهم
+
+550
+01:00:10,930 --> 01:00:22,710
+يصيروا، Y اتناشر X Z e أس Z Y تربيع DX DY DZ، إذا بدي
+
+551
+01:00:22,710 --> 01:00:28,000
+أغير الـ X، وإذا بدي أروح أرسم منطقة التكامل، مشان
+
+552
+01:00:28,000 --> 01:00:34,620
+أقلب حدود التكامل، يبقى لو جينا هيك وقلنا هذا محور
+
+553
+01:00:34,620 --> 01:00:44,460
+X وهذا محور Y وهذه نقطة الأصل اللي هي Z، عيد
+
+554
+01:00:44,460 --> 01:00:51,080
+نوافق من عندك يالا
+
+555
+01:00:51,080 --> 01:00:54,000
+اسمك ورقمك الجامعي وخلي نتفق عليهم
+
+556
+01:00:58,720 --> 01:01:05,940
+تمام، طيب بدنا نروح نرسم هذه المنطقة، جاي Y تساوي X
+
+557
+01:01:05,940 --> 01:01:10,640
+تربيع، Y تساوي X تربيع، من أول المعروفة، مشهورة
+
+558
+01:01:10,640 --> 01:01:17,780
+للجميع، يبقى هذا اللي بيقول Y تساوي X تربيع لغاية Y
+
+559
+01:01:17,780 --> 01:01:25,040
+تساوي كم؟ واحد، يبقى هذا الخط Y تساوي واحد، طيب الـ X
+
+560
+01:01:25,040 --> 01:01:29,520
+من وين لوين؟ الـ X من عند الـ Zero لغاية الـ واحد
+
+561
+01:01:29,520 --> 01:01:36,140
+هذا الـ X بـ Zero، هذه تقاطع الاثنين مع بعض بيعطينا
+
+562
+01:01:36,140 --> 01:01:41,540
+مين؟ الواحد، يبقى إحنا بس النصف اللي على اليمين
+
+563
+01:01:41,540 --> 01:01:47,570
+اللي عندنا، يبقى بدل ما كنا بدنا نكامل بالنسبة لـ Y
+
+564
+01:01:47,570 --> 01:01:53,110
+في الأول، هنكامل بالنسبة لـ X، يبقى بنروح نقطع، نرسم
+
+565
+01:01:53,110 --> 01:02:01,240
+خط يقطع منطقة التكامل وموازي لمحور X، يبقى هذا خط أفقي
+
+566
+01:02:01,240 --> 01:02:08,780
+من هنا لكذا، يكون X هنا Zero، ومن هنا X بقدر جذر
+
+567
+01:02:08,780 --> 01:02:15,960
+الـ Y، يبقى هنا X يساوي جذر الـ Y الموجب وليس السالب
+
+568
+01:02:15,960 --> 01:02:21,180
+لأن كل X موجب على الشكل اليمين، إذا بيصير عندي
+
+569
+01:02:21,180 --> 01:02:29,010
+من Zero لمين؟ لغاية جذر Y، طالعوا أنتم فوق، إيش كانت X
+
+570
+01:02:29,010 --> 01:02:33,990
+تربيع لواحد، اللي صار عندي X من عند Zero لغاية
+
+571
+01:02:33,990 --> 01:02:40,850
+جذر Y، ضلت عندي Y، بدأ يتغير من وين لوين؟ من صفر
+
+572
+01:02:40,850 --> 01:02:46,850
+لغاية واحد، يبقى من صفر لغاية واحد، بالشكل اللي
+
+573
+01:02:46,850 --> 01:02:51,250
+عندنا هذا، إذا بدنا نروح نكامل هذه الدالة أولا
+
+574
+01:02:51,540 --> 01:02:57,440
+بالنسبة لـ X، يبقى هذه تكامل من Zero لواحد، تكامل من
+
+575
+01:02:57,440 --> 01:03:05,980
+Zero لواحد لـ 6 X تربيع، والـ X هذه، ها بدنا نخليها
+
+576
+01:03:05,980 --> 01:03:15,320
+تتغير من Zero لغاية جذر الـ Y، لمن؟ لـ Z e أس Z Y
+
+577
+01:03:15,320 --> 01:03:19,380
+تربيع DY DZ
+
+578
+01:03:28,020 --> 01:03:35,200
+تكامل من صفر لواحد، تكامل من صفر لواحد، تكامل من صفر
+
+579
+01:03:35,200 --> 01:03:45,800
+لواحد، تكامل من صفر لواحد، تكامل من صفر لواحد
+
+580
+01:03:49,240 --> 01:03:53,460
+الآن بدك تكاملي بالنسبة لـ Y في الأول، والله بالنسبة
+
+581
+01:03:53,460 --> 01:03:58,700
+لـ Z في الأول، أي واحدة فيهم تمشي الحال، بس إذا بدك
+
+582
+01:03:58,700 --> 01:04:04,180
+تكاملي بالنسبة لـ Z، بيلزمك integration by parts لكن
+
+583
+01:04:04,180 --> 01:04:07,820
+إذا بدك تكاملي بالنسبة لـ Y، بتكاملي بالتعويض عادي جداً
+
+584
+01:04:07,820 --> 01:04:15,980
+إذا بروح بقول، حط لي T تساوي Y تربيع، يبقى DT تساوي 
+
+585
+01:04:15,980 --> 01:04:23,320
+2Y DY، يبقى نص DT بيعطينا Y DY، لكن عندنا الـ 6 خلاص مش هذه
+
+586
+01:04:23,320 --> 01:04:29,080
+على النص، يبقى هذا يا بنات بقدر أخليه، أخلي الـ 6 ليه
+
+587
+01:04:29,080 --> 01:04:36,200
+3 في 2، يبقى هذا الكلام بده يساوي ثلاثة برة، تكامل من
+
+588
+01:04:36,200 --> 01:04:45,000
+Zero لواحد، تكامل من Zero لواحد لـ 2 Y Z e أس Y
+
+589
+01:04:45,000 --> 01:04:54,780
+تربيع DY DZ، هذا الكلام بدي أشتغل عليه الآن، 2Y مع الـ DY
+
+590
+01:04:54,780 --> 01:05:00,020
+بدي أشيلها، بكتب بدل هذا DT، إذا صارت المسألة
+
+591
+01:05:00,020 --> 01:05:11,360
+ثلاثة تكامل من Zero لواحد وتكامل لـ Z e أس ZT DT
+
+592
+01:05:11,360 --> 01:05:12,560
+DZ
+
+593
+01:05:18,380 --> 01:05:25,100
+لو كانت الـ Y بواحد يبقى الـ T بواحد تربيعها بواحد، و
+
+594
+01:05:25,100 --> 01:05:29,140
+لو كانت بـ Zero بتعطيك هذه Zero، إذا أنت بقى حدود
+
+595
+01:05:29,140 --> 01:05:35,110
+التكامل كما هي، بدي أكامل بالنسبة لـ T، يبقى الثلاثة
+
+596
+01:05:35,110 --> 01:05:40,790
+ما لها دعوة، ومن Zero لواحد، والـ Z مقدار ثابت، و e
+
+597
+01:05:40,790 --> 01:05:51,750
+أس ZT على Z، والحكي هذا من Zero لواحد DZ، عظيم
+
+598
+01:05:51,750 --> 01:05:57,970
+الـ Z بتروح مع مين؟ مع الـ Z، وبالتالي بتقول المسألة
+
+599
+01:05:57,970 --> 01:06:04,710
+إلى ثلاثة تكامل من Zero لواحد لـ e أس Z ناقص واحد بـ Z
+
+600
+01:06:04,710 --> 01:06:15,500
+ناقص e أس Zero اللي هو واحد بـ Z، وبالتالي هذه ستصبح
+
+601
+01:06:15,500 --> 01:06:23,880
+ثلاثة e أس Z ناقص Z، وكل هذا الكلام من Zero لغاية
+
+602
+01:06:23,880 --> 01:06:32,820
+واحد، يبقى هذا الكلام بده يصير ثلاثة في e أس واحد ناقص
+
+603
+01:06:32,820 --> 01:06:40,650
+واحد، وهنا ناقص e أس Zero اللي هو بواحد، زائد Zero
+
+604
+01:06:40,650 --> 01:06:48,710
+مع السلامة، يبقى الجواب يساوي ثلاثة في e ناقص اثنين
+
+605
+01:06:48,710 --> 01:06:52,670
+هذه هي الإجابة نهائياً
+
+606
+01:07:13,380 --> 01:07:20,360
+السؤال السادس يا إخلاص، والكلام للسامعين، بيقول ما
+
+607
+01:07:20,360 --> 01:07:26,800
+يأتي، find the average value، يبقى شخصنا يا إخلاص
+
+608
+01:07:26,800 --> 01:07:33,740
+بالاسم، أن السؤال على الـ average value
+
+609
+01:07:34,550 --> 01:07:38,690
+بالفعل، نجاوب على السؤال اللي وعدناها فيه، what is
+
+610
+01:07:38,690 --> 01:07:48,610
+the average value of f of x, y وZ تساوي X زائد Y
+
+611
+01:07:48,610 --> 01:07:5
+
+667
+01:15:51,820 --> 01:16:00,240
+multiple of three وكذلك من سبعة وثلاثين لغاية
+
+668
+01:16:00,240 --> 01:16:07,280
+اربعة واربعين المسائل الفردية سأغلق الآن لل
+
+669
+01:16:07,280 --> 01:16:09,780
+section الذي يليه
+
+670
+01:16:33,680 --> 01:16:37,860
+تبقى ال section الذي به معلومات جديدة ما كناش
+
+671
+01:16:37,860 --> 01:16:45,180
+بنعرفها قبل ذلك section خمسة عشر السبعة بقول ما ستة
+
+672
+01:16:45,180 --> 01:16:53,100
+درجة بروحنا سبعة مباشرة بجود triple integrals
+
+673
+01:16:53,100 --> 01:16:59,880
+مكاملات ثلاثية in cylindrical
+
+674
+01:17:06,940 --> 01:17:17,300
+و الإحداثيات الأسطوانية
+
+675
+01:17:17,300 --> 01:17:20,640
+سنقسمه
+
+676
+01:17:20,640 --> 01:17:23,720
+إلى نقطتين النقطة الأولى
+
+677
+01:17:26,570 --> 01:17:34,610
+التكامل in cylindrical coordinates
+
+678
+01:17:34,610 --> 01:17:38,830
+الإحداثيات
+
+679
+01:17:38,830 --> 01:17:44,950
+الأسطوانية نعطي
+
+680
+01:17:44,950 --> 01:17:51,350
+definition ماذا؟ cylindrical
+
+681
+01:18:00,590 --> 01:18:11,990
+of a point P in space  الفرق
+
+682
+01:18:11,990 --> 01:18:29,750
+هو R و θ و Z  بحيث أن النقطة الأولى R and
+
+683
+01:18:29,750 --> 01:18:40,670
+θ هما الإحداثيات القطبية
+
+684
+01:18:40,670 --> 01:18:50,190
+الإحداثيات القطبية  of the vertical projection of the
+
+685
+01:18:50,190 --> 01:18:52,550
+vertical
+
+686
+01:18:57,340 --> 01:19:10,120
+projection that is a projection of P on the X Y
+
+687
+01:19:10,120 --> 01:19:21,980
+plane النقطة الثانية  هو Z is the rectangular
+
+688
+01:19:27,010 --> 01:19:33,030
+Rectangular Vertical Coordinate
+
+689
+01:19:33,030 --> 01:19:39,550
+يبقى
+
+690
+01:19:39,550 --> 01:19:48,190
+بناء عليه X  = R Cos θ و Y = R Cos
+
+691
+01:19:48,190 --> 01:19:56,760
+θ و Z كما هي  أو  X تربيع + Y تربيع = R
+
+692
+01:19:56,760 --> 01:20:04,220
+تربيع  و tan θ = Y/X
+
+693
+01:20:30,530 --> 01:20:34,110
+من يوم ما بدأنا نأخذ إحداثيات من الابتدائي
+
+694
+01:20:34,110 --> 01:20:39,530
+و الإعدادي و الثانوي  قضايا  لو دخلنا الجامعة و لو
+
+695
+01:20:39,530 --> 01:20:45,330
+دخلنا المستوى الأول الفصل الثاني و نحن نأخذ كل
+
+696
+01:20:45,330 --> 01:20:48,970
+Cartesian coordinates أو rectangular coordinates
+
+697
+01:20:48,970 --> 01:20:55,930
+إحداثيات ديكارتية أو إحداثيات مستطيلة طبعا طيب لكن
+
+698
+01:20:55,930 --> 01:21:01,250
+لما جئنا في calculus B  روحنا أخذنا من الإحداثيات
+
+699
+01:21:01,250 --> 01:21:05,120
+المستطيلة و جئنا  لإحداثيات cylindrical coordinatesاليوم إن
+
+700
+01:21:05,120 --> 01:21:08,000
+شاء الله نعطي نوعين طبعا  لا نحللها إلا نقطة النوع
+
+701
+01:21:08,000 --> 01:21:12,040
+الأول و بعدها نقطة النوع الثاني فيه نوعين آخرين
+
+702
+01:21:12,040 --> 01:21:16,800
+من الإحداثيات الذي هو الإحداثيات الأسطوانية
+
+703
+01:21:16,800 --> 01:21:21,660
+cylindrical coordinates و الإحداثيات الكروية
+
+704
+01:21:21,660 --> 01:21:27,820
+spherical coordinates الإحداثيات الكروية أو
+
+705
+01:21:27,820 --> 01:21:33,080
+الكروية تمام؟ يبقى هذه الإحداثيات ستبقينا
+
+706
+01:21:33,080 --> 01:21:35,620
+Missionary Coordinates اليوم و لنبقى مع ال
+
+707
+01:21:35,620 --> 01:21:40,040
+cylindrical coordinates الإحداثيات الأسطوانية هي
+
+708
+01:21:40,040 --> 01:21:45,880
+مزيج بين الإحداثيات القطبية و الإحداثيات
+
+709
+01:21:47,970 --> 01:21:53,010
+كيف  تُكتب  قال الـ cylindrical coordinates لنقطة P
+
+710
+01:21:53,010 --> 01:22:01,250
+in space S إحداثياتها  P,R,θ, Z Z  الذي هو الـ
+
+711
+01:22:01,250 --> 01:22:05,410
+Cartesian coordinates الـR و θ هما الإحداثيات
+
+712
+01:22:05,410 --> 01:22:10,660
+القطبية بحيث الـR و θ هما ال polar coordinates of
+
+713
+01:22:10,660 --> 01:22:16,540
+the vertical projection of B on the XY plane و Z
+
+714
+01:22:16,540 --> 01:22:20,720
+هي تبعت ال rectangular coordinate السؤال هو كيف ذلك؟
+
+715
+01:22:20,720 --> 01:22:25,140
+يقول لك اه استني شوية تعالى لو رحنا أخذنا المحاور
+
+716
+01:22:25,140 --> 01:22:29,660
+الشكل الذي عنها هذا
+
+717
+01:22:29,660 --> 01:22:34,320
+أقول عليها فإني في ال Cartesian X و في ال
+
+718
+01:22:34,320 --> 01:22:41,800
+Polar نقول θ = 0  يبقى θ = 0 هذا
+
+719
+01:22:41,800 --> 01:22:46,680
+في ال Cartesian نقول عليه Y  و في ال Polar نقول
+
+720
+01:22:46,680 --> 01:22:54,740
+θ = π/2  هذا Z و خلينا Z لأن ال
+
+721
+01:22:54,740 --> 01:23:00,110
+Polar ما عنديش إلا إحداثيين  حسنًا نأخذ نقطة مثل
+
+722
+01:23:00,110 --> 01:23:08,850
+النقطة هذه النقطة P إحداثياتها R, θ, Z  نريد
+
+723
+01:23:08,850 --> 01:23:13,990
+أن نرى أين R, θ, Z  فنحن ننزلها على
+
+724
+01:23:13,990 --> 01:23:20,590
+المستوى XY plane يبقى لو نزلناها عموديًا على ال
+
+725
+01:23:20,590 --> 01:23:30,470
+XY plane يبقى هذا الرأس  من هو؟ هو Z الموازي لمحور Z
+
+726
+01:23:30,470 --> 01:23:40,130
+طيب هذا  موازي لمحور Y  يبقى هذا  و هذا موازي
+
+727
+01:23:40,130 --> 01:23:44,970
+لمحور X يبقى
+
+728
+01:23:44,970 --> 01:23:51,360
+هذا Y يبقى يأتي بالشكل الذي عنده تمام طيب إذا
+
+729
+01:23:51,360 --> 01:23:58,340
+أين R و θ هذه؟ نقول لك بسيطة الخط المائل الذي عندك
+
+730
+01:23:58,340 --> 01:24:07,940
+هذا R الخط
+
+731
+01:24:07,940 --> 01:24:14,320
+الذي عندنا هذا يمثل R طيب أين θ؟ الزاوية التي
+
+732
+01:24:14,320 --> 01:24:20,550
+صنعتها مع الاتجاه الموجب لـ X-Axis يبقى هذه ثيتا
+
+733
+01:24:20,550 --> 01:24:27,770
+يبقى ثيتا و R تابعتان لمن؟ الإحداثيات القطبية إذا
+
+734
+01:24:27,770 --> 01:24:32,390
+لهذه النقطة الإحداثيات التابعة لها من هي يا بنات؟ R و
+
+735
+01:24:32,390 --> 01:24:38,050
+ثيتا و 0 لأن Z هنا 0 النقطة التي فوق التي
+
+736
+01:24:38,050 --> 01:24:45,010
+هي R, θ, Z يبقى هذه الإحداثيات القطبية مع
+
+737
+01:24:45,010 --> 01:24:50,450
+الإحداثيات الديكارتية يبقى أي نقطة نكتبها بدلالة
+
+738
+01:24:50,450 --> 01:24:56,930
+R و θ و Z  فبإختصار نسأل بعض الأسئلة
+
+739
+01:24:56,930 --> 01:25:04,530
+السؤال الأول لو قلت لك في الإحداثيات الأسطوانية R
+
+740
+01:25:04,530 --> 01:25:17,840
+= 0 تمثل من؟ فقط  origin يعني هنا هذه R محور
+
+741
+01:25:17,840 --> 01:25:22,800
+Z ممتاز فالإجابة التي أعطيتنا سلام هي إجابة دقيقة
+
+742
+01:25:22,800 --> 01:25:27,480
+مائة بالمائة و المصطلح مدام R = 0 نحن أين
+
+743
+01:25:27,480 --> 01:25:32,240
+على محور Z إذا في ال cylindrical coordinates R
+
+744
+01:25:32,240 --> 01:25:35,880
+= 0 تمثل من؟  حكيت بالتفصيل و برهن عليه شوية
+
+745
+01:25:36,070 --> 01:25:39,850
+لأن في بعض الأسئلة أخرى أريد أن أسألها طيب لو قلت لك
+
+746
+01:25:39,850 --> 01:25:46,610
+θ = θ node معادلة
+
+747
+01:25:46,610 --> 01:25:52,050
+ما الشكل؟ في ال polar كان خط مستقيم ال polar هو
+
+748
+01:25:52,050 --> 01:25:57,950
+الآن  مثل θ = 0 و θ = 0 كان خط
+
+749
+01:25:57,950 --> 01:26:03,660
+مستقيم لكن لو قلت لك θ = θ node في الفضاء لأن
+
+750
+01:26:03,660 --> 01:26:13,780
+نتكلم في مستوى الفضاء ماذا يمثل؟ يبقى
+
+751
+01:26:13,780 --> 01:26:18,900
+هذا يمثل plane بالشكل الذي عندنا الذي هو عمودي
+
+752
+01:26:18,900 --> 01:26:23,960
+على مستوى ال X Y plane حسنًا ستكون هذه المعلومات
+
+753
+01:26:23,960 --> 01:26:32,140
+التي هي بالنسبة لـ R = 0 طيب لو قلنا R =
+
+754
+01:26:32,140 --> 01:26:39,590
+A R = ماذا؟ R = ماذا؟ R = ماذا؟ R
+
+755
+01:26:39,590 --> 01:26:43,550
+= ماذا؟ R = ماذا؟ R = ماذا؟ R =
+
+756
+01:26:43,550 --> 01:26:46,450
+ماذا؟ R = ماذا؟ R = ماذا؟ R =
+
+757
+01:26:46,450 --> 01:26:50,430
+ماذا؟ R = ماذا؟ R = ماذا؟ R =
+
+758
+01:26:50,430 --> 01:26:51,250
+ماذا؟ R = ماذا؟ R = ماذا؟ R =
+
+759
+01:26:51,250 --> 01:26:52,710
+ماذا؟ R = ماذا؟ R = ماذا؟ R =
+
+760
+01:26:52,710 --> 01:26:57,170
+ماذا؟ R = ماذا؟ R =
+
+761
+01:27:07,550 --> 01:27:19,510
+is the equation of the z axis النقطة الأولى النقطة
+
+762
+01:27:19,510 --> 01:27:29,910
+الثانية R = a is an equation is an equation
+
+763
+01:27:29,910 --> 01:27:42,470
+of a cylinder of a cylinder with axis محور
+
+764
+01:27:42,470 --> 01:28:00,050
+تابعها along the z axis على محور z and radius الذي
+
+765
+01:28:00,050 --> 01:28:01,050
+هو a
+
+766
+01:28:06,290 --> 01:28:15,510
+مرة ثالثة θ = θ node is an equation of
+
+767
+01:28:15,510 --> 01:28:25,670
+a plane مستوى يحتوي .. يحتوي
+
+768
+01:28:25,670 --> 01:28:31,210
+the z-axis  يُقابِل
+
+769
+01:28:31,210 --> 01:28:34,830
+محور z  و يصنع
+
+770
+01:28:39,000 --> 01:28:43,720
+زاوية θ
+
+771
+01:28:43,720 --> 01:28:55,140
+node مع الـ positive x
+
+772
+01:28:55,140 --> 01:28:55,920
+-axis
+
+773
+01:29:01,410 --> 01:29:07,270
+يعني لو رحنا و رسمنا هناك باختصار و قلنا هذا محور
+
+774
+01:29:07,270 --> 01:29:14,610
+X هذا محور Y هذا محور Z و رحنا و رسمنا هذا ال
+
+775
+01:29:14,610 --> 01:29:28,190
+plane فكانت رسمته على الشكل الثاني  اعمل
+
+776
+01:29:28,190 --> 01:29:35,680
+زاوية مقدارها θ node مع من؟ مع محور X يبقى هذا ال
+
+777
+01:29:35,680 --> 01:29:42,960
+plane  الرأس المظلل معادلته θ = θ node لكن في
+
+778
+01:29:42,960 --> 01:29:47,140
+ال polar كان θ = θ node معادلة خط مستقيم
+
+779
+01:29:47,140 --> 01:29:53,800
+و في ال polar كانت R = A معادلة A  شهد يا بنات
+
+780
+01:29:53,800 --> 01:29:59,980
+في ال polar coordinates في ال plane دائرة مركزها
+
+781
+01:29:59,980 --> 01:30:04,740
+نقطة الأصل و نصف قطر يساوي a كم يكون واحد
+
+782
+01:30:04,740 --> 01:30:08,960
+أو غيره بشرط الذي سيكون موجبا لو كان سالبا نأخذ له
+
+783
+01:30:08,960 --> 01:30:16,380
+من ال absolute value نعطي مثال بسيط على ذلك يبقى
+
+784
+01:30:16,380 --> 01:30:20,720
+examples  أول
+
+785
+01:30:20,720 --> 01:30:30,270
+مثال يقول لي evaluate أحسب التكامل الثلاثي التالي
+
+786
+01:30:30,270 --> 01:30:38,910
+تكامل من 0 إلى 2 تكامل من R - 2 إلى
+
+787
+01:30:38,910 --> 01:30:45,990
+الجذر التربيعي ل 4 - R تربيع تكامل من 0
+
+788
+01:30:45,990 --> 01:30:56,090
+إلى 2  لباقي لمن؟ ل R في cos θ + 1 R هذه
+
+789
+01:30:56,090 --> 01:31:07,710
+R هذه θ هذه z يبقى R هذه R يبقى
+
+790
+01:31:07,710 --> 01:31:27,480
+يقول لي R dθ dz dr نكتبه هكذا كما هو بالترتيب
+
+791
+01:31:27,480 --> 01:31:34,160
+نشوف أول شيء نكامل بالنسبة لمن؟ إلى dθ
+
+792
+01:31:34,160 --> 01:31:38,600
+المسألة أصبحت كأنها ماذا؟ integration
+
+793
+01:31:40,730 --> 01:31:46,190
+من R - 2 للجذر التربيعي ل 4 - R تربيع
+
+794
+01:31:46,190 --> 01:31:52,850
+و تكامل من 0 إلى 2 لـ R تربيع cos θ
+
+795
+01:31:52,850 --> 01:32:01,390
++ R dθ dz dr يقول إنه يريد تكاملًا
+
+796
+01:32:01,390 --> 01:32:04,790
+بالنسبة لـ dθ  ما هذا التكامل سهل ما به
+
+797
+01:32:04,790 --> 01:32:11,420
+مشكلة يبقى هذا تكامل من 0 إلى 2 تكامل من R -
+
+798
+01:32:11,420 --> 01:32:19,360
+2 للجذر التربيعي ل 4 - R تربيع لـ  R
+
+799
+01:32:19,360 --> 01:32:27,580
+تربيع cos θ + R dθ dz dr كل هذا الكلام
+
+800
+01:32:27,580 --> 01:32:33,220
+من 0 لغاية 2π لـ dz dr
+
+801
+01:32:35,650 --> 01:32:41,470
+هذا بالنسبة  تكامل من 0 إلى 2 تكامل من R -
+
+802
+01:32:41,470 --> 01:32:47,810
+2 للجذر التربيعي ل 4 - R تربيع
+
+803
+01:32:50,060 --> 01:32:55,080
+هذا  مصطلح الربع الدائري  لن يكون  يبقى R - 2
+
+804
+01:32:55,080 --> 01:32:59,980
+نعوض بالقيم العليا ناقص القيم السفلى cos 2π
+
+805
+01:32:59,980 --> 01:33:04,540
+= cos 0 = 1 يبقى يصبح 1 يبقى
+
+806
+01:33:04,540 --> 01:33:12,460
+يصبح لي هذا -R تربيع و هذا يصير 2π
+
+807
+01:33:12,460 --> 01:33:21,390
+يبقى + 2π - cos 0 = 1 -  
+
+808
+01:33:21,390 --> 01:33:31,070
+يصبح + R تربيع - 0 في R الذي هو 0
+
+809
+01:33:59,450 --> 01:34:06,690
+تكامل من 0 إلى 2 تكامل من R - 2 للجذر
+
+810
+01:34:06,690 --> 01:34:12,550
+التربيعي لـ 4 - R تربيع هو -R تربيع
+
+811
+01:34:12,550 --> 01:34:19,400
+و + R تربيع مع بعض و ال 2π R يبقى 2π R
+
+812
+01:34:19,400 --> 01:34:26,620
+dz dr فهذا الكلام يساوي 2π خذها برا
+
+813
+01:34:26,620 --> 01:34:32,260
+و هو تكامل من 0 لغاية 2 و R ليس له علاقة في
+
+814
+01:34:32,260 --> 01:34:39,920
+الموضوع و تكامل dz = z من 2R - 2 إلى
+
+815
+01:34:39,920 --> 01:34:49,710
+الجذر التربيعي ل 4 - R تربيع لمن لـ R هذا
+
+816
+01:34:49,710 --> 01:34:56,570
+الكلام يساوي 2π تكامل من 0 إلى 2 لـ R
+
+817
+01:34:56,570 --> 01:35:04,510
+الجذر التربيعي لـ 4 - R تربيع - (R في R -2) كل هذا الكلام بالنسبة لمن لـ
+
+818
+01:35:04,510 --> 01:35:12,150
+R هذا يا بنات  اعمل لها تعويض  هكذا يأتي عندك هنا R
+
+819
+01:35:18,910 --> 01:35:24,910
+هنا 4 - R تربيع يبقى بإمكاني أن أضع R =
+
+820
+01:35:24,910 --> 01:35:30,640
+2 sin θ مثل calculus B و بإمكاني أن أشيل ال 4
+
+821
+01:35:30,640 --> 01:35:34,900
+- R تربيع  التي فيها كلها مرة واحدة و أضع بدلها أي
+
+822
+01:35:34,900 --> 01:35:39,640
+متغير لأن الذي برا هو مشتقة الذي جوا لكن لا زال لم يأتي
+
+823
+01:35:39,640 --> 01:35:47,400
+إشارة سالبة و إلى 2 يبدأ بناء عليه نذهب إلى التكامل
+
+824
+01:35:47,400 --> 01:35:55,820
+الأول نقول له ضع لي مثلا w = 4 - R تربيع يبقى dw =
+
+825
+01:35:55,820 --> 01:35:59,640
+-2R dR
+
+826
+01:36:04,350 --> 01:36:10,430
+R dR إذا أصبح هذا يا بنات الذي هو 2 في
+
+827
+01:36:10,430 --> 01:36:16,270
+التكامل أفضل من هذا سيصبح عندك R dR سنضع
+
+828
+01:36:16,270 --> 01:36:24,430
+بدلا منها -1/2 و هذا dw  و هذا الجذر التربيعي لـ w
+
+829
+01:36:24,430 --> 01:36:31,650
+ضاع عند حدود التكامل عندما تكون R = 2 يصير 0
+
+830
+01:36:32,680 --> 01:36:37,820
+عندما تكون R = 0 يصير كم؟ 4 تمام هذا الجزء
+
+831
+01:36:37,820 --> 01:36:44,140
+الأول الجزء الثاني -2π تكامل من 0
+
+832
+01:36:44,140 --> 01:36:54,820
+إلى 2 لـ R تربيع - R 2π R تربيع - R
+
+833
+01:36:54,820 --> 01:37:03,790
+ماذا؟ الذي فوق؟ يبقى R - 2 هذا يا بنات
+
+834
+01:37:03,790 --> 01:37:10,930
+يبقى هذا يصير 2R فقط يبقى هذا R - 2
+
+835
+01:37:14,580 --> 01:37:18,060
+هذا الكبير تحت الظروف آخذه من الشكل و أخضعها من
+
+836
+01:37:18,060 --> 01:37:24,620
+شرط الموجب و النص مع π يصبح π تكامل من 0 إلى 4
+
+837
+01:37:24,620 --> 01:37:36,740
+لـ w 1/2 dw - 2π R تكعيب / 3 - R تربيع
+
+838
+01:37:36,740 --> 01:37:45,600
+كل ذلك من 0 إلى 2  هذا π في w أس 3/2 / 3/2 من
+
+839
+01:37:45,600 --> 01:37:50,600
+عند ال 0 لغاية ال 4  و هذا
+
+840
+01:37:50,600 --> 01:37:54,160
+ناقص 2π في 8/3
+
+841
+01:38:08,070 --> 01:38:13,450
+أس 3/2  يعني هنا 4 أس 3/2
+
+842
+01:38:13,450 --> 01:38:19,590
+- 0 و هذا بالنسبة يصير -2π في
+
+843
+01:38:19,590 --> 01:38:27,090
+3 في 4 باطلنا ناقصها معها  يصبح  -4/3
+
+844
+01:38:27,090 --> 01:38:36,030
+و يساوي 2π/3  في هذا الجذر
+
+845
+01:38:36,030 --> 01:38:41,730
+التربيعي لـ 4 تكعيب يعني الذي هو
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/XhdO8919qXw_postprocess.srt b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/XhdO8919qXw_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..fbff3278138bf091aae2d4a05c1b55dcd111375d
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/XhdO8919qXw_postprocess.srt
@@ -0,0 +1,3412 @@
+1
+00:00:00,000 --> 00:00:02,680
+موسيقى
+
+2
+00:00:12,980 --> 00:00:17,380
+يبقى يا بنات احنا كنا بنتكلم في ال sections
+
+3
+00:00:17,380 --> 00:00:21,940
+الماضية عن ال double integrants يبقى تكاملين
+
+4
+00:00:21,940 --> 00:00:25,620
+واخدنا التكاملين الاتنين هدول في ال Cartesian
+
+5
+00:00:25,620 --> 00:00:30,760
+coordinates وكذلك في ال polar coordinates الآن من
+
+6
+00:00:30,760 --> 00:00:36,440
+التكاملين سنتقل إلى ثلاث تكاملات في الإحداثيات
+
+7
+00:00:36,440 --> 00:00:41,760
+الكارتيزية وكذلكسنشير إلى إحداثيات جديدة لم نكن
+
+8
+00:00:41,760 --> 00:00:46,360
+نعرفها من قبل إن شاء الله تعالى لكن هذا ال section
+
+9
+00:00:46,360 --> 00:00:52,060
+اللي هو 15-5 سيتكلم عن التكاملات الثلاثية في
+
+10
+00:00:52,060 --> 00:00:53,240
+الإحداثيات
+
+11
+00:00:55,540 --> 00:01:00,000
+يبقى triple integrals in rectangular coordinates
+
+12
+00:01:00,000 --> 00:01:06,320
+التكاملات الثلاثية في الإحداثيات الكارتيزية أو في
+
+13
+00:01:06,320 --> 00:01:10,760
+الإحداثيات المستطيلة rectangular مستطيل إذا لما
+
+14
+00:01:10,760 --> 00:01:13,740
+أقول إحداثيات مستطيلة والله إحداثيات كارتيزية
+
+15
+00:01:13,740 --> 00:01:20,240
+الإتنين are the same طيب بيقول هنا volume V الحجم
+
+16
+00:01:20,240 --> 00:01:22,700
+V of a closed bounded region
+
+17
+00:01:26,650 --> 00:01:30,190
+عندى حجم باجى بقول the volume d over closed
+
+18
+00:01:30,190 --> 00:01:36,350
+bounded region D in space S V بدى ساوية triple
+
+19
+00:01:36,350 --> 00:01:41,550
+integrals على المنطقة دى بالنسبة لدى V طبعا دى V
+
+20
+00:01:41,550 --> 00:01:46,670
+هي مناطق دي Dx Dy Dz او Dz Dy Dx اللى هم التلاتة
+
+21
+00:01:46,900 --> 00:01:51,020
+مضربات في بعض بصي اختصارا بيقول احنا DV زي ما في
+
+22
+00:01:51,020 --> 00:01:55,200
+حالة ال double integral بيقول دي ايه لكن دي ايه
+
+23
+00:01:55,200 --> 00:02:00,760
+بفهمانا دي اكس دي واي او دي واي دي اكس السؤال هو
+
+24
+00:02:00,760 --> 00:02:04,280
+how to evaluate the triple integrals يعني كيف بدنا
+
+25
+00:02:04,280 --> 00:02:10,340
+نعرف نحسب التكاملات الثلاثية بقوله بسيطة ثلاث
+
+26
+00:02:10,340 --> 00:02:13,800
+خطوات لرابع لها خطوة الأولى
+
+27
+00:02:41,250 --> 00:02:48,170
+الخطوة الثانيةبتقول sketch the projection R of the
+
+28
+00:02:48,170 --> 00:02:53,210
+solid on the XY plane يبقى المجسم اللي عندي فوق قد
+
+29
+00:02:53,210 --> 00:02:57,190
+أسقط على مين على مستوى ال X و اللي يبقى بتظهر رصمة
+
+30
+00:02:57,190 --> 00:03:01,570
+وين في ال plane مدار ظهرت انه الرصمة في ال plane
+
+31
+00:03:01,570 --> 00:03:05,930
+لما شوف X من وين لونه متغير و Y من وين لونه
+
+32
+00:03:05,930 --> 00:03:18,230
+وبالتالي حددت حدود التكاملمن هنا تحدد حدود
+
+33
+00:03:18,230 --> 00:03:25,790
+التكامل على المجال A تمام يبقى الخطوة الثانية
+
+34
+00:03:25,790 --> 00:03:34,490
+اتنين حددنا حدود التكامل بالنسبة لكل من X وYخطوة
+
+35
+00:03:34,490 --> 00:03:39,950
+التالتة كما كنا بنكمل في ال sections الماضية
+
+36
+00:03:39,950 --> 00:03:44,770
+integrated as in the previous sections
+
+37
+00:03:51,860 --> 00:03:58,180
+المنطقة دي للفوفيكس واي و zdv هي عبارة عن تكاملين
+
+38
+00:03:58,180 --> 00:04:02,440
+على R و اول حاجة يقول ان انا بكامل بالنسبة ل ميم ل
+
+39
+00:04:02,440 --> 00:04:07,140
+z يبقى بروح بكامل الدالة بالنسبة ل z و بعوض بحدود
+
+40
+00:04:07,140 --> 00:04:12,920
+التكامل بصير المثل لكل دلالة ميمX و Y يعني اتخلصنا
+
+41
+00:04:12,920 --> 00:04:16,540
+من قصة Z بالمرة نهائية وماظلش عندي لتكامل بالنسبة
+
+42
+00:04:16,540 --> 00:04:21,800
+ل X و Y بكامل زي ما كنت بكامل بال sections الماضية
+
+43
+00:04:21,800 --> 00:04:25,620
+إذا أفضل بالنسبة ل X بروح بكامل بالنسبة ل X إذا مش
+
+44
+00:04:25,620 --> 00:04:29,680
+أفضل بروح بكامل بالنسبة ل Y و هكذا إني احتاج تغيير
+
+45
+00:04:29,680 --> 00:04:36,400
+بروح بغير و هكذاأخر نقطة نظري في هذا ال section
+
+46
+00:04:36,400 --> 00:04:40,320
+بيقول اللي بدك تجيبه هي عن القيمة المتوسطة للدالة
+
+47
+00:04:40,320 --> 00:04:46,180
+the average value أو معدل الدالة f of x و y على
+
+48
+00:04:46,180 --> 00:04:51,980
+منطقة التكامل دي بعرفها إنها واحد على ال volume
+
+49
+00:04:51,980 --> 00:04:56,880
+تبع ال D و تلت تكاملات على ال D ل main لل function
+
+50
+00:04:56,880 --> 00:05:02,280
+L عندنا يبقى لما نأتي بجديد تلت تكاملات كما هياللي
+
+51
+00:05:02,280 --> 00:05:07,600
+هو المنطقة دي بروح أكملها وهكذا، يبقى هاي اللي
+
+52
+00:05:07,600 --> 00:05:11,280
+بيحصل عندنا، اللي هو الكلام اللي قلناه بدنا نبدأ
+
+53
+00:05:11,280 --> 00:05:19,470
+نطبقه عاملينأحسب اللي قدامنا هذا تكمل على x لديه z
+
+54
+00:05:19,470 --> 00:05:24,550
+dy dx طبعا ال z هتتغير من تلاتة لاربعة نقص x تربية
+
+55
+00:05:24,550 --> 00:05:29,430
+نقص y ال y هتتغير من zero لواحد نقص x تربية ال x
+
+56
+00:05:29,430 --> 00:05:33,450
+هتتغير من وين لوين من zero لغاية واحد
+
+57
+00:05:38,730 --> 00:05:43,370
+مقدارا ثابتة يبقى هذا الكلام بده يساوي integration
+
+58
+00:05:43,370 --> 00:05:49,030
+من zero لواحد integration من zero لناقص X تربيع ال
+
+59
+00:05:49,030 --> 00:05:55,650
+X مقدار ثابت مانوش داعو تكمل DZ بZ من عندي تلاتة
+
+60
+00:05:55,650 --> 00:05:59,090
+لغاية أربعة ناقص X تربيع ناقص Y
+
+61
+00:06:03,470 --> 00:06:09,810
+يبقى هذا الكلام يسوي تكامله من 0 ل1 من 0 ل1 ناقص X
+
+62
+00:06:09,810 --> 00:06:14,290
+تربيع X مالوش دعوة الان بنعوض بالقيم اللي فوق ناقص
+
+63
+00:06:14,290 --> 00:06:23,050
+اللي تحت يبقى 4 ناقص X تربيع ناقص Y ناقص 3 كل دي Y
+
+64
+00:06:23,360 --> 00:06:28,160
+دي اكس عندي اربعة وناقص ثلاثة بيبقى كده اش واحد
+
+65
+00:06:28,160 --> 00:06:33,220
+اتجهالة المسألة الى integration من zero لواحد من
+
+66
+00:06:33,220 --> 00:06:40,120
+zero لواحد ناقص X تربيع لواحد ناقص X تربيع ناقص Y
+
+67
+00:06:40,120 --> 00:06:46,300
+كله دي Y دي X ويسوء ال integration من zero لواحد
+
+68
+00:06:46,300 --> 00:06:50,380
+بدي اكامل بالنسبة دي Y كيف؟
+
+69
+00:06:53,620 --> 00:06:57,000
+يبقى دلت مضروبة في X يبقى بدي أفكها على طول الخط
+
+70
+00:06:57,000 --> 00:07:05,200
+يبقى هذا ب X وهذا ب X تكييب وهذا ب XY نقص XY
+
+71
+00:07:05,200 --> 00:07:09,020
+بالشكل اللي عندنا هذا DY DX الأهم اللي ده كامل
+
+72
+00:07:09,020 --> 00:07:13,920
+بالنسبة له Y يبقى كل ال X باعتبرهم constants يبقى
+
+73
+00:07:13,920 --> 00:07:22,060
+integration من 0 ل1 لل XY نقص X تكييب Y نقص X
+
+74
+00:07:28,870 --> 00:07:34,630
+نقص X تربيع هذا الكلام يبدو يساوي يبقى integration
+
+75
+00:07:34,630 --> 00:07:38,570
+من zero لغاية واحد تعوض يا بنات بالقيم اللي فوق
+
+76
+00:07:38,570 --> 00:07:44,370
+ناقص اللي تحت يبقى شبه الصغير X في واحد ناقص X
+
+77
+00:07:44,370 --> 00:07:52,630
+تربيع ناقص X تكيب في واحد ناقص X تربيع ناقص نصف X
+
+78
+00:07:52,630 --> 00:07:58,590
+في واحد ناقص X تربيعالكل تربيع كله بالنسبة لمين
+
+79
+00:07:58,590 --> 00:08:03,170
+إلى X يبقى هذا الكلام بتيساوي integration من Zero
+
+80
+00:08:03,170 --> 00:08:08,170
+لواحد بدا فك الأقواسم عشان أجمعهم مع بعض يبقى مصير
+
+81
+00:08:08,170 --> 00:08:17,030
+X ناقص X تكييب ناقص X تكييب كذلك وهنا زائر
+
+82
+00:08:20,730 --> 00:08:25,030
+بدي أفكر جوز و أضرب يبقى هذا لو فكناه بلغتي اللي
+
+83
+00:08:25,030 --> 00:08:31,790
+هو واحد نقص اتنين اكس تربيع زائد اكس أُس أربع بدي
+
+84
+00:08:31,790 --> 00:08:37,030
+اضرب في من؟ في نص اكس بالزائد ليه مش مصير عندي هنا
+
+85
+00:08:37,030 --> 00:08:44,670
+نقص نص اكس نقص في نقص بزايد نص في اتنين مع السلامة
+
+86
+00:08:44,670 --> 00:08:53,410
+بظل عندي جداش اكس تكعيدو بعد ذلك نقص نص X أُس خمسة
+
+87
+00:08:53,410 --> 00:09:00,850
+كله بالنسبة لمين إلى DX طب تعالى نجمع عندنا هنا X
+
+88
+00:09:00,850 --> 00:09:07,010
+و عندنا هنا نص X يبقى بالسالب بضل جداش نص X
+
+89
+00:09:07,010 --> 00:09:14,730
+بالموجة يبقى هذا الكلام تكامل من صفر لواحد لنص X
+
+90
+00:09:15,520 --> 00:09:20,020
+بعد ذلك انا عند هنا اكس تكييب سالب و اكس تكييب
+
+91
+00:09:20,020 --> 00:09:27,560
+موجة بماها السلامة بظل عندنا كم؟ نقص اكس تكييب بعد
+
+92
+00:09:27,560 --> 00:09:33,780
+ذلك عند هنا اكس أس خمسة و نقص نص اكس أس خمسة بظل
+
+93
+00:09:33,780 --> 00:09:41,730
+عندنا نص اكس أس خمسة بالموجة يبقى زائدمص اكس اص
+
+94
+00:09:41,730 --> 00:09:48,910
+خمسة كل هذا بالنسبة لمين الى DX هذا الكلام يساوي
+
+95
+00:09:48,910 --> 00:09:57,090
+بدي اكمل الان يبقى رابع اكس تربيع وعندك هنا ناقص
+
+96
+00:09:57,090 --> 00:10:06,250
+رابع اكس اص اربع وعندك هنا زائداللي هو مين؟ بنضيف
+
+97
+00:10:06,250 --> 00:10:11,190
+للأس واحد وبنقسم على الأس الجديد يعني واحد على
+
+98
+00:10:11,190 --> 00:10:17,210
+اتناشر X أس ستة بدنا
+
+99
+00:10:17,210 --> 00:10:20,630
+نعوض بالقيم اللي فوق نقص اللي تحت يبقى هذا الكلام
+
+100
+00:10:20,630 --> 00:10:28,490
+بده يساوي الرابع ماقص رابع زائد واحد على اتناشر
+
+101
+00:10:28,490 --> 00:10:35,100
+ناقص Zero الباقي كله Zero يبقى الجواب جديد1 على 12
+
+102
+00:10:35,100 --> 00:10:41,120
+فقط لغير قيمة هذا التكامل الثلاثي
+
+103
+00:10:59,790 --> 00:11:07,190
+بس أجب نجسمهم على حجم المنطقة بيحطيني جديش المتوسط
+
+104
+00:11:07,190 --> 00:11:12,330
+خلال فترة التكامل اذاكرك بكالة كلاسية برضه بجنبها
+
+105
+00:11:12,330 --> 00:11:16,730
+نحسب ال average للدالة فقولنا كل المكاملة دالة على
+
+106
+00:11:16,730 --> 00:11:21,450
+ال interval و بنقسم على طول ال interval بيحطيني
+
+107
+00:11:21,450 --> 00:11:26,980
+جديش المتوسط هذاإذا بدنا نحسب المتوسط بيحدث عند أي
+
+108
+00:11:26,980 --> 00:11:31,360
+نقمة برضه بجري من جيب النقاط إبريكال كلصية إبريكال
+
+109
+00:11:31,360 --> 00:11:35,840
+كلصية نفس الفكرة بالضبط تماما إذا نحسب التكاملات
+
+110
+00:11:35,840 --> 00:11:40,400
+الثلاثية على الدالة و نحسب التكامل الثلاثية على
+
+111
+00:11:40,400 --> 00:11:45,020
+المنطقة اللي نريد أن نتبعها لإننا نكمل عليه و نكسب
+
+112
+00:11:45,020 --> 00:11:49,520
+اتنين على بعض واحد على ال volume تبع الديل بثلاث
+
+113
+00:11:49,520 --> 00:11:52,120
+تكاملات على الديل الدالة
+
+114
+00:11:57,380 --> 00:12:02,360
+مش احنا بنكمل على المنطقة دي، بدي احسب كده حكم
+
+115
+00:12:02,360 --> 00:12:07,460
+المنطقة دي، كويس؟ حسبنابنحسب تلك التكاملات
+
+116
+00:12:07,460 --> 00:12:13,380
+الثلاثية على الدالة حسب نبقى اقسم هذا على هذا واحد
+
+117
+00:12:13,380 --> 00:12:18,160
+على مضروب هذا فوق في البصد وليس في المقام يبقى هذا
+
+118
+00:12:18,160 --> 00:12:21,240
+في البصد و هذا في المقام نقسم الدين على بعض بطلع
+
+119
+00:12:21,240 --> 00:12:28,480
+جدش متوسط دالة على هذه المنطقة نحسب
+
+120
+00:12:28,480 --> 00:12:33,300
+تلت تكاملات د دي ست دي واي دي اكس دحالة من الأول
+
+121
+00:12:34,060 --> 00:12:39,740
+كمان؟ يبقى جيبنا الحجم B كداش نسبة بعد هيك بروح
+
+122
+00:12:39,740 --> 00:12:45,740
+بحث بالتالتة كلمات لدالة على هذه المنطقة كويس؟
+
+123
+00:12:45,740 --> 00:12:49,600
+وبيكون جيب كداش من غرفة اكسم اتنين او اربعة تجيب
+
+124
+00:12:49,600 --> 00:12:51,720
+المنطقة واصل تلقى المنطقة تلقى المنطقة تلقى
+
+125
+00:12:51,720 --> 00:12:54,240
+المنطقة تلقى المنطقة تلقى المنطقة تلقى المنطقة
+
+126
+00:12:54,240 --> 00:12:54,400
+تلقى المنطقة تلقى المنطقة تلقى المنطقة تلقى
+
+127
+00:12:54,400 --> 00:12:57,080
+المنطقة تلقى المنطقة تلقى المنطقة تلقى المنطقة
+
+128
+00:12:57,080 --> 00:13:02,660
+تلقى المنطقة تلقى المنطقة تلقى المنطقة تلقى المنط
+
+129
+00:13:06,170 --> 00:13:13,870
+بتانى رقم اتنين بيقول لبعضه حاجة اسمه الى a وb نمر
+
+130
+00:13:13,870 --> 00:13:21,830
+a بيقول لي evaluate احسبلي integration من zero ل
+
+131
+00:13:21,830 --> 00:13:26,750
+one integration من سالب one ل zero integration من
+
+132
+00:13:26,750 --> 00:13:38,070
+zero ل y تاربيع ل dz dy dxالمطلوب التاني نمر به
+
+133
+00:13:38,070 --> 00:13:46,890
+rewrite rewrite قعد كتابة the integral the
+
+134
+00:13:46,890 --> 00:14:00,930
+integral التكامل as an equivalent as
+
+135
+00:14:00,930 --> 00:14:03,450
+an equivalent integral
+
+136
+00:14:07,260 --> 00:14:13,260
+in the order dy
+
+137
+00:14:13,260 --> 00:14:16,440
+dz
+
+138
+00:14:16,440 --> 00:14:22,460
+dx وراح
+
+139
+00:14:22,460 --> 00:14:28,120
+مش هذا احد أسئلة الكتاب رسملي الرسمة وقاللي احصل
+
+140
+00:14:28,120 --> 00:14:36,530
+نجي نرسم الرسمة يبقى الرسمة كتاليهذا محور X، هذا
+
+141
+00:14:36,530 --> 00:14:43,510
+محور Y، هذا محور Z، خلص معايا بنات، يبقى من هنا
+
+142
+00:14:43,510 --> 00:14:51,090
+مدهد على استقراره، ومن هنا جرسا موازي إليه، وطلع
+
+143
+00:14:51,090 --> 00:14:58,490
+رأسي هيكو من هنا طلع رأسي هيك و من هنا رسم موازي
+
+144
+00:14:58,490 --> 00:15:05,010
+لمحور X و من هنا موازي لمحور X الشكل اللي عندنا
+
+145
+00:15:05,010 --> 00:15:08,590
+هذا تمام؟
+
+146
+00:15:08,590 --> 00:15:13,610
+و
+
+147
+00:15:13,610 --> 00:15:20,290
+الراجل هنا هيك رسم لي قوس الشكل اللي عندنا هذا و
+
+148
+00:15:20,290 --> 00:15:22,370
+من هنا قوس الشكل اللي عندنا هذا
+
+149
+00:15:26,990 --> 00:15:30,910
+شايفين الخط الأزرق الجوسي من هات اللي فوق يبقى هذا
+
+150
+00:15:30,910 --> 00:15:37,510
+هو السطح العلوي تمام الشكل اللي عندنا هذا الأسود
+
+151
+00:15:37,510 --> 00:15:45,210
+اللي تحت هخططولك بالشكل الأسود هذا هو المستوى
+
+152
+00:15:45,210 --> 00:15:50,030
+السفلي اللي موجود في مستوى XY plane
+
+153
+00:15:57,330 --> 00:16:02,950
+طيب كل النقطة اللي عندنا هذه حط لإحداثيات كل نقطة
+
+154
+00:16:02,950 --> 00:16:09,570
+من هذه النقارة يبقى واحد و سالب واحد وزيرو النقطة
+
+155
+00:16:09,570 --> 00:16:14,710
+اللي عندنا هذه لفوق واحد وسالب واحد وواحد والنقطة
+
+156
+00:16:14,710 --> 00:16:20,910
+هذه Zero وسالب واحد وواحد اكتر من هيك ماتنيش
+
+157
+00:16:20,910 --> 00:16:26,390
+معلومات وهذه النقطة اللي بين اللي هي نقطة اللي هي
+
+158
+00:16:26,390 --> 00:16:26,590
+Zero
+
+159
+00:16:30,660 --> 00:16:33,840
+و اعطاني هذا النقطة اللي هي واحد و Zero Zero
+
+160
+00:16:33,840 --> 00:16:37,400
+تخيلين
+
+161
+00:16:37,400 --> 00:16:46,600
+انه الشكل الشكل الأزرق اللي فوق هذا هذا كله يعتبر
+
+162
+00:16:46,600 --> 00:16:52,880
+بنات المستوى العلويوحصر كل اللي منه تحت يبقى هذا
+
+163
+00:16:52,880 --> 00:16:58,020
+يعتبر السطح العلوي والمخطط بالأسود هذا يعتبر السطح
+
+164
+00:16:58,020 --> 00:17:03,960
+السفلي أو المستوى السفلي لهذا المجسم والمستوى اللي
+
+165
+00:17:03,960 --> 00:17:09,900
+عندنا هذا زي ما انتوا شايفين هذا موازن لل XZ plane
+
+166
+00:17:09,900 --> 00:17:15,380
+موازن له تماما قاللي احسبلي التكمل اللي فوق و بعد
+
+167
+00:17:15,380 --> 00:17:19,720
+هيكمطلوب التاني الـ rewrite the integral قعدت
+
+168
+00:17:19,720 --> 00:17:26,040
+كتابة هذا التكامل بمين؟ بتكامل مكافئله لكن مش
+
+169
+00:17:26,040 --> 00:17:35,520
+بالترتيب dz dy dx وإنما dy dz dx يعني هنا الأخير
+
+170
+00:17:35,520 --> 00:17:42,020
+خلّاه زي ما هو وجالب اتنين هذول مكان بعض إذن هنتر
+
+171
+00:17:42,020 --> 00:17:47,890
+نغير حدود التكامل طبقا لذلكوالروح نحسب التكامل هذا
+
+172
+00:17:47,890 --> 00:17:53,070
+السؤال هو يا ترى في كل التكاملين بيطلع إن قيمتهم
+
+173
+00:17:53,070 --> 00:17:58,010
+مختلفتين و الله نفس القيمة نفس القيمة لأن هذا حجب
+
+174
+00:17:58,010 --> 00:18:01,890
+ده و الله اطلع لغيره يبقى هذا بيطلع إن ايه نفس
+
+175
+00:18:01,890 --> 00:18:04,910
+القيمة يبقى باجي بقى منه الصليوشة
+
+176
+00:18:07,930 --> 00:18:13,270
+أول تكامل من 0 إلى 1 من سالب واحد إلى Zero وهذه
+
+177
+00:18:13,270 --> 00:18:20,570
+تكامل عادى جدا تكملها ب Z من Zero ل Y تربية Dy DX
+
+178
+00:18:23,130 --> 00:18:27,290
+نعود بالقيمة اللي فوق ناقص اللي تحت اللي تحت بـ0
+
+179
+00:18:27,290 --> 00:18:33,270
+يصير تكمل من 0 ل1 تكمل من سالق واحد إلى Zero ل Y
+
+180
+00:18:33,270 --> 00:18:41,190
+تربية Dy dx يساوي تكمل من Zero لواحد وبدأ أكمل
+
+181
+00:18:41,190 --> 00:18:47,590
+بالنسبة إلى Y يبقى Y تكيب على تلاتة من Zero لواحد
+
+182
+00:18:51,380 --> 00:18:59,400
+بتقول الى طول تكامل من zero ل واحد ل dx واحد تكيب
+
+183
+00:18:59,400 --> 00:19:03,840
+واحد على تلاتة يخليك برا ناقص ال zero مع السلامة
+
+184
+00:19:03,840 --> 00:19:13,300
+يبقى هذا كيف من أه أستنى شوية أستنى شوية ماشي ماشي
+
+185
+00:19:13,300 --> 00:19:20,990
+بسيطة جدايبقى هذا من سالب واحد إلى زيرو صحيح يبقى
+
+186
+00:19:20,990 --> 00:19:26,770
+من سالب واحد إلى زيرو القيمة اللى فوق بتروح بزيرو
+
+187
+00:19:26,770 --> 00:19:33,170
+تمام مع السلامة يبقى هذا الكلام بدى يصير هى الطول
+
+188
+00:19:33,170 --> 00:19:42,110
+برا ويتكمل من زيرو إلى واحد لزيرو ناقص ناقص واحد
+
+189
+00:19:42,110 --> 00:19:44,390
+لكل تكعيب DX
+
+190
+00:19:51,300 --> 00:19:59,060
+بنرجع كما كنا تكمل من zero لواحد ذا DX يبقى هذا
+
+191
+00:19:59,060 --> 00:20:05,160
+الكلام طول X كمان من zero لغاية واحد يبقى الجواب
+
+192
+00:20:05,160 --> 00:20:11,320
+يسوى قدر طول اذا بروح لنمر بيه من المسألة
+
+193
+00:20:33,900 --> 00:20:39,320
+خلّيني أقول معاكم مثلا في نمرة بي من المسألة بقال
+
+194
+00:20:39,320 --> 00:20:47,120
+لي اقلب حدود التكامل هتصير تكامل اتنين ثلاثة لديه
+
+195
+00:20:47,120 --> 00:20:54,360
+y دي زد دي اكس انا بروح اشوف له y ده تتغير من ويل
+
+196
+00:20:54,360 --> 00:21:01,580
+لويل بروح برسم خط موازي لمحور y ويقطع منطقة
+
+197
+00:21:01,580 --> 00:21:07,900
+التكاملوبتشوف قدش أقل قيمة لهذا الخط يعني أقل قيمة
+
+198
+00:21:07,900 --> 00:21:12,540
+بتاخدها Y و أكبر قيمة بتاخدها Y يبقى الخطش بتكون
+
+199
+00:21:12,540 --> 00:21:18,780
+بنات أفوقي وموازن لمحور Y يبقى بتاجي أرسمله خط
+
+200
+00:21:18,780 --> 00:21:24,250
+يبقى هذا الخطبتدا من وين يا بنات؟ بتدا من السطح
+
+201
+00:21:24,250 --> 00:21:32,150
+المائل وانتهى وين؟ على الـ Plane الرأس الموازي
+
+202
+00:21:32,150 --> 00:21:38,070
+لمحور XZ يبقى هاي الخط الأفق الموازي لمحور Y
+
+203
+00:21:38,070 --> 00:21:42,550
+النقطة هذه هي النقطة اللي جاية في الـ Plane اللي
+
+204
+00:21:42,550 --> 00:21:46,330
+فوق الـ Plane اللي فوق ايش كانت معادلته؟
+
+205
+00:21:48,600 --> 00:21:54,340
+Z تساوي Y تربيع صحيح ولا لأ لأن هذا الأفق الأرض
+
+206
+00:21:54,340 --> 00:22:01,460
+الأسود Z تساوي Zero إذا اللي فوق هذا الأزرق Z
+
+207
+00:22:01,460 --> 00:22:08,880
+تساوي Y تربيع هذا هاتف كان Z تساوي Y تربيع طب الآن
+
+208
+00:22:08,880 --> 00:22:14,300
+أنا بكمل أولا بالنسبة إلى Y يبقى Y ايش بالصين
+
+209
+00:22:23,640 --> 00:22:29,720
+الرسم كله على شمال الـ X Y Plane وليس على يمينه لو
+
+210
+00:22:29,720 --> 00:22:37,320
+كانت على يمينه لكانت Y بالموجة لكن نظرا لإنها على
+
+211
+00:22:37,320 --> 00:22:42,160
+شمال يعني في الجهة السالبة ل Yيبقى باجي بقول
+
+212
+00:22:42,160 --> 00:22:51,480
+المكافئة لها Y تساوي سالب جدر ال Z ممتاز
+
+213
+00:22:51,480 --> 00:22:58,900
+طيب ده السؤال هذه هو تعتبر القيمة الكبرى ولا
+
+214
+00:22:58,900 --> 00:23:04,660
+القيمة الصغرى لما نكمل بالنسبة ل Y الكبرى طيب إذا
+
+215
+00:23:04,660 --> 00:23:12,810
+بدنا نروح نجيب القيمة الصغرى هنابدي اعرف قيمة Y في
+
+216
+00:23:12,810 --> 00:23:18,170
+هذه الحالة طالع يا بنات قدش الطول هذا قدش الطول
+
+217
+00:23:18,170 --> 00:23:25,770
+هذا قدش هنا Y إذا هنا قدش تبقى سالب واحد يعني لين
+
+218
+00:23:25,770 --> 00:23:33,100
+الرأس هذا معادلة Y تساوي سالب واحد واضحة؟يبقى الـ
+
+219
+00:23:33,100 --> 00:23:38,880
+Plain ههه هيودة حقلك عليه سهم اللي غير مظلن
+
+220
+00:23:38,880 --> 00:23:45,640
+التظليل بيوصلوش هذا معادلة Y تساوي سالب واحد إذا Y
+
+221
+00:23:45,640 --> 00:23:51,960
+ستتغير من سالب واحد اللي هي قيمة الصورة إلى القيمة
+
+222
+00:23:51,960 --> 00:23:59,020
+الكبرى اللي هو سالب جذر زادطب الداجة هنا، كداش أقل
+
+223
+00:23:59,020 --> 00:24:05,600
+قيمة لزد و كداش أكبر قيمة لزد؟ من صفر لواحد، من
+
+224
+00:24:05,600 --> 00:24:13,420
+zero لواحد، كداش أقل قيمة ل X و أكبر قيمة ل X؟ من
+
+225
+00:24:13,420 --> 00:24:20,470
+صفر لواحد كذلك، من صفر لواحدطيب، لو الحجم هذا
+
+226
+00:24:20,470 --> 00:24:26,690
+مطلعش طول، يبقى شغلي غلط على كل الخط أو بكون غلط
+
+227
+00:24:26,690 --> 00:24:31,970
+مافي الحسابات، بروح اراجع معلوماتنا مرة ثانية طب
+
+228
+00:24:31,970 --> 00:24:35,370
+تعالوا نحسب هذا و نشوف كده شو بده يساوي يبقى
+
+229
+00:24:35,370 --> 00:24:42,870
+integration من zero لواحد لل Y من عند سالب واحد
+
+230
+00:24:42,870 --> 00:24:48,850
+لغاية سالب جذر ال Zوهنا DZ DX
+
+231
+00:24:50,740 --> 00:24:58,420
+يستخدم انتقال من 0 إلى 1 لناقص
+
+232
+00:24:58,420 --> 00:25:05,200
+جدر الـ z زائد واحد كل هذا ناقص جدر الـ z زائد
+
+233
+00:25:05,200 --> 00:25:05,740
+واحد
+
+234
+00:25:17,210 --> 00:25:20,330
+يبقى هذا الكلام بدل ساوي integration من zero
+
+235
+00:25:20,330 --> 00:25:24,930
+لواحد، بدي أكمل الدالة هذه بالنسبة إلى زد، هذه
+
+236
+00:25:24,930 --> 00:25:32,930
+تعتبر زد قص جداش؟ طولتين
+
+237
+00:25:32,930 --> 00:25:37,890
+زد قص تلاتة على اتنين بس بشارة سالب، يبقى سالب
+
+238
+00:25:37,890 --> 00:25:39,070
+طولتين
+
+239
+00:25:44,340 --> 00:25:50,620
+الحاجة ده كلها بنات من where ل where من zero لغاية
+
+240
+00:25:50,620 --> 00:25:55,920
+واحد ولسه بايل علينا دي xطب نعوض بالقيمة اللى فوق
+
+241
+00:25:55,920 --> 00:26:00,100
+ناقص اللى تحت يبقى هذا الكلام بده يساوي
+
+242
+00:26:00,100 --> 00:26:07,680
+integration من zero لواحد لسالب تلتين زائد واحد
+
+243
+00:26:07,680 --> 00:26:13,840
+ناقص zero بيروح مع السلامة كل هذا بالنسبة إلى مين؟
+
+244
+00:26:13,840 --> 00:26:22,930
+لدي x يبقى تكامل من zero لواحدلطول DX يبقى طول X
+
+245
+00:26:22,930 --> 00:26:29,110
+من Zero لواحد يبقى قديش ويسوى طول نفس الحجم اللي
+
+246
+00:26:29,110 --> 00:26:34,410
+طلعناها قبل قليل لو ما طلعش يبقى يا إما الحساب
+
+247
+00:26:34,410 --> 00:26:40,090
+عندنا غلط يا إما حدود التكامل اللي طلعناها مش
+
+248
+00:26:40,090 --> 00:26:46,790
+دقيقة لكن الحدود عندنا سليمة مائة بالمائةطيب نروح
+
+249
+00:26:46,790 --> 00:26:57,550
+ل example تلاتة بيقول
+
+250
+00:26:57,550 --> 00:26:59,190
+find the volume of the region
+
+251
+00:27:08,520 --> 00:27:20,120
+ما جدتش حجم المنطقة كانت from the cylinder اللي
+
+252
+00:27:20,120 --> 00:27:27,500
+اقطعت من الأسطولة x تربيع زائد y تربيع يساوي واحد
+
+253
+00:27:28,480 --> 00:27:38,280
+by the plains by the plains بالمستويين z يساوي
+
+254
+00:27:38,280 --> 00:27:47,180
+ناقص y and z يساوي زي و كذلك رسملي المنطقة
+
+255
+00:27:52,130 --> 00:27:58,110
+هذا محور X هذا محور Y هذا محور Z
+
+256
+00:28:40,930 --> 00:28:51,130
+X Y Z أكتر من ما أعطانيش معلومة لكن أعطاني هذا
+
+257
+00:28:51,130 --> 00:28:59,020
+اللي هو الواحدقال له اخر قال انا ثلاث سنة ثلاث سنة
+
+258
+00:28:59,020 --> 00:29:05,920
+في خطأ ترسل قال مات مات لحد هنا انا وقال في جيله
+
+259
+00:29:05,920 --> 00:29:12,920
+لغايتين وقال انا جيلي بالشكل ده كيف يا بسم الله
+
+260
+00:29:12,920 --> 00:29:19,160
+يحفظ انا المرحلس يالي واحد واهلي واحد بالشكل ده
+
+261
+00:29:24,270 --> 00:29:29,650
+يبقى زي السفين اللي أجب مير وهذا أجب أفقه يتلاقوا
+
+262
+00:29:29,650 --> 00:29:34,530
+مع بعض يبقى جزء كل مستوانة رأسي قاطعلها بمستوى
+
+263
+00:29:34,530 --> 00:29:41,010
+مائل وهذا المستوى أفضل فانه Z بيساوي واحد الان بدأ
+
+264
+00:29:41,010 --> 00:29:47,270
+أخطط كل مستوى من المستوين عشان نحدد كويس يبقى هذا
+
+265
+00:29:47,270 --> 00:29:52,650
+مستوى الأرض يعني مستوى مائل
+
+266
+00:29:56,040 --> 00:30:02,000
+المستوى الأزرق هو مستوى الأرض الـ XY Plane المستوى
+
+267
+00:30:02,000 --> 00:30:05,080
+المائل هو المستوى الفوق
+
+268
+00:30:17,320 --> 00:30:20,780
+يبقى المخطط في الأزرق اللي هو المستوى الأفقي Z
+
+269
+00:30:20,780 --> 00:30:26,380
+تساوي Zero والمخطط بالأسود اللي هو المستوى المائي
+
+270
+00:30:26,380 --> 00:30:31,880
+اللي هو Z يساوي سالب Y تربية إذا هذا الاطلين
+
+271
+00:30:31,880 --> 00:30:40,720
+معادلته Z تساوي سالب Y والمستوى الأفقي هذا اللي هو
+
+272
+00:30:40,720 --> 00:30:43,940
+Z تساوي كده؟ تساوي Zero
+
+273
+00:30:47,300 --> 00:30:51,620
+جالي هذا ليه جداش حجم المنطقة اللي قطعناها من
+
+274
+00:30:51,620 --> 00:30:57,020
+الأسطوان اللي عندنا دي بين ال two planes بقوله
+
+275
+00:30:57,020 --> 00:31:02,380
+بسيطة ال volume V طبعا مرسومة في الكتاب برضه رسمها
+
+276
+00:31:02,380 --> 00:31:12,080
+لها ال V هذه بدها تساوي تلت تكاملات لDZ DY DX
+
+277
+00:31:14,390 --> 00:31:19,590
+المستوى الأفقي هو z يساوي zero المستوى المائل z
+
+278
+00:31:19,590 --> 00:31:27,850
+يساوي one يبقى لو جيت رسم قطع منطقة التكامل من عند
+
+279
+00:31:27,850 --> 00:31:34,230
+المستوى الأفقي و جيت طالع رأسي موازي لمحور z قابل
+
+280
+00:31:34,230 --> 00:31:38,330
+المستوى المائل عند النقطة اللي فوق يبقى النقطة
+
+281
+00:31:38,330 --> 00:31:44,700
+اللي فوق كده يا بنات z يساوي one و هنا z كدهإذاً
+
+282
+00:31:44,700 --> 00:31:53,640
+بدي أقوله من Zero لغاية سالب Y مين ضال عندنا؟ مين
+
+283
+00:31:53,640 --> 00:31:59,060
+ضال عندنا ال X وY مشان تتوضحليك الصورة بدي أرسم
+
+284
+00:31:59,060 --> 00:32:04,200
+نصف الدائرة اللي عندنا هنا تمام؟ مشان أعرف برضه
+
+285
+00:32:04,200 --> 00:32:09,480
+نصف الدائرة بدي تغير من ويل لويل بعدين بقوله هذا
+
+286
+00:32:09,480 --> 00:32:17,920
+اللي هو محور X وهذا محور Yهذا X وهذا Y وهذه نقطة
+
+287
+00:32:17,920 --> 00:32:25,300
+الأصل Z X بدأ تتغير من عند السالب واحد لغاية
+
+288
+00:32:25,300 --> 00:32:33,240
+الواحد يبقى سالب واحد واحد هل احنا جهة Y الموجبة
+
+289
+00:32:33,240 --> 00:32:38,020
+ولا جهة Y السالبة جهة Y السالبة كبيرة الرسمة بدأ
+
+290
+00:32:38,020 --> 00:32:45,360
+تظهر أعلى محور X ولا أسفل محور Xأسفل المحور X يبقى
+
+291
+00:32:45,360 --> 00:32:52,940
+هذا يعتبر
+
+292
+00:32:52,940 --> 00:32:58,480
+هو ال domain تبع الدالة خطوة ثانية حدد ال domain
+
+293
+00:32:58,480 --> 00:33:04,460
+أي حددنا ال domain تبع الدالة إذا بدنا نكمل
+
+294
+00:33:04,460 --> 00:33:11,080
+بالنسبة ل Y في الأولبنروح و بنرسم خط يقطع منطقة
+
+295
+00:33:11,080 --> 00:33:17,900
+التكامل بالشكل عن هذا هو موازي المقور Y يبقى هنا Y
+
+296
+00:33:17,900 --> 00:33:26,260
+موجداش اما نها Zero طب هنا Y موجداش نرجع
+
+297
+00:33:26,260 --> 00:33:31,380
+لمينها دي معادلة الدائرة الدائرة ايش كانت X تربيه
+
+298
+00:33:31,380 --> 00:33:37,140
+زاد Y تربيه تساوي واحد انا بدي Yيبقى بصير عند مين
+
+299
+00:33:37,140 --> 00:33:43,780
+بصير عند Y تربيع يسوى واحد ناقص X تربيع إذا بناء
+
+300
+00:33:43,780 --> 00:33:50,720
+عليه Y تساوي زائد أو ناقص الجذر التربيع إلى واحد
+
+301
+00:33:50,720 --> 00:33:56,940
+ناقص X تربيع لكن Y سالبة ولا موجبة سالبة يبقى بصير
+
+302
+00:33:56,940 --> 00:34:03,780
+سالب الجذاب يبقى معنى هذا الكلام ان Yبدي احط تحت
+
+303
+00:34:03,780 --> 00:34:10,100
+هنا بنات Zero و فوق سالب الجدد Zero يبقى هذه Zero
+
+304
+00:34:10,100 --> 00:34:14,940
+تعتبر القيمة الكبرى وهذه الصغيرة لانها سالمة يبقى
+
+305
+00:34:14,940 --> 00:34:20,100
+باجي بقوله من سالب الجدر التربيع إلى واحد ناقص X
+
+306
+00:34:20,100 --> 00:34:29,360
+تربيع لغاية Zero ضالة ال X تتغير من سالب واحد إلى
+
+307
+00:34:29,360 --> 00:34:34,850
+واحديبقى من سالب واحد إلى واحد حددنا حدود التكامل
+
+308
+00:34:34,850 --> 00:34:38,630
+صح بضل بعد ذلك الشغل الروتيني يبقى .. زي ما انتوا
+
+309
+00:34:38,630 --> 00:34:42,910
+شايفيني بنتدرج في الأسئلة شوية شوية كل سؤال أدخل
+
+310
+00:34:42,910 --> 00:34:48,030
+مش التاني حتى نستوقع الموضوع، تفضلي يا عزيزي تعالي
+
+311
+00:34:48,030 --> 00:34:53,450
+هنا على اللوحة، شوف تعالي يلا، كوني مثال لغيرك
+
+312
+00:34:53,450 --> 00:34:57,450
+يعني هي تبرعت بنفسها، لأن قالت أنا مش فاهمة كيف
+
+313
+00:34:57,450 --> 00:35:00,960
+جيبنا حدود التكامليبقى خدوا بالك كيف بدنا نجيب
+
+314
+00:35:00,960 --> 00:35:07,220
+حدود التكمل أول حاجة، في مشكلة على ذات؟ بس خليني
+
+315
+00:35:07,220 --> 00:35:10,260
+مع هذا واحد واحد، إذا فهمنا هذا بكون أنا طيب
+
+316
+00:35:10,260 --> 00:35:15,460
+هتقولي دفتر بالله يا بنهاد؟ لأ دي دفتر، كويس تعيلي
+
+317
+00:35:15,460 --> 00:35:21,300
+الدفتر يعنى؟ واحد أفقي وواحد عمودي، يبقى الأفقي هو
+
+318
+00:35:21,300 --> 00:35:27,340
+هذاوالعمود اللى جاى من ورا هذا كويس انا بدي اجيب
+
+319
+00:35:27,340 --> 00:35:33,020
+من الماء المستوى الماء الهالى و هيك كويس يبقى زد
+
+320
+00:35:33,020 --> 00:35:40,620
+هنا بقداش صفر زد هنا معادلة زتين والزد يسوى ناقص
+
+321
+00:35:40,620 --> 00:35:46,200
+واحد صح ولا لا اذا بصير زد تتغير من zero يعني انا
+
+322
+00:35:46,200 --> 00:35:50,840
+بدأت الخط الأزرق اللى رسموه كدهمن عند الـ Z تساوي
+
+323
+00:35:50,840 --> 00:35:54,120
+Zero هنا لغاية Y لغاية ما جابلت المستوى ده بقى
+
+324
+00:35:54,120 --> 00:35:59,540
+واضحة الصورة يعني؟ طيب خلاص لما انقصت Z يبقى Z
+
+325
+00:35:59,540 --> 00:36:04,440
+تغيرت من Zero لواحد لناقص Y وده دفعك لتبقى بقى
+
+326
+00:36:04,440 --> 00:36:12,160
+عندي طيب المين عندي؟ طيب حدود ال Y و ال X ال Y و
+
+327
+00:36:12,160 --> 00:36:16,590
+ال X هو ال domain تبعي ده ليعني مين؟يعني نصف
+
+328
+00:36:16,590 --> 00:36:21,570
+الدائرة اللى عندناها تمام فجيت رسمت نصف الدائرة
+
+329
+00:36:21,570 --> 00:36:27,770
+قولت اه هى محور Y وهى محور X هذه مش ال Y الموجة
+
+330
+00:36:27,770 --> 00:36:33,890
+بجهة Y مين اذا يقول هى Y السلبي لنجعله نصف الدائرة
+
+331
+00:36:33,890 --> 00:36:38,770
+السفلية الان بدنا نحدد Y بده تتغير من و لا و ايه
+
+332
+00:36:38,770 --> 00:36:42,250
+يعني يا بنت احنا الان بدنا نشتغل زى ما كنا بنشتغل
+
+333
+00:36:42,250 --> 00:36:49,100
+وين في ال sections ال ماضىفقلنا برسم خط يوازي محور
+
+334
+00:36:49,100 --> 00:36:54,880
+Y و بشوف Y قداشة تاخد أقل قيمة لها و قداشة أكبر
+
+335
+00:36:54,880 --> 00:36:59,580
+قيمة لها و Y قدت أقل قيمة هي سارق الجدرى التربية
+
+336
+00:36:59,580 --> 00:37:01,340
+لو أحد ناقص X تربية
+
+337
+00:37:04,780 --> 00:37:11,940
+لأن Y عدنا بالسالب و Y موجبة كانت الرسمة فوق، يبقى
+
+338
+00:37:11,940 --> 00:37:18,160
+هنا أقل قيمة ل Y هي سالب الجدر و أكبر قيمة جداشإذا
+
+339
+00:37:18,160 --> 00:37:21,860
+Y تغيرت من سالب الجدران لغاية Zero، مين ضايق اللي
+
+340
+00:37:21,860 --> 00:37:26,640
+عندنا؟ من أين لغاية؟ واضحة هي، واضحة؟ بتكتسل في
+
+341
+00:37:26,640 --> 00:37:28,880
+اللي قبل يسأل، يلّا تكتسل، لأ ما انا كنت بدي أسأل
+
+342
+00:37:28,880 --> 00:37:32,780
+ليش، أنا خطأ، خدنا من عمودي من هناك، بس أنا لأ
+
+343
+00:37:32,780 --> 00:37:36,520
+عرفت اللي أعمل، لأ ما احنا في الأول اعطاني أجازة،
+
+344
+00:37:36,520 --> 00:37:39,840
+هدفش فيها مشكلة، هنا لما بدأي حد الحدود التكامل،
+
+345
+00:37:39,840 --> 00:37:44,580
+قاللي أول تكامل، بتكون بالنسبة لمن؟ بس هنا جد إيش
+
+346
+00:37:44,580 --> 00:37:50,960
+كان؟وهنا D زد يبقى هنا ل Y يبقى روحنا رسمنا خط
+
+347
+00:37:50,960 --> 00:37:57,620
+أفقي موازن لمحور Y وشوفنا Y بتتغير من ويلة ويلة حد
+
+348
+00:37:57,620 --> 00:38:03,460
+بتسأل تاني يا بنات؟ حد مش فاهمة؟ ها تخجليش، انت
+
+349
+00:38:03,460 --> 00:38:07,040
+بخليش على نفسك، تبخلي بالسؤال اللي تبخلي على حالك،
+
+350
+00:38:07,040 --> 00:38:15,320
+مش علينا، ها خلاص واضحة تمام؟ طيب بعد ايه؟بعد ما
+
+351
+00:38:15,320 --> 00:38:21,100
+حددنا حدود تكمل تحديدا سليما لم يبقى الا الروحان
+
+352
+00:38:21,100 --> 00:38:26,040
+كامل فباجي بقول هذا الكلام بده يساوي integration
+
+353
+00:38:26,040 --> 00:38:30,220
+من سالب واحد لواحد integration من سالب الجدرى
+
+354
+00:38:30,220 --> 00:38:37,000
+التربيعى لواحد ناقص X تربيعي لزيرو وتكمل DZ بZ
+
+355
+00:38:37,000 --> 00:38:41,700
+اللى فوق ناقص اللى تحت يبقى بس ناقص Y
+
+356
+00:38:46,200 --> 00:38:51,100
+إن كامل يبقى هذا الكلام يساوي integration من سالب
+
+357
+00:38:51,100 --> 00:38:57,840
+واحد لواحد تكمل ناقص Y بالناقص Y تربيع على اتنين
+
+358
+00:38:57,840 --> 00:39:03,440
+من سالب الجدرى التربيع لواحد ناقص X تربيع ل Zero
+
+359
+00:39:03,440 --> 00:39:10,280
+لDX يبقى هذا الكلام يساوي ناقص مُص خلّيك برا وهي
+
+360
+00:39:10,280 --> 00:39:15,280
+تكامل من سالب واحد إلى واحد القيمة اللي فوق
+
+361
+00:39:21,420 --> 00:39:29,960
+نقص الجذر التربيعي لواحد ناقص X تربيع لكل تربيع
+
+362
+00:39:29,960 --> 00:39:33,220
+بالشكل اللي عنده هذا ماله DX
+
+363
+00:39:35,660 --> 00:39:40,180
+عن حين لمّا ربع إشارة السلب مع السلامة بتظهر إشارة
+
+364
+00:39:40,180 --> 00:39:46,300
+السلب اللي برا والجدر مع السلامة السلب اللي برا مع
+
+365
+00:39:46,300 --> 00:39:50,580
+السلب اللي برا، مايصير؟ بالموجب، يبقى بتقول
+
+366
+00:39:50,580 --> 00:39:56,640
+المسألة إلى نص تكامل من سلب واحد إلى واحد لواحد
+
+367
+00:39:56,640 --> 00:40:06,640
+ناقص X تربيع DX فقط، لا غير طب السؤال هواللي جوا
+
+368
+00:40:06,640 --> 00:40:12,560
+هذا يا بنات even function ولا odd function ما هو
+
+369
+00:40:12,560 --> 00:40:14,800
+انت قولت odd و even لإن انا عارف منهم
+
+370
+00:40:25,760 --> 00:40:31,700
+يبقى هذه even function وحدود
+
+371
+00:40:31,700 --> 00:40:36,960
+التكامل نفسها بس واحدة موجة بواحدة سالبة يبقى نص
+
+372
+00:40:36,960 --> 00:40:44,760
+في اتنين تكامل من zero لواحدلواحد ناقص X تقريب DX
+
+373
+00:40:44,760 --> 00:40:51,160
+عظم النصف اتنين مع السلامة وبتقول المثل X ناقص X
+
+374
+00:40:51,160 --> 00:40:58,140
+تقريب على تلاتة من عند Zero لغاية الواحد يبقى
+
+375
+00:40:58,140 --> 00:41:05,280
+الجواب واحد ناقص تلت ناقص Zero مع السلامة بيظل
+
+376
+00:41:05,280 --> 00:41:06,480
+اليوم درجة
+
+377
+00:41:35,050 --> 00:41:38,050
+هذا كان المثال رقم 3
+
+378
+00:41:45,990 --> 00:41:49,650
+مثال رقم أربع بيقول find the volume of the region
+
+379
+00:41:49,650 --> 00:42:02,350
+find the volume of the region قدش حجم المنطقة
+
+380
+00:42:02,350 --> 00:42:08,050
+common to
+
+381
+00:42:08,050 --> 00:42:10,470
+the interior
+
+382
+00:42:16,410 --> 00:42:25,110
+إن ترى of the cylinders of the
+
+383
+00:42:25,110 --> 00:42:33,710
+cylinders x تربيع زائد y تربيع يساوي واحد and x
+
+384
+00:42:33,710 --> 00:42:38,390
+تربيع زائد z تربيع كله يساوي واحد
+
+385
+00:42:44,460 --> 00:42:50,220
+هذا لازم والله نمشي على بنات؟ ماشي
+
+386
+00:42:50,220 --> 00:42:56,080
+طيب نرجع لسؤالنا هذا مرة تان تانية بيقول ياتلي حجم
+
+387
+00:42:56,080 --> 00:43:02,020
+المنطقة المشتركة ما بين ال two cylinders الأتنين
+
+388
+00:43:02,020 --> 00:43:06,380
+اللي عندنا دول يبقى احنا فيه أن أسطوانتين
+
+389
+00:43:06,380 --> 00:43:13,420
+أسطوانتين في بينهم تقاطعيجب أن نعرف كم هي حجم
+
+390
+00:43:13,420 --> 00:43:19,420
+منطقة التقاطع بين الـ two cylinders كيف يعني؟ لو
+
+391
+00:43:19,420 --> 00:43:25,740
+جيت ودك هذا محور Z وهذا محور X وهذا محور Y تمام؟
+
+392
+00:43:25,740 --> 00:43:29,720
+يبقى الـ cylinders الأولى X تربيع زائد Y تربيع
+
+393
+00:43:29,720 --> 00:43:35,640
+تساوي واحد من المحور تبعها Z دائرة نصف قطرها يساوي
+
+394
+00:43:35,640 --> 00:43:41,310
+واحد وحوالين محور Zمن اين الى اين تنتهي كما ترغب
+
+395
+00:43:41,310 --> 00:43:42,330
+ان ترغب ان ترغب ان ترغب ان ترغب ان ترغب ان ترغب ان
+
+396
+00:43:42,330 --> 00:43:45,430
+ترغب ان ترغب ان ترغب ان ترغب ان ترغب ان ترغب ان
+
+397
+00:43:45,430 --> 00:43:46,930
+ترغب ان ترغب ان ترغب ان ترغب ان ترغب ان ترغب ان
+
+398
+00:43:46,930 --> 00:43:46,990
+ترغب ان ترغب ان ترغب ان ترغب ان ترغب ان ترغب ان
+
+399
+00:43:46,990 --> 00:43:47,050
+ترغب ان ترغب ان ترغب ان ترغب ان ترغب ان ترغب ان
+
+400
+00:43:47,050 --> 00:43:47,670
+ترغب ان ترغب ان ترغب ان ترغب ان ترغب ان ترغب ان
+
+401
+00:43:47,670 --> 00:43:57,350
+ترغب ان ترغب ان ترغب ان ترغب
+
+402
+00:43:57,350 --> 00:44:03,590
+ان ترغب ان
+
+403
+00:44:03,590 --> 00:44:08,290
+تفي تقابل بين الرقصية ومبين الأفقوية بدنا نجيب
+
+404
+00:44:08,290 --> 00:44:13,710
+جداش حجم منطقة التقابل طبعا زي ما تشاهدين كل من
+
+405
+00:44:13,710 --> 00:44:21,450
+الأسطولتين متماثلة بالنسبة لمستويات الإحداثية لذلك
+
+406
+00:44:21,450 --> 00:44:27,450
+هذول الأسطولتين بدون مياقة عامةفي الأسمنة الأربعة
+
+407
+00:44:27,450 --> 00:44:33,090
+والله في الأسمنة الثمانية في الثمانية في الثمانية
+
+408
+00:44:33,090 --> 00:44:39,230
+الأربعة احنا بكثير في ثمن واحد ونعمل في الثمن
+
+409
+00:44:39,230 --> 00:44:45,310
+الأول ونضربه في جدش طيب خلينا نشوف ما هو شكل الرسم
+
+410
+00:44:45,310 --> 00:44:52,750
+على الطبيعة أو جدش الحجم المحصور في الثمن الأول
+
+411
+00:44:53,030 --> 00:44:57,170
+مشان نتصور الوضع ومشان نعرف زيك بدأت اتغير من وين
+
+412
+00:44:57,170 --> 00:45:01,970
+لوين و ال X من وين لوين و ال Y من وين لوين صحيح؟
+
+413
+00:45:01,970 --> 00:45:07,470
+بقولكم كويس تعالوا نرسم مع بعض اللي هو ارسمت كله
+
+414
+00:45:07,470 --> 00:45:12,970
+من الاسطوانتين و بدي ارسم الجزء بس اللي جهة الغرفة
+
+415
+00:45:12,970 --> 00:45:16,990
+اللي جهتنا هذه و الباقي خلاص اللي مضروه في تمامي
+
+416
+00:45:16,990 --> 00:45:21,570
+بقولكم كويس يبقى باجي لمحاول الاحداثيات بهذا الشيء
+
+417
+00:45:25,040 --> 00:45:33,580
+هذا محور X هذا محور Y هذا محور Z يبقى الأسطوان
+
+418
+00:45:33,580 --> 00:45:41,800
+الرأسية يبقى الأسطوان الرأسية موازي لمحور Y ونص
+
+419
+00:45:41,800 --> 00:45:47,180
+وطول النوع يساوي واحد وننزل من هنا رأسي وأرسم
+
+420
+00:45:47,180 --> 00:45:54,110
+موازي لمحور Xبقوله يساوي واحد هو نزل رأسي بهذا
+
+421
+00:45:54,110 --> 00:46:01,130
+الشكل يبقى هذا هيك مجيني جزء من السطح اللي فوق و
+
+422
+00:46:01,130 --> 00:46:06,190
+هذا جزء من السطح اللي تعنى يبقى هذه مين يا بنات؟
+
+423
+00:46:06,190 --> 00:46:13,170
+يمثل ثمن الأسطوانة اللي هي مين؟ الأولى اللي محورها
+
+424
+00:46:13,170 --> 00:46:20,700
+محور الـZبعد ذلك نذهب للتانية للمحور Y و هرسمها
+
+425
+00:46:20,700 --> 00:46:26,680
+باللون الأزرق يبقى بداجي أخد طولي يساوي واحد يمثل
+
+426
+00:46:26,680 --> 00:46:35,360
+نصف القطر و أرسم أفقي هكذا تمام؟ و بداجي هنا نصف
+
+427
+00:46:35,360 --> 00:46:42,340
+يساوي واحد و أرسم أفقي بالشكل اللي عندناهدول اتنين
+
+428
+00:46:42,340 --> 00:46:47,820
+هيجيني جوس طبعا مش هيظهر هذا و هذا فبيكون من ناحية
+
+429
+00:46:47,820 --> 00:46:54,020
+تانية و من هنا هذا كمان مش هيظهر هيجيني بالشكل
+
+430
+00:46:54,020 --> 00:47:01,560
+اللي عندنا هذا و يجيني هذا رأسي هيك و هذا هيك فهي
+
+431
+00:47:01,560 --> 00:47:09,380
+ثمن الأسطوان الأفقي اتقاطعوا اتنين وين النقطة اللي
+
+432
+00:47:09,380 --> 00:47:09,800
+عندنا
+
+433
+00:47:13,310 --> 00:47:20,690
+طيب لما تقاطع في النقطة هذه هذا سطح منحني وهذا نزل
+
+434
+00:47:20,690 --> 00:47:25,770
+رأسي إذا بدي يكون في تقاطع ما بين السطح المنحني
+
+435
+00:47:25,770 --> 00:47:29,550
+اللي عندنا هذا والسطح المنحني اللي عندنا هذا
+
+436
+00:47:29,550 --> 00:47:33,430
+التقاطع هذا بيكون ظاهر لإنه جاي على المنطقة
+
+437
+00:47:33,430 --> 00:47:38,270
+المشتركة ما بين الإتنين يبقى بده يجين التقاطع
+
+438
+00:47:38,270 --> 00:47:39,630
+بالشكل اللي عندنا هذا
+
+439
+00:47:43,580 --> 00:47:49,440
+ها واضحة؟ طيب الآن السؤال هو حدد ان المنطقة بالضغط
+
+440
+00:47:49,440 --> 00:47:56,460
+تبعت التقاطع بس تصبر شوية الخط هذا ماله؟ مش انت
+
+441
+00:47:56,460 --> 00:48:02,640
+عندك منحنة هيه بالشكل هذا أفقي وجايك منحنة رأسي
+
+442
+00:48:02,640 --> 00:48:06,240
+اتنين هيتقاطعوا مع بعض بالخط الأزرق اللي انت شايفه
+
+443
+00:48:07,090 --> 00:48:13,710
+هيوط طلع هنا كويس هذا بنات سطح منحني الشكل لأن هذا
+
+444
+00:48:13,710 --> 00:48:20,450
+وهذا الوفق الأزرق كمان سطح منحني اتنين هتقع في
+
+445
+00:48:20,450 --> 00:48:26,870
+الخط الأزرق المتواصل اللي انتوا شايفينه هذا تمام؟
+
+446
+00:48:26,870 --> 00:48:33,010
+طيب يعني وين صارت منطقة التقاطع بالضبط؟ طلعيني
+
+447
+00:48:33,010 --> 00:48:41,180
+هخليها كل منطقة زرقاء غامقاءهذه هي من هنا وهذا
+
+448
+00:48:41,180 --> 00:48:46,500
+طبعا هذا مش هيظهر لأن هذا بيكون تاني، هذا بيكون في
+
+449
+00:48:46,500 --> 00:48:51,960
+مستوى ال X Y فلين مش هيظهر وهذا كمان يا بناه مش
+
+450
+00:48:51,960 --> 00:48:56,620
+هيظهر لأنه في الناحية التانية وهذا مش هيظهر يبقى
+
+451
+00:48:56,620 --> 00:49:02,090
+صارة المنطقة هذه كالتاليةهنرسم المستوى اللى فوق
+
+452
+00:49:02,090 --> 00:49:06,250
+والمستوى اللى تاعة اللى فوق طبعا مش مستوى حيكون
+
+453
+00:49:06,250 --> 00:49:14,690
+على شكل ميل يبجى هذا اللى فوق هكذا هذه كل المنطقة
+
+454
+00:49:14,690 --> 00:49:18,970
+اللى فوق طب وين المنطقة اللى تاعة المنطقة في
+
+455
+00:49:18,970 --> 00:49:26,930
+المستوى X Y Plain دى المنطقة هذه تمام؟
+
+456
+00:49:27,910 --> 00:49:39,850
+يبقى هذه المنطقة مرة تانية هذا خط
+
+457
+00:49:39,850 --> 00:49:44,170
+اللي فوق هو المستوى العلوي و اللي تحت هذا الأسود
+
+458
+00:49:44,170 --> 00:49:50,450
+هو المستوى السفلي يبقى
+
+459
+00:49:50,450 --> 00:49:55,010
+هذه المنطقة المشتركة بين الأسط والتانيةطبعا مش
+
+460
+00:49:55,010 --> 00:49:59,130
+واضحة الرسمة عندكم بالكتاب، الحلقة تبع أحد مسائل
+
+461
+00:49:59,130 --> 00:50:03,330
+الكتاب مش واضحة الرسمة، فهي وضحنالك للرسمة تماما
+
+462
+00:50:03,330 --> 00:50:08,370
+طيب، بدي أكمل أول حاجة بالنسبة إلى زد يبقى، بدي
+
+463
+00:50:08,370 --> 00:50:13,880
+أشوف زد بدت تتغير منين لوينيبقى بتروح اقوله بدي
+
+464
+00:50:13,880 --> 00:50:19,880
+اخد ال volume V اللي بيقول عنه يبقى تكامل اتنين
+
+465
+00:50:19,880 --> 00:50:27,840
+تلاتة ل DZ DY DX مثلا او DX DY CS يبقى بده يشوف ال
+
+466
+00:50:27,840 --> 00:50:33,500
+Z بدها تتغير من ويه اللويه حرصمه بخط أسود هدوء
+
+467
+00:50:33,500 --> 00:50:37,870
+الكلام لسا معينهأطلع من مستوى الأرض للمستوى الأسود
+
+468
+00:50:37,870 --> 00:50:42,630
+لغاية ما أقابل المستوى الأزرق مش المستوى الميلي
+
+469
+00:50:42,630 --> 00:50:49,010
+اللي جاي من فوق يبقى بدي أبدأ من هنا هه و أجي طالع
+
+470
+00:50:49,010 --> 00:50:53,130
+أرضه لغاية ما أقابل الميلي أقابل السطح اللي جايني
+
+471
+00:50:53,130 --> 00:50:59,750
+من فوق هنا زد يبقى ديني Zero تفاجئت يبقى من عند
+
+472
+00:50:59,750 --> 00:51:07,190
+Zero بدي أجي لهذاهذه يا ترى جاية على السطح الأوفقي
+
+473
+00:51:07,190 --> 00:51:12,970
+ولا على السطح الرأسي؟ أه جاية على السطح الأفقي،
+
+474
+00:51:12,970 --> 00:51:17,710
+منها داخل السطح الرأسي، جوا، مظبوط؟ إذا جاية على
+
+475
+00:51:17,710 --> 00:51:21,990
+وين؟ على السطح الأوفقي، طبعا السطح الأوفقي مين
+
+476
+00:51:21,990 --> 00:51:29,450
+هنا؟أيوة من هذه بتصير Z يساوي الجذر التربيعي لواحد
+
+477
+00:51:29,450 --> 00:51:35,930
+ناقص X تربية إذا هنا Z عند هذه النقطة بدأت ساوي
+
+478
+00:51:35,930 --> 00:51:41,210
+الجذر التربيعي لواحد ناقص X تربية وزي ما تشايفين
+
+479
+00:51:41,210 --> 00:51:46,310
+أخدنا الجذر الموجب وليس السالب لأنها أعلى المستوى
+
+480
+00:51:46,310 --> 00:51:51,070
+XY plane وليست أسفل المستوى XY plane
+
+481
+00:52:10,270 --> 00:52:15,850
+يبقى هذا Y وهذا X وهذا X
+
+482
+00:52:18,390 --> 00:52:26,350
+وهذا الرأس X وهذا جزء من دائرة أو ربعية دائرة يبقى
+
+483
+00:52:26,350 --> 00:52:30,970
+هذه الدائرة اللي عندنا بالشكل هذا انا بدي اكمل
+
+484
+00:52:30,970 --> 00:52:37,190
+بالنسبة الى Y يبقى بدي ارسم خط يوازي محور Y يبقى
+
+485
+00:52:37,190 --> 00:52:42,310
+لو روحت رسمت خط موازي لمحور Y هتيجي النقطة هذه
+
+486
+00:52:42,310 --> 00:52:49,110
+وهذه النقطة التانيةطب هنا Y يبقى كم؟ Zero لأن هنا
+
+487
+00:52:49,110 --> 00:52:56,130
+نقطة الأصل يبقى من عند Y تساوي Zero إلى Y أكثر كم
+
+488
+00:52:56,130 --> 00:53:01,250
+آه هذه الدائرة هي الدائرة الأولى تبعت الأسطوان
+
+489
+00:53:01,250 --> 00:53:05,710
+اللي نزل من فوق X تربية زائد Y تربية يساوي واحد
+
+490
+00:53:05,710 --> 00:53:12,910
+يبقى هنا Y تساوي الجدر يكتر بيه واحد ناقص X تربية
+
+491
+00:53:13,270 --> 00:53:20,950
+يبقى هنا الجذر التربيهي لواحد ناقص X تربيه ضالة
+
+492
+00:53:20,950 --> 00:53:29,170
+هنا مين ال X ستتغير من هنا لغاية هنا مابتدوش
+
+493
+00:53:29,170 --> 00:53:35,030
+النقطة في ال X؟ Zero وهذه الدائرة نصف قطرة يساوي
+
+494
+00:53:35,030 --> 00:53:38,830
+واحد يبقى هذه واحد وكذلك هذه
+
+495
+00:53:44,190 --> 00:53:48,550
+جبل مروحة كامل، حد بتسأل أي سؤال هنا في حدود
+
+496
+00:53:48,550 --> 00:53:57,330
+التكامل أو كيف جبناهم أو .. أو .. إلى آخرين؟
+
+497
+00:53:57,330 --> 00:54:03,990
+حط
+
+498
+00:54:03,990 --> 00:54:07,550
+دفاتك و تعالى أشوف كيف سؤالك بالضبط حط دفاتك و
+
+499
+00:54:07,550 --> 00:54:13,450
+تعالى طيب
+
+500
+00:54:14,440 --> 00:54:18,540
+تحكي عنية مستوى Z لما جيبناها بشي كانت على أفق
+
+501
+00:54:18,540 --> 00:54:22,940
+إيه؟ لأ على أفق إيه هي Z تساوي Zero له مستوى الأرض
+
+502
+00:54:22,940 --> 00:54:27,600
+بس هذا سطح جاي من فوق على الماء يعني أه أه على هي
+
+503
+00:54:27,600 --> 00:54:31,380
+و هي هذا هو الخط اللي هو جاي على سطوة يعني جيبناها
+
+504
+00:54:31,380 --> 00:54:34,760
+من المعادلة تبع السطوانة الأفقية أه بالضبط صحيح لو
+
+505
+00:54:34,760 --> 00:54:37,880
+كانت على ال .. لو كانت نجيبها من المعادلة اللي على
+
+506
+00:54:37,880 --> 00:54:41,780
+السطوانة الرأسية تقدر تجيبيها على السطوانة الرأسية
+
+507
+00:54:41,780 --> 00:54:45,840
+أكثر بقى دلوقتي نفسي واحدةفضل ايه، هي عندك استوانة
+
+508
+00:54:45,840 --> 00:54:51,640
+رأسية، كويس، هي استوانة رأسية وعندك الخط جاي في
+
+509
+00:54:51,640 --> 00:54:56,960
+المص، كيف بدك تجيبيها؟ لا يمكن تقضع الموازي إليها،
+
+510
+00:54:56,960 --> 00:55:05,280
+فيش تقضع أصلا، هذه
+
+511
+00:55:05,280 --> 00:55:11,020
+مانامش هاد هاد نكتب .. نكتب زد بتاع .. وين هي زد؟
+
+512
+00:55:11,020 --> 00:55:16,660
+وين هي زد فيها؟ مش موجودة يبقى صينك من أول مش صحيح
+
+513
+00:55:16,660 --> 00:55:21,980
+لما
+
+514
+00:55:21,980 --> 00:55:25,280
+نحدد .. لما نقول لبنات زد من كده إلى كده أو واي من
+
+515
+00:55:25,280 --> 00:55:29,060
+كده بتكون فيه تفاطة مش تفاطة يبقى مدرش ولا هاد
+
+516
+00:55:29,060 --> 00:55:33,300
+يبقى مدرش ألاك رسمت الخط اللي .. اللي عندي أسود
+
+517
+00:55:33,300 --> 00:55:37,990
+هذابقاطع مع المستوى الأفقي و بقاطع مع الميلت
+
+518
+00:55:37,990 --> 00:55:43,930
+الأسطوان الاجيني من فوق يعني السطح الأسطوان الأفقي
+
+519
+00:55:43,930 --> 00:55:51,400
+حد بتسمع أي سؤال تاني كمان؟ طيبيبقى مضالش فانا إلا
+
+520
+00:55:51,400 --> 00:55:59,240
+كامل يبقى هذه تكاملها بـ0 لـ1 ناقص
+
+521
+00:55:59,240 --> 00:56:05,520
+X تربيع ويتكاملها بـZ بالقيمة اللي فوق فقط لـ1
+
+522
+00:56:05,520 --> 00:56:07,220
+ناقص X تربيع
+
+523
+00:56:21,880 --> 00:56:31,840
+يبقى هذا الكلام
+
+524
+00:56:31,840 --> 00:56:35,180
+تكامل من zero لواحد واحد ناقص X تربيع
+
+525
+00:56:45,730 --> 00:56:51,610
+تكامل من صفر لواحد لواحد نقص X تربيع DX واللي هو
+
+526
+00:56:51,610 --> 00:56:57,450
+بده يساوي X نقص X تكيب على تلاتة كله من Zero لواحد
+
+527
+00:56:57,450 --> 00:57:06,850
+ويساوي واحد نقص طول ويساوي طول تين خلعت
+
+528
+00:57:06,850 --> 00:57:10,070
+نفسي جابت السؤال اللي جابله بس كل واحد شكل مش
+
+529
+00:57:10,070 --> 00:57:11,170
+علاقة بالتالت
+
+530
+00:57:37,260 --> 00:57:47,040
+كذا نسينا التمانية تمانية
+
+531
+00:57:47,040 --> 00:57:51,660
+تمانية تمانية تمانية تمانية تمانية تمانية تمانية
+
+532
+00:57:51,660 --> 00:57:57,060
+تمانية تمانية تمانية تمانية
+
+533
+00:58:07,180 --> 00:58:12,560
+السؤال الخامس بيقول
+
+534
+00:58:12,560 --> 00:58:13,820
+يحسبني التكامل
+
+535
+00:58:21,390 --> 00:58:36,130
+تكامل من 0 ل 1 تكامل من X تربيع لغاية 1 ل 12 X Z E
+
+536
+00:58:36,130 --> 00:58:43,750
+أُس Z Y تربيع DY DX
+
+537
+00:58:54,060 --> 00:58:59,200
+أول حاجة بدي اكمل بالنسبة الى one يبقى هدول كلهم
+
+538
+00:58:59,200 --> 00:59:05,440
+مال همامي ثوابت والزد ثابت يبقى انا بدي اكمل اكس
+
+539
+00:59:05,440 --> 00:59:06,720
+واي تربيع
+
+540
+00:59:15,600 --> 00:59:24,260
+إذا كتبناها على شكل Power Series، سنستطيع أن نضعها
+
+541
+00:59:24,260 --> 00:59:29,380
+هناك لما يقوش هذا المعقد هذا، تمام؟ يبقى في هذه
+
+542
+00:59:29,380 --> 00:59:34,300
+الحالة مصير، ماعناهاش إمكانية لهذه الشغلة، يبقى
+
+543
+00:59:34,300 --> 00:59:39,280
+بناءً عليه إجباري هغير ال order of integrationبدي
+
+544
+00:59:39,280 --> 00:59:44,780
+أغير ترتيب وضع التكامل يبقى بالشكل هذا مش حاجزا
+
+545
+00:59:44,780 --> 00:59:51,060
+طيب لو غيرت وضع التكامل يبقى بدي أخليها دي x dy
+
+546
+00:59:51,060 --> 00:59:55,500
+بصير هذا كله مقدار ثابت و هذا ثابت .. بصير هذه
+
+547
+00:59:55,500 --> 01:00:01,110
+تكامل x فقط لغايةيصبح معناها العملية سهلة جدا إذا
+
+548
+01:00:01,110 --> 01:00:06,430
+باجي بقوله هذا Y يسوي التكامل من الصفر الواحدة
+
+549
+01:00:06,430 --> 01:00:10,930
+اللي بنشلها فيه هذول تكاملين وبنشوف كيف بدهم
+
+550
+01:00:10,930 --> 01:00:22,710
+يصيروا Y اتناشر X Z E وز وY تربية DX DY DZ إذا بدي
+
+551
+01:00:22,710 --> 01:00:28,000
+أغير ال X و اذا بدي أروح أرسم منطقة التكاملمشان
+
+552
+01:00:28,000 --> 01:00:34,620
+أقلب حدود تتكامل يبقى لو جينا هيك و قولنا هذا محور
+
+553
+01:00:34,620 --> 01:00:44,460
+X و هذا محور Y و هذا نقطة الأصل اللي هي Z عيد
+
+554
+01:00:44,460 --> 01:00:51,080
+نوافق من عندك يالا
+
+555
+01:00:51,080 --> 01:00:54,000
+اسمك و رقمك الجامعة و خلي اتف عليهم
+
+556
+01:00:58,720 --> 01:01:05,940
+تمام طيب بدنا نروح نرسم هذه المنطقة جالي Y تساوي X
+
+557
+01:01:05,940 --> 01:01:10,640
+تربيع Y تساوي X تربيع الفرق الأولى المعروفة مشهورة
+
+558
+01:01:10,640 --> 01:01:17,780
+للكل يبقى هذا اللي يقول Y تساوي X تربيع لغاية Y
+
+559
+01:01:17,780 --> 01:01:25,040
+تساوي كم؟ واحد يبقى هذا الخط Y تساوي واحدطيب ال X
+
+560
+01:01:25,040 --> 01:01:29,520
+من وين لو ينجل ال X من عند ال Zero لغاية ال واحد
+
+561
+01:01:29,520 --> 01:01:36,140
+هذا ال X بال Zero هذه تقاطع لاتنين مع بعض بيعطينا
+
+562
+01:01:36,140 --> 01:01:41,540
+مين ال واحد يبقى احنا بس النصف اللي على اليمين
+
+563
+01:01:41,540 --> 01:01:47,570
+اللي عندنايبقى بدل ما كنا بدنا نكامل بالنسبة الى Y
+
+564
+01:01:47,570 --> 01:01:53,110
+في الأول هنكامل بالنسبة الى X يبقى بنروح نقطع نرسم
+
+565
+01:01:53,110 --> 01:02:01,240
+خط يقطع منطقة تكامل وموازن لمخوفاتيبقى هاي خط أفقي
+
+566
+01:02:01,240 --> 01:02:08,780
+من هنا كداش يكون X بقى هنا Zero ومن هنا X بقدر جدر
+
+567
+01:02:08,780 --> 01:02:15,960
+ال Y يبقى هنا X يساوي جدر ال Y الموجب وليس السالب
+
+568
+01:02:15,960 --> 01:02:21,180
+لأن كل X موجب على الشكل اليمين إذا بصير من عندي
+
+569
+01:02:21,180 --> 01:02:29,010
+Zero لمين لغاية جدر Yطالع انتوا فوق إيش كانت X
+
+570
+01:02:29,010 --> 01:02:33,990
+تربية ل واحد اللي صار عندي X من عند Zero لغاية
+
+571
+01:02:33,990 --> 01:02:40,850
+General Y ضلت عندي Y بدأ يتغير من وين ل وين من صفر
+
+572
+01:02:40,850 --> 01:02:46,850
+لغاية واحد يبقى من صفر لغاية واحد بالشكل اللي
+
+573
+01:02:46,850 --> 01:02:51,250
+عندنا هذا إذا بدنا نروح نكمل هذه الدالة أولا
+
+574
+01:02:51,540 --> 01:02:57,440
+بالنسبة ل X يبقى هذه تكامل من Zero ل واحد تكامل من
+
+575
+01:02:57,440 --> 01:03:05,980
+Zero ل واحد لستة X تربيع و ال X هذه ها بدنا نخليها
+
+576
+01:03:05,980 --> 01:03:15,320
+تتغير من Zero لغاية جدر ال Y لمن ل Z E أس Z Y
+
+577
+01:03:15,320 --> 01:03:19,380
+تربيع DYDZ
+
+578
+01:03:28,020 --> 01:03:35,200
+تكامل من صفر لواحد تكامل من صفر لواحد تكامل من صفر
+
+579
+01:03:35,200 --> 01:03:45,800
+لواحد تكامل من صفر لواحد تكامل من صفر لواحد
+
+580
+01:03:49,240 --> 01:03:53,460
+الان بدك تكمل بالنسبة ل Y في الأول و الله بالنسبة
+
+581
+01:03:53,460 --> 01:03:58,700
+ل Z في الأول أي واحدة فيهم تمشي الحال بس إذا بدك
+
+582
+01:03:58,700 --> 01:04:04,180
+تكمل بالنسبة ل Z بلزمك integration by parts لكن
+
+583
+01:04:04,180 --> 01:04:07,820
+إذا بدك تكمل بالنسبة ل Y تكمل بالتعويض عادي جدا
+
+584
+01:04:07,820 --> 01:04:15,980
+إذا بروح بقول حط لي T تساوي Y تربيع يبقى DT بتنير
+
+585
+01:04:15,980 --> 01:04:23,320
+YDYيبقى نص DT بيعطينا Y لكن عندنا ال 6 خلاص مش ده
+
+586
+01:04:23,320 --> 01:04:29,080
+على النص يبقى هذا يا بنات بقدر اخلى اخلى ال 6 ليه
+
+587
+01:04:29,080 --> 01:04:36,200
+3 في 2 يبقى هذا الكلام بده يساوي تلاتة برة تكمل من
+
+588
+01:04:36,200 --> 01:04:45,000
+Zero لواحد تكمل من Zero لواحد لإتنين YZ POZ Y
+
+589
+01:04:45,000 --> 01:04:54,780
+تربيةdy dz هذا الكلام بدرسه الآن اتنين y مع ال dy
+
+590
+01:04:54,780 --> 01:05:00,020
+بدي اشيله مكتب درم جديد دي تي إذا صارت المسألة
+
+591
+01:05:00,020 --> 01:05:11,360
+تلاتة تكامل من zero لواحد و تكامل ل z E أُس zt dt
+
+592
+01:05:11,360 --> 01:05:12,560
+dz
+
+593
+01:05:18,380 --> 01:05:25,100
+لو كانت ال Y بواحد يبقى ال T بواحد تربيته بواحد و
+
+594
+01:05:25,100 --> 01:05:29,140
+لو كانت ب Zero بتعطيك هذه Zero إذا انت بقى حدود
+
+595
+01:05:29,140 --> 01:05:35,110
+التكامل كما هيبدي اكابل بالنسبة E ل T يبقى التلاتة
+
+596
+01:05:35,110 --> 01:05:40,790
+بلاكش دعوة و من Zero ل واحد و ال Z مقدار ثابت و E
+
+597
+01:05:40,790 --> 01:05:51,750
+أس Z T على Z و الحكي هذا من Zero ل واحد دي Zعظم
+
+598
+01:05:51,750 --> 01:05:57,970
+الـ z بتروح مع مين؟ مع الـ z وبالتالي تقول المسألة
+
+599
+01:05:57,970 --> 01:06:04,710
+إلى تلاتة كامر من zero لواحد ل E of z هو واحد بz
+
+600
+01:06:04,710 --> 01:06:15,500
+ناقص E of zero اللي هو واحد بz وبالتاليهذه ستصبح
+
+601
+01:06:15,500 --> 01:06:23,880
+ثلاثة E أز ناقص Z وكل هذا الكلام من Zero لغاية
+
+602
+01:06:23,880 --> 01:06:32,820
+واحد يبقى هذا الكلام دسام ثلاثة في E أس واحد ناقص
+
+603
+01:06:32,820 --> 01:06:40,650
+واحدوهنا ناقص E of Zero اللي هو بواحد وزائد Zero
+
+604
+01:06:40,650 --> 01:06:48,710
+مع السلامة يبقى الجواب يساوي تلاتة في E ناقص اتنين
+
+605
+01:06:48,710 --> 01:06:52,670
+هذه هي الإجابة عن نهائي
+
+606
+01:07:13,380 --> 01:07:20,360
+السؤال السادس يا إخلاص والكلام للساميين يقول ما
+
+607
+01:07:20,360 --> 01:07:26,800
+يأتي find the average value يبقى نشخصنا يا إخلاص
+
+608
+01:07:26,800 --> 01:07:33,740
+بالاسم أن السؤالة على ال average value
+
+609
+01:07:34,550 --> 01:07:38,690
+بالقلب نجاوب على السؤال اللي وعدناها فيه what is
+
+610
+01:07:38,690 --> 01:07:48,610
+the average value of f of x, y وz تساوي x زائد y
+
+611
+01:07:48,610 --> 01:07:54,710
+نقص z over the
+
+612
+01:07:54,710 --> 01:08:01,910
+rectangular solid
+
+613
+01:08:09,490 --> 01:08:18,990
+first octant in the first octant بالثمن الأول
+
+614
+01:08:18,990 --> 01:08:26,370
+bounded by the
+
+615
+01:08:26,370 --> 01:08:34,670
+coordinate planes بمستويات
+
+616
+01:08:34,670 --> 01:08:37,130
+الإحداثيات
+
+617
+01:08:37,680 --> 01:08:46,460
+محدود بمستويات الإحداثيات and the planes and the
+
+618
+01:08:46,460 --> 01:08:54,660
+planes والمستويات X يساوي واحد Y يساوي واحد
+
+619
+01:09:12,500 --> 01:09:16,900
+نمسح الشكل اليمين هذه يا بنات خلاص؟
+
+620
+01:09:43,630 --> 01:09:48,510
+طيب مرة ثانية قال ياتي ال average value للدالة
+
+621
+01:09:48,510 --> 01:09:52,330
+اللى علناها دى على المنطقة المحدودة بمين
+
+622
+01:09:52,330 --> 01:09:57,590
+بالمسئولات X تساوي واحد و Y تساوي واحد و Z تساوي
+
+623
+01:09:57,590 --> 01:10:04,030
+اتنين تقول انا تصورت محور Z و محور X و محور Y X
+
+624
+01:10:04,030 --> 01:10:10,150
+تساوي واحد لمستوى اللى هناك مصبوط و Y تساوي واحد
+
+625
+01:10:10,150 --> 01:10:15,680
+لمستوى اللى هناكو Z يساوي 2 المستوى اللى فوق يبقى
+
+626
+01:10:15,680 --> 01:10:20,160
+المنطقة اللى عندنا مين هي الغرفة اللى احنا فيها صح
+
+627
+01:10:20,160 --> 01:10:26,060
+ولا لأ يعني حجم متوازى مستطيلات يبقى هذا مين هذا
+
+628
+01:10:26,060 --> 01:10:32,360
+يمثل المنطقة D تبع تلك التكامل إذا بروح بقوله D
+
+629
+01:10:32,360 --> 01:10:37,120
+بدي ساوي تكاملين تلاتة تبدأ ب Z
+
+630
+01:10:50,750 --> 01:10:56,190
+يبقى النتيجة هذه تساوي تكمل من صفر لواحد تكمل من
+
+631
+01:10:56,190 --> 01:11:05,090
+صفر لاثنينلمن لز من صفر لغاية اتنين ل dy dx يبقى
+
+632
+01:11:05,090 --> 01:11:11,070
+هذا الكلام بده يسوي تكامل من صفر لواحد وتكامل كذلك
+
+633
+01:11:11,070 --> 01:11:17,690
+من صفر لواحد دالي اتنين dy dx تكامل من صفر لواحد
+
+634
+01:11:17,690 --> 01:11:18,810
+اتنين مالوش دعوة
+
+635
+01:11:36,580 --> 01:11:42,700
+يبقى ال volume تبع المنطقة اللي احنا بنكمل عليها
+
+636
+01:11:42,700 --> 01:11:43,840
+يساوي اتنين
+
+637
+01:11:50,750 --> 01:12:08,610
+V of D V of D V of D V of D V of D V of D V
+
+638
+01:12:08,610 --> 01:12:20,210
+of D V of D V of D V of D V of D V of D V of D
+
+639
+01:12:20,280 --> 01:12:26,660
+أتنين تلاتة من Zero لأتنين من Zero لواحد من Zero
+
+640
+01:12:26,660 --> 01:12:36,120
+لواحد تكمل على D لمن؟ لدلة المعطاعة XY-Z كله
+
+641
+01:12:36,120 --> 01:12:39,700
+DZDYDX
+
+642
+01:12:39,700 --> 01:12:47,210
+هذا الكلام يساوي نص خليك برهوهيتكاملين من Zero ل
+
+643
+01:12:47,210 --> 01:12:53,490
+واحد من Zero ل واحد وبنكمل بالنسبة إلى Z يبقى XZ
+
+644
+01:12:53,490 --> 01:13:03,670
+-YZ-Z تربيع على الاتنين كله من Zero للإتنين ل DY
+
+645
+01:13:03,670 --> 01:13:11,520
+DX Y وشاويبقى نص هيبرة و هيتكاملين من Zero ل واحد
+
+646
+01:13:11,520 --> 01:13:15,760
+من Zero ل واحد و بدنا نعوض بالقيمة اللى فوق نقص
+
+647
+01:13:15,760 --> 01:13:20,580
+القيمة اللى تحت عن كل Z يبقى هنا ايش قصير عندنا يا
+
+648
+01:13:20,580 --> 01:13:30,200
+بنات اتنين X و هنا نقص اتنين زائد اه زائد زائد
+
+649
+01:13:30,200 --> 01:13:36,580
+اتنين Yوهنا بدأ أشيل هذه و أضع ما كانت اتنين بصير
+
+650
+01:13:36,580 --> 01:13:43,480
+أربع على اتنين باتنين يبقى ناقص اتنين فقط لغير الـ
+
+651
+01:13:43,480 --> 01:13:52,000
+dy بإكس بعدين بدروحة كامل بالنسبة لمن؟ بالنسبة إلى
+
+652
+01:13:52,000 --> 01:13:54,240
+y يبقى يساوي
+
+653
+01:14:13,680 --> 01:14:19,840
+يبقى هذا الكلام سوية نص خلّيك برا وهي تكمن من zero
+
+654
+01:14:19,840 --> 01:14:26,120
+إلى واحدبنعوض أشيل كل Y ونحط مكانها 1 يبقى بصير
+
+655
+01:14:26,120 --> 01:14:34,040
+عندنا هنا 2X وهنا زائد واحد وهنا ناقص اتنين
+
+656
+01:14:38,180 --> 01:14:45,540
+كله بالنسبة لمين إلى dx يبقى صارت نص تكامل من zero
+
+657
+01:14:45,540 --> 01:14:54,520
+لواحد لإتنين x ناقص واحد dx يبقى النتيجة تساوي نص
+
+658
+01:14:54,520 --> 01:14:59,520
+وهي تكامل من zero لواحد لمين
+
+659
+01:15:02,450 --> 01:15:09,050
+يبقى انكمل مباشرة يبقى
+
+660
+01:15:09,050 --> 01:15:15,490
+هذا ما تشير جدياش X تربية ناقص X كله من صفر لغاية
+
+661
+01:15:15,490 --> 01:15:22,650
+واحد يبقى نصف واحد ناقص واحد الحمد لله طلعت ب Zero
+
+662
+01:15:22,650 --> 01:15:28,510
+يبقى المتوسط تبع هذه الدالة بده يساوي Zeroولا
+
+663
+01:15:28,510 --> 01:15:33,830
+غرابة في ذلك ممكن يطلع zero ممكن يطلع رقم تاني إلى
+
+664
+01:15:33,830 --> 01:15:39,190
+آخرين لحد هنا stop بقى نتنتهى ال section وإلى يكون
+
+665
+01:15:39,190 --> 01:15:46,690
+أرقام المسائل اللي بنتحلوها حالا عاجلا من هذا ال
+
+666
+01:15:46,690 --> 01:15:49,550
+section من 1D33
+
+667
+01:15:51,820 --> 01:16:00,240
+multiple of three وكذلك من سبعة وتلاتين لغاية
+
+668
+01:16:00,240 --> 01:16:07,280
+اربعة واربعين المسائل الفردية سأغلق الآن لل
+
+669
+01:16:07,280 --> 01:16:09,780
+section اللذي يليه
+
+670
+01:16:33,680 --> 01:16:37,860
+تبقى ال section اللي جديد معلومات جديدة ماكناش
+
+671
+01:16:37,860 --> 01:16:45,180
+بنعرفها قبل هيك section خمستاشر السبعة بقول ما ستة
+
+672
+01:16:45,180 --> 01:16:53,100
+درجة بروحنا سبعة مباشرة بجود triple integrals
+
+673
+01:16:53,100 --> 01:16:59,880
+مكاملات ثلاثية in cylindrical
+
+674
+01:17:06,940 --> 01:17:17,300
+والتواصل الهواردنسي الهواردنسي
+
+675
+01:17:17,300 --> 01:17:20,640
+عنقسمه
+
+676
+01:17:20,640 --> 01:17:23,720
+إلى نقطتين النقطة الأولى
+
+677
+01:17:26,570 --> 01:17:34,610
+التكامل in cylindrical coordinates
+
+678
+01:17:34,610 --> 01:17:38,830
+الأحداثيات
+
+679
+01:17:38,830 --> 01:17:44,950
+الحالي الأوسطوانية نعطي
+
+680
+01:17:44,950 --> 01:17:51,350
+definition بقول ماذي؟ cylindrical
+
+681
+01:18:00,590 --> 01:18:11,990
+of a point P in space الفرق
+
+682
+01:18:11,990 --> 01:18:29,750
+is PR وθ وز in which بحيث أنمقطة الأولى الـR and
+
+683
+01:18:29,750 --> 01:18:40,670
+الـθية are the polar coordinates
+
+684
+01:18:40,670 --> 01:18:50,190
+احداثيات القطبية of the vertical projection of the
+
+685
+01:18:50,190 --> 01:18:52,550
+vertical
+
+686
+01:18:57,340 --> 01:19:10,120
+projection that is a projection of P on the X Y
+
+687
+01:19:10,120 --> 01:19:21,980
+plane النقطة الثانية يحدث Z is the rectangular
+
+688
+01:19:27,010 --> 01:19:33,030
+Rectangular Vertical Coordinate
+
+689
+01:19:33,030 --> 01:19:39,550
+يبقى
+
+690
+01:19:39,550 --> 01:19:48,190
+بناء عليه X بدأت ساوي R Cos θ و Y بدأت ساوي R Cos
+
+691
+01:19:48,190 --> 01:19:56,760
+θو Z زي ما هى او هدول X تربيع زاد Y تربيع تساوي R
+
+692
+01:19:56,760 --> 01:20:04,220
+تربيع and تانى فيتا بتساوي one على X
+
+693
+01:20:30,530 --> 01:20:34,110
+من يوم ما بدأنا ناخد إحداثيات من الإبتدائي
+
+694
+01:20:34,110 --> 01:20:39,530
+والإعدادي والثانوي قضايا لو دخلنا الجامعة و لو
+
+695
+01:20:39,530 --> 01:20:45,330
+دخلنا المستوى الأول الفصلي الثانيو احنا بناخد كله
+
+696
+01:20:45,330 --> 01:20:48,970
+Cartesian coordinates او rectangular coordinates
+
+697
+01:20:48,970 --> 01:20:55,930
+احداثيات كارتيزية او احداثيات مستطيلة طبعا طيب لكن
+
+698
+01:20:55,930 --> 01:21:01,250
+لما جينا في calculus B روحنا اخد من الاحداثيات
+
+699
+01:21:01,250 --> 01:21:05,120
+المستطيلة و نجينا coordinate coordinatesاليوم ان
+
+700
+01:21:05,120 --> 01:21:08,000
+شاء الله بنعطي نوعين طبعا مش حللها إلا نقطة النوع
+
+701
+01:21:08,000 --> 01:21:12,040
+الأول و بعدها نقطة النوع الثاني فيها نوعين أخرين
+
+702
+01:21:12,040 --> 01:21:16,800
+من الإحداثيات اللي هو الإحداثيات المستورانية
+
+703
+01:21:16,800 --> 01:21:21,660
+cylindrical coordinates والإحداثيات الرابعة
+
+704
+01:21:21,660 --> 01:21:27,820
+spherical coordinatesالإحداثيات الكورية أو
+
+705
+01:21:27,820 --> 01:21:33,080
+الكوراوية تمام؟ يبقى هالإحداثيات سيبقونا
+
+706
+01:21:33,080 --> 01:21:35,620
+Missionary Coordinates اليوم وخلينا مع ال
+
+707
+01:21:35,620 --> 01:21:40,040
+cylindrical coordinates الإحداثيات الأسطوانية هي
+
+708
+01:21:40,040 --> 01:21:45,880
+مزيج بين الإحداثيات الخطبية والإحداثيات
+
+709
+01:21:47,970 --> 01:21:53,010
+كيف كتالة قال الـ cylindrical coordinates لنقطة P
+
+710
+01:21:53,010 --> 01:22:01,250
+in space S إحداثياتها ل P,R,θ وZ Z اللي هي الـ
+
+711
+01:22:01,250 --> 01:22:05,410
+Cartesian coordinates الـR وثيتا هي الإحداثيات
+
+712
+01:22:05,410 --> 01:22:10,660
+القطبية بحيث الـR وثيتا هي ال polar coordinatesof
+
+713
+01:22:10,660 --> 01:22:16,540
+the vertical projection of B on the XY plane وزد
+
+714
+01:22:16,540 --> 01:22:20,720
+هي تبعت ال rectangular chord السؤال هو كيف ذلك؟
+
+715
+01:22:20,720 --> 01:22:25,140
+بيقولك اه استني شوية تعالى لو روحت أخدت المحاول
+
+716
+01:22:25,140 --> 01:22:29,660
+الشكل اللي عنها هذا
+
+717
+01:22:29,660 --> 01:22:34,320
+بقيني أقول عليها فانا في ال Cartesian Xوفي ال
+
+718
+01:22:34,320 --> 01:22:41,800
+Polar بقى نقول θ تساوي Zero يبقى θ تساوي Zero هذا
+
+719
+01:22:41,800 --> 01:22:46,680
+في ال Cartesian بقى نقول عليه Y وفي ال Polar بقى
+
+720
+01:22:46,680 --> 01:22:54,740
+نقول θ تساوي Pi على اتنين هذا Z وخلنا Z لإن ال
+
+721
+01:22:54,740 --> 01:23:00,110
+Polar ماعنديش إلا إحدىكويس بدنا نأخد نقطة زي
+
+722
+01:23:00,110 --> 01:23:08,850
+النقطة هذه النقطة P اليحداتي تبعها R و θ و Z بدنا
+
+723
+01:23:08,850 --> 01:23:13,990
+نشوف وين ال R و ال θ و ال Z فبنجب نسقطها على
+
+724
+01:23:13,990 --> 01:23:20,590
+المستوى XY plane يبقى لو نزلتها عمود رأسي على ال
+
+725
+01:23:20,590 --> 01:23:30,470
+XY planeيبقى الرأس هذا هو مين هو Z الموازن لمحور Z
+
+726
+01:23:30,470 --> 01:23:40,130
+طيب اتنين هذا موازن لمحور Y يبقى يؤفق و هذا موازن
+
+727
+01:23:40,130 --> 01:23:44,970
+لمحور X يبقى
+
+728
+01:23:44,970 --> 01:23:51,360
+هذا Y يبقى بده يجينا بالشكل اللي عندها تمامطب إذا
+
+729
+01:23:51,360 --> 01:23:58,340
+وين R و θ دي؟ بنقولك بسيطة الخط المائل اللي عندك
+
+730
+01:23:58,340 --> 01:24:07,940
+هذا R الخط
+
+731
+01:24:07,940 --> 01:24:14,320
+اللي عندنا هذا هذا يمثل R طب وين θ؟ الزاوية اللي
+
+732
+01:24:14,320 --> 01:24:20,550
+صنعهاعلى اتجاه الموجب للـ X-Axis يبقى هاي ثيتا
+
+733
+01:24:20,550 --> 01:24:27,770
+يبقى ثيتا و R تبعات مين؟ الإحداثية القطبية إذا
+
+734
+01:24:27,770 --> 01:24:32,390
+للنقطة هذه الإحداثية تبعها اللي و مين يا بنات؟ R و
+
+735
+01:24:32,390 --> 01:24:38,050
+ثيتا و Zero لأن Z هنا ب Zero النقطة اللي فوق اللي
+
+736
+01:24:38,050 --> 01:24:45,010
+هي R و ثيتا و Zيبقى هذه الإحداثيات القطبية مع
+
+737
+01:24:45,010 --> 01:24:50,450
+الإحداثيات الكارتيزية يبقى أي نقطة اكتبها بدلالة
+
+738
+01:24:50,450 --> 01:24:56,930
+الار والثيتا والز فبالإخاطرة اسأل بعض الأسئلة
+
+739
+01:24:56,930 --> 01:25:04,530
+السؤال الأول لو قلتلك في الإحداثيات الأسطوانية R
+
+740
+01:25:04,530 --> 01:25:17,840
+تساوي 0 تمثل مين؟ بس ال originيعني هنا هذه R محور
+
+741
+01:25:17,840 --> 01:25:22,800
+Z ممتاز فالإجابة اللي أعطتنا سلام هي إجابة دقيقة
+
+742
+01:25:22,800 --> 01:25:27,480
+مائة بالمائة والمصطلح مدام R تساوي Zero بأحنا وين
+
+743
+01:25:27,480 --> 01:25:32,240
+على محور Z إذا في ال cylindrical coordinates R
+
+744
+01:25:32,240 --> 01:25:35,880
+تساوي Zero تمثل مين؟ حكيت بالك بصوص وبره عليه شوية
+
+745
+01:25:36,070 --> 01:25:39,850
+لأن في بعض الأسئلة تانية بدي أسألها طيب لو قلت لك
+
+746
+01:25:39,850 --> 01:25:46,610
+θ تساوي θ node معادلة
+
+747
+01:25:46,610 --> 01:25:52,050
+إيه الشدد؟ في ال polar كانت خط مستقيم ال polar هو
+
+748
+01:25:52,050 --> 01:25:57,950
+الحالبوم زي θ تساوي zero و θ تساوي zero كانت خط
+
+749
+01:25:57,950 --> 01:26:03,660
+مستقيم لكن لو قلت لك θ تساوي θ node في الفراعيعشان
+
+750
+01:26:03,660 --> 01:26:13,780
+نتكلم في مستوى الفرارة ايش يمثل ايه؟ يبقى
+
+751
+01:26:13,780 --> 01:26:18,900
+هذا يمثلي plane بالشكل اللي عندنا اللي هو عمودي
+
+752
+01:26:18,900 --> 01:26:23,960
+على مستوى ال X Y plane كويس هيبقى هذه المعلومات
+
+753
+01:26:23,960 --> 01:26:32,140
+اللي هو بالنسبة ل R تساوي Zero طيب لو قلنا R تساوي
+
+754
+01:26:32,140 --> 01:26:39,590
+Aأرض تساوي إيه؟ أرض تساوي إيه؟ أرض تساوي إيه؟ أرض
+
+755
+01:26:39,590 --> 01:26:43,550
+تساوي إيه؟ أرض تساوي إيه؟ أرض تساوي إيه؟ أرض تساوي
+
+756
+01:26:43,550 --> 01:26:46,450
+إيه؟ أرض تساوي إيه؟ أرض تساوي إيه؟ أرض تساوي إيه؟
+
+757
+01:26:46,450 --> 01:26:50,430
+أرض تساوي إيه؟ أرض تساوي إيه؟ أرض تساوي إيه؟ أرض
+
+758
+01:26:50,430 --> 01:26:51,250
+تساوي إيه؟ أرض تساوي إيه؟ أرض تساوي إيه؟ أرض تساوي
+
+759
+01:26:51,250 --> 01:26:52,710
+إيه؟ أرض تساوي إيه؟ أرض تساوي إيه؟ أرض تساوي إيه؟
+
+760
+01:26:52,710 --> 01:26:57,170
+أرض تساوي إيه؟ أرض تساوي إيه؟ أرض تس
+
+761
+01:27:07,550 --> 01:27:19,510
+is the equation of the z axis المقطة الأولى المقطة
+
+762
+01:27:19,510 --> 01:27:29,910
+الثانية ال a تساوي a is an equation is an equation
+
+763
+01:27:29,910 --> 01:27:42,470
+of a cylinderVision of a cylinder with axis محور
+
+764
+01:27:42,470 --> 01:28:00,050
+تبعها along the z axis على محور z and radius اللي
+
+765
+01:28:00,050 --> 01:28:01,050
+هو a
+
+766
+01:28:06,290 --> 01:28:15,510
+مرة تلاتة ثيتا تساوي ثيتا نوت is an equation of
+
+767
+01:28:15,510 --> 01:28:25,670
+a plane لمستوى contains .. contains
+
+768
+01:28:25,670 --> 01:28:31,210
+the z-axis يجتمع
+
+769
+01:28:31,210 --> 01:28:34,830
+على محور z and makes
+
+770
+01:28:39,000 --> 01:28:43,720
+أن أنجل ثتا
+
+771
+01:28:43,720 --> 01:28:55,140
+نوت مع الـ positive x
+
+772
+01:28:55,140 --> 01:28:55,920
+-axis
+
+773
+01:29:01,410 --> 01:29:07,270
+يعني لو روحنا و رسمنا هناك باختصار و قلنا هذا محور
+
+774
+01:29:07,270 --> 01:29:14,610
+X هذا محور Y هذا محور Z و روحنا و رسمنا هذا ل
+
+775
+01:29:14,610 --> 01:29:28,190
+plane فكانت رسمته على الشكل التاني اعمل
+
+776
+01:29:28,190 --> 01:29:35,680
+زاوية مقدرها في Canonمع مين؟ مع محور X يبقى هذا ال
+
+777
+01:29:35,680 --> 01:29:42,960
+plane الرأس المظلل معادلته θ تساوي ثتا نوت لكن في
+
+778
+01:29:42,960 --> 01:29:47,140
+ال polar كان ثتا تساوي ثتا نوت معادلة خاط مستقيل
+
+779
+01:29:47,140 --> 01:29:53,800
+وفي ال polar كانت R تساوي A معادلة A شهد يا بنات
+
+780
+01:29:53,800 --> 01:29:59,980
+في ال polar coordinates في ال planeدائرة مركزها
+
+781
+01:29:59,980 --> 01:30:04,740
+نقطة الأصفر و نصف قطر هيساوي نساوي a كم يكون واحد
+
+782
+01:30:04,740 --> 01:30:08,960
+ولا غيره بشرط اللي هيكون موجة لو كان سالف باخدله
+
+783
+01:30:08,960 --> 01:30:16,380
+من ال absolute value نعطي مثال فسيط على ذلك يبقى
+
+784
+01:30:16,380 --> 01:30:20,720
+examples أول
+
+785
+01:30:20,720 --> 01:30:30,270
+مثال بيقول لي evaluate أحسبالتكامل الثلاثي التالي
+
+786
+01:30:30,270 --> 01:30:38,910
+لتكامل من zero لتنين تكامل من R ناقص اتنين الى
+
+787
+01:30:38,910 --> 01:30:45,990
+الجدرى التربية الى اربعة ناقص R تربيةتكامل من صفر
+
+788
+01:30:45,990 --> 01:30:56,090
+لإتنين باقي لمن؟ لـR في صين الـθيتا زائد واحد R دي
+
+789
+01:30:56,090 --> 01:31:07,710
+R دي ثيتا دي زيتا يبقى R دي R يبقى
+
+790
+01:31:07,710 --> 01:31:27,480
+يقل لي R دي ثيتاDZ DR كتبهم لهك زي ما هم بدريجي
+
+791
+01:31:27,480 --> 01:31:34,160
+نشوف أول حاجة بدي أكمل بالنسبة إلى مين إلى Dθ
+
+792
+01:31:34,160 --> 01:31:38,600
+المسألة صارت كإنها إيش هي integration
+
+793
+01:31:40,730 --> 01:31:46,190
+من R نقص اتنين للجدر التربية للاربع نقص R تربيع
+
+794
+01:31:46,190 --> 01:31:52,850
+وتكامل من صفر للاتنين ضايق لل R تربيع صيني الزاوية
+
+795
+01:31:52,850 --> 01:32:01,390
+ثيتا زائد R D ثيتا D زاد DR بيقول انه بده كامل
+
+796
+01:32:01,390 --> 01:32:04,790
+بالنسبة ل D ثيتا ايه بهذا التكامل سهل ماعناش فيه
+
+797
+01:32:04,790 --> 01:32:11,420
+مشكلةيبقى هاي تكامل من Zero لإتنين تكامل من R ناقص
+
+798
+01:32:11,420 --> 01:32:19,360
+اتنين للجدرش تربية للاربع ناقص R تربية لمن لسالب R
+
+799
+01:32:19,360 --> 01:32:27,580
+تربية قصين الزاوية ثيتا زائد R ثيتا كل هذا الكلام
+
+800
+01:32:27,580 --> 01:32:33,220
+من Zero لغاية اتنين Pi لD زاد DA
+
+801
+01:32:35,650 --> 01:32:41,470
+هذا بالنسبة تكامل من صفر للاتنين تكامل من R ناقص
+
+802
+01:32:41,470 --> 01:32:47,810
+اتنين للجذر التربيع للاربعة ناقص R تربيع
+
+803
+01:32:50,060 --> 01:32:55,080
+هذا مصحى ربع الربوطاني مش هتبقى يبقى R نقص اتنين
+
+804
+01:32:55,080 --> 01:32:59,980
+بتعوض بالقيم اللي فوق النقص اللي تحت كوصين اتنين
+
+805
+01:32:59,980 --> 01:33:04,540
+باي زي كوصين الصفر يعني بيبقى ادياش يبقى واحد يبقى
+
+806
+01:33:04,540 --> 01:33:12,460
+ببقى لدي جدياش سالب R تربيع وهذه تصير اتنين باي ا
+
+807
+01:33:12,460 --> 01:33:21,390
+يبقى زائد اتنين باي اناقص cosine صفر بواحد ما ناقص
+
+808
+01:33:21,390 --> 01:33:31,070
+بصير الزائد R تربيع ناقص Zero في R اللي هو ب Zero
+
+809
+01:33:59,450 --> 01:34:06,690
+تكامل من صفر للإتنين تكامل من R ناقص إتنين للجذر
+
+810
+01:34:06,690 --> 01:34:12,550
+التربيعي للأربعة ناقص R تربيع هو نجي ناقص R تربيع
+
+811
+01:34:12,550 --> 01:34:19,400
+وزاد R تربيع مع بعض والإتنين by Rيبقى اتنين باي ار
+
+812
+01:34:19,400 --> 01:34:26,620
+دي زد دي اه فهذا الكلام يساوي اتنين باي خليك برا
+
+813
+01:34:26,620 --> 01:34:32,260
+وهي تكامل من صفر لغاية اتنين والار مالهاش علاقة في
+
+814
+01:34:32,260 --> 01:34:39,920
+الموضوع وتكامل الدي زد بزد من ات ار ناقص اتنين الى
+
+815
+01:34:39,920 --> 01:34:49,710
+الجدر التربيه لاربع ناقص ار تربيه لمنلذي R هذا
+
+816
+01:34:49,710 --> 01:34:56,570
+الكلام يسمى نين بايت تكمن من صفر للاتنين لل R
+
+817
+01:34:56,570 --> 01:35:04,510
+الجذري التربية لاربعة ناقص R تربية ناقص اللي هو ال
+
+818
+01:35:04,510 --> 01:35:12,150
+R في ال R ناقص واحد كل هذا الكلام بالنسبة لمين لذي
+
+819
+01:35:12,150 --> 01:35:18,910
+Rهذا يا بنات أعمل لها تعويضة هيك بتجيش عندك هنا R
+
+820
+01:35:18,910 --> 01:35:24,910
+هنا أربع ناقص R تاربية يبقى بإمكاني أحط R يسوى
+
+821
+01:35:24,910 --> 01:35:30,640
+اتنين sin θ زي calculus Bو بإمكاني أشيل الأربعة
+
+822
+01:35:30,640 --> 01:35:34,900
+نقص الأرض اللي فيها كلها مرة واحدة و أحط بدلها أي
+
+823
+01:35:34,900 --> 01:35:39,640
+متغير لإن اللي برا هو مشتقة اللي جوا بس فلسة مجداش
+
+824
+01:35:39,640 --> 01:35:47,400
+إشارة سالف و لإتنينيبدأ بناء عليه بروح للتكافل
+
+825
+01:35:47,400 --> 01:35:55,820
+الأول بتقوله حطلي مثلا w يساوي 4-r ترمية يبقى dw
+
+826
+01:35:55,820 --> 01:35:59,640
+-2rdA
+
+827
+01:36:04,350 --> 01:36:10,430
+ر دي ار اذا صارت هذا يا بنات اللي هي اتنين في
+
+828
+01:36:10,430 --> 01:36:16,270
+التكامل افضل من كده بده يصير عندك الار دي ار هكتف
+
+829
+01:36:16,270 --> 01:36:24,430
+بدالها ناقص نص وهي الدي دابليو وهذه جذري ال دابليو
+
+830
+01:36:24,430 --> 01:36:31,650
+ضالت عند حدود التكامل لما تبقى ار باتنين مصير زيرو
+
+831
+01:36:32,680 --> 01:36:37,820
+عندما تبقى R بزيرو بصير كده؟ أربعة تمام هذا الجزء
+
+832
+01:36:37,820 --> 01:36:44,140
+الأول الجزء الثاني ناقص اتنين by تكامل من زيرو
+
+833
+01:36:44,140 --> 01:36:54,820
+لإتنين لر تربيه ناقص R ب R اتنين by ر تربيه ناقص R
+
+834
+01:36:54,820 --> 01:37:03,790
+ما لك؟ اللي فوق؟يبقى ار ناقص اتنين هذه يا بنات
+
+835
+01:37:03,790 --> 01:37:10,930
+يبقى هذي بصير اتنين ار فقط يبقى هذي ار ناقص اتنين
+
+836
+01:37:14,580 --> 01:37:18,060
+هذه الكبيرة تحت الظروف أجيبها من الشكل و أخضعها من
+
+837
+01:37:18,060 --> 01:37:24,620
+شرط السلف والنص مع البي بيبقى البي تكامل من 0 ل4
+
+838
+01:37:24,620 --> 01:37:36,740
+لW أص نص DW ناقص 2 بي R تكيب على 3 ناقص R تربيع
+
+839
+01:37:36,740 --> 01:37:45,600
+كله من 0 ل2هذه πاي في W أقصد تلاتة على اتنين على
+
+840
+01:37:45,600 --> 01:37:50,600
+تلاتة على اتنين من عند ال zero لغاية الأربعة وهذه
+
+841
+01:37:50,600 --> 01:37:54,160
+ناقصت اتنين باي في تمانية
+
+842
+01:38:08,070 --> 01:38:13,450
+أس تلاتة على اتنين يعني هنا أربعة أس تلاتة على
+
+843
+01:38:13,450 --> 01:38:19,590
+اتنين ناقص Zero وهذه بالنسبة تصير ناقص اتنين by
+
+844
+01:38:19,590 --> 01:38:27,090
+تلاتة في أربعة باطلناش ناقص بتمانية بظل ناقص أربعة
+
+845
+01:38:27,090 --> 01:38:36,030
+على تلاتة ويساوي اتنين by على تلاتة فيه هذاالجدر
+
+846
+01:38:36,030 --> 01:38:41,730
+التربيع لأربعة تكيب يعني اللي هي قداش تمانية يعني
+
+847
+01:38:41,730 --> 01:38:45,490
+اربعة وستين تحت الجدر التربيعي اللي هي التمانية
+
+848
+01:38:45,490 --> 01:38:53,330
+وهنا ناقص فناقصه بزائد تمانية باي على تلاتة وهنا
+
+849
+01:38:53,330 --> 01:39:01,210
+زائد نمف تمانية ستاشر باي على تلاتة زائد تمانية
+
+850
+01:39:01,210 --> 01:39:07,990
+بايع تلاتة ويسوء أربعة وعشرين باى يعني تمانية باى
+
+851
+01:39:07,990 --> 01:39:13,390
+تمانية باى على كل الخط يبقى هذه الإجابة المرة
+
+852
+01:39:13,390 --> 01:39:19,730
+القادمة ان شاء الله بنكمل هذا ال section حد بتحب
+
+853
+01:39:19,730 --> 01:39:24,250
+تسأل أي سؤال هنا يبقى اتوكر على الله
+
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/YDVEQJcaKaA.srt b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/YDVEQJcaKaA.srt
new file mode 100644
index 0000000000000000000000000000000000000000..429fb72ccf0c31a7278e3c645e1a4f6a180ff974
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/YDVEQJcaKaA.srt
@@ -0,0 +1,2376 @@
+1
+00:00:08,500 --> 00:00:12,800
+يبقى موضوعنا اليوم إن شاء الله تعالى موضوع the
+
+2
+00:00:12,800 --> 00:00:18,420
+top أو scalar product يعني حاصل الضرب القياسي
+
+3
+00:00:18,420 --> 00:00:25,050
+للمتجهين، هذا يوحي بتساؤل آخر، هل هناك حاصل ضرب
+
+4
+00:00:25,050 --> 00:00:30,750
+اتجاهي؟ الإجابة نعم، إذن نحن عندنا نوعين من
+
+5
+00:00:30,750 --> 00:00:35,290
+الضرب، الضرب القياسي والضرب الاتجاهي، الذي أخذناه
+
+6
+00:00:35,290 --> 00:00:40,950
+المرة الماضية كان حاصل ضرب scalar في vector، لكن
+
+7
+00:00:40,950 --> 00:00:44,730
+vector في vector لم نتحدث عنه في المرة الماضية، تمام؟
+
+8
+00:00:44,900 --> 00:00:48,820
+إذن، سنأخذ اليوم الـ dot أو الـ scalar product،
+
+9
+00:00:48,820 --> 00:00:53,360
+سنعطي تعريفنا للـ dot أو للـ scalar product ثم
+
+10
+00:00:53,360 --> 00:00:58,700
+كيفية العمل في هذا المجال، سنبدأ أول شيء بالـ
+
+11
+00:00:58,700 --> 00:01:04,480
+definition، سأقول هنا الـ definition، the
+
+12
+00:01:04,480 --> 00:01:04,900
+dot
+
+13
+00:01:14,670 --> 00:01:22,890
+of two vectors، الـ
+
+14
+00:01:22,890 --> 00:01:33,650
+U = U1، U2، U3 and الـ V =
+
+15
+00:01:33,650 --> 00:01:41,830
+V1، V2، V3 is defined
+
+16
+00:01:52,600 --> 00:01:59,760
+نضرب كل مركبة في نظيرتها، ونجمع هذه الأعداد، هذا يعطيني
+
+17
+00:01:59,760 --> 00:02:09,000
+رقماً، ليس vector، سأقول U1 V1 + U2 V2 +
+
+18
+00:02:09,000 --> 00:02:17,280
+U3 V3، هذا حاصل ضرب مركبات، إذن هذا يعطيني رقماً، إذن
+
+19
+00:02:17,280 --> 00:02:22,500
+الرقم الذي لدينا هذا هو عبارة عن حاصل الضرب
+
+20
+00:02:22,500 --> 00:02:27,400
+القياسي لمتجهين، لما نقول قياسي الناتج يساوي كمية
+
+21
+00:02:27,400 --> 00:02:33,200
+قياسية، طبعاً هناك تعريف آخر، هذا يُعتبر التعريف
+
+22
+00:02:33,200 --> 00:02:43,140
+الأول،  الـ U . V = طول الـ U × طول
+
+23
+00:02:43,140 --> 00:02:51,200
+الـ V × cos الزاوية θ، حيث θ هي
+
+24
+00:02:51,200 --> 00:02:57,760
+الزاوية بين الـ
+
+25
+00:02:57,760 --> 00:03:00,340
+U والـ V
+
+26
+00:03:07,510 --> 00:03:14,350
+إذن هناك صيغتان لحاصل الضرب القياسي لمتجهين، الصيغة
+
+27
+00:03:14,350 --> 00:03:19,410
+الأولى بضرب كل مركبة في نظيرتها وجمعها يعطينا
+
+28
+00:03:19,410 --> 00:03:24,790
+ناتج رقم، الصيغة الثانية طول المتجه الأول × طول
+
+29
+00:03:24,790 --> 00:03:30,050
+المتجه الثاني × جيب تمام الزاوية المحصورة بينهما
+
+30
+00:03:31,320 --> 00:03:36,320
+طبعاً واضح أنه لم تُوضع قيود على هذه الزاوية، السؤال هو
+
+31
+00:03:36,320 --> 00:03:40,840
+بما أن هذا رقم، لأن هذا الطول عبارة عن رقم، الطول
+
+32
+00:03:40,840 --> 00:03:44,580
+الثاني عبارة عن رقم، وجيب تمام الزاوية كذلك عبارة عن
+
+33
+00:03:44,580 --> 00:03:50,660
+رقم، لأن حاصل ضرب ثلاثة أرقام، السؤال هو هل يمكن
+
+34
+00:03:50,660 --> 00:03:59,840
+لحاصل الضرب هذا أن يكون كمية قياسية؟ ممكن يكون قياسياً
+
+35
+00:04:06,000 --> 00:04:11,280
+لأن هذا، سأضع الكلام هذا في صيغة remark
+
+36
+00:04:11,280 --> 00:04:19,100
+أولاً: لنفترض أني أريد إيجاد الزاوية ما بين
+
+37
+00:04:19,100 --> 00:04:22,780
+المتجهين، هذين المتجهين، وهي الزاوية θ، أريد
+
+38
+00:04:22,780 --> 00:04:27,320
+إيجادها من خلال العلاقة التي لدينا هذه، فأستطيع
+
+39
+00:04:27,320 --> 00:04:33,620
+أن أقول هنا cos الزاوية θ = U . V /
+
+40
+00:04:33,620 --> 00:04:39,440
+طول الـ U × طول الـ V، سأقسم الطرفين على طول الـ U
+
+41
+00:04:39,440 --> 00:04:45,360
+× طول الـ V، أريد θ، كما درسنا في calculus
+
+42
+00:04:45,360 --> 00:04:52,200
+بأُؤثر بـ cos⁻¹ على الطرفين، وبناءً عليه هذا
+
+43
+00:04:52,200 --> 00:04:59,300
+يصبح أن θ = cos⁻¹ للرقم U . V /
+
+44
+00:04:59,300 --> 00:05:02,500
+طول الـ U × طول الـ V
+
+45
+00:05:08,710 --> 00:05:16,330
+U . V ممكن يكون قيمة موجبة أكبر من الصفر، وهذا
+
+46
+00:05:16,330 --> 00:05:22,870
+الكلام لو كانت الزاوية θ زاوية حادة،  هذا
+
+47
+00:05:22,870 --> 00:05:33,130
+إذا θ is an obtuse or acute angle
+
+48
+00:05:35,590 --> 00:05:39,950
+هنا acute angle زاوية حادة، يعني محصورة من صفر
+
+49
+00:05:39,950 --> 00:05:44,130
+إلى 90 درجة، وجيب تمام الزاوية الحادة دائماً موجب
+
+50
+00:05:44,130 --> 00:05:51,550
+أو  positive، إذن لو قلت هذا الـ U، هذا
+
+51
+00:05:51,550 --> 00:05:58,070
+الـ V، هذا الـ U وهذا الـ V، وهذه الزاوية، على سبيل
+
+52
+00:05:58,070 --> 00:06:04,890
+المثال، هذه زاوية حادة، ثالثاً: الـ U
+
+53
+00:06:04,890 --> 00:06:10,890
+. V ممكن يكون less than zero، يعني كمية سالبة،
+
+54
+00:06:10,890 --> 00:06:19,810
+هذا يحدث لو كان θ is an obtuse angle،
+
+55
+00:06:19,810 --> 00:06:25,970
+obtuse angle، يعني زاوية منفرجة، يعني لو رسمت
+
+56
+00:06:25,970 --> 00:06:31,000
+الزاوية فكانت الزاوية بهذا الشكل، هذا الـ U، و
+
+57
+00:06:31,000 --> 00:06:35,060
+هذا الـ V، وهذه الزاوية، وهي الـ obtuse angle،
+
+58
+00:06:35,060 --> 00:06:40,360
+وهي الزاوية θ، طبعاً في الربع الثاني جيب
+
+59
+00:06:40,360 --> 00:06:47,160
+التمام كمية سالبة، وبالتالي الـ dot product سيُصبح
+
+60
+00:06:47,160 --> 00:06:50,420
+negative value، وهو كمية سالبة،
+
+61
+00:06:54,520 --> 00:07:00,180
+U . V ممكن يساوي صفر،  إذا كانت
+
+62
+00:07:00,180 --> 00:07:08,280
+الزاوية قائمة، هذا يعني إذا θ = π /
+
+63
+00:07:08,280 --> 00:07:15,200
+2، وهذا يحدث فقط
+
+64
+00:07:15,200 --> 00:07:19,740
+إذا الـ U والـ V
+
+65
+00:07:25,900 --> 00:07:30,640
+إذن إذا كان المتجهان متعامدان، كلمة
+
+66
+00:07:30,640 --> 00:07:33,780
+متعامدان معناها perpendicular،
+
+67
+00:07:51,070 --> 00:07:54,670
+المستقيمين متعامدان،  الـ two lines are
+
+68
+00:07:54,670 --> 00:08:01,590
+perpendicular، إذن
+
+69
+00:08:01,590 --> 00:08:05,910
+U . V = صفر، إذا كانت θ = π /
+
+70
+00:08:05,910 --> 00:08:12,550
+2، أو الـ U والـ V are orthogonal، خامساً:
+
+71
+00:08:12,550 --> 00:08:19,370
+لو سألتك السؤال التالي، وقلت لك لو أردت
+
+72
+00:08:19,370 --> 00:08:27,840
+U . U، هذا يعطينا ماذا؟ طول الـ U
+
+73
+00:08:27,840 --> 00:08:32,880
+× طول الـ U × cos الزاوية، كم الزاوية بين
+
+74
+00:08:32,880 --> 00:08:38,000
+المتجه نفسه؟ صفر، cos صفر = 1، إذن هذا يعطينا
+
+75
+00:08:38,000 --> 00:08:45,480
+طول الـ U²، لو أردت إيجاد
+
+76
+00:08:45,480 --> 00:08:50,600
+طول الـ U بدلالة الـ dot، فأخذ الجذر التربيعي
+
+77
+00:08:50,600 --> 00:08:56,560
+للطرفين، هذا يعطينا أن طول الـ U =
+
+78
+00:08:58,970 --> 00:09:06,750
+√U . U، لو أردت حسابه بدلالة المركبات،
+
+79
+00:09:06,750 --> 00:09:12,790
+سأقول هذا يساوي U1² + U
+
+80
+00:09:12,790 --> 00:09:21,110
+2² + U3²، إذن U . U
+
+81
+00:09:21,110 --> 00:09:24,570
+= طول الـ U × طول الـ U × cos الزاوية
+
+82
+00:09:24,570 --> 00:09:28,790
+الصفر، وهو 1، صحيح، إذن يصبح هذا طول الـ U
+
+83
+00:09:28,790 --> 00:09:34,670
+²، لو أخذنا الجذر التربيعي للطرفين، يصبح طول
+
+84
+00:09:34,670 --> 00:09:40,770
+المتجه U = √U . U، الـ U
+
+85
+00:09:40,770 --> 00:09:45,510
+. U، طبقاً للتعريف الذي كتبناه، يصبح V1
+
+86
+00:09:45,510 --> 00:09:51,790
+= U1، V2 = U2، V3 = U3، يصبح U1
+
+87
+00:09:51,790 --> 00:09:57,270
+² + U2² + U3² تحت الجذر التربيعي،
+
+88
+00:09:57,270 --> 00:10:04,190
+يعطيني طول المتجه U،  قياساً على ذلك، يمكن أن
+
+89
+00:10:04,190 --> 00:10:11,570
+نضيف ملاحظة من عندي، لو قلت لك I . I
+
+90
+00:10:13,220 --> 00:10:18,780
+كم يساوي؟ بدلاً من U . U، سأخذ I
+
+91
+00:10:18,780 --> 00:10:23,800
+. I،  الذي طوله 1، وطول الثاني 1، و
+
+92
+00:10:23,800 --> 00:10:28,160
+cos الزاوية صفر = 1، إذن كم؟ 1، صحيح، إذن
+
+93
+00:10:28,160 --> 00:10:34,680
+هذا = J . J = K . K
+
+94
+00:10:34,680 --> 00:10:36,420
+= 1، صحيح،
+
+95
+00:10:38,840 --> 00:10:46,140
+و لو قلت لك I . J، كم؟ صفر،
+
+96
+00:10:46,140 --> 00:10:50,580
+لأن الاثنين متعامدان، إذن حاصل الضرب هذا
+
+97
+00:10:50,580 --> 00:10:58,400
+= صفر،  J . K = K . I كلها تساوي
+
+98
+00:10:58,400 --> 00:11:06,080
+صفر، هذه بعض الخواص الأساسية،  سأطرح
+
+99
+00:11:06,080 --> 00:11:13,350
+كذلك تساؤلاً: هل Zero vector Orthogonal to any
+
+100
+00:11:13,350 --> 00:11:20,070
+vector؟ مرة أخرى،  لدينا Zero vector، Zero vector
+
+101
+00:11:20,070 --> 00:11:23,450
+يمكن كتابته  صفر في اتجاهي، صفر في اتجاهي،
+
+102
+00:11:23,450 --> 00:11:24,870
+صفر في اتجاهي، صفر في اتجاهي،
+
+103
+00:11:24,870 --> 00:11:29,870
+اتجاهي، هل Zero vector Orthogonal to any given
+
+104
+00:11:29,870 --> 00:11:32,330
+vector؟
+
+105
+00:11:42,150 --> 00:11:46,930
+سأزيل الـ U وأضع مكانه صفر . V، كم؟ سأحصل على
+
+106
+00:11:46,930 --> 00:11:52,790
+هذا، إذن الـ Zero vector is orthogonal to any
+
+107
+00:11:52,790 --> 00:11:58,330
+vector، حاصل الضرب القياسي لأي vector
+
+108
+00:11:58,330 --> 00:12:02,110
+مع Zero vector يعطينا ماذا؟ يعطينا الصفر،
+
+109
+00:12:02,110 --> 00:12:04,850
+سأسجل هذه النقطة 7
+
+110
+00:12:14,950 --> 00:12:25,290
+to any vector، السبب because، لو أخذنا الـ zero vector
+
+111
+00:12:25,290 --> 00:12:30,870
+. V، على سبيل المثال، هذا يقول لنا صفر في
+
+112
+00:12:30,870 --> 00:12:35,230
+اتجاه الـ I، صفر في اتجاه الـ J، صفر في اتجاه الـ K
+
+113
+00:12:35,230 --> 00:12:43,030
+.  V1 في اتجاه الـ I، V2 في اتجاه الـ J، V3 في
+
+114
+00:12:43,030 --> 00:12:48,410
+اتجاه الـ K، ننظر للمركبات المتناظرة، صفر × V
+
+115
+00:12:48,410 --> 00:12:53,850
+1 = صفر، صفر × V2 = صفر، صفر × V3
+
+116
+00:12:53,850 --> 00:12:59,290
+= صفر، الناتج = صفر، إذن بناءً عليه Zero
+
+117
+00:12:59,290 --> 00:13:04,910
+vector is orthogonal to any vector، قبل أن نواصل،
+
+118
+00:13:04,910 --> 00:13:12,650
+سناخذ بعض الأمثلة، examples، أول
+
+119
+00:13:12,650 --> 00:13:18,560
+مثال:  find the value of the constant α، find
+
+120
+00:13:18,560 --> 00:13:30,640
+the value of the constant α such that the
+
+121
+00:13:30,640 --> 00:13:31,100
+vectors
+
+122
+00:13:46,640 --> 00:13:58,380
+11J - 3K and الـ vector الثاني 2αI - αJ
+
+123
+00:13:58,380 --> 00:14:08,120
+الـ vector الثاني وهو V = 2αI - αJ - 5K are
+
+124
+00:14:08,120 --> 00:14:09,920
+orthogonal
+
+125
+00:14:16,890 --> 00:14:23,870
+سؤال مرة أخرى يقول: هات لي قيمة الثابت α، ولم يضع
+
+126
+00:14:23,870 --> 00:14:29,490
+عليها أي قيود، بحيث أن المتجهين هذين
+
+127
+00:14:29,490 --> 00:14:34,310
+يكونان متعامدين، إذا هذين المتجهين متعامدين،
+
+128
+00:14:34,310 --> 00:14:36,290
+فحاصل الضرب لهما كم؟
+
+129
+00:14:51,530 --> 00:14:59,330
+نأخذ U . V = 0، هذا يعني ماذا؟
+
+130
+00:14:59,330 --> 00:15:05,570
+نضرب المركبات المتناظرة،  يصبح 2α
+
+131
+00:15:05,570 --> 00:15:08,450
+× 0،  الذي بعده -α
+
+132
+00:15:12,310 --> 00:15:17,730
+× (-11)  الذي بعده -5 × (-3) = +15، كلها
+
+133
+00:15:17,730 --> 00:15:24,550
+تساو كم؟  تساوي 0، الآن هذه معادلة من الدرجة
+
+134
+00:15:24,550 --> 00:15:30,770
+الثانية في مجهول واحد، يمكن حلها وإيجاد هذا المجهول،
+
+135
+00:15:30,770 --> 00:15:36,650
+لو حللنا هذا المقدار الثلاثي على شكل أقواس،
+
+136
+00:15:36,650 --> 00:15:41,400
+هو يساوي 0، 2α، وهنا α، يعني
+
+137
+00:15:41,400 --> 00:15:47,460
+الـ 15 هذه  = 15 × 1 أو 3 × 5، إذن لو كتبت هنا 5، وهنا 3، و هنا -،
+
+138
+00:15:47,460 --> 00:15:55,980
+و هنا -، تصبح -5α و -3α،
+
+139
+00:15:55,980 --> 00:16:00,740
+بـ -،
+
+140
+00:16:00,740 --> 00:16:01,500
+بـ
+
+141
+00:16:22,750 --> 00:16:30,670
+إذن هاتان القيمتان المطلوبتان لـ α،
+
+142
+00:16:57,270 --> 00:17:06,490
+مثال آخر، example 2، يقول
+
+143
+00:17:06,490 --> 00:17:11,090
+let U =
+
+144
+00:17:11,090 --> 00:17:23,230
+3I - J - 2K and V = I +
+
+145
+00:17:23,230 --> 00:17:24,530
+2J
+
+146
+00:17:29,890 --> 00:17:38,870
+ماذا نريد؟  أولاً: U . V، ثانياً: the angle
+
+147
+00:17:38,870 --> 00:17:42,410
+between
+
+148
+00:17:42,410 --> 00:17:56,590
+U and V
+
+149
+00:17:56,590 --> 00:17:59,170
+انتهينا من المثال الأول، سأمحيه
+
+150
+00:18:17,750 --> 00:18:22,510
+سؤال آخر، لدينا U، لدينا V،  قال لي  U
+
+151
+00:18:22,510 --> 00:18:30,350
+. V،  أولاً: U . V، سأضرب
+
+152
+00:18:30,350 --> 00:18:34,810
+المركبات المتناظرة، 3 × 1
+
+153
+00:18:34,810 --> 00:18:35,610
+كم؟
+
+154
+00:19:03,290 --> 00:19:08,730
+النقطة الأولى التي أخذناها في الـ remark،  الزاوية = cos⁻¹
+
+155
+00:19:08,730 --> 00:19:18,730
+U . V / طول U × طول V، سأقول
+
+156
+00:19:18,730 --> 00:19:24,350
+طول U = √، المربع الأول 9، المربع الثاني 1، المربع
+
+157
+00:19:24,350 --> 00:19:30,550
+الثالث 4، إذن √14، سنحسب طول
+
+158
+00:19:30,550 --> 00:19:38,170
+المتجه الثاني V، √، المربع الأول 1، المربع الثاني 4، والمربع الثالث
+
+159
+00:19:38,170 --> 00:19:42,750
+أيضاً 4، √5،
+
+160
+00:19:42,750 --> 00:19:50,430
+إذن طول U × طول V = √14 × √5 =
+
+161
+00:19:50,430 --> 00:19:57,270
+√70،  إذن  θ = cos⁻¹
+
+162
+00:19:57,270 --> 00:20:03,220
+7 / √70،
+
+163
+00:20:03,220 --> 00:20:09,700
+=√14، تمام؟  إذن نحن لدينا θ = cos⁻¹
+
+164
+00:20:09,700 --> 00:20:15,740
+U . V / طول U × طول V،
+
+165
+00:20:15,740 --> 00:20:21,460
+= cos⁻¹
+
+166
+00:20:21,850 --> 00:20:26,650
+7/√70، من النقطة أ طلع 7، و هذا
+
+167
+00:20:26,650 --> 00:20:34,290
+√70، cos⁻¹  1/2، إذن θ
+
+168
+00:20:34,290 --> 00:20:42,950
+= كم؟  الزاوية التي جيب تمامها = 1/2،
+
+169
+00:20:42,950 --> 00:20:49,250
+نعلم أن جيب تمامها = 1/2  هي 60° =
+
+170
+00:20:49,250 --> 00:20:56,410
+π/3،  إذن θ =
+
+171
+00:20:56,410 --> 00:21:02,410
+π/3، هذه الزاوية
+
+172
+00:21:02,410 --> 00:21:06,710
+بين المتجهين، لاحظوا أن هذه الزاوية حادة،
+
+173
+00:21:06,710 --> 00:21:12,650
+وليس منفرجة، ولذلك  ستكون موجبة، وهي
+
+174
+00:21:12,650 --> 00:21:17,810
+7،  هذا يتفق مع الكلام النظري الذي ذكرناه
+
+175
+00:21:17,810 --> 00:21:23,510
+قبل قليل، سأنتقل الآن لبعض الخواص لـ dot
+
+176
+00:21:23,510 --> 00:21:30,830
+product، properties of
+
+177
+00:21:30,830 --> 00:21:40,270
+the dot product، خواص
+
+178
+00:21:40,270 --> 00:21:47,890
+حاصل الضرب القياسي، سأقول إذا U و V و
+
+179
+00:21:47,890 --> 00:22:03,340
+W أي متجهات،  و C ثابت،
+
+180
+00:22:03,340 --> 00:22:16,400
+then، أولاً: U . V = V . U، ثانياً:
+
+181
+00:22:16,400 --> 00:22:18,3
+
+223
+00:28:19,870 --> 00:28:29,230
+Dot الـ V زائد أربعة W لو رجعت للخاصية اللي عندنا و
+
+224
+00:28:29,230 --> 00:28:34,790
+الخاصية رقم تلاتة يبقى vector ضرب مجموع two
+
+225
+00:28:34,790 --> 00:28:38,750
+vectors بدي أوزع هذا الـ vector على مين؟ على الـ two
+
+226
+00:28:38,750 --> 00:28:43,550
+vectors اللي جوا يبقى بناء عليه هذا الكلام بده
+
+227
+00:28:43,550 --> 00:28:48,910
+يساوي تلاتة U كله كـ vector Dot الـ V
+
+228
+00:29:00,030 --> 00:29:10,610
+مرة تانية هذه التلاتة بقدر أخدها برا تمام كده هذه
+
+229
+00:29:10,610 --> 00:29:16,350
+التي هي تلاتة U dot الـ أربعة
+
+230
+00:29:37,150 --> 00:29:41,890
+هذا الكلام يبدو يساوي ثلاثة في أربعة = 12 يبقى هذه
+
+231
+00:29:41,890 --> 00:29:47,530
+ثلاثة في أربعة = اثني عشر
+
+232
+00:30:17,220 --> 00:30:22,920
+يبقى هاي قيمة المطلوب الأول من كل مثلث
+
+233
+00:30:22,920 --> 00:30:29,840
+المطلوب الثاني اللي هو نمرة V بيقول U نقص الـ V U
+
+234
+00:30:29,840 --> 00:30:38,960
+نقص الـ V U نقص الـ V dot اتنين U زائد L
+
+235
+00:30:52,250 --> 00:30:55,930
+ضربت الـ U في الـ vector الأخرى و أضربها لمين؟ في الـ
+
+236
+00:30:55,930 --> 00:31:02,470
+vector الثاني زائد الـ U dot الـ V اللي عملته لـ U
+
+237
+00:31:02,470 --> 00:31:11,390
+هروح أعمله لمين؟ لسالب V يبقى هذه سالب V dot اتنين
+
+238
+00:31:11,390 --> 00:31:20,310
+U اللي بعدها سالب V dot الـ V بالشكل اللي عندنا نعيد
+
+239
+00:31:20,310 --> 00:31:25,930
+ترتيب المطلوب يبقى هذا الكلام اتنين بتاخده برا بيظل
+
+240
+00:31:25,930 --> 00:31:37,270
+الـ U dot الـ U زائد U dot الـ V ناقص اتنين V dot الـ
+
+241
+00:31:37,270 --> 00:31:46,730
+U ناقص اللي هو طول الـ V تربيع الـ V dot الـ V طول الـ
+
+242
+00:31:46,730 --> 00:31:52,780
+V تربيع هذا الكلام يساوي هذه بنات بنفس القصة
+
+243
+00:31:52,780 --> 00:32:00,840
+بتعطينا طول الـ U تربيع يبقى هذه اتنين طول الـ U²
+
+244
+00:32:04,050 --> 00:32:10,550
+V Dot U و U Dot V  نفس الشيء الخاصية
+
+245
+00:32:10,550 --> 00:32:15,730
+الأولى U Dot V و V Dot U إذا هذه هي هذه طب واحدة
+
+246
+00:32:15,730 --> 00:32:22,250
+موجبة وواحدة سالبة يبقى إيه سالب U Dot V يبقى سالب
+
+247
+00:32:22,250 --> 00:32:30,170
+U Dot V خلصنا منها ناقص طول الـ V تربيع يبقى هذا
+
+248
+00:32:30,170 --> 00:32:31,570
+الكلام بده يساوي
+
+249
+00:32:41,090 --> 00:32:47,790
+وضرب الـ V اللي هو بـ 11 ناقص طول الـ V اللي هو خمسة
+
+250
+00:32:47,790 --> 00:32:54,030
+لكل تربيع طبعا هذه تسعة في اتنين = 18
+
+251
+00:32:54,030 --> 00:33:01,650
+18 ناقص 11 ناقص 25 ناقص 5
+
+252
+00:33:01,650 --> 00:33:05,010
+و20 ناقص 11 = -36
+
+253
+00:33:11,250 --> 00:33:18,370
+عشرة يبقى هذا هو المطلوب الثاني من المسألة بدنا
+
+254
+00:33:18,370 --> 00:33:24,690
+نروح للمطلوب الثالث طلعوني
+
+255
+00:33:24,690 --> 00:33:29,890
+في المطلوب الثالث كويس وفكروا كيف بدنا نجيب
+
+256
+00:33:29,890 --> 00:33:35,170
+المطلوب الثالث لأن أنا ما عنديش الـ vector U و الـ
+
+257
+00:33:41,020 --> 00:33:46,640
+اللي بده طول الـ U ناقص اتنين V لو بعرف الـ U و الـ
+
+258
+00:33:46,640 --> 00:33:52,500
+V كان صارت المسألة سهلة لكن أنا لا أعرف U ولا أعرف V طب
+
+259
+00:33:52,500 --> 00:33:58,040
+كيف نحل هذه المسألة؟ يلا اقترحوا علينا اقتراح
+
+260
+00:34:24,500 --> 00:34:29,140
+إحنا أخدنا مجموع لما نقول نقول اثنين يستوي نقول
+
+261
+00:34:29,140 --> 00:34:37,940
+الأول زي نقول الثاني  افتشل الكلام الحل
+
+262
+00:34:37,940 --> 00:34:46,740
+إيه؟ كدا كدا ها أنت سمعت
+
+263
+00:35:12,020 --> 00:35:21,140
+إذا أنا هنا باجي بقول نمرسي أنا عازمين اللي هو U
+
+264
+00:35:21,140 --> 00:35:24,700
+بالتربيع ناقص اثنين فيه الطول تبعه، بدي أخد
+
+265
+00:35:24,700 --> 00:35:28,500
+تربيعه، وشوف إيش بده يعطينا، وبعد هيك إن شاء الله
+
+266
+00:35:28,500 --> 00:35:33,760
+نحلها، يبقى باجي بقوله لو أخد طول الـ U
+
+267
+00:35:33,760 --> 00:35:34,840
+ناقص اثنين
+
+268
+00:35:40,560 --> 00:35:49,280
+يبقى بلغة الـ vectors هذا U ناقص 2B ضرب الـ U ناقص 2B
+
+269
+00:35:49,280 --> 00:35:55,380
+هزبط هيك؟ فبنعمل الفكرة اللي عملناها من هنا لضرب
+
+270
+00:35:55,380 --> 00:36:03,860
+هذا يبقى هذا شو بده يعطينا؟ بده يعطينا U ضرب الـ U
+
+271
+00:36:03,860 --> 00:36:08,420
+ناقص
+
+272
+00:36:08,420 --> 00:36:09,340
+الـ U
+
+273
+00:36:17,580 --> 00:36:25,260
+ناقص في ناقص في ناقص في ناقص في ناقص
+
+274
+00:36:25,260 --> 00:36:27,160
+في ناقص
+
+275
+00:36:32,250 --> 00:36:44,570
+يبقى U ضرب الـ V يبقى
+
+276
+00:36:44,570 --> 00:36:53,230
+U ضرب الـ V زائد أربعة طول الـ V تربيع V ضرب الـ V ليه
+
+277
+00:36:53,230 --> 00:36:54,770
+طول الـ V تربيع
+
+278
+00:37:13,600 --> 00:37:19,580
+طول الـ U  اللي هو قداش تلاتة يبقى تلاتة لكل
+
+279
+00:37:19,580 --> 00:37:28,640
+تربيع ناقص أربعة هذا U يا بنات ناقص أربعة U ضرب
+
+280
+00:37:28,640 --> 00:37:30,600
+الـ V اللي هو قداش بـ 11
+
+281
+00:37:34,380 --> 00:37:41,620
+أربعة في طول الـ V وين طول الـ V اللي هو خمسة الكل
+
+282
+00:37:41,620 --> 00:37:50,880
+تربيع هذا الكلام يساوي تسعة ناقص 44  خمسة
+
+283
+00:37:50,880 --> 00:37:56,640
+تربيع ليه خمسة وعشرين في أربعة = 100 يبقى زائد 100
+
+284
+00:37:57,310 --> 00:38:01,890
+عندك 109 بده أشيل منهم مين اللي مول هذا
+
+285
+00:38:01,890 --> 00:38:07,330
+موجب وهذا موجب يبقى هذا 109 بده أشيل منهم
+
+286
+00:38:07,330 --> 00:38:14,470
+44 بظل 65  يبقى 65
+
+287
+00:38:14,470 --> 00:38:21,330
+و60 بالموجب مين هذا؟ أنا لا أريد طول المتجه أنا
+
+288
+00:38:21,330 --> 00:38:25,590
+أريد طول المتجه إذا بأخذ الـ square root of both
+
+289
+00:38:25,590 --> 00:38:30,350
+sides بأخذ الجذر التربيعي للطرفين يبقى بناء على طول
+
+290
+00:38:30,350 --> 00:38:38,930
+الـ U ناقص 2V يساوي الـ square root من الـ 65
+
+291
+00:38:38,930 --> 00:38:44,730
+إذا أنا جبت الطول ههه هم لا يعرفوا شكل الـ U
+
+292
+00:39:12,030 --> 00:39:16,230
+طبعا ولا سؤال زيه في الكتاب وإنما جاء به في
+
+293
+00:39:16,230 --> 00:39:24,010
+امتحان 2005 ونشره طبعا نفس الفكرة ها، كويس؟ يبقى
+
+294
+00:39:24,010 --> 00:39:28,730
+هذا good exercise إيه المطلوب ديكوا فيه؟ امتحان في
+
+295
+00:39:28,730 --> 00:39:38,300
+2005 بيقول لو كان الـ V يساوي اثنين وطول الـ W يساوي
+
+296
+00:39:38,300 --> 00:39:47,300
+ثلاثة and the angle between and the angle between
+
+297
+00:39:47,300 --> 00:39:51,440
+the
+
+298
+00:39:51,440 --> 00:40:04,640
+angle between الـ V and الـ W is π على تلاتة فايند
+
+299
+00:40:04,640 --> 00:40:14,140
+هو إيش المطلوب اللي هو طول الـ V ناقص اثنين W the
+
+300
+00:40:14,140 --> 00:40:25,200
+length of the vector V ناقص اثنين W
+
+301
+00:40:39,460 --> 00:40:46,420
+V-2W الطول الكل تربيع و تبدأ تشتغل زي اللي فوق
+
+302
+00:40:46,420 --> 00:40:55,580
+يلا ونحسب كمان الجواب الـ answer الإجابة اثنين
+
+303
+00:40:55,580 --> 00:41:03,000
+جذر سبعة يلا مش هالنا التهيش قبل أن نجي لنقطة جدا
+
+304
+00:41:03,000 --> 00:41:05,020
+في هذا الـ section اسمها
+
+305
+00:41:24,980 --> 00:41:35,540
+بنحاول نسقط اللي هو متجه على متجه آخر حد راكوا
+
+306
+00:41:35,540 --> 00:41:44,080
+فيها مصطلح بيقولوا تلاتي صانده هاتي إيه؟ إيش؟
+
+307
+00:41:44,080 --> 00:41:52,460
+بنات؟ آه 100% بدي اعتبر هذه بنات عبارة عن vector
+
+308
+00:41:53,090 --> 00:41:58,500
+وهذا عبارة عن vector آخر بدي أحاول أسقط الـ vector
+
+309
+00:41:58,500 --> 00:42:03,020
+اللي فوق على الـ vector اللي تحت ونشوف إيش النتيجة
+
+310
+00:42:03,020 --> 00:42:07,680
+بدي يكون طبعا إحنا أخدنا زمان في المرحلة الثانوية
+
+311
+00:42:07,680 --> 00:42:14,420
+أنه مسقط مستقيم على مستقيم آخر هو مستقيم إلا إذا
+
+312
+00:42:14,420 --> 00:42:18,660
+كان عمودي عليه فالمسقط هو نقطة بالمثل إن أنا
+
+313
+00:42:18,660 --> 00:42:22,060
+بدي أسقط هذا الـ vector على هذا الـ vector بدي
+
+314
+00:42:22,060 --> 00:42:27,910
+يعطيني vector ثاني السؤال هو المسقط هذا بيكون
+
+315
+00:42:27,910 --> 00:42:32,990
+أطول من الـ vector الأصلي ولا أقصر منه ولا ممكن
+
+316
+00:42:32,990 --> 00:42:37,170
+يساوي .. ممكن
+
+317
+00:42:37,170 --> 00:42:43,070
+يساوي وارد وأقصر منه وارد لكن أكبر منه ما فيش
+
+318
+00:42:43,070 --> 00:42:47,390
+إمكانية على الإطلاق تمام؟ الكلام اللي أنا بقوله
+
+319
+00:42:47,390 --> 00:42:54,010
+هوضحه الآن من خلال الرسم لو أنا يا بنات عندي المتجه
+
+320
+00:42:54,010 --> 00:43:04,210
+V وعندي متجه آخر U بدي أسقط الـ U على V لحظة هذا
+
+321
+00:43:04,210 --> 00:43:11,190
+النقطة مشتركة يبقى هأدر بالمسطرة عشان أسقط ويسقط زي
+
+322
+00:43:11,190 --> 00:43:15,550
+ما هو يبقى النقطة هذه يا بنات رأس المتجه
+
+323
+00:43:20,320 --> 00:43:27,340
+عمودي بهذا الشكل يبقى المتجه تبع المسقط هو المتجه
+
+324
+00:43:27,340 --> 00:43:33,160
+اللي عندنا هذا الخط الأزرق هذا أو المتجه الأزرق
+
+325
+00:43:33,160 --> 00:43:39,520
+هذا هو المسقط اللي هسميه projection U على مين على
+
+326
+00:43:39,520 --> 00:43:43,000
+V وطبقه بالشكل التالي كلمة projection
+
+327
+00:43:47,010 --> 00:43:54,350
+وحط الـ V كـ index عندي الـ J يبقى يقرأ projection U
+
+328
+00:43:54,350 --> 00:44:01,350
+على V الزاوية
+
+329
+00:44:01,350 --> 00:44:07,490
+اللي بينهم كانت هذه θ زاوية حادة تمام؟ يبقى
+
+330
+00:44:07,490 --> 00:44:13,250
+الزاوية اللي عندنا هذه θ زاوية حادة بناء عليه بدي
+
+331
+00:44:13,250 --> 00:44:18,140
+أعرف هل الـ projection هذا بدي يكون positive ولا
+
+332
+00:44:18,140 --> 00:44:23,360
+negative يعني بدي أعرف قداش الطول تبعه بالضبط و
+
+333
+00:44:23,360 --> 00:44:29,960
+بدي أعرف قداش اتجاهه تمام فباجي أقول والله كويس الـ
+
+334
+00:44:29,960 --> 00:44:38,060
+vector هذا من هنا لهنا الطول تبعه له طول اليوم في
+
+335
+00:44:38,060 --> 00:44:42,830
+جيب تمام الزاوية ثيتا مين بيعطينا طول الـ
+
+336
+00:44:42,830 --> 00:44:47,730
+projection طول
+
+337
+00:44:47,730 --> 00:44:53,770
+الـ U على V يساوي طول الـ U في الـ cosine الزاوية
+
+338
+00:44:53,770 --> 00:45:01,490
+θ نهضة المستقيم الأزرق هذا أقصر من
+
+339
+00:45:01,490 --> 00:45:05,230
+طول
+
+340
+00:45:05,230 --> 00:45:10,830
+المتجه U طب لو كان الـ U عمودي على V الـ projection
+
+341
+00:45:10,830 --> 00:45:17,850
+هو الـ zero vector، مظبوط؟ طيب، بدنا نيجي ناخد
+
+342
+00:45:17,850 --> 00:45:24,150
+الحالة الثانية، لو كان هذا هو الـ vector V وكان هذا
+
+343
+00:45:24,150 --> 00:45:31,110
+هو الـ vector U وحبيت أسقط U على V حيث إن الزاوية
+
+344
+00:45:31,110 --> 00:45:33,890
+بينهما θ زاوية حادة
+
+345
+00:45:54,230 --> 00:46:00,490
+طول الـ U في الـ Cos الزاوية واتجاه
+
+346
+00:46:03,010 --> 00:46:07,190
+اتجاه الـ V هذا الأول سنة من الثانية هاروح للتانية
+
+347
+00:46:07,190 --> 00:46:11,370
+يبقى هو
+
+348
+00:46:11,370 --> 00:46:14,910
+طول الـ U في cos الزاوية θ هذا طول الـ
+
+349
+00:46:14,910 --> 00:46:20,250
+projection لكن اتجاهه هو اتجاه الـ V يعني في اتجاه
+
+350
+00:46:20,250 --> 00:46:26,250
+V على طول الـ V اللي هو متجه الوحدة في اتجاه من V
+
+351
+00:46:26,950 --> 00:46:31,770
+يجب أن تكون الـ projection تبع الـ U على V هو متجه
+
+352
+00:46:31,770 --> 00:46:35,390
+جديد في اتجاه المتجه V
+
+353
+00:46:53,080 --> 00:47:00,240
+هذا U إذا هذا طول المتجه U في cosine الزاوية θ
+
+354
+00:47:00,240 --> 00:47:07,600
+θ زاوية منفرجة إذا الجيب التمام سالب تمام إذا
+
+355
+00:47:07,600 --> 00:47:13,200
+لما بدي أجيب القول بالضبط بدي أقول طول المتجه هو و
+
+356
+00:47:13,200 --> 00:47:19,540
+هذا قيمة عددية موجبة في مين في cosine الزاوية θ
+
+357
+00:47:19,540 --> 00:47:25,120
+ولما كانت الزاوية θ زاوية منفرجة فأروح بقول في
+
+358
+00:47:25,120 --> 00:47:25,420
+مين
+
+359
+00:47:29,020 --> 00:47:34,440
+الأول طول المتجه هذا الـ absolute value لهذا الرقم
+
+360
+00:47:34,440 --> 00:47:39,100
+هيطلع سالب أخد absolute value وبطلع قيمة موجبة الـ
+
+361
+00:47:39,100 --> 00:47:45,380
+direction عكس اتجاه الـ V يعني إذا كان هذا الـ
+
+362
+00:47:45,380 --> 00:47:50,100
+projection في اتجاه الـ V على طول الـ V هذا هيكون في
+
+363
+00:47:50,100 --> 00:47:56,500
+اتجاه سالب في علقه يعني في عكس اتجاهه تماما بضبط،
+
+364
+00:47:56,500 --> 00:48:01,260
+تمام؟ الكلام اللي قلته لكم هذا شفوي بدنا نروح
+
+365
+00:48:01,260 --> 00:48:08,800
+ننصّحه ونكتبه كتابة، يبقى كيف كتابة كالتالي، بروح
+
+366
+00:48:08,800 --> 00:48:12,520
+بقول إن بدي أحط الكلام في صيغة النقاط التالية،
+
+367
+00:48:12,520 --> 00:48:13,200
+النقطة الأولى
+
+368
+00:48:23,130 --> 00:48:34,510
+between الـ U and الـ V is acute يعني لو كانت
+
+369
+00:48:34,510 --> 00:48:40,770
+زاوية حادة الـ projection تبع الـ U على الـ V
+
+370
+00:48:51,250 --> 00:49:00,890
+في cosine الزاوية θ and direction وفي الاتجاه V
+
+371
+00:49:00,890 --> 00:49:05,750
+على طول الـ V هذا طبعا لمتجه الوحدة في اتجاه
+
+372
+00:49:05,750 --> 00:49:12,670
+المتجه V ذكرناه في المحاضرة الماضية نمرة اثنين if
+
+373
+00:49:12,670 --> 00:49:16,830
+the angle θ
+
+374
+00:49:18,930 --> 00:49:25,970
+is obtuse لو
+
+375
+00:49:25,970 --> 00:49:33,810
+كانت زاوية منفرجة الـ projection تبع الـ U على V
+
+376
+00:49:33,810 --> 00:49:42,410
+has length اللي هو طول الـ U في absolute
+
+377
+00:49:42,410 --> 00:49:53,910
+value لـ cosine الزاوية V and direction والاتجاه
+
+378
+00:49:53,910 --> 00:50:02,850
+سالب V على طول الـ V يعني بنجيب cosine لـ opposite
+
+379
+00:50:02,850 --> 00:50:09,310
+direction of
+
+380
+00:50:09,310 --> 00:50:16,850
+V الاتجاه المعاكس للـ vector V تلاتة
+
+381
+00:50:49,890 --> 00:50:58,530
+المركبة القياسية of U المتجه U and
+
+382
+00:51:01,270 --> 00:51:13,850
+direction في اتجاه of V هذه
+
+383
+00:51:13,850 --> 00:51:19,930
+طول الـ U في Cos الزاوية θ ممكن أجيب لها صياغة
+
+384
+00:51:19,930 --> 00:51:26,010
+أخرى شو الصياغة الأخرى؟ هأبقالك بين قوسين not that
+
+385
+00:51:26,010 --> 00:51:37,420
+لحظة أن طول الـ U في cosine الزاوية θ يساوي لو
+
+386
+00:51:37,420 --> 00:51:42,320
+رجعت للـ dot product بين الـ U و الـ V في الهامشة
+
+387
+00:51:42,320 --> 00:51:49,680
+بنات قلنا أن الـ U dot الـ V يساوي طول الـ U في طول
+
+388
+00:51:49,680 --> 00:51:55,920
+الـ V في cosine الزاوية θ إذا طول الـ U في cosine
+
+389
+00:51:55,920 --> 00:51:59,740
+الزاوية θ يساوي U dot الـ V
+
+390
+00:52:15,140 --> 00:52:19,780
+الـ V أو طول الـ U اللي طلعناه اللي هو عبارة عن
+
+391
+00:52:19,780 --> 00:52:28,820
+الـ U دغري الـ U ضرب الـ V على طول الـ V بالشكل
+
+392
+00:52:28,820 --> 00:52:33,360
+العام أو
+
+393
+00:52:33,360 --> 00:52:41,420
+بقدر أحط هلك كمان في صيغة أخرى الـ U ضرب الـ V على
+
+394
+00:52:41,420 --> 00:52:49,520
+طول الـ V كأن واحد على طول V سكلار تعتبره مضروب في
+
+395
+00:52:49,520 --> 00:52:53,520
+الكل ماشي، مضروب في المتجهة الأولى ماشي، مضروب في
+
+396
+00:52:53,520 --> 00:52:56,940
+المتجهة الثانية ماشي، سيا، هادي، ورنهادي، كله are
+
+397
+00:52:56,94
+
+445
+00:58:49,810 --> 00:59:02,590
+زائد خمسة K زائد خمسة K، find نمرة A، بدنا لـ
+
+446
+00:59:02,590 --> 00:59:10,590
+projection تبع الـ U على V، نمرة B، بدنا this scalar
+
+447
+00:59:10,590 --> 00:59:16,670
+component، this scalar component
+
+448
+00:59:16,670 --> 00:59:19,030
+المركبة القيمية
+
+449
+00:59:40,110 --> 00:59:44,110
+مرة ثانية، نقرأ السؤال و نفهم ما هو المطلوب من هذا
+
+450
+00:59:44,110 --> 00:59:48,630
+السؤال بقول: لو كان الـ U و الـ V بالشكل اللي قدامنا
+
+451
+00:59:48,630 --> 00:59:52,990
+هذا طلب لـ projection تبع الـ U على V، إذا أنا لو
+
+452
+00:59:52,990 --> 00:59:58,830
+كتبت له هنا نمرة A، الـ projection تبع الـ U على V
+
+453
+00:59:58,830 --> 01:00:03,550
+أو الـ component of U in the direction of V،
+
+454
+01:00:03,550 --> 01:00:06,690
+الإتنين are the same، إذا مش أنا أجيب له الـ
+
+455
+01:00:06,690 --> 01:00:12,050
+projection بالـ U ضد الـ V، و بالـ V ضد
+
+456
+01:00:12,050 --> 01:00:16,190
+إيه، ده خلّيني أحسبهم من الأول، يبقى بدي أروح أخدي
+
+457
+01:00:16,190 --> 01:00:21,410
+الـ U ضد الـ V، يبقى بدي أضرب اللي هو العناصر
+
+458
+01:00:21,410 --> 01:00:28,180
+المتجهة: واحد في تلاتة، كده،شرطة، تلاتة ناقص 7 في 4
+
+459
+01:00:28,180 --> 01:00:37,460
+ناقص 28 زائد 3 في 5، اللي هو 15، يبقى هذا
+
+460
+01:00:37,460 --> 01:00:45,500
+الكلام بيساوي 15 و 3، 18، يبقى ناقص 10 بعد
+
+461
+01:00:45,500 --> 01:00:50,960
+ذلك، بيروح أجيب له الـ V، وضربت الـ V، يبقى المتجه في
+
+462
+01:00:50,960 --> 01:00:53,300
+نفسه، يبقى  مقداره هنا
+
+463
+01:01:02,510 --> 01:01:09,210
+16، 9، 25، 50
+
+464
+01:01:15,740 --> 01:01:26,540
+يبقى الـ U على V، يبقى
+
+465
+01:01:26,540 --> 01:01:34,580
+ناقص عشرة على خمسين في الـ vector اللي عندنا V، زي
+
+466
+01:01:34,580 --> 01:01:42,190
+ما هو: تلاتة I زائد أربعة J زائد خمسة K، طبعاً ناقص
+
+467
+01:01:42,190 --> 01:01:47,730
+عشرة على خمسين، اللي هو قد ايه؟ سالب خمس، إذا هذا الـ
+
+468
+01:01:47,730 --> 01:01:54,930
+vector بيصير سالب تلت أخماس في اتجاه الـ I، سالب أربع
+
+469
+01:01:54,930 --> 01:02:04,630
+أخماس في اتجاه الـ J، سالب خمسة أخماس في اتجاه K. يبقى هذا
+
+470
+01:02:04,630 --> 01:02:09,520
+اللي هو، أو الـ projection تبع الـ U في اتجاه مين؟
+
+471
+01:02:09,520 --> 01:02:14,960
+في اتجاه المتجه V، وهذا هو المطلوب الأول من السؤال
+
+472
+01:02:14,960 --> 01:02:20,320
+المطلوب الثاني، قال لي:  the scalar component of U in
+
+473
+01:02:20,320 --> 01:02:25,720
+the direction of V، يعني مين؟ يعني طول الـ U في
+
+474
+01:02:32,610 --> 01:02:40,430
+على طول الـ V، يبقى نمرة V، بعدين بقوله: V is scalar
+
+475
+01:02:40,430 --> 01:02:50,470
+component، اللي بده يطلع طول U في cosine الزاوية
+
+476
+01:02:50,470 --> 01:02:53,850
+تيتا، أو U dot
+
+477
+01:03:00,120 --> 01:03:05,920
+ضرب الـ V، هيو جدام الخطوة الأولى لو سالب عشرة، يبقى
+
+478
+01:03:05,920 --> 01:03:14,660
+سالب عشرة على طول الـ V، طبعاً احنا هنا جذر التربيع
+
+479
+01:03:14,660 --> 01:03:22,920
+اللي هو V ضد V، V ضد V، يبقى سالب عشرة V ضد V اللي هو
+
+480
+01:03:22,920 --> 01:03:31,240
+جذر بخمسين تحت الجذر، يبقى سالب عشرة على خمسين،  لير
+
+481
+01:03:39,490 --> 01:03:43,950
+إذا مش عاجبك جذر اتنين في المقام، بنقدر نوديه في
+
+482
+01:03:43,950 --> 01:03:49,310
+البسط عن طريق ضرب في جذر اتنين على جذر اتنين
+
+483
+01:03:49,310 --> 01:03:53,970
+يعني كده ضرب في كده، شغلة في واحد، صحية، يبقى هذا
+
+484
+01:03:53,970 --> 01:04:01,930
+بيطلع كده سالب جذر اتنين،  لـ scalar component تبع الـ
+
+485
+01:04:01,930 --> 01:04:07,570
+U في اتجاه L، بقيت عندنا في هذا الـ section نقطة
+
+486
+01:04:09,950 --> 01:04:19,330
+على صورة الـ remark،  ثانية يبقى writing vector
+
+487
+01:04:19,330 --> 01:04:28,030
+كتابة متجه as a sum of
+
+488
+01:04:28,030 --> 01:04:32,530
+orthogonal vectors
+
+489
+01:04:38,360 --> 01:04:42,360
+كتابة متجهات متجهات متجهات متجهات متجهات
+
+490
+01:04:42,360 --> 01:05:07,580
+متجهات متجهات متجهات
+
+491
+01:05:08,100 --> 01:05:17,120
+or two orthogonal vectors
+
+492
+01:05:17,120 --> 01:05:20,260
+vectors
+
+493
+01:05:20,260 --> 01:05:27,060
+as follows،  إتل
+
+494
+01:05:27,060 --> 01:05:37,220
+الـ U يساوي الـ projection تبع الـ U اتجاه الـ V زائد
+
+495
+01:05:42,500 --> 01:05:54,620
+في اتجاه الـ V، طبعاً
+
+496
+01:05:54,620 --> 01:06:02,640
+سؤال: كيف تم ذلك؟ مش هيك؟ لازم أقوله كويس، لو أنا
+
+497
+01:06:02,640 --> 01:06:10,120
+بنات، قلت هذا المتجه U، و روحت قلت هذا المتجه V، و
+
+498
+01:06:10,120 --> 01:06:12,140
+جينا من هنا، نزلنا عمود
+
+499
+01:06:30,020 --> 01:06:37,800
+البداية، أخد جمع المتجهات هندسياً، يبقى بقى اللي بقول
+
+500
+01:06:37,800 --> 01:06:45,380
+لو جت فترت هنا متجه، يبقى بصّي الـ projection، وهذا
+
+501
+01:06:45,380 --> 01:06:50,120
+المتجه في اتجاه دوري واحد، يبقى مجموع الاتنين
+
+502
+01:06:50,120 --> 01:06:54,000
+بعطيني المتجه الذي يقفل المثلث في الاتجاه الدوري
+
+503
+01:06:54,000 --> 01:06:56,000
+المضاد
+
+504
+01:07:09,680 --> 01:07:14,700
+المتجه الثاني اللي عندنا، هذا اللي الله أعلم منه
+
+505
+01:07:14,700 --> 01:07:23,020
+بده يساوي من؟ بده يساوي الـ U، إذا هذا المتجه اللي أنا
+
+506
+01:07:23,020 --> 01:07:29,400
+مش عارفه، بدي أعرف منه هو عبارة عن الـ U ناقص الـ
+
+507
+01:07:29,400 --> 01:07:35,320
+projection، يبقى هذا المتجه عبارة عن الـ U ناقص الـ
+
+508
+01:07:35,320 --> 01:07:37,540
+projection تبع الـ U
+
+509
+01:07:42,280 --> 01:07:50,260
+هو  تعامدين، يبقى هذا هو الـ U ناقص الـ projection تبع
+
+510
+01:07:50,260 --> 01:07:57,120
+الـ U على V، إذا المتجه U هو عبارة عن الـ projection
+
+511
+01:07:57,120 --> 01:08:02,550
+زي هذا، فعلاً هذا سرد وهذا موجه، لو جمعتهم مع
+
+512
+01:08:02,550 --> 01:08:07,470
+السلامة بيطلع لي عندي، بس المتجه بيهيأ بيهيأ بيهيأ
+
+513
+01:08:07,470 --> 01:08:12,110
+طيب أنا بدي أغيّر الصياغة هذه، بدي أصيغها صياغة
+
+514
+01:08:12,110 --> 01:08:15,090
+عملية، مش هنصيغها صياغة
+
+515
+01:08:33,750 --> 01:08:39,890
+زي إيه؟  أين السائلة؟
+
+516
+01:08:39,890 --> 01:08:46,450
+أنا
+
+517
+01:08:46,450 --> 01:08:52,550
+بجيبش أطوال في ثغور، أنا بجيب متجهات، جمع اتجاهي
+
+518
+01:08:52,550 --> 01:08:58,490
+زي القوة، محصلة القوة، يبقى كأن أنا عندي متجهين
+
+519
+01:08:59,250 --> 01:09:07,030
+بجيب أطوال، بقول لك بجيب محصلات متجهات، هذا متجه وهذا
+
+520
+01:09:07,030 --> 01:09:12,550
+متجه، يبقى محصلته هو المتجه الذي يقفل المثلث في اتجاه
+
+521
+01:09:12,550 --> 01:09:17,570
+الدوري المضاد، تمام؟ هو  بيحصل بعد ما نخلص الحل
+
+522
+01:09:17,570 --> 01:09:23,070
+الحين، تمام؟ يبقى بنرجع مرة ثانية، زائد الـ U
+
+523
+01:09:37,540 --> 01:09:41,940
+هل اتنين هدول متعامدين ولا لأ؟ بقول: آه والله، على
+
+524
+01:09:41,940 --> 01:09:49,080
+الرسم هذا وهذا هم متعامدين، صحيح ولا لأ؟ إحنا الـ
+
+525
+01:09:49,080 --> 01:09:54,860
+vector استطعنا كتابته على vector في اتجاه الـ V
+
+526
+01:10:01,570 --> 01:10:08,370
+هذا الرقم ماله مضاعفات الـ V، يبقى دوام في اتجاه الـ
+
+527
+01:10:08,370 --> 01:10:13,430
+V، أو parallel to V، موازٍ للـ V، يبقى هذا
+
+528
+01:10:32,810 --> 01:10:37,930
+عمودي على مين؟ عمودي على V
+
+529
+01:11:02,200 --> 01:11:06,300
+ماذا تجاهل فيه؟
+
+530
+01:11:06,300 --> 01:11:10,960
+والله إذا ضرب هذا طلع zero، بيكونوا اتنين هدول فعلاً
+
+531
+01:11:10,960 --> 01:11:13,080
+orthogonal، مظبوط؟
+
+532
+01:11:37,070 --> 01:11:44,790
+في bottle، نيجي الأن هذا رقم ولا لا، بروح مع الرقم
+
+533
+01:11:44,790 --> 01:11:53,170
+اللي تحت، قايلة، هذا الكلام بده يصير إبدالية صحيح
+
+534
+01:11:53,170 --> 01:11:59,830
+ولا لأ؟ يبقى هذا كأن الـ U ضد الـ V ناقص الـ U ضد الـ V
+
+535
+01:11:59,830 --> 01:12:04,430
+اللي فوق، يبقى كده إيش النتيجة؟ صفر، يبقى هذول
+
+536
+01:12:04,430 --> 01:12:08,710
+اتنين متعامدين، هذا السطر اللي كتبناه، محطوط
+
+537
+01:12:08,710 --> 01:12:13,870
+عندك في الكتاب على صيغة سؤال في التمرين، يبقى هاي
+
+538
+01:12:13,870 --> 01:12:17,690
+حدى نلالك السؤال، وإحنا بنشرح الجزء النظري، إذا يا
+
+539
+01:12:17,690 --> 01:12:25,760
+بنات، من الآن فصاعداً، أي vector بقدر أكتبه بدلالة جزء
+
+540
+01:12:25,760 --> 01:12:31,020
+في اتجاه الـ vector الآخر، وجزء ثاني عمودي على هذا الـ
+
+541
+01:12:31,020 --> 01:12:36,900
+vector الآخر، وبتيجي مسائل، إحنا في مسائل التمرين
+
+542
+01:12:36,900 --> 01:12:37,940
+على هذا الموضوع
+
+543
+01:12:49,170 --> 01:12:53,030
+مثال على الكلام اللي إحنا قلناه هذا
+
+544
+01:14:00,840 --> 01:14:14,760
+تبع V، بده يساوي I زائد اتنين J ناقص K، and a vector
+
+545
+01:14:14,760 --> 01:14:17,520
+Orthogonal
+
+546
+01:14:35,450 --> 01:14:43,930
+نرجع لسؤالنا مرة ثانية، اكتب لي المتجه U كمجموع two
+
+547
+01:14:43,930 --> 01:14:50,030
+vectors، واحد منهم موازٍ لـ V، وواحد ثاني عمودي على
+
+548
+01:14:50,030 --> 01:14:53,390
+V، الموازي لـ V هو مين يا بنات؟
+
+549
+01:15:02,160 --> 01:15:08,280
+العمودي هو U ناقص الـ projection، يبقى العمودي هو
+
+550
+01:15:08,280 --> 01:15:12,860
+في المثال هو إيجاد الـ projection، يبقى باجي بقول الـ
+
+551
+01:15:12,860 --> 01:15:13,660
+projection
+
+552
+01:15:29,050 --> 01:15:37,330
+متجه الـ U ضد الـ V، بيجي الـ U
+
+553
+01:15:37,330 --> 01:15:40,370
+ضد
+
+554
+01:15:40,370 --> 01:15:44,750
+الـ V، بيجي
+
+555
+01:15:44,750 --> 01:15:49,390
+الـ U
+
+556
+01:15:49,390 --> 01:15:52,430
+ضد
+
+557
+01:15:52,430 --> 01:15:53,850
+الـ V، بيجي الـ U ضد الـ V، بيجي الـ U ضد الـ V، بيجي الـ U
+
+558
+01:15:53,850 --> 01:15:53,910
+ضد الـ V، بيجي الـ U ضد الـ V، بيجي الـ U ضد الـ V، بيجي
+
+559
+01:15:53,910 --> 01:15:54,090
+بيجي الـ U ضد الـ V، بيجي الـ U ضد الـ V، بيجي الـ U ضد
+
+560
+01:15:54,090 --> 01:15:54,250
+الـ V، بيجي الـ U ضد الـ V، بيجي الـ U ضد الـ V، بيجي الـ U
+
+561
+01:15:54,250 --> 01:15:55,410
+ضد الـ V، بيجي الـ U ضد الـ V، بيجي الـ U ضد الـ V، بيجي
+
+562
+01:15:55,410 --> 01:15:55,570
+الـ U ضد الـ V، بيجي
+
+563
+01:16:00,130 --> 01:16:07,850
+كله في اتجاه من الـ V، يبقى هذا الكلام بده يساوي 16
+
+564
+01:16:07,850 --> 01:16:20,890
+و 12، 28 على 6 في الـ V، بنزله زي ما هو: I، اتنين J ناقص K
+
+565
+01:16:20,890 --> 01:16:26,210
+طبعاً هذه بتقسم على كده، عشان اتنين، هو أربعة عشر على
+
+566
+01:16:26,210 --> 01:16:37,110
+ثلاثة، وهو 14 على ثلاثة في I، اتنين J ناقص K، بناءً
+
+567
+01:16:37,110 --> 01:16:46,810
+عليه، الـ vector U بيساوي projection تبع الـ U على
+
+568
+01:16:46,810 --> 01:16:50,390
+V زائد الـ U
+
+569
+01:16:57,330 --> 01:17:03,290
+هذا اللي هو الـ main vector، parallel to v، هو هذا
+
+570
+01:17:03,290 --> 01:17:08,930
+orthogonal to v، الـ projection حسبناها، هي اللي
+
+571
+01:17:08,930 --> 01:17:15,790
+هو أربعة عشر على تلاتة I زائد ثمانية وعشرين على
+
+572
+01:17:15,790 --> 01:17:19,050
+تلاتة J ناقص أربعة عشر
+
+573
+01:17:37,060 --> 01:17:44,600
+ناقص اللي هو أربعة عشر على تلاتة I ناقص ثمانية
+
+574
+01:17:44,600 --> 01:17:51,820
+وعشرين على تلاتة J ناقص ثمانية وعشرين على تلاتة J
+
+575
+01:17:51,820 --> 01:18:00,680
+زائد أربعة عشر على تلاتة K، دخل إشارة السالب على كل
+
+576
+01:18:00,680 --> 01:18:04,700
+component من هذه الـ components، يبقى النتيجة
+
+577
+01:18:15,860 --> 01:18:22,800
+هذا الـ vector الأول،  زرعنا، بدا نجمع كل مركبة مع
+
+578
+01:18:22,800 --> 01:18:31,280
+نظيرتها: J ناقص إثنى عشر K ناقص الـ projection ناقص
+
+579
+01:18:31,280 --> 01:18:33,080
+اللي هو أربعة
+
+580
+01:18:54,360 --> 01:18:59,580
+من هذه الـ components، يبقى النتيجة أربعة عشر على
+
+581
+01:18:59,580 --> 01:19:06,580
+تلاتة I، ثمانية وعشرين على تلاتة J ناقص أربعة عشر
+
+582
+01:19:06,580 --> 01:19:15,500
+على تلاتة K، هذا الـ vector الأول، زرعنا نجمع كل مركبة
+
+583
+01:19:15,500 --> 01:19:21,180
+مع نظيرتها: تلاتة في ثمانية، أربعة وعشرين، شيل منهم
+
+584
+01:19:21,180 --> 01:19:23,980
+أربعة عشر، بظل عشرة
+
+585
+01:19:31,120 --> 01:19:36,900
+الجزء الثاني: تلاتة في أربعة، إثنى عشر بالموجب، من
+
+586
+01:19:36,900 --> 01:19:40,680
+ثمانية وعشرين إلى ستة عشر، يبقى اثنى عشر
+
+587
+01:19:46,270 --> 01:19:52,310
+بعدها: تلاتة في إثنى عشر، ستة وثلاثين، بدنا نشيل منها
+
+588
+01:19:52,310 --> 01:19:57,130
+إثنى عشر، بظل أربعة وعشرين على تلاتة، اللي هو ثمانية
+
+589
+01:19:57,130 --> 01:20:04,670
+يبقى ناقص ثمانية K، الشكل اللي عندها يبقى هنا
+
+590
+01:20:04,670 --> 01:20:12,050
+راجعها كمان مرة يا بنات، يبقى هذه بصير مرة ثانية
+
+591
+01:20:13,050 --> 01:20:18,310
+عندك تلاتة في إثنى عشر، ستة و ثلاثين، في ستة و
+
+592
+01:20:18,310 --> 01:20:22,410
+ثلاثين، في ستة و ثلاثين، في ستة و ثلاثين، في ستة و
+
+593
+01:20:22,410 --> 01:20:25,750
+ثلاثين، في ستة و ثلاثين، في ستة و ثلاثين، في ستة و
+
+594
+01:20:25,750 --> 01:20:26,730
+ثلاثين، في ستة و ثلاثين، في ستة و ثلاثين، في ستة و
+
+595
+01:20:26,730 --> 01:20:27,870
+ثلاثين، في ستة و ثلاثين، في ستة و ثلاثين، في ستة و
+
+596
+01:20:27,870 --> 01:20:29,230
+ثلاثين، في ستة و ثلاثين، في ستة و ثلاثين، في ستة و
+
+597
+01:20:29,230 --> 01:20:29,970
+ثلاثين، في ستة و ثلاثين، في ستة و ثلاثين، في ستة و
+
+598
+01:20:29,970 --> 01:20:33,450
+ثلاثين، في ستة و ثلاثين، في ستة و ثلاثين، في ستة و
+
+599
+01:20:33,450 --> 01:20:34,770
+ثلاثين، في ستة و
+
+600
+01:20:46,550 --> 01:20:50,690
+طبعاً، فيه، يبقى معادلة متجهات، اتنين هذول بقى لهم
+
+601
+01:20:50,690 --> 01:20:57,850
+اتنين متعامدين، لحد هنا stop، انتهاء الـ section
+
+602
+01:20:57,850 --> 01:21:05,930
+والآن بدنا نعطيكم أرقام المسائل المطلوب حلها، سؤال
+
+603
+01:21:05,930 --> 01:21:07,970
+اللي بدأ أسألكم إياه، روحتوا على الـ discussion
+
+604
+01:21:07,970 --> 01:21:12,690
+الأسبوع الماضي عليه
+
+605
+01:21:12,690 --> 01:21:14,390
+حد المناقشة عنكم
+
+606
+01:21:23,380 --> 01:21:28,140
+يبقى ده أنا قدامكم، لو ما جت coach بتروح للدّور و
+
+607
+01:21:28,140 --> 01:21:33,480
+عليها، وبلغوني: هل اجت ولا ما اجت، يبقى exercises
+
+608
+01:21:33,480 --> 01:21:41,040
+إثنى عشر، تلاتة، المسائل التالية: تلاتة، خمسة، سبعة،
+
+609
+01:21:41,040 --> 01:21:47,520
+أحد عشر، تلاتة عشر، سبعة عشر، تسعة و عشرين
+
+610
+01:22:16,240 --> 01:22:28,100
+يبقى الآن نروح لـ section 12-4، 12-4 اللي هو  cross أو
+
+611
+01:22:28,100 --> 01:22:33,400
+vector product
+
+612
+01:22:33,400 --> 01:22:38,480
+العنوان
+
+613
+01:22:38,480 --> 01:22:43,300
+اللي إحنا حاطينه، اسمه معناه: يعني لما نضرب two
+
+614
+01:22:43,300 --> 01:22:
+
+667
+01:29:50,160 --> 01:30:03,900
+أول مثال بيقول  الـ U تساوي 2I + 2I ناقص
+
+668
+01:30:03,900 --> 01:30:17,020
+J زائد K and الـ V تساوي 4I + 2J
+
+669
+01:30:32,630 --> 01:30:39,050
+A unit vector
+
+670
+01:30:39,050 --> 01:30:48,650
+متجه وحدة orthogonal to
+
+671
+01:30:48,650 --> 01:30:54,070
+both U and V
+
+672
+01:31:12,720 --> 01:31:20,560
+على التعريف رقم 2 يبقى بدي أعمل determinant I وJ
+
+673
+01:31:20,560 --> 01:31:25,620
+وK بدي أحط مركبات المتجه الأول 2
+
+674
+01:31:37,430 --> 01:31:43,670
+الثاني في الأول والمتجه الأول بحطّه بعدها هتطلع
+
+675
+01:31:43,670 --> 01:31:49,910
+نفس النتيجة بس بإشارة مخالفة في الإشارة طبعاً أخدت
+
+676
+01:31:49,910 --> 01:31:51,590
+من خواص المحددات في ثانوية
+
+677
+01:32:10,560 --> 01:32:16,860
+يبقى ماجيجي بيقول هاي  فيه بروح نشطة بالصف اللي
+
+678
+01:32:16,860 --> 01:32:22,400
+موجود فيه I واللي عاوز بيبقى هنا جداش مكس تين أ
+
+679
+01:32:22,400 --> 01:32:27,540
+الرئيسي هاي يبقى عندك المحدد الصغير هذا يبقى نحسب
+
+680
+01:32:27,540 --> 01:32:29,120
+ده أربع ناس القطر الرئيسي
+
+681
+01:32:41,270 --> 01:32:48,630
+في  أشطر بصفة وكذلك عامل من 2 في 2 بأربعة
+
+682
+01:32:48,630 --> 01:32:51,150
+ناقص 4 في 1
+
+683
+01:33:12,980 --> 01:33:18,900
+4 زائد 4 يبقى 4 زائد 4 بالشكل اللي
+
+684
+01:33:18,900 --> 01:33:25,920
+عندنا يبقى صار عندنا ناقص 4I هذا بيروح بـ Zero
+
+685
+01:33:25,920 --> 01:33:35,720
+زائد 8K يبقى هذا زائد 8K القيمة
+
+686
+01:33:35,720 --> 01:33:37,040
+المحدد تماماً
+
+687
+01:33:40,940 --> 01:33:46,780
+إذا صار عندنا شكل المحدد ناقص 4I زائد 8
+
+688
+01:33:46,780 --> 01:33:50,380
+K المطلوب الأول المطلوب الثاني قال لي هاتلي
+
+689
+01:33:50,380 --> 01:33:57,080
+unit vector orthogonal للـ  للاثنين هذا المتجه مش
+
+690
+01:33:57,080 --> 01:34:05,680
+هو عمودي على الاثنين يبقى هنا this vector is
+
+691
+01:34:05,680 --> 01:34:10,140
+orthogonal to
+
+692
+01:34:11,690 --> 01:34:21,790
+الـ U والـ V إذا المطلوب الثاني نمُرّ به قال
+
+693
+01:34:21,790 --> 01:34:26,390
+لي هاتي unit vector  يقول إيش بدّي أعمل؟
+
+694
+01:34:26,390 --> 01:34:29,890
+بدي أقسم هذا المتجه على طوله
+
+695
+01:34:41,950 --> 01:34:48,570
+على طول الـ U x V الـ U x V هو الـ -4I
+
+696
+01:35:02,250 --> 01:35:08,710
+يبقى U cross
+
+697
+01:35:08,710 --> 01:35:14,590
+V على طول U cross V يبقى  ثمانية على مربع
+
+698
+01:35:14,590 --> 01:35:21,130
+عدد 16  مربع العدد 64 هذا كله  ثمانية على ثمانين يبقى
+
+699
+01:35:21,130 --> 01:35:28,490
+ناقص 4I زائد 8K مقسوماً على جذر الثمانين
+
+700
+01:35:28,490 --> 01:35:34,270
+اللي هي 16 في 5 مظبوط 16 في 5 الثمانين
+
+701
+01:35:34,270 --> 01:35:40,910
+يبقى 4 جذر 5 طيب بناءً عليه هذا الكلام يبدو
+
+702
+01:35:40,910 --> 01:35:42,670
+يساوي ناقص
+
+703
+01:35:51,740 --> 01:35:56,260
+يا ناس لو .. لو روحت جبت طول المتجه هذا بتطلع واحد
+
+704
+01:35:56,260 --> 01:36:02,760
+صحيح؟ جرب ربع هذا .. ربع هذا بـ 4/5 يبقى
+
+705
+01:36:02,760 --> 01:36:07,040
+5/5 واحد صحيح؟ آخر مثال صغير
+
+706
+01:36:47,920 --> 01:36:52,610
+بيقول لو عملت cross product لمتجهين والـ dot
+
+707
+01:36:52,610 --> 01:37:00,150
+product لمتجهين وجبت مربع طول الـ cross product و
+
+708
+01:37:00,150 --> 01:37:04,410
+مربع الـ dot product  وجمعته بده يطلع طول المتجه U
+
+709
+01:37:04,410 --> 01:37:08,850
+تربيع × طول المتجه V تربيع هذا اللي عايزين نتحدث
+
+710
+01:37:08,850 --> 01:37:13,110
+عنه إذا بدنا نحاول نمسك أحد الطرفين ونوصل للطرف
+
+711
+01:37:13,110 --> 01:37:17,330
+الآخر أولاً نمسك أحد الطرفين ونوصله إلى نقطة ونمسك
+
+712
+01:37:17,330 --> 01:37:21,450
+الطرف الآخر ونوصله إلى نفس النقطة خلّينا نمسك
+
+713
+01:37:21,450 --> 01:37:28,110
+الطرف الأول اللي هو الـU cross الـV الكل تربيع زائد
+
+714
+01:37:28,110 --> 01:37:34,770
+U dot V الكل تربيع يساوي هذا بيساوي اللي هو طول الـU
+
+715
+01:37:34,770 --> 01:37:42,570
+في طول الـV في جيب تربيع الزاوية θ إذا لما قال تربيع
+
+716
+01:37:42,570 --> 01:37:51,290
+بسيط هذا تربيع وهذه تربيع  طول متجه
+
+717
+01:37:51,290 --> 01:38:00,130
+الوحدة والطول تبع متجه الوحدة الكل تربيع مش عرفنا
+
+718
+01:38:00,130 --> 01:38:04,530
+قبل شوية الـ cross product طول الـ U في طول الـ V في
+
+719
+01:38:04,530 --> 01:38:08,370
+جيب الزاوية في اتجاه متجه الوحدة N إذا لما أقول
+
+720
+01:38:08,370 --> 01:38:12,430
+هذا مربع الطول يبقى أخدت الأطوال كلها وربعتها
+
+721
+01:38:23,900 --> 01:38:29,700
+لكن هذا يصير تربيع يبقى هذا يصير تربيع تربيع تربيع
+
+722
+01:38:29,700 --> 01:38:36,420
+كده هذا طول البنات؟ واحد صحيح بهذا خلاص في عامل
+
+723
+01:38:36,420 --> 01:38:43,080
+مشترك ما بين الطرفين يبقى U تربيع طول الـ U تربيع
+
+724
+01:38:43,080 --> 01:38:47,440
+طول الـ V تربيع بظل sin تربيع ثيتا
+
+725
+01:38:51,930 --> 01:38:58,210
+هنا بواحد صحيح يبقى بصير طول الـ U تربيع × طول الـ V
+
+726
+01:38:58,210 --> 01:39:05,750
+تربيع ما هو المطلوب؟ خلاصنا؟ يبقى لحد هنا وقفنا
+
+727
+01:39:05,750 --> 01:39:10,750
+المرة الجاية بدنا ناخد إن شاء الله تعالى خواص الـ
+
+728
+01:39:10,750 --> 01:39:11,690
+cross product
+
+729
+01:39:21,410 --> 01:39:27,090
+أو أرضية للشيء اللي بدنا نِشرّحه حولها  فما جاية
+
+730
+01:39:27,090 --> 01:39:31,270
+تحتاجوا على الأرض بالضبط لأنك تاخده خمس دقائق، عشر
+
+731
+01:39:31,270 --> 01:39:35,390
+دقائق، خمس ساعات، خمس ساعات، فلاش أقفِل البابير و
+
+732
+01:39:35,390 --> 01:39:39,530
+أخليكِ برا هاي يا ولدي يا بني يا بني يا بني يا بني
+
+733
+01:39:39,530 --> 01:39:40,490
+يا بني يا بني يا بني يا بني يا بني يا بني يا بني
+
+734
+01:39:40,490 --> 01:39:44,570
+يا
+
+735
+01:39:44,570 --> 01:39:45,410
+بني
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/YDVEQJcaKaA_postprocess.srt b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/YDVEQJcaKaA_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..2de8c63e5319fafd78433a987c1b6d2ae4ebabc7
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/YDVEQJcaKaA_postprocess.srt
@@ -0,0 +1,2940 @@
+1
+00:00:08,500 --> 00:00:12,800
+يبقى موضوعنا اليوم ان شاء الله و تعالى موضوع the
+
+2
+00:00:12,800 --> 00:00:18,420
+top او scholar product يعني حاصل الضرب القياسي
+
+3
+00:00:18,420 --> 00:00:25,050
+لمتجهينهذا يوحي تساؤل آخر، هل هناك حاصل ضرب
+
+4
+00:00:25,050 --> 00:00:30,750
+إتجاهي؟ الإجابة نعم، إذا إحنا عندنا نوعين من
+
+5
+00:00:30,750 --> 00:00:35,290
+الضرب، الضرب القياسي والضرب الإتجاهي، اللي أخدناه
+
+6
+00:00:35,290 --> 00:00:40,950
+المرة الماضية كان حاصل ضرب scalar في vector، لكن
+
+7
+00:00:40,950 --> 00:00:44,730
+vector في vector ماتكلمناش في المرة الماضية، تمام؟
+
+8
+00:00:44,900 --> 00:00:48,820
+إذا اننا ناخد اليوم ال dot أو ال scholar product،
+
+9
+00:00:48,820 --> 00:00:53,360
+هنعطي تعريفنا ال dot أو ال scholar product ثم
+
+10
+00:00:53,360 --> 00:00:58,700
+كيفية الشغل في هذا المجال، تبقى هنبدأ أول شيء بال
+
+11
+00:00:58,700 --> 00:01:04,480
+definition، تبقى باجي بقول هنا ال definition، the
+
+12
+00:01:04,480 --> 00:01:04,900
+dot
+
+13
+00:01:14,670 --> 00:01:22,890
+of two vectors ال
+
+14
+00:01:22,890 --> 00:01:33,650
+U بده يساوي U1 و U3 و U2 و U3 and ال V بده يساوي
+
+15
+00:01:33,650 --> 00:01:41,830
+V1 و V2 و V3 is defined
+
+16
+00:01:52,600 --> 00:01:59,760
+بنضرب كل مركبة في نظيرتها وبنجمع هذا العدد بيعطيني
+
+17
+00:01:59,760 --> 00:02:09,000
+رقم مش vector يبقى باجي بقول U1 V1 زائد U2 V2 زائد
+
+18
+00:02:09,000 --> 00:02:17,280
+U3 V3 هذول حصل ضرب مركبات إذا هذا بيعطيني رقمإذاً
+
+19
+00:02:17,280 --> 00:02:22,500
+الرقم اللي عندنا هذا هه هو عبارة عن حاصل الضرب
+
+20
+00:02:22,500 --> 00:02:27,400
+القياسي لمنتجين لما يقول قياسي النتج يسوي كمية
+
+21
+00:02:27,400 --> 00:02:33,200
+قياسية طبعا هناك تعريف آخر يبقى هذا بتعتبر التعريف
+
+22
+00:02:33,200 --> 00:02:43,140
+رقمأقم اتنين ال u dot v بده يساوي طول ال u في طول
+
+23
+00:02:43,140 --> 00:02:51,200
+ال v في cosine زاوية theta where theta is the
+
+24
+00:02:51,200 --> 00:02:57,760
+angle between ال
+
+25
+00:02:57,760 --> 00:03:00,340
+u and ال v
+
+26
+00:03:07,510 --> 00:03:14,350
+إذا هناك صيغتان لحاصل الضرب القياسي لمتجههم الصيغة
+
+27
+00:03:14,350 --> 00:03:19,410
+الأولى بضرب الكل مركبة في نظيرتها و باجمع هيعطينا
+
+28
+00:03:19,410 --> 00:03:24,790
+ناتج رطل الصيغة الثانية طول المتجه الأول في طول
+
+29
+00:03:24,790 --> 00:03:30,050
+المتجه الثاني في جيب تمام الزاوية المحصورة بينهما
+
+30
+00:03:31,320 --> 00:03:36,320
+طبعا واضح انه محطتش قيود على هذه الزاوية السؤال هو
+
+31
+00:03:36,320 --> 00:03:40,840
+مدام هذا رقم لأن هذا الطول عبارة عن رقم الطول
+
+32
+00:03:40,840 --> 00:03:44,580
+الثاني عبارة عن رقم كوصين الزاوية كذلك عبارة عن
+
+33
+00:03:44,580 --> 00:03:50,660
+رقم لأن حاصر ضرب ثلاثة أرقام السؤال هو هل يمكن
+
+34
+00:03:50,660 --> 00:03:59,840
+لحاصر الضرب هذا أن يكون كمية ثالثة ممكن يكون ثقة
+
+35
+00:04:06,000 --> 00:04:11,280
+لأن هذا يبقى بدي أحط الكلام هذا في صيغة ال remark
+
+36
+00:04:11,280 --> 00:04:19,100
+التالف النقطة الأولىأفترضي بدي أجيب الزاوية ما بين
+
+37
+00:04:19,100 --> 00:04:22,780
+المتجهين اللي اتنين هدول اللي هي الزاوية θ بدي
+
+38
+00:04:22,780 --> 00:04:27,320
+أجيبها من مين من خلال العلاقة اللي عندنا هذه فبقدر
+
+39
+00:04:27,320 --> 00:04:33,620
+أقول هنا cosine الزاوية θ بدي أساوي U ضد ال V على
+
+40
+00:04:33,620 --> 00:04:39,440
+طول ال U في طول ال Vيبقى جسمت الطرفين على طول الـU
+
+41
+00:04:39,440 --> 00:04:45,360
+في طول الـV طب بدي الـθيتا زي ما درسنا في calculus
+
+42
+00:04:45,360 --> 00:04:52,200
+B بأثر بـcos inverse على الطرفين وبناء عليه هذا
+
+43
+00:04:52,200 --> 00:04:59,300
+بيصير أن الـθيتا تساوي cos inverse للرقم U ضد الـV
+
+44
+00:04:59,300 --> 00:05:02,500
+على طول الـU في طول الـV
+
+45
+00:05:08,710 --> 00:05:16,330
+ضد ال V ممكن يكون قيمة مجبة أكبر من الصفر واجتيش
+
+46
+00:05:16,330 --> 00:05:22,870
+هذا الكلام لو كانت الزاوية ثيتا زاوية حادة يبقى
+
+47
+00:05:22,870 --> 00:05:33,130
+هذا F ثيتا is an obtuse or acute angle
+
+48
+00:05:35,590 --> 00:05:39,950
+هيش acute angle زاوية حادة يعني محصورة من صفر
+
+49
+00:05:39,950 --> 00:05:44,130
+لغاية تسعين درجة وجيب تمام الزاوية حادة دائما او
+
+50
+00:05:44,130 --> 00:05:51,550
+ابدا positive يبقى اه اه لو جيت قلت هذا ال U هذا
+
+51
+00:05:51,550 --> 00:05:58,070
+ال V يبقى هذا ال U وهذا ال V وهذه الزاويتك على
+
+52
+00:05:58,070 --> 00:06:04,890
+سبيل المثال يبقى هذه زاوية حادة النقطة التالتةالـU
+
+53
+00:06:04,890 --> 00:06:10,890
+ضد الـV ممكن يكون less than zero يعني كمية سالبة
+
+54
+00:06:10,890 --> 00:06:19,810
+الكلام هذا بيحصل لو كان theta is an obtuse angle
+
+55
+00:06:19,810 --> 00:06:25,970
+obtuse angle يعني زاوية منفرجة يعني لو جيت رسمت
+
+56
+00:06:25,970 --> 00:06:31,000
+الزاوية فكانت الزاوية بالشكل هذايبقى هذا ال U و
+
+57
+00:06:31,000 --> 00:06:35,060
+هذا ال V و هذا الزاوية اللي هي ال object's angle
+
+58
+00:06:35,060 --> 00:06:40,360
+اللي هي الزاوية ثيتا طبعا في الربع الثاني جيب
+
+59
+00:06:40,360 --> 00:06:47,160
+التمام كمية صالبة وبالتالي ال dot product هيطلع
+
+60
+00:06:47,160 --> 00:06:50,420
+negative value اللي هو كمية صالبة
+
+61
+00:06:54,520 --> 00:07:00,180
+الـ V ممكن يساوي Zero ممكن يساوي Zero اقتناش إذا
+
+62
+00:07:00,180 --> 00:07:08,280
+الزاوية قائمة يبقى هذا الكلام F ثيتا تساوي باي على
+
+63
+00:07:08,280 --> 00:07:15,200
+اتنين وهذا الكلام F and
+
+64
+00:07:15,200 --> 00:07:19,740
+only F ال U and ال V
+
+65
+00:07:25,900 --> 00:07:30,640
+يبقى إذا كانوا المتجهات لاتنين متعمدين، يابانات
+
+66
+00:07:30,640 --> 00:07:33,780
+كلمة متعمد معناها perpendicular
+
+67
+00:07:51,070 --> 00:07:54,670
+المستقيمين متعامدان يبقى الـ two lines are
+
+68
+00:07:54,670 --> 00:08:01,590
+perpendicular يبقى
+
+69
+00:08:01,590 --> 00:08:05,910
+U ضد ال V بده يسوى Zero إذا كانت كذا تسوى بي على
+
+70
+00:08:05,910 --> 00:08:12,550
+اتنين أو ال U و ال V are orthogonalالنقطة الخامسة
+
+71
+00:08:12,550 --> 00:08:19,370
+لو جيت بناء عليه سألتك السؤال التالي وقلتك لو بدي
+
+72
+00:08:19,370 --> 00:08:27,840
+ال U ضد ال Uيبقى هذا الكلام يعطينا قداش طول ال U
+
+73
+00:08:27,840 --> 00:08:32,880
+في طول ال U في Cos الزاوية، قداش الزاوية بين
+
+74
+00:08:32,880 --> 00:08:38,000
+المتجة هو نفسه؟ Zero، Cos صفرة في قداش يا بنات؟
+
+75
+00:08:38,000 --> 00:08:45,480
+واحد، إذا هذا هيعطينا طول ال U تربيعطب لو بدى اجيب
+
+76
+00:08:45,480 --> 00:08:50,600
+طول ال U بدلالة ال dot إذا باخد ال square root
+
+77
+00:08:50,600 --> 00:08:56,560
+للطرفين يبقى هذا بدى يعطينا ان طول ال U بدى ساوي
+
+78
+00:08:58,970 --> 00:09:06,750
+أروت لل U ضد ال U لو بدى أحسب هذا بدلالة المركبات
+
+79
+00:09:06,750 --> 00:09:12,790
+فباجي بقول هذا الكلام يساوي ال U one تربيع زائد U
+
+80
+00:09:12,790 --> 00:09:21,110
+two تربيع زائد U three تربيعأذا الـ u ضد الـ u
+
+81
+00:09:21,110 --> 00:09:24,570
+بسوية طول الـ u في طول الـ u في الـ cosine الزاوية
+
+82
+00:09:24,570 --> 00:09:28,790
+الصفر اللي هو 1 صحيح إذا بصير أن هذا طول الـ u
+
+83
+00:09:28,790 --> 00:09:34,670
+تربيع لو بدأ أخد الجدر التربيع للطرفين يبقى طول
+
+84
+00:09:34,670 --> 00:09:40,770
+المتجه u يساوي ال square root للـ u ضد الـ u الـ u
+
+85
+00:09:40,770 --> 00:09:45,510
+ضد الـ u طبقا للتعريف اللي احنا كاتبينه بصير ال V1
+
+86
+00:09:45,510 --> 00:09:51,790
+هي U1و ال V2 هي U2 و ال V3 هي U3 إذا بيصير U1
+
+87
+00:09:51,790 --> 00:09:57,270
+square زائد U2 square زائد U3 square تحت ال square
+
+88
+00:09:57,270 --> 00:10:04,190
+root بيعطيني طول المتجه U قياسا على ذلك ممكن أروح
+
+89
+00:10:04,190 --> 00:10:11,570
+أحط مقطة زيادة من عند ال E6 لو جيت قلتلك I ضد I
+
+90
+00:10:13,220 --> 00:10:18,780
+كداش بده يساوي؟ هي بدل ال U ضد ال U بدأ أخد ال I
+
+91
+00:10:18,780 --> 00:10:23,800
+ضد ال I اللي هو طول الأول واحد وطول التاني واحد و
+
+92
+00:10:23,800 --> 00:10:28,160
+cosine الساوية صفرة بواحد يبقى بقداش واحد صحيح إذا
+
+93
+00:10:28,160 --> 00:10:34,680
+هذا بده يساوي ال J ضد ال J بده يساوي ال K ضد ال K
+
+94
+00:10:34,680 --> 00:10:36,420
+بده يساوي واحد صحيح
+
+95
+00:10:38,840 --> 00:10:46,140
+and لو جيت بقولتلك ال I ضد ال J قداش يا بنات؟ صفر
+
+96
+00:10:46,140 --> 00:10:50,580
+للإثنين are orthogonal يبقى ال dot product هذا في
+
+97
+00:10:50,580 --> 00:10:58,400
+Zero يسوى ال J ضد ال K يسوى ال K ضد ال I كله يسوى
+
+98
+00:10:58,400 --> 00:11:06,080
+كده؟ يسوى Zero يبقى هذه بعض الخواص الأساسية طب بدي
+
+99
+00:11:06,080 --> 00:11:13,350
+أطرح كمان تساؤلهل Zero vector Orthogonal to any
+
+100
+00:11:13,350 --> 00:11:20,070
+vector؟ مرة تانية أنا عند Zero vector Zero vector
+
+101
+00:11:20,070 --> 00:11:23,450
+قدر كتبات ومكتبات Zero في اتجاه انا، Zero في اتجاه
+
+102
+00:11:23,450 --> 00:11:24,870
+انا، Zero في اتجاه انا، Zero في اتجاه انا، Zero في
+
+103
+00:11:24,870 --> 00:11:29,870
+اتجاه انا هل Zero vector Orthogonal to any given
+
+104
+00:11:29,870 --> 00:11:32,330
+vector؟
+
+105
+00:11:42,150 --> 00:11:46,930
+بدي أشيل ال U و أحط مكانه Zero ضد ال V كدهش بدي
+
+106
+00:11:46,930 --> 00:11:52,790
+أطلع هدول إذا ال Zero vector is orthogonal to any
+
+107
+00:11:52,790 --> 00:11:58,330
+vector على طول خط المحاصر الطرف القاسي لأي vector
+
+108
+00:11:58,330 --> 00:12:02,110
+مع Zero vector بدي أعطينا مين؟ بدي أعطينا ال Zero
+
+109
+00:12:02,110 --> 00:12:04,850
+كمان هذه أحطيها سبعة
+
+110
+00:12:14,950 --> 00:12:25,290
+to any vector السبب because لو أخدت ال zero vector
+
+111
+00:12:25,290 --> 00:12:30,870
+ضد ال V على سبيل المثال يبقى هذا بيقولنا zero في
+
+112
+00:12:30,870 --> 00:12:35,230
+اتجاه ال I Zero في اتجاه ال J Zero في اتجاه ال K
+
+113
+00:12:35,230 --> 00:12:43,030
+ضد اللي هو V1 في اتجاه ال I V2 في اتجاه ال J V3 في
+
+114
+00:12:43,030 --> 00:12:48,410
+اتجاه ال Kنظر بالـ components المتناظرة Zero في V
+
+115
+00:12:48,410 --> 00:12:53,850
+واحد ب Zero Zero في V اتنين ب Zero Zero في V تلاتة
+
+116
+00:12:53,850 --> 00:12:59,290
+ب Zero يبقى الناتج يساوي Zero إذا بناء عليه Zero
+
+117
+00:12:59,290 --> 00:13:04,910
+vector is orthogonal to any vector قبل أن نواصل
+
+118
+00:13:04,910 --> 00:13:12,650
+ناخد بعض الأمثلة يبقى examples أول
+
+119
+00:13:12,650 --> 00:13:18,560
+مثلواللي find the value of the constant alpha find
+
+120
+00:13:18,560 --> 00:13:30,640
+the value of the constant alpha such that the
+
+121
+00:13:30,640 --> 00:13:31,100
+vectors
+
+122
+00:13:46,640 --> 00:13:58,380
+11j-3k and ال vector التاني 2αi-αj
+
+123
+00:13:58,380 --> 00:14:08,120
+ال vector التاني اللي هو v 2αi-αj-5k are
+
+124
+00:14:08,120 --> 00:14:09,920
+orthogonal
+
+125
+00:14:16,890 --> 00:14:23,870
+سؤال مرتين يقول هاتلي قيمة السابق أعفر ولم يضع
+
+126
+00:14:23,870 --> 00:14:29,490
+عليها أي قيود بحيث أن المنتجات الاتنين هذول اتنين
+
+127
+00:14:29,490 --> 00:14:34,310
+بيكونوا مالهم متعاملين، إذا اتنين هذول متعاملين
+
+128
+00:14:34,310 --> 00:14:36,290
+يبقى طبط ال product لهم جداش
+
+129
+00:14:51,530 --> 00:14:59,330
+بتاخد الـ U ضد ال V بده يساوي 0 هذا معناه إيه يلا
+
+130
+00:14:59,330 --> 00:15:05,570
+بتضرب ال components المتناظرة يبقى هذا اتنين Alpha
+
+131
+00:15:05,570 --> 00:15:08,450
+squared اللي بعده نقص Alpha
+
+132
+00:15:12,310 --> 00:15:17,730
+اللي بعده ناقص خمسة في ناقص تلاتة زائد خمستاشر كله
+
+133
+00:15:17,730 --> 00:15:24,550
+متساوي كده؟ متساوي Zero الان هذه معادلة من الدرجة
+
+134
+00:15:24,550 --> 00:15:30,770
+الثانية في مجهول واحد بقدر احلها واطلع هذا المجهول
+
+135
+00:15:30,770 --> 00:15:36,650
+لو روحنا حللنا هذا المقدار الثلاثي على شكل الأقواس
+
+136
+00:15:36,650 --> 00:15:41,400
+هو متساوي Zero باتنين Alpha وهنا Alphaهبعنى
+
+137
+00:15:41,400 --> 00:15:47,460
+الخمساشة دى مالاش إلا خمساشر في واحد أو تلاتة في
+
+138
+00:15:47,460 --> 00:15:55,980
+خمسة إذا لو جيت هنا قل خمسة و هنا تلاتة و هنا ناقص
+
+139
+00:15:55,980 --> 00:16:00,740
+و هنا ناقص تصير ناقص خمسة ألفة و ناقص ستة ألفة
+
+140
+00:16:00,740 --> 00:16:01,500
+بناقص
+
+141
+00:16:22,750 --> 00:16:30,670
+يبقى هذول القيمتين المطلوبتين لألفة
+
+142
+00:16:57,270 --> 00:17:06,490
+كمان مثال example two بيقول
+
+143
+00:17:06,490 --> 00:17:11,090
+let ال U يساوي
+
+144
+00:17:11,090 --> 00:17:23,230
+تلاتة I ناقص J ناقص اتنين K and ال V تساوي I زائد
+
+145
+00:17:23,230 --> 00:17:24,530
+اتنين J
+
+146
+00:17:29,890 --> 00:17:38,870
+أو ايش دولنا؟ نمرة A الـU ضد الـV نمرة B the angle
+
+147
+00:17:38,870 --> 00:17:42,410
+between
+
+148
+00:17:42,410 --> 00:17:56,590
+U and الـV أظن
+
+149
+00:17:56,590 --> 00:17:59,170
+انتهينا من المثال الأول يا بنات هذا نمسحه
+
+150
+00:18:17,750 --> 00:18:22,510
+سؤال مرة تانية، عند ال U عند ال V قال لي هدل ال U
+
+151
+00:18:22,510 --> 00:18:30,350
+ضد ال V فبجي بقوله نمرة A ال U ضد ال V بده يساعد
+
+152
+00:18:30,350 --> 00:18:34,810
+أضرب المركبات المتناضرة في بعضها، تلاتة في واحد
+
+153
+00:18:34,810 --> 00:18:35,610
+كدهاش
+
+154
+00:19:03,290 --> 00:19:08,730
+أول نقطة أخدناها في ال remark الزاوية تساوي cosine
+
+155
+00:19:08,730 --> 00:19:18,730
+inverseيو ضد ال V على طول ال U فطول ال V بقوله
+
+156
+00:19:18,730 --> 00:19:24,350
+كويس طول ال U بده يساوي اللي هو الجدر التربيه
+
+157
+00:19:24,350 --> 00:19:30,550
+لمربع الأول بتسعة مربع التاني واحد مربع اللي بعده
+
+158
+00:19:30,550 --> 00:19:38,170
+اللي هو أربعة يبقى square root لل 14بنروح نجيب طول
+
+159
+00:19:38,170 --> 00:19:42,750
+ال vector الثاني V يبقى الجدر التربيه لو المربع
+
+160
+00:19:42,750 --> 00:19:50,430
+الأول بواحد مربع الثاني باربعة ومربع التالت كذلك
+
+161
+00:19:50,430 --> 00:19:57,270
+بجدر بتسعة يبقى كمال square root لمان للاربعتاش من
+
+162
+00:19:57,270 --> 00:20:03,220
+الاتنين هدول بقدر اقول انطول الـU في طول الـV
+
+163
+00:20:03,220 --> 00:20:09,700
+تساوي كده 14، تمام؟ إذا إحنا عندنا ثيتا تساوي
+
+164
+00:20:09,700 --> 00:20:15,740
+cosine inverse للـU dot الـV على طول الـU في طول
+
+165
+00:20:15,740 --> 00:20:21,460
+مين في طول الـV، يرجع هذا بده يساوي cosine inverse
+
+166
+00:20:21,850 --> 00:20:26,650
+الـ U ضد V من النمرة A طالع تنة بسبعة وهذه
+
+167
+00:20:26,650 --> 00:20:34,290
+باربعتاشر يبقى Cos inverse لنص هنا أن عليه يبقى θ
+
+168
+00:20:34,290 --> 00:20:42,950
+تساوي مين الزاوية اللي جيب تمامها يساوي نص باي
+
+169
+00:20:42,950 --> 00:20:49,250
+علم؟ جيب تمامها يساوي نص صح جت ستين تساوي جت
+
+170
+00:20:49,250 --> 00:20:56,410
+تلاتين تساوينص يبقى باي على تلاتة يبقى تيتا تساوي
+
+171
+00:20:56,410 --> 00:21:02,410
+باي على تلاتة هذه اللي هي الإجابة او هذه الزاوية
+
+172
+00:21:02,410 --> 00:21:06,710
+ما بين الاتنين يبقى لاحظوا ان هذه الزاوية حادة و
+
+173
+00:21:06,710 --> 00:21:12,650
+لا مفرجة و لذلك تُكتبوا في كل عقيمة بوجب اللي هي
+
+174
+00:21:12,650 --> 00:21:17,810
+سابعة يبقى هذا يتفق مع الكلام النظري اللي ذكرناه
+
+175
+00:21:17,810 --> 00:21:23,510
+قبل قليلبنجي الأن يا بنات لبعض الخواص تبعات ضد ال
+
+176
+00:21:23,510 --> 00:21:30,830
+product يبقى بالدالي ل ال properties of
+
+177
+00:21:30,830 --> 00:21:40,270
+the product خواص
+
+178
+00:21:40,270 --> 00:21:47,890
+حاصل الضرب القياسي فبجي بقول F ال U و ال V and ال
+
+179
+00:21:47,890 --> 00:22:03,340
+Ware any vectors أي متجهات and الـ C is this color
+
+180
+00:22:03,340 --> 00:22:16,400
+then النقطة الأولى ال U بط ال V تساوي V بط ال U
+
+181
+00:22:16,400 --> 00:22:18,380
+النقطة الثانية
+
+182
+00:22:20,950 --> 00:22:35,650
+الـ C U ضد V يسوى U ضد CV يسوى C في U ضد V النقطة
+
+183
+00:22:35,650 --> 00:22:48,810
+التالتة U ضد V زائد W يسوى U ضد V زائد U ضد W
+
+184
+00:22:50,060 --> 00:22:56,700
+النقطة الرابعة والاخيرة الـ zero dot ال U بده
+
+185
+00:22:56,700 --> 00:23:00,420
+يساوي مين؟ بده يساوي ال zero
+
+186
+00:23:18,800 --> 00:23:26,100
+من هذه الخواصة بقول ال properties of the dot
+
+187
+00:23:26,100 --> 00:23:32,020
+product الخواص حصلت ضرب القياسي لمتجهين لو عندي
+
+188
+00:23:32,020 --> 00:23:39,640
+three vectors u وv وw وعندي c is scalar then ال u
+
+189
+00:23:39,640 --> 00:23:48,200
+ضد ال v تسوي v ضد ال uعملية الضرب القياسي عملية
+
+190
+00:23:48,200 --> 00:23:52,520
+إبدالية يبقى هذه بلغة الرياضات بقول عليها
+
+191
+00:23:52,520 --> 00:23:59,380
+commutative إبدالي هذه العملية بقول عليها
+
+192
+00:23:59,380 --> 00:24:03,300
+commutative
+
+193
+00:24:03,300 --> 00:24:09,840
+commutative يعني إبدالي إذا U ضط ال V يبدو سوى V
+
+194
+00:24:09,840 --> 00:24:12,440
+ضط ال U النقطة الثانية
+
+195
+00:24:15,480 --> 00:24:19,800
+الـ V يبقى الـ C ضربناه في المنتجة U و بعدين عملنا
+
+196
+00:24:19,800 --> 00:24:24,340
+ال dot المرة التانية أخدنا ال C ضربناه في ال V و
+
+197
+00:24:24,340 --> 00:24:29,000
+بعدين عملنا ال dot U dot CV أما أخدت ال U dot ال V
+
+198
+00:24:29,000 --> 00:24:34,440
+و النتج ضرب ال C على كل ثلاثة أمور تطلع عند نفسي
+
+199
+00:24:34,440 --> 00:24:42,500
+النتيجة طيبعملية الضربة القياسي تخضع لقانون
+
+200
+00:24:42,500 --> 00:24:46,320
+التوزيع أو ينطبق عليها قانون التوزيع الـ
+
+201
+00:24:46,320 --> 00:24:53,040
+Distributive Law يبقى U Dot V زائد U Dot W اللي
+
+202
+00:24:53,040 --> 00:24:58,700
+بعدها الـ Zero Dot U دو ساوي Zero السؤال هو الـ
+
+203
+00:24:58,700 --> 00:25:04,320
+Zero الأول هذاهل هو vector ولا scalar؟ vector وهذا
+
+204
+00:25:04,320 --> 00:25:09,100
+من هنا عامة الشركية الأولى مطاول والتانى مضورة
+
+205
+00:25:09,100 --> 00:25:12,700
+صغيرة يبقى اللى على اليمين اللى يساوى يا بنات هذا
+
+206
+00:25:12,700 --> 00:25:17,060
+scalar ال zero ال scalar واللى على الشمال هو ال
+
+207
+00:25:17,060 --> 00:25:21,280
+zero vector ومن هم أنا بدي أتميزي بينهم يبقى هذا
+
+208
+00:25:21,280 --> 00:25:25,640
+لإن مافيش حاجة اسمها ضط ما بين scalar و vector
+
+209
+00:25:32,330 --> 00:25:43,130
+.v بدي يسوي الـ zero scalar يبقى هذا scalar وهذا
+
+210
+00:25:43,130 --> 00:25:51,530
+ال zero وهذا اللي هو vector يبقى من هنا ييجي الفرق
+
+211
+00:25:51,530 --> 00:25:57,850
+بينهما نعطي مثال عملي على هذه الخواص يبقى examples
+
+212
+00:26:04,580 --> 00:26:07,280
+والـ f, u, v are vectors
+
+213
+00:26:33,030 --> 00:26:41,250
+و ال dot ما بين ال u و ال v ال u و dot ال v بدر
+
+214
+00:26:41,250 --> 00:26:54,030
+ساوي 11 and ال u dot ال w بدر ساوي 2 find او اشدون
+
+215
+00:26:54,030 --> 00:26:58,990
+نمر ايه تلاتة u dot
+
+216
+00:27:06,630 --> 00:27:11,970
+الـ U مينوس الـ V ضغط اتنين
+
+217
+00:27:40,500 --> 00:27:45,920
+مرة تانية نقرأ السؤال أو نتحدد ما هو اللي نريده
+
+218
+00:27:45,920 --> 00:27:50,270
+بالضبطيبقى بقول لو كان ال U و ال V و ال W are
+
+219
+00:27:50,270 --> 00:27:59,630
+vectors بحيث ان طول ال U يسوى 3 طول ال V يسوى 5 ال
+
+220
+00:27:59,630 --> 00:28:04,610
+product ما بين ال U و ال V يسوى 11 ال product ما
+
+221
+00:28:04,610 --> 00:28:09,370
+بين ال U و ال W يسوى 2 طلب عندي ثلاثة مطالب
+
+222
+00:28:09,370 --> 00:28:14,850
+المطلوب الأول ثلاثة U في V زائد الأربعة W
+
+223
+00:28:19,870 --> 00:28:29,230
+Dot ال V زائد أربعة W لو رجعت للخاص اللي عندنا و
+
+224
+00:28:29,230 --> 00:28:34,790
+الخاصة الخاصية رقم تلاتة يبقى vector ضرب مجموع two
+
+225
+00:28:34,790 --> 00:28:38,750
+vectors بدي أوزع هذا ال vector على مين؟ على ال two
+
+226
+00:28:38,750 --> 00:28:43,550
+vectors اللي جوا يبقى بناء عليه هذا الكلام بده
+
+227
+00:28:43,550 --> 00:28:48,910
+يساوي تلاتة U كله ك vector Dot ال V
+
+228
+00:29:00,030 --> 00:29:10,610
+مرة تانية هذه التلاتة بقدر أخدها برا تمام كده هذه
+
+229
+00:29:10,610 --> 00:29:16,350
+التي هي تلاتة you dot الاربعة
+
+230
+00:29:37,150 --> 00:29:41,890
+هذا الكلام يبدو يساوي ثلاثة في أربعة بارة يبقى هذه
+
+231
+00:29:41,890 --> 00:29:47,530
+ثلاثة في أربعة باطن عشر يضط دوي
+
+232
+00:30:17,220 --> 00:30:22,920
+يبقى هاي قيمة المطموب الأول من كل مثل بنانجل
+
+233
+00:30:22,920 --> 00:30:29,840
+المطموب التاني اللي هو نمرة V بيقول U نقص ال V U
+
+234
+00:30:29,840 --> 00:30:38,960
+نقص ال V U نقص ال V dot اتنين U زائد L
+
+235
+00:30:52,250 --> 00:30:55,930
+دربت ال U في ال vector أخرى و أضربها لمين؟ في ال
+
+236
+00:30:55,930 --> 00:31:02,470
+vector التاني زائد ال U بط ال V اللي عملته ل U
+
+237
+00:31:02,470 --> 00:31:11,390
+هروح أعمله لمين؟ لسالف V يبقى هذه سالف V بط اتنين
+
+238
+00:31:11,390 --> 00:31:20,310
+U اللي بعدها سالف V بط ال V بالشكل اللي عندنا نعيد
+
+239
+00:31:20,310 --> 00:31:25,930
+ترتيب المثليبقى هذا الكلام اتنين بتاخده برا بيظل
+
+240
+00:31:25,930 --> 00:31:37,270
+ال U dot ال U زائد U dot ال V ماقس اتنين V dot ال
+
+241
+00:31:37,270 --> 00:31:46,730
+U ماقس اللي هو طول ال V تربيع ال V dot ال V طول ال
+
+242
+00:31:46,730 --> 00:31:52,780
+V تربيع هذا الكلام يساويهذه بنات بنفس القصة
+
+243
+00:31:52,780 --> 00:32:00,840
+بتعطينا طول ال U تربيع يبقى هذه اتنين طول ال U²
+
+244
+00:32:04,050 --> 00:32:10,550
+V Dot U و U Dot V مش اتنين نفس الشيء الخاصية
+
+245
+00:32:10,550 --> 00:32:15,730
+الأولى U Dot V و V Dot U اذا هذه هي هذه طب واحدة
+
+246
+00:32:15,730 --> 00:32:22,250
+موجبة و اتنين سالب يبقى ايه سالب U Dot V يبقى سالب
+
+247
+00:32:22,250 --> 00:32:30,170
+U Dot V خلصنا منها ناقص طول ال V تربيع يبقى هذا
+
+248
+00:32:30,170 --> 00:32:31,570
+الكلام بده يساوي
+
+249
+00:32:41,090 --> 00:32:47,790
+وضد ال V اللي هو ب 11 ناقص طول ال V اللي هو خمسة
+
+250
+00:32:47,790 --> 00:32:54,030
+لكل تربية طبعا هذه تسعة في اتنين في تمانتاش
+
+251
+00:32:54,030 --> 00:33:01,650
+تمانتاش سالب احداش سالب خمسة وعشرين سالب خمسة
+
+252
+00:33:01,650 --> 00:33:05,010
+وعشرين وسالب احداش بسالب ستة وتلاتين
+
+253
+00:33:11,250 --> 00:33:18,370
+عشرة يبقى هذا هو المطلوب الثاني من المسألة بدنا
+
+254
+00:33:18,370 --> 00:33:24,690
+نروح للمطلوب التالت طلعوني
+
+255
+00:33:24,690 --> 00:33:29,890
+في المطلوب التالت كويس وفكروا كيف بدنا نجيب
+
+256
+00:33:29,890 --> 00:33:35,170
+المطلوب التالت لإن أنا ماعنديش ال vector u و ال
+
+257
+00:33:41,020 --> 00:33:46,640
+اللي بدى الطول ال U نقص اتنين V لو بعرف ال U و ال
+
+258
+00:33:46,640 --> 00:33:52,500
+V كان صارت الجزء سهل لكن أنا لاعرف U ولا عارف V طب
+
+259
+00:33:52,500 --> 00:33:58,040
+كيف نحل هالمسألة دي؟ يلا اقترحوا علينا اقتراح
+
+260
+00:34:24,500 --> 00:34:29,140
+أحنا أخدنا مجموع لما نقول نقول إثنين يستوي نقول
+
+261
+00:34:29,140 --> 00:34:37,940
+الأول زي نقول الثاني افتشل الكلام الحل
+
+262
+00:34:37,940 --> 00:34:46,740
+إيه؟ كدا كدا ها انت سمع
+
+263
+00:35:12,020 --> 00:35:21,140
+إذا أنا هنا باجي بقول نمرسيأنا عازمين اللي هو U
+
+264
+00:35:21,140 --> 00:35:24,700
+بالتربيع بنقص اتنين فيه الطول تبعه، بدي أخد
+
+265
+00:35:24,700 --> 00:35:28,500
+تربيعه، وشوف إيش بده بيعطينا، و بعد هيك القرآن ما
+
+266
+00:35:28,500 --> 00:35:33,760
+شاء الله حلها، يبقى باجي بقوله لو أخد طول ال U
+
+267
+00:35:33,760 --> 00:35:34,840
+ناقص اتنين
+
+268
+00:35:40,560 --> 00:35:49,280
+يبقى بلغة الـ vectors هذا U نقص 2B ضد الـ U نقص 2B
+
+269
+00:35:49,280 --> 00:35:55,380
+هزبط هيك؟ فبنعمل الفكرة اللي عملناها من هنا لضرب
+
+270
+00:35:55,380 --> 00:36:03,860
+هذا يبقى هذا شو بده يعطينا؟ يبده يعطينا U ضد الـ U
+
+271
+00:36:03,860 --> 00:36:08,420
+نقص
+
+272
+00:36:08,420 --> 00:36:09,340
+الـ U
+
+273
+00:36:17,580 --> 00:36:25,260
+نقص في نقص في نقص في نقص في نقص
+
+274
+00:36:25,260 --> 00:36:27,160
+في نقص
+
+275
+00:36:32,250 --> 00:36:44,570
+يبقى U ضد ال V يبقى
+
+276
+00:36:44,570 --> 00:36:53,230
+U ضد ال V زائد أربعة طول ال V تربية V ضد ال V ليه
+
+277
+00:36:53,230 --> 00:36:54,770
+طول ال V تربية
+
+278
+00:37:13,600 --> 00:37:19,580
+طول الـ U مات اللي هو قداش تلاتة يبقى تلاتة لكل
+
+279
+00:37:19,580 --> 00:37:28,640
+تربية ناقص أربعة هذا U يا بناتي ناقص أربعة U ضفت
+
+280
+00:37:28,640 --> 00:37:30,600
+ال V اللي هو قداش ب 11
+
+281
+00:37:34,380 --> 00:37:41,620
+أربعة في طول ال V وين طول ال V اللي هو خمسة الكل
+
+282
+00:37:41,620 --> 00:37:50,880
+تربيه هذا الكلام سوى تسعة ناقص أربعة وأربعين خمسة
+
+283
+00:37:50,880 --> 00:37:56,640
+تربيه ليه خمسة وعشرين في أربعة بمية يبقى زائد مية
+
+284
+00:37:57,310 --> 00:38:01,890
+عندك مية وتسعة بده اشيل منهم مين اللي مول ان هذا
+
+285
+00:38:01,890 --> 00:38:07,330
+موجب و هذا موجب يبقى هذا مية وتسعة بده اشيل منهم
+
+286
+00:38:07,330 --> 00:38:14,470
+اربع واربعين بظل خمسة و هنا كدهش ستة يبقى خمسة و
+
+287
+00:38:14,470 --> 00:38:21,330
+ستين بالموجب مين هذا؟أنا لا أريد طول المتجه أنا
+
+288
+00:38:21,330 --> 00:38:25,590
+أريد طول المتجه إذا باخد ال square root of both
+
+289
+00:38:25,590 --> 00:38:30,350
+sides باخد الجدر التربية للطرفين يبقى بناء على طول
+
+290
+00:38:30,350 --> 00:38:38,930
+ال U ونقص 2D يسوى ال square root من الخمس أو ستة
+
+291
+00:38:38,930 --> 00:38:44,730
+إذا أنا جبت الطول ههه هم لا يعرفوا شكل ال U
+
+292
+00:39:12,030 --> 00:39:16,230
+طبعا و لا سؤال زيه في الكتاب وإنما جيأ بيه في
+
+293
+00:39:16,230 --> 00:39:24,010
+امتحان 2005 ونشور طبعا نفس الفكرة ها، كويس؟ يبقى
+
+294
+00:39:24,010 --> 00:39:28,730
+هذا good exercise إيه المرنو ديكوا فيه؟ امتحان في
+
+295
+00:39:28,730 --> 00:39:38,300
+2005 بيقول لو كانالـ V يساوي اتنى وطول ال W يساوي
+
+296
+00:39:38,300 --> 00:39:47,300
+تلاتة and the angle between and the angle between
+
+297
+00:39:47,300 --> 00:39:51,440
+the
+
+298
+00:39:51,440 --> 00:40:04,640
+angle between ال V and ال W is Pi على تلاتةفايند
+
+299
+00:40:04,640 --> 00:40:14,140
+هو ايش دولة اللي هو طول ال V نقص اتنين W the
+
+300
+00:40:14,140 --> 00:40:25,200
+length of the vector V نقص اتنين W
+
+301
+00:40:39,460 --> 00:40:46,420
+V-2W الطول الكل تربيه و تبدأ تشتغل زي اللي فوق
+
+302
+00:40:46,420 --> 00:40:55,580
+يالا و نرشش الكمان الجواب الanswer الإجابة اتنين
+
+303
+00:40:55,580 --> 00:41:03,000
+جدر سبعة يالا مش هالنا التهيش قبل أن نجي لنقطة جدا
+
+304
+00:41:03,000 --> 00:41:05,020
+في هذا ال section اسمها
+
+305
+00:41:24,980 --> 00:41:35,540
+بنحاول نسقط اللى هو مفتجه على مفتجه الاخر حد راكوا
+
+306
+00:41:35,540 --> 00:41:44,080
+فيها مصطره بيقولوا تلاتي صانده هاتي ايه؟ ايش؟
+
+307
+00:41:44,080 --> 00:41:52,460
+بنات؟ اه 100% بدي اعتبر هذه بنات عبارة عن vector
+
+308
+00:41:53,090 --> 00:41:58,500
+وهذا عبارة عن vector آخربدي أحاول أسقط الـ vector
+
+309
+00:41:58,500 --> 00:42:03,020
+اللي فوق على ال vector اللي تحت و نشوف إيش النتج
+
+310
+00:42:03,020 --> 00:42:07,680
+بدي يكون طبعا احنا أخدنا زمان في المرحلة الثانوية
+
+311
+00:42:07,680 --> 00:42:14,420
+أنه مسقط مستقيم على مستقيم الآخر هو مستقيم إلا إذا
+
+312
+00:42:14,420 --> 00:42:18,660
+كان عمودي عليه فالمسقط هو main نقطة بالمثل إن أنا
+
+313
+00:42:18,660 --> 00:42:22,060
+بدي أسقط هذا ال vector على هذا ال vector بدي
+
+314
+00:42:22,060 --> 00:42:27,910
+يعطيني mainVector تاني السؤال هو المسقط هذا بيكون
+
+315
+00:42:27,910 --> 00:42:32,990
+أطول من ال vector الأصلي ولا أكثر منه ولا ممكن
+
+316
+00:42:32,990 --> 00:42:37,170
+يساوي .. ممكن
+
+317
+00:42:37,170 --> 00:42:43,070
+يساوي وارد و أكثر منه وارد لكن أكبر منه مافيش
+
+318
+00:42:43,070 --> 00:42:47,390
+إمكانية على الأطلع تمام؟ الكلام اللي أنا بقوله
+
+319
+00:42:47,390 --> 00:42:54,010
+هوضحه الآن من خلال الرسملو أنا يا بنات عندي المتجه
+
+320
+00:42:54,010 --> 00:43:04,210
+V وعندي متجه أخر U بدي أسقط ال U على V لحظة هذا
+
+321
+00:43:04,210 --> 00:43:11,190
+النقطة مشتركة يبقى هادر بالطل عشان أسقط ويسقط زي
+
+322
+00:43:11,190 --> 00:43:15,550
+ما هو يبقى النقطة هذه يا بنات رأس المتجه
+
+323
+00:43:20,320 --> 00:43:27,340
+عمودي بهذا الشكل يبقى المتجه تبع المسقط هو المتجه
+
+324
+00:43:27,340 --> 00:43:33,160
+اللي عندنا هذا الخط الأزرق هذا او المتجه الأزرق
+
+325
+00:43:33,160 --> 00:43:39,520
+هذا هو المسقط اللي هسميه projection U على مين على
+
+326
+00:43:39,520 --> 00:43:43,000
+فيه و بطبقه بالشكل التالي كلمة projection
+
+327
+00:43:47,010 --> 00:43:54,350
+وحط ال V ك index عندي ال J يبقى يقرأ projection U
+
+328
+00:43:54,350 --> 00:44:01,350
+على V الزاوية
+
+329
+00:44:01,350 --> 00:44:07,490
+اللي بينهم كانت هذه θ زاوية حاتة تمام؟ يبقى
+
+330
+00:44:07,490 --> 00:44:13,250
+الزاوية اللي عند هذه θ زاوية حاتة بناء عليه بدي
+
+331
+00:44:13,250 --> 00:44:18,140
+أعرف هل ال projection هذابدي اكون positive ولا
+
+332
+00:44:18,140 --> 00:44:23,360
+negative يعني بدي اعرف قداش الطول تبعه بالضبط و
+
+333
+00:44:23,360 --> 00:44:29,960
+بدي اعرف قداش اتجاهه تمام فباجي اقول والله كويس ال
+
+334
+00:44:29,960 --> 00:44:38,060
+vector هذا من هنا لهنا الطول تبعه له طول اليوم في
+
+335
+00:44:38,060 --> 00:44:42,830
+جيب تمام الزاوية ثيتا مين بيعطيناطول الـ
+
+336
+00:44:42,830 --> 00:44:47,730
+projection طول
+
+337
+00:44:47,730 --> 00:44:53,770
+الـ U على V يساوي طول الـ U في الـ cosine الزاوية
+
+338
+00:44:53,770 --> 00:45:01,490
+ميان الـ theta نهضة المستقيم الأزرق هذا أقصر من
+
+339
+00:45:01,490 --> 00:45:05,230
+طول
+
+340
+00:45:05,230 --> 00:45:10,830
+المتجه Uطب لو كان الـU عمودي على V بالـprojection
+
+341
+00:45:10,830 --> 00:45:17,850
+هو الـzero vector، مظبوط؟ طيب، بدنا نيجي ناخد
+
+342
+00:45:17,850 --> 00:45:24,150
+الحالة التانية، لو كان هذا هو الـvector V وكان هذا
+
+343
+00:45:24,150 --> 00:45:31,110
+هو الـvector U وحبيت أسقط U على V حيث إن الزاوية
+
+344
+00:45:31,110 --> 00:45:33,890
+بينهما θ زاوية A
+
+345
+00:45:54,230 --> 00:46:00,490
+طول الـ U في الـ Cos الزاوية واتجاه
+
+346
+00:46:03,010 --> 00:46:07,190
+تجاه ال V هذا الأول سنة من التانية هاروح للتانية
+
+347
+00:46:07,190 --> 00:46:11,370
+يبقى هو
+
+348
+00:46:11,370 --> 00:46:14,910
+طول ال U في قصين الزاوية تيتها هذا طول ال
+
+349
+00:46:14,910 --> 00:46:20,250
+projection لكن اتجاهه هو اتجاه ال V يعني في اتجاه
+
+350
+00:46:20,250 --> 00:46:26,250
+V على طول ال V اللي هو متجه الوحدة في اتجاه من V
+
+351
+00:46:26,950 --> 00:46:31,770
+يجب أن تكون الـ projection تبع الـ U على V هو متجه
+
+352
+00:46:31,770 --> 00:46:35,390
+جديد في اتجاه المتجه V
+
+353
+00:46:53,080 --> 00:47:00,240
+هذا U إذا هذا طول المتجه Uفى cosine الزاوية تيتا
+
+354
+00:47:00,240 --> 00:47:07,600
+تيتا زاوية منفرجة إذا الجيب التمام سالم تمام إذا
+
+355
+00:47:07,600 --> 00:47:13,200
+لما بدي أجيب القول بالضبط بدي أقول قول المتجه هي و
+
+356
+00:47:13,200 --> 00:47:19,540
+هذا قيمة عددية موجبة في مين في cosine الزاوية تيتا
+
+357
+00:47:19,540 --> 00:47:25,120
+ولما كانت الزاوية تيتا زاوية منفرجة فاروح بقول في
+
+358
+00:47:25,120 --> 00:47:25,420
+مين
+
+359
+00:47:29,020 --> 00:47:34,440
+الأول طول المتجه هذا ال absolute value لهذا الرقم
+
+360
+00:47:34,440 --> 00:47:39,100
+هيطلع سالب أخد absolute value و بطلع قيمة مجبرة ال
+
+361
+00:47:39,100 --> 00:47:45,380
+direction عكس اتجاه ال V يعني إذا كان هذا ال
+
+362
+00:47:45,380 --> 00:47:50,100
+projection في اتجاه ال V على طول ال V هذا هيكون في
+
+363
+00:47:50,100 --> 00:47:56,500
+اتجاه سالبفي علقه يعني في عكس اتجاهه تماما بضبط،
+
+364
+00:47:56,500 --> 00:48:01,260
+تمام؟ الكلام اللي قلتهلك هذا الشفوي بدنا نروح
+
+365
+00:48:01,260 --> 00:48:08,800
+أنصيه و نكتبه كتابة، يبقى كيف كتابة كالتالي، بروح
+
+366
+00:48:08,800 --> 00:48:12,520
+بقول ان بدي أحق الكلام في صيغة النقاط التالية،
+
+367
+00:48:12,520 --> 00:48:13,200
+النقطة الأولى
+
+368
+00:48:23,130 --> 00:48:34,510
+between الـU and الـV is accurate يعني لو كانت
+
+369
+00:48:34,510 --> 00:48:40,770
+زاوية حادة لـ projection تبع الـU على الـV
+
+370
+00:48:51,250 --> 00:49:00,890
+فى cosine الزاوية θ and direction وفى الاتجاه V
+
+371
+00:49:00,890 --> 00:49:05,750
+على طول الـ V هذا طبعا لمتجه الوحدة فى اتجاه
+
+372
+00:49:05,750 --> 00:49:12,670
+المتجه V ذكرناه فى المحاضرة الماضية نمرى اتنين if
+
+373
+00:49:12,670 --> 00:49:16,830
+the angle θ
+
+374
+00:49:18,930 --> 00:49:25,970
+is obvious لو
+
+375
+00:49:25,970 --> 00:49:33,810
+كانت زاوية منفرجة الـ projection تبع الـU على V
+
+376
+00:49:33,810 --> 00:49:42,410
+has length has length اللي هو طول الـU في absolute
+
+377
+00:49:42,410 --> 00:49:53,910
+value لكوصين الزاوية V anddirection والاتجاه
+
+378
+00:49:53,910 --> 00:50:02,850
+سالب V على فول ال V يعني بنجوسين ل opposite
+
+379
+00:50:02,850 --> 00:50:09,310
+direction of
+
+380
+00:50:09,310 --> 00:50:16,850
+V الاتجاه المعاكس لل vector V ثلاثة
+
+381
+00:50:49,890 --> 00:50:58,530
+المركبة القياسية of U المتجه U and
+
+382
+00:51:01,270 --> 00:51:13,850
+direction في اتجاه of V هذه
+
+383
+00:51:13,850 --> 00:51:19,930
+طول ال U في Cos الزاوية تيتا ممكن أجيب لها صياغة
+
+384
+00:51:19,930 --> 00:51:26,010
+أخرى شو الصياغة الأخرى؟ هأبقالك بين قسين؟ not that
+
+385
+00:51:26,010 --> 00:51:37,420
+لحظة أن طول ال Uفى cosine الزاوية تيتا يساوي لو
+
+386
+00:51:37,420 --> 00:51:42,320
+رجعت لل dot product بين ال U و ال V فى الهامشة
+
+387
+00:51:42,320 --> 00:51:49,680
+بنات قولنا ان ال U dot ال V يساوي طول ال U فى طول
+
+388
+00:51:49,680 --> 00:51:55,920
+ال V فى cosine الزاوية تيتا إذا طول ال U فى cosine
+
+389
+00:51:55,920 --> 00:51:59,740
+الزاوية تيتا يساوي U dot ال V
+
+390
+00:52:15,140 --> 00:52:19,780
+الـ V أو طول الـ U اللي طلعناه اللي هو عبارة عن
+
+391
+00:52:19,780 --> 00:52:28,820
+الـ U دُغري الـ U ضد ال V على طول ال V بالشكل
+
+392
+00:52:28,820 --> 00:52:33,360
+العام أو
+
+393
+00:52:33,360 --> 00:52:41,420
+بقدر أحط هلك كمان في صيغة أخرى الـ U ضد ال V على
+
+394
+00:52:41,420 --> 00:52:49,520
+طول ال Vكأن واحد على طول V-scalar تعتبره مضروف في
+
+395
+00:52:49,520 --> 00:52:53,520
+الكل ماشي، مضروف في المتجهة الأول ماشي، مضروف في
+
+396
+00:52:53,520 --> 00:52:56,940
+المتجهة التاني ماشي، سيان، هادي، ورنهادي، كله are
+
+397
+00:52:56,940 --> 00:53:02,960
+the same طب هل لو فكيت هذا يا تراج بيعطيني طول هذا
+
+398
+00:53:02,960 --> 00:53:08,200
+المقطع، الإجابة نعم، بدا فكرة طول الأول في طول
+
+399
+00:53:08,200 --> 00:53:12,040
+الثاني، طول الأول في طول اليوم، طول الثاني في قداش
+
+400
+00:53:13,050 --> 00:53:16,950
+وحد صحي للمتاجر الواحدة في cosine الزاوية بينهم
+
+401
+00:53:16,950 --> 00:53:21,770
+أكيد إذا صار طول ال U في cosine الزاوية أكيد إذا
+
+402
+00:53:21,770 --> 00:53:26,990
+يابا ندّي scalar component of ال vector U في اتجاه
+
+403
+00:53:26,990 --> 00:53:30,490
+ال vector value أبسل U أكيد طول ال U في cosine
+
+404
+00:53:30,490 --> 00:53:36,210
+الزاوية أكيد يابا أقول U dot V على طول ال V هذا
+
+405
+00:53:36,210 --> 00:53:39,630
+الكلام جيبته من وين؟ جيبته من خلال ال definition
+
+406
+00:53:39,630 --> 00:53:41,710
+تبع ال dot product
+
+407
+00:53:48,500 --> 00:53:53,640
+يبقى سواء كان هذا والله هذا الاتنين are the same
+
+408
+00:54:12,080 --> 00:54:17,760
+المثال هذا النقطة التانية بتحطها النقطة الرابعة
+
+409
+00:54:17,760 --> 00:54:23,140
+يبقى النقطة الرابعة لو بدي ال projection تبع ال U
+
+410
+00:54:23,140 --> 00:54:30,860
+في اتجاه المتجه B طول المتجه U في Cos الزاوية θ في
+
+411
+00:54:30,860 --> 00:54:31,460
+اتجاه
+
+412
+00:54:38,740 --> 00:54:42,680
+هذا الكلام ممكن يساوي يبقى هذا يمثل طول ال
+
+413
+00:54:42,680 --> 00:54:48,620
+projection وهذا يمثل مين؟ يمثلي اتجاهه يعني متجه
+
+414
+00:54:48,620 --> 00:54:53,040
+الواحدة في اتجاهه يبقى هذا كله على بعضه هو ال
+
+415
+00:54:53,040 --> 00:54:58,860
+projection تبع المتجه U في اتجاه المتجه من V لكن
+
+416
+00:54:58,860 --> 00:55:03,740
+انا عندي طول ال U في ال cosine يسوى القيمة اللي
+
+417
+00:55:03,740 --> 00:55:04,520
+عندنا هذه
+
+418
+00:55:08,070 --> 00:55:16,130
+عن هذه اليمين اللي هي U بط ال V على طول ال V في ال
+
+419
+00:55:16,130 --> 00:55:27,170
+V على طول ال V هذه بنات هي U بط ال V على طول ال V
+
+420
+00:55:27,170 --> 00:55:33,900
+تربية في اتجاه المتجاه Vالصياغة هذه جميلة جدا
+
+421
+00:55:33,900 --> 00:55:41,880
+والأجمل منها كذلك يضط ال V على V ضط ال V في اتجاه
+
+422
+00:55:41,880 --> 00:55:47,660
+المتجه V طيب
+
+423
+00:55:47,660 --> 00:55:52,200
+سؤال اللي بين قسين هذه من هذا كمية اتجاهية ولا
+
+424
+00:55:52,200 --> 00:55:59,460
+كمية قياسية يبقى الرقم مضروب في V الرقم هذا
+
+425
+00:56:24,170 --> 00:56:32,530
+هو ممكن يطلع أقل من V لكن هل يمكن أن يطلع أكبر من
+
+426
+00:56:32,530 --> 00:56:33,690
+V؟
+
+427
+00:56:42,340 --> 00:56:49,220
+لكن أكبر من ال V هذا الكلام مستبعد تماما واضحان
+
+428
+00:56:49,220 --> 00:56:54,540
+يرجع عمليا من الأن فسعنا نتعامل مع ال projection
+
+429
+00:56:54,540 --> 00:56:59,580
+تبع اليهو في اتجاه ال V بالطريقة اللي عندنا هنا طب
+
+430
+00:56:59,580 --> 00:57:03,520
+بدأ أسألكوا سؤال تاني لو جمت جرامة الوضع
+
+431
+00:57:15,610 --> 00:57:21,270
+أنت بصيغة والله ابنك يبقى هنا لو بدأت أخد ال
+
+432
+00:57:21,270 --> 00:57:27,290
+projection تبع ال V في اتجاه ال U بدأت تنتج و
+
+433
+00:57:27,290 --> 00:57:32,850
+لحالي هه بدون شغل و بدون كلام بس أني أدقق النظر في
+
+434
+00:57:32,850 --> 00:57:36,390
+النتيجة اللي عندنا هذا طلعوا يا بنات ال projection
+
+435
+00:57:36,390 --> 00:57:43,630
+تبع ال U على V U ضد ال V V V V يعني ال U ظهر بس
+
+436
+00:57:43,630 --> 00:57:48,190
+مرة واحدةيبقى انا بدي اخد ال projection تبع ال V
+
+437
+00:57:48,190 --> 00:57:55,010
+على U يبقى
+
+438
+00:57:55,010 --> 00:57:57,710
+انا بدي اخد ال projection تبع ال V على U يبقى انا
+
+439
+00:57:57,710 --> 00:57:58,710
+بدي اخد ال projection تبع ال V على U يبقى انا بدي
+
+440
+00:57:58,710 --> 00:58:05,130
+اخد ال projection تبع ال V على U يبقى
+
+441
+00:58:05,130 --> 00:58:10,810
+انا بدي اخد ال projection تبع ال V على U يبقى انا
+
+442
+00:58:10,810 --> 00:58:13,870
+بدي اخد ال projection تبع ال V على U
+
+443
+00:58:15,880 --> 00:58:20,980
+مرياضياً خلاص يبقى هذا اللي هو معنى ال projection
+
+444
+00:58:20,980 --> 00:58:25,420
+نعطي مثال عملي على ذلك example
+
+445
+00:58:49,810 --> 00:59:02,590
+زائد خمسة K زائد خمسة K find نمره A بدنا لـ
+
+446
+00:59:02,590 --> 00:59:10,590
+projection تبع الـ U على V نمره B بدنا this scalar
+
+447
+00:59:10,590 --> 00:59:16,670
+component this scalar component
+
+448
+00:59:16,670 --> 00:59:19,030
+المركبة القيمة
+
+449
+00:59:40,110 --> 00:59:44,110
+مرة ثانية نقرأ السؤال و نفهم ما هو المطلوب من هذا
+
+450
+00:59:44,110 --> 00:59:48,630
+السؤال بقول لو كان ال U و ال V بالشكل اللي قدامنا
+
+451
+00:59:48,630 --> 00:59:52,990
+هذا طلب ل projection تبع ال U على V إذا أنا لو
+
+452
+00:59:52,990 --> 00:59:58,830
+كتبت له هنا نمرة Aالـ projection تبع الـ U على V
+
+453
+00:59:58,830 --> 01:00:03,550
+أو الـ component of U in the direction of V،
+
+454
+01:00:03,550 --> 01:00:06,690
+الإتنين are the same إذا مش أنا أجيب له الـ
+
+455
+01:00:06,690 --> 01:00:12,050
+projection بالزمن الـU ضد الـV و بالزمن الـV ضد
+
+456
+01:00:12,050 --> 01:00:16,190
+إيه، ده خلّيني أحسبهم من الأول، يبقى بدي أروح أخدي
+
+457
+01:00:16,190 --> 01:00:21,410
+الـU ضد الـV، يبقى بدي أضرب اللي هو العناصر
+
+458
+01:00:21,410 --> 01:00:28,180
+المتنظرة، واحد في تلاتة كدهاشر، تلاتةماقص 7 في 4
+
+459
+01:00:28,180 --> 01:00:37,460
+بنقص جدال 28 زائد 3 في 5 اللي هو جدال 15 يبقى هذا
+
+460
+01:00:37,460 --> 01:00:45,500
+الكلام بدرساوي 15 و3 18 يبقى الجدال ناقص 10 بعد
+
+461
+01:00:45,500 --> 01:00:50,960
+ذلك بيروح أجيب له ال V وضعت ال V يبقى المتجه في
+
+462
+01:00:50,960 --> 01:00:53,300
+نفسه يبقاش مصير هنا
+
+463
+01:01:02,510 --> 01:01:09,210
+16 9 25 50
+
+464
+01:01:15,740 --> 01:01:26,540
+يبقى ال U على V يبقى
+
+465
+01:01:26,540 --> 01:01:34,580
+ناقص عشرة على خمسين في ال vector اللي عندنا V زي
+
+466
+01:01:34,580 --> 01:01:42,190
+ما هو تلاتة I زائد أربعة J زائد خمسة Kطبعا ناقص
+
+467
+01:01:42,190 --> 01:01:47,730
+عشر على خمسين اللي هو قداش سالب خمس إذا هذا ال
+
+468
+01:01:47,730 --> 01:01:54,930
+vector بصير سالب تلت أخمس في اتجاه ال I سالب أربع
+
+469
+01:01:54,930 --> 01:02:04,630
+أخمس في اتجاه ال J سالب كده كده فقط ناغية يبقى هذا
+
+470
+01:02:04,630 --> 01:02:09,520
+اللي هوأو الـ projection تبع الـ U في اتجاه مين؟
+
+471
+01:02:09,520 --> 01:02:14,960
+في اتجاه المتجه V وهذا هو المطلوب الأول من السؤال
+
+472
+01:02:14,960 --> 01:02:20,320
+المطلوب الثاني قل لي هتلي scalar component of U in
+
+473
+01:02:20,320 --> 01:02:25,720
+the direction of V يعني مين؟ يعني طول الـ U في
+
+474
+01:02:32,610 --> 01:02:40,430
+على طول ال V يبقى نمرة V بعدين بقوله V is scalar
+
+475
+01:02:40,430 --> 01:02:50,470
+component اللي بده يهيأ لطول U في cosine الزاوية
+
+476
+01:02:50,470 --> 01:02:53,850
+تيتا أو U dot
+
+477
+01:03:00,120 --> 01:03:05,920
+يضط ال V هيو جدام الخطوة الأولى لو سالب عشرة يبقى
+
+478
+01:03:05,920 --> 01:03:14,660
+سالب عشرة على طول ال Vطبعا احنا هنا الجدر التربية
+
+479
+01:03:14,660 --> 01:03:22,920
+اللي V ضد V V ضد V يبقى سلب عشرة V ضد V اللي هو
+
+480
+01:03:22,920 --> 01:03:31,240
+جدار بخمسين تحت الجدر يبقى سلب عشرة على خمسين لير
+
+481
+01:03:39,490 --> 01:03:43,950
+إذا مش عاجبك جدر اتنين في المقام بنقدر نوديه في
+
+482
+01:03:43,950 --> 01:03:49,310
+الـ bus عن طريق ضرب في جدر اتنين على جدر اتنين
+
+483
+01:03:49,310 --> 01:03:53,970
+يعني كده ضرب في كده شبنة في واحد صحية يبقى هذا
+
+484
+01:03:53,970 --> 01:04:01,930
+بيطلع كده سالب جدر اتنين ل scalar component تبع ال
+
+485
+01:04:01,930 --> 01:04:07,570
+U في اتجاه L بقيت عندنا في هذا ال section نقطة
+
+486
+01:04:09,950 --> 01:04:19,330
+على صورة الـ remark أث تانية يبقى writing vector
+
+487
+01:04:19,330 --> 01:04:28,030
+كتابة متجة as a sum of
+
+488
+01:04:28,030 --> 01:04:32,530
+orthogonal vectors
+
+489
+01:04:38,360 --> 01:04:42,360
+كتابة من اتجارات اتجارات اتجارات اتجارات اتجارات
+
+490
+01:04:42,360 --> 01:05:07,580
+اتجارات اتجارات اتجارات
+
+491
+01:05:08,100 --> 01:05:17,120
+or two orthogonal vectors
+
+492
+01:05:17,120 --> 01:05:20,260
+vectors
+
+493
+01:05:20,260 --> 01:05:27,060
+as follows اتل
+
+494
+01:05:27,060 --> 01:05:37,220
+ال U يساوي ال projection تبع ال U اتجاه ال V زائد
+
+495
+01:05:42,500 --> 01:05:54,620
+في اتجاه الـ V طبعا
+
+496
+01:05:54,620 --> 01:06:02,640
+سؤال كيف تم ذلك؟ مش هيك؟ لاجب أقوله كويس لو أنا
+
+497
+01:06:02,640 --> 01:06:10,120
+بنات قلت هذا المتجه U و روحت قلت هذا المتجه V و
+
+498
+01:06:10,120 --> 01:06:12,140
+جينا من هنا نزلنا عمون
+
+499
+01:06:30,020 --> 01:06:37,800
+البداية أخد جمع المتجهات هندسيا يبقى بقى اللي بقول
+
+500
+01:06:37,800 --> 01:06:45,380
+لو جت فترت هنا متجه يبقى بصية ال projection وهذا
+
+501
+01:06:45,380 --> 01:06:50,120
+المتجه في اتجاه دوري واحد يبقى الجامع الاتنين
+
+502
+01:06:50,120 --> 01:06:54,000
+بعطين المتجه الذي يقفل المثلث في الاتجاه الدوري
+
+503
+01:06:54,000 --> 01:06:56,000
+المضاد
+
+504
+01:07:09,680 --> 01:07:14,700
+المتجه التاني اللي عندنا هذا اللي الله أعلم منه
+
+505
+01:07:14,700 --> 01:07:23,020
+بده ساوي من؟ بده ساوي الـU إذا هذا المتجه اللي أنا
+
+506
+01:07:23,020 --> 01:07:29,400
+مش عارفه بده أعرف منه هو عبارة عن الـU ناقص ال
+
+507
+01:07:29,400 --> 01:07:35,320
+projection يبقى هذا المتجه عبارة عن الـU ناقص ال
+
+508
+01:07:35,320 --> 01:07:37,540
+projection تبع الـU
+
+509
+01:07:42,280 --> 01:07:50,260
+هو تعاملين يبقى هذا هو الـU ناقص لـprojection تبع
+
+510
+01:07:50,260 --> 01:07:57,120
+الـU على V إذا المتجه U هو عبارة عن الـprojection
+
+511
+01:07:57,120 --> 01:08:02,550
+زي هذا فعلا أنت هذا سرد و هذا موجةلو جمعتهم مع
+
+512
+01:08:02,550 --> 01:08:07,470
+السلامة بيظلمين عندى، بس المتجه يهيأو يهيأو يهيأو
+
+513
+01:08:07,470 --> 01:08:12,110
+طيب انا بديش يقو الصياغة هذه، بدي أصيغه صياغة
+
+514
+01:08:12,110 --> 01:08:15,090
+عملية، مش هنصيغه صياغة عملية
+
+515
+01:08:33,750 --> 01:08:39,890
+زي ايه؟ اين السائلة؟
+
+516
+01:08:39,890 --> 01:08:46,450
+انا
+
+517
+01:08:46,450 --> 01:08:52,550
+بجيبش اطوال في ثغور، انا بجيب متجهات، جمع اتجاهي
+
+518
+01:08:52,550 --> 01:08:58,490
+زي القوة، محصلة القوة، يبقى كأن انا عندي الدكتور
+
+519
+01:08:59,250 --> 01:09:07,030
+بجيب اشطول بقولك بجيب محصلات متجهات هذا متجه وهذا
+
+520
+01:09:07,030 --> 01:09:12,550
+متجه يبقى تحصل هو المتجه الذي يقفل المثلث في اتجاه
+
+521
+01:09:12,550 --> 01:09:17,570
+الدور المضادة تمام؟ هو بحالك بعد ما نخلص الحل
+
+522
+01:09:17,570 --> 01:09:23,070
+الحين تمام؟ يبقى بنرجع مرة تانية زائد ال U
+
+523
+01:09:37,540 --> 01:09:41,940
+هل اتنين هدول متعمدين ولا لأ؟ بقول اه والله على
+
+524
+01:09:41,940 --> 01:09:49,080
+الرسم هذا وهذا هم متعمدين صحيح ولا لأ؟ إحنا ال
+
+525
+01:09:49,080 --> 01:09:54,860
+vector يستطعنا كتابته على vector في اتجاه ال V
+
+526
+01:10:01,570 --> 01:10:08,370
+هذا الرقم ماله مضاعفات ال V يبقى دوام في اتجاه ال
+
+527
+01:10:08,370 --> 01:10:13,430
+V او parallel to V موازن لل V يبقى هذا
+
+528
+01:10:32,810 --> 01:10:37,930
+عمودي على مين؟ عمودي على V
+
+529
+01:11:02,200 --> 01:11:06,300
+ماذا تجاهل فيه؟
+
+530
+01:11:06,300 --> 01:11:10,960
+والله إذا ضد هذا طلع zero بيكونوا اتنين هدول فعلا
+
+531
+01:11:10,960 --> 01:11:13,080
+orthogonal، مظبوط؟
+
+532
+01:11:37,070 --> 01:11:44,790
+في bottle نيجي الأن هذا رقم ولا لا، بروح مع الرقم
+
+533
+01:11:44,790 --> 01:11:53,170
+اللي تحت، قايلة، هذا الكلام بده يستويإبدالية صحيح
+
+534
+01:11:53,170 --> 01:11:59,830
+ولا لأ؟ يبقى هذا كأن ال U ضد ال V نقص ال U ضد ال V
+
+535
+01:11:59,830 --> 01:12:04,430
+اللي دلت فوق يبقى كده إيش النتج؟ سافر يبقى هذول
+
+536
+01:12:04,430 --> 01:12:08,710
+اتنين في كرة ثقيلة هذا السطر اللي كتبنالك محطوط
+
+537
+01:12:08,710 --> 01:12:13,870
+عندك في الكتاب على صيغة سؤال في التمرين يبقى هاي
+
+538
+01:12:13,870 --> 01:12:17,690
+حد نلالك السؤال واحنا بنشرح الجزء النظري إذا يا
+
+539
+01:12:17,690 --> 01:12:25,760
+بنات من الآن فصاعداأي vector بقدر أكتبه بدلالة جزء
+
+540
+01:12:25,760 --> 01:12:31,020
+في اتجاه ال vector آخر وجزء ثاني عمودي على هذا ال
+
+541
+01:12:31,020 --> 01:12:36,900
+vector الآخر وبتيجي مسائل أحنا في مسائل التمرين
+
+542
+01:12:36,900 --> 01:12:37,940
+على هذا الموضوع
+
+543
+01:12:49,170 --> 01:12:53,030
+مثال على الكلام اللي احنا جايلينه هذا
+
+544
+01:14:00,840 --> 01:14:14,760
+تُب V بده يساوي I زيدي اتنين G ناقص K and a vector
+
+545
+01:14:14,760 --> 01:14:17,520
+Orthogonal
+
+546
+01:14:35,450 --> 01:14:43,930
+درجع لسؤالنا مرة ثانية، اكتبلي المتجه U كمجموع two
+
+547
+01:14:43,930 --> 01:14:50,030
+vectors، واحد منهم موازي ل V وواحد تاني عمودي على
+
+548
+01:14:50,030 --> 01:14:53,390
+V، الموازي ل V هو مين يا بنات؟
+
+549
+01:15:02,160 --> 01:15:08,280
+العمودي هو U نقص ال projection يبقى العمودي الفقري
+
+550
+01:15:08,280 --> 01:15:12,860
+في المثلة هو إيجاد ال projection يبقى باجي بقول ال
+
+551
+01:15:12,860 --> 01:15:13,660
+projection
+
+552
+01:15:29,050 --> 01:15:37,330
+متج ال U ضد ال V بيجي ال U
+
+553
+01:15:37,330 --> 01:15:40,370
+ضد
+
+554
+01:15:40,370 --> 01:15:44,750
+ال V بيجي
+
+555
+01:15:44,750 --> 01:15:49,390
+ال U
+
+556
+01:15:49,390 --> 01:15:52,430
+ضد
+
+557
+01:15:52,430 --> 01:15:53,850
+ال V بيجي ال U ضد ال V بيجي ال U ضد ال V بيجي ال U
+
+558
+01:15:53,850 --> 01:15:53,910
+ضد ال V بيجي ال U ضد ال V بيجي ال U ضد ال V بيجي
+
+559
+01:15:53,910 --> 01:15:54,090
+بيجي ال U ضد ال V بيجي ال U ضد ال V بيجي ال U ضد
+
+560
+01:15:54,090 --> 01:15:54,250
+ال V بيجي ال U ضد ال V بيجي ال U ضد ال V بيجي ال U
+
+561
+01:15:54,250 --> 01:15:55,410
+ضد ال V بيجي ال U ضد ال V بيجي ال U ضد ال V بيجي
+
+562
+01:15:55,410 --> 01:15:55,570
+ال U ضد ال V بيجي
+
+563
+01:16:00,130 --> 01:16:07,850
+كله في اتجاه من ال V يبقى هذا الكلام بده يساوي 16
+
+564
+01:16:07,850 --> 01:16:20,890
+و12 28 على 6 في ال V بنزله زي ما هو I نين G ناقص K
+
+565
+01:16:20,890 --> 01:16:26,210
+طبعا هذه بتكسب على كده عشان اتنين هو اربعتاشرعلى
+
+566
+01:16:26,210 --> 01:16:37,110
+ثلاثة وهو 14 على ثلاثة في I نين جي ناقس كي بناء
+
+567
+01:16:37,110 --> 01:16:46,810
+عليه ال vector U بيسافر ل projection تبع ال U على
+
+568
+01:16:46,810 --> 01:16:50,390
+V زائد ال U
+
+569
+01:16:57,330 --> 01:17:03,290
+هذا اللي هو في main vector parallel to v هو هذا
+
+570
+01:17:03,290 --> 01:17:08,930
+orthogonal to v ال projection حسبناها يجاهز اللي
+
+571
+01:17:08,930 --> 01:17:15,790
+هو اربعتاشر على تلاتة I زائد تمانية وعشرين على
+
+572
+01:17:15,790 --> 01:17:19,050
+تلاتة J نقص اربعتاشر
+
+573
+01:17:37,060 --> 01:17:44,600
+ناقص اللي هو اربعتاشر على تلاتة I ناقص تمانية
+
+574
+01:17:44,600 --> 01:17:51,820
+وعشرين على تلاتة J ناقص تمانية وعشرين على تلاتة J
+
+575
+01:17:51,820 --> 01:18:00,680
+زائد اربعتاشر على تلاتة K دخل اشارة السالب على كل
+
+576
+01:18:00,680 --> 01:18:04,700
+component من هذه ال components يبقى النتيجة
+
+577
+01:18:15,860 --> 01:18:22,800
+هذا الـ vector الأول زرع بدا نجمع كل مركبة مع
+
+578
+01:18:22,800 --> 01:18:31,280
+نظيرتها J ناقص اتناشر K ناقص ال projection ناقص
+
+579
+01:18:31,280 --> 01:18:33,080
+اللي هو اربعة
+
+580
+01:18:54,360 --> 01:18:59,580
+من هذه ال components يبقى النتيجة اربع تاشر على
+
+581
+01:18:59,580 --> 01:19:06,580
+تلاتة I تمانية وعشرين على تلاتة J ناقص اربع تاشر
+
+582
+01:19:06,580 --> 01:19:15,500
+على تلاتة K هذا ال vector الأول زار نجمع كل مركبة
+
+583
+01:19:15,500 --> 01:19:21,180
+مع نظيرتها تلاتة في تمانية باربعة وعشرين شيل منهم
+
+584
+01:19:21,180 --> 01:19:23,980
+اربع تاشر بظل عشرة
+
+585
+01:19:31,120 --> 01:19:36,900
+الجيل التاني تلاتة في أربعة باتناشر بالموجب من
+
+586
+01:19:36,900 --> 01:19:40,680
+تمانية وعشرين إلى ستة عشر يبقى النار
+
+587
+01:19:46,270 --> 01:19:52,310
+بعدها تلاتة في اتناش بستة وتلاتين بدنا نشيل منها
+
+588
+01:19:52,310 --> 01:19:57,130
+اتناش بظل اربعة وعشرين على تلاتة اللي هو تمانية
+
+589
+01:19:57,130 --> 01:20:04,670
+يبقى ناقص تمانية كيلو الشكل اللي عندها يبقى هنا
+
+590
+01:20:04,670 --> 01:20:12,050
+راجعها كمان مرة يا بنات يبقى هذه بصير مرة تانية
+
+591
+01:20:13,050 --> 01:20:18,310
+عندك تلاتة في اتناش في ستة و تلاتين في ستة و
+
+592
+01:20:18,310 --> 01:20:22,410
+تلاتين في ستة و تلاتين في ستة و تلاتين في ستة و
+
+593
+01:20:22,410 --> 01:20:25,750
+تلاتين في ستة و تلاتين في ستة و تلاتين في ستة و
+
+594
+01:20:25,750 --> 01:20:26,730
+تلاتين في ستة و تلاتين في ستة و تلاتين في ستة و
+
+595
+01:20:26,730 --> 01:20:27,870
+تلاتين في ستة و تلاتين في ستة و تلاتين في ستة و
+
+596
+01:20:27,870 --> 01:20:29,230
+تلاتين في ستة و تلاتين في ستة و تلاتين في ستة و
+
+597
+01:20:29,230 --> 01:20:29,970
+تلاتين في ستة و تلاتين في ستة و تلاتين في ستة و
+
+598
+01:20:29,970 --> 01:20:33,450
+تلاتين في ستة و تلاتين في ستة و تلاتين في ستة و
+
+599
+01:20:33,450 --> 01:20:34,770
+تلاتين في ستة و
+
+600
+01:20:46,550 --> 01:20:50,690
+طبعا، فيه، يبقى معاناته متجلة، اتنين هذول بقى لهم
+
+601
+01:20:50,690 --> 01:20:57,850
+اتنين متعامدين لحد هنا stop انتهاء ال section
+
+602
+01:20:57,850 --> 01:21:05,930
+والان بدنا نعطيكوا أرقام المسائل المطموض حلها سؤال
+
+603
+01:21:05,930 --> 01:21:07,970
+اللي بدأ أسالكوا ياه روحتوا على ال discussion
+
+604
+01:21:07,970 --> 01:21:12,690
+السبوع الماضي عليه
+
+605
+01:21:12,690 --> 01:21:14,390
+حد المناقش عنكم
+
+606
+01:21:23,380 --> 01:21:28,140
+يبقى ده انا قدناقيها لو ما جت coach بتروح الدور و
+
+607
+01:21:28,140 --> 01:21:33,480
+عليها و بلغوني هه اجت ولا ماجتش يبقى exercises
+
+608
+01:21:33,480 --> 01:21:41,040
+اتناشر تلاتة المسائل التالية تلاتة، خمسة، سبعة،
+
+609
+01:21:41,040 --> 01:21:47,520
+احداشر، تلاتاشر، سبعتاشر، تسعة و اتشرين
+
+610
+01:22:16,240 --> 01:22:28,100
+يبقى الآن نروح ل section 12-4 12-4 اللي هو نقرص او
+
+611
+01:22:28,100 --> 01:22:33,400
+vector product
+
+612
+01:22:33,400 --> 01:22:38,480
+العلوان
+
+613
+01:22:38,480 --> 01:22:43,300
+اللي احنا حاطينه اسمه معاه يعنيش لما نقطر two
+
+614
+01:22:43,300 --> 01:22:43,920
+vectors
+
+615
+01:22:49,160 --> 01:22:53,200
+قليل لذلك بناروح نكتب ال definition اللي عندنا هذا
+
+616
+01:22:53,200 --> 01:22:58,580
+و بعدين ناخد بعض الملاحظات عليه هيبقى definition
+
+617
+01:22:58,580 --> 01:23:08,200
+هحطه الصيغة الأولى اللي هي V a cross أو ال vector
+
+618
+01:23:08,200 --> 01:23:14,340
+a product of
+
+619
+01:23:14,340 --> 01:23:17,900
+two vectors of two
+
+620
+01:23:24,650 --> 01:23:37,330
+الـ V is defined by العرفة التالية U cross ال V في
+
+621
+01:23:37,330 --> 01:23:43,810
+درجة ساوية قول ال U في طول ال V في صين الزاوية
+
+622
+01:23:43,810 --> 01:23:48,090
+تيتا في اتجاه متجه الوحدة L
+
+623
+01:24:09,330 --> 01:24:15,290
+أو الـ V
+
+624
+01:24:15,290 --> 01:24:17,990
+عمودي على الإتنين
+
+625
+01:24:29,330 --> 01:24:35,430
+خلّينا نطرح الشوية للتالت، هل يمكن للـ cross
+
+626
+01:24:35,430 --> 01:24:42,930
+product لـ two vectors يطلع zero؟ ممكن، طيب الـ
+
+627
+01:24:42,930 --> 01:24:47,650
+zero هذا هو zero vector ولا zero شكلها؟ Zero
+
+628
+01:24:47,650 --> 01:24:48,210
+vector
+
+629
+01:24:56,050 --> 01:25:02,570
+بدي أضع هذا في صيغة الملاحظة التالية لو جيها تقولش
+
+630
+01:25:02,570 --> 01:25:09,050
+لك if ال U cross ال V بده يسوى ال zero vector
+
+631
+01:25:30,670 --> 01:25:36,310
+واحد منهم ممكن يكون zero او كلاهما ب zero الاحتمال
+
+632
+01:25:36,310 --> 01:25:41,550
+الثاني هذا الاحتمال الاول الاحتمال الثاني ممكن
+
+633
+01:25:41,550 --> 01:25:46,430
+يكونوا ادو ال zero او
+
+634
+01:25:46,430 --> 01:25:54,960
+180 يعني اتنين معاهم يكونوا are parallelوالتوازين
+
+635
+01:25:54,960 --> 01:25:58,700
+الانطباق يا بنات والتوازن اللي اكبره اتنين ارضه
+
+636
+01:25:58,700 --> 01:26:01,900
+سيء من ان ال vector vector انجلوب من مكان الى اي
+
+637
+01:26:01,900 --> 01:26:08,320
+مكان اخر موازن لهو يسوى في المقدار ال جباجي بقول
+
+638
+01:26:08,320 --> 01:26:15,280
+هنا يسوى zero then
+
+639
+01:26:15,280 --> 01:26:27,970
+lu and v are parallelthat is the
+
+640
+01:26:27,970 --> 01:26:36,550
+angle between you
+
+641
+01:26:36,550 --> 01:26:41,030
+and ال V is
+
+642
+01:26:47,350 --> 01:26:50,910
+يبقى لو كانت الزاوية بينهم zero او مية و تمانين
+
+643
+01:26:50,910 --> 01:26:57,230
+درجة بقول اتنين هدول مالهم متوازنة طيب لو جيت و
+
+644
+01:26:57,230 --> 01:27:02,150
+قولت هذا ال vector U و هذا ال vector التاني اللي
+
+645
+01:27:02,150 --> 01:27:06,670
+هو V و الزاوية اللي بينهم تيتا هي الزاوية اللي
+
+646
+01:27:06,670 --> 01:27:12,030
+عندها هتشوف وين ال cross product يبقى ال cross
+
+647
+01:27:12,030 --> 01:27:18,570
+product هو عبارة عن متجةعمودي على الاتنين يوجه هذا
+
+648
+01:27:18,570 --> 01:27:24,410
+U cross ال V الزاوية اللي عملها هنا زاوية قائمة
+
+649
+01:27:24,410 --> 01:27:30,130
+والزاوية هذه كمان مين زاوية قائمة زي و لا تشبه ال
+
+650
+01:27:30,130 --> 01:27:34,250
+corner اللي عندنا هذا عمودي على هذا ال vector و
+
+651
+01:27:34,250 --> 01:27:38,290
+عمودي على مين على ال vector إذا لو ضربت ال vector
+
+652
+01:27:38,290 --> 01:27:42,740
+هذا في ال vector هذا crossود يطلع vector منطبق على
+
+653
+01:27:42,740 --> 01:27:45,820
+ال corner اللي هناك تماماً بالضبط
+
+654
+01:28:09,230 --> 01:28:15,690
+بتساوي U1 في اتجاه I U2 في اتجاه J U3 في اتجاه K
+
+655
+01:28:27,200 --> 01:28:32,820
+فد ال U cross ال V، صيغة تانية، مابديش أقول طول
+
+656
+01:28:32,820 --> 01:28:36,560
+الأول في طول التاني في جيب الزاوية بينهما في اتجاه
+
+657
+01:28:36,560 --> 01:28:41,480
+M وإنما بطلع الشغل عملي بدلالة ال I و ال G و ال K
+
+658
+01:28:41,480 --> 01:28:47,800
+سمعت أظن بال determinants المحددات، طبعا كل كنتوا
+
+659
+01:28:47,800 --> 01:28:53,880
+عالي في الثانوية واخدتوا المصوفاتهذا المحدد تمام
+
+660
+01:28:53,880 --> 01:29:00,280
+يبقى هذا عبارة عن المحدد التاني بحط الصف الأول ال
+
+661
+01:29:00,280 --> 01:29:08,100
+I و ال J و ال K بعد هيك بحط مركبات المتجه الأول
+
+662
+01:29:08,100 --> 01:29:17,320
+اللي هو U U1 U2 U3 مركبات المتجه التاني V1
+
+663
+01:29:20,090 --> 01:29:27,150
+لو فكيت هذا المحدد بيطلع المتجر بدلالة I وJ وK
+
+664
+01:29:27,150 --> 01:29:32,690
+وهذا ما سناخده من خلال المثال أو من خلال بعض
+
+665
+01:29:32,690 --> 01:29:38,130
+الأمثلة توضح كيف بدنا أو يذكركوا تذكير بكيف يتفك
+
+666
+01:29:38,130 --> 01:29:44,290
+هذا المحدد تمام؟ إذا نعطيكي المثال التالي
+
+667
+01:29:50,160 --> 01:30:03,900
+أول مثال بيقول الف ال U تساوي اتنين I اتنين I ناقص
+
+668
+01:30:03,900 --> 01:30:17,020
+J زائد K and ال V تساوي اربعة I زائد اتنين J
+
+669
+01:30:32,630 --> 01:30:39,050
+A unit vector
+
+670
+01:30:39,050 --> 01:30:48,650
+متجه واحدة orthogonal to
+
+671
+01:30:48,650 --> 01:30:54,070
+both U and V
+
+672
+01:31:12,720 --> 01:31:20,560
+على التعريف رقم 2 يبقى بدي اعمل determinant I وJ
+
+673
+01:31:20,560 --> 01:31:25,620
+وK بدي احط مركبات المتجه الاول اتنين
+
+674
+01:31:37,430 --> 01:31:43,670
+الثاني في الأول والمتجه الأول بحطته بعدها هتطلع
+
+675
+01:31:43,670 --> 01:31:49,910
+نفسي النتيجة بس بإشارة وخالفة في الإشارة طبعا أخدت
+
+676
+01:31:49,910 --> 01:31:51,590
+من الخواص المحدد في ثانوية
+
+677
+01:32:10,560 --> 01:32:16,860
+يبقى ماجي بيقول هاي اي فيه بروح نشطة بالصف اللى
+
+678
+01:32:16,860 --> 01:32:22,400
+موجود فيه اي و اللى عاوز بيبقى هنا جداش مكس تين ا
+
+679
+01:32:22,400 --> 01:32:27,540
+الرئيسي هاي يبقى عندك المحدد الصغير هذا يبقى حاسب
+
+680
+01:32:27,540 --> 01:32:29,120
+ده اربع ناس القطة الرئيسية
+
+681
+01:32:41,270 --> 01:32:48,630
+في اشطر بصفه وكذلك عامل من اتنين في اتنين باربع
+
+682
+01:32:48,630 --> 01:32:51,150
+ناقص اربع في واحد
+
+683
+01:33:12,980 --> 01:33:18,900
+أربعة زائد أربعة يبقى أربعة زائد أربعة بالشكل اللي
+
+684
+01:33:18,900 --> 01:33:25,920
+عندنا يبقى صار عندنا ناقص أربعة I هذا بيروح ب Zero
+
+685
+01:33:25,920 --> 01:33:35,720
+زائد تمانية K يبقى هذا زائد تمانية K لغوية قيمة
+
+686
+01:33:35,720 --> 01:33:37,040
+المحدد تماما
+
+687
+01:33:40,940 --> 01:33:46,780
+إذا صار عندنا شكل المحدد ناقص أربع I زائد تمانية
+
+688
+01:33:46,780 --> 01:33:50,380
+كيلو المطموب الأول المطموب التاني قال لي هاتلي
+
+689
+01:33:50,380 --> 01:33:57,080
+unit vector orthogonal لمن للإتنين هذا المتجه مش
+
+690
+01:33:57,080 --> 01:34:05,680
+هو عمودي على الإتنين يبقى هنا this vector is
+
+691
+01:34:05,680 --> 01:34:10,140
+orthogonal to
+
+692
+01:34:11,690 --> 01:34:21,790
+بعض الـ U و الـ V إذا المطلوب التاني نمر بيه قال
+
+693
+01:34:21,790 --> 01:34:26,390
+لي هاتي unit vector في الهدايا، يقول إيش بدالي؟
+
+694
+01:34:26,390 --> 01:34:29,890
+بدي أقسم هذا المتجر على طولي
+
+695
+01:34:41,950 --> 01:34:48,570
+على طول الـ U x V الـ U x V هو الناقص 4I
+
+696
+01:35:02,250 --> 01:35:08,710
+يبقى U cross
+
+697
+01:35:08,710 --> 01:35:14,590
+V على طول U cross V يبقى نقطة أربعية زي 8 على مربع
+
+698
+01:35:14,590 --> 01:35:21,130
+عدد 16 مربع عدد 64هذا كله عقداش على تمانين يبقى
+
+699
+01:35:21,130 --> 01:35:28,490
+ناقص أربعة I زائد تمانية K مخسوما على جذر التمانين
+
+700
+01:35:28,490 --> 01:35:34,270
+اللي هي ستاش في خمسة مظبوط ستاش في خمسة التمانين
+
+701
+01:35:34,270 --> 01:35:40,910
+يبقى أربعة جذر خمسة طيب بناء عليه هذا الكلام يبدو
+
+702
+01:35:40,910 --> 01:35:42,670
+يساوي ناقص
+
+703
+01:35:51,740 --> 01:35:56,260
+يا ناس لو .. لو روحت جبت طول المتجه هذا بتطلع واحد
+
+704
+01:35:56,260 --> 01:36:02,760
+صحيح؟ جربي ربعي هذا .. ربعي هذا باربع أخمس يبقى
+
+705
+01:36:02,760 --> 01:36:07,040
+خمس أخمس واحد صحيح؟ آخر مثال صغير
+
+706
+01:36:47,920 --> 01:36:52,610
+بقول لو عملت cross product لمتجهينو الـ dot
+
+707
+01:36:52,610 --> 01:37:00,150
+product لمتجهين و جبت مربع طول ل cross product و
+
+708
+01:37:00,150 --> 01:37:04,410
+مربع ال dot product و جماعة بده يطلع طول المتجه U
+
+709
+01:37:04,410 --> 01:37:08,850
+تربية فطول المتجه V تربية هذا اللي عايزين نتحدث
+
+710
+01:37:08,850 --> 01:37:13,110
+عنه إذا بدنا نحاول نمسك أحد الطرفين و نوصل للطرف
+
+711
+01:37:13,110 --> 01:37:17,330
+الآخرأول نمسك أحد الطرفين و نوصله إلى نقطة و نمسك
+
+712
+01:37:17,330 --> 01:37:21,450
+الطرف الأخر و نوصله إلى نفس النقطة خلّينا نمسك
+
+713
+01:37:21,450 --> 01:37:28,110
+الطرف الأول اللي هو الـU cross الـV لكل تربيع زائد
+
+714
+01:37:28,110 --> 01:37:34,770
+U dot V لكل تربيع يساوي هذا بنادر اللي هو طول الـU
+
+715
+01:37:34,770 --> 01:37:42,570
+في طول الـV في صين الزاوية θ إذا لما قال لتربيع
+
+716
+01:37:42,570 --> 01:37:51,290
+بسيطوهذا تربيع وهذه تربيع ثمين في الطول تبع متجه
+
+717
+01:37:51,290 --> 01:38:00,130
+الوحدة والطول تبع متجه الوحدة الكل تربيع مش عرفنا
+
+718
+01:38:00,130 --> 01:38:04,530
+قبل شوية ال cross product طول ال U في طول ال V في
+
+719
+01:38:04,530 --> 01:38:08,370
+صين الزاوية في اتجاه متجه الوحدة N إذا لما أقول
+
+720
+01:38:08,370 --> 01:38:12,430
+هذا مربع الطول يبقى أخدت الأطوال كلها وربعتها
+
+721
+01:38:23,900 --> 01:38:29,700
+لكن هذا يصير تربيع يبقى هذا تصير تربيع تربيع تربيع
+
+722
+01:38:29,700 --> 01:38:36,420
+كده هذا طول البنات؟ واحد صحيح بهذا خلاص في عامل
+
+723
+01:38:36,420 --> 01:38:43,080
+مشترك ما بين الطرفين يبقى U تربيع طول ال U تربيع
+
+724
+01:38:43,080 --> 01:38:47,440
+طول ال V تربيع بظل Sin تربيع ثيتا
+
+725
+01:38:51,930 --> 01:38:58,210
+هنا بواحد صحيح يبقى بصير طول ال U تربية فطول ال V
+
+726
+01:38:58,210 --> 01:39:05,750
+تربية ما هو المطلوب؟ خلاصنا؟ يبقى لحد هنا وقفنا
+
+727
+01:39:05,750 --> 01:39:10,750
+المرة الجاية بدنا ناخد ان شاء الله تعالى خواص ل
+
+728
+01:39:10,750 --> 01:39:11,690
+cross product
+
+729
+01:39:21,410 --> 01:39:27,090
+أو أرضية للشيء اللي بدنا نشرها حولها بلاد فماجية
+
+730
+01:39:27,090 --> 01:39:31,270
+تحتروا على الارض بالضبط لإنك تاخدها خمس دقايق، عشر
+
+731
+01:39:31,270 --> 01:39:35,390
+دقايق، خمس ساعة، خمس ساعة، فلاش أقفل البابير و
+
+732
+01:39:35,390 --> 01:39:39,530
+أخليكي برا هاي يا ودي يا بني يا بني يا بني يا بني
+
+733
+01:39:39,530 --> 01:39:40,490
+يا بني يا بني يا بني يا بني يا بني يا بني يا بني
+
+734
+01:39:40,490 --> 01:39:44,570
+يا
+
+735
+01:39:44,570 --> 01:39:45,410
+بني
+
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/YDVEQJcaKaA_raw.srt b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/YDVEQJcaKaA_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..a42a9cf56671d183262d7b67307f864e7eddbe44
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/YDVEQJcaKaA_raw.srt
@@ -0,0 +1,2944 @@
+1
+00:00:08,500 --> 00:00:12,800
+يبقى موضوعنا اليوم ان شاء الله و تعالى موضوع the
+
+2
+00:00:12,800 --> 00:00:18,420
+top او scholar product يعني حاصل الضرب القياسي
+
+3
+00:00:18,420 --> 00:00:25,050
+لمتجهينهذا يوحي تساؤل آخر، هل هناك حاصل ضرب
+
+4
+00:00:25,050 --> 00:00:30,750
+إتجاهي؟ الإجابة نعم، إذا إحنا عندنا نوعين من
+
+5
+00:00:30,750 --> 00:00:35,290
+الضرب، الضرب القياسي والضرب الإتجاهي، اللي أخدناه
+
+6
+00:00:35,290 --> 00:00:40,950
+المرة الماضية كان حاصل ضرب scalar في vector، لكن
+
+7
+00:00:40,950 --> 00:00:44,730
+vector في vector ماتكلمناش في المرة الماضية، تمام؟
+
+8
+00:00:44,900 --> 00:00:48,820
+إذا اننا ناخد اليوم ال dot أو ال scholar product،
+
+9
+00:00:48,820 --> 00:00:53,360
+هنعطي تعريفنا ال dot أو ال scholar product ثم
+
+10
+00:00:53,360 --> 00:00:58,700
+كيفية الشغل في هذا المجال، تبقى هنبدأ أول شيء بال
+
+11
+00:00:58,700 --> 00:01:04,480
+definition، تبقى باجي بقول هنا ال definition، the
+
+12
+00:01:04,480 --> 00:01:04,900
+dot
+
+13
+00:01:14,670 --> 00:01:22,890
+of two vectors ال
+
+14
+00:01:22,890 --> 00:01:33,650
+U بده يساوي U1 و U3 و U2 و U3 and ال V بده يساوي
+
+15
+00:01:33,650 --> 00:01:41,830
+V1 و V2 و V3 is defined
+
+16
+00:01:52,600 --> 00:01:59,760
+بنضرب كل مركبة في نظيرتها وبنجمع هذا العدد بيعطيني
+
+17
+00:01:59,760 --> 00:02:09,000
+رقم مش vector يبقى باجي بقول U1 V1 زائد U2 V2 زائد
+
+18
+00:02:09,000 --> 00:02:17,280
+U3 V3 هذول حصل ضرب مركبات إذا هذا بيعطيني رقمإذاً
+
+19
+00:02:17,280 --> 00:02:22,500
+الرقم اللي عندنا هذا هه هو عبارة عن حاصل الضرب
+
+20
+00:02:22,500 --> 00:02:27,400
+القياسي لمنتجين لما يقول قياسي النتج يسوي كمية
+
+21
+00:02:27,400 --> 00:02:33,200
+قياسية طبعا هناك تعريف آخر يبقى هذا بتعتبر التعريف
+
+22
+00:02:33,200 --> 00:02:43,140
+رقمأقم اتنين ال u dot v بده يساوي طول ال u في طول
+
+23
+00:02:43,140 --> 00:02:51,200
+ال v في cosine زاوية theta where theta is the
+
+24
+00:02:51,200 --> 00:02:57,760
+angle between ال
+
+25
+00:02:57,760 --> 00:03:00,340
+u and ال v
+
+26
+00:03:07,510 --> 00:03:14,350
+إذا هناك صيغتان لحاصل الضرب القياسي لمتجههم الصيغة
+
+27
+00:03:14,350 --> 00:03:19,410
+الأولى بضرب الكل مركبة في نظيرتها و باجمع هيعطينا
+
+28
+00:03:19,410 --> 00:03:24,790
+ناتج رطل الصيغة الثانية طول المتجه الأول في طول
+
+29
+00:03:24,790 --> 00:03:30,050
+المتجه الثاني في جيب تمام الزاوية المحصورة بينهما
+
+30
+00:03:31,320 --> 00:03:36,320
+طبعا واضح انه محطتش قيود على هذه الزاوية السؤال هو
+
+31
+00:03:36,320 --> 00:03:40,840
+مدام هذا رقم لأن هذا الطول عبارة عن رقم الطول
+
+32
+00:03:40,840 --> 00:03:44,580
+الثاني عبارة عن رقم كوصين الزاوية كذلك عبارة عن
+
+33
+00:03:44,580 --> 00:03:50,660
+رقم لأن حاصر ضرب ثلاثة أرقام السؤال هو هل يمكن
+
+34
+00:03:50,660 --> 00:03:59,840
+لحاصر الضرب هذا أن يكون كمية ثالثة ممكن يكون ثقة
+
+35
+00:04:06,000 --> 00:04:11,280
+لأن هذا يبقى بدي أحط الكلام هذا في صيغة ال remark
+
+36
+00:04:11,280 --> 00:04:19,100
+التالف النقطة الأولىأفترضي بدي أجيب الزاوية ما بين
+
+37
+00:04:19,100 --> 00:04:22,780
+المتجهين اللي اتنين هدول اللي هي الزاوية θ بدي
+
+38
+00:04:22,780 --> 00:04:27,320
+أجيبها من مين من خلال العلاقة اللي عندنا هذه فبقدر
+
+39
+00:04:27,320 --> 00:04:33,620
+أقول هنا cosine الزاوية θ بدي أساوي U ضد ال V على
+
+40
+00:04:33,620 --> 00:04:39,440
+طول ال U في طول ال Vيبقى جسمت الطرفين على طول الـU
+
+41
+00:04:39,440 --> 00:04:45,360
+في طول الـV طب بدي الـθيتا زي ما درسنا في calculus
+
+42
+00:04:45,360 --> 00:04:52,200
+B بأثر بـcos inverse على الطرفين وبناء عليه هذا
+
+43
+00:04:52,200 --> 00:04:59,300
+بيصير أن الـθيتا تساوي cos inverse للرقم U ضد الـV
+
+44
+00:04:59,300 --> 00:05:02,500
+على طول الـU في طول الـV
+
+45
+00:05:08,710 --> 00:05:16,330
+ضد ال V ممكن يكون قيمة مجبة أكبر من الصفر واجتيش
+
+46
+00:05:16,330 --> 00:05:22,870
+هذا الكلام لو كانت الزاوية ثيتا زاوية حادة يبقى
+
+47
+00:05:22,870 --> 00:05:33,130
+هذا F ثيتا is an obtuse or acute angle
+
+48
+00:05:35,590 --> 00:05:39,950
+هيش acute angle زاوية حادة يعني محصورة من صفر
+
+49
+00:05:39,950 --> 00:05:44,130
+لغاية تسعين درجة وجيب تمام الزاوية حادة دائما او
+
+50
+00:05:44,130 --> 00:05:51,550
+ابدا positive يبقى اه اه لو جيت قلت هذا ال U هذا
+
+51
+00:05:51,550 --> 00:05:58,070
+ال V يبقى هذا ال U وهذا ال V وهذه الزاويتك على
+
+52
+00:05:58,070 --> 00:06:04,890
+سبيل المثال يبقى هذه زاوية حادة النقطة التالتةالـU
+
+53
+00:06:04,890 --> 00:06:10,890
+ضد الـV ممكن يكون less than zero يعني كمية سالبة
+
+54
+00:06:10,890 --> 00:06:19,810
+الكلام هذا بيحصل لو كان theta is an obtuse angle
+
+55
+00:06:19,810 --> 00:06:25,970
+obtuse angle يعني زاوية منفرجة يعني لو جيت رسمت
+
+56
+00:06:25,970 --> 00:06:31,000
+الزاوية فكانت الزاوية بالشكل هذايبقى هذا ال U و
+
+57
+00:06:31,000 --> 00:06:35,060
+هذا ال V و هذا الزاوية اللي هي ال object's angle
+
+58
+00:06:35,060 --> 00:06:40,360
+اللي هي الزاوية ثيتا طبعا في الربع الثاني جيب
+
+59
+00:06:40,360 --> 00:06:47,160
+التمام كمية صالبة وبالتالي ال dot product هيطلع
+
+60
+00:06:47,160 --> 00:06:50,420
+negative value اللي هو كمية صالبة
+
+61
+00:06:54,520 --> 00:07:00,180
+الـ V ممكن يساوي Zero ممكن يساوي Zero اقتناش إذا
+
+62
+00:07:00,180 --> 00:07:08,280
+الزاوية قائمة يبقى هذا الكلام F ثيتا تساوي باي على
+
+63
+00:07:08,280 --> 00:07:15,200
+اتنين وهذا الكلام F and
+
+64
+00:07:15,200 --> 00:07:19,740
+only F ال U and ال V
+
+65
+00:07:25,900 --> 00:07:30,640
+يبقى إذا كانوا المتجهات لاتنين متعمدين، يابانات
+
+66
+00:07:30,640 --> 00:07:33,780
+كلمة متعمد معناها perpendicular
+
+67
+00:07:51,070 --> 00:07:54,670
+المستقيمين متعامدان يبقى الـ two lines are
+
+68
+00:07:54,670 --> 00:08:01,590
+perpendicular يبقى
+
+69
+00:08:01,590 --> 00:08:05,910
+U ضد ال V بده يسوى Zero إذا كانت كذا تسوى بي على
+
+70
+00:08:05,910 --> 00:08:12,550
+اتنين أو ال U و ال V are orthogonalالنقطة الخامسة
+
+71
+00:08:12,550 --> 00:08:19,370
+لو جيت بناء عليه سألتك السؤال التالي وقلتك لو بدي
+
+72
+00:08:19,370 --> 00:08:27,840
+ال U ضد ال Uيبقى هذا الكلام يعطينا قداش طول ال U
+
+73
+00:08:27,840 --> 00:08:32,880
+في طول ال U في Cos الزاوية، قداش الزاوية بين
+
+74
+00:08:32,880 --> 00:08:38,000
+المتجة هو نفسه؟ Zero، Cos صفرة في قداش يا بنات؟
+
+75
+00:08:38,000 --> 00:08:45,480
+واحد، إذا هذا هيعطينا طول ال U تربيعطب لو بدى اجيب
+
+76
+00:08:45,480 --> 00:08:50,600
+طول ال U بدلالة ال dot إذا باخد ال square root
+
+77
+00:08:50,600 --> 00:08:56,560
+للطرفين يبقى هذا بدى يعطينا ان طول ال U بدى ساوي
+
+78
+00:08:58,970 --> 00:09:06,750
+أروت لل U ضد ال U لو بدى أحسب هذا بدلالة المركبات
+
+79
+00:09:06,750 --> 00:09:12,790
+فباجي بقول هذا الكلام يساوي ال U one تربيع زائد U
+
+80
+00:09:12,790 --> 00:09:21,110
+two تربيع زائد U three تربيعأذا الـ u ضد الـ u
+
+81
+00:09:21,110 --> 00:09:24,570
+بسوية طول الـ u في طول الـ u في الـ cosine الزاوية
+
+82
+00:09:24,570 --> 00:09:28,790
+الصفر اللي هو 1 صحيح إذا بصير أن هذا طول الـ u
+
+83
+00:09:28,790 --> 00:09:34,670
+تربيع لو بدأ أخد الجدر التربيع للطرفين يبقى طول
+
+84
+00:09:34,670 --> 00:09:40,770
+المتجه u يساوي ال square root للـ u ضد الـ u الـ u
+
+85
+00:09:40,770 --> 00:09:45,510
+ضد الـ u طبقا للتعريف اللي احنا كاتبينه بصير ال V1
+
+86
+00:09:45,510 --> 00:09:51,790
+هي U1و ال V2 هي U2 و ال V3 هي U3 إذا بيصير U1
+
+87
+00:09:51,790 --> 00:09:57,270
+square زائد U2 square زائد U3 square تحت ال square
+
+88
+00:09:57,270 --> 00:10:04,190
+root بيعطيني طول المتجه U قياسا على ذلك ممكن أروح
+
+89
+00:10:04,190 --> 00:10:11,570
+أحط مقطة زيادة من عند ال E6 لو جيت قلتلك I ضد I
+
+90
+00:10:13,220 --> 00:10:18,780
+كداش بده يساوي؟ هي بدل ال U ضد ال U بدأ أخد ال I
+
+91
+00:10:18,780 --> 00:10:23,800
+ضد ال I اللي هو طول الأول واحد وطول التاني واحد و
+
+92
+00:10:23,800 --> 00:10:28,160
+cosine الساوية صفرة بواحد يبقى بقداش واحد صحيح إذا
+
+93
+00:10:28,160 --> 00:10:34,680
+هذا بده يساوي ال J ضد ال J بده يساوي ال K ضد ال K
+
+94
+00:10:34,680 --> 00:10:36,420
+بده يساوي واحد صحيح
+
+95
+00:10:38,840 --> 00:10:46,140
+and لو جيت بقولتلك ال I ضد ال J قداش يا بنات؟ صفر
+
+96
+00:10:46,140 --> 00:10:50,580
+للإثنين are orthogonal يبقى ال dot product هذا في
+
+97
+00:10:50,580 --> 00:10:58,400
+Zero يسوى ال J ضد ال K يسوى ال K ضد ال I كله يسوى
+
+98
+00:10:58,400 --> 00:11:06,080
+كده؟ يسوى Zero يبقى هذه بعض الخواص الأساسية طب بدي
+
+99
+00:11:06,080 --> 00:11:13,350
+أطرح كمان تساؤلهل Zero vector Orthogonal to any
+
+100
+00:11:13,350 --> 00:11:20,070
+vector؟ مرة تانية أنا عند Zero vector Zero vector
+
+101
+00:11:20,070 --> 00:11:23,450
+قدر كتبات ومكتبات Zero في اتجاه انا، Zero في اتجاه
+
+102
+00:11:23,450 --> 00:11:24,870
+انا، Zero في اتجاه انا، Zero في اتجاه انا، Zero في
+
+103
+00:11:24,870 --> 00:11:29,870
+اتجاه انا هل Zero vector Orthogonal to any given
+
+104
+00:11:29,870 --> 00:11:32,330
+vector؟
+
+105
+00:11:42,150 --> 00:11:46,930
+بدي أشيل ال U و أحط مكانه Zero ضد ال V كدهش بدي
+
+106
+00:11:46,930 --> 00:11:52,790
+أطلع هدول إذا ال Zero vector is orthogonal to any
+
+107
+00:11:52,790 --> 00:11:58,330
+vector على طول خط المحاصر الطرف القاسي لأي vector
+
+108
+00:11:58,330 --> 00:12:02,110
+مع Zero vector بدي أعطينا مين؟ بدي أعطينا ال Zero
+
+109
+00:12:02,110 --> 00:12:04,850
+كمان هذه أحطيها سبعة
+
+110
+00:12:14,950 --> 00:12:25,290
+to any vector السبب because لو أخدت ال zero vector
+
+111
+00:12:25,290 --> 00:12:30,870
+ضد ال V على سبيل المثال يبقى هذا بيقولنا zero في
+
+112
+00:12:30,870 --> 00:12:35,230
+اتجاه ال I Zero في اتجاه ال J Zero في اتجاه ال K
+
+113
+00:12:35,230 --> 00:12:43,030
+ضد اللي هو V1 في اتجاه ال I V2 في اتجاه ال J V3 في
+
+114
+00:12:43,030 --> 00:12:48,410
+اتجاه ال Kنظر بالـ components المتناظرة Zero في V
+
+115
+00:12:48,410 --> 00:12:53,850
+واحد ب Zero Zero في V اتنين ب Zero Zero في V تلاتة
+
+116
+00:12:53,850 --> 00:12:59,290
+ب Zero يبقى الناتج يساوي Zero إذا بناء عليه Zero
+
+117
+00:12:59,290 --> 00:13:04,910
+vector is orthogonal to any vector قبل أن نواصل
+
+118
+00:13:04,910 --> 00:13:12,650
+ناخد بعض الأمثلة يبقى examples أول
+
+119
+00:13:12,650 --> 00:13:18,560
+مثلواللي find the value of the constant alpha find
+
+120
+00:13:18,560 --> 00:13:30,640
+the value of the constant alpha such that the
+
+121
+00:13:30,640 --> 00:13:31,100
+vectors
+
+122
+00:13:46,640 --> 00:13:58,380
+11j-3k and ال vector التاني 2αi-αj
+
+123
+00:13:58,380 --> 00:14:08,120
+ال vector التاني اللي هو v 2αi-αj-5k are
+
+124
+00:14:08,120 --> 00:14:09,920
+orthogonal
+
+125
+00:14:16,890 --> 00:14:23,870
+سؤال مرتين يقول هاتلي قيمة السابق أعفر ولم يضع
+
+126
+00:14:23,870 --> 00:14:29,490
+عليها أي قيود بحيث أن المنتجات الاتنين هذول اتنين
+
+127
+00:14:29,490 --> 00:14:34,310
+بيكونوا مالهم متعاملين، إذا اتنين هذول متعاملين
+
+128
+00:14:34,310 --> 00:14:36,290
+يبقى طبط ال product لهم جداش
+
+129
+00:14:51,530 --> 00:14:59,330
+بتاخد الـ U ضد ال V بده يساوي 0 هذا معناه إيه يلا
+
+130
+00:14:59,330 --> 00:15:05,570
+بتضرب ال components المتناظرة يبقى هذا اتنين Alpha
+
+131
+00:15:05,570 --> 00:15:08,450
+squared اللي بعده نقص Alpha
+
+132
+00:15:12,310 --> 00:15:17,730
+اللي بعده ناقص خمسة في ناقص تلاتة زائد خمستاشر كله
+
+133
+00:15:17,730 --> 00:15:24,550
+متساوي كده؟ متساوي Zero الان هذه معادلة من الدرجة
+
+134
+00:15:24,550 --> 00:15:30,770
+الثانية في مجهول واحد بقدر احلها واطلع هذا المجهول
+
+135
+00:15:30,770 --> 00:15:36,650
+لو روحنا حللنا هذا المقدار الثلاثي على شكل الأقواس
+
+136
+00:15:36,650 --> 00:15:41,400
+هو متساوي Zero باتنين Alpha وهنا Alphaهبعنى
+
+137
+00:15:41,400 --> 00:15:47,460
+الخمساشة دى مالاش إلا خمساشر في واحد أو تلاتة في
+
+138
+00:15:47,460 --> 00:15:55,980
+خمسة إذا لو جيت هنا قل خمسة و هنا تلاتة و هنا ناقص
+
+139
+00:15:55,980 --> 00:16:00,740
+و هنا ناقص تصير ناقص خمسة ألفة و ناقص ستة ألفة
+
+140
+00:16:00,740 --> 00:16:01,500
+بناقص
+
+141
+00:16:22,750 --> 00:16:30,670
+يبقى هذول القيمتين المطلوبتين لألفة
+
+142
+00:16:57,270 --> 00:17:06,490
+كمان مثال example two بيقول
+
+143
+00:17:06,490 --> 00:17:11,090
+let ال U يساوي
+
+144
+00:17:11,090 --> 00:17:23,230
+تلاتة I ناقص J ناقص اتنين K and ال V تساوي I زائد
+
+145
+00:17:23,230 --> 00:17:24,530
+اتنين J
+
+146
+00:17:29,890 --> 00:17:38,870
+أو ايش دولنا؟ نمرة A الـU ضد الـV نمرة B the angle
+
+147
+00:17:38,870 --> 00:17:42,410
+between
+
+148
+00:17:42,410 --> 00:17:56,590
+U and الـV أظن
+
+149
+00:17:56,590 --> 00:17:59,170
+انتهينا من المثال الأول يا بنات هذا نمسحه
+
+150
+00:18:17,750 --> 00:18:22,510
+سؤال مرة تانية، عند ال U عند ال V قال لي هدل ال U
+
+151
+00:18:22,510 --> 00:18:30,350
+ضد ال V فبجي بقوله نمرة A ال U ضد ال V بده يساعد
+
+152
+00:18:30,350 --> 00:18:34,810
+أضرب المركبات المتناضرة في بعضها، تلاتة في واحد
+
+153
+00:18:34,810 --> 00:18:35,610
+كدهاش
+
+154
+00:19:03,290 --> 00:19:08,730
+أول نقطة أخدناها في ال remark الزاوية تساوي cosine
+
+155
+00:19:08,730 --> 00:19:18,730
+inverseيو ضد ال V على طول ال U فطول ال V بقوله
+
+156
+00:19:18,730 --> 00:19:24,350
+كويس طول ال U بده يساوي اللي هو الجدر التربيه
+
+157
+00:19:24,350 --> 00:19:30,550
+لمربع الأول بتسعة مربع التاني واحد مربع اللي بعده
+
+158
+00:19:30,550 --> 00:19:38,170
+اللي هو أربعة يبقى square root لل 14بنروح نجيب طول
+
+159
+00:19:38,170 --> 00:19:42,750
+ال vector الثاني V يبقى الجدر التربيه لو المربع
+
+160
+00:19:42,750 --> 00:19:50,430
+الأول بواحد مربع الثاني باربعة ومربع التالت كذلك
+
+161
+00:19:50,430 --> 00:19:57,270
+بجدر بتسعة يبقى كمال square root لمان للاربعتاش من
+
+162
+00:19:57,270 --> 00:20:03,220
+الاتنين هدول بقدر اقول انطول الـU في طول الـV
+
+163
+00:20:03,220 --> 00:20:09,700
+تساوي كده 14، تمام؟ إذا إحنا عندنا ثيتا تساوي
+
+164
+00:20:09,700 --> 00:20:15,740
+cosine inverse للـU dot الـV على طول الـU في طول
+
+165
+00:20:15,740 --> 00:20:21,460
+مين في طول الـV، يرجع هذا بده يساوي cosine inverse
+
+166
+00:20:21,850 --> 00:20:26,650
+الـ U ضد V من النمرة A طالع تنة بسبعة وهذه
+
+167
+00:20:26,650 --> 00:20:34,290
+باربعتاشر يبقى Cos inverse لنص هنا أن عليه يبقى θ
+
+168
+00:20:34,290 --> 00:20:42,950
+تساوي مين الزاوية اللي جيب تمامها يساوي نص باي
+
+169
+00:20:42,950 --> 00:20:49,250
+علم؟ جيب تمامها يساوي نص صح جت ستين تساوي جت
+
+170
+00:20:49,250 --> 00:20:56,410
+تلاتين تساوينص يبقى باي على تلاتة يبقى تيتا تساوي
+
+171
+00:20:56,410 --> 00:21:02,410
+باي على تلاتة هذه اللي هي الإجابة او هذه الزاوية
+
+172
+00:21:02,410 --> 00:21:06,710
+ما بين الاتنين يبقى لاحظوا ان هذه الزاوية حادة و
+
+173
+00:21:06,710 --> 00:21:12,650
+لا مفرجة و لذلك تُكتبوا في كل عقيمة بوجب اللي هي
+
+174
+00:21:12,650 --> 00:21:17,810
+سابعة يبقى هذا يتفق مع الكلام النظري اللي ذكرناه
+
+175
+00:21:17,810 --> 00:21:23,510
+قبل قليلبنجي الأن يا بنات لبعض الخواص تبعات ضد ال
+
+176
+00:21:23,510 --> 00:21:30,830
+product يبقى بالدالي ل ال properties of
+
+177
+00:21:30,830 --> 00:21:40,270
+the product خواص
+
+178
+00:21:40,270 --> 00:21:47,890
+حاصل الضرب القياسي فبجي بقول F ال U و ال V and ال
+
+179
+00:21:47,890 --> 00:22:03,340
+Ware any vectors أي متجهات and الـ C is this color
+
+180
+00:22:03,340 --> 00:22:16,400
+then النقطة الأولى ال U بط ال V تساوي V بط ال U
+
+181
+00:22:16,400 --> 00:22:18,380
+النقطة الثانية
+
+182
+00:22:20,950 --> 00:22:35,650
+الـ C U ضد V يسوى U ضد CV يسوى C في U ضد V النقطة
+
+183
+00:22:35,650 --> 00:22:48,810
+التالتة U ضد V زائد W يسوى U ضد V زائد U ضد W
+
+184
+00:22:50,060 --> 00:22:56,700
+النقطة الرابعة والاخيرة الـ zero dot ال U بده
+
+185
+00:22:56,700 --> 00:23:00,420
+يساوي مين؟ بده يساوي ال zero
+
+186
+00:23:18,800 --> 00:23:26,100
+من هذه الخواصة بقول ال properties of the dot
+
+187
+00:23:26,100 --> 00:23:32,020
+product الخواص حصلت ضرب القياسي لمتجهين لو عندي
+
+188
+00:23:32,020 --> 00:23:39,640
+three vectors u وv وw وعندي c is scalar then ال u
+
+189
+00:23:39,640 --> 00:23:48,200
+ضد ال v تسوي v ضد ال uعملية الضرب القياسي عملية
+
+190
+00:23:48,200 --> 00:23:52,520
+إبدالية يبقى هذه بلغة الرياضات بقول عليها
+
+191
+00:23:52,520 --> 00:23:59,380
+commutative إبدالي هذه العملية بقول عليها
+
+192
+00:23:59,380 --> 00:24:03,300
+commutative
+
+193
+00:24:03,300 --> 00:24:09,840
+commutative يعني إبدالي إذا U ضط ال V يبدو سوى V
+
+194
+00:24:09,840 --> 00:24:12,440
+ضط ال U النقطة الثانية
+
+195
+00:24:15,480 --> 00:24:19,800
+الـ V يبقى الـ C ضربناه في المنتجة U و بعدين عملنا
+
+196
+00:24:19,800 --> 00:24:24,340
+ال dot المرة التانية أخدنا ال C ضربناه في ال V و
+
+197
+00:24:24,340 --> 00:24:29,000
+بعدين عملنا ال dot U dot CV أما أخدت ال U dot ال V
+
+198
+00:24:29,000 --> 00:24:34,440
+و النتج ضرب ال C على كل ثلاثة أمور تطلع عند نفسي
+
+199
+00:24:34,440 --> 00:24:42,500
+النتيجة طيبعملية الضربة القياسي تخضع لقانون
+
+200
+00:24:42,500 --> 00:24:46,320
+التوزيع أو ينطبق عليها قانون التوزيع الـ
+
+201
+00:24:46,320 --> 00:24:53,040
+Distributive Law يبقى U Dot V زائد U Dot W اللي
+
+202
+00:24:53,040 --> 00:24:58,700
+بعدها الـ Zero Dot U دو ساوي Zero السؤال هو الـ
+
+203
+00:24:58,700 --> 00:25:04,320
+Zero الأول هذاهل هو vector ولا scalar؟ vector وهذا
+
+204
+00:25:04,320 --> 00:25:09,100
+من هنا عامة الشركية الأولى مطاول والتانى مضورة
+
+205
+00:25:09,100 --> 00:25:12,700
+صغيرة يبقى اللى على اليمين اللى يساوى يا بنات هذا
+
+206
+00:25:12,700 --> 00:25:17,060
+scalar ال zero ال scalar واللى على الشمال هو ال
+
+207
+00:25:17,060 --> 00:25:21,280
+zero vector ومن هم أنا بدي أتميزي بينهم يبقى هذا
+
+208
+00:25:21,280 --> 00:25:25,640
+لإن مافيش حاجة اسمها ضط ما بين scalar و vector
+
+209
+00:25:32,330 --> 00:25:43,130
+.v بدي يسوي الـ zero scalar يبقى هذا scalar وهذا
+
+210
+00:25:43,130 --> 00:25:51,530
+ال zero وهذا اللي هو vector يبقى من هنا ييجي الفرق
+
+211
+00:25:51,530 --> 00:25:57,850
+بينهما نعطي مثال عملي على هذه الخواص يبقى examples
+
+212
+00:26:04,580 --> 00:26:07,280
+والـ f, u, v are vectors
+
+213
+00:26:33,030 --> 00:26:41,250
+و ال dot ما بين ال u و ال v ال u و dot ال v بدر
+
+214
+00:26:41,250 --> 00:26:54,030
+ساوي 11 and ال u dot ال w بدر ساوي 2 find او اشدون
+
+215
+00:26:54,030 --> 00:26:58,990
+نمر ايه تلاتة u dot
+
+216
+00:27:06,630 --> 00:27:11,970
+الـ U مينوس الـ V ضغط اتنين
+
+217
+00:27:40,500 --> 00:27:45,920
+مرة تانية نقرأ السؤال أو نتحدد ما هو اللي نريده
+
+218
+00:27:45,920 --> 00:27:50,270
+بالضبطيبقى بقول لو كان ال U و ال V و ال W are
+
+219
+00:27:50,270 --> 00:27:59,630
+vectors بحيث ان طول ال U يسوى 3 طول ال V يسوى 5 ال
+
+220
+00:27:59,630 --> 00:28:04,610
+product ما بين ال U و ال V يسوى 11 ال product ما
+
+221
+00:28:04,610 --> 00:28:09,370
+بين ال U و ال W يسوى 2 طلب عندي ثلاثة مطالب
+
+222
+00:28:09,370 --> 00:28:14,850
+المطلوب الأول ثلاثة U في V زائد الأربعة W
+
+223
+00:28:19,870 --> 00:28:29,230
+Dot ال V زائد أربعة W لو رجعت للخاص اللي عندنا و
+
+224
+00:28:29,230 --> 00:28:34,790
+الخاصة الخاصية رقم تلاتة يبقى vector ضرب مجموع two
+
+225
+00:28:34,790 --> 00:28:38,750
+vectors بدي أوزع هذا ال vector على مين؟ على ال two
+
+226
+00:28:38,750 --> 00:28:43,550
+vectors اللي جوا يبقى بناء عليه هذا الكلام بده
+
+227
+00:28:43,550 --> 00:28:48,910
+يساوي تلاتة U كله ك vector Dot ال V
+
+228
+00:29:00,030 --> 00:29:10,610
+مرة تانية هذه التلاتة بقدر أخدها برا تمام كده هذه
+
+229
+00:29:10,610 --> 00:29:16,350
+التي هي تلاتة you dot الاربعة
+
+230
+00:29:37,150 --> 00:29:41,890
+هذا الكلام يبدو يساوي ثلاثة في أربعة بارة يبقى هذه
+
+231
+00:29:41,890 --> 00:29:47,530
+ثلاثة في أربعة باطن عشر يضط دوي
+
+232
+00:30:17,220 --> 00:30:22,920
+يبقى هاي قيمة المطموب الأول من كل مثل بنانجل
+
+233
+00:30:22,920 --> 00:30:29,840
+المطموب التاني اللي هو نمرة V بيقول U نقص ال V U
+
+234
+00:30:29,840 --> 00:30:38,960
+نقص ال V U نقص ال V dot اتنين U زائد L
+
+235
+00:30:52,250 --> 00:30:55,930
+دربت ال U في ال vector أخرى و أضربها لمين؟ في ال
+
+236
+00:30:55,930 --> 00:31:02,470
+vector التاني زائد ال U بط ال V اللي عملته ل U
+
+237
+00:31:02,470 --> 00:31:11,390
+هروح أعمله لمين؟ لسالف V يبقى هذه سالف V بط اتنين
+
+238
+00:31:11,390 --> 00:31:20,310
+U اللي بعدها سالف V بط ال V بالشكل اللي عندنا نعيد
+
+239
+00:31:20,310 --> 00:31:25,930
+ترتيب المثليبقى هذا الكلام اتنين بتاخده برا بيظل
+
+240
+00:31:25,930 --> 00:31:37,270
+ال U dot ال U زائد U dot ال V ماقس اتنين V dot ال
+
+241
+00:31:37,270 --> 00:31:46,730
+U ماقس اللي هو طول ال V تربيع ال V dot ال V طول ال
+
+242
+00:31:46,730 --> 00:31:52,780
+V تربيع هذا الكلام يساويهذه بنات بنفس القصة
+
+243
+00:31:52,780 --> 00:32:00,840
+بتعطينا طول ال U تربيع يبقى هذه اتنين طول ال U²
+
+244
+00:32:04,050 --> 00:32:10,550
+V Dot U و U Dot V مش اتنين نفس الشيء الخاصية
+
+245
+00:32:10,550 --> 00:32:15,730
+الأولى U Dot V و V Dot U اذا هذه هي هذه طب واحدة
+
+246
+00:32:15,730 --> 00:32:22,250
+موجبة و اتنين سالب يبقى ايه سالب U Dot V يبقى سالب
+
+247
+00:32:22,250 --> 00:32:30,170
+U Dot V خلصنا منها ناقص طول ال V تربيع يبقى هذا
+
+248
+00:32:30,170 --> 00:32:31,570
+الكلام بده يساوي
+
+249
+00:32:41,090 --> 00:32:47,790
+وضد ال V اللي هو ب 11 ناقص طول ال V اللي هو خمسة
+
+250
+00:32:47,790 --> 00:32:54,030
+لكل تربية طبعا هذه تسعة في اتنين في تمانتاش
+
+251
+00:32:54,030 --> 00:33:01,650
+تمانتاش سالب احداش سالب خمسة وعشرين سالب خمسة
+
+252
+00:33:01,650 --> 00:33:05,010
+وعشرين وسالب احداش بسالب ستة وتلاتين
+
+253
+00:33:11,250 --> 00:33:18,370
+عشرة يبقى هذا هو المطلوب الثاني من المسألة بدنا
+
+254
+00:33:18,370 --> 00:33:24,690
+نروح للمطلوب التالت طلعوني
+
+255
+00:33:24,690 --> 00:33:29,890
+في المطلوب التالت كويس وفكروا كيف بدنا نجيب
+
+256
+00:33:29,890 --> 00:33:35,170
+المطلوب التالت لإن أنا ماعنديش ال vector u و ال
+
+257
+00:33:41,020 --> 00:33:46,640
+اللي بدى الطول ال U نقص اتنين V لو بعرف ال U و ال
+
+258
+00:33:46,640 --> 00:33:52,500
+V كان صارت الجزء سهل لكن أنا لاعرف U ولا عارف V طب
+
+259
+00:33:52,500 --> 00:33:58,040
+كيف نحل هالمسألة دي؟ يلا اقترحوا علينا اقتراح
+
+260
+00:34:24,500 --> 00:34:29,140
+أحنا أخدنا مجموع لما نقول نقول إثنين يستوي نقول
+
+261
+00:34:29,140 --> 00:34:37,940
+الأول زي نقول الثاني افتشل الكلام الحل
+
+262
+00:34:37,940 --> 00:34:46,740
+إيه؟ كدا كدا ها انت سمع
+
+263
+00:35:12,020 --> 00:35:21,140
+إذا أنا هنا باجي بقول نمرسيأنا عازمين اللي هو U
+
+264
+00:35:21,140 --> 00:35:24,700
+بالتربيع بنقص اتنين فيه الطول تبعه، بدي أخد
+
+265
+00:35:24,700 --> 00:35:28,500
+تربيعه، وشوف إيش بده بيعطينا، و بعد هيك القرآن ما
+
+266
+00:35:28,500 --> 00:35:33,760
+شاء الله حلها، يبقى باجي بقوله لو أخد طول ال U
+
+267
+00:35:33,760 --> 00:35:34,840
+ناقص اتنين
+
+268
+00:35:40,560 --> 00:35:49,280
+يبقى بلغة الـ vectors هذا U نقص 2B ضد الـ U نقص 2B
+
+269
+00:35:49,280 --> 00:35:55,380
+هزبط هيك؟ فبنعمل الفكرة اللي عملناها من هنا لضرب
+
+270
+00:35:55,380 --> 00:36:03,860
+هذا يبقى هذا شو بده يعطينا؟ يبده يعطينا U ضد الـ U
+
+271
+00:36:03,860 --> 00:36:08,420
+نقص
+
+272
+00:36:08,420 --> 00:36:09,340
+الـ U
+
+273
+00:36:17,580 --> 00:36:25,260
+نقص في نقص في نقص في نقص في نقص
+
+274
+00:36:25,260 --> 00:36:27,160
+في نقص
+
+275
+00:36:32,250 --> 00:36:44,570
+يبقى U ضد ال V يبقى
+
+276
+00:36:44,570 --> 00:36:53,230
+U ضد ال V زائد أربعة طول ال V تربية V ضد ال V ليه
+
+277
+00:36:53,230 --> 00:36:54,770
+طول ال V تربية
+
+278
+00:37:13,600 --> 00:37:19,580
+طول الـ U مات اللي هو قداش تلاتة يبقى تلاتة لكل
+
+279
+00:37:19,580 --> 00:37:28,640
+تربية ناقص أربعة هذا U يا بناتي ناقص أربعة U ضفت
+
+280
+00:37:28,640 --> 00:37:30,600
+ال V اللي هو قداش ب 11
+
+281
+00:37:34,380 --> 00:37:41,620
+أربعة في طول ال V وين طول ال V اللي هو خمسة الكل
+
+282
+00:37:41,620 --> 00:37:50,880
+تربيه هذا الكلام سوى تسعة ناقص أربعة وأربعين خمسة
+
+283
+00:37:50,880 --> 00:37:56,640
+تربيه ليه خمسة وعشرين في أربعة بمية يبقى زائد مية
+
+284
+00:37:57,310 --> 00:38:01,890
+عندك مية وتسعة بده اشيل منهم مين اللي مول ان هذا
+
+285
+00:38:01,890 --> 00:38:07,330
+موجب و هذا موجب يبقى هذا مية وتسعة بده اشيل منهم
+
+286
+00:38:07,330 --> 00:38:14,470
+اربع واربعين بظل خمسة و هنا كدهش ستة يبقى خمسة و
+
+287
+00:38:14,470 --> 00:38:21,330
+ستين بالموجب مين هذا؟أنا لا أريد طول المتجه أنا
+
+288
+00:38:21,330 --> 00:38:25,590
+أريد طول المتجه إذا باخد ال square root of both
+
+289
+00:38:25,590 --> 00:38:30,350
+sides باخد الجدر التربية للطرفين يبقى بناء على طول
+
+290
+00:38:30,350 --> 00:38:38,930
+ال U ونقص 2D يسوى ال square root من الخمس أو ستة
+
+291
+00:38:38,930 --> 00:38:44,730
+إذا أنا جبت الطول ههه هم لا يعرفوا شكل ال U
+
+292
+00:39:12,030 --> 00:39:16,230
+طبعا و لا سؤال زيه في الكتاب وإنما جيأ بيه في
+
+293
+00:39:16,230 --> 00:39:24,010
+امتحان 2005 ونشور طبعا نفس الفكرة ها، كويس؟ يبقى
+
+294
+00:39:24,010 --> 00:39:28,730
+هذا good exercise إيه المرنو ديكوا فيه؟ امتحان في
+
+295
+00:39:28,730 --> 00:39:38,300
+2005 بيقول لو كانالـ V يساوي اتنى وطول ال W يساوي
+
+296
+00:39:38,300 --> 00:39:47,300
+تلاتة and the angle between and the angle between
+
+297
+00:39:47,300 --> 00:39:51,440
+the
+
+298
+00:39:51,440 --> 00:40:04,640
+angle between ال V and ال W is Pi على تلاتةفايند
+
+299
+00:40:04,640 --> 00:40:14,140
+هو ايش دولة اللي هو طول ال V نقص اتنين W the
+
+300
+00:40:14,140 --> 00:40:25,200
+length of the vector V نقص اتنين W
+
+301
+00:40:39,460 --> 00:40:46,420
+V-2W الطول الكل تربيه و تبدأ تشتغل زي اللي فوق
+
+302
+00:40:46,420 --> 00:40:55,580
+يالا و نرشش الكمان الجواب الanswer الإجابة اتنين
+
+303
+00:40:55,580 --> 00:41:03,000
+جدر سبعة يالا مش هالنا التهيش قبل أن نجي لنقطة جدا
+
+304
+00:41:03,000 --> 00:41:05,020
+في هذا ال section اسمها
+
+305
+00:41:24,980 --> 00:41:35,540
+بنحاول نسقط اللى هو مفتجه على مفتجه الاخر حد راكوا
+
+306
+00:41:35,540 --> 00:41:44,080
+فيها مصطره بيقولوا تلاتي صانده هاتي ايه؟ ايش؟
+
+307
+00:41:44,080 --> 00:41:52,460
+بنات؟ اه 100% بدي اعتبر هذه بنات عبارة عن vector
+
+308
+00:41:53,090 --> 00:41:58,500
+وهذا عبارة عن vector آخربدي أحاول أسقط الـ vector
+
+309
+00:41:58,500 --> 00:42:03,020
+اللي فوق على ال vector اللي تحت و نشوف إيش النتج
+
+310
+00:42:03,020 --> 00:42:07,680
+بدي يكون طبعا احنا أخدنا زمان في المرحلة الثانوية
+
+311
+00:42:07,680 --> 00:42:14,420
+أنه مسقط مستقيم على مستقيم الآخر هو مستقيم إلا إذا
+
+312
+00:42:14,420 --> 00:42:18,660
+كان عمودي عليه فالمسقط هو main نقطة بالمثل إن أنا
+
+313
+00:42:18,660 --> 00:42:22,060
+بدي أسقط هذا ال vector على هذا ال vector بدي
+
+314
+00:42:22,060 --> 00:42:27,910
+يعطيني mainVector تاني السؤال هو المسقط هذا بيكون
+
+315
+00:42:27,910 --> 00:42:32,990
+أطول من ال vector الأصلي ولا أكثر منه ولا ممكن
+
+316
+00:42:32,990 --> 00:42:37,170
+يساوي .. ممكن
+
+317
+00:42:37,170 --> 00:42:43,070
+يساوي وارد و أكثر منه وارد لكن أكبر منه مافيش
+
+318
+00:42:43,070 --> 00:42:47,390
+إمكانية على الأطلع تمام؟ الكلام اللي أنا بقوله
+
+319
+00:42:47,390 --> 00:42:54,010
+هوضحه الآن من خلال الرسملو أنا يا بنات عندي المتجه
+
+320
+00:42:54,010 --> 00:43:04,210
+V وعندي متجه أخر U بدي أسقط ال U على V لحظة هذا
+
+321
+00:43:04,210 --> 00:43:11,190
+النقطة مشتركة يبقى هادر بالطل عشان أسقط ويسقط زي
+
+322
+00:43:11,190 --> 00:43:15,550
+ما هو يبقى النقطة هذه يا بنات رأس المتجه
+
+323
+00:43:20,320 --> 00:43:27,340
+عمودي بهذا الشكل يبقى المتجه تبع المسقط هو المتجه
+
+324
+00:43:27,340 --> 00:43:33,160
+اللي عندنا هذا الخط الأزرق هذا او المتجه الأزرق
+
+325
+00:43:33,160 --> 00:43:39,520
+هذا هو المسقط اللي هسميه projection U على مين على
+
+326
+00:43:39,520 --> 00:43:43,000
+فيه و بطبقه بالشكل التالي كلمة projection
+
+327
+00:43:47,010 --> 00:43:54,350
+وحط ال V ك index عندي ال J يبقى يقرأ projection U
+
+328
+00:43:54,350 --> 00:44:01,350
+على V الزاوية
+
+329
+00:44:01,350 --> 00:44:07,490
+اللي بينهم كانت هذه θ زاوية حاتة تمام؟ يبقى
+
+330
+00:44:07,490 --> 00:44:13,250
+الزاوية اللي عند هذه θ زاوية حاتة بناء عليه بدي
+
+331
+00:44:13,250 --> 00:44:18,140
+أعرف هل ال projection هذابدي اكون positive ولا
+
+332
+00:44:18,140 --> 00:44:23,360
+negative يعني بدي اعرف قداش الطول تبعه بالضبط و
+
+333
+00:44:23,360 --> 00:44:29,960
+بدي اعرف قداش اتجاهه تمام فباجي اقول والله كويس ال
+
+334
+00:44:29,960 --> 00:44:38,060
+vector هذا من هنا لهنا الطول تبعه له طول اليوم في
+
+335
+00:44:38,060 --> 00:44:42,830
+جيب تمام الزاوية ثيتا مين بيعطيناطول الـ
+
+336
+00:44:42,830 --> 00:44:47,730
+projection طول
+
+337
+00:44:47,730 --> 00:44:53,770
+الـ U على V يساوي طول الـ U في الـ cosine الزاوية
+
+338
+00:44:53,770 --> 00:45:01,490
+ميان الـ theta نهضة المستقيم الأزرق هذا أقصر من
+
+339
+00:45:01,490 --> 00:45:05,230
+طول
+
+340
+00:45:05,230 --> 00:45:10,830
+المتجه Uطب لو كان الـU عمودي على V بالـprojection
+
+341
+00:45:10,830 --> 00:45:17,850
+هو الـzero vector، مظبوط؟ طيب، بدنا نيجي ناخد
+
+342
+00:45:17,850 --> 00:45:24,150
+الحالة التانية، لو كان هذا هو الـvector V وكان هذا
+
+343
+00:45:24,150 --> 00:45:31,110
+هو الـvector U وحبيت أسقط U على V حيث إن الزاوية
+
+344
+00:45:31,110 --> 00:45:33,890
+بينهما θ زاوية A
+
+345
+00:45:54,230 --> 00:46:00,490
+طول الـ U في الـ Cos الزاوية واتجاه
+
+346
+00:46:03,010 --> 00:46:07,190
+تجاه ال V هذا الأول سنة من التانية هاروح للتانية
+
+347
+00:46:07,190 --> 00:46:11,370
+يبقى هو
+
+348
+00:46:11,370 --> 00:46:14,910
+طول ال U في قصين الزاوية تيتها هذا طول ال
+
+349
+00:46:14,910 --> 00:46:20,250
+projection لكن اتجاهه هو اتجاه ال V يعني في اتجاه
+
+350
+00:46:20,250 --> 00:46:26,250
+V على طول ال V اللي هو متجه الوحدة في اتجاه من V
+
+351
+00:46:26,950 --> 00:46:31,770
+يجب أن تكون الـ projection تبع الـ U على V هو متجه
+
+352
+00:46:31,770 --> 00:46:35,390
+جديد في اتجاه المتجه V
+
+353
+00:46:53,080 --> 00:47:00,240
+هذا U إذا هذا طول المتجه Uفى cosine الزاوية تيتا
+
+354
+00:47:00,240 --> 00:47:07,600
+تيتا زاوية منفرجة إذا الجيب التمام سالم تمام إذا
+
+355
+00:47:07,600 --> 00:47:13,200
+لما بدي أجيب القول بالضبط بدي أقول قول المتجه هي و
+
+356
+00:47:13,200 --> 00:47:19,540
+هذا قيمة عددية موجبة في مين في cosine الزاوية تيتا
+
+357
+00:47:19,540 --> 00:47:25,120
+ولما كانت الزاوية تيتا زاوية منفرجة فاروح بقول في
+
+358
+00:47:25,120 --> 00:47:25,420
+مين
+
+359
+00:47:29,020 --> 00:47:34,440
+الأول طول المتجه هذا ال absolute value لهذا الرقم
+
+360
+00:47:34,440 --> 00:47:39,100
+هيطلع سالب أخد absolute value و بطلع قيمة مجبرة ال
+
+361
+00:47:39,100 --> 00:47:45,380
+direction عكس اتجاه ال V يعني إذا كان هذا ال
+
+362
+00:47:45,380 --> 00:47:50,100
+projection في اتجاه ال V على طول ال V هذا هيكون في
+
+363
+00:47:50,100 --> 00:47:56,500
+اتجاه سالبفي علقه يعني في عكس اتجاهه تماما بضبط،
+
+364
+00:47:56,500 --> 00:48:01,260
+تمام؟ الكلام اللي قلتهلك هذا الشفوي بدنا نروح
+
+365
+00:48:01,260 --> 00:48:08,800
+أنصيه و نكتبه كتابة، يبقى كيف كتابة كالتالي، بروح
+
+366
+00:48:08,800 --> 00:48:12,520
+بقول ان بدي أحق الكلام في صيغة النقاط التالية،
+
+367
+00:48:12,520 --> 00:48:13,200
+النقطة الأولى
+
+368
+00:48:23,130 --> 00:48:34,510
+between الـU and الـV is accurate يعني لو كانت
+
+369
+00:48:34,510 --> 00:48:40,770
+زاوية حادة لـ projection تبع الـU على الـV
+
+370
+00:48:51,250 --> 00:49:00,890
+فى cosine الزاوية θ and direction وفى الاتجاه V
+
+371
+00:49:00,890 --> 00:49:05,750
+على طول الـ V هذا طبعا لمتجه الوحدة فى اتجاه
+
+372
+00:49:05,750 --> 00:49:12,670
+المتجه V ذكرناه فى المحاضرة الماضية نمرى اتنين if
+
+373
+00:49:12,670 --> 00:49:16,830
+the angle θ
+
+374
+00:49:18,930 --> 00:49:25,970
+is obvious لو
+
+375
+00:49:25,970 --> 00:49:33,810
+كانت زاوية منفرجة الـ projection تبع الـU على V
+
+376
+00:49:33,810 --> 00:49:42,410
+has length has length اللي هو طول الـU في absolute
+
+377
+00:49:42,410 --> 00:49:53,910
+value لكوصين الزاوية V anddirection والاتجاه
+
+378
+00:49:53,910 --> 00:50:02,850
+سالب V على فول ال V يعني بنجوسين ل opposite
+
+379
+00:50:02,850 --> 00:50:09,310
+direction of
+
+380
+00:50:09,310 --> 00:50:16,850
+V الاتجاه المعاكس لل vector V ثلاثة
+
+381
+00:50:49,890 --> 00:50:58,530
+المركبة القياسية of U المتجه U and
+
+382
+00:51:01,270 --> 00:51:13,850
+direction في اتجاه of V هذه
+
+383
+00:51:13,850 --> 00:51:19,930
+طول ال U في Cos الزاوية تيتا ممكن أجيب لها صياغة
+
+384
+00:51:19,930 --> 00:51:26,010
+أخرى شو الصياغة الأخرى؟ هأبقالك بين قسين؟ not that
+
+385
+00:51:26,010 --> 00:51:37,420
+لحظة أن طول ال Uفى cosine الزاوية تيتا يساوي لو
+
+386
+00:51:37,420 --> 00:51:42,320
+رجعت لل dot product بين ال U و ال V فى الهامشة
+
+387
+00:51:42,320 --> 00:51:49,680
+بنات قولنا ان ال U dot ال V يساوي طول ال U فى طول
+
+388
+00:51:49,680 --> 00:51:55,920
+ال V فى cosine الزاوية تيتا إذا طول ال U فى cosine
+
+389
+00:51:55,920 --> 00:51:59,740
+الزاوية تيتا يساوي U dot ال V
+
+390
+00:52:15,140 --> 00:52:19,780
+الـ V أو طول الـ U اللي طلعناه اللي هو عبارة عن
+
+391
+00:52:19,780 --> 00:52:28,820
+الـ U دُغري الـ U ضد ال V على طول ال V بالشكل
+
+392
+00:52:28,820 --> 00:52:33,360
+العام أو
+
+393
+00:52:33,360 --> 00:52:41,420
+بقدر أحط هلك كمان في صيغة أخرى الـ U ضد ال V على
+
+394
+00:52:41,420 --> 00:52:49,520
+طول ال Vكأن واحد على طول V-scalar تعتبره مضروف في
+
+395
+00:52:49,520 --> 00:52:53,520
+الكل ماشي، مضروف في المتجهة الأول ماشي، مضروف في
+
+396
+00:52:53,520 --> 00:52:56,940
+المتجهة التاني ماشي، سيان، هادي، ورنهادي، كله are
+
+397
+00:52:56,940 --> 00:53:02,960
+the same طب هل لو فكيت هذا يا تراج بيعطيني طول هذا
+
+398
+00:53:02,960 --> 00:53:08,200
+المقطع، الإجابة نعم، بدا فكرة طول الأول في طول
+
+399
+00:53:08,200 --> 00:53:12,040
+الثاني، طول الأول في طول اليوم، طول الثاني في قداش
+
+400
+00:53:13,050 --> 00:53:16,950
+وحد صحي للمتاجر الواحدة في cosine الزاوية بينهم
+
+401
+00:53:16,950 --> 00:53:21,770
+أكيد إذا صار طول ال U في cosine الزاوية أكيد إذا
+
+402
+00:53:21,770 --> 00:53:26,990
+يابا ندّي scalar component of ال vector U في اتجاه
+
+403
+00:53:26,990 --> 00:53:30,490
+ال vector value أبسل U أكيد طول ال U في cosine
+
+404
+00:53:30,490 --> 00:53:36,210
+الزاوية أكيد يابا أقول U dot V على طول ال V هذا
+
+405
+00:53:36,210 --> 00:53:39,630
+الكلام جيبته من وين؟ جيبته من خلال ال definition
+
+406
+00:53:39,630 --> 00:53:41,710
+تبع ال dot product
+
+407
+00:53:48,500 --> 00:53:53,640
+يبقى سواء كان هذا والله هذا الاتنين are the same
+
+408
+00:54:12,080 --> 00:54:17,760
+المثال هذا النقطة التانية بتحطها النقطة الرابعة
+
+409
+00:54:17,760 --> 00:54:23,140
+يبقى النقطة الرابعة لو بدي ال projection تبع ال U
+
+410
+00:54:23,140 --> 00:54:30,860
+في اتجاه المتجه B طول المتجه U في Cos الزاوية θ في
+
+411
+00:54:30,860 --> 00:54:31,460
+اتجاه
+
+412
+00:54:38,740 --> 00:54:42,680
+هذا الكلام ممكن يساوي يبقى هذا يمثل طول ال
+
+413
+00:54:42,680 --> 00:54:48,620
+projection وهذا يمثل مين؟ يمثلي اتجاهه يعني متجه
+
+414
+00:54:48,620 --> 00:54:53,040
+الواحدة في اتجاهه يبقى هذا كله على بعضه هو ال
+
+415
+00:54:53,040 --> 00:54:58,860
+projection تبع المتجه U في اتجاه المتجه من V لكن
+
+416
+00:54:58,860 --> 00:55:03,740
+انا عندي طول ال U في ال cosine يسوى القيمة اللي
+
+417
+00:55:03,740 --> 00:55:04,520
+عندنا هذه
+
+418
+00:55:08,070 --> 00:55:16,130
+عن هذه اليمين اللي هي U بط ال V على طول ال V في ال
+
+419
+00:55:16,130 --> 00:55:27,170
+V على طول ال V هذه بنات هي U بط ال V على طول ال V
+
+420
+00:55:27,170 --> 00:55:33,900
+تربية في اتجاه المتجاه Vالصياغة هذه جميلة جدا
+
+421
+00:55:33,900 --> 00:55:41,880
+والأجمل منها كذلك يضط ال V على V ضط ال V في اتجاه
+
+422
+00:55:41,880 --> 00:55:47,660
+المتجه V طيب
+
+423
+00:55:47,660 --> 00:55:52,200
+سؤال اللي بين قسين هذه من هذا كمية اتجاهية ولا
+
+424
+00:55:52,200 --> 00:55:59,460
+كمية قياسية يبقى الرقم مضروب في V الرقم هذا
+
+425
+00:56:24,170 --> 00:56:32,530
+هو ممكن يطلع أقل من V لكن هل يمكن أن يطلع أكبر من
+
+426
+00:56:32,530 --> 00:56:33,690
+V؟
+
+427
+00:56:42,340 --> 00:56:49,220
+لكن أكبر من ال V هذا الكلام مستبعد تماما واضحان
+
+428
+00:56:49,220 --> 00:56:54,540
+يرجع عمليا من الأن فسعنا نتعامل مع ال projection
+
+429
+00:56:54,540 --> 00:56:59,580
+تبع اليهو في اتجاه ال V بالطريقة اللي عندنا هنا طب
+
+430
+00:56:59,580 --> 00:57:03,520
+بدأ أسألكوا سؤال تاني لو جمت جرامة الوضع
+
+431
+00:57:15,610 --> 00:57:21,270
+أنت بصيغة والله ابنك يبقى هنا لو بدأت أخد ال
+
+432
+00:57:21,270 --> 00:57:27,290
+projection تبع ال V في اتجاه ال U بدأت تنتج و
+
+433
+00:57:27,290 --> 00:57:32,850
+لحالي هه بدون شغل و بدون كلام بس أني أدقق النظر في
+
+434
+00:57:32,850 --> 00:57:36,390
+النتيجة اللي عندنا هذا طلعوا يا بنات ال projection
+
+435
+00:57:36,390 --> 00:57:43,630
+تبع ال U على V U ضد ال V V V V يعني ال U ظهر بس
+
+436
+00:57:43,630 --> 00:57:48,190
+مرة واحدةيبقى انا بدي اخد ال projection تبع ال V
+
+437
+00:57:48,190 --> 00:57:55,010
+على U يبقى
+
+438
+00:57:55,010 --> 00:57:57,710
+انا بدي اخد ال projection تبع ال V على U يبقى انا
+
+439
+00:57:57,710 --> 00:57:58,710
+بدي اخد ال projection تبع ال V على U يبقى انا بدي
+
+440
+00:57:58,710 --> 00:58:05,130
+اخد ال projection تبع ال V على U يبقى
+
+441
+00:58:05,130 --> 00:58:10,810
+انا بدي اخد ال projection تبع ال V على U يبقى انا
+
+442
+00:58:10,810 --> 00:58:13,870
+بدي اخد ال projection تبع ال V على U
+
+443
+00:58:15,880 --> 00:58:20,980
+مرياضياً خلاص يبقى هذا اللي هو معنى ال projection
+
+444
+00:58:20,980 --> 00:58:25,420
+نعطي مثال عملي على ذلك example
+
+445
+00:58:49,810 --> 00:59:02,590
+زائد خمسة K زائد خمسة K find نمره A بدنا لـ
+
+446
+00:59:02,590 --> 00:59:10,590
+projection تبع الـ U على V نمره B بدنا this scalar
+
+447
+00:59:10,590 --> 00:59:16,670
+component this scalar component
+
+448
+00:59:16,670 --> 00:59:19,030
+المركبة القيمة
+
+449
+00:59:40,110 --> 00:59:44,110
+مرة ثانية نقرأ السؤال و نفهم ما هو المطلوب من هذا
+
+450
+00:59:44,110 --> 00:59:48,630
+السؤال بقول لو كان ال U و ال V بالشكل اللي قدامنا
+
+451
+00:59:48,630 --> 00:59:52,990
+هذا طلب ل projection تبع ال U على V إذا أنا لو
+
+452
+00:59:52,990 --> 00:59:58,830
+كتبت له هنا نمرة Aالـ projection تبع الـ U على V
+
+453
+00:59:58,830 --> 01:00:03,550
+أو الـ component of U in the direction of V،
+
+454
+01:00:03,550 --> 01:00:06,690
+الإتنين are the same إذا مش أنا أجيب له الـ
+
+455
+01:00:06,690 --> 01:00:12,050
+projection بالزمن الـU ضد الـV و بالزمن الـV ضد
+
+456
+01:00:12,050 --> 01:00:16,190
+إيه، ده خلّيني أحسبهم من الأول، يبقى بدي أروح أخدي
+
+457
+01:00:16,190 --> 01:00:21,410
+الـU ضد الـV، يبقى بدي أضرب اللي هو العناصر
+
+458
+01:00:21,410 --> 01:00:28,180
+المتنظرة، واحد في تلاتة كدهاشر، تلاتةماقص 7 في 4
+
+459
+01:00:28,180 --> 01:00:37,460
+بنقص جدال 28 زائد 3 في 5 اللي هو جدال 15 يبقى هذا
+
+460
+01:00:37,460 --> 01:00:45,500
+الكلام بدرساوي 15 و3 18 يبقى الجدال ناقص 10 بعد
+
+461
+01:00:45,500 --> 01:00:50,960
+ذلك بيروح أجيب له ال V وضعت ال V يبقى المتجه في
+
+462
+01:00:50,960 --> 01:00:53,300
+نفسه يبقاش مصير هنا
+
+463
+01:01:02,510 --> 01:01:09,210
+16 9 25 50
+
+464
+01:01:15,740 --> 01:01:26,540
+يبقى ال U على V يبقى
+
+465
+01:01:26,540 --> 01:01:34,580
+ناقص عشرة على خمسين في ال vector اللي عندنا V زي
+
+466
+01:01:34,580 --> 01:01:42,190
+ما هو تلاتة I زائد أربعة J زائد خمسة Kطبعا ناقص
+
+467
+01:01:42,190 --> 01:01:47,730
+عشر على خمسين اللي هو قداش سالب خمس إذا هذا ال
+
+468
+01:01:47,730 --> 01:01:54,930
+vector بصير سالب تلت أخمس في اتجاه ال I سالب أربع
+
+469
+01:01:54,930 --> 01:02:04,630
+أخمس في اتجاه ال J سالب كده كده فقط ناغية يبقى هذا
+
+470
+01:02:04,630 --> 01:02:09,520
+اللي هوأو الـ projection تبع الـ U في اتجاه مين؟
+
+471
+01:02:09,520 --> 01:02:14,960
+في اتجاه المتجه V وهذا هو المطلوب الأول من السؤال
+
+472
+01:02:14,960 --> 01:02:20,320
+المطلوب الثاني قل لي هتلي scalar component of U in
+
+473
+01:02:20,320 --> 01:02:25,720
+the direction of V يعني مين؟ يعني طول الـ U في
+
+474
+01:02:32,610 --> 01:02:40,430
+على طول ال V يبقى نمرة V بعدين بقوله V is scalar
+
+475
+01:02:40,430 --> 01:02:50,470
+component اللي بده يهيأ لطول U في cosine الزاوية
+
+476
+01:02:50,470 --> 01:02:53,850
+تيتا أو U dot
+
+477
+01:03:00,120 --> 01:03:05,920
+يضط ال V هيو جدام الخطوة الأولى لو سالب عشرة يبقى
+
+478
+01:03:05,920 --> 01:03:14,660
+سالب عشرة على طول ال Vطبعا احنا هنا الجدر التربية
+
+479
+01:03:14,660 --> 01:03:22,920
+اللي V ضد V V ضد V يبقى سلب عشرة V ضد V اللي هو
+
+480
+01:03:22,920 --> 01:03:31,240
+جدار بخمسين تحت الجدر يبقى سلب عشرة على خمسين لير
+
+481
+01:03:39,490 --> 01:03:43,950
+إذا مش عاجبك جدر اتنين في المقام بنقدر نوديه في
+
+482
+01:03:43,950 --> 01:03:49,310
+الـ bus عن طريق ضرب في جدر اتنين على جدر اتنين
+
+483
+01:03:49,310 --> 01:03:53,970
+يعني كده ضرب في كده شبنة في واحد صحية يبقى هذا
+
+484
+01:03:53,970 --> 01:04:01,930
+بيطلع كده سالب جدر اتنين ل scalar component تبع ال
+
+485
+01:04:01,930 --> 01:04:07,570
+U في اتجاه L بقيت عندنا في هذا ال section نقطة
+
+486
+01:04:09,950 --> 01:04:19,330
+على صورة الـ remark أث تانية يبقى writing vector
+
+487
+01:04:19,330 --> 01:04:28,030
+كتابة متجة as a sum of
+
+488
+01:04:28,030 --> 01:04:32,530
+orthogonal vectors
+
+489
+01:04:38,360 --> 01:04:42,360
+كتابة من اتجارات اتجارات اتجارات اتجارات اتجارات
+
+490
+01:04:42,360 --> 01:05:07,580
+اتجارات اتجارات اتجارات
+
+491
+01:05:08,100 --> 01:05:17,120
+or two orthogonal vectors
+
+492
+01:05:17,120 --> 01:05:20,260
+vectors
+
+493
+01:05:20,260 --> 01:05:27,060
+as follows اتل
+
+494
+01:05:27,060 --> 01:05:37,220
+ال U يساوي ال projection تبع ال U اتجاه ال V زائد
+
+495
+01:05:42,500 --> 01:05:54,620
+في اتجاه الـ V طبعا
+
+496
+01:05:54,620 --> 01:06:02,640
+سؤال كيف تم ذلك؟ مش هيك؟ لاجب أقوله كويس لو أنا
+
+497
+01:06:02,640 --> 01:06:10,120
+بنات قلت هذا المتجه U و روحت قلت هذا المتجه V و
+
+498
+01:06:10,120 --> 01:06:12,140
+جينا من هنا نزلنا عمون
+
+499
+01:06:30,020 --> 01:06:37,800
+البداية أخد جمع المتجهات هندسيا يبقى بقى اللي بقول
+
+500
+01:06:37,800 --> 01:06:45,380
+لو جت فترت هنا متجه يبقى بصية ال projection وهذا
+
+501
+01:06:45,380 --> 01:06:50,120
+المتجه في اتجاه دوري واحد يبقى الجامع الاتنين
+
+502
+01:06:50,120 --> 01:06:54,000
+بعطين المتجه الذي يقفل المثلث في الاتجاه الدوري
+
+503
+01:06:54,000 --> 01:06:56,000
+المضاد
+
+504
+01:07:09,680 --> 01:07:14,700
+المتجه التاني اللي عندنا هذا اللي الله أعلم منه
+
+505
+01:07:14,700 --> 01:07:23,020
+بده ساوي من؟ بده ساوي الـU إذا هذا المتجه اللي أنا
+
+506
+01:07:23,020 --> 01:07:29,400
+مش عارفه بده أعرف منه هو عبارة عن الـU ناقص ال
+
+507
+01:07:29,400 --> 01:07:35,320
+projection يبقى هذا المتجه عبارة عن الـU ناقص ال
+
+508
+01:07:35,320 --> 01:07:37,540
+projection تبع الـU
+
+509
+01:07:42,280 --> 01:07:50,260
+هو تعاملين يبقى هذا هو الـU ناقص لـprojection تبع
+
+510
+01:07:50,260 --> 01:07:57,120
+الـU على V إذا المتجه U هو عبارة عن الـprojection
+
+511
+01:07:57,120 --> 01:08:02,550
+زي هذا فعلا أنت هذا سرد و هذا موجةلو جمعتهم مع
+
+512
+01:08:02,550 --> 01:08:07,470
+السلامة بيظلمين عندى، بس المتجه يهيأو يهيأو يهيأو
+
+513
+01:08:07,470 --> 01:08:12,110
+طيب انا بديش يقو الصياغة هذه، بدي أصيغه صياغة
+
+514
+01:08:12,110 --> 01:08:15,090
+عملية، مش هنصيغه صياغة عملية
+
+515
+01:08:33,750 --> 01:08:39,890
+زي ايه؟ اين السائلة؟
+
+516
+01:08:39,890 --> 01:08:46,450
+انا
+
+517
+01:08:46,450 --> 01:08:52,550
+بجيبش اطوال في ثغور، انا بجيب متجهات، جمع اتجاهي
+
+518
+01:08:52,550 --> 01:08:58,490
+زي القوة، محصلة القوة، يبقى كأن انا عندي الدكتور
+
+519
+01:08:59,250 --> 01:09:07,030
+بجيب اشطول بقولك بجيب محصلات متجهات هذا متجه وهذا
+
+520
+01:09:07,030 --> 01:09:12,550
+متجه يبقى تحصل هو المتجه الذي يقفل المثلث في اتجاه
+
+521
+01:09:12,550 --> 01:09:17,570
+الدور المضادة تمام؟ هو بحالك بعد ما نخلص الحل
+
+522
+01:09:17,570 --> 01:09:23,070
+الحين تمام؟ يبقى بنرجع مرة تانية زائد ال U
+
+523
+01:09:37,540 --> 01:09:41,940
+هل اتنين هدول متعمدين ولا لأ؟ بقول اه والله على
+
+524
+01:09:41,940 --> 01:09:49,080
+الرسم هذا وهذا هم متعمدين صحيح ولا لأ؟ إحنا ال
+
+525
+01:09:49,080 --> 01:09:54,860
+vector يستطعنا كتابته على vector في اتجاه ال V
+
+526
+01:10:01,570 --> 01:10:08,370
+هذا الرقم ماله مضاعفات ال V يبقى دوام في اتجاه ال
+
+527
+01:10:08,370 --> 01:10:13,430
+V او parallel to V موازن لل V يبقى هذا
+
+528
+01:10:32,810 --> 01:10:37,930
+عمودي على مين؟ عمودي على V
+
+529
+01:11:02,200 --> 01:11:06,300
+ماذا تجاهل فيه؟
+
+530
+01:11:06,300 --> 01:11:10,960
+والله إذا ضد هذا طلع zero بيكونوا اتنين هدول فعلا
+
+531
+01:11:10,960 --> 01:11:13,080
+orthogonal، مظبوط؟
+
+532
+01:11:37,070 --> 01:11:44,790
+في bottle نيجي الأن هذا رقم ولا لا، بروح مع الرقم
+
+533
+01:11:44,790 --> 01:11:53,170
+اللي تحت، قايلة، هذا الكلام بده يستويإبدالية صحيح
+
+534
+01:11:53,170 --> 01:11:59,830
+ولا لأ؟ يبقى هذا كأن ال U ضد ال V نقص ال U ضد ال V
+
+535
+01:11:59,830 --> 01:12:04,430
+اللي دلت فوق يبقى كده إيش النتج؟ سافر يبقى هذول
+
+536
+01:12:04,430 --> 01:12:08,710
+اتنين في كرة ثقيلة هذا السطر اللي كتبنالك محطوط
+
+537
+01:12:08,710 --> 01:12:13,870
+عندك في الكتاب على صيغة سؤال في التمرين يبقى هاي
+
+538
+01:12:13,870 --> 01:12:17,690
+حد نلالك السؤال واحنا بنشرح الجزء النظري إذا يا
+
+539
+01:12:17,690 --> 01:12:25,760
+بنات من الآن فصاعداأي vector بقدر أكتبه بدلالة جزء
+
+540
+01:12:25,760 --> 01:12:31,020
+في اتجاه ال vector آخر وجزء ثاني عمودي على هذا ال
+
+541
+01:12:31,020 --> 01:12:36,900
+vector الآخر وبتيجي مسائل أحنا في مسائل التمرين
+
+542
+01:12:36,900 --> 01:12:37,940
+على هذا الموضوع
+
+543
+01:12:49,170 --> 01:12:53,030
+مثال على الكلام اللي احنا جايلينه هذا
+
+544
+01:14:00,840 --> 01:14:14,760
+تُب V بده يساوي I زيدي اتنين G ناقص K and a vector
+
+545
+01:14:14,760 --> 01:14:17,520
+Orthogonal
+
+546
+01:14:35,450 --> 01:14:43,930
+درجع لسؤالنا مرة ثانية، اكتبلي المتجه U كمجموع two
+
+547
+01:14:43,930 --> 01:14:50,030
+vectors، واحد منهم موازي ل V وواحد تاني عمودي على
+
+548
+01:14:50,030 --> 01:14:53,390
+V، الموازي ل V هو مين يا بنات؟
+
+549
+01:15:02,160 --> 01:15:08,280
+العمودي هو U نقص ال projection يبقى العمودي الفقري
+
+550
+01:15:08,280 --> 01:15:12,860
+في المثلة هو إيجاد ال projection يبقى باجي بقول ال
+
+551
+01:15:12,860 --> 01:15:13,660
+projection
+
+552
+01:15:29,050 --> 01:15:37,330
+متج ال U ضد ال V بيجي ال U
+
+553
+01:15:37,330 --> 01:15:40,370
+ضد
+
+554
+01:15:40,370 --> 01:15:44,750
+ال V بيجي
+
+555
+01:15:44,750 --> 01:15:49,390
+ال U
+
+556
+01:15:49,390 --> 01:15:52,430
+ضد
+
+557
+01:15:52,430 --> 01:15:53,850
+ال V بيجي ال U ضد ال V بيجي ال U ضد ال V بيجي ال U
+
+558
+01:15:53,850 --> 01:15:53,910
+ضد ال V بيجي ال U ضد ال V بيجي ال U ضد ال V بيجي
+
+559
+01:15:53,910 --> 01:15:53,910
+ال U ضد ال V بيجي ال U ضد ال V بيجي ال U ضد ال V
+
+560
+01:15:53,910 --> 01:15:54,090
+بيجي ال U ضد ال V بيجي ال U ضد ال V بيجي ال U ضد
+
+561
+01:15:54,090 --> 01:15:54,250
+ال V بيجي ال U ضد ال V بيجي ال U ضد ال V بيجي ال U
+
+562
+01:15:54,250 --> 01:15:55,410
+ضد ال V بيجي ال U ضد ال V بيجي ال U ضد ال V بيجي
+
+563
+01:15:55,410 --> 01:15:55,570
+ال U ضد ال V بيجي
+
+564
+01:16:00,130 --> 01:16:07,850
+كله في اتجاه من ال V يبقى هذا الكلام بده يساوي 16
+
+565
+01:16:07,850 --> 01:16:20,890
+و12 28 على 6 في ال V بنزله زي ما هو I نين G ناقص K
+
+566
+01:16:20,890 --> 01:16:26,210
+طبعا هذه بتكسب على كده عشان اتنين هو اربعتاشرعلى
+
+567
+01:16:26,210 --> 01:16:37,110
+ثلاثة وهو 14 على ثلاثة في I نين جي ناقس كي بناء
+
+568
+01:16:37,110 --> 01:16:46,810
+عليه ال vector U بيسافر ل projection تبع ال U على
+
+569
+01:16:46,810 --> 01:16:50,390
+V زائد ال U
+
+570
+01:16:57,330 --> 01:17:03,290
+هذا اللي هو في main vector parallel to v هو هذا
+
+571
+01:17:03,290 --> 01:17:08,930
+orthogonal to v ال projection حسبناها يجاهز اللي
+
+572
+01:17:08,930 --> 01:17:15,790
+هو اربعتاشر على تلاتة I زائد تمانية وعشرين على
+
+573
+01:17:15,790 --> 01:17:19,050
+تلاتة J نقص اربعتاشر
+
+574
+01:17:37,060 --> 01:17:44,600
+ناقص اللي هو اربعتاشر على تلاتة I ناقص تمانية
+
+575
+01:17:44,600 --> 01:17:51,820
+وعشرين على تلاتة J ناقص تمانية وعشرين على تلاتة J
+
+576
+01:17:51,820 --> 01:18:00,680
+زائد اربعتاشر على تلاتة K دخل اشارة السالب على كل
+
+577
+01:18:00,680 --> 01:18:04,700
+component من هذه ال components يبقى النتيجة
+
+578
+01:18:15,860 --> 01:18:22,800
+هذا الـ vector الأول زرع بدا نجمع كل مركبة مع
+
+579
+01:18:22,800 --> 01:18:31,280
+نظيرتها J ناقص اتناشر K ناقص ال projection ناقص
+
+580
+01:18:31,280 --> 01:18:33,080
+اللي هو اربعة
+
+581
+01:18:54,360 --> 01:18:59,580
+من هذه ال components يبقى النتيجة اربع تاشر على
+
+582
+01:18:59,580 --> 01:19:06,580
+تلاتة I تمانية وعشرين على تلاتة J ناقص اربع تاشر
+
+583
+01:19:06,580 --> 01:19:15,500
+على تلاتة K هذا ال vector الأول زار نجمع كل مركبة
+
+584
+01:19:15,500 --> 01:19:21,180
+مع نظيرتها تلاتة في تمانية باربعة وعشرين شيل منهم
+
+585
+01:19:21,180 --> 01:19:23,980
+اربع تاشر بظل عشرة
+
+586
+01:19:31,120 --> 01:19:36,900
+الجيل التاني تلاتة في أربعة باتناشر بالموجب من
+
+587
+01:19:36,900 --> 01:19:40,680
+تمانية وعشرين إلى ستة عشر يبقى النار
+
+588
+01:19:46,270 --> 01:19:52,310
+بعدها تلاتة في اتناش بستة وتلاتين بدنا نشيل منها
+
+589
+01:19:52,310 --> 01:19:57,130
+اتناش بظل اربعة وعشرين على تلاتة اللي هو تمانية
+
+590
+01:19:57,130 --> 01:20:04,670
+يبقى ناقص تمانية كيلو الشكل اللي عندها يبقى هنا
+
+591
+01:20:04,670 --> 01:20:12,050
+راجعها كمان مرة يا بنات يبقى هذه بصير مرة تانية
+
+592
+01:20:13,050 --> 01:20:18,310
+عندك تلاتة في اتناش في ستة و تلاتين في ستة و
+
+593
+01:20:18,310 --> 01:20:22,410
+تلاتين في ستة و تلاتين في ستة و تلاتين في ستة و
+
+594
+01:20:22,410 --> 01:20:25,750
+تلاتين في ستة و تلاتين في ستة و تلاتين في ستة و
+
+595
+01:20:25,750 --> 01:20:26,730
+تلاتين في ستة و تلاتين في ستة و تلاتين في ستة و
+
+596
+01:20:26,730 --> 01:20:27,870
+تلاتين في ستة و تلاتين في ستة و تلاتين في ستة و
+
+597
+01:20:27,870 --> 01:20:29,230
+تلاتين في ستة و تلاتين في ستة و تلاتين في ستة و
+
+598
+01:20:29,230 --> 01:20:29,970
+تلاتين في ستة و تلاتين في ستة و تلاتين في ستة و
+
+599
+01:20:29,970 --> 01:20:33,450
+تلاتين في ستة و تلاتين في ستة و تلاتين في ستة و
+
+600
+01:20:33,450 --> 01:20:34,770
+تلاتين في ستة و
+
+601
+01:20:46,550 --> 01:20:50,690
+طبعا، فيه، يبقى معاناته متجلة، اتنين هذول بقى لهم
+
+602
+01:20:50,690 --> 01:20:57,850
+اتنين متعامدين لحد هنا stop انتهاء ال section
+
+603
+01:20:57,850 --> 01:21:05,930
+والان بدنا نعطيكوا أرقام المسائل المطموض حلها سؤال
+
+604
+01:21:05,930 --> 01:21:07,970
+اللي بدأ أسالكوا ياه روحتوا على ال discussion
+
+605
+01:21:07,970 --> 01:21:12,690
+السبوع الماضي عليه
+
+606
+01:21:12,690 --> 01:21:14,390
+حد المناقش عنكم
+
+607
+01:21:23,380 --> 01:21:28,140
+يبقى ده انا قدناقيها لو ما جت coach بتروح الدور و
+
+608
+01:21:28,140 --> 01:21:33,480
+عليها و بلغوني هه اجت ولا ماجتش يبقى exercises
+
+609
+01:21:33,480 --> 01:21:41,040
+اتناشر تلاتة المسائل التالية تلاتة، خمسة، سبعة،
+
+610
+01:21:41,040 --> 01:21:47,520
+احداشر، تلاتاشر، سبعتاشر، تسعة و اتشرين
+
+611
+01:22:16,240 --> 01:22:28,100
+يبقى الآن نروح ل section 12-4 12-4 اللي هو نقرص او
+
+612
+01:22:28,100 --> 01:22:33,400
+vector product
+
+613
+01:22:33,400 --> 01:22:38,480
+العلوان
+
+614
+01:22:38,480 --> 01:22:43,300
+اللي احنا حاطينه اسمه معاه يعنيش لما نقطر two
+
+615
+01:22:43,300 --> 01:22:43,920
+vectors
+
+616
+01:22:49,160 --> 01:22:53,200
+قليل لذلك بناروح نكتب ال definition اللي عندنا هذا
+
+617
+01:22:53,200 --> 01:22:58,580
+و بعدين ناخد بعض الملاحظات عليه هيبقى definition
+
+618
+01:22:58,580 --> 01:23:08,200
+هحطه الصيغة الأولى اللي هي V a cross أو ال vector
+
+619
+01:23:08,200 --> 01:23:14,340
+a product of
+
+620
+01:23:14,340 --> 01:23:17,900
+two vectors of two
+
+621
+01:23:24,650 --> 01:23:37,330
+الـ V is defined by العرفة التالية U cross ال V في
+
+622
+01:23:37,330 --> 01:23:43,810
+درجة ساوية قول ال U في طول ال V في صين الزاوية
+
+623
+01:23:43,810 --> 01:23:48,090
+تيتا في اتجاه متجه الوحدة L
+
+624
+01:24:09,330 --> 01:24:15,290
+أو الـ V
+
+625
+01:24:15,290 --> 01:24:17,990
+عمودي على الإتنين
+
+626
+01:24:29,330 --> 01:24:35,430
+خلّينا نطرح الشوية للتالت، هل يمكن للـ cross
+
+627
+01:24:35,430 --> 01:24:42,930
+product لـ two vectors يطلع zero؟ ممكن، طيب الـ
+
+628
+01:24:42,930 --> 01:24:47,650
+zero هذا هو zero vector ولا zero شكلها؟ Zero
+
+629
+01:24:47,650 --> 01:24:48,210
+vector
+
+630
+01:24:56,050 --> 01:25:02,570
+بدي أضع هذا في صيغة الملاحظة التالية لو جيها تقولش
+
+631
+01:25:02,570 --> 01:25:09,050
+لك if ال U cross ال V بده يسوى ال zero vector
+
+632
+01:25:30,670 --> 01:25:36,310
+واحد منهم ممكن يكون zero او كلاهما ب zero الاحتمال
+
+633
+01:25:36,310 --> 01:25:41,550
+الثاني هذا الاحتمال الاول الاحتمال الثاني ممكن
+
+634
+01:25:41,550 --> 01:25:46,430
+يكونوا ادو ال zero او
+
+635
+01:25:46,430 --> 01:25:54,960
+180 يعني اتنين معاهم يكونوا are parallelوالتوازين
+
+636
+01:25:54,960 --> 01:25:58,700
+الانطباق يا بنات والتوازن اللي اكبره اتنين ارضه
+
+637
+01:25:58,700 --> 01:26:01,900
+سيء من ان ال vector vector انجلوب من مكان الى اي
+
+638
+01:26:01,900 --> 01:26:08,320
+مكان اخر موازن لهو يسوى في المقدار ال جباجي بقول
+
+639
+01:26:08,320 --> 01:26:15,280
+هنا يسوى zero then
+
+640
+01:26:15,280 --> 01:26:27,970
+lu and v are parallelthat is the
+
+641
+01:26:27,970 --> 01:26:36,550
+angle between you
+
+642
+01:26:36,550 --> 01:26:41,030
+and ال V is
+
+643
+01:26:47,350 --> 01:26:50,910
+يبقى لو كانت الزاوية بينهم zero او مية و تمانين
+
+644
+01:26:50,910 --> 01:26:57,230
+درجة بقول اتنين هدول مالهم متوازنة طيب لو جيت و
+
+645
+01:26:57,230 --> 01:27:02,150
+قولت هذا ال vector U و هذا ال vector التاني اللي
+
+646
+01:27:02,150 --> 01:27:06,670
+هو V و الزاوية اللي بينهم تيتا هي الزاوية اللي
+
+647
+01:27:06,670 --> 01:27:12,030
+عندها هتشوف وين ال cross product يبقى ال cross
+
+648
+01:27:12,030 --> 01:27:18,570
+product هو عبارة عن متجةعمودي على الاتنين يوجه هذا
+
+649
+01:27:18,570 --> 01:27:24,410
+U cross ال V الزاوية اللي عملها هنا زاوية قائمة
+
+650
+01:27:24,410 --> 01:27:30,130
+والزاوية هذه كمان مين زاوية قائمة زي و لا تشبه ال
+
+651
+01:27:30,130 --> 01:27:34,250
+corner اللي عندنا هذا عمودي على هذا ال vector و
+
+652
+01:27:34,250 --> 01:27:38,290
+عمودي على مين على ال vector إذا لو ضربت ال vector
+
+653
+01:27:38,290 --> 01:27:42,740
+هذا في ال vector هذا crossود يطلع vector منطبق على
+
+654
+01:27:42,740 --> 01:27:45,820
+ال corner اللي هناك تماماً بالضبط
+
+655
+01:28:09,230 --> 01:28:15,690
+بتساوي U1 في اتجاه I U2 في اتجاه J U3 في اتجاه K
+
+656
+01:28:27,200 --> 01:28:32,820
+فد ال U cross ال V، صيغة تانية، مابديش أقول طول
+
+657
+01:28:32,820 --> 01:28:36,560
+الأول في طول التاني في جيب الزاوية بينهما في اتجاه
+
+658
+01:28:36,560 --> 01:28:41,480
+M وإنما بطلع الشغل عملي بدلالة ال I و ال G و ال K
+
+659
+01:28:41,480 --> 01:28:47,800
+سمعت أظن بال determinants المحددات، طبعا كل كنتوا
+
+660
+01:28:47,800 --> 01:28:53,880
+عالي في الثانوية واخدتوا المصوفاتهذا المحدد تمام
+
+661
+01:28:53,880 --> 01:29:00,280
+يبقى هذا عبارة عن المحدد التاني بحط الصف الأول ال
+
+662
+01:29:00,280 --> 01:29:08,100
+I و ال J و ال K بعد هيك بحط مركبات المتجه الأول
+
+663
+01:29:08,100 --> 01:29:17,320
+اللي هو U U1 U2 U3 مركبات المتجه التاني V1
+
+664
+01:29:20,090 --> 01:29:27,150
+لو فكيت هذا المحدد بيطلع المتجر بدلالة I وJ وK
+
+665
+01:29:27,150 --> 01:29:32,690
+وهذا ما سناخده من خلال المثال أو من خلال بعض
+
+666
+01:29:32,690 --> 01:29:38,130
+الأمثلة توضح كيف بدنا أو يذكركوا تذكير بكيف يتفك
+
+667
+01:29:38,130 --> 01:29:44,290
+هذا المحدد تمام؟ إذا نعطيكي المثال التالي
+
+668
+01:29:50,160 --> 01:30:03,900
+أول مثال بيقول الف ال U تساوي اتنين I اتنين I ناقص
+
+669
+01:30:03,900 --> 01:30:17,020
+J زائد K and ال V تساوي اربعة I زائد اتنين J
+
+670
+01:30:32,630 --> 01:30:39,050
+A unit vector
+
+671
+01:30:39,050 --> 01:30:48,650
+متجه واحدة orthogonal to
+
+672
+01:30:48,650 --> 01:30:54,070
+both U and V
+
+673
+01:31:12,720 --> 01:31:20,560
+على التعريف رقم 2 يبقى بدي اعمل determinant I وJ
+
+674
+01:31:20,560 --> 01:31:25,620
+وK بدي احط مركبات المتجه الاول اتنين
+
+675
+01:31:37,430 --> 01:31:43,670
+الثاني في الأول والمتجه الأول بحطته بعدها هتطلع
+
+676
+01:31:43,670 --> 01:31:49,910
+نفسي النتيجة بس بإشارة وخالفة في الإشارة طبعا أخدت
+
+677
+01:31:49,910 --> 01:31:51,590
+من الخواص المحدد في ثانوية
+
+678
+01:32:10,560 --> 01:32:16,860
+يبقى ماجي بيقول هاي اي فيه بروح نشطة بالصف اللى
+
+679
+01:32:16,860 --> 01:32:22,400
+موجود فيه اي و اللى عاوز بيبقى هنا جداش مكس تين ا
+
+680
+01:32:22,400 --> 01:32:27,540
+الرئيسي هاي يبقى عندك المحدد الصغير هذا يبقى حاسب
+
+681
+01:32:27,540 --> 01:32:29,120
+ده اربع ناس القطة الرئيسية
+
+682
+01:32:41,270 --> 01:32:48,630
+في اشطر بصفه وكذلك عامل من اتنين في اتنين باربع
+
+683
+01:32:48,630 --> 01:32:51,150
+ناقص اربع في واحد
+
+684
+01:33:12,980 --> 01:33:18,900
+أربعة زائد أربعة يبقى أربعة زائد أربعة بالشكل اللي
+
+685
+01:33:18,900 --> 01:33:25,920
+عندنا يبقى صار عندنا ناقص أربعة I هذا بيروح ب Zero
+
+686
+01:33:25,920 --> 01:33:35,720
+زائد تمانية K يبقى هذا زائد تمانية K لغوية قيمة
+
+687
+01:33:35,720 --> 01:33:37,040
+المحدد تماما
+
+688
+01:33:40,940 --> 01:33:46,780
+إذا صار عندنا شكل المحدد ناقص أربع I زائد تمانية
+
+689
+01:33:46,780 --> 01:33:50,380
+كيلو المطموب الأول المطموب التاني قال لي هاتلي
+
+690
+01:33:50,380 --> 01:33:57,080
+unit vector orthogonal لمن للإتنين هذا المتجه مش
+
+691
+01:33:57,080 --> 01:34:05,680
+هو عمودي على الإتنين يبقى هنا this vector is
+
+692
+01:34:05,680 --> 01:34:10,140
+orthogonal to
+
+693
+01:34:11,690 --> 01:34:21,790
+بعض الـ U و الـ V إذا المطلوب التاني نمر بيه قال
+
+694
+01:34:21,790 --> 01:34:26,390
+لي هاتي unit vector في الهدايا، يقول إيش بدالي؟
+
+695
+01:34:26,390 --> 01:34:29,890
+بدي أقسم هذا المتجر على طولي
+
+696
+01:34:41,950 --> 01:34:48,570
+على طول الـ U x V الـ U x V هو الناقص 4I
+
+697
+01:35:02,250 --> 01:35:08,710
+يبقى U cross
+
+698
+01:35:08,710 --> 01:35:14,590
+V على طول U cross V يبقى نقطة أربعية زي 8 على مربع
+
+699
+01:35:14,590 --> 01:35:21,130
+عدد 16 مربع عدد 64هذا كله عقداش على تمانين يبقى
+
+700
+01:35:21,130 --> 01:35:28,490
+ناقص أربعة I زائد تمانية K مخسوما على جذر التمانين
+
+701
+01:35:28,490 --> 01:35:34,270
+اللي هي ستاش في خمسة مظبوط ستاش في خمسة التمانين
+
+702
+01:35:34,270 --> 01:35:40,910
+يبقى أربعة جذر خمسة طيب بناء عليه هذا الكلام يبدو
+
+703
+01:35:40,910 --> 01:35:42,670
+يساوي ناقص
+
+704
+01:35:51,740 --> 01:35:56,260
+يا ناس لو .. لو روحت جبت طول المتجه هذا بتطلع واحد
+
+705
+01:35:56,260 --> 01:36:02,760
+صحيح؟ جربي ربعي هذا .. ربعي هذا باربع أخمس يبقى
+
+706
+01:36:02,760 --> 01:36:07,040
+خمس أخمس واحد صحيح؟ آخر مثال صغير
+
+707
+01:36:47,920 --> 01:36:52,610
+بقول لو عملت cross product لمتجهينو الـ dot
+
+708
+01:36:52,610 --> 01:37:00,150
+product لمتجهين و جبت مربع طول ل cross product و
+
+709
+01:37:00,150 --> 01:37:04,410
+مربع ال dot product و جماعة بده يطلع طول المتجه U
+
+710
+01:37:04,410 --> 01:37:08,850
+تربية فطول المتجه V تربية هذا اللي عايزين نتحدث
+
+711
+01:37:08,850 --> 01:37:13,110
+عنه إذا بدنا نحاول نمسك أحد الطرفين و نوصل للطرف
+
+712
+01:37:13,110 --> 01:37:17,330
+الآخرأول نمسك أحد الطرفين و نوصله إلى نقطة و نمسك
+
+713
+01:37:17,330 --> 01:37:21,450
+الطرف الأخر و نوصله إلى نفس النقطة خلّينا نمسك
+
+714
+01:37:21,450 --> 01:37:28,110
+الطرف الأول اللي هو الـU cross الـV لكل تربيع زائد
+
+715
+01:37:28,110 --> 01:37:34,770
+U dot V لكل تربيع يساوي هذا بنادر اللي هو طول الـU
+
+716
+01:37:34,770 --> 01:37:42,570
+في طول الـV في صين الزاوية θ إذا لما قال لتربيع
+
+717
+01:37:42,570 --> 01:37:51,290
+بسيطوهذا تربيع وهذه تربيع ثمين في الطول تبع متجه
+
+718
+01:37:51,290 --> 01:38:00,130
+الوحدة والطول تبع متجه الوحدة الكل تربيع مش عرفنا
+
+719
+01:38:00,130 --> 01:38:04,530
+قبل شوية ال cross product طول ال U في طول ال V في
+
+720
+01:38:04,530 --> 01:38:08,370
+صين الزاوية في اتجاه متجه الوحدة N إذا لما أقول
+
+721
+01:38:08,370 --> 01:38:12,430
+هذا مربع الطول يبقى أخدت الأطوال كلها وربعتها
+
+722
+01:38:23,900 --> 01:38:29,700
+لكن هذا يصير تربيع يبقى هذا تصير تربيع تربيع تربيع
+
+723
+01:38:29,700 --> 01:38:36,420
+كده هذا طول البنات؟ واحد صحيح بهذا خلاص في عامل
+
+724
+01:38:36,420 --> 01:38:43,080
+مشترك ما بين الطرفين يبقى U تربيع طول ال U تربيع
+
+725
+01:38:43,080 --> 01:38:47,440
+طول ال V تربيع بظل Sin تربيع ثيتا
+
+726
+01:38:51,930 --> 01:38:58,210
+هنا بواحد صحيح يبقى بصير طول ال U تربية فطول ال V
+
+727
+01:38:58,210 --> 01:39:05,750
+تربية ما هو المطلوب؟ خلاصنا؟ يبقى لحد هنا وقفنا
+
+728
+01:39:05,750 --> 01:39:10,750
+المرة الجاية بدنا ناخد ان شاء الله تعالى خواص ل
+
+729
+01:39:10,750 --> 01:39:11,690
+cross product
+
+730
+01:39:21,410 --> 01:39:27,090
+أو أرضية للشيء اللي بدنا نشرها حولها بلاد فماجية
+
+731
+01:39:27,090 --> 01:39:31,270
+تحتروا على الارض بالضبط لإنك تاخدها خمس دقايق، عشر
+
+732
+01:39:31,270 --> 01:39:35,390
+دقايق، خمس ساعة، خمس ساعة، فلاش أقفل البابير و
+
+733
+01:39:35,390 --> 01:39:39,530
+أخليكي برا هاي يا ودي يا بني يا بني يا بني يا بني
+
+734
+01:39:39,530 --> 01:39:40,490
+يا بني يا بني يا بني يا بني يا بني يا بني يا بني
+
+735
+01:39:40,490 --> 01:39:44,570
+يا
+
+736
+01:39:44,570 --> 01:39:45,410
+بني
+
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/aAjYJyHQ2EE.srt b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/aAjYJyHQ2EE.srt
new file mode 100644
index 0000000000000000000000000000000000000000..53a7c1ee38a40005f41452557c13b7631107397a
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/aAjYJyHQ2EE.srt
@@ -0,0 +1,2483 @@
+1
+00:00:00,000 --> 00:00:02,700
+موسيقى
+
+2
+00:00:16,500 --> 00:00:21,540
+معادلات الخط المستقيم كانت المعادلات البارامترية
+
+3
+00:00:21,540 --> 00:00:26,440
+للخط المستقيم في الفراغ على صيغة x يساوي x0 زائد
+
+4
+00:00:26,440 --> 00:00:34,440
+v1t، وy يساوي y0 زائد v2t، وz يساوي z0 زائد v3t طبعا
+
+5
+00:00:34,440 --> 00:00:37,580
+x0، وy0، وz0 هي إحداثيات النقطة التي يمر
+
+6
+00:00:37,580 --> 00:00:43,240
+بهذا الخط المستقيم.  v1، v2، v3 هي الـ components  الـ
+
+7
+00:00:43,240 --> 00:00:48,580
+vector الموازي للخط المستقيم، وعطينا المرة
+
+8
+00:00:48,580 --> 00:00:52,980
+الماضية  على ذلك مثالا واحدا. الآن نروح لمثال رقم
+
+9
+00:00:52,980 --> 00:00:57,480
+اثنين. يبقى المثال رقم اثنين بقول: ما
+
+10
+00:01:03,110 --> 00:01:09,350
+five، اللي هو parametric equations، parametric
+
+11
+00:01:09,350 --> 00:01:15,730
+equations، المعادلات البارامترية  للخط، for the line، for
+
+12
+00:01:15,730 --> 00:01:26,750
+the line، للخط المستقيم، الذي يمر بالنقطة
+
+13
+00:01:26,750 --> 00:01:29,510
+اللي هي (2، 3، 0).
+
+14
+00:01:41,740 --> 00:01:52,480
+vectors، وعمودي على المتجهين:  u = i +
+
+15
+00:01:52,480 --> 00:02:02,000
+2j + 3k، والمتجه الثاني v =
+
+16
+00:02:02,000 --> 00:02:09,860
+3i + 4j + 5k.
+
+17
+00:02:15,470 --> 00:02:21,410
+نرجع لسؤالنا مرة ثانية، نقرأ السؤال جيدا،  نعرف نحدد
+
+18
+00:02:21,410 --> 00:02:26,010
+ما هو المطلوب، بناء عليه نعرف نشتغل بدقة، إن شاء
+
+19
+00:02:26,010 --> 00:02:30,710
+الله. يبقى بدنا المعادلة البارامترية للخط المستقيم.
+
+20
+00:02:30,710 --> 00:02:34,630
+يبقى بدنا المعادلات البارامترية الثلاثة هذه، بحيث
+
+21
+00:02:34,630 --> 00:02:38,770
+الخط المستقيم يمر بالنقطة (2، 3، 0). يبقى
+
+22
+00:02:38,770 --> 00:02:46,360
+الإحداثيات x0، y0، z0 معروفة. متجه يوازي
+
+23
+00:02:46,360 --> 00:02:50,580
+هذا الخط. بيقول لي هون: الـ line هذا يمر
+
+24
+00:02:50,580 --> 00:02:56,400
+بالنقطة هذه، وعمودي على المتجهين الاثنين هذول. طيب
+
+25
+00:02:56,400 --> 00:03:02,080
+كيف بقدر أجيب متجه عمودي على متجهين؟ شو بعملهم؟
+
+26
+00:03:02,080 --> 00:03:07,890
+cross product. لو عملت cross product بجيب vector
+
+27
+00:03:07,890 --> 00:03:12,850
+عمودي على كلا المتجهين، اللي بكون هو المتجه
+
+28
+00:03:12,850 --> 00:03:18,190
+المطلوب، حتى أتمكن من الحصول على معادلات الخط
+
+29
+00:03:18,190 --> 00:03:26,370
+المستقيم. إذا بدي أروح أجيب له الـ u × الـ v، يبقى
+
+30
+00:03:26,370 --> 00:03:29,010
+u × v يساوي المحدد
+
+31
+00:03:33,050 --> 00:03:40,610
+المتجه الأول (1، 2، 3)، مركبات المتجه الثاني (3، 4، 5).
+
+32
+00:03:43,420 --> 00:03:47,880
+يبقى على طول الخط هذا بده يساوي: نشطب الصف والعمود
+
+33
+00:03:47,880 --> 00:03:54,280
+(2 × 5 = 10) – (3 × 4 = 12) = -2i
+
+34
+00:03:54,280 --> 00:04:02,600
+اللي بعده: نشطب الصف والعمود (5 × 1 = 5) – (3 × 3 = 9) =
+
+35
+00:04:02,600 --> 00:04:06,140
+-4.  وهذا أصلا مش سالب،  بيبقى +10j
+
+36
+00:04:06,140 --> 00:04:10,680
+يبقى +10j. كيف؟
+
+37
+00:04:17,890 --> 00:04:24,550
+نشطب الصف والعمود: (1 × 4 = 4) – (2 × 3 = 6) = -2
+
+38
+00:04:24,550 --> 00:04:30,070
+مع السالب يبقى +2k. كلام سليم. اللي بعده:
+
+39
+00:04:30,070 --> 00:04:36,230
+نشطب الصف والعمود: (1 × 4 = 4) – (2 × 3 = 6) =
+
+40
+00:04:36,230 --> 00:04:46,210
+-2k. يبقى هذا الـ vector  orthogonal. يبقى
+
+41
+00:04:46,210 --> 00:04:55,430
+هذا parallel لمين؟ للخط. يبقى هذا الـ vector parallel
+
+42
+00:04:55,430 --> 00:04:58,610
+to
+
+43
+00:04:58,610 --> 00:05:02,150
+the required
+
+44
+00:05:02,150 --> 00:05:05,770
+line.
+
+45
+00:05:07,290 --> 00:05:12,590
+يبقى هذا الموازي للخط المطلوب، يعني
+
+46
+00:05:12,590 --> 00:05:17,930
+المطلوب اللي عليه. بدنا نشتغل بناء عليه. إذن أصبح الـ
+
+47
+00:05:17,930 --> 00:05:23,770
+parametric equations هي: x = x0 اللي هي 2
+
+48
+00:05:23,770 --> 00:05:29,670
+زائد المركبة اللي عندنا اللي هي -2، يبقى -
+
+49
+00:05:29,670 --> 00:05:37,590
+2t. يبقى 2 - 2t. المركبة الثانية اللي هي y بدها
+
+50
+00:05:37,590 --> 00:05:43,150
+تساوي المركبة الثانية اللي هي 3 زائد
+
+51
+00:05:46,370 --> 00:05:49,730
+10t. يبقى z، أو المعادلة الثالثة، المركبة عندنا z، والله
+
+52
+00:05:49,730 --> 00:05:55,530
+يسهل علينا. يبقى بضل +2t. والـ t هذه ماعليهاش
+
+53
+00:05:55,530 --> 00:06:01,170
+قيود. يبقى أكبر من -∞ وأقل من
+
+54
+00:06:01,170 --> 00:06:05,210
+∞. يبقى هذه معادلات البارامترية للخط
+
+55
+00:06:05,210 --> 00:06:10,210
+المستقيم اللي عندنا. نعطي كمان مثال رقم ثلاثة.
+
+56
+00:06:29,050 --> 00:06:39,230
+الخطوط المستقيمة التالية are intersecting
+
+57
+00:06:39,230 --> 00:06:46,450
+ولا parallel، or
+
+58
+00:06:46,450 --> 00:06:49,470
+skew،
+
+59
+00:06:49,470 --> 00:06:53,630
+if
+
+60
+00:06:53,630 --> 00:06:57,690
+they intersect.
+
+61
+00:07:00,560 --> 00:07:18,800
+إذا كان هناك تقاطع، احصل على نقاط التقاطع.
+
+62
+00:07:18,800 --> 00:07:23,520
+المستقيم الأول، L1، موضح بصيغة
+
+63
+00:07:23,520 --> 00:07:30,920
+البارامترية: x = 1 + 2t، و y =
+
+64
+00:07:30,920 --> 00:07:35,780
+-1 - t، و z =
+
+65
+00:07:38,260 --> 00:07:44,040
+3t. والمستقيم الثاني، L2، موضح بالشكل الثاني: x =
+
+66
+00:07:44,040 --> 00:07:54,240
+2 - s، و y = 3s، و z = 1 + s.
+
+67
+00:07:56,280 --> 00:08:03,940
+ثالثا، الخط على الصيغة. الـ L3 عبارة عن
+
+68
+00:08:03,940 --> 00:08:13,680
+الـ x = 5 + 2r، و y = 1 - r، و
+
+69
+00:08:13,680 --> 00:08:20,380
+z = 8 + 3r.
+
+70
+00:08:24,750 --> 00:08:29,930
+هنا بالنسبة لي ماعنديش قيود لا على t ولا s ولا r.
+
+71
+00:08:29,930 --> 00:08:35,290
+يبقى هذا على كل الـ real line.  بلاستيكية، نحاول
+
+72
+00:08:35,290 --> 00:08:37,710
+نشوف المستقيمات اللي عندنا هذه.
+
+73
+00:09:06,190 --> 00:09:12,130
+نرجع لسؤالنا مرة ثانية. بيعطيني ثلاثة مستقيمات: L1، و
+
+74
+00:09:12,130 --> 00:09:14,930
+L2، وL3. (تكرار لارقام الخطوط)
+
+75
+00:09:14,930 --> 00:09:16,850
+(تكرار لارقام الخطوط)
+
+76
+00:09:16,850 --> 00:09:22,070
+(تكرار لارقام الخطوط)
+
+77
+00:09:22,070 --> 00:09:23,030
+(تكرار لارقام الخطوط)
+
+78
+00:09:23,030 --> 00:09:25,010
+(تكرار لارقام الخطوط)
+
+79
+00:09:25,010 --> 00:09:25,090
+(تكرار لارقام الخطوط)
+
+80
+00:09:25,090 --> 00:09:26,330
+(تكرار لارقام الخطوط)
+
+81
+00:09:34,860 --> 00:09:45,500
+كويس. لما أقول اثنين متوازيين،
+
+82
+00:09:45,500 --> 00:09:51,560
+يبقى there is no intersection، مفيش تقاطع. طب كيف
+
+83
+00:09:51,560 --> 00:09:55,000
+بثبت أن two vectors are parallel؟
+
+84
+00:10:03,600 --> 00:10:09,640
+مستقيمين متخالفين، يعني لا تقاطع ولا توازي مهما المدى
+
+85
+00:10:09,640 --> 00:10:12,820
+هذا من -∞ إلى ∞، وهذا من ∞
+
+86
+00:10:12,820 --> 00:10:18,360
+إلى -∞. مافيش تقاطع، وليس هناك توازي. مثل
+
+87
+00:10:18,360 --> 00:10:23,100
+ذلك. لو جبت لك الـ corner اللي عندك هذا. هذا خط مستقيم
+
+88
+00:10:23,380 --> 00:10:27,880
+و الخط المستقيم اللي هو في القلي هناك، مهما أمددتهم
+
+89
+00:10:27,880 --> 00:10:31,220
+مافيش intersection ما بين الاثنين. يبقى هدول
+
+90
+00:10:31,220 --> 00:10:38,740
+بيسميهم skew lines، مستقيمات متخالفة. طيب نجي نشوف
+
+91
+00:10:38,740 --> 00:10:42,600
+إيش القصة الثانية كده؟ بدنا نثبت أن هدول متوازيين،
+
+92
+00:10:42,600 --> 00:10:47,400
+متقاطعين، متخالفين. بقول كويس. بدي أمسك المستقيم
+
+93
+00:10:47,400 --> 00:10:56,370
+الأول والثاني. هل هناك متجه يوازي المستقيم الأول من
+
+94
+00:10:56,370 --> 00:10:59,990
+خلال المعادلة هذه؟
+
+95
+00:11:08,280 --> 00:11:15,380
+هذا الـ vector يوازي المتجه الأول. وهذا الـ vector
+
+96
+00:11:15,380 --> 00:11:20,260
+الثاني يوازي
+
+97
+00:11:20,260 --> 00:11:21,880
+المتجه الثاني.
+
+98
+00:11:25,980 --> 00:11:30,980
+معناته المستقيمين متوازيين، صح ولا لا؟ طيب إذا كانوا
+
+99
+00:11:30,980 --> 00:11:34,620
+هدول ما هما متوازيين، يبقى المستقيمين غير متوازيين.
+
+100
+00:11:34,620 --> 00:11:39,880
+بيظل احتمال التقاطع أو التخالف، وبنبحث القصة هذه
+
+101
+00:11:39,880 --> 00:11:48,180
+ونشوف. يبقى باجي بقول هون: الـ one solution. الـ one
+
+102
+00:11:48,180 --> 00:11:54,380
+parallel to the vector
+
+103
+00:11:55,870 --> 00:12:03,170
+V1 هو مين؟ V1 هذا هجيبه من المعادلة: 2i
+
+104
+00:12:03,170 --> 00:12:11,870
+- j + 3k.  بعدين: الـ L2 parallel to the
+
+105
+00:12:11,870 --> 00:12:19,990
+vector، باجي هون اللي هو V2: -i + 3j
+
+106
+00:12:19,990 --> 00:12:23,770
++ k. السؤال
+
+107
+00:12:25,330 --> 00:12:30,150
+هل واحد من الاثنين هذول مضاعفات الآخر؟ مش ممكن.
+
+108
+00:12:30,150 --> 00:12:33,390
+يبقى المعنى بيقول: الاثنين هذول are not parallel.
+
+109
+00:12:33,390 --> 00:12:41,070
+وبالتالي الـ two lines are not parallel. يبقى هون L1
+
+110
+00:12:41,070 --> 00:12:54,050
+is not parallel to L2 because، السبب أن V1 is
+
+111
+00:13:02,600 --> 00:13:08,860
+وبالتالي لا يوجد توازي بين V1 وV2، وبالتالي لا
+
+112
+00:13:08,860 --> 00:13:13,920
+يمكن للـ two lines L1 وL2 يكونوا اثنين are
+
+113
+00:13:13,920 --> 00:13:21,020
+parallel. يبقى سقط التوازي. بظل احتمال التقاطع، الان
+
+114
+00:13:21,020 --> 00:13:26,040
+بدنا نحكم على المستقيمين: هم متخالفين ولا
+
+115
+00:13:26,040 --> 00:13:32,500
+المستقيمين متقاطعين؟ مش هنحكم بتحويل أي واحدة
+
+116
+00:13:32,500 --> 00:13:37,260
+فيهم. إذا استبعدت واحدة فيهم بتظل مين؟ بتظل الأخرى
+
+117
+00:13:37,260 --> 00:13:42,580
+إجباريا. يبقى جدلا أنا ببدأ أفترض أن الاثنين هم
+
+118
+00:13:42,580 --> 00:13:48,380
+متقاطعين، وأشوف إيش اللي بيوصلني.  يبقى هذا باجي
+
+119
+00:13:48,380 --> 00:13:55,580
+بقول: L1، L2، L3، L4، L5، L6، L7، L8، L9، L10، L11، L12، L13،
+
+120
+00:13:55,580 --> 00:14:01,280
+L14، L15، L16، L17، L18، L19، L20، L21، L22، L23، L24، L25،
+
+121
+00:14:01,280 --> 00:14:03,760
+L26، L27، L28، L29...(تكرار لرقم الخط)
+
+122
+00:14:03,760 --> 00:14:06,900
+(تكرار لرقم الخط)
+
+123
+00:14:06,900 --> 00:14:06,980
+(تكرار لرقم الخط)
+
+124
+00:14:06,980 --> 00:14:07,040
+(تكرار لرقم الخط)
+
+125
+00:14:07,040 --> 00:14:07,860
+(تكرار لرقم الخط)
+
+126
+00:14:07,860 --> 00:14:08,840
+(تكرار لرقم الخط)
+
+127
+00:14:14,330 --> 00:14:22,810
+بتكون 1 + 2t = 2 - s، و -1 - t = 3s، وعندنا هنا 3t
+
+128
+00:14:22,810 --> 00:14:31,650
+= 1 + s. هذول كم معادلة؟ ثلاث معادلات، و
+
+129
+00:14:31,650 --> 00:14:40,390
+كم مجهول؟ اثنين. يعني الحمد لله ربنا حط البركة
+
+130
+00:14:40,390 --> 00:14:44,090
+عشان نجيب t و s. بيكفينا اثنتين. عدد المعادلات يساوي
+
+131
+00:14:48,750 --> 00:14:52,090
+عدد المجاهيل. لكن ثلاث معادلات، يعني الحمد لله ربنا
+
+132
+00:14:52,090 --> 00:14:57,790
+حط البركة. okay، تمام. بقول كويس، خلينا نجرب نحل
+
+133
+00:14:57,790 --> 00:15:02,370
+المعادلتين الاثنتين هذول مع بعض، ونشوف إيش بده
+
+134
+00:15:02,370 --> 00:15:11,920
+يعطينا. يبقى هذا يعطينا: 1 + 2t = 2 - s.
+
+135
+00:15:11,920 --> 00:15:19,820
+المعادلة الثانية: نضربها في 2، يبقى -2 - 2t = 6s.
+
+136
+00:15:19,820 --> 00:15:28,880
+هنا -2 - 2t = 6s.
+
+137
+00:15:32,490 --> 00:15:40,870
+يبقى على اليسار -1، يبقى على اليمين
+
+138
+00:15:40,870 --> 00:15:46,050
+-s + 6s = 5s. يبقى -1 + 5s = 5s = 
+
+139
+00:15:46,050 --> 00:15:53,410
+2 +5s = -3 +5s, هذا معناه
+
+140
+00:15:53,410 --> 00:15:59,450
+أن -3 = 5s.  هذا معناه أن s
+
+141
+00:15:59,450 --> 00:16:01,850
+يساوي -3/5.
+
+142
+00:16:06,940 --> 00:16:11,920
+يبقى نعوض في أي من المعادلتين. لو جيت عوضت في
+
+143
+00:16:11,920 --> 00:16:16,640
+المعادلة الأولى. بس إذا عندي 1 + 2t
+
+144
+00:16:16,640 --> 00:16:25,120
+= 2 - s. s عندي = -3/5
+
+145
+00:16:37,740 --> 00:16:40,260
+(تكرار لرقم ثلاثه)
+
+146
+00:16:40,260 --> 00:16:43,220
+(تكرار لرقم ثلاثه)
+
+147
+00:16:43,220 --> 00:16:44,600
+(تكرار لرقم ثلاثه)
+
+148
+00:16:44,600 --> 00:16:45,140
+(تكرار لرقم ثلاثه)
+
+149
+00:16:45,140 --> 00:16:45,420
+(تكرار لرقم ثلاثه)
+
+150
+00:16:45,420 --> 00:16:48,300
+(تكرار لرقم ثلاثه)
+
+151
+00:16:48,300 --> 00:16:53,500
+(تكرار لرقم ثلاثه)
+
+152
+00:16:57,480 --> 00:17:04,880
+مرة ثانية، بقول: 3/5
+
+153
+00:17:04,880 --> 00:17:11,080
+= 2t، ومنها t = 3/10.
+
+154
+00:17:11,080 --> 00:17:14,590
+= 2t، ومنها t = 3/10.  يبقى حصلت على t
+
+155
+00:17:14,590 --> 00:17:21,790
+وحصلت هنا على s. إذا في تقاطع، لازم قيمة
+
+156
+00:17:21,790 --> 00:17:26,210
+المعادلة الثالثة هذه تساوي قيمة المعادلة هذه. إذا لم
+
+157
+00:17:26,210 --> 00:17:30,370
+تتساوي القيمتان، يبقى بيكون there is no
+
+158
+00:17:30,370 --> 00:17:35,430
+intersection. ماعنديش تقاطع بتاتا. يبقى بناء عليه
+
+159
+00:17:35,430 --> 00:17:40,590
+بيروح نعوض في المعادلة الثالثة.  هنسميها *
+
+160
+00:17:44,880 --> 00:17:52,140
+يبقى بتقول الان: substitute، عوض لي
+
+161
+00:17:52,140 --> 00:17:58,900
+in *. نحصل على إيش؟ يبقى عندي 3t
+
+162
+00:17:58,900 --> 00:18:07,920
+و t = 3/10 اللي هو الأصل. يساوي قد إيش؟ يساوي
+
+163
+00:18:07,920 --> 00:18:09,540
+الواحد.
+
+164
+00:18:13,590 --> 00:18:20,230
+هل هذول بيساووا بعض؟ ليش؟
+
+165
+00:18:20,230 --> 00:18:27,070
+لأن هذا 9/10، وهذا 12/5، يبقى 12
+
+166
+00:18:27,070 --> 00:18:33,690
+/5 لا يمكن أن تساوي 9/10. معنى هذا الكلام
+
+167
+00:18:33,690 --> 00:18:36,550
+أن المستقيمين الاثنين هذول لا يتقاطعان.
+
+168
+00:18:39,810 --> 00:18:51,270
+L1 و L2 لا يتقاطعان.
+
+169
+00:19:09,620 --> 00:19:16,060
+مستقيمان متخالفان. طيب احنا بحثنا الآن المستقيم الأول
+
+170
+00:19:16,060 --> 00:19:22,060
+مع الثالث. بدنا نبحث المستقيم الأول مع الثالث. يبقى
+
+171
+00:19:22,060 --> 00:19:29,300
+مرة ثانية بدي أقول: انتهينا من المطلوب الأول. V1، فرق
+
+172
+00:19:29,300 --> 00:19:38,260
+أو L1، فرق الـV1.
+
+173
+00:19:38,260 --> 00:19:38,900
+اللي عندنا.
+
+174
+00:19:53,720 --> 00:20:00,980
+parallel to V3، ويساوي 2i - j
+
+175
+00:20:07,660 --> 00:20:13,080
++ 3k. يبقى صار V1 وV2 are parallel
+
+223
+00:25:17,800 --> 00:25:23,110
+واحدة يا هذه يا هذه، أخذت هذه بتعوض قيمة A، أخذت هذه
+
+224
+00:25:23,110 --> 00:25:28,510
+بتعوض قيمة S، واضح أن S أسهل لأنها بجداش بواحد صحيح
+
+225
+00:25:28,510 --> 00:25:34,870
+إذا بدأ أقول X وY وZ أحداث النقطة، بدوا يساوي أنا
+
+226
+00:25:34,870 --> 00:25:40,710
+بدأ أمسك الـ L2 اللي هو اتنين ناقص واحد وتلاتة
+
+227
+00:25:50,240 --> 00:25:55,580
+نقطة التقاطع للمستقيمين الاتنين اللي عندنا هادول
+
+228
+00:25:55,580 --> 00:25:58,720
+طيب
+
+229
+00:25:58,720 --> 00:26:03,800
+ده حد هنا stop، انتهينا من النقطة الأولى من هذا الـ
+
+230
+00:26:03,800 --> 00:26:06,840
+section اللي ابتدأناها المرة الماضية
+
+231
+00:26:12,170 --> 00:26:20,590
+أي استفسار عندنا هنا؟ حد بيتسأل أي سؤال؟ طيب بروح
+
+232
+00:26:20,590 --> 00:26:22,830
+لـ لقال النقطة الثانية
+
+233
+00:26:52,540 --> 00:26:56,700
+النقطة الثانية يا بنات هي المسافة من نقطة إلى خط
+
+234
+00:26:56,700 --> 00:27:02,140
+مستقيم في الفرقة الـ
+
+235
+00:27:02,140 --> 00:27:06,160
+distance المسافة
+
+236
+00:27:06,160 --> 00:27:20,380
+from a point to a line in space
+
+237
+00:27:24,110 --> 00:27:29,730
+هنا نجيب المسافة ما بين نقطة وخط مستقيم بالفرعات
+
+238
+00:27:29,730 --> 00:27:38,130
+نفترض على سبيل المثال أن هذا هو line L، وأخذنا نقطة
+
+239
+00:27:38,130 --> 00:27:42,650
+وأن تكون هذه النقطة نقطة S مثلاً
+
+240
+00:27:45,440 --> 00:27:52,980
+بنجيب قداش المسافة ما بين النقطة S والـ Line L
+
+241
+00:27:52,980 --> 00:27:58,220
+بقول والله كويس، المسافة اللي وصلتك هذه مسافة هذه
+
+242
+00:27:58,220 --> 00:28:03,800
+مسافة هذه مسافة هذه مسافة، لكن في الحقيقة المسافة
+
+243
+00:28:03,800 --> 00:28:09,360
+الحقيقية هي المسافة العمودية بين هذه النقطة والخط
+
+244
+00:28:09,360 --> 00:28:16,160
+المستقيم، يعني بنروح ننزل عمود على الخط المستقيم من
+
+245
+00:28:16,160 --> 00:28:22,080
+هذه النقطة بهذا الشكل، يبقى
+
+246
+00:28:22,080 --> 00:28:28,540
+هذا عمود، يبقى هذا الـ distance دي مطلوب مننا نعرف
+
+247
+00:28:28,540 --> 00:28:33,900
+قداش مقدار الـ distance دي، طبعاً distance مسافة و
+
+248
+00:28:33,900 --> 00:28:39,140
+احنا بنشتغل في موضوع المتجهات، إذا بلزمني المتجهات
+
+249
+00:28:39,140 --> 00:28:44,920
+في معرفة هذه الـ distance، لذلك النقطة S هذه نقطة
+
+250
+00:28:44,920 --> 00:28:49,500
+معلومة معروفة عندي لأنهم يعطينا أحداثياتها والـ
+
+251
+00:28:49,500 --> 00:28:56,280
+line عندي معروف تمام، يبقى أنا مشان أجيب المسافة
+
+252
+00:28:56,280 --> 00:29:02,190
+هذه بروح أدور على vector موازٍ لهذا الـ line، وطبعاً
+
+253
+00:29:02,190 --> 00:29:05,190
+إذا الـ line معطى في الصيغة البارامترية، بيصير الـ
+
+254
+00:29:05,190 --> 00:29:09,510
+vector معروف، الـ vector معروف، والنقطة معروفة منهم
+
+255
+00:29:09,510 --> 00:29:14,530
+بقدر أجيب الـ distance، كيف؟ كالتالي بروح آخذ أي
+
+256
+00:29:14,530 --> 00:29:21,810
+نقطة موجودة على هذا الـ line، وليكن النقطة P، بأخذ
+
+257
+00:29:21,810 --> 00:29:29,590
+المتجه PS بالشكل اللي عندنا، يبقى هذا هو المتجه PS
+
+258
+00:29:31,180 --> 00:29:40,120
+PS يصنع زاوية مع المستقيم L أو مع المتجه
+
+259
+00:29:40,120 --> 00:29:48,940
+الموازٍ للـ line L، وليكن المتجه V الموازٍ للـ line L
+
+260
+00:29:48,940 --> 00:29:55,700
+يصنع زاوية مقدارها θ، صار
+
+261
+00:29:55,700 --> 00:30:02,790
+عندي مثلث قائم الزاوية، هذا طوله هو طول الـ P
+
+262
+00:30:02,790 --> 00:30:09,510
+S، وهذا أحد ضلعي القائمة، والزاوية θ اللي عندنا
+
+263
+00:30:09,510 --> 00:30:14,410
+هذه، حد فيكم بيقدر يجيب لي D بدلالة طول PS
+
+264
+00:30:14,410 --> 00:30:19,870
+والزاوية θ اللي هو PS يصنع الزاوية θ، يبقى
+
+265
+00:30:19,870 --> 00:30:25,910
+D تساوي PS طول المتجه في sin الزاوية
+
+266
+00:30:28,370 --> 00:30:33,370
+طيب، يبقى الحين قصتنا صارت معروفة، بس بدي أحول
+
+267
+00:30:33,370 --> 00:30:40,470
+الصياغة هذه بصياغة أخرى، تمام، فباجي بقول هنا the
+
+268
+00:30:40,470 --> 00:30:55,050
+distance d is given by، الـd يساوي طول الـPS في
+
+269
+00:30:55,050 --> 00:30:57,050
+مين؟ في sin الزاوية
+
+270
+00:30:59,640 --> 00:31:05,640
+طيب، نرجع بالذاكرة إلى الورقة، لو عندي متجهين U و V
+
+271
+00:31:05,640 --> 00:31:12,320
+وعملت لهم cross product، يبقى U cross V طول الـ U
+
+272
+00:31:12,320 --> 00:31:15,900
+في طول الـ V في sin الزاوية θ في اتجاه متجه
+
+273
+00:31:15,900 --> 00:31:21,420
+الوحدة M اللي هو خط طول بصورة U، طول U cross V
+
+274
+00:31:21,420 --> 00:31:25,500
+طول الـ U في طول الـ V في sin الزاوية θ، صح؟ إذا
+
+275
+00:31:25,500 --> 00:31:31,020
+لو كنت بجيب sin زاوية θ، بيصير طول الـ U cross V على طول
+
+276
+00:31:31,020 --> 00:31:36,220
+الـ U في طول الـ V، إذا الـ sin زاوية θ هذه بقدر
+
+277
+00:31:36,220 --> 00:31:44,460
+أشيلها وأقول هو طول الـ PS sin زاوية θ، θ
+
+278
+00:31:44,460 --> 00:31:53,680
+محصورة بين مين؟ بين PS و V، يبقى طول الـ PS cross الـ
+
+279
+00:31:53,680 --> 00:31:54,220
+V
+
+280
+00:31:59,160 --> 00:32:06,720
+على طول الـPS في طول الـV في
+
+281
+00:32:06,720 --> 00:32:11,760
+شغلة ممكن نختصرها بين البسط والمقام، طول الـPS مع
+
+282
+00:32:11,760 --> 00:32:18,500
+طول الـPS، ما قسمت على متجه، ما قسمت متجه، قسمت
+
+283
+00:32:18,500 --> 00:32:22,600
+على طول المتجه، يعني قسمت على scalar، يبقى من هنا
+
+284
+00:32:22,600 --> 00:32:29,660
+بيصير الـ distance D، بيصير طول الـ PS cross الـ V
+
+285
+00:32:29,660 --> 00:32:36,700
+على طول المتجه V، يبقى هذه وسيلة عملية على كيفية
+
+286
+00:32:36,700 --> 00:32:43,980
+الحصول على المسافة بين نقطة وخط مستقيم في الفراغ
+
+287
+00:32:43,980 --> 00:32:50,600
+يبقى يا بنات، بالبلدي هيك بنحكي، الآن لو في عندي نقطة
+
+288
+00:32:50,600 --> 00:32:55,060
+في الفراغ، وعندي خط مستقيم كده، بدي أجيب المسافة كده
+
+289
+00:32:55,060 --> 00:33:01,600
+بين هذه النقطة وذاك الخط المستقيم، ايش بلزمني؟ نقطة
+
+290
+00:33:01,600 --> 00:33:06,940
+معروفة، أحداثياتها، يمكن بدي أوجد أي نقطة على الخط
+
+291
+00:33:06,940 --> 00:33:12,660
+اللي اللي هسميها P، كويس، وبحتاج متجه موازٍ
+
+292
+00:33:34,740 --> 00:33:40,500
+طيب، أجت واحدة مش عارفة الرسمة، وعطيتها سؤال
+
+293
+00:33:48,170 --> 00:33:52,670
+وقلت لها: قيلي المسافة بين هذه النقطة وهذا الـ line
+
+294
+00:33:52,670 --> 00:33:56,210
+أجت على القانون اللي أخذت الـ tech tech اللي طلع
+
+295
+00:33:56,210 --> 00:34:05,370
+عليه، صفر، ما تفسيره؟ كلنا لهذا الاتجاه، ايوا
+
+296
+00:34:05,370 --> 00:34:11,470
+يبقى كم؟ قالت الأخت اسمك أنتِ؟ أفنان، أفنان زي ما قالت
+
+297
+00:34:11,470 --> 00:34:19,220
+أختها أفنان، هذه النقطة تبقى على نفس القرار المصطلح
+
+298
+00:34:30,710 --> 00:34:35,130
+معنى هذا الكلام أن هذه النقطة تقع على الخط
+
+299
+00:34:35,130 --> 00:34:40,890
+المستقيم مباشرةً، طيب stop لحد هنا، نيجي ناخد بعض
+
+300
+00:34:40,890 --> 00:34:45,970
+الأمثلة على الكلام اللي احنا جايين عليه، هذا أول مثال
+
+301
+00:34:45,970 --> 00:34:50,630
+examples، أول
+
+302
+00:34:50,630 --> 00:34:52,310
+مثال على هذا الموضوع
+
+303
+00:34:58,400 --> 00:35:02,520
+خدنا قداش المسافة من الـ point
+
+304
+00:35:11,650 --> 00:35:18,130
+وتلاتة to the line للخط
+
+305
+00:35:18,130 --> 00:35:27,770
+المستقيم X يساوي عشرة زائد أربعة T، وY يساوي ناقص
+
+306
+00:35:27,770 --> 00:35:34,270
+تلاتة، وZ يساوي أربعة T
+
+307
+00:35:44,390 --> 00:35:49,670
+سؤال مرة ثانية، بيعطيني خط مستقيم في الصيغة الـ
+
+308
+00:35:49,670 --> 00:35:55,210
+بارامترية، وبيعطيني نقطة يمر بها هذا الخط المستقيم
+
+309
+00:35:55,210 --> 00:36:01,330
+أو نقطة في الفراغ، فبدي أجيب قداش المسافة من هذه
+
+310
+00:36:01,330 --> 00:36:06,110
+النقطة إلى هذا الـ line، زي ما احنا شايفين بده نقطة
+
+311
+00:36:07,090 --> 00:36:11,850
+موجودة، والحمد لله موجودة، بدي vector موازٍ للـ line
+
+312
+00:36:11,850 --> 00:36:16,010
+اللي مطلوب أجيب المسافة بينه وبين النقطة، الـ vector
+
+313
+00:36:16,010 --> 00:36:20,770
+بجيبه من وين؟ من نفس المعادلة اللي عندنا، يبقى باجي
+
+314
+00:36:20,770 --> 00:36:26,590
+بقول بدي أجيب الـ vector الموازي لمين؟ لهذا الـ line
+
+315
+00:36:26,590 --> 00:36:29,070
+يبقى V يساوي
+
+316
+00:36:33,480 --> 00:36:39,960
+صفر المركبة، يبقى مع السلامة، يبقى زائد أربعة k
+
+317
+00:36:39,960 --> 00:36:49,120
+هذا parallel to the given line
+
+318
+00:36:52,900 --> 00:36:58,120
+يبقى هذا parallel to the given line، يبقى صار المتجه
+
+319
+00:36:58,120 --> 00:37:04,720
+الموازٍ موجود، والنقطة موجودة، تمام، طيب بدي المتجه P
+
+320
+00:37:04,720 --> 00:37:12,460
+S، معناته بدي النقطة P، أنا عندي هنا الـ S، يبقى نأخذ
+
+321
+00:37:12,460 --> 00:37:17,300
+النقطة اللي فوق، يبقى الـ S هي
+
+322
+00:37:17,300 --> 00:37:25,270
+النقطة واحد وأربعة وتلاتة، طيب، وP هذه
+
+323
+00:37:25,270 --> 00:37:29,510
+النقطة اللي بيمر فيها الخط المستقيم، اللي هي المركبة
+
+324
+00:37:29,510 --> 00:37:34,190
+الأولى لها عشرة، المركبة الثانية سالب تلاتة، واللي
+
+325
+00:37:34,190 --> 00:37:36,190
+بعدها كده؟ صفر
+
+326
+00:37:42,650 --> 00:37:49,190
+يساوي ناقص واحد ناقص عشرة، ناقص واحد ناقص عشرة في
+
+327
+00:37:49,190 --> 00:37:56,530
+اتجاه الـ I، اللي بعده أربعة زائد تلاتة، زائد أربعة
+
+328
+00:37:56,530 --> 00:38:02,910
+زائد تلاتة في اتجاه الـ J، اللي بعده تلاتة ناقص صفر
+
+329
+00:38:02,910 --> 00:38:11,430
+في اتجاه الـ K، يبقى ناقص 11 I زائد سبعة J زائد
+
+330
+00:38:11,430 --> 00:38:20,390
+تلاتة K زائد
+
+331
+00:38:20,390 --> 00:38:21,670
+تلاتة K
+
+332
+00:38:27,940 --> 00:38:37,600
+الـ V، يبقى الـ PS اللي هو سالب 11، 7، 3، الـ V 4، 0، 4
+
+333
+00:38:37,600 --> 00:38:49,600
+طبعاً I، J، K، الصف الثاني اللي هو من 4، 0، 4
+
+334
+00:38:49,600 --> 00:38:55,260
+بالشكل اللي عندنا، يبقى بالطريقة بأفك المحدد، هذا 7 في
+
+335
+00:38:55,260 --> 00:39:04,630
+4، 28، وعندك I، يبقى هنا 28 I، اللي
+
+336
+00:39:04,630 --> 00:39:11,850
+بعده بنفس طريقة العمود، بيصير ناقص 44 وناقص
+
+337
+00:39:11,850 --> 00:39:15,510
+12، يبقى ناقص 56
+
+338
+00:39:24,490 --> 00:39:31,610
+ناقص 28 K، ناقص 28 K، ناقص
+
+339
+00:39:31,610 --> 00:39:39,010
+28 K، ناقص 28
+
+340
+00:39:39,010 --> 00:39:39,550
+K
+
+341
+00:39:44,550 --> 00:39:52,550
+هذا PS cross V، بدنا طول المتجه هذا مقسوماً على
+
+342
+00:39:52,550 --> 00:39:58,810
+طول مين؟ على طول الـ V، يرجع الـ distance D بدها
+
+343
+00:39:58,810 --> 00:40:06,370
+تساوي طول الـ PS cross V مقسوماً على طول الـ V، و
+
+344
+00:40:06,370 --> 00:40:12,430
+يساوي، يبقى بدنا نروح ونربع المقادير اللي عندنا هنا
+
+345
+00:40:12,430 --> 00:40:20,170
+يبقى هذا بتساوي الـ square root، 28 تربيع خليها
+
+346
+00:40:20,170 --> 00:40:27,450
+لحالها، وهذا هنا بتصير 1 زائد 16 زائد 1
+
+347
+00:40:27,450 --> 00:40:36,590
+مقسوماً على، وين الـ V؟ هي الـ V، يبقى الجذر التربيعي لـ
+
+348
+00:40:36,590 --> 00:40:43,350
+16 زائد صفر زائد 16، يبقى
+
+349
+00:40:43,350 --> 00:40:48,970
+هذا الكلام يساوي الجذر التربيعي، هذا يا بنات اللي هي
+
+350
+00:40:48,970 --> 00:40:59,190
+4 تربيع في 7 تربيع في 6، على، وهذه اللي
+
+351
+00:40:59,190 --> 00:41:06,350
+هي 4، جذر 32، مظبوط؟ طيب، الـ 4 تربيع هذه لو
+
+352
+00:41:06,350 --> 00:41:12,520
+طلعت برا الجذر، بيضل قداش؟ 4، مظبوط، بيضل قداش؟
+
+353
+00:41:12,520 --> 00:41:17,540
+دي اللي هو 7 تربيع في 6، 7 في 7، 49 في 6، هي
+
+354
+00:41:17,540 --> 00:41:24,240
+49 في 6، 6 في 9، 54، 6 في 4، 24، 5
+
+355
+00:41:24,240 --> 00:41:30,320
+و29، يبقى 294 على جذر 32
+
+356
+00:41:30,320 --> 00:41:37,140
+على جذر 32
+
+357
+00:41:47,580 --> 00:41:54,060
+طيب، 28 هذه اللي ربعناها، وهذه اللي ربعناها، مظبوط
+
+358
+00:41:54,060 --> 00:42:00,420
+يبقى هذا الطول بده يساوي، تحت الجذر، يبقى هذا الجذر
+
+359
+00:42:00,420 --> 00:42:05,540
+التربيعي، بيجي، بيجي 7 جذر 6، صحيح، 7
+
+360
+00:42:09,660 --> 00:42:14,680
+على جذر 32، جذر 32 اللي هو جذر 2 في جذر
+
+361
+00:42:14,680 --> 00:42:21,140
+16، مظبوط، يبقى هنا 7 جذر 2 جذر 16 على
+
+362
+00:42:21,140 --> 00:42:26,920
+جذر 32، يبقى 7 جذر 3، هذا الطول، ان شاء الله، يعطيني كمان مثال
+
+363
+00:42:26,920 --> 00:42:30,680
+الله يعطيكِ كمان مثال
+
+364
+00:42:59,880 --> 00:43:05,380
+يبقى example two، verify
+
+365
+00:43:05,380 --> 00:43:13,020
+أتأكد أنه that the lines
+
+366
+00:43:13,020 --> 00:43:19,360
+الخطوط المستقيمة، الـ one اللي هو L1، اللي هو X
+
+367
+00:43:19,360 --> 00:43:26,780
+يساوي اتنين زائد T، X يساوي اتنين زائد T، وY تساوي
+
+368
+00:43:26,780 --> 00:43:28,420
+ناقص اتنين
+
+369
+00:43:36,150 --> 00:43:49,550
+L2، X يساوي 1 زائد 2T، Y
+
+370
+00:43:49,550 --> 00:44:01,270
+يساوي 3 ناقص 4T، Z يساوي 5 ناقص 2T، تلاتة
+
+371
+00:44:05,950 --> 00:44:13,930
+and find the distance between them، and find the
+
+372
+00:44:13,930 --> 00:44:21,890
+distance between them
+
+373
+00:44:44,560 --> 00:44:52,700
+هو بيقول: يثبت أن الخطين متوازيان، ومن ثم أوجد الـ
+
+374
+00:44:52,700 --> 00:44:57,800
+distance ما بين الخطين المتوازيين الاتنين، كويس
+
+375
+00:44:57,800 --> 00:45:01,600
+يبقى بدي أشوف هل هذول الاتنين متوازيين ولا، يعني هل الـ
+
+376
+00:45:01,600 --> 00:45:06,560
+vector الذي يوازي المتجه الأول يوازي الـ vector
+
+377
+00:45:06,560 --> 00:45:11,120
+الذي يوازي الخط الثاني ولا لأ، فباجي بقول له، الأهم
+
+378
+00:45:11,120 --> 00:45:11,720
+solution
+
+379
+00:45:33,270 --> 00:45:44,050
+2i - 4j - 2k، parallel to L2، parallel to L2
+
+380
+00:45:49,850 --> 00:45:55,990
+V2 يساوي... بدي آخذ اتنين عامل مشترك، بضل عندي I
+
+381
+00:45:55,990 --> 00:46:03,590
+ناقص اتنين J، ناقص K، اللي هو اتنين في هذا مين؟ اتنين
+
+382
+00:46:03,590 --> 00:46:13,350
+V1، يبقى هذا بدي يعطينا أن V1 and V2 are parallel
+
+383
+00:46:13,350 --> 00:46:26,020
+هذا بدي يعطينا أن L1 and L2 are parallel lines
+
+384
+00:46:26,020 --> 00:46:31,660
+تبقى إثبات النقطة المطلوبة الأول، أن هذول الاتنين متوازيين، لو جيت افترضت على سبيل المثال أن هذا الـ one
+
+385
+00:46:31,660 --> 00:46:37,960
+وهذا الـ two الموازي له، هذا L1 وهذا L2، على سبيل
+
+386
+00:46:37,960 --> 00:46:45,590
+المثال، كويس، يبقى الـ L1 هو المستقيم الأول، مظبوط، بدي
+
+387
+00:46:52,430 --> 00:46:58,390
+أفترض أنه بيمر بنقطة ما، مين النقطة التي يمر بها
+
+388
+00:46:58,390 --> 00:47:04,450
+المستقيم الأول؟ 2، سالب 2، 1، لو افترضت أن
+
+390
+00:47:11,290 --> 00:47:18,830
+وسالب اتنين وواحد، نقطة ثانية هنا على المستقيم
+
+391
+00:47:18,830 --> 00:47:24,550
+الثاني، بدي اسميها P، الـ P 1، 3، 5
+
+392
+00:47:24,550 --> 00:47:31,550
+يبقى 1، 3، 5، بدي أجيب المسافة ما بين
+
+393
+
+445
+00:52:58,860 --> 00:53:06,560
+وقلت هذا المستوى وذهبت سميت هذا المستوى M أخذت
+
+446
+00:53:06,560 --> 00:53:13,400
+متجه عمودي عليه بهذا الشكل طلع هذا المتجه اللي هو
+
+447
+00:53:13,400 --> 00:53:23,260
+عمودي عليه وسميته المتجه N  A I زائد B J زائد C K
+
+448
+00:53:23,260 --> 00:53:31,750
+مثلاً قاطعوا النقطة اللي عندنا تمام؟ المتجه هذا
+
+449
+00:53:31,750 --> 00:53:38,930
+epsilon مرّ في نقطة والـكن النقطة في نوضة x نوضة و
+
+450
+00:53:38,930 --> 00:53:44,450
+y نوضة و z نوضة تبقى عندي معلومة عندي شغلتين الآن
+
+451
+00:53:44,450 --> 00:53:50,690
+تمام متجه عمودي على المستوى ونقطة تقع في المستوى
+
+452
+00:53:50,690 --> 00:53:54,990
+يعني يمرّ بها هذا المستوى من خلال الكلام اللي
+
+453
+00:53:54,990 --> 00:54:01,970
+قدامنا هذا بدي أحاول أجيب قَدْ أَش معادلة هذا المستوى
+
+454
+00:54:01,970 --> 00:54:07,070
+بقول كويس عشان أجيب المعادلة بروح آخذ أي نقطة
+
+455
+00:54:07,070 --> 00:54:12,890
+موجودة في هذا المستوى طبعاً أذكركم بشغلة لو قلت أي
+
+456
+00:54:12,890 --> 00:54:17,430
+مستوى الطاولة اللي عندنا هنا وهذا متجه عمودي على
+
+457
+00:54:17,430 --> 00:54:22,990
+الطاولة، إذا عمودي على أي متجه أو أي مستقيم موجود
+
+458
+00:54:22,990 --> 00:54:27,630
+في مستوى الطاولة اللي عندنا هنا تمام يبقى بناءً
+
+459
+00:54:27,630 --> 00:54:36,330
+عليه لو أخذت نقطة ثانية هنا وسميتها XYZ أو الـ P
+
+460
+00:54:36,330 --> 00:54:38,310
+XYZ
+
+461
+00:54:42,080 --> 00:54:50,480
+يوجد متجه من P نود إلى P بهذا الشكل، إيش علاقة
+
+462
+00:54:50,480 --> 00:54:57,720
+متجه P نود P بالمتجه L؟ أيوة، الاثنين are orthogonal
+
+463
+00:54:57,720 --> 00:55:06,340
+يبقى هنا باجي بقول له ده أو نقول إن الكلمتين قبل، بحط
+
+464
+00:55:06,340 --> 00:55:06,980
+المعادلة
+
+465
+00:55:13,210 --> 00:55:26,730
+that أن الـ plane M passes.. passes through الـ
+
+466
+00:55:26,730 --> 00:55:35,790
+P node و X node و Y node و Z node and normal to
+
+467
+00:55:35,790 --> 00:55:44,720
+the vector عمودي على المتجه N، وA في اتجاه I، P في
+
+468
+00:55:44,720 --> 00:55:51,180
+اتجاه الـ J، وC في اتجاه الـ K، let
+
+469
+00:55:51,180 --> 00:56:03,720
+P أو X أو Y أو Z be any point أو be a point نقطة
+
+470
+00:56:03,720 --> 00:56:13,270
+in the plane  الآن
+
+471
+00:56:13,270 --> 00:56:26,890
+الـ vector n أو الـ vectors n and الـ P note PR أو
+
+472
+00:56:26,890 --> 00:56:27,430
+orthogonal
+
+473
+00:56:37,270 --> 00:56:47,570
+يبقى معنى هذا الكلام أن الـ vector أولاً الـ N dot P
+
+474
+00:56:47,570 --> 00:56:50,350
+not P بده يساوي صفر
+
+475
+00:56:54,990 --> 00:57:02,590
+بدي أشيل الـ N وأضع قيمته يبقى AI زائد BJ
+
+476
+00:57:02,590 --> 00:57:09,830
+زائد CK Dot المتجهة الثانية، المتجهة الثانية اللي
+
+477
+00:57:09,830 --> 00:57:17,750
+هو X ناقص X node في اتجاه الـ I زائد Y ناقص Y node
+
+478
+00:57:17,750 --> 00:57:25,370
+في اتجاه الـ J، Z ناقص Z node كله في اتجاه الـ K، كل
+
+479
+00:57:25,370 --> 00:57:31,770
+هذا الكلام يجب أن يساوي كم؟ يجب أن يساوي 0، نعمل الـ
+
+480
+00:57:31,770 --> 00:57:37,930
+dot product فيما بينهم يبقى صار الـ A في الـ X ناقص الـ X knot
+
+481
+00:57:37,930 --> 00:57:44,610
+زائد B في الـ Y ناقص الـ Y knot زائد C
+
+482
+00:57:44,610 --> 00:57:46,010
+في الـ Z ناقص
+
+483
+00:57:58,130 --> 00:58:01,870
+بالسالب، أضيفها على الجهة اليمنى
+
+484
+00:58:11,600 --> 00:58:18,120
+الآن الـ X0 والـ Y0 والـ Z0 نقاط معلومة أو مركبات معلومة، الـ
+
+485
+00:58:18,120 --> 00:58:22,340
+A والـ B والـ C هي مركبات المتجه العمودي المعلومة
+
+486
+00:58:22,340 --> 00:58:28,000
+إذاً هذا كله يشكل قَدْ أَش بنات؟ رقم واحد، يبقى صار
+
+487
+00:58:28,000 --> 00:58:34,780
+المعادلة AX زائد BY زائد CZ
+
+488
+00:58:37,860 --> 00:58:46,740
+رقم واحد وليكن D، ودي بيكون X نوت، Y نوت، Z نوت
+
+489
+00:58:46,740 --> 00:58:51,420
+نوت طيب؟
+
+490
+00:58:51,420 --> 00:58:58,440
+طيب كويس، يبقى احنا جبنا هذه معادلة الـ equation
+
+491
+00:58:58,440 --> 00:59:12,100
+يبقى هذه هي equation of the plane M، إذاً من الآن
+
+492
+00:59:12,100 --> 00:59:18,280
+فصاعداً، مشان أجيب معادلة plane بدي متجه عمودي على
+
+493
+00:59:18,280 --> 00:59:22,500
+هذا الـ plane، اثنين، بدي نقطة يمر بها الـ plane
+
+494
+00:59:22,500 --> 00:59:27,020
+وبالتالي بصير المعادلة بسيطة جداً، حد بيحب يسأل أي
+
+495
+00:59:27,020 --> 00:59:32,740
+سؤال هنا قبل أن نذهب إلى الأمثلة؟ لا بدّ تسأل، تسأل
+
+496
+00:59:36,570 --> 00:59:42,450
+إيش فيه حياة؟ قالت عائشة رضي الله عنها، تسأل النبي
+
+497
+00:59:42,450 --> 00:59:47,690
+صلى الله عليه وسلم عن أدق الأشياء في حياة
+
+498
+00:59:52,690 --> 00:59:57,730
+السنة، بيجي الصحابة يسألوها عن تصرّف النبي صلى الله
+
+499
+00:59:57,730 --> 01:00:04,150
+عليه وسلم، لذلك أحلى ما نقول، حاجة تسألي، ما تضلكيش
+
+500
+01:00:04,150 --> 01:00:09,750
+ساكته، وتعودي أنك تسألي حتى لو كان سؤالك غلط، تسألي
+
+501
+01:00:09,750 --> 01:00:12,790
+غلط، كل مرة جاي تسألي، غلط، غلط، تسألي، صحّي
+
+502
+01:00:21,210 --> 01:00:26,070
+لكن من خلال التساؤل بتثبتي المعلومة، غالباً، المال
+
+503
+01:00:26,070 --> 01:00:32,850
+والمال، وزميلاتك بصير أنت قدوة لهم، حاضر، بالنسبة لي
+
+504
+01:00:32,850 --> 01:00:37,610
+سؤال، معادلة الـ plane اللي كانت عليه الشكل ax زائد by زائد
+
+505
+01:00:37,610 --> 01:00:41,830
+cz يساوي d، حيث الـ a والـ b والـ c هي مركبات المتجهة
+
+506
+01:00:41,830 --> 01:00:47,840
+العمودي على الـ plane، الآن نبدأ نأخذ أمثلة على هذا
+
+507
+01:00:47,840 --> 01:00:54,640
+الكلام، أول
+
+508
+01:00:54,640 --> 01:01:02,540
+بدأ يقول find an
+
+509
+01:01:02,540 --> 01:01:10,700
+equation for the plane
+
+510
+01:01:10,700 --> 01:01:12,000
+satisfying
+
+511
+01:01:18,630 --> 01:01:27,030
+الأولى، يمرّ أيه؟ the plane passes
+
+512
+01:01:27,030 --> 01:01:33,490
+through يمرّ
+
+513
+01:01:33,490 --> 01:01:42,310
+بالنقطة اللي هي P، وإحداثياتها اثنين، وأربعة،
+
+514
+01:01:42,310 --> 01:01:47,250
+وخمسة، and perpendicular to the line and
+
+515
+01:01:47,250 --> 01:01:50,570
+perpendicular
+
+516
+01:01:50,570 --> 01:01:53,950
+to
+
+517
+01:01:53,950 --> 01:01:58,450
+the line الخطّ
+
+518
+01:01:58,450 --> 01:02:08,910
+المستقيم X يساوي خمسة زائد T، والـ Y يساوي واحد زائد
+
+519
+01:02:08,910 --> 01:02:12,090
+ثلاثة T، والـ Z يساوي
+
+520
+01:02:20,570 --> 01:02:27,870
+هذه معادلة المستوى اللي يحقق، يمرّ أيه؟ الـ plane يمرّ
+
+521
+01:02:27,870 --> 01:02:33,790
+بالنقطة هذه، وفي نفس الوقت عمودي على هذا الخط، أنا مش
+
+522
+01:02:33,790 --> 01:02:39,540
+هأجيب معادلة الـ plane، بدي نقطة يمرّ بها، ومين؟ متجه
+
+523
+01:02:39,540 --> 01:02:44,120
+عمودي على هذا الخط، هو أجيب لهذا الخط، عمودي على
+
+524
+01:02:44,120 --> 01:02:50,480
+الخطّ المستقيم، هل أنا بقدر أجيب متجه يوازي هذا الخطّ
+
+525
+01:02:50,480 --> 01:02:57,020
+المستقيم؟ اللي هو مين؟ تمام، يبقى باجي بقول له هنا
+
+526
+01:02:57,020 --> 01:03:04,420
+solution، the vector اللي
+
+527
+01:03:04,420 --> 01:03:04,680
+هو
+
+528
+01:03:07,560 --> 01:03:18,160
+يبقى I زائد ثلاثة J زائد أربعة K، parallel to the
+
+529
+01:03:18,160 --> 01:03:27,100
+given line، طب قال لي الـ plane عمودي على هذا الـ line،
+
+530
+01:03:27,100 --> 01:03:31,980
+إذاً الـ plane عمودي على هذا الـ vector، يبقى هذا
+
+531
+01:03:31,980 --> 01:03:36,600
+يعطينا أن الـ vector
+
+532
+01:03:38,420 --> 01:03:49,820
+اللي هو سميته V is normal to the plane، يبقى هذا
+
+533
+01:03:49,820 --> 01:03:56,540
+عمودي على مين؟ على مسافة، صار الـ vector العمودي على
+
+534
+01:03:56,540 --> 01:04:02,160
+الـ plane معروف، والنقطة معروفة، يبقى هذا تعويض مباشر
+
+535
+01:04:02,160 --> 01:04:12,560
+يبقى بقى اللي بقوله، equation of الـ plane العمودي
+
+536
+01:04:12,560 --> 01:04:18,440
+AX
+
+537
+01:04:18,440 --> 01:04:24,900
+يساوي  زائد BY زائد CZ
+
+538
+01:04:31,530 --> 01:04:38,070
+بصير عندي هنا، I بواحد، يبقى X، الـ P بثلاثة، والـ C
+
+539
+01:04:38,070 --> 01:04:44,110
+بأربعة، زائد، بدي أساوي، واحد في الـ X نود اللي بقدّاش؟
+
+540
+01:04:44,110 --> 01:04:51,910
+اثنين، زائد ثلاثة في الـ Y نود اللي بأربعة، زائد اللي
+
+541
+01:04:51,910 --> 01:04:58,390
+هو C اللي بأربعة في قدّاش؟ P خمسة، يبقى قصدي هنا
+
+542
+01:04:58,390 --> 01:04:59,790
+قدّاش الـ X؟
+
+543
+01:05:21,810 --> 01:05:26,470
+هذا المطلوب الأول من السؤال، المطلوب الثاني
+
+544
+01:05:35,570 --> 01:05:43,650
+passes through يمرّ
+
+545
+01:05:43,650 --> 01:05:52,430
+بـ the intersecting
+
+546
+01:05:52,430 --> 01:06:02,450
+lines يمرّ بالخطين المتقاطعين اللي هو L1، معادلاته
+
+547
+01:06:02,450 --> 01:06:12,250
+هي X يساوي T، والـ Y تساوي اثنين ناقص T، والـ Z تساوي
+
+548
+01:06:12,250 --> 01:06:23,750
+واحد زائد T، والـ L2 معادلته اللي هو X يساوي اثنين
+
+549
+01:06:23,750 --> 01:06:29,830
+زائد اثنين S، والـ Y بدها تساوي
+
+550
+01:06:34,290 --> 01:06:48,110
+تساوي ستة زائد خمسة S، الشكل اللي عندنا هذا كويس
+
+551
+01:06:48,110 --> 01:06:49,890
+مرتين
+
+552
+01:06:51,690 --> 01:06:56,830
+سؤال بيقول، إيش يعني؟ أنا عندي plane، الـ plane هذا يمرّ
+
+553
+01:06:56,830 --> 01:07:03,150
+بخطين مستقيمين متقاطعين، يعني لو تصوّرت هذول اثنين
+
+554
+01:07:03,150 --> 01:07:08,930
+في مستوى رقيق، يبقى مروا بهما مين؟ مستوى، المستوى
+
+555
+01:07:08,930 --> 01:07:13,030
+هذا، أنا بدي المعادلة تبعه، عشان أجيب المعادلة تبعه
+
+556
+01:07:13,030 --> 01:07:15,570
+فبدي نقطة تقع فيه
+
+557
+01:07:25,310 --> 01:07:32,570
+عمودي على الاثنين، يعني عمودي على مستويهما، مشان هيك
+
+558
+01:07:32,570 --> 01:07:41,950
+بدنا نروح نجيب المتجه الأول الموازي لـ L1، نجيب V1
+
+559
+01:07:41,950 --> 01:07:53,530
+اللي هو بده يساوي I وهنا ناقص J وهنا زائد K، هذا
+
+560
+01:07:53,530 --> 01:08:04,790
+parallel to L1، والـ V2 طبعاً هنا بقول solution، أولاً، والـ
+
+561
+01:08:04,790 --> 01:08:14,850
+الـ V2 يساوي 2I وهنا زائد 5J وهنا زائد خمسة K
+
+562
+01:08:14,850 --> 01:08:18,030
+parallel to L2
+
+563
+01:08:25,350 --> 01:08:31,310
+Okay، ومركبات الـ V1 واحد وسالب واحد وواحد، ومركبات
+
+564
+01:08:31,310 --> 01:08:38,370
+الـ V2 اثنين وواحد وخمسة، بالشكل العام بدي أفكّ هذا
+
+565
+01:08:38,370 --> 01:08:43,430
+المحدد، يعني هذا الكلام بيدرسه، سالب خمسة وسالب
+
+566
+01:08:43,430 --> 01:08:50,410
+واحد وسالب ستة في اتجاه الـ I، اللي بعده خمسة ناقص
+
+567
+01:08:50,410 --> 01:08:57,820
+اثنين وناقص ثلاثة في اتجاه الـ J، اللي بعده واحد
+
+568
+01:08:57,820 --> 01:09:03,760
+زائد اثنين زائد ثلاثة K، يبقى زائد ثلاثة K
+
+569
+01:09:03,760 --> 01:09:09,900
+إذاً هذا المتجه عمودي على المتجهين الاثنين، يبقى
+
+570
+01:09:09,900 --> 01:09:22,060
+عمودي على مستويهما، this vector is normal to the
+
+571
+01:09:22,060 --> 01:09:23,340
+plate
+
+572
+01:09:25,460 --> 01:09:30,280
+هذا جيد، جبت المتجه العمودي على المستوى، بدي نقطة
+
+573
+01:09:30,280 --> 01:09:37,210
+تقع في هذا المستوى، في كم واحدة؟ أنت...المتّقاطعين
+
+574
+01:09:37,210 --> 01:09:42,170
+الاثنين يقعوا في الـ plane، كل واحد منهم يمرّ بنقطة
+
+575
+01:09:42,170 --> 01:09:47,050
+يبقى هذا الحمد لله، نحط البركة، بدل النقطة، خذ أي
+
+576
+01:09:47,050 --> 01:09:51,530
+واحدة فيهم، وبيطلع نفس المعادلة، نحط النقطة الأولى
+
+577
+01:09:51,530 --> 01:09:56,310
+والنقطة الثانية، شوف ما تطلعش نفس المعادلة، إذا
+
+578
+01:09:56,310 --> 01:10:04,530
+بدأت أقول take مثلاً P not اللي هي واحد...أيه
+
+579
+01:10:04,530 --> 01:10:17,590
+قصدي؟ صفر واثنين وواحد، that lie on the line L1
+
+580
+01:10:17,590 --> 01:10:22,650
+ومن
+
+581
+01:10:22,650 --> 01:10:28,650
+ثم تقع وين؟ تقع على الـ plane، التي تقع on the line
+
+582
+01:10:28,650 --> 01:10:38,810
+L1 and on الـ plane، وكذلك على المستوى، إذاً المتجه
+
+583
+01:10:38,810 --> 01:10:45,630
+موجود، يبقى بالمعادلة، يبقى ناقص ستة X ناقص
+
+584
+01:10:45,630 --> 01:10:54,250
+ثلاثة Y زائد ثلاثة Z يساوي ناقص ستة في صفر وهنا
+
+585
+01:10:54,250 --> 01:11:00,860
+ناقص ثلاثة في اثنين وهنا زائد ثلاثة في واحد، إذاً صارت
+
+586
+01:11:00,860 --> 01:11:06,860
+المعادلة ناقص ستة X ناقص ثلاثة Y زائد ثلاثة Z
+
+587
+01:11:06,860 --> 01:11:13,980
+يساوي ناقص ستة زائد ثلاثة يبقى ناقص ثلاثة، أو ممكن
+
+588
+01:11:13,980 --> 01:11:21,600
+أقول لو قسمت كله على ناقص ثلاثة، بيضل قدّاش عندي؟ اثنين
+
+589
+01:11:21,600 --> 01:11:29,600
+X زائد Y ناقص Z يساوي قدّاش؟ يساوي واحد، هذه معادلة
+
+590
+01:11:29,600 --> 01:11:40,420
+الـ plane المطلوبة، طيب نمرّ على السؤال، جالس اثنين فاصل
+
+591
+01:11:40,420 --> 01:11:48,000
+أترونيكوينز، اثنين فاصل أترونيكوينز
+
+592
+01:11:49,790 --> 01:12:01,510
+the point الذي يمرّ بالخطّ المستقيم P (2, 1, -1) and
+
+593
+01:12:01,510 --> 01:12:11,090
+perpendicular to
+
+594
+01:12:11,090 --> 01:12:18,550
+the line of intersection to the line of
+
+595
+01:12:21,980 --> 01:12:30,160
+Intersection of the planes ده
+
+596
+01:12:30,160 --> 01:12:34,380
+المستويين اللي هو اثنين X
+
+597
+01:12:39,550 --> 01:12:46,610
+هو الـ X زائد اثنين Y زائد Z
+
+598
+01:13:22,370 --> 01:13:27,150
+نرجع لسؤالنا مرة ثانية، بيقول، بدي معادلة plane اللي
+
+599
+01:13:27,150 --> 01:13:32,030
+يمرّ بهذه النقطة، الحمد لله، تمام، ضال عندي مين؟ متجه
+
+600
+01:13:32,030 --> 01:13:37,770
+عمودي عليه، بقول له أيوة، and perpendicular to the
+
+601
+01:13:37,770 --> 01:13:41,330
+line of intersection of the two planes، وهذا الـ
+
+602
+01:13:41,330 --> 01:13:47,030
+plane عمودي على خطّ تقاطع الـ two planes اللي عندنا
+
+603
+01:13:47,030 --> 01:13:54,330
+هذول تمام؟ أيوة، الآن بدي أشوف خطّ التقاطع على هذا
+
+604
+01:13:54,330 --> 01:13:59,230
+اللي عندنا، على جُلّ الـ employment يكون عمود الانتقال
+
+605
+01:13:59,230 --> 01:14:06,690
+ده هو الشكل، وهي اسم العالم، ودي دفتركي معاكي، تسيبي
+
+606
+01:14:06,690 --> 01:14:08,190
+الشنطة، ودي دفتركي معاكي
+
+607
+01:14:17,480 --> 01:14:26,140
+تمام تمام، خليه هكذا موجه على البنات، هي
+
+608
+01:14:26,140 --> 01:14:29,820
+عندي، بنات الصفحتين اللي أجبرتهم، اعتبرهم مستويين
+
+609
+01:14:29,820 --> 01:14:36,330
+متقاطعين، إذا في عندي متجه عمودي على المستوى الأول
+
+610
+01:14:36,330 --> 01:14:41,630
+وفي متجه ثاني عمودي على المستوى الثاني، لو ما
+
+611
+01:14:41,630 --> 01:14:46,530
+عملت لهم cross product بيطلع متجه عمودي على الاثنين
+
+612
+01:14:46,530 --> 01:14:52,010
+يعني موازي لمين؟ موازي لخطّ التقاطع، يبقى الـ plane
+
+613
+01:14:52,010 --> 01:14:57,650
+العمودي على خطّ التقاطع بيكون عمودي على مين؟ على
+
+614
+01:14:57,650 --> 01:15:02,120
+تبع الـ cross product اللي عندنا، مرة ثانية بقول أنا
+
+615
+01:15:02,120 --> 01:15:10,100
+عندي هذا الـ plane وهذا الـ plane، أخذت
+
+616
+01:15:10,100 --> 01:15:15,020
+المتجه هذا عمودي على الـ plane الأول، والمتجه هذا
+
+617
+
+667
+01:22:25,460 --> 01:22:29,220
+بين الـplain يبقى بدي إحداثي النقطة اللي عندنا هذا
+
+668
+01:22:29,220 --> 01:22:36,060
+يبقى عند التقاطع بتكون x و y و z هذه هي x و y و z
+
+669
+01:22:36,060 --> 01:22:46,120
+هذه صح ولا لأ؟ يبقى باجي بقوله هنا the point of
+
+670
+01:22:46,120 --> 01:22:49,480
+intersection
+
+671
+01:22:49,480 --> 01:23:01,060
+we have نحصل على علامات أربعة في اثنين
+
+672
+01:23:01,060 --> 01:23:13,720
+زائد ثلاثة T اللي بعدها زائد خمسة، نقص أربعة T، نقص
+
+673
+01:23:13,720 --> 01:23:21,540
+اثنين في زي خمسة زائد T، الكل بتساوي تقريباً ثمانية
+
+674
+01:23:21,540 --> 01:23:28,540
+عشرة، لأن X هنا وهي X هنا، و Y هنا وهنا عند نقطة
+
+675
+01:23:28,540 --> 01:23:34,560
+التقاطع مشتركة ما بين الاثنين، طب بدأ أفكر ثمانية
+
+676
+01:23:34,560 --> 01:23:36,460
+زائد اثنا عشر
+
+677
+01:23:40,210 --> 01:23:47,630
+-20T - 10 - 2T - 18
+
+678
+01:24:02,280 --> 01:24:09,100
+عشرة T وعندك هنا ضالعة سالب عشرة فقط، وثمانية أفضل
+
+679
+01:24:09,100 --> 01:24:13,800
+قدر سالب اثنين، وأحطهم على الشكة الثانية بده يساوي
+
+680
+01:24:13,800 --> 01:24:21,000
+عشرين، ومنها T تساوي قدر سالب اثنين، فلو كانت T
+
+681
+01:24:21,000 --> 01:24:26,000
+بسالِب اثنين، بصير التقاطع ما بين الـline وما بين
+
+682
+01:24:26,000 --> 01:24:32,000
+من وما بين اللي فلاني، يجب أن أضع مكانها سالب اثنين
+
+683
+01:24:32,000 --> 01:24:37,660
+في معادلة الخط المستقيم، بحصل على نقطة التقاطع اللي
+
+684
+01:24:37,660 --> 01:24:48,840
+بروح بقوله هنا the point of intersection of X, Y,
+
+685
+01:24:49,460 --> 01:24:58,320
+Z، اثنين زائد ثلاثة في ناقص اثنين
+
+686
+01:24:58,320 --> 01:25:07,160
+الـY ناقص أربعة في T اللي هي ناقص اثنين، والـZ خمسة
+
+687
+01:25:07,160 --> 01:25:13,880
+ناقص اثنين، يبقى هذه بدها تساوي ناقص أربعة
+
+688
+01:25:16,650 --> 01:25:22,530
+وهنا ثلاثة، يبقى هذه النقطة تقاطع المستوى مع الـ
+
+689
+01:25:22,530 --> 01:25:31,150
+plane، الآن نعطي كمان مثال example
+
+690
+01:25:50,760 --> 01:25:59,240
+المعادلة البارامترية of
+
+691
+01:25:59,240 --> 01:26:10,100
+the line of intersection of
+
+692
+01:26:10,100 --> 01:26:20,960
+the planes، بالمستويات الاثنين، ثلاثة X ناقص ستة Y
+
+693
+01:26:20,960 --> 01:26:30,620
+ناقص اثنين Z يساوي ثلاثة، واثنين X زائد Y، اثنين X
+
+694
+01:26:30,620 --> 01:26:35,120
+زائد Y ناقص اثنين Z يساوي ثمانية
+
+695
+01:27:12,310 --> 01:27:16,290
+سؤال مرة ثانية، بيقول لي هذه المعادلات الـ
+
+696
+01:27:16,290 --> 01:27:22,530
+بارامترية للخط المستقيم اللي هو عبارة عن تقاطع لـ
+
+697
+01:27:22,530 --> 01:27:26,630
+planes، طب لما طلعنا إحدى الطالبات برة، اتجهت لضفنك
+
+698
+01:27:26,630 --> 01:27:31,810
+شوية، طب كان عندنا two planes بالشكل اللي عندنا
+
+699
+01:27:31,810 --> 01:27:39,750
+اثنين، وتقاطعوا في الخط اللي عندنا، الآن بالتقاطع وفي
+
+700
+01:27:39,750 --> 01:27:45,590
+الخط المستقيم، نريد معادلة البارامترية لهذا
+
+701
+01:27:45,590 --> 01:27:51,130
+الخط المستقيم، لذلك أنا لن أجلب المعادلة البارامترية
+
+702
+01:27:51,130 --> 01:27:58,770
+لهذا الخط المستقيم، بل أجلب متجه موازٍ، تمام؟
+
+703
+01:27:58,770 --> 01:28:02,370
+ورغم ذلك، نريد نقطة تقع عليه
+
+704
+01:28:17,540 --> 01:28:24,720
+ونحن رسمنا الـtwo vectors، العمليات على الاثنين، و
+
+705
+01:28:24,720 --> 01:28:29,740
+عملنا cross product، بطلع المتجه الموازي لمين؟ للخط
+
+706
+01:28:29,740 --> 01:28:35,200
+التقاطع، وأنا مش هجيب معادلة خط مستقيم، بلزم المتجه
+
+707
+01:28:35,200 --> 01:28:42,070
+الموازي لخط التقاطع، موجه هذا في الأول، وبعد هيك ندور
+
+708
+01:28:42,070 --> 01:28:48,310
+على نقطة تقع على هذا الخط بالضبط، تماماً، بقول كويس
+
+709
+01:28:48,310 --> 01:28:53,910
+هذول متجهين اثنين، بقدر أجيب العمودي على الأول، و
+
+710
+01:28:53,910 --> 01:28:58,490
+العمودي على الثاني، وأعمل لهم cross product، بيطلع
+
+711
+01:28:58,490 --> 01:29:03,570
+الموازي لخط التقاطع، مظبوط؟ يبقى بالداخل أقول له
+
+712
+01:29:03,570 --> 01:29:11,040
+in one اللي هو بده يساوي ثلاثة I ناقص ستة J ناقص
+
+713
+01:29:11,040 --> 01:29:25,420
+اثنين K، normal to the first plane، الآن
+
+714
+01:29:25,420 --> 01:29:34,090
+المتجه الأول، into اللي هو عبارة عن اثنين I زائد J
+
+715
+01:29:34,090 --> 01:29:46,010
+ناقص اثنين K، normal to the second، يبقى بدي أجيب N1
+
+716
+01:29:54,970 --> 01:30:02,670
+يبقى مركبات المتجه الأول: ثلاثة، ناقص ستة، ناقص اثنين
+
+717
+01:30:02,670 --> 01:30:10,410
+اثنين، واحد، ناقص اثنين، اثنا عشر
+
+718
+01:30:10,410 --> 01:30:14,450
+زائد اثنين يبقى أربعة عشر R
+
+719
+01:30:18,680 --> 01:30:26,840
+ستة، زائد أربعة، ويظل ناقص اثنين مع ناقص يظل زائد
+
+720
+01:30:26,840 --> 01:30:36,820
+اثنين J، اللي بعده ثلاثة زائد اثنا عشر يساوي خمسة عشر
+
+721
+01:30:36,820 --> 01:30:41,280
+K، طيب
+
+722
+01:30:41,280 --> 01:30:46,140
+يبقى in one، in two، هذا parallel to the line of
+
+723
+01:30:46,140 --> 01:30:55,480
+intersection، تبقى باجي بقوله هنا: the vector N1 cross
+
+724
+01:30:55,480 --> 01:31:15,040
+N2، parallel to the line of intersection of
+
+725
+01:31:15,040 --> 01:31:16,400
+the
+
+726
+01:31:21,290 --> 01:31:28,730
+طيب، إيش مطلبنا؟ نقطة تقع على خط التقاطع، يالا،
+
+727
+01:31:28,730 --> 01:31:36,610
+من أين سنأتي بهذه النقطة؟ نقطة مشتركة بين الـtwo
+
+728
+01:31:36,610 --> 01:31:42,510
+planes، تقع على خط التقاطع، تقع في الـplane الأول
+
+729
+01:31:42,510 --> 01:31:42,790
+وفي
+
+730
+01:32:13,350 --> 01:32:20,100
+أو بأي رقم آخر، معادلتين في X و Y بحيث هما مع بعض
+
+731
+01:32:20,100 --> 01:32:24,420
+بجيب نفس الفكرة اللي طرحتيها، ولو أنهم خربطوا شوية
+
+732
+01:32:24,420 --> 01:32:28,300
+معادلات بكرة، بس تطرح عملية كويسة، تطرح الفكرة تمام
+
+733
+01:32:28,300 --> 01:32:35,160
+إذا بنروح نأخذ Z بصفر، أو X بصفر، أو Y بصفر، أي
+
+734
+01:32:35,160 --> 01:32:39,300
+واحدة منهم، بأخذ واحدة بس، بضل متغيرين في معادلتين
+
+735
+01:32:39,300 --> 01:32:44,660
+بحيث هما مع بعض، بس سنتين مع بعض، ثلاث معادلات ورا
+
+736
+01:32:44,660 --> 01:32:49,900
+معادلتين وما كناش بنطلع برة المعادلتين، تنحلش
+
+737
+01:32:49,900 --> 01:32:55,460
+موجود للجهات، بروح بحط قيمة معينة لأحد المتغيرات
+
+738
+01:32:55,460 --> 01:33:03,580
+والأخذ Z على سبيل المثال، باجي بقول هنا: what قيمة
+
+739
+01:33:03,580 --> 01:33:09,690
+الـZ تساوي قيمة، ليس القرآن اللي نزل من السماء، لازم
+
+740
+01:33:09,690 --> 01:33:13,590
+Z بصفر، ممكن تاخذ Z بواحد، باثنين، بسالب ثلاثة، زي
+
+741
+01:33:13,590 --> 01:33:19,490
+ما بدك، يبقى لما Z تساوي صفر، قَد Z تساوي صفر
+
+742
+01:33:19,490 --> 01:33:24,830
+ويجد نقص العالم تعالى على الـplane الأول، بدأ أحط Z
+
+743
+01:33:24,830 --> 01:33:27,730
+بصفر، كيف تصير ثلاثة X ناقص
+
+744
+01:33:31,360 --> 01:33:38,940
+ناقص ستة Y يساوي ثلاثة، المعادلة الثانية اثنين X زائد
+
+745
+01:33:38,940 --> 01:33:47,520
+Y، اثنين X زائد Y يساوي اثنين، الآن بدي أحل المعادلتين
+
+746
+01:33:47,520 --> 01:33:53,160
+مع بعض، المعادلة الأولى بدي أدخلها زي ما هي، ناقص ستة
+
+747
+01:33:53,160 --> 01:33:54,600
+Y يساوي ثلاثة
+
+748
+01:34:02,370 --> 01:34:07,390
+يساوي اثنا عشر، أجمعهن، بروح أجمع هدول مع بعض بيصير إيش؟
+
+749
+01:34:07,390 --> 01:34:14,230
+خمسة عشر X يساوي خمسة عشر، يبقى الـX تساوي كده؟ واحد
+
+750
+01:34:14,230 --> 01:34:24,530
+لما الـX تساوي واحد، يبقى الـY كده؟ صفر، يبقى هذا
+
+751
+01:34:24,530 --> 01:34:30,150
+يعطيك أن Y تساوي صفر، يبقى الصفر
+
+752
+01:34:38,990 --> 01:34:45,050
+Z بصفر، و Y بصفر، و X بواحد، أين تقع هذه النقطة
+
+753
+01:34:45,050 --> 01:34:52,330
+on the line of intersection of the two planes، يبقى
+
+754
+01:34:52,330 --> 01:35:04,830
+هذه الـY on the line of intersection
+
+755
+01:35:06,740 --> 01:35:16,300
+of the given planes، هذا جيد، الآن صارت النقطة
+
+756
+01:35:16,300 --> 01:35:23,960
+موجودة، والمتجه الموازي اللي هو موجود، إذا بقدر أجيب
+
+757
+01:35:23,960 --> 01:35:27,420
+المعادلة البارامترية، لأنه قال لي في المثال find
+
+758
+01:35:27,420 --> 01:35:32,620
+parametric equations، إذا بناء عليه بقول له the
+
+759
+01:35:32,620 --> 01:35:36,240
+parametric
+
+760
+01:35:39,050 --> 01:35:53,990
+of the line of intersection of the given planes
+
+761
+01:36:07,560 --> 01:36:16,720
+يبقى زائد أربعة عشر T، و Y يساوي، Y not بصفر، يبقى
+
+762
+01:36:16,720 --> 01:36:23,920
+طلع أن أنا ما قلتش اثنين T، يبقى اثنين T، و Z بصفر
+
+763
+01:36:23,920 --> 01:36:31,180
+وخمسة عشر T، في قيود على T، يبقى T أكبر من سالب
+
+764
+01:36:31,180 --> 01:36:31,740
+Infinity
+
+765
+01:36:37,610 --> 01:36:43,850
+لحد هنا انتهت الأمثلة على هذا النقطة اللي هي
+
+766
+01:36:43,850 --> 01:36:47,790
+النقطة رقم ثلاثة من هذا الـsection، نفس الله لها
+
+767
+01:36:47,790 --> 01:36:52,930
+النقطة رقم أربعة، والنقطة رقم خمسة طبعاً مش حاضر
+
+768
+01:36:52,930 --> 01:36:57,830
+حاجة اليوم، الله يعطيك العافية، ونكمل المرة القادمة
+
+769
+01:36:57,830 --> 01:37:00,110
+إن شاء الله تعالى
+
+770
+01:37:04,270 --> 01:37:05,370
+الحاجب السليسي والعالمي
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/aAjYJyHQ2EE_postprocess.srt b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/aAjYJyHQ2EE_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..729af785f8ddca30bde92f8d3cbcdbe88bb57d2e
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/aAjYJyHQ2EE_postprocess.srt
@@ -0,0 +1,3080 @@
+1
+00:00:00,000 --> 00:00:02,700
+موسيقى
+
+2
+00:00:16,500 --> 00:00:21,540
+معادلات الخط المستقيم كانت المعادلات البرامترية
+
+3
+00:00:21,540 --> 00:00:26,440
+للخط المستقيم في الفرار على صيغة x يساوي x0 زايد
+
+4
+00:00:26,440 --> 00:00:34,440
+v1t وy يساوي y0 زايد v2tبتساوي Z نوت زائد V3T طبعا
+
+5
+00:00:34,440 --> 00:00:37,580
+X نوت و Y نوت و Z نوت هي احداثيات النقطة التي يمر
+
+6
+00:00:37,580 --> 00:00:43,240
+بهذا الخط المستقيم V1 V2 V3 هي ال components تبعة
+
+7
+00:00:43,240 --> 00:00:48,580
+ال vector الموازنة من الخط المستقيم وعطينا المرة
+
+8
+00:00:48,580 --> 00:00:52,980
+الماضية على ذلك مثلا واحد الألب نروح لمثال رقم
+
+9
+00:00:52,980 --> 00:00:57,480
+اتنين يبقى المثال رقم اتنين بقول ما
+
+10
+00:01:03,110 --> 00:01:09,350
+five اللي هو parametric equations parametric
+
+11
+00:01:09,350 --> 00:01:15,730
+equations المعادلات ال parametric for the line for
+
+12
+00:01:15,730 --> 00:01:26,750
+the line للقطة المستقيم through الذي يمر بالنقطة
+
+13
+00:01:26,750 --> 00:01:29,510
+اللي هي اتنين
+
+14
+00:01:41,740 --> 00:01:52,480
+vectors وعمودي على المتجهات اللي هو U تساوي I زائد
+
+15
+00:01:52,480 --> 00:02:02,000
+اتنين J زائد تلاتة K and المتجه الثاني V يساوي
+
+16
+00:02:02,000 --> 00:02:09,860
+تلاتة I زائد اربعة J زائد خمسة K
+
+17
+00:02:15,470 --> 00:02:21,410
+نرجع لسؤالنا مرة ثانية نقرأ السؤال جيدا نعرف انحدد
+
+18
+00:02:21,410 --> 00:02:26,010
+ما هو المطلوب بناء عليه ان نعرف نشتغل بدقة ان شاء
+
+19
+00:02:26,010 --> 00:02:30,710
+الله يبقى ليهدد المعادلة القارامترية للخط المستقيم
+
+20
+00:02:30,710 --> 00:02:34,630
+يبقى بدنا المعادلات اللي قدامنا التلاتة هذه بحيث
+
+21
+00:02:34,630 --> 00:02:38,770
+الخط المستقيم يمر بالنقطة 2 تلاتة زير يبقى
+
+22
+00:02:38,770 --> 00:02:46,360
+الاحداثية X node وY node وZ node معروفةمتجه يوازي
+
+23
+00:02:46,360 --> 00:02:50,580
+هذا الخط المستخمش بيقول لي هون ال line هذا مقرب
+
+24
+00:02:50,580 --> 00:02:56,400
+النقطة هذه و عمودي على المتجهين الأثنين هذول طيب
+
+25
+00:02:56,400 --> 00:03:02,080
+كيف بقدر أجيب متجه عمودي على متجهين شو بعملهم
+
+26
+00:03:02,080 --> 00:03:07,890
+cross productلو عملت cross product بجيب vector
+
+27
+00:03:07,890 --> 00:03:12,850
+عمودي على كل المل المتجه اللي بكون هو المتجه
+
+28
+00:03:12,850 --> 00:03:18,190
+المطلوب حتى أتمكن من الحصول على معادلات الخط
+
+29
+00:03:18,190 --> 00:03:26,370
+المستقل إذا بدي أروح أجيب له ال U cross ال V يبقى
+
+30
+00:03:26,370 --> 00:03:29,010
+U cross ال V يسوى المحدد
+
+31
+00:03:33,050 --> 00:03:40,610
+المتجه الأول 1 2 3 مركبات المتجه التاني 3 4 5
+
+32
+00:03:43,420 --> 00:03:47,880
+يبقى على طول الخط هذا بده يسوي نشطة بصفه و عموده
+
+33
+00:03:47,880 --> 00:03:54,280
+نين في خمسة بعشرة ناقص اتناشت بيبقى ناقص اتنين I
+
+34
+00:03:54,280 --> 00:04:02,600
+اللي بعد نشطة بصفه و عموده خمسة ناقص خمستاشر بيبقى
+
+35
+00:04:02,600 --> 00:04:06,140
+ناقص عشرة و هذا أصلا مش هرت ناقص بيبقى زائد عشرة
+
+36
+00:04:06,140 --> 00:04:10,680
+يبقى زائد عشرة G كيف؟
+
+37
+00:04:17,890 --> 00:04:24,550
+صفه و عموده يبقى خمسة ناقص ستة يبقى ناقص أربعة مع
+
+38
+00:04:24,550 --> 00:04:30,070
+الناقص يبقى زائد أربعة جيه كلام سليم اللي بقناه
+
+39
+00:04:30,070 --> 00:04:36,230
+مشطب صفه و عموده يبقى أربعة ناقص ستة يبقى قداش
+
+40
+00:04:36,230 --> 00:04:46,210
+ناقص اتنين كيه يبقى هذا ال vector أورثجوناليبقى
+
+41
+00:04:46,210 --> 00:04:55,430
+هذا parallel لمين لللعين يبقى هذا vector parallel
+
+42
+00:04:55,430 --> 00:04:58,610
+to
+
+43
+00:04:58,610 --> 00:05:02,150
+required
+
+44
+00:05:02,150 --> 00:05:05,770
+line
+
+45
+00:05:07,290 --> 00:05:12,590
+يبقى هذا مالموازي للخط اللي مطوب علي الكوارث، يعني
+
+46
+00:05:12,590 --> 00:05:17,930
+مطوب اللي عليها بدنا نوشبناء عليه إذا أصبح ال
+
+47
+00:05:17,930 --> 00:05:23,770
+parametric equations هي X يساوي X نول اللي هي 2
+
+48
+00:05:23,770 --> 00:05:29,670
+زائد المركبة اللي عندنا اللي هي ناقص 2 يبقى ناقص
+
+49
+00:05:29,670 --> 00:05:37,590
+2T يبقى 2 ناقص 2T المركبة التانية اللي هي Y بدها
+
+50
+00:05:37,590 --> 00:05:43,150
+تساوي المركبة التانية اللي هي 3 وعنا زائد
+
+51
+00:05:46,370 --> 00:05:49,730
+يبقى Z أو المعادلة التالتة المركبة علينا Z و الله
+
+52
+00:05:49,730 --> 00:05:55,530
+يسهل عليها يبقى بظل ناقص اتنين T وT هذه ماعليهاش
+
+53
+00:05:55,530 --> 00:06:01,170
+قيود يبقى اكبر من سالب Infinity و اقل منين اقل من
+
+54
+00:06:01,170 --> 00:06:05,210
+Infinity يبقى هذه معادلات ال Parameterية للخط
+
+55
+00:06:05,210 --> 00:06:10,210
+المستقيم اللي عندنا نعطي كمان مثال رقم تلاتة
+
+56
+00:06:29,050 --> 00:06:39,230
+الخطوط المستقيمة التالية are intersecting
+
+57
+00:06:39,230 --> 00:06:46,450
+ولا parallel or
+
+58
+00:06:46,450 --> 00:06:49,470
+skew
+
+59
+00:06:49,470 --> 00:06:53,630
+if
+
+60
+00:06:53,630 --> 00:06:57,690
+they intersect
+
+61
+00:07:00,560 --> 00:07:18,800
+اذا كان هناك تقاطة، احصل على نقاط التقاطة
+
+62
+00:07:18,800 --> 00:07:23,520
+المستقيم الأول الحديد هو الرمز الـ1موضة في صيغة
+
+63
+00:07:23,520 --> 00:07:30,920
+البرامترية X يساوي واحد زائد اتنين T وال Y تساوي
+
+64
+00:07:30,920 --> 00:07:35,780
+ناقص واحد ناقص T وال Z تساوي
+
+65
+00:07:38,260 --> 00:07:44,040
+والمستقيم التاني L2 موقع الشكل التاني X يساوي
+
+66
+00:07:44,040 --> 00:07:54,240
+اتنين ناقص S وY تساوي تلاتة S وZ تساوي واحد زائد S
+
+67
+00:07:56,280 --> 00:08:03,940
+لتلاتة مقطع على الصيغة الهمين ال L تلاتة عبارة عن
+
+68
+00:08:03,940 --> 00:08:13,680
+ال X يساوي خمسة زائد اتنين R وال Y يساوي واحد ناقص
+
+69
+00:08:13,680 --> 00:08:20,380
+R وال Z تساوي تمانية زائد تلاتة R
+
+70
+00:08:24,750 --> 00:08:29,930
+هنا بالنسبالي ماعنديش قيود لا على T ولا S ولا R
+
+71
+00:08:29,930 --> 00:08:35,290
+يبقى هذا على كل الـ real line بلاستيكنات نحاول
+
+72
+00:08:35,290 --> 00:08:37,710
+نشوف المستقيمات اللي عندنا هذه
+
+73
+00:09:06,190 --> 00:09:12,130
+نرجع لسؤالنا مرة تانية بيعطيني ثلاثة مستقيمات L1 و
+
+74
+00:09:12,130 --> 00:09:14,930
+L2 و L3 و L4 و L5 و L6 و L7 و L8 و L9 و L10 و L10
+
+75
+00:09:14,930 --> 00:09:16,850
+و L10 و L11 و L12 و L12 و L13 و L13 و L14 و L15 و
+
+76
+00:09:16,850 --> 00:09:22,070
+L15 و L16 و L17 و L18 و L19 و L19 و L20 و L21 و
+
+77
+00:09:22,070 --> 00:09:23,030
+L22 و L22 و L22 و L22 و L22 و L22 و L22 و L22 و
+
+78
+00:09:23,030 --> 00:09:25,010
+L22 و L22 و L22 و L22 و L22 و L22 و L22 و L22 و
+
+79
+00:09:25,010 --> 00:09:25,090
+L22 و L22 و L22 و L22 و L22 و L22 و L22 و L22 و
+
+80
+00:09:25,090 --> 00:09:26,330
+L22 و L22 و L22 و L22 و L22 و L22 و L
+
+81
+00:09:34,860 --> 00:09:45,500
+كويس لما اقول اتنين متوازين
+
+82
+00:09:45,500 --> 00:09:51,560
+يبقى there is no intersection مفيش بالمرة طب كيف
+
+83
+00:09:51,560 --> 00:09:55,000
+بثبت ان two vectors are parallel
+
+84
+00:10:03,600 --> 00:10:09,640
+مستقيمين متخلفين يعني لا تقاطع ولا توازن مهما المد
+
+85
+00:10:09,640 --> 00:10:12,820
+هذا من سلب infinity إلى infinity وهذا من infinity
+
+86
+00:10:12,820 --> 00:10:18,360
+إلى سلب infinity مافيش تقاطع وليس هناك توازن مثل
+
+87
+00:10:18,360 --> 00:10:23,100
+ذلك لو جدتك ال corner اللي عندك هذا هذا خط مستقيم
+
+88
+00:10:23,380 --> 00:10:27,880
+والخط المستقيم اللي هو في القلي هناك مهما اتمنديهم
+
+89
+00:10:27,880 --> 00:10:31,220
+مافيش intersection ما بين الاثنين يبقى هدول
+
+90
+00:10:31,220 --> 00:10:38,740
+بيسميهم as QV lines مستقيمات متخالفة طيب نجي نشوف
+
+91
+00:10:38,740 --> 00:10:42,600
+ايش قصة تانية كده بدنا نثبت ان هدول متوازين
+
+92
+00:10:42,600 --> 00:10:47,400
+متقاطعين متخالفين بقول كويسة بدي امسك المستقيم
+
+93
+00:10:47,400 --> 00:10:56,370
+الأول والثانيهل هناك متجه يوازي المستقيم الأول من
+
+94
+00:10:56,370 --> 00:10:59,990
+خلال المعادلة هذه؟
+
+95
+00:11:08,280 --> 00:11:15,380
+هذا الـ vector يوازي المتجه الأول وهذا ال vector
+
+96
+00:11:15,380 --> 00:11:20,260
+تاني يوازي
+
+97
+00:11:20,260 --> 00:11:21,880
+المتجه الثاني
+
+98
+00:11:25,980 --> 00:11:30,980
+معناته المستقيمين متوازين صح ولا لا طيب إذا كانوا
+
+99
+00:11:30,980 --> 00:11:34,620
+هدول مهماش متوازين يبقى المستقيمين غير متوازين
+
+100
+00:11:34,620 --> 00:11:39,880
+بيظل احتمال التقاطع أو التخالف وبنبحث القصة هذه
+
+101
+00:11:39,880 --> 00:11:48,180
+ونشوف يبقى باجي بقول هنا ال one solution ال one
+
+102
+00:11:48,180 --> 00:11:54,380
+parallel to the vector
+
+103
+00:11:55,870 --> 00:12:03,170
+V1 هو مين V1 هذا هجيبه من نفسي المعادل اتنين I
+
+104
+00:12:03,170 --> 00:12:11,870
+ناقص J زائد تلاتة K بعد هي ال L2 parallel to the
+
+105
+00:12:11,870 --> 00:12:19,990
+vector باجي هنا اللي هو V2 ناقص I زائد تلاتة J
+
+106
+00:12:19,990 --> 00:12:23,770
+زائد K السؤال
+
+107
+00:12:25,330 --> 00:12:30,150
+هل واحد من الاتنين هدول مضاعفات الآخر؟ مش ممكن
+
+108
+00:12:30,150 --> 00:12:33,390
+يبقى المعنى تقول اتنين هدول are not parallel
+
+109
+00:12:33,390 --> 00:12:41,070
+وبالتالي ال two lines are not parallel يبقى هنا L1
+
+110
+00:12:41,070 --> 00:12:54,050
+is not parallel to L2 because السبب ان V1 is
+
+111
+00:13:02,600 --> 00:13:08,860
+بالتالي لا يوجد توازي بين ال V1 و V2 وبالتالي لا
+
+112
+00:13:08,860 --> 00:13:13,920
+يمكن لـ two lines L1 و L2 يكونوا اتنين are
+
+113
+00:13:13,920 --> 00:13:21,020
+parallel يبقى سبعة التوازن بظل احتمالي التقاطعالان
+
+114
+00:13:21,020 --> 00:13:26,040
+بدنا نحكم علي المستقيمين هم متخالفين ولا
+
+115
+00:13:26,040 --> 00:13:32,500
+المستقيمين متقاطعين مش هنحكم بتحول السبعة واحدة
+
+116
+00:13:32,500 --> 00:13:37,260
+فيهم إذا استبعت واحدة فيهم بتظل مين؟ بتظل الأخرى
+
+117
+00:13:37,260 --> 00:13:42,580
+إجباري يبقى جدلا انا بدأ افترض ان اتنين هم
+
+118
+00:13:42,580 --> 00:13:48,380
+متقاطعين وشوف ايش اللي بتوصل ليش يبقى هذا باجي
+
+119
+00:13:48,380 --> 00:13:55,580
+يقول FL1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13
+
+120
+00:13:55,580 --> 00:14:01,280
+L14 L15 L16 L17 L18 L19 L20 L21 L22 L23 L24 L25
+
+121
+00:14:01,280 --> 00:14:03,760
+L26 L27 L28 L29 L29 L29 L29 L29 L29 L29 L29 L29
+
+122
+00:14:03,760 --> 00:14:06,900
+L29 L29 L29 L29 L29 L29 L29 L29 L29 L29 L29 L29
+
+123
+00:14:06,900 --> 00:14:06,980
+L29 L29 L29 L29 L29 L29 L29 L29 L29 L29 L29 L29
+
+124
+00:14:06,980 --> 00:14:07,040
+L29 L29 L29 L29 L29 L29 L29 L29 L29 L29 L29 L29
+
+125
+00:14:07,040 --> 00:14:07,860
+L29 L29 L29 L29 L29 L29 L29 L29 L29 L29 L29 L29
+
+126
+00:14:07,860 --> 00:14:08,840
+L29 L29 L29
+
+127
+00:14:14,330 --> 00:14:22,810
+بتكون واحد زائد اتنين T بتساوي اتنين ناقص S وناقص
+
+128
+00:14:22,810 --> 00:14:31,650
+واحد ناقص T بتساوي تلاتة S وعندنا هنا تلاتة T
+
+129
+00:14:31,650 --> 00:14:40,390
+بتساوية واحد زائد Sهذول كام معادلة؟ تلات معادلة و
+
+130
+00:14:40,390 --> 00:14:44,090
+كام مجهول؟ اتنين يعني الحمد لله ربنا حط البركة
+
+131
+00:14:44,090 --> 00:14:48,750
+عشان نجيب TOS بيكفينا تنتين عدد المعادلات يساوي
+
+132
+00:14:48,750 --> 00:14:52,090
+عدد المجاهيين لكن تلات معادلة يعني الحمد لله ربنا
+
+133
+00:14:52,090 --> 00:14:57,790
+حط البركة okay تمام بقول كويس خلينا نجرب نحل
+
+134
+00:14:57,790 --> 00:15:02,370
+المعادلتين الاتنين هذول مع بعض و نشوف إيش بده
+
+135
+00:15:02,370 --> 00:15:11,920
+يعطينايبقى هذا يعطينا ما يبتي 1 زائد 2t تساوي 2
+
+136
+00:15:11,920 --> 00:15:19,820
+ناقص s المعادلة التانية بيضربها في 2 يبقى ناقص 2
+
+137
+00:15:19,820 --> 00:15:28,880
+هنا ناقص 2t يبقى ناقص 6s
+
+138
+00:15:32,490 --> 00:15:40,870
+يبقى على الشمال ناقص واحد يبقى على الشجر اليمين
+
+139
+00:15:40,870 --> 00:15:46,050
+ناقص اس وست اس يبقى ناقص خمس اس يبقى ناقص اتنين
+
+140
+00:15:46,050 --> 00:15:53,410
+زائد خمس اس يبقى ناقص اتنين زائد خمس اس هذا معناته
+
+141
+00:15:53,410 --> 00:15:59,450
+ان ناقص تلاتة يبقى ناقص خمس اس هذا معناته ان اس
+
+142
+00:15:59,450 --> 00:16:01,850
+يسوى ناقص تلاتة
+
+143
+00:16:06,940 --> 00:16:11,920
+يبقى عوض في أي من المعادلة تانية لو جيت عوض في
+
+144
+00:16:11,920 --> 00:16:16,640
+المعادلة الأولى بس إذا عندي واحد زائد اتنين T
+
+145
+00:16:16,640 --> 00:16:25,120
+يساوي اتنين ناقص اتنين ناقص S، S عندي بتلات أخمس
+
+146
+00:16:37,740 --> 00:16:40,260
+عشرة و تلاتة و تلاتة و تلاتة و تلاتة و تلاتة و
+
+147
+00:16:40,260 --> 00:16:43,220
+تلاتة و تلاتة و تلاتة و تلاتة و تلاتة و تلاتة و
+
+148
+00:16:43,220 --> 00:16:44,600
+تلاتة و تلاتة و تلاتة و تلاتة و تلاتة و تلاتة و
+
+149
+00:16:44,600 --> 00:16:45,140
+تلاتة و تلاتة و تلاتة و تلاتة و تلاتة و تلاتة و
+
+150
+00:16:45,140 --> 00:16:45,420
+تلاتة و تلاتة و تلاتة و تلاتة و تلاتة و تلاتة و
+
+151
+00:16:45,420 --> 00:16:48,300
+تلاتة و تلاتة و تلاتة و تلاتة و تلاتة و تلاتة و
+
+152
+00:16:48,300 --> 00:16:53,500
+تلاتة و تلاتة و تلاتة و
+
+153
+00:16:57,480 --> 00:17:04,880
+مرة تانية بقول تلتاشة على خمسة تمان
+
+154
+00:17:04,880 --> 00:17:11,080
+أخمس تساوي اتنين T ومنها T تساوي أربع أخمس تساوي
+
+155
+00:17:11,080 --> 00:17:14,590
+اتنين T ومنها T تساوي أربع أخمسيبقى حصلت على T
+
+156
+00:17:14,590 --> 00:17:21,790
+وحصلت هنا على مين على S إذا في تقاطع لازم قيمة
+
+157
+00:17:21,790 --> 00:17:26,210
+المعادلة التالتة هذه تسوي قيمة المعادلة هذه إذا لم
+
+158
+00:17:26,210 --> 00:17:30,370
+تتساوي القيمتان يبقى بيكون there is no
+
+159
+00:17:30,370 --> 00:17:35,430
+intersection ماعنديش تقاطع بتاتة يبقى بناء عليه
+
+160
+00:17:35,430 --> 00:17:40,590
+بيروح أعوض في المعادلة التالتة هسميها ك star
+
+161
+00:17:44,880 --> 00:17:52,140
+يبقى بتقول الان substitute عوضلي
+
+162
+00:17:52,140 --> 00:17:58,900
+in star نحصل على ايش يبقى قصير عندي تلاتة فيتي
+
+163
+00:17:58,900 --> 00:18:07,920
+وانتي لاربع اخلاص اللي هو الاصل يساوي قداش يساوي
+
+164
+00:18:07,920 --> 00:18:09,540
+الواحد
+
+165
+00:18:13,590 --> 00:18:20,230
+هل هدول بيساووا بعض؟ ليش؟
+
+166
+00:18:20,230 --> 00:18:27,070
+لأن هذا خمسين وهذا كده اتناشر على خمسة يبقى اتناشر
+
+167
+00:18:27,070 --> 00:18:33,690
+على خمسة لا يمكن انها تساوي خمسين معناه هذا الكلام
+
+168
+00:18:33,690 --> 00:18:36,550
+ان المستقيمات الاتنين هدول بتقاطعوا
+
+169
+00:18:39,810 --> 00:18:51,270
+L1 و L2 لا يتقاطعون
+
+170
+00:19:09,620 --> 00:19:16,060
+مستقيمان متخلفة طيب احنا بحثنا الان المستقيم الاول
+
+171
+00:19:16,060 --> 00:19:22,060
+مع الثالث بدنا نبحث المستقيم الاول مع التالت يبقى
+
+172
+00:19:22,060 --> 00:19:29,300
+مرة تانية بدي اقول ان انتهينا المطلوب الاول V1 فرق
+
+173
+00:19:29,300 --> 00:19:38,260
+او L1 فرق ال V1
+
+174
+00:19:38,260 --> 00:19:38,900
+اللي عندنا
+
+175
+00:19:53,720 --> 00:20:00,980
+Parallel to V3 ويسافر 2I-J
+
+176
+00:20:07,660 --> 00:20:13,080
+يبقى صار V1 و V2 are parallel يبقى هذا بدي أعطيلك
+
+177
+00:20:13,080 --> 00:20:27,380
+ان V1 parallel to V2 so L1 and L2 are parallel
+
+178
+00:20:27,380 --> 00:20:32,160
+line يبقى
+
+179
+00:20:32,160 --> 00:20:40,190
+دول خطين متوازن تهيأنا بالأول مع التالتمع التالت
+
+180
+00:20:40,190 --> 00:20:55,130
+الان تطلعينى ل V1 و V2 V1 و V3 هى V2 و
+
+181
+00:20:55,130 --> 00:21:01,630
+V3 هى V2 هى V3 هى V3 هى V3 هى V3 هى V3 هى V3 هى V3
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+182
+00:21:01,630 --> 00:21:01,850
+هى V3 هى V3 هى V3 هى V3 هى V3 هى V3 هى V3 هى V3 هى
+
+183
+00:21:01,850 --> 00:21:05,050
+V3 هى V3 هى V3 هى V3 هى V3 هى V3 هى V3 هى V3 هى V3
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+184
+00:21:05,050 --> 00:21:05,090
+V3 هى V3 هى V3 هى V3 هى V3 هى V3 هى V3 هى V3 هى V3
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+185
+00:21:05,090 --> 00:21:11,510
+هى V3 هى V3 هى V3 هى V3 هى V3 هى V3 هال L2 و L3
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+186
+00:21:11,510 --> 00:21:24,070
+ليسوا مرتبطين السبب لأن V2
+
+187
+00:21:24,070 --> 00:21:27,010
+و V3
+
+188
+00:21:35,730 --> 00:21:42,330
+هيبقى هدول غير متوازية ضال احتمال التقاطع واحتمال
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+189
+00:21:42,330 --> 00:21:48,130
+مين التخالف التكتيك اللي اتبعته هنا هه هه هه هه هه
+
+190
+00:21:48,130 --> 00:21:48,310
+هه هه هه هه هه هه هه هه هه هه هه هه هه هه هه هه هه
+
+191
+00:21:48,310 --> 00:21:49,710
+هه هه هه هه هه هه هه هه هه هه هه هه هه هه هه هه هه
+
+192
+00:21:49,710 --> 00:21:51,410
+هه هه هه هه هه هه هه هه هه هه هه هه هه هه هه هه هه
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+193
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+هه هه هه هه هه هه هه هه هه هه هه هه هه هه هه هه هه
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+194
+00:21:53,070 --> 00:22:03,390
+هه هه هه هه هه هه هه هه هه هه هه هه هه هه هه
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+195
+00:22:03,390 --> 00:22:12,040
+ههلو حصل ان ال X للتاني هي X للتالت و Y للتاني هي
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+196
+00:22:12,040 --> 00:22:20,340
+X للتالت و هكذا يجب ان يكون اذا كان 2-S يكون 5
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+197
+00:22:20,340 --> 00:22:22,700
+زائد 2A
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+198
+00:22:30,000 --> 00:22:36,440
+بعدها واحد زائد اس بده يساوي واحد زائد اس بده
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+00:22:36,440 --> 00:22:45,120
+يساوي تمانية زائد تلاتة بقول كويس ايش رايك اجمع
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+00:22:45,120 --> 00:22:51,700
+الأولى والتالتة مرة واحدة نسيب التانية يبقى لو
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+201
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+جمعتهم بتروح الاس مع الاس بيظل في الشجة الشمال جدا
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+يعنيثلاثة تساوي تلت
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+عشرة يبقى ال R تساوي سالب اتنين الآن بدي اعوض في
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+اي من المعادلة تانية الأولى او التالتة سيانةبالـ S
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+الـ R عندي بسلب 2 لو روحت عوضت في الأولى يجب ان
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+209
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+يبقى الـ S تساوي قدر واحد الان المعادل اللي ما
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+اشتغلتش عليها اليمينمعادلة رقم اتنين إذا بدي أشيل
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+S و أضع مكانها واحد بصير الطرف الشمال كم؟ تلاتة
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+بدي أشيل هنا و أضع مكانها سالفي اتنين بصير كم؟
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+تلاتة يبقى اتنين هذول are intersect يبقى هذه
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+214
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+نسميها المعادلة star substitute
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+215
+00:24:23,420 --> 00:24:33,420
+ان استاء ويجد بدي اشير عندك تلاتة في اس اللي هي
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+216
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+واحد يساوي واحد ناقص ناقص اتنين يعني تلاتة بدها
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+تساوي تلاتة اذا معناه هذا الكلام الخاطئ هدول مالهم
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+بدهم يتقاطعوا
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+219
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+يبقى كذلك الاتنين والتلاتة
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+220
+00:25:00,780 --> 00:25:04,460
+مقاومة
+
+221
+00:25:04,460 --> 00:25:11,940
+في المقاومة يلّا
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+222
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+نجيب نقطة التقاطع تبع الخط الاتنين هذين تاخدي أي
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+00:25:17,800 --> 00:25:23,110
+واحدة يا هذه يا هذهأخذت هذي بتعوض قيمة A أخذت هذي
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+225
+00:25:28,510 --> 00:25:34,870
+إذا بدأ أقول X وY وZ أحداث النقطة بدوا يساوي انا
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+00:25:34,870 --> 00:25:40,710
+بدأ أمسك ال L2 اللي هو اتنين ناقص واحد وتلاتة
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+227
+00:25:50,240 --> 00:25:55,580
+نقطة التقاطع للمستقيمين الاتنين اللي عندناها دوة
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+228
+00:25:55,580 --> 00:25:58,720
+طيب
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+229
+00:25:58,720 --> 00:26:03,800
+ده حد هنا stop انتهينا من النقطة الأولى من هذا ال
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+230
+00:26:03,800 --> 00:26:06,840
+section اللي ابتدأناها المرة الماضية
+
+231
+00:26:12,170 --> 00:26:20,590
+أي استفسار عندنا هنا؟ حد بتسأل أي سؤال؟ طيب بروح
+
+232
+00:26:20,590 --> 00:26:22,830
+لقال النقطة الثانية
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+233
+00:26:52,540 --> 00:26:56,700
+النقطة الثانية يا بنات هي المسافة من نقطة إلى خط
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+234
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+مستقيم في الفرقة الـ
+
+235
+00:27:02,140 --> 00:27:06,160
+distance المسافة
+
+236
+00:27:06,160 --> 00:27:20,380
+from a point from a point to a line and space
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+237
+00:27:24,110 --> 00:27:29,730
+هنا نجيب المسافة ما بين نقطة وخط مستقيم بالفرعات
+
+238
+00:27:29,730 --> 00:27:38,130
+نفترض على سبيل المثال ان هذا هو line L واخدنا نقطة
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+239
+00:27:38,130 --> 00:27:42,650
+وان تكون هذه النقطة نقطة S مثلا
+
+240
+00:27:45,440 --> 00:27:52,980
+بنجيب قداش المسافة ما بين النقطة S و Main و Line L
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+241
+00:27:52,980 --> 00:27:58,220
+بقول والله كويس المسافة اللى وصلتك هذه مسافة هذه
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+242
+00:27:58,220 --> 00:28:03,800
+مسافة هذه مسافة هذه مسافة لكن في الحقيقة المسافة
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+243
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+الحقيقية هي المسافةالعمودية بين هذه النقطة والخط
+
+244
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+المستقيم يعني بنروح نزل عمود على الخط المستقيم من
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+245
+00:28:16,160 --> 00:28:22,080
+هذه النقطة بهذا الشكل يبقى
+
+246
+00:28:22,080 --> 00:28:28,540
+هذا عمود يبقى هذا ال distance دي مطلوب مننا نعرف
+
+247
+00:28:28,540 --> 00:28:33,900
+قداش مقدار ال distance ديطبعا distance مسافة و
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+248
+00:28:33,900 --> 00:28:39,140
+احنا بنشغل في موضوع المتجهات إذا بلزمني المتجهات
+
+249
+00:28:39,140 --> 00:28:44,920
+في معرفة هذه ال distance لذلك النقطة S هذه نقطة
+
+250
+00:28:44,920 --> 00:28:49,500
+معلومة معروفة عندى لإنهم يعطينا أحداثياتها و ال
+
+251
+00:28:49,500 --> 00:28:56,280
+line عند ال معروف تمام يبقى أنا مشان أجيب المسافة
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+252
+00:28:56,280 --> 00:29:02,190
+هذه بتروح أدور على vector موازي لهذا ال lineو طبعا
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+253
+00:29:02,190 --> 00:29:05,190
+إذا ال line مُعطَى في الصيغة البرامترية بصير ال
+
+254
+00:29:05,190 --> 00:29:09,510
+vector معروف ال vector معروف و النقطة معروفة منهم
+
+255
+00:29:09,510 --> 00:29:14,530
+بقدر أجيب ال distance كيف؟ كالتالت بروح أخد أي
+
+256
+00:29:14,530 --> 00:29:21,810
+نقطة موجودة على هذا ال line و لتكن النقطة P باخد
+
+257
+00:29:21,810 --> 00:29:29,590
+المتجه PS بالشكل اللي عندنا يبقى هذا هو المتجه PS
+
+258
+00:29:31,180 --> 00:29:40,120
+PS صنعني مع المستقيم L أو مع المتجه
+
+259
+00:29:40,120 --> 00:29:48,940
+الموازي لل line L وليكن المتجه V الموازي لل line L
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+260
+00:29:48,940 --> 00:29:55,700
+صنعني زاوية مقدارها θيتا صار
+
+261
+00:29:55,700 --> 00:30:02,790
+عندي مثلث قائم الزاوية الطلع هذا طولههو طول الـ P
+
+262
+00:30:02,790 --> 00:30:09,510
+S وهذا أحد ضلعي القائمة والزاوية تيتا اللي عندنا
+
+263
+00:30:09,510 --> 00:30:14,410
+هذه حد فيكم بتقدر تجيب لي D بدلالة طول P S
+
+264
+00:30:14,410 --> 00:30:19,870
+والزاوية تيتا اللي هو P S في صين الزاوية تيتا يبقى
+
+265
+00:30:19,870 --> 00:30:25,910
+D تساوي P S طول المتجة في صين الزاوية
+
+266
+00:30:28,370 --> 00:30:33,370
+طيب يبقى الحين قصتنا صارت معروفة بس بدي أحول
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+267
+00:30:33,370 --> 00:30:40,470
+الصياغ هذه بصياغة أخرى تمام فباجي بقول هنا the
+
+268
+00:30:40,470 --> 00:30:55,050
+distance d is given from الـd يسوى طول الـP S في
+
+269
+00:30:55,050 --> 00:30:57,050
+مين؟ في صيني الزاوية
+
+270
+00:30:59,640 --> 00:31:05,640
+طيب نرجع بالذاكرة إلى الوراق لو عندي متجهين U و V
+
+271
+00:31:05,640 --> 00:31:12,320
+وعملت لهم cross product يبقى U cross ال B طول ال U
+
+272
+00:31:12,320 --> 00:31:15,900
+فطول ال B في الصينة الزاوية تيتا في اتجاه متجه
+
+273
+00:31:15,900 --> 00:31:21,420
+الوحدة M اللي هو خط طول بصورة U طول U cross ال B
+
+274
+00:31:21,420 --> 00:31:25,500
+طول ال U فطول ال U في الصينة الزاوية تيتا صح؟ إذا
+
+275
+00:31:25,500 --> 00:31:31,020
+لو كنت جيب صينة زاوية تيتابصير طول ال U V على طول
+
+276
+00:31:31,020 --> 00:31:36,220
+ال U في طول ال V إذا ال sin زاوية تيتا هذه بقدر
+
+277
+00:31:36,220 --> 00:31:44,460
+أشيلها و أقول هو طول ال PS sin زاوية تيتا تيتا
+
+278
+00:31:44,460 --> 00:31:53,680
+محصورة بين مين؟ بين PS و V يبقى طول ال PS cross ال
+
+279
+00:31:53,680 --> 00:31:54,220
+V
+
+280
+00:31:59,160 --> 00:32:06,720
+على طول الـPS في طول الـV في
+
+281
+00:32:06,720 --> 00:32:11,760
+شغلة ممكن نختصرها بين البصد والمقارنة طول الـPS مع
+
+282
+00:32:11,760 --> 00:32:18,500
+طول الـPS ما قسمتش على متج هه ماقسمت متج هه قسمت
+
+283
+00:32:18,500 --> 00:32:22,600
+على طول المتجه يعني قسم على الـscalarيبقى من هنا
+
+284
+00:32:22,600 --> 00:32:29,660
+بيصير ال distance D بيصير طول ال PS across ال V
+
+285
+00:32:29,660 --> 00:32:36,700
+على طول المتجه V يبقى هذه وسيلة عملية على كيفية
+
+286
+00:32:36,700 --> 00:32:43,980
+الحصول على المسافة بين نقطة وخط مستقيم في الفرعات
+
+287
+00:32:43,980 --> 00:32:50,600
+يبقى يا بناتبالبلد هيك نحكي الان لو فى عندى نقطة
+
+288
+00:32:50,600 --> 00:32:55,060
+فى الفراغ وعندي خط مستقيم كده اجيب المسافة كدهش
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+289
+00:32:55,060 --> 00:33:01,600
+بين هذه النقطة وذاك الخط المستقيم ايش بالزمنى نقطة
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+290
+00:33:01,600 --> 00:33:06,940
+معروفة احدثيتها يمكن بدي اوجد اى نقطة على الخط
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+291
+00:33:06,940 --> 00:33:12,660
+اللى اللى هسميها P كويس وبيدي متجة يوازن
+
+292
+00:33:34,740 --> 00:33:40,500
+طيب أجت واحدة مش عارفة الرسمة وعطيتها سؤال
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+293
+00:33:48,170 --> 00:33:52,670
+و تلها كيلي المسافة بين هذه النقطة و هذا ال line
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+294
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+أجت على القانون اللي أخدت ال tech tech اللي طلع
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+295
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+عليه جسر الصفارة ما تفسيره كلنا لهذه الاتجاه ايوا
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+296
+00:34:05,370 --> 00:34:11,470
+يبقى كم قالت الأخش اسمك إنت أفنان أفنان زي ما قالت
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+297
+00:34:11,470 --> 00:34:19,220
+أختك أفنانهذه النقطة تبقى على نفس القرار المصطلح
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+298
+00:34:30,710 --> 00:34:35,130
+معنى هذا الكلام ان هذه النقطة تقع على الخط
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+299
+00:34:35,130 --> 00:34:40,890
+المستقيم مباشرة طيب stop لحد هنا نيجي ناخد بعض
+
+300
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+الأمثلة على الكلام اللي احنا جاي له هذا اول مثال
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+301
+00:34:45,970 --> 00:34:50,630
+examples اول
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+302
+00:34:50,630 --> 00:34:52,310
+مثال على هذا الموضوع
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+303
+00:34:58,400 --> 00:35:02,520
+خدنا قداش المسافة من الـ point
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+304
+00:35:11,650 --> 00:35:18,130
+وتلاتة to the line للخط
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+00:35:18,130 --> 00:35:27,770
+المستقيم X يساوي عشرة زائد أربعة T وY يساوي ناقص
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+306
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+تلاتة وZ يساوي أربعة T
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+307
+00:35:44,390 --> 00:35:49,670
+سؤال مرة تانية ماتيني خط مستقيم في الصيغة ال
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+308
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+parameterية وماتيني نقطة يمر بها هذا الخط المستقيم
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+أو نقطة في الفرار فجالي قداشي المسافة من هذه
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+النقطة إلى هذا ال line زي ما احنا شايفين بده نقطة
+
+311
+00:36:07,090 --> 00:36:11,850
+موجودة و الحمد لله موجودة بدي vector موازي ال line
+
+312
+00:36:11,850 --> 00:36:16,010
+اللي مطلوب يجيب المسافة بينه وبين النقطة ال vector
+
+313
+00:36:16,010 --> 00:36:20,770
+بجيبه من وين؟ من نفس المعادلة اللي عندنا يبقى باجي
+
+314
+00:36:20,770 --> 00:36:26,590
+بقول بدي أجيب ال vector الموازي لمين لهذا ال line
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+315
+00:36:26,590 --> 00:36:29,070
+يبقى V تساوي
+
+316
+00:36:33,480 --> 00:36:39,960
+زيرو المركبة يبقى مع السلامة يبقى زائد أربعة key
+
+317
+00:36:39,960 --> 00:36:49,120
+هذا parallel to the given line
+
+318
+00:36:52,900 --> 00:36:58,120
+يبقى هذا given to the given line يبقى صار المتجه
+
+319
+00:36:58,120 --> 00:37:04,720
+الموازي موجود والنقطة موجودة تمام طيب بدي المتجه P
+
+320
+00:37:04,720 --> 00:37:12,460
+S معناته بدي النقطة P أنا عند هنا ال S يبقى ناقطي
+
+321
+00:37:12,460 --> 00:37:17,300
+النقطة المواطعة اللي هي المواطعة فوق يبقى ال S هي
+
+322
+00:37:17,300 --> 00:37:25,270
+النقطة السالف واحدة واربعة وتلاتة طيب و Pهذه
+
+323
+00:37:25,270 --> 00:37:29,510
+اللقطة اللي بمرقها الخط المستقيل اللي هي المركبة
+
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+00:37:29,510 --> 00:37:34,190
+الأولى لها عشرة المركبة التانية سالم تلاتة والا
+
+325
+00:37:34,190 --> 00:37:36,190
+بعدها كده؟ Zero
+
+326
+00:37:42,650 --> 00:37:49,190
+يساوي ناقص واحد ناقص عشرة ناقص واحد ناقص عشرة في
+
+327
+00:37:49,190 --> 00:37:56,530
+اتجاه ال I اللي بعده أربعة زائد تلاتة زائد أربعة
+
+328
+00:37:56,530 --> 00:38:02,910
+زائد تلاتة في اتجاه ال J اللي بعده تلاتة ناقص Zero
+
+329
+00:38:02,910 --> 00:38:11,430
+في اتجاه ال K يبقى ناقص 11 Iزائد سبعة جيب زائد
+
+330
+00:38:11,430 --> 00:38:20,390
+تلاتة كيب زائد
+
+331
+00:38:20,390 --> 00:38:21,670
+تلاتة كيب
+
+332
+00:38:27,940 --> 00:38:37,600
+الـ V يبقى الـ P S اللي هو سالب 11 7 3 ال V 404
+
+333
+00:38:37,600 --> 00:38:49,600
+طبعا I و J و K و الصفة التالت اللي هو من 4 و 0 و 4
+
+334
+00:38:49,600 --> 00:38:55,260
+بالشكل اللي عندنا يبقى بالدرجة أفك المحدد هذا 7 في
+
+335
+00:38:55,260 --> 00:39:04,630
+4تمنية وعشرين وعندك I يبقى هنا تمنية وعشرين I اللي
+
+336
+00:39:04,630 --> 00:39:11,850
+بعده نشطة بصفه عموده بصير ناقص اربعة واربعين وناقص
+
+337
+00:39:11,850 --> 00:39:15,510
+اتناشر يبقى ناقص ستة وخمسين
+
+338
+00:39:24,490 --> 00:39:31,610
+نقص تمانية وعشرين كيلو نقص تمانية وعشرين كيلو نقص
+
+339
+00:39:31,610 --> 00:39:39,010
+تمانية وعشرين كيلو نقص تمانية وعشرين
+
+340
+00:39:39,010 --> 00:39:39,550
+كيلو
+
+341
+00:39:44,550 --> 00:39:52,550
+هذا P S cross ال V بدنا طول المتجه هذا مقسوما على
+
+342
+00:39:52,550 --> 00:39:58,810
+طول مين؟ على طول ال V يرجع ال distance D بدها
+
+343
+00:39:58,810 --> 00:40:06,370
+تساوي طول ال P S cross ال V مقسوما على طول ال V و
+
+344
+00:40:06,370 --> 00:40:12,430
+يسافريبقى بدنا نروح و نربع المقادير اللي عندنا هنا
+
+345
+00:40:12,430 --> 00:40:20,170
+يبقى هذا بتساوي ال square ربما 28 تربيع خليها
+
+346
+00:40:20,170 --> 00:40:27,450
+لحالي و هذا هنا بتصير واحد زائد اربعة زائد واحد
+
+347
+00:40:27,450 --> 00:40:36,590
+مقسوما على وين ال V هي ال Vيبقى الجذر التربيعي ل
+
+348
+00:40:36,590 --> 00:40:43,350
+16 زائد 16 يبقى
+
+349
+00:40:43,350 --> 00:40:48,970
+هذا الكلام يساوي الجذر التربيعي هذه بنات اللي هي
+
+350
+00:40:48,970 --> 00:40:59,190
+أربعة تربية في سبعة تربية في ستة على و هذه اللي
+
+351
+00:40:59,190 --> 00:41:06,350
+أربعة جذر اتنىمظهر؟ طيب الأربعة الترابيه هذه لو
+
+352
+00:41:06,350 --> 00:41:12,520
+طلعت برا الجدرق وضار قداش، أربعةمظبوط بيضال جدشان
+
+353
+00:41:12,520 --> 00:41:17,540
+دي اللي هو سبعة تربية في ستة سبعة في سبعة بتسعة
+
+354
+00:41:17,540 --> 00:41:24,240
+واربعين في ستة هي تسعة واربعين في ستة ستة في تسعة
+
+355
+00:41:24,240 --> 00:41:30,320
+واربعة وخمسين ستة في أربعة واربعة وعشرين وخمسة
+
+356
+00:41:30,320 --> 00:41:37,140
+وتسعة وعشرين يبقى اتنين اربعة وتسعين على جذر اتنين
+
+357
+00:41:47,580 --> 00:41:54,060
+طيب 28 هذه اللي ربعناها و هذه اللي ربعناها مظبوط
+
+358
+00:41:54,060 --> 00:42:00,420
+يبقى هذا الطول بده يساوي تحت الجدر يبقى هذا الجدر
+
+359
+00:42:00,420 --> 00:42:05,540
+التربيعي تيجي لأ تيجي سبعة جدر ستة صحيح سبعة
+
+360
+00:42:09,660 --> 00:42:14,680
+على جدر اتنين وجدر ستة اللي هو جدر اتنين في جدر
+
+361
+00:42:14,680 --> 00:42:21,140
+تلاتة مظلوم يبقى هنا سبعة جدر اتنين جدر تلاتة على
+
+362
+00:42:21,140 --> 00:42:26,920
+جدر اتنين يبقى السابعة جدر تلاتة هذا الطول الا ان
+
+363
+00:42:26,920 --> 00:42:30,680
+الله يعطي كمان مثال
+
+364
+00:42:59,880 --> 00:43:05,380
+يبقى example two verify
+
+365
+00:43:05,380 --> 00:43:13,020
+اتأكد انه that the lines
+
+366
+00:43:13,020 --> 00:43:19,360
+الخطوط المستقيمة ال one اللي هو main اللي هو X
+
+367
+00:43:19,360 --> 00:43:26,780
+يساوي اتنين زائد T X يساوي اتنين زائد T و Y تساوي
+
+368
+00:43:26,780 --> 00:43:28,420
+ناقص اتنين
+
+369
+00:43:36,150 --> 00:43:49,550
+1-t L2 X يساوي 1 زائد 2T Y
+
+370
+00:43:49,550 --> 00:44:01,270
+يساوي 3-4T Z يساوي 5-2T R تلالي
+
+371
+00:44:05,950 --> 00:44:13,930
+and find the distance between them and find the
+
+372
+00:44:13,930 --> 00:44:21,890
+distance between them
+
+373
+00:44:44,560 --> 00:44:52,700
+هو يقول يثبت ان الخطين متوازيان ومن ثم اتل ال
+
+374
+00:44:52,700 --> 00:44:57,800
+distance ما بين الخطين المتوازيان الاتنين كويس
+
+375
+00:44:57,800 --> 00:45:01,600
+يبقى بدى اشوف هل هدول اتنين متوازيان لأ يعني هل ال
+
+376
+00:45:01,600 --> 00:45:06,560
+vector اللذي يوازي المتجه الأول يوازي ال vector
+
+377
+00:45:06,560 --> 00:45:11,120
+اللذي يوازي الخط الثاني ولا لأ فبجي بقوله الأهم
+
+378
+00:45:11,120 --> 00:45:11,720
+solution
+
+379
+00:45:33,270 --> 00:45:44,050
+2i-4j-2k parallel to l2 parallel to l2
+
+380
+00:45:49,850 --> 00:45:55,990
+V2 يساوي .. بدي أخد اتنين عامل مشترك بضل عندي I
+
+381
+00:45:55,990 --> 00:46:03,590
+نقص اتنين J نقص K اللي هو اتنين فيه هذا مين؟ اتنين
+
+382
+00:46:03,590 --> 00:46:13,350
+V1 يبقى هذا بدي يعطينا ان V1 and V2 are parallel
+
+383
+00:46:13,350 --> 00:46:26,020
+هذا بدي يعطينا ان L1 andلتو are parallel lines
+
+384
+00:46:26,020 --> 00:46:31,660
+تبقى اثبات نظر المطلوب الاول ان اتنين هدول ما لهم
+
+385
+00:46:31,660 --> 00:46:37,960
+متوازين لو جت افترضت على سبيل المثال ان هذا ال one
+
+386
+00:46:37,960 --> 00:46:45,590
+و هذا ال two الموازي لههذا L1 وهذا L2 على سبيل
+
+387
+00:46:45,590 --> 00:46:52,430
+المثال كويس يبقى ال L1 هو المستقيم الأول مظبوط بدا
+
+388
+00:46:52,430 --> 00:46:58,390
+افترض انه بيمر بنقطة ما مين النقطة اللتي يمر بها
+
+389
+00:46:58,390 --> 00:47:04,450
+المستقيم الأول 2 سالب 2 هو 1 لو افترض ان
+
+390
+00:47:11,290 --> 00:47:18,830
+و سالب اتنين و واحد نقطة تانية هنا على المستقيم
+
+391
+00:47:18,830 --> 00:47:24,550
+التاني بدي أسميها P ال P لي واحد و تلاتة و خمسة
+
+392
+00:47:24,550 --> 00:47:31,550
+يبقى واحد و تلاتة و خمسة جالي هاجل المسافة ما بين
+
+393
+00:47:31,550 --> 00:47:37,210
+الخطين المستقيمين بقوله كويس بدي أجي من هنا أنزل
+
+394
+00:47:37,210 --> 00:47:37,790
+عنوان
+
+395
+00:47:43,720 --> 00:47:53,980
+هو نفس المسافة إذا أنا صار عندى متجه اسمه yes يبقى
+
+396
+00:47:53,980 --> 00:47:59,180
+ماشي ناشي بال distance هذي بدي الموازي ل L2 من
+
+397
+00:47:59,180 --> 00:48:05,960
+الموازي ل L2 اللي هو V2 اللي عندنا هذا تمام يبقى
+
+398
+00:48:05,960 --> 00:48:13,760
+هذا المتجه اللي هو V2 اللي عندناخلصنا يبقى V موجود
+
+399
+00:48:13,760 --> 00:48:18,080
+ضايق بس أجيب له PS و بالتالي مشكلتنا خلصت يبقى
+
+400
+00:48:18,080 --> 00:48:27,540
+بتاجي لمين؟ لـPS الشكل اللي عندنا هذا يبقى 2-1 في
+
+401
+00:48:27,540 --> 00:48:31,760
+اتجاه I زائد نقص 2
+
+402
+00:48:42,150 --> 00:48:50,670
+نقص اربعة كيك نقص
+
+403
+00:48:50,670 --> 00:48:55,730
+اربعة كيك نقص اربعة كيك نقص اربعة كيك نقص اربعة
+
+404
+00:48:55,730 --> 00:48:56,490
+كيك نقص اربعة كيك نقص اربعة كيك نقص اربعة كيك نقص
+
+405
+00:48:56,490 --> 00:48:56,590
+اربعة كيك نقص اربعة كيك نقص اربعة كيك نقص اربعة
+
+406
+00:48:56,590 --> 00:48:56,610
+كيك نقص اربعة كيك نقص اربعة كيك نقص اربعة كيك نقص
+
+407
+00:48:56,610 --> 00:48:58,290
+كيك نقص اربعة كيك نقص اربعة كيك نقص اربعة كيك نقص
+
+408
+00:48:58,290 --> 00:49:05,310
+اربعة كيك نقص اربعة كيك نقص اربعة كي
+
+409
+00:49:14,520 --> 00:49:25,120
+عشرة ناقص ستة في اتجاه الاعلى مرتين عشرة بالموجة
+
+410
+00:49:25,120 --> 00:49:29,360
+سالب ستة يظل سالب ستة في اتجاه الاعلى ليه بعد؟
+
+411
+00:49:33,410 --> 00:49:40,990
+زائد تمانية يبقى ضل زائد سبعة مع شرط الناقص بناقص
+
+412
+00:49:40,990 --> 00:49:46,950
+سبعة genes اتنين
+
+413
+00:49:46,950 --> 00:49:53,030
+و تمانية صح ستة كلامك مظبوط أصابت امرأة وأختها عمر
+
+414
+00:49:57,100 --> 00:50:03,960
+مشط بصفه وعموده يبقى ناقص أربعة وزائد عشرة بغير
+
+415
+00:50:03,960 --> 00:50:12,340
+زائد ستة يبقى زائد ستة K الان بدي أجيب قداش الطول
+
+416
+00:50:12,340 --> 00:50:16,640
+تبعه أو بدي أجيب ال distance دي يبقى ال distance
+
+417
+00:50:16,640 --> 00:50:25,400
+دي بدها تساوي طول ال PS cross ال V2 مقسوماعلى قول
+
+418
+00:50:25,400 --> 00:50:32,380
+الـ V2 ويساوي الجدرى التربية طول الـ PSI يبقى 36
+
+419
+00:50:32,380 --> 00:50:41,520
+زائد 36 زائد 36 على الجدرى التربية الى V2 اللي هو
+
+420
+00:50:41,520 --> 00:50:44,140
+4 زائد 16
+
+421
+00:50:47,830 --> 00:50:52,830
+كل جدر واحد ستة و تلاتين و ستة و تلاتين و ستة و
+
+422
+00:50:52,830 --> 00:50:54,450
+تلاتين و ستة و تلاتين و ستة و تلاتين و ستة و
+
+423
+00:50:54,450 --> 00:50:58,370
+تلاتين و ستة و تلاتين و ستة و تلاتين و ستة و
+
+424
+00:50:58,370 --> 00:51:02,910
+تلاتين و ستة و تلاتين و ستة و تلاتين و ستة و
+
+425
+00:51:02,910 --> 00:51:03,610
+تلاتين و ستة و تلاتين و ستة و تلاتين و ستة و
+
+426
+00:51:03,610 --> 00:51:05,350
+تلاتين و ستة و تلاتين و ستة و تلاتين و ستة و
+
+427
+00:51:05,350 --> 00:51:12,750
+تلاتين و ستة و تلاتين و ستة و تلاتين و ستة و
+
+428
+00:51:12,750 --> 00:51:18,660
+تلاتين و ستيبقى على أربعة فيها اتنين وتمانية
+
+429
+00:51:18,660 --> 00:51:22,940
+وعشرين على أربعة فيها السبعة وعشرين وعلى أربعة
+
+430
+00:51:22,940 --> 00:51:29,720
+فيها ستة وعلى تلاتة فيها تسعة وعلى تلاتة فيها
+
+431
+00:51:29,720 --> 00:51:36,280
+اتنين يبقى تلاتة على جذر اتنين هذه المسافة ما بين
+
+432
+00:51:36,280 --> 00:51:43,920
+الخطين المتوازين اللي عندناطيب نجي الان بنطلع
+
+433
+00:51:43,920 --> 00:51:49,240
+النقطة الثالثة من هذا ال section النقطة التالتة
+
+434
+00:51:49,240 --> 00:51:54,460
+equation of
+
+435
+00:51:54,460 --> 00:51:58,220
+a plane
+
+436
+00:51:58,220 --> 00:51:59,860
+in space
+
+437
+00:52:08,810 --> 00:52:14,950
+يجب أن نجي لمعادلة المستوى في الفرق سواء كان مستوى
+
+438
+00:52:14,950 --> 00:52:18,450
+أفقي أو رأسي أو مائي أو كيف ما يكون يكون لدينا
+
+439
+00:52:18,450 --> 00:52:25,790
+مشكلة لدينا معادلة عامة لهذا المستوى باستخدام ال
+
+440
+00:52:25,790 --> 00:52:26,130
+vector
+
+441
+00:52:30,790 --> 00:52:35,550
+معادلة هذا المستوى بلزمني ال vector عمودي عليه
+
+442
+00:52:35,550 --> 00:52:41,110
+وبلزمني النقطة يمر بيه لهذا المستوى بس شغلتين زي
+
+443
+00:52:41,110 --> 00:52:45,330
+ما في ال line بدي مسافة بين و بين هذا ال line بدي
+
+444
+00:52:45,330 --> 00:52:51,110
+نقطة و بدي متجهي ودي لأ انا بدي متجه عمودي عليه
+
+445
+00:52:58,860 --> 00:53:06,560
+و قلت هذا المستوى و روحت سميت هذا المستوى M أخدت
+
+446
+00:53:06,560 --> 00:53:13,400
+متجه عمودي عليه بهذا الشكل طلع هذا المتجه اللي هو
+
+447
+00:53:13,400 --> 00:53:23,260
+عمودي عليه و سميته المتجه N A I زائد B J زائد C K
+
+448
+00:53:23,260 --> 00:53:31,750
+مثلا قاطعوا النقطة اللي عندناتمام؟ المتجر هذا
+
+449
+00:53:31,750 --> 00:53:38,930
+epsilon مر في نقطة و التكن النقطة في نوضه x نوضه و
+
+450
+00:53:38,930 --> 00:53:44,450
+y نوضه و z نوضهتبقى عني معلومة عندي شغلتين الآن
+
+451
+00:53:44,450 --> 00:53:50,690
+تمام منتجة عمودي على المستوى و نقطة تقع في المستوى
+
+452
+00:53:50,690 --> 00:53:54,990
+يعني امر بها هذا المستوى من خلال الكلام اللي
+
+453
+00:53:54,990 --> 00:54:01,970
+قدامنا هذا بدي احاول اجيب قداش معادلة هذا المستوى
+
+454
+00:54:01,970 --> 00:54:07,070
+بقول كويس عشان اجيب المعادلة بروح اخد اي نقطة
+
+455
+00:54:07,070 --> 00:54:12,890
+موجودة في هذا المستوىطبعاً بنذكركم بشغلة لو قلت أي
+
+456
+00:54:12,890 --> 00:54:17,430
+مستوى الطاولة اللي عندنا هنا وهذا متجه عمودي على
+
+457
+00:54:17,430 --> 00:54:22,990
+الطاولة إذا عمودي على أي متجه أو أي مستقيم موجود
+
+458
+00:54:22,990 --> 00:54:27,630
+في مستوى الطاولة اللي عندنا هنا تمام يبقى بناء
+
+459
+00:54:27,630 --> 00:54:36,330
+عليه لو أخدت نقطة تانية هنا وسميتها XYZ أو ال P
+
+460
+00:54:36,330 --> 00:54:38,310
+XYZ
+
+461
+00:54:42,080 --> 00:54:50,480
+يوجد متجة من P نود الى P بهذه الشكلة ايش علاقة
+
+462
+00:54:50,480 --> 00:54:57,720
+متجة P نود P بالمتجة L ايوة اتنين are orthogonal
+
+463
+00:54:57,720 --> 00:55:06,340
+يبقى هنا باجي بقوله ده او نقول ان كلمتين قبل بحط
+
+464
+00:55:06,340 --> 00:55:06,980
+المعادلة
+
+465
+00:55:13,210 --> 00:55:26,730
+that أنه the plane M passes .. passes through الـ
+
+466
+00:55:26,730 --> 00:55:35,790
+P node و X node و Y node و Z node and normal to
+
+467
+00:55:35,790 --> 00:55:44,720
+the vectorوعمودي على المتجد N وA في اتجاه I P في
+
+468
+00:55:44,720 --> 00:55:51,180
+اتجاه الـ J وC في اتجاه الـ K let
+
+469
+00:55:51,180 --> 00:56:03,720
+P أو X أو Y أو Z be any point أو be a point نقطة
+
+470
+00:56:03,720 --> 00:56:13,270
+in the planeم الان
+
+471
+00:56:13,270 --> 00:56:26,890
+ال vector n او ال vectors n and ال P note PR او
+
+472
+00:56:26,890 --> 00:56:27,430
+orthogonal
+
+473
+00:56:37,270 --> 00:56:47,570
+يبقى معنى هذا الكلام ان ال vector اولا ال N dot P
+
+474
+00:56:47,570 --> 00:56:50,350
+not P بده يساوي زيه
+
+475
+00:56:54,990 --> 00:57:02,590
+بدي أشيل ال N و أضع القيمة بتاعي يبقى AI زائد BJ
+
+476
+00:57:02,590 --> 00:57:09,830
+زائد CK Dot المتجهة الثانية المتجهة التانية اللي
+
+477
+00:57:09,830 --> 00:57:17,750
+هو X ناقص X node في اتجاه ال I زائد Y ناقص Y node
+
+478
+00:57:17,750 --> 00:57:25,370
+في اتجاه ال J Z ناقص Z node كله في اتجاهالـ K كل
+
+479
+00:57:25,370 --> 00:57:31,770
+هذا الكلام يجب أن يسوى كم؟ يجب أن يسوى 0 نعمل الـ
+
+480
+00:57:31,770 --> 00:57:37,930
+dot product فيما بينهم يبقى صار الـ A في الـ X مقص
+
+481
+00:57:37,930 --> 00:57:44,610
+الـ X knot زائد B في الـ Y مقص الـ Y knot زائد C
+
+482
+00:57:44,610 --> 00:57:46,010
+في الـ Z مقص
+
+483
+00:57:58,130 --> 00:58:01,870
+بالسالب هضيفها على الشجة اليمين
+
+484
+00:58:11,600 --> 00:58:18,120
+الان ال X0 وY0 وZ0 نقاط معلومة أو مركبات معلومة ال
+
+485
+00:58:18,120 --> 00:58:22,340
+A والB والC هي المركبات المتجه العمودي المعلومة
+
+486
+00:58:22,340 --> 00:58:28,000
+إذاً هذا كله يشكل لقداشا بنات رقم واحد يبقى صلة
+
+487
+00:58:28,000 --> 00:58:34,780
+المعادلة AX زائد BY زائد C زاد
+
+488
+00:58:37,860 --> 00:58:46,740
+رقم واحد وليكن دي ودي بيكون اكس نوت بي نوت سي زي
+
+489
+00:58:46,740 --> 00:58:51,420
+نوت طيب؟
+
+490
+00:58:51,420 --> 00:58:58,440
+طيب كويس يبقى احنا جيبنا هذه معادلة ال equation
+
+491
+00:58:58,440 --> 00:59:12,100
+يبقى هذه ده equation of theA plane M إذا من الآن
+
+492
+00:59:12,100 --> 00:59:18,280
+فصاعدا مشان أجيب معادلة plane بدي متجه عمودي على
+
+493
+00:59:18,280 --> 00:59:22,500
+هذا ال plane اتنين بده نقطة يمر بها ال plane
+
+494
+00:59:22,500 --> 00:59:27,020
+وبالتالي بصير المعادلة بسيطة جدا حد بتحب تسأل أي
+
+495
+00:59:27,020 --> 00:59:32,740
+سؤال هنا قبل أن نذهب إلى الأمثلة لابد تسأل تسأل
+
+496
+00:59:36,570 --> 00:59:42,450
+إيش في حياة؟ قالت عايشة رضي الله عنها تسأل النبي
+
+497
+00:59:42,450 --> 00:59:47,690
+صلى الله عليه وسلم عن أدق الأشياء في حياة
+
+498
+00:59:52,690 --> 00:59:57,730
+السنة بيجي الصحابة يسألوها عن تصرف النبي صلى الله
+
+499
+00:59:57,730 --> 01:00:04,150
+عليه وسلم لذلك أحلى ما نقول حاجة تسألي ماتضلقيش
+
+500
+01:00:04,150 --> 01:00:09,750
+ساكتة وتعودي أنك تسألي حتى لو كان سوالك غلط تسألي
+
+501
+01:00:09,750 --> 01:00:12,790
+غلط كل مرة جاي تسألي غلط غلط تسألي صحي
+
+502
+01:00:21,210 --> 01:00:26,070
+لكن من خلال التساؤل بتثبت المعلوم غالب المال
+
+503
+01:00:26,070 --> 01:00:32,850
+والمال وزميلاتك بصير انت قدوة لهم حاضر بالنسبالي
+
+504
+01:00:32,850 --> 01:00:37,610
+سؤال عدلة ال plane اللي كانت عليه شكل ax زي بي زي
+
+505
+01:00:37,610 --> 01:00:41,830
+cz يساوي d حيث ال a والb والc هي المركبات المتجهة
+
+506
+01:00:41,830 --> 01:00:47,840
+العمودي على ال planeالان بدأ ناخد أمثلة على هذا
+
+507
+01:00:47,840 --> 01:00:54,640
+الكلام أول
+
+508
+01:00:54,640 --> 01:01:02,540
+بدا يقول find an
+
+509
+01:01:02,540 --> 01:01:10,700
+equation for the plane
+
+510
+01:01:10,700 --> 01:01:12,000
+satisfying
+
+511
+01:01:18,630 --> 01:01:27,030
+الأولى نمر ايه؟ the plane passes
+
+512
+01:01:27,030 --> 01:01:33,490
+through يمر
+
+513
+01:01:33,490 --> 01:01:42,310
+بالنقطة اللي هي P والي حدثية تبعتها اتنين واربعة
+
+514
+01:01:42,310 --> 01:01:47,250
+وخمسةand perpendicular to the line and
+
+515
+01:01:47,250 --> 01:01:50,570
+perpendicular
+
+516
+01:01:50,570 --> 01:01:53,950
+to
+
+517
+01:01:53,950 --> 01:01:58,450
+the line الخط
+
+518
+01:01:58,450 --> 01:02:08,910
+المستقيم X يساوي خمسة زائد T وال Y يساوي واحد زائد
+
+519
+01:02:08,910 --> 01:02:12,090
+تلاتة T وال Z يساوي
+
+520
+01:02:20,570 --> 01:02:27,870
+هذه معادلة المستوى اللي يحقق نمر أيه ال plane يمر
+
+521
+01:02:27,870 --> 01:02:33,790
+بالنقطة هذه وفي نفس لقطة عمودي على هذا الخط أنا مش
+
+522
+01:02:33,790 --> 01:02:39,540
+هنجيب معادلة ال plane بدي نقطة يمر بهاومين؟ متجه
+
+523
+01:02:39,540 --> 01:02:44,120
+عمودي على هذا الكليل هو أجلب لهذا الكليل عمودي على
+
+524
+01:02:44,120 --> 01:02:50,480
+الخط المستقيم هل أنا بقدر أجيب متجه يوازي هذا الخط
+
+525
+01:02:50,480 --> 01:02:57,020
+المستقيم؟ اللي هو مين؟ تمام يبقى باجي بقوله هنا
+
+526
+01:02:57,020 --> 01:03:04,420
+solution the vector اللي
+
+527
+01:03:04,420 --> 01:03:04,680
+هو
+
+528
+01:03:07,560 --> 01:03:18,160
+يبقى I زائد تلاتة J زائد أربعة K parallel to the
+
+529
+01:03:18,160 --> 01:03:27,100
+given line طب قالي لـ plane عمودي على هذا ال line
+
+530
+01:03:27,100 --> 01:03:31,980
+إذا لـ plane عمودي على هذا ال vector يبقى هذا
+
+531
+01:03:31,980 --> 01:03:36,600
+يعطينا ان ال vector
+
+532
+01:03:38,420 --> 01:03:49,820
+اللي هو سمته V is normal to the plane يبقى هذا
+
+533
+01:03:49,820 --> 01:03:56,540
+عمودي على مين على مسافة صار ال vector العمودي على
+
+534
+01:03:56,540 --> 01:04:02,160
+ال plane معروف والنقطة معروفة يبقى هذه تعويض مباشر
+
+535
+01:04:02,160 --> 01:04:12,560
+يبقى بقى اللي بقول ال question ofالمطلع العمودي
+
+536
+01:04:12,560 --> 01:04:18,440
+AX
+
+537
+01:04:18,440 --> 01:04:24,900
+يساوي ازايد BY زايد CZ
+
+538
+01:04:31,530 --> 01:04:38,070
+بنصارى عندى هنا I بواحد يبقى X الـ P بثلاثة والـ C
+
+539
+01:04:38,070 --> 01:04:44,110
+باربعة زده بدي نسوي واحد في ال X نوض اللى بقداش
+
+540
+01:04:44,110 --> 01:04:51,910
+اتنين زائد تلاتة في ال Y نوض اللى اربعة زائد اللى
+
+541
+01:04:51,910 --> 01:04:58,390
+هو C اللى باربعة في قداش P خمسة يبقى قصيرة ان هنا
+
+542
+01:04:58,390 --> 01:04:59,790
+قداش ال X
+
+543
+01:05:21,810 --> 01:05:26,470
+هذا المطلوب الأول من السؤال المطلوب التاني
+
+544
+01:05:35,570 --> 01:05:43,650
+passes through يمر
+
+545
+01:05:43,650 --> 01:05:52,430
+بـ the intersecting
+
+546
+01:05:52,430 --> 01:06:02,450
+lines يمر بالخطين المتقطعين اللي هو L1 المعادلات
+
+547
+01:06:02,450 --> 01:06:12,250
+هي Xيساوي T وال Y تساوي اتنين ناقص T وال Z تساوي
+
+548
+01:06:12,250 --> 01:06:23,750
+واحد زائد T وال L تو معادلته اللي هو X يساوي اتنين
+
+549
+01:06:23,750 --> 01:06:29,830
+زائد اتنين S وال Y بدها تساوي
+
+550
+01:06:34,290 --> 01:06:48,110
+تساوي ستة زائد خمس اسم الشكل اللي عندنا هذا كويس
+
+551
+01:06:48,110 --> 01:06:49,890
+مرتين
+
+552
+01:06:51,690 --> 01:06:56,830
+سؤال بيقول مياتي أنا عندي plane ال plane هذا يمر
+
+553
+01:06:56,830 --> 01:07:03,150
+بخطين مستقيمين متقاطعين يعني لو تصورت هذول اتنين
+
+554
+01:07:03,150 --> 01:07:08,930
+في مستوى رقاطة يبقوا مروا بهم مين؟ مستوى المستوى
+
+555
+01:07:08,930 --> 01:07:13,030
+هذا انا بدي المعادلة تبعه عشان اجيب المعادلة تبعه
+
+556
+01:07:13,030 --> 01:07:15,570
+فبدي نقطة تقع فيه
+
+557
+01:07:25,310 --> 01:07:32,570
+عروضي على الإثنين يعني عروضي على مستويهم مشان هيك
+
+558
+01:07:32,570 --> 01:07:41,950
+بدنا نروح نجيب المتجه الأول الموازي ل L1 يجيب V1
+
+559
+01:07:41,950 --> 01:07:53,530
+اللي هو بده يساوي I وهنا ناقص J وهنا زائد K هذا
+
+560
+01:07:53,530 --> 01:08:04,790
+parallelto L1 و ال V2 طبعا هنا بقول solution أول و
+
+561
+01:08:04,790 --> 01:08:14,850
+ال V2 يساوي 2I وهنا زائد J وهنا زائد خمسة K
+
+562
+01:08:14,850 --> 01:08:18,030
+parallel to L2
+
+563
+01:08:25,350 --> 01:08:31,310
+Okay وركبات ال V1 واحد و سالب واحد و واحد وركبات
+
+564
+01:08:31,310 --> 01:08:38,370
+ال V2 اتنين و واحد و خمسة بالشكل العام بدي افك هذا
+
+565
+01:08:38,370 --> 01:08:43,430
+المحدد يعني هذا الكلام بدرساه سالب خمسة و سالب
+
+566
+01:08:43,430 --> 01:08:50,410
+واحد و سالب ستة في اتجاه ال R اللي بعده خمسة نقص
+
+567
+01:08:50,410 --> 01:08:57,820
+اتنين و ناقص تلاتة في اتجاه ال Jاللي بعده واحد
+
+568
+01:08:57,820 --> 01:09:03,760
+زائد اتنين زائد تلاتة كيلو يبقى زائد تلاتة كيلو
+
+569
+01:09:03,760 --> 01:09:09,900
+إذا هذا المتجه عمودي على المتجهين الإتنين يبقى
+
+570
+01:09:09,900 --> 01:09:22,060
+عمودي على مستويهما this vector is normal to the
+
+571
+01:09:22,060 --> 01:09:23,340
+plate
+
+572
+01:09:25,460 --> 01:09:30,280
+هذا جيد، فجبت المتجه العمودي على المستوى، بدي نقطة
+
+573
+01:09:30,280 --> 01:09:37,210
+تقع في هذا المستوى، في كام واحدة؟ انت ..المفصقين
+
+574
+01:09:37,210 --> 01:09:42,170
+الاتنين يقعوا في الـ plan كل واحد منهم يمر بنقطة
+
+575
+01:09:42,170 --> 01:09:47,050
+يبقى هاي الحمد للار نحط البركة بدل النقطة خدي أي
+
+576
+01:09:47,050 --> 01:09:51,530
+واحدة فيهم و بيطلع نفسي المعادلة نحط النقطة الأولى
+
+577
+01:09:51,530 --> 01:09:56,310
+والنقطة الثانية سيال ماتطلعاش نفسي المعادلة اذا
+
+578
+01:09:56,310 --> 01:10:04,530
+بدأت اقول take مثلا P not herاللي هي واحد .. ايه
+
+579
+01:10:04,530 --> 01:10:17,590
+قصدي؟ Zero واتنين وواحد that lie on the line L1
+
+580
+01:10:17,590 --> 01:10:22,650
+ومن
+
+581
+01:10:22,650 --> 01:10:28,650
+ثم تقع وين؟ تقع على ال flame التي تقع on the line
+
+582
+01:10:28,650 --> 01:10:38,810
+L1 and onلـ plane وكذلك على المستوى إذا المتجه
+
+583
+01:10:38,810 --> 01:10:45,630
+موجود يبقى بالدعوة الضغطية يبقى ناقص ستة X ناقص
+
+584
+01:10:45,630 --> 01:10:54,250
+تلاتة Y زائد تلاتة Z يساوي ناقص ستة في Zero وهنا
+
+585
+01:10:54,250 --> 01:11:00,860
+ناقص تلاتة في اتنين وهنا زائد تلاتة في واحدإذا صرت
+
+586
+01:11:00,860 --> 01:11:06,860
+المعادلة ناقص ستة X ناقص تلاتة Y زائد تلاتة Z
+
+587
+01:11:06,860 --> 01:11:13,980
+يساوي ناقص ستة وزائد تلاتة يبقى ناقص تلاتة أو ممكن
+
+588
+01:11:13,980 --> 01:11:21,600
+أقول لو قسم كله على ناقص تلاتةمضال قداش عندي اتنين
+
+589
+01:11:21,600 --> 01:11:29,600
+X زائد Y ناقص Z يساوي كده؟ يساوي واحد هذه معادلة
+
+590
+01:11:29,600 --> 01:11:40,420
+plane المطلوبة طيب نمرسي من السؤال جالس اتنين فاصل
+
+591
+01:11:40,420 --> 01:11:48,000
+اترونيكوينز اتنين فاصل اترونيكوينز
+
+592
+01:11:49,790 --> 01:12:01,510
+the point اللذي يمر بالخط المستقيم P2 1-1 and
+
+593
+01:12:01,510 --> 01:12:11,090
+perpendicular to
+
+594
+01:12:11,090 --> 01:12:18,550
+the line of intersection to the line of
+
+595
+01:12:21,980 --> 01:12:30,160
+Intersection of the planes ده
+
+596
+01:12:30,160 --> 01:12:34,380
+المستويات الإتنين اللي هو اتنين X
+
+597
+01:12:39,550 --> 01:12:46,610
+هو ال X زائد اتنين Y زائد Z
+
+598
+01:13:22,370 --> 01:13:27,150
+نرجع لسؤالنا مرة تانية بيقول يبدي معاكد plane اللي
+
+599
+01:13:27,150 --> 01:13:32,030
+يمر بهذه النقطة الحمد لله تمام، ضال عند مين؟ متجه
+
+600
+01:13:32,030 --> 01:13:37,770
+عمودي عليه، بقول له أيوة and perpendicular to the
+
+601
+01:13:37,770 --> 01:13:41,330
+line of intersection of the two planes وهذا ال
+
+602
+01:13:41,330 --> 01:13:47,030
+plane عمودي على خط تقاطع ال two planes اللي عندنا
+
+603
+01:13:47,030 --> 01:13:54,330
+هذاتمام؟ ايوة، الان بدي اشوف خط التقاط على هذا
+
+604
+01:13:54,330 --> 01:13:59,230
+اللي عندنا ع جل ال employment يكون عمود الانتقال
+
+605
+01:13:59,230 --> 01:14:06,690
+ده هو الشكل وهي اسم العالم وهدي دفترك معاكي، تسيب
+
+606
+01:14:06,690 --> 01:14:08,190
+الشنطة وهدي دفترك معاكي
+
+607
+01:14:17,480 --> 01:14:26,140
+تمام تمام خليه هك موجه على البنات هى
+
+608
+01:14:26,140 --> 01:14:29,820
+عندى بنات الصفحاتين اللى اجبرتهم اعتبرهم مستويين
+
+609
+01:14:29,820 --> 01:14:36,330
+متقاطعينإذا في عندي متجه عمودي على المستوى الأول
+
+610
+01:14:36,330 --> 01:14:41,630
+وفي متجه تاني عمودي على المستوى الثاني لو ما
+
+611
+01:14:41,630 --> 01:14:46,530
+عملتلهم cross product بيطلع متجه عمودي على الاتنين
+
+612
+01:14:46,530 --> 01:14:52,010
+يعني موازي لمين؟ موازي لخط التقاطع يبقى ليه plane
+
+613
+01:14:52,010 --> 01:14:57,650
+العمودي على خط التقاطع بيكون عمودي على مين؟ على
+
+614
+01:14:57,650 --> 01:15:02,120
+تبع ال cross product اللي عندنامرة تانية بقول انا
+
+615
+01:15:02,120 --> 01:15:10,100
+عندى هذا plane و هذا plane اتخذت
+
+616
+01:15:10,100 --> 01:15:15,020
+المتجه هذا عمودي على ال plane الأولوالمتجه هذا
+
+617
+01:15:15,020 --> 01:15:19,080
+عمودي على ال plane التاني عملتله cross product
+
+618
+01:15:19,080 --> 01:15:25,860
+بيطلع متجه موازي لخط التقاطة تمام؟ بالمتجه الموازي
+
+619
+01:15:25,860 --> 01:15:30,020
+لخط التقاطة بيكون عمودي على مين؟ على ال plane
+
+620
+01:15:30,020 --> 01:15:35,520
+المطلوب وهذا حصل الكلام اللي شفته هذا على الطبيعة
+
+621
+01:15:35,520 --> 01:15:45,070
+بدنا نحسبه حساباطيب نجي الأن لل planes هذول بدي
+
+622
+01:15:45,070 --> 01:15:50,090
+أجيب العمودي على كل plane من ال planes اللي عندنا
+
+623
+01:15:50,090 --> 01:15:58,650
+هذا يبقى فاللي بقوله هي ال solution ان
+
+624
+01:15:58,650 --> 01:16:09,570
+ال vector اللي عندنا هذا معنو Normal to the first
+
+625
+01:16:09,570 --> 01:16:10,230
+plane
+
+626
+01:16:13,240 --> 01:16:19,580
+او بدنا نحط لحظة شوية هنا بدنا نكتب قداش يساوي انه
+
+627
+01:16:19,580 --> 01:16:28,340
+اللي هو بده يساوي اتنين I اتنين I زائد G ناقص K
+
+628
+01:16:28,340 --> 01:16:41,840
+زائد G ناقص K هذا normal to the first plane على
+
+629
+01:16:41,840 --> 01:16:48,300
+المستوى الأولان اتنين متجه التاني بدي اسافر اللي
+
+630
+01:16:48,300 --> 01:16:55,720
+هو I زائد اتنين G زائد K I زائد اتنين G زائد K
+
+631
+01:16:55,720 --> 01:17:03,900
+normal to the second plane في المستوى التالف
+
+632
+01:17:12,490 --> 01:17:14,070
+الجهد اللي بده يعطينا
+
+633
+01:17:51,390 --> 01:17:58,810
+مالغة ده parallel to the line of intersection of
+
+634
+01:17:58,810 --> 01:18:08,610
+the two planes يبقى هذا vector parallel to the
+
+635
+01:18:08,610 --> 01:18:15,350
+line of intersection
+
+636
+01:18:16,850 --> 01:18:26,550
+of the two planes يبقى ايش علاقته بالـ plane اللي
+
+637
+01:18:26,550 --> 01:18:36,230
+مطلوب عمودي عليه هذا parallel and hence ومن ثم
+
+638
+01:18:36,230 --> 01:18:44,210
+normal to the plane يبقى
+
+639
+01:18:44,210 --> 01:18:49,610
+صار فيه نقطة في الـ planeوفي متجه عمودي عليه بس
+
+640
+01:18:49,610 --> 01:18:57,470
+قصتنا زالة يبقى باجي بقول له تلاتة X ناقص تلاتة Y
+
+641
+01:18:57,470 --> 01:19:04,650
+زائد تلاتة Z بده يساوي تلاتة فيه إحداث النقطة قديش
+
+642
+01:19:04,650 --> 01:19:09,130
+قلي اتنين وهنا ناقص تلاتة في
+
+643
+01:19:14,600 --> 01:19:24,680
+يبقى هذا الكلام يبقى يساوي 6-3-3 ويساوي 0 يبقى 3x
+
+644
+01:19:24,680 --> 01:19:36,100
+-3y زائد 3z يساوي 0 او x-y زائد z يساوي 0 هذه
+
+645
+01:19:36,100 --> 01:19:39,740
+معادلة ال plane المطلوبة
+
+646
+01:19:43,740 --> 01:19:50,260
+طيب نعطي كمان مثال ان
+
+647
+01:19:50,260 --> 01:19:54,760
+تلاحظك كل مثال بفكرة مختلفة يعني هذا A و B و C
+
+648
+01:19:54,760 --> 01:19:59,500
+كأنه إيه السؤال لحاله منفصل عن B منفصل عن C يبقى
+
+649
+01:19:59,500 --> 01:20:01,440
+هذه أسئلة منفصلة عن بعض
+
+650
+01:20:18,540 --> 01:20:27,280
+المثال الثاني هو أن
+
+651
+01:20:27,280 --> 01:20:33,520
+تجد نقطة الانتقال تجد نقطة
+
+652
+01:20:33,520 --> 01:20:37,160
+الانتقال
+
+653
+01:20:37,160 --> 01:20:43,600
+نقطة
+
+654
+01:20:43,600 --> 01:20:45,480
+التقاطع للطريقة
+
+655
+01:20:49,280 --> 01:21:02,300
+للخط المستقيم X بده يساوي اتنين زائد تلاتة T وال Y
+
+656
+01:21:02,300 --> 01:21:12,760
+يساوي ناقص اربعة T وال Z يساوي خمسة زائد T خمسة
+
+657
+01:21:12,760 --> 01:21:16,480
+زائد T with اتنين with
+
+658
+01:21:18,360 --> 01:21:29,260
+إتنين مع المستوى اللي هو قداشة أربعة X زائد خمسة Y
+
+659
+01:21:29,260 --> 01:21:36,380
+زائد خمسة Y نقص اتنين Z يساوي تمانتاش
+
+660
+01:21:47,210 --> 01:21:53,730
+مثال ثاني قال لهذا النقطة التقاطة الخط المستقيم
+
+661
+01:21:53,730 --> 01:21:59,470
+المُعطَر في صيغة البرامج هي بمعادلات الـ 3 X سواء
+
+662
+01:21:59,470 --> 01:22:07,410
+2 زائد 3T Y سواء نقص 4T Z سواء 5 زائد T مع الـ
+
+663
+01:22:07,410 --> 01:22:10,770
+Plane يبقى أنا عند الـ Plane و فيه خط مستقيم
+
+664
+01:22:10,770 --> 01:22:16,020
+اتقاطعوا مع بعضبدي قداش احداثي النقطة التقاطعة
+
+665
+01:22:16,020 --> 01:22:20,900
+اللى موجودة عندنا تمام بقول يعني ايش يعني النقطة
+
+666
+01:22:20,900 --> 01:22:25,460
+مشتركة ما بين الخط المستقيم و ما بين ال main و ما
+
+667
+01:22:25,460 --> 01:22:29,220
+بين ال plain يبقى بدي احداثي النقطة اللى عندنا هذا
+
+668
+01:22:29,220 --> 01:22:36,060
+يبقى عند التقاطعة بتكون x و y و z هذه هي x و y و z
+
+669
+01:22:36,060 --> 01:22:46,120
+هذه صح ولا لأ يبقى باجي بقوله هناthe point of
+
+670
+01:22:46,120 --> 01:22:49,480
+intersection
+
+671
+01:22:49,480 --> 01:23:01,060
+we have نحصل علامات اربع في اتنين
+
+672
+01:23:01,060 --> 01:23:13,720
+زائد تلاتة T اللي بعدها زائد خمسةنقص اربعة T نقص
+
+673
+01:23:13,720 --> 01:23:21,540
+اتنين في زي خمسة زائد T كله بتسوي تقريبا تمانية
+
+674
+01:23:21,540 --> 01:23:28,540
+عشر لأن X هنا وهي X هنا وY هنا وهنا عند نقطة
+
+675
+01:23:28,540 --> 01:23:34,560
+التقاطع مشتركة ما بين الاتنين طب بدأ افكر تمانية
+
+676
+01:23:34,560 --> 01:23:36,460
+زائد اتناشر
+
+677
+01:23:40,210 --> 01:23:47,630
+-20T-10-2T-18
+
+678
+01:24:02,280 --> 01:24:09,100
+عشرة T وعندك هنا ضالانه سالب عشر فقط و تمانية أفضل
+
+679
+01:24:09,100 --> 01:24:13,800
+قدر سالي باتنين واتيهم على الشكة التانية بده يساوي
+
+680
+01:24:13,800 --> 01:24:21,000
+عشرين ومنها T تساوي قدر سالي باتنين فلو كانت T
+
+681
+01:24:21,000 --> 01:24:26,000
+بسالي باتنين بصير التقاطع ما بين ال line و ما بين
+
+682
+01:24:26,000 --> 01:24:32,000
+من و ما بين اللي فلانيجب ان اضع مكانها سالك اتنين
+
+683
+01:24:32,000 --> 01:24:37,660
+في معادلة الخط المستقيم بحصل على نقطة التقطة اللي
+
+684
+01:24:37,660 --> 01:24:48,840
+بروح بقوله هنا the point of intersection of X, Y,
+
+685
+01:24:49,460 --> 01:24:58,320
+Zاليك صندوق جديد بإتنين زائد تلاتة في ناقص اتنين
+
+686
+01:24:58,320 --> 01:25:07,160
+ال Y ناقص اربعة في T اللي هي ناقص اتنين وال Z خمسة
+
+687
+01:25:07,160 --> 01:25:13,880
+ناقص اتنين يبقى هذه بدها تساوي ناقص اربعة
+
+688
+01:25:16,650 --> 01:25:22,530
+وهنا تلاتة يبقى هذه النقطة تقاطع المستوى مع ال
+
+689
+01:25:22,530 --> 01:25:31,150
+plane الان نعطي كمان مثال example
+
+690
+01:25:50,760 --> 01:25:59,240
+المعادلة الفارامترية of
+
+691
+01:25:59,240 --> 01:26:10,100
+the line of intersection of
+
+692
+01:26:10,100 --> 01:26:20,960
+the planesبالمستويات الاتنين تلاتة X ناقص ستة Y
+
+693
+01:26:20,960 --> 01:26:30,620
+ناقص اتنين Z يسوى تلاتة و اتنين X زائد Y اتنين X
+
+694
+01:26:30,620 --> 01:26:35,120
+زائد Y ناقص اتنين Z يسوى مان
+
+695
+01:27:12,310 --> 01:27:16,290
+سؤال مرة تانية بيقول لي هذه المعادلات ال
+
+696
+01:27:16,290 --> 01:27:22,530
+parameterية للخط المستقيم اللي هو عبارة عن تقاطة ل
+
+697
+01:27:22,530 --> 01:27:26,630
+planes طب لما طلعنا احد الطالبات برا اتجه لضفنك
+
+698
+01:27:26,630 --> 01:27:31,810
+شوية طب كان عندنا two planes بالشكل اللي عندنا
+
+699
+01:27:31,810 --> 01:27:39,750
+اتنين و تقاطين في الحرف اللي عندنالأن بالقاطة وفي
+
+700
+01:27:39,750 --> 01:27:45,590
+الخط المستقيم نريد كمية المعادلات البرامدرية لهذا
+
+701
+01:27:45,590 --> 01:27:51,130
+قطار المستقيم لذلك أنا لن أجلب المعادلة البرامدرية
+
+702
+01:27:51,130 --> 01:27:58,770
+لهذا القطار المستقيم بل أجلب متجة يورزين تمام؟
+
+703
+01:27:58,770 --> 01:28:02,370
+ورغم ذلك نريد نقطة تقع عليه
+
+704
+01:28:17,540 --> 01:28:24,720
+و احنا رسمنا ال two vectors العمليات على الاتنين و
+
+705
+01:28:24,720 --> 01:28:29,740
+عملنا cross product بدأ المنتجة الموازن لمين؟ لخط
+
+706
+01:28:29,740 --> 01:28:35,200
+التقاطة وانا مش هنجيب معادلة خط مستقيم بلزم المنتج
+
+707
+01:28:35,200 --> 01:28:42,070
+موازن لخط التقاطةموجه هذا في الأول و بعد هيك ندور
+
+708
+01:28:42,070 --> 01:28:48,310
+على النقطة تقع على هذا الخط بالضبط تماما بقول كويس
+
+709
+01:28:48,310 --> 01:28:53,910
+هدول محتجهات اثنين بقدر اجيب العمودي على الأول و
+
+710
+01:28:53,910 --> 01:28:58,490
+العمودي على التاني و اعمل لهم cross product بطلع
+
+711
+01:28:58,490 --> 01:29:03,570
+الموازي لخط التقاطة، مظبوط؟ يبقى بالداخل اقول له
+
+712
+01:29:03,570 --> 01:29:11,040
+in one اللي هو بده يساويثلاثة I نقصي تجي نقصي
+
+713
+01:29:11,040 --> 01:29:25,420
+اتنين كي normal to the first plane الان
+
+714
+01:29:25,420 --> 01:29:34,090
+المفترض الاول into اللي هو عبارة عن اتنين Iزائد G
+
+715
+01:29:34,090 --> 01:29:46,010
+نقص اتنين K Normal to the second إبليك بدي أجيب N1
+
+716
+01:29:54,970 --> 01:30:02,670
+يبقى مراكبات المتجه الاول تلاتة مقص ستة مقص اتنين
+
+717
+01:30:02,670 --> 01:30:10,410
+اتنين واحد مقص اتنين اتناشر
+
+718
+01:30:10,410 --> 01:30:14,450
+زائد اتنين يبقى اربعتاشر R
+
+719
+01:30:18,680 --> 01:30:26,840
+ستة وزائد أربعة ويظل ناقص اتنين مع ناقص يظل زائد
+
+720
+01:30:26,840 --> 01:30:36,820
+اتنين J اللي بعده تلاتة زائد اتناش ويساوي خمستاشر
+
+721
+01:30:36,820 --> 01:30:41,280
+K طيب
+
+722
+01:30:41,280 --> 01:30:46,140
+يبقى in one in two هذا parallel to the line of
+
+723
+01:30:46,140 --> 01:30:55,480
+intersectionتبقى باجي بقوله هنا ذا vector N1 cross
+
+724
+01:30:55,480 --> 01:31:15,040
+N2 parallel to the line of intersection of
+
+725
+01:31:15,040 --> 01:31:16,400
+the
+
+726
+01:31:21,290 --> 01:31:28,730
+طيب، إيش مضالبتنا؟ نقطة تقع على خط التقاطة، يالا،
+
+727
+01:31:28,730 --> 01:31:36,610
+من أين سنتي بهذه النقطة؟ نقطة مشتركة بين الـ two
+
+728
+01:31:36,610 --> 01:31:42,510
+planes، تقع على خط التقاطة، تقع في الـplane الأول
+
+729
+01:31:42,510 --> 01:31:42,790
+وفي
+
+730
+01:32:13,350 --> 01:32:20,100
+أو بأي رقم آخرمعادلتين في X و Y بحيث هما مع بعض
+
+731
+01:32:20,100 --> 01:32:24,420
+بجيب نفس الفكرة اللي طرحتيها ولو انهم خربحوا شوية
+
+732
+01:32:24,420 --> 01:32:28,300
+عادلين بكرة بس تطرح عملية كويسة تطرح الفكرة تمام
+
+733
+01:32:28,300 --> 01:32:35,160
+اذا بنروح اخد Z بزيرو او X بزيرو او Y بزيرو اي
+
+734
+01:32:35,160 --> 01:32:39,300
+واحدة منهم باخد واحدة بس بضل متغيرين في معادلتين
+
+735
+01:32:39,300 --> 01:32:44,660
+بحيث هما مع بعض بس سنتين مع بعضتلات معادلات ورا
+
+736
+01:32:44,660 --> 01:32:49,900
+معادلتين وماكنتش بتطلعوا برا المعادلتين تنحلش
+
+737
+01:32:49,900 --> 01:32:55,460
+موجود للجهات بروح بحط قيمة معندي لأحد المتغيرات
+
+738
+01:32:55,460 --> 01:33:03,580
+والتكن زد على سبيل المثال باجي بقول هنا what قطيل
+
+739
+01:33:03,580 --> 01:33:09,690
+الزد تساوي زيلةليس القرآن اللي نزل من السماء لازم
+
+740
+01:33:09,690 --> 01:33:13,590
+زت بزيرو ممكن تاخد زت بواحد باتنين بسلب تلاتة زي
+
+741
+01:33:13,590 --> 01:33:19,490
+ما بدك يبقى لما زت تساوي زيرو قد زت تساوي زيرو
+
+742
+01:33:19,490 --> 01:33:24,830
+ويجد نقص العالم تعالى على ال plan الأول بدأ أحط زت
+
+743
+01:33:24,830 --> 01:33:27,730
+بزيرو كيف تصير تلاتة اكس نقص
+
+744
+01:33:31,360 --> 01:33:38,940
+نقص ستة Y يسوى تلاتة المعادلة التانية اتنين X زائد
+
+745
+01:33:38,940 --> 01:33:47,520
+Y اتنين X زائد Y يسوى اتنين الان بدي احل المعادلات
+
+746
+01:33:47,520 --> 01:33:53,160
+مع بعض المعادلة الأولى بدي ادخلها زي ما هي نقص ستة
+
+747
+01:33:53,160 --> 01:33:54,600
+Y يسوى تلاتة
+
+748
+01:34:02,370 --> 01:34:07,390
+يساوي اتناش اجمعين بروح هدول مع بعض بيصير ايش
+
+749
+01:34:07,390 --> 01:34:14,230
+خمستاشر X يساوي خمستاشر يبقى ال X تساوي كده؟ واحد
+
+750
+01:34:14,230 --> 01:34:24,530
+لما ال X تساوي واحد يبقى Y كده؟ Zero يبقى هذا
+
+751
+01:34:24,530 --> 01:34:30,150
+يعطيك ان Y تساوي Zero يبقى الاسفار
+
+752
+01:34:38,990 --> 01:34:45,050
+زت بزيرو و Y بزيرو و يكسب واحد أين تقع هذه النقطة
+
+753
+01:34:45,050 --> 01:34:52,330
+on the line of intersection of the two planes يبقى
+
+754
+01:34:52,330 --> 01:35:04,830
+هذه الـ Y on the line of intersection
+
+755
+01:35:06,740 --> 01:35:16,300
+of the given planes هذا جيد الآن صارت النقطة
+
+756
+01:35:16,300 --> 01:35:23,960
+موجودة والمتجه الموازي اللي هو موجود إذا بقدر أجيب
+
+757
+01:35:23,960 --> 01:35:27,420
+المعادلة ال parameterية لأنه قال لي في المثلة find
+
+758
+01:35:27,420 --> 01:35:32,620
+parametric equations إذا بناء عليه بقول له the
+
+759
+01:35:32,620 --> 01:35:36,240
+parametric
+
+760
+01:35:39,050 --> 01:35:53,990
+of the line of intersection of the given planes
+
+761
+01:36:07,560 --> 01:36:16,720
+يبقى زائد اربعتاشر T وY يساوي Y not بزيرو يبقى
+
+762
+01:36:16,720 --> 01:36:23,920
+طالع ان انا ما قلتش اتنين T يبقى اتنين T وZ بزيرو
+
+763
+01:36:23,920 --> 01:36:31,180
+وخمستاشر T في قيود على T يبقى T اكبر من سالة
+
+764
+01:36:31,180 --> 01:36:31,740
+Infinity
+
+765
+01:36:37,610 --> 01:36:43,850
+لحد هنا انتهت الأمثلة على هذا النقطة اللي هي
+
+766
+01:36:43,850 --> 01:36:47,790
+النقطة الرقم تلاتة من هذا ال section نفس الله لها
+
+767
+01:36:47,790 --> 01:36:52,930
+النقطة الرقم أربعة والنقطة رقم خامسة طبعا مش حاضر
+
+768
+01:36:52,930 --> 01:36:57,830
+حاجة اليوم الله يعطيك العافية ونكمل المرة القادمة
+
+769
+01:36:57,830 --> 01:37:00,110
+إن شاء الله تعالى
+
+770
+01:37:04,270 --> 01:37:05,370
+الحاجب السليسي والعالمي
+
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/aAjYJyHQ2EE_raw.json b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/aAjYJyHQ2EE_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..77c281d59ca4840f16cd94880433c1ad1d4180d0
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/aAjYJyHQ2EE_raw.json
@@ -0,0 +1 @@
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659.99, "text": "هل هناك متجه يوازي المستقيم الأول من خلال المعادلة هذه؟", "tokens": [3224, 1211, 34105, 4117, 44650, 7435, 3224, 7251, 2407, 31377, 1829, 9673, 14851, 4587, 32640, 16247, 12610, 9154, 16490, 1211, 6027, 9673, 3615, 18513, 37977, 29538, 22807], "avg_logprob": -0.11872209794819355, "compression_ratio": 1.188235294117647, "no_speech_prob": 0.0, "words": [{"start": 649.65, "end": 650.17, "word": "هل", "probability": 0.954833984375}, {"start": 650.17, "end": 650.97, "word": " هناك", "probability": 0.953857421875}, {"start": 650.97, "end": 652.19, "word": " متجه", "probability": 0.9482421875}, {"start": 652.19, "end": 652.79, "word": " يوازي", "probability": 0.94677734375}, {"start": 652.79, "end": 653.45, "word": " المستقيم", "probability": 0.9593505859375}, {"start": 653.45, "end": 653.95, "word": " الأول", "probability": 0.97900390625}, {"start": 653.95, "end": 656.37, "word": " من", "probability": 0.1866455078125}, {"start": 656.37, "end": 658.77, "word": " خلال", 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متوازين بيظل احتمال التقاطع أو التخالف وبنبحث القصة هذه ونشوف يبقى باجي بقول هنا ال one solution ال one parallel to the vector", "tokens": [2304, 3615, 8315, 47395, 9673, 14851, 4587, 32640, 9957, 44650, 2407, 31377, 9957, 20328, 5016, 49429, 20193, 23032, 1829, 3555, 11933, 15730, 25961, 14407, 8032, 3215, 12610, 3714, 16095, 33599, 44650, 2407, 31377, 9957, 7251, 3555, 4587, 7578, 9673, 14851, 4587, 32640, 9957, 32771, 13546, 44650, 2407, 31377, 9957, 4724, 1829, 19913, 1211, 1975, 33753, 2304, 6027, 16712, 4587, 41193, 3615, 34051, 16712, 9778, 6027, 5172, 46599, 1863, 49628, 12984, 25062, 9381, 3660, 29538, 4032, 1863, 8592, 38688, 7251, 3555, 4587, 7578, 4724, 26108, 1829, 4724, 39648, 34105, 2423, 472, 3827, 2423, 472, 8952, 281, 264, 8062], "avg_logprob": -0.16788902863556024, "compression_ratio": 1.7142857142857142, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 685.98, "end": 686.68, "word": "معناته", "probability": 0.82745361328125}, {"start": 686.68, "end": 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هدول are not parallel وبالتالي ال two lines are not parallel يبقى هنا L1 is not parallel to L2 because السبب ان V1 is", "tokens": [3224, 1211, 36764, 24401, 9154, 2423, 9307, 1863, 9957, 8032, 3215, 12610, 3714, 11242, 45761, 5172, 9307, 6024, 95, 34740, 22807, 37893, 3714, 43020, 7251, 3555, 4587, 7578, 9673, 3615, 1863, 7578, 6055, 39648, 1975, 2655, 1863, 9957, 8032, 3215, 12610, 366, 406, 8952, 46599, 6027, 2655, 6027, 1829, 2423, 732, 3876, 366, 406, 8952, 7251, 3555, 4587, 7578, 34105, 441, 16, 307, 406, 8952, 281, 441, 17, 570, 21136, 3555, 3555, 16472, 691, 16, 307], "avg_logprob": -0.23599837352703143, "compression_ratio": 1.5722543352601157, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 745.33, "end": 745.83, "word": "هل", "probability": 0.8935546875}, {"start": 745.83, "end": 746.41, "word": " واحد", "probability": 0.943359375}, {"start": 746.41, "end": 746.69, "word": " من", "probability": 0.9892578125}, {"start": 746.69, "end": 747.13, "word": " الاتنين", 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line", "probability": 0.76806640625}, {"start": 2163.21, "end": 2163.89, "word": " زي", "probability": 0.8125}, {"start": 2163.89, "end": 2163.99, "word": " ما", "probability": 0.927734375}, {"start": 2163.99, "end": 2164.13, "word": " احنا", "probability": 0.8653971354166666}, {"start": 2164.13, "end": 2164.69, "word": " شايفين", "probability": 0.9276123046875}, {"start": 2164.69, "end": 2165.51, "word": " بده", "probability": 0.4847412109375}, {"start": 2165.51, "end": 2166.11, "word": " نقطة", "probability": 0.9754231770833334}], "temperature": 1.0}, {"id": 82, "seek": 218907, "start": 2167.09, "end": 2189.07, "text": "موجودة و الحمد لله موجودة بدي vector موازي ال line اللي مطلوب يجيب المسافة بينه وبين النقطة ال vector بجيبه من وين؟ من نفس المعادلة اللي عندنا يبقى باجي بقول بدي أجيب ال vector الموازي لمين لهذا ال line يبقى V تساوي", "tokens": [2304, 29245, 23328, 3660, 4032, 21542, 2304, 3215, 24976, 3224, 3714, 29245, 23328, 3660, 4724, 16254, 8062, 3714, 2407, 31377, 1829, 2423, 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"text": "يبقى هذا given to the given line يبقى صار المتجه الموازي موجود والنقطة موجودة تمام طيب بدي المتجه P S معناته بدي النقطة P أنا عند هنا ال S يبقى ناقطي النقطة المواطعة اللي هي المواطعة فوق يبقى ال S هي النقطة السالف واحدة واربعة وتلاتة طيب و P", "tokens": [1829, 3555, 4587, 7578, 23758, 2212, 281, 264, 2212, 1622, 7251, 3555, 4587, 7578, 20328, 9640, 9673, 2655, 7435, 3224, 9673, 2407, 31377, 1829, 3714, 29245, 23328, 16070, 1863, 47432, 3660, 3714, 29245, 23328, 3660, 46811, 10943, 23032, 1829, 3555, 4724, 16254, 9673, 2655, 7435, 3224, 430, 318, 20449, 8315, 47395, 4724, 16254, 28239, 47432, 3660, 430, 41850, 43242, 34105, 2423, 318, 7251, 3555, 4587, 7578, 8717, 995, 4587, 9566, 1829, 28239, 47432, 3660, 9673, 2407, 41193, 27884, 13672, 1829, 39896, 9673, 2407, 41193, 27884, 6156, 30543, 7251, 3555, 4587, 7578, 2423, 318, 39896, 28239, 47432, 3660, 21136, 6027, 5172, 36764, 24401, 3660, 4032, 9640, 3555, 27884, 4032, 2655, 1211, 9307, 3660, 23032, 1829, 3555, 4032, 430], 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"text": "زائد سبعة جيب زائد تلاتة كيب زائد تلاتة كيب", "tokens": [11622, 16373, 3215, 8608, 3555, 27884, 10874, 1829, 3555, 30767, 16373, 3215, 6055, 1211, 9307, 3660, 9122, 1829, 3555, 30767, 16373, 3215, 6055, 1211, 9307, 3660, 9122, 1829, 3555], "avg_logprob": -0.47213542461395264, "compression_ratio": 1.5294117647058822, "no_speech_prob": 7.748603820800781e-07, "words": [{"start": 2287.77, "end": 2288.83, "word": "زائد", "probability": 0.4560750325520833}, {"start": 2288.83, "end": 2289.79, "word": " سبعة", "probability": 0.84130859375}, {"start": 2289.79, "end": 2290.33, "word": " جيب", "probability": 0.592529296875}, {"start": 2290.33, "end": 2291.43, "word": " زائد", "probability": 0.93701171875}, {"start": 2291.43, "end": 2292.29, "word": " تلاتة", "probability": 0.9422607421875}, {"start": 2292.29, "end": 2293.31, "word": " كيب", "probability": 0.5799153645833334}, {"start": 2293.31, "end": 2300.39, "word": " زائد", "probability": 0.6678263346354166}, {"start": 2300.39, "end": 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0.2261962890625}, {"start": 2480.62, "end": 2481.26, "word": " تسعة", "probability": 0.9794921875}, {"start": 2481.26, "end": 2482.06, "word": " واربعين", "probability": 0.951171875}, {"start": 2482.06, "end": 2482.32, "word": " في", "probability": 0.990234375}, {"start": 2482.32, "end": 2483.06, "word": " ستة", "probability": 0.9947916666666666}, {"start": 2483.06, "end": 2483.68, "word": " ستة", "probability": 0.9114583333333334}, {"start": 2483.68, "end": 2483.8, "word": " في", "probability": 0.96142578125}, {"start": 2483.8, "end": 2484.24, "word": " تسعة", "probability": 0.9894205729166666}, {"start": 2484.24, "end": 2484.88, "word": " واربعة", "probability": 0.7926025390625}, {"start": 2484.88, "end": 2485.76, "word": " وخمسين", "probability": 0.99013671875}, {"start": 2485.76, "end": 2486.68, "word": " ستة", "probability": 0.9352213541666666}, {"start": 2486.68, "end": 2486.82, "word": " في", "probability": 0.9912109375}, {"start": 2486.82, "end": 2487.26, "word": " أربعة", "probability": 0.7698567708333334}, {"start": 2487.26, "end": 2488.06, "word": " واربعة", "probability": 0.8489990234375}, {"start": 2488.06, "end": 2489.08, "word": " وعشرين", "probability": 0.94970703125}, {"start": 2489.08, "end": 2490.32, "word": " وخمسة", "probability": 0.99111328125}, {"start": 2490.32, "end": 2490.92, "word": " وتسعة", "probability": 0.82666015625}, {"start": 2490.92, "end": 2491.62, "word": " وعشرين", "probability": 0.970458984375}, {"start": 2491.62, "end": 2492.12, "word": " يبقى", "probability": 0.74896240234375}, {"start": 2492.12, "end": 2492.74, "word": " اتنين", "probability": 0.680389404296875}, {"start": 2492.74, "end": 2493.24, "word": " اربعة", "probability": 0.8597005208333334}, {"start": 2493.24, "end": 2494.1, "word": " وتسعين", "probability": 0.9267578125}, {"start": 2494.1, "end": 2495.06, "word": " على", "probability": 0.87841796875}, {"start": 2495.06, "end": 2496.16, "word": " جذر", "probability": 0.8759765625}, {"start": 2496.16, "end": 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2508.82, "word": "طيب", "probability": 0.6952311197916666}, {"start": 2508.82, "end": 2510.06, "word": " 28", "probability": 0.376220703125}, {"start": 2510.06, "end": 2511.16, "word": " هذه", "probability": 0.389892578125}, {"start": 2511.16, "end": 2511.34, "word": " اللي", "probability": 0.8603515625}, {"start": 2511.34, "end": 2512.14, "word": " ربعناها", "probability": 0.78701171875}, {"start": 2512.14, "end": 2512.26, "word": " و", "probability": 0.58935546875}, {"start": 2512.26, "end": 2512.5, "word": " هذه", "probability": 0.81005859375}, {"start": 2512.5, "end": 2512.64, "word": " اللي", "probability": 0.986083984375}, {"start": 2512.64, "end": 2513.26, "word": " ربعناها", "probability": 0.980078125}, {"start": 2513.26, "end": 2514.06, "word": " مظبوط", "probability": 0.84384765625}, {"start": 2514.06, "end": 2514.68, "word": " يبقى", "probability": 0.913818359375}, {"start": 2514.68, "end": 2515.04, "word": " هذا", "probability": 0.74169921875}, {"start": 2515.04, "end": 2515.58, "word": " الطول", "probability": 0.6573486328125}, {"start": 2515.58, "end": 2516.48, "word": " بده", "probability": 0.500244140625}, {"start": 2516.48, "end": 2517.02, "word": " يساوي", "probability": 0.81427001953125}, {"start": 2517.02, "end": 2517.9, "word": " تحت", "probability": 0.989501953125}, {"start": 2517.9, "end": 2518.64, "word": " الجدر", "probability": 0.9694010416666666}, {"start": 2518.64, "end": 2519.54, "word": " يبقى", "probability": 0.9488525390625}, {"start": 2519.54, "end": 2519.86, "word": " هذا", "probability": 0.91748046875}, {"start": 2519.86, "end": 2520.42, "word": " الجدر", "probability": 0.9850260416666666}, {"start": 2520.42, "end": 2521.66, "word": " التربيعي", "probability": 0.89287109375}, {"start": 2521.66, "end": 2522.32, "word": " تيجي", "probability": 0.847900390625}, {"start": 2522.32, "end": 2522.58, "word": " لأ", "probability": 0.6708984375}, {"start": 2522.58, "end": 2522.88, "word": " تيجي", "probability": 0.908447265625}, {"start": 2522.88, "end": 2523.22, "word": " سبعة", "probability": 0.8567708333333334}, {"start": 2523.22, "end": 2523.52, "word": " جدر", "probability": 0.9820963541666666}, {"start": 2523.52, "end": 2523.92, "word": " ستة", "probability": 0.9339192708333334}, {"start": 2523.92, "end": 2524.66, "word": " صحيح", "probability": 0.9801025390625}, {"start": 2524.66, "end": 2525.54, "word": " سبعة", "probability": 0.92333984375}], "temperature": 1.0}, {"id": 97, "seek": 255067, "start": 2529.66, "end": 2550.68, "text": "على جدر اتنين وجدر ستة اللي هو جدر اتنين في جدر تلاتة مظلوم يبقى هنا سبعة جدر اتنين جدر تلاتة على جدر اتنين يبقى السابعة جدر تلاتة هذا الطول الا ان الله يعطي كمان مثال", "tokens": [3615, 23942, 10874, 3215, 2288, 1975, 2655, 1863, 9957, 49610, 3215, 2288, 8608, 2655, 3660, 13672, 1829, 31439, 10874, 3215, 2288, 1975, 2655, 1863, 9957, 8978, 10874, 3215, 2288, 6055, 1211, 9307, 3660, 3714, 19913, 1211, 20498, 7251, 3555, 4587, 7578, 34105, 8608, 3555, 27884, 10874, 3215, 2288, 1975, 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"probability": 0.9305013020833334}, {"start": 2540.36, "end": 2540.92, "word": " تلاتة", "probability": 0.975341796875}, {"start": 2540.92, "end": 2541.14, "word": " على", "probability": 0.78662109375}, {"start": 2541.14, "end": 2541.58, "word": " جدر", "probability": 0.9934895833333334}, {"start": 2541.58, "end": 2542.1, "word": " اتنين", "probability": 0.99072265625}, {"start": 2542.1, "end": 2542.84, "word": " يبقى", "probability": 0.981201171875}, {"start": 2542.84, "end": 2543.58, "word": " السابعة", "probability": 0.83935546875}, {"start": 2543.58, "end": 2544.42, "word": " جدر", "probability": 0.9840494791666666}, {"start": 2544.42, "end": 2545.24, "word": " تلاتة", "probability": 0.9881591796875}, {"start": 2545.24, "end": 2545.74, "word": " هذا", "probability": 0.888671875}, {"start": 2545.74, "end": 2546.32, "word": " الطول", "probability": 0.973876953125}, {"start": 2546.32, "end": 2546.68, "word": " الا", "probability": 0.262939453125}, {"start": 2546.68, "end": 2546.92, 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"end": 2593.88, "word": " الخطوط", "probability": 0.640283203125}, {"start": 2593.88, "end": 2595.28, "word": " المستقيمة", "probability": 0.9783203125}, {"start": 2595.28, "end": 2596.08, "word": " ال", "probability": 0.89990234375}, {"start": 2596.08, "end": 2596.64, "word": " one", "probability": 0.78125}, {"start": 2596.64, "end": 2597.12, "word": " اللي", "probability": 0.895751953125}, {"start": 2597.12, "end": 2597.3, "word": " هو", "probability": 0.876953125}, {"start": 2597.3, "end": 2597.66, "word": " main", "probability": 0.157470703125}, {"start": 2597.66, "end": 2598.7, "word": " اللي", "probability": 0.73876953125}, {"start": 2598.7, "end": 2598.9, "word": " هو", "probability": 0.93212890625}, {"start": 2598.9, "end": 2599.36, "word": " X", "probability": 0.25927734375}, {"start": 2599.36, "end": 2599.88, "word": " يساوي", "probability": 0.74957275390625}, {"start": 2599.88, "end": 2600.32, "word": " اتنين", "probability": 0.946044921875}, {"start": 2600.32, "end": 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"seek": 264127, "start": 2616.15, "end": 2641.27, "text": "1-t L2 X يساوي 1 زائد 2T Y يساوي 3-4T Z يساوي 5-2T R تلالي", "tokens": [16, 12, 83, 441, 17, 1783, 7251, 3794, 995, 45865, 502, 30767, 16373, 3215, 568, 51, 398, 7251, 3794, 995, 45865, 805, 12, 19, 51, 1176, 7251, 3794, 995, 45865, 1025, 12, 17, 51, 497, 6055, 1211, 6027, 1829], "avg_logprob": -0.32539062649011613, "compression_ratio": 1.1714285714285715, "no_speech_prob": 7.748603820800781e-07, "words": [{"start": 2616.15, "end": 2616.81, "word": "1", "probability": 0.1304931640625}, {"start": 2616.81, "end": 2618.03, "word": "-t", "probability": 0.5487060546875}, {"start": 2618.03, "end": 2620.11, "word": " L2", "probability": 0.63232421875}, {"start": 2620.11, "end": 2621.73, "word": " X", "probability": 0.3369140625}, {"start": 2621.73, "end": 2622.87, "word": " يساوي", "probability": 0.71435546875}, {"start": 2622.87, "end": 2624.15, "word": " 1", "probability": 0.7451171875}, {"start": 2624.15, "end": 2624.81, "word": " 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"start": 2645.95, "end": 2661.89, "text": "and find the distance between them and find the distance between them", "tokens": [474, 915, 264, 4560, 1296, 552, 293, 915, 264, 4560, 1296, 552], "avg_logprob": -0.35637020147763765, "compression_ratio": 1.6428571428571428, "no_speech_prob": 0.0, "words": [{"start": 2645.95, "end": 2646.93, "word": "and", "probability": 0.08819580078125}, {"start": 2646.93, "end": 2647.29, "word": " find", "probability": 0.92822265625}, {"start": 2647.29, "end": 2647.49, "word": " the", "probability": 0.87646484375}, {"start": 2647.49, "end": 2647.89, "word": " distance", "probability": 0.93994140625}, {"start": 2647.89, "end": 2648.31, "word": " between", "probability": 0.93212890625}, {"start": 2648.31, "end": 2648.89, "word": " them", "probability": 0.93603515625}, {"start": 2648.89, "end": 2650.47, "word": " and", "probability": 0.73388671875}, {"start": 2650.47, "end": 2652.03, "word": " find", "probability": 0.86181640625}, {"start": 2652.03, "end": 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L1", "probability": 0.90576171875}, {"start": 2808.75, "end": 2809.01, "word": " هو", "probability": 0.97509765625}, {"start": 2809.01, "end": 2809.81, "word": " المستقيم", "probability": 0.970947265625}, {"start": 2809.81, "end": 2810.47, "word": " الأول", "probability": 0.95849609375}, {"start": 2810.47, "end": 2811.87, "word": " مظبوط", "probability": 0.728759765625}, {"start": 2811.87, "end": 2812.43, "word": " بدا", "probability": 0.376953125}, {"start": 2812.43, "end": 2812.91, "word": " افترض", "probability": 0.9453125}, {"start": 2812.91, "end": 2813.93, "word": " انه", "probability": 0.87841796875}, {"start": 2813.93, "end": 2814.67, "word": " بيمر", "probability": 0.7861328125}, {"start": 2814.67, "end": 2815.77, "word": " بنقطة", "probability": 0.79583740234375}, {"start": 2815.77, "end": 2816.33, "word": " ما", "probability": 0.82470703125}, {"start": 2816.33, "end": 2817.03, "word": " مين", "probability": 0.6580810546875}, {"start": 2817.03, "end": 2817.53, "word": " 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"probability": 0.9320068359375}, {"start": 2844.55, "end": 2845.29, "word": " يبقى", "probability": 0.9295654296875}, {"start": 2845.29, "end": 2845.91, "word": " واحد", "probability": 0.973388671875}, {"start": 2845.91, "end": 2846.45, "word": " و", "probability": 0.9072265625}, {"start": 2846.45, "end": 2847.33, "word": " تلاتة", "probability": 0.962890625}, {"start": 2847.33, "end": 2847.65, "word": " و", "probability": 0.99755859375}, {"start": 2847.65, "end": 2848.65, "word": " خمسة", "probability": 0.934814453125}, {"start": 2848.65, "end": 2849.99, "word": " جالي", "probability": 0.6788736979166666}, {"start": 2849.99, "end": 2850.43, "word": " هاجل", "probability": 0.5634765625}, {"start": 2850.43, "end": 2851.17, "word": " المسافة", "probability": 0.971923828125}, {"start": 2851.17, "end": 2851.37, "word": " ما", "probability": 0.544921875}, {"start": 2851.37, "end": 2851.55, "word": " بين", "probability": 0.984375}, {"start": 2851.55, "end": 2852.21, "word": " الخطين", 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اللي عندنا هذا تمام يبقى هذا المتجه اللي هو V2 اللي عندنا", "tokens": [3224, 2407, 8717, 36178, 9673, 3794, 31845, 3660, 11933, 15730, 41850, 20328, 9640, 43242, 7578, 44650, 7435, 3224, 24525, 2304, 3224, 2086, 7251, 3555, 4587, 7578, 3714, 33599, 1829, 8717, 33599, 1829, 20666, 4560, 8032, 8848, 1829, 4724, 16254, 9673, 2407, 31377, 1829, 5296, 441, 17, 9154, 9673, 2407, 31377, 1829, 5296, 441, 17, 13672, 1829, 31439, 691, 17, 13672, 1829, 43242, 8315, 23758, 46811, 10943, 7251, 3555, 4587, 7578, 23758, 9673, 2655, 7435, 3224, 13672, 1829, 31439, 691, 17, 13672, 1829, 43242, 8315], "avg_logprob": -0.31838234592886533, "compression_ratio": 1.8132530120481927, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 2863.72, "end": 2864.68, "word": "هو", "probability": 0.304901123046875}, {"start": 2864.68, "end": 2865.64, "word": " نفس", "probability": 0.53924560546875}, {"start": 2865.64, "end": 2866.7, "word": " المسافة", "probability": 0.9600830078125}, {"start": 2866.7, 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"word": " اللي", "probability": 0.916015625}, {"start": 2883.44, "end": 2883.84, "word": " عندنا", "probability": 0.94482421875}, {"start": 2883.84, "end": 2884.22, "word": " هذا", "probability": 0.8994140625}, {"start": 2884.22, "end": 2885.0, "word": " تمام", "probability": 0.66552734375}, {"start": 2885.0, "end": 2885.96, "word": " يبقى", "probability": 0.9437255859375}, {"start": 2885.96, "end": 2886.28, "word": " هذا", "probability": 0.85009765625}, {"start": 2886.28, "end": 2887.24, "word": " المتجه", "probability": 0.976806640625}, {"start": 2887.24, "end": 2888.04, "word": " اللي", "probability": 0.93017578125}, {"start": 2888.04, "end": 2888.52, "word": " هو", "probability": 0.9765625}, {"start": 2888.52, "end": 2890.1, "word": " V2", "probability": 0.970703125}, {"start": 2890.1, "end": 2890.48, "word": " اللي", "probability": 0.92529296875}, {"start": 2890.48, "end": 2890.86, "word": " عندنا", "probability": 0.9658203125}], "temperature": 1.0}, {"id": 108, "seek": 291176, "start": 2891.6, "end": 2911.76, "text": "خلصنا يبقى V موجود ضايق بس أجيب له PS و بالتالي مشكلتنا خلصت يبقى بتاجي لمين؟ لـPS الشكل اللي عندنا هذا يبقى 2-1 في اتجاه I زائد نقص 2", "tokens": [9778, 1211, 9381, 8315, 7251, 3555, 4587, 7578, 691, 3714, 29245, 23328, 48812, 47302, 4587, 4724, 3794, 5551, 7435, 1829, 3555, 46740, 8168, 4032, 20666, 2655, 6027, 1829, 37893, 28820, 2655, 8315, 16490, 1211, 9381, 2655, 7251, 3555, 4587, 7578, 39894, 26108, 1829, 32767, 9957, 22807, 5296, 39184, 6273, 25124, 28820, 13672, 1829, 43242, 8315, 23758, 7251, 3555, 4587, 7578, 568, 12, 16, 8978, 1975, 2655, 7435, 40294, 286, 30767, 16373, 3215, 8717, 4587, 9381, 568], "avg_logprob": -0.4293831261721524, "compression_ratio": 1.4838709677419355, "no_speech_prob": 1.1742115020751953e-05, "words": [{"start": 2891.6, "end": 2892.4, "word": "خلصنا", "probability": 0.5239410400390625}, {"start": 2892.4, "end": 2892.98, "word": " يبقى", "probability": 0.84710693359375}, {"start": 2892.98, "end": 2893.16, 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"word": " the", "probability": 0.92626953125}, {"start": 3714.19, "end": 3714.89, "word": " line", "probability": 0.95361328125}, {"start": 3714.89, "end": 3718.45, "word": " الخط", "probability": 0.95751953125}, {"start": 3718.45, "end": 3719.63, "word": " المستقيم", "probability": 0.9483642578125}, {"start": 3719.63, "end": 3721.39, "word": " X", "probability": 0.24658203125}, {"start": 3721.39, "end": 3722.49, "word": " يساوي", "probability": 0.65863037109375}, {"start": 3722.49, "end": 3723.47, "word": " خمسة", "probability": 0.9334716796875}, {"start": 3723.47, "end": 3724.33, "word": " زائد", "probability": 0.742919921875}, {"start": 3724.33, "end": 3724.79, "word": " T", "probability": 0.888671875}, {"start": 3724.79, "end": 3725.69, "word": " وال", "probability": 0.374755859375}, {"start": 3725.69, "end": 3726.19, "word": " Y", "probability": 0.58056640625}, {"start": 3726.19, "end": 3727.23, "word": " يساوي", "probability": 0.9803466796875}, {"start": 3727.23, "end": 3727.91, "word": " واحد", "probability": 0.982666015625}, {"start": 3727.91, "end": 3728.91, "word": " زائد", "probability": 0.962890625}, {"start": 3728.91, "end": 3729.71, "word": " تلاتة", "probability": 0.9443359375}, {"start": 3729.71, "end": 3730.07, "word": " T", "probability": 0.87841796875}, {"start": 3730.07, "end": 3730.85, "word": " وال", "probability": 0.8427734375}, {"start": 3730.85, "end": 3731.13, "word": " Z", "probability": 0.64453125}, {"start": 3731.13, "end": 3732.09, "word": " يساوي", "probability": 0.9874267578125}], "temperature": 1.0}, {"id": 140, "seek": 375661, "start": 3740.57, "end": 3756.61, "text": "هذه معادلة المستوى اللي يحقق نمر أيه ال plane يمر بالنقطة هذه وفي نفس لقطة عمودي على هذا الخط أنا مش هنجيب معادلة ال plane بدي نقطة يمر بها", "tokens": [3224, 24192, 20449, 18513, 37977, 9673, 14851, 2407, 7578, 13672, 1829, 7251, 5016, 4587, 4587, 8717, 29973, 36632, 3224, 2423, 5720, 7251, 29973, 20666, 1863, 47432, 3660, 29538, 4032, 41185, 8717, 36178, 5296, 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"probability": 0.21435546875}, {"start": 3746.99, "end": 3747.37, "word": " plane", "probability": 0.330078125}, {"start": 3747.37, "end": 3747.87, "word": " يمر", "probability": 0.959716796875}, {"start": 3747.87, "end": 3748.63, "word": " بالنقطة", "probability": 0.9554443359375}, {"start": 3748.63, "end": 3749.03, "word": " هذه", "probability": 0.791015625}, {"start": 3749.03, "end": 3749.63, "word": " وفي", "probability": 0.830078125}, {"start": 3749.63, "end": 3749.95, "word": " نفس", "probability": 0.995849609375}, {"start": 3749.95, "end": 3750.37, "word": " لقطة", "probability": 0.658935546875}, {"start": 3750.37, "end": 3751.05, "word": " عمودي", "probability": 0.9801025390625}, {"start": 3751.05, "end": 3751.33, "word": " على", "probability": 0.88232421875}, {"start": 3751.33, "end": 3751.77, "word": " هذا", "probability": 0.73876953125}, {"start": 3751.77, "end": 3752.39, "word": " الخط", "probability": 0.95849609375}, {"start": 3752.39, "end": 3753.59, "word": " أنا", 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اللي هو مين؟ تمام يبقى باجي بقوله هنا solution the vector اللي هو", "tokens": [20498, 9957, 22807, 44650, 7435, 3224, 6225, 2304, 2407, 16254, 15844, 23758, 2423, 28820, 26895, 31439, 5551, 7435, 46152, 46740, 15730, 2423, 28820, 26895, 6225, 2304, 2407, 16254, 15844, 33962, 9566, 9673, 14851, 4587, 32640, 8032, 1211, 41850, 4724, 28543, 2288, 5551, 7435, 1829, 3555, 44650, 7435, 3224, 7251, 2407, 31377, 1829, 23758, 33962, 9566, 9673, 14851, 4587, 32640, 22807, 13672, 1829, 31439, 3714, 9957, 22807, 46811, 10943, 7251, 3555, 4587, 7578, 4724, 26108, 1829, 4724, 39648, 3224, 34105, 3827, 264, 8062, 13672, 1829, 31439], "avg_logprob": -0.17996002248553342, "compression_ratio": 1.8100558659217878, "no_speech_prob": 4.172325134277344e-07, "words": [{"start": 3757.82, "end": 3758.64, "word": "ومين؟", "probability": 0.4850260416666667}, {"start": 3758.64, "end": 3759.54, "word": " متجه", "probability": 0.9435221354166666}, {"start": 3759.54, "end": 3760.2, "word": " عمودي", "probability": 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0.95263671875}, {"start": 3767.28, "end": 3767.58, "word": " أنا", "probability": 0.79931640625}, {"start": 3767.58, "end": 3768.06, "word": " بقدر", "probability": 0.7890625}, {"start": 3768.06, "end": 3768.6, "word": " أجيب", "probability": 0.93798828125}, {"start": 3768.6, "end": 3769.38, "word": " متجه", "probability": 0.99072265625}, {"start": 3769.38, "end": 3769.88, "word": " يوازي", "probability": 0.9105224609375}, {"start": 3769.88, "end": 3770.12, "word": " هذا", "probability": 0.93505859375}, {"start": 3770.12, "end": 3770.48, "word": " الخط", "probability": 0.989501953125}, {"start": 3770.48, "end": 3771.54, "word": " المستقيم؟", "probability": 0.9130859375}, {"start": 3771.54, "end": 3771.76, "word": " اللي", "probability": 0.909423828125}, {"start": 3771.76, "end": 3771.88, "word": " هو", "probability": 0.958984375}, {"start": 3771.88, "end": 3773.04, "word": " مين؟", "probability": 0.9176432291666666}, {"start": 3773.04, "end": 3775.18, "word": " تمام", "probability": 0.6849365234375}, {"start": 3775.18, "end": 3775.72, "word": " يبقى", "probability": 0.816162109375}, {"start": 3775.72, "end": 3776.1, "word": " باجي", "probability": 0.8527018229166666}, {"start": 3776.1, "end": 3776.66, "word": " بقوله", "probability": 0.88671875}, {"start": 3776.66, "end": 3777.02, "word": " هنا", "probability": 0.93701171875}, {"start": 3777.02, "end": 3778.12, "word": " solution", "probability": 0.94287109375}, {"start": 3778.12, "end": 3780.62, "word": " the", "probability": 0.357421875}, {"start": 3780.62, "end": 3781.34, "word": " vector", "probability": 0.78271484375}, {"start": 3781.34, "end": 3784.42, "word": " اللي", "probability": 0.9775390625}, {"start": 3784.42, "end": 3784.68, "word": " هو", "probability": 0.990234375}], "temperature": 1.0}, {"id": 142, "seek": 381660, "start": 3787.56, "end": 3816.6, "text": "يبقى I زائد تلاتة J زائد أربعة K parallel to the given line طب قالي لـ plane عمودي على هذا ال line إذا لـ plane عمودي على هذا ال vector يبقى هذا يعطينا ان ال vector", "tokens": [1829, 3555, 4587, 7578, 286, 30767, 16373, 3215, 6055, 1211, 9307, 3660, 508, 30767, 16373, 3215, 5551, 25513, 27884, 591, 8952, 281, 264, 2212, 1622, 23032, 3555, 50239, 1829, 5296, 39184, 5720, 6225, 2304, 2407, 16254, 15844, 23758, 2423, 1622, 11933, 15730, 5296, 39184, 5720, 6225, 2304, 2407, 16254, 15844, 23758, 2423, 8062, 7251, 3555, 4587, 7578, 23758, 7251, 3615, 9566, 1829, 8315, 16472, 2423, 8062], "avg_logprob": -0.3148320975588329, "compression_ratio": 1.6241610738255035, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 3787.56, "end": 3788.0, "word": "يبقى", "probability": 0.721435546875}, {"start": 3788.0, "end": 3788.24, "word": " I", "probability": 0.150634765625}, {"start": 3788.24, "end": 3789.5, "word": " زائد", "probability": 0.4593505859375}, {"start": 3789.5, "end": 3790.24, "word": " تلاتة", "probability": 0.85498046875}, {"start": 3790.24, "end": 3790.64, "word": " J", "probability": 0.69580078125}, {"start": 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"end": 3806.04, "word": " عمودي", "probability": 0.9814453125}, {"start": 3806.04, "end": 3806.3, "word": " على", "probability": 0.87646484375}, {"start": 3806.3, "end": 3806.64, "word": " هذا", "probability": 0.87890625}, {"start": 3806.64, "end": 3806.8, "word": " ال", "probability": 0.91015625}, {"start": 3806.8, "end": 3807.1, "word": " line", "probability": 0.8447265625}, {"start": 3807.1, "end": 3807.56, "word": " إذا", "probability": 0.85302734375}, {"start": 3807.56, "end": 3807.88, "word": " لـ", "probability": 0.80615234375}, {"start": 3807.88, "end": 3808.22, "word": " plane", "probability": 0.76708984375}, {"start": 3808.22, "end": 3809.08, "word": " عمودي", "probability": 0.9730224609375}, {"start": 3809.08, "end": 3809.32, "word": " على", "probability": 0.90625}, {"start": 3809.32, "end": 3809.8, "word": " هذا", "probability": 0.970703125}, {"start": 3809.8, "end": 3810.08, "word": " ال", "probability": 0.9609375}, {"start": 3810.08, "end": 3810.46, "word": " vector", 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هذا اللي عندنا ع جل ال employment يكون عمود الانتقال ده هو الشكل وهي اسم العالم وهدي دفترك معاكي، تسيب الشنطة وهدي دفترك معاكي", "tokens": [39237, 10943, 22807, 1975, 1829, 2407, 3660, 12399, 2423, 7649, 4724, 16254, 1975, 8592, 38688, 16490, 9566, 16712, 4587, 41193, 15844, 23758, 13672, 1829, 43242, 8315, 6225, 10874, 1211, 2423, 11949, 7251, 30544, 6225, 2304, 23328, 2423, 7649, 2655, 4587, 6027, 11778, 3224, 31439, 25124, 28820, 37037, 1829, 24525, 2304, 18863, 45340, 37037, 16254, 11778, 5172, 2655, 31747, 20449, 995, 4117, 1829, 12399, 6055, 3794, 1829, 3555, 25124, 1863, 9566, 3660, 37037, 16254, 11778, 5172, 2655, 31747, 20449, 995, 4117, 1829], "avg_logprob": -0.3845274342996318, "compression_ratio": 1.7117647058823529, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 4427.95, "end": 4429.15, "word": "تمام؟", "probability": 0.6714680989583334}, {"start": 4429.15, "end": 4430.53, "word": " ايوة،", "probability": 0.718212890625}, {"start": 4430.53, "end": 4431.39, 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"text": "المعادلة الفارامترية of the line of intersection of the planes", "tokens": [6027, 2304, 3615, 18513, 37977, 27188, 9640, 10943, 2655, 2288, 10632, 295, 264, 1622, 295, 15236, 295, 264, 14952], "avg_logprob": -0.3949218690395355, "compression_ratio": 1.051948051948052, "no_speech_prob": 0.0, "words": [{"start": 5150.760000000001, "end": 5152.160000000001, "word": "المعادلة", "probability": 0.6636962890625}, {"start": 5152.160000000001, "end": 5153.56, "word": " الفارامترية", "probability": 0.6609293619791666}, {"start": 5153.56, "end": 5159.24, "word": " of", "probability": 0.283203125}, {"start": 5159.24, "end": 5160.56, "word": " the", "probability": 0.79541015625}, {"start": 5160.56, "end": 5162.14, "word": " line", "probability": 0.8857421875}, {"start": 5162.14, "end": 5163.36, "word": " of", "probability": 0.96923828125}, {"start": 5163.36, "end": 5165.58, "word": " intersection", "probability": 0.810546875}, {"start": 5165.58, "end": 5170.1, "word": " of", "probability": 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"probability": 0.6376953125}, {"start": 5803.73, "end": 5803.85, "word": " هي", "probability": 0.8779296875}, {"start": 5803.85, "end": 5804.31, "word": " النقطة", "probability": 0.8143717447916666}, {"start": 5804.31, "end": 5804.99, "word": " الرقم", "probability": 0.974609375}, {"start": 5804.99, "end": 5805.67, "word": " تلاتة", "probability": 0.8681640625}, {"start": 5805.67, "end": 5805.81, "word": " من", "probability": 0.9638671875}, {"start": 5805.81, "end": 5806.07, "word": " هذا", "probability": 0.716796875}, {"start": 5806.07, "end": 5806.19, "word": " ال", "probability": 0.74169921875}, {"start": 5806.19, "end": 5806.63, "word": " section", "probability": 0.3076171875}, {"start": 5806.63, "end": 5807.41, "word": " نفس", "probability": 0.729248046875}, {"start": 5807.41, "end": 5807.61, "word": " الله", "probability": 0.499755859375}, {"start": 5807.61, "end": 5807.79, "word": " لها", "probability": 0.5687255859375}, {"start": 5807.79, "end": 5808.11, "word": " النقطة", "probability": 0.9449869791666666}, {"start": 5808.11, "end": 5808.43, "word": " الرقم", "probability": 0.86865234375}, {"start": 5808.43, "end": 5808.95, "word": " أربعة", "probability": 0.8448893229166666}, {"start": 5808.95, "end": 5809.91, "word": " والنقطة", "probability": 0.84625244140625}, {"start": 5809.91, "end": 5810.55, "word": " رقم", "probability": 0.9635416666666666}, {"start": 5810.55, "end": 5812.05, "word": " خامسة", "probability": 0.869873046875}, {"start": 5812.05, "end": 5812.47, "word": " طبعا", "probability": 0.8427734375}, {"start": 5812.47, "end": 5812.69, "word": " مش", "probability": 0.60546875}, {"start": 5812.69, "end": 5812.93, "word": " حاضر", "probability": 0.7635091145833334}, {"start": 5812.93, "end": 5813.15, "word": " حاجة", "probability": 0.6495361328125}, {"start": 5813.15, "end": 5813.61, "word": " اليوم", "probability": 0.973876953125}, {"start": 5813.61, "end": 5814.19, "word": " الله", "probability": 0.81298828125}, {"start": 5814.19, "end": 5814.51, "word": " يعطيك", "probability": 0.78857421875}, {"start": 5814.51, "end": 5815.11, "word": " العافية", "probability": 0.7586263020833334}, {"start": 5815.11, "end": 5816.53, "word": " ونكمل", "probability": 0.683837890625}, {"start": 5816.53, "end": 5816.99, "word": " المرة", "probability": 0.949951171875}, {"start": 5816.99, "end": 5817.83, "word": " القادمة", "probability": 0.9938151041666666}, {"start": 5817.83, "end": 5818.43, "word": " إن", "probability": 0.689453125}, {"start": 5818.43, "end": 5818.91, "word": " شاء", "probability": 0.9814453125}, {"start": 5818.91, "end": 5819.29, "word": " الله", "probability": 0.9423828125}, {"start": 5819.29, "end": 5820.11, "word": " تعالى", "probability": 0.98876953125}], "temperature": 1.0}, {"id": 214, "seek": 582537, "start": 5824.27, "end": 5825.37, "text": "الحاجب السليسي والعالمي", "tokens": [6027, 5016, 26108, 3555, 21136, 20292, 3794, 1829, 16070, 3615, 45340, 1829], "avg_logprob": -0.5715144230769231, "compression_ratio": 0.9777777777777777, "no_speech_prob": 0.0, "words": [{"start": 5824.27, "end": 5824.59, "word": "الحاجب", "probability": 0.432952880859375}, {"start": 5824.59, "end": 5825.03, "word": " السليسي", "probability": 0.78369140625}, {"start": 5825.03, "end": 5825.37, "word": " والعالمي", "probability": 0.646728515625}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 5836.08, "duration_after_vad": 5062.097218750028}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/aAjYJyHQ2EE_raw.srt b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/aAjYJyHQ2EE_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f7dd7f393ff345ebe001b693095db5b2e68c69ec
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/aAjYJyHQ2EE_raw.srt
@@ -0,0 +1,3108 @@
+1
+00:00:00,000 --> 00:00:02,700
+موسيقى
+
+2
+00:00:16,500 --> 00:00:21,540
+معادلات الخط المستقيم كانت المعادلات البرامترية
+
+3
+00:00:21,540 --> 00:00:26,440
+للخط المستقيم في الفرار على صيغة x يساوي x0 زايد
+
+4
+00:00:26,440 --> 00:00:34,440
+v1t وy يساوي y0 زايد v2tبتساوي Z نوت زائد V3T طبعا
+
+5
+00:00:34,440 --> 00:00:37,580
+X نوت و Y نوت و Z نوت هي احداثيات النقطة التي يمر
+
+6
+00:00:37,580 --> 00:00:43,240
+بهذا الخط المستقيم V1 V2 V3 هي ال components تبعة
+
+7
+00:00:43,240 --> 00:00:48,580
+ال vector الموازنة من الخط المستقيم وعطينا المرة
+
+8
+00:00:48,580 --> 00:00:52,980
+الماضية على ذلك مثلا واحد الألب نروح لمثال رقم
+
+9
+00:00:52,980 --> 00:00:57,480
+اتنين يبقى المثال رقم اتنين بقول ما
+
+10
+00:01:03,110 --> 00:01:09,350
+five اللي هو parametric equations parametric
+
+11
+00:01:09,350 --> 00:01:15,730
+equations المعادلات ال parametric for the line for
+
+12
+00:01:15,730 --> 00:01:26,750
+the line للقطة المستقيم through الذي يمر بالنقطة
+
+13
+00:01:26,750 --> 00:01:29,510
+اللي هي اتنين
+
+14
+00:01:41,740 --> 00:01:52,480
+vectors وعمودي على المتجهات اللي هو U تساوي I زائد
+
+15
+00:01:52,480 --> 00:02:02,000
+اتنين J زائد تلاتة K and المتجه الثاني V يساوي
+
+16
+00:02:02,000 --> 00:02:09,860
+تلاتة I زائد اربعة J زائد خمسة K
+
+17
+00:02:15,470 --> 00:02:21,410
+نرجع لسؤالنا مرة ثانية نقرأ السؤال جيدا نعرف انحدد
+
+18
+00:02:21,410 --> 00:02:26,010
+ما هو المطلوب بناء عليه ان نعرف نشتغل بدقة ان شاء
+
+19
+00:02:26,010 --> 00:02:30,710
+الله يبقى ليهدد المعادلة القارامترية للخط المستقيم
+
+20
+00:02:30,710 --> 00:02:34,630
+يبقى بدنا المعادلات اللي قدامنا التلاتة هذه بحيث
+
+21
+00:02:34,630 --> 00:02:38,770
+الخط المستقيم يمر بالنقطة 2 تلاتة زير يبقى
+
+22
+00:02:38,770 --> 00:02:46,360
+الاحداثية X node وY node وZ node معروفةمتجه يوازي
+
+23
+00:02:46,360 --> 00:02:50,580
+هذا الخط المستخمش بيقول لي هون ال line هذا مقرب
+
+24
+00:02:50,580 --> 00:02:56,400
+النقطة هذه و عمودي على المتجهين الأثنين هذول طيب
+
+25
+00:02:56,400 --> 00:03:02,080
+كيف بقدر أجيب متجه عمودي على متجهين شو بعملهم
+
+26
+00:03:02,080 --> 00:03:07,890
+cross productلو عملت cross product بجيب vector
+
+27
+00:03:07,890 --> 00:03:12,850
+عمودي على كل المل المتجه اللي بكون هو المتجه
+
+28
+00:03:12,850 --> 00:03:18,190
+المطلوب حتى أتمكن من الحصول على معادلات الخط
+
+29
+00:03:18,190 --> 00:03:26,370
+المستقل إذا بدي أروح أجيب له ال U cross ال V يبقى
+
+30
+00:03:26,370 --> 00:03:29,010
+U cross ال V يسوى المحدد
+
+31
+00:03:33,050 --> 00:03:40,610
+المتجه الأول 1 2 3 مركبات المتجه التاني 3 4 5
+
+32
+00:03:43,420 --> 00:03:47,880
+يبقى على طول الخط هذا بده يسوي نشطة بصفه و عموده
+
+33
+00:03:47,880 --> 00:03:54,280
+نين في خمسة بعشرة ناقص اتناشت بيبقى ناقص اتنين I
+
+34
+00:03:54,280 --> 00:04:02,600
+اللي بعد نشطة بصفه و عموده خمسة ناقص خمستاشر بيبقى
+
+35
+00:04:02,600 --> 00:04:06,140
+ناقص عشرة و هذا أصلا مش هرت ناقص بيبقى زائد عشرة
+
+36
+00:04:06,140 --> 00:04:10,680
+يبقى زائد عشرة G كيف؟
+
+37
+00:04:17,890 --> 00:04:24,550
+صفه و عموده يبقى خمسة ناقص ستة يبقى ناقص أربعة مع
+
+38
+00:04:24,550 --> 00:04:30,070
+الناقص يبقى زائد أربعة جيه كلام سليم اللي بقناه
+
+39
+00:04:30,070 --> 00:04:36,230
+مشطب صفه و عموده يبقى أربعة ناقص ستة يبقى قداش
+
+40
+00:04:36,230 --> 00:04:46,210
+ناقص اتنين كيه يبقى هذا ال vector أورثجوناليبقى
+
+41
+00:04:46,210 --> 00:04:55,430
+هذا parallel لمين لللعين يبقى هذا vector parallel
+
+42
+00:04:55,430 --> 00:04:58,610
+to
+
+43
+00:04:58,610 --> 00:05:02,150
+required
+
+44
+00:05:02,150 --> 00:05:05,770
+line
+
+45
+00:05:07,290 --> 00:05:12,590
+يبقى هذا مالموازي للخط اللي مطوب علي الكوارث، يعني
+
+46
+00:05:12,590 --> 00:05:17,930
+مطوب اللي عليها بدنا نوشبناء عليه إذا أصبح ال
+
+47
+00:05:17,930 --> 00:05:23,770
+parametric equations هي X يساوي X نول اللي هي 2
+
+48
+00:05:23,770 --> 00:05:29,670
+زائد المركبة اللي عندنا اللي هي ناقص 2 يبقى ناقص
+
+49
+00:05:29,670 --> 00:05:37,590
+2T يبقى 2 ناقص 2T المركبة التانية اللي هي Y بدها
+
+50
+00:05:37,590 --> 00:05:43,150
+تساوي المركبة التانية اللي هي 3 وعنا زائد
+
+51
+00:05:46,370 --> 00:05:49,730
+يبقى Z أو المعادلة التالتة المركبة علينا Z و الله
+
+52
+00:05:49,730 --> 00:05:55,530
+يسهل عليها يبقى بظل ناقص اتنين T وT هذه ماعليهاش
+
+53
+00:05:55,530 --> 00:06:01,170
+قيود يبقى اكبر من سالب Infinity و اقل منين اقل من
+
+54
+00:06:01,170 --> 00:06:05,210
+Infinity يبقى هذه معادلات ال Parameterية للخط
+
+55
+00:06:05,210 --> 00:06:10,210
+المستقيم اللي عندنا نعطي كمان مثال رقم تلاتة
+
+56
+00:06:29,050 --> 00:06:39,230
+الخطوط المستقيمة التالية are intersecting
+
+57
+00:06:39,230 --> 00:06:46,450
+ولا parallel or
+
+58
+00:06:46,450 --> 00:06:49,470
+skew
+
+59
+00:06:49,470 --> 00:06:53,630
+if
+
+60
+00:06:53,630 --> 00:06:57,690
+they intersect
+
+61
+00:07:00,560 --> 00:07:18,800
+اذا كان هناك تقاطة، احصل على نقاط التقاطة
+
+62
+00:07:18,800 --> 00:07:23,520
+المستقيم الأول الحديد هو الرمز الـ1موضة في صيغة
+
+63
+00:07:23,520 --> 00:07:30,920
+البرامترية X يساوي واحد زائد اتنين T وال Y تساوي
+
+64
+00:07:30,920 --> 00:07:35,780
+ناقص واحد ناقص T وال Z تساوي
+
+65
+00:07:38,260 --> 00:07:44,040
+والمستقيم التاني L2 موقع الشكل التاني X يساوي
+
+66
+00:07:44,040 --> 00:07:54,240
+اتنين ناقص S وY تساوي تلاتة S وZ تساوي واحد زائد S
+
+67
+00:07:56,280 --> 00:08:03,940
+لتلاتة مقطع على الصيغة الهمين ال L تلاتة عبارة عن
+
+68
+00:08:03,940 --> 00:08:13,680
+ال X يساوي خمسة زائد اتنين R وال Y يساوي واحد ناقص
+
+69
+00:08:13,680 --> 00:08:20,380
+R وال Z تساوي تمانية زائد تلاتة R
+
+70
+00:08:24,750 --> 00:08:29,930
+هنا بالنسبالي ماعنديش قيود لا على T ولا S ولا R
+
+71
+00:08:29,930 --> 00:08:35,290
+يبقى هذا على كل الـ real line بلاستيكنات نحاول
+
+72
+00:08:35,290 --> 00:08:37,710
+نشوف المستقيمات اللي عندنا هذه
+
+73
+00:09:06,190 --> 00:09:12,130
+نرجع لسؤالنا مرة تانية بيعطيني ثلاثة مستقيمات L1 و
+
+74
+00:09:12,130 --> 00:09:14,930
+L2 و L3 و L4 و L5 و L6 و L7 و L8 و L9 و L10 و L10
+
+75
+00:09:14,930 --> 00:09:16,850
+و L10 و L11 و L12 و L12 و L13 و L13 و L14 و L15 و
+
+76
+00:09:16,850 --> 00:09:22,070
+L15 و L16 و L17 و L18 و L19 و L19 و L20 و L21 و
+
+77
+00:09:22,070 --> 00:09:23,030
+L22 و L22 و L22 و L22 و L22 و L22 و L22 و L22 و
+
+78
+00:09:23,030 --> 00:09:25,010
+L22 و L22 و L22 و L22 و L22 و L22 و L22 و L22 و
+
+79
+00:09:25,010 --> 00:09:25,090
+L22 و L22 و L22 و L22 و L22 و L22 و L22 و L22 و
+
+80
+00:09:25,090 --> 00:09:25,090
+L22 و L22 و L22 و L22 و L22 و L22 و L22 و L22 و
+
+81
+00:09:25,090 --> 00:09:26,330
+L22 و L22 و L22 و L22 و L22 و L22 و L
+
+82
+00:09:34,860 --> 00:09:45,500
+كويس لما اقول اتنين متوازين
+
+83
+00:09:45,500 --> 00:09:51,560
+يبقى there is no intersection مفيش بالمرة طب كيف
+
+84
+00:09:51,560 --> 00:09:55,000
+بثبت ان two vectors are parallel
+
+85
+00:10:03,600 --> 00:10:09,640
+مستقيمين متخلفين يعني لا تقاطع ولا توازن مهما المد
+
+86
+00:10:09,640 --> 00:10:12,820
+هذا من سلب infinity إلى infinity وهذا من infinity
+
+87
+00:10:12,820 --> 00:10:18,360
+إلى سلب infinity مافيش تقاطع وليس هناك توازن مثل
+
+88
+00:10:18,360 --> 00:10:23,100
+ذلك لو جدتك ال corner اللي عندك هذا هذا خط مستقيم
+
+89
+00:10:23,380 --> 00:10:27,880
+والخط المستقيم اللي هو في القلي هناك مهما اتمنديهم
+
+90
+00:10:27,880 --> 00:10:31,220
+مافيش intersection ما بين الاثنين يبقى هدول
+
+91
+00:10:31,220 --> 00:10:38,740
+بيسميهم as QV lines مستقيمات متخالفة طيب نجي نشوف
+
+92
+00:10:38,740 --> 00:10:42,600
+ايش قصة تانية كده بدنا نثبت ان هدول متوازين
+
+93
+00:10:42,600 --> 00:10:47,400
+متقاطعين متخالفين بقول كويسة بدي امسك المستقيم
+
+94
+00:10:47,400 --> 00:10:56,370
+الأول والثانيهل هناك متجه يوازي المستقيم الأول من
+
+95
+00:10:56,370 --> 00:10:59,990
+خلال المعادلة هذه؟
+
+96
+00:11:08,280 --> 00:11:15,380
+هذا الـ vector يوازي المتجه الأول وهذا ال vector
+
+97
+00:11:15,380 --> 00:11:20,260
+تاني يوازي
+
+98
+00:11:20,260 --> 00:11:21,880
+المتجه الثاني
+
+99
+00:11:25,980 --> 00:11:30,980
+معناته المستقيمين متوازين صح ولا لا طيب إذا كانوا
+
+100
+00:11:30,980 --> 00:11:34,620
+هدول مهماش متوازين يبقى المستقيمين غير متوازين
+
+101
+00:11:34,620 --> 00:11:39,880
+بيظل احتمال التقاطع أو التخالف وبنبحث القصة هذه
+
+102
+00:11:39,880 --> 00:11:48,180
+ونشوف يبقى باجي بقول هنا ال one solution ال one
+
+103
+00:11:48,180 --> 00:11:54,380
+parallel to the vector
+
+104
+00:11:55,870 --> 00:12:03,170
+V1 هو مين V1 هذا هجيبه من نفسي المعادل اتنين I
+
+105
+00:12:03,170 --> 00:12:11,870
+ناقص J زائد تلاتة K بعد هي ال L2 parallel to the
+
+106
+00:12:11,870 --> 00:12:19,990
+vector باجي هنا اللي هو V2 ناقص I زائد تلاتة J
+
+107
+00:12:19,990 --> 00:12:23,770
+زائد K السؤال
+
+108
+00:12:25,330 --> 00:12:30,150
+هل واحد من الاتنين هدول مضاعفات الآخر؟ مش ممكن
+
+109
+00:12:30,150 --> 00:12:33,390
+يبقى المعنى تقول اتنين هدول are not parallel
+
+110
+00:12:33,390 --> 00:12:41,070
+وبالتالي ال two lines are not parallel يبقى هنا L1
+
+111
+00:12:41,070 --> 00:12:54,050
+is not parallel to L2 because السبب ان V1 is
+
+112
+00:13:02,600 --> 00:13:08,860
+بالتالي لا يوجد توازي بين ال V1 و V2 وبالتالي لا
+
+113
+00:13:08,860 --> 00:13:13,920
+يمكن لـ two lines L1 و L2 يكونوا اتنين are
+
+114
+00:13:13,920 --> 00:13:21,020
+parallel يبقى سبعة التوازن بظل احتمالي التقاطعالان
+
+115
+00:13:21,020 --> 00:13:26,040
+بدنا نحكم علي المستقيمين هم متخالفين ولا
+
+116
+00:13:26,040 --> 00:13:32,500
+المستقيمين متقاطعين مش هنحكم بتحول السبعة واحدة
+
+117
+00:13:32,500 --> 00:13:37,260
+فيهم إذا استبعت واحدة فيهم بتظل مين؟ بتظل الأخرى
+
+118
+00:13:37,260 --> 00:13:42,580
+إجباري يبقى جدلا انا بدأ افترض ان اتنين هم
+
+119
+00:13:42,580 --> 00:13:48,380
+متقاطعين وشوف ايش اللي بتوصل ليش يبقى هذا باجي
+
+120
+00:13:48,380 --> 00:13:55,580
+يقول FL1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13
+
+121
+00:13:55,580 --> 00:14:01,280
+L14 L15 L16 L17 L18 L19 L20 L21 L22 L23 L24 L25
+
+122
+00:14:01,280 --> 00:14:03,760
+L26 L27 L28 L29 L29 L29 L29 L29 L29 L29 L29 L29
+
+123
+00:14:03,760 --> 00:14:06,900
+L29 L29 L29 L29 L29 L29 L29 L29 L29 L29 L29 L29
+
+124
+00:14:06,900 --> 00:14:06,980
+L29 L29 L29 L29 L29 L29 L29 L29 L29 L29 L29 L29
+
+125
+00:14:06,980 --> 00:14:07,040
+L29 L29 L29 L29 L29 L29 L29 L29 L29 L29 L29 L29
+
+126
+00:14:07,040 --> 00:14:07,040
+L29 L29 L29 L29 L29 L29 L29 L29 L29 L29 L29 L29
+
+127
+00:14:07,040 --> 00:14:07,860
+L29 L29 L29 L29 L29 L29 L29 L29 L29 L29 L29 L29
+
+128
+00:14:07,860 --> 00:14:07,860
+L29 L29 L29 L29 L29 L29 L29 L29 L29 L29 L29 L29
+
+129
+00:14:07,860 --> 00:14:08,840
+L29 L29 L29
+
+130
+00:14:14,330 --> 00:14:22,810
+بتكون واحد زائد اتنين T بتساوي اتنين ناقص S وناقص
+
+131
+00:14:22,810 --> 00:14:31,650
+واحد ناقص T بتساوي تلاتة S وعندنا هنا تلاتة T
+
+132
+00:14:31,650 --> 00:14:40,390
+بتساوية واحد زائد Sهذول كام معادلة؟ تلات معادلة و
+
+133
+00:14:40,390 --> 00:14:44,090
+كام مجهول؟ اتنين يعني الحمد لله ربنا حط البركة
+
+134
+00:14:44,090 --> 00:14:48,750
+عشان نجيب TOS بيكفينا تنتين عدد المعادلات يساوي
+
+135
+00:14:48,750 --> 00:14:52,090
+عدد المجاهيين لكن تلات معادلة يعني الحمد لله ربنا
+
+136
+00:14:52,090 --> 00:14:57,790
+حط البركة okay تمام بقول كويس خلينا نجرب نحل
+
+137
+00:14:57,790 --> 00:15:02,370
+المعادلتين الاتنين هذول مع بعض و نشوف إيش بده
+
+138
+00:15:02,370 --> 00:15:11,920
+يعطينايبقى هذا يعطينا ما يبتي 1 زائد 2t تساوي 2
+
+139
+00:15:11,920 --> 00:15:19,820
+ناقص s المعادلة التانية بيضربها في 2 يبقى ناقص 2
+
+140
+00:15:19,820 --> 00:15:28,880
+هنا ناقص 2t يبقى ناقص 6s
+
+141
+00:15:32,490 --> 00:15:40,870
+يبقى على الشمال ناقص واحد يبقى على الشجر اليمين
+
+142
+00:15:40,870 --> 00:15:46,050
+ناقص اس وست اس يبقى ناقص خمس اس يبقى ناقص اتنين
+
+143
+00:15:46,050 --> 00:15:53,410
+زائد خمس اس يبقى ناقص اتنين زائد خمس اس هذا معناته
+
+144
+00:15:53,410 --> 00:15:59,450
+ان ناقص تلاتة يبقى ناقص خمس اس هذا معناته ان اس
+
+145
+00:15:59,450 --> 00:16:01,850
+يسوى ناقص تلاتة
+
+146
+00:16:06,940 --> 00:16:11,920
+يبقى عوض في أي من المعادلة تانية لو جيت عوض في
+
+147
+00:16:11,920 --> 00:16:16,640
+المعادلة الأولى بس إذا عندي واحد زائد اتنين T
+
+148
+00:16:16,640 --> 00:16:25,120
+يساوي اتنين ناقص اتنين ناقص S، S عندي بتلات أخمس
+
+149
+00:16:37,740 --> 00:16:40,260
+عشرة و تلاتة و تلاتة و تلاتة و تلاتة و تلاتة و
+
+150
+00:16:40,260 --> 00:16:43,220
+تلاتة و تلاتة و تلاتة و تلاتة و تلاتة و تلاتة و
+
+151
+00:16:43,220 --> 00:16:44,600
+تلاتة و تلاتة و تلاتة و تلاتة و تلاتة و تلاتة و
+
+152
+00:16:44,600 --> 00:16:45,140
+تلاتة و تلاتة و تلاتة و تلاتة و تلاتة و تلاتة و
+
+153
+00:16:45,140 --> 00:16:45,420
+تلاتة و تلاتة و تلاتة و تلاتة و تلاتة و تلاتة و
+
+154
+00:16:45,420 --> 00:16:45,420
+تلاتة و تلاتة و تلاتة و تلاتة و تلاتة و تلاتة و
+
+155
+00:16:45,420 --> 00:16:48,300
+تلاتة و تلاتة و تلاتة و تلاتة و تلاتة و تلاتة و
+
+156
+00:16:48,300 --> 00:16:53,500
+تلاتة و تلاتة و تلاتة و
+
+157
+00:16:57,480 --> 00:17:04,880
+مرة تانية بقول تلتاشة على خمسة تمان
+
+158
+00:17:04,880 --> 00:17:11,080
+أخمس تساوي اتنين T ومنها T تساوي أربع أخمس تساوي
+
+159
+00:17:11,080 --> 00:17:14,590
+اتنين T ومنها T تساوي أربع أخمسيبقى حصلت على T
+
+160
+00:17:14,590 --> 00:17:21,790
+وحصلت هنا على مين على S إذا في تقاطع لازم قيمة
+
+161
+00:17:21,790 --> 00:17:26,210
+المعادلة التالتة هذه تسوي قيمة المعادلة هذه إذا لم
+
+162
+00:17:26,210 --> 00:17:30,370
+تتساوي القيمتان يبقى بيكون there is no
+
+163
+00:17:30,370 --> 00:17:35,430
+intersection ماعنديش تقاطع بتاتة يبقى بناء عليه
+
+164
+00:17:35,430 --> 00:17:40,590
+بيروح أعوض في المعادلة التالتة هسميها ك star
+
+165
+00:17:44,880 --> 00:17:52,140
+يبقى بتقول الان substitute عوضلي
+
+166
+00:17:52,140 --> 00:17:58,900
+in star نحصل على ايش يبقى قصير عندي تلاتة فيتي
+
+167
+00:17:58,900 --> 00:18:07,920
+وانتي لاربع اخلاص اللي هو الاصل يساوي قداش يساوي
+
+168
+00:18:07,920 --> 00:18:09,540
+الواحد
+
+169
+00:18:13,590 --> 00:18:20,230
+هل هدول بيساووا بعض؟ ليش؟
+
+170
+00:18:20,230 --> 00:18:27,070
+لأن هذا خمسين وهذا كده اتناشر على خمسة يبقى اتناشر
+
+171
+00:18:27,070 --> 00:18:33,690
+على خمسة لا يمكن انها تساوي خمسين معناه هذا الكلام
+
+172
+00:18:33,690 --> 00:18:36,550
+ان المستقيمات الاتنين هدول بتقاطعوا
+
+173
+00:18:39,810 --> 00:18:51,270
+L1 و L2 لا يتقاطعون
+
+174
+00:19:09,620 --> 00:19:16,060
+مستقيمان متخلفة طيب احنا بحثنا الان المستقيم الاول
+
+175
+00:19:16,060 --> 00:19:22,060
+مع الثالث بدنا نبحث المستقيم الاول مع التالت يبقى
+
+176
+00:19:22,060 --> 00:19:29,300
+مرة تانية بدي اقول ان انتهينا المطلوب الاول V1 فرق
+
+177
+00:19:29,300 --> 00:19:38,260
+او L1 فرق ال V1
+
+178
+00:19:38,260 --> 00:19:38,900
+اللي عندنا
+
+179
+00:19:53,720 --> 00:20:00,980
+Parallel to V3 ويسافر 2I-J
+
+180
+00:20:07,660 --> 00:20:13,080
+يبقى صار V1 و V2 are parallel يبقى هذا بدي أعطيلك
+
+181
+00:20:13,080 --> 00:20:27,380
+ان V1 parallel to V2 so L1 and L2 are parallel
+
+182
+00:20:27,380 --> 00:20:32,160
+line يبقى
+
+183
+00:20:32,160 --> 00:20:40,190
+دول خطين متوازن تهيأنا بالأول مع التالتمع التالت
+
+184
+00:20:40,190 --> 00:20:55,130
+الان تطلعينى ل V1 و V2 V1 و V3 هى V2 و
+
+185
+00:20:55,130 --> 00:21:01,630
+V3 هى V2 هى V3 هى V3 هى V3 هى V3 هى V3 هى V3 هى V3
+
+186
+00:21:01,630 --> 00:21:01,850
+هى V3 هى V3 هى V3 هى V3 هى V3 هى V3 هى V3 هى V3 هى
+
+187
+00:21:01,850 --> 00:21:05,050
+V3 هى V3 هى V3 هى V3 هى V3 هى V3 هى V3 هى V3 هى V3
+
+188
+00:21:05,050 --> 00:21:05,050
+هى V3 هى V3 هى V3 هى V3 هى V3 هى V3 هى V3 هى V3 هى
+
+189
+00:21:05,050 --> 00:21:05,090
+V3 هى V3 هى V3 هى V3 هى V3 هى V3 هى V3 هى V3 هى V3
+
+190
+00:21:05,090 --> 00:21:11,510
+هى V3 هى V3 هى V3 هى V3 هى V3 هى V3 هال L2 و L3
+
+191
+00:21:11,510 --> 00:21:24,070
+ليسوا مرتبطين السبب لأن V2
+
+192
+00:21:24,070 --> 00:21:27,010
+و V3
+
+193
+00:21:35,730 --> 00:21:42,330
+هيبقى هدول غير متوازية ضال احتمال التقاطع واحتمال
+
+194
+00:21:42,330 --> 00:21:48,130
+مين التخالف التكتيك اللي اتبعته هنا هه هه هه هه هه
+
+195
+00:21:48,130 --> 00:21:48,310
+هه هه هه هه هه هه هه هه هه هه هه هه هه هه هه هه هه
+
+196
+00:21:48,310 --> 00:21:49,710
+هه هه هه هه هه هه هه هه هه هه هه هه هه هه هه هه هه
+
+197
+00:21:49,710 --> 00:21:51,410
+هه هه هه هه هه هه هه هه هه هه هه هه هه هه هه هه هه
+
+198
+00:21:51,410 --> 00:21:53,070
+هه هه هه هه هه هه هه هه هه هه هه هه هه هه هه هه هه
+
+199
+00:21:53,070 --> 00:22:03,390
+هه هه هه هه هه هه هه هه هه هه هه هه هه هه هه
+
+200
+00:22:03,390 --> 00:22:12,040
+ههلو حصل ان ال X للتاني هي X للتالت و Y للتاني هي
+
+201
+00:22:12,040 --> 00:22:20,340
+X للتالت و هكذا يجب ان يكون اذا كان 2-S يكون 5
+
+202
+00:22:20,340 --> 00:22:22,700
+زائد 2A
+
+203
+00:22:30,000 --> 00:22:36,440
+بعدها واحد زائد اس بده يساوي واحد زائد اس بده
+
+204
+00:22:36,440 --> 00:22:45,120
+يساوي تمانية زائد تلاتة بقول كويس ايش رايك اجمع
+
+205
+00:22:45,120 --> 00:22:51,700
+الأولى والتالتة مرة واحدة نسيب التانية يبقى لو
+
+206
+00:22:51,700 --> 00:22:56,320
+جمعتهم بتروح الاس مع الاس بيظل في الشجة الشمال جدا
+
+207
+00:22:56,320 --> 00:23:03,970
+يعنيثلاثة تساوي تلت
+
+208
+00:23:03,970 --> 00:23:13,850
+عشر زائد خمسة R هذا معناه ان خمسة R يساوي ناقص
+
+209
+00:23:13,850 --> 00:23:21,470
+عشرة يبقى ال R تساوي سالب اتنين الآن بدي اعوض في
+
+210
+00:23:21,470 --> 00:23:27,820
+اي من المعادلة تانية الأولى او التالتة سيانةبالـ S
+
+211
+00:23:27,820 --> 00:23:32,380
+الـ R عندي بسلب 2 لو روحت عوضت في الأولى يجب ان
+
+212
+00:23:32,380 --> 00:23:41,100
+تشتغل عيندي اتنين ناقص S بده يساوي خمسة ناقص أربعة
+
+213
+00:23:41,100 --> 00:23:48,120
+يبقى هنا بصير عندي اللي هو اتنين ناقص S يساوي واحد
+
+214
+00:23:48,120 --> 00:23:54,400
+يبقى الـ S تساوي قدر واحد الان المعادل اللي ما
+
+215
+00:23:54,400 --> 00:23:59,830
+اشتغلتش عليها اليمينمعادلة رقم اتنين إذا بدي أشيل
+
+216
+00:23:59,830 --> 00:24:04,130
+S و أضع مكانها واحد بصير الطرف الشمال كم؟ تلاتة
+
+217
+00:24:04,130 --> 00:24:09,610
+بدي أشيل هنا و أضع مكانها سالفي اتنين بصير كم؟
+
+218
+00:24:09,610 --> 00:24:15,450
+تلاتة يبقى اتنين هذول are intersect يبقى هذه
+
+219
+00:24:15,450 --> 00:24:19,650
+نسميها المعادلة star substitute
+
+220
+00:24:23,420 --> 00:24:33,420
+ان استاء ويجد بدي اشير عندك تلاتة في اس اللي هي
+
+221
+00:24:33,420 --> 00:24:42,720
+واحد يساوي واحد ناقص ناقص اتنين يعني تلاتة بدها
+
+222
+00:24:42,720 --> 00:24:47,740
+تساوي تلاتة اذا معناه هذا الكلام الخاطئ هدول مالهم
+
+223
+00:24:47,740 --> 00:24:49,940
+بدهم يتقاطعوا
+
+224
+00:24:54,260 --> 00:25:00,780
+يبقى كذلك الاتنين والتلاتة
+
+225
+00:25:00,780 --> 00:25:04,460
+مقاومة
+
+226
+00:25:04,460 --> 00:25:11,940
+في المقاومة يلّا
+
+227
+00:25:11,940 --> 00:25:17,800
+نجيب نقطة التقاطع تبع الخط الاتنين هذين تاخدي أي
+
+228
+00:25:17,800 --> 00:25:23,110
+واحدة يا هذه يا هذهأخذت هذي بتعوض قيمة A أخذت هذي
+
+229
+00:25:23,110 --> 00:25:28,510
+بتعوض قيمة S واضح أن S أسهل لإنها بجداش بواحد صحيح
+
+230
+00:25:28,510 --> 00:25:34,870
+إذا بدأ أقول X وY وZ أحداث النقطة بدوا يساوي انا
+
+231
+00:25:34,870 --> 00:25:40,710
+بدأ أمسك ال L2 اللي هو اتنين ناقص واحد وتلاتة
+
+232
+00:25:50,240 --> 00:25:55,580
+نقطة التقاطع للمستقيمين الاتنين اللي عندناها دوة
+
+233
+00:25:55,580 --> 00:25:58,720
+طيب
+
+234
+00:25:58,720 --> 00:26:03,800
+ده حد هنا stop انتهينا من النقطة الأولى من هذا ال
+
+235
+00:26:03,800 --> 00:26:06,840
+section اللي ابتدأناها المرة الماضية
+
+236
+00:26:12,170 --> 00:26:20,590
+أي استفسار عندنا هنا؟ حد بتسأل أي سؤال؟ طيب بروح
+
+237
+00:26:20,590 --> 00:26:22,830
+لقال النقطة الثانية
+
+238
+00:26:52,540 --> 00:26:56,700
+النقطة الثانية يا بنات هي المسافة من نقطة إلى خط
+
+239
+00:26:56,700 --> 00:27:02,140
+مستقيم في الفرقة الـ
+
+240
+00:27:02,140 --> 00:27:06,160
+distance المسافة
+
+241
+00:27:06,160 --> 00:27:20,380
+from a point from a point to a line and space
+
+242
+00:27:24,110 --> 00:27:29,730
+هنا نجيب المسافة ما بين نقطة وخط مستقيم بالفرعات
+
+243
+00:27:29,730 --> 00:27:38,130
+نفترض على سبيل المثال ان هذا هو line L واخدنا نقطة
+
+244
+00:27:38,130 --> 00:27:42,650
+وان تكون هذه النقطة نقطة S مثلا
+
+245
+00:27:45,440 --> 00:27:52,980
+بنجيب قداش المسافة ما بين النقطة S و Main و Line L
+
+246
+00:27:52,980 --> 00:27:58,220
+بقول والله كويس المسافة اللى وصلتك هذه مسافة هذه
+
+247
+00:27:58,220 --> 00:28:03,800
+مسافة هذه مسافة هذه مسافة لكن في الحقيقة المسافة
+
+248
+00:28:03,800 --> 00:28:09,360
+الحقيقية هي المسافةالعمودية بين هذه النقطة والخط
+
+249
+00:28:09,360 --> 00:28:16,160
+المستقيم يعني بنروح نزل عمود على الخط المستقيم من
+
+250
+00:28:16,160 --> 00:28:22,080
+هذه النقطة بهذا الشكل يبقى
+
+251
+00:28:22,080 --> 00:28:28,540
+هذا عمود يبقى هذا ال distance دي مطلوب مننا نعرف
+
+252
+00:28:28,540 --> 00:28:33,900
+قداش مقدار ال distance ديطبعا distance مسافة و
+
+253
+00:28:33,900 --> 00:28:39,140
+احنا بنشغل في موضوع المتجهات إذا بلزمني المتجهات
+
+254
+00:28:39,140 --> 00:28:44,920
+في معرفة هذه ال distance لذلك النقطة S هذه نقطة
+
+255
+00:28:44,920 --> 00:28:49,500
+معلومة معروفة عندى لإنهم يعطينا أحداثياتها و ال
+
+256
+00:28:49,500 --> 00:28:56,280
+line عند ال معروف تمام يبقى أنا مشان أجيب المسافة
+
+257
+00:28:56,280 --> 00:29:02,190
+هذه بتروح أدور على vector موازي لهذا ال lineو طبعا
+
+258
+00:29:02,190 --> 00:29:05,190
+إذا ال line مُعطَى في الصيغة البرامترية بصير ال
+
+259
+00:29:05,190 --> 00:29:09,510
+vector معروف ال vector معروف و النقطة معروفة منهم
+
+260
+00:29:09,510 --> 00:29:14,530
+بقدر أجيب ال distance كيف؟ كالتالت بروح أخد أي
+
+261
+00:29:14,530 --> 00:29:21,810
+نقطة موجودة على هذا ال line و لتكن النقطة P باخد
+
+262
+00:29:21,810 --> 00:29:29,590
+المتجه PS بالشكل اللي عندنا يبقى هذا هو المتجه PS
+
+263
+00:29:31,180 --> 00:29:40,120
+PS صنعني مع المستقيم L أو مع المتجه
+
+264
+00:29:40,120 --> 00:29:48,940
+الموازي لل line L وليكن المتجه V الموازي لل line L
+
+265
+00:29:48,940 --> 00:29:55,700
+صنعني زاوية مقدارها θيتا صار
+
+266
+00:29:55,700 --> 00:30:02,790
+عندي مثلث قائم الزاوية الطلع هذا طولههو طول الـ P
+
+267
+00:30:02,790 --> 00:30:09,510
+S وهذا أحد ضلعي القائمة والزاوية تيتا اللي عندنا
+
+268
+00:30:09,510 --> 00:30:14,410
+هذه حد فيكم بتقدر تجيب لي D بدلالة طول P S
+
+269
+00:30:14,410 --> 00:30:19,870
+والزاوية تيتا اللي هو P S في صين الزاوية تيتا يبقى
+
+270
+00:30:19,870 --> 00:30:25,910
+D تساوي P S طول المتجة في صين الزاوية
+
+271
+00:30:28,370 --> 00:30:33,370
+طيب يبقى الحين قصتنا صارت معروفة بس بدي أحول
+
+272
+00:30:33,370 --> 00:30:40,470
+الصياغ هذه بصياغة أخرى تمام فباجي بقول هنا the
+
+273
+00:30:40,470 --> 00:30:55,050
+distance d is given from الـd يسوى طول الـP S في
+
+274
+00:30:55,050 --> 00:30:57,050
+مين؟ في صيني الزاوية
+
+275
+00:30:59,640 --> 00:31:05,640
+طيب نرجع بالذاكرة إلى الوراق لو عندي متجهين U و V
+
+276
+00:31:05,640 --> 00:31:12,320
+وعملت لهم cross product يبقى U cross ال B طول ال U
+
+277
+00:31:12,320 --> 00:31:15,900
+فطول ال B في الصينة الزاوية تيتا في اتجاه متجه
+
+278
+00:31:15,900 --> 00:31:21,420
+الوحدة M اللي هو خط طول بصورة U طول U cross ال B
+
+279
+00:31:21,420 --> 00:31:25,500
+طول ال U فطول ال U في الصينة الزاوية تيتا صح؟ إذا
+
+280
+00:31:25,500 --> 00:31:31,020
+لو كنت جيب صينة زاوية تيتابصير طول ال U V على طول
+
+281
+00:31:31,020 --> 00:31:36,220
+ال U في طول ال V إذا ال sin زاوية تيتا هذه بقدر
+
+282
+00:31:36,220 --> 00:31:44,460
+أشيلها و أقول هو طول ال PS sin زاوية تيتا تيتا
+
+283
+00:31:44,460 --> 00:31:53,680
+محصورة بين مين؟ بين PS و V يبقى طول ال PS cross ال
+
+284
+00:31:53,680 --> 00:31:54,220
+V
+
+285
+00:31:59,160 --> 00:32:06,720
+على طول الـPS في طول الـV في
+
+286
+00:32:06,720 --> 00:32:11,760
+شغلة ممكن نختصرها بين البصد والمقارنة طول الـPS مع
+
+287
+00:32:11,760 --> 00:32:18,500
+طول الـPS ما قسمتش على متج هه ماقسمت متج هه قسمت
+
+288
+00:32:18,500 --> 00:32:22,600
+على طول المتجه يعني قسم على الـscalarيبقى من هنا
+
+289
+00:32:22,600 --> 00:32:29,660
+بيصير ال distance D بيصير طول ال PS across ال V
+
+290
+00:32:29,660 --> 00:32:36,700
+على طول المتجه V يبقى هذه وسيلة عملية على كيفية
+
+291
+00:32:36,700 --> 00:32:43,980
+الحصول على المسافة بين نقطة وخط مستقيم في الفرعات
+
+292
+00:32:43,980 --> 00:32:50,600
+يبقى يا بناتبالبلد هيك نحكي الان لو فى عندى نقطة
+
+293
+00:32:50,600 --> 00:32:55,060
+فى الفراغ وعندي خط مستقيم كده اجيب المسافة كدهش
+
+294
+00:32:55,060 --> 00:33:01,600
+بين هذه النقطة وذاك الخط المستقيم ايش بالزمنى نقطة
+
+295
+00:33:01,600 --> 00:33:06,940
+معروفة احدثيتها يمكن بدي اوجد اى نقطة على الخط
+
+296
+00:33:06,940 --> 00:33:12,660
+اللى اللى هسميها P كويس وبيدي متجة يوازن
+
+297
+00:33:34,740 --> 00:33:40,500
+طيب أجت واحدة مش عارفة الرسمة وعطيتها سؤال
+
+298
+00:33:48,170 --> 00:33:52,670
+و تلها كيلي المسافة بين هذه النقطة و هذا ال line
+
+299
+00:33:52,670 --> 00:33:56,210
+أجت على القانون اللي أخدت ال tech tech اللي طلع
+
+300
+00:33:56,210 --> 00:34:05,370
+عليه جسر الصفارة ما تفسيره كلنا لهذه الاتجاه ايوا
+
+301
+00:34:05,370 --> 00:34:11,470
+يبقى كم قالت الأخش اسمك إنت أفنان أفنان زي ما قالت
+
+302
+00:34:11,470 --> 00:34:19,220
+أختك أفنانهذه النقطة تبقى على نفس القرار المصطلح
+
+303
+00:34:30,710 --> 00:34:35,130
+معنى هذا الكلام ان هذه النقطة تقع على الخط
+
+304
+00:34:35,130 --> 00:34:40,890
+المستقيم مباشرة طيب stop لحد هنا نيجي ناخد بعض
+
+305
+00:34:40,890 --> 00:34:45,970
+الأمثلة على الكلام اللي احنا جاي له هذا اول مثال
+
+306
+00:34:45,970 --> 00:34:50,630
+examples اول
+
+307
+00:34:50,630 --> 00:34:52,310
+مثال على هذا الموضوع
+
+308
+00:34:58,400 --> 00:35:02,520
+خدنا قداش المسافة من الـ point
+
+309
+00:35:11,650 --> 00:35:18,130
+وتلاتة to the line للخط
+
+310
+00:35:18,130 --> 00:35:27,770
+المستقيم X يساوي عشرة زائد أربعة T وY يساوي ناقص
+
+311
+00:35:27,770 --> 00:35:34,270
+تلاتة وZ يساوي أربعة T
+
+312
+00:35:44,390 --> 00:35:49,670
+سؤال مرة تانية ماتيني خط مستقيم في الصيغة ال
+
+313
+00:35:49,670 --> 00:35:55,210
+parameterية وماتيني نقطة يمر بها هذا الخط المستقيم
+
+314
+00:35:55,210 --> 00:36:01,330
+أو نقطة في الفرار فجالي قداشي المسافة من هذه
+
+315
+00:36:01,330 --> 00:36:06,110
+النقطة إلى هذا ال line زي ما احنا شايفين بده نقطة
+
+316
+00:36:07,090 --> 00:36:11,850
+موجودة و الحمد لله موجودة بدي vector موازي ال line
+
+317
+00:36:11,850 --> 00:36:16,010
+اللي مطلوب يجيب المسافة بينه وبين النقطة ال vector
+
+318
+00:36:16,010 --> 00:36:20,770
+بجيبه من وين؟ من نفس المعادلة اللي عندنا يبقى باجي
+
+319
+00:36:20,770 --> 00:36:26,590
+بقول بدي أجيب ال vector الموازي لمين لهذا ال line
+
+320
+00:36:26,590 --> 00:36:29,070
+يبقى V تساوي
+
+321
+00:36:33,480 --> 00:36:39,960
+زيرو المركبة يبقى مع السلامة يبقى زائد أربعة key
+
+322
+00:36:39,960 --> 00:36:49,120
+هذا parallel to the given line
+
+323
+00:36:52,900 --> 00:36:58,120
+يبقى هذا given to the given line يبقى صار المتجه
+
+324
+00:36:58,120 --> 00:37:04,720
+الموازي موجود والنقطة موجودة تمام طيب بدي المتجه P
+
+325
+00:37:04,720 --> 00:37:12,460
+S معناته بدي النقطة P أنا عند هنا ال S يبقى ناقطي
+
+326
+00:37:12,460 --> 00:37:17,300
+النقطة المواطعة اللي هي المواطعة فوق يبقى ال S هي
+
+327
+00:37:17,300 --> 00:37:25,270
+النقطة السالف واحدة واربعة وتلاتة طيب و Pهذه
+
+328
+00:37:25,270 --> 00:37:29,510
+اللقطة اللي بمرقها الخط المستقيل اللي هي المركبة
+
+329
+00:37:29,510 --> 00:37:34,190
+الأولى لها عشرة المركبة التانية سالم تلاتة والا
+
+330
+00:37:34,190 --> 00:37:36,190
+بعدها كده؟ Zero
+
+331
+00:37:42,650 --> 00:37:49,190
+يساوي ناقص واحد ناقص عشرة ناقص واحد ناقص عشرة في
+
+332
+00:37:49,190 --> 00:37:56,530
+اتجاه ال I اللي بعده أربعة زائد تلاتة زائد أربعة
+
+333
+00:37:56,530 --> 00:38:02,910
+زائد تلاتة في اتجاه ال J اللي بعده تلاتة ناقص Zero
+
+334
+00:38:02,910 --> 00:38:11,430
+في اتجاه ال K يبقى ناقص 11 Iزائد سبعة جيب زائد
+
+335
+00:38:11,430 --> 00:38:20,390
+تلاتة كيب زائد
+
+336
+00:38:20,390 --> 00:38:21,670
+تلاتة كيب
+
+337
+00:38:27,940 --> 00:38:37,600
+الـ V يبقى الـ P S اللي هو سالب 11 7 3 ال V 404
+
+338
+00:38:37,600 --> 00:38:49,600
+طبعا I و J و K و الصفة التالت اللي هو من 4 و 0 و 4
+
+339
+00:38:49,600 --> 00:38:55,260
+بالشكل اللي عندنا يبقى بالدرجة أفك المحدد هذا 7 في
+
+340
+00:38:55,260 --> 00:39:04,630
+4تمنية وعشرين وعندك I يبقى هنا تمنية وعشرين I اللي
+
+341
+00:39:04,630 --> 00:39:11,850
+بعده نشطة بصفه عموده بصير ناقص اربعة واربعين وناقص
+
+342
+00:39:11,850 --> 00:39:15,510
+اتناشر يبقى ناقص ستة وخمسين
+
+343
+00:39:24,490 --> 00:39:31,610
+نقص تمانية وعشرين كيلو نقص تمانية وعشرين كيلو نقص
+
+344
+00:39:31,610 --> 00:39:39,010
+تمانية وعشرين كيلو نقص تمانية وعشرين
+
+345
+00:39:39,010 --> 00:39:39,550
+كيلو
+
+346
+00:39:44,550 --> 00:39:52,550
+هذا P S cross ال V بدنا طول المتجه هذا مقسوما على
+
+347
+00:39:52,550 --> 00:39:58,810
+طول مين؟ على طول ال V يرجع ال distance D بدها
+
+348
+00:39:58,810 --> 00:40:06,370
+تساوي طول ال P S cross ال V مقسوما على طول ال V و
+
+349
+00:40:06,370 --> 00:40:12,430
+يسافريبقى بدنا نروح و نربع المقادير اللي عندنا هنا
+
+350
+00:40:12,430 --> 00:40:20,170
+يبقى هذا بتساوي ال square ربما 28 تربيع خليها
+
+351
+00:40:20,170 --> 00:40:27,450
+لحالي و هذا هنا بتصير واحد زائد اربعة زائد واحد
+
+352
+00:40:27,450 --> 00:40:36,590
+مقسوما على وين ال V هي ال Vيبقى الجذر التربيعي ل
+
+353
+00:40:36,590 --> 00:40:43,350
+16 زائد 16 يبقى
+
+354
+00:40:43,350 --> 00:40:48,970
+هذا الكلام يساوي الجذر التربيعي هذه بنات اللي هي
+
+355
+00:40:48,970 --> 00:40:59,190
+أربعة تربية في سبعة تربية في ستة على و هذه اللي
+
+356
+00:40:59,190 --> 00:41:06,350
+أربعة جذر اتنىمظهر؟ طيب الأربعة الترابيه هذه لو
+
+357
+00:41:06,350 --> 00:41:12,520
+طلعت برا الجدرق وضار قداش، أربعةمظبوط بيضال جدشان
+
+358
+00:41:12,520 --> 00:41:17,540
+دي اللي هو سبعة تربية في ستة سبعة في سبعة بتسعة
+
+359
+00:41:17,540 --> 00:41:24,240
+واربعين في ستة هي تسعة واربعين في ستة ستة في تسعة
+
+360
+00:41:24,240 --> 00:41:30,320
+واربعة وخمسين ستة في أربعة واربعة وعشرين وخمسة
+
+361
+00:41:30,320 --> 00:41:37,140
+وتسعة وعشرين يبقى اتنين اربعة وتسعين على جذر اتنين
+
+362
+00:41:47,580 --> 00:41:54,060
+طيب 28 هذه اللي ربعناها و هذه اللي ربعناها مظبوط
+
+363
+00:41:54,060 --> 00:42:00,420
+يبقى هذا الطول بده يساوي تحت الجدر يبقى هذا الجدر
+
+364
+00:42:00,420 --> 00:42:05,540
+التربيعي تيجي لأ تيجي سبعة جدر ستة صحيح سبعة
+
+365
+00:42:09,660 --> 00:42:14,680
+على جدر اتنين وجدر ستة اللي هو جدر اتنين في جدر
+
+366
+00:42:14,680 --> 00:42:21,140
+تلاتة مظلوم يبقى هنا سبعة جدر اتنين جدر تلاتة على
+
+367
+00:42:21,140 --> 00:42:26,920
+جدر اتنين يبقى السابعة جدر تلاتة هذا الطول الا ان
+
+368
+00:42:26,920 --> 00:42:30,680
+الله يعطي كمان مثال
+
+369
+00:42:59,880 --> 00:43:05,380
+يبقى example two verify
+
+370
+00:43:05,380 --> 00:43:13,020
+اتأكد انه that the lines
+
+371
+00:43:13,020 --> 00:43:19,360
+الخطوط المستقيمة ال one اللي هو main اللي هو X
+
+372
+00:43:19,360 --> 00:43:26,780
+يساوي اتنين زائد T X يساوي اتنين زائد T و Y تساوي
+
+373
+00:43:26,780 --> 00:43:28,420
+ناقص اتنين
+
+374
+00:43:36,150 --> 00:43:49,550
+1-t L2 X يساوي 1 زائد 2T Y
+
+375
+00:43:49,550 --> 00:44:01,270
+يساوي 3-4T Z يساوي 5-2T R تلالي
+
+376
+00:44:05,950 --> 00:44:13,930
+and find the distance between them and find the
+
+377
+00:44:13,930 --> 00:44:21,890
+distance between them
+
+378
+00:44:44,560 --> 00:44:52,700
+هو يقول يثبت ان الخطين متوازيان ومن ثم اتل ال
+
+379
+00:44:52,700 --> 00:44:57,800
+distance ما بين الخطين المتوازيان الاتنين كويس
+
+380
+00:44:57,800 --> 00:45:01,600
+يبقى بدى اشوف هل هدول اتنين متوازيان لأ يعني هل ال
+
+381
+00:45:01,600 --> 00:45:06,560
+vector اللذي يوازي المتجه الأول يوازي ال vector
+
+382
+00:45:06,560 --> 00:45:11,120
+اللذي يوازي الخط الثاني ولا لأ فبجي بقوله الأهم
+
+383
+00:45:11,120 --> 00:45:11,720
+solution
+
+384
+00:45:33,270 --> 00:45:44,050
+2i-4j-2k parallel to l2 parallel to l2
+
+385
+00:45:49,850 --> 00:45:55,990
+V2 يساوي .. بدي أخد اتنين عامل مشترك بضل عندي I
+
+386
+00:45:55,990 --> 00:46:03,590
+نقص اتنين J نقص K اللي هو اتنين فيه هذا مين؟ اتنين
+
+387
+00:46:03,590 --> 00:46:13,350
+V1 يبقى هذا بدي يعطينا ان V1 and V2 are parallel
+
+388
+00:46:13,350 --> 00:46:26,020
+هذا بدي يعطينا ان L1 andلتو are parallel lines
+
+389
+00:46:26,020 --> 00:46:31,660
+تبقى اثبات نظر المطلوب الاول ان اتنين هدول ما لهم
+
+390
+00:46:31,660 --> 00:46:37,960
+متوازين لو جت افترضت على سبيل المثال ان هذا ال one
+
+391
+00:46:37,960 --> 00:46:45,590
+و هذا ال two الموازي لههذا L1 وهذا L2 على سبيل
+
+392
+00:46:45,590 --> 00:46:52,430
+المثال كويس يبقى ال L1 هو المستقيم الأول مظبوط بدا
+
+393
+00:46:52,430 --> 00:46:58,390
+افترض انه بيمر بنقطة ما مين النقطة اللتي يمر بها
+
+394
+00:46:58,390 --> 00:47:04,450
+المستقيم الأول 2 سالب 2 هو 1 لو افترض ان
+
+395
+00:47:11,290 --> 00:47:18,830
+و سالب اتنين و واحد نقطة تانية هنا على المستقيم
+
+396
+00:47:18,830 --> 00:47:24,550
+التاني بدي أسميها P ال P لي واحد و تلاتة و خمسة
+
+397
+00:47:24,550 --> 00:47:31,550
+يبقى واحد و تلاتة و خمسة جالي هاجل المسافة ما بين
+
+398
+00:47:31,550 --> 00:47:37,210
+الخطين المستقيمين بقوله كويس بدي أجي من هنا أنزل
+
+399
+00:47:37,210 --> 00:47:37,790
+عنوان
+
+400
+00:47:43,720 --> 00:47:53,980
+هو نفس المسافة إذا أنا صار عندى متجه اسمه yes يبقى
+
+401
+00:47:53,980 --> 00:47:59,180
+ماشي ناشي بال distance هذي بدي الموازي ل L2 من
+
+402
+00:47:59,180 --> 00:48:05,960
+الموازي ل L2 اللي هو V2 اللي عندنا هذا تمام يبقى
+
+403
+00:48:05,960 --> 00:48:13,760
+هذا المتجه اللي هو V2 اللي عندناخلصنا يبقى V موجود
+
+404
+00:48:13,760 --> 00:48:18,080
+ضايق بس أجيب له PS و بالتالي مشكلتنا خلصت يبقى
+
+405
+00:48:18,080 --> 00:48:27,540
+بتاجي لمين؟ لـPS الشكل اللي عندنا هذا يبقى 2-1 في
+
+406
+00:48:27,540 --> 00:48:31,760
+اتجاه I زائد نقص 2
+
+407
+00:48:42,150 --> 00:48:50,670
+نقص اربعة كيك نقص
+
+408
+00:48:50,670 --> 00:48:55,730
+اربعة كيك نقص اربعة كيك نقص اربعة كيك نقص اربعة
+
+409
+00:48:55,730 --> 00:48:56,490
+كيك نقص اربعة كيك نقص اربعة كيك نقص اربعة كيك نقص
+
+410
+00:48:56,490 --> 00:48:56,590
+اربعة كيك نقص اربعة كيك نقص اربعة كيك نقص اربعة
+
+411
+00:48:56,590 --> 00:48:56,610
+كيك نقص اربعة كيك نقص اربعة كيك نقص اربعة كيك نقص
+
+412
+00:48:56,610 --> 00:48:56,610
+اربعة كيك نقص اربعة كيك نقص اربعة كيك نقص اربعة
+
+413
+00:48:56,610 --> 00:48:58,290
+كيك نقص اربعة كيك نقص اربعة كيك نقص اربعة كيك نقص
+
+414
+00:48:58,290 --> 00:49:05,310
+اربعة كيك نقص اربعة كيك نقص اربعة كي
+
+415
+00:49:14,520 --> 00:49:25,120
+عشرة ناقص ستة في اتجاه الاعلى مرتين عشرة بالموجة
+
+416
+00:49:25,120 --> 00:49:29,360
+سالب ستة يظل سالب ستة في اتجاه الاعلى ليه بعد؟
+
+417
+00:49:33,410 --> 00:49:40,990
+زائد تمانية يبقى ضل زائد سبعة مع شرط الناقص بناقص
+
+418
+00:49:40,990 --> 00:49:46,950
+سبعة genes اتنين
+
+419
+00:49:46,950 --> 00:49:53,030
+و تمانية صح ستة كلامك مظبوط أصابت امرأة وأختها عمر
+
+420
+00:49:57,100 --> 00:50:03,960
+مشط بصفه وعموده يبقى ناقص أربعة وزائد عشرة بغير
+
+421
+00:50:03,960 --> 00:50:12,340
+زائد ستة يبقى زائد ستة K الان بدي أجيب قداش الطول
+
+422
+00:50:12,340 --> 00:50:16,640
+تبعه أو بدي أجيب ال distance دي يبقى ال distance
+
+423
+00:50:16,640 --> 00:50:25,400
+دي بدها تساوي طول ال PS cross ال V2 مقسوماعلى قول
+
+424
+00:50:25,400 --> 00:50:32,380
+الـ V2 ويساوي الجدرى التربية طول الـ PSI يبقى 36
+
+425
+00:50:32,380 --> 00:50:41,520
+زائد 36 زائد 36 على الجدرى التربية الى V2 اللي هو
+
+426
+00:50:41,520 --> 00:50:44,140
+4 زائد 16
+
+427
+00:50:47,830 --> 00:50:52,830
+كل جدر واحد ستة و تلاتين و ستة و تلاتين و ستة و
+
+428
+00:50:52,830 --> 00:50:54,450
+تلاتين و ستة و تلاتين و ستة و تلاتين و ستة و
+
+429
+00:50:54,450 --> 00:50:58,370
+تلاتين و ستة و تلاتين و ستة و تلاتين و ستة و
+
+430
+00:50:58,370 --> 00:51:02,910
+تلاتين و ستة و تلاتين و ستة و تلاتين و ستة و
+
+431
+00:51:02,910 --> 00:51:03,610
+تلاتين و ستة و تلاتين و ستة و تلاتين و ستة و
+
+432
+00:51:03,610 --> 00:51:05,350
+تلاتين و ستة و تلاتين و ستة و تلاتين و ستة و
+
+433
+00:51:05,350 --> 00:51:05,350
+تلاتين و ستة و تلاتين و ستة و تلاتين و ستة و
+
+434
+00:51:05,350 --> 00:51:12,750
+تلاتين و ستة و تلاتين و ستة و تلاتين و ستة و
+
+435
+00:51:12,750 --> 00:51:18,660
+تلاتين و ستيبقى على أربعة فيها اتنين وتمانية
+
+436
+00:51:18,660 --> 00:51:22,940
+وعشرين على أربعة فيها السبعة وعشرين وعلى أربعة
+
+437
+00:51:22,940 --> 00:51:29,720
+فيها ستة وعلى تلاتة فيها تسعة وعلى تلاتة فيها
+
+438
+00:51:29,720 --> 00:51:36,280
+اتنين يبقى تلاتة على جذر اتنين هذه المسافة ما بين
+
+439
+00:51:36,280 --> 00:51:43,920
+الخطين المتوازين اللي عندناطيب نجي الان بنطلع
+
+440
+00:51:43,920 --> 00:51:49,240
+النقطة الثالثة من هذا ال section النقطة التالتة
+
+441
+00:51:49,240 --> 00:51:54,460
+equation of
+
+442
+00:51:54,460 --> 00:51:58,220
+a plane
+
+443
+00:51:58,220 --> 00:51:59,860
+in space
+
+444
+00:52:08,810 --> 00:52:14,950
+يجب أن نجي لمعادلة المستوى في الفرق سواء كان مستوى
+
+445
+00:52:14,950 --> 00:52:18,450
+أفقي أو رأسي أو مائي أو كيف ما يكون يكون لدينا
+
+446
+00:52:18,450 --> 00:52:25,790
+مشكلة لدينا معادلة عامة لهذا المستوى باستخدام ال
+
+447
+00:52:25,790 --> 00:52:26,130
+vector
+
+448
+00:52:30,790 --> 00:52:35,550
+معادلة هذا المستوى بلزمني ال vector عمودي عليه
+
+449
+00:52:35,550 --> 00:52:41,110
+وبلزمني النقطة يمر بيه لهذا المستوى بس شغلتين زي
+
+450
+00:52:41,110 --> 00:52:45,330
+ما في ال line بدي مسافة بين و بين هذا ال line بدي
+
+451
+00:52:45,330 --> 00:52:51,110
+نقطة و بدي متجهي ودي لأ انا بدي متجه عمودي عليه
+
+452
+00:52:58,860 --> 00:53:06,560
+و قلت هذا المستوى و روحت سميت هذا المستوى M أخدت
+
+453
+00:53:06,560 --> 00:53:13,400
+متجه عمودي عليه بهذا الشكل طلع هذا المتجه اللي هو
+
+454
+00:53:13,400 --> 00:53:23,260
+عمودي عليه و سميته المتجه N A I زائد B J زائد C K
+
+455
+00:53:23,260 --> 00:53:31,750
+مثلا قاطعوا النقطة اللي عندناتمام؟ المتجر هذا
+
+456
+00:53:31,750 --> 00:53:38,930
+epsilon مر في نقطة و التكن النقطة في نوضه x نوضه و
+
+457
+00:53:38,930 --> 00:53:44,450
+y نوضه و z نوضهتبقى عني معلومة عندي شغلتين الآن
+
+458
+00:53:44,450 --> 00:53:50,690
+تمام منتجة عمودي على المستوى و نقطة تقع في المستوى
+
+459
+00:53:50,690 --> 00:53:54,990
+يعني امر بها هذا المستوى من خلال الكلام اللي
+
+460
+00:53:54,990 --> 00:54:01,970
+قدامنا هذا بدي احاول اجيب قداش معادلة هذا المستوى
+
+461
+00:54:01,970 --> 00:54:07,070
+بقول كويس عشان اجيب المعادلة بروح اخد اي نقطة
+
+462
+00:54:07,070 --> 00:54:12,890
+موجودة في هذا المستوىطبعاً بنذكركم بشغلة لو قلت أي
+
+463
+00:54:12,890 --> 00:54:17,430
+مستوى الطاولة اللي عندنا هنا وهذا متجه عمودي على
+
+464
+00:54:17,430 --> 00:54:22,990
+الطاولة إذا عمودي على أي متجه أو أي مستقيم موجود
+
+465
+00:54:22,990 --> 00:54:27,630
+في مستوى الطاولة اللي عندنا هنا تمام يبقى بناء
+
+466
+00:54:27,630 --> 00:54:36,330
+عليه لو أخدت نقطة تانية هنا وسميتها XYZ أو ال P
+
+467
+00:54:36,330 --> 00:54:38,310
+XYZ
+
+468
+00:54:42,080 --> 00:54:50,480
+يوجد متجة من P نود الى P بهذه الشكلة ايش علاقة
+
+469
+00:54:50,480 --> 00:54:57,720
+متجة P نود P بالمتجة L ايوة اتنين are orthogonal
+
+470
+00:54:57,720 --> 00:55:06,340
+يبقى هنا باجي بقوله ده او نقول ان كلمتين قبل بحط
+
+471
+00:55:06,340 --> 00:55:06,980
+المعادلة
+
+472
+00:55:13,210 --> 00:55:26,730
+that أنه the plane M passes .. passes through الـ
+
+473
+00:55:26,730 --> 00:55:35,790
+P node و X node و Y node و Z node and normal to
+
+474
+00:55:35,790 --> 00:55:44,720
+the vectorوعمودي على المتجد N وA في اتجاه I P في
+
+475
+00:55:44,720 --> 00:55:51,180
+اتجاه الـ J وC في اتجاه الـ K let
+
+476
+00:55:51,180 --> 00:56:03,720
+P أو X أو Y أو Z be any point أو be a point نقطة
+
+477
+00:56:03,720 --> 00:56:13,270
+in the planeم الان
+
+478
+00:56:13,270 --> 00:56:26,890
+ال vector n او ال vectors n and ال P note PR او
+
+479
+00:56:26,890 --> 00:56:27,430
+orthogonal
+
+480
+00:56:37,270 --> 00:56:47,570
+يبقى معنى هذا الكلام ان ال vector اولا ال N dot P
+
+481
+00:56:47,570 --> 00:56:50,350
+not P بده يساوي زيه
+
+482
+00:56:54,990 --> 00:57:02,590
+بدي أشيل ال N و أضع القيمة بتاعي يبقى AI زائد BJ
+
+483
+00:57:02,590 --> 00:57:09,830
+زائد CK Dot المتجهة الثانية المتجهة التانية اللي
+
+484
+00:57:09,830 --> 00:57:17,750
+هو X ناقص X node في اتجاه ال I زائد Y ناقص Y node
+
+485
+00:57:17,750 --> 00:57:25,370
+في اتجاه ال J Z ناقص Z node كله في اتجاهالـ K كل
+
+486
+00:57:25,370 --> 00:57:31,770
+هذا الكلام يجب أن يسوى كم؟ يجب أن يسوى 0 نعمل الـ
+
+487
+00:57:31,770 --> 00:57:37,930
+dot product فيما بينهم يبقى صار الـ A في الـ X مقص
+
+488
+00:57:37,930 --> 00:57:44,610
+الـ X knot زائد B في الـ Y مقص الـ Y knot زائد C
+
+489
+00:57:44,610 --> 00:57:46,010
+في الـ Z مقص
+
+490
+00:57:58,130 --> 00:58:01,870
+بالسالب هضيفها على الشجة اليمين
+
+491
+00:58:11,600 --> 00:58:18,120
+الان ال X0 وY0 وZ0 نقاط معلومة أو مركبات معلومة ال
+
+492
+00:58:18,120 --> 00:58:22,340
+A والB والC هي المركبات المتجه العمودي المعلومة
+
+493
+00:58:22,340 --> 00:58:28,000
+إذاً هذا كله يشكل لقداشا بنات رقم واحد يبقى صلة
+
+494
+00:58:28,000 --> 00:58:34,780
+المعادلة AX زائد BY زائد C زاد
+
+495
+00:58:37,860 --> 00:58:46,740
+رقم واحد وليكن دي ودي بيكون اكس نوت بي نوت سي زي
+
+496
+00:58:46,740 --> 00:58:51,420
+نوت طيب؟
+
+497
+00:58:51,420 --> 00:58:58,440
+طيب كويس يبقى احنا جيبنا هذه معادلة ال equation
+
+498
+00:58:58,440 --> 00:59:12,100
+يبقى هذه ده equation of theA plane M إذا من الآن
+
+499
+00:59:12,100 --> 00:59:18,280
+فصاعدا مشان أجيب معادلة plane بدي متجه عمودي على
+
+500
+00:59:18,280 --> 00:59:22,500
+هذا ال plane اتنين بده نقطة يمر بها ال plane
+
+501
+00:59:22,500 --> 00:59:27,020
+وبالتالي بصير المعادلة بسيطة جدا حد بتحب تسأل أي
+
+502
+00:59:27,020 --> 00:59:32,740
+سؤال هنا قبل أن نذهب إلى الأمثلة لابد تسأل تسأل
+
+503
+00:59:36,570 --> 00:59:42,450
+إيش في حياة؟ قالت عايشة رضي الله عنها تسأل النبي
+
+504
+00:59:42,450 --> 00:59:47,690
+صلى الله عليه وسلم عن أدق الأشياء في حياة
+
+505
+00:59:52,690 --> 00:59:57,730
+السنة بيجي الصحابة يسألوها عن تصرف النبي صلى الله
+
+506
+00:59:57,730 --> 01:00:04,150
+عليه وسلم لذلك أحلى ما نقول حاجة تسألي ماتضلقيش
+
+507
+01:00:04,150 --> 01:00:09,750
+ساكتة وتعودي أنك تسألي حتى لو كان سوالك غلط تسألي
+
+508
+01:00:09,750 --> 01:00:12,790
+غلط كل مرة جاي تسألي غلط غلط تسألي صحي
+
+509
+01:00:21,210 --> 01:00:26,070
+لكن من خلال التساؤل بتثبت المعلوم غالب المال
+
+510
+01:00:26,070 --> 01:00:32,850
+والمال وزميلاتك بصير انت قدوة لهم حاضر بالنسبالي
+
+511
+01:00:32,850 --> 01:00:37,610
+سؤال عدلة ال plane اللي كانت عليه شكل ax زي بي زي
+
+512
+01:00:37,610 --> 01:00:41,830
+cz يساوي d حيث ال a والb والc هي المركبات المتجهة
+
+513
+01:00:41,830 --> 01:00:47,840
+العمودي على ال planeالان بدأ ناخد أمثلة على هذا
+
+514
+01:00:47,840 --> 01:00:54,640
+الكلام أول
+
+515
+01:00:54,640 --> 01:01:02,540
+بدا يقول find an
+
+516
+01:01:02,540 --> 01:01:10,700
+equation for the plane
+
+517
+01:01:10,700 --> 01:01:12,000
+satisfying
+
+518
+01:01:18,630 --> 01:01:27,030
+الأولى نمر ايه؟ the plane passes
+
+519
+01:01:27,030 --> 01:01:33,490
+through يمر
+
+520
+01:01:33,490 --> 01:01:42,310
+بالنقطة اللي هي P والي حدثية تبعتها اتنين واربعة
+
+521
+01:01:42,310 --> 01:01:47,250
+وخمسةand perpendicular to the line and
+
+522
+01:01:47,250 --> 01:01:50,570
+perpendicular
+
+523
+01:01:50,570 --> 01:01:53,950
+to
+
+524
+01:01:53,950 --> 01:01:58,450
+the line الخط
+
+525
+01:01:58,450 --> 01:02:08,910
+المستقيم X يساوي خمسة زائد T وال Y يساوي واحد زائد
+
+526
+01:02:08,910 --> 01:02:12,090
+تلاتة T وال Z يساوي
+
+527
+01:02:20,570 --> 01:02:27,870
+هذه معادلة المستوى اللي يحقق نمر أيه ال plane يمر
+
+528
+01:02:27,870 --> 01:02:33,790
+بالنقطة هذه وفي نفس لقطة عمودي على هذا الخط أنا مش
+
+529
+01:02:33,790 --> 01:02:39,540
+هنجيب معادلة ال plane بدي نقطة يمر بهاومين؟ متجه
+
+530
+01:02:39,540 --> 01:02:44,120
+عمودي على هذا الكليل هو أجلب لهذا الكليل عمودي على
+
+531
+01:02:44,120 --> 01:02:50,480
+الخط المستقيم هل أنا بقدر أجيب متجه يوازي هذا الخط
+
+532
+01:02:50,480 --> 01:02:57,020
+المستقيم؟ اللي هو مين؟ تمام يبقى باجي بقوله هنا
+
+533
+01:02:57,020 --> 01:03:04,420
+solution the vector اللي
+
+534
+01:03:04,420 --> 01:03:04,680
+هو
+
+535
+01:03:07,560 --> 01:03:18,160
+يبقى I زائد تلاتة J زائد أربعة K parallel to the
+
+536
+01:03:18,160 --> 01:03:27,100
+given line طب قالي لـ plane عمودي على هذا ال line
+
+537
+01:03:27,100 --> 01:03:31,980
+إذا لـ plane عمودي على هذا ال vector يبقى هذا
+
+538
+01:03:31,980 --> 01:03:36,600
+يعطينا ان ال vector
+
+539
+01:03:38,420 --> 01:03:49,820
+اللي هو سمته V is normal to the plane يبقى هذا
+
+540
+01:03:49,820 --> 01:03:56,540
+عمودي على مين على مسافة صار ال vector العمودي على
+
+541
+01:03:56,540 --> 01:04:02,160
+ال plane معروف والنقطة معروفة يبقى هذه تعويض مباشر
+
+542
+01:04:02,160 --> 01:04:12,560
+يبقى بقى اللي بقول ال question ofالمطلع العمودي
+
+543
+01:04:12,560 --> 01:04:18,440
+AX
+
+544
+01:04:18,440 --> 01:04:24,900
+يساوي ازايد BY زايد CZ
+
+545
+01:04:31,530 --> 01:04:38,070
+بنصارى عندى هنا I بواحد يبقى X الـ P بثلاثة والـ C
+
+546
+01:04:38,070 --> 01:04:44,110
+باربعة زده بدي نسوي واحد في ال X نوض اللى بقداش
+
+547
+01:04:44,110 --> 01:04:51,910
+اتنين زائد تلاتة في ال Y نوض اللى اربعة زائد اللى
+
+548
+01:04:51,910 --> 01:04:58,390
+هو C اللى باربعة في قداش P خمسة يبقى قصيرة ان هنا
+
+549
+01:04:58,390 --> 01:04:59,790
+قداش ال X
+
+550
+01:05:21,810 --> 01:05:26,470
+هذا المطلوب الأول من السؤال المطلوب التاني
+
+551
+01:05:35,570 --> 01:05:43,650
+passes through يمر
+
+552
+01:05:43,650 --> 01:05:52,430
+بـ the intersecting
+
+553
+01:05:52,430 --> 01:06:02,450
+lines يمر بالخطين المتقطعين اللي هو L1 المعادلات
+
+554
+01:06:02,450 --> 01:06:12,250
+هي Xيساوي T وال Y تساوي اتنين ناقص T وال Z تساوي
+
+555
+01:06:12,250 --> 01:06:23,750
+واحد زائد T وال L تو معادلته اللي هو X يساوي اتنين
+
+556
+01:06:23,750 --> 01:06:29,830
+زائد اتنين S وال Y بدها تساوي
+
+557
+01:06:34,290 --> 01:06:48,110
+تساوي ستة زائد خمس اسم الشكل اللي عندنا هذا كويس
+
+558
+01:06:48,110 --> 01:06:49,890
+مرتين
+
+559
+01:06:51,690 --> 01:06:56,830
+سؤال بيقول مياتي أنا عندي plane ال plane هذا يمر
+
+560
+01:06:56,830 --> 01:07:03,150
+بخطين مستقيمين متقاطعين يعني لو تصورت هذول اتنين
+
+561
+01:07:03,150 --> 01:07:08,930
+في مستوى رقاطة يبقوا مروا بهم مين؟ مستوى المستوى
+
+562
+01:07:08,930 --> 01:07:13,030
+هذا انا بدي المعادلة تبعه عشان اجيب المعادلة تبعه
+
+563
+01:07:13,030 --> 01:07:15,570
+فبدي نقطة تقع فيه
+
+564
+01:07:25,310 --> 01:07:32,570
+عروضي على الإثنين يعني عروضي على مستويهم مشان هيك
+
+565
+01:07:32,570 --> 01:07:41,950
+بدنا نروح نجيب المتجه الأول الموازي ل L1 يجيب V1
+
+566
+01:07:41,950 --> 01:07:53,530
+اللي هو بده يساوي I وهنا ناقص J وهنا زائد K هذا
+
+567
+01:07:53,530 --> 01:08:04,790
+parallelto L1 و ال V2 طبعا هنا بقول solution أول و
+
+568
+01:08:04,790 --> 01:08:14,850
+ال V2 يساوي 2I وهنا زائد J وهنا زائد خمسة K
+
+569
+01:08:14,850 --> 01:08:18,030
+parallel to L2
+
+570
+01:08:25,350 --> 01:08:31,310
+Okay وركبات ال V1 واحد و سالب واحد و واحد وركبات
+
+571
+01:08:31,310 --> 01:08:38,370
+ال V2 اتنين و واحد و خمسة بالشكل العام بدي افك هذا
+
+572
+01:08:38,370 --> 01:08:43,430
+المحدد يعني هذا الكلام بدرساه سالب خمسة و سالب
+
+573
+01:08:43,430 --> 01:08:50,410
+واحد و سالب ستة في اتجاه ال R اللي بعده خمسة نقص
+
+574
+01:08:50,410 --> 01:08:57,820
+اتنين و ناقص تلاتة في اتجاه ال Jاللي بعده واحد
+
+575
+01:08:57,820 --> 01:09:03,760
+زائد اتنين زائد تلاتة كيلو يبقى زائد تلاتة كيلو
+
+576
+01:09:03,760 --> 01:09:09,900
+إذا هذا المتجه عمودي على المتجهين الإتنين يبقى
+
+577
+01:09:09,900 --> 01:09:22,060
+عمودي على مستويهما this vector is normal to the
+
+578
+01:09:22,060 --> 01:09:23,340
+plate
+
+579
+01:09:25,460 --> 01:09:30,280
+هذا جيد، فجبت المتجه العمودي على المستوى، بدي نقطة
+
+580
+01:09:30,280 --> 01:09:37,210
+تقع في هذا المستوى، في كام واحدة؟ انت ..المفصقين
+
+581
+01:09:37,210 --> 01:09:42,170
+الاتنين يقعوا في الـ plan كل واحد منهم يمر بنقطة
+
+582
+01:09:42,170 --> 01:09:47,050
+يبقى هاي الحمد للار نحط البركة بدل النقطة خدي أي
+
+583
+01:09:47,050 --> 01:09:51,530
+واحدة فيهم و بيطلع نفسي المعادلة نحط النقطة الأولى
+
+584
+01:09:51,530 --> 01:09:56,310
+والنقطة الثانية سيال ماتطلعاش نفسي المعادلة اذا
+
+585
+01:09:56,310 --> 01:10:04,530
+بدأت اقول take مثلا P not herاللي هي واحد .. ايه
+
+586
+01:10:04,530 --> 01:10:17,590
+قصدي؟ Zero واتنين وواحد that lie on the line L1
+
+587
+01:10:17,590 --> 01:10:22,650
+ومن
+
+588
+01:10:22,650 --> 01:10:28,650
+ثم تقع وين؟ تقع على ال flame التي تقع on the line
+
+589
+01:10:28,650 --> 01:10:38,810
+L1 and onلـ plane وكذلك على المستوى إذا المتجه
+
+590
+01:10:38,810 --> 01:10:45,630
+موجود يبقى بالدعوة الضغطية يبقى ناقص ستة X ناقص
+
+591
+01:10:45,630 --> 01:10:54,250
+تلاتة Y زائد تلاتة Z يساوي ناقص ستة في Zero وهنا
+
+592
+01:10:54,250 --> 01:11:00,860
+ناقص تلاتة في اتنين وهنا زائد تلاتة في واحدإذا صرت
+
+593
+01:11:00,860 --> 01:11:06,860
+المعادلة ناقص ستة X ناقص تلاتة Y زائد تلاتة Z
+
+594
+01:11:06,860 --> 01:11:13,980
+يساوي ناقص ستة وزائد تلاتة يبقى ناقص تلاتة أو ممكن
+
+595
+01:11:13,980 --> 01:11:21,600
+أقول لو قسم كله على ناقص تلاتةمضال قداش عندي اتنين
+
+596
+01:11:21,600 --> 01:11:29,600
+X زائد Y ناقص Z يساوي كده؟ يساوي واحد هذه معادلة
+
+597
+01:11:29,600 --> 01:11:40,420
+plane المطلوبة طيب نمرسي من السؤال جالس اتنين فاصل
+
+598
+01:11:40,420 --> 01:11:48,000
+اترونيكوينز اتنين فاصل اترونيكوينز
+
+599
+01:11:49,790 --> 01:12:01,510
+the point اللذي يمر بالخط المستقيم P2 1-1 and
+
+600
+01:12:01,510 --> 01:12:11,090
+perpendicular to
+
+601
+01:12:11,090 --> 01:12:18,550
+the line of intersection to the line of
+
+602
+01:12:21,980 --> 01:12:30,160
+Intersection of the planes ده
+
+603
+01:12:30,160 --> 01:12:34,380
+المستويات الإتنين اللي هو اتنين X
+
+604
+01:12:39,550 --> 01:12:46,610
+هو ال X زائد اتنين Y زائد Z
+
+605
+01:13:22,370 --> 01:13:27,150
+نرجع لسؤالنا مرة تانية بيقول يبدي معاكد plane اللي
+
+606
+01:13:27,150 --> 01:13:32,030
+يمر بهذه النقطة الحمد لله تمام، ضال عند مين؟ متجه
+
+607
+01:13:32,030 --> 01:13:37,770
+عمودي عليه، بقول له أيوة and perpendicular to the
+
+608
+01:13:37,770 --> 01:13:41,330
+line of intersection of the two planes وهذا ال
+
+609
+01:13:41,330 --> 01:13:47,030
+plane عمودي على خط تقاطع ال two planes اللي عندنا
+
+610
+01:13:47,030 --> 01:13:54,330
+هذاتمام؟ ايوة، الان بدي اشوف خط التقاط على هذا
+
+611
+01:13:54,330 --> 01:13:59,230
+اللي عندنا ع جل ال employment يكون عمود الانتقال
+
+612
+01:13:59,230 --> 01:14:06,690
+ده هو الشكل وهي اسم العالم وهدي دفترك معاكي، تسيب
+
+613
+01:14:06,690 --> 01:14:08,190
+الشنطة وهدي دفترك معاكي
+
+614
+01:14:17,480 --> 01:14:26,140
+تمام تمام خليه هك موجه على البنات هى
+
+615
+01:14:26,140 --> 01:14:29,820
+عندى بنات الصفحاتين اللى اجبرتهم اعتبرهم مستويين
+
+616
+01:14:29,820 --> 01:14:36,330
+متقاطعينإذا في عندي متجه عمودي على المستوى الأول
+
+617
+01:14:36,330 --> 01:14:41,630
+وفي متجه تاني عمودي على المستوى الثاني لو ما
+
+618
+01:14:41,630 --> 01:14:46,530
+عملتلهم cross product بيطلع متجه عمودي على الاتنين
+
+619
+01:14:46,530 --> 01:14:52,010
+يعني موازي لمين؟ موازي لخط التقاطع يبقى ليه plane
+
+620
+01:14:52,010 --> 01:14:57,650
+العمودي على خط التقاطع بيكون عمودي على مين؟ على
+
+621
+01:14:57,650 --> 01:15:02,120
+تبع ال cross product اللي عندنامرة تانية بقول انا
+
+622
+01:15:02,120 --> 01:15:10,100
+عندى هذا plane و هذا plane اتخذت
+
+623
+01:15:10,100 --> 01:15:15,020
+المتجه هذا عمودي على ال plane الأولوالمتجه هذا
+
+624
+01:15:15,020 --> 01:15:19,080
+عمودي على ال plane التاني عملتله cross product
+
+625
+01:15:19,080 --> 01:15:25,860
+بيطلع متجه موازي لخط التقاطة تمام؟ بالمتجه الموازي
+
+626
+01:15:25,860 --> 01:15:30,020
+لخط التقاطة بيكون عمودي على مين؟ على ال plane
+
+627
+01:15:30,020 --> 01:15:35,520
+المطلوب وهذا حصل الكلام اللي شفته هذا على الطبيعة
+
+628
+01:15:35,520 --> 01:15:45,070
+بدنا نحسبه حساباطيب نجي الأن لل planes هذول بدي
+
+629
+01:15:45,070 --> 01:15:50,090
+أجيب العمودي على كل plane من ال planes اللي عندنا
+
+630
+01:15:50,090 --> 01:15:58,650
+هذا يبقى فاللي بقوله هي ال solution ان
+
+631
+01:15:58,650 --> 01:16:09,570
+ال vector اللي عندنا هذا معنو Normal to the first
+
+632
+01:16:09,570 --> 01:16:10,230
+plane
+
+633
+01:16:13,240 --> 01:16:19,580
+او بدنا نحط لحظة شوية هنا بدنا نكتب قداش يساوي انه
+
+634
+01:16:19,580 --> 01:16:28,340
+اللي هو بده يساوي اتنين I اتنين I زائد G ناقص K
+
+635
+01:16:28,340 --> 01:16:41,840
+زائد G ناقص K هذا normal to the first plane على
+
+636
+01:16:41,840 --> 01:16:48,300
+المستوى الأولان اتنين متجه التاني بدي اسافر اللي
+
+637
+01:16:48,300 --> 01:16:55,720
+هو I زائد اتنين G زائد K I زائد اتنين G زائد K
+
+638
+01:16:55,720 --> 01:17:03,900
+normal to the second plane في المستوى التالف
+
+639
+01:17:12,490 --> 01:17:14,070
+الجهد اللي بده يعطينا
+
+640
+01:17:51,390 --> 01:17:58,810
+مالغة ده parallel to the line of intersection of
+
+641
+01:17:58,810 --> 01:18:08,610
+the two planes يبقى هذا vector parallel to the
+
+642
+01:18:08,610 --> 01:18:15,350
+line of intersection
+
+643
+01:18:16,850 --> 01:18:26,550
+of the two planes يبقى ايش علاقته بالـ plane اللي
+
+644
+01:18:26,550 --> 01:18:36,230
+مطلوب عمودي عليه هذا parallel and hence ومن ثم
+
+645
+01:18:36,230 --> 01:18:44,210
+normal to the plane يبقى
+
+646
+01:18:44,210 --> 01:18:49,610
+صار فيه نقطة في الـ planeوفي متجه عمودي عليه بس
+
+647
+01:18:49,610 --> 01:18:57,470
+قصتنا زالة يبقى باجي بقول له تلاتة X ناقص تلاتة Y
+
+648
+01:18:57,470 --> 01:19:04,650
+زائد تلاتة Z بده يساوي تلاتة فيه إحداث النقطة قديش
+
+649
+01:19:04,650 --> 01:19:09,130
+قلي اتنين وهنا ناقص تلاتة في
+
+650
+01:19:14,600 --> 01:19:24,680
+يبقى هذا الكلام يبقى يساوي 6-3-3 ويساوي 0 يبقى 3x
+
+651
+01:19:24,680 --> 01:19:36,100
+-3y زائد 3z يساوي 0 او x-y زائد z يساوي 0 هذه
+
+652
+01:19:36,100 --> 01:19:39,740
+معادلة ال plane المطلوبة
+
+653
+01:19:43,740 --> 01:19:50,260
+طيب نعطي كمان مثال ان
+
+654
+01:19:50,260 --> 01:19:54,760
+تلاحظك كل مثال بفكرة مختلفة يعني هذا A و B و C
+
+655
+01:19:54,760 --> 01:19:59,500
+كأنه إيه السؤال لحاله منفصل عن B منفصل عن C يبقى
+
+656
+01:19:59,500 --> 01:20:01,440
+هذه أسئلة منفصلة عن بعض
+
+657
+01:20:18,540 --> 01:20:27,280
+المثال الثاني هو أن
+
+658
+01:20:27,280 --> 01:20:33,520
+تجد نقطة الانتقال تجد نقطة
+
+659
+01:20:33,520 --> 01:20:37,160
+الانتقال
+
+660
+01:20:37,160 --> 01:20:43,600
+نقطة
+
+661
+01:20:43,600 --> 01:20:45,480
+التقاطع للطريقة
+
+662
+01:20:49,280 --> 01:21:02,300
+للخط المستقيم X بده يساوي اتنين زائد تلاتة T وال Y
+
+663
+01:21:02,300 --> 01:21:12,760
+يساوي ناقص اربعة T وال Z يساوي خمسة زائد T خمسة
+
+664
+01:21:12,760 --> 01:21:16,480
+زائد T with اتنين with
+
+665
+01:21:18,360 --> 01:21:29,260
+إتنين مع المستوى اللي هو قداشة أربعة X زائد خمسة Y
+
+666
+01:21:29,260 --> 01:21:36,380
+زائد خمسة Y نقص اتنين Z يساوي تمانتاش
+
+667
+01:21:47,210 --> 01:21:53,730
+مثال ثاني قال لهذا النقطة التقاطة الخط المستقيم
+
+668
+01:21:53,730 --> 01:21:59,470
+المُعطَر في صيغة البرامج هي بمعادلات الـ 3 X سواء
+
+669
+01:21:59,470 --> 01:22:07,410
+2 زائد 3T Y سواء نقص 4T Z سواء 5 زائد T مع الـ
+
+670
+01:22:07,410 --> 01:22:10,770
+Plane يبقى أنا عند الـ Plane و فيه خط مستقيم
+
+671
+01:22:10,770 --> 01:22:16,020
+اتقاطعوا مع بعضبدي قداش احداثي النقطة التقاطعة
+
+672
+01:22:16,020 --> 01:22:20,900
+اللى موجودة عندنا تمام بقول يعني ايش يعني النقطة
+
+673
+01:22:20,900 --> 01:22:25,460
+مشتركة ما بين الخط المستقيم و ما بين ال main و ما
+
+674
+01:22:25,460 --> 01:22:29,220
+بين ال plain يبقى بدي احداثي النقطة اللى عندنا هذا
+
+675
+01:22:29,220 --> 01:22:36,060
+يبقى عند التقاطعة بتكون x و y و z هذه هي x و y و z
+
+676
+01:22:36,060 --> 01:22:46,120
+هذه صح ولا لأ يبقى باجي بقوله هناthe point of
+
+677
+01:22:46,120 --> 01:22:49,480
+intersection
+
+678
+01:22:49,480 --> 01:23:01,060
+we have نحصل علامات اربع في اتنين
+
+679
+01:23:01,060 --> 01:23:13,720
+زائد تلاتة T اللي بعدها زائد خمسةنقص اربعة T نقص
+
+680
+01:23:13,720 --> 01:23:21,540
+اتنين في زي خمسة زائد T كله بتسوي تقريبا تمانية
+
+681
+01:23:21,540 --> 01:23:28,540
+عشر لأن X هنا وهي X هنا وY هنا وهنا عند نقطة
+
+682
+01:23:28,540 --> 01:23:34,560
+التقاطع مشتركة ما بين الاتنين طب بدأ افكر تمانية
+
+683
+01:23:34,560 --> 01:23:36,460
+زائد اتناشر
+
+684
+01:23:40,210 --> 01:23:47,630
+-20T-10-2T-18
+
+685
+01:24:02,280 --> 01:24:09,100
+عشرة T وعندك هنا ضالانه سالب عشر فقط و تمانية أفضل
+
+686
+01:24:09,100 --> 01:24:13,800
+قدر سالي باتنين واتيهم على الشكة التانية بده يساوي
+
+687
+01:24:13,800 --> 01:24:21,000
+عشرين ومنها T تساوي قدر سالي باتنين فلو كانت T
+
+688
+01:24:21,000 --> 01:24:26,000
+بسالي باتنين بصير التقاطع ما بين ال line و ما بين
+
+689
+01:24:26,000 --> 01:24:32,000
+من و ما بين اللي فلانيجب ان اضع مكانها سالك اتنين
+
+690
+01:24:32,000 --> 01:24:37,660
+في معادلة الخط المستقيم بحصل على نقطة التقطة اللي
+
+691
+01:24:37,660 --> 01:24:48,840
+بروح بقوله هنا the point of intersection of X, Y,
+
+692
+01:24:49,460 --> 01:24:58,320
+Zاليك صندوق جديد بإتنين زائد تلاتة في ناقص اتنين
+
+693
+01:24:58,320 --> 01:25:07,160
+ال Y ناقص اربعة في T اللي هي ناقص اتنين وال Z خمسة
+
+694
+01:25:07,160 --> 01:25:13,880
+ناقص اتنين يبقى هذه بدها تساوي ناقص اربعة
+
+695
+01:25:16,650 --> 01:25:22,530
+وهنا تلاتة يبقى هذه النقطة تقاطع المستوى مع ال
+
+696
+01:25:22,530 --> 01:25:31,150
+plane الان نعطي كمان مثال example
+
+697
+01:25:50,760 --> 01:25:59,240
+المعادلة الفارامترية of
+
+698
+01:25:59,240 --> 01:26:10,100
+the line of intersection of
+
+699
+01:26:10,100 --> 01:26:20,960
+the planesبالمستويات الاتنين تلاتة X ناقص ستة Y
+
+700
+01:26:20,960 --> 01:26:30,620
+ناقص اتنين Z يسوى تلاتة و اتنين X زائد Y اتنين X
+
+701
+01:26:30,620 --> 01:26:35,120
+زائد Y ناقص اتنين Z يسوى مان
+
+702
+01:27:12,310 --> 01:27:16,290
+سؤال مرة تانية بيقول لي هذه المعادلات ال
+
+703
+01:27:16,290 --> 01:27:22,530
+parameterية للخط المستقيم اللي هو عبارة عن تقاطة ل
+
+704
+01:27:22,530 --> 01:27:26,630
+planes طب لما طلعنا احد الطالبات برا اتجه لضفنك
+
+705
+01:27:26,630 --> 01:27:31,810
+شوية طب كان عندنا two planes بالشكل اللي عندنا
+
+706
+01:27:31,810 --> 01:27:39,750
+اتنين و تقاطين في الحرف اللي عندنالأن بالقاطة وفي
+
+707
+01:27:39,750 --> 01:27:45,590
+الخط المستقيم نريد كمية المعادلات البرامدرية لهذا
+
+708
+01:27:45,590 --> 01:27:51,130
+قطار المستقيم لذلك أنا لن أجلب المعادلة البرامدرية
+
+709
+01:27:51,130 --> 01:27:58,770
+لهذا القطار المستقيم بل أجلب متجة يورزين تمام؟
+
+710
+01:27:58,770 --> 01:28:02,370
+ورغم ذلك نريد نقطة تقع عليه
+
+711
+01:28:17,540 --> 01:28:24,720
+و احنا رسمنا ال two vectors العمليات على الاتنين و
+
+712
+01:28:24,720 --> 01:28:29,740
+عملنا cross product بدأ المنتجة الموازن لمين؟ لخط
+
+713
+01:28:29,740 --> 01:28:35,200
+التقاطة وانا مش هنجيب معادلة خط مستقيم بلزم المنتج
+
+714
+01:28:35,200 --> 01:28:42,070
+موازن لخط التقاطةموجه هذا في الأول و بعد هيك ندور
+
+715
+01:28:42,070 --> 01:28:48,310
+على النقطة تقع على هذا الخط بالضبط تماما بقول كويس
+
+716
+01:28:48,310 --> 01:28:53,910
+هدول محتجهات اثنين بقدر اجيب العمودي على الأول و
+
+717
+01:28:53,910 --> 01:28:58,490
+العمودي على التاني و اعمل لهم cross product بطلع
+
+718
+01:28:58,490 --> 01:29:03,570
+الموازي لخط التقاطة، مظبوط؟ يبقى بالداخل اقول له
+
+719
+01:29:03,570 --> 01:29:11,040
+in one اللي هو بده يساويثلاثة I نقصي تجي نقصي
+
+720
+01:29:11,040 --> 01:29:25,420
+اتنين كي normal to the first plane الان
+
+721
+01:29:25,420 --> 01:29:34,090
+المفترض الاول into اللي هو عبارة عن اتنين Iزائد G
+
+722
+01:29:34,090 --> 01:29:46,010
+نقص اتنين K Normal to the second إبليك بدي أجيب N1
+
+723
+01:29:54,970 --> 01:30:02,670
+يبقى مراكبات المتجه الاول تلاتة مقص ستة مقص اتنين
+
+724
+01:30:02,670 --> 01:30:10,410
+اتنين واحد مقص اتنين اتناشر
+
+725
+01:30:10,410 --> 01:30:14,450
+زائد اتنين يبقى اربعتاشر R
+
+726
+01:30:18,680 --> 01:30:26,840
+ستة وزائد أربعة ويظل ناقص اتنين مع ناقص يظل زائد
+
+727
+01:30:26,840 --> 01:30:36,820
+اتنين J اللي بعده تلاتة زائد اتناش ويساوي خمستاشر
+
+728
+01:30:36,820 --> 01:30:41,280
+K طيب
+
+729
+01:30:41,280 --> 01:30:46,140
+يبقى in one in two هذا parallel to the line of
+
+730
+01:30:46,140 --> 01:30:55,480
+intersectionتبقى باجي بقوله هنا ذا vector N1 cross
+
+731
+01:30:55,480 --> 01:31:15,040
+N2 parallel to the line of intersection of
+
+732
+01:31:15,040 --> 01:31:16,400
+the
+
+733
+01:31:21,290 --> 01:31:28,730
+طيب، إيش مضالبتنا؟ نقطة تقع على خط التقاطة، يالا،
+
+734
+01:31:28,730 --> 01:31:36,610
+من أين سنتي بهذه النقطة؟ نقطة مشتركة بين الـ two
+
+735
+01:31:36,610 --> 01:31:42,510
+planes، تقع على خط التقاطة، تقع في الـplane الأول
+
+736
+01:31:42,510 --> 01:31:42,790
+وفي
+
+737
+01:32:13,350 --> 01:32:20,100
+أو بأي رقم آخرمعادلتين في X و Y بحيث هما مع بعض
+
+738
+01:32:20,100 --> 01:32:24,420
+بجيب نفس الفكرة اللي طرحتيها ولو انهم خربحوا شوية
+
+739
+01:32:24,420 --> 01:32:28,300
+عادلين بكرة بس تطرح عملية كويسة تطرح الفكرة تمام
+
+740
+01:32:28,300 --> 01:32:35,160
+اذا بنروح اخد Z بزيرو او X بزيرو او Y بزيرو اي
+
+741
+01:32:35,160 --> 01:32:39,300
+واحدة منهم باخد واحدة بس بضل متغيرين في معادلتين
+
+742
+01:32:39,300 --> 01:32:44,660
+بحيث هما مع بعض بس سنتين مع بعضتلات معادلات ورا
+
+743
+01:32:44,660 --> 01:32:49,900
+معادلتين وماكنتش بتطلعوا برا المعادلتين تنحلش
+
+744
+01:32:49,900 --> 01:32:55,460
+موجود للجهات بروح بحط قيمة معندي لأحد المتغيرات
+
+745
+01:32:55,460 --> 01:33:03,580
+والتكن زد على سبيل المثال باجي بقول هنا what قطيل
+
+746
+01:33:03,580 --> 01:33:09,690
+الزد تساوي زيلةليس القرآن اللي نزل من السماء لازم
+
+747
+01:33:09,690 --> 01:33:13,590
+زت بزيرو ممكن تاخد زت بواحد باتنين بسلب تلاتة زي
+
+748
+01:33:13,590 --> 01:33:19,490
+ما بدك يبقى لما زت تساوي زيرو قد زت تساوي زيرو
+
+749
+01:33:19,490 --> 01:33:24,830
+ويجد نقص العالم تعالى على ال plan الأول بدأ أحط زت
+
+750
+01:33:24,830 --> 01:33:27,730
+بزيرو كيف تصير تلاتة اكس نقص
+
+751
+01:33:31,360 --> 01:33:38,940
+نقص ستة Y يسوى تلاتة المعادلة التانية اتنين X زائد
+
+752
+01:33:38,940 --> 01:33:47,520
+Y اتنين X زائد Y يسوى اتنين الان بدي احل المعادلات
+
+753
+01:33:47,520 --> 01:33:53,160
+مع بعض المعادلة الأولى بدي ادخلها زي ما هي نقص ستة
+
+754
+01:33:53,160 --> 01:33:54,600
+Y يسوى تلاتة
+
+755
+01:34:02,370 --> 01:34:07,390
+يساوي اتناش اجمعين بروح هدول مع بعض بيصير ايش
+
+756
+01:34:07,390 --> 01:34:14,230
+خمستاشر X يساوي خمستاشر يبقى ال X تساوي كده؟ واحد
+
+757
+01:34:14,230 --> 01:34:24,530
+لما ال X تساوي واحد يبقى Y كده؟ Zero يبقى هذا
+
+758
+01:34:24,530 --> 01:34:30,150
+يعطيك ان Y تساوي Zero يبقى الاسفار
+
+759
+01:34:38,990 --> 01:34:45,050
+زت بزيرو و Y بزيرو و يكسب واحد أين تقع هذه النقطة
+
+760
+01:34:45,050 --> 01:34:52,330
+on the line of intersection of the two planes يبقى
+
+761
+01:34:52,330 --> 01:35:04,830
+هذه الـ Y on the line of intersection
+
+762
+01:35:06,740 --> 01:35:16,300
+of the given planes هذا جيد الآن صارت النقطة
+
+763
+01:35:16,300 --> 01:35:23,960
+موجودة والمتجه الموازي اللي هو موجود إذا بقدر أجيب
+
+764
+01:35:23,960 --> 01:35:27,420
+المعادلة ال parameterية لأنه قال لي في المثلة find
+
+765
+01:35:27,420 --> 01:35:32,620
+parametric equations إذا بناء عليه بقول له the
+
+766
+01:35:32,620 --> 01:35:36,240
+parametric
+
+767
+01:35:39,050 --> 01:35:53,990
+of the line of intersection of the given planes
+
+768
+01:36:07,560 --> 01:36:16,720
+يبقى زائد اربعتاشر T وY يساوي Y not بزيرو يبقى
+
+769
+01:36:16,720 --> 01:36:23,920
+طالع ان انا ما قلتش اتنين T يبقى اتنين T وZ بزيرو
+
+770
+01:36:23,920 --> 01:36:31,180
+وخمستاشر T في قيود على T يبقى T اكبر من سالة
+
+771
+01:36:31,180 --> 01:36:31,740
+Infinity
+
+772
+01:36:37,610 --> 01:36:43,850
+لحد هنا انتهت الأمثلة على هذا النقطة اللي هي
+
+773
+01:36:43,850 --> 01:36:47,790
+النقطة الرقم تلاتة من هذا ال section نفس الله لها
+
+774
+01:36:47,790 --> 01:36:52,930
+النقطة الرقم أربعة والنقطة رقم خامسة طبعا مش حاضر
+
+775
+01:36:52,930 --> 01:36:57,830
+حاجة اليوم الله يعطيك العافية ونكمل المرة القادمة
+
+776
+01:36:57,830 --> 01:37:00,110
+إن شاء الله تعالى
+
+777
+01:37:04,270 --> 01:37:05,370
+الحاجب السليسي والعالمي
+
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/cjA4GBt8ijs.srt b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/cjA4GBt8ijs.srt
new file mode 100644
index 0000000000000000000000000000000000000000..5e86b12634ca0bdcdc8ce41459061c92764eb042
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/cjA4GBt8ijs.srt
@@ -0,0 +1,2701 @@
+1
+00:00:13,720 --> 00:00:20,400
+بسم الله الرحمن الرحيم نرجع الآن لما كنا نستعرضه اللي
+
+2
+00:00:20,400 --> 00:00:24,640
+ابتدأنا به المرة الماضية، المرة الماضية قلنا كيف نتحول
+
+3
+00:00:24,640 --> 00:00:28,120
+من Cartesian coordinates إلى cylindrical
+
+4
+00:00:28,120 --> 00:00:33,690
+coordinates، فقلنا نقطة P (X, Y, Z) في الإحداثيات
+
+5
+00:00:33,690 --> 00:00:38,410
+الكارتزية، ودي  قابلتها في الإحداثيات  الأسطوانية الـ
+
+6
+00:00:38,410 --> 00:00:44,250
+cylindrical coordinates  اللي هو Z بتبقى زي ما هي
+
+7
+00:00:44,250 --> 00:00:52,410
+dx dy هستبدلها بـ r dr dθ،  و أخذنا على ذلك مثال واحد في
+
+8
+00:00:52,410 --> 00:00:57,090
+المحاضرة الماضية، الآن  نأخذ المثال رقم اثنين.
+
+9
+00:01:02,140 --> 00:01:07,700
+نقلب من الإحداثيات الكارتزية to an equivalent
+
+10
+00:01:07,700 --> 00:01:11,520
+integral in cylindrical coordinates إلى تكامل
+
+11
+00:01:11,520 --> 00:01:17,980
+المكافئ له،  بس في الإحداثيات الأسطوانية، ومن ثم نبدأ
+
+12
+00:01:17,980 --> 00:01:21,800
+نحسب التكامل في الإحداثيات الأسطوانية.
+
+13
+00:01:30,080 --> 00:01:34,860
+الآن نحول إلى cylindrical coordinates، x تربيع زي
+
+14
+00:01:34,860 --> 00:01:40,360
+ما نوع تربيعها؟ هي عبارة عن r تربيع، dz كما هي
+
+15
+00:01:40,360 --> 00:01:47,440
+ما لها أي أشكال، بجي لمين؟ بدل dx dy بقول r dr
+
+16
+00:01:47,440 --> 00:01:54,320
+dθ، إذا حدود z ستبقى كما هي.
+
+17
+00:02:02,230 --> 00:02:10,390
+r في cos الزاوية، بدي أجيب عندي dx dy بدي
+
+18
+00:02:10,390 --> 00:02:16,290
+أستبدلها بـ r dr dθ، بدي أعرف r بدها تتغير من وين لوين، و
+
+19
+00:02:16,290 --> 00:02:20,070
+كذلك θ بدها تتغير من وين لوين، لذلك بروح ارسم
+
+20
+00:02:20,070 --> 00:02:25,890
+منطقة التكامل اللي عندي، هذه كيف كانت كارتزية، و
+
+21
+00:02:25,890 --> 00:02:29,170
+كيف بدي أحولها إلى cylindrical coordinates.
+
+22
+00:02:38,450 --> 00:02:43,470
+بعد الـ dz، بدأ يجيني dx، يبقى الحدود هذه هي حدود
+
+23
+00:02:43,470 --> 00:02:49,210
+x، الـ x بتبدأ من صفر لغاية
+
+24
+00:02:49,210 --> 00:02:54,770
+الجذر الموجب، بيبقى عندها تكون جهتي اليمين، جهات
+
+25
+00:02:54,770 --> 00:02:59,150
+اليمين، يعني x جهات الشمال ما عنديش، تمام؟ طيب هذه
+
+26
+00:02:59,150 --> 00:03:03,130
+معادلة ليش؟ لما أقول x يساوي الجذر التربيعي لو
+
+27
+00:03:03,130 --> 00:03:07,790
+واحد ناقص y تربيع، لو ربعت الطرفين، بصير دائرة
+
+28
+00:03:07,790 --> 00:03:13,030
+مركزها نقطة الأصل ونصف قطرها يساوي واحد، صحيح بس مش
+
+29
+00:03:13,030 --> 00:03:17,680
+اللي على الشمال، ما لي فيها، يبقى أنا بأخذ اليمين.
+
+30
+00:03:17,680 --> 00:03:23,640
+طب هل كل نصف دائرة، ولا ربع دائرة؟ بدي أجيب الحدود تبع
+
+31
+00:03:23,640 --> 00:03:28,560
+الـ y، الـ y بتبدأ من سالب واحد لغاية
+
+32
+00:03:28,560 --> 00:03:34,340
+واحد، يبقى منطقة التكامل كلها المنطقة المظللة
+
+33
+00:03:34,340 --> 00:03:50,050
+اللي عندنا، طيب هذه عبارة عن نصف دائرة، r ستتغير
+
+34
+00:03:50,050 --> 00:03:56,370
+من صفر إلى أي نقطة على محيط الدائرة، من صفر لغاية
+
+35
+00:03:56,370 --> 00:04:05,050
+واحد، لغاية واحد، لإيش؟ وين ما ترسمي هذا الخط، المسافة
+
+36
+00:04:05,050 --> 00:04:14,410
+من هنا لهنا مسافة ثابتة، هيبقى اللي عندي θ بتبدأ
+
+37
+00:04:14,410 --> 00:04:18,350
+تتغير، إذا ابتديت عند السالب واحد وجايه طالعة لغاية
+
+38
+00:04:18,350 --> 00:04:24,690
+الواحد، من وين لوين؟ من سالب π/2 إلى π/2.
+
+39
+00:04:24,690 --> 00:04:31,270
+لما حددنا حدود التكامل صح، يبقى لك شغل روتيني.
+
+40
+00:04:31,270 --> 00:04:36,430
+يبقى أول شيء بتكامل بالنسبة لمن؟ لـ z، يبقى الـ r
+
+41
+00:04:36,430 --> 00:04:40,690
+هذا مقدار ثابت، ما لي علاقة بالموضوع، يبقى بوضحه كامل
+
+42
+00:04:40,690 --> 00:04:43,770
+بره، يبقى هذا الكلام بنستخدم integration
+
+43
+00:05:04,410 --> 00:05:09,010
+يبقى المثال اللي عندي، التكامل من سالب π/2
+
+44
+00:05:09,010 --> 00:05:13,230
+إلى π/2، تكامل من صفر لغاية
+
+45
+00:05:13,230 --> 00:05:17,010
+الواحد، من صفر،  بنعوض بالقيم اللي فوق، النقص اللي
+
+46
+00:05:17,010 --> 00:05:22,290
+تحت، اللي بيبقى بس القيم اللي فوق، وعندنا كمان r
+
+47
+00:05:26,720 --> 00:05:35,020
+cos الزاوية θ، في dr في dθ، إذا هذا بدي
+
+48
+00:05:35,020 --> 00:05:40,320
+يعطيني ما يأتي، يبقى التكامل من سالب π/2
+
+49
+00:05:40,320 --> 00:05:47,580
+إلى π/2، وهذه تكاملها 5/5 من
+
+50
+00:05:47,580 --> 00:05:53,520
+صفر لواحد، لسه ضايل عندي cos θ في dθ
+
+51
+00:05:54,240 --> 00:05:57,940
+بنعوض بالقيمة اللي فوق، هيجيب لي 5، والقيمة اللي
+
+52
+00:05:57,940 --> 00:06:03,080
+تحت هيجيب لي صفر، يبقى 5 مقدار ثابت، فأقوله كمان
+
+53
+00:06:03,080 --> 00:06:09,380
+خليه برة، يبقى 5 تكامل من سالب π/2 إلى
+
+54
+00:06:09,380 --> 00:06:18,720
+π/2، لـ cos θ dθ، cos θ dθ،
+
+55
+00:06:18,720 --> 00:06:25,800
+even، هذا الرقم هو نفس الرقم بإشارة مخالفة، إذا
+
+56
+00:06:25,800 --> 00:06:31,260
+بستخدم خاصية الـ even، يبقى هذا الكلام 2/5
+
+57
+00:06:31,260 --> 00:06:38,320
+تكامل من صفر إلى π/2، لـ cos θ dθ،
+
+58
+00:06:38,320 --> 00:06:47,080
+يبقى هذا الكلام يبدو يساوي 5 × 2/5، وتكامل cos
+
+59
+00:06:47,080 --> 00:06:49,520
+θ،
+
+60
+00:06:58,410 --> 00:07:03,150
+cos π/2 بواحد، و cos صفر بصفر، إذا
+
+61
+00:07:03,150 --> 00:07:14,670
+الجواب يساوي 2/5.  النقطة
+
+62
+00:07:14,670 --> 00:07:19,850
+الثانية، و
+
+63
+00:07:19,850 --> 00:07:26,630
+to find the volume of the region، find the volume
+
+64
+00:07:27,950 --> 00:07:35,370
+of the region،  كم حجم المنطقة bounded by the
+
+65
+00:07:35,370 --> 00:07:42,050
+cylinder، bounded by
+
+66
+00:07:42,050 --> 00:07:53,850
+the cylinder، والمحدودة بالأسطوانة x تربيع زائد y
+
+67
+00:07:53,850 --> 00:08:05,050
+تربيع تساوي أربعة، and the planes، بالمستويين z
+
+68
+00:08:05,050 --> 00:08:15,350
+بتساوي صفر، and، والمستوى الثاني x زائد y زائد z
+
+69
+00:08:15,350 --> 00:08:18,430
+بتساوي أربعة.
+
+70
+00:08:33,500 --> 00:08:38,640
+هذا السؤال يختلف عن السؤالين السابقين، السؤالين
+
+71
+00:08:38,640 --> 00:08:43,460
+السابقين كان بيعطيني حدود التكامل جاهزة،  أعمل عليها
+
+72
+00:08:43,460 --> 00:08:48,140
+تكامل، الأول كان مباشر، الثاني كان بدنا نغير حدود
+
+73
+00:08:48,140 --> 00:08:52,580
+التكامل من كارتزية إلى cylindrical coordinates،
+
+74
+00:08:52,580 --> 00:08:57,160
+لكن هذا لا،  ما أعطاني، وقال أنت بتحدد حدود التكامل
+
+75
+00:08:57,160 --> 00:09:02,560
+لوحدك، بقوله ماشي الحال، يبقى أنا بدي أبدأ أحط
+
+76
+00:09:02,560 --> 00:09:08,840
+التكاملات الثلاثة اللي عندنا، هي ثلاثة تكاملات لـ dV،
+
+77
+00:09:08,840 --> 00:09:20,470
+dV بدي أقول عليها dz r dr dθ،  شكلها، بدي أبدأ بـ z،
+
+78
+00:09:20,470 --> 00:09:25,170
+قال الـ region محدودة ما بين الـ cylinder هذه، and
+
+79
+00:09:25,170 --> 00:09:30,830
+the planes، وفي عندي مستويين، المستوى الأول z يساوي
+
+80
+00:09:30,830 --> 00:09:35,230
+صفر، الـ xy plane، يعني مستوى الأرض اللي إحنا
+
+81
+00:09:35,230 --> 00:09:40,510
+قاعدين عليها، وهذا مستوى x زائد y زائد z يساوي
+
+82
+00:09:40,510 --> 00:09:46,050
+أربعة، إذا z تتغير من وين؟ من عندي الصفر لغاية
+
+83
+00:09:46,050 --> 00:09:53,110
+هذا، هذا z قد ايش؟ يساوي 4 ناقص x ناقص y، يبقى 4
+
+84
+00:09:53,110 --> 00:10:01,550
+ناقص x ناقص y، تمام، بدي أجي أشوف حدود الـ r والـ θ.
+
+85
+00:10:01,550 --> 00:10:06,550
+مشان أشوف حدود الـ r والـ θ، بدي أجي أشوف الـ cylinder
+
+86
+00:10:06,550 --> 00:10:09,790
+اللي عندنا، السيلندر اللي عندنا هذا مين محوره يا
+
+87
+00:10:09,790 --> 00:10:16,120
+بنات؟ محور z، لأنه الرمز الغائب، وتقاطعها مع المستوى
+
+88
+00:10:16,120 --> 00:10:22,220
+xy plane بيكون على شكل دائرة مركزها النقطة الأصل، و
+
+89
+00:10:22,220 --> 00:10:28,200
+نصف قطرها يساوي اثنين، تمام تمام، إذا لو جيت قلت هذه
+
+90
+00:10:28,200 --> 00:10:34,420
+المحاور اللي عندنا، هذا محور x، وهذا محور y، وهذا
+
+91
+00:10:34,420 --> 00:10:41,030
+نقطة الأصل z، يبقى هذا بده يكون دائرة، الشكل اللي
+
+92
+00:10:41,030 --> 00:10:47,790
+عندنا هذا، يبقى هي الدائرة اللي موجودة، إذا r على
+
+93
+00:10:47,790 --> 00:10:53,010
+هذه الدائرة ستتغير من أين إلى أين؟ من صفر لغاية
+
+94
+00:10:53,010 --> 00:11:00,330
+كم؟ لغاية اثنين، لماذا؟ لأن نصف قطر دائرة هذه ثابت
+
+95
+00:11:00,330 --> 00:11:06,880
+أينما تروح تجد r تساوي صفر، و r تساوي هنا قد ايش؟
+
+96
+00:11:06,880 --> 00:11:12,480
+اثنين، طيب كويس، ضايل اللي عندنا مين؟ θ، θ
+
+97
+00:11:12,480 --> 00:11:16,560
+بالنسبة لدار أسطوانة نازلة من فوق، يبقى θ حتة
+
+98
+00:11:16,560 --> 00:11:22,540
+تتغير من وين لوين؟ من صفر لغاية 2π، يبقى
+
+99
+00:11:22,540 --> 00:11:30,300
+من صفر لغاية 2π، طيب مش مشكلة،  أظل لو
+
+100
+00:11:30,300 --> 00:11:34,460
+أكملها بالنسبة لـ z في الأول، لأنها هذه من ضمن مين؟
+
+101
+00:11:34,840 --> 00:11:40,420
+من ضمن المتغيرات الثلاثة تبع الـ cylindrical
+
+102
+00:11:40,420 --> 00:11:44,600
+coordinates، يبقى ما أجي أقول هذا الكلام بده يساوي
+
+103
+00:11:44,600 --> 00:11:50,420
+تكامل من صفر لـ 2π، تكامل من صفر لغاية اثنين،
+
+104
+00:11:50,420 --> 00:11:58,080
+تكامل dz، اللي هي f(z) من عند صفر لغاية 4 ناقص
+
+105
+00:11:58,080 --> 00:12:04,380
+x ناقص y، وظل عندي برة r dr dθ.
+
+106
+00:12:07,090 --> 00:12:16,030
+هذا الكلام يجب أن يساوي هذا
+
+107
+00:12:16,030 --> 00:12:23,890
+الكلام، يجب أن يتكامل من 0 إلى 2π، تكامل من 0 إلى
+
+108
+00:12:23,890 --> 00:12:32,130
+2، نعوض بالقيمة، 4 ناقص x ناقص y ناقص الصفر،
+
+109
+00:12:32,130 --> 00:12:41,750
+وهنا ضل r dr dθ، وما عجلك عن قومك يا موسى،
+
+110
+00:12:41,750 --> 00:12:49,070
+يعني أربعة، وبعدين في القرآن في سورة الأعراف، ويدعو
+
+111
+00:12:49,070 --> 00:12:54,350
+الإنسان بالشر دعاءه بالخير، وكان الإنسان عجولاً،
+
+112
+00:12:54,350 --> 00:13:00,030
+باستعجال دائمًا، أو أبدًا، لأنك لا تستعجلنا، واصبر حتى
+
+113
+00:13:00,030 --> 00:13:08,010
+يأتيك اليقين، طيب عارفين إيش معنى اليقين؟ أيوة
+
+114
+00:13:08,010 --> 00:13:14,550
+الموت، اليقين هو أحد أسماء الموت، يبقى هنا حتى..
+
+115
+00:13:14,550 --> 00:13:18,670
+هنا لا نقصد الموت، ولكن نقصد اللي هو الإجابة اللي
+
+116
+00:13:18,670 --> 00:13:23,810
+أنتم بتسألوا عليها هنا، يبقى هذا الكلام يساوي من
+
+117
+00:13:23,810 --> 00:13:29,600
+صفر لـ 2π، ومن هنا من صفر للاثنين، من صفر
+
+118
+00:13:29,600 --> 00:13:34,300
+للاثنين، هذه حدود  r، إذا لازم أحول الـ Cartesian
+
+119
+00:13:34,300 --> 00:13:38,740
+هذه المعادلات إلى cylindrical، إذا بدي أشيل الـ x
+
+120
+00:13:38,740 --> 00:13:43,640
+وأحط مكانها r cos θ، وبدي أشيل الـ y وأحط مكانها
+
+121
+00:13:43,640 --> 00:13:53,200
+r sin θ، إذا هذه يا بنات تصير 4 - r تربيع cos θ - r تربيع
+
+122
+00:13:53,200 --> 00:14:00,600
+sin θ، كل هذا dr، إذا شلت الـ x وحطيت مكانها r cos θ،
+
+123
+00:14:00,600 --> 00:14:10,400
+وشلت الـ y وحطيت مكانها r sin θ، اللي قمنا في
+
+124
+00:14:10,400 --> 00:14:15,460
+الـ cylindrical coordinates، وضربت في r، فصرت
+
+125
+00:14:15,460 --> 00:14:19,680
+المعادلة قدامي بهذا الشكل، الآن بيتكامل بالنسبة لمن؟
+
+126
+00:14:19,680 --> 00:14:25,830
+لـ r، الـ integration من صفر لـ 2π هذه بـ 2 r تربيع
+
+127
+00:14:25,830 --> 00:14:32,110
+مضروبة بـ4 - 2 r تكعيب في cos θ -
+
+128
+00:14:32,110 --> 00:14:40,890
+2 r تكعيب في cos الزاوية θ، وهذه ناقص 2 r تكعيب في sin
+
+129
+00:14:40,890 --> 00:14:47,190
+الزاوية θ، والكلام هذا من صفر لاثنين، dθ، يبقى هذا
+
+130
+00:14:47,190 --> 00:14:55,400
+الكلام بيتكامل من صفر إلى 2π،  بنعوض بالقيم
+
+131
+00:14:55,400 --> 00:15:02,020
+اللي فوق ناقصها تحت، طبعًا تحت صفر، صفر، صفر، مع
+
+132
+00:15:02,020 --> 00:15:06,800
+السلامة، بتظهر بس القيم اللي فوق، بدي أشيل كل r وأحط
+
+133
+00:15:06,800 --> 00:15:11,560
+مكانها اثنين، يبقى هنا اثنين تربيع، أربعة في
+
+134
+00:15:11,560 --> 00:15:16,600
+اثنين، بثمانية، يبقى هذه ثمانية، وهنا ناقص برضه ثمانية
+
+135
+00:15:16,600 --> 00:15:24,010
+على ثلاثة، يبقى ثمانية على ثلاثة، و sin الزاوية θ،
+
+136
+00:15:24,010 --> 00:15:30,670
+وهنا ناقص ثمانية على ثلاثة sin الزاوية θ في dθ،
+
+137
+00:15:30,670 --> 00:15:37,890
+وهنا ناقص ثمانية على ثلاثة sin الزاوية θ، في dθ.
+
+138
+00:15:37,890 --> 00:15:38,650
+.
+
+139
+00:16:06,630 --> 00:16:12,930
+طيب نكمل التكامل هنا، هذا الكلام بده يساوي ثمانية
+
+140
+00:16:12,930 --> 00:16:19,430
+θ، واللي بعده cos  زائد ناقص 8/3 cos
+
+141
+00:16:19,430 --> 00:16:27,030
+زاوية θ، واللي بعده زائد 8/3 cos
+
+142
+00:16:27,030 --> 00:16:33,460
+الزاوية θ، وكله من صفر لـ 2π،  لذا نجد أن نعوض بحدود التكامل، هادئة
+
+143
+00:16:33,460 --> 00:16:38,180
+من هادئة θ وحطيت 2π بيصير 16π، cos
+
+144
+00:16:38,180 --> 00:16:44,300
+2π، ظهرت كاملة يعني أنها صفر، يبقى هذا هنا
+
+145
+00:16:44,300 --> 00:16:50,180
+أقل من صفر،  cos 2π بواحد،  تمام،
+
+146
+00:16:50,180 --> 00:16:56,200
+.
+
+147
+00:17:02,660 --> 00:17:10,880
+صفر، صفر، و cos صفر بواحد، يبقى ناقص 8/3
+
+148
+00:17:10,880 --> 00:17:16,020
+الفوق، ناقص اللي تحت، يبقى الجواب بتعطينا قدر
+
+149
+00:17:16,020 --> 00:17:21,620
+16π + 1،  وتسهل وتسهل، ده حد فيكم  بيسأل أي
+
+150
+00:17:21,620 --> 00:17:27,360
+سؤال، يعني إحنا إذا حددنا حدود التكامل صح، بيصير
+
+151
+00:17:27,360 --> 00:17:34,650
+الشغل الباقي كله عندنا شغل روتيني، مثال، مثال أربعة،
+
+152
+00:17:34,650 --> 00:17:38,310
+you
+
+153
+00:17:38,310 --> 00:17:43,650
+gonna find the volume of the region، find the
+
+154
+00:17:43,650 --> 00:17:55,330
+volume of the region، كم حجم المنطقة bounded above
+
+155
+00:17:55,330 --> 00:17:59,830
+bounded above،
+
+156
+00:18:13,460 --> 00:18:24,780
+يساوي 5 - x تربيع - y تربيع، and below، ومن
+
+157
+00:18:24,780 --> 00:18:37,680
+أسفل، by the paraboloid، كذلك بالـ paraboloid
+
+158
+00:18:40,450 --> 00:18:49,310
+اللي هو z تساوي 4x تربيع زائد 4y
+
+159
+00:18:49,310 --> 00:19:08,830
+تربيع، نمسح
+
+160
+00:19:08,830 --> 00:19:09,850
+الشجرة دي كلها،
+
+161
+00:19:32,010 --> 00:19:38,410
+خلاص نرجع لسؤال هذا مرة ثانية، السؤال بيقول لي هذه
+
+162
+00:19:38,410 --> 00:19:43,530
+حجم المنطقة المحدودة من أعلى بالـ paraboloid اللي
+
+163
+00:19:43,530 --> 00:19:49,970
+قدامنا هنا، ومن أسفل بالـ paraboloid السابق، طبعًا رسمة
+
+164
+00:19:49,970 --> 00:19:54,630
+الـ paraboloid هذا مر علينا من ضمن الرسومات الستة،
+
+165
+00:19:54,630 --> 00:20:00,650
+مظهر؟ كويس؟ إذا بدنا نرسم كل واحد فيهم ونحدد
+
+166
+00:20:00,650 --> 00:20:05,260
+وين المنطقة المشتركة اللي هو بدنا إياها، لو جيت للـ
+
+167
+00:20:05,260 --> 00:20:10,440
+paraboloid الأول، ورحت أخذت المحاور بالشكل اللي
+
+168
+00:20:10,440 --> 00:20:18,400
+عندها، يبقى هذا محور x، وهذا محور y، وهذا محور z،
+
+169
+00:20:18,400 --> 00:20:22,820
+بالداخل للـ paraboloid الأول، لو كان الـ paraboloid
+
+170
+00:20:22,820 --> 00:20:30,260
+الأول هو z تساوي x تربيع زائد y تربيع، لو كان الـ
+
+171
+00:20:30,260 --> 00
+
+223
+00:25:49,740 --> 00:25:54,500
+عندنا هذا تمام، يمكن لو جئت أسقطها بلاتك تجيلك هذه
+
+224
+00:25:54,500 --> 00:26:00,220
+هناك، و تجيلك هذه الثانية هناك، اللي فوق دائرة يمكن
+
+225
+00:26:00,220 --> 00:26:02,360
+تلاقي هذه كمان دائرة
+
+226
+00:26:07,400 --> 00:26:14,060
+الآن بدي أعرف كده ثيتا، و كده R، أظن واضح من الدائرة
+
+227
+00:26:14,060 --> 00:26:19,060
+هذه أن ثيتا في الدائرة من صفر لـاثنين باي، يفج هذه
+
+228
+00:26:19,060 --> 00:26:23,460
+من Zero لـاثنين باي، مع أني مشكلة فيها، المشكلة
+
+229
+00:26:23,460 --> 00:26:29,600
+أين هي؟ في الـR، بدي أعرف كده نصف قطر هذه
+
+230
+00:26:29,600 --> 00:26:35,820
+الدائرة نفسها هي الدائرة اللي فوق هذه بالضبط تماماً
+
+231
+00:26:35,820 --> 00:26:41,620
+تماماً، يبقى هذا لو عرفت قداش R، اللي منك بحلّنا
+
+232
+00:26:41,620 --> 00:26:46,640
+الإشكالية من تقول لك كيف نجيب R من الدائرة اللي
+
+233
+00:26:46,640 --> 00:26:50,700
+فوق؟
+
+234
+00:26:50,700 --> 00:26:55,780
+يلا نشوف بسيطة وسهلة جداً كمان، very easy
+
+235
+00:27:01,890 --> 00:27:07,450
+بنجيب ايش؟ كويس
+
+236
+00:27:07,450 --> 00:27:12,470
+الدائرة هذه يا بنات مشتقة على كل من الـ two
+
+237
+00:27:12,470 --> 00:27:18,010
+surfaces، إذا بدنا نسوي المعادلتين في بعض بكون خلصت
+
+238
+00:27:18,010 --> 00:27:23,090
+من المشكلة دي، طيب باجي بقوله اه ماهي z فوق خمسة
+
+239
+00:27:23,090 --> 00:27:28,510
+ناقص R تربيع، و z تعتبر أربعة R تربيع، وهذه الدائرة
+
+240
+00:27:28,510 --> 00:27:33,740
+هي مشتركة ما بين الاثنين، يبقى الذد في هذه اللحظة
+
+241
+00:27:33,740 --> 00:27:38,840
+لازم تساوي مين؟ الذد الثاني، إذا بناء عليه الذد
+
+242
+00:27:38,840 --> 00:27:46,600
+عندها هتسوي خمسة ناقص R تربيع، وتساوي أربعة R تربيع،
+
+243
+00:27:46,600 --> 00:27:52,260
+يبقى بناء عليه هذه هتعطيك ايش؟ هتعطيك أنه خمسة R
+
+244
+00:27:52,260 --> 00:27:58,420
+تربيع بده يساوي خمسة، يبقى الـ R تربيع تساوي واحد،
+
+245
+00:27:58,420 --> 00:28:05,510
+يبقى الـ R بتساوي واحد، يبقى الـ R ستتغير من
+
+246
+00:28:05,510 --> 00:28:10,910
+الـ zero من النقطة هذه إلى أي نقطة على محيط الدائرة
+
+247
+00:28:10,910 --> 00:28:16,550
+يعني من النقطة هذه إلى أي نقطة على محيط الدائرة
+
+248
+00:28:16,550 --> 00:28:23,770
+يبقى هنا R تساوي واحد، وهنا R تساوي واحد كذلك، يبقى
+
+249
+00:28:23,770 --> 00:28:30,140
+من Zero لغاية واحد، يبقى الآن حددنا حدود التكامل
+
+250
+00:28:30,140 --> 00:28:35,820
+تحديداً سليماً، ما فيه أي إشكالية، وبالتالي لم يبقى
+
+251
+00:28:35,820 --> 00:28:40,120
+علي إلا أن أقوم بالتكامل لأن كل المسألة كتبتها
+
+252
+00:28:40,120 --> 00:28:44,340
+الآن في الـ cylindrical coordinates بقى، اللي بقولك
+
+253
+00:28:44,340 --> 00:28:50,900
+بويس، يبقى هذا الكلام بالساوي integration من Zero
+
+254
+00:28:50,900 --> 00:28:55,580
+لإثنين باي، integration من Zero لواحد، تكامل
+
+255
+00:29:21,240 --> 00:29:25,100
+يبقى هذا الكلام اللي يعطيني integration من Zero
+
+256
+00:29:25,100 --> 00:29:30,380
+لإثنين باي، من Zero لغاية الواحد، طالع عندك هنا
+
+257
+00:29:30,380 --> 00:29:40,400
+لمين؟ لخمسة ناقص خمسة R تربيع، كله هنا في RDRdθ
+
+258
+00:29:40,400 --> 00:29:46,100
+ثيتا، أو أنشأناها، فقلنا هذا الكلام بدل يساوي
+
+259
+00:29:46,100 --> 00:29:50,840
+integration من zero للاثنين باي، integration من zero
+
+260
+00:29:50,840 --> 00:30:01,520
+لواحد، لمين؟ لخمسة R ناقص خمسة R تكعيب، كله dθ، اه دي
+
+261
+00:30:01,520 --> 00:30:06,980
+ثيتا، دخلنا R اللي برا داخل الجوة، طيب مش نايل إلا
+
+262
+00:30:06,980 --> 00:30:11,220
+كام؟ يبقى هذا الكلام بدل يساوي integration من zero
+
+263
+00:30:11,220 --> 00:30:19,520
+لإثنين باي، وهذه خمسة R تربيع على الاثنين، وهذه ناقص
+
+264
+00:30:19,520 --> 00:30:26,460
+خمسة على أربعة R أس أربعة، والكلام هذا كله من
+
+265
+00:30:26,460 --> 00:30:31,680
+zero لغاية الواحد، وهذه dθ، اليومين بتبتدي ثيتا
+
+266
+00:30:36,080 --> 00:30:42,020
+بتعود القيمة اللي فوق يا بناتي، بالخمسة على اثنين - 5
+
+267
+00:30:42,020 --> 00:30:50,240
+على 4 - 0، مع السلامة، كله في dθ، يبقى بضالة ان دي قداش
+
+268
+00:30:50,240 --> 00:31:01,740
+5 على 4، و من 0 الى 2π،  لـ dθ، يبقى 5 على 4θ من 0 الى
+
+269
+00:31:01,740 --> 00:31:09,900
+2π، واللي يبدأ يساوي 5 على 4 في 2π، طبعاً بضل اللي
+
+270
+00:31:09,900 --> 00:31:17,400
+يُعطيه خمسة باي على الاثنين، هذا حجم المنطقة اللي
+
+271
+00:31:17,400 --> 00:31:23,170
+عليها، يبقى بنات إذا قرأنا السؤال قراءة سليمة، و
+
+272
+00:31:23,170 --> 00:31:28,870
+الرسم كان معروف، الشكل المعطيني له سبق الدراسة، و
+
+273
+00:31:28,870 --> 00:31:33,870
+قبل ذلك، بيصير عملية الرسم بسيطة جداً، و من الرسم باجي
+
+274
+00:31:33,870 --> 00:31:38,910
+بحدد حدود التكامل، وبالتالي تبقى انتهت المشكلة أو
+
+275
+00:31:38,910 --> 00:31:44,710
+بكون انحلّ السؤال بسهولة، ويسط حد بتحفظ أي سؤال هنا
+
+276
+00:31:46,300 --> 00:31:49,680
+نذهب للنصف الثاني على الـ Spherical Coordinates
+
+277
+00:31:49,680 --> 00:31:58,160
+نذهب
+
+278
+00:31:58,160 --> 00:32:04,580
+للنصف الثاني
+
+279
+00:32:04,580 --> 00:32:08,620
+على الـ Spherical Coordinates
+
+280
+00:32:30,710 --> 00:32:35,210
+الشطر الثاني من هذا الـ section يقول integration
+
+281
+00:32:35,210 --> 00:32:38,450
+and spherical coordinates
+
+282
+00:32:55,760 --> 00:33:03,520
+التكامل في الإحداثيات
+
+283
+00:33:03,520 --> 00:33:07,280
+الكروية أو الكُوراوية
+
+284
+00:33:27,410 --> 00:33:37,370
+point P in space P
+
+285
+00:33:37,370 --> 00:33:50,130
+of ρ، وفاي، وثيتا، in which بحيث
+
+286
+00:33:50,130 --> 00:33:59,960
+أن النقطة الأولى ρ is the distance، wrong is the
+
+287
+00:33:59,960 --> 00:34:12,200
+distance، المسافة from P to the origin
+
+288
+00:34:12,200 --> 00:34:20,280
+النقطة P، لأن النقطة P هي الأصل، النقطة الثانية φ
+
+289
+00:34:22,170 --> 00:34:35,430
+is the angle، is the angle، هي الزاوية التي الـ RP، الـ
+
+290
+00:34:35,430 --> 00:34:48,470
+makes، التي  يصنعها الـ RP مع الـ positive z
+
+291
+00:34:48,470 --> 00:34:50,350
+axis
+
+292
+00:34:53,340 --> 00:35:02,220
+فاي هذه محصورة فقط من زيرو لغاية باي ناقص تلاتة
+
+293
+00:35:02,220 --> 00:35:06,380
+الثيتا هي الثيتا الأولانية تبعاتنا، تبع الـ
+
+294
+00:35:06,380 --> 00:35:16,800
+cylindrical، والـ θ is the angle، هي الزاوية from
+
+295
+00:35:16,800 --> 00:35:20,460
+cylindrical
+
+296
+00:35:28,660 --> 00:35:30,980
+الذات الـ Cylindrical Core
+
+297
+00:35:57,520 --> 00:36:03,060
+بنروح نرسم اللي هو الإحداثيات الجديدة في الـ
+
+298
+00:36:03,060 --> 00:36:06,040
+spherical coordinates، طبعاً احنا بنرسم الإحداثيات
+
+299
+00:36:06,040 --> 00:36:12,140
+القديمة بدلالة X وY وZ، فمثلاً لو جئت تقول خذي
+
+300
+00:36:12,140 --> 00:36:18,960
+للنقطة اللي عندها، وهذه في الإحداثيات الديكارتية P X
+
+301
+00:36:18,960 --> 00:36:27,860
+Y Z، إذا في الإحداثيات الجديدة بنوصل النقطة هذه P ρ
+
+302
+00:36:27,860 --> 00:36:36,420
+وفاي وثيتا، السؤال هو أين ρ وأين فاي وأين ثيتا؟
+
+303
+00:36:36,420 --> 00:36:41,040
+بقول لك اه، قال لك ρ هنا هي المسافة من النقطة P إلى
+
+304
+00:36:41,040 --> 00:36:46,820
+نقطة الأصل، يبقى باجي بوصل هذه النقطة لنقطة الأصل
+
+305
+00:36:46,820 --> 00:36:54,680
+بيعطيني مين؟ بيعطيني ρ، عرفنا الإحداثي الأول، بعدها
+
+306
+00:36:54,680 --> 00:36:59,520
+قال الزاوية Φ هي الزاوية المحصورة ما بين ρ والـ
+
+307
+00:36:59,520 --> 00:37:05,540
+الاتجاه الموجب للـ Z Axis، يبقى Φ كأنها بدأ يكون
+
+308
+00:37:05,540 --> 00:37:11,200
+الخط مطبق على Z وبدأ يفتح بالشكل هذا، فسمينا
+
+309
+00:37:11,200 --> 00:37:13,480
+الزاوية هذه اللي هي الزاوية Φ
+
+310
+00:37:17,180 --> 00:37:21,340
+طب يجب أن أعرف أين الـR وأين الـθيتا، بروح يا بنات
+
+311
+00:37:21,340 --> 00:37:27,060
+نسقط النقطة P على المستوى XY Plane، يعني لو جئت
+
+312
+00:37:27,060 --> 00:37:32,680
+أسقط النقطة P على المستوى XY Plane، تبدأ تجينا P عند
+
+313
+00:37:32,680 --> 00:37:37,860
+النقطة اللي عندنا هذا، بعدين بقول كويس، هذا موازٍ
+
+314
+00:37:37,860 --> 00:37:48,570
+لمحور Y، وهذا موازٍ لمحور X، تمام؟ يبقى صار عندنا هذا
+
+315
+00:37:48,570 --> 00:37:58,110
+هو Y، وهذا هو مين؟ X، افترض هذا هو X وهذا هو Y، لو جئت
+
+316
+00:37:58,110 --> 00:38:04,310
+وصلت من نقطة الأصل لغاية هذا، فأنت عارف تقول مين
+
+317
+00:38:04,310 --> 00:38:11,850
+بيكون هذا في الـ cylindrical R، ممتاز جداً، يبقى هذا R
+
+318
+00:38:11,850 --> 00:38:16,250
+في الـcylindrical، والزاوية هذه بتكون هي مين؟ هي
+
+319
+00:38:16,250 --> 00:38:24,320
+الزاوية ثيتا، إذن حددنا له ρ، حددنا له فاي، حددنا له
+
+320
+00:38:24,320 --> 00:38:29,500
+من ثيتا، ليه الإحداثيات الجديدة، يبقى ثيتا هو الخط
+
+321
+00:38:29,500 --> 00:38:34,120
+الذي يصنعه مع R تبع الـcylindrical، وطبعاً الحاجة
+
+322
+00:38:34,120 --> 00:38:36,200
+يقول لك هي كروية كدا يا عزيزي، بس احنا رشتنا في
+
+323
+00:38:36,200 --> 00:38:41,720
+البداية، يبقى هذا R اللي هو تبع الـcylindrical عامل
+
+324
+00:38:41,720 --> 00:38:45,560
+ليه زاوية ثيتا، يبقى ثيتا جات لي تبعت من تبعت
+
+325
+00:38:45,560 --> 00:38:51,010
+الـcylindrical coordinate، طيب و الـ Φ هيها، و الـ
+
+326
+00:38:51,010 --> 00:38:58,050
+role اللي عندنا هذه، هل في علاقة رابطة ما بين الـ R
+
+327
+00:38:58,050 --> 00:39:05,990
+و ما بين الـ Φ مثلاً، و الـ R في كده، فالحين أنا بنعت
+
+328
+00:39:05,990 --> 00:39:12,590
+هذا الطول، لو جئت أسقطه على محور Z، يعني نزلت من
+
+329
+00:39:12,590 --> 00:39:19,160
+هنا عمود على محور Z، الطول هذا قد ايش؟ بيقول من نقطة
+
+330
+00:39:19,160 --> 00:39:27,600
+الأصل، من هنا لغاية ρ في كوساين الزاوية Φ، يبقى Z
+
+331
+00:39:27,600 --> 00:39:33,780
+في هذه الحالة بدها تساوي ρ في كوساين الـ Φ، طيب
+
+332
+00:39:33,780 --> 00:39:41,340
+وين ρ ساين الـ Φ؟ يلا نشوف ρ ساين الـ Φ مين بده
+
+333
+00:39:41,340 --> 00:39:48,420
+يطلع؟ هذا عمود على الـ XY Plane، يعني عمودي على أي
+
+334
+00:39:48,420 --> 00:39:52,820
+مستقيم موجود في الـ XY Plane، يعني الزاوية هذه
+
+335
+00:39:52,820 --> 00:40:02,500
+زاوية كم؟ تسعين درجة، يبقى هو ρ ساين الـ Φ هو R
+
+336
+00:40:02,500 --> 00:40:08,360
+يبقى R اللي عندنا هذه يا بنات هي ρ ساين الـ Φ
+
+337
+00:40:08,360 --> 00:40:17,420
+يبقى هذه ρ ساين الـ Φ، عرفنا ايش العلاقة ما بين الـ
+
+338
+00:40:17,420 --> 00:40:24,380
+spherical ومين؟ و الـ cylindrical، وبعد قليل هأجمع لك
+
+339
+00:40:24,380 --> 00:40:28,680
+الاثنين مع الـ cartesian ونشوف ايش اللي بده يصير، بس
+
+340
+00:40:28,680 --> 00:40:33,360
+عندي في بعض التساؤلات بدي أحاول أطرحها، وأشوف ايش
+
+341
+00:40:33,360 --> 00:40:38,500
+رأيكم فيها، ايش معناها؟ طيب يا بنات لو قلت لك احنا
+
+342
+00:40:38,500 --> 00:40:45,050
+الآن نتكلم spherical، وهي Spherical Coordinates أو
+
+343
+00:40:45,050 --> 00:40:49,930
+cylindrical، بعدين نروح للـ Spherical، لو قلت لك R
+
+344
+00:40:49,930 --> 00:40:55,550
+يساوي Zero، R اللي عندنا هذا يساوي Zero، بيعطيني
+
+345
+00:40:55,550 --> 00:41:01,790
+ايش؟ محور Z، ممتاز جداً، يبقى R تساوي Zero، والمطروح
+
+346
+00:41:01,790 --> 00:41:06,570
+الذي هو محور Z، يبقى R تساوي Zero بيعطيك دائماً، و
+
+347
+00:41:06,570 --> 00:41:11,760
+أبداً من محور Z، يبقى لنا خاطرة نكتب هذا الكلام على
+
+348
+00:41:11,760 --> 00:41:22,520
+شكل اللي هو الملاحظات التالية. يبقى دي مارك هذا
+
+349
+00:41:22,520 --> 00:41:25,260
+الكلام اللي قالته سلامة هو الكلام اللي قلناه المرة
+
+350
+00:41:25,260 --> 00:41:29,100
+الماضية، يعني ما كان جديد، يعني هو كلام ذكرناه
+
+351
+00:41:29,100 --> 00:41:29,920
+قبل ذلك.
+
+352
+00:41:36,200 --> 00:41:40,320
+ρ تساوي ثلاثة، ρ تساوي أربعة، ρ تساوي عشرة، هذا
+
+353
+00:41:40,320 --> 00:41:46,080
+ايش يمثل يا أمل؟ يعني جئنا هناك وقلنا ρ تساوي
+
+354
+00:41:46,080 --> 00:41:52,080
+خمسة، ρ خمسة، ρ خمسة، ρ خمسة، ρ خمسة، ρ خمسة،
+
+355
+00:41:52,080 --> 00:41:52,820
+ρ خمسة، ρ خمسة، ρ خمسة، ρ خمسة، ρ خمسة، ρ
+
+356
+00:41:52,820 --> 00:41:52,900
+خمسة، ρ خمسة، ρ خمسة، ρ خمسة، ρ خمسة، ρ خمسة،
+
+357
+00:41:52,900 --> 00:41:53,860
+ρ خمسة، ρ خمسة، ρ خمسة، ρ خمسة، ρ خمسة، ρ
+
+358
+00:41:53,860 --> 00:42:00,130
+خمسة، ρ خمسة،Sphere، عقلي خطر، يعني يعطيك كرة
+
+359
+00:42:00,130 --> 00:42:05,630
+مركزها نقطة الأصل ونصف قطرها يساوي A، يبقى ρ تساوي
+
+360
+00:42:05,630 --> 00:42:20,730
+A، is a sphere with center at the origin and
+
+361
+00:42:20,730 --> 00:42:22,150
+radius
+
+362
+00:42:27,090 --> 00:42:36,070
+النقطة الثانية، يبقى في تساوي في نوت، يبقى في تساوي في
+
+363
+00:42:36,070 --> 00:42:45,010
+نوت، يبقى في تساوي في نوت، يبقى في تساوي في نوت، يبقى
+
+364
+00:42:45,010 --> 00:42:46,350
+في تساوي في نوت، يبقى في تساوي في نوت، يبقى في تساوي في
+
+365
+00:42:46,350 --> 00:42:47,290
+نوت، يبقى في تساوي في نوت، يبقى في تساوي في نوت، يبقى
+
+366
+00:42:47,290 --> 00:42:52,370
+في تساوي في نوت، يبقى في تساوي في نوت، اعمل 30 درجة، هاي 30 درجة
+
+367
+00:42:52,370 --> 00:42:57,450
+هاي كامل، جلب اللي فيه، هاي 30 درجة، وداير
+
+368
+00:42:57,450 --> 00:43:05,890
+ما يدور 30 درجة، شو بيطلع عندي؟ كرة
+
+369
+00:43:05,890 --> 00:43:14,130
+مخروط، كويس، إذا بيطلع عندي مخروط دائري قائم، إذا
+
+370
+00:43:14,130 --> 00:43:20,200
+بيطلع عندي مخروط، يبقى في تساوي في نوت تمثل مين؟ تمثل
+
+371
+00:43:20,200 --> 00:43:26,320
+مخروط دائري قائم، رأسه واقع عند نقطة الأصل، و open
+
+372
+00:43:26,320 --> 00:43:32,940
+up، مفتوح لوين؟ إلى أعلى، يبقى هذه في تساوي في نوت
+
+373
+00:43:32,940 --> 00:43:42,440
+عبارة عن مخروط، يبقى هذه equation of a cone، مخروط
+
+374
+00:43:42,440 --> 00:43:55,920
+with vertex، with vertex at the origin، عند نقطة
+
+375
+00:43:55,920 --> 00:44:06,400
+الأصل، at the origin and open، مفتوح إلى أعلى، إذا
+
+376
+00:44:06,400 --> 00:44:07,620
+كانت والله
+
+377
+00:44:13,900 --> 00:44:20,160
+يبقى لما تبقى في نوت من صفر لغاية تسعين، المخروط
+
+378
+00:44:20,160 --> 00:44:26,540
+يكون مفتوح لوين؟ أو لو خليناها أكثر من تسعين يعني
+
+379
+00:44:26,540 --> 00:44:32,640
+امشي امشي امشي، تسعين، نزلت كمان شوية، يبقى ايش يصير؟
+
+380
+00:44:32,640 --> 00:44:40,000
+مخروط رأسه نازل، open down، مفتوح الى أسفل
+
+381
+00:44:40,000 --> 00:44:43,480
+يبقى باجي بقول الـ open down
+
+382
+00:44:46,960 --> 00:44:58,140
+open down، مفتوح الى أسفل، if Φ أكبر من مين؟ من
+
+383
+00:44:58,140 --> 00:45:03,260
+π على اثنين، طيب أنت تكلمت على أقل من π على اثنين
+
+384
+00:45:03,260 --> 00:45:07,060
+وقلنا مخروط مفتوح الى أعلى، أكبر من π على اثنين
+
+385
+00:45:07,060 --> 00:45:09,960
+مخروط مفتوح الى أعلى، طب لو كان π على اثنين
+
+386
+00:45:17,610 --> 00:45:30,470
+بعدين افتح افتح افتح افتح افتح افتح افتح
+
+387
+00:45:30,470 --> 00:45:37,590
+افتح افتح افتح افتح افتح افتح
+
+388
+00:45:47,510 --> 00:45:57,050
+يبقى هذا المستوى XY، قلت عندنا اللي هو العلاقة
+
+389
+00:45:57,050 --> 00:46:02,330
+اللي بتربط هدول كلهم مع بعض، أو لو حبينا نعطي رسم
+
+390
+00:46:02,330 --> 00:46:09,210
+يعني سريع لهذه
+
+445
+00:53:23,990 --> 00:53:33,350
+من صفر لغاية باي على أربع والتالي من zero لغاية
+
+446
+00:53:33,350 --> 00:53:47,160
+six في  الـ رو كوساين الفاي  الـ رو ساين الفاي d رو
+
+447
+00:53:47,160 --> 00:53:55,120
+دي فاي دي ثيتا التكامل
+
+448
+00:53:55,120 --> 00:54:05,400
+الأول وهي التكامل الثاني وهذا لازم يشغل بالنسبة
+
+449
+00:54:05,400 --> 00:54:13,120
+إلى رو يبقى  الـ ساين والـ كوساين ليس دعوة رو تكعيب تكاملها
+
+450
+00:54:21,870 --> 00:54:31,550
+سك الفاي  لمين؟ لكوساين الفاي ساين الفاي دي فاي دي
+
+451
+00:54:31,550 --> 00:54:35,910
+ثيتا اللي ما فيش ميزة ما بين الفاي وثيتا خليها زي ما هي
+
+452
+00:54:35,910 --> 00:54:43,410
+طول شوية هذا الكلام بده يساوي رابع خليه برا لغاية
+
+453
+00:54:43,410 --> 00:54:48,130
+كامل من Zero لإثنين باي كامل من Zero لغاية Pi على
+
+454
+00:54:48,130 --> 00:54:56,130
+أربعة يبقى هذا شو بيصير سك أس أربعة يبقى سك أس
+
+455
+00:54:56,130 --> 00:55:06,030
+أربعة في و هنا كوساين الفاي كوساين الفاي و دي فاي دي
+
+456
+00:55:06,030 --> 00:55:14,190
+ثيتا ناقص zero بتروح مع السلامة يبقى آلة المسألة
+
+457
+00:55:22,520 --> 00:55:28,000
+زيرو نقاط باي على أربعة في اختصارات يا بنات لو
+
+458
+00:55:28,000 --> 00:55:31,660
+أخذت كوساين اه سك واحدة بصير واحد على كوساين
+
+459
+00:55:31,660 --> 00:55:38,350
+بتروح مع هذه يبقى بظل سك تكعيب ساين يبقى هذه بيصير
+
+460
+00:55:38,350 --> 00:55:49,670
+سك تكعيب  ساين في دي فاي دي ثيتا يبقى مرة ثانية هي
+
+461
+00:55:49,670 --> 00:55:54,770
+الرابع تكامل من zero لإثنين باي تكامل من zero
+
+462
+00:55:54,770 --> 00:56:03,170
+لغاية باي على أربع بدنا نكامل هذه سهلة
+
+463
+00:56:03,170 --> 00:56:08,540
+very easy لا بأخليها سك أيه زي ما هي يبقى ، بس لو
+
+464
+00:56:08,540 --> 00:56:13,880
+نزلتها إيش مصرية؟ Cos فوق Cos فقعدت ست ساعة. هذه
+
+465
+00:56:13,880 --> 00:56:21,200
+بقدر أقول أنّه واحد على Cos أو أقول لك خليها فوق هذه
+
+466
+00:56:21,200 --> 00:56:29,080
+كأنها Cos فاي أس سالب ثلاثة صح ولا لأ؟ واحد على
+
+467
+00:56:29,080 --> 00:56:37,070
+Cos لو طلعت من الـ Cos فاي أس سالب ثلاثة أليست مشتقة
+
+468
+00:56:37,070 --> 00:56:46,710
+الـ cosine بس بده إشارة سالب يبقى هذه فيها سالب دي
+
+469
+00:56:46,710 --> 00:56:51,530
+cosine الفاي و الـ d ثيتا ده إيه يا برة ما له علاقة
+
+470
+00:56:51,530 --> 00:56:59,210
+بالموضوع يبقى هذا الكلام يساوي ربع تكامل من zero
+
+471
+00:56:59,210 --> 00:57:07,110
+لإثنين باي واشتغل إيه كل كامل يبقى بالساين cos فان
+
+472
+00:57:07,110 --> 00:57:16,090
+كوساين ناقص اثنين على ناقص اثنين وعند كده الشرط الناقص
+
+473
+00:57:16,090 --> 00:57:22,330
+اللي كانت برا هيها جابلها وضايل عندنا هذا الحكي من
+
+474
+00:57:22,330 --> 00:57:29,890
+عند الـ zero لغاية Pi على 4 وهي دي فترة يبقى ناقص
+
+475
+00:57:29,890 --> 00:57:36,970
+وناقص نص تطلع برا مع الرموز بيصير كده؟ تمام و
+
+476
+00:57:36,970 --> 00:57:42,150
+بيصير عندي تكامل من zero لإثنين باي و تعالي نعود
+
+477
+00:57:42,150 --> 00:57:46,790
+للقيمة اللي فوق ناقص القيمة اللي تحت يبقى إيش بيصير
+
+478
+00:57:46,790 --> 00:57:56,830
+عندي واحد على cosine باي على أربع الكل تربيع ناقص
+
+479
+00:57:56,830 --> 00:58:06,540
+واحد على cos 0 الكل تربيع بالنسبة الى Dθ يبقى هذا
+
+480
+00:58:06,540 --> 00:58:13,820
+الكلام متساوي 8 جتا 45 يعني واحد على جذر اثنين
+
+481
+00:58:13,820 --> 00:58:19,900
+فتصير إيه نصف بنقلب فوق تصير اثنين يبقى هاي
+
+482
+00:58:19,900 --> 00:58:25,840
+التكامل من 0 لإثنين باي وهي اثنين ناقص cos 0
+
+483
+00:58:25,840 --> 00:58:34,190
+تربيع واحد على واحد ناقص واحد يبقى هاي ناقص واحد
+
+484
+00:58:34,190 --> 00:58:37,550
+يبقى
+
+485
+00:58:37,550 --> 00:58:42,890
+هاي كل اللي عندنا المفضل بالنسبة الى D ثيتا هو
+
+486
+00:58:42,890 --> 00:58:51,250
+يساوي تم تكامل من zero لإثنين باي فقط d ثيتا
+
+487
+00:58:51,250 --> 00:58:59,870
+يبقى يساوي ثمن ثيتا من zero لإثنين باي ويساوي ثمن
+
+488
+00:58:59,870 --> 00:59:07,650
+في إثنين باي يبقى باي على أربعة نعتبر هذا أكثر
+
+489
+00:59:38,580 --> 00:59:43,320
+بطريقة ما اتناولها جاية بيه في إحدى الامتحانات
+
+490
+00:59:43,320 --> 00:59:48,760
+للناس اللي زيكم واحنا عنها هنقدر نعطيك إياها كمثال
+
+491
+00:59:48,760 --> 00:59:57,140
+أقول find the volume of the region find the
+
+492
+00:59:57,140 --> 01:00:09,530
+volume of the region قد إيش حجم المنطقة bounded below
+
+493
+01:00:09,530 --> 01:00:14,870
+bounded below
+
+494
+01:00:14,870 --> 01:00:23,250
+والمحدودة من أسفل بالـ مخروط بالـ مخروط
+
+495
+01:00:23,250 --> 01:00:34,170
+بالمخروط Z تساوي الجذر التربيعي ل X تربيع زائد Y
+
+496
+01:00:34,170 --> 01:00:47,420
+تربيع and above ومن أعلى بالـ plane بالـ plane
+
+497
+01:00:47,420 --> 01:01:03,040
+بالمستوى Z تساوي واحد by using by using امرأة
+
+498
+01:01:03,040 --> 01:01:06,000
+cylindrical coordinates
+
+499
+01:01:09,160 --> 01:01:17,120
+Cylindrical Coordinates لمرة بيه Spherical
+
+500
+01:01:17,120 --> 01:01:29,800
+Coordinates Spherical
+
+501
+01:01:29,800 --> 01:01:31,300
+Coordinates
+
+502
+01:01:53,380 --> 01:01:59,020
+نرجع لسؤالنا مرة ثانية بيقول في عندي منطقة مغلقة
+
+503
+01:01:59,020 --> 01:02:06,400
+ومحدودة من أسفل بمين؟ بالـ مخروط اللي هو Z
+
+504
+01:02:06,400 --> 01:02:11,520
+يساوي الجذر التربيعي ل X تربيع زائد Y تربيع and
+
+505
+01:02:11,520 --> 01:02:17,250
+above ومن أعلى بالـ plane Z يساوي واحد بنجيب هذا
+
+506
+01:02:17,250 --> 01:02:22,550
+الحجم مرتين مرة باستخدام cylindrical coordinates و
+
+507
+01:02:22,550 --> 01:02:26,630
+مرة باستخدام spherical coordinates بيطلعوا اجابتين
+
+508
+01:02:26,630 --> 01:02:32,810
+زي بعض ولا مختلفين؟ نفس الحجم تمام بس بطريقتين
+
+509
+01:02:32,810 --> 01:02:40,620
+مختلفتين ياريت نروح نرسم الشغل هذا و نشوف كيف بعدين
+
+510
+01:02:40,620 --> 01:02:50,520
+يومين نحسب المظبوط تبع المثلث هذا X هذا Y هذا Z
+
+511
+01:02:50,520 --> 01:02:59,400
+و روح ارسم المخروط اللي عندنا بيكون المخروط بالشكل
+
+512
+01:02:59,400 --> 01:03:10,060
+اللي عندنا هذا Xوالمستوى الأفقي Z يساوي واحد يبقى
+
+513
+01:03:10,060 --> 01:03:17,560
+هذا المستوى هو Z يساوي واحد وهذا المخروط هو Z يساوي
+
+514
+01:03:17,560 --> 01:03:24,240
+الجذر التربيعي ل X تربيع زائد Y تربيع شو رأيك احنا
+
+515
+01:03:24,240 --> 01:03:29,340
+بنتكلم على مين؟ على cylindrical في الأول. مدام
+
+516
+01:03:29,340 --> 01:03:35,340
+cylindrical يبقى هذا يبقى الجذر التربيعي اللي
+
+517
+01:03:35,340 --> 01:03:42,000
+هو قدره R يبقى Z يساوي R تمام؟ ما اجي اقوله كويس
+
+518
+01:03:42,000 --> 01:03:48,640
+يبقى الـ volume اللي احنا بدنا إياه يعني ثلاثة تكاملات
+
+519
+01:03:48,640 --> 01:03:50,200
+التي يزد
+
+520
+01:03:59,540 --> 01:04:07,500
+يبقى أنا بدي ارسم خط يقطع منطقة التكامل وموازي لمحور
+
+521
+01:04:07,500 --> 01:04:14,680
+Z يبقى بداجي هنا ارسم خط من هنا و اجي طالع رأسي
+
+522
+01:04:14,680 --> 01:04:20,460
+موازي لمحور Z بالشكل اللي عندنا هذا لغاية ما
+
+523
+01:04:20,460 --> 01:04:27,400
+يقطع اللي هو Z يساوي واحد يبقى هنا Z يساوي قد إيش؟ R
+
+524
+01:04:27,400 --> 01:04:34,560
+هنا Z يساوي قد إيش؟ واحد يبقى هنا R وهنا واحد ضلع الـ
+
+525
+01:04:34,560 --> 01:04:40,760
+R يبقى الـ R بدي أسقط المجسم هذا كله على مين؟ على
+
+526
+01:04:40,760 --> 01:04:47,550
+الـ XY Plane يبقى المسقط هيكون يا بنات دائرة
+
+527
+01:04:47,550 --> 01:04:53,370
+يبقى بتصير المسقط اللي عندنا هي دائرة أها لو جيت
+
+528
+01:04:53,370 --> 01:04:58,590
+قلت هاي وهنا وهاي وهنا بالضبط تماما وهذا ماشي
+
+529
+01:04:58,590 --> 01:05:04,570
+دغري يبقى بدها تكون عند مين؟ الدائرة اللي عندنا هذا
+
+530
+01:05:04,570 --> 01:05:05,050
+الشكل
+
+531
+01:05:09,350 --> 01:05:13,890
+طيب، بدي أعرف قد إيش نصف قطر هذه الدائرة في
+
+532
+01:05:13,890 --> 01:05:19,150
+الإحداثيات القطبية أو ما هي معادلة هذه الدائرة في
+
+533
+01:05:19,150 --> 01:05:22,790
+الإحداثيات القطبية، طب كيف؟ كيف عرفتيها واحد يعني؟
+
+534
+01:05:22,790 --> 01:05:26,290
+تمام
+
+535
+01:05:26,290 --> 01:05:33,270
+تمام، يبقى بروح بقوله هنا Z تساوي واحد و Z تساوي R
+
+536
+01:05:33,270 --> 01:05:37,870
+من هذول الإثنين مع بعض بساويهم بعض يبقى الـ R تساوي
+
+537
+01:05:37,870 --> 01:05:43,890
+قد إيش؟ واحد إذًا الـ R ستبدأ من هنا إلى أي نقطة على
+
+538
+01:05:43,890 --> 01:05:48,090
+محيط الدائرة أو من هنا إلى أي نقطة على محيط
+
+539
+01:05:48,090 --> 01:05:52,750
+الدائرة وبيكون هذا كله R يساوي واحد يبقى الـ R
+
+540
+01:05:52,750 --> 01:06:00,180
+ستتغير من Zero لغاية واحد طب θ هتتغير من 0 ل 2 باي
+
+541
+01:06:00,180 --> 01:06:07,260
+يبقى من 0 لغاية 2 باي ويساوي integration من 0 ل 2
+
+542
+01:06:07,260 --> 01:06:13,900
+باي integration من 0 ل 1 تكامل الـ dZ اللي هي Z من
+
+543
+01:06:13,900 --> 01:06:22,580
+عند R لغاية 1 وظل عندي RdRdθ يبقى آلة المسألة هي
+
+544
+01:06:22,580 --> 01:06:31,210
+تكامل من Zero لغاية 2 باي من 0 لغاية 1 للواحد ناقص R
+
+545
+01:06:31,210 --> 01:06:38,510
+في RdRd ثانية أعوض من القيمة اللي فوق ناقص لتحت
+
+546
+01:06:38,510 --> 01:06:44,730
+بدي أدخل الـ R هذا داخل الـ  ∫ فبيصير عندي تكاملين من
+
+547
+01:06:44,730 --> 01:06:50,350
+Zero لإثنين باي والتكامل الثاني من Zero لواحد للـ
+
+548
+01:06:50,350 --> 01:06:58,210
+R ناقص R تربيع dR d ثيتا التكامل يبدأ integration
+
+549
+01:06:58,210 --> 01:07:04,210
+من Zero لغاية إثنين باي ده من  ل R تربيع على اثنين
+
+550
+01:07:04,210 --> 01:07:11,590
+ناقص R تكعيب على ثلاثة كل الحكي هذا من عند الـ Zero
+
+551
+01:07:11,590 --> 01:07:18,010
+لغاية الواحد d ثيتا هذا بده يساوي
+
+552
+01:07:18,010 --> 01:07:22,250
+integration من zero لغاية إثنين باي بدي أعوض بالقيم
+
+553
+01:07:22,250 --> 01:07:29,490
+اللي فوق بقى نص ناقص ثلث يبقى نص ناقص ثلث و ناقص zero
+
+554
+01:07:29,490 --> 01:07:36,710
+بيروح كله d ثيتا يبقى تكامل من zero لإثنين باي
+
+555
+01:07:36,710 --> 01:07:43,530
+لمين؟ لسُدس d ثيتا إذًا بيصير هذا سُدس
+
+556
+01:07:52,950 --> 01:08:06,170
+باي على ثلاثة باي على ثلاثة
+
+557
+01:08:06,170 --> 01:08:13,850
+باي على ثلاثة باي على ثلاثة باي على ثلاثة في احتمال
+
+558
+01:08:13,850 --> 01:08:21,070
+يكون التكامل غلط في احتمال حدود التكامل غلط الأخرى
+
+559
+01:08:21,070 --> 01:08:29,750
+إن شاء الله لا نقع في الخطأ إيه الآن بدنا نروح
+
+560
+01:08:29,750 --> 01:08:39,630
+نشتغل في اللي هو الـ spherical coordinates ده
+
+561
+01:08:39,630 --> 01:08:49,600
+يا عزيزي هأقوله  بمفرداته بدي تكامل  إثنين ثلاثة رو تربيع
+
+562
+01:08:49,600 --> 01:09:02,960
+ساين فاي d رو d فاي d تيتا نيجي لـ رو تتغير من أين إلى أين يبقى رو هتبدأ من أين يا
+
+563
+01:09:02,960 --> 01:09:06,820
+بنات؟ من نقطة الأصل ونتجه  نطلع طالعين لغاية ما
+
+564
+01:09:06,820 --> 01:09:12,900
+نجابل وين؟ المستوى اللي فوق اللي هو Z يساوي واحد إذًا لو
+
+565
+01:09:12,900 --> 01:09:19,000
+جينا طالعين بهذا الشكل لغاية ما جابلنا السطح اللي
+
+566
+01:09:19,000 --> 01:09:24,600
+فوق يبقى روحنا بقد إيش؟ Zero اتفقنا يبقى هاي روحنا
+
+567
+01:09:24,600 --> 01:09:32,320
+Zero روحنا فوق بقد إيش؟
+
+568
+01:09:32,320 --> 01:09:35,540
+مين هو اللي فوق؟ Z تساوي واحد طب مين هي Z في الـ
+
+569
+01:09:40,590 --> 01:09:45,610
+spherical؟ رو كوساين فاي بيبقى صارت قصته سهلة يبقى
+
+570
+01:09:45,610 --> 01:09:51,390
+هذه اللي هو Z تساوي واحد يعني الـ رو كوساين
+
+571
+01:09:51,390 --> 01:09:59,180
+الفاي يساوي واحد يبقى رو كده  شبهها سك الفاي لأن
+
+572
+01:09:59,180 --> 01:10:05,200
+واحد على سك اضرب الطرفين بس الـ رو بسك الفاي إذًا
+
+573
+01:10:05,200 --> 01:10:10,460
+الـ رو تتغير من zero لغاية سك الفاي طب إذًا نيجي لـ
+
+574
+01:10:10,460 --> 01:10:18,730
+فاي تتغير من أين لأين؟ يبقى فاي تتغير من المحور
+
+575
+01:10:18,730 --> 01:10:25,870
+Z لغاية  الخط اللي عندنا هذا إذًا لو عرفنا قد إيش
+
+576
+01:10:25,870 --> 01:10:30,970
+معادلة هذا الخط بتبقى قصتنا محلولة يلا قد إيش؟
+
+577
+01:10:30,970 --> 01:10:41,090
+يلا بس يطلع يعني .. يعني شوفوا لي كيف ممكن نجيبها
+
+578
+01:10:41,090 --> 01:10:47,420
+هيك يلا
+
+579
+01:10:47,420 --> 01:10:51,760
+إيه حسب جربوا قولوا لي كيف أنا ما بديش أعطيكم جوااب،
+
+580
+01:10:51,760 --> 01:10:54,680
+بدي إياك أنتِ تشغلي مخك شوية يلا
+
+581
+01:11:03,000 --> 01:11:11,660
+شوفوا قد إيش تقاطع المستوى اللي فوق مع المخروط يعني
+
+582
+01:11:11,660 --> 01:11:19,460
+بقول Z تساوي R  Z تساوي 1 صحيح ولا لأ؟ يلا نشوف
+
+583
+01:11:19,460 --> 01:11:23,740
+المستوى
+
+584
+01:11:23,740 --> 01:11:30,700
+اللي فوق شو معادلته؟ رو كوساين فاي صحيح ولا لأ؟
+
+585
+01:11:30,700 --> 01:11:37,620
+وشوف اللي تحت بصراحة هو هذا يلا أيوة
+
+586
+01:11:39,510 --> 01:11:43,410
+صحيح زيه
+
+587
+01:11:43,410 --> 01:11:49,930
+يساوي R ممتاز
+
+588
+01:11:49,930 --> 01:11:59,830
+هي R بقد إيش عادي ممتاز جدًّا يبقى رو كوساين فاي واللي
+
+589
+01:11:59,830 --> 01:12:04,930
+فوق الـ رو كوساين فاي يبقى حاليًا الإشكالية تمام
+
+590
+01:12:05,200 --> 01:12:09,520
+يبقى يا بنات بروح بأكتب في الهامش بقول المستوى اللي
+
+591
+01:12:09,520 --> 01:12:16,140
+فوق اللي هو Z  اللي هو رو كوساين فاي و اللي
+
+592
+01:12:16,140 --> 01:12:23,440
+تحت Z تساوي R و الـ R اللي هو رو كوساين الفاي يبقى
+
+593
+01:12:23,440 --> 01:12:30,660
+رو كوساين الفاي هذه اللي هي هذه اللي هي R لو
+
+594
+01:12:30,660 --> 01:12:36,820
+قسمنا الطرفين على رو بيصير كوساين فاي بده يساوي
+
+595
+01:12:36,820 --> 01:12:41,280
+الـ ساين فاي أو لو قسمنا على الـ كوساين فاي بيصير
+
+596
+01:12:41,280 --> 01:12:47,580
+واحد يساوي تان فاي من الزاوية اللي تانها يساوي
+
+597
+01:12:47,580 --> 01:12:59,030
+واحد 45 درجة يبقى من 90 نقاط 45 درجة طبعًا شايفين
+
+598
+01:12:59,030 --> 01:13:06,090
+كيف جابت الزاوية؟ الآن هذا صار معادلة فاي تساوي باي
+
+599
+01:13:06,090 --> 01:13:10,850
+على أربع الخط اللي عندنا هنا يبقى الزاوية هذه كلها
+
+600
+01:13:10,850 --> 01:13:14,750
+صارت كده شبه بنات اللي هي باي على أربع اللي هي
+
+601
+01:13:14,750 --> 01:13:20,030
+الزاوية فاي  مرات أقولها لأنها very important  خبصت
+
+602
+01:13:20,030 --> 01:13:24,460
+فيها بتروح المسألة يبقى مرة ثانية بدي أجيب قد إيش
+
+603
+01:13:24,460 --> 01:13:28,560
+مقدار الزاوية فاي اللي عندنا بقول آه تعالي
+
+604
+01:13:28,560 --> 01:13:34,710
+ناخذها من خط التقاطع هذا مع المستوى اللي فوق تمامًا هذا
+
+605
+01:13:34,710 --> 01:13:40,830
+جاي من مين؟ من معادلة المخروط Z تساوي R وهذا
+
+606
+01:13:40,830 --> 01:13:45,910
+اللي فوق جاي من Z تساوي واحد إذًا بدي أساوي هذول
+
+607
+01:13:45,910 --> 01:13:50,770
+هذول بمين؟ ببعض طيب بأجي بقوله Z اللي فوق في الـ
+
+608
+01:13:50,770 --> 01:13:57,230
+spherical هي رو كوساين فاي يبقى رو كوساين فاي
+
+609
+01:13:57,230 --> 01:14:03,500
+بيبقى تساوي اللي تحت اللي هي مين؟ اللي بيبقى تساوي
+
+610
+01:14:03,500 --> 01:14:08,760
+رو ساين فاي اللي هي R يبقى صار رو كوساين فاي
+
+611
+01:14:08,760 --> 01:14:12,960
+بيبقى يساوي رو ساين فاي قسمنا على رو صار الـ كوساين
+
+612
+01:14:12,960 --> 01:14:17,120
+بيبقى يساوي ساين قسمنا على كل كوساين بيصير ساين على كوساين
+
+613
+01:14:
+
+667
+01:22:07,280 --> 01:22:11,980
+بنقلب دي حجم المنطقة المحظورة من الأسفل بالـ X Y
+
+668
+01:22:11,980 --> 01:22:18,680
+Plane و من الجوانب بالاسفير، يبقى أنا عندي هنا بنا
+
+669
+01:22:18,680 --> 01:22:28,140
+اسفير كويس، هاي ها بدي أرسم بالشكل اللي عندنا هذا، هاي
+
+670
+01:22:28,140 --> 01:22:36,250
+القاعدة قلب الـ X Y Plane، يبقى هذا مش هيبقى كويس، و
+
+671
+01:22:36,250 --> 01:22:41,690
+هذا هيجينا هيك، و الاسفير بدأ يرسم من فوق، يبقى تظهر
+
+672
+01:22:41,690 --> 01:22:46,970
+الاسفير بالشكل اللي عندنا هذا، و الناحية التانية
+
+673
+01:22:46,970 --> 01:22:53,250
+بالشكل هذا، كويس، يبقى هذا النصف العلوي من الاسفير
+
+674
+01:22:53,250 --> 01:23:04,460
+النصف السفلي ما رسمناهوش، يبقى الاسفير يبقى
+
+675
+01:23:04,460 --> 01:23:13,660
+الاسفير يبقى الاسفير
+
+676
+01:23:13,660 --> 01:23:18,360
+يبقى الاسفير
+
+677
+01:23:18,360 --> 01:23:21,060
+يبقى الاسفير يبقى الاسفر يبقى الاسفر يبقى الاسفر
+
+678
+01:23:21,240 --> 01:23:24,980
+يبقى بده يجينا هذا من الناحية اللي عندنا هذه
+
+679
+01:23:24,980 --> 01:23:30,680
+وبالتالي بده يصير عندنا من المخروط على الشكل اللي
+
+680
+01:23:30,680 --> 01:23:37,420
+عندنا هذا، يعني أنتم بنات كأن المخروط هذا تجويف
+
+681
+01:23:37,420 --> 01:23:41,960
+للكرة، الكرة اللي اتصورناها مصمتة، و أخدنا النصف العلوي
+
+682
+01:23:41,960 --> 01:23:47,780
+نزلنا فيه ثقب على شكل مخروط بالشكل اللي قدامك هذا
+
+683
+01:23:47,780 --> 01:23:49,340
+يبقى اللي فوق
+
+684
+01:23:54,670 --> 01:23:59,030
+الجزء العلوي لبعض المخروط كله، وجوده لأ، يبقى هذا
+
+685
+01:23:59,030 --> 01:24:04,970
+بنشيله تماماً من راسنا، يبقى هذا كأنه مالوش وجود
+
+686
+01:24:04,970 --> 01:24:09,430
+بالمرة، كويس
+
+687
+01:24:09,430 --> 01:24:15,710
+يبقى صار يعني الدائرة كأنه إحنا اللي هو على الجوانب
+
+688
+01:24:15,710 --> 01:24:21,650
+فقط، يبقى على الجوانب هذه الـ r تساوي إثنين هنا
+
+689
+01:24:21,650 --> 01:24:25,850
+مخروط في الداخل اللي هو r تساوي 5/3
+
+690
+01:24:25,850 --> 01:24:32,370
+والأرض هي الـ X Y plane، كويس، بدل الـ volume V فبقول
+
+691
+01:24:32,370 --> 01:24:43,790
+لهم V تساوي ثلث تكاملات لـ  r تربيع sin φ d r d
+
+692
+01:24:43,790 --> 01:24:51,080
+φ d θ، ليجي لـ r، روح تبدأ من هنا من هنا من نقطة
+
+693
+01:24:51,080 --> 01:24:57,120
+الأصل لغاية أي نقطة على محيط الكرة، يبقى هنا كده؟
+
+694
+01:24:57,120 --> 01:25:04,920
+r تساوي إثنين، يبقى من 0 لغاية 2، يجي لـ
+
+695
+01:25:04,920 --> 01:25:11,280
+5؟ 5 هذا كله فرق مش علاقة فيه، يبقى المجسم
+
+696
+01:25:11,280 --> 01:25:17,810
+هيبدأ من هنا لغاية الـ 5 هذه، فاضية اللي فوق، يبقى
+
+697
+01:25:17,810 --> 01:25:24,890
+في حتى تغير من وين لوين؟ من π/3 إلى π/2
+
+698
+01:25:24,890 --> 01:25:32,270
+يمشي من π/3 لغاية π/2
+
+699
+01:25:32,270 --> 01:25:36,770
+طبعاً بعض البنات هتجي تقولي، هه لو سرقت رحلتك، هتقولي
+
+700
+01:25:36,770 --> 01:25:40,730
+من 0 لغاية π/3، هذا كلام غلط، تتكلمي
+
+701
+01:25:40,730 --> 01:25:44,530
+في الفراغ، أنا بدي لحاجة باللي ضايل اللي بعدها، طبعاً
+
+702
+01:25:44,530 --> 01:25:49,110
+يبدأ من π/3 لـ π، طيب، ضل θ واضحة أصلاً
+
+703
+01:25:49,110 --> 01:25:58,630
+θ من الصفر لغاية كده؟ 2π، دوس خط الرسمة كلها
+
+704
+01:25:58,630 --> 01:26:08,970
+بتصير الدائرة اللي تحت، هي من 0 لغاية 2π، كيف؟
+
+705
+01:26:08,970 --> 01:26:15,450
+لو قلنا حد المخروط صحيح، إحنا ما بنعش المخروط هدف
+
+706
+01:26:15,450 --> 01:26:20,530
+فرع، تمام؟ يبقى هاي اللي بيحصل، يبقى هذا الكلام
+
+707
+01:26:20,530 --> 01:26:27,520
+يدوسي التكامل من 0 لغاية 2π، و تكامل من π/3
+
+708
+01:26:27,520 --> 01:26:35,400
+لغاية π/2، لـ r، تكعيبك على 3
+
+709
+01:26:35,400 --> 01:26:41,900
+من 0 لغاية من 0 لغاية 2، من 0 لغاية
+
+710
+01:26:41,900 --> 01:26:49,700
+2، ويظل عندي sin φ d φ d θ، يعني من هذا
+
+711
+01:26:49,700 --> 01:26:53,620
+الكلام، الدنيا تصبح 8/3، 8/3
+
+712
+01:26:53,620 --> 01:26:59,420
+خليك برا، أي 8/3، و بقى لدي تكاملين من
+
+713
+01:26:59,420 --> 01:27:03,840
+π/3 إلى π/2، و من 0 لغاية
+
+714
+01:27:03,840 --> 01:27:11,060
+2π، من 0 لغاية 2π، لمين؟ لـ sin
+
+715
+01:27:11,060 --> 01:27:18,900
+φ d φ d θ، و 0 برنامج كويس، بدنا
+
+716
+01:27:18,900 --> 01:27:24,510
+الكامل، يبقى هذا الكلام يساوي 8/3 تكامل من
+
+717
+01:27:24,510 --> 01:27:31,330
+0 لإثنين π لـ -cos φ من π/3
+
+718
+01:27:31,330 --> 01:27:38,670
+لغاية π/2، d θ، و يساوي 8/3
+
+719
+01:27:38,670 --> 01:27:44,230
+على 3 تكامل من 0 لإثنين π،
+
+720
+01:27:46,850 --> 01:27:55,210
+يبقى نقص مع نقص بصير الزائد، و هنا جتا 60 يبقى
+
+721
+01:27:55,210 --> 01:28:03,370
+بـ 1/2، d θ، يبقى هذا الكلام بده يساوي 4/3
+
+722
+01:28:03,370 --> 01:28:10,060
+تكامل من 0 للإثنين π لـ d θ، 4/3
+
+723
+01:28:10,060 --> 01:28:16,620
+في θ من 0 للإثنين π، 4/3
+
+724
+01:28:16,620 --> 01:28:23,220
+في إثنين π، و يساوي 8π/3
+
+725
+01:28:23,220 --> 01:28:28,480
+آخر مثال في محاضرة اليوم، مثال رقم
+
+726
+01:28:44,880 --> 01:28:57,980
+molar region المنطقة الصغرى كانت from و المقطوعة من
+
+727
+01:28:57,980 --> 01:29:00,660
+the solid sphere
+
+728
+01:29:08,160 --> 01:29:16,260
+R أقل من أو يساوي 2، لإطلين
+
+729
+01:29:16,260 --> 01:29:21,100
+بالمستوى Z تساوي 1
+
+730
+01:30:00,070 --> 01:30:06,770
+بقول لكِ حجم المنطقة الصغرى المقطوعة من الكرة اللي
+
+731
+01:30:06,770 --> 01:30:11,490
+عندها دي بالـ Plane Z تساوي مين؟ تساوي واحدة، أقول
+
+732
+01:30:11,490 --> 01:30:14,650
+لكِ، استخدموا ارصدوا من الرسمة و نشوف إيه الدينامكس
+
+733
+01:30:14,650 --> 01:30:21,370
+يبقى لو جهت خذ اللي هو المحاور الثلاثة هذا X هذا Y
+
+734
+01:30:21,370 --> 01:30:26,810
+هذا Z، الآن لما أقول r تساوي 2، يبقى كرة
+
+735
+01:30:27,130 --> 01:30:31,870
+مركزها نقطة الأصل، نصف قطرها يساوي كده؟ يساوي 2
+
+736
+01:30:31,870 --> 01:30:44,810
+يبقى كأن الكرة عليها الشكل اللي عندنا هذا، يبقى
+
+737
+01:30:44,810 --> 01:30:49,790
+هذه الكرة في شكلها العام، طبعاً ما بدي أقطعها
+
+738
+01:30:49,790 --> 01:30:55,360
+بالمستوى اللي هو مين؟ Z يساوي 1، إذا بدي أجي على
+
+739
+01:30:55,360 --> 01:31:00,500
+المستوى هيك، و أجي و آخده بالشكل اللي عندنا
+
+740
+01:31:00,500 --> 01:31:06,080
+هذا هيك، و من هنا أجي و أقول هذه المستوى اللي عندنا
+
+741
+01:31:06,080 --> 01:31:12,540
+و الـ Z بده يساوي 1، إذا قطع الدائرة قطع الكرة
+
+742
+01:31:12,540 --> 01:31:17,000
+اللي عندنا على شكل دائرة، الشكل اللي عندنا هذا
+
+743
+01:31:20,140 --> 01:31:24,460
+و هذا اللي تحت كله شيلناه، مش لازمه، شيلناه بالمرة.
+
+744
+01:31:25,140 --> 01:31:31,100
+إذا صار عندي مين؟ الجزء اللي فوق هذا فقط لا غير.
+
+745
+01:31:33,640 --> 01:31:39,000
+اللي هو شكله شكل إيه يا بنات؟ بس شكله بالبلدي هيك
+
+746
+01:31:39,000 --> 01:31:47,360
+شكل إيش؟ طاقية، مظبوط، يبقى كأنه إحنا بدنا نجيب حجم
+
+747
+01:31:47,360 --> 01:31:52,580
+الطاقية القروية اللي عندنا دي، طبعاً، و باقي الكرة
+
+748
+01:31:52,580 --> 01:31:55,760
+اللي تحت هذا مالوش لازمة، مش موجود عندي من الأصل
+
+749
+01:31:55,760 --> 01:32:00,200
+طبعاً أنه جاي، بدي الجزء الصغير، هاي اللي كبير تحت
+
+750
+01:32:00,200 --> 01:32:04,840
+وصغير فوق، إذا إحنا علاقتنا مع الجزء الصغير ما تبقى
+
+751
+01:32:04,840 --> 01:32:08,100
+بسيطة، يبقى إحنا بدنا V
+
+752
+01:32:16,590 --> 01:32:24,590
+d φ d r d θ d φ d φ d φ d φ d φ d φ d φ d φ d φ
+
+753
+01:32:24,590 --> 01:32:25,610
+d φ d φ d φ d φ d φ d φ d φ d φ d φ d φ d φ d φ d φ d φ
+
+754
+01:32:25,610 --> 01:32:26,190
+d φ d φ d φ d φ d φ d φ d φ d φ d φ d φ d φ d φ d φ d φ
+
+755
+01:32:26,190 --> 01:32:30,190
+d φ d φ d φ d φ d φ d φ d φ d φ d φ d φ d φ d φ d φ d φ
+
+756
+01:32:30,190 --> 01:32:33,790
+d φ d φ d φ d φ
+
+757
+01:32:33,790 --> 01:32:33,990
+d φ d φ d φ d φ d φ d φ d φ d φ d φ d φ d φ d φ d φ d φ d φ
+
+758
+01:32:33,990 --> 01:32:37,450
+d φ d φ
+
+759
+01:32:37,450 --> 01:32:43,590
+d
+
+760
+01:32:44,950 --> 01:32:51,570
+قطعت منطقة التكامل لغاية ما وصلت للحدود الإقليمية
+
+761
+01:32:51,570 --> 01:32:58,510
+يبقى هنا أقل قيمة لـ r هنا، و أكبر قيمة لـ r هنا
+
+762
+01:32:58,510 --> 01:33:09,490
+فمجدداً r هنا؟ sec φ، أيوة، بتجي تقوليلي z في
+
+763
+01:33:09,490 --> 01:33:15,390
+الإحداثيات الكروية هي z تساوي r cos φ
+
+764
+01:33:15,390 --> 01:33:21,410
+يعني بتجي تقوليلي هنا z تساوي r cos φ
+
+765
+01:33:21,410 --> 01:33:27,230
+اللي هو 1، تمام، إذا r تساوي sec φ
+
+766
+01:33:27,230 --> 01:33:33,210
+يبقى أقل قيمة لـ r هي sec φ، و أكبر قيمة كده
+
+767
+01:33:35,800 --> 01:33:39,500
+للنصف القطر تبعها أنه أقل من أو يساوي 2، يعني
+
+768
+01:33:39,500 --> 01:33:45,620
+الكرة المصمتة كلها، دي، طيب نجي لـ φ، φ بتغير
+
+769
+01:33:45,620 --> 01:33:50,820
+من وين لوين؟ من 0 لغاية π/2، كده أعرف كده إيش
+
+770
+01:33:50,820 --> 01:33:56,820
+الـ φ، كده تبقى يلا، طيب ماشي، θ بقد إيش؟ نرجع
+
+771
+01:33:56,820 --> 01:34:03,660
+لفاية، بس قولولي θ من وين لوين؟ من 0 لإثنين π
+
+772
+01:34:07,220 --> 01:34:12,140
+مع قصد الـ φ هتبدأ من هنا، إذا هتبدأ من الـ 0
+
+773
+01:34:12,140 --> 01:34:19,660
+لـ قد إيش؟ الله أعلم، لأننا وعرفنا قد إيش معادلة هذا
+
+774
+01:34:19,660 --> 01:34:26,680
+الخط بيكون، و عرفنا φ تساوي قد إيش، يلا قد إحنا
+
+775
+01:34:26,680 --> 01:34:31,820
+رسمنا لكم، و رسمنا الخط و شوفوا كيف يمكنكم تحسبوا φ
+
+776
+01:34:31,820 --> 01:34:35,660
+من خلال الرسم اللي قدامكم هذا
+
+777
+01:34:49,200 --> 01:35:02,060
+يلا، أيوة صحيح، هاي z تساوي 1، مضبوط، صحيح
+
+778
+01:35:02,060 --> 01:35:09,320
+و r تساوي 2، ممتاز جداً، يبقى البنات بتقول لكم
+
+779
+01:35:09,320 --> 01:35:14,200
+خذوا صباح، أبو سمها، دانا ما يأتي، بتقولوا اللي فوق
+
+780
+01:35:14,200 --> 01:35:19,800
+اللي هي باتنين، يقول يا r تساوي 2، و هذه الـ
+
+781
+01:35:19,800 --> 01:35:24,740
+دائرة، لأن الليط لين z يساوي 1، في الإحداثيات
+
+782
+01:35:24,740 --> 01:35:31,800
+الكروية، يبقى z، و r cos φ بدها تساوي
+
+783
+01:35:31,800 --> 01:35:41,090
+واحد، يبقى صار عندنا r = 2، cos φ =
+
+784
+01:35:41,090 --> 01:35:45,430
+cos φ = cos φ = cos φ
+
+785
+01:35:45,430 --> 01:35:46,770
+= cos φ = cos φ = cos φ
+
+786
+01:35:46,770 --> 01:35:47,030
+= cos φ = cos φ = cos φ
+
+787
+01:35:47,030 --> 01:35:47,070
+= cos φ = cos φ = cos φ
+
+788
+01:35:47,070 --> 01:35:48,230
+= cos φ = cos φ = cos φ
+
+789
+01:35:48,230 --> 01:35:54,890
+= cos φ = cos φ = cos φ
+
+790
+01:35:54,890 --> 01:35:59,190
+cos φ =
+
+791
+01:36:02,390 --> 01:36:05,390
+By integration من 0 لإثنين π، By integration من
+
+792
+01:36:05,390 --> 01:36:06,650
+0 لـ π/3، By integration من 0 لـ
+
+793
+01:36:06,650 --> 01:36:10,230
+π/3، By integration من 0 لـ π/3
+
+794
+01:36:10,230 --> 01:36:11,750
+By integration من 0 لـ π/3، By
+
+795
+01:36:11,750 --> 01:36:12,170
+integration من 0 لـ π/3، By integration
+
+796
+01:36:12,170 --> 01:36:12,290
+من 0 لـ π/3، By integration من 0 لـ
+
+797
+01:36:12,290 --> 01:36:14,910
+π/3، By integration من 0 لـ π/3
+
+798
+01:36:14,910 --> 01:36:15,770
+By integration من 0 لـ π/3، By
+
+799
+01:36:15,770 --> 01:36:16,750
+integration من 0 لـ π/3، By integration
+
+800
+01:36:16,750 --> 01:36:20,210
+من 0 لـ π/3، By integration من 0 لـ
+
+801
+01:36:20,210 --> 01:36:23,050
+π/3، By integration من 0 لـ π/3
+
+802
+01:36:23,050 --> 01:36:26,110
+By integration من 0 لـ π/3، By
+
+803
+01:36:26,110 --> 01:36:31,870
+integration من 0 لـ π/3، By integration
+
+804
+01:36:31,870 --> 01:36:42,440
+من 0، طبعاً، و هنا sin φ، و هنا d φ d θ، إذا
+
+805
+01:36:42,440 --> 01:36:49,520
+صار هذا الطول تكاملين من 0 لإثنين π، من 0
+
+806
+01:36:49,520 --> 01:36:59,060
+لـ π/3، لـ 8 sin φ، و هنا ناقص بدي
+
+807
+01:36:59,060 --> 01:37:00,600
+أسوي زي اللي قبل يا بنات
+
+808
+01:37:06,750 --> 01:37:17,250
+tan φ، كل هذا في φ d θ، هذا
+
+809
+01:37:17,250 --> 01:37:27,390
+لحالها كإنها يشبه tan φ d، tan φ عملناها
+
+810
+01:37:27,390 --> 01:37:33,720
+بالضبط تماماً، يبقى بالنهاية كامل، يبقى طول التكامل من 0
+
+811
+01:37:33,720 --> 01:37:43,580
+لإثنين π، و -8 cos φ، و هذه بقى
+
+812
+01:37:43,580 --> 01:37:52,860
+- 8 tan² φ، كله على 2، من 0 لغاية
+
+813
+01:37:52,860 --> 01:38:03,450
+π/3، d θ، يبقى الثلث integration من
+
+814
+01:38:03,450 --> 01:38:08,790
+0 لغاية إثنين π، ليجي فتعوض π/3، جتا
+
+815
+01:38:08,790 --> 01:38:17,530
+60 بـ 1/2، مع الثمانية بتعطيك -4، نفس بدنا نجي
+
+816
+01:38:17,530 --> 01:38:25,150
+لـ ظل الـ 60، يعني جا 60 على جتا 60، جذر
+
+817
+01:38:25,150 --> 01:38:34,400
+3، أمان مظبوط، جذر 3 و تربيع 3
+
+818
+01:38:34,400 --> 01:38:41,200
+و على 2 طبعاً، هاي عوض بالقيم اللي فوق ناقص اللي
+
+819
+01:38:41,200 --> 01:38:46,680
+تحت، ناقص مع ناقص بصير زائد، 8 - 0 =
+
+820
+01:38:46,680 --> 01:38:54,460
+8، وظل الـ 0 بـ 0 فقط لا غير، كله في d θ، طب
+
+821
+01:38:54,460 --> 01:38:55,160
+اطلعي
+
+822
+01:38:59,050 --> 01:39:05,710
+5.5 من 8 بظل 2.5 يعني 5/2، شرفونه برا، يبقى طول في 5/2 في
+
+823
+01:39:05,710 --> 01:39:12,610
+تكامل من 0 لإثنين π لـ d θ، يبقى هذا الكلام
+
+824
+01:39:12,610 --> 01:39:22,110
+يساوي 5/6، و هنا θ من 0 لغاية إثنين π
+
+825
+01:39:22,110 --> 01:39:29,570
+يبقى 5/6 لـ إثنين π، و يساوي 5π/3
+
+826
+01:39:29,570 --> 01:39:39,530
+اللي هو مقدار هذا التكامل، بنروح لـ exercises
+
+827
+01:39:45,890 --> 01:39:53,190
+خمسة عشر، سبعة، exercises، خمسة عشر، سبعة، المسائل
+
+828
+01:39:53,190 --> 01:40:00,530
+التالية، 3، 5، 7، 9، 3، 5، 7
+
+829
+01:40:00,530 --> 01:40:10,730
+9، 15، 18، 19، 23، 25
+
+830
+01:40:10,730 --> 01:40:22,260
+25، 28، 30، 34، 7
+
+831
+01:40:22,260 --> 01:40:33,360
+30، 45، 47، 49
+
+832
+01:40:33,360 --> 01:40:42,740
+52، 53، 54، 57
+
+833
+01:40:42,740 --> 01:40:49,620
+57، 59، 62
+
+834
+01:40:52,520 --> 01:40:56,280
+يبقى يوم الأربعاء إن شاء الله القادم،
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/cjA4GBt8ijs_postprocess.srt b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/cjA4GBt8ijs_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..9c34a2f014339f34b6e0074857d3d3a8e231ed75
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/cjA4GBt8ijs_postprocess.srt
@@ -0,0 +1,3404 @@
+1
+00:00:13,720 --> 00:00:20,400
+بسم الله الرحمن الرحيم نرجع الآن لستشين اللي
+
+2
+00:00:20,400 --> 00:00:24,640
+ابتدأنا المرة الماضية المرة الماضية قلنا كيف نتحول
+
+3
+00:00:24,640 --> 00:00:28,120
+من Cartesian coordinates إلى cylindrical
+
+4
+00:00:28,120 --> 00:00:33,690
+coordinatesفقلنا نقطة P X Y و Z في الإحداثيات
+
+5
+00:00:33,690 --> 00:00:38,410
+الكارتزية و دي جابلها في الإحداثيات القسطوانية الـ
+
+6
+00:00:38,410 --> 00:00:44,250
+cylindrical coordinates اللي هو Z بتبقى زي ما هي
+
+7
+00:00:44,250 --> 00:00:52,410
+DX DY هستدلها بRDR Dθ واخدنا على ذلك مثال واحد في
+
+8
+00:00:52,410 --> 00:00:57,090
+المحاضرة الماضية الآن بناخد المثالة رقم اتنين
+
+9
+00:01:02,140 --> 00:01:07,700
+بنقلب من الإحداثيات الكارتيزية to an equivalent
+
+10
+00:01:07,700 --> 00:01:11,520
+integral in cylindrical coordinates إلى تكامل
+
+11
+00:01:11,520 --> 00:01:17,980
+المكافئ له بس في الإحداثيات الأسطانية ومن ثم بدأ
+
+12
+00:01:17,980 --> 00:01:21,800
+نحسب التكامل في الإحداثيات الأسطانية
+
+13
+00:01:30,080 --> 00:01:34,860
+الان نحول الى cylindrical coordinates X تربيه زي
+
+14
+00:01:34,860 --> 00:01:40,360
+نوع التربيه هي عبارة عن مين R تربيه دي زد كما هي
+
+15
+00:01:40,360 --> 00:01:47,440
+مالهاش اي اشكالين بجي لمين بدل دي X دي Y بقول ر دي
+
+16
+00:01:47,440 --> 00:01:54,320
+ار دي ثيتر اذا الحدود زد ستبقى كما هي
+
+17
+00:02:02,230 --> 00:02:10,390
+ر في قصين الزاويةبدي ايجي عندي دي x دي y بدي
+
+18
+00:02:10,390 --> 00:02:16,290
+استبدلها بRDRDθ بدي اعرف R بدي اتغير من وين لوين و
+
+19
+00:02:16,290 --> 00:02:20,070
+كذلك θ بدي اتغير من وين لوين لذلك بروح ارسم
+
+20
+00:02:20,070 --> 00:02:25,890
+المنطقة التكامل اللي عندها هذه كيف كانت كارتزيا و
+
+21
+00:02:25,890 --> 00:02:29,170
+كيف بدي احولها الى cylindrical coordinates
+
+22
+00:02:38,450 --> 00:02:43,470
+بعد ال DZ بدأ يجيني DX يبقى الحدود هذه هي حدود
+
+23
+00:02:43,470 --> 00:02:49,210
+امام ال X ال X بدأ تبدأ من اندي ال zero لغاية
+
+24
+00:02:49,210 --> 00:02:54,770
+الجذر الموجة بيبقى عندها تكون جهتي اليمينجهات
+
+25
+00:02:54,770 --> 00:02:59,150
+اليمين يعني X جهات الشمال ماعنديش تمام ؟ طيب هذه
+
+26
+00:02:59,150 --> 00:03:03,130
+معادلة ليش لما اقول X يساوي الجدري التربيهي لو
+
+27
+00:03:03,130 --> 00:03:07,790
+واحد ناقص Y تربيه لو ربعت الطرفين وانا بصير دائرة
+
+28
+00:03:07,790 --> 00:03:13,030
+مركزها نقطة الأصل و نسقطها يساوي واحد صحيح بس مش
+
+29
+00:03:13,030 --> 00:03:17,680
+اللي على الشمال ماليش فيهايبقى نادي باسميني اليمين
+
+30
+00:03:17,680 --> 00:03:23,640
+طب هل كل نصف دائرة و لا ربع دائرة بيدجل الحدود تبع
+
+31
+00:03:23,640 --> 00:03:28,560
+ال Y جل ال Y بدأ تبدأ من أيدي السالف واحد لغاية
+
+32
+00:03:28,560 --> 00:03:34,340
+مين الواحد يبقى منطقة التكامل كلها المنطقة المضللة
+
+33
+00:03:34,340 --> 00:03:50,050
+اللي عندنا طيبهذه عبارة عن نصف دائرة ر ستتغير
+
+34
+00:03:50,050 --> 00:03:56,370
+من zero إلى أي نقطة على محيط الدائرة من صفر لغاية
+
+35
+00:03:56,370 --> 00:04:05,050
+واحدلغاية واحد لإيش؟ وين ما ترسمي هذا الخط المسافة
+
+36
+00:04:05,050 --> 00:04:14,410
+من هنا لهنا مسافة ثابتة هيبقى اللي عندى θ تبدأ
+
+37
+00:04:14,410 --> 00:04:18,350
+تتغير إذا ابتديت عند السلب واحد و جايب طالع لغاية
+
+38
+00:04:18,350 --> 00:04:24,690
+الواحد، من وين لوين؟ من سالب باي على اتنين إلى باي
+
+39
+00:04:24,690 --> 00:04:31,270
+على اتنينلما حد حدد تكمر صح يبقى لك شغل روتيني
+
+40
+00:04:31,270 --> 00:04:36,430
+يبقى أول شي بتكمل بالنسبة لمان الذي زد يبقى الار
+
+41
+00:04:36,430 --> 00:04:40,690
+هذي مقدر ثابت مليش علاقة بالموضوع يبقى بضوحة كامل
+
+42
+00:04:40,690 --> 00:04:43,770
+فبقى يبقى هذا الكلام يستخدم integration
+
+43
+00:05:04,410 --> 00:05:09,010
+يبقى الة المثلة اللى عندى الى تكامل من سالب باى
+
+44
+00:05:09,010 --> 00:05:13,230
+على اتنين كده باى على اتنين تكامل من Zero لغاية
+
+45
+00:05:13,230 --> 00:05:17,010
+الواحد ال Zero بتعاون بالقيم اللى فوق النقص اللى
+
+46
+00:05:17,010 --> 00:05:22,290
+تحته اللى بيبقى بس القيم اللى فوق وعنا كمان R
+
+47
+00:05:26,720 --> 00:05:35,020
+كوصين الزاوية ثيتا في DR في D ثيتا إذا هذا بدي
+
+48
+00:05:35,020 --> 00:05:40,320
+يعطيني ما يأتي يبقى اي تكامل من سالف باي على اتنين
+
+49
+00:05:40,320 --> 00:05:47,580
+إلى باي على اتنين وهذه تكملها أقص خمسة على خمسة من
+
+50
+00:05:47,580 --> 00:05:53,520
+Zero لواحد لسه بضايل عندي كوصين ثيتا في D ثيتا
+
+51
+00:05:54,240 --> 00:05:57,940
+بنعوض بالقيمة اللي فوق هيجيبلي خمس والقيمة اللي
+
+52
+00:05:57,940 --> 00:06:03,080
+تحت هيجيبلي zero يبقى خمس مقدار ثابت فأقوله كمان
+
+53
+00:06:03,080 --> 00:06:09,380
+خليك برا يبقى خمس تكامل من سالف πاي على اتنين إلى
+
+54
+00:06:09,380 --> 00:06:18,720
+باي على اتنين ل cosine ثيتا دي ثيتا cosine ثيتا دي
+
+55
+00:06:18,720 --> 00:06:25,800
+ثيتاeven هذا الرقم هو نفس الرقم بإشارة مخالفة إذا
+
+56
+00:06:25,800 --> 00:06:31,260
+بستخدم خاصية ال even يبقى هذا الكلام اتنين على
+
+57
+00:06:31,260 --> 00:06:38,320
+خمسة تكامل من zero ل pi على اتنين ل cosine theta d
+
+58
+00:06:38,320 --> 00:06:47,080
+theta يبقى هذا الكلام يبدو يسوى خمسين اتنين على
+
+59
+00:06:47,080 --> 00:06:49,520
+خمسة وتكامل ال cosine
+
+60
+00:06:58,410 --> 00:07:03,150
+صين البي على اتنين بواحد وصين زيرو بزيرو إذا
+
+61
+00:07:03,150 --> 00:07:14,670
+الجواب يساوي نين على خمسة لثالث
+
+62
+00:07:14,670 --> 00:07:19,850
+نتة و
+
+63
+00:07:19,850 --> 00:07:26,630
+ل find the volume of the region find the volume
+
+64
+00:07:27,950 --> 00:07:35,370
+of the region قدش حجم المنطقة bounded by the
+
+65
+00:07:35,370 --> 00:07:42,050
+cylinder bounded by
+
+66
+00:07:42,050 --> 00:07:53,850
+the cylinder والمحدودة بالاسطوالةx تربيع زائد y
+
+67
+00:07:53,850 --> 00:08:05,050
+تربيع تساوي أربعة and the airplanes بالمستويين z
+
+68
+00:08:05,050 --> 00:08:15,350
+بتساوي zero and المستوى التاني x زائد y زائد z
+
+69
+00:08:15,350 --> 00:08:18,430
+بتساوي اللي هو أربعة
+
+70
+00:08:33,500 --> 00:08:38,640
+هذا السؤال يختلف عن السؤالين السابقين السؤالين
+
+71
+00:08:38,640 --> 00:08:43,460
+السابقين كان ميعطيني حدود التكامل وجاهز بعث عليها
+
+72
+00:08:43,460 --> 00:08:48,140
+كامل الأول كان مباشر التاني كان بدنا نغير حدود
+
+73
+00:08:48,140 --> 00:08:52,580
+التكامل من كارتيزيا إلى cylindrical coordinates
+
+74
+00:08:52,580 --> 00:08:57,160
+لكن هذا لا اعطاني وقال انت بتحدد حدود التكامل
+
+75
+00:08:57,160 --> 00:09:02,560
+لوحدك بقوله ماشي الحاليبقى انا بدي ابدأ احط
+
+76
+00:09:02,560 --> 00:09:08,840
+التكامنات الثلاثة اللي عندنا اي تلت تكامنات ل DV
+
+77
+00:09:08,840 --> 00:09:20,470
+DV بدي اقول عليها DZ وR DR Dθ شكلانهابدي ابدأ زد
+
+78
+00:09:20,470 --> 00:09:25,170
+قال ال region محدودة ما بين ال cylinder هذي and
+
+79
+00:09:25,170 --> 00:09:30,830
+the planes وفي عندي مستوين المستوى الأول زد يساوي
+
+80
+00:09:30,830 --> 00:09:35,230
+zero لهمين ال XY فلان يعني مستوى الأرض اللي احنا
+
+81
+00:09:35,230 --> 00:09:40,510
+قاعدين عليها وهذا مستوى X زائد Y زائد Z يساوي
+
+82
+00:09:40,510 --> 00:09:46,050
+أربعة إذا زد تتغير من وينمن عندي الـ zero لغاية
+
+83
+00:09:46,050 --> 00:09:53,110
+هذا هذا Z قدش ساوي أربعة ناقص X ناقص Y يبقى أربعة
+
+84
+00:09:53,110 --> 00:10:01,550
+ناقص X ناقص Y تمام بداجي أشوف حدود ال R والثيتا
+
+85
+00:10:01,550 --> 00:10:06,550
+مشان أشوف حدود ال R والثيتا بداجي أشوف السيلندر
+
+86
+00:10:06,550 --> 00:10:09,790
+اللي عندنا السيلندر اللي عندنا هذا مين محورها يا
+
+87
+00:10:09,790 --> 00:10:16,120
+بناتيمحور Z لأنه الرمز الغائب وتقاطعها مع المستوى
+
+88
+00:10:16,120 --> 00:10:22,220
+XY Plane بيكون على شكل دائرة مركزها النقطة الأصل و
+
+89
+00:10:22,220 --> 00:10:28,200
+نصف قطر هيساوي اتنين تمام تمام إذا لو جيت قلت هذه
+
+90
+00:10:28,200 --> 00:10:34,420
+المحاور اللي عندنا هذا محور X وهذا محور Y وهذا
+
+91
+00:10:34,420 --> 00:10:41,030
+نقطة الأصل Zيبقى هذا بدأ يكون دائرة الشكل اللي
+
+92
+00:10:41,030 --> 00:10:47,790
+عندنا هذا يبقى هي الدائرة اللي موجودة إذا R على
+
+93
+00:10:47,790 --> 00:10:53,010
+هذه الدائرة ستتغير من أين إلى أين؟ من Zero لغاية
+
+94
+00:10:53,010 --> 00:11:00,330
+كم؟ لغاية اتنين لماذا؟ لأن نصف قطر دائرة هذه ثابت
+
+95
+00:11:00,330 --> 00:11:06,880
+أين ما تروح تجد R تساوي Zeroوارت ساوي هنا قداش
+
+96
+00:11:06,880 --> 00:11:12,480
+اتنين طيب كويس ضايق اللي عندنا مين ثيتا ثيتا
+
+97
+00:11:12,480 --> 00:11:16,560
+بالنسبة لدار نصطوانة نازلة من فوق يبقى ثيتا حتى
+
+98
+00:11:16,560 --> 00:11:22,540
+تتغير من و لا و اين من صفر لغاية اتنين بايت يبقى
+
+99
+00:11:22,540 --> 00:11:30,300
+من zero لغاية اتنين بايت طيب مش مشكلة اظل لو
+
+100
+00:11:30,300 --> 00:11:34,460
+اكملها بالنسبة لزيد في الأول لإنها هذه من ضمن مين
+
+101
+00:11:34,840 --> 00:11:40,420
+من ضمن المتغيرات التلاتة تبع الـ Cylindrical
+
+102
+00:11:40,420 --> 00:11:44,600
+Coordinates يبقى ماجي بقول هذا الكلام بده يساوي
+
+103
+00:11:44,600 --> 00:11:50,420
+تكامل من صفر لإتنين باي تكامل من Zero لغاية اتنين
+
+104
+00:11:50,420 --> 00:11:58,080
+تكامل ال DZ اللي هي FZ من عند Zero لغاية أربع ناقص
+
+105
+00:11:58,080 --> 00:12:04,380
+X ناقص Y وظل عندي برا RDRDZ
+
+106
+00:12:07,090 --> 00:12:16,030
+هذا الكلام يجب أن يساوي هذا
+
+107
+00:12:16,030 --> 00:12:23,890
+الكلام يجب أن يتكامل من 0 إلى 2 باي تكامل من 0 إلى
+
+108
+00:12:23,890 --> 00:12:32,130
+2 نعوض بالقيمة ناقص 4 ناقص X ناقص Y ناقص الـ Zero
+
+109
+00:12:32,130 --> 00:12:41,750
+وهنا ضللنا RDRDithita وما عجلك عن قومك يا موسى
+
+110
+00:12:41,750 --> 00:12:49,070
+يعني أربعه وبعدين في القرآن في سورة الأسرار ويدعو
+
+111
+00:12:49,070 --> 00:12:54,350
+الإنسان بالشر دعاءه بالخير وكان الإنسان عجولة
+
+112
+00:12:54,350 --> 00:13:00,030
+باستعجل دائما أو أبدا لأنك لا تستعجلنا واصبرنا حتى
+
+113
+00:13:00,030 --> 00:13:08,010
+يأتيكن اليقينطيب عارفين إيش معنى اليقين؟ ايوة
+
+114
+00:13:08,010 --> 00:13:14,550
+الموت اليقين هو أحد أسماء الموت يبقى هنا حتى ..
+
+115
+00:13:14,550 --> 00:13:18,670
+هنا لا نقصد موت ولكن نقصد اللي هو الإجابة اللي
+
+116
+00:13:18,670 --> 00:13:23,810
+أنتوا بتسألوا عليها هنا يبقى هذا الكلام يساوي من
+
+117
+00:13:23,810 --> 00:13:29,600
+zero لإتنين byومن هنا من Zero للإتنين من Zero
+
+118
+00:13:29,600 --> 00:13:34,300
+للإتنين هذه حدوط لل R إذا لازم أحوّل ال kart easy
+
+119
+00:13:34,300 --> 00:13:38,740
+ان هذه اللامعين إلى cylindrical إذا بدي أشيل ال X
+
+120
+00:13:38,740 --> 00:13:43,640
+و أحط مكانها R Cos θ و بدي أشيل ال Y و أحط مكانها
+
+121
+00:13:43,640 --> 00:13:53,200
+R Sin θ إذا هذه يا بنات تصير 4R ناقص R تربيع في
+
+122
+00:13:53,200 --> 00:14:00,600
+Cos الزاوية θنقص R تربيع في Sine الزاوية تيتا كل
+
+123
+00:14:00,600 --> 00:14:10,400
+هذا DRZ إذا شيلت ال X وحطيت مكانها R Cosine تيتا
+
+124
+00:14:10,400 --> 00:14:15,460
+وشيلت ال Y وحطيت مكانها R Sine تيتا اللي وقمتهم في
+
+125
+00:14:15,460 --> 00:14:19,680
+الـ cylindrical coordinates وضربت في R فصرت
+
+126
+00:14:19,680 --> 00:14:25,830
+المعادلة قدامي بهذا الشكل الان بيتكمل بالنسبةلمن؟
+
+127
+00:14:25,830 --> 00:14:32,110
+لR الـ integration من Zero لإتنين بايت هذي باتنين
+
+128
+00:14:32,110 --> 00:14:40,890
+R تربيع مفقود؟ طيب هذي ناقص طول R تكييب في cosine
+
+129
+00:14:40,890 --> 00:14:47,190
+الزاوية ثيتا وهذي ناقص طول R تكييب في sine الزاوية
+
+130
+00:14:47,190 --> 00:14:55,400
+ثيتا والكلام من Zero لإتنين لديه ثيتايبقى هذا
+
+131
+00:14:55,400 --> 00:15:02,020
+الكلام مدة ساعة من Zero لإتنين By L بتعوض بالقيم
+
+132
+00:15:02,020 --> 00:15:06,800
+اللي فوق نقصها لتحت طبعا لتحت Zero Zero Zero مع
+
+133
+00:15:06,800 --> 00:15:11,560
+السلامة بتظهر بس القيم اللي فوت بدي أشيل كل R و
+
+134
+00:15:11,560 --> 00:15:16,600
+أحط مكانها اتنين يبقى هنا اتنين تاربية اربعة في
+
+135
+00:15:16,600 --> 00:15:24,010
+اتنين بتمانية يبقى هاي تمانيةوهنا ناقص برضه تمانية
+
+136
+00:15:24,010 --> 00:15:30,670
+على تلاتة يبقى تمانية على تلاتة وsin الزاوية ثيتا
+
+137
+00:15:30,670 --> 00:15:37,890
+وهنا ناقص تمانية على تلاتة sin الزاوية ثيتا في دي
+
+138
+00:15:37,890 --> 00:15:38,650
+ثيتا
+
+139
+00:16:06,630 --> 00:16:12,930
+طيب نجم كامل هنا تجه هذا الكلام بده يساوى تمانية
+
+140
+00:16:12,930 --> 00:16:19,430
+ثيتا واللي بعده ال cosine بالزائد نخص تمانية على
+
+141
+00:16:19,430 --> 00:16:27,030
+تلاتة cosine زاوية ثيتا واللي بعده زائد تمانية على
+
+142
+00:16:27,030 --> 00:16:33,460
+تلاتةبكوصين الزاوية تيتا وكله من zero لما تقدرش
+
+143
+00:16:33,460 --> 00:16:38,180
+لما تتنين باى لذا نجد ان عوض بحدود التكامل هادئة
+
+144
+00:16:38,180 --> 00:16:44,300
+من هادئة تيتا وحطت تنين باى بيصير ست عشر باى صيني
+
+145
+00:16:44,300 --> 00:16:50,180
+اتنين باى ضهورة كاملة يعني انه زيرو يبقى هادئ هنا
+
+146
+00:16:50,180 --> 00:16:56,200
+اقل من زيرو تما الكوصين اتنين باى بواحد تمازز
+
+147
+00:17:02,660 --> 00:17:10,880
+zero zero وصين صفر و واحد يبقى ناقص تمانية على
+
+148
+00:17:10,880 --> 00:17:16,020
+تلاتة الفون ناقص اللي تحت يبقى ال job بتعطينا قدير
+
+149
+00:17:16,020 --> 00:17:21,620
+ستاشر و واحد و تسهل و تسهل ده حد فيكم بتسأل أي
+
+150
+00:17:21,620 --> 00:17:27,360
+سؤال يعني إحنا إذا حددنا حدود التكامل صح بصير
+
+151
+00:17:27,360 --> 00:17:34,650
+الشغل الباقي كله عندنا شغل روتينيمثال مثال اربعة
+
+152
+00:17:34,650 --> 00:17:38,310
+you
+
+153
+00:17:38,310 --> 00:17:43,650
+gonna find the volume of the region find the
+
+154
+00:17:43,650 --> 00:17:55,330
+volume of the region جدش حجب المنطقة bounded above
+
+155
+00:17:55,330 --> 00:17:59,830
+bounded above
+
+156
+00:18:13,460 --> 00:18:24,780
+يساوي خمسة ناقص X تربيع ناقص Y تربيع and below ومن
+
+157
+00:18:24,780 --> 00:18:37,680
+أسفل by the paraboloid كذلك بالparaboloid
+
+158
+00:18:40,450 --> 00:18:49,310
+اللي هو الـ z تساوية أربعة X تربيع زائد أربعة Y
+
+159
+00:18:49,310 --> 00:19:08,830
+تربيع نمسح
+
+160
+00:19:08,830 --> 00:19:09,850
+الشجرة دي كلها
+
+161
+00:19:32,010 --> 00:19:38,410
+خلاص نرجع لسؤال هذا مرة تانية السؤال بيقول ليهذه
+
+162
+00:19:38,410 --> 00:19:43,530
+حجم المنطقة المحدودة من أعلى بالparaboloid اللي
+
+163
+00:19:43,530 --> 00:19:49,970
+قدامنا هنا ومن أسفل بالparaboloid السابق طبعا رسمة
+
+164
+00:19:49,970 --> 00:19:54,630
+الparaboloid هذا مر علينا من ضمن الرسومات الستة،
+
+165
+00:19:54,630 --> 00:20:00,650
+مظهر؟ كويس؟ إذا بدنا نجد رسم كل واحد فيهم ونحدد
+
+166
+00:20:00,650 --> 00:20:05,260
+وين المنطقة المشتركة اللي هو بدوياهالو جيت لل
+
+167
+00:20:05,260 --> 00:20:10,440
+Paraboloid الأول و روحت أخذت المحاور بالشكل اللي
+
+168
+00:20:10,440 --> 00:20:18,400
+عنها يبقى هذا محور X وهذا محور Y وهذا محور Z
+
+169
+00:20:18,400 --> 00:20:22,820
+بالداخل لل Paraboloid الأول لو كان ال Paraboloid
+
+170
+00:20:22,820 --> 00:20:30,260
+الأول هو Z تساوي X تربية زائد Y تربيةلو كان ال
+
+171
+00:20:30,260 --> 00:20:33,760
+paraboloid الأول مش بالشكل الأول كان X تربيه زائد
+
+172
+00:20:33,760 --> 00:20:38,780
+و ات تربيه إذا ال paraboloid جينه زيها و من هنا
+
+173
+00:20:38,780 --> 00:20:44,740
+على شكل ذهب Circular paraboloid تمام لكن لما تبقى
+
+174
+00:20:44,740 --> 00:20:49,580
+سابقة اتنين إشارة سالف يبقى بديه اللي بيصير بدل ما
+
+175
+00:20:49,580 --> 00:20:53,560
+هو مفتوح إلى أعلى بيصير مفتوح إلى أعلى للأسفل يبقى
+
+176
+00:20:53,560 --> 00:20:57,760
+بديه يصير ال paraboloid بالشكل اللي قلناه طيب راح
+
+177
+00:20:57,760 --> 00:20:59,260
+أضفنا له خمسة
+
+178
+00:21:01,620 --> 00:21:07,260
+المقدار خمسة إذا الرسمة في هذه الحالة بتاخد الشكل
+
+179
+00:21:07,260 --> 00:21:12,520
+التالي بيدهد على استقالته وال Paraboloid بيجيه
+
+180
+00:21:12,520 --> 00:21:20,540
+بشكل هذا الشكل تمام؟ وهذه القاعدة عبارة عن دائرة
+
+181
+00:21:20,540 --> 00:21:27,310
+الشكل اللي عندها هذه النقطة كده يا عزيزي؟5 يبقى
+
+182
+00:21:27,310 --> 00:21:36,710
+هذه 005 يبقى 005 على محور الزرد نجي لل Paraboloid
+
+183
+00:21:36,710 --> 00:21:42,010
+الثاني Paraboloid الثاني الزرد يسوى أربع نقص اكس
+
+184
+00:21:42,010 --> 00:21:47,450
+زائد X ترمية زائد Y ترمية يبقى هذا Parabola رقصه
+
+185
+00:21:47,450 --> 00:21:51,730
+نقطة الأصل المفتوح لوين لأعلى يبقى حرصه بلون تاني
+
+186
+00:21:51,730 --> 00:21:55,390
+يبقى بدجيك ال Parabola بهذا الشكل
+
+187
+00:21:58,230 --> 00:22:01,910
+و يتقاطع مع ال parabola اللى عندنا في ال
+
+188
+00:22:01,910 --> 00:22:07,790
+paraboloid التانى هذاهي الدائرة اللي عندناها يبقى
+
+189
+00:22:07,790 --> 00:22:11,990
+هذا ال paraboloid الثاني اللي هو مفتوح لعله هذا
+
+190
+00:22:11,990 --> 00:22:17,810
+مفتوح لأسفل يبقى احنا بدنا حجم المنطقة المحصورة
+
+191
+00:22:17,810 --> 00:22:23,210
+بين من؟ بين ال two paraboloids يبقى كأنه بقول ايش؟
+
+192
+00:22:23,210 --> 00:22:28,750
+بدي حجم ال paraboloid اللي عندنا هذا مضافة للي حجم
+
+193
+00:22:28,750 --> 00:22:33,000
+الطاقية اللي فوقيبقى هذا لما نقصه لتحت بظل اللي
+
+194
+00:22:33,000 --> 00:22:38,720
+فوق هذه على شكل ايه؟ على شكل طاقية يبقى بدنا حجم
+
+195
+00:22:38,720 --> 00:22:44,040
+المنطقة هذه كله بقوله كويس يبقى احنا بدنا نحدد
+
+196
+00:22:44,040 --> 00:22:48,800
+حدود التكمل تحديدا سليما وبالتالي بصير مسلتنا
+
+197
+00:22:48,800 --> 00:22:54,320
+بسيطة يبقى بقوله ال volume V اللي بده اياه يبقى
+
+198
+00:22:54,320 --> 00:22:57,780
+solution ال volume V
+
+199
+00:23:03,060 --> 00:23:09,520
+نبدأ من DZ و بعدها RDRD
+
+200
+00:23:13,960 --> 00:23:19,880
+بالـ Parabolid اللي فوق الأسود هذا معادلته Z يسوى
+
+201
+00:23:19,880 --> 00:23:24,980
+كمسة نقص X تربيع نقص Y تربيع يعني إيش؟ يعني
+
+202
+00:23:24,980 --> 00:23:33,160
+معادلته هذها اللي هي Z تسوى خمسة نقص X تربيع زي Y
+
+203
+00:23:33,160 --> 00:23:39,060
+تربيع تمام؟ طيب هذه خمسة نقص بدي أحولها إلى
+
+204
+00:23:39,060 --> 00:23:44,990
+الـCylindricalيبقى X تربيع زاد و تربيع عبارة عن Y
+
+205
+00:23:44,990 --> 00:23:50,910
+تربيع يبقى خمسة نفس R square تمام تمام نيجي لل
+
+206
+00:23:50,910 --> 00:23:56,970
+Parabolic التالي صاحبنا هذا اللي هو الأزرق كويس Z
+
+207
+00:23:56,970 --> 00:24:05,050
+تساوي أربعة في X تربيع زاد Y تربيع إذا هذا الكلام
+
+208
+00:24:05,050 --> 00:24:14,520
+بتساوي كده؟ أربعة R تربيعطب كويس نيجي نحدد حدود
+
+209
+00:24:14,520 --> 00:24:20,460
+التكامل بالنسبة إلى مين؟ إلى زد يبقى بدأ أروح أخد
+
+210
+00:24:20,460 --> 00:24:28,900
+أي نقطة على سطح الفرابل السفلي و أرسم موازن لمحور
+
+211
+00:24:28,900 --> 00:24:35,700
+زد و يقطع منطقة مين؟ منطقة التكامل يبقى بداجي طالع
+
+212
+00:24:35,700 --> 00:24:43,990
+هك امشي امشي جابلنا هنايبقى قابلنا السطح السفلي
+
+213
+00:24:43,990 --> 00:24:48,710
+عند هذه النقطة وقابلنا السطح العلوية عند هذه
+
+214
+00:24:48,710 --> 00:24:54,570
+النقطة يبقى هذه النقطة ايش بتكون يا بنات؟ اربعة ار
+
+215
+00:24:54,570 --> 00:25:01,110
+تربيع يعني ز عند هذه النقطة لأي نقطة على محيط
+
+216
+00:25:01,110 --> 00:25:08,510
+الفرابل السفلي بتبقى اربعة ار تربيعو Z هي لها عند
+
+217
+00:25:08,510 --> 00:25:16,030
+هذه النقطة Z يساوي خمسة ناقص R تربيع إذا Z اللي
+
+218
+00:25:16,030 --> 00:25:22,830
+عندنا دي ستتغير من أقل قيمة إلى أكبر قيمة من عند
+
+219
+00:25:22,830 --> 00:25:32,710
+الأربع R تربيع لخمسة ناقص R تربيع مين ضللنا؟ R
+
+220
+00:25:32,710 --> 00:25:38,780
+وThetaأريد أن أعرف أين الـr و الـθ و أيضًا أين
+
+221
+00:25:38,780 --> 00:25:44,860
+منطقة التقاطع تبعتهم؟ هذه لو جيت أسقطها على الـr
+
+222
+00:25:44,860 --> 00:25:49,740
+على من؟ على الـxy المشي هنا حدد ال domain اللي
+
+223
+00:25:49,740 --> 00:25:54,500
+عندنا هذا تمام يمكن لو جيت أسقطها بلاتك تجيلك هذه
+
+224
+00:25:54,500 --> 00:26:00,220
+هناك و تجيلك هذه التانية هناك اللي فوق دائرة يمكن
+
+225
+00:26:00,220 --> 00:26:02,360
+تلاقي هذه كمان دائرة
+
+226
+00:26:07,400 --> 00:26:14,060
+الان بدي اعرف كده تيتا و كده R اظن واضح من الدائرة
+
+227
+00:26:14,060 --> 00:26:19,060
+هذه ان تيتا في الدائرة من صفر لاثنين بايم يفجه هذه
+
+228
+00:26:19,060 --> 00:26:23,460
+من Zero لاثنين بايم مع اني مشكلة فيها المشكلة
+
+229
+00:26:23,460 --> 00:26:29,600
+دايلة وين؟ في الـR بدي اعرف كده نصف قطر هذه
+
+230
+00:26:29,600 --> 00:26:35,820
+الدائرة هميست هي الدائرة اللي فوق هذه بالضبط تماما
+
+231
+00:26:35,820 --> 00:26:41,620
+تمامايبقى هذا لو عرفت قداش R اللي منك بحلنا
+
+232
+00:26:41,620 --> 00:26:46,640
+الإشكالية مين تقولك كيف نجيب R من الدائرة اللي
+
+233
+00:26:46,640 --> 00:26:50,700
+فوق؟
+
+234
+00:26:50,700 --> 00:26:55,780
+يلا نشوف بسيطة وسهلة جدا كمان very easy
+
+235
+00:27:01,890 --> 00:27:07,450
+بنجيب ايش؟ كويس
+
+236
+00:27:07,450 --> 00:27:12,470
+الدائرة هذه يا بنات مشتقة على كل من ال two
+
+237
+00:27:12,470 --> 00:27:18,010
+surfaces اذا بدنا نسوي المعادلتين في بعض بكون خلصت
+
+238
+00:27:18,010 --> 00:27:23,090
+من المشكلة دي طيب باجي بقوله اه ماهي z فوق خمسة
+
+239
+00:27:23,090 --> 00:27:28,510
+ناقص R تربية و z تعتبر اربعة R تربية وهذه الدائرة
+
+240
+00:27:28,510 --> 00:27:33,740
+هي مشتركة ما بين الاتنينيبقى الذد في هذه اللحظة
+
+241
+00:27:33,740 --> 00:27:38,840
+لازم تسوى مين؟ الذد التاني، إذا بناء عليه الذد
+
+242
+00:27:38,840 --> 00:27:46,600
+عندها هتسوى خمسة ناقص R تربيع وتسوى أربعة R تربيع،
+
+243
+00:27:46,600 --> 00:27:52,260
+يبقى بناء عليه هذه هتعطيك إيش؟ هتعطيك إنه خمسة R
+
+244
+00:27:52,260 --> 00:27:58,420
+تربيع بده يسوى خمسة، يبقى ال R تربيع تسوى واحد،
+
+245
+00:27:58,420 --> 00:28:05,510
+يبقى ال R كتش بده تسوى بنانة1 يبقى ال R ستتغير من
+
+246
+00:28:05,510 --> 00:28:10,910
+ال zero من النقطة هذه إلى أي نقطة على محيط الدائرة
+
+247
+00:28:10,910 --> 00:28:16,550
+يعني من النقطة هذه إلى أي نقطة على محيط الدائرة
+
+248
+00:28:16,550 --> 00:28:23,770
+يبقى هنا R تساوي واحد وهنا R تساوي واحد كذلك يبقى
+
+249
+00:28:23,770 --> 00:28:30,140
+من Zero لغاية واحديبقى الآن حددنا حدود التكامل
+
+250
+00:28:30,140 --> 00:28:35,820
+تحديدا سليما مافيش فيه أي إشكالية وبالتالي لم يبقى
+
+251
+00:28:35,820 --> 00:28:40,120
+علي إلا أن أقوم بالتكامل لأن كل المسألة كتبتها
+
+252
+00:28:40,120 --> 00:28:44,340
+الآن في الـ cylindrical coordinates بقى اللي بقولك
+
+253
+00:28:44,340 --> 00:28:50,900
+بويس يبقى هذا الكلام بالساوي integration من zero
+
+254
+00:28:50,900 --> 00:28:55,580
+لإتنين by integration من zero لواحد تكامل
+
+255
+00:29:21,240 --> 00:29:25,100
+يبقى هذا الكلام اللي يعطيني integration من Zero
+
+256
+00:29:25,100 --> 00:29:30,380
+لإتنين باي من Zero لغاية الواحد طالع عندك هنا
+
+257
+00:29:30,380 --> 00:29:40,400
+لمين؟ لخمسة ناقص خمسة R تربيع كله هنا في RDRدى
+
+258
+00:29:40,400 --> 00:29:46,100
+تيتا او انشئتنا فقولنا هذا الكلام بدل ساوية
+
+259
+00:29:46,100 --> 00:29:50,840
+integration من zero للاثنين by integration من zero
+
+260
+00:29:50,840 --> 00:30:01,520
+لواحد لمين لخمسة R ناقص خمسة R تكيب كله دى اه دى
+
+261
+00:30:01,520 --> 00:30:06,980
+تيتا دخلنا R اللى برا داخل الجوز طيب مش نايل إلا
+
+262
+00:30:06,980 --> 00:30:11,220
+كامليبقى هذا الكلاب بدل يساوي integration من zero
+
+263
+00:30:11,220 --> 00:30:19,520
+لإتنين باي وهذه خمسة R تربيع على الإتنين وهذه ناقص
+
+264
+00:30:19,520 --> 00:30:26,460
+خمسة على أربعة R أقصى أربعة والكلاب هذا كله من
+
+265
+00:30:26,460 --> 00:30:31,680
+zero لغاية الواحد وهذه ان اليومين تبتدي تيتا
+
+266
+00:30:36,080 --> 00:30:42,020
+بتعود القيمة اللي فوق يا بناتي بالخمسة على اتنين-5
+
+267
+00:30:42,020 --> 00:30:50,240
+على 4-0 مع السلامة كله في Dθ يبقى بضالة ان دي قداش
+
+268
+00:30:50,240 --> 00:31:01,740
+5 على 4 و من 0 لل 2π لل Dθ يبقى 5 على 4θ من 0 لل
+
+269
+00:31:01,740 --> 00:31:09,900
+2π و اللي يبدأ تساوي 5 على 4 في 2πطبعا بضل اللي
+
+270
+00:31:09,900 --> 00:31:17,400
+يديه خمسة by على الإتنين هذا حجم المنطقة اللي
+
+271
+00:31:17,400 --> 00:31:23,170
+عليهايبقى بنات إذا قرأنا السؤال قراءة سليمة و
+
+272
+00:31:23,170 --> 00:31:28,870
+الرسم كان معروف الشكل المعطيني له سبق الدراسة و
+
+273
+00:31:28,870 --> 00:31:33,870
+قبل ذلك بصير عملية الرسم بسيطة جدا و من الرسم باجي
+
+274
+00:31:33,870 --> 00:31:38,910
+بحدد حدود التكامن وبالتالي تبقى انتهت المشكلة أو
+
+275
+00:31:38,910 --> 00:31:44,710
+بكون انحل السؤال بسهولة ويسط حد بتحفظ اي سؤال هنا
+
+276
+00:31:46,300 --> 00:31:49,680
+نذهب للنصف الثاني على الـ Spherical Coordinates
+
+277
+00:31:49,680 --> 00:31:58,160
+نذهب
+
+278
+00:31:58,160 --> 00:32:04,580
+للنصف الثاني
+
+279
+00:32:04,580 --> 00:32:08,620
+على الـ Spherical Coordinates
+
+280
+00:32:30,710 --> 00:32:35,210
+الشطر التاني من هذا ال section يقول integration
+
+281
+00:32:35,210 --> 00:32:38,450
+and spherical coordinates
+
+282
+00:32:55,760 --> 00:33:03,520
+التكامل في الأحداثيات
+
+283
+00:33:03,520 --> 00:33:07,280
+الكورية أو الكوراوية
+
+284
+00:33:27,410 --> 00:33:37,370
+point P in space P
+
+285
+00:33:37,370 --> 00:33:50,130
+of رو وفاي وثيتا in which بحيث
+
+286
+00:33:50,130 --> 00:33:59,960
+ان النقطة الأولى رو is the distancewrong is the
+
+287
+00:33:59,960 --> 00:34:12,200
+distance المسافة from P from P to the origin
+
+288
+00:34:12,200 --> 00:34:20,280
+النقطة P لأن النقطة P هي الأصل النقطة الثانية five
+
+289
+00:34:22,170 --> 00:34:35,430
+is the angle is the angle هي الزاوية اللي ال RP ال
+
+290
+00:34:35,430 --> 00:34:48,470
+mix اللي بيعمل هالي RP with the positive z
+
+291
+00:34:48,470 --> 00:34:50,350
+axis
+
+292
+00:34:53,340 --> 00:35:02,220
+فاي هذه محصورة فقط من زيرو لغاية بارت مرة تلاتة
+
+293
+00:35:02,220 --> 00:35:06,380
+الثيتا هي الثيتا الأولانية تبعاتنا تبع بالسي
+
+294
+00:35:06,380 --> 00:35:16,800
+ليندريكل والبورت is the angle هي الزاوية from
+
+295
+00:35:16,800 --> 00:35:20,460
+cylindrical
+
+296
+00:35:28,660 --> 00:35:30,980
+الذات الـ Cylindrical Core
+
+297
+00:35:57,520 --> 00:36:03,060
+بنروح نرسم اللي هو الاحداثيات الجديدة في الـ
+
+298
+00:36:03,060 --> 00:36:06,040
+spherical coordinates طبعا احنا بنرسم الاحداثيات
+
+299
+00:36:06,040 --> 00:36:12,140
+القديمة بدلالة X وY وZ فمثلا لو جيه تقول خدي
+
+300
+00:36:12,140 --> 00:36:18,960
+للنقطة اللي عندها وهذه في الاحداثيات الكارتزية P X
+
+301
+00:36:18,960 --> 00:36:27,860
+Y Zإذا في الإحداثيات الجديدة بنوصل النقطة هذه P رو
+
+302
+00:36:27,860 --> 00:36:36,420
+وفاي وثيتا السؤال هو أين رو و أين فاي و أين ثيتا؟
+
+303
+00:36:36,420 --> 00:36:41,040
+بقولك أه قالك رو هنا هي المسافة من النقطة P إلى
+
+304
+00:36:41,040 --> 00:36:46,820
+نقطة الأصل يبقى باجي بوصل هذه النقطة لنقطة الأصل
+
+305
+00:36:46,820 --> 00:36:54,680
+بيعطيني مين؟ بيعطيني روعرفنا الأحداث الأول بعدها
+
+306
+00:36:54,680 --> 00:36:59,520
+قال الزاوية Phi هي الزاوية المحصورة ما بين روه
+
+307
+00:36:59,520 --> 00:37:05,540
+والاتجاه الموجب لل Z Axis يبقى Phi كأنها بدأ يكون
+
+308
+00:37:05,540 --> 00:37:11,200
+الخط مطبق على Z وبدأ يفتح بالشكل هذا فسمينا
+
+309
+00:37:11,200 --> 00:37:13,480
+الزاوية هذه اللي هي الزاوية Phi
+
+310
+00:37:17,180 --> 00:37:21,340
+طب يجب أن أعرف أين الـR و أين الـθيتا بروح يا بنات
+
+311
+00:37:21,340 --> 00:37:27,060
+نسقط النقطة P على المستوى XY Plane يعني لو جيت
+
+312
+00:37:27,060 --> 00:37:32,680
+أسقط النقطة P على المستوى XY Plane بدأ تجينا P عند
+
+313
+00:37:32,680 --> 00:37:37,860
+النقطة اللي عندنا هذا بعدين بقول كويس هذا موازي
+
+314
+00:37:37,860 --> 00:37:48,570
+لمحور Y وهذا موازي لمحور X تمام؟ يبقىصار عندنا هذا
+
+315
+00:37:48,570 --> 00:37:58,110
+هو Y وهذا هو مين؟ X يفكر هذا هو X وهذا هو Y لو جيت
+
+316
+00:37:58,110 --> 00:38:04,310
+وصلت من نقطة الأصل لغاية هذا فانت عارف تقول مين
+
+317
+00:38:04,310 --> 00:38:11,850
+بيكون هذا في ال cylindricalR ممتاز جدا يبقى هذا R
+
+318
+00:38:11,850 --> 00:38:16,250
+في الـcylindrical والزاوية هذه بتكون هي مين؟ هي
+
+319
+00:38:16,250 --> 00:38:24,320
+الزاوية ثيتاإذاً حددنا له رو حددنا له فاي حددنا له
+
+320
+00:38:24,320 --> 00:38:29,500
+من ثيتا ليه الإحداثيات الجديدة يبقى ثيتا هو الخط
+
+321
+00:38:29,500 --> 00:38:34,120
+اللي بيعمله ليه R تبع الـcylindrical وطبعا الحاجة
+
+322
+00:38:34,120 --> 00:38:36,200
+يقولك هي أسفرية كدا يا عزيزي بس احنا رشتنا في
+
+323
+00:38:36,200 --> 00:38:41,720
+البداية يبقى هذا R اللي هو تبع الـcylindrical عامل
+
+324
+00:38:41,720 --> 00:38:45,560
+ليه زاوية ثيتا يبقى ثيتا جالي تبعت من تبعت
+
+325
+00:38:45,560 --> 00:38:51,010
+الـcylindrical coordinateطيب و الـ Phi هيها و ال
+
+326
+00:38:51,010 --> 00:38:58,050
+role اللي عندنا هذه هل في علاقة ابتردة ما بين ال R
+
+327
+00:38:58,050 --> 00:39:05,990
+و ما بين ال Phi مثلا و ال R في كده فالحين انا بنعت
+
+328
+00:39:05,990 --> 00:39:12,590
+هذا الطلعة لو جيت أسقطه على محور Z يعني نزلت من
+
+329
+00:39:12,590 --> 00:39:19,160
+هنا عمود على محور Z الطول هذا جديش بيقولمن نقطة
+
+330
+00:39:19,160 --> 00:39:27,600
+الأصل من هنا لغاية رو في كوساين الزاوية فيه يبقى Z
+
+331
+00:39:27,600 --> 00:39:33,780
+في هذه الحالة بدها ساوية رو في كوساين الفيه طيب
+
+332
+00:39:33,780 --> 00:39:41,340
+وين رو ساين الفيه؟ يلا اشوف رو ساين الفيه مين بده
+
+333
+00:39:41,340 --> 00:39:48,420
+يطلع؟هذا عمود على ال X Y Plane يعني عمودي على أي
+
+334
+00:39:48,420 --> 00:39:52,820
+مستقيل موجود في ال X Y Plane يعني الزاوية هذه
+
+335
+00:39:52,820 --> 00:40:02,500
+زاوية كم؟ تسعين درجة يبقى هو رو صين الفايف هو R
+
+336
+00:40:02,500 --> 00:40:08,360
+يبقى R اللي عندنا هذه يا بنات هي رو صين الفايف
+
+337
+00:40:08,360 --> 00:40:17,420
+يبقى هذهفي صين الفاي عرفنا إيش العلاقة ما بين ال
+
+338
+00:40:17,420 --> 00:40:24,380
+spherical ومين و ال cylindrical وبعد قليل هجمعلك
+
+339
+00:40:24,380 --> 00:40:28,680
+اتنين مع ال cartesian ونشوف إيش اللي بده يصير بس
+
+340
+00:40:28,680 --> 00:40:33,360
+عندي في بعض التساؤلات بدي أحاول أطرحها و أشوف إيش
+
+341
+00:40:33,360 --> 00:40:38,500
+رأيكوا فيها إيش معناها طيب يا بنات لو قلتلك احنا
+
+342
+00:40:38,500 --> 00:40:45,050
+الآن بتكلم sphericalوهي Aspirical Coordinates او
+
+343
+00:40:45,050 --> 00:40:49,930
+سيلندري كانوا بعدين بروح لل Aspirical لو قلت لك R
+
+344
+00:40:49,930 --> 00:40:55,550
+يساوي Zero R اللي عندنا هذا بيساوي Zero بيعطيني
+
+345
+00:40:55,550 --> 00:41:01,790
+ايش؟ محور Z ممتاز جدا يبقى R تساوي Zero والمطروح
+
+346
+00:41:01,790 --> 00:41:06,570
+اللي هو محور Z يبقى R تساوي Zero بيعطيكي دائما و
+
+347
+00:41:06,570 --> 00:41:11,760
+أبدا من محور Zيبقى لنا خاطرة نكتب هذا الكلام على
+
+348
+00:41:11,760 --> 00:41:22,520
+شكل اللي هو الملاحظات التالية. يبقى دي مارك هذا
+
+349
+00:41:22,520 --> 00:41:25,260
+الكلام اللي قالته سلامه هو الكلام اللي قلناه المرة
+
+350
+00:41:25,260 --> 00:41:29,100
+الماضية، يعني ما كنتش جديد، يعني هو كلام ذكرناه
+
+351
+00:41:29,100 --> 00:41:29,920
+قبل ذلك.
+
+352
+00:41:36,200 --> 00:41:40,320
+رو تساوي ثلاثة، رو تساوي أربعة، رو تساوي عشرة. هذا
+
+353
+00:41:40,320 --> 00:41:46,080
+إيش يمثل الأملاء؟ يعني جينا هناك وقلنا رو تساوي
+
+354
+00:41:46,080 --> 00:41:52,080
+خمسة، رو خمسة، رو خمسة، رو خمسة، رو خمسة، رو خمسة،
+
+355
+00:41:52,080 --> 00:41:52,820
+رو خمسة، رو خمسة، رو خمسة، رو خمسة، رو خمسة، رو
+
+356
+00:41:52,820 --> 00:41:52,900
+خمسة، رو خمسة، رو خمسة، رو خمسة، رو خمسة، رو خمسة،
+
+357
+00:41:52,900 --> 00:41:53,860
+رو خمسة، رو خمسة، رو خمسة، رو خمسة، رو خمسة، رو
+
+358
+00:41:53,860 --> 00:42:00,130
+خمسة، رو خمسSphere عقول الخطر يعني بيعطيك كرة
+
+359
+00:42:00,130 --> 00:42:05,630
+مركزها نقطة الأصل و نصفه ما هيساوي A يبقى روتس
+
+360
+00:42:05,630 --> 00:42:20,730
+ساوي A is a sphere with centers at the origin and
+
+361
+00:42:20,730 --> 00:42:22,150
+radius
+
+362
+00:42:27,090 --> 00:42:36,070
+النقطة الثانية يبقى في تسوي في نوت يبقى في تسوي في
+
+363
+00:42:36,070 --> 00:42:45,010
+نوت يبقى في تسوي في نوت يبقى في تسوي في نوت يبقى
+
+364
+00:42:45,010 --> 00:42:46,350
+في تسوي في نوت يبقى في تسوي في نوت يبقى في تسوي في
+
+365
+00:42:46,350 --> 00:42:47,290
+نوت يبقى في تسوي في نوت يبقى في تسوي في نوت يبقى
+
+366
+00:42:47,290 --> 00:42:52,370
+في تسفي الدرجة اعمل تلاتين درجة هاي تلاتين درجة
+
+367
+00:42:52,370 --> 00:42:57,450
+هاتي كمال جلب اللي فيه هاي تلاتين درجة وداير
+
+368
+00:42:57,450 --> 00:43:05,890
+مايدور تلاتين درجة شو بطلع عندي كرة
+
+369
+00:43:05,890 --> 00:43:14,130
+اي مخروض كويس اذا بطلع عندي مخروض دائري قائم اذا
+
+370
+00:43:14,130 --> 00:43:20,200
+بطلع عندي كونيبقى في تسوى في نوت تمثل مين؟ تمثل
+
+371
+00:43:20,200 --> 00:43:26,320
+مخروض دائري قائم رأسه عاميا عند نقطة الأصل و open
+
+372
+00:43:26,320 --> 00:43:32,940
+up مفتوح لوين؟ إلى أعلى يبقى هذه في تسوى في نوت
+
+373
+00:43:32,940 --> 00:43:42,440
+عبارة عن مخروض يبقى هذه equation of a cone مخروض
+
+374
+00:43:42,440 --> 00:43:55,920
+man with vertexwith vertex at the origin عند نقطة
+
+375
+00:43:55,920 --> 00:44:06,400
+الأصل at the origin and open أ مفتوح إلى أعلى إذا
+
+376
+00:44:06,400 --> 00:44:07,620
+كانت والله
+
+377
+00:44:13,900 --> 00:44:20,160
+يبقى لما تبقى في نوت من صفر لغاية تسعين المخروض
+
+378
+00:44:20,160 --> 00:44:26,540
+يكون مفتوح لوين؟ او لو خلناها ازيد عن تسعين يعني
+
+379
+00:44:26,540 --> 00:44:32,640
+امشي امشي امشي تسعين نزلت كمان شوية يبقى ايش مصير؟
+
+380
+00:44:32,640 --> 00:44:40,000
+مخروض رأسه عنده نقص له open down مفتوح الى أسفل
+
+381
+00:44:40,000 --> 00:44:43,480
+يبقى باجي بقول ال open down
+
+382
+00:44:46,960 --> 00:44:58,140
+open down مفتوح الى أسفل اف why not أكبر من مين من
+
+383
+00:44:58,140 --> 00:45:03,260
+by على اتنين طيب انت تكلمت على أقل من by على اتنين
+
+384
+00:45:03,260 --> 00:45:07,060
+وقلنا مخروط مفتوح الى أعلى أكبر من by على اتنين
+
+385
+00:45:07,060 --> 00:45:09,960
+مخروط مفتوح الى أعلى طب لو كان by على اتنين
+
+386
+00:45:17,610 --> 00:45:30,470
+بعدين افتح افتح افتح افتح افتح افتح افتح
+
+387
+00:45:30,470 --> 00:45:37,590
+افتح افتح افتح افتح افتح افتح
+
+388
+00:45:47,510 --> 00:45:57,050
+يبقى هذا المستوى XY بقلت عندنا اللي هو العلاقة
+
+389
+00:45:57,050 --> 00:46:02,330
+اللي بتربط هدول كلهم مع بعض او لو حبينا نعطي رسم
+
+390
+00:46:02,330 --> 00:46:09,210
+يعني سريع لهذه الشغلات تالي بقول بالشكل التالي
+
+391
+00:46:23,160 --> 00:46:31,360
+هذا X هذا Y هذا Z لان يا بنات باجي بقول هي المخروط
+
+392
+00:46:31,360 --> 00:46:41,060
+الأول يبقى هي عندي Phi node يبقى مفتوح لان هذا
+
+393
+00:46:41,060 --> 00:46:49,030
+الكلام لو كان Phi node ماله؟أقل من Pi على 2 يبقى
+
+394
+00:46:49,030 --> 00:46:56,130
+هذا Phi node أقل من Pi على 2 فلو حصل أن Phi node
+
+395
+00:46:56,130 --> 00:47:04,590
+عبارة عن Pi على 2 سنحصل على المستوى اللي عندنا هذا
+
+396
+00:47:04,590 --> 00:47:11,450
+بهذا الشكل يبقى هذا كله يصير من المستوى اللي عندنا
+
+397
+00:47:11,450 --> 00:47:18,710
+هذا وهذا من الناحية الثانيةيبقى هذا بيصير في نوت
+
+398
+00:47:18,710 --> 00:47:25,430
+تسوى باي على اتنين يعني ال X Y plane الحالة
+
+399
+00:47:25,430 --> 00:47:33,550
+التالتة لو كان عندنا المحاور بهذا الشكل وقولنا هذا
+
+400
+00:47:33,550 --> 00:47:42,310
+محور X هذا محور Y هذا محور Z المخروض بيقلب و يسير
+
+401
+00:47:42,310 --> 00:47:50,070
+الى أسفليبقى بدي أجيك المخروط بالشكل التالي ايو
+
+402
+00:47:50,070 --> 00:47:57,750
+حيصير هيك و هذا هو بالشكل اللي عندك هذا يبقى هذا
+
+403
+00:47:57,750 --> 00:48:05,630
+five هيهاباي نول أكبر من من ميل من باي على اتنين
+
+404
+00:48:05,630 --> 00:48:09,550
+يعني لو كانت الزاوية زاوية منفرجة بدي انقلب
+
+405
+00:48:09,550 --> 00:48:16,410
+المخروض ويصير لوين ويصير الى أسفل الأن بدنا نيجي
+
+406
+00:48:16,410 --> 00:48:22,010
+العلاقة اللى بتربط بين المتغيرات هذه كلها فبدي
+
+407
+00:48:22,010 --> 00:48:25,190
+اكتب the relation between the
+
+408
+00:48:30,020 --> 00:48:40,180
+between العلاقة بين الـ spherical و
+
+409
+00:48:40,180 --> 00:48:49,960
+ال Cartesian and cylindrical and cylindrical
+
+410
+00:49:10,370 --> 00:49:17,070
+طيب خلينا نبدأ بالفيلم اللي حكينا عليه هنا رو او R
+
+411
+00:49:17,070 --> 00:49:24,630
+تساوي رو في صين الفا يبقى هنا ال R تساوي ال رو في
+
+412
+00:49:24,630 --> 00:49:29,350
+صين الفا زيادة
+
+413
+00:49:29,350 --> 00:49:37,070
+على ذلك لو بدي ال Z ال Z تساوي ال رو في كوصين الفا
+
+414
+00:49:38,130 --> 00:49:47,230
+لو جيتنا ال X في الـ cylindrical coordinates هي R
+
+415
+00:49:47,230 --> 00:49:53,940
+في الـ cosine الزاويةطبعا بدي احولها الى spherical
+
+416
+00:49:53,940 --> 00:49:58,960
+يبقى في ال spherical ايش بدي اتصير؟ بدي اشيل ال R
+
+417
+00:49:58,960 --> 00:50:07,540
+و احط عندي رو ساين فاي يبقى هنا رو ساين فاي كساين
+
+418
+00:50:07,540 --> 00:50:16,340
+تيك طب ال Yيكون لدينا R في صين الزاوية تيتا يبقى
+
+419
+00:50:16,340 --> 00:50:22,500
+في الـ spherical الراو في صين الفاي في صين مين في
+
+420
+00:50:22,500 --> 00:50:29,520
+صين الزاوية تيتا طيب سؤال شو العلاقة ما بين الراو
+
+421
+00:50:29,520 --> 00:50:35,760
+و ال X و ال Y و ال Z هذا
+
+422
+00:50:35,760 --> 00:50:47,510
+X وهذا Y وهذا Zيبقى روح كده تساوي X تربيع زائد Y
+
+423
+00:50:47,510 --> 00:50:53,970
+تربيع زائد Z تربيع تحت الجذر التربيعي يبقى روح
+
+424
+00:50:53,970 --> 00:51:00,760
+تساوي ال square rootX تربيع زائد Y تربيع زائد Z
+
+425
+00:51:00,760 --> 00:51:06,500
+تربيع طب لو بدى اكتبها cylindrical يبقى
+
+426
+00:51:06,500 --> 00:51:13,440
+cylindrical بيساوي الجذر التربيعى ل R تربيع زائد Z
+
+427
+00:51:13,440 --> 00:51:18,860
+تربيع لأن X تربيع زائد Y تربيع اللى هو تسامين اللى
+
+428
+00:51:18,860 --> 00:51:25,380
+هو R تربيع طب لو بدى DV يا ماناتى DV
+
+429
+00:51:27,720 --> 00:51:51,380
+الذي يعني دي زد دي واي دي اكس دي اكس
+
+430
+00:51:51,380 --> 00:51:55,860
+دي اكس
+
+431
+00:51:55,860 --> 00:51:56,720
+دي اكس دي اكس دي اكس دي اكس دي اكس دي اكس دي اكس
+
+432
+00:51:56,720 --> 00:51:56,780
+دي اكس دي اكس دي اكس دي اكس دي اكس دي اكس دي اكس
+
+433
+00:51:58,250 --> 00:52:03,450
+تمام؟ يبقى هذه المعلومات الأساسية إلا أن الان لم
+
+434
+00:52:03,450 --> 00:52:08,730
+يبقى في هذا section إلا أن نعطي بعض الأمثلة. حد
+
+435
+00:52:08,730 --> 00:52:15,500
+إليها يتسأل في الكلام اللي قدامها؟ كيف؟ صحيحيعني
+
+436
+00:52:15,500 --> 00:52:20,760
+لما نقول لزميلتكوا لو كان هذا رو شو مسقط على ال XY
+
+437
+00:52:20,760 --> 00:52:26,720
+Plane؟ نقول لك R ليش؟ ان هو ينزل عمودة، مصبوط،
+
+438
+00:52:26,720 --> 00:52:31,900
+يبقى R هو مسقطة اللي هو ال raw sine فعلا حد بيسأل
+
+439
+00:52:31,900 --> 00:52:36,900
+أي سؤال تاني؟
+
+440
+00:52:36,900 --> 00:52:42,540
+يبقى
+
+441
+00:52:42,540 --> 00:52:44,980
+الناس كلها في السيلندر كلها بنضرب فيه
+
+442
+00:52:56,420 --> 00:53:09,280
+أول مثال على ذلك هو
+
+443
+00:53:09,280 --> 00:53:11,380
+اللي يحسب التكامل التالي
+
+444
+00:53:16,510 --> 00:53:23,990
+إتنين ثلاثة الأول من صفر لغاية اتنين باي والتالي
+
+445
+00:53:23,990 --> 00:53:33,350
+من صفر لغاية باي على أربع والتالي من zero لغاية
+
+446
+00:53:33,350 --> 00:53:47,160
+six في لروت كوساين الفاى لروت ربيع صين الفاىد رو
+
+447
+00:53:47,160 --> 00:53:55,120
+دي فاي دي ثيتا التكامل
+
+448
+00:53:55,120 --> 00:54:05,400
+الأول وهي التكامل التاني وهذا لازم يشغل بالنسبة
+
+449
+00:54:05,400 --> 00:54:13,120
+إلى رو يبقى الصين والقصين ليس دعوة رو تكيب تكاملها
+
+450
+00:54:21,870 --> 00:54:31,550
+سك الفاي لمين لكوساين الفاي لصين الفاي دي فاي دي
+
+451
+00:54:31,550 --> 00:54:35,910
+ثيتا اللي ماك ميزة ما بين الفاي وثيتا خلي دينها
+
+452
+00:54:35,910 --> 00:54:43,410
+طول شوية هذا الكلام بده يساوي رابع خليه برا لغاية
+
+453
+00:54:43,410 --> 00:54:48,130
+كامل من Zero لإتنين بايت كامل من Zero لغاية Pi على
+
+454
+00:54:48,130 --> 00:54:56,130
+أربعيبقى هذا شو بيصير سك أُس أربعة يبقى سك أُس
+
+455
+00:54:56,130 --> 00:55:06,030
+أربعة في و هنا كوصين الفي كوصين الفي و دي في دي
+
+456
+00:55:06,030 --> 00:55:14,190
+ثيتا ناقص zero بتروح مع السلام يبقى آلة المسألة
+
+457
+00:55:22,520 --> 00:55:28,000
+زيرو نقاط باية على أربعة في اختصارات يا بناتي لو
+
+458
+00:55:28,000 --> 00:55:31,660
+أخدت كوساين اه سك واحدة بصير واحدة على كوساين
+
+459
+00:55:31,660 --> 00:55:38,350
+بتروح مع هذه يبقى بظل سك تكيب ساينيبقى هذه بيصير
+
+460
+00:55:38,350 --> 00:55:49,670
+سكتة كيب في صين في دي في دي ثيتا يبقى مرة ثانية هي
+
+461
+00:55:49,670 --> 00:55:54,770
+الرابع تكامل من zero للاتنين باي تكامل من zero
+
+462
+00:55:54,770 --> 00:56:03,170
+لغاية باي على أربع بدنا نكامل هذه سهلة
+
+463
+00:56:03,170 --> 00:56:08,540
+very easyلا بأخليها سكتة أيه بزي ما يبقى ، بس لو
+
+464
+00:56:08,540 --> 00:56:13,880
+نزلتها إيش مصرية؟ Cos فوق Cos فقعدت ست ساعة. هذه
+
+465
+00:56:13,880 --> 00:56:21,200
+بقدر أقول انه واحد على Cos او أقولك خليها فوق هذه
+
+466
+00:56:21,200 --> 00:56:29,080
+كأنها Cos فاي أس سالب تلاتة صح ولا لأ؟ واحد على
+
+467
+00:56:29,080 --> 00:56:37,070
+Cos لو طلعت من ال Cos فاي أس سالب تلاتةأليست مشتقة
+
+468
+00:56:37,070 --> 00:56:46,710
+الـ cosine بس بده إشارة سالب يبقى هذه فيه سالب دي
+
+469
+00:56:46,710 --> 00:56:51,530
+cosine الفاية و الـ dt ده أيه يا بره مالعش علاقة
+
+470
+00:56:51,530 --> 00:56:59,210
+بالموضوع يبقى هذا الكلام يستاوي لربع تكمل من zero
+
+471
+00:56:59,210 --> 00:57:07,110
+لإتنين و اشتغلش ايه كل كامل يبقاش بالصيانةcos فان
+
+472
+00:57:07,110 --> 00:57:16,090
+قص ناقص اتنين على ناقص اتنين وعند كده الشرط الناقص
+
+473
+00:57:16,090 --> 00:57:22,330
+اللي كانت برا هيها جابلها وضايل عندنا هذا الحكي من
+
+474
+00:57:22,330 --> 00:57:29,890
+عند ال zero لغاية Pi على 4 وهي دي فترة يبقى ناقص
+
+475
+00:57:29,890 --> 00:57:36,970
+وناقصو نص تطلع برا مع الرموز بيصير كده؟ تمام و
+
+476
+00:57:36,970 --> 00:57:42,150
+بيصير عندي تكامل من zero لإتنين باي و تعالى نعود
+
+477
+00:57:42,150 --> 00:57:46,790
+للقيمة اللى فوق ناقص القيمة اللى تحت يبقى اش بيصير
+
+478
+00:57:46,790 --> 00:57:56,830
+عندي واحد على cosine باي على أربع الكل تقريبا ناقص
+
+479
+00:57:56,830 --> 00:58:06,540
+واحدعلى cos 0 الكل تربيع بالنسبة الى Dθ يبقى هذا
+
+480
+00:58:06,540 --> 00:58:13,820
+الكلام متساوي 8 جتا 45 ابنات واحد على جدر تنارقها
+
+481
+00:58:13,820 --> 00:58:19,900
+فتصير ايه نصف بنقلب فوق تصير اتنين يبقى هاي
+
+482
+00:58:19,900 --> 00:58:25,840
+التكامن من 0 للإتنين باى وهي اتنين ناقص cos 0
+
+483
+00:58:25,840 --> 00:58:34,190
+تربيعواحد على واحد مناقص واحد يبقى هاي ناقص واحد
+
+484
+00:58:34,190 --> 00:58:37,550
+يبقى
+
+485
+00:58:37,550 --> 00:58:42,890
+هاي كل اللي عندنا المفضل بالنسبة الى D ثيتا هو
+
+486
+00:58:42,890 --> 00:58:51,250
+يساوي تمت تكامن من zero للاثنين byفقط الذي ثيتا
+
+487
+00:58:51,250 --> 00:58:59,870
+يبقى يساوي تمن ثيتا من zero للإتنين by ويساوي تمن
+
+488
+00:58:59,870 --> 00:59:07,650
+في إتنين by يبقى by على أربع نقدار هذا أكتر
+
+489
+00:59:38,580 --> 00:59:43,320
+بطرقة ما اتناولها جيئة بيه في احدى التمتحانات
+
+490
+00:59:43,320 --> 00:59:48,760
+للناس اللي زيكم واحنا عنها هنقدر نعطيكيها كمثال
+
+491
+00:59:48,760 --> 00:59:57,140
+اقول find your volume of the region find the
+
+492
+00:59:57,140 --> 01:00:09,530
+volume of the regionقداش حجم المنطقة bounded below
+
+493
+01:00:09,530 --> 01:00:14,870
+bounded below
+
+494
+01:00:14,870 --> 01:00:23,250
+والمحدودة من أسفل باليكون باليكون
+
+495
+01:00:23,250 --> 01:00:34,170
+بالمخروج Z تساوي الجذر التربيع ال X تربيع زائد Y
+
+496
+01:00:34,170 --> 01:00:47,420
+تربيعand above ومن أعلى by the plane by the plane
+
+497
+01:00:47,420 --> 01:01:03,040
+بالمستوى z تساوي واحد by using by using امرأة
+
+498
+01:01:03,040 --> 01:01:06,000
+cylindrical coordinates
+
+499
+01:01:09,160 --> 01:01:17,120
+Cylindrical Coordinates لمرة بيه Spherical
+
+500
+01:01:17,120 --> 01:01:29,800
+Coordinates Spherical
+
+501
+01:01:29,800 --> 01:01:31,300
+Coordinates
+
+502
+01:01:53,380 --> 01:01:59,020
+نرجع لسؤالنا مرة تانية بيقول في عندي منطقة مغلقة
+
+503
+01:01:59,020 --> 01:02:06,400
+ومحدودة بيه من أسفل بمين بيه المخروط اللي هو z
+
+504
+01:02:06,400 --> 01:02:11,520
+يساوي الجدر التربيع ال x تربيع زائد y تربيع and
+
+505
+01:02:11,520 --> 01:02:17,250
+above ومن أعلى بال plane z يساوي واحدبنجيب هذا
+
+506
+01:02:17,250 --> 01:02:22,550
+الحجم مرتين مرة باستخدام cylindrical coordinates و
+
+507
+01:02:22,550 --> 01:02:26,630
+مرة باستخدام spherical coordinates بيطلعوا جبتين
+
+508
+01:02:26,630 --> 01:02:32,810
+زي بعض و لا مختلفين نفس الحجم تمام بس بطريقتين
+
+509
+01:02:32,810 --> 01:02:40,620
+مختلفتين ياريت أروح نرسم الشغل هذه و نشوف كيفبعدين
+
+510
+01:02:40,620 --> 01:02:50,520
+يومين نحسب المظبوط تبع المثل هذا X هذا Y هذا Z
+
+511
+01:02:50,520 --> 01:02:59,400
+وروح ترسم المخروض اللي عندنا بيكان المخروض بالشكل
+
+512
+01:02:59,400 --> 01:03:10,060
+اللي عندنا هذا Xوالمستوى الأفقي z يساوي واحد يبقى
+
+513
+01:03:10,060 --> 01:03:17,560
+هذا المستوى هو z يساوي واحد وهذا المخرج هو z يساوي
+
+514
+01:03:17,560 --> 01:03:24,240
+جدر التربية إلى x تربية زائد y تربيةشو رايك احنا
+
+515
+01:03:24,240 --> 01:03:29,340
+بنتكلم على مين؟ على cylindrical في الأول. مدام
+
+516
+01:03:29,340 --> 01:03:35,340
+cylindrical يبقى هذا يبقى جدرخ كبير لارتربية اللي
+
+517
+01:03:35,340 --> 01:03:42,000
+هو قدرة A يبقى Z يساوي A تمام؟ ماجي بقوله كويس
+
+518
+01:03:42,000 --> 01:03:48,640
+يبقى ال volume اللي احنا بدنا يعني تلت تكاملات
+
+519
+01:03:48,640 --> 01:03:50,200
+التي يزد
+
+520
+01:03:59,540 --> 01:04:07,500
+يبقى انا بدي ارسم خط يقطع منطقة تكامل وموازن لمحور
+
+521
+01:04:07,500 --> 01:04:14,680
+Z يبقى بداجي هنا ارسم خط من هنا و اجي طالع رأسي
+
+522
+01:04:14,680 --> 01:04:20,460
+موازن لمحور Z بالشكل اللي عندنا هذا هيكلغاية ما
+
+523
+01:04:20,460 --> 01:04:27,400
+قبل اللي هو Z يساوي واحد يبقى هنا Z يساوي قداش R
+
+524
+01:04:27,400 --> 01:04:34,560
+هنا Z يساوي قداش واحد يبقى هنا R وهنا واحد ضالة ال
+
+525
+01:04:34,560 --> 01:04:40,760
+R يبقى ال R بدي أسحب المجسم هذا كله على مين؟ على
+
+526
+01:04:40,760 --> 01:04:47,550
+ال XY Plane يبقى المصعدش هيكون يا بنات كذلكدائرة
+
+527
+01:04:47,550 --> 01:04:53,370
+يبقى بتصير المصطفى اللى عندنا هي دائرة اها لو جيت
+
+528
+01:04:53,370 --> 01:04:58,590
+قلت هاي و هنا و هاي و هنا بالضبط تماما و هذا ماشي
+
+529
+01:04:58,590 --> 01:05:04,570
+دغري يبقى بدها تكون عند مين الدائرة اللى عندنا هذا
+
+530
+01:05:04,570 --> 01:05:05,050
+الشكل
+
+531
+01:05:09,350 --> 01:05:13,890
+طيب، بدأ أعرف قداش نصف قطر هذه الدائرة في
+
+532
+01:05:13,890 --> 01:05:19,150
+الإحداثيات القصوية أو ما هي معادلة هذه الدائرة في
+
+533
+01:05:19,150 --> 01:05:22,790
+الإحداث الأولى، طب كيف؟ كيف عرفتيها واحد يعني؟
+
+534
+01:05:22,790 --> 01:05:26,290
+تمام
+
+535
+01:05:26,290 --> 01:05:33,270
+تمام، يبقى بروح بقوله هنا Zتساوي واحد و Z تساوي R
+
+536
+01:05:33,270 --> 01:05:37,870
+من هذول التنتير مع بعض بسويهم بعض يبقى ال R تساوي
+
+537
+01:05:37,870 --> 01:05:43,890
+قداش واحد إذا ال R ستبدأ من هنا إلى أي نقطة على
+
+538
+01:05:43,890 --> 01:05:48,090
+محيط الدائرة أو من هنا إلى أي نقطة على محيط
+
+539
+01:05:48,090 --> 01:05:52,750
+الدائرة وبيكون هذا كله R يساوي واحد يبقى ال R
+
+540
+01:05:52,750 --> 01:06:00,180
+ستتغير من Zero لغاية واحدطب θ هتتغير من 0 ل2 باى
+
+541
+01:06:00,180 --> 01:06:07,260
+يبقى من 0 لغاية 2 باى ويساوي integration من 0 ل2
+
+542
+01:06:07,260 --> 01:06:13,900
+باى integration من 0 ل1 تكمل ال DZ اللي هي Z من
+
+543
+01:06:13,900 --> 01:06:22,580
+عند R لغاية 1 وظل عندي RDRDθ يبقى آلة المسألة إلى
+
+544
+01:06:22,580 --> 01:06:31,210
+تكمل من Zeroلغاية 2 باي من 0 لغاية 1 للواحد ناقص R
+
+545
+01:06:31,210 --> 01:06:38,510
+في RDR D ثانية اعوض من القيمة اللي فوق ناقص لتاعة
+
+546
+01:06:38,510 --> 01:06:44,730
+بدي ادخل ال R هذا دخل ال O فبصير عندي تكاملينمن
+
+547
+01:06:44,730 --> 01:06:50,350
+Zero للإتنين باي والتكامل التاني من Zero لواحد لل
+
+548
+01:06:50,350 --> 01:06:58,210
+R ناقص R تربيع DR D ثيتا الكامل يبدأ integration
+
+549
+01:06:58,210 --> 01:07:04,210
+من Zero لغاية اتنين باي ده من لل R تربيع على اتنين
+
+550
+01:07:04,210 --> 01:07:11,590
+ناقص R تكامل على تلاتة كل الحكي هذا من عند ال Zero
+
+551
+01:07:11,590 --> 01:07:18,010
+لغاية الواحد ده منلدى فيتا هذا بدى يساوي
+
+552
+01:07:18,010 --> 01:07:22,250
+integration من zero لغاية اتنين باى بدى عوض بالقيم
+
+553
+01:07:22,250 --> 01:07:29,490
+اللى فوق بقى نص نقص طول يبقى نص نقص طول و نقص zero
+
+554
+01:07:29,490 --> 01:07:36,710
+بيروح كله لدى فيتا يبقى تكامل من zero للاتنين باى
+
+555
+01:07:36,710 --> 01:07:43,530
+لمين لسادس دى فيتا إذا المصير هذا سادس
+
+556
+01:07:52,950 --> 01:08:06,170
+باي على ثلاث باي على ثلاث
+
+557
+01:08:06,170 --> 01:08:13,850
+باي على ثلاث باي على ثلاث باي على ثلاثفي احتمال
+
+558
+01:08:13,850 --> 01:08:21,070
+يكون التكامل غلط في احتمال قدود التكامل غلط الاخري
+
+559
+01:08:21,070 --> 01:08:29,750
+ان شاء الله لا نقع في الخطأ ايه الآن بدنا نروح
+
+560
+01:08:29,750 --> 01:08:39,630
+نشتغل فيه اللي هو الـ spherical coordinates ده
+
+561
+01:08:39,630 --> 01:08:49,600
+يا عزيزي هقوله نمرا فيهبدي تكامل اتنين ثلاثة روتا
+
+562
+01:08:49,600 --> 01:09:02,960
+ربيع فايل الفايل دي رو دي فايل دي تيتا نيجي لروب
+
+563
+01:09:02,960 --> 01:09:06,820
+تتغير من أين اللي وين يبقى روحة تبدأ من أين يا
+
+564
+01:09:06,820 --> 01:09:12,900
+بنات؟ من نقطة الأصلوتجهي نطلع طالعين لغاية ما
+
+565
+01:09:12,900 --> 01:09:19,000
+نجابل وين المستوى اللى فوق له Z يساوي واحد اذا لو
+
+566
+01:09:19,000 --> 01:09:24,600
+جينا طالعين بهذا الشكل لغاية ما جابلنا السطح اللى
+
+567
+01:09:24,600 --> 01:09:32,320
+فوق يبقى روحنا بقداش Zero اتفقنا يبقى هاي روحنا
+
+568
+01:09:32,320 --> 01:09:35,540
+Zero روحنا فوق بقداش
+
+569
+01:09:40,590 --> 01:09:45,610
+مين هو اللي فوق؟ Z تساويها طب مين هي Z في ال
+
+570
+01:09:45,610 --> 01:09:51,390
+spherical؟ رو كوساين فاي بيبقى صارت قصته سهلة يبقى
+
+571
+01:09:51,390 --> 01:09:59,180
+هدئها اللي هو Zتساوي واحد يعني ال row في cosine
+
+572
+01:09:59,180 --> 01:10:05,200
+الفاي يساوي واحد يبقى روه كده شبنها سك الفاي لإن
+
+573
+01:10:05,200 --> 01:10:10,460
+واحد على سك اضرب الطرفين بس ال row بسك الفاي إذا
+
+574
+01:10:10,460 --> 01:10:18,730
+ال row تتغير من zero لغاية سك الفايطب إذا نجي لـ
+
+575
+01:10:18,730 --> 01:10:25,870
+Phi تتغير من واحد لواحد ، يبقى Phi تتغير من المحور
+
+576
+01:10:25,870 --> 01:10:30,970
+ضد لواء الخطة اللي عندنا هذا. إذا لو عرفت قداش
+
+577
+01:10:30,970 --> 01:10:41,090
+معادلة هذا الخط بتبقى قصتنا محلولة. يالا قداش؟
+
+578
+01:10:41,090 --> 01:10:47,420
+يلا بس يطلعيعني .. يعني تشوفوالي كيف ممكن نجيبها
+
+579
+01:10:47,420 --> 01:10:51,760
+هيك يلا
+
+580
+01:10:51,760 --> 01:10:54,680
+ايه حسب جربه، قوليلي كيف، أنا مابديش أعطيك دوري،
+
+581
+01:10:54,680 --> 01:11:03,000
+بديك أنت تشغل مخك شوية يلا
+
+582
+01:11:03,000 --> 01:11:11,660
+شوف قداشر تقاطع المستوى اللي فوق مع المخروجيعني
+
+583
+01:11:11,660 --> 01:11:19,460
+تقلق Z تساوي 4 Z تساوي 1 صحيح ولا لأ؟ يلّا نشوف
+
+584
+01:11:19,460 --> 01:11:23,740
+المستوى
+
+585
+01:11:23,740 --> 01:11:30,700
+اللي فوق شو معادلته؟ روت ساوسيك 5 صحيح ولا لأ؟
+
+586
+01:11:30,700 --> 01:11:37,620
+وشوفوا اللي تحت بصرفين هو هذا يلّا ايوة
+
+587
+01:11:39,510 --> 01:11:43,410
+صحيح زيته
+
+588
+01:11:43,410 --> 01:11:49,930
+ساوي R ممتاز
+
+589
+01:11:49,930 --> 01:11:59,830
+هي R بقداش عادى ممتاز جدا يبقى روه صين الفاى واللي
+
+590
+01:11:59,830 --> 01:12:04,930
+فوق الروه كوصين الفاى يبقى حاليا الإشكالية تمام
+
+591
+01:12:05,200 --> 01:12:09,520
+يبقى يا بنات بروح تاك في الهامش بقول المستوى اللي
+
+592
+01:12:09,520 --> 01:12:16,140
+فوق اللي هو Z زد اللي هو رو كو صين الفاية و اللي
+
+593
+01:12:16,140 --> 01:12:23,440
+تحت Z تساوي R و ال R اللي هو برو صين الفاية يبقى
+
+594
+01:12:23,440 --> 01:12:30,660
+رو في صين الفاية هذه ه ه اللي هي منك اللي هي Rلو
+
+595
+01:12:30,660 --> 01:12:36,820
+قسمنا الطرفين على روه بيصير cosine فاى بده يسوى
+
+596
+01:12:36,820 --> 01:12:41,280
+الـ sine فاى او لو قسمنا على ال cosine فاى بيصير
+
+597
+01:12:41,280 --> 01:12:47,580
+واحد يسوى تاني الفاى من الزاوية اللي ضلها يسوى
+
+598
+01:12:47,580 --> 01:12:59,030
+واحد 45 درجة يبقى من 90 نقاط 45 درجة طبعاشايفين
+
+599
+01:12:59,030 --> 01:13:06,090
+كيف الصندوق جاها؟ الآن هذا صار معادلة في تساوي باي
+
+600
+01:13:06,090 --> 01:13:10,850
+على أربع الخط اللي عندنا هنا يبقى الزاوية هذه كلها
+
+601
+01:13:10,850 --> 01:13:14,750
+صارت كده شبنات اللي هي باي على أربع اللي هي
+
+602
+01:13:14,750 --> 01:13:20,030
+الزاوية في مرتين أقولها لإنها very important خبصت
+
+603
+01:13:20,030 --> 01:13:24,460
+فيها بتروح المسألةيبقى مرة تانية بدي اجيب قداش
+
+604
+01:13:24,460 --> 01:13:28,560
+مقدار الزاوية في ال file اللي عندنا بقول اه تعالى
+
+605
+01:13:28,560 --> 01:13:34,710
+ناخده تخط التقاطع هذا مع المستوى اللي فوق تمامهذا
+
+606
+01:13:34,710 --> 01:13:40,830
+جاي من مين؟ من معادلة الكون المخروط z تساوي a وهذا
+
+607
+01:13:40,830 --> 01:13:45,910
+اللي فوق جايين من z تساوي واحد إذا بدي أساوي اتنين
+
+608
+01:13:45,910 --> 01:13:50,770
+هدول بمين؟ ببعض طيب باجي بقوله z اللي فوق freely
+
+609
+01:13:50,770 --> 01:13:57,230
+spherical هي rho cosine فاي يبقى rho cosine فاي
+
+610
+01:13:57,230 --> 01:14:03,500
+بيبقى تساوي اللي تحت اللي هي مين؟اللي بيبدأ تسوي
+
+611
+01:14:03,500 --> 01:14:08,760
+رو صين الفاي اللي هي R يبقى صار رو قصين الفاي
+
+612
+01:14:08,760 --> 01:14:12,960
+بيبقى يسوي رو صين فاي قسمنا على رو صار القصين
+
+613
+01:14:12,960 --> 01:14:17,120
+بيبقى يسوي صين قسمنا على كل صين بيصير صين على قصين
+
+614
+01:14:17,120 --> 01:14:23,640
+اللي هي تان فاي يسوي مين واحد ومنها هذا بيقولك أن
+
+615
+01:14:23,640 --> 01:14:29,260
+فاي تسوي باي على أربع يبقى فاي تتغير من Zero لغاية
+
+616
+01:14:29,260 --> 01:14:34,390
+باي على رمية ضايد عندناتختلفت عن الـcylindrical
+
+617
+01:14:34,390 --> 01:14:39,250
+وعن الـspherical لما هي .. يبقى هذه لم تحدث إلى أي
+
+618
+01:14:39,250 --> 01:14:44,950
+تغيير يبقى Zero لغاية الدنيا الفارقة طيب تعالوا
+
+619
+01:14:44,950 --> 01:14:50,570
+نحسن إذا ما طلعش طيعة تلاتة معناته في الشغل غلط يا
+
+620
+01:14:50,570 --> 01:14:54,490
+إما حدودنا غلط يا إما طريقتنا في التكامل غلط وإن
+
+621
+01:14:54,490 --> 01:14:58,850
+شاء الله مايحصلش فهي يبقى المروحة الكامل فين؟
+
+622
+01:15:24,950 --> 01:15:30,810
+هذا الكلام بده يسوي يتلت خليك برا وهي من zero
+
+623
+01:15:30,810 --> 01:15:37,620
+لغاية 2pi وهي من zero لغاية pi على 4العوض بالقيمة
+
+624
+01:15:37,620 --> 01:15:43,740
+اللى فوق يبقى شوف الصغير يبقى سك تك عيب اللى هو
+
+625
+01:15:43,740 --> 01:15:53,020
+فاي في صين الفاي في دي فاي في دي فيتا لأن هذا
+
+626
+01:15:53,020 --> 01:15:58,760
+الكلام بده ساوي طول integration من zero لإتنين فاي
+
+627
+01:16:03,120 --> 01:16:09,320
+ما رأيك هذه سك تاخد منها سك واحدة وانزلها تحت بصير
+
+628
+01:16:09,320 --> 01:16:14,400
+cosine بصير sine على cosine اللي هو مين بتان يبقى
+
+629
+01:16:14,400 --> 01:16:24,540
+بده يصير هذه سك تربيع فاي تان الفاي بفاي دفين
+
+630
+01:16:24,540 --> 01:16:33,720
+مظبوط؟ هذا الكلام بده يصير طولتكمل من 0 ل2 باى
+
+631
+01:16:33,720 --> 01:16:45,120
+تكمل من 0 لباى على 4 لمين لتان الفاى دى تان الفاى
+
+632
+01:16:45,120 --> 01:16:54,460
+دى ثيتا تفضل التان ب 6 ترميق الشلدسكتر بيع الفاى
+
+633
+01:16:54,460 --> 01:17:00,540
+مع دى فاى وكتبت بدالها دى تان الفاى يبقى كأنه انا
+
+634
+01:17:00,540 --> 01:17:05,860
+بكمل اكس دى اكس يبقى بضطري فى بس للأس واحد و اقسم
+
+635
+01:17:05,860 --> 01:17:12,360
+على الأس الجديد يبقى هى التلت برا وهى تكمل من زيرو
+
+636
+01:17:12,360 --> 01:17:20,360
+لاتنين باى وهدى تان تربيع فاى على الاتنينمن Zero
+
+637
+01:17:20,360 --> 01:17:30,280
+لغاية Pi على أربعة لدى ثيتا مصفى تلت بقدرش بسدس
+
+638
+01:17:30,280 --> 01:17:34,620
+وغاية كامل من Zero لإتنين Pi
+
+639
+01:17:48,920 --> 01:17:57,380
+بس عندي واحد دي ثيتا يبقى هنا سُدس وثيتا ومن zero
+
+640
+01:17:57,380 --> 01:18:04,640
+divide اتنين by او سُدس اتنين by او باية تلاتة
+
+641
+01:18:04,640 --> 01:18:10,900
+معناته شغلنا صحيح ولا خمأة في ذلك حد مش حابب تسأل
+
+642
+01:18:10,900 --> 01:18:16,680
+أي شوية هنا لسه في عندنا مشاكل كتير كما أناهي
+
+643
+01:18:16,680 --> 01:18:24,520
+تساوى الأيوة مش
+
+644
+01:18:24,520 --> 01:18:29,660
+هيها بالضبط هي الدائرة اللي عندها دي و أسقطها
+
+645
+01:18:29,660 --> 01:18:33,880
+تماما مش أسقط الدائرة يعني بمعنى أخر أسقط المجسم
+
+646
+01:18:33,880 --> 01:18:38,500
+كله فظهرت المنطقة المصممة اللي هي على شكل قصة أو
+
+647
+01:18:38,500 --> 01:18:41,880
+على شكل دائرة هي الدائرة اللي فوت بالضبط لأن هذا
+
+648
+01:18:41,880 --> 01:18:45,760
+نزل عمود وهذا نزل عمود صحيح
+
+649
+01:18:53,260 --> 01:18:59,060
+هي ربط تبدأ من النقطة هذه لغاية اي نقطة على
+
+650
+01:18:59,060 --> 01:19:09,940
+الدائرة اللى فوق لما
+
+651
+01:19:09,940 --> 01:19:12,880
+احنا هنا مش هدى تقع على ال y axis ولا لا
+
+652
+01:19:16,950 --> 01:19:21,030
+يختيروا اسم أي خط هنا بيصير عندك مثلث طايم ده اه
+
+653
+01:19:21,030 --> 01:19:24,630
+بده يوصل الهدوء ان بيصير هذه المثلث القايم الزاوية
+
+654
+01:19:24,630 --> 01:19:28,930
+فوق طيب
+
+655
+01:19:28,930 --> 01:19:35,850
+انت بتشغلي cartesian يعني الان احنا بدنا mean
+
+656
+01:19:35,850 --> 01:19:38,210
+spherical اه دي لبالك
+
+657
+01:20:04,500 --> 01:20:08,980
+طب كان هذا هو المثال الرقم اتنين بدنا نروح لمثال
+
+658
+01:20:08,980 --> 01:20:16,000
+رقم تلاتة مثال رقم تلاتة find the volume of the
+
+659
+01:20:16,000 --> 01:20:26,180
+solid find the volume of the solid بدنا نقدرش حجم
+
+660
+01:20:26,180 --> 01:20:29,120
+المجسم bounded below
+
+661
+01:20:33,930 --> 01:20:45,530
+من أسفل By The XY Plane XY Plane
+
+662
+01:20:45,530 --> 01:20:56,710
+On Sides On Sides من الجانب By The Sphere By The
+
+663
+01:20:56,710 --> 01:21:09,890
+Sphere بالكرة روتو ساوي بنيتand above ومن أعلى by
+
+664
+01:21:09,890 --> 01:21:18,490
+the whole بالمخروج by تساوي by على
+
+665
+01:21:33,770 --> 01:21:45,150
+المنطقة اللي عندنا يبقى هذا اللي هو محور X وهذا
+
+666
+01:21:45,150 --> 01:21:51,930
+محور Y وهذا الرأس اللي هو محور Z
+
+667
+01:22:07,280 --> 01:22:11,980
+بنقلب دي حجم المنطقة المحظورة من الأسفل بال X Y
+
+668
+01:22:11,980 --> 01:22:18,680
+Plane و من الجوانب بالاسفير يبقى أنا عند هنا بنا
+
+669
+01:22:18,680 --> 01:22:28,140
+اسفير كويس هاي ها بدي أرسم بالشكل اللي عنا هذا هاي
+
+670
+01:22:28,140 --> 01:22:36,250
+القاعدة قلب ال X Y Plane يبقى هذا مش هيبقىكويس و
+
+671
+01:22:36,250 --> 01:22:41,690
+هذا هيجينا هيك و الاسفير بدأ يرسم من فوق يبقى تظهر
+
+672
+01:22:41,690 --> 01:22:46,970
+الاسفير بالشكل اللي عندنا هذا و الناحية التانية
+
+673
+01:22:46,970 --> 01:22:53,250
+بالشكل هذا كويس يبقى هذا النصف العلوي من الاسفير
+
+674
+01:22:53,250 --> 01:23:04,460
+النصف والسفلي ما رسمناهوشيبقى الاسفير يبقى
+
+675
+01:23:04,460 --> 01:23:13,660
+الاسفير يبقى الاسفير
+
+676
+01:23:13,660 --> 01:23:18,360
+يبقى الاسفير
+
+677
+01:23:18,360 --> 01:23:21,060
+يبقى الاسفير يبقى الاسفر يبقى الاسفر يبقى الاسفر
+
+678
+01:23:21,240 --> 01:23:24,980
+يبقى بده يجينا هذا من الناحية اللي عندنا هذه
+
+679
+01:23:24,980 --> 01:23:30,680
+وبالتالي بده يصير عندنا من المخروض على الشكل اللي
+
+680
+01:23:30,680 --> 01:23:37,420
+عندنا هذا يعني انت بنات كأن المخروض هذا تجويف
+
+681
+01:23:37,420 --> 01:23:41,960
+للكرة الكرة اللي اتصورناها مصمة واخدنا نصف العلوي
+
+682
+01:23:41,960 --> 01:23:47,780
+نزلنا فيها ثقب على شكل مخروج بالشكل اللي قدامك هذا
+
+683
+01:23:47,780 --> 01:23:49,340
+يبقى اللي فوق
+
+684
+01:23:54,670 --> 01:23:59,030
+الجزء العلوي لبعض المخروط كله وجود لأ يبقى هذا
+
+685
+01:23:59,030 --> 01:24:04,970
+بنشيله تماما من راسنا يبقى هذا كأنه مالوش وجود
+
+686
+01:24:04,970 --> 01:24:09,430
+بالمرة كويس
+
+687
+01:24:09,430 --> 01:24:15,710
+يبقى صار يعني الدارة كأنه احنا اللي هو على الجوالب
+
+688
+01:24:15,710 --> 01:24:21,650
+فقط يبقى على الجوالب هذه ال road تساوي اتنين هنا
+
+689
+01:24:21,650 --> 01:24:25,850
+مخروط في الداخل اللي هو five تساوي fiveعلى تلاتة
+
+690
+01:24:25,850 --> 01:24:32,370
+والأرض هي ال X Y plane كويس بدل ال volume V فبقول
+
+691
+01:24:32,370 --> 01:24:43,790
+لهم V تساوي تلت تكاملات ل رو تربيع ف sin ف D رو D
+
+692
+01:24:43,790 --> 01:24:51,080
+في دي ثي ليجي ل روروح تبدأ من هنا من هنا من نقطة
+
+693
+01:24:51,080 --> 01:24:57,120
+الأصل لغاية أي نقطة على محيط الكرة يبقى هنا كده؟
+
+694
+01:24:57,120 --> 01:25:04,920
+روح تساوي اتنين يبقى من zero لغاية اتنين يجي ليه
+
+695
+01:25:04,920 --> 01:25:11,280
+five؟ five هذا كله فرق مش علاقة فيه يبقى المجسم
+
+696
+01:25:11,280 --> 01:25:17,810
+هيبدأ من هنا لغاية الفاية هذه فاضية اللي فوقيبقى
+
+697
+01:25:17,810 --> 01:25:24,890
+في حتى تغير من وين لوين من باية ثلاثة الى باية
+
+698
+01:25:24,890 --> 01:25:32,270
+اتنين يمشي من باية على تلاتة لغاية في على اتنين
+
+699
+01:25:32,270 --> 01:25:36,770
+طبعا بعض البنات هتجي تقولي هه لو سرقت رحلتك هتقولي
+
+700
+01:25:36,770 --> 01:25:40,730
+من zero لغاية باية على تلاتة هذا كلام غلط تتكلمي
+
+701
+01:25:40,730 --> 01:25:44,530
+في الفراغ انا بدي لحاجة باللي ضايل اللي بعدهاطبعا
+
+702
+01:25:44,530 --> 01:25:49,110
+يبدأ من باية تلاتة لباية طيب ضل تيتا واضحة اصلا
+
+703
+01:25:49,110 --> 01:25:58,630
+تيتا من الصفر لغاية كده؟2π دوس خط الرسمة كلها
+
+704
+01:25:58,630 --> 01:26:08,970
+بتصير الدائرة اللى تحتجه من 0 لغاية 2π كيف؟
+
+705
+01:26:08,970 --> 01:26:15,450
+لو قولنا حد المخروض صحيح احنا مابنعش المخروض هدف
+
+706
+01:26:15,450 --> 01:26:20,530
+فرعام تمام؟ يبقى هاي اللى بيحصل يبقى هذا الكلام
+
+707
+01:26:20,530 --> 01:26:27,520
+يدوسى التكامل من 0 لغاية 2πوتكامل من πاية على
+
+708
+01:26:27,520 --> 01:26:35,400
+تلاتة لغاية باية على اتنين لروح تكييبك على تلاتة
+
+709
+01:26:35,400 --> 01:26:41,900
+من Zero لغاية من Zero لغاية اتنين من Zero لغاية
+
+710
+01:26:41,900 --> 01:26:49,700
+اتنين ويظل عندى sin فاية D فاية D ثيتا يعني من هذا
+
+711
+01:26:49,700 --> 01:26:53,620
+الكلام الدنيا تصبح تمانية على تلاتةتمنى على تلاتة
+
+712
+01:26:53,620 --> 01:26:59,420
+خليك برا أي تمانية على تلاتة و بقى لدي تكاملين من
+
+713
+01:26:59,420 --> 01:27:03,840
+باية على تلاتة الى باية على اتنين و من Zero لغاية
+
+714
+01:27:03,840 --> 01:27:11,060
+اتنين باية من Zero لغاية اتنين باية لمين لصين
+
+715
+01:27:11,060 --> 01:27:18,900
+الفاية D فاية D تيتا و Zero برنامج كويس بدنا
+
+716
+01:27:18,900 --> 01:27:24,510
+الكامليبقى هذا الكلام يسوى تمانية ع تلاتة تكامل من
+
+717
+01:27:24,510 --> 01:27:31,330
+Zero لإتنين باي لناقص cosine الفاعي من باية ع
+
+718
+01:27:31,330 --> 01:27:38,670
+تلاتة لغاية باية على اتنين لدى ثيتا ويسوى تمانية
+
+719
+01:27:38,670 --> 01:27:44,230
+على تلاتة تكامل من Zero لإتنين باية ع تلاتة
+
+720
+01:27:46,850 --> 01:27:55,210
+يبقى نقص مع نقص بالصير الزائد و هنا جتا ستين يبقى
+
+721
+01:27:55,210 --> 01:28:03,370
+داشت بنص دي ثيتا يبقى هذا الكلام بده يساوي أربعة
+
+722
+01:28:03,370 --> 01:28:10,060
+على تلاتة تكامل من zero للإتنين by للدي ثيتاأربع
+
+723
+01:28:10,060 --> 01:28:16,620
+على تلاتة تيتا من Zero للإتنين باى أربع على تلاتة
+
+724
+01:28:16,620 --> 01:28:23,220
+في إتنين باى ويساوي تمانية باى على بين على تلاتة
+
+725
+01:28:23,220 --> 01:28:28,480
+آخر مثال في محاضرة اليوم مثال رقم
+
+726
+01:28:44,880 --> 01:28:57,980
+molar region المنطقة الصغرى كانت from والمقطوعة من
+
+727
+01:28:57,980 --> 01:29:00,660
+the solid sphere
+
+728
+01:29:08,160 --> 01:29:16,260
+R أقل من أو يساوي 2π لإطلين
+
+729
+01:29:16,260 --> 01:29:21,100
+بالمستوى Z تساوي 1
+
+730
+01:30:00,070 --> 01:30:06,770
+بقولتلي حجم المنطقة الصغرى المطقوعة من الكورة اللى
+
+731
+01:30:06,770 --> 01:30:11,490
+عندها دى بالـ Plane Z تساوي مين؟ تساوي واحدة اقول
+
+732
+01:30:11,490 --> 01:30:14,650
+لكوا يستخدموا ارصدوا من الرسمة ونشوف كإيه الدينامس
+
+733
+01:30:14,650 --> 01:30:21,370
+يبقى لو جهت خد اللى هو المحاول التلاتة هذا X هذا Y
+
+734
+01:30:21,370 --> 01:30:26,810
+هذا Z الان لما اقول روتو تساوي اتنين يبقى كورة
+
+735
+01:30:27,130 --> 01:30:31,870
+مركزها نقطة الأصبع نصف قطرة يساوي كده؟ يساوي اتنين
+
+736
+01:30:31,870 --> 01:30:44,810
+يبقى كأن الكورة عليا الشكل اللي عندنا هذا يبقى
+
+737
+01:30:44,810 --> 01:30:49,790
+هذا الكورة في شكلها العام طبعا مابدي اقطعها
+
+738
+01:30:49,790 --> 01:30:55,360
+بالمستوى اللي همين Z يساوي واحدإذا بدى أجي على
+
+739
+01:30:55,360 --> 01:31:00,500
+المستوى الطوب هيك و أجي و أاخده بالشكل اللي عنده
+
+740
+01:31:00,500 --> 01:31:06,080
+هذا هيك و من هنا أجي و أقول هذه المستوى اللي عندنا
+
+741
+01:31:06,080 --> 01:31:12,540
+و الـ Z بده يساوي واحدة إذا قطع الدائرة قطع القرة
+
+742
+01:31:12,540 --> 01:31:17,000
+اللي عندنا على شكل دائرة الشكل اللي عندنا هذا
+
+743
+01:31:20,140 --> 01:31:24,460
+وهذا اللي تحت كله شيلناه مش لزمن ، شيلناه بالمرة.
+
+744
+01:31:25,140 --> 01:31:31,100
+إذا صار عند مين الجزء اللي فوق هذا فقط لا غير.
+
+745
+01:31:33,640 --> 01:31:39,000
+اللي هو شكله شكل إيه يا بنات؟ بس شكله بالبلد هيك
+
+746
+01:31:39,000 --> 01:31:47,360
+شكل إيش؟ طاقيةمظبوط يبقى كأنه احنا بدنا نجيب حجم
+
+747
+01:31:47,360 --> 01:31:52,580
+الطاقية القروية اللى عندناها دى طبعا و باقى الكرة
+
+748
+01:31:52,580 --> 01:31:55,760
+اللى تحت هذا مالوش لزوم مش موجود عندى من الأصل
+
+749
+01:31:55,760 --> 01:32:00,200
+طبعا انه جالى بدى الجزء الصغير هاي اللى كبير تحت
+
+750
+01:32:00,200 --> 01:32:04,840
+وصغير فوق اذا احنا علاقتنا مع الجزء الصغير مايبقوا
+
+751
+01:32:04,840 --> 01:32:08,100
+بسيطة يبقى احنا بدنا V
+
+752
+01:32:16,590 --> 01:32:24,590
+فاين الفاين دي روى دي فاين دي فاين دي دي دي دي دي
+
+753
+01:32:24,590 --> 01:32:25,610
+دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي
+
+754
+01:32:25,610 --> 01:32:26,190
+دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي
+
+755
+01:32:26,190 --> 01:32:30,190
+دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي
+
+756
+01:32:30,190 --> 01:32:33,790
+دي دي دي دي دي دي دي دي
+
+757
+01:32:33,790 --> 01:32:33,990
+دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي
+
+758
+01:32:33,990 --> 01:32:37,450
+دي دي دي
+
+759
+01:32:37,450 --> 01:32:43,590
+د
+
+760
+01:32:44,950 --> 01:32:51,570
+قطعت منطقة التكامل لغاية ما وصلت الحدود الاقليمية
+
+761
+01:32:51,570 --> 01:32:58,510
+يبقى هنا اقل قيمة لرو هنا و اكبر قيمة لرو هنا
+
+762
+01:32:58,510 --> 01:33:09,490
+فمجددش رو هنا؟ زيت تلب واحد ايوةبتجي تقوليلي z في
+
+763
+01:33:09,490 --> 01:33:15,390
+الإحداثيات الكوروية هي z تساوي ال raw cosine الفاي
+
+764
+01:33:15,390 --> 01:33:21,410
+يعني بتجي تقوليلي هنا z تساوي ال raw cosine الفاي
+
+765
+01:33:21,410 --> 01:33:27,230
+اللي هو واحد تمام إذا ال raw تساوي كده سك الفاي
+
+766
+01:33:27,230 --> 01:33:33,210
+يبقى أقل قيمة ل raw هي سك الفاي وأكبر قيمة كده
+
+767
+01:33:35,800 --> 01:33:39,500
+للنصف القطر تبعها انه بالاقل من او سوى اتنين يعني
+
+768
+01:33:39,500 --> 01:33:45,620
+الكرة المصممة كلها دي طيب نجي ليه فاي فاي ستة تغير
+
+769
+01:33:45,620 --> 01:33:50,820
+من وين لوين من الان لغاية اتنين كده اعرف كده اش
+
+770
+01:33:50,820 --> 01:33:56,820
+الفاية كده تبقى يالا طب ماشي theta بقداش نرجع
+
+771
+01:33:56,820 --> 01:34:03,660
+لفاية بس قولولي theta من وين لوين من zero لاتنين
+
+772
+01:34:07,220 --> 01:34:12,140
+مع قصد الـ Phi هتبدأ من هنا إذا هتبدأ من الـ Zero
+
+773
+01:34:12,140 --> 01:34:19,660
+لأن قداش الله أعلم لأننا وعرفنا قداش معادلة هذا
+
+774
+01:34:19,660 --> 01:34:26,680
+الخط بيكون وعرفنا Phi تساوي قداش يالا قد احنا
+
+775
+01:34:26,680 --> 01:34:31,820
+رششناكوا ورسمنا الخط وشوفوا كيف يمكنوا تحسبوا Phi
+
+776
+01:34:31,820 --> 01:34:35,660
+من خلال الرسم اللي قدامكوا هذه
+
+777
+01:34:49,200 --> 01:35:02,060
+يلا ايوة صحيح هاي زيت تساوي واحد مضمون صحيح
+
+778
+01:35:02,060 --> 01:35:09,320
+وراه تساوي اتنينممتاز جدا يبقى البنات بتقولكوا
+
+779
+01:35:09,320 --> 01:35:14,200
+اخدوا صباح ابو سمها دانا ما يأتي بتقولوا اللي فوق
+
+780
+01:35:14,200 --> 01:35:19,800
+اللي هي باتنينيقول يا راتو ساوى اتنين وهذه ال E
+
+781
+01:35:19,800 --> 01:35:24,740
+دائرة لان لليط لين زد يساوي واحد في الاحداثيات
+
+782
+01:35:24,740 --> 01:35:31,800
+الكوروية يبقى Z ال وبرو كساين الفاي بدها تساوي
+
+783
+01:35:31,800 --> 01:35:41,090
+واحد يبقى صار عندنا E اتنينكو ساين الفاى بيبقى كو
+
+784
+01:35:41,090 --> 01:35:45,430
+ساين الفاى بيبقى كو ساين الفاى بيبقى كو ساين الفاى
+
+785
+01:35:45,430 --> 01:35:46,770
+بيبقى كو ساين الفاى بيبقى كو ساين الفاى بيبقى كو
+
+786
+01:35:46,770 --> 01:35:47,030
+ساين الفاى بيبقى كو ساين الفاى بيبقى كو ساين الفاى
+
+787
+01:35:47,030 --> 01:35:47,070
+بيبقى كو ساين الفاى بيبقى كو ساين الفاى بيبقى كو
+
+788
+01:35:47,070 --> 01:35:48,230
+ساين الفاى بيبقى كو ساين الفاى بيبقى كو ساين الفاى
+
+789
+01:35:48,230 --> 01:35:54,890
+بيبقى كو ساين الفاى بيبقى كو ساين الفاى بيبقى كو
+
+790
+01:35:54,890 --> 01:35:59,190
+ساين الفاى بيبقى كو س
+
+791
+01:36:02,390 --> 01:36:05,390
+By integration من Zero لإتنين By integration من
+
+792
+01:36:05,390 --> 01:36:06,650
+Zero لإت باية تلاتة By integration من Zero لإت
+
+793
+01:36:06,650 --> 01:36:10,230
+باية تلاتة By integration من Zero لإت باية تلاتة
+
+794
+01:36:10,230 --> 01:36:11,750
+By integration من Zero لإت باية تلاتة By
+
+795
+01:36:11,750 --> 01:36:12,170
+integration من Zero لإت باية تلاتة By integration
+
+796
+01:36:12,170 --> 01:36:12,290
+من Zero لإت باية تلاتة By integration من Zero لإت
+
+797
+01:36:12,290 --> 01:36:14,910
+باية تلاتة By integration من Zero لإت باية تلاتة
+
+798
+01:36:14,910 --> 01:36:15,770
+By integration من Zero لإت باية تلاتة By
+
+799
+01:36:15,770 --> 01:36:16,750
+integration من Zero لإت باية تلاتة By integration
+
+800
+01:36:16,750 --> 01:36:20,210
+من Zero لإت باية تلاتة By integration من Zero لإت
+
+801
+01:36:20,210 --> 01:36:23,050
+باية تلاتة By integration من Zero لإت باية تلاتة
+
+802
+01:36:23,050 --> 01:36:26,110
+By integration من Zero لإت باية تلاتة By
+
+803
+01:36:26,110 --> 01:36:31,870
+integration من Zero لإت باية تلاتة By integration
+
+804
+01:36:31,870 --> 01:36:42,440
+من Zero لطبعا و هنا sin فاي و هنا دي فاي دي إذا
+
+805
+01:36:42,440 --> 01:36:49,520
+صار هذا الطول تكاملين من zero لإتنين باى من zero
+
+806
+01:36:49,520 --> 01:36:59,060
+لباية باى ع تلاتة لتمانية sin فاي و هنا ناقص بدي
+
+807
+01:36:59,060 --> 01:37:00,600
+أسوي زي اللي قبل يا بنات
+
+808
+01:37:06,750 --> 01:37:17,250
+تان فاى كل هذا فيه فاى دى تى هذه
+
+809
+01:37:17,250 --> 01:37:27,390
+لحالها كإنها يشبه تان الفاى دى تان الفاى عاملناها
+
+810
+01:37:27,390 --> 01:37:33,720
+بالضبط تماما يبقى بالنار كامل يبقى طولتكامل من صفر
+
+811
+01:37:33,720 --> 01:37:43,580
+للإتنين باي وناقص تمانية في cosine الفاي وهذه بقى
+
+812
+01:37:43,580 --> 01:37:52,860
+ناقص تان تربيع الفاي كله على إتنين من Zero لغاية
+
+813
+01:37:52,860 --> 01:38:03,450
+باي على تلاتة لديه ثيتا يبقى التلتintegration من
+
+814
+01:38:03,450 --> 01:38:08,790
+zero لغاية اتنين by ليه فتعوض ال باية تلتة جتا
+
+815
+01:38:08,790 --> 01:38:17,530
+ستين بنص مع التمانية بتعطيك سالب اربع نفس بدنا نجي
+
+816
+01:38:17,530 --> 01:38:25,150
+لمان لظل الستين يعني جا ستين على جتا ستين جزر
+
+817
+01:38:25,150 --> 01:38:34,400
+تلاتة امان مظبوطجدر تلاتة وتربيه تلاتة
+
+818
+01:38:34,400 --> 01:38:41,200
+وعلى اتنين طبعا هاي عوض بالقيم اللي فوق ناقص اللي
+
+819
+01:38:41,200 --> 01:38:46,680
+تحت ناقص مع ناقص بيصير زائد تمانين نقصين سفر اك
+
+820
+01:38:46,680 --> 01:38:54,460
+واحد وظل السفر بسفر فقط لا غير كله في دي فيتر طب
+
+821
+01:38:54,460 --> 01:38:55,160
+اطلعي
+
+822
+01:38:59,050 --> 01:39:05,710
+خمسة و نصف من تمانية بظل اتنين و نصف يعني خمسة على
+
+823
+01:39:05,710 --> 01:39:12,610
+اتنين شرفونه برا يبقى طول في خمسة على اتنين في
+
+824
+01:39:12,610 --> 01:39:22,110
+تكامل من Zero لإتنين Pi لديه ثيتايبقى هذا الكلام
+
+825
+01:39:22,110 --> 01:39:29,570
+يساوي خمس أسداس و هنا ثيتا من zero لغاية اتنين باي
+
+826
+01:39:29,570 --> 01:39:39,530
+يبقى خمس أسداس لمين لاتنين باي ويساوي خمسة باي على
+
+827
+01:39:39,530 --> 01:39:45,890
+تلاتة اللي هو مقدار هذا التكامل بنروح ل exercises
+
+828
+01:39:45,890 --> 01:39:53,190
+خمستاشر السابعة exercisesخمس تاشر سبعة المسائل
+
+829
+01:39:53,190 --> 01:40:00,530
+التالية تلاتة خمسة سابعة تسعة تلاتة خمسة سابعة
+
+830
+01:40:00,530 --> 01:40:10,730
+تسعة خمس تاشر تمانتاش تسعة تاشر تلاتة وعشرين خمسة
+
+831
+01:40:10,730 --> 01:40:22,260
+وعشرين تمانية وعشرين تلاتين اربعة وتلاتينسبعة و
+
+832
+01:40:22,260 --> 01:40:33,360
+تلاتين خمسة و اربعين سبعة و اربعين تسعة و اربعين
+
+833
+01:40:33,360 --> 01:40:42,740
+اتنين و خمسين تلاتة و خمسين اربعة و خمسين سبعة و
+
+834
+01:40:42,740 --> 01:40:49,620
+خمسين و تسعة و خمسين و اتنين و ستين
+
+835
+01:40:52,520 --> 01:40:56,280
+يبقى يوم الأربعاء ان شاء الله القادم فبناخد ال
+
+836
+01:40:56,280 --> 01:41:01,220
+section الأخير في هذا الشبهر.
+
+837
+01:41:04,780 --> 01:41:13,180
+حد بتحب تسأل أي سؤالينا؟
+
+838
+01:41:13,180 --> 01:41:17,220
+هل
+
+839
+01:41:17,220 --> 01:41:25,860
+عيناكم؟ شايفة الإدارة هذه؟وشايفان الكرة هذه اتنين
+
+840
+01:41:25,860 --> 01:41:29,420
+اتقطعوا مع بعض عندها نقطة صارت هذه نقطة مشتركة
+
+841
+01:41:29,420 --> 01:41:33,940
+كثيرة بينهم لما وصلت من نقطة الأصل إلى هذه النقطة
+
+842
+01:41:33,940 --> 01:41:38,220
+طلع الخط اللي عندنا هذا الخط هذا بدي أحاول أجيب
+
+843
+01:41:38,220 --> 01:41:43,220
+معادله بقول كويس الكرة هذه رو كساوين اتنين
+
+844
+01:41:43,220 --> 01:41:50,180
+والمستوى هذا Z يساوي واحد Z في ال spherical هي رو
+
+845
+01:41:50,180 --> 01:41:55,440
+كساين الفعلصارت روب اتنين وروب كوصين الفاى بقدرش
+
+846
+01:41:55,440 --> 01:42:01,140
+بقى بواحد يبقى ده ساوى اتنين بعض يبقى صار اتنين
+
+847
+01:42:01,140 --> 01:42:06,080
+كوصين الفاى بدرة ساوية واحد يبقى كوصين الفاى
+
+848
+01:42:06,080 --> 01:42:12,300
+بساوية نصف يبقى فاى صارت بقدرش خلاصنا عايزين
+
+849
+01:42:12,300 --> 01:42:15,760
+نسوينا واحدة قابلة السؤال المثال اللى جابله برضه
+
+850
+01:42:15,760 --> 01:42:19,960
+بنفس الطريقة يبقى بنفس الطريقة حد لايه تسوى الآخر
+
+851
+01:42:22,280 --> 01:42:23,820
+يا الله تعالى تعالى
+
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/cjA4GBt8ijs_raw.srt b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/cjA4GBt8ijs_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..ea0a52f0f259f53004399a03fb4acd1220f88ef9
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/cjA4GBt8ijs_raw.srt
@@ -0,0 +1,3444 @@
+1
+00:00:13,720 --> 00:00:20,400
+بسم الله الرحمن الرحيم نرجع الآن لستشين اللي
+
+2
+00:00:20,400 --> 00:00:24,640
+ابتدأنا المرة الماضية المرة الماضية قلنا كيف نتحول
+
+3
+00:00:24,640 --> 00:00:28,120
+من Cartesian coordinates إلى cylindrical
+
+4
+00:00:28,120 --> 00:00:33,690
+coordinatesفقلنا نقطة P X Y و Z في الإحداثيات
+
+5
+00:00:33,690 --> 00:00:38,410
+الكارتزية و دي جابلها في الإحداثيات القسطوانية الـ
+
+6
+00:00:38,410 --> 00:00:44,250
+cylindrical coordinates اللي هو Z بتبقى زي ما هي
+
+7
+00:00:44,250 --> 00:00:52,410
+DX DY هستدلها بRDR Dθ واخدنا على ذلك مثال واحد في
+
+8
+00:00:52,410 --> 00:00:57,090
+المحاضرة الماضية الآن بناخد المثالة رقم اتنين
+
+9
+00:01:02,140 --> 00:01:07,700
+بنقلب من الإحداثيات الكارتيزية to an equivalent
+
+10
+00:01:07,700 --> 00:01:11,520
+integral in cylindrical coordinates إلى تكامل
+
+11
+00:01:11,520 --> 00:01:17,980
+المكافئ له بس في الإحداثيات الأسطانية ومن ثم بدأ
+
+12
+00:01:17,980 --> 00:01:21,800
+نحسب التكامل في الإحداثيات الأسطانية
+
+13
+00:01:30,080 --> 00:01:34,860
+الان نحول الى cylindrical coordinates X تربيه زي
+
+14
+00:01:34,860 --> 00:01:40,360
+نوع التربيه هي عبارة عن مين R تربيه دي زد كما هي
+
+15
+00:01:40,360 --> 00:01:47,440
+مالهاش اي اشكالين بجي لمين بدل دي X دي Y بقول ر دي
+
+16
+00:01:47,440 --> 00:01:54,320
+ار دي ثيتر اذا الحدود زد ستبقى كما هي
+
+17
+00:02:02,230 --> 00:02:10,390
+ر في قصين الزاويةبدي ايجي عندي دي x دي y بدي
+
+18
+00:02:10,390 --> 00:02:16,290
+استبدلها بRDRDθ بدي اعرف R بدي اتغير من وين لوين و
+
+19
+00:02:16,290 --> 00:02:20,070
+كذلك θ بدي اتغير من وين لوين لذلك بروح ارسم
+
+20
+00:02:20,070 --> 00:02:25,890
+المنطقة التكامل اللي عندها هذه كيف كانت كارتزيا و
+
+21
+00:02:25,890 --> 00:02:29,170
+كيف بدي احولها الى cylindrical coordinates
+
+22
+00:02:38,450 --> 00:02:43,470
+بعد ال DZ بدأ يجيني DX يبقى الحدود هذه هي حدود
+
+23
+00:02:43,470 --> 00:02:49,210
+امام ال X ال X بدأ تبدأ من اندي ال zero لغاية
+
+24
+00:02:49,210 --> 00:02:54,770
+الجذر الموجة بيبقى عندها تكون جهتي اليمينجهات
+
+25
+00:02:54,770 --> 00:02:59,150
+اليمين يعني X جهات الشمال ماعنديش تمام ؟ طيب هذه
+
+26
+00:02:59,150 --> 00:03:03,130
+معادلة ليش لما اقول X يساوي الجدري التربيهي لو
+
+27
+00:03:03,130 --> 00:03:07,790
+واحد ناقص Y تربيه لو ربعت الطرفين وانا بصير دائرة
+
+28
+00:03:07,790 --> 00:03:13,030
+مركزها نقطة الأصل و نسقطها يساوي واحد صحيح بس مش
+
+29
+00:03:13,030 --> 00:03:17,680
+اللي على الشمال ماليش فيهايبقى نادي باسميني اليمين
+
+30
+00:03:17,680 --> 00:03:23,640
+طب هل كل نصف دائرة و لا ربع دائرة بيدجل الحدود تبع
+
+31
+00:03:23,640 --> 00:03:28,560
+ال Y جل ال Y بدأ تبدأ من أيدي السالف واحد لغاية
+
+32
+00:03:28,560 --> 00:03:34,340
+مين الواحد يبقى منطقة التكامل كلها المنطقة المضللة
+
+33
+00:03:34,340 --> 00:03:50,050
+اللي عندنا طيبهذه عبارة عن نصف دائرة ر ستتغير
+
+34
+00:03:50,050 --> 00:03:56,370
+من zero إلى أي نقطة على محيط الدائرة من صفر لغاية
+
+35
+00:03:56,370 --> 00:04:05,050
+واحدلغاية واحد لإيش؟ وين ما ترسمي هذا الخط المسافة
+
+36
+00:04:05,050 --> 00:04:14,410
+من هنا لهنا مسافة ثابتة هيبقى اللي عندى θ تبدأ
+
+37
+00:04:14,410 --> 00:04:18,350
+تتغير إذا ابتديت عند السلب واحد و جايب طالع لغاية
+
+38
+00:04:18,350 --> 00:04:24,690
+الواحد، من وين لوين؟ من سالب باي على اتنين إلى باي
+
+39
+00:04:24,690 --> 00:04:31,270
+على اتنينلما حد حدد تكمر صح يبقى لك شغل روتيني
+
+40
+00:04:31,270 --> 00:04:36,430
+يبقى أول شي بتكمل بالنسبة لمان الذي زد يبقى الار
+
+41
+00:04:36,430 --> 00:04:40,690
+هذي مقدر ثابت مليش علاقة بالموضوع يبقى بضوحة كامل
+
+42
+00:04:40,690 --> 00:04:43,770
+فبقى يبقى هذا الكلام يستخدم integration
+
+43
+00:05:04,410 --> 00:05:09,010
+يبقى الة المثلة اللى عندى الى تكامل من سالب باى
+
+44
+00:05:09,010 --> 00:05:13,230
+على اتنين كده باى على اتنين تكامل من Zero لغاية
+
+45
+00:05:13,230 --> 00:05:17,010
+الواحد ال Zero بتعاون بالقيم اللى فوق النقص اللى
+
+46
+00:05:17,010 --> 00:05:22,290
+تحته اللى بيبقى بس القيم اللى فوق وعنا كمان R
+
+47
+00:05:26,720 --> 00:05:35,020
+كوصين الزاوية ثيتا في DR في D ثيتا إذا هذا بدي
+
+48
+00:05:35,020 --> 00:05:40,320
+يعطيني ما يأتي يبقى اي تكامل من سالف باي على اتنين
+
+49
+00:05:40,320 --> 00:05:47,580
+إلى باي على اتنين وهذه تكملها أقص خمسة على خمسة من
+
+50
+00:05:47,580 --> 00:05:53,520
+Zero لواحد لسه بضايل عندي كوصين ثيتا في D ثيتا
+
+51
+00:05:54,240 --> 00:05:57,940
+بنعوض بالقيمة اللي فوق هيجيبلي خمس والقيمة اللي
+
+52
+00:05:57,940 --> 00:06:03,080
+تحت هيجيبلي zero يبقى خمس مقدار ثابت فأقوله كمان
+
+53
+00:06:03,080 --> 00:06:09,380
+خليك برا يبقى خمس تكامل من سالف πاي على اتنين إلى
+
+54
+00:06:09,380 --> 00:06:18,720
+باي على اتنين ل cosine ثيتا دي ثيتا cosine ثيتا دي
+
+55
+00:06:18,720 --> 00:06:25,800
+ثيتاeven هذا الرقم هو نفس الرقم بإشارة مخالفة إذا
+
+56
+00:06:25,800 --> 00:06:31,260
+بستخدم خاصية ال even يبقى هذا الكلام اتنين على
+
+57
+00:06:31,260 --> 00:06:38,320
+خمسة تكامل من zero ل pi على اتنين ل cosine theta d
+
+58
+00:06:38,320 --> 00:06:47,080
+theta يبقى هذا الكلام يبدو يسوى خمسين اتنين على
+
+59
+00:06:47,080 --> 00:06:49,520
+خمسة وتكامل ال cosine
+
+60
+00:06:58,410 --> 00:07:03,150
+صين البي على اتنين بواحد وصين زيرو بزيرو إذا
+
+61
+00:07:03,150 --> 00:07:14,670
+الجواب يساوي نين على خمسة لثالث
+
+62
+00:07:14,670 --> 00:07:19,850
+نتة و
+
+63
+00:07:19,850 --> 00:07:26,630
+ل find the volume of the region find the volume
+
+64
+00:07:27,950 --> 00:07:35,370
+of the region قدش حجم المنطقة bounded by the
+
+65
+00:07:35,370 --> 00:07:42,050
+cylinder bounded by
+
+66
+00:07:42,050 --> 00:07:53,850
+the cylinder والمحدودة بالاسطوالةx تربيع زائد y
+
+67
+00:07:53,850 --> 00:08:05,050
+تربيع تساوي أربعة and the airplanes بالمستويين z
+
+68
+00:08:05,050 --> 00:08:15,350
+بتساوي zero and المستوى التاني x زائد y زائد z
+
+69
+00:08:15,350 --> 00:08:18,430
+بتساوي اللي هو أربعة
+
+70
+00:08:33,500 --> 00:08:38,640
+هذا السؤال يختلف عن السؤالين السابقين السؤالين
+
+71
+00:08:38,640 --> 00:08:43,460
+السابقين كان ميعطيني حدود التكامل وجاهز بعث عليها
+
+72
+00:08:43,460 --> 00:08:48,140
+كامل الأول كان مباشر التاني كان بدنا نغير حدود
+
+73
+00:08:48,140 --> 00:08:52,580
+التكامل من كارتيزيا إلى cylindrical coordinates
+
+74
+00:08:52,580 --> 00:08:57,160
+لكن هذا لا اعطاني وقال انت بتحدد حدود التكامل
+
+75
+00:08:57,160 --> 00:09:02,560
+لوحدك بقوله ماشي الحاليبقى انا بدي ابدأ احط
+
+76
+00:09:02,560 --> 00:09:08,840
+التكامنات الثلاثة اللي عندنا اي تلت تكامنات ل DV
+
+77
+00:09:08,840 --> 00:09:20,470
+DV بدي اقول عليها DZ وR DR Dθ شكلانهابدي ابدأ زد
+
+78
+00:09:20,470 --> 00:09:25,170
+قال ال region محدودة ما بين ال cylinder هذي and
+
+79
+00:09:25,170 --> 00:09:30,830
+the planes وفي عندي مستوين المستوى الأول زد يساوي
+
+80
+00:09:30,830 --> 00:09:35,230
+zero لهمين ال XY فلان يعني مستوى الأرض اللي احنا
+
+81
+00:09:35,230 --> 00:09:40,510
+قاعدين عليها وهذا مستوى X زائد Y زائد Z يساوي
+
+82
+00:09:40,510 --> 00:09:46,050
+أربعة إذا زد تتغير من وينمن عندي الـ zero لغاية
+
+83
+00:09:46,050 --> 00:09:53,110
+هذا هذا Z قدش ساوي أربعة ناقص X ناقص Y يبقى أربعة
+
+84
+00:09:53,110 --> 00:10:01,550
+ناقص X ناقص Y تمام بداجي أشوف حدود ال R والثيتا
+
+85
+00:10:01,550 --> 00:10:06,550
+مشان أشوف حدود ال R والثيتا بداجي أشوف السيلندر
+
+86
+00:10:06,550 --> 00:10:09,790
+اللي عندنا السيلندر اللي عندنا هذا مين محورها يا
+
+87
+00:10:09,790 --> 00:10:16,120
+بناتيمحور Z لأنه الرمز الغائب وتقاطعها مع المستوى
+
+88
+00:10:16,120 --> 00:10:22,220
+XY Plane بيكون على شكل دائرة مركزها النقطة الأصل و
+
+89
+00:10:22,220 --> 00:10:28,200
+نصف قطر هيساوي اتنين تمام تمام إذا لو جيت قلت هذه
+
+90
+00:10:28,200 --> 00:10:34,420
+المحاور اللي عندنا هذا محور X وهذا محور Y وهذا
+
+91
+00:10:34,420 --> 00:10:41,030
+نقطة الأصل Zيبقى هذا بدأ يكون دائرة الشكل اللي
+
+92
+00:10:41,030 --> 00:10:47,790
+عندنا هذا يبقى هي الدائرة اللي موجودة إذا R على
+
+93
+00:10:47,790 --> 00:10:53,010
+هذه الدائرة ستتغير من أين إلى أين؟ من Zero لغاية
+
+94
+00:10:53,010 --> 00:11:00,330
+كم؟ لغاية اتنين لماذا؟ لأن نصف قطر دائرة هذه ثابت
+
+95
+00:11:00,330 --> 00:11:06,880
+أين ما تروح تجد R تساوي Zeroوارت ساوي هنا قداش
+
+96
+00:11:06,880 --> 00:11:12,480
+اتنين طيب كويس ضايق اللي عندنا مين ثيتا ثيتا
+
+97
+00:11:12,480 --> 00:11:16,560
+بالنسبة لدار نصطوانة نازلة من فوق يبقى ثيتا حتى
+
+98
+00:11:16,560 --> 00:11:22,540
+تتغير من و لا و اين من صفر لغاية اتنين بايت يبقى
+
+99
+00:11:22,540 --> 00:11:30,300
+من zero لغاية اتنين بايت طيب مش مشكلة اظل لو
+
+100
+00:11:30,300 --> 00:11:34,460
+اكملها بالنسبة لزيد في الأول لإنها هذه من ضمن مين
+
+101
+00:11:34,840 --> 00:11:40,420
+من ضمن المتغيرات التلاتة تبع الـ Cylindrical
+
+102
+00:11:40,420 --> 00:11:44,600
+Coordinates يبقى ماجي بقول هذا الكلام بده يساوي
+
+103
+00:11:44,600 --> 00:11:50,420
+تكامل من صفر لإتنين باي تكامل من Zero لغاية اتنين
+
+104
+00:11:50,420 --> 00:11:58,080
+تكامل ال DZ اللي هي FZ من عند Zero لغاية أربع ناقص
+
+105
+00:11:58,080 --> 00:12:04,380
+X ناقص Y وظل عندي برا RDRDZ
+
+106
+00:12:07,090 --> 00:12:16,030
+هذا الكلام يجب أن يساوي هذا
+
+107
+00:12:16,030 --> 00:12:23,890
+الكلام يجب أن يتكامل من 0 إلى 2 باي تكامل من 0 إلى
+
+108
+00:12:23,890 --> 00:12:32,130
+2 نعوض بالقيمة ناقص 4 ناقص X ناقص Y ناقص الـ Zero
+
+109
+00:12:32,130 --> 00:12:41,750
+وهنا ضللنا RDRDithita وما عجلك عن قومك يا موسى
+
+110
+00:12:41,750 --> 00:12:49,070
+يعني أربعه وبعدين في القرآن في سورة الأسرار ويدعو
+
+111
+00:12:49,070 --> 00:12:54,350
+الإنسان بالشر دعاءه بالخير وكان الإنسان عجولة
+
+112
+00:12:54,350 --> 00:13:00,030
+باستعجل دائما أو أبدا لأنك لا تستعجلنا واصبرنا حتى
+
+113
+00:13:00,030 --> 00:13:08,010
+يأتيكن اليقينطيب عارفين إيش معنى اليقين؟ ايوة
+
+114
+00:13:08,010 --> 00:13:14,550
+الموت اليقين هو أحد أسماء الموت يبقى هنا حتى ..
+
+115
+00:13:14,550 --> 00:13:18,670
+هنا لا نقصد موت ولكن نقصد اللي هو الإجابة اللي
+
+116
+00:13:18,670 --> 00:13:23,810
+أنتوا بتسألوا عليها هنا يبقى هذا الكلام يساوي من
+
+117
+00:13:23,810 --> 00:13:29,600
+zero لإتنين byومن هنا من Zero للإتنين من Zero
+
+118
+00:13:29,600 --> 00:13:34,300
+للإتنين هذه حدوط لل R إذا لازم أحوّل ال kart easy
+
+119
+00:13:34,300 --> 00:13:38,740
+ان هذه اللامعين إلى cylindrical إذا بدي أشيل ال X
+
+120
+00:13:38,740 --> 00:13:43,640
+و أحط مكانها R Cos θ و بدي أشيل ال Y و أحط مكانها
+
+121
+00:13:43,640 --> 00:13:53,200
+R Sin θ إذا هذه يا بنات تصير 4R ناقص R تربيع في
+
+122
+00:13:53,200 --> 00:14:00,600
+Cos الزاوية θنقص R تربيع في Sine الزاوية تيتا كل
+
+123
+00:14:00,600 --> 00:14:10,400
+هذا DRZ إذا شيلت ال X وحطيت مكانها R Cosine تيتا
+
+124
+00:14:10,400 --> 00:14:15,460
+وشيلت ال Y وحطيت مكانها R Sine تيتا اللي وقمتهم في
+
+125
+00:14:15,460 --> 00:14:19,680
+الـ cylindrical coordinates وضربت في R فصرت
+
+126
+00:14:19,680 --> 00:14:25,830
+المعادلة قدامي بهذا الشكل الان بيتكمل بالنسبةلمن؟
+
+127
+00:14:25,830 --> 00:14:32,110
+لR الـ integration من Zero لإتنين بايت هذي باتنين
+
+128
+00:14:32,110 --> 00:14:40,890
+R تربيع مفقود؟ طيب هذي ناقص طول R تكييب في cosine
+
+129
+00:14:40,890 --> 00:14:47,190
+الزاوية ثيتا وهذي ناقص طول R تكييب في sine الزاوية
+
+130
+00:14:47,190 --> 00:14:55,400
+ثيتا والكلام من Zero لإتنين لديه ثيتايبقى هذا
+
+131
+00:14:55,400 --> 00:15:02,020
+الكلام مدة ساعة من Zero لإتنين By L بتعوض بالقيم
+
+132
+00:15:02,020 --> 00:15:06,800
+اللي فوق نقصها لتحت طبعا لتحت Zero Zero Zero مع
+
+133
+00:15:06,800 --> 00:15:11,560
+السلامة بتظهر بس القيم اللي فوت بدي أشيل كل R و
+
+134
+00:15:11,560 --> 00:15:16,600
+أحط مكانها اتنين يبقى هنا اتنين تاربية اربعة في
+
+135
+00:15:16,600 --> 00:15:24,010
+اتنين بتمانية يبقى هاي تمانيةوهنا ناقص برضه تمانية
+
+136
+00:15:24,010 --> 00:15:30,670
+على تلاتة يبقى تمانية على تلاتة وsin الزاوية ثيتا
+
+137
+00:15:30,670 --> 00:15:37,890
+وهنا ناقص تمانية على تلاتة sin الزاوية ثيتا في دي
+
+138
+00:15:37,890 --> 00:15:38,650
+ثيتا
+
+139
+00:16:06,630 --> 00:16:12,930
+طيب نجم كامل هنا تجه هذا الكلام بده يساوى تمانية
+
+140
+00:16:12,930 --> 00:16:19,430
+ثيتا واللي بعده ال cosine بالزائد نخص تمانية على
+
+141
+00:16:19,430 --> 00:16:27,030
+تلاتة cosine زاوية ثيتا واللي بعده زائد تمانية على
+
+142
+00:16:27,030 --> 00:16:33,460
+تلاتةبكوصين الزاوية تيتا وكله من zero لما تقدرش
+
+143
+00:16:33,460 --> 00:16:38,180
+لما تتنين باى لذا نجد ان عوض بحدود التكامل هادئة
+
+144
+00:16:38,180 --> 00:16:44,300
+من هادئة تيتا وحطت تنين باى بيصير ست عشر باى صيني
+
+145
+00:16:44,300 --> 00:16:50,180
+اتنين باى ضهورة كاملة يعني انه زيرو يبقى هادئ هنا
+
+146
+00:16:50,180 --> 00:16:56,200
+اقل من زيرو تما الكوصين اتنين باى بواحد تمازز
+
+147
+00:17:02,660 --> 00:17:10,880
+zero zero وصين صفر و واحد يبقى ناقص تمانية على
+
+148
+00:17:10,880 --> 00:17:16,020
+تلاتة الفون ناقص اللي تحت يبقى ال job بتعطينا قدير
+
+149
+00:17:16,020 --> 00:17:21,620
+ستاشر و واحد و تسهل و تسهل ده حد فيكم بتسأل أي
+
+150
+00:17:21,620 --> 00:17:27,360
+سؤال يعني إحنا إذا حددنا حدود التكامل صح بصير
+
+151
+00:17:27,360 --> 00:17:34,650
+الشغل الباقي كله عندنا شغل روتينيمثال مثال اربعة
+
+152
+00:17:34,650 --> 00:17:38,310
+you
+
+153
+00:17:38,310 --> 00:17:43,650
+gonna find the volume of the region find the
+
+154
+00:17:43,650 --> 00:17:55,330
+volume of the region جدش حجب المنطقة bounded above
+
+155
+00:17:55,330 --> 00:17:59,830
+bounded above
+
+156
+00:18:13,460 --> 00:18:24,780
+يساوي خمسة ناقص X تربيع ناقص Y تربيع and below ومن
+
+157
+00:18:24,780 --> 00:18:37,680
+أسفل by the paraboloid كذلك بالparaboloid
+
+158
+00:18:40,450 --> 00:18:49,310
+اللي هو الـ z تساوية أربعة X تربيع زائد أربعة Y
+
+159
+00:18:49,310 --> 00:19:08,830
+تربيع نمسح
+
+160
+00:19:08,830 --> 00:19:09,850
+الشجرة دي كلها
+
+161
+00:19:32,010 --> 00:19:38,410
+خلاص نرجع لسؤال هذا مرة تانية السؤال بيقول ليهذه
+
+162
+00:19:38,410 --> 00:19:43,530
+حجم المنطقة المحدودة من أعلى بالparaboloid اللي
+
+163
+00:19:43,530 --> 00:19:49,970
+قدامنا هنا ومن أسفل بالparaboloid السابق طبعا رسمة
+
+164
+00:19:49,970 --> 00:19:54,630
+الparaboloid هذا مر علينا من ضمن الرسومات الستة،
+
+165
+00:19:54,630 --> 00:20:00,650
+مظهر؟ كويس؟ إذا بدنا نجد رسم كل واحد فيهم ونحدد
+
+166
+00:20:00,650 --> 00:20:05,260
+وين المنطقة المشتركة اللي هو بدوياهالو جيت لل
+
+167
+00:20:05,260 --> 00:20:10,440
+Paraboloid الأول و روحت أخذت المحاور بالشكل اللي
+
+168
+00:20:10,440 --> 00:20:18,400
+عنها يبقى هذا محور X وهذا محور Y وهذا محور Z
+
+169
+00:20:18,400 --> 00:20:22,820
+بالداخل لل Paraboloid الأول لو كان ال Paraboloid
+
+170
+00:20:22,820 --> 00:20:30,260
+الأول هو Z تساوي X تربية زائد Y تربيةلو كان ال
+
+171
+00:20:30,260 --> 00:20:33,760
+paraboloid الأول مش بالشكل الأول كان X تربيه زائد
+
+172
+00:20:33,760 --> 00:20:38,780
+و ات تربيه إذا ال paraboloid جينه زيها و من هنا
+
+173
+00:20:38,780 --> 00:20:44,740
+على شكل ذهب Circular paraboloid تمام لكن لما تبقى
+
+174
+00:20:44,740 --> 00:20:49,580
+سابقة اتنين إشارة سالف يبقى بديه اللي بيصير بدل ما
+
+175
+00:20:49,580 --> 00:20:53,560
+هو مفتوح إلى أعلى بيصير مفتوح إلى أعلى للأسفل يبقى
+
+176
+00:20:53,560 --> 00:20:57,760
+بديه يصير ال paraboloid بالشكل اللي قلناه طيب راح
+
+177
+00:20:57,760 --> 00:20:59,260
+أضفنا له خمسة
+
+178
+00:21:01,620 --> 00:21:07,260
+المقدار خمسة إذا الرسمة في هذه الحالة بتاخد الشكل
+
+179
+00:21:07,260 --> 00:21:12,520
+التالي بيدهد على استقالته وال Paraboloid بيجيه
+
+180
+00:21:12,520 --> 00:21:20,540
+بشكل هذا الشكل تمام؟ وهذه القاعدة عبارة عن دائرة
+
+181
+00:21:20,540 --> 00:21:27,310
+الشكل اللي عندها هذه النقطة كده يا عزيزي؟5 يبقى
+
+182
+00:21:27,310 --> 00:21:36,710
+هذه 005 يبقى 005 على محور الزرد نجي لل Paraboloid
+
+183
+00:21:36,710 --> 00:21:42,010
+الثاني Paraboloid الثاني الزرد يسوى أربع نقص اكس
+
+184
+00:21:42,010 --> 00:21:47,450
+زائد X ترمية زائد Y ترمية يبقى هذا Parabola رقصه
+
+185
+00:21:47,450 --> 00:21:51,730
+نقطة الأصل المفتوح لوين لأعلى يبقى حرصه بلون تاني
+
+186
+00:21:51,730 --> 00:21:55,390
+يبقى بدجيك ال Parabola بهذا الشكل
+
+187
+00:21:58,230 --> 00:22:01,910
+و يتقاطع مع ال parabola اللى عندنا في ال
+
+188
+00:22:01,910 --> 00:22:07,790
+paraboloid التانى هذاهي الدائرة اللي عندناها يبقى
+
+189
+00:22:07,790 --> 00:22:11,990
+هذا ال paraboloid الثاني اللي هو مفتوح لعله هذا
+
+190
+00:22:11,990 --> 00:22:17,810
+مفتوح لأسفل يبقى احنا بدنا حجم المنطقة المحصورة
+
+191
+00:22:17,810 --> 00:22:23,210
+بين من؟ بين ال two paraboloids يبقى كأنه بقول ايش؟
+
+192
+00:22:23,210 --> 00:22:28,750
+بدي حجم ال paraboloid اللي عندنا هذا مضافة للي حجم
+
+193
+00:22:28,750 --> 00:22:33,000
+الطاقية اللي فوقيبقى هذا لما نقصه لتحت بظل اللي
+
+194
+00:22:33,000 --> 00:22:38,720
+فوق هذه على شكل ايه؟ على شكل طاقية يبقى بدنا حجم
+
+195
+00:22:38,720 --> 00:22:44,040
+المنطقة هذه كله بقوله كويس يبقى احنا بدنا نحدد
+
+196
+00:22:44,040 --> 00:22:48,800
+حدود التكمل تحديدا سليما وبالتالي بصير مسلتنا
+
+197
+00:22:48,800 --> 00:22:54,320
+بسيطة يبقى بقوله ال volume V اللي بده اياه يبقى
+
+198
+00:22:54,320 --> 00:22:57,780
+solution ال volume V
+
+199
+00:23:03,060 --> 00:23:09,520
+نبدأ من DZ و بعدها RDRD
+
+200
+00:23:13,960 --> 00:23:19,880
+بالـ Parabolid اللي فوق الأسود هذا معادلته Z يسوى
+
+201
+00:23:19,880 --> 00:23:24,980
+كمسة نقص X تربيع نقص Y تربيع يعني إيش؟ يعني
+
+202
+00:23:24,980 --> 00:23:33,160
+معادلته هذها اللي هي Z تسوى خمسة نقص X تربيع زي Y
+
+203
+00:23:33,160 --> 00:23:39,060
+تربيع تمام؟ طيب هذه خمسة نقص بدي أحولها إلى
+
+204
+00:23:39,060 --> 00:23:44,990
+الـCylindricalيبقى X تربيع زاد و تربيع عبارة عن Y
+
+205
+00:23:44,990 --> 00:23:50,910
+تربيع يبقى خمسة نفس R square تمام تمام نيجي لل
+
+206
+00:23:50,910 --> 00:23:56,970
+Parabolic التالي صاحبنا هذا اللي هو الأزرق كويس Z
+
+207
+00:23:56,970 --> 00:24:05,050
+تساوي أربعة في X تربيع زاد Y تربيع إذا هذا الكلام
+
+208
+00:24:05,050 --> 00:24:14,520
+بتساوي كده؟ أربعة R تربيعطب كويس نيجي نحدد حدود
+
+209
+00:24:14,520 --> 00:24:20,460
+التكامل بالنسبة إلى مين؟ إلى زد يبقى بدأ أروح أخد
+
+210
+00:24:20,460 --> 00:24:28,900
+أي نقطة على سطح الفرابل السفلي و أرسم موازن لمحور
+
+211
+00:24:28,900 --> 00:24:35,700
+زد و يقطع منطقة مين؟ منطقة التكامل يبقى بداجي طالع
+
+212
+00:24:35,700 --> 00:24:43,990
+هك امشي امشي جابلنا هنايبقى قابلنا السطح السفلي
+
+213
+00:24:43,990 --> 00:24:48,710
+عند هذه النقطة وقابلنا السطح العلوية عند هذه
+
+214
+00:24:48,710 --> 00:24:54,570
+النقطة يبقى هذه النقطة ايش بتكون يا بنات؟ اربعة ار
+
+215
+00:24:54,570 --> 00:25:01,110
+تربيع يعني ز عند هذه النقطة لأي نقطة على محيط
+
+216
+00:25:01,110 --> 00:25:08,510
+الفرابل السفلي بتبقى اربعة ار تربيعو Z هي لها عند
+
+217
+00:25:08,510 --> 00:25:16,030
+هذه النقطة Z يساوي خمسة ناقص R تربيع إذا Z اللي
+
+218
+00:25:16,030 --> 00:25:22,830
+عندنا دي ستتغير من أقل قيمة إلى أكبر قيمة من عند
+
+219
+00:25:22,830 --> 00:25:32,710
+الأربع R تربيع لخمسة ناقص R تربيع مين ضللنا؟ R
+
+220
+00:25:32,710 --> 00:25:38,780
+وThetaأريد أن أعرف أين الـr و الـθ و أيضًا أين
+
+221
+00:25:38,780 --> 00:25:44,860
+منطقة التقاطع تبعتهم؟ هذه لو جيت أسقطها على الـr
+
+222
+00:25:44,860 --> 00:25:49,740
+على من؟ على الـxy المشي هنا حدد ال domain اللي
+
+223
+00:25:49,740 --> 00:25:54,500
+عندنا هذا تمام يمكن لو جيت أسقطها بلاتك تجيلك هذه
+
+224
+00:25:54,500 --> 00:26:00,220
+هناك و تجيلك هذه التانية هناك اللي فوق دائرة يمكن
+
+225
+00:26:00,220 --> 00:26:02,360
+تلاقي هذه كمان دائرة
+
+226
+00:26:07,400 --> 00:26:14,060
+الان بدي اعرف كده تيتا و كده R اظن واضح من الدائرة
+
+227
+00:26:14,060 --> 00:26:19,060
+هذه ان تيتا في الدائرة من صفر لاثنين بايم يفجه هذه
+
+228
+00:26:19,060 --> 00:26:23,460
+من Zero لاثنين بايم مع اني مشكلة فيها المشكلة
+
+229
+00:26:23,460 --> 00:26:29,600
+دايلة وين؟ في الـR بدي اعرف كده نصف قطر هذه
+
+230
+00:26:29,600 --> 00:26:35,820
+الدائرة هميست هي الدائرة اللي فوق هذه بالضبط تماما
+
+231
+00:26:35,820 --> 00:26:41,620
+تمامايبقى هذا لو عرفت قداش R اللي منك بحلنا
+
+232
+00:26:41,620 --> 00:26:46,640
+الإشكالية مين تقولك كيف نجيب R من الدائرة اللي
+
+233
+00:26:46,640 --> 00:26:50,700
+فوق؟
+
+234
+00:26:50,700 --> 00:26:55,780
+يلا نشوف بسيطة وسهلة جدا كمان very easy
+
+235
+00:27:01,890 --> 00:27:07,450
+بنجيب ايش؟ كويس
+
+236
+00:27:07,450 --> 00:27:12,470
+الدائرة هذه يا بنات مشتقة على كل من ال two
+
+237
+00:27:12,470 --> 00:27:18,010
+surfaces اذا بدنا نسوي المعادلتين في بعض بكون خلصت
+
+238
+00:27:18,010 --> 00:27:23,090
+من المشكلة دي طيب باجي بقوله اه ماهي z فوق خمسة
+
+239
+00:27:23,090 --> 00:27:28,510
+ناقص R تربية و z تعتبر اربعة R تربية وهذه الدائرة
+
+240
+00:27:28,510 --> 00:27:33,740
+هي مشتركة ما بين الاتنينيبقى الذد في هذه اللحظة
+
+241
+00:27:33,740 --> 00:27:38,840
+لازم تسوى مين؟ الذد التاني، إذا بناء عليه الذد
+
+242
+00:27:38,840 --> 00:27:46,600
+عندها هتسوى خمسة ناقص R تربيع وتسوى أربعة R تربيع،
+
+243
+00:27:46,600 --> 00:27:52,260
+يبقى بناء عليه هذه هتعطيك إيش؟ هتعطيك إنه خمسة R
+
+244
+00:27:52,260 --> 00:27:58,420
+تربيع بده يسوى خمسة، يبقى ال R تربيع تسوى واحد،
+
+245
+00:27:58,420 --> 00:28:05,510
+يبقى ال R كتش بده تسوى بنانة1 يبقى ال R ستتغير من
+
+246
+00:28:05,510 --> 00:28:10,910
+ال zero من النقطة هذه إلى أي نقطة على محيط الدائرة
+
+247
+00:28:10,910 --> 00:28:16,550
+يعني من النقطة هذه إلى أي نقطة على محيط الدائرة
+
+248
+00:28:16,550 --> 00:28:23,770
+يبقى هنا R تساوي واحد وهنا R تساوي واحد كذلك يبقى
+
+249
+00:28:23,770 --> 00:28:30,140
+من Zero لغاية واحديبقى الآن حددنا حدود التكامل
+
+250
+00:28:30,140 --> 00:28:35,820
+تحديدا سليما مافيش فيه أي إشكالية وبالتالي لم يبقى
+
+251
+00:28:35,820 --> 00:28:40,120
+علي إلا أن أقوم بالتكامل لأن كل المسألة كتبتها
+
+252
+00:28:40,120 --> 00:28:44,340
+الآن في الـ cylindrical coordinates بقى اللي بقولك
+
+253
+00:28:44,340 --> 00:28:50,900
+بويس يبقى هذا الكلام بالساوي integration من zero
+
+254
+00:28:50,900 --> 00:28:55,580
+لإتنين by integration من zero لواحد تكامل
+
+255
+00:29:21,240 --> 00:29:25,100
+يبقى هذا الكلام اللي يعطيني integration من Zero
+
+256
+00:29:25,100 --> 00:29:30,380
+لإتنين باي من Zero لغاية الواحد طالع عندك هنا
+
+257
+00:29:30,380 --> 00:29:40,400
+لمين؟ لخمسة ناقص خمسة R تربيع كله هنا في RDRدى
+
+258
+00:29:40,400 --> 00:29:46,100
+تيتا او انشئتنا فقولنا هذا الكلام بدل ساوية
+
+259
+00:29:46,100 --> 00:29:50,840
+integration من zero للاثنين by integration من zero
+
+260
+00:29:50,840 --> 00:30:01,520
+لواحد لمين لخمسة R ناقص خمسة R تكيب كله دى اه دى
+
+261
+00:30:01,520 --> 00:30:06,980
+تيتا دخلنا R اللى برا داخل الجوز طيب مش نايل إلا
+
+262
+00:30:06,980 --> 00:30:11,220
+كامليبقى هذا الكلاب بدل يساوي integration من zero
+
+263
+00:30:11,220 --> 00:30:19,520
+لإتنين باي وهذه خمسة R تربيع على الإتنين وهذه ناقص
+
+264
+00:30:19,520 --> 00:30:26,460
+خمسة على أربعة R أقصى أربعة والكلاب هذا كله من
+
+265
+00:30:26,460 --> 00:30:31,680
+zero لغاية الواحد وهذه ان اليومين تبتدي تيتا
+
+266
+00:30:36,080 --> 00:30:42,020
+بتعود القيمة اللي فوق يا بناتي بالخمسة على اتنين-5
+
+267
+00:30:42,020 --> 00:30:50,240
+على 4-0 مع السلامة كله في Dθ يبقى بضالة ان دي قداش
+
+268
+00:30:50,240 --> 00:31:01,740
+5 على 4 و من 0 لل 2π لل Dθ يبقى 5 على 4θ من 0 لل
+
+269
+00:31:01,740 --> 00:31:09,900
+2π و اللي يبدأ تساوي 5 على 4 في 2πطبعا بضل اللي
+
+270
+00:31:09,900 --> 00:31:17,400
+يديه خمسة by على الإتنين هذا حجم المنطقة اللي
+
+271
+00:31:17,400 --> 00:31:23,170
+عليهايبقى بنات إذا قرأنا السؤال قراءة سليمة و
+
+272
+00:31:23,170 --> 00:31:28,870
+الرسم كان معروف الشكل المعطيني له سبق الدراسة و
+
+273
+00:31:28,870 --> 00:31:33,870
+قبل ذلك بصير عملية الرسم بسيطة جدا و من الرسم باجي
+
+274
+00:31:33,870 --> 00:31:38,910
+بحدد حدود التكامن وبالتالي تبقى انتهت المشكلة أو
+
+275
+00:31:38,910 --> 00:31:44,710
+بكون انحل السؤال بسهولة ويسط حد بتحفظ اي سؤال هنا
+
+276
+00:31:46,300 --> 00:31:49,680
+نذهب للنصف الثاني على الـ Spherical Coordinates
+
+277
+00:31:49,680 --> 00:31:58,160
+نذهب
+
+278
+00:31:58,160 --> 00:32:04,580
+للنصف الثاني
+
+279
+00:32:04,580 --> 00:32:08,620
+على الـ Spherical Coordinates
+
+280
+00:32:30,710 --> 00:32:35,210
+الشطر التاني من هذا ال section يقول integration
+
+281
+00:32:35,210 --> 00:32:38,450
+and spherical coordinates
+
+282
+00:32:55,760 --> 00:33:03,520
+التكامل في الأحداثيات
+
+283
+00:33:03,520 --> 00:33:07,280
+الكورية أو الكوراوية
+
+284
+00:33:27,410 --> 00:33:37,370
+point P in space P
+
+285
+00:33:37,370 --> 00:33:50,130
+of رو وفاي وثيتا in which بحيث
+
+286
+00:33:50,130 --> 00:33:59,960
+ان النقطة الأولى رو is the distancewrong is the
+
+287
+00:33:59,960 --> 00:34:12,200
+distance المسافة from P from P to the origin
+
+288
+00:34:12,200 --> 00:34:20,280
+النقطة P لأن النقطة P هي الأصل النقطة الثانية five
+
+289
+00:34:22,170 --> 00:34:35,430
+is the angle is the angle هي الزاوية اللي ال RP ال
+
+290
+00:34:35,430 --> 00:34:48,470
+mix اللي بيعمل هالي RP with the positive z
+
+291
+00:34:48,470 --> 00:34:50,350
+axis
+
+292
+00:34:53,340 --> 00:35:02,220
+فاي هذه محصورة فقط من زيرو لغاية بارت مرة تلاتة
+
+293
+00:35:02,220 --> 00:35:06,380
+الثيتا هي الثيتا الأولانية تبعاتنا تبع بالسي
+
+294
+00:35:06,380 --> 00:35:16,800
+ليندريكل والبورت is the angle هي الزاوية from
+
+295
+00:35:16,800 --> 00:35:20,460
+cylindrical
+
+296
+00:35:28,660 --> 00:35:30,980
+الذات الـ Cylindrical Core
+
+297
+00:35:57,520 --> 00:36:03,060
+بنروح نرسم اللي هو الاحداثيات الجديدة في الـ
+
+298
+00:36:03,060 --> 00:36:06,040
+spherical coordinates طبعا احنا بنرسم الاحداثيات
+
+299
+00:36:06,040 --> 00:36:12,140
+القديمة بدلالة X وY وZ فمثلا لو جيه تقول خدي
+
+300
+00:36:12,140 --> 00:36:18,960
+للنقطة اللي عندها وهذه في الاحداثيات الكارتزية P X
+
+301
+00:36:18,960 --> 00:36:27,860
+Y Zإذا في الإحداثيات الجديدة بنوصل النقطة هذه P رو
+
+302
+00:36:27,860 --> 00:36:36,420
+وفاي وثيتا السؤال هو أين رو و أين فاي و أين ثيتا؟
+
+303
+00:36:36,420 --> 00:36:41,040
+بقولك أه قالك رو هنا هي المسافة من النقطة P إلى
+
+304
+00:36:41,040 --> 00:36:46,820
+نقطة الأصل يبقى باجي بوصل هذه النقطة لنقطة الأصل
+
+305
+00:36:46,820 --> 00:36:54,680
+بيعطيني مين؟ بيعطيني روعرفنا الأحداث الأول بعدها
+
+306
+00:36:54,680 --> 00:36:59,520
+قال الزاوية Phi هي الزاوية المحصورة ما بين روه
+
+307
+00:36:59,520 --> 00:37:05,540
+والاتجاه الموجب لل Z Axis يبقى Phi كأنها بدأ يكون
+
+308
+00:37:05,540 --> 00:37:11,200
+الخط مطبق على Z وبدأ يفتح بالشكل هذا فسمينا
+
+309
+00:37:11,200 --> 00:37:13,480
+الزاوية هذه اللي هي الزاوية Phi
+
+310
+00:37:17,180 --> 00:37:21,340
+طب يجب أن أعرف أين الـR و أين الـθيتا بروح يا بنات
+
+311
+00:37:21,340 --> 00:37:27,060
+نسقط النقطة P على المستوى XY Plane يعني لو جيت
+
+312
+00:37:27,060 --> 00:37:32,680
+أسقط النقطة P على المستوى XY Plane بدأ تجينا P عند
+
+313
+00:37:32,680 --> 00:37:37,860
+النقطة اللي عندنا هذا بعدين بقول كويس هذا موازي
+
+314
+00:37:37,860 --> 00:37:48,570
+لمحور Y وهذا موازي لمحور X تمام؟ يبقىصار عندنا هذا
+
+315
+00:37:48,570 --> 00:37:58,110
+هو Y وهذا هو مين؟ X يفكر هذا هو X وهذا هو Y لو جيت
+
+316
+00:37:58,110 --> 00:38:04,310
+وصلت من نقطة الأصل لغاية هذا فانت عارف تقول مين
+
+317
+00:38:04,310 --> 00:38:11,850
+بيكون هذا في ال cylindricalR ممتاز جدا يبقى هذا R
+
+318
+00:38:11,850 --> 00:38:16,250
+في الـcylindrical والزاوية هذه بتكون هي مين؟ هي
+
+319
+00:38:16,250 --> 00:38:24,320
+الزاوية ثيتاإذاً حددنا له رو حددنا له فاي حددنا له
+
+320
+00:38:24,320 --> 00:38:29,500
+من ثيتا ليه الإحداثيات الجديدة يبقى ثيتا هو الخط
+
+321
+00:38:29,500 --> 00:38:34,120
+اللي بيعمله ليه R تبع الـcylindrical وطبعا الحاجة
+
+322
+00:38:34,120 --> 00:38:36,200
+يقولك هي أسفرية كدا يا عزيزي بس احنا رشتنا في
+
+323
+00:38:36,200 --> 00:38:41,720
+البداية يبقى هذا R اللي هو تبع الـcylindrical عامل
+
+324
+00:38:41,720 --> 00:38:45,560
+ليه زاوية ثيتا يبقى ثيتا جالي تبعت من تبعت
+
+325
+00:38:45,560 --> 00:38:51,010
+الـcylindrical coordinateطيب و الـ Phi هيها و ال
+
+326
+00:38:51,010 --> 00:38:58,050
+role اللي عندنا هذه هل في علاقة ابتردة ما بين ال R
+
+327
+00:38:58,050 --> 00:39:05,990
+و ما بين ال Phi مثلا و ال R في كده فالحين انا بنعت
+
+328
+00:39:05,990 --> 00:39:12,590
+هذا الطلعة لو جيت أسقطه على محور Z يعني نزلت من
+
+329
+00:39:12,590 --> 00:39:19,160
+هنا عمود على محور Z الطول هذا جديش بيقولمن نقطة
+
+330
+00:39:19,160 --> 00:39:27,600
+الأصل من هنا لغاية رو في كوساين الزاوية فيه يبقى Z
+
+331
+00:39:27,600 --> 00:39:33,780
+في هذه الحالة بدها ساوية رو في كوساين الفيه طيب
+
+332
+00:39:33,780 --> 00:39:41,340
+وين رو ساين الفيه؟ يلا اشوف رو ساين الفيه مين بده
+
+333
+00:39:41,340 --> 00:39:48,420
+يطلع؟هذا عمود على ال X Y Plane يعني عمودي على أي
+
+334
+00:39:48,420 --> 00:39:52,820
+مستقيل موجود في ال X Y Plane يعني الزاوية هذه
+
+335
+00:39:52,820 --> 00:40:02,500
+زاوية كم؟ تسعين درجة يبقى هو رو صين الفايف هو R
+
+336
+00:40:02,500 --> 00:40:08,360
+يبقى R اللي عندنا هذه يا بنات هي رو صين الفايف
+
+337
+00:40:08,360 --> 00:40:17,420
+يبقى هذهفي صين الفاي عرفنا إيش العلاقة ما بين ال
+
+338
+00:40:17,420 --> 00:40:24,380
+spherical ومين و ال cylindrical وبعد قليل هجمعلك
+
+339
+00:40:24,380 --> 00:40:28,680
+اتنين مع ال cartesian ونشوف إيش اللي بده يصير بس
+
+340
+00:40:28,680 --> 00:40:33,360
+عندي في بعض التساؤلات بدي أحاول أطرحها و أشوف إيش
+
+341
+00:40:33,360 --> 00:40:38,500
+رأيكوا فيها إيش معناها طيب يا بنات لو قلتلك احنا
+
+342
+00:40:38,500 --> 00:40:45,050
+الآن بتكلم sphericalوهي Aspirical Coordinates او
+
+343
+00:40:45,050 --> 00:40:49,930
+سيلندري كانوا بعدين بروح لل Aspirical لو قلت لك R
+
+344
+00:40:49,930 --> 00:40:55,550
+يساوي Zero R اللي عندنا هذا بيساوي Zero بيعطيني
+
+345
+00:40:55,550 --> 00:41:01,790
+ايش؟ محور Z ممتاز جدا يبقى R تساوي Zero والمطروح
+
+346
+00:41:01,790 --> 00:41:06,570
+اللي هو محور Z يبقى R تساوي Zero بيعطيكي دائما و
+
+347
+00:41:06,570 --> 00:41:11,760
+أبدا من محور Zيبقى لنا خاطرة نكتب هذا الكلام على
+
+348
+00:41:11,760 --> 00:41:22,520
+شكل اللي هو الملاحظات التالية. يبقى دي مارك هذا
+
+349
+00:41:22,520 --> 00:41:25,260
+الكلام اللي قالته سلامه هو الكلام اللي قلناه المرة
+
+350
+00:41:25,260 --> 00:41:29,100
+الماضية، يعني ما كنتش جديد، يعني هو كلام ذكرناه
+
+351
+00:41:29,100 --> 00:41:29,920
+قبل ذلك.
+
+352
+00:41:36,200 --> 00:41:40,320
+رو تساوي ثلاثة، رو تساوي أربعة، رو تساوي عشرة. هذا
+
+353
+00:41:40,320 --> 00:41:46,080
+إيش يمثل الأملاء؟ يعني جينا هناك وقلنا رو تساوي
+
+354
+00:41:46,080 --> 00:41:52,080
+خمسة، رو خمسة، رو خمسة، رو خمسة، رو خمسة، رو خمسة،
+
+355
+00:41:52,080 --> 00:41:52,820
+رو خمسة، رو خمسة، رو خمسة، رو خمسة، رو خمسة، رو
+
+356
+00:41:52,820 --> 00:41:52,900
+خمسة، رو خمسة، رو خمسة، رو خمسة، رو خمسة، رو خمسة،
+
+357
+00:41:52,900 --> 00:41:53,860
+رو خمسة، رو خمسة، رو خمسة، رو خمسة، رو خمسة، رو
+
+358
+00:41:53,860 --> 00:42:00,130
+خمسة، رو خمسSphere عقول الخطر يعني بيعطيك كرة
+
+359
+00:42:00,130 --> 00:42:05,630
+مركزها نقطة الأصل و نصفه ما هيساوي A يبقى روتس
+
+360
+00:42:05,630 --> 00:42:20,730
+ساوي A is a sphere with centers at the origin and
+
+361
+00:42:20,730 --> 00:42:22,150
+radius
+
+362
+00:42:27,090 --> 00:42:36,070
+النقطة الثانية يبقى في تسوي في نوت يبقى في تسوي في
+
+363
+00:42:36,070 --> 00:42:45,010
+نوت يبقى في تسوي في نوت يبقى في تسوي في نوت يبقى
+
+364
+00:42:45,010 --> 00:42:46,350
+في تسوي في نوت يبقى في تسوي في نوت يبقى في تسوي في
+
+365
+00:42:46,350 --> 00:42:46,350
+نوت يبقى في تسوي في نوت يبقى في تسوي في نوت يبقى
+
+366
+00:42:46,350 --> 00:42:46,350
+في تسوي في نوت يبقى في تسوي في نوت يبقى في تسوي في
+
+367
+00:42:46,350 --> 00:42:46,350
+نوت يبقى في تسوي في نوت يبقى في تسوي في نوت يبقى
+
+368
+00:42:46,350 --> 00:42:46,350
+في تسوي في نوت يبقى في تسوي في نوت يبقى في تسوي في
+
+369
+00:42:46,350 --> 00:42:47,290
+نوت يبقى في تسوي في نوت يبقى في تسوي في نوت يبقى
+
+370
+00:42:47,290 --> 00:42:52,370
+في تسفي الدرجة اعمل تلاتين درجة هاي تلاتين درجة
+
+371
+00:42:52,370 --> 00:42:57,450
+هاتي كمال جلب اللي فيه هاي تلاتين درجة وداير
+
+372
+00:42:57,450 --> 00:43:05,890
+مايدور تلاتين درجة شو بطلع عندي كرة
+
+373
+00:43:05,890 --> 00:43:14,130
+اي مخروض كويس اذا بطلع عندي مخروض دائري قائم اذا
+
+374
+00:43:14,130 --> 00:43:20,200
+بطلع عندي كونيبقى في تسوى في نوت تمثل مين؟ تمثل
+
+375
+00:43:20,200 --> 00:43:26,320
+مخروض دائري قائم رأسه عاميا عند نقطة الأصل و open
+
+376
+00:43:26,320 --> 00:43:32,940
+up مفتوح لوين؟ إلى أعلى يبقى هذه في تسوى في نوت
+
+377
+00:43:32,940 --> 00:43:42,440
+عبارة عن مخروض يبقى هذه equation of a cone مخروض
+
+378
+00:43:42,440 --> 00:43:55,920
+man with vertexwith vertex at the origin عند نقطة
+
+379
+00:43:55,920 --> 00:44:06,400
+الأصل at the origin and open أ مفتوح إلى أعلى إذا
+
+380
+00:44:06,400 --> 00:44:07,620
+كانت والله
+
+381
+00:44:13,900 --> 00:44:20,160
+يبقى لما تبقى في نوت من صفر لغاية تسعين المخروض
+
+382
+00:44:20,160 --> 00:44:26,540
+يكون مفتوح لوين؟ او لو خلناها ازيد عن تسعين يعني
+
+383
+00:44:26,540 --> 00:44:32,640
+امشي امشي امشي تسعين نزلت كمان شوية يبقى ايش مصير؟
+
+384
+00:44:32,640 --> 00:44:40,000
+مخروض رأسه عنده نقص له open down مفتوح الى أسفل
+
+385
+00:44:40,000 --> 00:44:43,480
+يبقى باجي بقول ال open down
+
+386
+00:44:46,960 --> 00:44:58,140
+open down مفتوح الى أسفل اف why not أكبر من مين من
+
+387
+00:44:58,140 --> 00:45:03,260
+by على اتنين طيب انت تكلمت على أقل من by على اتنين
+
+388
+00:45:03,260 --> 00:45:07,060
+وقلنا مخروط مفتوح الى أعلى أكبر من by على اتنين
+
+389
+00:45:07,060 --> 00:45:09,960
+مخروط مفتوح الى أعلى طب لو كان by على اتنين
+
+390
+00:45:17,610 --> 00:45:30,470
+بعدين افتح افتح افتح افتح افتح افتح افتح
+
+391
+00:45:30,470 --> 00:45:37,590
+افتح افتح افتح افتح افتح افتح
+
+392
+00:45:47,510 --> 00:45:57,050
+يبقى هذا المستوى XY بقلت عندنا اللي هو العلاقة
+
+393
+00:45:57,050 --> 00:46:02,330
+اللي بتربط هدول كلهم مع بعض او لو حبينا نعطي رسم
+
+394
+00:46:02,330 --> 00:46:09,210
+يعني سريع لهذه الشغلات تالي بقول بالشكل التالي
+
+395
+00:46:23,160 --> 00:46:31,360
+هذا X هذا Y هذا Z لان يا بنات باجي بقول هي المخروط
+
+396
+00:46:31,360 --> 00:46:41,060
+الأول يبقى هي عندي Phi node يبقى مفتوح لان هذا
+
+397
+00:46:41,060 --> 00:46:49,030
+الكلام لو كان Phi node ماله؟أقل من Pi على 2 يبقى
+
+398
+00:46:49,030 --> 00:46:56,130
+هذا Phi node أقل من Pi على 2 فلو حصل أن Phi node
+
+399
+00:46:56,130 --> 00:47:04,590
+عبارة عن Pi على 2 سنحصل على المستوى اللي عندنا هذا
+
+400
+00:47:04,590 --> 00:47:11,450
+بهذا الشكل يبقى هذا كله يصير من المستوى اللي عندنا
+
+401
+00:47:11,450 --> 00:47:18,710
+هذا وهذا من الناحية الثانيةيبقى هذا بيصير في نوت
+
+402
+00:47:18,710 --> 00:47:25,430
+تسوى باي على اتنين يعني ال X Y plane الحالة
+
+403
+00:47:25,430 --> 00:47:33,550
+التالتة لو كان عندنا المحاور بهذا الشكل وقولنا هذا
+
+404
+00:47:33,550 --> 00:47:42,310
+محور X هذا محور Y هذا محور Z المخروض بيقلب و يسير
+
+405
+00:47:42,310 --> 00:47:50,070
+الى أسفليبقى بدي أجيك المخروط بالشكل التالي ايو
+
+406
+00:47:50,070 --> 00:47:57,750
+حيصير هيك و هذا هو بالشكل اللي عندك هذا يبقى هذا
+
+407
+00:47:57,750 --> 00:48:05,630
+five هيهاباي نول أكبر من من ميل من باي على اتنين
+
+408
+00:48:05,630 --> 00:48:09,550
+يعني لو كانت الزاوية زاوية منفرجة بدي انقلب
+
+409
+00:48:09,550 --> 00:48:16,410
+المخروض ويصير لوين ويصير الى أسفل الأن بدنا نيجي
+
+410
+00:48:16,410 --> 00:48:22,010
+العلاقة اللى بتربط بين المتغيرات هذه كلها فبدي
+
+411
+00:48:22,010 --> 00:48:25,190
+اكتب the relation between the
+
+412
+00:48:30,020 --> 00:48:40,180
+between العلاقة بين الـ spherical و
+
+413
+00:48:40,180 --> 00:48:49,960
+ال Cartesian and cylindrical and cylindrical
+
+414
+00:49:10,370 --> 00:49:17,070
+طيب خلينا نبدأ بالفيلم اللي حكينا عليه هنا رو او R
+
+415
+00:49:17,070 --> 00:49:24,630
+تساوي رو في صين الفا يبقى هنا ال R تساوي ال رو في
+
+416
+00:49:24,630 --> 00:49:29,350
+صين الفا زيادة
+
+417
+00:49:29,350 --> 00:49:37,070
+على ذلك لو بدي ال Z ال Z تساوي ال رو في كوصين الفا
+
+418
+00:49:38,130 --> 00:49:47,230
+لو جيتنا ال X في الـ cylindrical coordinates هي R
+
+419
+00:49:47,230 --> 00:49:53,940
+في الـ cosine الزاويةطبعا بدي احولها الى spherical
+
+420
+00:49:53,940 --> 00:49:58,960
+يبقى في ال spherical ايش بدي اتصير؟ بدي اشيل ال R
+
+421
+00:49:58,960 --> 00:50:07,540
+و احط عندي رو ساين فاي يبقى هنا رو ساين فاي كساين
+
+422
+00:50:07,540 --> 00:50:16,340
+تيك طب ال Yيكون لدينا R في صين الزاوية تيتا يبقى
+
+423
+00:50:16,340 --> 00:50:22,500
+في الـ spherical الراو في صين الفاي في صين مين في
+
+424
+00:50:22,500 --> 00:50:29,520
+صين الزاوية تيتا طيب سؤال شو العلاقة ما بين الراو
+
+425
+00:50:29,520 --> 00:50:35,760
+و ال X و ال Y و ال Z هذا
+
+426
+00:50:35,760 --> 00:50:47,510
+X وهذا Y وهذا Zيبقى روح كده تساوي X تربيع زائد Y
+
+427
+00:50:47,510 --> 00:50:53,970
+تربيع زائد Z تربيع تحت الجذر التربيعي يبقى روح
+
+428
+00:50:53,970 --> 00:51:00,760
+تساوي ال square rootX تربيع زائد Y تربيع زائد Z
+
+429
+00:51:00,760 --> 00:51:06,500
+تربيع طب لو بدى اكتبها cylindrical يبقى
+
+430
+00:51:06,500 --> 00:51:13,440
+cylindrical بيساوي الجذر التربيعى ل R تربيع زائد Z
+
+431
+00:51:13,440 --> 00:51:18,860
+تربيع لأن X تربيع زائد Y تربيع اللى هو تسامين اللى
+
+432
+00:51:18,860 --> 00:51:25,380
+هو R تربيع طب لو بدى DV يا ماناتى DV
+
+433
+00:51:27,720 --> 00:51:51,380
+الذي يعني دي زد دي واي دي اكس دي اكس
+
+434
+00:51:51,380 --> 00:51:55,860
+دي اكس
+
+435
+00:51:55,860 --> 00:51:56,720
+دي اكس دي اكس دي اكس دي اكس دي اكس دي اكس دي اكس
+
+436
+00:51:56,720 --> 00:51:56,780
+دي اكس دي اكس دي اكس دي اكس دي اكس دي اكس دي اكس
+
+437
+00:51:58,250 --> 00:52:03,450
+تمام؟ يبقى هذه المعلومات الأساسية إلا أن الان لم
+
+438
+00:52:03,450 --> 00:52:08,730
+يبقى في هذا section إلا أن نعطي بعض الأمثلة. حد
+
+439
+00:52:08,730 --> 00:52:15,500
+إليها يتسأل في الكلام اللي قدامها؟ كيف؟ صحيحيعني
+
+440
+00:52:15,500 --> 00:52:20,760
+لما نقول لزميلتكوا لو كان هذا رو شو مسقط على ال XY
+
+441
+00:52:20,760 --> 00:52:26,720
+Plane؟ نقول لك R ليش؟ ان هو ينزل عمودة، مصبوط،
+
+442
+00:52:26,720 --> 00:52:31,900
+يبقى R هو مسقطة اللي هو ال raw sine فعلا حد بيسأل
+
+443
+00:52:31,900 --> 00:52:36,900
+أي سؤال تاني؟
+
+444
+00:52:36,900 --> 00:52:42,540
+يبقى
+
+445
+00:52:42,540 --> 00:52:44,980
+الناس كلها في السيلندر كلها بنضرب فيه
+
+446
+00:52:56,420 --> 00:53:09,280
+أول مثال على ذلك هو
+
+447
+00:53:09,280 --> 00:53:11,380
+اللي يحسب التكامل التالي
+
+448
+00:53:16,510 --> 00:53:23,990
+إتنين ثلاثة الأول من صفر لغاية اتنين باي والتالي
+
+449
+00:53:23,990 --> 00:53:33,350
+من صفر لغاية باي على أربع والتالي من zero لغاية
+
+450
+00:53:33,350 --> 00:53:47,160
+six في لروت كوساين الفاى لروت ربيع صين الفاىد رو
+
+451
+00:53:47,160 --> 00:53:55,120
+دي فاي دي ثيتا التكامل
+
+452
+00:53:55,120 --> 00:54:05,400
+الأول وهي التكامل التاني وهذا لازم يشغل بالنسبة
+
+453
+00:54:05,400 --> 00:54:13,120
+إلى رو يبقى الصين والقصين ليس دعوة رو تكيب تكاملها
+
+454
+00:54:21,870 --> 00:54:31,550
+سك الفاي لمين لكوساين الفاي لصين الفاي دي فاي دي
+
+455
+00:54:31,550 --> 00:54:35,910
+ثيتا اللي ماك ميزة ما بين الفاي وثيتا خلي دينها
+
+456
+00:54:35,910 --> 00:54:43,410
+طول شوية هذا الكلام بده يساوي رابع خليه برا لغاية
+
+457
+00:54:43,410 --> 00:54:48,130
+كامل من Zero لإتنين بايت كامل من Zero لغاية Pi على
+
+458
+00:54:48,130 --> 00:54:56,130
+أربعيبقى هذا شو بيصير سك أُس أربعة يبقى سك أُس
+
+459
+00:54:56,130 --> 00:55:06,030
+أربعة في و هنا كوصين الفي كوصين الفي و دي في دي
+
+460
+00:55:06,030 --> 00:55:14,190
+ثيتا ناقص zero بتروح مع السلام يبقى آلة المسألة
+
+461
+00:55:22,520 --> 00:55:28,000
+زيرو نقاط باية على أربعة في اختصارات يا بناتي لو
+
+462
+00:55:28,000 --> 00:55:31,660
+أخدت كوساين اه سك واحدة بصير واحدة على كوساين
+
+463
+00:55:31,660 --> 00:55:38,350
+بتروح مع هذه يبقى بظل سك تكيب ساينيبقى هذه بيصير
+
+464
+00:55:38,350 --> 00:55:49,670
+سكتة كيب في صين في دي في دي ثيتا يبقى مرة ثانية هي
+
+465
+00:55:49,670 --> 00:55:54,770
+الرابع تكامل من zero للاتنين باي تكامل من zero
+
+466
+00:55:54,770 --> 00:56:03,170
+لغاية باي على أربع بدنا نكامل هذه سهلة
+
+467
+00:56:03,170 --> 00:56:08,540
+very easyلا بأخليها سكتة أيه بزي ما يبقى ، بس لو
+
+468
+00:56:08,540 --> 00:56:13,880
+نزلتها إيش مصرية؟ Cos فوق Cos فقعدت ست ساعة. هذه
+
+469
+00:56:13,880 --> 00:56:21,200
+بقدر أقول انه واحد على Cos او أقولك خليها فوق هذه
+
+470
+00:56:21,200 --> 00:56:29,080
+كأنها Cos فاي أس سالب تلاتة صح ولا لأ؟ واحد على
+
+471
+00:56:29,080 --> 00:56:37,070
+Cos لو طلعت من ال Cos فاي أس سالب تلاتةأليست مشتقة
+
+472
+00:56:37,070 --> 00:56:46,710
+الـ cosine بس بده إشارة سالب يبقى هذه فيه سالب دي
+
+473
+00:56:46,710 --> 00:56:51,530
+cosine الفاية و الـ dt ده أيه يا بره مالعش علاقة
+
+474
+00:56:51,530 --> 00:56:59,210
+بالموضوع يبقى هذا الكلام يستاوي لربع تكمل من zero
+
+475
+00:56:59,210 --> 00:57:07,110
+لإتنين و اشتغلش ايه كل كامل يبقاش بالصيانةcos فان
+
+476
+00:57:07,110 --> 00:57:16,090
+قص ناقص اتنين على ناقص اتنين وعند كده الشرط الناقص
+
+477
+00:57:16,090 --> 00:57:22,330
+اللي كانت برا هيها جابلها وضايل عندنا هذا الحكي من
+
+478
+00:57:22,330 --> 00:57:29,890
+عند ال zero لغاية Pi على 4 وهي دي فترة يبقى ناقص
+
+479
+00:57:29,890 --> 00:57:36,970
+وناقصو نص تطلع برا مع الرموز بيصير كده؟ تمام و
+
+480
+00:57:36,970 --> 00:57:42,150
+بيصير عندي تكامل من zero لإتنين باي و تعالى نعود
+
+481
+00:57:42,150 --> 00:57:46,790
+للقيمة اللى فوق ناقص القيمة اللى تحت يبقى اش بيصير
+
+482
+00:57:46,790 --> 00:57:56,830
+عندي واحد على cosine باي على أربع الكل تقريبا ناقص
+
+483
+00:57:56,830 --> 00:58:06,540
+واحدعلى cos 0 الكل تربيع بالنسبة الى Dθ يبقى هذا
+
+484
+00:58:06,540 --> 00:58:13,820
+الكلام متساوي 8 جتا 45 ابنات واحد على جدر تنارقها
+
+485
+00:58:13,820 --> 00:58:19,900
+فتصير ايه نصف بنقلب فوق تصير اتنين يبقى هاي
+
+486
+00:58:19,900 --> 00:58:25,840
+التكامن من 0 للإتنين باى وهي اتنين ناقص cos 0
+
+487
+00:58:25,840 --> 00:58:34,190
+تربيعواحد على واحد مناقص واحد يبقى هاي ناقص واحد
+
+488
+00:58:34,190 --> 00:58:37,550
+يبقى
+
+489
+00:58:37,550 --> 00:58:42,890
+هاي كل اللي عندنا المفضل بالنسبة الى D ثيتا هو
+
+490
+00:58:42,890 --> 00:58:51,250
+يساوي تمت تكامن من zero للاثنين byفقط الذي ثيتا
+
+491
+00:58:51,250 --> 00:58:59,870
+يبقى يساوي تمن ثيتا من zero للإتنين by ويساوي تمن
+
+492
+00:58:59,870 --> 00:59:07,650
+في إتنين by يبقى by على أربع نقدار هذا أكتر
+
+493
+00:59:38,580 --> 00:59:43,320
+بطرقة ما اتناولها جيئة بيه في احدى التمتحانات
+
+494
+00:59:43,320 --> 00:59:48,760
+للناس اللي زيكم واحنا عنها هنقدر نعطيكيها كمثال
+
+495
+00:59:48,760 --> 00:59:57,140
+اقول find your volume of the region find the
+
+496
+00:59:57,140 --> 01:00:09,530
+volume of the regionقداش حجم المنطقة bounded below
+
+497
+01:00:09,530 --> 01:00:14,870
+bounded below
+
+498
+01:00:14,870 --> 01:00:23,250
+والمحدودة من أسفل باليكون باليكون
+
+499
+01:00:23,250 --> 01:00:34,170
+بالمخروج Z تساوي الجذر التربيع ال X تربيع زائد Y
+
+500
+01:00:34,170 --> 01:00:47,420
+تربيعand above ومن أعلى by the plane by the plane
+
+501
+01:00:47,420 --> 01:01:03,040
+بالمستوى z تساوي واحد by using by using امرأة
+
+502
+01:01:03,040 --> 01:01:06,000
+cylindrical coordinates
+
+503
+01:01:09,160 --> 01:01:17,120
+Cylindrical Coordinates لمرة بيه Spherical
+
+504
+01:01:17,120 --> 01:01:29,800
+Coordinates Spherical
+
+505
+01:01:29,800 --> 01:01:31,300
+Coordinates
+
+506
+01:01:53,380 --> 01:01:59,020
+نرجع لسؤالنا مرة تانية بيقول في عندي منطقة مغلقة
+
+507
+01:01:59,020 --> 01:02:06,400
+ومحدودة بيه من أسفل بمين بيه المخروط اللي هو z
+
+508
+01:02:06,400 --> 01:02:11,520
+يساوي الجدر التربيع ال x تربيع زائد y تربيع and
+
+509
+01:02:11,520 --> 01:02:17,250
+above ومن أعلى بال plane z يساوي واحدبنجيب هذا
+
+510
+01:02:17,250 --> 01:02:22,550
+الحجم مرتين مرة باستخدام cylindrical coordinates و
+
+511
+01:02:22,550 --> 01:02:26,630
+مرة باستخدام spherical coordinates بيطلعوا جبتين
+
+512
+01:02:26,630 --> 01:02:32,810
+زي بعض و لا مختلفين نفس الحجم تمام بس بطريقتين
+
+513
+01:02:32,810 --> 01:02:40,620
+مختلفتين ياريت أروح نرسم الشغل هذه و نشوف كيفبعدين
+
+514
+01:02:40,620 --> 01:02:50,520
+يومين نحسب المظبوط تبع المثل هذا X هذا Y هذا Z
+
+515
+01:02:50,520 --> 01:02:59,400
+وروح ترسم المخروض اللي عندنا بيكان المخروض بالشكل
+
+516
+01:02:59,400 --> 01:03:10,060
+اللي عندنا هذا Xوالمستوى الأفقي z يساوي واحد يبقى
+
+517
+01:03:10,060 --> 01:03:17,560
+هذا المستوى هو z يساوي واحد وهذا المخرج هو z يساوي
+
+518
+01:03:17,560 --> 01:03:24,240
+جدر التربية إلى x تربية زائد y تربيةشو رايك احنا
+
+519
+01:03:24,240 --> 01:03:29,340
+بنتكلم على مين؟ على cylindrical في الأول. مدام
+
+520
+01:03:29,340 --> 01:03:35,340
+cylindrical يبقى هذا يبقى جدرخ كبير لارتربية اللي
+
+521
+01:03:35,340 --> 01:03:42,000
+هو قدرة A يبقى Z يساوي A تمام؟ ماجي بقوله كويس
+
+522
+01:03:42,000 --> 01:03:48,640
+يبقى ال volume اللي احنا بدنا يعني تلت تكاملات
+
+523
+01:03:48,640 --> 01:03:50,200
+التي يزد
+
+524
+01:03:59,540 --> 01:04:07,500
+يبقى انا بدي ارسم خط يقطع منطقة تكامل وموازن لمحور
+
+525
+01:04:07,500 --> 01:04:14,680
+Z يبقى بداجي هنا ارسم خط من هنا و اجي طالع رأسي
+
+526
+01:04:14,680 --> 01:04:20,460
+موازن لمحور Z بالشكل اللي عندنا هذا هيكلغاية ما
+
+527
+01:04:20,460 --> 01:04:27,400
+قبل اللي هو Z يساوي واحد يبقى هنا Z يساوي قداش R
+
+528
+01:04:27,400 --> 01:04:34,560
+هنا Z يساوي قداش واحد يبقى هنا R وهنا واحد ضالة ال
+
+529
+01:04:34,560 --> 01:04:40,760
+R يبقى ال R بدي أسحب المجسم هذا كله على مين؟ على
+
+530
+01:04:40,760 --> 01:04:47,550
+ال XY Plane يبقى المصعدش هيكون يا بنات كذلكدائرة
+
+531
+01:04:47,550 --> 01:04:53,370
+يبقى بتصير المصطفى اللى عندنا هي دائرة اها لو جيت
+
+532
+01:04:53,370 --> 01:04:58,590
+قلت هاي و هنا و هاي و هنا بالضبط تماما و هذا ماشي
+
+533
+01:04:58,590 --> 01:05:04,570
+دغري يبقى بدها تكون عند مين الدائرة اللى عندنا هذا
+
+534
+01:05:04,570 --> 01:05:05,050
+الشكل
+
+535
+01:05:09,350 --> 01:05:13,890
+طيب، بدأ أعرف قداش نصف قطر هذه الدائرة في
+
+536
+01:05:13,890 --> 01:05:19,150
+الإحداثيات القصوية أو ما هي معادلة هذه الدائرة في
+
+537
+01:05:19,150 --> 01:05:22,790
+الإحداث الأولى، طب كيف؟ كيف عرفتيها واحد يعني؟
+
+538
+01:05:22,790 --> 01:05:26,290
+تمام
+
+539
+01:05:26,290 --> 01:05:33,270
+تمام، يبقى بروح بقوله هنا Zتساوي واحد و Z تساوي R
+
+540
+01:05:33,270 --> 01:05:37,870
+من هذول التنتير مع بعض بسويهم بعض يبقى ال R تساوي
+
+541
+01:05:37,870 --> 01:05:43,890
+قداش واحد إذا ال R ستبدأ من هنا إلى أي نقطة على
+
+542
+01:05:43,890 --> 01:05:48,090
+محيط الدائرة أو من هنا إلى أي نقطة على محيط
+
+543
+01:05:48,090 --> 01:05:52,750
+الدائرة وبيكون هذا كله R يساوي واحد يبقى ال R
+
+544
+01:05:52,750 --> 01:06:00,180
+ستتغير من Zero لغاية واحدطب θ هتتغير من 0 ل2 باى
+
+545
+01:06:00,180 --> 01:06:07,260
+يبقى من 0 لغاية 2 باى ويساوي integration من 0 ل2
+
+546
+01:06:07,260 --> 01:06:13,900
+باى integration من 0 ل1 تكمل ال DZ اللي هي Z من
+
+547
+01:06:13,900 --> 01:06:22,580
+عند R لغاية 1 وظل عندي RDRDθ يبقى آلة المسألة إلى
+
+548
+01:06:22,580 --> 01:06:31,210
+تكمل من Zeroلغاية 2 باي من 0 لغاية 1 للواحد ناقص R
+
+549
+01:06:31,210 --> 01:06:38,510
+في RDR D ثانية اعوض من القيمة اللي فوق ناقص لتاعة
+
+550
+01:06:38,510 --> 01:06:44,730
+بدي ادخل ال R هذا دخل ال O فبصير عندي تكاملينمن
+
+551
+01:06:44,730 --> 01:06:50,350
+Zero للإتنين باي والتكامل التاني من Zero لواحد لل
+
+552
+01:06:50,350 --> 01:06:58,210
+R ناقص R تربيع DR D ثيتا الكامل يبدأ integration
+
+553
+01:06:58,210 --> 01:07:04,210
+من Zero لغاية اتنين باي ده من لل R تربيع على اتنين
+
+554
+01:07:04,210 --> 01:07:11,590
+ناقص R تكامل على تلاتة كل الحكي هذا من عند ال Zero
+
+555
+01:07:11,590 --> 01:07:18,010
+لغاية الواحد ده منلدى فيتا هذا بدى يساوي
+
+556
+01:07:18,010 --> 01:07:22,250
+integration من zero لغاية اتنين باى بدى عوض بالقيم
+
+557
+01:07:22,250 --> 01:07:29,490
+اللى فوق بقى نص نقص طول يبقى نص نقص طول و نقص zero
+
+558
+01:07:29,490 --> 01:07:36,710
+بيروح كله لدى فيتا يبقى تكامل من zero للاتنين باى
+
+559
+01:07:36,710 --> 01:07:43,530
+لمين لسادس دى فيتا إذا المصير هذا سادس
+
+560
+01:07:52,950 --> 01:08:06,170
+باي على ثلاث باي على ثلاث
+
+561
+01:08:06,170 --> 01:08:13,850
+باي على ثلاث باي على ثلاث باي على ثلاثفي احتمال
+
+562
+01:08:13,850 --> 01:08:21,070
+يكون التكامل غلط في احتمال قدود التكامل غلط الاخري
+
+563
+01:08:21,070 --> 01:08:29,750
+ان شاء الله لا نقع في الخطأ ايه الآن بدنا نروح
+
+564
+01:08:29,750 --> 01:08:39,630
+نشتغل فيه اللي هو الـ spherical coordinates ده
+
+565
+01:08:39,630 --> 01:08:49,600
+يا عزيزي هقوله نمرا فيهبدي تكامل اتنين ثلاثة روتا
+
+566
+01:08:49,600 --> 01:09:02,960
+ربيع فايل الفايل دي رو دي فايل دي تيتا نيجي لروب
+
+567
+01:09:02,960 --> 01:09:06,820
+تتغير من أين اللي وين يبقى روحة تبدأ من أين يا
+
+568
+01:09:06,820 --> 01:09:12,900
+بنات؟ من نقطة الأصلوتجهي نطلع طالعين لغاية ما
+
+569
+01:09:12,900 --> 01:09:19,000
+نجابل وين المستوى اللى فوق له Z يساوي واحد اذا لو
+
+570
+01:09:19,000 --> 01:09:24,600
+جينا طالعين بهذا الشكل لغاية ما جابلنا السطح اللى
+
+571
+01:09:24,600 --> 01:09:32,320
+فوق يبقى روحنا بقداش Zero اتفقنا يبقى هاي روحنا
+
+572
+01:09:32,320 --> 01:09:35,540
+Zero روحنا فوق بقداش
+
+573
+01:09:40,590 --> 01:09:45,610
+مين هو اللي فوق؟ Z تساويها طب مين هي Z في ال
+
+574
+01:09:45,610 --> 01:09:51,390
+spherical؟ رو كوساين فاي بيبقى صارت قصته سهلة يبقى
+
+575
+01:09:51,390 --> 01:09:59,180
+هدئها اللي هو Zتساوي واحد يعني ال row في cosine
+
+576
+01:09:59,180 --> 01:10:05,200
+الفاي يساوي واحد يبقى روه كده شبنها سك الفاي لإن
+
+577
+01:10:05,200 --> 01:10:10,460
+واحد على سك اضرب الطرفين بس ال row بسك الفاي إذا
+
+578
+01:10:10,460 --> 01:10:18,730
+ال row تتغير من zero لغاية سك الفايطب إذا نجي لـ
+
+579
+01:10:18,730 --> 01:10:25,870
+Phi تتغير من واحد لواحد ، يبقى Phi تتغير من المحور
+
+580
+01:10:25,870 --> 01:10:30,970
+ضد لواء الخطة اللي عندنا هذا. إذا لو عرفت قداش
+
+581
+01:10:30,970 --> 01:10:41,090
+معادلة هذا الخط بتبقى قصتنا محلولة. يالا قداش؟
+
+582
+01:10:41,090 --> 01:10:47,420
+يلا بس يطلعيعني .. يعني تشوفوالي كيف ممكن نجيبها
+
+583
+01:10:47,420 --> 01:10:51,760
+هيك يلا
+
+584
+01:10:51,760 --> 01:10:54,680
+ايه حسب جربه، قوليلي كيف، أنا مابديش أعطيك دوري،
+
+585
+01:10:54,680 --> 01:11:03,000
+بديك أنت تشغل مخك شوية يلا
+
+586
+01:11:03,000 --> 01:11:11,660
+شوف قداشر تقاطع المستوى اللي فوق مع المخروجيعني
+
+587
+01:11:11,660 --> 01:11:19,460
+تقلق Z تساوي 4 Z تساوي 1 صحيح ولا لأ؟ يلّا نشوف
+
+588
+01:11:19,460 --> 01:11:23,740
+المستوى
+
+589
+01:11:23,740 --> 01:11:30,700
+اللي فوق شو معادلته؟ روت ساوسيك 5 صحيح ولا لأ؟
+
+590
+01:11:30,700 --> 01:11:37,620
+وشوفوا اللي تحت بصرفين هو هذا يلّا ايوة
+
+591
+01:11:39,510 --> 01:11:43,410
+صحيح زيته
+
+592
+01:11:43,410 --> 01:11:49,930
+ساوي R ممتاز
+
+593
+01:11:49,930 --> 01:11:59,830
+هي R بقداش عادى ممتاز جدا يبقى روه صين الفاى واللي
+
+594
+01:11:59,830 --> 01:12:04,930
+فوق الروه كوصين الفاى يبقى حاليا الإشكالية تمام
+
+595
+01:12:05,200 --> 01:12:09,520
+يبقى يا بنات بروح تاك في الهامش بقول المستوى اللي
+
+596
+01:12:09,520 --> 01:12:16,140
+فوق اللي هو Z زد اللي هو رو كو صين الفاية و اللي
+
+597
+01:12:16,140 --> 01:12:23,440
+تحت Z تساوي R و ال R اللي هو برو صين الفاية يبقى
+
+598
+01:12:23,440 --> 01:12:30,660
+رو في صين الفاية هذه ه ه اللي هي منك اللي هي Rلو
+
+599
+01:12:30,660 --> 01:12:36,820
+قسمنا الطرفين على روه بيصير cosine فاى بده يسوى
+
+600
+01:12:36,820 --> 01:12:41,280
+الـ sine فاى او لو قسمنا على ال cosine فاى بيصير
+
+601
+01:12:41,280 --> 01:12:47,580
+واحد يسوى تاني الفاى من الزاوية اللي ضلها يسوى
+
+602
+01:12:47,580 --> 01:12:59,030
+واحد 45 درجة يبقى من 90 نقاط 45 درجة طبعاشايفين
+
+603
+01:12:59,030 --> 01:13:06,090
+كيف الصندوق جاها؟ الآن هذا صار معادلة في تساوي باي
+
+604
+01:13:06,090 --> 01:13:10,850
+على أربع الخط اللي عندنا هنا يبقى الزاوية هذه كلها
+
+605
+01:13:10,850 --> 01:13:14,750
+صارت كده شبنات اللي هي باي على أربع اللي هي
+
+606
+01:13:14,750 --> 01:13:20,030
+الزاوية في مرتين أقولها لإنها very important خبصت
+
+607
+01:13:20,030 --> 01:13:24,460
+فيها بتروح المسألةيبقى مرة تانية بدي اجيب قداش
+
+608
+01:13:24,460 --> 01:13:28,560
+مقدار الزاوية في ال file اللي عندنا بقول اه تعالى
+
+609
+01:13:28,560 --> 01:13:34,710
+ناخده تخط التقاطع هذا مع المستوى اللي فوق تمامهذا
+
+610
+01:13:34,710 --> 01:13:40,830
+جاي من مين؟ من معادلة الكون المخروط z تساوي a وهذا
+
+611
+01:13:40,830 --> 01:13:45,910
+اللي فوق جايين من z تساوي واحد إذا بدي أساوي اتنين
+
+612
+01:13:45,910 --> 01:13:50,770
+هدول بمين؟ ببعض طيب باجي بقوله z اللي فوق freely
+
+613
+01:13:50,770 --> 01:13:57,230
+spherical هي rho cosine فاي يبقى rho cosine فاي
+
+614
+01:13:57,230 --> 01:14:03,500
+بيبقى تساوي اللي تحت اللي هي مين؟اللي بيبدأ تسوي
+
+615
+01:14:03,500 --> 01:14:08,760
+رو صين الفاي اللي هي R يبقى صار رو قصين الفاي
+
+616
+01:14:08,760 --> 01:14:12,960
+بيبقى يسوي رو صين فاي قسمنا على رو صار القصين
+
+617
+01:14:12,960 --> 01:14:17,120
+بيبقى يسوي صين قسمنا على كل صين بيصير صين على قصين
+
+618
+01:14:17,120 --> 01:14:23,640
+اللي هي تان فاي يسوي مين واحد ومنها هذا بيقولك أن
+
+619
+01:14:23,640 --> 01:14:29,260
+فاي تسوي باي على أربع يبقى فاي تتغير من Zero لغاية
+
+620
+01:14:29,260 --> 01:14:34,390
+باي على رمية ضايد عندناتختلفت عن الـcylindrical
+
+621
+01:14:34,390 --> 01:14:39,250
+وعن الـspherical لما هي .. يبقى هذه لم تحدث إلى أي
+
+622
+01:14:39,250 --> 01:14:44,950
+تغيير يبقى Zero لغاية الدنيا الفارقة طيب تعالوا
+
+623
+01:14:44,950 --> 01:14:50,570
+نحسن إذا ما طلعش طيعة تلاتة معناته في الشغل غلط يا
+
+624
+01:14:50,570 --> 01:14:54,490
+إما حدودنا غلط يا إما طريقتنا في التكامل غلط وإن
+
+625
+01:14:54,490 --> 01:14:58,850
+شاء الله مايحصلش فهي يبقى المروحة الكامل فين؟
+
+626
+01:15:24,950 --> 01:15:30,810
+هذا الكلام بده يسوي يتلت خليك برا وهي من zero
+
+627
+01:15:30,810 --> 01:15:37,620
+لغاية 2pi وهي من zero لغاية pi على 4العوض بالقيمة
+
+628
+01:15:37,620 --> 01:15:43,740
+اللى فوق يبقى شوف الصغير يبقى سك تك عيب اللى هو
+
+629
+01:15:43,740 --> 01:15:53,020
+فاي في صين الفاي في دي فاي في دي فيتا لأن هذا
+
+630
+01:15:53,020 --> 01:15:58,760
+الكلام بده ساوي طول integration من zero لإتنين فاي
+
+631
+01:16:03,120 --> 01:16:09,320
+ما رأيك هذه سك تاخد منها سك واحدة وانزلها تحت بصير
+
+632
+01:16:09,320 --> 01:16:14,400
+cosine بصير sine على cosine اللي هو مين بتان يبقى
+
+633
+01:16:14,400 --> 01:16:24,540
+بده يصير هذه سك تربيع فاي تان الفاي بفاي دفين
+
+634
+01:16:24,540 --> 01:16:33,720
+مظبوط؟ هذا الكلام بده يصير طولتكمل من 0 ل2 باى
+
+635
+01:16:33,720 --> 01:16:45,120
+تكمل من 0 لباى على 4 لمين لتان الفاى دى تان الفاى
+
+636
+01:16:45,120 --> 01:16:54,460
+دى ثيتا تفضل التان ب 6 ترميق الشلدسكتر بيع الفاى
+
+637
+01:16:54,460 --> 01:17:00,540
+مع دى فاى وكتبت بدالها دى تان الفاى يبقى كأنه انا
+
+638
+01:17:00,540 --> 01:17:05,860
+بكمل اكس دى اكس يبقى بضطري فى بس للأس واحد و اقسم
+
+639
+01:17:05,860 --> 01:17:12,360
+على الأس الجديد يبقى هى التلت برا وهى تكمل من زيرو
+
+640
+01:17:12,360 --> 01:17:20,360
+لاتنين باى وهدى تان تربيع فاى على الاتنينمن Zero
+
+641
+01:17:20,360 --> 01:17:30,280
+لغاية Pi على أربعة لدى ثيتا مصفى تلت بقدرش بسدس
+
+642
+01:17:30,280 --> 01:17:34,620
+وغاية كامل من Zero لإتنين Pi
+
+643
+01:17:48,920 --> 01:17:57,380
+بس عندي واحد دي ثيتا يبقى هنا سُدس وثيتا ومن zero
+
+644
+01:17:57,380 --> 01:18:04,640
+divide اتنين by او سُدس اتنين by او باية تلاتة
+
+645
+01:18:04,640 --> 01:18:10,900
+معناته شغلنا صحيح ولا خمأة في ذلك حد مش حابب تسأل
+
+646
+01:18:10,900 --> 01:18:16,680
+أي شوية هنا لسه في عندنا مشاكل كتير كما أناهي
+
+647
+01:18:16,680 --> 01:18:24,520
+تساوى الأيوة مش
+
+648
+01:18:24,520 --> 01:18:29,660
+هيها بالضبط هي الدائرة اللي عندها دي و أسقطها
+
+649
+01:18:29,660 --> 01:18:33,880
+تماما مش أسقط الدائرة يعني بمعنى أخر أسقط المجسم
+
+650
+01:18:33,880 --> 01:18:38,500
+كله فظهرت المنطقة المصممة اللي هي على شكل قصة أو
+
+651
+01:18:38,500 --> 01:18:41,880
+على شكل دائرة هي الدائرة اللي فوت بالضبط لأن هذا
+
+652
+01:18:41,880 --> 01:18:45,760
+نزل عمود وهذا نزل عمود صحيح
+
+653
+01:18:53,260 --> 01:18:59,060
+هي ربط تبدأ من النقطة هذه لغاية اي نقطة على
+
+654
+01:18:59,060 --> 01:19:09,940
+الدائرة اللى فوق لما
+
+655
+01:19:09,940 --> 01:19:12,880
+احنا هنا مش هدى تقع على ال y axis ولا لا
+
+656
+01:19:16,950 --> 01:19:21,030
+يختيروا اسم أي خط هنا بيصير عندك مثلث طايم ده اه
+
+657
+01:19:21,030 --> 01:19:24,630
+بده يوصل الهدوء ان بيصير هذه المثلث القايم الزاوية
+
+658
+01:19:24,630 --> 01:19:28,930
+فوق طيب
+
+659
+01:19:28,930 --> 01:19:35,850
+انت بتشغلي cartesian يعني الان احنا بدنا mean
+
+660
+01:19:35,850 --> 01:19:38,210
+spherical اه دي لبالك
+
+661
+01:20:04,500 --> 01:20:08,980
+طب كان هذا هو المثال الرقم اتنين بدنا نروح لمثال
+
+662
+01:20:08,980 --> 01:20:16,000
+رقم تلاتة مثال رقم تلاتة find the volume of the
+
+663
+01:20:16,000 --> 01:20:26,180
+solid find the volume of the solid بدنا نقدرش حجم
+
+664
+01:20:26,180 --> 01:20:29,120
+المجسم bounded below
+
+665
+01:20:33,930 --> 01:20:45,530
+من أسفل By The XY Plane XY Plane
+
+666
+01:20:45,530 --> 01:20:56,710
+On Sides On Sides من الجانب By The Sphere By The
+
+667
+01:20:56,710 --> 01:21:09,890
+Sphere بالكرة روتو ساوي بنيتand above ومن أعلى by
+
+668
+01:21:09,890 --> 01:21:18,490
+the whole بالمخروج by تساوي by على
+
+669
+01:21:33,770 --> 01:21:45,150
+المنطقة اللي عندنا يبقى هذا اللي هو محور X وهذا
+
+670
+01:21:45,150 --> 01:21:51,930
+محور Y وهذا الرأس اللي هو محور Z
+
+671
+01:22:07,280 --> 01:22:11,980
+بنقلب دي حجم المنطقة المحظورة من الأسفل بال X Y
+
+672
+01:22:11,980 --> 01:22:18,680
+Plane و من الجوانب بالاسفير يبقى أنا عند هنا بنا
+
+673
+01:22:18,680 --> 01:22:28,140
+اسفير كويس هاي ها بدي أرسم بالشكل اللي عنا هذا هاي
+
+674
+01:22:28,140 --> 01:22:36,250
+القاعدة قلب ال X Y Plane يبقى هذا مش هيبقىكويس و
+
+675
+01:22:36,250 --> 01:22:41,690
+هذا هيجينا هيك و الاسفير بدأ يرسم من فوق يبقى تظهر
+
+676
+01:22:41,690 --> 01:22:46,970
+الاسفير بالشكل اللي عندنا هذا و الناحية التانية
+
+677
+01:22:46,970 --> 01:22:53,250
+بالشكل هذا كويس يبقى هذا النصف العلوي من الاسفير
+
+678
+01:22:53,250 --> 01:23:04,460
+النصف والسفلي ما رسمناهوشيبقى الاسفير يبقى
+
+679
+01:23:04,460 --> 01:23:13,660
+الاسفير يبقى الاسفير
+
+680
+01:23:13,660 --> 01:23:18,360
+يبقى الاسفير
+
+681
+01:23:18,360 --> 01:23:21,060
+يبقى الاسفير يبقى الاسفر يبقى الاسفر يبقى الاسفر
+
+682
+01:23:21,060 --> 01:23:21,060
+يبقى الاسفر يبقى الاسفر يبقى الاسفر يبقى الاسفر
+
+683
+01:23:21,060 --> 01:23:21,060
+يبقى الاسفر يبقى الاسفر يبقى الاسفر يبقى الاسفر
+
+684
+01:23:21,060 --> 01:23:21,060
+يبقى الاسفر يبقى الاسفر يبقى الاسفر يبقى الاسفر
+
+685
+01:23:21,060 --> 01:23:21,060
+يبقى الاسفر يبقى الاسفر يبقى الاسفر يبقى الاسفر
+
+686
+01:23:21,060 --> 01:23:21,060
+يبقى الاسفر يبقى الاسفر يبقى الاسفر يبقى الاسفر
+
+687
+01:23:21,240 --> 01:23:24,980
+يبقى بده يجينا هذا من الناحية اللي عندنا هذه
+
+688
+01:23:24,980 --> 01:23:30,680
+وبالتالي بده يصير عندنا من المخروض على الشكل اللي
+
+689
+01:23:30,680 --> 01:23:37,420
+عندنا هذا يعني انت بنات كأن المخروض هذا تجويف
+
+690
+01:23:37,420 --> 01:23:41,960
+للكرة الكرة اللي اتصورناها مصمة واخدنا نصف العلوي
+
+691
+01:23:41,960 --> 01:23:47,780
+نزلنا فيها ثقب على شكل مخروج بالشكل اللي قدامك هذا
+
+692
+01:23:47,780 --> 01:23:49,340
+يبقى اللي فوق
+
+693
+01:23:54,670 --> 01:23:59,030
+الجزء العلوي لبعض المخروط كله وجود لأ يبقى هذا
+
+694
+01:23:59,030 --> 01:24:04,970
+بنشيله تماما من راسنا يبقى هذا كأنه مالوش وجود
+
+695
+01:24:04,970 --> 01:24:09,430
+بالمرة كويس
+
+696
+01:24:09,430 --> 01:24:15,710
+يبقى صار يعني الدارة كأنه احنا اللي هو على الجوالب
+
+697
+01:24:15,710 --> 01:24:21,650
+فقط يبقى على الجوالب هذه ال road تساوي اتنين هنا
+
+698
+01:24:21,650 --> 01:24:25,850
+مخروط في الداخل اللي هو five تساوي fiveعلى تلاتة
+
+699
+01:24:25,850 --> 01:24:32,370
+والأرض هي ال X Y plane كويس بدل ال volume V فبقول
+
+700
+01:24:32,370 --> 01:24:43,790
+لهم V تساوي تلت تكاملات ل رو تربيع ف sin ف D رو D
+
+701
+01:24:43,790 --> 01:24:51,080
+في دي ثي ليجي ل روروح تبدأ من هنا من هنا من نقطة
+
+702
+01:24:51,080 --> 01:24:57,120
+الأصل لغاية أي نقطة على محيط الكرة يبقى هنا كده؟
+
+703
+01:24:57,120 --> 01:25:04,920
+روح تساوي اتنين يبقى من zero لغاية اتنين يجي ليه
+
+704
+01:25:04,920 --> 01:25:11,280
+five؟ five هذا كله فرق مش علاقة فيه يبقى المجسم
+
+705
+01:25:11,280 --> 01:25:17,810
+هيبدأ من هنا لغاية الفاية هذه فاضية اللي فوقيبقى
+
+706
+01:25:17,810 --> 01:25:24,890
+في حتى تغير من وين لوين من باية ثلاثة الى باية
+
+707
+01:25:24,890 --> 01:25:32,270
+اتنين يمشي من باية على تلاتة لغاية في على اتنين
+
+708
+01:25:32,270 --> 01:25:36,770
+طبعا بعض البنات هتجي تقولي هه لو سرقت رحلتك هتقولي
+
+709
+01:25:36,770 --> 01:25:40,730
+من zero لغاية باية على تلاتة هذا كلام غلط تتكلمي
+
+710
+01:25:40,730 --> 01:25:44,530
+في الفراغ انا بدي لحاجة باللي ضايل اللي بعدهاطبعا
+
+711
+01:25:44,530 --> 01:25:49,110
+يبدأ من باية تلاتة لباية طيب ضل تيتا واضحة اصلا
+
+712
+01:25:49,110 --> 01:25:58,630
+تيتا من الصفر لغاية كده؟2π دوس خط الرسمة كلها
+
+713
+01:25:58,630 --> 01:26:08,970
+بتصير الدائرة اللى تحتجه من 0 لغاية 2π كيف؟
+
+714
+01:26:08,970 --> 01:26:15,450
+لو قولنا حد المخروض صحيح احنا مابنعش المخروض هدف
+
+715
+01:26:15,450 --> 01:26:20,530
+فرعام تمام؟ يبقى هاي اللى بيحصل يبقى هذا الكلام
+
+716
+01:26:20,530 --> 01:26:27,520
+يدوسى التكامل من 0 لغاية 2πوتكامل من πاية على
+
+717
+01:26:27,520 --> 01:26:35,400
+تلاتة لغاية باية على اتنين لروح تكييبك على تلاتة
+
+718
+01:26:35,400 --> 01:26:41,900
+من Zero لغاية من Zero لغاية اتنين من Zero لغاية
+
+719
+01:26:41,900 --> 01:26:49,700
+اتنين ويظل عندى sin فاية D فاية D ثيتا يعني من هذا
+
+720
+01:26:49,700 --> 01:26:53,620
+الكلام الدنيا تصبح تمانية على تلاتةتمنى على تلاتة
+
+721
+01:26:53,620 --> 01:26:59,420
+خليك برا أي تمانية على تلاتة و بقى لدي تكاملين من
+
+722
+01:26:59,420 --> 01:27:03,840
+باية على تلاتة الى باية على اتنين و من Zero لغاية
+
+723
+01:27:03,840 --> 01:27:11,060
+اتنين باية من Zero لغاية اتنين باية لمين لصين
+
+724
+01:27:11,060 --> 01:27:18,900
+الفاية D فاية D تيتا و Zero برنامج كويس بدنا
+
+725
+01:27:18,900 --> 01:27:24,510
+الكامليبقى هذا الكلام يسوى تمانية ع تلاتة تكامل من
+
+726
+01:27:24,510 --> 01:27:31,330
+Zero لإتنين باي لناقص cosine الفاعي من باية ع
+
+727
+01:27:31,330 --> 01:27:38,670
+تلاتة لغاية باية على اتنين لدى ثيتا ويسوى تمانية
+
+728
+01:27:38,670 --> 01:27:44,230
+على تلاتة تكامل من Zero لإتنين باية ع تلاتة
+
+729
+01:27:46,850 --> 01:27:55,210
+يبقى نقص مع نقص بالصير الزائد و هنا جتا ستين يبقى
+
+730
+01:27:55,210 --> 01:28:03,370
+داشت بنص دي ثيتا يبقى هذا الكلام بده يساوي أربعة
+
+731
+01:28:03,370 --> 01:28:10,060
+على تلاتة تكامل من zero للإتنين by للدي ثيتاأربع
+
+732
+01:28:10,060 --> 01:28:16,620
+على تلاتة تيتا من Zero للإتنين باى أربع على تلاتة
+
+733
+01:28:16,620 --> 01:28:23,220
+في إتنين باى ويساوي تمانية باى على بين على تلاتة
+
+734
+01:28:23,220 --> 01:28:28,480
+آخر مثال في محاضرة اليوم مثال رقم
+
+735
+01:28:44,880 --> 01:28:57,980
+molar region المنطقة الصغرى كانت from والمقطوعة من
+
+736
+01:28:57,980 --> 01:29:00,660
+the solid sphere
+
+737
+01:29:08,160 --> 01:29:16,260
+R أقل من أو يساوي 2π لإطلين
+
+738
+01:29:16,260 --> 01:29:21,100
+بالمستوى Z تساوي 1
+
+739
+01:30:00,070 --> 01:30:06,770
+بقولتلي حجم المنطقة الصغرى المطقوعة من الكورة اللى
+
+740
+01:30:06,770 --> 01:30:11,490
+عندها دى بالـ Plane Z تساوي مين؟ تساوي واحدة اقول
+
+741
+01:30:11,490 --> 01:30:14,650
+لكوا يستخدموا ارصدوا من الرسمة ونشوف كإيه الدينامس
+
+742
+01:30:14,650 --> 01:30:21,370
+يبقى لو جهت خد اللى هو المحاول التلاتة هذا X هذا Y
+
+743
+01:30:21,370 --> 01:30:26,810
+هذا Z الان لما اقول روتو تساوي اتنين يبقى كورة
+
+744
+01:30:27,130 --> 01:30:31,870
+مركزها نقطة الأصبع نصف قطرة يساوي كده؟ يساوي اتنين
+
+745
+01:30:31,870 --> 01:30:44,810
+يبقى كأن الكورة عليا الشكل اللي عندنا هذا يبقى
+
+746
+01:30:44,810 --> 01:30:49,790
+هذا الكورة في شكلها العام طبعا مابدي اقطعها
+
+747
+01:30:49,790 --> 01:30:55,360
+بالمستوى اللي همين Z يساوي واحدإذا بدى أجي على
+
+748
+01:30:55,360 --> 01:31:00,500
+المستوى الطوب هيك و أجي و أاخده بالشكل اللي عنده
+
+749
+01:31:00,500 --> 01:31:06,080
+هذا هيك و من هنا أجي و أقول هذه المستوى اللي عندنا
+
+750
+01:31:06,080 --> 01:31:12,540
+و الـ Z بده يساوي واحدة إذا قطع الدائرة قطع القرة
+
+751
+01:31:12,540 --> 01:31:17,000
+اللي عندنا على شكل دائرة الشكل اللي عندنا هذا
+
+752
+01:31:20,140 --> 01:31:24,460
+وهذا اللي تحت كله شيلناه مش لزمن ، شيلناه بالمرة.
+
+753
+01:31:25,140 --> 01:31:31,100
+إذا صار عند مين الجزء اللي فوق هذا فقط لا غير.
+
+754
+01:31:33,640 --> 01:31:39,000
+اللي هو شكله شكل إيه يا بنات؟ بس شكله بالبلد هيك
+
+755
+01:31:39,000 --> 01:31:47,360
+شكل إيش؟ طاقيةمظبوط يبقى كأنه احنا بدنا نجيب حجم
+
+756
+01:31:47,360 --> 01:31:52,580
+الطاقية القروية اللى عندناها دى طبعا و باقى الكرة
+
+757
+01:31:52,580 --> 01:31:55,760
+اللى تحت هذا مالوش لزوم مش موجود عندى من الأصل
+
+758
+01:31:55,760 --> 01:32:00,200
+طبعا انه جالى بدى الجزء الصغير هاي اللى كبير تحت
+
+759
+01:32:00,200 --> 01:32:04,840
+وصغير فوق اذا احنا علاقتنا مع الجزء الصغير مايبقوا
+
+760
+01:32:04,840 --> 01:32:08,100
+بسيطة يبقى احنا بدنا V
+
+761
+01:32:16,590 --> 01:32:24,590
+فاين الفاين دي روى دي فاين دي فاين دي دي دي دي دي
+
+762
+01:32:24,590 --> 01:32:25,610
+دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي
+
+763
+01:32:25,610 --> 01:32:26,190
+دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي
+
+764
+01:32:26,190 --> 01:32:30,190
+دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي
+
+765
+01:32:30,190 --> 01:32:33,790
+دي دي دي دي دي دي دي دي
+
+766
+01:32:33,790 --> 01:32:33,990
+دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي
+
+767
+01:32:33,990 --> 01:32:33,990
+دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي
+
+768
+01:32:33,990 --> 01:32:37,450
+دي دي دي
+
+769
+01:32:37,450 --> 01:32:43,590
+د
+
+770
+01:32:44,950 --> 01:32:51,570
+قطعت منطقة التكامل لغاية ما وصلت الحدود الاقليمية
+
+771
+01:32:51,570 --> 01:32:58,510
+يبقى هنا اقل قيمة لرو هنا و اكبر قيمة لرو هنا
+
+772
+01:32:58,510 --> 01:33:09,490
+فمجددش رو هنا؟ زيت تلب واحد ايوةبتجي تقوليلي z في
+
+773
+01:33:09,490 --> 01:33:15,390
+الإحداثيات الكوروية هي z تساوي ال raw cosine الفاي
+
+774
+01:33:15,390 --> 01:33:21,410
+يعني بتجي تقوليلي هنا z تساوي ال raw cosine الفاي
+
+775
+01:33:21,410 --> 01:33:27,230
+اللي هو واحد تمام إذا ال raw تساوي كده سك الفاي
+
+776
+01:33:27,230 --> 01:33:33,210
+يبقى أقل قيمة ل raw هي سك الفاي وأكبر قيمة كده
+
+777
+01:33:35,800 --> 01:33:39,500
+للنصف القطر تبعها انه بالاقل من او سوى اتنين يعني
+
+778
+01:33:39,500 --> 01:33:45,620
+الكرة المصممة كلها دي طيب نجي ليه فاي فاي ستة تغير
+
+779
+01:33:45,620 --> 01:33:50,820
+من وين لوين من الان لغاية اتنين كده اعرف كده اش
+
+780
+01:33:50,820 --> 01:33:56,820
+الفاية كده تبقى يالا طب ماشي theta بقداش نرجع
+
+781
+01:33:56,820 --> 01:34:03,660
+لفاية بس قولولي theta من وين لوين من zero لاتنين
+
+782
+01:34:07,220 --> 01:34:12,140
+مع قصد الـ Phi هتبدأ من هنا إذا هتبدأ من الـ Zero
+
+783
+01:34:12,140 --> 01:34:19,660
+لأن قداش الله أعلم لأننا وعرفنا قداش معادلة هذا
+
+784
+01:34:19,660 --> 01:34:26,680
+الخط بيكون وعرفنا Phi تساوي قداش يالا قد احنا
+
+785
+01:34:26,680 --> 01:34:31,820
+رششناكوا ورسمنا الخط وشوفوا كيف يمكنوا تحسبوا Phi
+
+786
+01:34:31,820 --> 01:34:35,660
+من خلال الرسم اللي قدامكوا هذه
+
+787
+01:34:49,200 --> 01:35:02,060
+يلا ايوة صحيح هاي زيت تساوي واحد مضمون صحيح
+
+788
+01:35:02,060 --> 01:35:09,320
+وراه تساوي اتنينممتاز جدا يبقى البنات بتقولكوا
+
+789
+01:35:09,320 --> 01:35:14,200
+اخدوا صباح ابو سمها دانا ما يأتي بتقولوا اللي فوق
+
+790
+01:35:14,200 --> 01:35:19,800
+اللي هي باتنينيقول يا راتو ساوى اتنين وهذه ال E
+
+791
+01:35:19,800 --> 01:35:24,740
+دائرة لان لليط لين زد يساوي واحد في الاحداثيات
+
+792
+01:35:24,740 --> 01:35:31,800
+الكوروية يبقى Z ال وبرو كساين الفاي بدها تساوي
+
+793
+01:35:31,800 --> 01:35:41,090
+واحد يبقى صار عندنا E اتنينكو ساين الفاى بيبقى كو
+
+794
+01:35:41,090 --> 01:35:45,430
+ساين الفاى بيبقى كو ساين الفاى بيبقى كو ساين الفاى
+
+795
+01:35:45,430 --> 01:35:46,770
+بيبقى كو ساين الفاى بيبقى كو ساين الفاى بيبقى كو
+
+796
+01:35:46,770 --> 01:35:47,030
+ساين الفاى بيبقى كو ساين الفاى بيبقى كو ساين الفاى
+
+797
+01:35:47,030 --> 01:35:47,070
+بيبقى كو ساين الفاى بيبقى كو ساين الفاى بيبقى كو
+
+798
+01:35:47,070 --> 01:35:48,230
+ساين الفاى بيبقى كو ساين الفاى بيبقى كو ساين الفاى
+
+799
+01:35:48,230 --> 01:35:54,890
+بيبقى كو ساين الفاى بيبقى كو ساين الفاى بيبقى كو
+
+800
+01:35:54,890 --> 01:35:59,190
+ساين الفاى بيبقى كو س
+
+801
+01:36:02,390 --> 01:36:05,390
+By integration من Zero لإتنين By integration من
+
+802
+01:36:05,390 --> 01:36:06,650
+Zero لإت باية تلاتة By integration من Zero لإت
+
+803
+01:36:06,650 --> 01:36:10,230
+باية تلاتة By integration من Zero لإت باية تلاتة
+
+804
+01:36:10,230 --> 01:36:11,750
+By integration من Zero لإت باية تلاتة By
+
+805
+01:36:11,750 --> 01:36:12,170
+integration من Zero لإت باية تلاتة By integration
+
+806
+01:36:12,170 --> 01:36:12,290
+من Zero لإت باية تلاتة By integration من Zero لإت
+
+807
+01:36:12,290 --> 01:36:14,910
+باية تلاتة By integration من Zero لإت باية تلاتة
+
+808
+01:36:14,910 --> 01:36:15,770
+By integration من Zero لإت باية تلاتة By
+
+809
+01:36:15,770 --> 01:36:16,750
+integration من Zero لإت باية تلاتة By integration
+
+810
+01:36:16,750 --> 01:36:20,210
+من Zero لإت باية تلاتة By integration من Zero لإت
+
+811
+01:36:20,210 --> 01:36:23,050
+باية تلاتة By integration من Zero لإت باية تلاتة
+
+812
+01:36:23,050 --> 01:36:26,110
+By integration من Zero لإت باية تلاتة By
+
+813
+01:36:26,110 --> 01:36:31,870
+integration من Zero لإت باية تلاتة By integration
+
+814
+01:36:31,870 --> 01:36:42,440
+من Zero لطبعا و هنا sin فاي و هنا دي فاي دي إذا
+
+815
+01:36:42,440 --> 01:36:49,520
+صار هذا الطول تكاملين من zero لإتنين باى من zero
+
+816
+01:36:49,520 --> 01:36:59,060
+لباية باى ع تلاتة لتمانية sin فاي و هنا ناقص بدي
+
+817
+01:36:59,060 --> 01:37:00,600
+أسوي زي اللي قبل يا بنات
+
+818
+01:37:06,750 --> 01:37:17,250
+تان فاى كل هذا فيه فاى دى تى هذه
+
+819
+01:37:17,250 --> 01:37:27,390
+لحالها كإنها يشبه تان الفاى دى تان الفاى عاملناها
+
+820
+01:37:27,390 --> 01:37:33,720
+بالضبط تماما يبقى بالنار كامل يبقى طولتكامل من صفر
+
+821
+01:37:33,720 --> 01:37:43,580
+للإتنين باي وناقص تمانية في cosine الفاي وهذه بقى
+
+822
+01:37:43,580 --> 01:37:52,860
+ناقص تان تربيع الفاي كله على إتنين من Zero لغاية
+
+823
+01:37:52,860 --> 01:38:03,450
+باي على تلاتة لديه ثيتا يبقى التلتintegration من
+
+824
+01:38:03,450 --> 01:38:08,790
+zero لغاية اتنين by ليه فتعوض ال باية تلتة جتا
+
+825
+01:38:08,790 --> 01:38:17,530
+ستين بنص مع التمانية بتعطيك سالب اربع نفس بدنا نجي
+
+826
+01:38:17,530 --> 01:38:25,150
+لمان لظل الستين يعني جا ستين على جتا ستين جزر
+
+827
+01:38:25,150 --> 01:38:34,400
+تلاتة امان مظبوطجدر تلاتة وتربيه تلاتة
+
+828
+01:38:34,400 --> 01:38:41,200
+وعلى اتنين طبعا هاي عوض بالقيم اللي فوق ناقص اللي
+
+829
+01:38:41,200 --> 01:38:46,680
+تحت ناقص مع ناقص بيصير زائد تمانين نقصين سفر اك
+
+830
+01:38:46,680 --> 01:38:54,460
+واحد وظل السفر بسفر فقط لا غير كله في دي فيتر طب
+
+831
+01:38:54,460 --> 01:38:55,160
+اطلعي
+
+832
+01:38:59,050 --> 01:39:05,710
+خمسة و نصف من تمانية بظل اتنين و نصف يعني خمسة على
+
+833
+01:39:05,710 --> 01:39:12,610
+اتنين شرفونه برا يبقى طول في خمسة على اتنين في
+
+834
+01:39:12,610 --> 01:39:22,110
+تكامل من Zero لإتنين Pi لديه ثيتايبقى هذا الكلام
+
+835
+01:39:22,110 --> 01:39:29,570
+يساوي خمس أسداس و هنا ثيتا من zero لغاية اتنين باي
+
+836
+01:39:29,570 --> 01:39:39,530
+يبقى خمس أسداس لمين لاتنين باي ويساوي خمسة باي على
+
+837
+01:39:39,530 --> 01:39:45,890
+تلاتة اللي هو مقدار هذا التكامل بنروح ل exercises
+
+838
+01:39:45,890 --> 01:39:53,190
+خمستاشر السابعة exercisesخمس تاشر سبعة المسائل
+
+839
+01:39:53,190 --> 01:40:00,530
+التالية تلاتة خمسة سابعة تسعة تلاتة خمسة سابعة
+
+840
+01:40:00,530 --> 01:40:10,730
+تسعة خمس تاشر تمانتاش تسعة تاشر تلاتة وعشرين خمسة
+
+841
+01:40:10,730 --> 01:40:22,260
+وعشرين تمانية وعشرين تلاتين اربعة وتلاتينسبعة و
+
+842
+01:40:22,260 --> 01:40:33,360
+تلاتين خمسة و اربعين سبعة و اربعين تسعة و اربعين
+
+843
+01:40:33,360 --> 01:40:42,740
+اتنين و خمسين تلاتة و خمسين اربعة و خمسين سبعة و
+
+844
+01:40:42,740 --> 01:40:49,620
+خمسين و تسعة و خمسين و اتنين و ستين
+
+845
+01:40:52,520 --> 01:40:56,280
+يبقى يوم الأربعاء ان شاء الله القادم فبناخد ال
+
+846
+01:40:56,280 --> 01:41:01,220
+section الأخير في هذا الشبهر.
+
+847
+01:41:04,780 --> 01:41:13,180
+حد بتحب تسأل أي سؤالينا؟
+
+848
+01:41:13,180 --> 01:41:17,220
+هل
+
+849
+01:41:17,220 --> 01:41:25,860
+عيناكم؟ شايفة الإدارة هذه؟وشايفان الكرة هذه اتنين
+
+850
+01:41:25,860 --> 01:41:29,420
+اتقطعوا مع بعض عندها نقطة صارت هذه نقطة مشتركة
+
+851
+01:41:29,420 --> 01:41:33,940
+كثيرة بينهم لما وصلت من نقطة الأصل إلى هذه النقطة
+
+852
+01:41:33,940 --> 01:41:38,220
+طلع الخط اللي عندنا هذا الخط هذا بدي أحاول أجيب
+
+853
+01:41:38,220 --> 01:41:43,220
+معادله بقول كويس الكرة هذه رو كساوين اتنين
+
+854
+01:41:43,220 --> 01:41:50,180
+والمستوى هذا Z يساوي واحد Z في ال spherical هي رو
+
+855
+01:41:50,180 --> 01:41:55,440
+كساين الفعلصارت روب اتنين وروب كوصين الفاى بقدرش
+
+856
+01:41:55,440 --> 01:42:01,140
+بقى بواحد يبقى ده ساوى اتنين بعض يبقى صار اتنين
+
+857
+01:42:01,140 --> 01:42:06,080
+كوصين الفاى بدرة ساوية واحد يبقى كوصين الفاى
+
+858
+01:42:06,080 --> 01:42:12,300
+بساوية نصف يبقى فاى صارت بقدرش خلاصنا عايزين
+
+859
+01:42:12,300 --> 01:42:15,760
+نسوينا واحدة قابلة السؤال المثال اللى جابله برضه
+
+860
+01:42:15,760 --> 01:42:19,960
+بنفس الطريقة يبقى بنفس الطريقة حد لايه تسوى الآخر
+
+861
+01:42:22,280 --> 01:42:23,820
+يا الله تعالى تعالى
+
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/dSJIcUHEpZw.srt b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/dSJIcUHEpZw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..22ef133126a7010bc3ef5840af3b1149396e1222
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/dSJIcUHEpZw.srt
@@ -0,0 +1,2530 @@
+1
+00:00:00,000 --> 00:00:02,680
+موسيقى
+
+2
+00:00:25,330 --> 00:00:30,110
+الآن بالمعادلة اللي هو شبكة 13، المرة الماضية أخذنا
+
+3
+00:00:30,110 --> 00:00:33,910
+أول section، واليوم نأخذ ثانية section، المرة اللي
+
+4
+00:00:33,910 --> 00:00:37,190
+فاتت كان vector valued function limit لهذا ال
+
+5
+00:00:37,190 --> 00:00:40,170
+vector، الـ derivative لهذا الـ vector، الـ continuity
+
+6
+00:00:40,170 --> 00:00:45,030
+لهذا الـ vector، وما يتعلق بها، اللي دلوقت بدنا نروح
+
+7
+00:00:45,030 --> 00:00:49,650
+للـ integrals لهذه الـ vector valued functions، فبيجي
+
+8
+00:00:49,650 --> 00:00:55,520
+بقول integrals of vector functions، تكامل اللي هي
+
+9
+00:00:55,520 --> 00:01:02,340
+الدوال الاتجاهية. هنقسم الـ section هذا إلى نقطتين.
+
+10
+00:01:02,340 --> 00:01:06,920
+النقطة الأولى نتحدث عن الـ indefinite integrals.
+
+11
+00:01:06,920 --> 00:01:12,300
+يعني التكاملات غير المحدودة، ثم نذهب بعد ذلك إلى الـ
+
+12
+00:01:12,300 --> 00:01:18,090
+definite integrals، التي هي التكاملات المحدودة. سنعطي
+
+13
+00:01:18,090 --> 00:01:22,890
+تعريف لكل واحدة منهم، ثم بعد ذلك نأخذ بعض الأمثلة
+
+14
+00:01:22,890 --> 00:01:27,990
+على التعريفات اللي سنعطيها. يبقى أول definition في
+
+15
+00:01:27,990 --> 00:01:33,590
+هذا الموضوع، definition اللي
+
+16
+00:01:33,590 --> 00:01:36,290
+هو تبع الـ indefinite integral.
+
+17
+00:01:46,900 --> 00:01:57,520
+بنعرف فعلاً  F(t) بيتساوى F(t) في اتجاه I، زي
+
+18
+00:01:57,520 --> 00:02:02,440
+الـ G(t) في اتجاه الـ J، زي الـ H(t) في اتجاه
+
+19
+00:02:02,440 --> 00:02:12,800
+الـ K، where حيث الـ F، والـ G، والـ H are
+
+20
+00:02:12,800 --> 00:02:14,460
+integrable functions.
+
+21
+00:02:20,130 --> 00:02:27,690
+دول قابلة للتكامل، of T قابلة للتكامل في المتغير T.
+
+22
+00:02:27,690 --> 00:02:31,730
+then تكامل
+
+23
+00:02:31,730 --> 00:02:41,430
+الـ R(t) dt بتساوي تكامل للـ F(t) dt كله في
+
+24
+00:02:41,430 --> 00:02:49,940
+اتجاه I، زائد تكامل للـ G(t) dt كله في اتجاه J، زائد
+
+25
+00:02:49,940 --> 00:02:59,780
+تكامل للـ H(t) dt كله في اتجاه الـ K. كنا كاملنا
+
+26
+00:02:59,780 --> 00:03:09,200
+بنضيف زائد constant C، where C is a constant vector.
+
+27
+00:03:18,680 --> 00:03:24,100
+نمر اثنين، باعتبار هذا نمر واحد، ونمر اثنين اللي هو
+
+28
+00:03:24,100 --> 00:03:28,780
+definite integrals.
+
+29
+00:03:28,780 --> 00:03:37,220
+التكاملات المحددة، التكاملات
+
+30
+00:03:37,220 --> 00:03:45,880
+المحددة زي إيه؟ زي التكامل من A إلى B للـ R(t)
+
+31
+00:03:48,640 --> 00:03:57,220
+بتساوي تكامل من A إلى B للـ F(t) dt كله في اتجاه
+
+32
+00:03:57,220 --> 00:04:05,360
+I، زائد تكامل من A إلى B للـ G(t) dt كله في اتجاه
+
+33
+00:04:05,360 --> 00:04:09,480
+J، زائد تكامل من A إلى B
+
+34
+00:04:26,150 --> 00:04:30,270
+نرجع للكلام اللي كتبته على اللوح، لأنه بدنا نبدأ
+
+35
+00:04:30,270 --> 00:04:35,070
+تطبيقات عليه، قبل أن نبدأ هذه التطبيقات، نحاول نفهم
+
+36
+00:04:35,070 --> 00:04:40,690
+كل نقطة موجودة عندنا هنا. نأتي للتعريف الأول اللي
+
+37
+00:04:40,690 --> 00:04:44,670
+هو تعريف الـ independent integral للـ vector valued
+
+38
+00:04:44,670 --> 00:04:50,940
+function، نتجاهل تكاملات غير المحدودة. فبجب أقول لو كان
+
+39
+00:04:50,940 --> 00:04:54,960
+الـ R(t) يساوي F(t) في اتجاه I، زي G(t) في اتجاه G(t)
+
+40
+00:04:54,960 --> 00:05:00,880
+زي H(t) في اتجاه K، حيث الـ F، والـ G، والـ H هم integrable
+
+41
+00:05:00,880 --> 00:05:06,920
+functions. نرجع إلى Calculus A، بنقول ممكن الدالة تكون
+
+42
+00:05:06,920 --> 00:05:11,800
+قابلة للاشتقاق، وممكن ما تكونش، وممكن تكون قابلة
+
+43
+00:05:11,800 --> 00:05:18,120
+للتكامل، وممكن ما تكونش. السؤال هو: متى تكون الدالة
+
+44
+00:05:18,120 --> 00:05:22,200
+قابلة للتكامل؟ حد يذكر condition واحد فقط.
+
+45
+00:05:22,200 --> 00:05:27,720
+أجل أن تكون متصلة، ممتازة جداً. إذًا لو كانت الدالة
+
+46
+00:05:27,720 --> 00:05:34,940
+دالة متصلة، إذًا هذه الدالة قابلة للتكامل. اثنين: معنى
+
+47
+00:05:34,940 --> 00:05:40,660
+التكامل المحدود هو المساحة بين المنحنى ومحور X.
+
+48
+00:05:40,660 --> 00:05:46,340
+مقدار هذه المساحة يساوي عملياً قيمة التكامل.
+
+49
+00:05:47,100 --> 00:05:51,100
+لازم تكون الدالة F، وG، وH، هذول الثلاثة are
+
+50
+00:05:51,100 --> 00:05:55,960
+integrable functions. انتهى الكلام، يبقى بروح بعتبر في
+
+51
+00:05:55,960 --> 00:06:01,300
+التكامل المحدود، على أنه تكامل لكل مركبة من هذه
+
+52
+00:06:01,300 --> 00:06:05,480
+المركبات، بدل ما أقول هنا زائد constant one، هنا
+
+53
+00:06:05,480 --> 00:06:09,600
+زائد constant two، هنا constant three، بقول لهم
+
+54
+00:06:09,600 --> 00:06:13,440
+أجمعهم كلهم constant واحد، اللي هو هسميه main الـ C.
+
+55
+00:06:13,440 --> 00:06:21,570
+السؤال: هل الـ constant هذا scalar ولا vector؟ أنا
+
+56
+00:06:21,570 --> 00:06:24,710
+أسأل: إحنا الـ function العادية اللي بيكون تكاملها
+
+57
+00:06:24,710 --> 00:06:29,370
+ليست function اتجاهية، بيبقى نقول زائد constant، و
+
+58
+00:06:29,370 --> 00:06:33,590
+scalar، اثنين، ثلاثة، زيرو، أربعة، الآخَرين، مضبوط؟
+
+59
+00:06:33,590 --> 00:06:38,630
+طيب هل الـ C هذا constant vector ولا constant
+
+60
+00:06:38,630 --> 00:06:43,850
+scalar؟ constant vector. لحد لو كان... لو كان
+
+61
+00:06:43,850 --> 00:06:47,630
+scalar، كيف بدي أجمع مع الـ vectors هذه؟ مش ممكنية.
+
+62
+00:06:47,630 --> 00:06:50,950
+إذًا لازم يكون هذا الـ C هو عبارة
+
+63
+00:07:15,110 --> 00:07:18,330
+بتكون رقم في اتجاه الـ I، رقم في اتجاه الـ J، رقم في
+
+64
+00:07:18,330 --> 00:07:22,910
+اتجاه الـ K، اللي هو اللي لو جينا لـ definite
+
+65
+00:07:22,910 --> 00:07:28,230
+integrals، التكاملات المحدودة، فالتكامل على الـ R(t)
+
+66
+00:07:28,230 --> 00:07:32,310
+dt من إيه؟ اللي بيبدأ يسمى التكامل على كل مركبة
+
+67
+00:07:32,310 --> 00:07:37,590
+من هذه المركبات، وفي هذه الحالة بقولش زائد
+
+68
+00:07:37,590 --> 00:07:41,690
+constant، تماماً كما درسنا في Calculus التكامل
+
+69
+00:07:41,690 --> 00:07:46,330
+المحدود. بنحطلش constant، وبنطلع القيمة بتاعته، بنعوض
+
+70
+00:07:46,330 --> 00:07:49,830
+بالقيمة اللي فوق، ناقص القيمة اللي تحت، بعد ما نكامل
+
+71
+00:07:49,830 --> 00:07:54,590
+بنطلع القيمة الحقيقية لمقدار التكامل. الآن نبدأ نأخذ
+
+72
+00:07:54,590 --> 00:08:00,010
+أمثلة على كل من الـ two definitions، الاثنين هدول.
+
+73
+00:08:00,010 --> 00:08:01,510
+يبقى examples.
+
+74
+00:08:07,150 --> 00:08:12,130
+أول مثال، أول مثال يبقى نديله سؤال عشرة من الكتاب
+
+75
+00:08:12,130 --> 00:08:19,350
+بيقول لي evaluate the
+
+76
+00:08:19,350 --> 00:08:28,630
+following integral. احسب لي
+
+77
+00:08:28,630 --> 00:08:35,770
+التكامل التالي integration من zero لغاية five
+
+78
+00:09:04,120 --> 00:09:09,530
+يبقى بنا نـحسب تكامل الـ vector valued function من
+
+79
+00:09:09,530 --> 00:09:14,870
+النقطة zero لغاية النقطة باي. بقول هذا التكامل
+
+80
+00:09:14,870 --> 00:09:22,030
+يساوي، هأكمل، four you never know، هايه يساوي أظن 60
+
+81
+00:09:22,030 --> 00:09:29,110
+سهل تكامله. لكن تان تربيع ماشي
+
+82
+00:09:29,110 --> 00:09:34,970
+بنحولها بدلالة المتطابقات المثلثية إلى دالة يمكن
+
+83
+00:09:34,970 --> 00:09:40,470
+تكاملها. إذا هذا الكلام بده يساوي تكامل من zero إلى
+
+84
+00:09:40,470 --> 00:09:48,510
+باي ل sec t في اتجاه الـ I، زائد تان تربيع، عملت اللي هي
+
+85
+00:09:48,510 --> 00:09:55,800
+sec تربيع t ناقص واحد، كله في اتجاه الـ J، ناقص اللي
+
+86
+00:09:55,800 --> 00:10:01,640
+هو t في sin t في اتجاه مين؟ في اتجاه الـ K.
+
+87
+00:10:01,640 --> 00:10:07,840
+بالنسبة إلى D، هذا الكلام يساوي، نكمل السيك في قداش
+
+88
+00:10:07,840 --> 00:10:18,840
+من Calculus B، قداش؟ أيوة، الصوت قليل، اسمعني.
+
+89
+00:10:18,840 --> 00:10:25,240
+absolute value لـ sec t زائد tan t. يبقى هذا الـ
+
+90
+00:10:25,240 --> 00:10:33,200
+absolute value لـ sec t زائد tan t، كل هذا الكلام من
+
+91
+00:10:33,200 --> 00:10:37,870
+zero لغاية باي في اتجاه الـ I، زائد، طبعاً مذكرة
+
+92
+00:10:37,870 --> 00:10:43,290
+الكريمانات، sec t ما أقدرش أكملها مباشرة، فبروح بضربها
+
+93
+00:10:43,290 --> 00:10:47,490
+في مقدار وبقسم عليه، شو المقدار هذا؟ بضرب في sec
+
+94
+00:10:47,490 --> 00:10:52,170
+زائد tan، وبقسم على sec زائد tan. بصير البسط هو تفاضل
+
+95
+00:10:52,170 --> 00:10:56,670
+المقام، يبقى الجواب هو absolute value لمن؟ للمقام.
+
+96
+00:10:56,670 --> 00:11:03,570
+اللي بعده، زائد، آه، ما نقدرش، تفاضل الـ tan، تفاضل الـ tan
+
+97
+00:11:05,040 --> 00:11:13,440
+sec تربيع. إذا تكامل الـ sec تربيع هو tan، يبقى tan t ناقص
+
+98
+00:11:13,440 --> 00:11:19,460
+t، كل هذا الكلام من وين لوين؟ من zero لغاية باي في
+
+99
+00:11:19,460 --> 00:11:25,600
+اتجاه الـ J، ناقص، آه، استنى شوية، هذه ما لها اللي إيش
+
+100
+00:11:26,980 --> 00:11:30,840
+الكسور الجزئية ولا لا؟ مش الكسور الجزئية،
+
+101
+00:11:30,840 --> 00:11:35,500
+integration by parts، تكامل بالتجزئة، يبقى بدي آخذ
+
+102
+00:11:35,500 --> 00:11:36,840
+جزء الـ derivatives.
+
+103
+00:12:00,880 --> 00:12:09,620
+هو لوحده. طبعاً لو كان الـ n هو عدد صحيح موجب، إذا بقول
+
+104
+00:12:09,620 --> 00:12:17,140
+تكامل x أس n في cos x، أو x أس n في sin x، أو x
+
+105
+00:12:17,140 --> 00:12:23,840
+أس n في sin x، أو x أس n في cos x، أو الـ x أس n
+
+106
+00:12:23,840 --> 00:12:28,580
+في e أس ax، أو الـ x أس n في a to the power x.
+
+107
+00:12:28,580 --> 00:12:32,920
+يبقى الست حالات، من حد أشوفهم بروح بعملهم الجدول
+
+108
+00:12:32,920 --> 00:12:38,560
+مباشرة. مشتقة الـ t بواحد، تكامل الـ sin بسالب
+
+109
+00:12:38,560 --> 00:12:43,840
+cos t، مشتقة الواحد بزيرو، تكامل هذا بناقص
+
+110
+00:12:43,840 --> 00:12:48,870
+sin t، وبروح بخدم قاعدة الإشارات، ببدأ بزائد، ناقص،
+
+111
+00:12:48,870 --> 00:12:52,970
+زائد، ناقص، لغاية ما تنتهي المسألة اللي عندي هذه.
+
+112
+00:12:52,970 --> 00:13:04,610
+بصير ناقص، وعندك هنا ناقص t cos t، وهنا زائد sin t.
+
+113
+00:13:04,610 --> 00:13:11,980
+كل هذا الكلام من zero لغاية pi في اتجاه الـ K. هذا
+
+114
+00:13:11,980 --> 00:13:15,460
+الكلام يساوي، فالدعوة من القيمة اللي فوق ناقص
+
+115
+00:13:15,460 --> 00:13:21,720
+القيمة اللي تحت. يبقى هذا الـ in absolute value. بدأ  أجي لـ 16. إذا نسيها بقول الـ sec هي مقلوب من الـ
+
+116
+00:13:21,720 --> 00:13:26,700
+cos 180، سالب واحد، واحد على سالب واحد اللي هو
+
+117
+00:13:26,700 --> 00:13:32,960
+سالب واحد تمام، اللي بدي assign ال by. يبقى جيب
+
+118
+00:13:32,960 --> 00:13:39,670
+الـ 180، عفواً، ضل الـ 180. يبقى جيب الـ 180 على جيب
+
+119
+00:13:39,670 --> 00:13:45,850
+الـ 180. جيب الـ 180 بزيرو، وجيب الـ 180 بسالب واحد يبقى
+
+120
+00:13:45,850 --> 00:13:51,070
+بزيرو. يبقى ناقص واحد ناقص زيرو على فوق، ناقص لن 0 1
+
+121
+00:14:01,540 --> 00:14:06,820
+و tan 0 اللي هو بزيرو. هاي خلصنا الـ term الأول هذا
+
+122
+00:14:06,820 --> 00:14:14,580
+كله في اتجاه مين؟ في اتجاه الـ I. زائد، ها tan pi
+
+123
+00:14:14,580 --> 00:14:23,540
+اللي هو قداش؟ بزيرو. ناقص pi ناقص زيرو، زائد زيرو في
+
+124
+00:14:23,540 --> 00:14:30,860
+اتجاه الـ G. tan pi بزيرو. سالب pi. ها ينقص tan zero
+
+125
+00:14:30,860 --> 00:14:35,600
+بزيرو، و t بزيرو، مع السلامة اللي بعضه. ناقص ناقص بصير
+
+126
+00:14:35,600 --> 00:14:42,260
+جمع، زائد، ها قصر مية ثمانين بسالب واحد، مع سالب
+
+127
+00:14:42,260 --> 00:14:46,040
+بصير إشارة ناقص.
+
+128
+00:14:49,580 --> 00:14:53,720
+الشرط الناقص بدي أدخله زائد، وبدي أدخله سالب جوا
+
+129
+00:14:53,720 --> 00:15:00,560
+بصير عندك كلامياً موجب pi، و cos مية وثمانين بسالب
+
+130
+00:15:00,560 --> 00:15:09,480
+واحد، زائد زيرو ناقص زيرو ناقص زيرو، كله بزيرو في
+
+131
+00:15:09,480 --> 00:15:13,500
+اتجاه الـ k.
+
+132
+00:15:13,500 --> 00:15:18,160
+طبعاً ناقص يصير هذا زائد زيرو ما عليك. يبقى هذه بدها
+
+133
+00:15:18,160 --> 00:15:25,740
+تساويلن absolute value لسالب واحد اللي هو واحد، لإن
+
+134
+00:15:25,740 --> 00:15:30,520
+الواحد بـ zero، ولإن الواحد بـ zero في إطار مع
+
+135
+00:15:30,520 --> 00:15:35,680
+السلامة. يبقى هاي الـ zero. نأتي لبعض، همضلش عندي، هذه
+
+136
+00:15:35,680 --> 00:15:40,160
+هنا بلد في اتجاه الـ J، يبقى
+
+137
+00:15:40,160 --> 00:15:46,800
+ناقص باي في اتجاه الـ J، وبعدها ناقص باي في اتجاه
+
+138
+00:15:46,800 --> 00:15:55,040
+الـ K. أو نتيجة التكامل هو ناقص pi J زائد K. يبقى هذه
+
+139
+00:15:55,040 --> 00:16:04,140
+نتيجة التكامل لهذه المسألة. نأخذ كمان سؤال، سؤال اثنين
+
+140
+00:16:04,140 --> 00:16:14,120
+اللي هو سؤال ستة عشر من الكتاب، يقول لي F، الـ R''(t)
+
+141
+00:16:14,120 --> 00:16:21,960
+بيكون ناقص I زائد J زائد K، ناقص مضروب في الكل، والـ
+
+142
+00:16:21,960 --> 00:16:28,040
+R عند الـ zero، والـ R عند الـ zero بيكون 10 I
+
+143
+00:16:28,040 --> 00:16:38,600
+زائد 10 J زائد 10 K، والـ dR على dt
+
+144
+00:16:47,820 --> 00:16:53,080
+أو جدلنا الـ R(0)
+
+145
+00:17:23,110 --> 00:17:27,410
+يبقى السؤال يقول: لو كانت المشتقة الثانية لـ R(t)
+
+146
+00:17:27,410 --> 00:17:32,690
+يساوي ناقص I زائد J زائد K، وكانت R عند الـ zero هو
+
+147
+00:17:32,690 --> 00:17:38,590
+المتجه الثابت 10 I زائد 10 J زائد 10 K، وكانت
+
+148
+00:17:38,590 --> 00:17:44,010
+المشتقة لـ R بالنسبة إلى dt عند t تساوي zero تساوي
+
+149
+00:17:44,010 --> 00:17:47,730
+zero، السؤال هو: هل الـ zero هذا مختلف عن الـ zero
+
+150
+00:17:47,730 --> 00:17:52,500
+هذا؟ من أين؟ طبعاً بيختلف اختلافاً كليا، هذا p is
+
+151
+00:17:52,500 --> 00:17:56,520
+scalar، لكن هذا main vector، لأن R(t) في الأصل هو
+
+152
+00:17:56,520 --> 00:18:00,200
+vector valued function، فمشتقته هي vector كذلك. إذا
+
+153
+00:18:00,200 --> 00:18:04,800
+هذا هو الـ zero vector، ومن هنا عملته لك على شكل
+
+154
+00:18:04,800 --> 00:18:10,580
+اللي هو مطول شوية، بحيث يختلف تماماً عن هذا. قال لي
+
+155
+00:18:10,580 --> 00:18:15,360
+هزل الـ R(t)، يبقى ملعقين الـ R''(t).
+
+156
+00:18:15,360 --> 00:18:21,400
+وطلب مني، يعني إيه؟ مرتين.
+
+157
+00:18:21,400 --> 00:18:27,460
+كل مرة يطلع ثابت للتكامل، لأن هذا ما هو إيش؟ تكامل
+
+158
+00:18:27,460 --> 00:18:31,920
+محدود زي السؤال اللي قبله، تمام؟ إذا المثال الأول
+
+159
+00:18:31,920 --> 00:18:35,680
+كان على الحالة الثانية، والمثال الثاني على مين؟ على
+
+160
+00:18:35,680 --> 00:18:40,770
+الحالة الأولى. يبقى إحنا عندنا هذا بده يروح أكامله.
+
+161
+00:18:40,770 --> 00:18:48,510
+يبقى بده آخذ تكامل للـ R'(t) dt، بده يساوي تكامل
+
+162
+00:18:48,510 --> 00:18:58,190
+لـ -I +J+K كله بالنسبة الى dt، طيب
+
+163
+00:19:01,200 --> 00:19:05,920
+هذا اشتقاق مرتين، بدنا نكامل مرة، نخلص من المشتقة
+
+164
+00:19:05,920 --> 00:19:09,940
+الأولى. هتبقى اللي عندنا مين؟ الـ R'(t) اللي
+
+165
+00:19:09,940 --> 00:19:17,260
+هي dR على dt، هدول اثنين. بدنا نكامل هذه، يبقى ناقص t
+
+166
+00:19:17,260 --> 00:19:22,360
+في اتجاه الـ I، ناقص t في اتجاه الـ J، ناقص t في اتجاه
+
+167
+00:19:22,360 --> 00:19:31,270
+الـ K، زائد constant C1. هذا ثابت ولا vector؟ يعني
+
+168
+00:19:31,270 --> 00:19:35,210
+scalar ولا vector؟ vector طبعاً. بدنا نع
+
+223
+00:26:18,120 --> 00:26:21,200
+T
+
+224
+00:26:21,200 --> 00:26:32,790
+تساوي A to T، تساوي B،  ويتقلل البنسوي تكامل من A
+
+225
+00:26:32,790 --> 00:26:42,470
+إلى B للجذر التربيعي لمن؟ لـ dx على dt لكل تربيع،
+
+226
+00:26:42,470 --> 00:26:51,950
+dy على dt لكل تربيع، dz على dt لكل تربيع، والتكامل
+
+227
+00:26:51,950 --> 00:26:58,390
+هذا كله بالنسبة لمن؟ بالنسبة إلى dt. طبعاً هذا بده
+
+228
+00:26:58,390 --> 00:27:06,630
+يساوي تكامل من a إلى b. هذا مين يا بنات؟ المرة اللي
+
+229
+00:27:06,630 --> 00:27:16,170
+فاتت، طول الـ a، طول
+
+230
+00:27:16,170 --> 00:27:19,910
+الـ a، ممتاز جداً. يعني هذا مقدار السرعة
+
+231
+00:27:22,860 --> 00:27:32,340
+هو الـ vector P بالنسبة إلى DT. مرة ثانية باجي بقول
+
+232
+00:27:32,340 --> 00:27:38,350
+طول smooth curve، المقطع بالعلاقة اللي عندنا هذه من
+
+233
+00:27:38,350 --> 00:27:43,250
+النقطة A إلى B، حيث T  يزيد من النقطة A إلى نقطة B
+
+234
+00:27:43,250 --> 00:27:48,390
+بُعرّفه كتالي: L يساوي integration من A إلى B للجذر
+
+235
+00:27:48,390 --> 00:27:52,090
+التربيعي لـ DX على DT لكل تربيع، زي الـ DY على DT لكل
+
+236
+00:27:52,090 --> 00:27:56,390
+تربيع، زي الـ DZ على DT لكل تربيع. يبقى X وY وZ هنا
+
+237
+00:27:56,390 --> 00:28:02,510
+أجَت مكان اللي جاب الـ F والـ G، و هي هي فانكشن في
+
+238
+00:28:02,510 --> 00:28:11,160
+T. هذا المقدار هو طول متجه السرعة
+
+239
+00:28:28,030 --> 00:28:34,990
+السؤال هو: احنا على المحاور الكارتيزية، بدأنا نبدأ
+
+240
+00:28:34,990 --> 00:28:37,890
+من نقطة الأصل، ونتحرك عليه، ونقول واحد، اثنين، ثلاثة،
+
+241
+00:28:37,890 --> 00:28:41,330
+أربعة، وأشياء ثانية: سالب واحد، سالب اثنين، وإيه كده.
+
+242
+00:28:41,330 --> 00:28:45,230
+بالنسبة لمحور y. طب المنحنى اللي في الفراغ هذا
+
+243
+00:28:45,230 --> 00:28:50,770
+كيف بنساوي فيه؟ بقول بسيطة جداً: تختار نقطة بتسميها
+
+244
+00:28:50,770 --> 00:28:51,290
+الـ base
+
+245
+00:29:08,380 --> 00:29:18,700
+يبقى ده smooth curve، المنحنى الأمثل، is scaled
+
+246
+00:29:24,330 --> 00:29:35,370
+is a scale، الرقم يعني، like a number، like a
+
+247
+00:29:35,370 --> 00:29:46,290
+number line، مثل خط الأعداد تماماً، as shown in the
+
+248
+00:29:46,290 --> 00:29:49,570
+figure، كما هو مبَرسَم
+
+249
+00:30:16,860 --> 00:30:25,040
+عند نقطة PRT، نقطة PRT، نقطة PRT، نقطة PRT، نقطة PRT
+
+250
+00:30:25,040 --> 00:30:31,910
+نقطة PRT، نقطة PRT، نقطة PRT، نقطة. هذا اثنين، هذا
+
+251
+00:30:31,910 --> 00:30:38,470
+ثلاثة، هذا أربعة، خمسة، ستة، وهكذا. هذا مشيت وين
+
+252
+00:30:38,470 --> 00:30:43,490
+عليه؟ مشيت على الشمال، بدأ يقول هنا سالب واحد،
+
+253
+00:30:43,490 --> 00:30:49,270
+سالب اثنين، وهكذا. يبقى ترقيم المنحنى في الفراغ زي
+
+254
+00:30:49,270 --> 00:30:55,040
+ترقيم خط الأعداد تماماً. طيب، في أنا كمان تعريف
+
+255
+00:30:55,040 --> 00:31:00,300
+آخر، بيقول: طبعاً أنتو شايفين أن أنا قادم هنا S of T
+
+256
+00:31:00,300 --> 00:31:04,240
+لكن إيش S of T؟ أنتو لسه مش عارفين، يبقى الآن بدي
+
+257
+00:31:04,240 --> 00:31:11,140
+أعطي تعريف للـ S of T. يبقى الـ definition the
+
+258
+00:31:11,140 --> 00:31:20,760
+directed distance، المسافة
+
+259
+00:31:20,760 --> 00:31:21,740
+المباشرة
+
+260
+00:31:24,400 --> 00:31:36,360
+along a smooth curve from the
+
+261
+00:31:36,360 --> 00:31:43,800
+base point
+
+262
+00:31:43,800 --> 00:31:57,560
+من النقطة البداية. الـ S of T بده يساوي تكامل من T
+
+263
+00:31:57,560 --> 00:32:09,000
+naught إلى T لـ V of Tau D Tau. ولو بدو يساوي
+
+264
+00:32:09,000 --> 00:32:17,540
+تكامل من T naught إلى T للجذر التربيعي لـ X prime
+
+265
+00:32:17,540 --> 00:32:27,150
+of Tau لكل تربيع، زائد y prime of tau لكل
+
+266
+00:32:27,150 --> 00:32:38,050
+تربيع، زائد z prime of tau لكل تربيع، كله d tau
+
+267
+00:32:59,370 --> 00:33:07,830
+هذه التسمية لها اسم آخر، يبقى also وكذلك اللي هو S
+
+268
+00:33:07,830 --> 00:33:14,270
+of T is called the arc length parameter
+
+269
+00:33:38,770 --> 00:33:54,710
+والذي يكون هو تزايداً في اتجاه in the direction of
+
+270
+00:33:54,710 --> 00:33:56,050
+increasing T
+
+271
+00:33:58,730 --> 00:34:03,110
+increasing T، جاية زايد
+
+272
+00:34:39,960 --> 00:34:45,320
+بنرجع للتعريف اللي احنا كاتبينه مرة ثانية. التعريف
+
+273
+00:34:45,320 --> 00:34:49,540
+بيقول: الـ directed distance along a smooth curve C
+
+274
+00:34:49,540 --> 00:34:53,740
+يبقى المنحنى هذا بيسميه المنحنى C. هذا يا بنات كأنه
+
+275
+00:34:53,740 --> 00:34:58,500
+المنحنى الأزرق اللي احنا رسمينه هنا تماماً. ما هو
+
+276
+00:34:58,500 --> 00:35:05,660
+from the base point T0، من عند النقطة T0، is كتالي:
+
+277
+00:35:05,660 --> 00:35:14,080
+بقول: S of T هو تكامل من T0 لغاية T للـ V of TAU D TAU
+
+278
+00:35:14,080 --> 00:35:18,780
+طبعاً السؤال اللي بيخطر على بالك: شو TAU هذا؟ مش هيك؟
+
+279
+00:35:18,780 --> 00:35:24,420
+بيقول لك: أبداً. مش احنا بنكامل بالنسبة إلى T؟ إذن لو خلّيت
+
+280
+00:35:24,420 --> 00:35:30,260
+من T نقطة إلى T، وكانت هذه الدالة بدلالة T
+
+281
+00:35:40,910 --> 00:35:45,750
+بعد ما كامل، بعوّض بحدود اللي فوق ناقص اللي تحت، بصير عندي
+
+282
+00:35:45,750 --> 00:35:51,330
+دالة في T. يبقى هذا تاو، أي رمز بدك إياه يعني. كتبتَه تاو
+
+283
+00:35:51,330 --> 00:35:56,030
+أنت، وكتبته epsilon، واحد يكتب له xi، وواحد يقول
+
+284
+00:35:56,030 --> 00:36:00,690
+له xi، وكده، حق الرمز اللي يعجبك. مع أنه مش مشكلة، لكن
+
+285
+00:36:00,690 --> 00:36:04,830
+اصطلح عليه أن أرمزه بالرمز تاو. أي رمز بدنا إياه يعني.
+
+286
+00:36:05,300 --> 00:36:10,240
+طيب، يبقى من هنا، طول الـ V of tau، وتشيل x prime
+
+287
+00:36:10,240 --> 00:36:13,540
+of tau تربيع، و y prime of tau تربيع، و z prime of
+
+288
+00:36:13,540 --> 00:36:17,020
+tau تربيع، كل التكوين تحت الـ d tau. وبعد ما كامل
+
+289
+00:36:17,020 --> 00:36:21,580
+بعض، وحدود التكوين تطلع دالة في T، main في T. أبقى
+
+290
+00:36:21,580 --> 00:36:27,920
+بستنى شوية، بستنى شو الفرق بين التعريف الأول و
+
+291
+00:36:27,920 --> 00:36:33,600
+التعريف الثاني؟ لأن أنا شايفهم زي بعض، ولا لا؟ طلع
+
+292
+00:36:33,600 --> 00:36:38,070
+هنا كويس. أنا قايل هنا الـ length، التكامل من a لـ b،
+
+293
+00:36:38,070 --> 00:36:44,130
+لرقمين، عددين تمام. هذا المشتق الأولى، والمشتق
+
+294
+00:36:44,130 --> 00:36:47,590
+الأولى للمركبة، وتربيعها. هذا
+
+295
+00:36:47,590 --> 00:36:52,310
+المشتق الأولى، والمشتق الأولى للمركبة، وتربيعها. طيب،
+
+296
+00:36:52,310 --> 00:36:56,530
+الفرق بينهم، بس هذا يكون من رقمين، هذا يكون من
+
+297
+00:36:56,530 --> 00:37:03,090
+الرقم إلى متغير T ليس إلا. إذن اللي فوق هو اللي تحت
+
+298
+00:37:03,090 --> 00:37:10,710
+شكله. طيب، في فارق بينهما؟ في فارق ما بين الـ two
+
+299
+00:37:10,710 --> 00:37:17,210
+definitions؟ طلعوا فيه كويس، واضح يعني. كلامك حد
+
+300
+00:37:17,210 --> 00:37:20,050
+تقدر تجيب له شو الفرق ما بين الاثنين؟
+
+301
+00:37:25,390 --> 00:37:27,370
+ماما؟ بصراحة، بصراحة، بصراحة، بصراحة، بصراحة، بصراحة
+
+302
+00:37:27,370 --> 00:37:28,230
+بصراحة، بصراحة، بصراحة، بصراحة، بصراحة، بصراحة، بصراحة
+
+303
+00:37:28,230 --> 00:37:30,630
+بصراحة، بصراحة، بصراحة، بصراحة، بصراحة، بصراحة، بصراحة
+
+304
+00:37:30,630 --> 00:37:31,210
+بصراحة، بصراحة، بصراحة، بصراحة، بصراحة، بصراحة، بصراحة
+
+305
+00:37:31,210 --> 00:37:31,530
+بصراحة، بصراحة، بصراحة، بصراحة، بصراحة، بصراحة، بصراحة
+
+306
+00:37:31,530 --> 00:37:34,610
+بصراحة، بصراحة، بصراحة، بصراحة، بصراحة، بصراحة، بصراحة
+
+307
+00:37:34,610 --> 00:37:40,230
+بصراحة، بصراحة، بصراحة. الأول من رقم، قيمة محددة،
+
+308
+00:37:40,230 --> 00:37:45,510
+يبقى أنا يا بنات في الحالة الأولى بجيب رقم، طول
+
+309
+00:37:45,510 --> 00:37:50,510
+القوس اللي عندنا على فترة محددة. هذا التعريف الأول،
+
+310
+00:37:50,510 --> 00:37:59,070
+النتيجة رقم. النتيجة الثانية دالة في T، لأنها بتقول
+
+311
+00:37:59,070 --> 00:38:05,350
+من T نقطة إلى T ثانية، بتطلع لي T، وهو المسافة
+
+312
+00:38:05,350 --> 00:38:10,870
+عند أي لحظة. يعني هو الطول عند أي لحظة. اختار اللحظة
+
+313
+00:38:10,870 --> 00:38:14,810
+اللي بدك إياها. يعني كأنه قاصر. التعريف الأول هو
+
+314
+00:38:14,810 --> 00:38:19,430
+حالة خاصة من مين؟ من التعريف الثاني. صحيح ولا لأ؟
+
+315
+00:38:19,430 --> 00:38:23,850
+يبقى الحالة الأولى هو طول محدد على فترة محددة. هذا
+
+316
+00:38:23,850 --> 00:38:31,230
+طول المنحنى عند أي لحظة بدك تجيب عليها.
+
+317
+00:38:31,550 --> 00:38:35,630
+هذا لو جيت كاملته، هيطلع بدلالة T. ولما أعوّض بحدود
+
+318
+00:38:35,630 --> 00:38:40,650
+التكامل، بصير بدلالة T. ومن هنا سمّيته الـ S of T. مين
+
+319
+00:38:40,650 --> 00:38:45,250
+الـ S of T؟ الـ directed distance along this smooth
+
+320
+00:38:45,250 --> 00:38:50,690
+curve، المسافة المباشرة على مين؟ على اللي هو
+
+321
+00:38:50,690 --> 00:38:54,670
+المنحنى اللي عندنا. لحظة كتبت لك هنا S of T، وقلنا
+
+322
+00:38:54,670 --> 00:38:58,010
+لك شو S of T؟ وقلنا مش عارفين، فراحنا عرفنا لك S of
+
+323
+00:38:58,010 --> 00:39:03,440
+T. S of T يا بسميه directed distance على كل المنحنى، يا
+
+324
+00:39:03,440 --> 00:39:09,180
+بسميه arc length parameter للمنحنى. SDC، يعني إيش
+
+325
+00:39:09,180 --> 00:39:13,180
+معناه parameter؟ يا بنت، بالعربي parameter
+
+326
+00:39:14,420 --> 00:39:19,780
+هذا الـ parameter، ليس قيمة معروفة، قيمة معروفة. هو وسيط
+
+327
+00:39:19,780 --> 00:39:23,720
+يعني واحد يدخل بين اثنين. لماذا؟ لأن المنحنى نكتبه
+
+328
+00:39:23,720 --> 00:39:28,520
+بدلالة X وY دائماً وأبداً. إذن دخلت T في المصطلح، فتكون T
+
+329
+00:39:28,520 --> 00:39:33,080
+دخلتها وسيط، وقلت X function في T، وY function في T،
+
+330
+00:39:33,080 --> 00:39:38,220
+اللي بسميه وسيط، أو parameter. إذن الـ S of T، يا بسميه
+
+331
+00:39:38,220 --> 00:39:41,960
+الـ directed distance، يا بسميه الـ arc length parameter
+
+332
+00:39:41,960 --> 00:39:49,320
+للمنحنى. arc length parameter، هذا يتزايد في اتجاه تزايد
+
+333
+00:39:49,320 --> 00:39:53,240
+تزايد
+
+334
+00:39:53,240 --> 00:39:54,800
+تزايد تزايد تزايد تزايد تزايد تزايد تزايد تزايد
+
+335
+00:39:54,800 --> 00:39:55,620
+تزايد تزايد تزايد تزايد تزايد تزايد تزايد تزايد
+
+336
+00:39:55,620 --> 00:39:56,660
+تزايد تزايد تزايد تزايد تزايد تزايد تزايد تزايد
+
+337
+00:39:56,660 --> 00:40:01,120
+تزايد تزايد تزايد تزايد تزايد تزايد تزايد تزايد
+
+338
+00:40:01,120 --> 00:40:05,000
+تزايد تزايد تزايد تزايد تزايد تزايد تزايد تزايد
+
+339
+00:40:05,000 --> 00:40:11,700
+تزا
+
+340
+00:40:16,650 --> 00:40:20,070
+طبعاً مش هيبقى عليك في الرسوم الكلام اللي احنا كتبناه قبل
+
+341
+00:40:20,070 --> 00:40:24,810
+المثال. لو جيت قلت يا بنات هذه النقطة هي الـ base
+
+342
+00:40:24,810 --> 00:40:31,870
+point، الـ base point، النقطة لـ P of T node، يعني عندي
+
+343
+00:40:31,870 --> 00:40:37,750
+الـ T node، كانت النقطة هذه، تمام؟ وراحنا أخذنا نقطة
+
+344
+00:40:37,750 --> 00:40:43,590
+ثانية، زي النقطة هذه، اللي عند أي لحظة. يبقى هذه الـ P
+
+345
+00:40:43,590 --> 00:40:49,370
+of T. كان عندنا هذا الـ vector الأساسي، وهذا صار الـ
+
+346
+00:40:49,370 --> 00:40:55,310
+vector الجديد، اللي هو R of T. لكن هذا الـ vector
+
+347
+00:40:55,310 --> 00:41:02,410
+اللي هو R of T، هذا الـ vector اللي هو R of T0. طب
+
+348
+00:41:02,410 --> 00:41:07,390
+وين الـ directed distance S of T؟ باجي بقول: الخط
+
+349
+00:41:07,390 --> 00:41:14,230
+الغامق اللي عندنا هذا، الخط الأسود هذا كله، هذا يا بنات
+
+350
+00:41:14,230 --> 00:41:18,950
+اللي هو الـ S of T، اللي هي المسافة المباشرة من
+
+351
+00:41:18,950 --> 00:41:23,410
+النقطة، لأن الـ base point، إلى أي نقطة تقع على
+
+352
+00:41:23,410 --> 00:41:28,830
+المنحنى. عرفنا وين الـ S of T؟ طيب، إذن النقطة هذه
+
+353
+00:41:28,830 --> 00:41:33,710
+معروفة عددياً، والنقطة هذه معروفة عددياً، صار اللي
+
+354
+00:41:33,710 --> 00:41:40,530
+هو طول المنحنى. طب، نأخذ مثال توضيح على ذلك، بيقول
+
+355
+00:42:15,820 --> 00:42:25,420
+Find the length of the given. Find the length of the
+
+356
+00:42:25,420 --> 00:42:29,960
+given portion
+
+357
+00:42:29,960 --> 00:42:37,600
+of
+
+358
+00:42:37,600 --> 00:42:38,280
+the curve
+
+359
+00:42:45,710 --> 00:42:52,950
+find the arc length parameter. find the arc length
+
+360
+00:42:52,950 --> 00:42:59,350
+parameter. parameter
+
+361
+00:42:59,350 --> 00:43:08,290
+اللي هو S of T. For T naught، بدنا نساوي كده، بدنا نساوي
+
+362
+00:43:08,290 --> 00:43:13,030
+نساوي solution
+
+363
+00:43:20,890 --> 00:43:27,710
+المطلوب الأول، قال لي: هات طول القوس اللي هو من المنحنى
+
+364
+00:43:27,710 --> 00:43:33,230
+على الفترة اللي احنا حددناها. من منحنى الـ R of T
+
+365
+00:43:33,230 --> 00:43:37,930
+في معادلاتنا هذه، بدي أعرف قداش طول القوس على
+
+366
+00:43:37,930 --> 00:43:43,190
+الفترة اللي بدها تتغير فيها T من سالب أربعة
+
+367
+00:43:43,190 --> 00:43:49,730
+لغاية الـ zero. بدي أعرف قداش طول المنحنى في هذه
+
+368
+00:43:49,730 --> 00:43:56,370
+الفترة. مش هنجيب طول المنحنى بقى، شو بدي أعمل؟ بدي
+
+369
+00:43:56,370 --> 00:44:03,290
+أجيب المشتقات الأولى لمعادلة المنحنى. طب كويس، الآن لو
+
+370
+00:44:03,290 --> 00:44:10,740
+جيت بدي أحسب الـ DX على DT، يبقى بدي مشتق الثاني، مش
+
+371
+00:44:10,740 --> 00:44:15,920
+هذا X، وهذا Y، وهذا Z، تمام؟ واحنا كتبنا DX على DT
+
+372
+00:44:15,920 --> 00:44:20,160
+لكل تربيع، زي الـ DY على DT لكل تربيع، زي الـ DZ على
+
+373
+00:44:20,160 --> 00:44:25,060
+DT لكل تربيع، كله تحت، من تحت الجذر. إذن أنا بدي
+
+374
+00:44:25,060 --> 00:44:33,580
+أجيب له DX على DT، يعني D على DT لمن؟ من X
+
+375
+00:44:39,850 --> 00:44:47,270
+إذن أنا مشتقتها كده. حاصل ضرب دالتين، مشتقة الدالة
+
+376
+00:44:47,270 --> 00:44:53,470
+الأولى في الدالة الثانية، زائد الدالة الأولى
+
+377
+00:44:56,740 --> 00:45:02,580
+في مشترك الـ cos، بسالب sin. أو إذا كنت تاخد E أس T
+
+378
+00:45:02,580 --> 00:45:10,680
+عامل مشترك، بيبقى الـ cos T ناقص sin T، بشكل يعني
+
+379
+00:45:10,680 --> 00:45:16,260
+بلزم تربيعها، خلينا نطبعها بالمرة. يبقى يا بنات، لو
+
+380
+00:45:16,260 --> 00:45:24,280
+جيت أخذت DX على DT لكل تربيع، يبقى E أس اثنين T
+
+381
+00:45:24,280 --> 00:45:33,630
+في cos تربيع T ناقص اثنين cos T sin T زائد
+
+382
+00:45:33,630 --> 00:45:41,530
+sin تربيع T. ويبقى يساوي E أس اثنين T في cos
+
+383
+00:45:41,530 --> 00:45:47,130
+تربيع زائد sin تربيع، يبقى واحد. يبقى واحد ناقص
+
+384
+00:45:47,130 --> 00:45:53,030
+اثنين cos T sin T. كيف؟
+
+385
+00:45:54,470 --> 00:45:59,410
+ماشي، بنفع أقول sin 2t، بنفع، صحيح. طيب، بنروح نجيب
+
+386
+00:45:59,410 --> 00:46:07,150
+اللي هو الـ dy على dt، يساوي. وإذا الـ y هكذا بنفس
+
+387
+00:46:07,150 --> 00:46:14,150
+الطريقة، بدي أشتقها: مشتقة الأول في sin t، زائد E أس
+
+388
+00:46:14,150 --> 00:46:20,590
+t في مين؟ في تفاضل الـ sin، اللي هو cos t، اللي هو بده
+
+389
+00:46:20,590 --> 00:46:30,460
+يساوي E أس اثنين t في sine of T زائد cosine of T. الربع
+
+390
+00:46:30,460 --> 00:46:37,880
+يبقى هذا بده يعطيكِ أن dy على dt كل تربيع
+
+445
+00:53:50,010 --> 00:54:03,970
+26 units along the curve from
+
+446
+00:54:03,970 --> 00:54:13,890
+the point من النقطة 0 و5 و0
+
+447
+00:54:18,580 --> 00:54:31,940
+direction of increasing arc
+
+448
+00:54:31,940 --> 00:54:32,360
+length
+
+449
+00:55:01,460 --> 00:55:07,660
+نرجع لسؤالنا مرة ثانية، بقول: هاتلي النقطة التي تقع
+
+450
+00:55:07,660 --> 00:55:14,780
+على المنحنى اللي قدامنا والتي تكون على بعد 26π من
+
+451
+00:55:14,780 --> 00:55:18,920
+وحدات الطول units along the curve، يعني من وحدات
+
+452
+00:55:18,920 --> 00:55:25,460
+طول تبع المنحنى من عند النقطة 0، 5، 0 في اتجاه
+
+453
+00:55:25,460 --> 00:55:32,080
+تزايد طول المنحنى. يعني لو جينا افترضنا أن أنا
+
+454
+00:55:32,080 --> 00:55:37,360
+عندي منحنى بالشكل اللي عندنا هذا، وجئت أخذت النقطة
+
+455
+00:55:37,360 --> 00:55:42,160
+اللي عندنا هذه، اللي كانت base point، الإحداثي تبع
+
+456
+00:55:42,160 --> 00:55:48,520
+هذه النقطة اللي هو صفر، وخمسة، وصفر. يعني x، و y، و
+
+457
+00:55:48,520 --> 00:55:55,760
+z تساوي صفر، ووصلنا إلى هذه النقطة وفي اتجاه تزايد
+
+458
+00:55:55,760 --> 00:56:01,360
+طول القوس arc length، في اتجاهه زي الـ R كله
+
+459
+00:56:01,360 --> 00:56:06,420
+يعني في اتجاهه زي الـ S of T، فكان هذا هو الـ
+
+460
+00:56:06,420 --> 00:56:14,200
+S of T، المسافة هذه حسبتها عملياً، طلعت 26
+
+461
+00:56:14,200 --> 00:56:19,600
+باي، يبقى الطول يا بنات على المنحنى هذا من عند
+
+462
+00:56:19,600 --> 00:56:25,100
+النقطة اللي عندنا هذه لغاية النقطة هذه، الخط الأزرق
+
+463
+00:56:25,100 --> 00:56:34,490
+هذا الخط...  مين؟ السكرتير العام
+
+464
+00:56:34,490 --> 00:56:39,270
+للأمم المتحدة. طب مين اللي كان جابله؟ كوفي عنان،
+
+465
+00:56:39,270 --> 00:56:42,890
+هم عينوا الخط الأزرق اللي جاي بيحط نخش وبيعملوا له
+
+466
+00:56:42,890 --> 00:56:47,670
+خط على حدود لبنان وفلسطين وبيشتغلوا على كيفهم
+
+467
+00:56:47,960 --> 00:56:52,440
+تمام؟ يبقى احنا الخط الأزرق تبعنا هذا طوله 26
+
+468
+00:56:52,440 --> 00:56:57,580
+باي، بدأ من النقطة صفر، خمسة، وصفر، وانتهى
+
+469
+00:56:57,580 --> 00:57:02,380
+في النقطة اللي عندنا هذه. ايش سؤالنا؟ سؤالنا بيقول لي
+
+470
+00:57:02,380 --> 00:57:08,560
+هاتلي النقطة اللي عندك هذه، بدك تعرفي قداش إحداثيات
+
+471
+00:57:08,560 --> 00:57:13,710
+النقطة هذه. والله كويس، النقطة هذه معلومة، والطول
+
+472
+00:57:13,710 --> 00:57:17,950
+معلوم، إذا نضل عليه. بس إحداثية النقطة دي بتبقى
+
+473
+00:57:17,950 --> 00:57:23,730
+قصتنا سادة، مظبوط؟ أيوة، يبقى بدنا نيجي نعرف قداش
+
+474
+00:57:23,730 --> 00:57:28,830
+إحداثيات النقطة اللي موجودة عندنا، بدنا نشوف يا
+
+475
+00:57:28,830 --> 00:57:32,990
+بنات الـ directed distance من النقطة هذه لغاية
+
+476
+00:57:32,990 --> 00:57:37,050
+النقطة هذه، عشان تعرف لي كده الـ t عند النقطة دي، و بدي أعرف كده الـ t عند النقطة التانية
+
+477
+00:57:37,050 --> 00:57:42,690
+وإذا عرفت التنتين، بصير إحداثيات النقطة هذه x، وهذا
+
+478
+00:57:42,690 --> 00:57:47,790
+y، وهذا z، بصير قصتنا سهلة، مظبوط؟ طيب، إذا بدي أعرف كده
+
+479
+00:57:47,790 --> 00:57:55,510
+إحداثيات النقطة اللي عندنا هذه، الإحداثيات موجودة
+
+480
+00:57:55,510 --> 00:57:59,950
+ككارتيزيان x، y، و z، لكن أنا بدي أجيب الـ parameter t
+
+481
+00:57:59,950 --> 00:58:04,430
+عند هذه النقطة كده، بده يساوي... تمام، شوفوا كيف بدنا
+
+482
+00:58:04,430 --> 00:58:08,770
+نحسب كده t نوت، عشان بعدين وين ما تقابلك تعرفي
+
+483
+00:58:08,770 --> 00:58:12,910
+تعرفيها. طلع يا بنتي، الحين أنا عندي مين؟ عندي اللي هو
+
+484
+00:58:19,860 --> 00:58:28,620
+الـ x ده تساوي كده؟ خمسة sin t، الإحداثي الأول اللي
+
+485
+00:58:28,620 --> 00:58:34,980
+بيسموها ده x، صح ولا لأ؟ إذا هذا بيساوي كده؟ بيساوي
+
+486
+00:58:34,980 --> 00:58:38,420
+صفر. مين
+
+487
+00:58:38,420 --> 00:58:43,880
+الزاوية اللي جيبها sin بيساوي صفر؟ يا صفر، يا باي، يا
+
+488
+00:58:43,880 --> 00:58:49,340
+اتنين باي. هي دي المشكلة. يبقى هنا هذا بدي يعطيني أن
+
+489
+00:58:49,340 --> 00:58:54,580
+t ياما صفر، ياما باي، ياما اتنين باي، وبعدها تبدأ
+
+490
+00:58:54,580 --> 00:59:01,980
+دورة جديدة. هم نمسك التانية. التانية y تساوي خمسة cos
+
+491
+00:59:01,980 --> 00:59:10,200
+t، وخمسة cos t تساوي كم؟ خمسة. هذا معناته أن cos t
+
+492
+00:59:10,200 --> 00:59:15,700
+تساوي كم؟ واحد. هذا معناته أن t تساوي كم؟ مين الزاوية
+
+493
+00:59:15,700 --> 00:59:21,720
+اللي cos بتاعها يساوي واحد؟ يبقى ياما صفر، ياما اتنين
+
+494
+00:59:21,720 --> 00:59:26,560
+باي. باي لأ، لأن sin بتاعها بيساوي سالب واحد. يبقى واحدة من
+
+495
+00:59:26,560 --> 00:59:34,300
+هدول. z تساوي قداش؟ 12 t، ويساوي صفر. هنا
+
+496
+00:59:34,300 --> 00:59:40,880
+ما فيش عندي إلا t تساوي قداش؟ الآن صار عندي تلات
+
+497
+00:59:40,880 --> 00:59:46,300
+نقاط، وأين القيمة المشتركة بين التلات نقاط؟ مش عندي
+
+498
+00:59:46,300 --> 00:59:52,800
+إلا صفر، صفر، صفر. يبقى هذا معناته أن t تساوي صفر.
+
+499
+00:59:52,800 --> 00:59:58,880
+إذا عندي نقطة صفر، وخمسة، وصفر، كانت t تساوي قداش؟
+
+500
+00:59:58,880 --> 01:00:04,020
+صفر، اللي هي t نوت. يبقى t نوت اللي عندنا هذا بدها
+
+501
+01:00:04,020 --> 01:00:09,940
+تساوي مين؟ بدها تساوي صفر. why؟ طب ما أعطيني قداش
+
+502
+01:00:09,940 --> 01:00:15,140
+طول الـ directed distance، بده أشوف t عند نهاية
+
+503
+01:00:15,140 --> 01:00:19,630
+المسافة اللي عندنا هناك، ده ايش كان؟ إذا عرفت بتبقى
+
+504
+01:00:19,630 --> 01:00:24,030
+انحلت مشكلتي. بدي أجيبها من وين؟ بدي أجيبها من الـ S
+
+505
+01:00:24,030 --> 01:00:28,550
+of t. طب الـ S of t بدي أجيبها من وين؟ من الدالة اللي
+
+506
+01:00:28,550 --> 01:00:32,070
+عندك، بدك تروح تشتقها، وتربع المركبات تحت الجذر
+
+507
+01:00:32,070 --> 01:00:38,790
+مظبوط ولا لأ؟ إذا بناء عليه بدي أروح أجيب من؟ أجيب
+
+508
+01:00:38,790 --> 01:00:42,970
+الـ v، والله بلاش نجيب الـ v في الأول
+
+509
+01:00:47,190 --> 01:00:53,150
+يبقى بنا نجيب الـ v بالأول. يبقى الـ v of t بدها تساوي
+
+510
+01:00:53,150 --> 01:01:01,130
+dr على dt، اللي هو مين؟ خمسة cos t في اتجاه i ناقص
+
+511
+01:01:01,130 --> 01:01:08,910
+خمسة sin t في اتجاه j زائد 12 في اتجاه k. بدي طول
+
+512
+01:01:08,910 --> 01:01:15,370
+الـ v، يبقى طول الـ v بدها تساوي الجذر التربيعي لمربع
+
+513
+01:01:15,370 --> 01:01:22,720
+المركبات: 25 cos تربيع t، 25 sin تربيع t،
+
+514
+01:01:22,720 --> 01:01:32,200
+زائد 144. يساوي square
+
+515
+01:01:32,200 --> 01:01:38,060
+root. لو أخدت 25 عامل مشترك يا بنات، بضل كده؟
+
+516
+01:01:38,060 --> 01:01:43,580
+sin تربيع زائد cos تربيع، اللي هو واحد، زائد 144،
+
+517
+01:01:43,580 --> 01:01:50,670
+و169 تحت
+
+518
+01:01:50,670 --> 01:01:56,850
+الجذر، جذر 13. بعدين بقول لك كويس، يبقى الـ S
+
+519
+01:01:56,850 --> 01:02:05,470
+of t يساوي تكامل من t نوت، اللي هي صفر، لعند
+
+520
+01:02:05,470 --> 01:02:10,670
+الـ t اللي أنا مش عارفها، لـ absolute value
+
+521
+01:02:10,670 --> 01:02:14,610
+اللي هي v of tau d tau
+
+522
+01:02:20,770 --> 01:02:28,670
+لـ 13 d tau. يبقى 13 tau من صفر إلى t، ويسمى
+
+523
+01:02:28,670 --> 01:02:36,430
+كده 13 t. طيب، تمام، 13 t عملياً كده شو سوى
+
+524
+01:02:36,430 --> 01:02:38,950
+يا بنات؟ 26 باي
+
+525
+01:02:51,430 --> 01:02:58,390
+يبقى عند هذه النقطة
+
+526
+01:02:58,390 --> 01:03:00,410
+يبقى t يساوي 2 باي
+
+527
+01:03:04,160 --> 01:03:11,400
+يبقى تكامل من صفر إلى t لـ v of tau d tau، يبقى تكامل من
+
+528
+01:03:11,400 --> 01:03:20,640
+صفر إلى t لـ 13 d tau. يبقى تكامل من صفر إلى t لـ v of
+
+529
+01:03:20,640 --> 01:03:25,120
+tau d tau، يبقى تكامل من صفر إلى t لـ 13 d tau، أو الـ
+
+530
+01:03:25,120 --> 01:03:30,360
+arc length parameter. يبقى الـ 13 t هو معطيني أصلاً
+
+531
+01:03:30,360 --> 01:03:38,040
+بقداش؟ بـ 26 باي. ومنها t بقداش؟ بـ 2 باي. إذا عند
+
+532
+01:03:38,040 --> 01:03:43,790
+النقطة الأخيرة هذه، إذا عرفنا t بقد ايه؟ بتنين
+
+533
+01:03:43,790 --> 01:03:48,050
+باي. إذا عرفنا t بتنين باي، إذا ما بقدر أعرف النقطة
+
+534
+01:03:48,050 --> 01:03:52,030
+اللي هو ايه؟ اللي بدنا إياها. لو طلب النقطة اللي عندها
+
+535
+01:03:52,030 --> 01:03:57,950
+يكون قطعنا على الـ arc length مسافة مقدارها 26
+
+536
+01:03:57,950 --> 01:04:04,130
+باي، بقول له: آه، النقطة اللي بدنا إياها، يبقى z
+
+537
+01:04:04,130 --> 01:04:04,850
+point
+
+538
+01:04:10,150 --> 01:04:14,890
+قداش الـ x أصلاً عندها؟ منا خمسة sin t، والـ t بقداش؟
+
+539
+01:04:14,890 --> 01:04:22,430
+اتنين باي. يبقى خمسة sin اتنين باي، والتانية خمسة
+
+540
+01:04:22,430 --> 01:04:30,490
+cos اتنين باي، والتالتة 12 في اتنين باي
+
+541
+01:04:30,490 --> 01:04:34,310
+بالشكل اللي عندنا هذا، واللي هي بدها تساوي sin
+
+542
+01:04:34,310 --> 01:04:38,150
+اتنين باي بقداش؟ صفر. cos اتنين باي
+
+544
+01:04:58,740 --> 01:05:05,660
+مثال رقم 2 من الكتاب، وفي كمان سؤال زيه في الكتاب
+
+545
+01:05:11,050 --> 01:05:14,210
+بتاع رقم 3 بيقولنا: find the length of the curve
+
+546
+01:05:14,210 --> 01:05:25,610
+find the length of the curve، قداش طول المنحنى من
+
+547
+01:05:25,610 --> 01:05:32,590
+المنحنى r of t، بده يساوي t تربيع في اتجاه الـ i
+
+548
+01:05:32,590 --> 01:05:41,260
+زائد 2t في اتجاه الـ j زائد ln t في اتجاه الـ k from
+
+549
+01:05:41,260 --> 01:05:44,720
+the
+
+550
+01:05:44,720 --> 01:05:53,180
+point من النقطة اللي هي واحد، واتنين، وصفر to
+
+551
+01:05:53,180 --> 01:06:03,980
+للنقطة e تربيع، واتنين e، وواحد، where حيث t أكبر
+
+552
+01:06:03,980 --> 01:06:04,560
+من الصفر
+
+553
+01:06:13,910 --> 01:06:20,310
+مرة تانية قال لي: هات لي قداش طول المنحنى المُعطى
+
+554
+01:06:20,310 --> 01:06:23,870
+اللي عندنا هذا، من النقطة اللي عندنا هذه لغاية
+
+555
+01:06:23,870 --> 01:06:29,430
+النقطة هذه، حيث t أكبر من الصفر. بقول له: كويس، احنا
+
+556
+01:06:29,430 --> 01:06:35,230
+مش هنجيب طول المنحنى، بدي قيمتين عدديتين، بدي t
+
+557
+01:06:35,230 --> 01:06:40,170
+تساوي كده، و t تساوي كده، مش هيعطيني إحداثيات نقطة
+
+558
+01:06:43,050 --> 01:06:49,270
+أيوة، بس ايش بالمجلوب إحنا كيف آه؟ أنت عندك هنا دول
+
+559
+01:06:49,270 --> 01:06:56,150
+إحداثيات نقطة، دول x، و y، و z، وأنت عندك هاي x، وهاي y،
+
+560
+01:06:56,150 --> 01:07:01,750
+وهاي z، مظبوط؟ إذا بدك تشوف إن كل نقطة من هذه
+
+561
+01:07:01,750 --> 01:07:10,550
+النقاط، فبجي بقول له: الـ x، والـ y، والـ z، x، y، z
+
+562
+01:07:10,550 --> 01:07:20,980
+اللي عبارة عن مين؟ t تربيع، واتنين t، و ln t. يبقى
+
+563
+01:07:20,980 --> 01:07:25,360
+بالنسبة للنقطة الأولى بدي أعرف قداش مقدار t
+
+564
+01:07:25,360 --> 01:07:35,100
+تباجي بقول له: عند النقطة الأولى (1، 2، 0)
+
+565
+01:07:35,100 --> 01:07:35,380
+زين
+
+566
+01:07:40,070 --> 01:07:47,250
+الـ x اللي هي t تربيع تساوي كده؟ تساوي واحد، اللي
+
+567
+01:07:47,250 --> 01:07:54,010
+بعدها الـ y اللي هي 2t تساوي اتنين، اللي
+
+568
+01:07:54,010 --> 01:08:02,810
+بعدها ln t تساوي صفر. هذه قيم بتعطيك أن t زيادة أو
+
+569
+01:08:02,810 --> 01:08:07,690
+ناقص واحد. بس هو قال لي t أكبر من الصفر، يبقى يا
+
+570
+01:08:07,690 --> 01:08:11,570
+سالم واحد، صف على شجرة. يبقى هذا بدي يعطيني أن t
+
+571
+01:08:11,570 --> 01:08:17,690
+تساوي واحد. هذا بدي يعطيك أن t تساوي واحد. طيب مين
+
+572
+01:08:17,690 --> 01:08:22,190
+اللي ln بتاعها يساوي الصفر؟ واحد، إن واحد يساوي صفر، هذا
+
+573
+01:08:22,190 --> 01:08:29,510
+بدي يعطيك أن t تساوي واحد. إذا من هذول التلاتة بقول
+
+574
+01:08:29,510 --> 01:08:38,570
+t تساوي واحد. في النقطة الآن الثانية عند النقطة
+
+575
+01:08:38,570 --> 01:08:47,170
+الثانية e تربيع، واتنين e، وواحد. وهذا t تربيع
+
+576
+01:08:47,170 --> 01:08:55,670
+بده يساوي e تربيع، و 2t بده يساوي 2e، و ln
+
+577
+01:08:55,670 --> 01:09:01,470
+t يساوي كده؟ يساوي واحد. هذه ايش بتعطيكي لما تأخدي
+
+578
+01:09:01,470 --> 01:09:07,650
+جذر تربيعي للطرفين؟ t يساوي e. وهذا
+
+579
+01:09:07,650 --> 01:09:14,210
+بتعطيكي t يساوي e. وهذا بتعطيكي أن t تساوي الـ
+
+580
+01:09:14,210 --> 01:09:21,350
+e. أخذوا في نفس القيمة، يبقى هنا t تساوي من e من
+
+581
+01:09:21,350 --> 01:09:23,090
+اللي أكبر؟ الواحد، والله الـ e
+
+582
+01:09:25,910 --> 01:09:34,850
+إذا بدنا نروح نجيب الـ v of t، يبقى باجي بقول v of t
+
+583
+01:09:34,850 --> 01:09:44,970
+يساوي: يبقى 2t في اتجاه i زائد 2 في اتجاه j زائد 1
+
+584
+01:09:44,970 --> 01:09:48,950
+على t في اتجاه k.
+
+585
+01:10:04,740 --> 01:10:11,000
+السؤال قال لي هات لمن؟ هات لـ l للمنحنى هذا، بروح
+
+586
+01:10:11,000 --> 01:10:19,860
+بقول: l، l بدي أساوي تكامل من واحد لغاية الـ e للجذر
+
+587
+01:10:19,860 --> 01:10:25,820
+التربيعي لمربع المركبات اللي عندي، ايش بيصير؟ أربعة
+
+588
+01:10:25,820 --> 01:10:34,620
+t تربيع زائد أربعة زائد واحد على t تربيع dt. يبقى
+
+589
+01:10:34,620 --> 01:10:40,040
+هذا الكلام يساوي تكامل من واحد لغاية الـ e
+
+590
+01:10:40,040 --> 01:10:46,060
+للسquare root، بعد توحيد المقامات كله على t تربيع
+
+591
+01:10:46,060 --> 01:10:53,860
+بيصير أربعة t أس أربعة زائد أربعة t تربيع زائد واحد
+
+592
+01:10:53,860 --> 01:11:01,560
+كله dt. هذا الكلام يساوي تكامل من واحد إلى e للجذر
+
+593
+01:11:01,560 --> 01:11:12,020
+التربيعي. البسط مربع كامل يا بنات؟ البسط مربع كامل؟ مش
+
+594
+01:11:12,020 --> 01:11:17,200
+مربع كامل؟ طب والله شوفوا قداش: 2t تربيع
+
+595
+01:11:17,200 --> 01:11:21,880
+زائد واحد الكل تربيع. فكّي الجذر ده، شوفوا هو اللي
+
+596
+01:11:21,880 --> 01:11:22,300
+فوق
+
+597
+01:11:25,070 --> 01:11:30,530
+يبقى مربع كامل ولا لأ؟ جاهز وخالص. طيب، هذه كمية
+
+598
+01:11:30,530 --> 01:11:36,350
+مربعة، وكمية مربعة تحت الجذر من واحد إلى e، أعداد
+
+599
+01:11:36,350 --> 01:11:43,450
+موجبة، إذا كله بيطلع بقيمة موجبة. يبقى 2t تربيع زائد
+
+600
+01:11:43,450 --> 01:11:51,460
+واحد على t dt، يعني تكامل من اللي هو الواحد لغاية الـ e
+
+601
+01:11:51,460 --> 01:12:01,640
+لـ 2t زائد واحد على t dt. التكامل يبقى t تربيع على
+
+602
+01:12:01,640 --> 01:12:07,460
+اتنين زائد ln الـ t أو
+
+603
+01:12:07,460 --> 01:12:13,160
+absolute value لـ t، وكل هذا الكلام من واحد لغاية
+
+604
+01:12:13,160 --> 01:12:17,100
+الـ e، يبقى e تربيع
+
+605
+01:12:28,430 --> 01:12:36,530
+يبقى الجواب قدر e تربيع ناقص واحد. إذا طول المنحنى يساوي e تربيع ناقص واحد
+
+606
+01:12:36,530 --> 01:12:40,330
+الآن للمقطع الثاني من هذا الـ section، اللي هو
+
+607
+01:12:40,330 --> 01:12:44,570
+الـ speed، مقدار السرعة on اسمه
+
+608
+01:12:44,570 --> 01:12:51,890
+speed
+
+609
+01:13:27,290 --> 01:13:40,890
+بالنسبة لـ S of t، بدي
+
+610
+01:13:40,890 --> 01:13:51
+
+667
+01:20:17,800 --> 01:20:19,260
+تعريف Definition
+
+668
+01:20:26,480 --> 01:20:35,720
+unit tangent vector of
+
+669
+01:20:35,720 --> 01:20:42,900
+a smooth curve R
+
+670
+01:20:42,900 --> 01:20:47,220
+of T is
+
+671
+01:20:47,220 --> 01:20:59,650
+T  ده تساوي dR على ds واللي هي بالأساس عملياً الـ V
+
+672
+01:20:59,650 --> 01:21:01,770
+على طول الـ V
+
+673
+01:21:51,320 --> 01:21:57,040
+بنرجع للكلام اللي كتبناه مرة ثانية، نحاول نستنتج
+
+674
+01:21:57,040 --> 01:22:02,360
+متجه طوله الواحدة، اللي هو واحد صحيح، وبالتالي هيكون
+
+675
+01:22:02,360 --> 01:22:08,340
+unit vector، وبنبيّن أن هذا المتجه هو المتجه المماس
+
+676
+01:22:08,340 --> 01:22:12,300
+للمنحنى، هبقى أقول مئة unit tangent vector
+
+677
+01:22:12,300 --> 01:22:18,480
+هديله الرقم ٦، أحنا بنعرف أن سرعة V هي dR على dt لو
+
+678
+01:22:18,480 --> 01:22:21,180
+أعطينا vector-valued function، اشتقيناها، بيعطينا
+
+679
+01:22:21,180 --> 01:22:25,640
+مين السرعة، واشتقيناها مرة ثانية بيعطينا مين؟ العجلة، الـ
+
+680
+01:22:25,640 --> 01:22:29,480
+acceleration، خلّينا مع السرعة اللي هي dR على dt،
+
+681
+01:22:29,480 --> 01:22:35,480
+اتجاه الـ V دائماً وأبداً هو اتجاه مماس للمنحنى،
+
+682
+01:22:35,480 --> 01:22:40,590
+يعني لو كان عندي منحنى بالشكل اللي عندنا هذا، وقلنا
+
+683
+01:22:40,590 --> 01:22:47,370
+هذا محور X، وهذا محور Y، وهذا محور Z، وروحنا رسمنا
+
+684
+01:22:47,370 --> 01:22:54,770
+معادلة المنحنى، أو رسمنا رسمة المنحنى عند أي لحظة،
+
+685
+01:22:54,770 --> 01:23:00,670
+فكان المنحنى بهذا الشكل على سبيل المثال، يبقى هذا
+
+686
+01:23:00,670 --> 01:23:05,270
+المنحنى عند أي لحظة، وروحنا أخذنا أي نقطة موجودة
+
+687
+01:23:05,270 --> 01:23:10,880
+عليه، ولتكن هذه النقطة مثلاً، النقطة اللي عندها، يبقى
+
+688
+01:23:10,880 --> 01:23:18,900
+هذا يمثل مين؟  r(t)، المتجه الموضعي عند أي لحظة ابتداءً
+
+689
+01:23:18,900 --> 01:23:25,600
+من مين؟ من نقطة الأصل، اللي هي z، اتجاه الحركة هو
+
+690
+01:23:25,600 --> 01:23:32,080
+عبارة عن اتجاه السرعة، وهذا هو اتجاه مماس للمنحنى
+
+691
+01:23:32,080 --> 01:23:37,360
+عند النقطة، اتجاه المماس يكون بالشكل اللي عندنا هذا،
+
+692
+01:23:37,360 --> 01:23:44,160
+هذا الشكل، يبقى هذا المماس اللي هو اتجاه مين؟ اتجاه
+
+693
+01:23:44,160 --> 01:23:49,040
+السرعة طبعاً، طيب، اتجاه السرعة اللي أخذناه ليه
+
+694
+01:23:49,040 --> 01:23:56,920
+متجه طول الوحدة، هذا هسميه متجه T، اللي هو V على طول
+
+695
+01:23:56,920 --> 01:24:01,780
+الـ V هذا،
+
+696
+01:24:01,780 --> 01:24:05,920
+بيكون، فاللي هي اللي هنا، بيقول الفلوس، الـ dR على
+
+697
+01:24:05,920 --> 01:24:12,840
+dt، طب، نعرف طوله،  مربع المركبات تحت الجذر،  T، قسمنا
+
+698
+01:24:12,840 --> 01:24:18,620
+الـ V على طول الـ V، الأهم أن أثبت أن هذا فعلاً هو الـ
+
+699
+01:24:18,620 --> 01:24:22,680
+tangent vector، والطول بتاعه يساوي الواحد الصحيح.
+
+700
+01:24:22,680 --> 01:24:28,820
+أظن ds على dt، كتبناها قبل قليل هنا، كانت دالة موجبة،
+
+701
+01:24:28,820 --> 01:24:35,260
+مشتقتها أكبر من الـ zero، طب لو قلبناها، بتبقى أكبر
+
+702
+01:24:35,260 --> 01:24:38,160
+من الـ zero، ولا بيصير أقل من الـ zero، يعني لو
+
+703
+01:24:38,160 --> 01:24:42,640
+قلت لك خمسة مثلاً، ممكنها تبتدي، بيصير خمسة أكبر من الـ
+
+704
+01:24:42,640 --> 01:24:46,800
+zero، ولا لا، إذا المقلوب هو أكبر من الـ zero، لكن الـ
+
+705
+01:24:46,800 --> 01:24:53,220
+dt على ds هذه هي واحد على ds على dt، مين الـ ds على
+
+706
+01:24:53,220 --> 01:24:59,500
+dt؟ طول الـ V، إذا بقدر أقول واحد على طول الـ V، بيهدم مين؟
+
+707
+01:24:59,500 --> 01:25:05,240
+دي، dR على ds، بقول لك لو روحنا اشتقينا R بالنسبة
+
+708
+01:25:05,240 --> 01:25:11,100
+لـ S، يعني اشتقينا R بالنسبة لبارامتر S، ما هو
+
+709
+01:25:11,100 --> 01:25:15,710
+بقدرش أنا أجيب البارامتر S إلا إذا كان عندي main
+
+710
+01:25:15,710 --> 01:25:22,090
+r(t)، يعني الـ s(t) بتبدأ تعتمد عملياً على r(t)،
+
+711
+01:25:22,090 --> 01:25:27,250
+يعني لو افترضنا الـ R بالنسبة للـ S، نفس الكلام،  بتفضل
+
+712
+01:25:27,250 --> 01:25:32,110
+الـ R بالنسبة للـ T،  بتفضل الـ T بالنسبة للـ S، لأن الـ R
+
+713
+01:25:32,110 --> 01:25:36,650
+function of T، والـ S كذلك function of T، يعني بقدر
+
+714
+01:25:36,650 --> 01:25:41,330
+أدخل الوسيط أو الـ parameter T ما بينهم، الـ dR
+
+715
+01:25:41,330 --> 01:25:46,450
+على dt هي مين؟ الـ V، إذا بدي أشيلها وأضع مكانها
+
+716
+01:25:46,450 --> 01:25:52,590
+الـ V، الـ dt على dR، واحد على طول الـ V، إذا هذا
+
+717
+01:25:52,590 --> 01:25:56,690
+بيصير الـ V على طول الـ V، اللي هو مين؟ الـ unit
+
+718
+01:25:56,690 --> 01:26:01,350
+tangent vector، بيكون هذا هو الـ unit tangent لو كان طوله
+
+719
+01:26:01,350 --> 01:26:06,910
+واحد صحيح، إذا بدي أجيب طول الـ dR على ds، يبقى هو
+
+720
+01:26:06,910 --> 01:26:11,410
+طول الـ V اللي طالع عندنا، على طول الـ V، طول الـ V
+
+721
+01:26:11,410 --> 01:26:15,710
+على طول الـ V، لو طلع واحد صحيح، يبقى فعلاً هذا عبارة
+
+722
+01:26:15,710 --> 01:26:20,090
+عن unit vector اللي حسّميته طبقاً لهذا الـ definition،
+
+723
+01:26:20,090 --> 01:26:24,770
+يبقى هو الـ unit tangent vector، لو أجاني السؤال وقال
+
+724
+01:26:24,770 --> 01:26:29,550
+لي: هات لي الـ unit tangent vector للمنحنى الفلاني، بشتقّ
+
+725
+01:26:29,550 --> 01:26:33,530
+بيكون هذا السرعة، بجيب طوله، بيكون هذا الـ speed،
+
+726
+01:26:33,530 --> 01:26:37,090
+بقسم الاثنين على بعض، بيكون هذا الـ unit tangent
+
+727
+01:26:37,090 --> 01:26:41,990
+vector،  تقول هذا الكلام؟ الكلام اللي أنا بقوله هعطي
+
+728
+01:26:41,990 --> 01:26:47,910
+عليه مثال، إذن بدنا نروح للمثال الأخير في هذا الـ
+
+729
+01:26:47,910 --> 01:26:51,530
+section، يبقى
+
+730
+01:26:51,530 --> 01:26:52,090
+example
+
+731
+01:27:03,690 --> 01:27:13,570
+sin t زائد cos t، كله في اتجاه i، زائد t
+
+732
+01:27:13,570 --> 01:27:21,530
+cos t ناقص sin t، كله في اتجاه j، و t
+
+733
+01:27:21,530 --> 01:27:30,130
+greater than zero، المطلوب الأول دي بقى is find the
+
+734
+01:27:30,130 --> 01:27:42,460
+speed، المطلوب الثاني find the unit tangent
+
+735
+01:27:42,460 --> 01:27:48,260
+vector of
+
+736
+01:27:48,260 --> 01:27:57,040
+the curve، المطلوب الثالث find the length of
+
+737
+01:27:57,040 --> 01:28:06,530
+the curve،  أوجد الطول أو المسافة، كده، شوفوا،
+
+738
+01:28:06,530 --> 01:28:14,450
+المنحنى for على الفترة التي t أكبر من أو تساوي
+
+739
+01:28:14,450 --> 01:28:22,170
+جذر ٢، وأقل من أو يساوي ٢، كده،
+
+740
+01:28:22,170 --> 01:28:30,650
+طيب،
+
+741
+01:28:30,650 --> 01:28:38,060
+أرفع هذا السؤال مرة ثانية، معطيني
+
+742
+01:28:39,180 --> 01:28:44,940
+position vector، متجه موضعي، لدالة ما، اللي هو main r(
+
+743
+01:28:44,940 --> 01:28:49,840
+t) تساوي t sin t زائد cos t في اتجاه i، زائد t cos t
+
+744
+01:28:49,840 --> 01:28:55,160
+ناقص sin t في اتجاه مين؟ في اتجاه الـ j، قال لي: أوجد
+
+745
+01:28:55,160 --> 01:29:00,320
+الـ speed، إذا مشان أجيب الـ speed، بتروح أشتق، مظبوط؟
+
+746
+01:29:00,320 --> 01:29:04,940
+طبعاً ما عنديش k، الـ k كان معاملها يساوي zero،
+
+747
+01:29:04,940 --> 01:29:11,890
+تمام، هبقى أقول له كويس، هذا يعتبر من الـ x، وهذا يعتبر
+
+748
+01:29:11,890 --> 01:29:20,490
+من الـ y، إذا بدي أجيب له الـ dx على dt،  مشتقة هذه،
+
+749
+01:29:20,490 --> 01:29:26,110
+يبقى الجزء الأول، مشتقة حاصل ضرب دالتين،  بقاعدة، بتقول له
+
+750
+01:29:26,110 --> 01:29:38,890
+sin t زي t في cos t ناقص sin t، يبقى بدها تساوي t
+
+751
+01:29:38,890 --> 01:29:49,450
+في cos t، هذه، هتروح معاها، طيب، بدي أجيب له dy على dt،
+
+752
+01:30:13,280 --> 01:30:19,680
+يبقى السرعة v as a function of t بدها تساوي اللي
+
+753
+01:30:19,680 --> 01:30:32,100
+هو t cos t في اتجاه i، ناقص t sin t في اتجاه j، فبجيب
+
+754
+01:30:32,100 --> 01:30:42,030
+أقول له ليه speed، اللي بده يساوي، طول الـ v، طول الـ v اللي
+
+755
+01:30:42,030 --> 01:30:48,370
+هو الجذر التربيعي لمربع المركبات، t تربيع cos تربيع
+
+756
+01:30:48,370 --> 01:30:57,650
+t زائد t تربيع sin تربيع t، يساوي، Descant
+
+757
+01:30:57,650 --> 01:31:02,570
+root لـ t تربيع عامل مشترك، طلع، sin تربيع زائد cos
+
+758
+01:31:02,570 --> 01:31:09,400
+تربيع، اللي هو بواحد، تحت الجذر، بـ t، يبقى مقدار السرعة
+
+759
+01:31:09,400 --> 01:31:15,240
+عند أي لحظة بدي إياها، هي عبارة عن مين؟ عبارة عن t،
+
+760
+01:31:15,240 --> 01:31:21,340
+إذا خلصنا من المطلب الأول، المطلب الثاني قال لي هذا
+
+761
+01:31:21,340 --> 01:31:28,580
+الـ unit tangent vector، بقول: بلغة بسيطة، اليونت هذا،
+
+762
+01:31:28,580 --> 01:31:33,180
+نمرأ a الأول؟  مضاد إلى نمرأ b، اليونت
+
+763
+01:31:36,000 --> 01:31:47,300
+tangent vector، اللي هو v، بتكون t، t بده يساوي
+
+764
+01:31:47,300 --> 01:31:54,340
+الـ v على طول الـ v، هو يساوي الـ v، المتجه اللي عندنا
+
+765
+01:31:54,340 --> 01:32:02,280
+اللي هو t cos t في اتجاه i، ناقص t sin t في
+
+766
+01:32:02,280 --> 01:32:09,620
+اتجاه j، كله مقسوم على مين؟ على t، إذا أصبح t
+
+767
+01:32:09,620 --> 01:32:15,580
+بده يساوي cos t في اتجاه i، ناقص sin t في
+
+768
+01:32:15,580 --> 01:32:22,080
+اتجاه مين؟ في اتجاه j، طيب، السؤال هو: هل هذا
+
+769
+01:32:22,080 --> 01:32:23,580
+فعلاً unit vector؟
+
+770
+01:32:27,490 --> 01:32:31,210
+بطلع واحد، فعلاً unit vector، بربع المركبات
+
+771
+01:32:31,210 --> 01:32:33,870
+اللي عندك، cos تربيع زائد sin تربيع، اللي بتطلع
+
+772
+01:32:33,870 --> 01:32:38,310
+مجموعة واحد، يعني فعلاً هذا هو مين؟ هو الـ unit vector،
+
+773
+01:32:38,310 --> 01:32:43,330
+اللي طلع، طب، المطلوب الثالث،  قال لي: هات لي الـ length تبع
+
+774
+01:32:43,330 --> 01:32:49,070
+الـ curve على الفترة من جذر ٢ لغاية ٢،
+
+775
+01:32:49,070 --> 01:32:55,870
+إذا، بأجي أقول له: بدنا الـ length اللي بيساوي تكامل من
+
+776
+01:32:55,870 --> 01:33:03,370
+وين لوين؟ من جذر ٢ لغاية ٢، لمين؟ لطول الـ v،
+
+777
+01:33:03,370 --> 01:33:10,990
+كداش طول الـ v؟ t، هاي، بروح أحسب من جديد، يبقى خلاص،
+
+778
+01:33:10,990 --> 01:33:16,870
+بشيل الجذر كله هذا، وحسبناها وخلصنا، يبقى بقول له
+
+779
+01:33:16,870 --> 01:33:24,150
+فقط t dt، من وين جبناها؟ من طول الـ v هاي اللي عندك،
+
+780
+01:33:25,080 --> 01:33:27,940
+يبقى الموجود خلاص، في اشتقاق وما بضيع وقته، وحاسب من
+
+781
+01:33:27,940 --> 01:33:35,220
+الأول، جديد، فإيه، جاهز، إذا حطينا، يبقى هذا قدر نص t
+
+782
+01:33:35,220 --> 01:33:43,060
+تربيع، من جذر ٢ لغاية ٢، ويساوي النص في ٤
+
+783
+01:33:43,060 --> 01:33:50,470
+ناقص ٢، نص في ٢ يساوي واحد، إذا طول هذا الجزء
+
+784
+01:33:50,470 --> 01:33:55,850
+من المنحنى يساوي واحد صحيح، طيب، نجي للـ exercises،
+
+785
+01:33:55,850 --> 01:34:06,590
+ثلاثة عشر، ثلاثة، طيب،
+
+786
+01:34:06,590 --> 01:34:10,830
+نجي للـ exercises ثلاثة عشر،
+
+787
+01:34:10,830 --> 01:34:18,330
+ثلاثة، المسائل من واحد لخمسة عشر، من واحد،
+
+788
+01:34:27,680 --> 01:34:31,360
+ببدأ أسأل السؤال الثاني، يوم الاثنين افتتحنا
+
+789
+01:34:31,360 --> 01:34:35,260
+discussion، يعني جت لكم المادة اسمها كم section،
+
+790
+01:34:35,260 --> 01:34:40,520
+غطيتوا فيها أربعة، كويس، يعني أربعة كل section معقول،
+
+791
+01:34:40,520 --> 01:34:46,900
+كويس،  تعويضية، ماشي، ممتاز، يعني اليوم نخلص الـ
+
+792
+01:34:46,900 --> 01:34:47,700
+chapter، معناته،
+
+793
+01:34:52,120 --> 01:34:56,900
+كيف؟ يعني يبقى تقولوا لي الامتحان داخله chapter
+
+794
+01:34:56,900 --> 01:35:01,460
+١٣ كله، يعني كمان المحاضرة المُشرحة المرة القادمة
+
+795
+01:35:01,460 --> 01:35:06,220
+اللي هو section ١٣، أربعة داخله في الامتحان، فلازم
+
+796
+01:35:06,220 --> 01:35:11,680
+تغطوا الـ chapter ١٣ كله قبل الامتحان، ماشي؟ كويس،
+
+797
+01:35:11,680 --> 01:35:16,220
+سأعطيكم العافية، حتى هنا اليوم يكفي، والمرة القادمة إن
+
+798
+01:35:16,220 --> 01:35:16,800
+شاء الله
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/dSJIcUHEpZw_raw.json b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/dSJIcUHEpZw_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..a873ea99fd9e11a2025145f97b19378b1b63ffab
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/dSJIcUHEpZw_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 268, "start": 0.0, "end": 2.68, "text": "موسيقى", "tokens": [2304, 41779, 1829, 4587, 7578], "avg_logprob": -0.3717447817325592, "compression_ratio": 0.5714285714285714, "no_speech_prob": 0.0029811859130859375, "words": [{"start": 0.0, "end": 2.68, "word": "موسيقى", "probability": 0.7352294921875}], "temperature": 1.0}, {"id": 2, "seek": 5329, "start": 25.33, "end": 53.29, "text": "الان بالمعاصلة اللى هو شبكة 13 المرة الماضية اخدنا اول section و اليوم بناخد تانية section المرة اللى فات كان vector valued function limit لهذا ال vector ال derivative لهذا ال vector ال continuity لهذا ال vector وما يتعلق بها اللى دلوقت بدنا نروح لل integrals لهذه ال vector valued functions فبجي بقول integrals of vector functions", "tokens": [6027, 7649, 20666, 2304, 3615, 33546, 37977, 13672, 7578, 31439, 13412, 3555, 4117, 3660, 3705, 9673, 25720, 9673, 46958, 10632, 1975, 9778, 3215, 8315, 1975, 12610, 3541, 4032, 45595, 20498, 44945, 47283, 3215, 6055, 7649, 10632, 3541, 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592.06, "end": 616.66, "text": "كله في اتجاه ال J ناقص اللي هو T في ال sign T في اتجاه مين في اتجاه ال K بالنسبة الى D هذا الكلام يساوي نكمل السكة في قداش من Calculus B قداش؟ ايوة علي صوت قليل اسمع", "tokens": [28820, 3224, 8978, 1975, 2655, 7435, 40294, 2423, 508, 8717, 995, 4587, 9381, 13672, 1829, 31439, 314, 8978, 2423, 1465, 314, 8978, 1975, 2655, 7435, 40294, 3714, 9957, 8978, 1975, 2655, 7435, 40294, 2423, 591, 20666, 1863, 35457, 3660, 2423, 7578, 413, 23758, 2423, 28820, 10943, 7251, 3794, 995, 45865, 8717, 24793, 1211, 21136, 4117, 3660, 8978, 12174, 3215, 33599, 9154, 3511, 36002, 363, 12174, 3215, 33599, 22807, 1975, 1829, 2407, 3660, 6225, 20292, 20328, 35473, 12174, 20292, 1211, 24525, 2304, 3615], "avg_logprob": -0.2801204797733261, "compression_ratio": 1.5930232558139534, "no_speech_prob": 0.0, "words": [{"start": 592.06, "end": 592.54, "word": "كله", "probability": 0.669921875}, {"start": 592.54, "end": 592.64, "word": " في", "probability": 0.841796875}, {"start": 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تكمن", "probability": 0.90283203125}, {"start": 3796.04, "end": 3796.04, "word": " من", "probability": 0.962890625}, {"start": 3796.04, "end": 3797.0, "word": " 0", "probability": 0.7890625}, {"start": 3797.0, "end": 3797.82, "word": " إلى", "probability": 0.97802734375}, {"start": 3797.82, "end": 3798.2, "word": " T", "probability": 0.9931640625}, {"start": 3798.2, "end": 3798.7, "word": " لـ", "probability": 0.82177734375}, {"start": 3798.7, "end": 3800.64, "word": " V", "probability": 0.14794921875}, {"start": 3800.64, "end": 3800.64, "word": " of", "probability": 0.93115234375}, {"start": 3800.64, "end": 3801.3, "word": " Tau", "probability": 0.9736328125}, {"start": 3801.3, "end": 3801.3, "word": " D", "probability": 0.98876953125}, {"start": 3801.3, "end": 3801.6, "word": " Tau", "probability": 0.9228515625}, {"start": 3801.6, "end": 3802.28, "word": " يبقى", "probability": 0.8941650390625}, {"start": 3802.28, "end": 3802.94, "word": " تكمن", "probability": 0.9466145833333334}, 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481926, "start": 4796.82, "end": 4819.26, "text": "على طول ال V و يسوى طول ال V على طول ال V و يسوى واحد صحيح لك هذا سوف يعطيك ان DR على DS is a unit vector نعطيه تعريف Definition", "tokens": [3615, 23942, 23032, 12610, 2423, 691, 4032, 7251, 3794, 2407, 7578, 23032, 12610, 2423, 691, 15844, 23032, 12610, 2423, 691, 4032, 7251, 3794, 2407, 7578, 36764, 24401, 20328, 5016, 1829, 5016, 5296, 4117, 23758, 8608, 38688, 37495, 9566, 1829, 4117, 16472, 12118, 15844, 15816, 307, 257, 4985, 8062, 8717, 3615, 9566, 1829, 3224, 37279, 16572, 5172, 46245, 849], "avg_logprob": -0.3577860280618829, "compression_ratio": 1.4885496183206106, "no_speech_prob": 3.5762786865234375e-07, "words": [{"start": 4796.82, "end": 4797.42, "word": "على", "probability": 0.51837158203125}, {"start": 4797.42, "end": 4797.88, "word": " طول", "probability": 0.993896484375}, {"start": 4797.88, "end": 4798.12, "word": " ال", "probability": 0.7275390625}, {"start": 4798.12, "end": 4798.4, "word": " V", "probability": 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4803.54, "end": 4804.0, "word": " صحيح", "probability": 0.8475341796875}, {"start": 4804.0, "end": 4804.3, "word": " لك", "probability": 0.5443115234375}, {"start": 4804.3, "end": 4804.86, "word": " هذا", "probability": 0.6025390625}, {"start": 4804.86, "end": 4805.3, "word": " سوف", "probability": 0.2352294921875}, {"start": 4805.3, "end": 4805.84, "word": " يعطيك", "probability": 0.770263671875}, {"start": 4805.84, "end": 4806.66, "word": " ان", "probability": 0.5048828125}, {"start": 4806.66, "end": 4807.78, "word": " DR", "probability": 0.490478515625}, {"start": 4807.78, "end": 4808.46, "word": " على", "probability": 0.72900390625}, {"start": 4808.46, "end": 4809.28, "word": " DS", "probability": 0.94580078125}, {"start": 4809.28, "end": 4810.36, "word": " is", "probability": 0.099853515625}, {"start": 4810.36, "end": 4811.22, "word": " a", "probability": 0.66357421875}, {"start": 4811.22, "end": 4811.94, "word": " unit", "probability": 0.94287109375}, {"start": 4811.94, "end": 4813.84, "word": " vector", "probability": 0.97216796875}, {"start": 4813.84, "end": 4817.8, "word": " نعطيه", "probability": 0.7724609375}, {"start": 4817.8, "end": 4818.5, "word": " تعريف", "probability": 0.98486328125}, {"start": 4818.5, "end": 4819.26, "word": " Definition", "probability": 0.661865234375}], "temperature": 1.0}, {"id": 180, "seek": 485522, "start": 4826.48, "end": 4855.22, "text": "unit tangent vector of a smooth curve R of T is T ده تساوي DR على DS", "tokens": [409, 270, 27747, 8062, 295, 257, 5508, 7605, 497, 295, 314, 307, 314, 11778, 3224, 6055, 3794, 995, 45865, 12118, 15844, 15816], "avg_logprob": -0.42934781572093134, "compression_ratio": 0.9285714285714286, "no_speech_prob": 0.0, "words": [{"start": 4826.48, "end": 4827.4, "word": "unit", "probability": 0.57867431640625}, {"start": 4827.4, "end": 4829.26, "word": " tangent", "probability": 0.59130859375}, {"start": 4829.26, "end": 4831.48, "word": " vector", "probability": 0.94677734375}, {"start": 4831.48, "end": 4835.72, "word": " of", "probability": 0.88134765625}, {"start": 4835.72, "end": 4837.82, "word": " a", "probability": 0.90869140625}, {"start": 4837.82, "end": 4838.34, "word": " smooth", "probability": 0.615234375}, {"start": 4838.34, "end": 4839.18, "word": " curve", "probability": 0.96875}, {"start": 4839.18, "end": 4842.9, "word": " R", "probability": 0.537109375}, {"start": 4842.9, "end": 4843.3, "word": " of", "probability": 0.59619140625}, {"start": 4843.3, "end": 4843.7, "word": " T", "probability": 0.9091796875}, {"start": 4843.7, "end": 4847.22, "word": " is", "probability": 0.331298828125}, {"start": 4847.22, "end": 4849.7, "word": " T", "probability": 0.8642578125}, {"start": 4849.7, "end": 4851.78, "word": " ده", "probability": 0.474365234375}, {"start": 4851.78, "end": 4852.38, "word": " تساوي", "probability": 0.8126220703125}, {"start": 4852.38, "end": 4853.24, "word": " DR", "probability": 0.185546875}, {"start": 4853.24, "end": 4854.76, "word": " على", "probability": 0.72900390625}, {"start": 4854.76, "end": 4855.22, "word": " DS", "probability": 0.9189453125}], "temperature": 1.0}, {"id": 181, "seek": 486177, "start": 4856.05, "end": 4861.77, "text": "واللي هي بالاسامة عمليا ال V على قول ال V", "tokens": [2407, 6027, 20292, 39896, 20666, 32277, 10943, 3660, 6225, 2304, 20292, 995, 2423, 691, 15844, 12174, 12610, 2423, 691], "avg_logprob": -0.3712890759110451, "compression_ratio": 1.126984126984127, "no_speech_prob": 0.0, "words": [{"start": 4856.05, "end": 4856.49, "word": "واللي", "probability": 0.8767903645833334}, {"start": 4856.49, "end": 4856.59, "word": " هي", "probability": 0.435302734375}, {"start": 4856.59, "end": 4857.79, "word": " بالاسامة", "probability": 0.5157470703125}, {"start": 4857.79, "end": 4858.97, "word": " عمليا", "probability": 0.77801513671875}, {"start": 4858.97, "end": 4859.19, "word": " ال", "probability": 0.62646484375}, {"start": 4859.19, "end": 4859.65, "word": " V", "probability": 0.77490234375}, {"start": 4859.65, "end": 4860.61, "word": " على", "probability": 0.88623046875}, {"start": 4860.61, "end": 4861.27, "word": " قول", "probability": 0.90576171875}, {"start": 4861.27, "end": 4861.53, "word": " ال", "probability": 0.6494140625}, {"start": 4861.53, "end": 4861.77, "word": " V", "probability": 0.6240234375}], "temperature": 1.0}, {"id": 182, "seek": 493368, "start": 4911.32, "end": 4933.68, "text": "بنرجع الكلام اللي كاتبينه مرة ثانية نحاول نستنتج متجة طوله الواحدة اللي هو واحد صحيح وبالتالي هيكون unit vector وبنبين ان هذا المتجه هو المتجه المماس للمنعنى هبقى جيب اقول مئة unit tangent vector هديله الرقم 6", "tokens": [3555, 1863, 47341, 3615, 2423, 28820, 10943, 13672, 1829, 9122, 9307, 3555, 9957, 3224, 3714, 25720, 38637, 7649, 10632, 8717, 5016, 995, 12610, 8717, 14851, 29399, 7435, 44650, 7435, 3660, 23032, 12610, 3224, 2423, 14407, 24401, 3660, 13672, 1829, 31439, 36764, 24401, 20328, 5016, 1829, 5016, 46599, 6027, 2655, 6027, 1829, 39896, 30544, 4985, 8062, 4032, 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"probability": 0.4765625}, {"start": 4930.94, "end": 4931.28, "word": " unit", "probability": 0.60107421875}, {"start": 4931.28, "end": 4931.84, "word": " tangent", "probability": 0.8837890625}, {"start": 4931.84, "end": 4932.3, "word": " vector", "probability": 0.966796875}, {"start": 4932.3, "end": 4932.88, "word": " هديله", "probability": 0.72998046875}, {"start": 4932.88, "end": 4933.32, "word": " الرقم", "probability": 0.8001302083333334}, {"start": 4933.32, "end": 4933.68, "word": " 6", "probability": 0.68212890625}], "temperature": 1.0}, {"id": 183, "seek": 495788, "start": 4934.52, "end": 4957.88, "text": "أحنا بنعرف أن غلصة V هي DR على DT لو أعطينا vector value of function اشتقناها بيعطينا مين السرعة و اشتقناها كم مرة بيعطينا مين العجل ال acceleration خلّينا مع السرعة اللي هي DR على DT اتجاه ال V دائما و أبدا هو اتجاه مماصل الملحنة يعني لو كان عندي محاول", "tokens": [10721, 5016, 8315, 44945, 3615, 28480, 14739, 32771, 1211, 9381, 3660, 691, 39896, 12118, 15844, 413, 51, 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مين؟", "probability": 0.8982747395833334}, {"start": 5156.09, "end": 5156.69, "word": " الـUnit", "probability": 0.53558349609375}, {"start": 5156.69, "end": 5157.31, "word": " Tangent", "probability": 0.86083984375}, {"start": 5157.31, "end": 5157.49, "word": " D", "probability": 0.66943359375}], "temperature": 1.0}, {"id": 192, "seek": 518260, "start": 5157.89, "end": 5182.61, "text": "بيكون هذا هو ال unit tangent لو كان طوله واحد صحيح إذا بدي أجيب طول ال DR على DS يبقى هو طول ال V اللي طالع عندنا على طول ال V بطول ال V على طول ال V لو جداش واحد صحيح يبقى فعلا هذا عبارة عن unit vector اللي حسمي طبقا لهذا ال definition يبقى هو ال unit tangent vector", "tokens": [3555, 1829, 30544, 23758, 31439, 2423, 4985, 27747, 45164, 25961, 23032, 12610, 3224, 36764, 24401, 20328, 5016, 1829, 5016, 11933, 15730, 4724, 16254, 5551, 7435, 1829, 3555, 23032, 12610, 2423, 12118, 15844, 15816, 7251, 3555, 4587, 7578, 31439, 23032, 12610, 2423, 691, 13672, 1829, 23032, 6027, 3615, 43242, 8315, 15844, 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"probability": 0.8684895833333334}, {"start": 5490.44, "end": 5490.82, "word": " مضاد", "probability": 0.3184814453125}, {"start": 5490.82, "end": 5491.02, "word": " إلى", "probability": 0.76025390625}, {"start": 5491.02, "end": 5491.52, "word": " نمرأ", "probability": 0.9435221354166666}, {"start": 5491.52, "end": 5491.82, "word": " B", "probability": 0.6279296875}, {"start": 5491.82, "end": 5493.18, "word": " اليونت", "probability": 0.8976236979166666}], "temperature": 1.0}, {"id": 204, "seek": 551850, "start": 5496.0, "end": 5518.5, "text": "Tangent vector اللي هو V بتقى الـT T بده يساوي الـV على طول الـV هو يساوي الـV المتجه اللي عندنا اللي هو T هو Sine T في اتجاه I", "tokens": [51, 656, 317, 8062, 13672, 1829, 31439, 691, 39894, 4587, 7578, 2423, 39184, 51, 314, 47525, 3224, 7251, 3794, 995, 45865, 2423, 39184, 53, 15844, 23032, 12610, 2423, 39184, 53, 31439, 7251, 3794, 995, 45865, 2423, 39184, 53, 9673, 2655, 7435, 3224, 13672, 1829, 43242, 8315, 13672, 1829, 31439, 314, 31439, 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{"start": 5507.3, "end": 5508.8, "word": " الـV", "probability": 0.700439453125}, {"start": 5508.8, "end": 5509.72, "word": " على", "probability": 0.90869140625}, {"start": 5509.72, "end": 5510.32, "word": " طول", "probability": 0.96875}, {"start": 5510.32, "end": 5510.8, "word": " الـV", "probability": 0.9176432291666666}, {"start": 5510.8, "end": 5511.58, "word": " هو", "probability": 0.314453125}, {"start": 5511.58, "end": 5512.16, "word": " يساوي", "probability": 0.932373046875}, {"start": 5512.16, "end": 5513.08, "word": " الـV", "probability": 0.90478515625}, {"start": 5513.08, "end": 5513.58, "word": " المتجه", "probability": 0.8702392578125}, {"start": 5513.58, "end": 5513.74, "word": " اللي", "probability": 0.8681640625}, {"start": 5513.74, "end": 5514.34, "word": " عندنا", "probability": 0.880859375}, {"start": 5514.34, "end": 5514.98, "word": " اللي", "probability": 0.982421875}, {"start": 5514.98, "end": 5515.22, "word": " هو", "probability": 0.98486328125}, {"start": 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{"start": 5537.58, "end": 5538.64, "word": " الجهة", "probability": 0.9158528645833334}, {"start": 5538.64, "end": 5540.18, "word": " طيب", "probability": 0.7409261067708334}, {"start": 5540.18, "end": 5540.86, "word": " السؤال", "probability": 0.9078776041666666}, {"start": 5540.86, "end": 5541.1, "word": " هو", "probability": 0.98779296875}, {"start": 5541.1, "end": 5541.8, "word": " هل", "probability": 0.93115234375}, {"start": 5541.8, "end": 5542.08, "word": " هذا", "probability": 0.91357421875}, {"start": 5542.08, "end": 5542.44, "word": " فعلا", "probability": 0.9156901041666666}, {"start": 5542.44, "end": 5542.72, "word": " unit", "probability": 0.5732421875}, {"start": 5542.72, "end": 5543.58, "word": " vector؟", "probability": 0.89697265625}], "temperature": 1.0}, {"id": 206, "seek": 557659, "start": 5547.49, "end": 5576.59, "text": "بطلع واحد فعلا unit vector بربي على المُركّبات اللي عندك وصية تربيه زاد وصية تربيه اللي فتطلع مجدش واحد يعني فعلا هذا هو مين هو ال unit vector 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"word": " كله", "probability": 0.976318359375}, {"start": 5708.08, "end": 5708.62, "word": " قبل", "probability": 0.997802734375}, {"start": 5708.62, "end": 5710.0, "word": " الامتحان", "probability": 0.9912109375}, {"start": 5710.0, "end": 5710.96, "word": " ماشي؟", "probability": 0.893310546875}, {"start": 5710.96, "end": 5711.68, "word": " كويس", "probability": 0.9747721354166666}, {"start": 5711.68, "end": 5712.1, "word": " ساعطيكوا", "probability": 0.5835978190104166}, {"start": 5712.1, "end": 5712.6, "word": " العافية", "probability": 0.9754231770833334}, {"start": 5712.6, "end": 5713.3, "word": " حد", "probability": 0.763916015625}, {"start": 5713.3, "end": 5713.5, "word": " هنا", "probability": 0.98095703125}, {"start": 5713.5, "end": 5713.8, "word": " اليوم", "probability": 0.98095703125}, {"start": 5713.8, "end": 5714.52, "word": " بيكفي", "probability": 0.9591064453125}, {"start": 5714.52, "end": 5715.38, "word": " و", "probability": 0.62255859375}, {"start": 5715.38, "end": 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/dSJIcUHEpZw_raw.srt b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/dSJIcUHEpZw_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..1fee315eedebef1100543b77919b6de553fbb22d
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/dSJIcUHEpZw_raw.srt
@@ -0,0 +1,3228 @@
+1
+00:00:00,000 --> 00:00:02,680
+موسيقى
+
+2
+00:00:25,330 --> 00:00:30,110
+الان بالمعاصلة اللى هو شبكة 13 المرة الماضية اخدنا
+
+3
+00:00:30,110 --> 00:00:33,910
+اول section و اليوم بناخد تانية section المرة اللى
+
+4
+00:00:33,910 --> 00:00:37,190
+فات كان vector valued function limit لهذا ال
+
+5
+00:00:37,190 --> 00:00:40,170
+vector ال derivative لهذا ال vector ال continuity
+
+6
+00:00:40,170 --> 00:00:45,030
+لهذا ال vector وما يتعلق بها اللى دلوقت بدنا نروح
+
+7
+00:00:45,030 --> 00:00:49,650
+لل integrals لهذه ال vector valued functions فبجي
+
+8
+00:00:49,650 --> 00:00:55,520
+بقول integrals of vector functionsتكامل اللي هي
+
+9
+00:00:55,520 --> 00:01:02,340
+الدوال الاتجاهية هنقسم ال section هذا إلى نقطتين
+
+10
+00:01:02,340 --> 00:01:06,920
+النقطة الأولى بنتحدث عن ال indefinite integrals
+
+11
+00:01:06,920 --> 00:01:12,300
+يعني التكاملات غير المحدودة ثم نذهب بعد ذلك إلى ال
+
+12
+00:01:12,300 --> 00:01:18,090
+definite integralsالتي هي التكاملات المحدودة سنعطي
+
+13
+00:01:18,090 --> 00:01:22,890
+تعريف لكل واحدة منهم ثم بعد ذلك ناخد بعض الأمثلة
+
+14
+00:01:22,890 --> 00:01:27,990
+على التعريفات اللي سنعطيها يبقى أول definition في
+
+15
+00:01:27,990 --> 00:01:33,590
+هذا الموضوع definition اللي
+
+16
+00:01:33,590 --> 00:01:36,290
+هو تبع ال indefinite integral
+
+17
+00:01:46,900 --> 00:01:57,520
+بنعرف فعلاً F R of T بيتساوى F of T في اتجاه I زي
+
+18
+00:01:57,520 --> 00:02:02,440
+الـ G of T في اتجاه الـ J زي الـ H of T في اتجاه
+
+19
+00:02:02,440 --> 00:02:12,800
+الـ K where حيث الـ F و الـ G و الـ H are
+
+20
+00:02:12,800 --> 00:02:14,460
+integrable functions
+
+21
+00:02:20,130 --> 00:02:27,690
+دول قابلة للتكامل of T قابلة للتكامل في المتغير T
+
+22
+00:02:27,690 --> 00:02:31,730
+then تكامل
+
+23
+00:02:31,730 --> 00:02:41,430
+لل R of T DT بتساوي تكامل لل F of T DT كله في
+
+24
+00:02:41,430 --> 00:02:49,940
+اتجاه I زائد تكامل لل G of T DT كله في اتجاه Jزائد
+
+25
+00:02:49,940 --> 00:02:59,780
+تكامل لل H of T DT كله في اتجاه الـ K كنا كاملنا
+
+26
+00:02:59,780 --> 00:03:09,200
+بنضيف زائد constant C where C is a constant vector
+
+27
+00:03:18,680 --> 00:03:24,100
+نمر اتنين، باعتبر هذا نمر واحد ونمر اتنين اللي هو
+
+28
+00:03:24,100 --> 00:03:28,780
+definite integrals
+
+29
+00:03:28,780 --> 00:03:37,220
+التكاملات المحزوظة التكاملات
+
+30
+00:03:37,220 --> 00:03:45,880
+المحزوظة زي ايه؟ زي التكامل من A إلى B لـR of T
+
+31
+00:03:48,640 --> 00:03:57,220
+بتساوي تكامل من A إلى B لل F of T DT كله في اتجاه
+
+32
+00:03:57,220 --> 00:04:05,360
+I زائد تكامل من A إلى B لل G of T DT كله في اتجاه
+
+33
+00:04:05,360 --> 00:04:09,480
+J زائد تكامل من A إلى B
+
+34
+00:04:26,150 --> 00:04:30,270
+نرجع للكلام اللي كتبته على اللوح لأنه بدنا نبدأ
+
+35
+00:04:30,270 --> 00:04:35,070
+تطبيقات عليه قبل أن نبدأ هذه التطبيقات نحاول نفهم
+
+36
+00:04:35,070 --> 00:04:40,690
+كل نقطة موجودة عندنا هنا ننجي للتعريف الأول اللي
+
+37
+00:04:40,690 --> 00:04:44,670
+هو تعريف ال independent integral لل vector valued
+
+38
+00:04:44,670 --> 00:04:50,940
+function يتجاه تكملات غير المحدودةفبجب اقول لو كان
+
+39
+00:04:50,940 --> 00:04:54,960
+ال R of T يسوى F of T في اتجاه I زي G و في اتجاه G
+
+40
+00:04:54,960 --> 00:05:00,880
+زي H و في اتجاه K حيث ال F والG والH هم انتجرابل
+
+41
+00:05:00,880 --> 00:05:06,920
+فانكشنبنرجع الى Calculus A بنقول ممكن الدالة تكون
+
+42
+00:05:06,920 --> 00:05:11,800
+قابلة للاشتقاء و ممكن ما تكونش و ممكن تكون قابلة
+
+43
+00:05:11,800 --> 00:05:18,120
+للتكامل و ممكن ما تكونش السؤال هو متى تكون الدالة
+
+44
+00:05:18,120 --> 00:05:22,200
+قابلة للتكامل؟ حد من الذكرة condition واحد فقط
+
+45
+00:05:22,200 --> 00:05:27,720
+نغشت انها تبقى متصلة ممتازة جدا، إذالو كانت الدالة
+
+46
+00:05:27,720 --> 00:05:34,940
+دالة متصلة إذا هذه الدالة قابلة للتكامل اتنين معنى
+
+47
+00:05:34,940 --> 00:05:40,660
+التكامل المحدود هو المساحة بين المنحلة ومحور X
+
+48
+00:05:40,660 --> 00:05:46,340
+مقدار هذه المساحة يسوى عمليا قيمة من قيمة التكامل
+
+49
+00:05:47,100 --> 00:05:51,100
+لازم تكون الدالة F وG وH هذول التلاتة are
+
+50
+00:05:51,100 --> 00:05:55,960
+integrable functions ان حد ذلك يبقى بروح بعضه في
+
+51
+00:05:55,960 --> 00:06:01,300
+التكامل المحدود على انه تكامل لكل مركبة من هذه
+
+52
+00:06:01,300 --> 00:06:05,480
+المركبات بدل ما اقول هنا زائد constant one هنا
+
+53
+00:06:05,480 --> 00:06:09,600
+زائد constant two هنا constant three بقول لهم
+
+54
+00:06:09,600 --> 00:06:13,440
+اجمعهم كلهم constant واحد اللي هو هسميه main ال C
+
+55
+00:06:13,440 --> 00:06:21,570
+السؤال هوهل ال constant هذا scalar ولا vector؟أنا
+
+56
+00:06:21,570 --> 00:06:24,710
+سؤال احنا ال function العادية اللي بيكون كاملة
+
+57
+00:06:24,710 --> 00:06:29,370
+ليست function اتجاهية بيبقى نقول ذات كونستانت و
+
+58
+00:06:29,370 --> 00:06:33,590
+اسكالر اثنين، تلاتة، زيرو، اربع، الاخرين، مضبوط؟
+
+59
+00:06:33,590 --> 00:06:38,630
+طب هل ال C هذا constant vector ولا constant
+
+60
+00:06:38,630 --> 00:06:43,850
+scalar؟ constant vector لحد لو كان .. لو كان
+
+61
+00:06:43,850 --> 00:06:47,630
+scalar كيف بدي أجمع مع ال vectors هذه؟ مش ممكنية،
+
+62
+00:06:47,630 --> 00:06:50,950
+إذا لازم يكون هذا ال C هو عبارة
+
+63
+00:07:15,110 --> 00:07:18,330
+بتكون رقم في اتجاه الـ I رقم في اتجاه الـ J رقم في
+
+64
+00:07:18,330 --> 00:07:22,910
+اتجاه الـ Kاللي هاللي لو جينا لإنتى في light
+
+65
+00:07:22,910 --> 00:07:28,230
+integrals التكاملات المحدودة فالتكامل على ال R of
+
+66
+00:07:28,230 --> 00:07:32,310
+T DT من ايه؟ اللي بيبدو يسمى التكامل على كل مركبة
+
+67
+00:07:32,310 --> 00:07:37,590
+من؟هذه المُركّبات وفي هذه الحالة بقولش زائد
+
+68
+00:07:37,590 --> 00:07:41,690
+constant تماما كما دُرس فيه Calculus التكامل
+
+69
+00:07:41,690 --> 00:07:46,330
+المحدود بنحطلش constant و بنطلع القيمة بتبعته بعوض
+
+70
+00:07:46,330 --> 00:07:49,830
+بالقيمة اللى فوق نقص القيمة اللى تحت بعد ما نكامل
+
+71
+00:07:49,830 --> 00:07:54,590
+بطلع القيمة الحقيقية لمهم للتكامل الان بدأ ناخد
+
+72
+00:07:54,590 --> 00:08:00,010
+أمثلة على كل من ال two definitions الاتنين هدول
+
+73
+00:08:00,010 --> 00:08:01,510
+يبقى examples
+
+74
+00:08:07,150 --> 00:08:12,130
+أول مثال أول مثال يبقى ندله سؤال عشرة من الكتاب
+
+75
+00:08:12,130 --> 00:08:19,350
+بيقول لي evaluate the
+
+76
+00:08:19,350 --> 00:08:28,630
+following integral احسبلي
+
+77
+00:08:28,630 --> 00:08:35,770
+التكامل التالي integration من zero لغاية five
+
+78
+00:09:04,120 --> 00:09:09,530
+يبقى بنا نحسبتكامل ال vector valued function من
+
+79
+00:09:09,530 --> 00:09:14,870
+النقطة zero لغاية النقطة باي بقول هذا التكامل
+
+80
+00:09:14,870 --> 00:09:22,030
+يساوي هكمل four you never know هايه يساوي اظن 60
+
+81
+00:09:22,030 --> 00:09:29,110
+سهل تكاملهالكن تان تربيع ماشي
+
+82
+00:09:29,110 --> 00:09:34,970
+بنحولها بدلالة المتطابقات المثلثية إلى دالة يمكن
+
+83
+00:09:34,970 --> 00:09:40,470
+تكاملها إذا هذا الكلام بده يساوي تكامل من zero إلى
+
+84
+00:09:40,470 --> 00:09:48,510
+باي لsec T اتجاه ال I زي تان تربيع عملات اللي هي
+
+85
+00:09:48,510 --> 00:09:55,800
+sec تربية T ناقص واحدكله في اتجاه ال J ناقص اللي
+
+86
+00:09:55,800 --> 00:10:01,640
+هو T في ال sign T في اتجاه مين في اتجاه ال K
+
+87
+00:10:01,640 --> 00:10:07,840
+بالنسبة الى D هذا الكلام يساوي نكمل السكة في قداش
+
+88
+00:10:07,840 --> 00:10:18,840
+من Calculus B قداش؟ ايوة علي صوت قليل اسمعلن
+
+89
+00:10:18,840 --> 00:10:25,240
+absolute value ل 6T زائد تان T يبقى هذا لن
+
+90
+00:10:25,240 --> 00:10:33,200
+absolute value ل 6T زائد تان T كل هذا الكلام من
+
+91
+00:10:33,200 --> 00:10:37,870
+zero لغاية باي في اتجاه ال I زائدطبعا مذكرة
+
+92
+00:10:37,870 --> 00:10:43,290
+الكريمانات سك تي ماقدرش اكملها مباشرة فبروح بضربها
+
+93
+00:10:43,290 --> 00:10:47,490
+في مقدار و بقسم عليه شو المقدار هذا بضرب في سك
+
+94
+00:10:47,490 --> 00:10:52,170
+زائد تان و بقسم على سك زائد تان بصير البسط و تفاضل
+
+95
+00:10:52,170 --> 00:10:56,670
+المقام يبقى الجواب لم absolute value لمن؟ للمقام
+
+96
+00:10:56,670 --> 00:11:03,570
+اللي بعده زائد اه مقدش تفاضل التان تفاضل التان
+
+97
+00:11:05,040 --> 00:11:13,440
+سكتربيع إذا تكاول السكتربيع هو تان يبقى تان ت ناقص
+
+98
+00:11:13,440 --> 00:11:19,460
+ت كل هذا الكلام من وين لوين من zero لغاية باي في
+
+99
+00:11:19,460 --> 00:11:25,600
+اتجاه ال J ناقص اه استنى شوية هذه مالاش اللي ايش
+
+100
+00:11:26,980 --> 00:11:30,840
+الكسور الجزئية ولا لا؟ مش الكسور الجزئية
+
+101
+00:11:30,840 --> 00:11:35,500
+integration by parts تكامل بالتجزيه يبقى بدى اخد
+
+102
+00:11:35,500 --> 00:11:36,840
+جزء ال derivatives
+
+103
+00:12:00,880 --> 00:12:09,620
+هو لوحدهطبعا لو كان ال N هو عدد صحيح موجد إذا بقول
+
+104
+00:12:09,620 --> 00:12:17,140
+تكامل X أُس N في Cos X أو X أُس N في Sin X أو X
+
+105
+00:12:17,140 --> 00:12:23,840
+أُس N في Sin X أو X أُس N في Cos X أوالـ X أُس N
+
+106
+00:12:23,840 --> 00:12:28,580
+في E أُس A X أو الـ X أُس N في A to the power X
+
+107
+00:12:28,580 --> 00:12:32,920
+يبقى الست حالتها من حد أشوفهم بروح بعملهم الجدول
+
+108
+00:12:32,920 --> 00:12:38,560
+مباشرة مشتقة الـ T بواحد تكمل الـ Sine بسالب
+
+109
+00:12:38,560 --> 00:12:43,840
+Cosine الـ T مشتقة الواحد بزيرو تكمل هذا بناقص
+
+110
+00:12:43,840 --> 00:12:48,870
+Sine Tو بروح بتخدم قاعدة الإشارات ببدأ بزائد ناقص
+
+111
+00:12:48,870 --> 00:12:52,970
+زائد ناقص لغاية ما تنتهي المسألة اللي عندي هذه
+
+112
+00:12:52,970 --> 00:13:04,610
+بصير ناقص و عندك هنا ناقص T Cos T و هنا زائد Sin T
+
+113
+00:13:04,610 --> 00:13:11,980
+كل هذا الكلام من Zero لغاية Pi في اتجاه الـKهذا
+
+114
+00:13:11,980 --> 00:13:15,460
+الكلام يسافر فالدعوة من القيمة اللى فوق ناقص
+
+115
+00:13:15,460 --> 00:13:21,720
+القيمة اللى تحت يبقى هذا ال in absolute value بدأى
+
+116
+00:13:21,720 --> 00:13:26,700
+اجي ل 16 إذا نسيها بقول ال سك هي مقلوب من ال
+
+117
+00:13:26,700 --> 00:13:32,960
+cosine 180 سالب واحد واحد على سالب واحد اللى هو
+
+118
+00:13:32,960 --> 00:13:39,670
+سالب واحد تمام اللى بدى assign ال byيبقى جيب
+
+119
+00:13:39,670 --> 00:13:45,850
+الـ180 عفواً ضل الـ180 يبقى جيب الـ180 على جيت
+
+120
+00:13:45,850 --> 00:13:51,070
+الـ180 جيب الـ180 بزيرو وجيت الـ180 بسلب واحد يبقى
+
+121
+00:13:51,070 --> 00:14:01,540
+بزيرو يبقى ناقص واحد ناقص زيرو على فوق ناقص لن0 1
+
+122
+00:14:01,540 --> 00:14:06,820
+و tan 0 اللي هو بزيرو هاي خلصنا ال term الأول هذا
+
+123
+00:14:06,820 --> 00:14:14,580
+كله في اتجاه مين؟ في اتجاه ال I زاد ها tan باي
+
+124
+00:14:14,580 --> 00:14:23,540
+اللي هو قداش بزيرو ناقص باي ناقص زيرو زائد زيرو في
+
+125
+00:14:23,540 --> 00:14:30,860
+اتجاه ال G tan باي بزيرو سالف باي هاينقص تان زيرو
+
+126
+00:14:30,860 --> 00:14:35,600
+بزيرو و تي بزيرو مع السلامة اللي بعضه نقص نقص بصير
+
+127
+00:14:35,600 --> 00:14:42,260
+جملات زائد ه قصارى مية تمانين بسالب واحد مع سالب
+
+128
+00:14:42,260 --> 00:14:46,040
+بصير مؤاشرة نقص
+
+129
+00:14:49,580 --> 00:14:53,720
+الشرط النقص بدي أدخله زائد و بدي أدخله سالب جوا
+
+130
+00:14:53,720 --> 00:15:00,560
+بصير عندك كلاميا موجة باي و كسايمية و تمانين بسالب
+
+131
+00:15:00,560 --> 00:15:09,480
+واحد زائد زيرو ناقص زيرو ناقص زيرو كله بزيرو في
+
+132
+00:15:09,480 --> 00:15:13,500
+اتجاه الكيك
+
+133
+00:15:13,500 --> 00:15:18,160
+طبعا ناقص يصير هذا زائد زيرو ما عليك يبقى هذه بدها
+
+134
+00:15:18,160 --> 00:15:25,740
+تساويلن absolute value لسالب واحد اللي هو واحد لإن
+
+135
+00:15:25,740 --> 00:15:30,520
+الواحد ب zero و لإن الواحد ب zero في أيطار مع
+
+136
+00:15:30,520 --> 00:15:35,680
+السلامة يبقى هاي ال zero نجي لبعض، همضلش عندي، هذي
+
+137
+00:15:35,680 --> 00:15:40,160
+هنا بلد في اتجاه ال J يبقى
+
+138
+00:15:40,160 --> 00:15:46,800
+ناقص باي في اتجاه ال J و لبعدها ناقص باي في اتجاه
+
+139
+00:15:46,800 --> 00:15:55,040
+ال Kأو نتيجة التكامل هو ناقص by J زائد K يبقى هذه
+
+140
+00:15:55,040 --> 00:16:04,140
+نتيجة التكامل لهذه المثل ناخد كمان سؤال سؤال اتنين
+
+141
+00:16:04,140 --> 00:16:14,120
+اللي هو سؤال ستاشر من الكتاب يقول لي Fالـ RW' of T
+
+142
+00:16:14,120 --> 00:16:21,960
+بيكون ناقص I زائد J زائد K ناقص مضلوب في الكل والـ
+
+143
+00:16:21,960 --> 00:16:28,040
+R عند الـ Zero والـ R عند الـ Zero بيكون عشرة I
+
+144
+00:16:28,040 --> 00:16:38,600
+زائد عشرة J زائد عشرة K و الـ DR على DT
+
+145
+00:16:47,820 --> 00:16:53,080
+أو جدلنا الـ R of G
+
+146
+00:17:23,110 --> 00:17:27,410
+يبقى السؤال يقول، لو كانت المشتقة الثانية لR of T
+
+147
+00:17:27,410 --> 00:17:32,690
+يسوى نقص I زائد G زائد K وكانت R عند الـ Zero هو
+
+148
+00:17:32,690 --> 00:17:38,590
+المتجه الثابت عشرة I زائد عشرة G زائد عشرة K وكانت
+
+149
+00:17:38,590 --> 00:17:44,010
+المشتقة لR بالنسبة إلى DT عند T تساوي Zero تساوي
+
+150
+00:17:44,010 --> 00:17:47,730
+Zero السؤال هو، هل الـ Zero هذا مختلف عن الـ Zero
+
+151
+00:17:47,730 --> 00:17:52,500
+هذا من أين؟طبعاً بيختلف اختلافاً كليا هذا P is
+
+152
+00:17:52,500 --> 00:17:56,520
+scalar لكن هذا main vector لأن R of T في الأصل هو
+
+153
+00:17:56,520 --> 00:18:00,200
+vector valued function فمشتقته هي vector كذلك إذا
+
+154
+00:18:00,200 --> 00:18:04,800
+هذا هو ال zero vector ومن هنا عملته لك على شكل
+
+155
+00:18:04,800 --> 00:18:10,580
+اللي هو مطاول شوية بحيث يختلف عالمين عن هذاقال لي
+
+156
+00:18:10,580 --> 00:18:15,360
+هزل ال R of T يبقى ملعقين ال R double prime of T
+
+157
+00:18:15,360 --> 00:18:21,400
+وطلب من يعني أيه؟ مارتين
+
+158
+00:18:21,400 --> 00:18:27,460
+كل مرة يطلع لثابت لتكامل لأن هذا ما هو اش تكامل
+
+159
+00:18:27,460 --> 00:18:31,920
+محدود زي السؤال اللي قبله تمام؟ إذا المثال الأول
+
+160
+00:18:31,920 --> 00:18:35,680
+كان على الحالة الثانية والمثال الثاني على مين؟ على
+
+161
+00:18:35,680 --> 00:18:40,770
+الحالة الأولىيبقى احنا عندنا هذا بده روح اكامله
+
+162
+00:18:40,770 --> 00:18:48,510
+يبقى بده اخد تكامل لل R' of T DT بده يساوي تكامل
+
+163
+00:18:48,510 --> 00:18:58,190
+لـ I J K كله بالنسبة الى DT طيب
+
+164
+00:19:01,200 --> 00:19:05,920
+هذا اشتقاق مرتين بدا كامل مرة نخلص من المشتقة
+
+165
+00:19:05,920 --> 00:19:09,940
+الأولى هبقى اللي عندنا مين ال R prime of D اللي
+
+166
+00:19:09,940 --> 00:19:17,260
+همين D R على D T هدوي سوا بدا كامل هذه يبقى ناقص T
+
+167
+00:19:17,260 --> 00:19:22,360
+في اتجاه ال I ناقص T في اتجاه ال J ناقص T في اتجاه
+
+168
+00:19:22,360 --> 00:19:31,270
+ال K زائد كونسالـ C1 هذا ثابت و لا vectorيعني
+
+169
+00:19:31,270 --> 00:19:35,210
+scalar ولا vector؟ vector طبعاً بدنا نعرف مين هو
+
+170
+00:19:35,210 --> 00:19:40,310
+ال vector اللي عندنا هنا بقول اه ارجع شوية ميعطيني
+
+171
+00:19:40,310 --> 00:19:45,410
+معلومة هذه المعلومة بده أحاول أستفيد منها جالي لما
+
+172
+00:19:45,410 --> 00:19:49,790
+T تساوي Zero بده تبقى المشتقة الأولى ل R of T بده
+
+173
+00:19:49,790 --> 00:19:54,950
+ساوي مين؟ Zero إذا هشيل كل T و أحط مكانها؟ Zero
+
+174
+00:19:54,950 --> 00:20:02,330
+يبقى بناء عليه هذا بده يعطيناإن دي R على دي T عند
+
+175
+00:20:02,330 --> 00:20:06,990
+الـ T بدها تساوي زيرو بده يساوي هاي المستقبل إذا
+
+176
+00:20:06,990 --> 00:20:12,710
+هشيل كل T و أحط مكانها زيرو يبقى و يساوي زيرو في
+
+177
+00:20:12,710 --> 00:20:17,110
+اتجاه ال I زائد زيرو في اتجاه ال J زائد زيرو في
+
+178
+00:20:17,110 --> 00:20:18,930
+اتجاه ال K زائد C
+
+179
+00:20:25,920 --> 00:20:31,660
+يبقى هذا كله بده يساوي الـ zero vector بناء عليه
+
+180
+00:20:31,660 --> 00:20:35,820
+الـ C1 بده يساوي كده ال zero
+
+181
+00:20:54,520 --> 00:21:00,440
+طيب اللي بد ال R of T يبقى كامل الطرفين يبقى بناء
+
+182
+00:21:00,440 --> 00:21:07,560
+عليه R of T سوى نقص نص T تربيه في اتجاه I نقص نص T
+
+183
+00:21:07,560 --> 00:21:14,040
+تربيه في اتجاه J نقص نص T تربيه في اتجاه K زائد
+
+184
+00:21:14,040 --> 00:21:21,420
+constant من C2عند الـ T تساوي 0 قداش بده يساوي لإن
+
+185
+00:21:21,420 --> 00:21:28,340
+هو ماتين ال R of 0 يعني عند T تساوي 0 فباجي بقوله
+
+186
+00:21:28,340 --> 00:21:34,600
+ال R of 0 بده يساوي، بدي أشيل كل T و أحط مكانها
+
+187
+00:21:34,600 --> 00:21:41,580
+Zero يبقى هذا Zero Zero Zero يبقى Zero زائد C2طب
+
+188
+00:21:41,580 --> 00:21:47,200
+ال R of Zero قال لي هي عشرة I زائد عشرة J زائد
+
+189
+00:21:47,200 --> 00:21:53,220
+عشرة K معناه هذا الكلام انه C2 يسوى عشرة I زائد
+
+190
+00:21:53,220 --> 00:21:58,380
+عشرة J زائد عشرة K فالان علينا ال vector valid
+
+191
+00:21:58,380 --> 00:22:03,080
+function اللي بده إياها ليه R of T نقص نص
+
+192
+00:22:11,370 --> 00:22:21,450
+زائد له C2 له بعشرة I زائد عشرة J زائد عشرة K بدي
+
+193
+00:22:21,450 --> 00:22:27,710
+أجمع المراكبات المتناضرة يبقى عشرة ناقص نص T تربيع
+
+194
+00:22:27,710 --> 00:22:33,530
+في اتجاه ال I زائد عشرة ناقص نص T تربيع في اتجاه
+
+195
+00:22:33,530 --> 00:22:40,910
+ال Jزائد عشرة نقص نص T تربية في اتجاه main في
+
+196
+00:22:40,910 --> 00:22:49,730
+اتجاه ال K هذه كلها اليمين R of T اللي طلع لحد
+
+197
+00:22:49,730 --> 00:22:54,210
+هنا بكفينا النقطة هذه من هذا ال section وبتروح
+
+198
+00:22:54,210 --> 00:23:00,990
+اتحلول المسائل مناللي هو تلات و عشر اتنين المسائل
+
+199
+00:23:00,990 --> 00:23:09,830
+من واحد الى ستاش الأدء المسائل الفردية كافي الباقي
+
+200
+00:23:09,830 --> 00:23:11,030
+كلهم مش لزمني
+
+201
+00:23:44,590 --> 00:23:49,610
+ننتقل الان الى ال section اللذي يليه اللي هو
+
+202
+00:23:49,610 --> 00:23:54,150
+تلتاشر تلاتة اللي بتكلم عن ال arc linked in space
+
+203
+00:23:54,150 --> 00:24:00,570
+يبقى بالداخل ال section تلتاشر تلاتة اللي هو ال
+
+204
+00:24:00,570 --> 00:24:07,450
+arc linked in space
+
+205
+00:24:34,960 --> 00:24:39,950
+لما نقول arc length يا بنات in spaceيبقى احنا
+
+206
+00:24:39,950 --> 00:24:45,850
+عندنا منحنى فى الفرق و بدنا نعرف كده شطول جزء من
+
+207
+00:24:45,850 --> 00:24:50,390
+المنحنى على فترة ما فانا بسمى arc length يعني طول
+
+208
+00:24:50,390 --> 00:24:56,300
+القوس فى الفرق in space فى الفرقسأقسم إلى ثلاث
+
+209
+00:24:56,300 --> 00:24:59,920
+نقاط أول نقطة سأحسب الـ arc length النقطة التانية
+
+210
+00:24:59,920 --> 00:25:04,160
+هي speed اللي هي مقدار صدر الجسم يسيره في الفرار
+
+211
+00:25:04,160 --> 00:25:09,080
+النقطة التالتة ال unit tangent vector للمنحنة
+
+212
+00:25:09,080 --> 00:25:13,600
+عندها نقطة يبقى أنا عند المنحنة في الفرار سأحسب ال
+
+213
+00:25:13,600 --> 00:25:17,460
+tangent إلى أين عندها نقطة خلّيني مع النقطة الأولى
+
+214
+00:25:17,460 --> 00:25:23,400
+سأعطيها تعريف ونشوف كيف سنستخدم هذا التعريف يبقى
+
+215
+00:25:23,400 --> 00:25:23,980
+definition
+
+216
+00:25:32,150 --> 00:25:40,130
+of a small curve R
+
+217
+00:25:40,130 --> 00:25:47,910
+of T بده يساوي X of T في اتجاه I Y of T في اتجاه J
+
+218
+00:25:47,910 --> 00:25:57,190
+زائد Z of T في اتجاه K والـ A أقل من أو يساوي T
+
+219
+00:25:57,190 --> 00:26:03,160
+أقل من أو يساوي B يعني T محصورةما بين ال A و ال B
+
+220
+00:26:03,160 --> 00:26:08,080
+as T
+
+221
+00:26:08,080 --> 00:26:11,200
+increases
+
+222
+00:26:11,200 --> 00:26:18,120
+from
+
+223
+00:26:18,120 --> 00:26:21,200
+T
+
+224
+00:26:21,200 --> 00:26:32,790
+تساوي A to T تساوي B as يتقلل البنسوي تكامل من A
+
+225
+00:26:32,790 --> 00:26:42,470
+إلى B للجدر التربيعي لمن؟ لـ dx على dt لكل تربيع،
+
+226
+00:26:42,470 --> 00:26:51,950
+dy على dt لكل تربيع، dz على dt لكل تربيع، والتكامل
+
+227
+00:26:51,950 --> 00:26:58,390
+هذا كله بالنسبة لمن؟ بالنسبة إلى dtطبعاً هذا بده
+
+228
+00:26:58,390 --> 00:27:06,630
+يسوي تكامل من a إلى b هذا مين يا بنات المرة اللي
+
+229
+00:27:06,630 --> 00:27:16,170
+فاتت طول ال a طول
+
+230
+00:27:16,170 --> 00:27:19,910
+ال a ممتاز جدا يعني هذا مقدار السرعة
+
+231
+00:27:22,860 --> 00:27:32,340
+هو ال vector P بالنسبة الى DT مرة تانية باجي بقول
+
+232
+00:27:32,340 --> 00:27:38,350
+طول smooth curve المقطع بالعلاقة اللى عندنا هذهمن
+
+233
+00:27:38,350 --> 00:27:43,250
+النقطة A الى B حيث T انكريز من النقطة A الى نقطة B
+
+234
+00:27:43,250 --> 00:27:48,390
+بعرفه كتالة L يسوى integration من A الى B للجدر
+
+235
+00:27:48,390 --> 00:27:52,090
+التربية لDX على DT لكل تربية زي ال DIY على DT لكل
+
+236
+00:27:52,090 --> 00:27:56,390
+تربية زي ال DZ على DT لكل تربية يبقى X وY وZ هنا
+
+237
+00:27:56,390 --> 00:28:02,510
+أجت مكان اللي جاب ال F والG ولدش هي هي فانكشن في
+
+238
+00:28:02,510 --> 00:28:11,160
+100 في Tهذا المقدار هو طول متجه السرعة
+
+239
+00:28:28,030 --> 00:28:34,990
+السؤال هو احنا على المحاور الكارتيزية بدأنا نبدأ
+
+240
+00:28:34,990 --> 00:28:37,890
+من نقطة الأصل و نتحرك عليه و نقول واحد اتنين تلاتة
+
+241
+00:28:37,890 --> 00:28:41,330
+أربعة و اشيجر تانية سالب واحد سالب اتنين و ايه كده
+
+242
+00:28:41,330 --> 00:28:45,230
+بالنسبالي محور وايه طب المنحلة اللي في الفراغ هذا
+
+243
+00:28:45,230 --> 00:28:50,770
+كيف بنسوي فيه بقوله بسيطة جدا تختار نقطة بتسميها
+
+244
+00:28:50,770 --> 00:28:51,290
+ال base
+
+245
+00:29:08,380 --> 00:29:18,700
+يبقى ده smooth curve المنحنة الاملة is scaled
+
+246
+00:29:24,330 --> 00:29:35,370
+is a scale الرقم يعني like number like
+
+247
+00:29:35,370 --> 00:29:46,290
+number line مثل خط الأعداد تماما as shown in the
+
+248
+00:29:46,290 --> 00:29:49,570
+figure كما هو بيتبرسل
+
+249
+00:30:16,860 --> 00:30:25,040
+عند نقطة PRT نقطة PRT نقطة PRT نقطة PRT نقطة PRT
+
+250
+00:30:25,040 --> 00:30:31,910
+نقطة PRT نقطة PRT نقطة PRT نقطةهذا اتنين، هذا
+
+251
+00:30:31,910 --> 00:30:38,470
+تلاتة، هذا اربع، خمسة، ستة، وهكذا، هذا مشيت وين
+
+252
+00:30:38,470 --> 00:30:43,490
+عالي منه؟ مشيت ع الشمال، بدأ يقول هنا سالب واحد،
+
+253
+00:30:43,490 --> 00:30:49,270
+سالب اتنين، وهكذا، يبقى برقم المنحنى في الفراغ زي
+
+254
+00:30:49,270 --> 00:30:55,040
+ترقيم خط الاعداد تماما بالضعفطيب في انا كمان تعريف
+
+255
+00:30:55,040 --> 00:31:00,300
+اخر بيقول طبعا انتوا شايفين ان انا قادم هنا S of T
+
+256
+00:31:00,300 --> 00:31:04,240
+لكن ايش S of T انتوا لسه مش عارفين يبقى الان بدي
+
+257
+00:31:04,240 --> 00:31:11,140
+اعطي تعريف لل S of T يبقى ال definition the
+
+258
+00:31:11,140 --> 00:31:20,760
+directed distance المسافة
+
+259
+00:31:20,760 --> 00:31:21,740
+المباشرة
+
+260
+00:31:24,400 --> 00:31:36,360
+along a smooth curve from the
+
+261
+00:31:36,360 --> 00:31:43,800
+base point
+
+262
+00:31:43,800 --> 00:31:57,560
+من النقطة البداية ال S of Tبدو يساوي تكامل من T
+
+263
+00:31:57,560 --> 00:32:09,000
+naught إلى T لقول ال V of Tau D Tau و لو بدو يساوي
+
+264
+00:32:09,000 --> 00:32:17,540
+تكامل من T naught إلى T للجذر الترابيعي ل X prime
+
+265
+00:32:17,540 --> 00:32:27,150
+of Tau كل ترابيعزائد y prime of tau لكل
+
+266
+00:32:27,150 --> 00:32:38,050
+تربيع زائد z prime of tau لكل تربيع كله d tau
+
+267
+00:32:59,370 --> 00:33:07,830
+هذه التسمية إلى اسم آخر يبقى also وكذلك اللي هو S
+
+268
+00:33:07,830 --> 00:33:14,270
+of T is called the arc length parameter
+
+269
+00:33:38,770 --> 00:33:54,710
+والذي يكون هو تزايدا in the direction of
+
+270
+00:33:54,710 --> 00:33:56,050
+increasing T
+
+271
+00:33:58,730 --> 00:34:03,110
+increasing T جادة زايد
+
+272
+00:34:39,960 --> 00:34:45,320
+بنرجع للتعريف اللي احنا كاتبينه مرة ثانية التعريف
+
+273
+00:34:45,320 --> 00:34:49,540
+بيقول الـ directed distance along a smooth curve C
+
+274
+00:34:49,540 --> 00:34:53,740
+يبقى الملحنة هذا بيسميه الملحنة C هذا يا بنات كأنه
+
+275
+00:34:53,740 --> 00:34:58,500
+الملحنة الأزرق اللي احنا رسمينه هنا تماما مانو
+
+276
+00:34:58,500 --> 00:35:05,660
+from the base point T0 من عند النقطة T0 is كتالي
+
+277
+00:35:05,660 --> 00:35:14,080
+بقول S of T هو تكمل من T0لغاية T لل V of TAU D TAU
+
+278
+00:35:14,080 --> 00:35:18,780
+طبعا السؤال اللي يحط على بعضك شو TAU هذا؟ مش هيك؟
+
+279
+00:35:18,780 --> 00:35:24,420
+بيقولك أبدا مش احنا بنكمل بالنسبة إلى T إذا لو خلت
+
+280
+00:35:24,420 --> 00:35:30,260
+من T نقطة إلى T وكانت هذه الدالة بدلالة T
+
+281
+00:35:40,910 --> 00:35:45,750
+بعد كامل بعوض بحدود اللي فوق نقص لتحت بصير عندي
+
+282
+00:35:45,750 --> 00:35:51,330
+دالة في Tيبقى هذا تاو اي رمز بدك يعني كتبته تاو
+
+283
+00:35:51,330 --> 00:35:56,030
+انت و كتبيه epsilon واحد يكتب ليه xi و واحد يقول
+
+284
+00:35:56,030 --> 00:36:00,690
+ليه xi و كده حق الرمز اللي يعجبك مع أنه مشكلة لكن
+
+285
+00:36:00,690 --> 00:36:04,830
+اصطلح عليه ان ارمزله بالرمز تاو اي رمز بدنا يعني
+
+286
+00:36:05,300 --> 00:36:10,240
+طيب يبقى من هنا لطول ال view of tau و تشيل x prime
+
+287
+00:36:10,240 --> 00:36:13,540
+of tau تربيه و y prime of tau تربيه و z prime of
+
+288
+00:36:13,540 --> 00:36:17,020
+tau تربيه كل التكوين يسبل ال d tau و بعد ما كامل
+
+289
+00:36:17,020 --> 00:36:21,580
+بعض و حدود التكوين تطلع دالة في main في T أبقى
+
+290
+00:36:21,580 --> 00:36:27,920
+بستنى شوية بستنى شو الفرق بين التعريف الأول و
+
+291
+00:36:27,920 --> 00:36:33,600
+التعريف التاني لأن أنا شايفهم زي بعض ولا لا طلع
+
+292
+00:36:33,600 --> 00:36:38,070
+هنا كويسانا قايل هنا ال length ال تكامل من a لب ا
+
+293
+00:36:38,070 --> 00:36:44,130
+لب رقمين عددين تمام هذا المشتق الأولى والمشتق
+
+294
+00:36:44,130 --> 00:36:47,590
+الأولى والمشتق الأولى للمركبة ورقم ربعها هذا
+
+295
+00:36:47,590 --> 00:36:52,310
+المشتق الأولى والمشتق الأولى للمركبة ورقم ربعهاطيب
+
+296
+00:36:52,310 --> 00:36:56,530
+الفرق بينهم بس هذا تكون من الرقمين هذا تكون من
+
+297
+00:36:56,530 --> 00:37:03,090
+الرقم إلى متغير T ليس إلا إذا اللي فوق هو اللي تحت
+
+298
+00:37:03,090 --> 00:37:10,710
+شكله طيب في فارق بينهما؟ في فارق ما بين ال two
+
+299
+00:37:10,710 --> 00:37:17,210
+definitions؟ طلعوا فيهم كويس واضح يعني كلامك حد
+
+300
+00:37:17,210 --> 00:37:20,050
+تقدر تجيب ليه شو الفرق ما بين الاتنين؟
+
+301
+00:37:25,390 --> 00:37:27,370
+ماما؟ بصراحة بصراحة بصراحة بصراحة بصراحة بصراحة
+
+302
+00:37:27,370 --> 00:37:28,230
+بصراحة بصراحة بصراحة بصراحة بصراحة بصراحة بصراحة
+
+303
+00:37:28,230 --> 00:37:30,630
+بصراحة بصراحة بصراحة بصراحة بصراحة بصراحة بصراحة
+
+304
+00:37:30,630 --> 00:37:31,210
+بصراحة بصراحة بصراحة بصراحة بصراحة بصراحة بصراحة
+
+305
+00:37:31,210 --> 00:37:31,530
+بصراحة بصراحة بصراحة بصراحة بصراحة بصراحة بصراحة
+
+306
+00:37:31,530 --> 00:37:34,610
+بصراحة بصراحة بصراحة بصراحة بصراحة بصراحة بصراحة
+
+307
+00:37:34,610 --> 00:37:40,230
+بصراحة بصراحة بصراحةالأول من ضعيف رقم قيمة محددة
+
+308
+00:37:40,230 --> 00:37:45,510
+يبقى أنا يا بنات في الحالة الأولى بجيب رقم الوطول
+
+309
+00:37:45,510 --> 00:37:50,510
+القوس اللى عندنا على فترة محددة هذا التعريف الأول
+
+310
+00:37:50,510 --> 00:37:59,070
+النتيجة رقمالنتيجة الثانية دالة في T لأنها بتقول
+
+311
+00:37:59,070 --> 00:38:05,350
+من T نضله رقم إلى T التاني بتطلع لي T وهو المسافة
+
+312
+00:38:05,350 --> 00:38:10,870
+عند أي لحظة يعني هو طول عند أي لحظة اختار اللحظة
+
+313
+00:38:10,870 --> 00:38:14,810
+اللي بدك إياها يعني كأنه قصير التعريف الأول هو
+
+314
+00:38:14,810 --> 00:38:19,430
+حالة خاصة من مين من التعريف الثاني صحيح ولا لأ
+
+315
+00:38:19,430 --> 00:38:23,850
+يبقى الحالة الأولة هو طول محدد على فترة محددةهذا
+
+316
+00:38:23,850 --> 00:38:31,230
+طول المدحانة عند اي لحظة بدك يجيب عليها
+
+317
+00:38:31,550 --> 00:38:35,630
+هذا لو جيت كامده هيطلع بدلالة T ولمّا أعوض بحدود
+
+318
+00:38:35,630 --> 00:38:40,650
+التكامل بصير بدلالة T ومن هنا سمنها ال S of T مين
+
+319
+00:38:40,650 --> 00:38:45,250
+ال S of T الى ال direct distance along this small
+
+320
+00:38:45,250 --> 00:38:50,690
+curve المسافة المباشرة على مين؟ على اللي هو
+
+321
+00:38:50,690 --> 00:38:54,670
+المنحنى اللي عندنا لحظة كتبتولك هنا S of T وقلنا
+
+322
+00:38:54,670 --> 00:38:58,010
+لك شو S of T وقلنا مش عارفين فروحنا عرفنا لك S of
+
+323
+00:38:58,010 --> 00:39:03,440
+TS of T يا بسميه Direct Distance على كل المنحنة يا
+
+324
+00:39:03,440 --> 00:39:09,180
+بسميه Arc Length Parameter للمنحنة SDC يعني ايش
+
+325
+00:39:09,180 --> 00:39:13,180
+معناه Parameter يا بنت بالعربي Parameter
+
+326
+00:39:14,420 --> 00:39:19,780
+هذا البرامتر ليس تلجة معروفية تلجة معروفية هو وسيط
+
+327
+00:39:19,780 --> 00:39:23,720
+يعني واحد يدخل بين اتنين لماذا؟ لأن المنحنة نكتب
+
+328
+00:39:23,720 --> 00:39:28,520
+دلالة X وY دائما وابدا إذا دخلت T في المصي فتكون T
+
+329
+00:39:28,520 --> 00:39:33,080
+دخلتها وسيط وقلت X function في T وY function في T
+
+330
+00:39:33,080 --> 00:39:38,220
+اللي بسمي وسيط أو parameter إذا ال S of T يا بسمي
+
+331
+00:39:38,220 --> 00:39:41,960
+ال direct distance يا بسمي ال arc length parameter
+
+332
+00:39:41,960 --> 00:39:49,320
+للمنحنة Tاركلينج بارامتر هذا يتزايد في اتجاه تزايد
+
+333
+00:39:49,320 --> 00:39:53,240
+تزايد
+
+334
+00:39:53,240 --> 00:39:54,800
+تزايد تزايد تزايد تزايد تزايد تزايد تزايد تزايد
+
+335
+00:39:54,800 --> 00:39:55,620
+تزايد تزايد تزايد تزايد تزايد تزايد تزايد تزايد
+
+336
+00:39:55,620 --> 00:39:56,660
+تزايد تزايد تزايد تزايد تزايد تزايد تزايد تزايد
+
+337
+00:39:56,660 --> 00:40:01,120
+تزايد تزايد تزايد تزايد تزايد تزايد تزايد تزايد
+
+338
+00:40:01,120 --> 00:40:01,120
+تزايد تزايد تزايد تزايد تزايد تزايد تزايد تزايد
+
+339
+00:40:01,120 --> 00:40:05,000
+تزايد تزايد تزايد تزايد تزايد تزايد تزايد تزايد
+
+340
+00:40:05,000 --> 00:40:11,700
+تزا
+
+341
+00:40:16,650 --> 00:40:20,070
+طبعا مش هيبيلك ع الرسل الكلام اللي احنا كتبهله قبل
+
+342
+00:40:20,070 --> 00:40:24,810
+المثال لو جيت قلت يا بنات هذه النقطة هي ال base
+
+343
+00:40:24,810 --> 00:40:31,870
+point ال base point النقطة ل P of T node يعني عندي
+
+344
+00:40:31,870 --> 00:40:37,750
+ال T node كانت النقطة هذه تمام؟ وروحنا أخدنا نقطة
+
+345
+00:40:37,750 --> 00:40:43,590
+تانية زي النقطة هذه اللي عند أي لحظة يبقى هذه ال P
+
+346
+00:40:43,590 --> 00:40:49,370
+of Tكان عندنا هذا ال vector الأساسي وهذا صار ال
+
+347
+00:40:49,370 --> 00:40:55,310
+vector الجديد اللي هو R of T لكن هذا ال vector
+
+348
+00:40:55,310 --> 00:41:02,410
+اللي هو R of T هذا ال vector اللي هو R of T0 طب
+
+349
+00:41:02,410 --> 00:41:07,390
+وين ال directed distance S of T؟ باجي بقول خط
+
+350
+00:41:07,390 --> 00:41:14,230
+الغامق اللي عندنا هذا خط الأسود هذا كلههذا بنات
+
+351
+00:41:14,230 --> 00:41:18,950
+اللي هو ال S of T اللي هي المسافة المباشرة من
+
+352
+00:41:18,950 --> 00:41:23,410
+النقطة لأن ال base point إلى أي نقطة تقع على
+
+353
+00:41:23,410 --> 00:41:28,830
+المنحنة عرفنا وين ال S of T؟ طيب إذا النقطة هذه
+
+354
+00:41:28,830 --> 00:41:33,710
+معروفة عدديًا والنقطة هذه معروفة عدديًا صار اللي
+
+355
+00:41:33,710 --> 00:41:40,530
+هو الوطول المنحنة طب ناصر مثال توضيح على ذلك بيقول
+
+356
+00:42:15,820 --> 00:42:25,420
+Find the length of the givenFind the length of the
+
+357
+00:42:25,420 --> 00:42:29,960
+given portion
+
+358
+00:42:29,960 --> 00:42:37,600
+of
+
+359
+00:42:37,600 --> 00:42:38,280
+the curb
+
+360
+00:42:45,710 --> 00:42:52,950
+find the arglym parameter find the arglym
+
+361
+00:42:52,950 --> 00:42:59,350
+parameter parameter
+
+362
+00:42:59,350 --> 00:43:08,290
+اللي هو S of T F T naught بدت ساوي كده بدت ساوي
+
+363
+00:43:08,290 --> 00:43:13,030
+ساوي solution
+
+364
+00:43:20,890 --> 00:43:27,710
+المقول الأول جالي هدى طول الجزر اللى هو من المنحنى
+
+365
+00:43:27,710 --> 00:43:33,230
+على الفترة اللى احنا حددناها من المنحنى هى R of T
+
+366
+00:43:33,230 --> 00:43:37,930
+في جامعاتنا التجاهية بدي اعرف قداش طول الجزر على
+
+367
+00:43:37,930 --> 00:43:43,190
+الفترة اللى بدها تتغير فيها D من سالب للاربعة
+
+368
+00:43:43,190 --> 00:43:49,730
+لغاية ال zero بدي اعرف قداش طول المنحنى في هذه
+
+369
+00:43:49,730 --> 00:43:56,370
+الفترةمش هنجيب طول المنحنى بقى شو بدي أعمل؟ بدي
+
+370
+00:43:56,370 --> 00:44:03,290
+أجيب المستقل أولى لمعادلة المنحنى طب كويس، الآن لو
+
+371
+00:44:03,290 --> 00:44:10,740
+جيت بدي أحسب الـDX على DDيبقى بدى مشتق التاني مش
+
+372
+00:44:10,740 --> 00:44:15,920
+هاد X و هاد Y و هاد Z تمام و احنا كتبنا DX على DT
+
+373
+00:44:15,920 --> 00:44:20,160
+لكل تربيع زي ال DY على DT لكل تربيع زي ال DZ على
+
+374
+00:44:20,160 --> 00:44:25,060
+DT لكل تربيع كله تحت من تحت الجذر اذا انا بدي
+
+375
+00:44:25,060 --> 00:44:33,580
+اجيبله DX على DT يعني D على DT لمن؟ من X
+
+376
+00:44:39,850 --> 00:44:47,270
+إذا أنا مشتقت كده؟ حاصل ضرب دلتين مشتقت الدالة
+
+377
+00:44:47,270 --> 00:44:53,470
+الأولى في الدالة الثانية زائد الدالة الأولى
+
+378
+00:44:56,740 --> 00:45:02,580
+مشتركة ال cos بسالب sin او اذا كنت تاخد E أس T
+
+379
+00:45:02,580 --> 00:45:10,680
+عامل مشترك بيبقى ال cos T ناقص sin T بشكل يعني
+
+380
+00:45:10,680 --> 00:45:16,260
+بلزم تربيعها خلينا نطبعها بالمرة يبقى يا بنات لو
+
+381
+00:45:16,260 --> 00:45:24,280
+جيتك واخدت DX على DT لكل تربيع يبقى E أس اتنين T
+
+382
+00:45:24,280 --> 00:45:33,630
+فيهكوصين تربيع T نقص اتنين كوصين T كوصين T زائد
+
+383
+00:45:33,630 --> 00:45:41,530
+كوصين تربيع T ويبقى ساوي E باس اتنين T فيه كوصين
+
+384
+00:45:41,530 --> 00:45:47,130
+تربيع زائد كوصين تربيع يبقى واحد يبقى واحد نقص
+
+385
+00:45:47,130 --> 00:45:53,030
+اتنين كوصين T كوصين T كيف؟
+
+386
+00:45:54,470 --> 00:45:59,410
+ماشي بنفع اقول sin 2t بنفع صحيح طيب بناروح نجيب
+
+387
+00:45:59,410 --> 00:46:07,150
+اللي هو ال dy على dt يساوي وإذا ال y هاجر بنفس
+
+388
+00:46:07,150 --> 00:46:14,150
+الطريقة بدي اشتقها مشتقة الأول في sin t زائد a أس
+
+389
+00:46:14,150 --> 00:46:20,590
+t في مين في تفاضل ال sin لكو sin t اللي هو بده
+
+390
+00:46:20,590 --> 00:46:30,460
+يساوي a أس 2tفي sine of T زائد cosine of T الربع
+
+391
+00:46:30,460 --> 00:46:37,880
+يبقى هذا بده يعطيكي ان dy على dt كل تربيع بده
+
+392
+00:46:37,880 --> 00:46:45,100
+يساوي E أس اتنين T مربع دي بنفس الطريقة sine تربيع
+
+393
+00:46:45,100 --> 00:46:54,920
+Tزي ايدي اتنين Sine T Cos T زائد Cos تربيه T الو E
+
+394
+00:46:54,920 --> 00:47:04,040
+أس اتنين T في واحد زي ايدي اتنين Sine T Cos T اظن
+
+395
+00:47:04,040 --> 00:47:08,900
+انت مشتقتها هي نفسها و تربيها سهل E أس اتنين T
+
+396
+00:47:08,900 --> 00:47:13,420
+يبقى سهل يبقى بده اقول له ال length L
+
+397
+00:47:22,050 --> 00:47:25,850
+مربع الأولى E أس اتنين T مربع الأولى E أس اتنين T
+
+398
+00:47:25,850 --> 00:47:33,210
+مربع الأولى E أس اتنين T مربع الأولى E أس اتنين T
+
+399
+00:47:33,210 --> 00:47:40,040
+مربع الأولى E أس اتنين Tنقص اتنين Sine T Cos T
+
+400
+00:47:40,040 --> 00:47:50,480
+زائد واحد زائد اتنين Sine T Cos T زائد مربع
+
+401
+00:47:50,480 --> 00:47:57,440
+المشتقة الأخيرة اللي هو E قصة اتنين T كل هذا
+
+402
+00:47:57,440 --> 00:48:04,780
+الكلام تحت الجدر تكمل بالنسبة إلى T يبقى يساوي
+
+403
+00:48:05,080 --> 00:48:09,400
+Integration من سالب لن أربعة لغاية الـ zero لل
+
+404
+00:48:09,400 --> 00:48:16,420
+square root لل E أس اتنين T فيه هذا ال term بروح
+
+405
+00:48:16,420 --> 00:48:20,860
+مع ال term هذا يظل واحد زائد واحد يساوي كده اتنين
+
+406
+00:48:20,860 --> 00:48:28,140
+زائد E أس اتنين T DT اللي هو يطلع كدهتلاتة E أُس
+
+407
+00:48:28,140 --> 00:48:38,360
+اتنين T يعني جدر تلاتة تكامل E أُس T DT من سالب لم
+
+408
+00:48:38,360 --> 00:48:45,220
+أربعة لغاية زيارة اتنين زائد واحد يبقى تلاتة
+
+409
+00:48:45,220 --> 00:48:49,740
+المقدار تحت الجدر يبقى جدر تلاتة وضع الجدر E أُس
+
+410
+00:48:49,740 --> 00:48:57,010
+اتنين E أُس Tبديها كامل يبقى ويساوي جدر تلاتة في
+
+411
+00:48:57,010 --> 00:49:03,850
+تكامل EOST بالـ EOSTSL من ناقص لن أربعة لغاية زيرو
+
+412
+00:49:03,850 --> 00:49:10,550
+يبقى يساوي جدر تلاتة فيه فتعود بالقيمة اللي فوق
+
+413
+00:49:10,550 --> 00:49:15,790
+ناقص القيمة اللي تحتها EOSTL من ناقص
+
+414
+00:49:15,790 --> 00:49:23,580
+EOS ناقص لن أربعة جدر تلاتة في واحد نافعحط الناقص
+
+415
+00:49:23,580 --> 00:49:29,060
+فوق بصير أربع عوص قداش ناقص واحد يعني قداش ربع
+
+416
+00:49:29,060 --> 00:49:35,460
+والإي واللن مع السلامة يبقى ناقص ربع واحد ناقص ربع
+
+417
+00:49:35,460 --> 00:49:41,800
+مضل قداش تلت تربع في جدر تلاتة يبقى بتلاتة جدر
+
+418
+00:49:41,800 --> 00:49:48,060
+تلاتة على أربع هذا طول مين طول الجزء من القوس على
+
+419
+00:49:48,060 --> 00:49:59,990
+الفترة المعطاةهذا لسه كله مين مطلوب الأول ايه عندك
+
+420
+00:49:59,990 --> 00:50:07,850
+اخر سطر يعني اخر سطر Eost زي دي لا Eost هدف Eost
+
+421
+00:50:07,850 --> 00:50:17,370
+صحيح وهذه ربعناها ومشت صح تمام 100% تمامطيب يبقى
+
+422
+00:50:17,370 --> 00:50:23,670
+تجيبنا طول اللي هو المنحنة L المطلوب التاني قلي هت
+
+423
+00:50:23,670 --> 00:50:28,390
+ال arc length parameter عند T not تساومين تزاوي
+
+424
+00:50:28,390 --> 00:50:35,590
+Zero او قلي هت ال direct distance بقوله A نمر بيد
+
+425
+00:50:35,590 --> 00:50:41,990
+ال S of T اللي هو عبارة عن تكامل من Zero إلى T
+
+426
+00:50:41,990 --> 00:50:52,680
+ليش؟ لأنه قلي عند T not تساوي Zeroلمن؟ لطول
+
+427
+00:50:52,680 --> 00:51:02,300
+ال V of T DT صحيح؟ طيب ال V of T مش هي اللي احسب
+
+428
+00:51:02,300 --> 00:51:10,700
+احسب حسبناها لغاية ما وصلنا هنا لجدر تلاتة E of T
+
+429
+00:51:10,700 --> 00:51:17,600
+صح؟ يبقى هذه يساوي تكاملطبعا هنا بشان اقول كلام
+
+430
+00:51:17,600 --> 00:51:26,680
+دقيقة بقول V of TAU D TAU لان هنا التكامل هنا نسبة
+
+431
+00:51:26,680 --> 00:51:36,060
+الارتي يبقى بناتها جذر تلاتة E أس TAU D TAU و
+
+432
+00:51:36,060 --> 00:51:43,440
+الكلام من Zero لغاية ال T جذر تلاتة خليك برا و
+
+433
+00:51:43,440 --> 00:51:44,940
+تكامل E أس TAU
+
+434
+00:51:51,710 --> 00:52:01,430
+يبقى هذا جدر تلاتة في E Os T ناقص E Os Zero يبقى
+
+435
+00:52:01,430 --> 00:52:09,450
+الجواب جدر تلاتة في E Os T ناقص واحد هذا ال direct
+
+436
+00:52:09,450 --> 00:52:12,490
+line distance at any point
+
+437
+00:52:26,170 --> 00:52:33,030
+طيب هذا هو المثال الأول، الأن نعطيكي مثال ثاني لكن
+
+438
+00:52:33,030 --> 00:52:35,010
+بفكرة جديدة
+
+439
+00:52:57,730 --> 00:53:03,630
+مثال رقم اتنين اللي
+
+440
+00:53:03,630 --> 00:53:08,150
+هو السؤال التسعة من الكتاب بقول find a port on the
+
+441
+00:53:08,150 --> 00:53:08,530
+care
+
+442
+00:53:17,360 --> 00:53:26,220
+curve هات النقطة اللي على المنحنى a cot t ببر ساوي
+
+443
+00:53:26,220 --> 00:53:34,880
+خمسة sine t في اتجاه ال I زائد خمسة cosine t في
+
+444
+00:53:34,880 --> 00:53:42,340
+اتجاه ال J زائد اتناشر t في اتجاه ال K at a
+
+445
+00:53:42,340 --> 00:53:43,180
+distance
+
+446
+00:53:50,010 --> 00:54:03,970
+26 units by units along the curve from
+
+447
+00:54:03,970 --> 00:54:13,890
+the point من النقطة 0 و 5 و 0
+
+448
+00:54:18,580 --> 00:54:31,940
+direction and direction of increasing arc
+
+449
+00:54:31,940 --> 00:54:32,360
+length
+
+450
+00:55:01,460 --> 00:55:07,660
+نرجع لسؤالنا مرة ثانية بقول هاتلي النقطة التي تقع
+
+451
+00:55:07,660 --> 00:55:14,780
+على المنحدة اللي قدامنا والتي تكون على بعد 26π من
+
+452
+00:55:14,780 --> 00:55:18,920
+وحدات الطول units along the curve يعني من وحدات
+
+453
+00:55:18,920 --> 00:55:25,460
+طول تبعات المنحدة من عند النقطة 0 5 0 في اتجاه
+
+454
+00:55:25,460 --> 00:55:32,080
+تزايد من تزايد المنحدة يعني لو جينا افترضناان انا
+
+455
+00:55:32,080 --> 00:55:37,360
+عندى منحرة بالشكل اللى عندنا هذا و جيت اخدت النقطة
+
+456
+00:55:37,360 --> 00:55:42,160
+اللى عندنا هذه اللى كانت base point الاحداثى تبع
+
+457
+00:55:42,160 --> 00:55:48,520
+هذه النقطة اللى هو zero وخمسة و zero يعني x و y و
+
+458
+00:55:48,520 --> 00:55:55,760
+z تساوي zero ووصلنا الى هذه النقطة وفي اتجاه تزايد
+
+459
+00:55:55,760 --> 00:56:01,360
+من اللى هو ال arc lengthفي اتجاهاتها زي ال R كله
+
+460
+00:56:01,360 --> 00:56:06,420
+يعني في اتجاهاتها زي ال S of T فكان هذا main هو ال
+
+461
+00:56:06,420 --> 00:56:14,200
+S of T المسافة هذه حسبتها عمليا لجلها ستة و عشرين
+
+462
+00:56:14,200 --> 00:56:19,600
+بايت يبقى الطول يا بنات على المنحنة هذا من عند
+
+463
+00:56:19,600 --> 00:56:25,100
+النقطة اللي عندنا هذه لغاية النقطة هذه الخط الأزرق
+
+464
+00:56:25,100 --> 00:56:34,490
+هذا لخط بنكبونمين مان كيمون؟ مين؟ السكرتير العام
+
+465
+00:56:34,490 --> 00:56:39,270
+للأمم المتحدة، طب مين اللي كان جابله؟ كوفي عنان،
+
+466
+00:56:39,270 --> 00:56:42,890
+هم تعينوا الخط الأذرك اللي جال بيحط نخش و بيعملوله
+
+467
+00:56:42,890 --> 00:56:47,670
+خط على حدود لبنان و فلسطين و بيشتغلوا على كيفهم
+
+468
+00:56:47,960 --> 00:56:52,440
+تمام؟ يبقى احنا الخط الأزرق تبعنا هذا طوله ستة
+
+469
+00:56:52,440 --> 00:56:57,580
+وعشرين بايت بدأ من النقطة زيرو خمسة وزيرو وانتهى
+
+470
+00:56:57,580 --> 00:57:02,380
+في النقطة اللى عندنا هذه ايش سؤالنا؟ سؤالنا بيقولى
+
+471
+00:57:02,380 --> 00:57:08,560
+هدل النقطة اللى عندك هذى بدك تعرفى قداش احداثيات
+
+472
+00:57:08,560 --> 00:57:13,710
+النقطة هذى والله كويس النقطة هذى معلومةوالطول
+
+473
+00:57:13,710 --> 00:57:17,950
+معلوم، إذا نضل عليه، بس إحداثية النقطة دي بتبقى
+
+474
+00:57:17,950 --> 00:57:23,730
+قصتنا سادة، مظبوط؟ أيوة، يبقى بدنا نيجي نعرف قداش
+
+475
+00:57:23,730 --> 00:57:28,830
+إحداثيات النقطة اللي موجودة عندنا بدنا نشوف يا
+
+476
+00:57:28,830 --> 00:57:32,990
+بنات ال directed distance من النقطة هذه لغاية
+
+477
+00:57:32,990 --> 00:57:37,050
+النقطة هذهمشان تعرفلي كده الدرجة اللى بدنا نعرف
+
+478
+00:57:37,050 --> 00:57:42,690
+كده T نقطة ده و بدي أعرف كده T عند النقطة التانية
+
+479
+00:57:42,690 --> 00:57:47,790
+و إذا عرفت التنتين بصير أحداثيات النقطة هذا X وهذا
+
+480
+00:57:47,790 --> 00:57:55,510
+Y وهذا Z بصير قصتنا سهلةمظبوط طيب اذا بدي اعرف كده
+
+481
+00:57:55,510 --> 00:57:59,950
+احداث النقطة اللى عندنا هذه الاحداثيات موجودة
+
+482
+00:57:59,950 --> 00:58:04,430
+ككارتيزن X Y و Z لكن انا بدي جيبه ال parameter T
+
+483
+00:58:04,430 --> 00:58:08,770
+عند هذه النقطة كده بده يساوي تمام شوفوا كيف بدنا
+
+484
+00:58:08,770 --> 00:58:12,910
+نحسب كده T نوت عشان بعدك وين ما تقابلك تعرفي
+
+485
+00:58:12,910 --> 00:58:19,190
+تعزبيا طلع يا بنتك الحين انا عندي مين عندي اللي هو
+
+486
+00:58:19,860 --> 00:58:28,620
+الـ X ده تساوي كده؟ خمسة صين T الإحداث الأولة اللي
+
+487
+00:58:28,620 --> 00:58:34,980
+بيجموها ده X صح ولا لأ؟ إذا هذا بيساوي كده؟ بيساوي
+
+488
+00:58:34,980 --> 00:58:38,420
+Zero مين
+
+489
+00:58:38,420 --> 00:58:43,880
+الزاوية اللي جيبها بيساوي Zero؟ يا Zero يا باي يا
+
+490
+00:58:43,880 --> 00:58:49,340
+اتنين باي هي ده مشكلة يبقى هنا هذا بدي يعطيني انه
+
+491
+00:58:49,340 --> 00:58:54,580
+Tياما zero ياما باى ياما اتنين باى وبعدها تبدأ
+
+492
+00:58:54,580 --> 00:59:01,980
+دورة جديدة هم نمسك التانية التانية Y تسوى خمسة cos
+
+493
+00:59:01,980 --> 00:59:10,200
+T وخمسة cos T تسوى كم؟ خمسة هذا معناته ان cos T
+
+494
+00:59:10,200 --> 00:59:15,700
+تسوى كم؟ واحد هذا معناته ان T تسوى كم؟ مين الزاوية
+
+495
+00:59:15,700 --> 00:59:21,720
+اللي جيبت مابا يسوى واحد؟يبقى ياما صفر ياما اتنين
+
+496
+00:59:21,720 --> 00:59:26,560
+باى باى لأ لإن انتصارنا بيسالب واحد يبقى واحدة من
+
+497
+00:59:26,560 --> 00:59:34,300
+هدول بداخل ز ز يساوي قداش اتناشر T ويساوي Zero هنا
+
+498
+00:59:34,300 --> 00:59:40,880
+مافيش عندي الا T تساوي قداش الآن صار عندي تلات
+
+499
+00:59:40,880 --> 00:59:46,300
+نقاط و أين القيمة المشتركة بين التلات نقاط مش عندي
+
+500
+00:59:46,300 --> 00:59:52,800
+الا Zero Zero Zeroيبقى هذا معناته ان T تساوي Zero
+
+501
+00:59:52,800 --> 00:59:58,880
+إذا عندي نقطة Zero وخمسة و Zero كانت T تساوي جداش
+
+502
+00:59:58,880 --> 01:00:04,020
+Zero اللي هي T نوت يبقى T نوت اللي عندنا هذا بدها
+
+503
+01:00:04,020 --> 01:00:09,940
+تساوي مين؟ بدها تساوي Zero Why؟ طب ماعطيني جداش
+
+504
+01:00:09,940 --> 01:00:15,140
+طول ال Direct Distance بده أشوف T عند نهاية
+
+505
+01:00:15,140 --> 01:00:19,630
+المسافة اللي عندنا هناكده إش كانة إذا عرفت بتبقى
+
+506
+01:00:19,630 --> 01:00:24,030
+انحلت مشكلتي بدي أجيبها من وين؟ بدي أجيبها من ال S
+
+507
+01:00:24,030 --> 01:00:28,550
+of T طب ال S of T بدي أجيبها من وين؟ من الدلة اللي
+
+508
+01:00:28,550 --> 01:00:32,070
+عندك بديك تروح تشتقها و تربع المركبة تحت الجدر
+
+509
+01:00:32,070 --> 01:00:38,790
+مظبوط ولا لا؟ إذا بناء عليه بدي أروح أجيب من؟ أجيب
+
+510
+01:00:38,790 --> 01:00:42,970
+قول ال V و الله بلاش نجيب V في الأول
+
+511
+01:00:47,190 --> 01:00:53,150
+يبقى بنا نجيب ال V بالأول يبقى ال V of T بديه ساوي
+
+512
+01:00:53,150 --> 01:01:01,130
+DR على DT اللي هو مين؟ خمسة Cos T في اتجاه I ناقص
+
+513
+01:01:01,130 --> 01:01:08,910
+خمسة Sin T في اتجاه الجهة زائد اتماع شركي بدي طول
+
+514
+01:01:08,910 --> 01:01:15,370
+ال V يبقى طول ال V بديه ساوي الجذري التربيعي لمربع
+
+515
+01:01:15,370 --> 01:01:22,720
+المركباتخمسة وعشرين وصين تربية T خمسة وعشرين وصين
+
+516
+01:01:22,720 --> 01:01:32,200
+تربية T زائد مية واربعة واربعين يساوي ال square
+
+517
+01:01:32,200 --> 01:01:38,060
+root لو أخدت خمسة وعشرين عامل مشتركة بنات بضل كده؟
+
+518
+01:01:38,060 --> 01:01:43,580
+صين تربية زاد كصين تربية له واحد، صحيح زائد مية
+
+519
+01:01:43,580 --> 01:01:50,670
+واربعة واربعين، كدهش بتلعب؟مية وتسعة وستين تحت
+
+520
+01:01:50,670 --> 01:01:56,850
+الجدر في جدار تلاتة عشر بعدين بقولك كويس يبقى ال S
+
+521
+01:01:56,850 --> 01:02:05,470
+of T يساوي تكامل من T naught اللي هي ب Zero لعند
+
+522
+01:02:05,470 --> 01:02:10,670
+ال T اللي أنا مش عارفها لمن؟ ل ال absolute value
+
+523
+01:02:10,670 --> 01:02:14,610
+اللي هي V of Tau D Tau
+
+524
+01:02:20,770 --> 01:02:28,670
+لتلتاشر D TAU يبقى تلتاشر TAU من Zero إلى T ويسمى
+
+525
+01:02:28,670 --> 01:02:36,430
+كده تلتاشر T طيب تمام تلتاشر T عامليا كده شو سوى
+
+526
+01:02:36,430 --> 01:02:38,950
+بنات؟ ستة واشرين بايت
+
+527
+01:02:51,430 --> 01:02:58,390
+يبقى عند هذه النقطة
+
+528
+01:02:58,390 --> 01:03:00,410
+يبقى T يساوي 26 باي
+
+529
+01:03:04,160 --> 01:03:11,400
+يبقى تكمن من 0 إلى T ل V of Tau D Tau يبقى تكمن من
+
+530
+01:03:11,400 --> 01:03:20,640
+0 إلى T لـ 13 D Tau يبقى تكمن من 0 إلى T لـ V of
+
+531
+01:03:20,640 --> 01:03:25,120
+Tau D Tau يبقى تكمن من 0 إلى T لـ 13 D Tauأو الـ
+
+532
+01:03:25,120 --> 01:03:30,360
+arc lens parameter يبقى التلتاشر T هو معتهالي أصلا
+
+533
+01:03:30,360 --> 01:03:38,040
+بقداش ب 26 باي ومنها T بقداش ب 2 باي، إذا عند
+
+534
+01:03:38,040 --> 01:03:43,790
+النقطة الأخيرة هذههه اذا تعرف T بقدر ايه؟ بتنين
+
+535
+01:03:43,790 --> 01:03:48,050
+باى اذا عرف T بتنين باى اذا ما بقدر اعرف النقطة
+
+536
+01:03:48,050 --> 01:03:52,030
+اللي هو ايه اللي بدوياها لو طلب النقطة اللي عندها
+
+537
+01:03:52,030 --> 01:03:57,950
+بيكون قطعنا على ال arc lens مسافة مقدرها ستة
+
+538
+01:03:57,950 --> 01:04:04,130
+وعشرين باى بقوله اه النقطة اللي بدوياها يبقى Z
+
+539
+01:04:04,130 --> 01:04:04,850
+point
+
+540
+01:04:10,150 --> 01:04:14,890
+كداش ال X أصلا عندها مناد خمسة صين T و ال T بقدرش
+
+541
+01:04:14,890 --> 01:04:22,430
+اتنين باى يبقى خمسة صين اتنين باى و التانية خمسة
+
+542
+01:04:22,430 --> 01:04:30,490
+كوصين اتنين باى و التالتة اتناشر في اتنين باى
+
+543
+01:04:30,490 --> 01:04:34,310
+بالشكل اللي عندنا هذا و اللي هي بدها تساوي صين
+
+544
+01:04:34,310 --> 01:04:38,150
+اتنين باى بقدرش Zero cosine اتنين باى
+
+545
+01:04:58,740 --> 01:05:05,660
+مثال رقم 2 من الكتاب وفي كمان سؤال زيه في الكتاب
+
+546
+01:05:11,050 --> 01:05:14,210
+بتاع الرقم 3 بيقولنا find the length of the curve
+
+547
+01:05:14,210 --> 01:05:25,610
+find the length of the curve قداش طول المنحنة من
+
+548
+01:05:25,610 --> 01:05:32,590
+المنحنة R of T بده يساوي T تربيع في اتجاه ال I
+
+549
+01:05:32,590 --> 01:05:41,260
+زائد 2T في اتجاه ال J زائد Ln T في اتجاه ال Kfrom
+
+550
+01:05:41,260 --> 01:05:44,720
+the
+
+551
+01:05:44,720 --> 01:05:53,180
+point من النقطة اللي هي واحد و اتنين و zero to
+
+552
+01:05:53,180 --> 01:06:03,980
+للنقطة E تربيع و اتنين E و واحد where حيث T أكبر
+
+553
+01:06:03,980 --> 01:06:04,560
+من الzero
+
+554
+01:06:13,910 --> 01:06:20,310
+مرة تانية قال لي هاتلي قداش طول المنحنى المُعطى
+
+555
+01:06:20,310 --> 01:06:23,870
+اللى عندنا هذا من النقطة اللى عندنا هذه لغاية
+
+556
+01:06:23,870 --> 01:06:29,430
+النقطة هذه حيث T أكبر من من الزرع بقوله كويس احنا
+
+557
+01:06:29,430 --> 01:06:35,230
+مش هنجيب طول المنحنى بدي قيمتين عدديتين بدي T
+
+558
+01:06:35,230 --> 01:06:40,170
+تساوي كده وT تساوي كده مش ميعطيني احداثيات نقطة
+
+559
+01:06:43,050 --> 01:06:49,270
+ايوة بس ايش بالمجلوك اينا كيف اه انت عندك هنا دول
+
+560
+01:06:49,270 --> 01:06:56,150
+احدثية نقطة دول X و Y و Z و انت عندك هاي X و هاي Y
+
+561
+01:06:56,150 --> 01:07:01,750
+و هاي Z مظبوط اذا بدك يشوف ان كل نقطة من هذه
+
+562
+01:07:01,750 --> 01:07:10,550
+النقاط فبجي بقوله ال X و ال Y و ال Z X و Y و Z
+
+563
+01:07:10,550 --> 01:07:20,980
+اللي عبارة عن مينT تربيع و اتنين T و لين T يبقى
+
+564
+01:07:20,980 --> 01:07:25,360
+بالداجة عند النقطة الأولى بدى اعرف قداش مقدار T
+
+565
+01:07:25,360 --> 01:07:35,100
+تباجى بقوله add النقطة الأولى D Y الواحد و اتنين و
+
+566
+01:07:35,100 --> 01:07:35,380
+زين
+
+567
+01:07:40,070 --> 01:07:47,250
+الاكس اللى بتى تربية تساوي كده؟ تساوي واحد اللى
+
+568
+01:07:47,250 --> 01:07:54,010
+بعدها ال Y اللى بداش بتنين T تساوي اتنين اللى
+
+569
+01:07:54,010 --> 01:08:02,810
+بعدها لان T تساوي زيوهذه قدرات بتعطيك ان تزايد او
+
+570
+01:08:02,810 --> 01:08:07,690
+ناقص واحد بس هو قال لي ت أكبر من ال zero يبقى يا
+
+571
+01:08:07,690 --> 01:08:11,570
+سالم واحد صف على شجرة يبقى هذا بدي يعطيني ان ت
+
+572
+01:08:11,570 --> 01:08:17,690
+تساوي واحد هذا بدي يعطيك ان ت تساوي جدا طيب مين
+
+573
+01:08:17,690 --> 01:08:22,190
+اللي لنه يساوي ال zero واحد ان واحد يساوي zero هذا
+
+574
+01:08:22,190 --> 01:08:29,510
+بدي يعطيك ان ت تساوي واحد اذا من هذول التلاتةبقول
+
+575
+01:08:29,510 --> 01:08:38,570
+T تساوي واحد في الدرجة الان ال D Y عند النقطة
+
+576
+01:08:38,570 --> 01:08:47,170
+اليمين E تربيع و اتنين E و واحد و هذا ال T تربيع
+
+577
+01:08:47,170 --> 01:08:55,670
+بده يساوي E تربيع و اتنين T بده يساوي اتنين Eو لن
+
+578
+01:08:55,670 --> 01:09:01,470
+تي يساوي كده؟ يساوي واحد هذي ايش بتعطيكي لما تاخد
+
+579
+01:09:01,470 --> 01:09:07,650
+جدرى التربيه على الطرفين؟ تي يساوي من ال اي وهذا
+
+580
+01:09:07,650 --> 01:09:14,210
+بتعطيكي تي يساوي ال اي وهذا بتعطيكي ان تي تساوي ال
+
+581
+01:09:14,210 --> 01:09:21,350
+اي اتخذوا في نفس القيمة يبقى هنا تي تساوي من اي من
+
+582
+01:09:21,350 --> 01:09:23,090
+اللي اكبر؟ الواحد و الله ال اي
+
+583
+01:09:25,910 --> 01:09:34,850
+إذا بدنا نروح نجي بال V of T يبقى باجي بقول V of T
+
+584
+01:09:34,850 --> 01:09:44,970
+يساوي يبقى 2T في اتجاه I زائد 2 في اتجاه J زائد 1
+
+585
+01:09:44,970 --> 01:09:48,950
+على T في اتجاه M في اتجاه K
+
+586
+01:10:04,740 --> 01:10:11,000
+السؤال قال لي هات لمن؟ هات لـ L للمنحنة هذا بروح
+
+587
+01:10:11,000 --> 01:10:19,860
+بقول ل L L بدي أسوي تكامل من واحد لغاية ال E للجذر
+
+588
+01:10:19,860 --> 01:10:25,820
+التربيعي لمربع المركبة اللي عندي، إيش بيصير؟ أربعة
+
+589
+01:10:25,820 --> 01:10:34,620
+T تربيع زائد أربعة زائد واحد على T تربية DTيبقى
+
+590
+01:10:34,620 --> 01:10:40,040
+هذا الكلام يساوي تكامل من واحد لغاية الـA
+
+591
+01:10:40,040 --> 01:10:46,060
+للـsquare root بدا واحد المقامات كله على T تربية
+
+592
+01:10:46,060 --> 01:10:53,860
+بصير أربعة T أس أربعة زائد أربعة T تربية زائد واحد
+
+593
+01:10:53,860 --> 01:11:01,560
+كله DT هذا الكلام يساوي تكامل من واحد إلى E للجدر
+
+594
+01:11:01,560 --> 01:11:12,020
+تربيعيالبسط مربع كامل يا بنات؟ البسط مربع كامل؟ مش
+
+595
+01:11:12,020 --> 01:11:17,200
+مربع كامل؟ طب والله شوفين الجداش اتنين ت ترابية
+
+596
+01:11:17,200 --> 01:11:21,880
+زائد واحد لكل ترابية فكلي الجثة ده شوفين هو اللي
+
+597
+01:11:21,880 --> 01:11:22,300
+فوق
+
+598
+01:11:25,070 --> 01:11:30,530
+يبقى مربع كامل ولا لا؟ جاهز وخالص طيب هذه كمية
+
+599
+01:11:30,530 --> 01:11:36,350
+مربعة وكمية مربعة تحت الجدد من 1 إلى E أعدادا
+
+600
+01:11:36,350 --> 01:11:43,450
+موجبة إذا كله بيطلع بقيمة موجبة يبقى 2T تربية زائد
+
+601
+01:11:43,450 --> 01:11:51,460
+1 على T DT يعني تكامل من اللي هو الواحدلغاية الـ E
+
+602
+01:11:51,460 --> 01:12:01,640
+لـ 2T زائد واحد عالك DT الكامل يبقى T تربيع على
+
+603
+01:12:01,640 --> 01:12:07,460
+اتنين على اتنين الله سهل عليها زائد لن الـ T أو
+
+604
+01:12:07,460 --> 01:12:13,160
+absolute value لـ T وكل هذا الكلام من واحد لغاية
+
+605
+01:12:13,160 --> 01:12:17,100
+الـ E يبقى E تربيع
+
+606
+01:12:28,430 --> 01:12:36,530
+يبقى الجواب قدر E تربية إذا طول المنحنة يساوي E
+
+607
+01:12:36,530 --> 01:12:40,330
+تربية الروح
+
+608
+01:12:40,330 --> 01:12:44,570
+الآن للمقطة الثانية من هذا ال section اللي هو ال
+
+609
+01:12:44,570 --> 01:12:51,890
+speed مقدار السرعة on اسمه
+
+610
+01:13:27,290 --> 01:13:40,890
+بالنسبة لـ S of T بدي
+
+611
+01:13:40,890 --> 01:13:51,890
+أشتغل
+
+612
+01:13:51,890 --> 01:13:57,600
+الطرفين هناشارستين كوتيلة حسبناها دا وساق بدي
+
+613
+01:13:57,600 --> 01:14:02,860
+أشتقها بس بصير هذا اشتقاق لمين للتكامل اخدنا
+
+614
+01:14:02,860 --> 01:14:07,660
+اشتقاق للتكامل في calculus ايه؟ حدا .. حدا مذكرا
+
+615
+01:14:07,660 --> 01:14:13,200
+ايش اسم هالنظرية؟ اللي هو التفاضل للتكامل؟
+
+616
+01:14:13,200 --> 01:14:19,800
+fundamental equilibrium of calculus ممتاز جدا يبقى
+
+617
+01:14:19,800 --> 01:14:31,820
+هنا بقول هنا bythe fundamental theorem
+
+618
+01:14:31,820 --> 01:14:35,760
+of
+
+619
+01:14:35,760 --> 01:14:40,920
+calculus ايش
+
+620
+01:14:40,920 --> 01:14:48,440
+بده يصير ال DS على DT بده يساوي اللي جوا هذي بشيل
+
+621
+01:14:48,440 --> 01:14:57,120
+كلته و بحط مكانها باسمين Tيبقى طول ال Z of T إيش
+
+622
+01:14:57,120 --> 01:15:01,320
+رايك؟ طول
+
+623
+01:15:01,320 --> 01:15:06,920
+يبقى طول يبقى قيمة موجبة إذا هذه معناته معناها
+
+624
+01:15:06,920 --> 01:15:12,220
+أكبر من ال Zero مدام المشتقة أكبر من Zero يبقى ال
+
+625
+01:15:12,220 --> 01:15:18,700
+S of T ممكن تكون Decrease يبقى مش إمكانية يبقى هذا
+
+626
+01:15:18,700 --> 01:15:29,640
+معناتهإن ال S of T is an increasing function يبقى
+
+627
+01:15:29,640 --> 01:15:37,020
+هذه تزيادية على طول الخط طيب طول ال V مش هو هذا
+
+628
+01:15:37,020 --> 01:15:37,980
+اللي خدناها
+
+629
+01:15:41,450 --> 01:15:46,990
+إذا مشتقة ال arc length parameter بتعطينا ميه؟
+
+630
+01:15:46,990 --> 01:15:53,370
+بتعطينا مقدار ال speed لجسم متحرك مقدار السرعة
+
+631
+01:15:53,370 --> 01:16:01,650
+بالنسبة له الحركة
+
+632
+01:16:01,650 --> 01:16:07,070
+عندنا على smooth curve هل يمكن لهذا المقدار أن
+
+633
+01:16:07,070 --> 01:16:12,260
+يكون في يوم من الأيام صفر؟يبقى المضمون دائما و
+
+634
+01:16:12,260 --> 01:16:18,480
+أبدا أكبر من الـ 0 و لا يمكن أن تسوى من الـ 0 يبقى
+
+635
+01:16:18,480 --> 01:16:28,000
+بنكتفها لنحظة بسيطة هيك for a small curve للمنحنة
+
+636
+01:16:28,000 --> 01:16:35,200
+الأملس ال DS على DT دائما و أبدا أكبر من الـ 0
+
+637
+01:16:35,200 --> 01:16:46,250
+becauseطول ال V لا يمكن
+
+638
+01:16:46,250 --> 01:16:51,910
+أن تكون Zero في يوم من الأيام هذا سيعطينا ان ال S
+
+639
+01:16:51,910 --> 01:17:04,330
+of T is an increasing function of T كما زعمنا قبل
+
+640
+01:17:04,330 --> 01:17:04,970
+قليل
+
+641
+01:17:09,860 --> 01:17:14,840
+بنجي لآخر النقطة من هذا ال section اللي هو النقطة
+
+642
+01:17:14,840 --> 01:17:28,820
+رقم 3 اللي هو unit tangent vector هديله رمز T جاية
+
+643
+01:17:28,820 --> 01:17:33,900
+من كلمة tangent we
+
+644
+01:17:33,900 --> 01:17:44,130
+know that احنا بنعرف انهV Velocity V
+
+645
+01:17:44,130 --> 01:17:51,210
+Velocity V Velocity
+
+646
+01:17:51,210 --> 01:17:52,230
+V Velocity V Velocity V Velocity V Velocity V
+
+647
+01:17:52,230 --> 01:17:52,230
+Velocity V Velocity V Velocity V Velocity V
+
+648
+01:17:52,230 --> 01:17:52,230
+Velocity V Velocity V Velocity V Velocity V
+
+649
+01:17:52,230 --> 01:17:52,590
+Velocity V Velocity V Velocity V Velocity V
+
+650
+01:17:52,590 --> 01:17:52,590
+Velocity V Velocity V Velocity V Velocity V
+
+651
+01:17:52,590 --> 01:17:52,590
+Velocity V Velocity V Velocity V Velocity V
+
+652
+01:17:52,590 --> 01:17:52,590
+Velocity V Velocity V Velocity V Velocity V
+
+653
+01:17:52,590 --> 01:17:52,590
+Velocity V Velocity V Velocity V Velocity V
+
+654
+01:17:52,590 --> 01:17:52,590
+Velocity V Velocity V Velocity V Velocity V
+
+655
+01:17:52,590 --> 01:17:52,590
+Velocity V Velocity V Velocity V Velocity V
+
+656
+01:17:52,590 --> 01:17:52,650
+Velocity V Velocity V Velocity V Velocity V
+
+657
+01:17:52,650 --> 01:17:56,990
+Velocity V Velocity V Velocity V Velocity V
+
+658
+01:17:56,990 --> 01:18:05,310
+Velocity V Velocity V Velocity V Velocity
+
+659
+01:18:05,310 --> 01:18:07,130
+V Velocity
+
+660
+01:18:08,940 --> 01:18:19,420
+the unit tangent vector T
+
+661
+01:18:19,420 --> 01:18:26,320
+بدي يساوي ال V على طول ال V هذا بيعطينا ال unit
+
+662
+01:18:26,320 --> 01:18:30,780
+tangent vector بدي
+
+663
+01:18:30,780 --> 01:18:36,880
+أحاول أثبت لك ان مقوله فعلا يساوي واحد صحيح فبجي
+
+664
+01:18:36,880 --> 01:18:45,490
+بقول senseبما أن الـ DS على DT أكبر من الـ Zero
+
+665
+01:18:45,490 --> 01:18:54,750
+نحن لدينا أن الـ DT على DS كذلك أكبر من الـ Zero
+
+666
+01:18:54,750 --> 01:19:03,790
+هذا يجب أن يعطيك أن الـ DT على DS يجب أن يكون واحد
+
+667
+01:19:03,790 --> 01:19:12,650
+على DS على DTاللي هو بده يساوي واحد على طول ال V
+
+668
+01:19:12,650 --> 01:19:26,730
+ثم الـDR على DS بده يساوي اللي هو DR على DT في DT
+
+669
+01:19:26,730 --> 01:19:34,470
+على DS هذا الأول اللي هو عبارة عن الصرعة D والتاني
+
+670
+01:19:34,470 --> 01:19:42,860
+اللي هو واحدعلى طول الـ V ويساوي الـ V على طول الـ
+
+671
+01:19:42,860 --> 01:19:49,740
+V ويساوي الـ T etc. لو حبيت اتأكد الطول تلعب فضل
+
+672
+01:19:49,740 --> 01:19:57,880
+بقول طول الـ D A على D S يساوي الطول الـ Vعلى طول
+
+673
+01:19:57,880 --> 01:20:04,000
+ال V و يسوى طول ال V على طول ال V و يسوى واحد صحيح
+
+674
+01:20:04,000 --> 01:20:13,840
+لك هذا سوف يعطيك ان DR على DS is a unit vector
+
+675
+01:20:13,840 --> 01:20:17,800
+نعطيه
+
+676
+01:20:17,800 --> 01:20:19,260
+تعريف Definition
+
+677
+01:20:26,480 --> 01:20:35,720
+unit tangent vector of
+
+678
+01:20:35,720 --> 01:20:42,900
+a smooth curve R
+
+679
+01:20:42,900 --> 01:20:47,220
+of T is
+
+680
+01:20:47,220 --> 01:20:59,650
+T ده تساوي DR على DSواللي هي بالاسامة عمليا ال V
+
+681
+01:20:59,650 --> 01:21:01,770
+على قول ال V
+
+682
+01:21:51,320 --> 01:21:57,040
+بنرجع الكلام اللي كاتبينه مرة ثانية نحاول نستنتج
+
+683
+01:21:57,040 --> 01:22:02,360
+متجة طوله الواحدة اللي هو واحد صحيح وبالتالي هيكون
+
+684
+01:22:02,360 --> 01:22:08,340
+unit vector وبنبين ان هذا المتجه هو المتجه المماس
+
+685
+01:22:08,340 --> 01:22:12,300
+للمنعنى هبقى جيب اقول مئة unit tangent vector
+
+686
+01:22:12,300 --> 01:22:18,480
+هديله الرقم 6أحنا بنعرف أن غلصة V هي DR على DT لو
+
+687
+01:22:18,480 --> 01:22:21,180
+أعطينا vector value of function اشتقناها بيعطينا
+
+688
+01:22:21,180 --> 01:22:25,640
+مين السرعة و اشتقناها كم مرة بيعطينا مين العجل ال
+
+689
+01:22:25,640 --> 01:22:29,480
+acceleration خلّينا مع السرعة اللي هي DR على DT
+
+690
+01:22:29,480 --> 01:22:35,480
+اتجاه ال V دائما و أبدا هو اتجاه مماصل الملحنة
+
+691
+01:22:35,480 --> 01:22:40,590
+يعني لو كان عندي محاولبالشكل اللي عندنا هذا وقلنا
+
+692
+01:22:40,590 --> 01:22:47,370
+هذا محور X وهذا محور Y وهذا محور Z وروحنا رسمنا
+
+693
+01:22:47,370 --> 01:22:54,770
+معادلة المنحنة او رسمنا رسمة المنحنة عند اي لحظة
+
+694
+01:22:54,770 --> 01:23:00,670
+فكان المنحنة بهذا الشكل على سبيل المثال يبقى هذا
+
+695
+01:23:00,670 --> 01:23:05,270
+المنحنة عند اي لحظة وروحنا اخدنا اي نقطة موجودة
+
+696
+01:23:05,270 --> 01:23:10,880
+عليهوالتكن هذه النقطة مثلا النقطة اللى عندها يبقى
+
+697
+01:23:10,880 --> 01:23:18,900
+هذا يمثل مين؟ RT لمتجه الموضوع عند اى لحظة ابتداء
+
+698
+01:23:18,900 --> 01:23:25,600
+من مين؟ من نقطة الاصل اللى دى Z اتجاه الحركة هو
+
+699
+01:23:25,600 --> 01:23:32,080
+عبارة عن اتجاه السرعة وهذا هو اتجاه مماس للمنحنة
+
+700
+01:23:32,080 --> 01:23:37,360
+عند النقطة اتجاه النبات يكون بالشكل اللى عندناهك
+
+701
+01:23:37,360 --> 01:23:44,160
+هذا الشكل يبقى هذا المماز اللي هو اتجاه مين؟ اتجاه
+
+702
+01:23:44,160 --> 01:23:49,040
+السرعة طبعا طيب اتجاه السرعة اللي اواخدتها ليه
+
+703
+01:23:49,040 --> 01:23:56,920
+متجه طول الوحدة هذا هسميه متجه T اللي هو V على طول
+
+704
+01:23:56,920 --> 01:24:01,780
+ال V هذا
+
+705
+01:24:01,780 --> 01:24:05,920
+بيكويس فاللي هي اللي هنا بيقول الفلوس ال EDR على
+
+706
+01:24:05,920 --> 01:24:12,840
+DTطب نعرف طوله المربع المركبات تحت الجدار T قسمنا
+
+707
+01:24:12,840 --> 01:24:18,620
+ال V على طول ال V الأهم ان اثبت ان هذا فعلا هو ال
+
+708
+01:24:18,620 --> 01:24:22,680
+tangent vector و الطول سبعه يساوي الواحد الصحيح
+
+709
+01:24:22,680 --> 01:24:28,820
+اظن DS على DT كتبناها قبل قليل هنا كانت دالة موجبة
+
+710
+01:24:28,820 --> 01:24:35,260
+مشتقتها اكبر من من ال zero طب لو غلبتهابتبقى أكبر
+
+711
+01:24:35,260 --> 01:24:38,160
+من الـ zero ولا بيصير أقل من الـ zero يعني لو
+
+712
+01:24:38,160 --> 01:24:42,640
+قلتلك خمسة مثلا ممكنها تبتش بيصير خمس أكبر من الـ
+
+713
+01:24:42,640 --> 01:24:46,800
+zero ولا لا إذا المقلب هو أكبر من الـ zero لكن ال
+
+714
+01:24:46,800 --> 01:24:53,220
+DT على DS هذه هي واحد على DS على DT مين ال DS على
+
+715
+01:24:53,220 --> 01:24:59,500
+DT طول ال Vإذا بقدر أقول واحد على طول ال بيهدمين
+
+716
+01:24:59,500 --> 01:25:05,240
+دي ات اي على دي اس بقولك لو روحنا اشتقنا R بالنسبة
+
+717
+01:25:05,240 --> 01:25:11,100
+ل S يعني اشتقنا R بالنسبة لل R بارامتر S ما هو
+
+718
+01:25:11,100 --> 01:25:15,710
+بقدرش انا اجيبالارك برامتر S إلا إذا كان عندي main
+
+719
+01:25:15,710 --> 01:25:22,090
+R of T يعني ال S of T بدأ تعتمد عالميا على R of T
+
+720
+01:25:22,090 --> 01:25:27,250
+يعني لو افضلت ال R بالنسبة ال S ينفس الكلام تفضل
+
+721
+01:25:27,250 --> 01:25:32,110
+ال R بالنسبة ال T تفضل ال T بالنسبة ال S لإن ال R
+
+722
+01:25:32,110 --> 01:25:36,650
+function of T و ال S كذلك function of T يعني بقدر
+
+723
+01:25:36,650 --> 01:25:41,330
+أدخل الوسيط أو ال parameter T ما بين الطب الـDR
+
+724
+01:25:41,330 --> 01:25:46,450
+على DT هي مين؟ الـV، إذا بدي أشيلها و أضع مكانها
+
+725
+01:25:46,450 --> 01:25:52,590
+الـV الـDT على DR، واحد على طول الـV، إذا هذا
+
+726
+01:25:52,590 --> 01:25:56,690
+بيصير الـV على طول الـV، اللي هو مين؟ الـUnit
+
+727
+01:25:56,690 --> 01:26:01,350
+Tangent Dبيكون هذا هو ال unit tangent لو كان طوله
+
+728
+01:26:01,350 --> 01:26:06,910
+واحد صحيح إذا بدي أجيب طول ال DR على DS يبقى هو
+
+729
+01:26:06,910 --> 01:26:11,410
+طول ال V اللي طالع عندنا على طول ال V بطول ال V
+
+730
+01:26:11,410 --> 01:26:15,710
+على طول ال V لو جداش واحد صحيح يبقى فعلا هذا عبارة
+
+731
+01:26:15,710 --> 01:26:20,090
+عن unit vector اللي حسمي طبقا لهذا ال definition
+
+732
+01:26:20,090 --> 01:26:24,770
+يبقى هو ال unit tangent vectorلو أجالي السؤال وقال
+
+733
+01:26:24,770 --> 01:26:29,550
+لي هات لل unit tangent vector للمنطقة الفلاني بشتق
+
+734
+01:26:29,550 --> 01:26:33,530
+بيكون هذا السرعة بجيب طوله بيكون هذا ال speed
+
+735
+01:26:33,530 --> 01:26:37,090
+باقسم اتنين على بعض بيكون هذا ال unit tangent
+
+736
+01:26:37,090 --> 01:26:41,990
+vector تقول هذا السورة؟ الكلام اللي أنا بقوله هعطي
+
+737
+01:26:41,990 --> 01:26:47,910
+عليه مثال إذن بدنا نروح للمثال الأخير في هذا ال
+
+738
+01:26:47,910 --> 01:26:51,530
+section يبقى
+
+739
+01:26:51,530 --> 01:26:52,090
+example
+
+740
+01:27:03,690 --> 01:27:13,570
+sine of T زائد cosine of T كله في اتجاه I زائد T
+
+741
+01:27:13,570 --> 01:27:21,530
+cosine of T ناقص sine of T كله في اتجاه J وT
+
+742
+01:27:21,530 --> 01:27:30,130
+greater than zero المقول الأول دي بقى is find the
+
+743
+01:27:30,130 --> 01:27:42,460
+speedمفتاح الصراعي نمره بـ find the unit tangent
+
+744
+01:27:42,460 --> 01:27:48,260
+vector of
+
+745
+01:27:48,260 --> 01:27:57,040
+the curve of the curve نمره C find the length of
+
+746
+01:27:57,040 --> 01:28:06,530
+the curve find the lengthأو الذكية كده شقول
+
+747
+01:28:06,530 --> 01:28:14,450
+المنحنى four على الفترة التي تي أكبر من أو تساوي
+
+748
+01:28:14,450 --> 01:28:22,170
+جدر اتنين وأقل من أو يساوي كده اتنين
+
+749
+01:28:22,170 --> 01:28:30,650
+قلبي
+
+750
+01:28:30,650 --> 01:28:38,060
+أرفع هناسؤال مرة ثانية معطيني
+
+751
+01:28:39,180 --> 01:28:44,940
+Position vector متجه موضوع لدالة ما الهو main R of
+
+752
+01:28:44,940 --> 01:28:49,840
+T ساوية T sin T زائد cos T في اتجاه I زائد T cos T
+
+753
+01:28:49,840 --> 01:28:55,160
+not sin T في اتجاه من؟ في اتجاه ال J قال هدى قداش
+
+754
+01:28:55,160 --> 01:29:00,320
+ال speed إذا مشان أجيبه ال speed بتروح أشتق مظبوط
+
+755
+01:29:00,320 --> 01:29:04,940
+طبعا ماعنديش K ال K كانوا المعامل تبعها يساوي Zero
+
+756
+01:29:04,940 --> 01:29:11,890
+تمام هبقى قوله كويسةهذا تعتبر من الـ X وهذا تعتبر
+
+757
+01:29:11,890 --> 01:29:20,490
+من الـ Y إذا بدي أجيب له الـ DX على DT، خويصة هذه
+
+758
+01:29:20,490 --> 01:29:26,110
+يبقى الجزء الأول مشتقت حاصل ضرب داليتين بقش بتقوله
+
+759
+01:29:26,110 --> 01:29:38,890
+sin T زي T في cos T مناقص sin Tيبقى بدها تساوي T
+
+760
+01:29:38,890 --> 01:29:49,450
+في Cos T هذه هتروح معاها طيب بدي أجيب له Dy على Dt
+
+761
+01:30:13,280 --> 01:30:19,680
+يبقى السرعة V as a function of T بيدها تساوي اللي
+
+762
+01:30:19,680 --> 01:30:32,100
+هو T هو sine of T في اتجاه I مقص T في اتجاه G فبجب
+
+763
+01:30:32,100 --> 01:30:42,030
+اقول له ليه speedاللي بدأ يساوي O لل V O لل V اللي
+
+764
+01:30:42,030 --> 01:30:48,370
+هو الجذري التربيعي لمربع المُركّبات T تربيع cosine
+
+765
+01:30:48,370 --> 01:30:57,650
+تربيع T زائد T تربيع sine تربيع T يساوي Descant
+
+766
+01:30:57,650 --> 01:31:02,570
+Root ل T تربيع عامل مشترك طبقه sin تربيع زائد sin
+
+767
+01:31:02,570 --> 01:31:09,400
+تربيع اللي هو بواحدتحت الجذر ب T يبقى مقدار السرعة
+
+768
+01:31:09,400 --> 01:31:15,240
+عند اي لحظة بدي اياها هي عبارة عنين؟ عبارة عن T
+
+769
+01:31:15,240 --> 01:31:21,340
+إذا خلصنا من المطلب الأول المطلب الثاني قال لي هذا
+
+770
+01:31:21,340 --> 01:31:28,580
+ال unit tangent vector بقول لغة بسيطة اليونت هذا
+
+771
+01:31:28,580 --> 01:31:33,180
+نمرأ ايه الأول؟ مضاد إلى نمرأ B اليونت
+
+772
+01:31:36,000 --> 01:31:47,300
+Tangent vector اللي هو V بتقى الـT T بده يساوي
+
+773
+01:31:47,300 --> 01:31:54,340
+الـV على طول الـV هو يساوي الـV المتجه اللي عندنا
+
+774
+01:31:54,340 --> 01:32:02,280
+اللي هو T هو Sine T في اتجاه Iنقص T Sine T في
+
+775
+01:32:02,280 --> 01:32:09,620
+اتجاه الجهة كله مقسم على مين؟ على T إذا أصبح T
+
+776
+01:32:09,620 --> 01:32:15,580
+بدرساوي وSine T في اتجاه الأعلى نقص Sine T في
+
+777
+01:32:15,580 --> 01:32:22,080
+اتجاه مين؟ في اتجاه الجهة طيب السؤال هو هل هذا
+
+778
+01:32:22,080 --> 01:32:23,580
+فعلا unit vector؟
+
+779
+01:32:27,490 --> 01:32:31,210
+بطلع واحد فعلا unit vector بربي على المُركّبات
+
+780
+01:32:31,210 --> 01:32:33,870
+اللي عندك وصية تربيه زاد وصية تربيه اللي فتطلع
+
+781
+01:32:33,870 --> 01:32:38,310
+مجدش واحد يعني فعلا هذا هو مين هو ال unit vector
+
+782
+01:32:38,310 --> 01:32:43,330
+اللي طلع طب المطلوب التالت جالي هاد لل length تبع
+
+783
+01:32:43,330 --> 01:32:49,070
+ال curve على الفترة من جدر اتنين لغاية من اتنين
+
+784
+01:32:49,070 --> 01:32:55,870
+اذا باجب اقوله بدنا ال length اللي يسوى تكامل من
+
+785
+01:32:55,870 --> 01:33:03,370
+وين لوينمن جدر اتنين لغاية اتنين لمين؟ لقول ال V
+
+786
+01:33:03,370 --> 01:33:10,990
+كداش طول ال V؟ T هاي بروح أحسب من جديد يبقى خلاص
+
+787
+01:33:10,990 --> 01:33:16,870
+بشيل الجدر كله هذا و حسبناها و خلصنا يبقى بقوله
+
+788
+01:33:16,870 --> 01:33:24,150
+فقط T D T من وين جبتها؟ من قول ال V هاي اللي عندك
+
+789
+01:33:25,080 --> 01:33:27,940
+يبقى الموجود خلاص في إشتعاق وما بضيع وقته وحاسب من
+
+790
+01:33:27,940 --> 01:33:35,220
+أول لجديد فايه جاهز إذا حاطنا يبقى هذا قدر نص تيه
+
+791
+01:33:35,220 --> 01:33:43,060
+تربيع من جذر يتنين لغاية اتنين ويساوي النص في أربع
+
+792
+01:33:43,060 --> 01:33:50,470
+نقص اتنين نص في اتنين يساوي واحدإذا طول هذا الجزء
+
+793
+01:33:50,470 --> 01:33:55,850
+من المنحنى يساوي واحد صحيح تابي نجي ال exercises
+
+794
+01:33:55,850 --> 01:34:06,590
+تلتاشر تلاتة تابي
+
+795
+01:34:06,590 --> 01:34:10,830
+نجي ال exercises تلتاشر
+
+796
+01:34:10,830 --> 01:34:18,330
+تلاتة المسائل من واحد لخمستاشر من واحد
+
+797
+01:34:27,680 --> 01:34:31,360
+بدا أسأل السؤال التاني يوم اتنين افتتحتوا
+
+798
+01:34:31,360 --> 01:34:35,260
+discussion يعني اجتكوا الميدا اسمها كام section
+
+799
+01:34:35,260 --> 01:34:40,520
+غطيتوا فيها اربعة كويس يعني اربعة كل section معقول
+
+800
+01:34:40,520 --> 01:34:46,900
+كويس تعويضية ماشي ممتاز يعني اليوم اتخلص ال
+
+801
+01:34:46,900 --> 01:34:47,700
+chapter معناته
+
+802
+01:34:52,120 --> 01:34:56,900
+كيف؟ يعني يبقى تقولولها الامتحان داخل فيه chapter
+
+803
+01:34:56,900 --> 01:35:01,460
+13 كله يعني كمان المحاضرة المشرحة المرة القادمة
+
+804
+01:35:01,460 --> 01:35:06,220
+اللي هو section 13 أربعة داخل فيه الامتحان فلازم
+
+805
+01:35:06,220 --> 01:35:11,680
+اتغطي ال chapter 13 كله قبل الامتحان ماشي؟ كويس
+
+806
+01:35:11,680 --> 01:35:16,220
+ساعطيكوا العافية حد هنا اليوم بيكفي و المرة جاء ان
+
+807
+01:35:16,220 --> 01:35:16,800
+شاء الله
+
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/iMvxudRFYy4.srt b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/iMvxudRFYy4.srt
new file mode 100644
index 0000000000000000000000000000000000000000..ae3aff7aecfa64b00edc08aa97e23b3ccb9be255
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/iMvxudRFYy4.srt
@@ -0,0 +1,2687 @@
+1
+00:00:00,000 --> 00:00:02,680
+موسيقى
+
+2
+00:00:08,960 --> 00:00:14,660
+بسم الله الرحمن الرحيم، بدأنا في المحاضرة الماضية
+
+3
+00:00:14,660 --> 00:00:19,300
+عن هنا، اللي هو الـ chapter 12 اللي كان بيتحدث عن
+
+4
+00:00:19,300 --> 00:00:23,400
+الـ vectors، الـ dot product، الـ cross product، الـ
+
+5
+00:00:23,400 --> 00:00:28,020
+lines and the planes، وكذلك بعض المجسمات اللي هي
+
+6
+00:00:28,020 --> 00:00:31,640
+الستة أنواع من المجسمات بالإضافة إلى الـ
+
+7
+00:00:31,640 --> 00:00:35,830
+cylinders، اللي هي الأسطوانات. الآن ننتقل إلى chapter
+
+8
+00:00:35,830 --> 00:00:39,990
+13 اللي بيتحدث عن الـ vector valued functions and
+
+9
+00:00:39,990 --> 00:00:44,650
+functions in a space. يبقى احنا الآن بدنا ننتقل إلى
+
+10
+00:00:44,650 --> 00:00:49,850
+المعادلات الاتجاهية. قبل ذلك، قبل chapter 12 وقبل
+
+11
+00:00:49,850 --> 00:00:54,320
+هذا الـ chapter، كان شغلنا على معادلات عادية أو على
+
+12
+00:00:54,320 --> 00:00:58,040
+الـ functions العادية. ننتقل إلى الـ functions
+
+13
+00:00:58,040 --> 00:01:02,920
+الاتجاهية، وسندرس حركة الجسيمات في الفراغ.
+
+14
+00:01:08,090 --> 00:01:13,670
+بدنا الـ velocity تبعه، بدنا الـ acceleration، بدنا
+
+15
+00:01:13,670 --> 00:01:17,930
+مقدار السرعة، اللي هي الـ speed، إلى آخره، تمام؟
+
+16
+00:01:17,930 --> 00:01:22,150
+هنقسم الجسم إلى عدة sections، أول section منهم اللي
+
+17
+00:01:22,150 --> 00:01:26,870
+بيتحدث عن الـ curves in space، المنحنيات في الفراغ.
+
+18
+00:01:27,340 --> 00:01:33,720
+وكذلك المماسات لهذه المنحنيات. يبقى curves in space
+
+19
+00:01:33,720 --> 00:01:38,920
+and their tangents، والمماسات لهذه المنحنيات طبعا عند
+
+20
+00:01:38,920 --> 00:01:43,820
+أي نقطة موجودة على هذه المنحنيات. أول حاجة: التعريف
+
+21
+00:01:43,820 --> 00:01:49,340
+للـ curve في الـ space. إيش معنى الـ curve؟ ثم ننتقل
+
+22
+00:01:49,340 --> 00:01:51,180
+إلى باقي التعريفات.
+
+23
+00:01:54,460 --> 00:02:03,840
+النقطة الأولى: a curve in space، المنحنى في الفراغ
+
+24
+00:02:03,840 --> 00:02:16,260
+is the particle’s path. Is the particle’s path.
+
+25
+00:02:16,260 --> 00:02:20,900
+يعني مسار الجسيم، particle’s path.
+
+26
+00:02:28,850 --> 00:02:37,850
+defined by the points، بالنقط
+
+27
+00:02:37,850 --> 00:02:49,650
+اللي هي x، و y، و z is equal to f of t، و g of t،
+
+28
+00:02:49,650 --> 00:02:58,790
+و h of t، والـ T موجودة في الـ interval I، والـ I اللي
+
+29
+00:02:58,790 --> 00:03:11,470
+هي الـ time interval. الـ I is a time interval.  دُمّرَتْ
+
+30
+00:03:11,470 --> 00:03:19,410
+اثنين: a position vector، a position vector.
+
+31
+00:03:21,990 --> 00:03:29,570
+اتجاه الموضع، of a particle، mass of a particle،
+
+32
+00:03:29,570 --> 00:03:35,670
+mass in
+
+33
+00:03:35,670 --> 00:03:40,290
+space as
+
+34
+00:03:45,210 --> 00:03:53,510
+الـ R of T، فهو يساوي الـ  OP vector، فهو يساوي
+
+35
+00:03:53,510 --> 00:04:00,850
+f of T في اتجاه I، زائد g of T في اتجاه J، زائد h of
+
+36
+00:04:00,850 --> 00:04:10,250
+T في اتجاه K، والـ T موجودة في الـ Interval I. This
+
+37
+00:04:10,250 --> 00:04:21,770
+vector، هذا المتجه، this vector is called، بنسميه
+
+38
+00:04:21,770 --> 00:04:23,390
+the vector valued function.
+
+39
+00:05:02,080 --> 00:05:08,980
+الآن بدنا نجيء إلى الحركة في الفراغ، فباجي بقول الـ
+
+40
+00:05:08,980 --> 00:05:12,520
+curves in space، يبقى المنحنيات في الفراغ، and their
+
+41
+00:05:12,520 --> 00:05:18,760
+tangents، والمماسات لهذه المنحنيات. بدنا نجيء للتعريف
+
+42
+00:05:18,760 --> 00:05:24,930
+الأول. يجب أن أقول: a curve in space، المنحنى في الفراغ
+
+43
+00:05:24,930 --> 00:05:30,070
+is the particle’s path، والمسار للجسيم، that
+
+44
+00:05:30,070 --> 00:05:34,150
+defined by the points، هذا المسار عند أي نقطة وعند
+
+45
+00:05:34,150 --> 00:05:41,610
+أي لحظة، بأن أعرف إحداثيات x، y، و z. كل من x، y، و z هي
+
+46
+00:05:41,610 --> 00:05:47,910
+functions في متغير آخر، المتغير هذا بدي أسميه T، و نظراً
+
+47
+00:05:47,910 --> 00:05:52,710
+لأن الحركة مرتبطة بالزمن، بدي أسميه T، موجودة في الـ
+
+48
+00:05:52,710 --> 00:05:58,510
+I، الـ I is a time interval، يبقى هي الفترة الزمنية
+
+49
+00:05:58,510 --> 00:06:02,350
+اللي أنا بدي أدرس الحركة عليها، الـ time interval،
+
+50
+00:06:02,350 --> 00:06:08,640
+الفترة الزمنية التي يتحرك فيها الجسم في الفراغ. هذه
+
+51
+00:06:08,640 --> 00:06:12,900
+النقطة، اللي هيجيب كل النقاط، كيف يعني؟ لو جينا نقول
+
+52
+00:06:12,900 --> 00:06:17,500
+افترض أن جسم في الفراغ اتحرك، وكان المنحنى بالشكل
+
+53
+00:06:17,500 --> 00:06:22,550
+اللي عنده، المنحنى هذا اللي احنا شايفينه، لا يعني
+
+54
+00:06:22,550 --> 00:06:27,250
+أنه بيتقطع مع نفسه، ترى بالك، لأن هذا رسم في الفراغ، مش
+
+55
+00:06:27,250 --> 00:06:31,650
+تقول المنحنى بيتقطع عند النقطة هذه، لا بيتقطعش، هذا أي
+
+56
+00:06:31,650 --> 00:06:40,010
+حركة في الهواء. طيب، يبقى عند أي لحظة، أي نقطة موجودة
+
+57
+00:06:40,010 --> 00:06:44,660
+هنا أو هنا أو هنا أو في أي مكان، أقول الإحداثيات
+
+58
+00:06:44,660 --> 00:06:51,020
+تبعها x، و y، و z، وكل من x، و y، و z هي function في
+
+59
+00:06:51,020 --> 00:06:56,060
+T، حيث T اللي هو الـ Time أو ما إلى ذلك. هذا
+
+60
+00:06:56,060 --> 00:06:59,360
+بالنسبة لي، التعريف اللي هو التعريف الثاني، بقول: إذا
+
+61
+00:06:59,360 --> 00:07:03,980
+position vector، متجه الموضع، of a particle moves
+
+62
+00:07:03,980 --> 00:07:08,600
+in space، لجسم يتحرك في الفراغ، بدي أعبر عنها وأقول
+
+63
+00:07:08,600 --> 00:07:16,010
+هي R of T، يساوي المتجه OP. يعني لو جئت أخذ أي نقطة
+
+64
+00:07:16,010 --> 00:07:22,470
+زي النقطة هذه مثلاً، على مسار الجسيم، سميتها x، و y، و
+
+65
+00:07:22,470 --> 00:07:31,510
+z، كل من x، و y، و z هي عبارة عن f of T، و g of T، و h of
+
+66
+00:07:31,510 --> 00:07:37,010
+T بهذا الشكل. يبقى في الفراغ، النقطة لها ثلاثة
+
+67
+00:07:37,010 --> 00:07:44,120
+إحداثيات. ذهبتُ ورسمتُ المتجه من الـ origin لغاية هذه
+
+68
+00:07:44,120 --> 00:07:50,080
+النقطة. الشكل اللي عندنا هذا، هذا المتجه سمّيته R of
+
+69
+00:07:50,080 --> 00:07:57,180
+T، يبقى الـ vector R of T الذي يبدأ من نقطة الأصل
+
+70
+00:07:57,180 --> 00:08:02,020
+إلى أي نقطة موجودة على المنحنى، هسمي الـ position
+
+71
+00:08:02,020 --> 00:08:08,750
+vector، اللي هو متجه الموضع، عند أي لحظة. يبقى سمّيته
+
+72
+00:08:08,750 --> 00:08:15,470
+المتجه RT، المتجه RT بدي أكتبه as a vector، كمتجه
+
+73
+00:08:15,470 --> 00:08:20,610
+فباجي بقول هو عبارة عن f of T في اتجاه I، زي g of T
+
+74
+00:08:20,610 --> 00:08:25,970
+في اتجاه J، زي h of T في اتجاه K. يبقى كل مركبة من
+
+75
+00:08:25,970 --> 00:08:32,370
+هذه المركبات تعتبر مركبة في اتجاه ما. لما بدي أكتب
+
+76
+00:08:32,370 --> 00:08:37,540
+متجه الموضع as a position vector، الـ position
+
+77
+00:08:37,540 --> 00:08:40,820
+vector هذا يا بنات هو اللي بيسمّيه vector valued
+
+78
+00:08:40,820 --> 00:08:46,150
+function، اللي هو الأولاني اللي احنا قلنا عليه، اللي
+
+79
+00:08:46,150 --> 00:08:51,050
+هو هي الـ curves اللي عندنا، curves in space، المنحنى
+
+80
+00:08:51,050 --> 00:08:57,430
+ده متجه الموضع عند أي لحظة أو عند أي نقطة موجودة
+
+81
+00:08:57,430 --> 00:09:01,890
+عليه. هسميها الـ R of T، بدلالة T، بدلالة هذه
+
+82
+00:09:01,890 --> 00:09:06,690
+المركبات. يبقى الخط اللي احنا شايفينه هذا هو المسار
+
+83
+00:09:06,690 --> 00:09:07,990
+تبع الجسيم.
+
+84
+00:09:14,340 --> 00:09:19,960
+هو أي vector من نقطة الأصل إلى أي نقطة تقع على هذا
+
+85
+00:09:19,960 --> 00:09:26,580
+المنحنى. وبالتالي الـ R of T، بسمّيها الـ vector valued
+
+86
+00:09:26,580 --> 00:09:31,460
+function.  Function. لكل مركبة من هذه المركبات هي
+
+87
+00:09:31,460 --> 00:09:33,480
+عبارة عن function.
+
+88
+00:09:41,170 --> 00:09:45,590
+اللي موجودة في time interval. إذا أطلع قيم، ومن هنا
+
+89
+00:09:45,590 --> 00:09:50,210
+سميناها valued. إذا هذا المتجه الموضع بسميه vector
+
+90
+00:09:50,210 --> 00:09:57,230
+valued function. إذا بناء عليه، كأننا مع دالة جديدة
+
+91
+00:09:57,510 --> 00:10:01,630
+غير الدوال اللي اتعرفنا عليها في calculus A
+
+92
+00:10:01,630 --> 00:10:06,450
+و calculus B. بقى نقول في calculus A: y تساوي f of x،
+
+93
+00:10:06,450 --> 00:10:11,950
+في الـ polar: r تساوي f of θ، تمام؟ إذا احنا هنا باجي
+
+94
+00:10:11,950 --> 00:10:16,210
+بقول الـ R of T هي f of T في اتجاه الـ I، g of T في
+
+95
+00:10:16,210 --> 00:10:20,750
+اتجاه الـ J، h of T في اتجاه الـ K. يبقى هذه الدالة
+
+96
+00:10:20,750 --> 00:10:25,670
+اتجاهية في الفراغ. إذا، مدام دالة، بدنا نروح نشوف الـ
+
+97
+00:10:25,670 --> 00:10:28,430
+limit لهذه الدالة، وبدنا نروح نشوف الـ
+
+98
+00:10:28,430 --> 00:10:32,070
+differentiation لهذه الدالة، والـ integral لهذه
+
+99
+00:10:32,070 --> 00:10:36,430
+الدالة. يعني كل الأشياء التي درست على الدالة
+
+100
+00:10:36,430 --> 00:10:41,630
+العادية من التعرض، هنطبقها على الدالة اللي قدامنا هذه.
+
+101
+00:10:42,010 --> 00:10:46,390
+يبقى أول نقطة بدي أشير إليها، اللي هي limit and
+
+102
+00:10:46,390 --> 00:10:52,010
+continuity لهذه الدالة. كيف بدنا نروح نحسبها؟ يبقى
+
+103
+00:10:52,010 --> 00:11:00,430
+بدي أحط عنوان صغير، اللي هو limits and continuity،
+
+104
+00:11:00,430 --> 00:11:06,390
+النهايات
+
+105
+00:11:06,390 --> 00:11:10,190
+والاتصال لهذه الدالة. هعطي definition.
+
+106
+00:11:12,990 --> 00:11:19,850
+definition، بقول: Let R of T يساوي f of T في
+
+107
+00:11:19,850 --> 00:11:26,930
+اتجاه I، زائد g of T في اتجاه J، زائد h of T في
+
+108
+00:11:26,930 --> 00:11:38,250
+اتجاه K، is a vector، is a vector valued function.
+
+109
+00:11:38,250 --> 00:11:40,610
+then
+
+110
+00:11:44,880 --> 00:11:53,860
+للـ R of T، لما T بدها تروح إلى T naught، is defined by
+
+111
+00:11:53,860 --> 00:12:07,620
+as defined by، بعرفها بالتالي: limit للـ R of T، لما T
+
+112
+00:12:07,620 --> 00:12:11,060
+بدها تروح لـ T naught، بده يساوي
+
+113
+00:12:13,820 --> 00:12:18,720
+للـ f of T، لما T بدها تروح إلى T naught، في اتجاه الـ
+
+114
+00:12:18,720 --> 00:12:26,780
+I، زائد limit للـ g of T، لما T بدها تروح لـ T naught، زائد
+
+115
+00:12:26,780 --> 00:12:33,380
+limit، طبعاً في اتجاه الـ J، limit الـ h of T، لما T
+
+116
+00:12:33,380 --> 00:12:38,360
+بدها تروح إلى T naught، في اتجاه الـ K، في اتجاه الـ
+
+117
+00:12:38,360 --> 00:12:38,600
+K.
+
+118
+00:12:47,470 --> 00:12:51,970
+بنرجع لهذا التعريف مرة ثانية. أنا عندي vector valued
+
+119
+00:12:51,970 --> 00:12:56,190
+function على الصيغة R of T، سواء f of T في اتجاه
+
+120
+00:12:56,190 --> 00:13:00,750
+الـ I، زي g of T في اتجاه الـ J، زي h of T في
+
+121
+00:13:00,750 --> 00:13:05,670
+اتجاه الـ K. بدي أعرف الـ limit لهذه الـ function.
+
+122
+00:13:05,670 --> 00:13:10,370
+فبقول: limit لهذه الـ function هي limit للـ R of T، لما
+
+123
+00:13:10,370 --> 00:13:15,760
+تبدأ تروح لـ T naught. هذه شو تساوي؟ الـ Limit لهذه الدالة
+
+124
+00:13:15,760 --> 00:13:21,160
+تعني Limit لكل مركبة من هذه المركبات. إذا باجي
+
+125
+00:13:21,160 --> 00:13:24,260
+limit للمركبة الأولى في اتجاه الـ I، limit
+
+126
+00:13:24,260 --> 00:13:27,360
+للمركبة الثانية في اتجاه الـ J، limit للمركبة
+
+127
+00:13:27,360 --> 00:13:32,580
+الثالثة في اتجاه الـ K. نفترض حسبنا هذه الـ limits،
+
+128
+00:13:32,580 --> 00:13:39,720
+وطلعت L1 في اتجاه الـ I، L2 في اتجاه الـ J، L3 في
+
+129
+00:13:39,720 --> 00:13:40,920
+اتجاه الـ K.
+
+130
+00:13:43,580 --> 00:13:47,460
+أول شيء يجب أن نفهمه يا بنات هو أن الـ vector
+
+131
+00:13:47,460 --> 00:13:51,560
+-valued function، لو أخذت لها limit، يجب أن يخرج
+
+132
+00:13:51,560 --> 00:13:55,220
+كمان vector، ليس مثل الدوال العادية، الدوال العادية
+
+133
+00:13:55,220 --> 00:13:59,060
+اللي أخذت لها limit، تخرج constant، مظبوط أم لا؟ لكن
+
+134
+00:13:59,060 --> 00:14:04,600
+هنا يجب أن يخرج vector مكون من ثلاث مركبات، يمكن
+
+135
+00:14:04,600 --> 00:14:09,650
+بعضها صفر، ويمكن بعضها غير الصفر، ويمكن الـ limit تطلع
+
+136
+00:14:09,650 --> 00:14:13,810
+does not exist، كمان كما سنرى بعد قليل إن شاء الله.
+
+137
+00:14:13,810 --> 00:14:17,790
+تعالى يعني، ممكن الـ limit تكون exist، وممكن الـ
+
+138
+00:14:17,790 --> 00:14:23,230
+limit تكون does not exist، تماماً مثل الدوال العادية.
+
+139
+00:14:23,230 --> 00:14:31,210
+يبقى هذا اختصاراً، بقول: هذا الـ L، يجب أن نفهم إنه
+
+140
+00:14:31,210 --> 00:14:37,930
+vector، ولما نكتبه، سأضع عليه سهم لأعرف إن هذا
+
+141
+00:14:37,930 --> 00:14:42,190
+vector. طب السؤال هو: هل هذا يا بنات constant
+
+142
+00:14:42,190 --> 00:14:47,600
+vector؟ والله الـ vector هذا متغير. لما نأخذ الـ limit،
+
+143
+00:14:47,600 --> 00:14:51,940
+ها constant vector، لأن كل واحد هيعطيني قيمة، اللي
+
+144
+00:14:51,940 --> 00:14:55,120
+هو الـ one، والثانية الـ two، والثالثة الـ three. إذا
+
+145
+00:14:55,120 --> 00:14:59,040
+هذا بدو يطلع عندي limit constant vector، زي ما الـ
+
+146
+00:14:59,040 --> 00:15:02,420
+limit تبعت الـ function العادية كنا بنطلعها scalar
+
+147
+00:15:02,420 --> 00:15:08,900
+أو constant، تمام. طيب، نعطي كمان definition ثاني.
+
+148
+00:15:18,380 --> 00:15:30,040
+The function R of T is continuous، تبقى الدالة متصلة، at
+
+149
+00:15:30,040 --> 00:15:40,360
+a point، عند النقطة T تساوي T naught، in its domain،
+
+150
+00:15:40,360 --> 00:15:54,270
+in its domain، في المجال تبع هذه الدالة، if the limit للـ R
+
+151
+00:15:54,270 --> 00:16:00,930
+of T، لما T بدها تروح لـ T naught، بدها تساوي R of T
+
+152
+00:16:00,930 --> 00:16:06,770
+naught، also، وكذلك.
+
+153
+00:16:07,950 --> 00:16:15,230
+الـ R of T بيكون f of T في اتجاه I، زائد g of T في
+
+154
+00:16:15,230 --> 00:16:23,390
+اتجاه J، زائد h of T في اتجاه K، is continuous، is
+
+155
+00:16:23,390 --> 00:16:36,470
+continuous، دالة متصلة، at T تساوي T naught if and only if
+
+156
+00:16:42,860 --> 00:16:55,240
+and الـ h are continuous at T تساوي T naught.
+
+157
+00:17:26,820 --> 00:17:31,780
+أخذنا تعريف الـ curve في الـ space، وبعد ذلك عرفنا
+
+158
+00:17:31,780 --> 00:17:35,100
+الـ vector-valued function، والآن بدنا نجيء للـ limit
+
+159
+00:17:35,100 --> 00:17:38,800
+للـ vector-valued function، والـ continuity، طبعاً
+
+160
+00:17:38,800 --> 00:17:43,680
+عرفنا الـ limit، والـ limit للـ vector-valued function
+
+161
+00:17:43,680 --> 00:17:48,860
+بيطلع كمان اللي هو constant vector. بدنا نجيء الآن
+
+162
+00:17:48,860 --> 00:17:53,520
+للـ continuity، الـ Continuity لهذه الدالة. بقول الـ
+
+163
+00:17:53,520 --> 00:17:58,160
+vector function R of T بتبقى continuous عند نقطة
+
+164
+00:17:58,160 --> 00:18:02,200
+T تساوي T naught اللي موجودة في domain هذه
+
+165
+00:18:02,200 --> 00:18:06,240
+الدالة، إذا والله الـ limit للـ R of T، لما T بتروح لـ
+
+166
+00:18:06,240 --> 00:18:12,440
+T naught، تساوي مين؟ R of T naught. السؤال هو: هل اختلف هذا
+
+167
+00:18:12,440 --> 00:18:18,060
+التعريف عن تعريف الـ continuity لدالة عادية؟ في
+
+168
+00:18:18,060 --> 00:18:19,140
+اختلاف بينهم؟
+
+169
+00:18:26,970 --> 00:18:32,150
+الدالة بقول عنها continuous عند نقطة إذا كان قيمة
+
+170
+00:18:32,150 --> 00:18:37,250
+الدالة عند تلك النقطة تساوي نهاية الدالة عند تلك
+
+171
+00:18:37,250 --> 00:18:37,830
+النقطة.
+
+172
+00:18:43,720 --> 00:18:48,140
+مش هذا التعريف، وروحنا قسمنا هذا التعريف إلى ثلاث
+
+173
+00:18:48,140 --> 00:18:54,700
+نقاط، في calculus one، وسميناها الـ continuity test، يعني
+
+174
+00:18:
+
+223
+00:24:55,980 --> 00:25:00,200
+الكلمة لكن في كل علم من العلوم لها مصطلح مختلف،
+
+224
+00:25:00,200 --> 00:25:04,400
+مثلاً vector عنا إيش بيقولون عليها إحنا، لكن طبعاً
+
+225
+00:25:04,400 --> 00:25:08,380
+كلية الطب عندنا بيقولوا، الـ vector بيسموه
+
+226
+00:25:08,380 --> 00:25:13,740
+حامل جرثوم، طبعاً اللي بحمل جرثوم بيتحرك، فالـ
+
+227
+00:25:13,740 --> 00:25:17,440
+vector عندهم بيسموه، بترجموه حامل جرثوم، لكن إحنا
+
+228
+00:25:17,440 --> 00:25:21,620
+بيقولوا متجه، إذا كلمة في اللغة الإنجليزية إذا
+
+229
+00:25:21,620 --> 00:25:26,300
+جينا نبعد عن اللغة الأدبية وبدنا نحطها كمصطلح
+
+230
+00:25:26,300 --> 00:25:32,380
+يختلف طبعاً المعنى، متقارب لكن يختلف من علم إلى علم
+
+231
+00:25:32,380 --> 00:25:38,530
+آخر ترجمة لهذا المصطلح، طيب برجع مرة ثانية، بقول الـ R
+
+232
+00:25:38,530 --> 00:25:42,910
+of T is called smooth، يعني منحنى أملس إذا تحقق
+
+233
+00:25:42,910 --> 00:25:48,910
+شرطان، الشرط الأول أن دي R على دي T is continuous
+
+234
+00:25:48,910 --> 00:25:53,630
+يعني لو اشتقيت الـ vector valued function، بدي المشتقة
+
+235
+00:25:53,630 --> 00:25:59,810
+تكون دالة متصلة، إثنين، بدي المشتقة ممنوعة تساوي
+
+236
+00:25:59,810 --> 00:26:00,170
+zero
+
+237
+00:26:03,570 --> 00:26:09,070
+هذه وقتها تبقى متصلة إذا كانت المركبات الثلاث 
+
+238
+00:26:09,070 --> 00:26:14,430
+continuous، المشتقة الأولى للمركبات الثلاث، يعني DF
+
+239
+00:26:14,430 --> 00:26:17,790
+على DT، و DG على DT، و DH على DT
+
+240
+00:26:21,260 --> 00:26:27,160
+هذه النقطة الأولى، النقطة الثانية، مش كلهم Zero يعني
+
+241
+00:26:27,160 --> 00:26:30,460
+ممكن تبقى واحدة بـ Zero، والثانية بـ Zero، بس الثالثة
+
+242
+00:26:30,460 --> 00:26:37,260
+ممنوعة تكون بـ Zero، لإيش؟ لأن الـ DR على DT لا تساوي
+
+243
+00:26:37,260 --> 00:26:40,320
+Zero، لكن المركبة تلقاها واحدة بـ Zero ما في مشكلة لو
+
+244
+00:26:40,320 --> 00:26:43,000
+كانت اثنتين بـ Zero، ما في مشكلة، لكن إذا الثلاث بـ
+
+245
+00:26:43,000 --> 00:26:48,280
+Zero، إذا بطل المنحنى smooth curve، هذا بدي
+
+246
+00:26:48,280 --> 00:26:54,700
+يخليني أسأل السؤال التالي: هل يمكن للجسيم أن يتوقف
+
+247
+00:26:54,700 --> 00:27:00,560
+على الـ smooth curve؟ ممكن يوقف؟ ممنوع، لأنه بدي
+
+248
+00:27:00,560 --> 00:27:03,580
+equal to zero، في هذه الحالة يبقى المستقلات هذه
+
+249
+00:27:03,580 --> 00:27:09,320
+كلها equal to zero، طب اثنتين؟ هل يمكن على الـ smooth
+
+250
+00:27:09,320 --> 00:27:15,380
+curve أن يحصل عندي كاسب يعني أنه يطاف حد في المنحنى
+
+251
+00:27:15,660 --> 00:27:21,700
+أو يكون عندي corner، طبعاً لا، لأن الدالة غير قابلة
+
+252
+00:27:21,700 --> 00:27:25,800
+للاشتقاق عند الكاسب، والـ corner مش هيك اللي أخدت
+
+253
+00:27:25,800 --> 00:27:31,760
+فكرة الفلسفة، إذا على اسمه كـ there is no cusp، و
+
+254
+00:27:31,760 --> 00:27:36,020
+كمان there is no corner، ما فيش عندي على المرحلة ده
+
+255
+00:27:36,020 --> 00:27:40,520
+ده نكتب المرحلة كويسة هنا، يعني مجرد تركيز ليس
+
+256
+00:27:52,720 --> 00:28:01,620
+هنا على المنحنى الأملس لا يوجد كورنر، لا يوجد
+
+257
+00:28:01,620 --> 00:28:05,840
+كورنر
+
+258
+00:28:05,840 --> 00:28:11,380
+أو كاسب، لا هذا ولا ذلك
+
+259
+00:28:21,230 --> 00:28:30,130
+أول مثال بيقول  اللي هو الـ R of T بدها تساوي E أس
+
+260
+00:28:30,130 --> 00:28:37,930
+ناقص T في اتجاه الـ I زائد T ناقص واحد على T زائد
+
+261
+00:28:37,930 --> 00:28:46,590
+واحد في اتجاه الـ J زائد تان Inverse T في اتجاه من؟
+
+262
+00:28:46,590 --> 00:28:48,210
+في اتجاه الـ K
+
+263
+00:28:50,950 --> 00:28:56,510
+Limit للـ R of T لما T بدها تروح
+
+264
+00:29:09,730 --> 00:29:14,570
+يقول خد R of T يساوي E أس ناقص T في اتجاه I زي T
+
+265
+00:29:14,570 --> 00:29:18,650
+ناقص واحد على T زائد واحد في اتجاه J زي 10 inverse
+
+266
+00:29:18,650 --> 00:29:23,750
+T في اتجاه K، جالي هات النهاية لهذه الدالة لما T بدأ
+
+267
+00:29:23,750 --> 00:29:27,370
+تروح إلى ما لا نهاية، حسب الـ definition اللي كتبناه في
+
+268
+00:29:27,370 --> 00:29:28,650
+طريقة الخريطة تبع الـ level
+
+269
+00:29:34,190 --> 00:29:39,410
+تبدأ تروح لما لا نهاية، تبدأ تسوي limit لكل مركبة
+
+270
+00:29:39,410 --> 00:29:43,990
+من هذه المركبات لما تبدأ تروح لما لا نهاية، هذه
+
+271
+00:29:43,990 --> 00:29:49,310
+limit لما تبدأ تروح لما لا نهاية، E أس ناقص D يا بنات هي
+
+272
+00:29:49,310 --> 00:29:56,370
+عبارة عن مين؟ صفر، ممتاز، يبقى صفر في اتجاه الـ I، T ناقص 1 على T زائد 1 في اتجاه الـ J، طبعاً
+
+273
+00:29:56,370 --> 00:30:04,190
+limit  المفترض
+
+274
+00:30:04,190 --> 00:30:07,870
+اللي عندنا، يبقى limit لما T بدأ تروح لما لا نهاية
+
+275
+00:30:07,870 --> 00:30:15,650
+لمن؟ لـ T ناقص واحد على T زائد واحد في اتجاه الـ J
+
+276
+00:30:15,650 --> 00:30:21,910
+زائد limit لـ تان Inverse T لما T بدأ تروح لما لا
+
+278
+00:30:28,410 --> 00:30:29,010
+نهاية
+
+279
+00:30:35,050 --> 00:30:39,110
+بنروح نحسب الـ limit لكل الـ functions من الـ
+
+280
+00:30:39,110 --> 00:30:43,250
+function الثلاث هنا لما تيجي تروح لما لا نهاية
+
+281
+00:30:43,250 --> 00:30:47,670
+الطريقة المباشرة، سيرجع تجي 0، و 1، 0،  أقصى ما لا
+
+282
+00:30:47,670 --> 00:30:52,310
+نهاية، ما لا نهاية، 1 على ما لا نهاية بـ zero، يبقى
+
+283
+00:30:52,310 --> 00:30:53,810
+النتيجة الأولى
+
+284
+00:30:56,470 --> 00:31:00,510
+نجي للثانية، لما نعوض  طريقنا عشان نوصل لما لا نهاية على
+
+285
+00:31:00,510 --> 00:31:05,750
+ما لا نهاية، قدامي طريقين، الطريق الأول أنه أستخدم قاعدة
+
+286
+00:31:05,750 --> 00:31:10,350
+لوبيتال، اشتق البسط على اشتق المقام، أو اقسم
+
+287
+00:31:10,350 --> 00:31:14,050
+كل من البسط والمقام على T المرفوعة لأعلى أس في
+
+288
+00:31:14,050 --> 00:31:18,590
+المقام، وبعد هيك بروح أعوض، يبقى سواء كانت هذه أو
+
+289
+00:31:18,590 --> 00:31:23,390
+تلك الـ limit لها، يبقى ده واحد صحيح، يبقى هنا
+
+290
+00:31:26,740 --> 00:31:32,040
+بنانيجي الـ limit لـ تان Inverse T، بقى يا إثنين،
+
+291
+00:31:32,040 --> 00:31:36,580
+يعني المذاكرين ما يحفظوا تان Inverse حد، مش مسمى، مش
+
+292
+00:31:36,580 --> 00:31:40,840
+عارفة، بنرسمه يعني، مش مستاهل، طيب لو ذكرنا نتذكر
+
+293
+00:31:40,840 --> 00:31:46,580
+بمنحنى تان Inverse، يبقى اللي بيقول هذا X وهذا Y
+
+294
+00:31:46,580 --> 00:31:51,480
+وهذه النقطة اللي عندنا  بـ باي على إثنين، وهذه النقطة
+
+295
+00:31:51,480 --> 00:31:55,200
+الثانية اللي هي سالب باي على إثنين، لو جيت رسمت
+
+296
+00:31:55,200 --> 00:32:00,760
+المنحنى، المنحنى بده يمر بنقطة الأصل، والمنحنى بيكون
+
+297
+00:32:01,080 --> 00:32:05,860
+اللي هو باللون الأزرق اللي عندنا هذا، جاي وبيجي
+
+298
+00:32:05,860 --> 00:32:12,680
+نازل، الشكل عندنا، طبعاً واضح أنه هذه الـ limit لما الـ
+
+299
+00:32:12,680 --> 00:32:17,440
+X بدها تروح لما لا نهاية، أقصى قيمة بياخدها المنحنى
+
+300
+00:32:17,440 --> 00:32:22,140
+هي باي على إثنين، ولما راح ياخذ قيمة سالبة بيصير قيمة
+
+301
+00:32:22,140 --> 00:32:27,560
+إذا الـ domain كل الـ real line، والـ range من سالب
+
+302
+00:32:27,560 --> 00:32:32,320
+باي على إثنين لغاية باي على إثنين، يبقى هذه زائد
+
+303
+00:32:32,320 --> 00:32:38,630
+باي على إثنين في اتجاه من الـ K، لحظة أن النتيجة
+
+304
+00:32:38,630 --> 00:32:43,830
+تساوي J زائد باي على إثنين في اتجاه الـ K، which is
+
+305
+00:32:43,830 --> 00:32:49,350
+a vector، كما زعمنا قبل قليل، يبقى limit الـ vector
+
+306
+00:32:49,350 --> 00:32:55,070
+valued function هو constant vector، متجه ثابت زي ما
+
+307
+00:32:55,070 --> 00:32:59,170
+إنتوا شايفين، نجي لمثال رقم إثنين، example two
+
+308
+00:33:02,560 --> 00:33:07,300
+الحاجة اسمها إلى نقطتين، النقطة الأولى نمرّ بـ الـ
+
+309
+00:33:07,300 --> 00:33:16,280
+vector function، الدالة المتجهة اللي هو الـ R of T to Z
+
+310
+00:33:16,280 --> 00:33:23,860
+هو sign T في اتجاه الـ I زائد sign T
+
+311
+00:33:27,620 --> 00:33:34,260
+الـ R of T تساوي sin T في اتجاه I زائد sin
+
+312
+00:33:34,260 --> 00:33:38,580
+T في اتجاه J زائد T في اتجاه
+
+313
+00:33:42,100 --> 00:33:46,960
+السؤال هو: هل الـ vector value دي continuous ولا غير
+
+314
+00:33:46,960 --> 00:33:52,700
+continuous؟ نجيب نشوف المركبات، الـ cos T هل لها
+
+315
+00:33:52,700 --> 00:33:57,040
+نقطة عندها بيصير غير معرفة؟ إذا دي continuous على
+
+316
+00:33:57,040 --> 00:34:00,720
+طول، والـ sign طبعاً عارفين أنها بتترجح بين واحد وسالب
+
+317
+00:34:00,720 --> 00:34:05,040
+واحد، من سالب ما لا نهاية لما لا نهاية، لأنها بتردّ الأرض واملأ
+
+318
+00:34:05,040 --> 00:34:10,480
+عليها، تمام؟ والـ T هذه لأنها خطية من الدرجة
+
+319
+00:34:10,480 --> 00:34:14,720
+الأولى، يعني كأنها polynomial من الدرجة الأولى،
+
+320
+00:34:14,720 --> 00:34:18,280
+واحنا الـ polynomial بنعرف أنها متصلة على طول الخط
+
+321
+00:34:18,280 --> 00:34:24,000
+يبقى أن الـ vector function هذه is continuous
+
+322
+00:34:25,670 --> 00:34:37,710
+for all T، هو السبب because each of cos T و sin T
+
+323
+00:34:37,710 --> 00:34:52,110
+and T، because each is continuous for all T، نمرّ
+
+324
+00:34:52,110 --> 00:34:52,450
+بها.
+
+325
+00:35:02,780 --> 00:35:13,280
+R of T يساوي cos T في اتجاه I زائد sin T في
+
+326
+00:35:13,280 --> 00:35:27,760
+اتجاه J زائد دالة R ل T في اتجاه K is discontinuous
+
+327
+00:35:29,400 --> 00:35:40,400
+غير متصلة، بالله الرحمن، والسبب at every integer، عند
+
+328
+00:35:40,400 --> 00:35:49,600
+أي عدد صحيح، because السبب أن الـ limit لدالة الأرض
+
+329
+00:35:49,600 --> 00:35:55,440
+ل T لما تبدأ تروح لل C does
+
+330
+00:35:56,980 --> 00:36:05,020
+not exist، والـ C is an integer
+
+331
+00:36:12,540 --> 00:36:16,640
+المثال الأول يا بناتي اللي هو نمرة A، بيانا فيه
+
+332
+00:36:16,640 --> 00:36:20,120
+أن الـ vector valued function continuous، لأنه ثلاث
+
+333
+00:36:20,120 --> 00:36:26,200
+مركبات continuous، في الآخر واحد نجي لـ example T
+
+334
+00:36:26,200 --> 00:36:29,000
+بيقول الـ vector valued function على الشكل اللي إحنا
+
+335
+00:36:29,440 --> 00:36:38,160
+دالة، المركبة الأولى والثانية دالة
+
+336
+00:36:38,160 --> 00:36:45,200
+السلمية، أو دالة الدرجية، أو step function، أو إحنا
+
+337
+00:36:45,200 --> 00:36:50,380
+بنسميها دالة الأرض، لو كانت لفوق بنسميها دالة السقف
+
+338
+00:36:50,380 --> 00:36:56,200
+الـ ceiling function، لكن هذه اللي هو floor function
+
+339
+00:36:56,200 --> 00:37:03,920
+اللي هو دالة الأرض، أي رقم أعلى من أي عدد صحيح كله
+
+340
+00:37:03,920 --> 00:37:08,440
+بنزّله لمين؟ لنفس العدد الصحيح، فمثلاً الدالة هذه لو
+
+341
+00:37:08,440 --> 00:37:12,760
+كانت الـ T اللي عندي واحد وتسعة من عشرة، بتنزل للواحد
+
+342
+00:37:12,760 --> 00:37:19,620
+لو كانت سبعة من عشرة، بتنزل للصفر، لو كانت ناقص سبعة
+
+343
+00:37:19,620 --> 00:37:25,950
+من عشرة، بتنزل للسالب واحد، وهكذا، تمام؟ يبقى هذه بنزلها
+
+344
+00:37:25,950 --> 00:37:32,290
+لو جيت عند كل عدد صحيح وبدي آخد الـ limit، إذا بروح
+
+345
+00:37:32,290 --> 00:37:36,130
+بأخد الـ limit من اليمين والـ limit من اليسار عند
+
+346
+00:37:36,130 --> 00:37:40,400
+العدد الصحيح، لا يمكن أن الـ two limits يتساووا، بيكون
+
+347
+00:37:40,400 --> 00:37:44,980
+الفرق بينهم واحد صحيح دائماً وأبداً، يعني من هنا
+
+348
+00:37:44,980 --> 00:37:47,860
+ممكن أجيها zero، ومن هنا واحد، من هنا واحد، من هنا
+
+349
+00:37:47,860 --> 00:37:49,340
+نصف، من هنا إثنين، من هنا إثنين، ومن هنا إثنين، ومن
+
+350
+00:37:49,340 --> 00:37:49,460
+هنا إثنين، ومن هنا إثنين، ومن هنا إثنين، ومن
+
+351
+00:37:49,460 --> 00:37:49,600
+هنا إثنين، ومن هنا إثنين، ومن هنا إثنين، ومن
+
+352
+00:37:49,600 --> 00:37:50,000
+هنا إثنين، ومن هنا إثنين، ومن هنا إثنين، ومن
+
+353
+00:37:50,000 --> 00:37:50,160
+هنا إثنين، ومن هنا إثنين، ومن هنا إثنين، ومن
+
+354
+00:37:50,160 --> 00:37:51,780
+هنا إثنين، ومن هنا إثنين، ومن هنا إثنين، ومن
+
+355
+00:37:51,780 --> 00:37:56,520
+هنا إثنين، ومن هنا إثنين، ومن هنا إثنين، ومن
+
+356
+00:37:56,520 --> 00:37:59,180
+هنا إثنين،
+
+357
+00:38:01,480 --> 00:38:07,940
+كتبنا لك C is an integer، يبقى C عدد صحيح، إذا لا
+
+358
+00:38:07,940 --> 00:38:12,540
+يمكن لهذا الـ limit أن  ت exist، يبقى لا يمكن للـ
+
+359
+00:38:12,540 --> 00:38:17,980
+function هذه أن تكون continuous، تمام؟ هذا بالنسبة
+
+360
+00:38:17,980 --> 00:38:22,640
+لمين؟ للـ continuity، نأخذ كمان مثل هذا
+
+361
+00:38:35,870 --> 00:38:45,270
+زائد ربع T تربيع زائد واحد، كل هذا في اتجاه I زائد تان
+
+362
+00:38:45,270 --> 00:38:54,130
+Inverse T في اتجاه J زائد T E أس T في اتجاه K
+
+363
+00:39:05,650 --> 00:39:12,850
+مشتقة هذه الدالة عند T تساوي واحد، تساوي
+
+364
+00:39:30,500 --> 00:39:34,100
+إذا عشان نعرف المشتقة عند الواحد الصحيح، بنروح نشتق
+
+365
+00:39:34,100 --> 00:39:40,000
+الدالة، وبعد ذلك نعوض بالواحد الصحيح، يبقى solution
+
+366
+00:39:40,000 --> 00:39:43,200
+دي
+
+367
+00:39:43,200 --> 00:39:50,920
+دي R على دي T، أو R prime of T، تمام؟ هذا اللي هي R
+
+368
+00:39:50,920 --> 00:39:59,060
+prime of T، وتساوي، تفاضل تان واحد على الداخلية ضرب
+
+369
+00:39:59,060 --> 00:40:04,960
+مشتقة ما بداخلها، يبقى واحد على T تربيع زائد واحد
+
+370
+00:40:04,960 --> 00:40:09,680
+ضرب مشتقة ما بداخل القوس، اللي هو 2T في اتجاه
+
+371
+00:40:09,680 --> 00:40:17,150
+الـ J، تان Inverse of one over one plus T square in
+
+372
+00:40:17,150 --> 00:40:25,370
+the direction of J، المشتقة حاصل ضرب قوسين، يبقى هذه
+
+373
+00:40:25,370 --> 00:40:32,290
+زائد E أس T زائد T في E أس T في اتجاه الـ K
+
+374
+00:40:32,290 --> 00:40:39,610
+المشتقة E أس T في E أس T نفسها، جالي هات للـ R
+
+375
+00:40:39,610 --> 00:40:44,370
+prime of one، بقول الـ R prime of one بدي يساوي، إذا
+
+376
+00:40:44,370 --> 00:40:49,530
+بدي أشيل كل T وأحط مكانها واحد صحيح، البسط هنا
+
+377
+00:40:49,530 --> 00:40:53,310
+بـ إثنين، واحد تربيعه واحد زائد واحد، بـ إثنين، إثنين
+
+378
+00:40:53,310 --> 00:41:01,670
+على إثنين، يبقى I فقط، نغم، ليه؟ بعد، ها، تبقى واحد،
+
+379
+00:41:01,670 --> 00:41:07,130
+يبقى بصير نص، يبقى زائد نص في اتجاه الـ J، اللي
+
+380
+00:41:07,130 --> 00:41:17,290
+بعدها E زائد E، لو قديش ب 2E، يبقى زائد 2E في اتجاه K
+
+381
+00:41:17,290 --> 00:41:22,690
+يبقى المشتقة كذلك من نهايتها vector، ولما نعوض بها
+
+382
+00:41:22,690 --> 00:41:28,570
+بها عندها نقطة صار main، صار constant vector، السؤال
+
+383
+00:41:28,570 --> 00:41:29,230
+الرابع
+
+384
+00:41:39,220 --> 00:41:48,100
+R of T بقدر زاوية اللي هو T تكعيب في اتجاه I زائد
+
+385
+00:42:05,850 --> 00:42:09,910
+هل المنحنى اللي قدامنا هذا منحنى أملس أم لا؟ سبق أن قلنا
+
+386
+00:42:09,910 --> 00:42:14,790
+له we don't know، أنا ما بعرفش، لكن أنا بروح أشوف هل
+
+387
+00:42:14,790 --> 00:42:20,050
+الشرطين متحققين ولا لا، تبعات من الـ smooth curve، شرط
+
+388
+00:42:20,050 --> 00:42:24,930
+الأول، بده أجيب المشتقة الأولى، وأبين أن الثلاث
+
+389
+00:42:24,930 --> 00:42:30,570
+مشتقات اللي عندنا are continuous، نمراً واحد، نمراً
+
+390
+00:42:30,570 --> 00:42:36,260
+اثنين، ممكن يكونوا بعضهم ب صفر، لكن ليس كلهم بصفر، إذا
+
+391
+00:42:36,260 --> 00:42:36,820
+كانوا أفضل، واحدة ما يكونوا، أفضل، واحدة ما يكونوا
+
+392
+00:42:36,820 --> 00:42:38,440
+أفضل، واحدة ما يكونوا، أفضل، واحدة ما يكونوا أفضل
+
+3
+
+445
+00:48:46,050 --> 00:48:52,930
+الـ V هو اتجاه السرعة، هو
+
+446
+00:48:52,930 --> 00:49:05,850
+اتجاه السرعة، اللي هو اتجاه الحركة
+
+447
+00:49:05,850 --> 00:49:11,570
+وهو اتجاه الحركة، وهو
+
+448
+00:49:14,710 --> 00:49:23,550
+variation of motion، أو هو اتجاه الحركة
+
+449
+00:50:16,790 --> 00:50:19,190
+متجه العجلة
+
+450
+00:50:29,650 --> 00:50:43,850
+a small curve للمرحلة الأملس لفلوستي، كما
+
+451
+00:50:43,850 --> 00:50:50,450
+لا يساوي صفراً أبداً
+
+452
+00:50:50,450 --> 00:50:56,760
+يمكن أن تساوي صفراً، يبقى هذا يعني كلمة اللي
+
+453
+00:50:56,760 --> 00:51:05,520
+أعتقد، بظبط، stop، ليه أعتقد بظبط
+
+454
+00:51:05,520 --> 00:51:15,000
+ما تستطيع التوقف، لا يتوقع أن  بظبط يعكس اتجاهه
+
+455
+00:51:15,000 --> 00:51:18,220
+بظبط
+
+456
+00:51:18,220 --> 00:51:20,460
+ما يعكس
+
+457
+00:51:39,390 --> 00:51:49,030
+الأمثلة، The Tangent Line، خط
+
+458
+00:51:49,030 --> 00:51:58,370
+الماس، اسمه الـ Curve، المرحلة
+
+459
+00:51:58,370 --> 00:51:58,950
+الأولى
+
+460
+00:52:23,960 --> 00:52:35,660
+السهم، كتابة، هي الرسالة التي
+
+461
+00:52:35,660 --> 00:52:45,960
+تتجه من النقطة، تتجه من النقطة
+
+462
+00:53:02,210 --> 00:53:11,530
+Parallel، الذي في نفس الوقت يكون موازياً لـ V of T0
+
+463
+00:53:11,530 --> 00:53:18,430
+اللي هو Velocity Vector
+
+464
+00:54:19,100 --> 00:54:23,920
+طب أنا أخذته في المرحلة الثانوية، في حساب التفاضل
+
+465
+00:54:23,920 --> 00:54:29,360
+والتكامل، أن تفاضل المسافة يعطيني السرعة
+
+466
+00:54:29,360 --> 00:54:35,050
+وتفاضل السرعة يعطيني العجلة، هنا في الـ
+
+467
+00:54:35,050 --> 00:54:39,270
+vector value of function، نفس الطريقة بالضرب، وبقدر
+
+468
+00:54:39,270 --> 00:54:44,590
+أجيب السرعة مقداراً واتجاهاً، مقداراً، أجيب طول متجه
+
+469
+00:54:44,590 --> 00:54:49,270
+السرعة، كده، شو يكون مقدار الـ speed، اتجاهاً، بقسم
+
+470
+00:54:49,270 --> 00:54:53,590
+متجه السرعة على طوله، يعطيني الـ direction، أو
+
+471
+00:54:53,590 --> 00:55:00,960
+يعطيني متجه الوحدة في اتجاه الحركة، فمثلاً بقول له
+
+472
+00:55:00,960 --> 00:55:05,560
+كان الـ R of T هو الـ position vector للجسم
+
+473
+00:55:05,560 --> 00:55:09,540
+المتحرك على منحنى، small curve، على
+
+474
+00:55:09,540 --> 00:55:14,660
+منحنى أملس، بدي الـ V of T، بروح بشتق المنحنى
+
+475
+00:55:14,660 --> 00:55:18,260
+من  الأسفل إلى T، وهذا يصيح الـ particles
+
+476
+00:55:18,260 --> 00:55:24,640
+velocity vector، متجه سرعة الجسيم، that is a tangent
+
+477
+00:55:24,640 --> 00:55:30,620
+والذي يكون مماساً للمنحنى، كيف يعني؟ ما أجي
+
+478
+00:55:30,620 --> 00:55:34,980
+بقول، لو جينا للمنحنى اللي رسمناه قبل شوية، وروح
+
+479
+00:55:34,980 --> 00:55:41,660
+نقول هذا محور X، وهذا محور Y، وهذا محور Z، نفترض
+
+480
+00:55:41,660 --> 00:55:48,480
+الجسيم كان ماشياً بالشكل اللي رسمناه، ورحت بدي أوجد
+
+481
+00:55:48,480 --> 00:55:54,940
+اللي هو متجه السرعة عند هذه النقطة، على سبيل
+
+482
+00:55:54,940 --> 00:56:01,980
+المثال، بقول له بدي متجه الموضع من نقطة الأصل إلى هذه
+
+483
+00:56:01,980 --> 00:56:10,160
+النقطة، يبقى هذا هو متجه الموضع، هذا اللي هو R of T، الـ
+
+484
+00:56:10,160 --> 00:56:15,600
+R of T، لو روحت افاضلتها، بحصل على متجه السرعة، وين
+
+485
+00:56:15,600 --> 00:56:22,960
+بدي يكون متجه السرعة؟ اتجاه مماس لمن؟ للمنحنى عند
+
+486
+00:56:22,960 --> 00:56:24,240
+هذه النقطة
+
+487
+00:56:33,760 --> 00:56:41,580
+V of T، V of T، هو متجه السرعة، متجه السرعة يمثل اتجاه
+
+488
+00:56:41,580 --> 00:56:48,220
+الحركة، ويمثل اتجاه السرعة، وهو عبارة عن مشتقة الـ
+
+489
+00:56:48,220 --> 00:56:50,020
+position vector
+
+490
+00:56:55,800 --> 00:57:02,600
+يبقى هذا بسميه متجه السرعة، والذي يكون مماساً للمنحنى
+
+491
+00:57:02,600 --> 00:57:08,400
+إذا رسمناها، مماس للمنحنى عند النقطة، مقدار هذه
+
+492
+00:57:08,400 --> 00:57:12,040
+السرعة، مقدار هذه السرعة بسميها speed
+
+493
+00:57:34,840 --> 00:57:39,910
+النقطة الرابعة، بدي أيه؟ بروح بأشتق أيه؟ طبعاً الـ
+
+494
+00:57:39,910 --> 00:57:44,310
+acceleration، هي مشتقة الـ V بالنسبة إلى T، المشتقة
+
+495
+00:57:44,310 --> 00:57:49,050
+الأولى، أو المشتقة الثانية لـ vector valued
+
+496
+00:57:49,050 --> 00:57:52,430
+functions، أو للـ position vector، اللي هو R of T
+
+497
+00:57:52,430 --> 00:57:54,730
+يعني D تربيع R على D تربيع T
+
+498
+00:57:58,420 --> 00:58:03,680
+على الـ smooth curve، قال، الوصف، لا يمكن أن تساوي
+
+499
+00:58:03,680 --> 00:58:09,940
+صفراً، لأن إذا V تساوي صفراً، معناته المشتقات اللي
+
+500
+00:58:09,940 --> 00:58:15,230
+اشتقناهم هنا بده تساوي صفراً، وهذا يناقض الشرط الثاني
+
+501
+00:58:15,230 --> 00:58:21,070
+من شروط smooth curve، يبقى لا يمكن أن يتوقف الجسيم
+
+502
+00:58:21,070 --> 00:58:26,150
+مش عاجزاكوا بس، الـ particle does not stop،  لا يتوقف
+
+503
+00:58:26,150 --> 00:58:31,130
+and does not reverse its direction، يعني ما يروح يعكس
+
+504
+00:58:31,130 --> 00:58:34,570
+اتجاه الحركة، أنه لو اتجاه... لو افترضنا أنه ماشي
+
+505
+00:58:34,570 --> 00:58:38,290
+في هذا الاتجاه، وبعدين بده يعكس، يعني بده يصل إلى
+
+506
+00:58:38,290 --> 00:58:44,910
+نقطة تنعدم السرعة عندها، ويبدأ يرجع ثانيةً، عند هذه
+
+507
+00:58:44,910 --> 00:58:48,910
+النقطة، صار مقدار السرعة يساوي صفراً، إذاً على
+
+508
+00:58:48,910 --> 00:58:54,970
+الـ smooth curve، ما عنديش توقف للجسم، ما عنديش أن
+
+509
+00:58:54,970 --> 00:58:58,330
+الجسم يعود على نفس الخط اللي هاجي عليه، اللي هو
+
+510
+00:58:58,330 --> 00:59:02,300
+reverse its direction، يبقى هذه ملاحظة من خلال
+
+511
+00:59:02,300 --> 00:59:07,560
+التعريف تبع الـ smooth curve، آخر نقطة عندي اللي
+
+512
+00:59:07,560 --> 00:59:11,000
+هو tangent line، طبعاً لو رجعنا للعنوان اللي احنا
+
+513
+00:59:11,000 --> 00:59:15,360
+كاتبينه، كاتبين الـ curves and tangent lines، وحتى
+
+514
+00:59:15,360 --> 00:59:19,360
+الآن لم نتحدث عن الـ tangent line، يبقى نيجي للـ
+
+515
+00:59:19,360 --> 00:59:23,400
+tangent line، فبأعود للـ tangent line to a smooth
+
+516
+00:59:23,400 --> 00:59:29,830
+curve، لمنحنى أملس، مقطع بهذا الشكل، هذه النقطة، هو
+
+517
+00:59:29,830 --> 00:59:36,310
+الخط الذي يمر بالنقطة F of T node، وG of T node، وH
+
+518
+00:59:36,310 --> 00:59:41,890
+of T node، هذه أصلاً مركبات X، Y، وZ، يعني إحداثيات نقطة
+
+519
+00:59:41,890 --> 00:59:46,550
+إذا، مشان أجيب إحداثيات نقطة، بدي أشيل كل T، وأعوض
+
+520
+00:59:46,550 --> 00:59:50,650
+بقيمة T node، لأن أنا بحصل على ثلاثة أرقام، الثلاثة
+
+521
+00:59:50,650 --> 00:59:55,410
+أرقام بيكونوا هم الـ components لـ position
+
+522
+00:59:55,410 --> 01:00:01,070
+vector، اللي عندها بدي أحسب التمام، طيب يبقى هي جدنا
+
+523
+01:00:01,070 --> 01:00:08,130
+نقطة تقع على الخط المستقيم، الـ line، هذا بدي يكون
+
+524
+01:00:08,130 --> 01:00:14,530
+parallel to V node، لمتجه السرعة عند نقطة T node
+
+525
+01:00:14,530 --> 01:00:22,020
+يعني الـ tangent، بدي يكون هنا؟ لا، الـ
+
+526
+01:00:22,020 --> 01:00:25,540
+vector، أنا بقدر أنقله زي ما بدي، بس الـ tangent بدي
+
+527
+01:00:25,540 --> 01:00:29,320
+يكون مماساً عند تلك النقطة، مظبوط ولا لا؟ إذا الـ
+
+528
+01:00:29,320 --> 01:00:33,900
+tangent، هذا، بدي يكون مطابقاً تماماً على V، يبقى
+
+529
+01:00:33,900 --> 01:00:40,420
+هو المتجه، في بالضبط عند الكمية النقطة، واحنا أخذنا
+
+530
+01:00:40,420 --> 01:00:46,040
+اللي هو في section 12-5، بدي معادلة الـ، أو المعادلة
+
+531
+01:00:46,040 --> 01:00:50,520
+البارامترية للخط المستقيم، بيلزمني شغلتين، الشغلة
+
+532
+01:00:50,520 --> 01:00:56,470
+الأولى، النقطة التي تقع عليه، وهي الحمد لله موجودة، المتجه
+
+533
+01:00:56,470 --> 01:01:04,150
+الذي يوازي المماس هو متجه السرعة عند تلك النقطة
+
+534
+01:01:04,150 --> 01:01:10,430
+وبالتالي، بقدر أجيب معادلة خط التماس للمنحنى عند تلك
+
+535
+01:01:10,430 --> 01:01:14,810
+النقطة، هل بتحب تسأل أي سؤال هنا قبل أن ندخل إلى
+
+536
+01:01:14,810 --> 01:01:21,040
+الأمثلة، عن السرعة، عن الـ acceleration، عن الـ
+
+537
+01:01:21,040 --> 01:01:25,160
+direction، عن الـ speed، عن الـ tangent، إيش ما عندي
+
+538
+01:01:25,160 --> 01:01:27,420
+أسئلة؟ مفيش؟
+
+539
+01:01:30,880 --> 01:01:36,120
+المعنى، بنات، أننا نأخذ بعض الأمثلة على اللي هو بعض
+
+540
+01:01:36,120 --> 01:01:40,720
+الـ definitions اللي أشرنا إليها، وتعرفنا عليها قبل
+
+541
+01:01:40,720 --> 01:01:46,120
+قليل، أول مثال من هذه الأمثلة هو، لِهذِه المعادلات الـ
+
+542
+01:01:46,120 --> 01:01:52,060
+بارامترية للخط الذي يكون مماساً للمنحنى اللي
+
+543
+01:01:52,060 --> 01:01:57,540
+عنده، عند T node يساوي E، قديش E؟ هذه قيمة عددية
+
+544
+01:02:01,490 --> 01:02:07,970
+مش سامع، العدد، قديش؟ اثنين وسبعة من عشرة
+
+545
+01:02:07,970 --> 01:02:12,790
+تقريباً، يبقى احنا بنعرف أنه
+
+546
+01:02:18,060 --> 01:02:22,480
+يعني عندي اثنين وسبعة من عشرة تقريباً، مشان أعرف
+
+547
+01:02:22,480 --> 01:02:28,680
+التالية، بدي شغلتين، بدي نقطة يمر بها من المنحنى
+
+548
+01:02:28,680 --> 01:02:37,460
+معناته بدي أجيب F of E، وG of E، وH of E، يبقى آجي
+
+549
+01:02:37,460 --> 01:02:40,240
+بقول له هنا، دي point
+
+550
+01:02:55,850 --> 01:03:01,610
+لأن الـ E بقى قيمة أو واحدة، يبقى هنا للتوضيح، أكتب
+
+551
+01:03:01,610 --> 01:03:02,530
+لأن الـ E
+
+552
+01:03:17,360 --> 01:03:27,540
+وE ناقص واحد على E زائد واحد، وE، هذه النقطة lie on
+
+553
+01:03:27,540 --> 01:03:33,900
+the line، يبقى هذه تقع على الخط اللي احنا بدنا نجيب
+
+554
+01:03:33,900 --> 01:03:39,000
+معادلته، ابتداءً، يبقى أنا جبت له الآن اللي بده إياه، H
+
+555
+01:03:39,000 --> 01:03:45,380
+of T نوت، وG of T نوت، وH of T نوت، بدي أجيب متجه
+
+556
+01:03:45,380 --> 01:03:52,300
+يوازي هذا الـ line، من المتجه، يجب أن يكون V of T نوت
+
+557
+01:03:52,300 --> 01:03:58,440
+شو  حمله؟ يبقى بده أروح أشتق الـ R of T، يبقى بروح
+
+558
+01:03:58,440 --> 01:04:08,290
+بقول له الـ V as a function of T،  d R على d T، نشتق، لأن
+
+559
+01:04:08,290 --> 01:04:17,010
+T بدأ  جبنا في اتجاه مين؟ في اتجاه I، زائد نشتق
+
+560
+01:04:17,010 --> 01:04:20,450
+هذه البسط في مشتقة المقام
+
+561
+01:04:30,790 --> 01:04:36,610
+على مربع المقام الأصلي، T زائد واحد الكل تربيع، في
+
+562
+01:04:36,610 --> 01:04:45,130
+اتجاه الـ J، زائد هذه حاصل ضرب، دليل T في ln الـ T
+
+563
+01:04:45,130 --> 01:04:52,690
+ناقص واحد على T، يعني واحد زائد ln الـ T، كله في اتجاه
+
+564
+01:04:52,690 --> 01:04:55,510
+مين؟ في اتجاه الـ K
+
+565
+01:04:59,880 --> 01:05:07,940
+يبقى الـ V of E، يبقى واحد على E في اتجاه الـ I، هذه
+
+566
+01:05:07,940 --> 01:05:13,280
+مع هذه، الله يسهل عليها، بضلّ نِقدر نجيبها، زائد
+
+567
+01:05:13,280 --> 01:05:19,540
+اثنين على E زائد واحد الكل تربيع
+
+568
+01:05:30,080 --> 01:05:35,460
+يبقى النقطة موجودة، والمتجه الذي يوازي الـ line
+
+569
+01:05:35,460 --> 01:05:42,200
+موجود، إذا بقدر أقول له، the parametric
+
+570
+01:05:42,200 --> 01:05:51,240
+equation for the tangent line
+
+571
+01:06:20,840 --> 01:06:28,360
+زائد اثنين على E زائد واحد الكل تربيع في T، والـ Z
+
+572
+01:06:28,360 --> 01:06:37,260
+يساوي E زائد اثنين T، هذه الـ Parametric
+
+573
+01:06:37,260 --> 01:06:43,040
+Equations، لمن؟ لمعادلات الخط المستقيم الذي بدي
+
+574
+01:06:43,040 --> 01:06:48,680
+يكون مماساً للمنحنى عند هذه النقطة
+
+575
+01:07:18,330 --> 01:07:23,790
+مطلوب الأول، نمرأة، find the particle's path
+
+576
+01:07:31,570 --> 01:07:39,130
+المسار تبع الجسيم، in terms of
+
+577
+01:07:39,130 --> 01:07:49,570
+x and y، بدلالة x و y، نمرة ب، find
+
+578
+01:07:49,570 --> 01:07:58,190
+the particle's velocity، أو find the particle's
+
+579
+01:08:04,250 --> 01:08:12,310
+and acceleration، and acceleration، والعجلة
+
+580
+01:08:12,310 --> 01:08:20,910
+acceleration vectors، متجهات السرعة والعجلة، at T
+
+581
+01:08:20,910 --> 01:08:24,390
+تساوي باي على ستة
+
+582
+01:09:09,630 --> 01:09:14,450
+يجب أن أنا أشتغل في المركبة x و y، والمركبة z بـ 0
+
+583
+01:09:14,450 --> 01:09:19,850
+أنا
+
+584
+01:09:19,850 --> 01:09:24,290
+أشتغل في المركبة x و y، والمركبة z بـ 0، أنا أشتغل في
+
+585
+01:09:24,290 --> 01:09:25,070
+الـ x و الـ y، والمركبة z بـ 0، أنا أشتغل في الـ x و
+
+586
+01:09:25,070 --> 01:09:29,620
+y، والمركبة الثالثة بـ 0، المطلب الثاني هو كم السرعة
+
+587
+01:09:29,620 --> 01:09:35,940
+والعجلة عند T0 يساوي كم؟ باي على ستة، إذا خلّيني أجي
+
+588
+01:09:35,940 --> 01:09:39,540
+للمطلوب الأول، المطلوب الأول، من أين بدي أجيب له X
+
+589
+01:09:39,540 --> 01:09:49,600
+وY؟ هذه المركبة X في اتجاه I، وهذه Y في اتجاه J، يبقى
+
+590
+01:09:49,600 --> 01:09:57,810
+هنا كأنه X بده يساوي اللي هو cos اثنين T، والـ Y
+
+591
+01:09:57,810 --> 01:10:06,220
+بده يساوي ثلاثة sin اثنين T، لما جاء لي هذا السؤال بالمعادلة
+
+592
+01:10:06,220 --> 01:10:11,980
+بدلالة x و y، يعني كأنه بيقول إيه؟ إشْ احذف T من
+
+593
+01:10:11,980 --> 01:10:17,380
+المعادلتين، تتخلص من T، السؤال هو كيف يا بنات
+
+594
+01:10:17,380 --> 01:10:23,700
+نتخلص من T بين المعادلتين، ونخليها بدلالة x و y
+
+595
+01:10:23,700 --> 01:10:29,220
+إيش
+
+596
+01:10:29,220 --> 01:10:30,320
+نعمل بالضبط ثانيةً
+
+597
+01:10:38,040 --> 01:10:44,240
+ماشي، والثانية زيها، وجهة نظر سليمة، 100%، في واحد
+
+598
+01:10:44,240 --> 01:10:50,780
+عنده رأي آخر، آه
+
+599
+01:10:50,780 --> 01:11:03,540
+ما له؟ يعني بدك تقول اثنين sin cos، عقدناها أكثر، صحيح
+
+600
+01:11:03,540 --> 01:11:07,980
+يمكن نفكر بهذا الاتجاه، بدون ما أجي لمعكوس الدوال
+
+601
+01:11:07,980 --> 01:11:15,150
+المثلثية، لطرح الخلاصة، بقول كيف هذه؟ بقدر أقول x يساوي
+
+602
+01:11:15,150 --> 01:11:21,310
+cos اثنين t، وهذه y على ثلاثة يساوي sin اثنين t
+
+603
+01:11:21,310 --> 01:11:27,390
+إذا، لو ربعنا الطرفين وجمعنا، بكون اتخلصت منين؟ من الـ T
+
+604
+01:11:27,390 --> 01:11:31,090
+وبتظلّ المعادلة بدلالة x و y، زي ما هو طالب، إذا لو
+
+605
+01:11:31,090 --> 01:11:36,430
+روحنا ربعنا، يا بنات، بقول x تربيع على ثلاثة الكل
+
+606
+01:11:36,430 --> 01:11:42,870
+تربيع، يساوي cos تربيع اثنين T زائد sin تربيع اثنين
+
+607
+01:11:42,870 --> 01:11:50,470
+T، أو، شو هيّ؟ قلنا x تربيع زائد y تربيع على
+
+608
+01:11:50,470 --> 01:11:53,630
+تسعة، يساوي كده إيش؟ واحد
+
+609
+01:11:58,820 --> 01:12:04,440
+Ellipse، دائرة، Ellipse، طيب، مين الـ major axis، أو
+
+610
+01:12:04,440 --> 01:12:13,100
+الـ axis الأكبر؟ محور X ولا محور Y؟ Y طبعاً، لأنه
+
+611
+01:12:13,100 --> 01:12:16,800
+بحكم من خلال الرقم الكبير اللي في المقام، هذه
+
+612
+01:12:16,800 --> 01:12:23,900
+باعتبارها x على واحد، وهذا من y، كثير على 9، يبقى هذا
+
+613
+01:12:23,900 --> 01:12:24,840
+Ellipse
+
+614
+01:12:29,120 --> 01:12:45,820
+Center at the origin and the major axis along
+
+615
+01:12:47,010 --> 01:12:54,110
+
+667
+01:20:01,090 --> 01:20:08,180
+شبناتهو أحد على اثنين الجدر في مشتقة ما تحت الجدر
+
+668
+01:20:08,180 --> 01:20:13,200
+اللي هو اثنين T بتروح اثنين مع اثنين و ببقى بس
+
+669
+01:20:13,200 --> 01:20:15,880
+عندي T على الجدر التالي
+
+670
+01:20:43,850 --> 01:20:53,170
+واحد على جذر اثنين K بدي الـ acceleration A as a
+
+671
+01:20:53,170 --> 01:21:00,650
+function of T يبقى اللي هي DV على DT بدي اشتغل
+
+672
+01:21:00,650 --> 01:21:07,190
+كمان مرة يبقى المقام في مشتقة البسط باثنين T
+
+673
+01:21:07,190 --> 01:21:09,170
+تربيع زائد واحد
+
+674
+01:21:15,860 --> 01:21:24,080
+المقام الأصلي في اتجاه الـ R إذا المقام في مشتقة
+
+675
+01:21:24,080 --> 01:21:32,120
+البسط بـ 0 ناقص البسط في مشتقة المقام على مربع
+
+676
+01:21:32,120 --> 01:21:34,100
+المقام الأصلي
+
+677
+01:22:06,760 --> 01:22:11,520
+طيب كنت هأضيع وقت ورق وأنا بأبسط لكن بنقول نبسط
+
+678
+01:22:11,520 --> 01:22:16,420
+ماعنداش مشكلة لو حبينا نرتبها ههه  فيطلع عندي اثنين
+
+679
+01:22:16,420 --> 01:22:21,480
+T تربيع وهنا ناقص أربعة T تربيع فبقى ناقص اثنين T
+
+680
+01:22:21,480 --> 01:22:28,220
+تربيع زائد اثنين ناقص اثنين T تربيع زائد اثنين على
+
+681
+01:22:28,220 --> 01:22:34,020
+T تربيع زائد واحد الكل تربيع اللي فاتجاه
+
+682
+01:22:41,050 --> 01:22:47,230
+الـ J زائد هذه لو أحط لها المقامات يا بنات أو هذه
+
+683
+01:22:47,230 --> 01:22:51,650
+اثنين بتروح مع اثنين اللي عندها هذه لو أحط لها
+
+684
+01:22:51,650 --> 01:22:55,390
+المقامات الـ J اللي بنزل هنا وبنضربها بـ T تربيع
+
+685
+01:22:55,390 --> 01:23:03,070
+زائد واحد ناقص T تربيع يبقى بيظل عندي قديش بس واحد
+
+686
+01:23:12,860 --> 01:23:17,520
+مرة ثانية لو وحدت المقامات بده ينزل الجذر هذا تحت
+
+687
+01:23:17,520 --> 01:23:22,760
+الجذر في الجذر بيطير بيظل T تربيع ناقص واحد ناقص T
+
+688
+01:23:22,760 --> 01:23:29,040
+تربيع بيظل قديش عندي بس واحد على المقام بالشكل اللي
+
+689
+01:23:29,040 --> 01:23:32,580
+عندنا هذا بدي أجيب له قديش العجلة
+
+690
+01:23:40,510 --> 01:23:47,910
+وهذا عند الواحد بصير ناقص J عند الواحد بصير اثنين
+
+691
+01:23:47,910 --> 01:23:52,410
+على اثنين اللي هو ناقص J وهذا عند الواحد اللي هو
+
+692
+01:23:52,410 --> 01:23:57,070
+جذر اثنين وهنا اثنين بواحد على اثنين جذر اثنين
+
+693
+01:23:57,070 --> 01:23:58,470
+زائد
+
+694
+01:24:11,550 --> 01:24:16,070
+بنكتب التربيعية تبعها صح أصاب امرأة وأختها عمر
+
+695
+01:24:16,070 --> 01:24:22,530
+يبقى دي اثنين على أربعة اللي هو نص نص جي المفروض
+
+696
+01:24:22,530 --> 01:24:28,210
+يبقى هذا نص جي وهذه واحد على اثنين جذر اثنين جي
+
+697
+01:24:28,210 --> 01:24:35,170
+يبقى جبنا له المطلوب الأول المطلوب الثاني نمبر بيه
+
+698
+01:24:35,170 --> 01:24:38,090
+جاي بيديه الـ speed عند هذه
+
+699
+01:24:44,960 --> 01:24:51,560
+اللي هي الطول المتجه اللي يبدأ يساوي
+
+700
+01:24:51,560 --> 01:25:01,610
+الجذر التربيعي لمربع المركبات الواحد زائد ربع زائد
+
+701
+01:25:01,610 --> 01:25:09,730
+نصف  ويصبح عضل نصف زائد ربع في ثلث ربع زائد
+
+702
+01:25:09,730 --> 01:25:16,850
+واحد في سبعة على أربعة يبقى الجذر التربيعي لسبعة
+
+703
+01:25:16,850 --> 01:25:22,610
+على أربعة يبقى جذر سبعة على الاثنين مقدار السرعة.
+
+704
+01:25:23,370 --> 01:25:31,030
+يعني بدل Direction of Motion يرجع الـ Direction of
+
+705
+01:25:31,030 --> 01:25:41,950
+motion بيساوي الـ V على طول الـ V طول الـ V موجود والـ
+
+706
+01:25:41,950 --> 01:25:46,910
+V هو موجود وين هو؟ بده Direction يرجع  بصيرها
+
+707
+01:25:46,910 --> 01:25:48,730
+بنات؟ اللي هو وين؟
+
+708
+01:25:52,160 --> 01:26:02,360
+زائد نصف J زائد واحد على جذر اثنين K الكل مقسوم على جذر
+
+709
+01:26:02,360 --> 01:26:09,160
+سبعة على اثنين ويساوي اثنين على جذر سبعة في اتجاه
+
+710
+01:26:09,160 --> 01:26:17,040
+الـ I زائد واحد على جذر سبعة في اتجاه الـ J زائد
+
+711
+01:26:17,040 --> 01:26:31,500
+اثنين على جذر الـ K طيب
+
+712
+01:26:31,500 --> 01:26:37,860
+الآن بدنا نيجي بعد هذا الكلام للمطلوب المركزي
+
+713
+01:26:37,860 --> 01:26:42,900
+لِإيجاد الزاوية بين الاثنين عشان أجيب الزاوية بدي
+
+714
+01:26:42,900 --> 01:26:49,060
+يعني بعدين متجهة A و V بقول خد dot product بجيبها
+
+715
+01:26:49,060 --> 01:26:50,320
+بقول الـ A
+
+716
+01:27:00,660 --> 01:27:07,000
+يبقى باتجاه هذه الـ A وهذه الـ B يبقى ضرب هذا قديش
+
+717
+01:27:07,000 --> 01:27:16,360
+النتيجة تبعد I0 اللي بعديها ناقص نصف في جذر في نصف
+
+718
+01:27:16,360 --> 01:27:18,140
+ناقص ربع
+
+719
+01:27:24,140 --> 01:27:29,060
+جذر اثنين واحد على جذر اثنين اللي هو بربع يبقى
+
+720
+01:27:29,060 --> 01:27:39,520
+زائد ربع يساوي هو الجذر التربيعي لمربع المركبات
+
+721
+01:27:39,520 --> 01:27:46,280
+اللي هو ربع زائد اللي هو اثنين جذر اثنين على ثمانية
+
+722
+01:27:46,280 --> 01:27:50,340
+في الجذر التربيعي
+
+723
+01:27:59,650 --> 01:28:03,490
+يوجد كوساين في الزاوية ثيتا هذا ليس قديش أبناء أنا
+
+724
+01:28:03,490 --> 01:28:07,410
+أنا
+
+725
+01:28:07,410 --> 01:28:07,610
+أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا
+
+726
+01:28:07,610 --> 01:28:08,950
+أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا
+
+727
+01:28:08,950 --> 01:28:16,530
+أنا أنا أنا أنا أنا أنا أنا أنا
+
+728
+01:28:16,530 --> 01:28:27,590
+أنا أنا
+
+729
+01:28:27,590 --> 01:28:29,410
+أنا  أ
+
+730
+01:28:35,660 --> 01:28:44,560
+اكسيلريشن أورثوغونال التي تساوي واحد عند هذه
+
+731
+01:28:44,560 --> 01:28:48,220
+النقطة الذين يكونوا متعامدين
+
+732
+01:29:44,000 --> 01:29:50,600
+Differentiable Vector Functions of T
+
+733
+01:30:08,660 --> 01:30:20,460
+و C أي C صغير أي كمية قياسية أي
+
+734
+01:30:20,460 --> 01:30:28,900
+كمية قياسية أي  Any Differentiable Any
+
+735
+01:30:28,900 --> 01:30:37,660
+Differentiable Scalar Function Then
+
+736
+01:30:42,890 --> 01:30:54,650
+على DT لِـ قِيمة الـ C يساوي جذر اثنين الـ D على DT لـ
+
+737
+01:30:54,650 --> 01:30:55,310
+C صغير
+
+738
+01:31:36,390 --> 01:31:48,370
+أو U' of T زائد أو ناقص V' of T  الـ D على DT
+
+739
+01:31:48,370 --> 01:32:02,530
+لـ U ضرب الـ V U' ضرب الـ V زائد U ضرب V'  الـ D
+
+740
+01:32:16,420 --> 01:32:28,620
+DV على DT  الـ D على DT لـ U as a function
+
+741
+01:32:28,620 --> 01:32:36,020
+of T بده يساوي الـ U prime للـ F of T
+
+742
+01:33:10,900 --> 01:33:17,220
+قواعد الاشتقاق لا تختلف عن قواعد الاشتقاق التي
+
+743
+01:33:17,220 --> 01:33:21,760
+تعرفنا عليهم في الدوال العادية فبقول لو كان U و
+
+744
+01:33:21,760 --> 01:33:25,980
+V قابلين
+
+745
+01:33:25,980 --> 01:33:31,380
+للاشتقاق وكان C الكبير هو constant vector و
+
+746
+01:33:31,380 --> 01:33:37,250
+c الصغير هو عبارة عن scalar والـ F scalar function
+
+747
+01:33:37,250 --> 01:33:43,310
+يعني زي cos T زي sin T زي tan inverse T زي T تربيع
+
+748
+01:33:43,310 --> 01:33:47,430
+زي T تربيع ناقص خمسة إلى آخره يعني دالة ليست
+
+749
+01:33:47,430 --> 01:33:52,710
+اتجاهية ومن هنا بسميها scalar function يعني دالة
+
+750
+01:33:52,710 --> 01:33:55,210
+قياسية  دب مشتقتها
+
+751
+01:34:01,340 --> 01:34:07,500
+مشتقة أي متجه ثابت يساوي صفر لأنها كلها مقادير ثابتة
+
+752
+01:34:07,500 --> 01:34:14,900
+بعد هيك مشتقة الـ scalar C في الدالة الاتجاهية U
+
+753
+01:34:20,040 --> 01:34:24,020
+هو الـ main function اللي هي الـ U لو كان هذا الـ
+
+754
+01:34:24,020 --> 01:34:29,120
+scalar وهذا الـ U يبقى بدل مكانة C رقم بدي آخذ
+
+755
+01:34:29,120 --> 01:34:33,440
+سؤال بدل main الـ scalar function F فبقى يقول
+
+756
+01:34:33,440 --> 01:34:36,620
+مُستقلّة الـ function في الـ vector valued
+
+757
+01:34:36,620 --> 01:34:40,920
+function زي الـ function في مُستقلّة الـ vector valued
+
+758
+01:34:40,920 --> 01:34:46,060
+function اللي عندنا هنا قانون التوزيع زي
+
+759
+01:34:53,500 --> 01:34:57,120
+الأولى في مشتقة الثانية زائد الثانية في مشتقة الأولى
+
+760
+01:34:57,120 --> 01:35:05,440
+يعني ايش مشتقة حاصل ضرب دالتين قياسيتين الترتيب
+
+761
+01:35:05,440 --> 01:35:11,320
+ضروري ليس ضروري لأنّ dot product is commutative نيجي
+
+762
+01:35:11,320 --> 01:35:15,820
+على الـ product هذا اللي بده الترتيب يعني هذا اللي
+
+763
+01:35:15,820 --> 01:35:20,480
+قلت لك U prime ضرب V وقلت لك V prime ضرب U مافي مشكلة
+
+764
+01:35:31,760 --> 01:35:36,900
+الأولى في الثانية زائد الأولى في مشتقتها بخلي كل
+
+765
+01:35:36,900 --> 01:35:42,760
+واحد في موقعه وبشتقه في موقعه وبستخدم مشتقة
+
+766
+01:35:42,760 --> 01:35:48,760
+حاصل ضرب دالتين هنا chain rule لو الـ U  cannot
+
+767
+01:35:48,760 --> 01:35:53,460
+function في main في scalar function أخرى بقول الـ U
+
+768
+01:35:53,460 --> 01:35:58,560
+prime F of T وبضربه في مشتقة main مشتقة هذه الـ
+
+769
+01:35:58,560 --> 01:36:01,100
+function  آخر نقطة في هذا
+
+770
+01:36:07,100 --> 01:36:11,340
+الـ vector functions
+
+771
+01:36:11,340 --> 01:36:16,580
+of a constant
+
+772
+01:36:40,370 --> 01:36:53,790
+الـ vector function of T as الـ R of T is of
+
+773
+01:37:09,550 --> 01:37:20,750
+R of T  الـ DR على DT بده يساوي زيرو هذا ايش معناه؟
+
+774
+01:37:20,750 --> 01:37:27,970
+يبقى هذا means ان الـ R of T and
+
+775
+01:38:01,270 --> 01:38:07,190
+الـ R of T of constant length  دالة قبل الاشتقاق لكن
+
+776
+01:38:07,190 --> 01:38:12,490
+القوة تبعها يساوي مقدارا ثابتا ضمن الـ R of T ضد
+
+777
+01:38:12,490 --> 01:38:16,790
+الـ DR على DT بدل يساوي Zero هذا يعني ان الدالة لو
+
+778
+01:38:16,790 --> 01:38:21,750
+مشتقتها هاتين اللي بيكونوا مالهم متعامدان R او
+
+779
+01:38:21,750 --> 01:38:26,590
+أورثوغونال بدنا نبرهن صحة هذا الكلام يبقى احنا عندنا
+
+780
+01:38:26,590 --> 01:38:29,630
+R of T is of constant length
+
+781
+01:38:36,690 --> 01:38:48,570
+طول R of T كده؟ طول R of T طول
+
+782
+01:38:48,570 --> 01:38:53,070
+R of T كده؟
+
+783
+01:38:53,070 --> 01:39:01,490
+طول مصدر ثابت يبقى هذا ايش؟ هذا أعطاني رقم كلام
+
+784
+01:39:15,120 --> 01:39:26,260
+DR على DT ضرب DR على DT بطل R of T كده مُستقل
+
+785
+01:39:26,260 --> 01:39:32,460
+المقدار الثابت؟ Zero تمام احتمال ما يبقاش اللي حصل
+
+786
+01:39:32,460 --> 01:39:39,340
+عندنا  بناء هل هذا وهذا مختلف عن بعض الـ dot
+
+787
+01:39:39,340 --> 01:39:42,280
+is commutative يبقى انه مش هيكون عندي
+
+788
+01:39:46,130 --> 01:39:52,390
+R ضرب DR على DT بده يساوي Zero هذا معناته ان الـ R of
+
+789
+01:39:52,390 --> 01:39:59,390
+T ضرب DR على DT بده يساوي كده Zero وهو المقلوب
+
+790
+01:39:59,390 --> 01:40:04,770
+يعني صار الـ R of T و DR على DT اثنين
+
+791
+01:40:18,060 --> 01:40:29,620
+the vector قيل لي ان المتجه R of T يساوي خمسة كوساين
+
+792
+01:40:29,620 --> 01:40:32,940
+E في اتجاه I زائد خمسة
+
+793
+01:40:52,360 --> 01:41:05,920
+والثابت is orthogonal to
+
+794
+01:41:05,920 --> 01:41:06,900
+its derivative
+
+795
+01:41:21,120 --> 01:41:26,310
+عليه البركة وكان بيبين لي ان المتجه هذا طوله ثابت
+
+796
+01:41:26,310 --> 01:41:30,190
+إذا بروح أحسب قديش الطول تبعه وأشوف قديش هو ثابت
+
+797
+01:41:30,190 --> 01:41:36,990
+فبجي بقول الطول تبع الـ R of T يساوي الـ square root
+
+798
+01:41:36,990 --> 01:41:43,990
+لمربع المركبات قديش هذه خمسة وعشرين cosine تربيع تي
+
+799
+01:41:43,990 --> 01:41:50,250
+زائد خمسة وعشرين sin تربيع تي زائد اثنا عشر في اثنا عشر
+
+800
+01:41:50,250 --> 01:41:55,540
+القد ايش يبقى 144 يبقى هذا الكلام يساوي الجذر
+
+801
+01:41:55,540 --> 01:42:01,560
+التربيعي لو أخد 25 عامل مشترك بيطلع قديش تربيع تربيع
+
+802
+01:42:01,560 --> 01:42:06,460
+تربيع تربيع تربيع تربيع تربيع تربيع تربيع تربيع
+
+803
+01:42:06,460 --> 01:42:09,120
+تربيع تربيع تربيع تربيع تربيع تربيع تربيع تربيع
+
+804
+01:42:09,120 --> 01:42:14,040
+تربيع تربيع تربيع تربيع تربيع تربيع تربيع تربيع
+
+805
+01:42:14,040 --> 01:42:16,980
+تربيع تربيع تربيع تربيع تربيع تربيع تربيع تربيع
+
+806
+01:42:16,980 --> 01:42:17,080
+تربيع تربيع تربيع تربيع تربيع تربيع تربيع تربيع
+
+807
+01:42:20,220 --> 01:42:26,780
+ده مئة وتسعة وستون اللي هو قديش ثلاثة عشر اذا نجد
+
+808
+01:42:26,780 --> 01:42:31,320
+الدالة هذه او الـ vector عند أي لحظة الطول دائما
+
+809
+01:42:31,320 --> 01:42:40,300
+أبدا ثابت ويساوي قديش ثلاثة عشر Sir دي vector او ده
+
+810
+01:42:40,300 --> 01:42:54,000
+given given vector is of Palestine لأن لو
+
+811
+01:42:54,000 --> 01:42:58,520
+ضربت الـ vector فيه واشتقيت هذا سيكون جداء Zero
+
+812
+01:42:58,520 --> 01:43:03,660
+أنا حسبت عملي يبقى الـ R of T موجودة هنا ضايل عليها
+
+813
+01:43:03,660 --> 01:43:12,320
+بس mean DR على DT يبقى DR على DT يساوي سالب خمسة
+
+814
+01:43:15,760 --> 01:43:24,860
+زائد خمسة كوساين T في اتجاه الـ J زائد Zero ايه
+
+815
+01:43:24,860 --> 01:43:34,440
+بده أخد R of T Dot DR على DT هنا
+
+816
+01:43:34,440 --> 01:43:41,400
+هذي في هذي كده  بيصير ناقص خمسة وعشرين Sin كوساين
+
+817
+01:43:41,400 --> 01:43:49,700
+يبقى ناقص خمسة وعشرين ساين تي كوساين تي اللي بعدها
+
+818
+01:43:49,700 --> 01:43:57,800
+زائد خمسة وعشرين ساين تي كوساين تي زائد خمسة وعشرين
+
+819
+01:43:57,800 --> 01:44:05,140
+ساين تي كوساين تي زائد زيرو وهي سواء كده؟ يبقى اثنين
+
+820
+01:44:05,140 --> 01:44:17,710
+ضربها أورثوغونال الـ R of T and الـ D على DT R of
+
+821
+01:44:17,710 --> 01:44:25,110
+T مولانا خديني الآن أرقام المثال تبعد ثلاثة عشر واحد
+
+822
+01:44:25,110 --> 01:44:26,810
+في الـ exercises
+
+823
+01:44:40,260 --> 01:44:51,140
+وخمسة عشر وسبعة عشر وتسعة عشر واثنين وعشرة لهنا
+
+824
+01:44:51,140 --> 01:44:53,980
+انتهى الـ section يعطيكم العافية
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/iMvxudRFYy4_raw.srt b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/iMvxudRFYy4_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..dc2964559bc696382df0a22a4e58e764ac9602fd
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/iMvxudRFYy4_raw.srt
@@ -0,0 +1,3372 @@
+1
+00:00:00,000 --> 00:00:02,680
+موسيقى
+
+2
+00:00:08,960 --> 00:00:14,660
+بسم الله الرحمن الرحيم بدأنا في المحاضرة الماضية
+
+3
+00:00:14,660 --> 00:00:19,300
+عن هنا اللي هو ال chapter اتناشر اللي كان بتحدث عن
+
+4
+00:00:19,300 --> 00:00:23,400
+ال vectors ال dot product ال cross product ال
+
+5
+00:00:23,400 --> 00:00:28,020
+lines and the planes و كذلك بعض المجسمات اللي هي
+
+6
+00:00:28,020 --> 00:00:31,640
+الستة تنوع من المجسمات بالاضافة إلى مين إلى ال
+
+7
+00:00:31,640 --> 00:00:35,830
+cylinders اللي هي الأسطولاتالان بنتقل الى chapter
+
+8
+00:00:35,830 --> 00:00:39,990
+13 اللى بتحدث عن ال vector valued functions and
+
+9
+00:00:39,990 --> 00:00:44,650
+functions in a space يبقى احنا الان بدنا ننتقل الى
+
+10
+00:00:44,650 --> 00:00:49,850
+المعادلات الاتجاهية قبل ذلك قبل chapter 12 وقبل
+
+11
+00:00:49,850 --> 00:00:54,320
+هذا ال chapter كان شغلنا على معادلات عاديةأو على
+
+12
+00:00:54,320 --> 00:00:58,040
+الـ functions عادية ننتقل الى الـ functions
+
+13
+00:00:58,040 --> 00:01:02,920
+التجاهية وسندرس حركة الجسيمات في الفرق
+
+14
+00:01:08,090 --> 00:01:13,670
+بدنا ال velocity تبعته، بدنا ال acceleration، بدنا
+
+15
+00:01:13,670 --> 00:01:17,930
+مقدار السرعة، اللي هي ال speed إلى آخرى، تمام؟
+
+16
+00:01:17,930 --> 00:01:22,150
+هنقهن جسمه إلى عدة section، أول section منهم اللي
+
+17
+00:01:22,150 --> 00:01:26,870
+بتحدث عن ال curves in space المنحنيات في الفرق
+
+18
+00:01:27,340 --> 00:01:33,720
+وكذلك الممثات لهذه المنحنات يبقى curves in space
+
+19
+00:01:33,720 --> 00:01:38,920
+and their tangents والممثات لهذه المنحنات طبعا عند
+
+20
+00:01:38,920 --> 00:01:43,820
+أي نقطة موجودة على هذا المنحنات اول حاجة التعريف
+
+21
+00:01:43,820 --> 00:01:49,340
+لل curve في ال space إيش معنى ال curve ثم ننتقل
+
+22
+00:01:49,340 --> 00:01:51,180
+إلى باقي التعريفات
+
+23
+00:01:54,460 --> 00:02:03,840
+النقطة الأولى a curve in space المنحنة في الفرار
+
+24
+00:02:03,840 --> 00:02:16,260
+is the particles path is the particles path
+
+25
+00:02:16,260 --> 00:02:20,900
+يعني مسار الجسيم particles path
+
+26
+00:02:28,850 --> 00:02:37,850
+defined by the points بالنقا
+
+27
+00:02:37,850 --> 00:02:49,650
+اللي هي امان x و y و z is equal to f of t و g of t
+
+28
+00:02:49,650 --> 00:02:58,790
+و h of tو ال T موجودة في ال interval I و ال I اللي
+
+29
+00:02:58,790 --> 00:03:11,470
+هي ال time interval ال I is a time interval دمرة
+
+30
+00:03:11,470 --> 00:03:19,410
+اتنين a position vector a position vector
+
+31
+00:03:21,990 --> 00:03:29,570
+واتجاه الموضع of a particle mass of a particle
+
+32
+00:03:29,570 --> 00:03:35,670
+mass in
+
+33
+00:03:35,670 --> 00:03:40,290
+space as
+
+34
+00:03:45,210 --> 00:03:53,510
+الـ R of T فهو يساوي الـ O P L A Vector فهو يساوي
+
+35
+00:03:53,510 --> 00:04:00,850
+F of T في اتجاه I زائد G of T في اتجاه J زائد H of
+
+36
+00:04:00,850 --> 00:04:10,250
+T في اتجاه K وT موجودة في الـ Interval I. This
+
+37
+00:04:10,250 --> 00:04:21,770
+vectorهذا المنتجة this vector is called بنسميه
+
+38
+00:04:21,770 --> 00:04:23,390
+the vector valued function
+
+39
+00:05:02,080 --> 00:05:08,980
+الان بدنا نجي الى الحركة في الفرق فباجي بقول ال
+
+40
+00:05:08,980 --> 00:05:12,520
+cares in space يبقى المنحنيات في الفرق and their
+
+41
+00:05:12,520 --> 00:05:18,760
+tangents والممثات لهذه المنحنيات بدنا نجي للتعريف
+
+42
+00:05:18,760 --> 00:05:24,930
+الأوليجب أقول a curve in space المنحنة في الفرارة
+
+43
+00:05:24,930 --> 00:05:30,070
+is the particles path والمسار الريدوسي من ما that
+
+44
+00:05:30,070 --> 00:05:34,150
+defined by the points هذا المسار عند أي لقطة و عند
+
+45
+00:05:34,150 --> 00:05:41,610
+أي لحظة بأن أرفع تكتالي X Y و Z كل من X Y و Z هي
+
+46
+00:05:41,610 --> 00:05:47,910
+function في متغير آخرالمتغير هذا بدي أسميه T ونظرا
+
+47
+00:05:47,910 --> 00:05:52,710
+لإن الحركة مرتبطة بالزمن بدي أسميه T موجودة في ال
+
+48
+00:05:52,710 --> 00:05:58,510
+I ال I is a time interval يبقى هي الفترة الزمنية
+
+49
+00:05:58,510 --> 00:06:02,350
+اللي أنا بدي أدرس الحركة عليه ال time interval
+
+50
+00:06:02,350 --> 00:06:08,640
+الفترة الزمنية اللتي يتحرك فيها الجسم في الفرقهذه
+
+51
+00:06:08,640 --> 00:06:12,900
+النقطة اللي هيجيب كل النقاط كيف يعني لو جيها تقول
+
+52
+00:06:12,900 --> 00:06:17,500
+افترض ان اليوسيف الفراغ اتحرك وكان المنحرق بالشكل
+
+53
+00:06:17,500 --> 00:06:22,550
+اللي عندهاالمنحنى هذا اللي احنا شايفينه لا يعني
+
+54
+00:06:22,550 --> 00:06:27,250
+انه بتقطع مع نفسه ترى بالك لأن هذا رسم في الفرق مش
+
+55
+00:06:27,250 --> 00:06:31,650
+تقول المنحنى بتقطع عند النقطة هذه لا بتقطعش هذا اي
+
+56
+00:06:31,650 --> 00:06:40,010
+حركة في الهواء طيب يبقى عند اي لحظة اي نقطة موجودة
+
+57
+00:06:40,010 --> 00:06:44,660
+هنا او هنا او هنا او في اي مكانهأقول الإحداثيات
+
+58
+00:06:44,660 --> 00:06:51,020
+تبعتها X وY وZ وكل من X وY وZ هي function في main
+
+59
+00:06:51,020 --> 00:06:56,060
+في T حيث T اللي هو الـTime أو ما إلى ذلك هذا
+
+60
+00:06:56,060 --> 00:06:59,360
+بالنسبالي التعريف اللي هو التعريف التاني بقول إذا
+
+61
+00:06:59,360 --> 00:07:03,980
+position vector متجه الموضوع of a particle moves
+
+62
+00:07:03,980 --> 00:07:08,600
+in space لجسم يتحرك في الفرار بدي أعبر عنها و أقول
+
+63
+00:07:08,600 --> 00:07:16,010
+هي R of T يساوي المتجه O Pيعني لو جيت اخد اي نقطة
+
+64
+00:07:16,010 --> 00:07:22,470
+زي النقطة هذه مثلا على مصاري الجثير سميتها X و Y و
+
+65
+00:07:22,470 --> 00:07:31,510
+Z كل من X و Y و Z هي عبارة عن F of T و G of T و H
+
+66
+00:07:31,510 --> 00:07:37,010
+of T بهذا الشكل يبقى في الفرقاء النقطة لها ثلاثة
+
+67
+00:07:37,010 --> 00:07:44,120
+احداثية روحت رسمت المتجةمن الـ origin لغاية هذه
+
+68
+00:07:44,120 --> 00:07:50,080
+النقطة الشكل اللي عندنا هذا هذا المتجر سميته R of
+
+69
+00:07:50,080 --> 00:07:57,180
+D يبقى ال vector R of D الذي يبدأ من نقطة الأصل
+
+70
+00:07:57,180 --> 00:08:02,020
+إلى أي نقطة موجودة على المنحنة هسمي ال position
+
+71
+00:08:02,020 --> 00:08:08,750
+vector اللي هو متجر الموضوع عند أي لحظةيبقى سميته
+
+72
+00:08:08,750 --> 00:08:15,470
+المتجه RT المتجه RT بدي اكتبه as a vector كمتجه
+
+73
+00:08:15,470 --> 00:08:20,610
+فباجي بقول هو عبارة عن F of T في اتجاه I زي T of T
+
+74
+00:08:20,610 --> 00:08:25,970
+في اتجاه J زي H of T في اتجاه K يبقى كل مركبة من
+
+75
+00:08:25,970 --> 00:08:32,370
+هذه المركبات تعتبر مركبة في اتجاه ما لما بدي اكتب
+
+76
+00:08:32,370 --> 00:08:37,540
+متجه الموضع as a position vectorالـ position
+
+77
+00:08:37,540 --> 00:08:40,820
+vector هذا يا بنات هو اللي بيسميه vector valued
+
+78
+00:08:40,820 --> 00:08:46,150
+function اللي هو الأولوان اللي احنا قلنا عليهاللي
+
+79
+00:08:46,150 --> 00:08:51,050
+هو هي ال curves اللي عندنا curves in space المنحنة
+
+80
+00:08:51,050 --> 00:08:57,430
+ده متجه الموضوع عند اي لحظة او عند اي نقطة موجودة
+
+81
+00:08:57,430 --> 00:09:01,890
+عليه هسميها ال R of T بدلالة main بدلالة هذه
+
+82
+00:09:01,890 --> 00:09:06,690
+المركبات يبقى الخط اللي احنا شايفينه هذا هو المسار
+
+83
+00:09:06,690 --> 00:09:07,990
+تبع الجسيم
+
+84
+00:09:14,340 --> 00:09:19,960
+هو أي vector من نقطة الأصل إلى أي نقطة تقع على هذا
+
+85
+00:09:19,960 --> 00:09:26,580
+المنحلة وبالتالي ال R of T بسميها ال vector valued
+
+86
+00:09:26,580 --> 00:09:31,460
+function Function لكل مركبة من هذه المركبات هي
+
+87
+00:09:31,460 --> 00:09:33,480
+عبارة عن function
+
+88
+00:09:41,170 --> 00:09:45,590
+اللي موجودة في time interval إذا بطلع قيم ومن هنا
+
+89
+00:09:45,590 --> 00:09:50,210
+سميناها valued إذا هذا المتجه الموضع بسميه vector
+
+90
+00:09:50,210 --> 00:09:57,230
+valued function إذا بناء عليه كأننا مع دالة جديدة
+
+91
+00:09:57,510 --> 00:10:01,630
+غير الدول اللي اتعرفت عليها في calculus A
+
+92
+00:10:01,630 --> 00:10:06,450
+وcalculus B بقى نقول في calculus A Y تساوي F of X
+
+93
+00:10:06,450 --> 00:10:11,950
+في ال polar R تساوي F of Z تمام؟ إذا إحنا هنا باجي
+
+94
+00:10:11,950 --> 00:10:16,210
+بقول ال R of T يهي F of T في اتجاه ال I، G of T في
+
+95
+00:10:16,210 --> 00:10:20,750
+اتجاه ال J، H of T في اتجاه ال K يبقى هذه الدالة
+
+96
+00:10:20,750 --> 00:10:25,670
+اتجارية في الفرقإذا مدام دالة بدنا نروح نشوف ال
+
+97
+00:10:25,670 --> 00:10:28,430
+limit لهذه الدالة وبدنا نروح نشوف ال
+
+98
+00:10:28,430 --> 00:10:32,070
+differentiation لهذه الدالة و ال integral لهذه
+
+99
+00:10:32,070 --> 00:10:36,430
+الدالة يعني كل الأشياء التي دُرست على الدالة
+
+100
+00:10:36,430 --> 00:10:41,630
+العادية من التعرض الهلمين للدالة اللي قدامنا هذه
+
+101
+00:10:42,010 --> 00:10:46,390
+يبقى أول نقطة بدي أشير إليها اللي هي limit and
+
+102
+00:10:46,390 --> 00:10:52,010
+continuity لهذه الدالة كيف بدنا نروح نحسبها يبقى
+
+103
+00:10:52,010 --> 00:11:00,430
+بداتي أحط أغنان صغير اللي هو limits and continuity
+
+104
+00:11:00,430 --> 00:11:06,390
+النهايات
+
+105
+00:11:06,390 --> 00:11:10,190
+والاتصال لهذه الدالة هعطي definition
+
+106
+00:11:12,990 --> 00:11:19,850
+definition بقول ماتي F R of T يساوي F of T في
+
+107
+00:11:19,850 --> 00:11:26,930
+اتجاه I زائد G of T في اتجاه J زائد H of T في
+
+108
+00:11:26,930 --> 00:11:38,250
+اتجاه K is a vector is a vector valued function
+
+109
+00:11:38,250 --> 00:11:40,610
+then
+
+110
+00:11:44,880 --> 00:11:53,860
+لل R of T لما T بدها تروح إلى T نوت is defined by
+
+111
+00:11:53,860 --> 00:12:07,620
+as defined by بعرفك التالي limit لل R of T لما T
+
+112
+00:12:07,620 --> 00:12:11,060
+بدها تروح ل T نوت بده يساوي
+
+113
+00:12:13,820 --> 00:12:18,720
+للـ F of T لما T بدأ تروح إلى T node في اتجاه الـ
+
+114
+00:12:18,720 --> 00:12:26,780
+I زائد limit للـ G of T لما T بدأ تنست P node زائد
+
+115
+00:12:26,780 --> 00:12:33,380
+limit طبعا في اتجاه الـ J limit الـ H of T لما T
+
+116
+00:12:33,380 --> 00:12:38,360
+بدأ تروح إلى T node في اتجاه الـ Main في اتجاه الـ
+
+117
+00:12:38,360 --> 00:12:38,600
+K
+
+118
+00:12:47,470 --> 00:12:51,970
+بنرجع لهذا التعريف مرة ثانية انا عندي vector valid
+
+119
+00:12:51,970 --> 00:12:56,190
+function على الصيغة R of T سواء F of T في اتجاه
+
+120
+00:12:56,190 --> 00:13:00,750
+الـR زي الـG of T في اتجاه الـK زي الـH of T في
+
+121
+00:13:00,750 --> 00:13:05,670
+اتجاه الـK بدي اعرف ال limit لهذه ال function
+
+122
+00:13:05,670 --> 00:13:10,370
+فبقول limit لهذه ال function هي limit للR of T لما
+
+123
+00:13:10,370 --> 00:13:15,760
+تبدأ تروح لتينوت هذه شو تساويالـ Limit لهذه الدالة
+
+124
+00:13:15,760 --> 00:13:21,160
+تعني Limit لكل مُركّبة من هذه المُركّبات إذا باجي
+
+125
+00:13:21,160 --> 00:13:24,260
+Limit للمُركّبة الأولى في اتجاه الـI Limit
+
+126
+00:13:24,260 --> 00:13:27,360
+للمُركّبة التانية في اتجاه الـJ Limit للمُركّبة
+
+127
+00:13:27,360 --> 00:13:32,580
+التالتة في اتجاه الـK نفترض حسبنا هذه ال Limits
+
+128
+00:13:32,580 --> 00:13:39,720
+وطلعت L1 في اتجاه الـI L2 في اتجاه الـJ L3 في
+
+129
+00:13:39,720 --> 00:13:40,920
+اتجاه الـK
+
+130
+00:13:43,580 --> 00:13:47,460
+أول شيء يجب أن نفهمه يا بنات هو أن الـ vector
+
+131
+00:13:47,460 --> 00:13:51,560
+-valued function لو أخدت لها limit يجب أن يخرج
+
+132
+00:13:51,560 --> 00:13:55,220
+كمان vector ليس مثل الدول العادية، الدول العادية
+
+133
+00:13:55,220 --> 00:13:59,060
+اللي أخدت لها limit تخرج constant مظبوط أم لا؟ لكن
+
+134
+00:13:59,060 --> 00:14:04,600
+هنا يجب أن يخرج vector مكون من ثلاث مركبات، يمكن
+
+135
+00:14:04,600 --> 00:14:09,650
+بعضها صفر ويمكن بعضها غير الصفرويمكن ال limit تطلع
+
+136
+00:14:09,650 --> 00:14:13,810
+does not exist كمان كما سنرى بعد قليل ان شاء الله
+
+137
+00:14:13,810 --> 00:14:17,790
+تعالى يعني ممكن ال limit تكون exist و ممكن ال
+
+138
+00:14:17,790 --> 00:14:23,230
+limit تكون does not exist تماما مثل الدوال العادية
+
+139
+00:14:23,230 --> 00:14:31,210
+يبقى هذا اختصارا بقول الهذا الـ L يجب أن نفهم إنه
+
+140
+00:14:31,210 --> 00:14:37,930
+Vector، ولمّا لا نخطط، سأضع عليه سهم لأعرف إن هذا
+
+141
+00:14:37,930 --> 00:14:42,190
+Vector طب السؤال هو هل هذا يا بنات constant،
+
+142
+00:14:42,190 --> 00:14:47,600
+vector؟ والله ال vector هذا متغيرلما ناخد ال limit
+
+143
+00:14:47,600 --> 00:14:51,940
+ها constant vector لأن كل واحد هيعطيني قيمة اللي
+
+144
+00:14:51,940 --> 00:14:55,120
+هو ال ال one والتانية ال two والتالتة ال three إذا
+
+145
+00:14:55,120 --> 00:14:59,040
+هذا بدو يطلع عندي limit constant vector زي ما ال
+
+146
+00:14:59,040 --> 00:15:02,420
+limit تبعت ال function العادية كنا بنطلعها scalar
+
+147
+00:15:02,420 --> 00:15:08,900
+أو constant تمام طيب نعطي كمان definition تاني
+
+148
+00:15:18,380 --> 00:15:30,040
+function R of T is continuous تبقى دالة مبتصلة at
+
+149
+00:15:30,040 --> 00:15:40,360
+a point عند النقطة T تساوي T naught in its domain
+
+150
+00:15:40,360 --> 00:15:54,270
+Mits domain في المجال تبع هذه الدالة F limit لل R
+
+151
+00:15:54,270 --> 00:16:00,930
+of T لما T بدى تروح الى T naught بدى يسوى R of T
+
+152
+00:16:00,930 --> 00:16:06,770
+naught also وكذلك
+
+153
+00:16:07,950 --> 00:16:15,230
+الـ R of T بيكون F of T في اتجاه I زائد G of T في
+
+154
+00:16:15,230 --> 00:16:23,390
+اتجاه J زائد H of T في اتجاه K is continuous is
+
+155
+00:16:23,390 --> 00:16:36,470
+continuous دالة متصلة at T بيكون T0 F and only F
+
+156
+00:16:42,860 --> 00:16:55,240
+and الـ h are continuous and T ده ساوي T note
+
+157
+00:17:26,820 --> 00:17:31,780
+أخذنا تعريف الـ Curve في الـ space و بعد ذلك عرفنا
+
+158
+00:17:31,780 --> 00:17:35,100
+الـ vector-valid function والآن بدنا نجي ال limit
+
+159
+00:17:35,100 --> 00:17:38,800
+لل vector-valid function و ال continuity طبعا
+
+160
+00:17:38,800 --> 00:17:43,680
+عرفنا ال limit و ال limit لل vector-valid function
+
+161
+00:17:43,680 --> 00:17:48,860
+بيطلع كمان اللي هو constant vector بدنا نجي الآن
+
+162
+00:17:48,860 --> 00:17:53,520
+لل continuityالـ Continuity لهذه الدالة بقول الـ
+
+163
+00:17:53,520 --> 00:17:58,160
+vector function R of T بتبقى continuous عند نقطة
+
+164
+00:17:58,160 --> 00:18:02,200
+أو التقن تبت سوى T node اللي موجودة في domain هذه
+
+165
+00:18:02,200 --> 00:18:06,240
+الدالة إذا والله ال limit ال R of T لما ت بتروح ل
+
+166
+00:18:06,240 --> 00:18:12,440
+T node تسوى مين R of T node السؤال هو هل اختلف هذا
+
+167
+00:18:12,440 --> 00:18:18,060
+التعريف عن تعريف ال continuity لدالة عالية؟ في
+
+168
+00:18:18,060 --> 00:18:19,140
+خلاف بينهم؟
+
+169
+00:18:26,970 --> 00:18:32,150
+الدالة بقول عنها continuous عند نقطة إذا كان قيمة
+
+170
+00:18:32,150 --> 00:18:37,250
+الدالة عند تلك النقطة تساوي نهاية الدالة عند تلك
+
+171
+00:18:37,250 --> 00:18:37,830
+النقطة
+
+172
+00:18:43,720 --> 00:18:48,140
+مش هاد التعريف وروحنا جسمنا هذا التعريف إلى ثلاث
+
+173
+00:18:48,140 --> 00:18:54,700
+نقاط يكالكوا نص إيه وسمينا ال continuity test يعني
+
+174
+00:18:54,700 --> 00:18:58,160
+كيف بدي اختبر الدالة هتكون continuous ولا لأ وقلنا
+
+175
+00:18:58,160 --> 00:19:02,130
+أول شيء بنشوف هل الدالة معرفةعند هذه النقطة ولا
+
+176
+00:19:02,130 --> 00:19:06,970
+لأ؟ condition اتحقق الأول ماشي condition التاني هل
+
+177
+00:19:06,970 --> 00:19:11,330
+ال limit عند هذه النقطة exist ولا لأ؟ إذا exist في
+
+178
+00:19:11,330 --> 00:19:15,730
+الأول ماشي تحقق الشرطة يبقى بظلمين عند الشرطة
+
+179
+00:19:15,730 --> 00:19:22,540
+التالت إذا تساوت القيمتهامع ال condition بمعنى ان
+
+180
+00:19:22,540 --> 00:19:26,640
+قيمة الدالة عند هذا نقطة سواء نهاية الدالة عند تلك
+
+181
+00:19:26,640 --> 00:19:30,060
+النقطة، إذا بقول الدالة continuous عند هذا نقطة،
+
+182
+00:19:30,060 --> 00:19:33,920
+هذا ما دُلس فيه كالكلاصين، هنا لو طلعت لهذا
+
+183
+00:19:33,920 --> 00:19:38,600
+التعريف يبقى نهاية الدالة عند T تساوي T note تساوي
+
+184
+00:19:38,600 --> 00:19:42,320
+قيمة الدالة عند T note، إذا هو نفس التعريف تبع
+
+185
+00:19:42,320 --> 00:19:47,300
+الكلاصين، لم نغير فيه شيءالان يا بقول التعريف هيك
+
+186
+00:19:47,300 --> 00:19:53,300
+يا بروح بقول ان الدالة دي continuous إذا كانت كل
+
+187
+00:19:53,300 --> 00:19:57,560
+مركبة من المركبات تبع ال vector value function
+
+188
+00:19:57,560 --> 00:20:02,500
+continuous عند نفس ال D تسوى من؟T0 يبقى هذا
+
+189
+00:20:02,500 --> 00:20:07,460
+التعريف اقول also ممكن اعيد صياغته بطريقة اخرى و
+
+190
+00:20:07,460 --> 00:20:10,160
+اقول ال vector valued function هذي continuous عند
+
+191
+00:20:10,160 --> 00:20:15,660
+T تسوى T0 اذا و فقط اذا كان ال F والG والH التنتين
+
+192
+00:20:15,660 --> 00:20:21,350
+كانوا continuous عند تلك النقطةحد إلها أي سؤال في
+
+193
+00:20:21,350 --> 00:20:24,850
+ال continuity أو ال limit أو ما إلى ذلك طبعا هنرجع
+
+194
+00:20:24,850 --> 00:20:29,590
+نشتغل هذا بأمثلة بعد قليل ان شاء الله حد بتحب تسأل
+
+195
+00:20:29,590 --> 00:20:34,610
+أسئلة قبل أن أذهب إلى تعريف جديد و هو اشتقاق
+
+196
+00:20:34,610 --> 00:20:38,270
+الدالة أو الدالة و اكتشف تبقى differential أو ما
+
+197
+00:20:38,270 --> 00:20:44,230
+إلى ذلك حد بتحب تسأل نبقى ننتقل إلى تعريف جديد
+
+198
+00:20:44,230 --> 00:20:48,030
+definition the
+
+199
+00:20:48,030 --> 00:20:57,280
+vector functionVector function R of T هو F of T في
+
+200
+00:20:57,280 --> 00:21:03,380
+اتجاه I زائد G of T في اتجاه J زائد H of T في
+
+201
+00:21:03,380 --> 00:21:05,100
+اتجاه K
+
+202
+00:21:21,180 --> 00:21:30,540
+والـ G and الـ H have derivatives
+
+203
+00:21:30,540 --> 00:21:38,440
+.. have derivatives at الـ OT and
+
+204
+00:21:50,890 --> 00:21:59,290
+يبقى دي اف على دي تي في اتجاه الاي زائد دي جي على
+
+205
+00:21:59,290 --> 00:22:03,490
+دي تي في اتجاه الجي زائد دي اتش على دي تي في اتجاه
+
+206
+00:22:03,490 --> 00:22:03,490
+الاي
+
+207
+00:22:19,450 --> 00:22:26,670
+R of T is called is
+
+208
+00:22:26,670 --> 00:22:33,110
+called smooth if
+
+209
+00:22:33,110 --> 00:22:44,570
+dA على dT is continuous يعني إذا كانت المستقبل
+
+210
+00:22:44,570 --> 00:22:54,710
+أولى في هذه المنحلةدالة متصلة وDR على DT لا يكون
+
+211
+00:22:54,710 --> 00:23:06,870
+اقل لـ 0، هذا يعني ان اذا الـ
+
+212
+00:23:06,870 --> 00:23:13,590
+F و G و الأرض لديها درجة مستمرة
+
+213
+00:23:18,000 --> 00:23:24,720
+continuous first derivatives
+
+214
+00:23:24,720 --> 00:23:31,340
+and
+
+215
+00:23:31,340 --> 00:23:41,320
+df على dt و dg على dt and
+
+216
+00:24:32,710 --> 00:24:37,550
+المنحنى R of T is called smooth كيش يعني smooth؟
+
+217
+00:24:37,550 --> 00:24:39,950
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+218
+00:24:39,950 --> 00:24:40,270
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+219
+00:24:40,270 --> 00:24:42,030
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+220
+00:24:42,030 --> 00:24:43,970
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+221
+00:24:43,970 --> 00:24:45,010
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+222
+00:24:45,010 --> 00:24:48,810
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+223
+00:24:48,810 --> 00:24:55,980
+لألأن كل كلمة في اللغة لها مصطلحة، يعني بتلاقي نفس
+
+224
+00:24:55,980 --> 00:25:00,200
+الكلمة لكن في كل علم من العلوم لها مصطلح مختلف،
+
+225
+00:25:00,200 --> 00:25:04,400
+مثلا vector عنا إيش بيقولون عليها إحنا، لكن طبعا
+
+226
+00:25:04,400 --> 00:25:08,380
+كلية الطب عندنا بيقولوش أنا متجر، ال vector بيسموه
+
+227
+00:25:08,380 --> 00:25:13,740
+حامل جرثوميطبعا اللي بحمل جرثوم بتحرك مظبوط فال
+
+228
+00:25:13,740 --> 00:25:17,440
+vector عندهم بيسموه بترجموه حامل جرثوم لكن احنا
+
+229
+00:25:17,440 --> 00:25:21,620
+بيقول اه متجه إذا كلمة في اللغة الإنجليزية إذا
+
+230
+00:25:21,620 --> 00:25:26,300
+جينا نبعدنا عن اللغة الأدابية و بدنا نحطها كمصطلح
+
+231
+00:25:26,300 --> 00:25:32,380
+يختلف طبعا المعنى متقارف لكن يختلف من علم إلى علم
+
+232
+00:25:32,380 --> 00:25:38,530
+آخر ترجمة هذا المصطلح طيب برجع مرة تانيةبقول ال R
+
+233
+00:25:38,530 --> 00:25:42,910
+of T is called smooth يعني منحنى أملس إذا تحقق
+
+234
+00:25:42,910 --> 00:25:48,910
+شرطان الشرط الأول ان دي R على دي T is continuous
+
+235
+00:25:48,910 --> 00:25:53,630
+يعني لو اشتقت ال vector valued function بد المشتقة
+
+236
+00:25:53,630 --> 00:25:59,810
+تكون دالة متاصلة إتنين بد المشتقة ممنوعة تساوي
+
+237
+00:25:59,810 --> 00:26:00,170
+zero
+
+238
+00:26:03,570 --> 00:26:09,070
+هذه وقتها تبقى متصلة إذا كانت المركبات التلاتة
+
+239
+00:26:09,070 --> 00:26:14,430
+continuous المشتقة الأولى للمركبات التلاتة يعني DF
+
+240
+00:26:14,430 --> 00:26:17,790
+على DT وDG على DT وDH على DT
+
+241
+00:26:21,260 --> 00:26:27,160
+هذا النقطة الأولى النقطة التانية مش كلهم Zero يعني
+
+242
+00:26:27,160 --> 00:26:30,460
+ممكن تبقى واحدة ب Zero والتانية ب Zero بس التالتة
+
+243
+00:26:30,460 --> 00:26:37,260
+ممنوعة تكون ب Zero لإيش؟ لأن ال DR على DT لا تساوي
+
+244
+00:26:37,260 --> 00:26:40,320
+Zero لكن المركبة تلقاه واحدة ب Zero مافي مشكلة لو
+
+245
+00:26:40,320 --> 00:26:43,000
+كانت انتين ب Zero مافي مشكلة لكن إذا التلاتة ب
+
+246
+00:26:43,000 --> 00:26:48,280
+Zero إذا بطل المرحلة سيرمان Smooth Curveهذا بدى
+
+247
+00:26:48,280 --> 00:26:54,700
+يخلينى اسأل السؤال التالى هل يمكن للجسيم ان يتوقف
+
+248
+00:26:54,700 --> 00:27:00,560
+على ال smooth curve ممكن يوقف؟ ممنوع لأنه بدى
+
+249
+00:27:00,560 --> 00:27:03,580
+equal to zero في هذه الحالة يبقى المستقلات هذه
+
+250
+00:27:03,580 --> 00:27:09,320
+كلها equal to zero طب اتنين هل يمكن على ال smooth
+
+251
+00:27:09,320 --> 00:27:15,380
+curve ان يحصل عندي كسب يعني انهيطاف حد في المنحنة
+
+252
+00:27:15,660 --> 00:27:21,700
+أو يكون عندى corner طبعا لا لأن الدالة غير قابلة
+
+253
+00:27:21,700 --> 00:27:25,800
+للاشتفاخ عند القصب و ال corner مش هيك اللي أخدت
+
+254
+00:27:25,800 --> 00:27:31,760
+فكرة الفلسفين إذا على اسمه ك there is no casb و
+
+255
+00:27:31,760 --> 00:27:36,020
+كمان there is no corner مافيش عندي على المرحلة ده
+
+256
+00:27:36,020 --> 00:27:40,520
+ده نكتب هالمرحلة كويسة هنا يعني مجرد تركيزه ليس
+
+257
+00:27:52,720 --> 00:28:01,620
+هنا على المنحنى الأبلس لا يوجد كورنار لا يوجد
+
+258
+00:28:01,620 --> 00:28:05,840
+كورنار
+
+259
+00:28:05,840 --> 00:28:11,380
+أو نوركسف لا هذا ولا ذلك
+
+260
+00:28:21,230 --> 00:28:30,130
+أول مثال بيقول اللي هت ال R of T بدها تساوي E أس
+
+261
+00:28:30,130 --> 00:28:37,930
+ناقص T في اتجاه ال I زائد T ناقص واحد على T زائد
+
+262
+00:28:37,930 --> 00:28:46,590
+واحد في اتجاه ال J زائد تان Inverse T في اتجاه من؟
+
+263
+00:28:46,590 --> 00:28:48,210
+في اتجاه ال K
+
+264
+00:28:50,950 --> 00:28:56,510
+Limit للR of T لما T بدها تروح
+
+265
+00:29:09,730 --> 00:29:14,570
+يقول خد R of T يساوي E و اصلاغس T في اتجاه I زي T
+
+266
+00:29:14,570 --> 00:29:18,650
+ناطس واحد على T زايد واحد في اتجاه J زي 10 inverse
+
+267
+00:29:18,650 --> 00:29:23,750
+T في اتجاه K جالي هات لنهاية هذه الدالة لما T بدأ
+
+268
+00:29:23,750 --> 00:29:27,370
+تروح الى N فارغ حسب ال definition اللي كتبناه في
+
+269
+00:29:27,370 --> 00:29:28,650
+طريقة الخريط تبع ال level
+
+270
+00:29:34,190 --> 00:29:39,410
+تبدأ تروح لل infinity تبدأ تسوي limit لكل مُركّبة
+
+271
+00:29:39,410 --> 00:29:43,990
+من هذه المُركّبات لما تبدأ تروح إليها infinity هذه
+
+272
+00:29:43,990 --> 00:29:49,310
+limit لما تبدأ تروح لل infinity EOS-D يا بنات هي
+
+273
+00:29:49,310 --> 00:29:56,370
+عبارة عن مين؟ 1 على EOS-D ممتاز يبقى 1 على EOS-D
+
+274
+00:29:56,370 --> 00:30:04,190
+في اتجاه الـI T-1 T زائد 1 في اتجاه الـJطبعاً
+
+275
+00:30:04,190 --> 00:30:07,870
+limit المفتر
+
+276
+00:30:07,870 --> 00:30:15,650
+اللي عندنا يبقى limit لما T بدأ تروح الى infinity
+
+277
+00:30:15,650 --> 00:30:21,910
+لمن؟ ل T ناقص واحد على T زائد واحد في اتجاه ال J
+
+278
+00:30:21,910 --> 00:30:28,410
+زائد limit لتان inverse T لما T بدأ تروح الى
+
+279
+00:30:28,410 --> 00:30:29,010
+infinity
+
+280
+00:30:35,050 --> 00:30:39,110
+بنروح نحسب ال limit لكل ال functions من ال
+
+281
+00:30:39,110 --> 00:30:43,250
+function z التلاتة هنا لما تيجي تروح لمالة نهاية
+
+282
+00:30:43,250 --> 00:30:47,670
+التعود المباشر سيرجع تجي 2 و 7 من 10 أقص مالة
+
+283
+00:30:47,670 --> 00:30:52,310
+نهاية مالة نهاية 1 على مالة نهاية ب zero يبقى
+
+284
+00:30:52,310 --> 00:30:53,810
+النتيجة الأولى
+
+285
+00:30:56,470 --> 00:31:00,510
+نجي لتانى لما نعوض طريقنا عشان نبصير infinity على
+
+286
+00:31:00,510 --> 00:31:05,750
+infinity قدامى طريقين طريق الاول انه استخدم قاعدة
+
+287
+00:31:05,750 --> 00:31:10,350
+لبتال اشتغد دلت البسط على اشتغد دلت المقام او اقسم
+
+288
+00:31:10,350 --> 00:31:14,050
+كل من البسط والمقام على T المرفوعة ليه اكبر أس في
+
+289
+00:31:14,050 --> 00:31:18,590
+المقام و بعد هيك بروح اعوض يبقى سواء كانت هذه او
+
+290
+00:31:18,590 --> 00:31:23,390
+تلك ال limit لها يبقى ده واحد صحيح يبقى هنا
+
+291
+00:31:26,740 --> 00:31:32,040
+بنانيجي ال limit ل 10 inverse T، بقى يا اتنين،
+
+292
+00:31:32,040 --> 00:31:36,580
+يعني المذاكرين مالحدد 10 inverseحد مش مسمى مش
+
+293
+00:31:36,580 --> 00:31:40,840
+عارفه بنرسمه يعني مش مستاهل طيب لو ذكرنا تذكر
+
+294
+00:31:40,840 --> 00:31:46,580
+بمنحلة تام inverse يبقى بالي بيقول هذا X وهذا Y
+
+295
+00:31:46,580 --> 00:31:51,480
+وهذا النقطة اللي عندنا بي على اتنين وهذا النقطة
+
+296
+00:31:51,480 --> 00:31:55,200
+التانية اللي يسالب بي على اتنين لو جيت رسمت
+
+297
+00:31:55,200 --> 00:32:00,760
+المنحلة المنحلة بده يمر بنقطة الأصل والمنحلة بيكون
+
+298
+00:32:01,080 --> 00:32:05,860
+اللي هو باللون الأزرق اللي عندنا هذا جاي وبيجي
+
+299
+00:32:05,860 --> 00:32:12,680
+نازل الشكل عندناطبعا واضح انه هذه ال limit لما ال
+
+300
+00:32:12,680 --> 00:32:17,440
+X بدها تروح لما لا نهاية اكتر موقيمة بياخد المنحنة
+
+301
+00:32:17,440 --> 00:32:22,140
+هي من باي على اتنين و لما ربك ياخذ فه بيصير قدر
+
+302
+00:32:22,140 --> 00:32:27,560
+اذا ال domain كل ال real line و ال range من سالب
+
+303
+00:32:27,560 --> 00:32:32,320
+باي على اتنين لغاية باي على اتنين يبقى هذه زائد
+
+304
+00:32:32,320 --> 00:32:38,630
+بايعلى اتنين في اتجاه من الـ K لحظة ان النتيجة
+
+305
+00:32:38,630 --> 00:32:43,830
+تساوي J زائد Pi على اتنين في اتجاه الـ K which is
+
+306
+00:32:43,830 --> 00:32:49,350
+a vector كما زعمنا قبل قليل يبقى limit the vector
+
+307
+00:32:49,350 --> 00:32:55,070
+valued function هو constant vector متجه ثابت زي ما
+
+308
+00:32:55,070 --> 00:32:59,170
+انتوا شايفين نجي لمثال رقم اتنين example two
+
+309
+00:33:02,560 --> 00:33:07,300
+الحاجة اسمه الى نقطتين النقطة الأولى نمر ايه ال
+
+310
+00:33:07,300 --> 00:33:16,280
+vector function الدلد التجارية اللي ال R of T to Z
+
+311
+00:33:16,280 --> 00:33:23,860
+هو sign T في اتجاه ال I زائد sign T
+
+312
+00:33:27,620 --> 00:33:34,260
+الـ R of T فساوية for Sine T في اتجاه I زائد Sine
+
+313
+00:33:34,260 --> 00:33:38,580
+T في اتجاه J زائد T في اتجاه
+
+314
+00:33:42,100 --> 00:33:46,960
+السؤال هو هل ال vector value دي continuous ولا غير
+
+315
+00:33:46,960 --> 00:33:52,700
+continuous نجيب نشوف المركبات ال cosine t هل لها
+
+316
+00:33:52,700 --> 00:33:57,040
+نقطة عندها بصير غير معرفة إذا دي continuous على
+
+317
+00:33:57,040 --> 00:34:00,720
+طول و ال sign طبعا عارفين أنها تترجح بين واحد و
+
+318
+00:34:00,720 --> 00:34:05,040
+سالف واحد من سالف infinity لأن يرد الله الأرض وامل
+
+319
+00:34:05,040 --> 00:34:10,480
+عليهاتمام؟ والـ T هذه لأنها خطوية من الدرجة
+
+320
+00:34:10,480 --> 00:34:14,720
+الأولى، يعني كأنها polynomial من الدرجة الأولى،
+
+321
+00:34:14,720 --> 00:34:18,280
+واحنا ال polynomial بنعرف أنها متصلة على طول الخط
+
+322
+00:34:18,280 --> 00:34:24,000
+يبقى أن ال vector function هذه as continuous
+
+323
+00:34:25,670 --> 00:34:37,710
+for all T هو السبب because each of cos T وsin T
+
+324
+00:34:37,710 --> 00:34:52,110
+and T because each is continuous for all T نمر
+
+325
+00:34:52,110 --> 00:34:52,450
+باين
+
+326
+00:35:02,780 --> 00:35:13,280
+R of T يساوي LU Cos T في اتجاه I زائد Sin T في
+
+327
+00:35:13,280 --> 00:35:27,760
+اتجاه J زائد دلة R لT في اتجاه K is discontinuous
+
+328
+00:35:29,400 --> 00:35:40,400
+غير متصلة بالله الرحمن والسبب at every integer عند
+
+329
+00:35:40,400 --> 00:35:49,600
+أي عدد صحيح because السبب ان الlimit لدلة الأرض
+
+330
+00:35:49,600 --> 00:35:55,440
+التي لما تبدأ تروح للـC does
+
+331
+00:35:56,980 --> 00:36:05,020
+ن exist و الـ C is an integer
+
+332
+00:36:12,540 --> 00:36:16,640
+المثال الأول يا بناتي اللي هو نمره A بياننا فيه
+
+333
+00:36:16,640 --> 00:36:20,120
+انه ال vector valid function continuous لأنه ثلاث
+
+334
+00:36:20,120 --> 00:36:26,200
+مركبات continuous في آخر واحد نجي لال example T
+
+335
+00:36:26,200 --> 00:36:29,000
+بيقول ال vector valid function على الشكل اللي لنا
+
+336
+00:36:29,440 --> 00:36:38,160
+ضالة المركبة الأولى والثانية دل
+
+337
+00:36:38,160 --> 00:36:45,200
+السلمية أو دل الدرجية أو step function أو احنا
+
+338
+00:36:45,200 --> 00:36:50,380
+بنسميها دالة الأرض لو كانت لفوق بنسميها دالة السقف
+
+339
+00:36:50,380 --> 00:36:56,200
+ال sailing function لكن هذه اللي هو floor function
+
+340
+00:36:56,200 --> 00:37:03,920
+اللي هو دالة الأرضأي رقم أعلى من أي عدد صحيح كله
+
+341
+00:37:03,920 --> 00:37:08,440
+بنزله لمين لنفس العدد الصحيح فمثلا الدالة هذه لو
+
+342
+00:37:08,440 --> 00:37:12,760
+كانت التي اللي عندي واحد وتسعة من عشرة تنزل الواحد
+
+343
+00:37:12,760 --> 00:37:19,620
+لو كانت سبعة من عشرة تنزل للصفر لو كانت ناقص سبعة
+
+344
+00:37:19,620 --> 00:37:25,950
+من عشرةتنزل الاخص واحد و هكذا تمام يبقى هذه بنزلة
+
+345
+00:37:25,950 --> 00:37:32,290
+لو جيت عند كل عدد صحيح و بدي اخد ال limit إذا بروح
+
+346
+00:37:32,290 --> 00:37:36,130
+باخد ال limit من اليمين و ال limit من الشمال عند
+
+347
+00:37:36,130 --> 00:37:40,400
+الحدد الصحيح لا يمكن ان ال two limits يتزاوىيكون
+
+348
+00:37:40,400 --> 00:37:44,980
+الفرق بينهم واحد صحيح دائما و أبدًا، يعني من هنا
+
+349
+00:37:44,980 --> 00:37:47,860
+ممكن أجيها Zero و من هنا واحد، من هنا واحد، من هنا
+
+350
+00:37:47,860 --> 00:37:49,340
+حتة، من هنا اتنين، من هنا اتنين، و من هنا اتنين، و
+
+351
+00:37:49,340 --> 00:37:49,460
+من هنا اتنين، و من هنا اتنين، و من هنا اتنين، و من
+
+352
+00:37:49,460 --> 00:37:49,600
+هنا اتنين، و من هنا اتنين، و من هنا اتنين، و من
+
+353
+00:37:49,600 --> 00:37:50,000
+هنا اتنين، و من هنا اتنين، و من هنا اتنين، و من
+
+354
+00:37:50,000 --> 00:37:50,160
+هنا اتنين، و من هنا اتنين، و من هنا اتنين، و من
+
+355
+00:37:50,160 --> 00:37:51,780
+هنا اتنين، و من هنا اتنين، و من هنا اتنين، و من
+
+356
+00:37:51,780 --> 00:37:56,520
+هنا اتنين، و من هنا اتنين، و من هنا اتنين، و من
+
+357
+00:37:56,520 --> 00:37:59,180
+هنا اتنين،
+
+358
+00:38:01,480 --> 00:38:07,940
+كتبنا لك c is an integer يبقى c حدث صحيح إذا لا
+
+359
+00:38:07,940 --> 00:38:12,540
+يمكن لهذا ال limit ان تبقى exist يبقى لا يمكن لل
+
+360
+00:38:12,540 --> 00:38:17,980
+function هذه ان تبقى continuous تمام هذا بالنسبة
+
+361
+00:38:17,980 --> 00:38:22,640
+لمين ل ال continuity ناخد كمان مثل هذا
+
+362
+00:38:35,870 --> 00:38:45,270
+زائد ربيع زائد واحد كل هذا في اتجاه I زائد لتان
+
+363
+00:38:45,270 --> 00:38:54,130
+انفرست T في اتجاه J زائد T P أس T في اتجاه K
+
+364
+00:39:05,650 --> 00:39:12,850
+مشتقت هذه الدالة عند تنون تساوي واحد صحيح
+
+365
+00:39:30,500 --> 00:39:34,100
+إذا عشان نعرف المشتق عن الواحد الصحيح بندروح اشتق
+
+366
+00:39:34,100 --> 00:39:40,000
+الدالة وبعد ذلك اعوض بالواحد الصحيح يبقى solution
+
+367
+00:39:40,000 --> 00:39:43,200
+دي
+
+368
+00:39:43,200 --> 00:39:50,920
+اعلى دي تي او R prime of T تمام هذا اللي هي R
+
+369
+00:39:50,920 --> 00:39:59,060
+prime of T وتساويتفاضل الان واحد على الداخلية ضرب
+
+370
+00:39:59,060 --> 00:40:04,960
+مشتقة ما بداخلها يبقى واحد على T تربيع الزائد واحد
+
+371
+00:40:04,960 --> 00:40:09,680
+ضرب مشتقة ما داشر الامر اللي هو اتنين T في اتجاه
+
+372
+00:40:09,680 --> 00:40:17,150
+الانTen inverse of one over one plus T square in
+
+373
+00:40:17,150 --> 00:40:25,370
+the direction of J المشتقة حاصل ضرب غلطين يبقى هذه
+
+374
+00:40:25,370 --> 00:40:32,290
+زائد E of T زائد T في E of T في اتجاه الـ K
+
+375
+00:40:32,290 --> 00:40:39,610
+المشتقة E of T في E of T itselfجالي هات للاري
+
+376
+00:40:39,610 --> 00:40:44,370
+prime of one بقول الاري prime of one بدي يسوي، إذا
+
+377
+00:40:44,370 --> 00:40:49,530
+بدي أشيل كل T و أحط مكانها واحد صحيح، البس هنا
+
+378
+00:40:49,530 --> 00:40:53,310
+باتنين، واحد تربيهك واحد زائد واحد، باتنين اتنين
+
+379
+00:40:53,310 --> 00:41:01,670
+على اتنين، يبقى I فقط نغم، ليه بعد؟ ها، تيب واحد،
+
+380
+00:41:01,670 --> 00:41:07,130
+يبقى بصير نص، يبقى زائد نص، في اتجاه ال Jاللي
+
+381
+00:41:07,130 --> 00:41:17,290
+بعدها E زائد E لو قدش ب 2E يبقى زائد 2E في اتجاه P
+
+382
+00:41:17,290 --> 00:41:22,690
+يبقى المشتقة كذلك من اتهائها vector و لما نعوضها
+
+383
+00:41:22,690 --> 00:41:28,570
+بها عندها نقطة صار main صار constant vector السؤال
+
+384
+00:41:28,570 --> 00:41:29,230
+الرابع
+
+385
+00:41:39,220 --> 00:41:48,100
+R of T بقدر زاوية اللي هو T تكييب في اتجاه I زائد
+
+386
+00:42:05,850 --> 00:42:09,910
+هل المنحنى اللى قدامنا هذا منحنى ام لا سبق ان نقول
+
+387
+00:42:09,910 --> 00:42:14,790
+له we don't know انا ماعرفش لكن انا بروح اشوف هل
+
+388
+00:42:14,790 --> 00:42:20,050
+الشرطين متحققين ولا لا تبعات من ال small curve شرط
+
+389
+00:42:20,050 --> 00:42:24,930
+الاول فده اجيب المشتقة الاولى وابينه ان التلت
+
+390
+00:42:24,930 --> 00:42:30,570
+مشتقات اللى عندنا are continuous نمرا واحد نمرا
+
+391
+00:42:30,570 --> 00:42:36,260
+اتنينممكن يكونوا بعضهم بـ0، لكن ليس كلهم بـ0، إذا
+
+392
+00:42:36,260 --> 00:42:36,820
+كانوا أفضل واحدة ما يكونوا أفضل واحدة ما يكونوا
+
+393
+00:42:36,820 --> 00:42:38,440
+أفضل واحدة ما يكونوا أفضل واحدة ما يكونوا أفضل
+
+394
+00:42:38,440 --> 00:42:40,100
+واحدة ما يكونوا أفضل واحدة ما يكونوا أفضل واحدة ما
+
+395
+00:42:40,100 --> 00:42:41,280
+يكونوا أفضل واحدة ما يكونوا أفضل واحدة ما يكونوا
+
+396
+00:42:41,280 --> 00:42:41,400
+أفضل واحدة ما يكونوا أفضل واحدة ما يكونوا أفضل
+
+397
+00:42:41,400 --> 00:42:42,280
+واحدة ما يكونوا أفضل واحدة ما يكونوا أفضل واحدة ما
+
+398
+00:42:42,280 --> 00:42:42,480
+يكونوا أفضل واحدة ما يكونوا أفضل واحدة ما يكونوا
+
+399
+00:42:42,480 --> 00:42:44,780
+أفضل واحدة ما يكونوا أفضل واحدة ما يكونوا أ
+
+400
+00:43:05,980 --> 00:43:15,730
+الـ F of T والـ G of T والS of Tهذه Polynomial من
+
+401
+00:43:15,730 --> 00:43:18,550
+الدرجة الثانية وهذه Polynomial من الدرجة الأولى
+
+402
+00:43:18,550 --> 00:43:21,590
+وهذه Polynomial من الدرجة الأولى واحنا بنعرف من
+
+403
+00:43:21,590 --> 00:43:25,410
+Calculus أن Polynomial continuous عالمين على كلهم
+
+404
+00:43:25,410 --> 00:43:31,090
+إذا ال first derivatives للمركبات التلاتة are
+
+405
+00:43:31,090 --> 00:43:37,520
+continuous إذا انتحقق الشرط اللي عندنا هذاطيب شرط
+
+406
+00:43:37,520 --> 00:43:43,200
+الأول تحقق بدي المشتقة الثانية هل هناك رقم في
+
+407
+00:43:43,200 --> 00:43:48,860
+الدنيا بتقدر تاخديه يخلط ثلاث مراكبات صفر في آن
+
+408
+00:43:48,860 --> 00:43:54,280
+واحد تقول خد ال T ب Zero بقولك صح بيخل المراكبة
+
+409
+00:43:54,280 --> 00:43:58,320
+الأولى ب Zero و الأخيرة ب Zero لكن اللي في الناصر
+
+410
+00:43:58,320 --> 00:44:06,910
+لأ طب لو أخدت الرقم مثلا طولتلت بيخلي هذا زيرو لكن
+
+411
+00:44:06,910 --> 00:44:11,490
+هل بيخلي هذا و هذا زيرو لا يوجد رقم في الدنيا
+
+412
+00:44:11,490 --> 00:44:18,090
+بيخلي التلت مركبات تسوي زيرو في آن واحد لذا هذا
+
+413
+00:44:18,090 --> 00:44:26,350
+الملحانة ماله is a small k يا رباه يبقى هنا the
+
+414
+00:44:26,350 --> 00:44:28,190
+function
+
+415
+00:44:32,230 --> 00:44:44,150
+نقص اتنين and اتنين T are continuous for all T
+
+416
+00:44:44,150 --> 00:44:49,150
+because they
+
+417
+00:44:49,150 --> 00:45:01,930
+are polynomials لأنه كثيرات الحدود and not
+
+418
+00:45:02,730 --> 00:45:15,150
+all zero at any point مش كلهم zero عند أي نقطة
+
+419
+00:45:15,150 --> 00:45:23,360
+يبقى معاها كل من حلماله smooth curveThe given
+
+420
+00:45:23,360 --> 00:45:33,180
+curve R of T تكيّب في اتجاه I تلاتة T تربيع نقص
+
+421
+00:45:33,180 --> 00:45:38,000
+اتنين T في اتجاه J تربيع في اتجاه K
+
+422
+00:45:53,430 --> 00:45:57,890
+طبعا احنا في أول ساعة يعني كنا اتكلمنا عن ال
+
+423
+00:45:57,890 --> 00:46:00,690
+curves و ال tangents و العنوان اللي احنا رافعينه
+
+424
+00:46:00,690 --> 00:46:05,030
+لكن العنوان الرئيسي تبع ال chapter قلنا and motion
+
+425
+00:46:05,030 --> 00:46:10,090
+in space و الحركة وين في الفرار إذا في جسم يتحرك
+
+426
+00:46:10,090 --> 00:46:14,720
+يعني معناته بدأت كله سرعةوإذا كانت لا تتحرك بسرعة
+
+427
+00:46:14,720 --> 00:46:20,740
+متوسطة فهي كلها عجلة تمام؟ إذا هنجي لتعريف كل من
+
+428
+00:46:20,740 --> 00:46:31,800
+السرعة والعجلة ومقدار السرعة Definition if R of T
+
+429
+00:46:31,800 --> 00:46:33,140
+is
+
+430
+00:46:39,760 --> 00:46:47,980
+الـ vector لو كان هذا متجه الموضوع ف a particle
+
+431
+00:46:47,980 --> 00:46:53,980
+moving هيبقى
+
+432
+00:46:53,980 --> 00:47:00,080
+يتحرك along a
+
+433
+00:47:00,080 --> 00:47:04,860
+smooth curve يتحرك
+
+434
+00:47:04,860 --> 00:47:06,800
+على مرحلة أملاس
+
+435
+00:47:09,280 --> 00:47:18,860
+f in space في الفرار then النقطة
+
+436
+00:47:18,860 --> 00:47:30,400
+الأولى dv of t اللي يبدأ يساوي dr على dv is called
+
+437
+00:47:30,400 --> 00:47:35,380
+the particles
+
+438
+00:47:35,380 --> 00:47:37,820
+velocity
+
+439
+00:47:41,480 --> 00:47:51,120
+vector متجه الصراع للجثير that is والذي يكون
+
+440
+00:47:51,120 --> 00:47:57,040
+مماثًا
+
+441
+00:47:57,040 --> 00:48:07,600
+that is a tangent والذي يكون مماثًا to the curve
+
+442
+00:48:13,610 --> 00:48:22,270
+طول الـ V طول المتجر V is
+
+443
+00:48:22,270 --> 00:48:26,430
+called the
+
+444
+00:48:26,430 --> 00:48:32,730
+particle speed the particle's
+
+445
+00:48:32,730 --> 00:48:46,050
+speed مقدار سرعته الجثيم تلاتة ال Vمقسومة على طول
+
+446
+00:48:46,050 --> 00:48:52,930
+ال V is the direction of the velocity is the
+
+447
+00:48:52,930 --> 00:49:05,850
+direction of the velocity اللي هو اتجاه الصراحة
+
+448
+00:49:05,850 --> 00:49:11,570
+and is the direction of motion and is
+
+449
+00:49:14,710 --> 00:49:23,550
+فايريشن او موشي او يهو اتجاه الحاجة
+
+450
+00:50:16,790 --> 00:50:19,190
+متجه العجلة
+
+451
+00:50:29,650 --> 00:50:43,850
+a small curve للمرحلة الأملة لفلوستي as
+
+452
+00:50:43,850 --> 00:50:50,450
+never zero ده
+
+453
+00:50:50,450 --> 00:50:56,760
+يمكن أن تساوي zeroيبقى هذا بدي يعني كلمة اللي
+
+454
+00:50:56,760 --> 00:51:05,520
+بعتقد بظبط stop ليه بعتقد بظبط
+
+455
+00:51:05,520 --> 00:51:15,000
+مات stop لا يتوقع ان بظبط reverse its direction
+
+456
+00:51:15,000 --> 00:51:18,220
+بظبط
+
+457
+00:51:18,220 --> 00:51:20,460
+مات reverse
+
+458
+00:51:39,390 --> 00:51:49,030
+الأمثلة The Tangent Line خط
+
+459
+00:51:49,030 --> 00:51:58,370
+التماس باسمه الـ Curve المرحلة
+
+460
+00:51:58,370 --> 00:51:58,950
+الأولى
+
+461
+00:52:23,960 --> 00:52:35,660
+الساوية كتابة هي الرسالة التي
+
+462
+00:52:35,660 --> 00:52:45,960
+تتجه من النقطة التي تتجه من النقطة
+
+463
+00:53:02,210 --> 00:53:11,530
+Parallel الذي في نفس الوقت يكون موازن لV of T0
+
+464
+00:53:11,530 --> 00:53:18,430
+اللي هو Velocity Vector
+
+465
+00:54:19,100 --> 00:54:23,920
+طب أنا أخدته في المرحلة الثانوية في حساب التفاضل
+
+466
+00:54:23,920 --> 00:54:29,360
+والتكامل أن تفاضل المسافة بيعطيني main السرعة
+
+467
+00:54:29,360 --> 00:54:35,050
+وتفاضل السرعة بيعطيني main اللي هي العجلهنا في ال
+
+468
+00:54:35,050 --> 00:54:39,270
+vector value of function نفس الطريقة بالضرب و بقدر
+
+469
+00:54:39,270 --> 00:54:44,590
+اجيب السرعة مقدارا و اتجاها مقدارا بجيب طول متجه
+
+470
+00:54:44,590 --> 00:54:49,270
+السرعة كده شهو يكون مقدار ال speed اتجاها بقسم
+
+471
+00:54:49,270 --> 00:54:53,590
+متجه السرعة على طوله بيعطيني ال direction او
+
+472
+00:54:53,590 --> 00:55:00,960
+بيعطيني متجه الوحدة في اتجاه الحركة فمثلا بقوللو
+
+473
+00:55:00,960 --> 00:55:05,560
+كان الـR of T هو الـposition vector لـparticle
+
+474
+00:55:05,560 --> 00:55:09,540
+موبق للجسم المتعرك على لومبيا small curve على
+
+475
+00:55:09,540 --> 00:55:14,660
+محلقة أملاست داليةبدي ال V of T بروح بشتق المنحنة
+
+476
+00:55:14,660 --> 00:55:18,260
+من اسم الامام الى T وهذا بيصيح ال particles
+
+477
+00:55:18,260 --> 00:55:24,640
+velocity vector متجه سرعة اليسير that is a tangent
+
+478
+00:55:24,640 --> 00:55:30,620
+والذي يكون مماثل الامام للمنحنة كيف يعني؟ ماجي
+
+479
+00:55:30,620 --> 00:55:34,980
+بقول لو جينا المنحنة اللي رسمناها قبل شوية وروح
+
+480
+00:55:34,980 --> 00:55:41,660
+نقولها هذا محور X وهذا محور Y وهذا محور Zنفترض
+
+481
+00:55:41,660 --> 00:55:48,480
+الجثير كان ماشي بالشكل اللي علناه و روحت بدي وين
+
+482
+00:55:48,480 --> 00:55:54,940
+اللي هو متجه تبع الصراع عند هذه النقطة على سبيل
+
+483
+00:55:54,940 --> 00:56:01,980
+المثال بقوله بدي متجه الموضع من نقطة الأصل إلى هذه
+
+484
+00:56:01,980 --> 00:56:10,160
+النقطة يبقى هذا هو متجه الموضع هذا اللي هو ROTالـ
+
+485
+00:56:10,160 --> 00:56:15,600
+R of T لو روحت فاضلتها بحصل على متجه السرعة، وين
+
+486
+00:56:15,600 --> 00:56:22,960
+بدي يكون متجه السرعة؟ اتجاه مماس لمين للملحنة عند
+
+487
+00:56:22,960 --> 00:56:24,240
+هذه النقطة
+
+488
+00:56:33,760 --> 00:56:41,580
+VRT VRT هو متجه السرعة متجه السرعة يمثل اتجاه
+
+489
+00:56:41,580 --> 00:56:48,220
+الحركة ويمثل اتجاه السرعة وهو عبارة عن مشتقة ال
+
+490
+00:56:48,220 --> 00:56:50,020
+position vector
+
+491
+00:56:55,800 --> 00:57:02,600
+يبقى هذا بسميه متجه السرعة والذي يكون مماس للمنحنة
+
+492
+00:57:02,600 --> 00:57:08,400
+اذا رسمناها مماس للمنحنة النقطة التانية مقدار هذه
+
+493
+00:57:08,400 --> 00:57:12,040
+السرعة مقدار هذه السرعة بسميها speed
+
+494
+00:57:34,840 --> 00:57:39,910
+النقطة الرابعةبدي ايه بروح باشت ايه طبعا ال
+
+495
+00:57:39,910 --> 00:57:44,310
+acceleration هي مشتقة ال V بالنسبة الى T المشتقة
+
+496
+00:57:44,310 --> 00:57:49,050
+الاولى او المشتقة الثانية لمان لل vector valued
+
+497
+00:57:49,050 --> 00:57:52,430
+functions او لل position vector اللي همان R of T
+
+498
+00:57:52,430 --> 00:57:54,730
+يعني D Square R على D T
+
+499
+00:57:58,420 --> 00:58:03,680
+على ال smooth curve قال الوصي لا يمكن أن تساوي
+
+500
+00:58:03,680 --> 00:58:09,940
+Zero لإن إذا V زوات Zero معناته المشتقات اللي
+
+501
+00:58:09,940 --> 00:58:15,230
+اشتقناهم هنا بده تساوي Zeroوهذا يناقض الشرط التاني
+
+502
+00:58:15,230 --> 00:58:21,070
+من شروط smooth curve يبقى لا يمكن أن يتوقف اتنين
+
+503
+00:58:21,070 --> 00:58:26,150
+مش عاجزاكوا بس ال particle does not stop بتوقفش
+
+504
+00:58:26,150 --> 00:58:31,130
+and does not replace its direction يعني مروحش يعكس
+
+505
+00:58:31,130 --> 00:58:34,570
+اتجاه الحركة انه لو اتجاه .. لو افترضنا انه ماشي
+
+506
+00:58:34,570 --> 00:58:38,290
+في هذا الاتجاه و بعدين بده يعكس يعني بده يصل إلى
+
+507
+00:58:38,290 --> 00:58:44,910
+نقطة تنعدم الصراع عنده ويبدأ يرجع تانيعند هذه
+
+508
+00:58:44,910 --> 00:58:48,910
+النقطة صار مقدار السرعة يسوي جداية زيرو، اذا ان
+
+509
+00:58:48,910 --> 00:58:54,970
+على ال smooth curve ماعنديش توقف للجسم، ماعنديش ان
+
+510
+00:58:54,970 --> 00:58:58,330
+الجسم يعود على نفس الخط اللي هاجي عليه، اللي هو
+
+511
+00:58:58,330 --> 00:59:02,300
+reverse its directionيبقى هذه ملاحظة من خلال
+
+512
+00:59:02,300 --> 00:59:07,560
+التعريف تبع main ل smooth curve آخر نقطة عندي اللي
+
+513
+00:59:07,560 --> 00:59:11,000
+هو tangent line طبعا لو رجحنا للعنوان اللي احنا
+
+514
+00:59:11,000 --> 00:59:15,360
+كاتبينه كاتبين ال curves and tangent lines وحتى
+
+515
+00:59:15,360 --> 00:59:19,360
+الآن لم نتحدث عن ال tangent line يبقى بنا نيجي لل
+
+516
+00:59:19,360 --> 00:59:23,400
+tangent line فبعور في ال tangent line to a smooth
+
+517
+00:59:23,400 --> 00:59:29,830
+curve لمنحنا أملس مقطع بهذا الشكل هذا النقطةهو
+
+518
+00:59:29,830 --> 00:59:36,310
+الخط الذي يمر بالنقطة F of T node وG of T node وH
+
+519
+00:59:36,310 --> 00:59:41,890
+of T node هذه أصلا مركبات X Y وZ يعني إحداثية نقطة
+
+520
+00:59:41,890 --> 00:59:46,550
+إذا مشان أجيب إحداثية نقطة بدي أشيل كل T و أعوض
+
+521
+00:59:46,550 --> 00:59:50,650
+بقيمة T node لأن أنا بحصل على ثلاثة أرقام الثلاثة
+
+522
+00:59:50,650 --> 00:59:55,410
+أرقام بيكون هم ال components لنهية ال position
+
+523
+00:59:55,410 --> 01:00:01,070
+vector اللي عندها بدي أحسب التأجدطيب يبقى هي جدنا
+
+524
+01:00:01,070 --> 01:00:08,130
+نقطة تقع على الخط المستقيم ال line هذا بدي يكون
+
+525
+01:00:08,130 --> 01:00:14,530
+parallel to V node لمتجه السرعة عند نقطة T node
+
+526
+01:00:14,530 --> 01:00:22,020
+يعني ال tangent بدي يكون هنابدي يكون هنا؟ لا ال
+
+527
+01:00:22,020 --> 01:00:25,540
+vector أنا بقدر أنقله زي ما بدي، بس ال tangent بدي
+
+528
+01:00:25,540 --> 01:00:29,320
+يكون ممس عند تلك النقطة، مظبوط ولا لا؟ إذا ال
+
+529
+01:00:29,320 --> 01:00:33,900
+tangent دي أبدا بدي يكون مطابق تماما على V، يبقى
+
+530
+01:00:33,900 --> 01:00:40,420
+هو المتجهفي بالضبط عند الكمين النقطة واحنا أخدنا
+
+531
+01:00:40,420 --> 01:00:46,040
+اللي هو في section 12-5 بدي معادلة ال أو المعادلة
+
+532
+01:00:46,040 --> 01:00:50,520
+ال parameterية للخط المستقيم بلزمني شغلتين الشغلة
+
+533
+01:00:50,520 --> 01:00:56,470
+الأولى النقطة تقع عليه وهي الحمد لله موجودةالمتجه
+
+534
+01:00:56,470 --> 01:01:04,150
+اللي يوازي المماس هو متجه السرعة عند تلك النقطة
+
+535
+01:01:04,150 --> 01:01:10,430
+وبالتالي بقدر أجيب لمخط التماس للمنحنة عند تلك
+
+536
+01:01:10,430 --> 01:01:14,810
+النقطة حد بتحب تسأل أي سؤال هنا قبل أن ندخل إلى
+
+537
+01:01:14,810 --> 01:01:21,040
+الأمثلةعن السرعة، عن ال acceleration، عن ال
+
+538
+01:01:21,040 --> 01:01:25,160
+direction، عن ال speed، عن ال tangent، إيش ماعندي
+
+539
+01:01:25,160 --> 01:01:27,420
+كسلي؟ مفيش؟
+
+540
+01:01:30,880 --> 01:01:36,120
+المعنى بنات أننا ناخد بعض الأمثلة على اللي هو بعض
+
+541
+01:01:36,120 --> 01:01:40,720
+ال definitions اللي أشرنا اليها واتعرفنا عليها قبل
+
+542
+01:01:40,720 --> 01:01:46,120
+قليل أول مثال من هذه الأمثلة هو لهد المعادلات ال
+
+543
+01:01:46,120 --> 01:01:52,060
+parameterية للخط اللي يكون مماثل للمنحنة اللي
+
+544
+01:01:52,060 --> 01:01:57,540
+عندها دي عند T node يساوي E قداشر E هذه بنت عددية
+
+545
+01:02:01,490 --> 01:02:07,970
+مش سامع العدد اللي يقدرش اتنين وسبعة من عشرة
+
+546
+01:02:07,970 --> 01:02:12,790
+تقريبا يبقى احنا بنا نعرف انه
+
+547
+01:02:18,060 --> 01:02:22,480
+يعني عندي اتنين وسبعة من عشرة تقريبا مشان اعرف
+
+548
+01:02:22,480 --> 01:02:28,680
+التنين بدي شغلتين بدي نقطة يمر بيها من المنحنة
+
+549
+01:02:28,680 --> 01:02:37,460
+معناته بدي اجيب F of E وG of E وH of E يبقى باجي
+
+550
+01:02:37,460 --> 01:02:40,240
+بقوله هنا دي point
+
+551
+01:02:55,850 --> 01:03:01,610
+لن ال E بقى درجة او واحدة يبقى هنا بس للتوضيح اكتب
+
+552
+01:03:01,610 --> 01:03:02,530
+لن ال E
+
+553
+01:03:17,360 --> 01:03:27,540
+و E نقص واحد على E زائد واحد و E نقطة هذه lie on
+
+554
+01:03:27,540 --> 01:03:33,900
+the lineيبقى هذه تبقى على الخط اللي احنا بدنا نجيب
+
+555
+01:03:33,900 --> 01:03:39,000
+المعادلة ابتدا يبقى انا جبتله الان اللي بده اياه H
+
+556
+01:03:39,000 --> 01:03:45,380
+of T نوت وG of T نوت وH of T نوت بده اجيب متجه
+
+557
+01:03:45,380 --> 01:03:52,300
+يوازي هذا ال line من المتجه يجب ان يكون V of T نوت
+
+558
+01:03:52,300 --> 01:03:58,440
+شو حمله يبقى بده اروح اشتغل ال R of T يبقى بروح
+
+559
+01:03:58,440 --> 01:04:08,290
+بقولهالـ V as a function of T لـDR على DT نشتق لأن
+
+560
+01:04:08,290 --> 01:04:17,010
+T بدأ جبنان في اتجاه ماين؟ في اتجاه I زائر نشتق
+
+561
+01:04:17,010 --> 01:04:20,450
+هذه المقام في مشتقة البصد
+
+562
+01:04:30,790 --> 01:04:36,610
+على مربع المقام الأصلي T زائد واحد الكل تربية في
+
+563
+01:04:36,610 --> 01:04:45,130
+اتجاه ال J زائد هذه حاصل ضرب دليل T T في لن ال T
+
+564
+01:04:45,130 --> 01:04:52,690
+لواحد على T يعني واحد زائد لن ال T كله في اتجاه
+
+565
+01:04:52,690 --> 01:04:55,510
+مين؟ في اتجاه ال K
+
+566
+01:04:59,880 --> 01:05:07,940
+يبقى ال V of E يبقى واحد على E في اتجاه ال I هادي
+
+567
+01:05:07,940 --> 01:05:13,280
+مع هادي الله يسهل عليها بضلان نقدر جبنان زائد
+
+568
+01:05:13,280 --> 01:05:19,540
+اتنين على E زائد واحد لكل تربيع
+
+569
+01:05:30,080 --> 01:05:35,460
+يبقى النقطة موجودة والمتجه اللي يوازي ال line
+
+570
+01:05:35,460 --> 01:05:42,200
+موجود اذا بقدر اقوله the parametric
+
+571
+01:05:42,200 --> 01:05:51,240
+equation for the tangent line
+
+572
+01:06:20,840 --> 01:06:28,360
+زائد اتنين على E زائد واحد لكل تربيه في T والـ Z
+
+573
+01:06:28,360 --> 01:06:37,260
+يساوي E زائد اتنين T في هذا ال Parametric
+
+574
+01:06:37,260 --> 01:06:43,040
+Equations لمين؟ لمعادلات الخط المستخيم اللي بدي
+
+575
+01:06:43,040 --> 01:06:48,680
+يكون مماس للملحنة عند هذه النقطة
+
+576
+01:07:18,330 --> 01:07:23,790
+مطلوب الأول نمرأه find the particles path
+
+577
+01:07:31,570 --> 01:07:39,130
+المصاد تبع الجثيم in terms of
+
+578
+01:07:39,130 --> 01:07:49,570
+x and y بدللة x و y نمرى ب find
+
+579
+01:07:49,570 --> 01:07:58,190
+the particles velocity أو find the particles
+
+580
+01:08:04,250 --> 01:08:12,310
+and acceleration and acceleration والعجلة
+
+581
+01:08:12,310 --> 01:08:20,910
+acceleration vectors متجهات السرعة والعجلة at T
+
+582
+01:08:20,910 --> 01:08:24,390
+تساوي باي على ستة
+
+583
+01:09:09,630 --> 01:09:14,450
+يجب ان انا اشتغل في الفرق و المركبة الثالثة بـ0
+
+584
+01:09:14,450 --> 01:09:19,850
+انا
+
+585
+01:09:19,850 --> 01:09:24,290
+اشتغل في الفرق و المركبة الثالثة بـ0 انا اشتغل في
+
+586
+01:09:24,290 --> 01:09:25,070
+الفرق و المركبة الثالثة بـ0 انا اشتغل في الفرق و
+
+587
+01:09:25,070 --> 01:09:29,620
+المركبة الثالثة بـ0المطلب التاني هو كم السرعة
+
+588
+01:09:29,620 --> 01:09:35,940
+والعجلة عند T0 يساوي كم Y على سنة اذا خلّيني أجي
+
+589
+01:09:35,940 --> 01:09:39,540
+المطلوب الأول المطلوب الأول من أين بدي أجيب له X
+
+590
+01:09:39,540 --> 01:09:49,600
+وY هذي المركبة X في اتجاه I وهذه Y في اتجاه G يبقى
+
+591
+01:09:49,600 --> 01:09:57,810
+هنا كإنه Xيدها الساوي اللي هو cosine اتنين T وال Y
+
+592
+01:09:57,810 --> 01:10:06,220
+بده يساوي تلاتة sin اتنين Tلما جالي هت للمعادلة
+
+593
+01:10:06,220 --> 01:10:11,980
+بدلالة x و y يعني كأنه بيقول ايه اش احذف ت من
+
+594
+01:10:11,980 --> 01:10:17,380
+المعادلتين بتتخلص من ت السؤال هو كيف يا ملات
+
+595
+01:10:17,380 --> 01:10:23,700
+بتتخلص من ت بين المعادلتين ونخليها بدلالة x و y
+
+596
+01:10:23,700 --> 01:10:29,220
+ايش
+
+597
+01:10:29,220 --> 01:10:30,320
+نعمل بالضبط تاني
+
+598
+01:10:38,040 --> 01:10:44,240
+ماشي و التانية زيها وجهة نظر السليمان 100% في واحد
+
+599
+01:10:44,240 --> 01:10:50,780
+عندها رأي اخر اه
+
+600
+01:10:50,780 --> 01:11:03,540
+مالهيعني بدك تقول اتنين sin cos عقدناها اكتر صحيح
+
+601
+01:11:03,540 --> 01:11:07,980
+يمكن نفكر بهذا الاتجاه بدون ما اجي لمعكوس الدول
+
+602
+01:11:07,980 --> 01:11:15,150
+المثلثية لطرحة الخلاصبقول كيف هذي بقدر اقول x يسوى
+
+603
+01:11:15,150 --> 01:11:21,310
+cosine اتنين t و هذي y على تلاتة يسوى sin اتنين t
+
+604
+01:11:21,310 --> 01:11:27,390
+إذا لو بعت الطرفين و جمعت بكون اتخلصت منين من ال T
+
+605
+01:11:27,390 --> 01:11:31,090
+و بتظل المثلة بدلت x و y زي ما هو طالب إذا لو
+
+606
+01:11:31,090 --> 01:11:36,430
+روحنا رابعنا يا بنات بقول x تربيةعلى تلاتة كل
+
+607
+01:11:36,430 --> 01:11:42,870
+تربيع يسوى Cos تربيع اتنين T زائد Sin تربيع اتنين
+
+608
+01:11:42,870 --> 01:11:50,470
+T او ان شويتولنا فقولنا X تربيع زائد Y تربيع على
+
+609
+01:11:50,470 --> 01:11:53,630
+تسعة يسوى كده ايش؟ واحد
+
+610
+01:11:58,820 --> 01:12:04,440
+Ellipse دائرة Ellipse طب مين ال major axis او
+
+611
+01:12:04,440 --> 01:12:13,100
+الفوك ال axis تبع محور X ولا محور Y؟ Y طبعا لإنه
+
+612
+01:12:13,100 --> 01:12:16,800
+بحكم من خلال الرقم الكبير اللي في المقام هذه
+
+613
+01:12:16,800 --> 01:12:23,900
+باعتبارها X على 1 وهذا من Y كتير على 9 يبقى هذا
+
+614
+01:12:23,900 --> 01:12:24,840
+Ellipse
+
+615
+01:12:29,120 --> 01:12:45,820
+Center at the origin and the major axis along
+
+616
+01:12:47,010 --> 01:12:54,110
+the y axis يعني الاستقالة تبعته بده تكون وين فوق
+
+617
+01:12:54,110 --> 01:12:58,510
+قوتها على اي حالة على هذا السطر و نص دول مجرد
+
+618
+01:12:58,510 --> 01:13:03,330
+توضية لكن بسموهش المعادلة هذه هي معادلة من معادلة
+
+619
+01:13:05,000 --> 01:13:08,180
+بنجي للمطلوب التاني يبقى بناتنا بيقولي هات
+
+620
+01:13:08,180 --> 01:13:12,780
+المعادلة يعني بدي أضيع T بين المعادلة إيش ميكون
+
+621
+01:13:12,780 --> 01:13:18,600
+شكله ميكون بأي طريقة رياضية صحيحة نجي للمطلوب
+
+622
+01:13:18,600 --> 01:13:22,340
+التاني بيقولي هد ال particles velocity and
+
+623
+01:13:22,340 --> 01:13:27,360
+acceleration بقوله بسيطة أنا المطلوب التاني نمرا B
+
+624
+01:13:27,360 --> 01:13:34,500
+بدي ال V of T يبقى اللي هى DR على DTيعني بدي ارجع
+
+625
+01:13:34,500 --> 01:13:40,080
+للمعادلة واشتغل اتفاض القصاي بسالب صين بمشتقة
+
+626
+01:13:40,080 --> 01:13:45,100
+الزاوية له اتنين صين اتنين T في اتجاه مين؟ في
+
+627
+01:13:45,100 --> 01:13:52,800
+اتجاه ال I زائد ستة قصين اتنين T في اتجاه الجي
+
+628
+01:13:52,800 --> 01:13:59,360
+بالمرة احسب له ال V and ال Y على ستة
+
+629
+01:14:01,850 --> 01:14:06,630
+إذا بدأ أشيل كل T و أضع مكانها باي على ستة بسيطة
+
+630
+01:14:06,630 --> 01:14:12,390
+عندها أن أناقص اتنين Sine of I على تلاتة في اتجاه
+
+631
+01:14:12,390 --> 01:14:21,610
+I زائد ستة و Sine of I على تلاتة في اتجاه J شيلت
+
+632
+01:14:21,610 --> 01:14:26,210
+ال T و أضعت مكانها باي على ستة و اختصرت يبقى
+
+633
+01:14:26,210 --> 01:14:32,980
+نتيجته ساعةالأعلى من هنا جهة ستين اللي هي بجدر
+
+634
+01:14:32,980 --> 01:14:40,280
+تلاتة على اتنين يبقى سالب جدر تلاتة في اتجاه ال I
+
+635
+01:14:40,280 --> 01:14:47,680
+اللي بعدها جهتها ستين نص في ستة بالتلاتة زائد
+
+636
+01:14:47,680 --> 01:14:54,500
+تلاتة في اتجاه ال J بعد هيك تبدأ ال acceleration A
+
+637
+01:14:54,500 --> 01:15:02,280
+يبقى اللي DVهذه ال V بنتد عنها هشتغها تمام مرة
+
+638
+01:15:02,280 --> 01:15:09,040
+يبقى ناقص اربعة كوصين اتنين T في اتجاه I زي ناقص
+
+639
+01:15:09,040 --> 01:15:17,480
+اتناشر صين اتنين T في اتجاه Jبدي أجيب له الـ
+
+640
+01:15:17,480 --> 01:15:23,280
+acceleration عند النقطة باي على ستة يبقى تساوي
+
+641
+01:15:23,280 --> 01:15:30,500
+ناقص أربعة قساين باي على تلاتة في اتجاه الـ I ناقص
+
+642
+01:15:30,500 --> 01:15:37,400
+اتناشر sign باي على تلاتة في اتجاه الجهة والتي
+
+643
+01:15:37,400 --> 01:15:40,180
+بدأت تساوي جتها ستين
+
+644
+01:15:46,780 --> 01:15:53,340
+الجدر التلاتة على اتنين يبقى مناقش ستة جدر تلاتة
+
+645
+01:15:53,340 --> 01:15:59,840
+في اتجاه مين في اتجاه ال جيك دي بقى حسبناله ال
+
+646
+01:15:59,840 --> 01:16:06,260
+acceleration و ال velocity و معادلة المسار كذلك
+
+647
+01:16:06,260 --> 01:16:09,100
+عند النقطة المضغوطة
+
+648
+01:16:49,030 --> 01:16:57,590
+تتجاه الـ I زائد تان Inverse T بتجاه الـ J زائد
+
+649
+01:16:57,590 --> 01:17:05,470
+الجذر التربيه اللتي تربيها زائد واحد تتجاه ال K at
+
+650
+01:17:05,470 --> 01:17:12,910
+P بساوي واحد في عين رجلنا مرتين
+
+651
+01:17:22,920 --> 01:17:45,920
+Velocity Velocity Velocity
+
+652
+01:17:45,920 --> 01:17:46,240
+Velocity Velocity Velocity Velocity Velocity
+
+653
+01:17:46,240 --> 01:17:46,240
+Velocity Velocity Velocity Velocity Velocity
+
+654
+01:17:46,240 --> 01:17:46,240
+Velocity Velocity Velocity Velocity Velocity
+
+655
+01:17:46,240 --> 01:17:47,780
+Velocity Velocity Velocity Velocity Velocity
+
+656
+01:17:47,780 --> 01:17:47,780
+Velocity Velocity Velocity Velocity Velocity
+
+657
+01:17:47,780 --> 01:17:47,780
+Velocity Velocity Velocity Velocity Velocity
+
+658
+01:17:47,780 --> 01:17:47,780
+Velocity Velocity Velocity Velocity Velocity
+
+659
+01:17:47,780 --> 01:17:47,780
+Velocity Velocity Velocity Velocity Velocity
+
+660
+01:17:47,780 --> 01:17:47,780
+Velocity Velocity Velocity Velocity Velocity
+
+661
+01:17:47,780 --> 01:17:47,780
+Velocity Velocity Velocity Velocity Velocity
+
+662
+01:17:47,780 --> 01:17:47,780
+Velocity Velocity Velocity Velocity Velocity
+
+663
+01:17:47,780 --> 01:17:47,800
+Velocity Velocity Velocity Velocity Velocity
+
+664
+01:17:47,800 --> 01:17:47,800
+Velocity Velocity Velocity Velocity Velocity
+
+665
+01:17:47,800 --> 01:17:49,120
+Velocity Velocity Velocity Velocity Velocity
+
+666
+01:17:49,120 --> 01:17:49,920
+Velocity Vel
+
+667
+01:18:05,040 --> 01:18:11,120
+angle between اللي
+
+668
+01:18:11,120 --> 01:18:17,160
+هو ال velocity and
+
+669
+01:18:17,160 --> 01:18:22,660
+acceleration vectors
+
+670
+01:19:08,780 --> 01:19:14,760
+السرعة والعجلة مطلوب التاني كده كده السرعة مقدارا
+
+671
+01:19:14,760 --> 01:19:20,660
+واتجاها كده ال particle كده ال speed وكده اتجاه ال
+
+672
+01:19:20,660 --> 01:19:24,600
+direction of motion كده اتجاه السرعة اللي ما كتبنا
+
+673
+01:19:24,600 --> 01:19:29,300
+قبل قليل وبعدها كده اعرف كده الزاوية بين السرعة
+
+674
+01:19:29,300 --> 01:19:33,460
+والعجلة عند T تساوي واحد
+
+675
+01:19:45,550 --> 01:19:51,310
+ت ويسار اتنين ت على ت تربيه زائد واحد في اتجاه ال
+
+676
+01:19:51,310 --> 01:19:56,490
+I وكان ال inverse فاضل لها قبل قليل فكانت واحد على
+
+677
+01:19:56,490 --> 01:20:01,090
+واحد زائد ت تربيه في اتجاه ال J متفاضل الجدرف جدا
+
+678
+01:20:01,090 --> 01:20:08,180
+شبناتهو احد على اتنين الجدر في مشتقة ما تحت الجدر
+
+679
+01:20:08,180 --> 01:20:13,200
+اللي هو اتنين T بتروح اتنين مع اتنين و ببقى بس
+
+680
+01:20:13,200 --> 01:20:15,880
+عندي T على الجدر التالي
+
+681
+01:20:43,850 --> 01:20:53,170
+واحد على جدري اتنين K بدي ال acceleration A as a
+
+682
+01:20:53,170 --> 01:21:00,650
+function of T يبقى اللي هى DV على DT بدي اشتغل
+
+683
+01:21:00,650 --> 01:21:07,190
+كمان مرة يبقى المقام في مشتقة الفاصلة باتنين T
+
+684
+01:21:07,190 --> 01:21:09,170
+تربية زائد واحد
+
+685
+01:21:15,860 --> 01:21:24,080
+المقام الأصلي في اتجاه الـR إذا المقام في مشتقة
+
+686
+01:21:24,080 --> 01:21:32,120
+البصد بـ0 ناقص البصد في مشتقة المقام على مربع
+
+687
+01:21:32,120 --> 01:21:34,100
+المقام الأصلي
+
+688
+01:22:06,760 --> 01:22:11,520
+طيب كنتش أضيع وقت ورق وانا بسط لكن بنقول بسط بنبسط
+
+689
+01:22:11,520 --> 01:22:16,420
+ماعنداش مشكلة لو حبينا نرتبها هه فاطلع عندى اتنين
+
+690
+01:22:16,420 --> 01:22:21,480
+T تربيع و هنا ناقص اربعة T تربيع فبقى ناقص اتنين T
+
+691
+01:22:21,480 --> 01:22:28,220
+تربيع زائد اتنين ناقص اتنين T تربيع زائد اتنين على
+
+692
+01:22:28,220 --> 01:22:34,020
+T تربيع زائد واحد لكل تربيع اللى فاتجه
+
+693
+01:22:41,050 --> 01:22:47,230
+الـ J زائد هذه لو احطلها المقامات يا بنات او هذه
+
+694
+01:22:47,230 --> 01:22:51,650
+اتنين بتروح مع اتنين اللي عندها هذه لو احطلها
+
+695
+01:22:51,650 --> 01:22:55,390
+المقامات الـ J اللي بنزل هنا وبصينا اندي T تربية
+
+696
+01:22:55,390 --> 01:23:03,070
+زائد واحد ناقص T تربية يبقى بيظل عندي جداش بس واحد
+
+697
+01:23:12,860 --> 01:23:17,520
+مرة تانية لو وحدت المقامات بده ينزل الجدر هذا تحت
+
+698
+01:23:17,520 --> 01:23:22,760
+الجدر في الجدر بطير بظل ت تربيع ناقص واحد ناقص ت
+
+699
+01:23:22,760 --> 01:23:29,040
+تربيع بظل قداش عندي بس واحد على المقام الشكل اللي
+
+700
+01:23:29,040 --> 01:23:32,580
+عندنا هذا بدي اجيب له قداش العجلة
+
+701
+01:23:40,510 --> 01:23:47,910
+وهذا عند الواحد بصير ناقص J عند الواحد بصير اتنين
+
+702
+01:23:47,910 --> 01:23:52,410
+على اتنين اللي هو ناقص J وهذا عند الواحد اللي هو
+
+703
+01:23:52,410 --> 01:23:57,070
+جذري اتنين وهنا اتنين بواحد على اتنين جذري اتنين
+
+704
+01:23:57,070 --> 01:23:58,470
+زائد
+
+705
+01:24:11,550 --> 01:24:16,070
+بنكتب التربيهة تبعها صح أصابة امرأة و أختها عمر
+
+706
+01:24:16,070 --> 01:24:22,530
+يبقى دي اتنين على اربع اللي هو مص مص جي المفروض
+
+707
+01:24:22,530 --> 01:24:28,210
+يبقى هذا مص جي و هذه واحد على اتنين جدر اتنين جي
+
+708
+01:24:28,210 --> 01:24:35,170
+يبقى جيبناله المطلوب الأول المطلوب التاني نمربيه
+
+709
+01:24:35,170 --> 01:24:38,090
+جالي بيديه ال speed عند هذه
+
+710
+01:24:44,960 --> 01:24:51,560
+اليد اللي هي الطول المتجه فيه و اللي يبدأ تساوي
+
+711
+01:24:51,560 --> 01:25:01,610
+الجدر التربيعي لمربع المركبات الواحدزائد ربع زائد
+
+712
+01:25:01,610 --> 01:25:09,730
+نص ويسبب عضل نص غالب زائد ربع في تلت تربع زائد
+
+713
+01:25:09,730 --> 01:25:16,850
+واحد في سبعة على أربع يبقى الجدر التربيهي لسبعة
+
+714
+01:25:16,850 --> 01:25:22,610
+على أربع يبقى جدر سبعة على الإتنين مقدار السرعة.
+
+715
+01:25:23,370 --> 01:25:31,030
+يعني بدل Direction of Motionيرجع الـ Direction of
+
+716
+01:25:31,030 --> 01:25:41,950
+motion بيساوي ال V على طول ال V طول ال V موجود وال
+
+717
+01:25:41,950 --> 01:25:46,910
+V هيو موجود وينه هيو؟ بده Direction يرجعش بصيرها
+
+718
+01:25:46,910 --> 01:25:48,730
+بنات؟ اللي هو اين؟
+
+719
+01:25:52,160 --> 01:26:02,360
+زائد نص J زائد واحد على جدر اتنين K كله مقسومة جدر
+
+720
+01:26:02,360 --> 01:26:09,160
+سبعة على اتنين ويسار اتنين على جدر سبعة في اتجاه
+
+721
+01:26:09,160 --> 01:26:17,040
+ال I زائد واحد على جدر سبعة في اتجاه ال J زائد
+
+722
+01:26:17,040 --> 01:26:31,500
+اتنين على جدرالـ K طيب
+
+723
+01:26:31,500 --> 01:26:37,860
+الان بدنا نيجي بعد هذا الكلام للمطبوخ التركيزي
+
+724
+01:26:37,860 --> 01:26:42,900
+لانجل ما بين الاتنين عشان اجيب الانجل بدي الزاوية
+
+725
+01:26:42,900 --> 01:26:49,060
+يعني بعدين موجهة A و V بقول خد ضبط product بجباجي
+
+726
+01:26:49,060 --> 01:26:50,320
+بقول ال A
+
+727
+01:27:00,660 --> 01:27:07,000
+يبقى بالتاجة هذه الـA وهذه الـB يبقى طُبط هذا جداش
+
+728
+01:27:07,000 --> 01:27:16,360
+الرجل تبعد I0 اللي بعدينا ناقص نص في جدار في نص
+
+729
+01:27:16,360 --> 01:27:18,140
+ناقص ربع
+
+730
+01:27:24,140 --> 01:27:29,060
+جدري اتنين واحد على جدري اتنين اللي هو بربع يبقى
+
+731
+01:27:29,060 --> 01:27:39,520
+زائد ربع يساوي هو للجدري التربيعي لمربع المركبات
+
+732
+01:27:39,520 --> 01:27:46,280
+اللي هو ربع زائد اللي هو اتنين جدري اتنين على تمت
+
+733
+01:27:46,280 --> 01:27:50,340
+في الجدري التربيعي
+
+734
+01:27:59,650 --> 01:28:03,490
+يوجد كوصينة في الزاوية تيتا هذا ليس جداش أبناء انا
+
+735
+01:28:03,490 --> 01:28:07,410
+انا
+
+736
+01:28:07,410 --> 01:28:07,410
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+737
+01:28:07,410 --> 01:28:07,410
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+738
+01:28:07,410 --> 01:28:07,610
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+739
+01:28:07,610 --> 01:28:08,950
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+740
+01:28:08,950 --> 01:28:08,950
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+741
+01:28:08,950 --> 01:28:08,950
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+742
+01:28:08,950 --> 01:28:16,530
+انا انا انا انا انا انا انا انا انا
+
+743
+01:28:16,530 --> 01:28:16,530
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+744
+01:28:16,530 --> 01:28:27,590
+انا انا
+
+745
+01:28:27,590 --> 01:28:29,410
+انا ا
+
+746
+01:28:35,660 --> 01:28:44,560
+أكسليريشن أورثجولان التى تساوي واحدة عند هذه
+
+747
+01:28:44,560 --> 01:28:48,220
+النقطة الذين يكونوا بالهم متعامدين
+
+748
+01:29:44,000 --> 01:29:50,600
+Differentiable Vector Functions of T
+
+749
+01:30:08,660 --> 01:30:20,460
+و C Any C Small Any Scalar أي
+
+750
+01:30:20,460 --> 01:30:28,900
+كمية قياسية Any ال Earth Any Differentiable Any
+
+751
+01:30:28,900 --> 01:30:37,660
+Differentiable Scalar Function Then
+
+752
+01:30:42,890 --> 01:30:54,650
+على DT لكرتة الـ C بساوي زرد اتنين ال D على DT لـ
+
+753
+01:30:54,650 --> 01:30:55,310
+C Small
+
+754
+01:31:36,390 --> 01:31:48,370
+أو U' of T زائد او ناطس V' of T الأربع ال D على DT
+
+755
+01:31:48,370 --> 01:32:02,530
+ل U بُط ال V U' بُط ال V زائد U بُط V' الخامس ال D
+
+756
+01:32:16,420 --> 01:32:28,620
+DV على DT الثالث الـ D على DT لـ U as a function
+
+757
+01:32:28,620 --> 01:32:36,020
+of T بده يساوي الـ U prime لل F of T
+
+758
+01:33:10,900 --> 01:33:17,220
+القواعد الاشتقاق لا يختلف عن قواعد الاشتقاق اللي
+
+759
+01:33:17,220 --> 01:33:21,760
+اتعرفنا فيهم على الدوال العادلين فبقول لو كان U و
+
+760
+01:33:21,760 --> 01:33:25,980
+P قابل
+
+761
+01:33:25,980 --> 01:33:31,380
+الاشتقاق و كان capital C هو constant vector و
+
+762
+01:33:31,380 --> 01:33:37,250
+small c هو عبارة عن scalarوالـ F scalar function
+
+763
+01:33:37,250 --> 01:33:43,310
+يعني زي cos T زي sin T زي tan inverse T زي T تربية
+
+764
+01:33:43,310 --> 01:33:47,430
+زي T تربية نقص خمسية إلى آخرين يعني دالة ليست
+
+765
+01:33:47,430 --> 01:33:52,710
+اتجاهية ومن هنا بسميها scalar function يعني دالة
+
+766
+01:33:52,710 --> 01:33:55,210
+قياسية دب مشتقتي
+
+767
+01:34:01,340 --> 01:34:07,500
+مشتاقة أي مرتجة ثابت يساوي ان كلها مقادير ثابتة
+
+768
+01:34:07,500 --> 01:34:14,900
+بعد هيك مشتاقة ال scalar C في الدالة الاتجاهية U
+
+769
+01:34:20,040 --> 01:34:24,020
+هو الـ main function اللي هي الـ U لو كان هذا الـ
+
+770
+01:34:24,020 --> 01:34:29,120
+scalar و هذا الـ U يبقى بدل مكانة C رقم بدي أخد
+
+771
+01:34:29,120 --> 01:34:33,440
+سؤال بدل main الـ scalar function F فبقى يقول
+
+772
+01:34:33,440 --> 01:34:36,620
+مستقل مستقلة ال function في ال vector valued
+
+773
+01:34:36,620 --> 01:34:40,920
+function زي ال function في مستقلة ال vector valued
+
+774
+01:34:40,920 --> 01:34:46,060
+function اللي عندنا هنا قانون التوزيع زي
+
+775
+01:34:53,500 --> 01:34:57,120
+الأولى في مشتقة التانية زادتانى في مشتقة الأولى
+
+776
+01:34:57,120 --> 01:35:05,440
+يعني ايش مشتقة حاصل ضرب دلتين تصدر قياسي ترتيب
+
+777
+01:35:05,440 --> 01:35:11,320
+ضروري ليس ضروري لضد product is commutative نيجي
+
+778
+01:35:11,320 --> 01:35:15,820
+على ال product هذا اللي بده الترتيب يعني هذا اللي
+
+779
+01:35:15,820 --> 01:35:20,480
+قلت لك U prime TV و قلت لك V prime ضد U مافي مشكلة
+
+780
+01:35:31,760 --> 01:35:36,900
+الأولى في الثانية زائد الأولى في مشتقتها بخلي كل
+
+781
+01:35:36,900 --> 01:35:42,760
+واحد في موقعه و بشتقه ا في موقعه و بستخدم مشتقة
+
+782
+01:35:42,760 --> 01:35:48,760
+حصل ضال دالتين هنا chain rule لو ال U cannot
+
+783
+01:35:48,760 --> 01:35:53,460
+function في main في scalar function أخرى بقول ال U
+
+784
+01:35:53,460 --> 01:35:58,560
+prime F of T و بضره في مشتقة main مشتقة هذه ال
+
+785
+01:35:58,560 --> 01:36:01,100
+function أخر نقطة في هذا
+
+786
+01:36:07,100 --> 01:36:11,340
+الـ vector functions
+
+787
+01:36:11,340 --> 01:36:16,580
+of a constant
+
+788
+01:36:40,370 --> 01:36:53,790
+الـ vector function of T as ال R of T is of
+
+789
+01:37:09,550 --> 01:37:20,750
+ROT بطي الـDR على DT بده ساوي زيرو هذا إيش معناه؟
+
+790
+01:37:20,750 --> 01:37:27,970
+يبقى هذا means ان الـ ROT and
+
+791
+01:38:01,270 --> 01:38:07,190
+الـ R of T of constant length دلّة قبل اشتقاق لكن
+
+792
+01:38:07,190 --> 01:38:12,490
+القوة تبعها يسوى مقدارا ثابتا ضمن الـ R of T ضد
+
+793
+01:38:12,490 --> 01:38:16,790
+الـDR على DT بدل ساوى Zero هذا يعني أن الدل لو
+
+794
+01:38:16,790 --> 01:38:21,750
+مشتقت هاتين اللي بيكونوا مالوا متعامدان R او
+
+795
+01:38:21,750 --> 01:38:26,590
+رثوبالة بدنا نبره انصحة هذا الكلام يبقى احنا عندنا
+
+796
+01:38:26,590 --> 01:38:29,630
+R of T is of constant length
+
+797
+01:38:36,690 --> 01:38:48,570
+طول R of T كده؟ طول R of T طول
+
+798
+01:38:48,570 --> 01:38:53,070
+R of T كده؟
+
+799
+01:38:53,070 --> 01:39:01,490
+طول مصدر ثالث يبقى هذا إيش؟ هذا اعطاني رقم كلام
+
+800
+01:39:15,120 --> 01:39:26,260
+DR على DT زائد DR على DT بطل ROT كده مستقلة
+
+801
+01:39:26,260 --> 01:39:32,460
+المقدار الثابت؟ Zero تمام احتمال يبقاش اللي حصل
+
+802
+01:39:32,460 --> 01:39:39,340
+عندنا بناه هل هذا هو وهذا ولا مختلف عن بعض ال dot
+
+803
+01:39:39,340 --> 01:39:42,280
+is commutative يبقى انه مش مصير عندي
+
+804
+01:39:46,130 --> 01:39:52,390
+بط DR على DT بده يساوي Zero هذا معناته ان ال R of
+
+805
+01:39:52,390 --> 01:39:59,390
+T بط DR على DT بده يساوي كدهش Zero وهو المقلوب
+
+806
+01:39:59,390 --> 01:40:04,770
+يعني صار ال R of T وDR على DT اتنين
+
+807
+01:40:18,060 --> 01:40:29,620
+the vector قيللي إن المتجد R of T يساوي خمسة أساية
+
+808
+01:40:29,620 --> 01:40:32,940
+E في اتجاه I زائد خمسة
+
+809
+01:40:52,360 --> 01:41:05,920
+والثابت is orthogonal to
+
+810
+01:41:05,920 --> 01:41:06,900
+its derivative
+
+811
+01:41:21,120 --> 01:41:26,310
+عليه البركةوكان بيبين لي ان المتجه هذا طوله ثابت
+
+812
+01:41:26,310 --> 01:41:30,190
+إذا بروح أحسب قداش الطول تبعه واشوف قداشه ثابت
+
+813
+01:41:30,190 --> 01:41:36,990
+فبجي بقول الطول تبع ال R of T يسوى ال square root
+
+814
+01:41:36,990 --> 01:41:43,990
+لمربع المركمات قداش هذه خمسة وعشرين cosine تربيتي
+
+815
+01:41:43,990 --> 01:41:50,250
+زائد خمسة وعشرين sin تربيتي زائد اتناش في اتناش
+
+816
+01:41:50,250 --> 01:41:55,540
+القداشيبقى 144 يبقى هذا الكلام لساوي الجدر
+
+817
+01:41:55,540 --> 01:42:01,560
+التربيعي لو أخد 25 عامل مشترك بطول قدر تربية تربية
+
+818
+01:42:01,560 --> 01:42:06,460
+تربية تربية تربية تربية تربية تربية تربية تربية
+
+819
+01:42:06,460 --> 01:42:09,120
+تربية تربية تربية تربية تربية تربية تربية تربية
+
+820
+01:42:09,120 --> 01:42:14,040
+تربية تربية تربية تربية تربية تربية تربية تربية
+
+821
+01:42:14,040 --> 01:42:16,980
+تربية تربية تربية تربية تربية تربية تربية تربية
+
+822
+01:42:16,980 --> 01:42:17,080
+تربية تربية تربية تربية تربية تربية تربية تربية
+
+823
+01:42:17,080 --> 01:42:17,080
+تربية تربية تربية تربية تربية تربية تربية تربية
+
+824
+01:42:17,080 --> 01:42:17,080
+تربية تربية تربية تربية تربية تربية تربية تربية
+
+825
+01:42:17,080 --> 01:42:17,080
+تربية تربية ترب
+
+826
+01:42:20,220 --> 01:42:26,780
+ده مية و تسعة و ستين اللي هو جداش تلاتاش إذا نيد
+
+827
+01:42:26,780 --> 01:42:31,320
+دال هادي أو ال vector عند أي لحظة الطول دائما و
+
+828
+01:42:31,320 --> 01:42:40,300
+أبدا ثابت و يسوى جداش تلاتاش Sir دي vector أو ده
+
+829
+01:42:40,300 --> 01:42:54,000
+given given vector is of Palestineلأن لو
+
+830
+01:42:54,000 --> 01:42:58,520
+ضربت ال vector فيه و إشتغته هذا سيكون جدال Zero
+
+831
+01:42:58,520 --> 01:43:03,660
+أنا حسبت عملي يبقى ال R of T موجودة هنا ضايل عليها
+
+832
+01:43:03,660 --> 01:43:12,320
+بس mean DR على DT يبقى DR على DT يسوى سالم خمسة
+
+833
+01:43:15,760 --> 01:43:24,860
+زائد خمسة كوساين T في اتجاه الـ J زائد Zero ايه
+
+834
+01:43:24,860 --> 01:43:34,440
+بدا اخد R over T Dot DR على DT هنا
+
+835
+01:43:34,440 --> 01:43:41,400
+هذي في هذي كده شبلات ناقص خمسة وعشرين Sin كوساين
+
+836
+01:43:41,400 --> 01:43:49,700
+يبقى ناقص خمسة وعشرينصين تي كوسين تي اللي بعدها
+
+837
+01:43:49,700 --> 01:43:57,800
+زائد خمسة وعشرين صين تي كوسين تي زائد خمسة وعشرين
+
+838
+01:43:57,800 --> 01:44:05,140
+صين تي كوسين تي زائد زيرو وهي سواء كده؟ يبقى اتنين
+
+839
+01:44:05,140 --> 01:44:17,710
+ضمنها أورثغنات ال R of T and ال Dعلى دي تي ار او
+
+840
+01:44:17,710 --> 01:44:25,110
+تر مولانا خديني الآن أرقام المثال تبعد تلتاشر واحد
+
+841
+01:44:25,110 --> 01:44:26,810
+في ال exercises
+
+842
+01:44:40,260 --> 01:44:51,140
+وخمستاشر وسبعتاشر وزسعتاشر واثنين وعشرة لهنا
+
+843
+01:44:51,140 --> 01:44:53,980
+انتهى ال section يعطيكوا العافية
+
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/ismnVpIzntA_postprocess.srt b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/ismnVpIzntA_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..4038eeb1d05b8e7c7e1f34c02597e3888736dc02
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/ismnVpIzntA_postprocess.srt
@@ -0,0 +1,3532 @@
+1
+00:00:00,000 --> 00:00:02,680
+موسيقى
+
+2
+00:00:13,400 --> 00:00:17,700
+بسم الله الرحمن الرحيم نرجع الان نكمل ال section
+
+3
+00:00:17,700 --> 00:00:21,120
+تبع المرة الماضية أخدنا مجموعة من الأمثلة وضع لنا
+
+4
+00:00:21,120 --> 00:00:24,640
+مثال أخير يقول مثال اللي قدامنا على اللي هو حدث
+
+5
+00:00:24,640 --> 00:00:29,420
+المثال بيقول ما يأتي by the volume of the solid in
+
+6
+00:00:29,420 --> 00:00:33,660
+the first octant bounded bythe coordinate planes
+
+7
+00:00:33,660 --> 00:00:37,720
+the cylinder x تربية زائد y تربية يساوي أربعة and
+
+8
+00:00:37,720 --> 00:00:42,760
+the plane z زائد y يساوي تلاتة إذن احنا في عندنا
+
+9
+00:00:42,760 --> 00:00:48,880
+مجسم هذا المجسم ده محدود
+
+10
+00:00:48,880 --> 00:00:54,340
+من أعلى و كذلك محدود من أسفل كيف؟ قاللي هذا المجسم
+
+11
+00:00:54,340 --> 00:01:01,290
+موجود في الثمني الأولو محاط بمستويات الاحداثيات
+
+12
+00:01:01,290 --> 00:01:06,130
+bounded by the coordinate planes يبقى هاي مستويات
+
+13
+00:01:06,130 --> 00:01:11,790
+الاحداثيات اللي عندنا والسيلندر والاسطوانة X تربيه
+
+14
+00:01:11,790 --> 00:01:16,930
+زاد Y تربيه تسوى أربعة and the plane Y زائد Z بده
+
+15
+00:01:16,930 --> 00:01:22,330
+يسوى كده تلاتة طيب احنا بيمكن اروح نرسم هذه
+
+16
+00:01:22,330 --> 00:01:25,930
+المنطقة ولو انه ليس بالضرورة لأن المرة اللي فاتت
+
+17
+00:01:25,930 --> 00:01:31,130
+أخدنا ال volumeتكاملين عالمين على ال z لل function
+
+18
+00:01:31,130 --> 00:01:36,430
+دي اكس دي واي او دي واي دي اكس بجيب الحجب لكن اذا
+
+19
+00:01:36,430 --> 00:01:40,010
+حاببنا نستزيد و نعرف ما هو الشكل بنقول الشكل
+
+20
+00:01:40,010 --> 00:01:45,550
+كالتالي خلّي بالكم معناه الان لو جيت كنت هذا محور
+
+21
+00:01:45,550 --> 00:01:54,790
+X وهذا محور Y وهذا محور Z الشكل يعني هذا Y كبرناه
+
+22
+00:01:54,790 --> 00:02:04,440
+شويةهذا محور Y وهذا محور Z يقل المجسم محاض
+
+23
+00:02:04,440 --> 00:02:09,780
+بمستويات الإحداثية يبقى المستوى XY منشجع المستوى
+
+24
+00:02:09,780 --> 00:02:14,280
+YZ منشجع المستوى XY منشجع ليش انه يقل في الثمن
+
+25
+00:02:14,280 --> 00:02:19,820
+الأول يبقى في الثمن اللي جهتنا هذاقال لي هو في
+
+26
+00:02:19,820 --> 00:02:23,580
+عندي أسطوانة يبقى الأسطوانة يا بنات لو روحنا و
+
+27
+00:02:23,580 --> 00:02:28,240
+قولنا هذه هي مين هذه هي الأسطوانة اللي عندنا هذا
+
+28
+00:02:28,240 --> 00:02:32,440
+جزء منها اللي في الثمن اللي جهتنا بقيتها بتكون
+
+29
+00:02:32,440 --> 00:02:36,100
+وين؟ في الشجرة التانية ماعناش علاقة فيها احنا إنا
+
+30
+00:02:36,100 --> 00:02:40,720
+علاقة وين؟ في اللي جهتنا كويس يبقى بدأ فيجي جزء من
+
+31
+00:02:40,720 --> 00:02:45,280
+الأسطوانة يجي لي هنا كمان بالشكل اللي عندها دايما
+
+32
+00:02:46,230 --> 00:02:51,350
+واضح كويس لأن الأسطوان لسه لها جزء باقي ها جوز زي
+
+33
+00:02:51,350 --> 00:02:55,630
+هيك ترسمش استني شوية بس بدي أريك إياها و بعد هيك
+
+34
+00:02:55,630 --> 00:02:59,850
+همسحها لإنه بدنا نجيب المستوى يبقى فاق الأسطوان
+
+35
+00:02:59,850 --> 00:03:04,290
+هتيجيك زي هيك بالشكل اللي عندنا هذايبقى بده يجيكي
+
+36
+00:03:04,290 --> 00:03:08,410
+هذا الجزء بالشكل هذا يبقى هذا الجزء من الوصوان
+
+37
+00:03:08,410 --> 00:03:13,070
+اللي وين لجهتنا لكن في عندنا شغلة تانية ايش الشغلة
+
+38
+00:03:13,070 --> 00:03:18,350
+التانية اللي محطة من اعلى بالمستوى y زائد z يسوى
+
+39
+00:03:18,350 --> 00:03:22,330
+كدهش يسوى تلاتة اللي فوق هذا مستوى افق اللي احنا
+
+40
+00:03:22,330 --> 00:03:29,430
+رسمينه هذا مستوى موازي لهذابنروح نرسم هذا المستوى
+
+41
+00:03:29,430 --> 00:03:34,190
+لما قالي المستوى y زائد z يساوي تلاتة بجي بقوله لو
+
+42
+00:03:34,190 --> 00:03:39,910
+كانت z ب zero يبقى y بتجيني تلاتة إذا في عندي نقطة
+
+43
+00:03:39,910 --> 00:03:43,370
+عن هذه اللي هو الأسطولة نصف قطرة الدفعة تبعها
+
+44
+00:03:43,370 --> 00:03:49,730
+قداشر اتنين يبقى تلاتة بتجيني هنا مصبوط إذا
+
+45
+00:03:49,730 --> 00:03:57,470
+المستوى هيمر بنقطة zero وتلاتة وزيدز بزيرو و X في
+
+46
+00:03:57,470 --> 00:04:01,590
+الاصل مش موجودة يعني بزيرو بضل انمين و Y تساوي
+
+47
+00:04:01,590 --> 00:04:06,890
+تلاتة طيب بدي اجيب التقطع مع محور Z من فوق يبقى
+
+48
+00:04:06,890 --> 00:04:13,310
+بحط Y عندي بقداش بزيرو تصير Z بقداش تلاتة يبقى بده
+
+49
+00:04:13,310 --> 00:04:18,950
+يجينا عنها هاتف لو جيتك و افترض جدلا ان هذه النقطة
+
+50
+00:04:18,950 --> 00:04:25,950
+هي زيرو و زيرو و تلاتةيبقى بيننا نرسم هذا المستوى
+
+51
+00:04:25,950 --> 00:04:33,390
+بلون أخر يبقى
+
+52
+00:04:33,390 --> 00:04:36,710
+بيجي بقول أنا عندي مستوى بالشكل اللي عندي هذا
+
+53
+00:04:42,450 --> 00:04:49,370
+و يجينا من هنا على اللي هو هذا بالضبط و ايه بجيته
+
+54
+00:04:49,370 --> 00:04:54,470
+هك بهذا الشكل و بدي جيك المستوى بالشكل اللي عندها
+
+55
+00:04:54,470 --> 00:05:02,010
+لأن الأزرق هو المستوى من y زائد z سوى قداش تلاتة
+
+56
+00:05:02,010 --> 00:05:08,210
+إذا هذا الأزرق هو اللي يخلين z زائد y سوى قداش
+
+57
+00:05:08,210 --> 00:05:14,280
+تلاتةإذا يا بنات هذا المستوى هيقص الأسطوان الجزء
+
+58
+00:05:14,280 --> 00:05:19,140
+هذا اللي فوق مش هيظهر ايوة يبقى هتظهر وين نقطة
+
+59
+00:05:19,140 --> 00:05:24,500
+عندنا زي مين زي النقطة اللي عندنا هذه تمام ويصير
+
+60
+00:05:24,500 --> 00:05:31,580
+عندي قوس قوس موخود بهذا الشكل يبقى الخط الأسود هذا
+
+61
+00:05:31,580 --> 00:05:37,280
+هما هذا كله هينقص ويروح بصير مالوش وجودة
+
+62
+00:05:39,720 --> 00:05:47,040
+يبقى بصير ان هذا المستوى المائل من فوق هذا هو
+
+63
+00:05:47,040 --> 00:05:51,420
+المستوى الأزرق اللى موجود عندنا فوق اللى هو مين هو
+
+64
+00:05:51,420 --> 00:05:57,180
+y زائد z يساوي تلاتة ليش انه جزء من المستوى الأزرق
+
+65
+00:05:57,180 --> 00:06:01,160
+اللى احنا شايفه انه يبقى هذا اللى فوق هو كمان z
+
+66
+00:06:01,160 --> 00:06:05,580
+زائد y يساوي تلاتة نفس المستوى اللى احنا بنحكي
+
+67
+00:06:05,580 --> 00:06:13,210
+عليه طيبيبقى لان بدنا نروح نجيب قداش مقدار الحجم
+
+68
+00:06:13,210 --> 00:06:16,790
+اللي عندنا هذا ماخديني بقى كويس يبقى اللي تحت هذه
+
+69
+00:06:16,790 --> 00:06:23,550
+عبارة عن دائرة او جزء من دائرة ربعي الدائرة وهي
+
+70
+00:06:23,550 --> 00:06:27,870
+على الطبيعة لو حبيت اوريهالك بقولك هذا اللي هو
+
+71
+00:06:27,870 --> 00:06:32,710
+محور X وهذا محور Y حسب ما هو موجود على الطبيعة على
+
+72
+00:06:32,710 --> 00:06:36,510
+الرسمة وهي الدائرة اللي عندنا بالشكل اللي عندنا
+
+73
+00:06:36,510 --> 00:06:41,870
+هذايبقى هذه المنطقة المظللة هي المنطقة المظللة
+
+74
+00:06:41,870 --> 00:06:47,770
+اللى تحت الأدنى طبعا يجب ان اقوله بدي ال volume V
+
+75
+00:06:47,770 --> 00:06:56,290
+solution بدي ال volume V إذا بدي سوى تكامل على
+
+76
+00:06:56,290 --> 00:07:04,570
+مين؟ على Z دي ايه على المنطقة A مش هكذا المرة اللى
+
+77
+00:07:04,570 --> 00:07:09,070
+فاتت؟الـ Volume المحصور بين مجسم بين سطح فوق
+
+78
+00:07:09,070 --> 00:07:13,190
+ومستوى الـ XY plane هو بالشكل اللي عندنا هذا
+
+79
+00:07:13,190 --> 00:07:17,330
+واطلنا اكوا على ذلك مثالين هذا هو المثال الرقم
+
+80
+00:07:17,330 --> 00:07:21,910
+تلاتة يبقى هذا الكلام بديه يسوي تكاملين بدي اشيل
+
+81
+00:07:21,910 --> 00:07:27,550
+ال Z و احط قيمتها كده كم تزد هنا بنات تلاتة ناقص Y
+
+82
+00:07:27,550 --> 00:07:34,100
+يبقى تلاتة ناقص Y هي قيمة ال Zبدي اتكامل بالنسبة
+
+83
+00:07:34,100 --> 00:07:38,660
+الى X بمشي الحال في الاول او بدي اتكامل بالنسبة
+
+84
+00:07:38,660 --> 00:07:41,800
+الى Y بمشي الحال سواء كان هذه او تلك الاتنين
+
+85
+00:07:41,800 --> 00:07:47,020
+بيهدئي لنفس النتيجة اذا بروح اشوف X بدها تتغير من
+
+86
+00:07:47,020 --> 00:07:53,160
+وين لوين فبجي على المنطقة التكامل و برسم خط يقطع
+
+87
+00:07:53,160 --> 00:08:00,160
+منطقة التكامل وموازن لمحور X كده ايش قيمة X عند
+
+88
+00:08:00,160 --> 00:08:00,760
+هذه النقطة
+
+89
+00:08:04,210 --> 00:08:10,270
+هنا لم يكن هناك قيمة x على محور واحد قيمة x هو 0
+
+90
+00:08:10,270 --> 00:08:14,910
+من هنا مش هي نقطة الأصل يبقى على محور واحد قيمة x
+
+91
+00:08:14,910 --> 00:08:20,170
+بزيرو أنا ارسل خط مودي لمحور x أيه في أصل التوضيع
+
+92
+00:08:20,170 --> 00:08:26,430
+تمام يبقى هنا x تساوي 0 الخط اللي عندي هذا الجثة
+
+93
+00:08:26,430 --> 00:08:32,830
+ده معادلة مين؟مقادرة الأسطوانة أو قاعدة الأسطوانة
+
+94
+00:08:32,830 --> 00:08:37,750
+وهي عبارة عن دائرة إذا بدّر أجيب قداش X تساوي من
+
+95
+00:08:37,750 --> 00:08:43,530
+هنا قداش X تساوي أربعة ناقص Y تربيع تحت الجدر
+
+96
+00:08:43,530 --> 00:08:49,110
+التربيع إذا إن هنا بيكون ال X بتساوي الجدر التربيع
+
+97
+00:08:49,110 --> 00:08:54,710
+لأربعة ناقص Y تربيعاللي هي معادلة مين؟ معادلة
+
+98
+00:08:54,710 --> 00:09:01,510
+الدائرة اللي عندها إذا ال X ستتغير من Zero لغاية
+
+99
+00:09:01,510 --> 00:09:08,430
+كدهش لغاية الجذري التربيعي لأربعة ناقص Y تربيع بلت
+
+100
+00:09:08,430 --> 00:09:13,310
+عندي Y ده تتغير من وين و وين بناها من صفر لغاية
+
+101
+00:09:13,310 --> 00:09:17,450
+اتنين لأن نصف قطر القاعدة اللي هو كدهش باتنين هذا
+
+102
+00:09:17,450 --> 00:09:22,870
+النقطة اللي هي اتنينيبقى من 0 ل 2 إذا كتبنا
+
+103
+00:09:22,870 --> 00:09:27,210
+المعادلة صحيحة صارت مسألتنا بسيطة جدا خلاص شغل
+
+104
+00:09:27,210 --> 00:09:30,950
+روتيني ضال بنكامل ونطلع كمية ال volume اللي عندنا
+
+105
+00:09:30,950 --> 00:09:35,730
+كويس فبعدين بكمل بقول هذا الكلام بدى يساوي
+
+106
+00:09:35,730 --> 00:09:41,100
+integration من 0 ل 2لتلاتة ناقص y مالكش دعوة كله
+
+107
+00:09:41,100 --> 00:09:45,960
+constant و تكامله نسبة ل dx اللي هو ب X و الكلام
+
+108
+00:09:45,960 --> 00:09:52,040
+هذا من zero لجدري التربيع لاربع ناقص y تربيع dy أو
+
+109
+00:09:52,040 --> 00:09:57,880
+ان شئتولنا فقولنا تكامل من صفر للإتنين لتلاتة ناقص
+
+110
+00:09:57,880 --> 00:10:04,240
+y الجدري التربيع لاربع ناقص y تربيع ناقص zero بروح
+
+111
+00:10:04,240 --> 00:10:06,000
+و كل هذا ب 100
+
+112
+00:10:12,140 --> 00:10:17,180
+ما بيكونش إذا بدنا نروح نكامل الدالة اللي عندنا
+
+113
+00:10:17,180 --> 00:10:25,180
+هذه و نشوف كيف بدنا نكاملها تمام؟ قدامك بدل الخيار
+
+114
+00:10:25,180 --> 00:10:31,680
+اتنين لو جيت طلعت فصلت إلى جزين قلت تلاتة في الجذر
+
+115
+00:10:31,680 --> 00:10:35,640
+ناقص واي في الجذر ناقص واي في الجذر بصير اللي برا
+
+116
+00:10:35,640 --> 00:10:40,500
+الجذر هومش تقت ما تحت الجذر بيصير سهل لكن تلاتة في
+
+117
+00:10:40,500 --> 00:10:45,700
+الجذر ماليش إلا Trigonometric Substitution يبقى
+
+118
+00:10:45,700 --> 00:10:49,440
+مدام هيك خليها كلها على بعضها Trigonometric
+
+119
+00:10:49,440 --> 00:10:55,560
+Substitution يعني التعويض بدالة مثلثية أيوة نرجع ل
+
+120
+00:10:55,560 --> 00:11:01,980
+Calculus B Calculus B أخدنا section فيه في التكامل
+
+121
+00:11:01,980 --> 00:11:07,580
+اللي هو التعويض بدالة مثلثيةولا لو كان عندى جذر
+
+122
+00:11:07,580 --> 00:11:12,620
+بقدر اطيّر هذا الجذر بالتعويضة المثلثية بس بده
+
+123
+00:11:12,620 --> 00:11:18,320
+تعويضة مثلثية مناسبة مش اي تعويضة بطل على القيمة
+
+124
+00:11:18,320 --> 00:11:22,240
+اللى تحت الجذر والله إذا الإشارة بالموجة بين
+
+125
+00:11:22,240 --> 00:11:27,580
+القمسات بتعويضة بدلالي الطاقة وإذا كان ناقص بطل عن
+
+126
+00:11:27,580 --> 00:11:32,820
+ناقص هل هو للمتغير والله المقدار الثامنإذا للمقدار
+
+127
+00:11:32,820 --> 00:11:37,400
+الثابت التعويضة بدلالة سيك ثيتا وإذا كان الإشارة
+
+128
+00:11:37,400 --> 00:11:42,460
+السلبية المتغيرة يبقى التعويضة بدلالة ساين الزاوية
+
+129
+00:11:42,460 --> 00:11:48,080
+ثيتا إذا تعوضتنا هنا كم ستكون تلقاه اتنين ساين
+
+130
+00:11:48,080 --> 00:11:48,780
+ثيتا
+
+131
+00:11:55,920 --> 00:12:01,540
+Y تساوي اتنين في صين الزاوية تيتا وطبعا تيتا
+
+132
+00:12:01,540 --> 00:12:07,100
+مخصورة بين سالب باي على اتنين و باي على اتنين يبقى
+
+133
+00:12:07,100 --> 00:12:14,900
+DY تساوي اتنين Cos θ Dθ إذا انقلت المسألة إلى
+
+134
+00:12:14,900 --> 00:12:21,860
+الشكل التالي تساوي تكامل و هنا تلاتة ناقص اتنين
+
+135
+00:12:21,860 --> 00:12:28,060
+صين الزاوية تيتا اتنينصين الزاوية ثيتا في الجذر
+
+136
+00:12:28,060 --> 00:12:35,580
+التربيهي ليه؟ مين؟ أربعة ناقص أربعة في صين تربية
+
+137
+00:12:35,580 --> 00:12:41,360
+الزاوية ثيتا في دي اكس اللي هو باتنين قصين ثيتا في
+
+138
+00:12:41,360 --> 00:12:49,130
+دي ثيتا مين ضايق عندي يا بنات؟ حدود التكاملبعدين
+
+139
+00:12:49,130 --> 00:12:53,670
+بقوله لما نكون ال Y ب 2 يبقى بده أشيل Y و أحط
+
+140
+00:12:53,670 --> 00:12:58,630
+مكانها 2 معناته sine theta كده تساوي واحد مين
+
+141
+00:12:58,630 --> 00:13:02,550
+الزاوية اللي جيبها تساوي واحد باي على اتنين يبقى
+
+142
+00:13:02,550 --> 00:13:08,830
+بده يصير هنا باي على اتنين بعد هيك لو كانت ال Y ب
+
+143
+00:13:08,830 --> 00:13:13,950
+Zero حط Zero بصير sine theta تساوي Zero يبقى ب
+
+144
+00:13:13,950 --> 00:13:20,910
+Zero إذاحدود التكامل المكافئة لـ0 و 2 لما كان
+
+145
+00:13:20,910 --> 00:13:27,210
+المتغير Y هي 0 و باية 2 لما صار المتغير بدلالة θ
+
+146
+00:13:27,210 --> 00:13:32,250
+يبقى صار عندنا التكامل هذا طيب نجرّط بمثلتنا هك و
+
+147
+00:13:32,250 --> 00:13:38,450
+نشوف قداش ماتطلع هذه قداش بتطلع يا بناتأربعة واحد
+
+148
+00:13:38,450 --> 00:13:41,670
+نقص sin تربيع اللي هو cos تربيع تطلع من تحت الجانب
+
+149
+00:13:41,670 --> 00:13:46,810
+باتنين cosine وعندي اتنين cosine يبقى أربعة خليها
+
+150
+00:13:46,810 --> 00:13:51,310
+برا وضل عندي cosine تربيع يبقى الأربعة بتطلع برا
+
+151
+00:13:51,310 --> 00:13:56,450
+هنا ههه و باجي بقول تكامل من zero to pi على اتنين
+
+152
+00:13:56,450 --> 00:14:02,830
+لتلاتة نقص اتنين sin زاوية ثيتا في cosine تربيع
+
+153
+00:14:02,830 --> 00:14:10,740
+ثيتا في d ثيتاطب بدأ افك هذه يبقى هذه بدها تساوي
+
+154
+00:14:10,740 --> 00:14:23,360
+اللي همين 3×4 ب12 تكامل من 0 لغاية Pi على 4 لcos²θ
+
+155
+00:14:23,360 --> 00:14:31,850
+dθ ناقصهندك أربعة في اتنين بتمانية وهيتكاول من صفر
+
+156
+00:14:31,850 --> 00:14:38,070
+لغاية باي على اتنين لمين؟ لـ sin θ cos تربيع θ sin
+
+157
+00:14:38,070 --> 00:14:42,190
+θ cos تربيع θ في dθ
+
+158
+00:14:44,700 --> 00:14:49,400
+فكت الأقواص ووزعت التكامل لكل واحدة منهم طبعا
+
+159
+00:14:49,400 --> 00:14:53,960
+الأولين ماقدرش أكملها إلا أحولها بدلالة ضعف
+
+160
+00:14:53,960 --> 00:14:59,280
+الزاوية Cos تربيع نص في واحد زائد Cos اتنين فيها
+
+161
+00:14:59,280 --> 00:15:04,320
+يبقى هذه يا بنات بدأت تصير اتناشر مضروبة في نص في
+
+162
+00:15:04,320 --> 00:15:08,180
+تكامل من Zero لغاية Pi باي على اتنين
+
+163
+00:15:13,480 --> 00:15:18,580
+يبقى من zero ل πاى على اتنين لواحد زائد كوصين
+
+164
+00:15:18,580 --> 00:15:22,900
+اتنين في ده كله في دي دي ده
+
+165
+00:15:30,180 --> 00:15:38,440
+8 تكامل من 0 لπ على 2 ل cos تربية فيتا شو رايك sin
+
+166
+00:15:38,440 --> 00:15:45,680
+فيتا بفيتا أليست هي مشتقة cos فيتا صح ولا لا يبقى
+
+167
+00:15:45,680 --> 00:15:53,220
+بقدر اتبع هذه هي D لفو sin فيتا بس مشتقة ال cosine
+
+168
+00:15:53,220 --> 00:15:59,760
+ابسالب sin يبقى هذه لو خلتها موجة بقي ماسويتش شيء
+
+169
+00:16:00,510 --> 00:16:06,790
+يبقى أبدًا شيلت sin θ cos θ و كتبها دالها d cos θ
+
+170
+00:16:06,790 --> 00:16:11,330
+تمام يبقى صارت المثلة بالشكل اللي قدامنا هذا طيب
+
+171
+00:16:11,330 --> 00:16:16,890
+اتناشر في نص القداش بستة وهذه عبارة عن ثيتا زائد
+
+172
+00:16:16,890 --> 00:16:21,910
+sin اتنين ثيتا على اتنين الكلام من zero لغاية pi
+
+173
+00:16:21,910 --> 00:16:28,900
+على اتنينوهذه زائد تمانية على تلاتة كوصين تكييب
+
+174
+00:16:28,900 --> 00:16:35,340
+ثيتا من zero لغاية كده؟ باي على اتنين هذا الكلام
+
+175
+00:16:35,340 --> 00:16:42,540
+يسوى ستة في باي على اتنين زائد بدا اشيل ثيتا و احط
+
+176
+00:16:42,540 --> 00:16:45,260
+باي على اتنين و اتروح اتنين مع اتنين و يبقى sign
+
+177
+00:16:45,260 --> 00:16:46,360
+باي كده؟
+
+178
+00:16:54,070 --> 00:17:12,250
+زائد تمانية على تلاتة في نقص
+
+179
+00:17:12,250 --> 00:17:15,110
+نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص
+
+180
+00:17:15,110 --> 00:17:18,730
+نقص نقص نقص نقص نقص نقص نقص نقص نقصناقص تمانية على
+
+181
+00:17:18,730 --> 00:17:24,690
+تلاتة يعني قداش كله على تلاتة تسعة بايت ناقص
+
+182
+00:17:24,690 --> 00:17:30,490
+تمانية كله على تلاتة مقدار الحجم المطلوب
+
+183
+00:17:57,700 --> 00:17:58,600
+امسحها بنات
+
+184
+00:18:21,480 --> 00:18:24,720
+طب الحكي اللى اتحاكناه من اول ما بدأنا هذا ال
+
+185
+00:18:24,720 --> 00:18:28,460
+chapter و الى يومنا هذا حتى هذه اللحظة كان على ال
+
+186
+00:18:28,460 --> 00:18:32,220
+double integral in cartesian coordinates كان
+
+187
+00:18:32,220 --> 00:18:37,060
+المتغيرات x y لكن احنا روحنا في كل كلاص بيدرسنا
+
+188
+00:18:37,060 --> 00:18:41,380
+احداثيات جديدة سميناها ال polar coordinates فماهي
+
+189
+00:18:41,380 --> 00:18:44,780
+اخبار ال double integral in polar coordinates هذا
+
+190
+00:18:44,780 --> 00:18:47,760
+موضوع ال section 15-4
+
+191
+00:19:15,060 --> 00:19:20,940
+يبقى التكاملات الثنائية في الإحداثيات القطبية
+
+192
+00:19:23,230 --> 00:19:26,650
+نعطي تعريف وبناء على هذا التعريف نبدأ نشتغل
+
+193
+00:19:26,650 --> 00:19:35,030
+Definition بيقول ما يأتي definition f ال function
+
+194
+00:19:35,030 --> 00:19:40,090
+f كانت دالة في r و theta بدل ما كنا نقول x و y
+
+195
+00:19:40,090 --> 00:19:50,660
+هنقول r و theta is defined function دالة معرفةover
+
+196
+00:19:50,660 --> 00:20:02,920
+a region a over a region a bounded bounded by the
+
+197
+00:20:02,920 --> 00:20:13,040
+rays by the rays بالشعيني theta تساوي alpha و
+
+198
+00:20:13,040 --> 00:20:24,150
+theta تساوي beta and by the continuousand by the
+
+199
+00:20:24,150 --> 00:20:36,470
+continuous curves بالمنحنيات المتصلة R تساوي G1 of
+
+200
+00:20:36,470 --> 00:20:48,450
+theta وR تساوي G2 of theta G2 of theta with
+
+201
+00:20:50,370 --> 00:20:55,390
+الـ zero أقل من أو يساوي g1 of theta أقل من أو
+
+202
+00:20:55,390 --> 00:21:04,010
+يساوي g2 of theta نحن ندفع الانتجار نحن ندفع
+
+203
+00:21:04,010 --> 00:21:07,650
+الانتجار
+
+204
+00:21:07,650 --> 00:21:13,330
+of
+
+205
+00:21:13,330 --> 00:21:22,400
+ال function f of r و theta overالـ Region R by
+
+206
+00:21:22,400 --> 00:21:32,760
+تكاملين على الـ R لمين؟ للـ F of R وثيتا D A يسوى
+
+207
+00:21:32,760 --> 00:21:44,720
+تكاملين للـ F of R وثيتا في الـ R D R D ثيتاوهنا r
+
+208
+00:21:44,720 --> 00:21:51,840
+تساوي g1 of theta وهنا r تساوي g2 of theta وهنا
+
+209
+00:21:51,840 --> 00:21:59,940
+theta تساوي alpha وهنا theta تساوي beta command
+
+210
+00:21:59,940 --> 00:22:08,020
+definition تاني the area the
+
+211
+00:22:08,020 --> 00:22:15,210
+area of a closed bounded region of aبقرة مغلقة
+
+212
+00:22:15,210 --> 00:22:20,090
+بقرة
+
+213
+00:22:20,090 --> 00:22:37,210
+مغلقة بقرة مغلقة بقرة مغلقة بقرة مغلقة بقرة مغلقة
+
+214
+00:22:42,790 --> 00:22:55,290
+احداثيات القطبية الـ
+
+215
+00:22:55,290 --> 00:23:03,990
+A تساوي تكاملين على R لـ D A والرمز يساوي تكاملين
+
+216
+00:23:03,990 --> 00:23:07,730
+على R لـ R DR D
+
+217
+00:23:16,120 --> 00:23:21,420
+أيه اللي بتحكي؟ ولا
+
+218
+00:23:21,420 --> 00:23:27,520
+يهمك بسيطة
+
+219
+00:23:27,520 --> 00:23:32,160
+ايه
+
+220
+00:23:32,160 --> 00:23:41,820
+هو جمال public exercises عشر اتنين مثال من تسعة
+
+221
+00:23:41,820 --> 00:23:52,930
+لغاية أربعة تمثيلmultiple of three مباعظة تلاتة
+
+222
+00:23:52,930 --> 00:24:00,790
+ومن سبعة وخمسين لغاية خمسة وستين في العالم
+
+223
+00:24:15,470 --> 00:24:20,090
+نرجع الكلام اللي احنا كاتبينه و نحاول نفهم كل نقطة
+
+224
+00:24:20,090 --> 00:24:25,110
+احنا كاتبينها وسنحاول نرسم حتى نوضح الكلام اللي
+
+225
+00:24:25,110 --> 00:24:29,970
+بين ايدنا هذا لذلك لو روحت اخدت محاور يبقى من هذا
+
+226
+00:24:29,970 --> 00:24:34,230
+الشكل و روحت قلت هذا θ تساوي zero
+
+227
+00:24:38,330 --> 00:24:42,290
+اللي هو الاحداثيات القطبية او المحاور في الاحداث
+
+228
+00:24:42,290 --> 00:24:46,150
+القطبية المكتوب تقول x و y بقول θ تساوي zero و θ
+
+229
+00:24:46,150 --> 00:24:52,410
+تساوي باي على اتنى جيت رسمت اللي هو المنحليين
+
+230
+00:25:04,030 --> 00:25:12,550
+يبقى اتنين دوال موجبة يبقى وتنتين واحدة منهم اكبر
+
+231
+00:25:12,550 --> 00:25:17,530
+من التانية فمثلا لو روحت قلت على سبيل المثال هذا
+
+232
+00:25:17,530 --> 00:25:24,560
+المنحنى R تساوي G one of thetaو جينا يقولنا فيها
+
+233
+00:25:24,560 --> 00:25:34,020
+المنحنة تاني كان بالشكل هذا R تساوي G E2 of θ قال
+
+234
+00:25:34,020 --> 00:25:41,060
+لي θ هذه اتغيرت من θ تساوي Alpha قلت هذا الخط θ
+
+235
+00:25:41,060 --> 00:25:48,500
+تساوي Alpha إلى الخط التاني θ تساوي Beta اذا ما
+
+236
+00:25:48,500 --> 00:25:52,280
+بدت بقول
+
+237
+00:25:52,280 --> 00:25:57,350
+مرة تانيةمن خلال الـ definition هذا بدنا نحدد
+
+238
+00:25:57,350 --> 00:26:03,010
+منطقة التكامل اللي عندنا طبعا هي يصير θ تتغير من θ
+
+239
+00:26:03,010 --> 00:26:07,630
+تسوى Alpha إلى θ تسوى Beta يعني عند الخط θ تسوى
+
+240
+00:26:07,630 --> 00:26:12,570
+Alpha إلى الخط θ تسوى Beta لكن R اتغيرت من G1 of θ
+
+241
+00:26:12,570 --> 00:26:18,580
+لمين ل G2 of θ فصالي مينبالشكل اللي عندنا هذا بقيت
+
+242
+00:26:18,580 --> 00:26:23,780
+المشكلة اولا عن R من اين جاء بعد ما اعطينا جزء
+
+243
+00:26:23,780 --> 00:26:26,500
+النظر التابع اللي هو ال polar coordinates او ال
+
+244
+00:26:26,500 --> 00:26:29,800
+double integral ال polar coordinates نبدأ في اخذ
+
+245
+00:26:29,800 --> 00:26:34,200
+بعض اللامثلة قال لي اوصفلي المنطقة المرسومة يعني
+
+246
+00:26:34,200 --> 00:26:38,600
+هو اعطاني هذه الرسمة كويس الرسمة موجودة في الكتابة
+
+247
+00:26:38,600 --> 00:26:43,690
+السؤال في الكتابةهو قال لي عبر عن هذه الرسمة وهي
+
+248
+00:26:43,690 --> 00:26:49,070
+ضللتك إياها بمين بالإحداثيات القطبية، أعطاني هذا
+
+249
+00:26:49,070 --> 00:26:53,230
+واحد و أعطاني هنا جدر ثلاثة، بهذا الطول جدر ثلاثة،
+
+250
+00:26:53,230 --> 00:26:58,510
+بحسب فيثة غورفالضلة التانية كم؟ اتنين يبقى احنا
+
+251
+00:26:58,510 --> 00:27:03,830
+امام مثلة تلاتين ستين واحد وجذر تلاتة واثنين من
+
+252
+00:27:03,830 --> 00:27:06,950
+خواص المثلة التلاتين الستين الدولة المقابلة زوج
+
+253
+00:27:06,950 --> 00:27:12,990
+تلاتين يساوي نص الوتر يبقى هيوم يساوي كم نص الوتر
+
+254
+00:27:12,990 --> 00:27:17,600
+يبقى هذا زوج تلاتين درجة وهذا زوج الإيمان60 درجة
+
+255
+00:27:17,600 --> 00:27:22,000
+باي على تلاتة وديك باي على ستة إذا بدنا نعبر عن
+
+256
+00:27:22,000 --> 00:27:26,160
+هذه هه بمين بالإحداثية القطبية بقوله المنطقة
+
+257
+00:27:26,160 --> 00:27:31,020
+المضللة محصورة بين theta تساوي zero و theta تساوي
+
+258
+00:27:31,020 --> 00:27:36,080
+قداش باي على تلاتة ضايل عندنا R بدنا نعرف من وين
+
+259
+00:27:36,080 --> 00:27:40,660
+لوين يفجأر يا بنات بده يبدأ من النقطة الأصل اللي
+
+260
+00:27:40,660 --> 00:27:45,100
+عنده ويظل رايح لغاية ما يجيب الميمما يقابل الخط
+
+261
+00:27:45,100 --> 00:27:49,960
+اللى عندنا هذا اللى هو الرأسي طب هذا معطى كارتيزيا
+
+262
+00:27:49,960 --> 00:27:55,040
+انا بديه polar بقول هذا الخط اللى هو مين
+
+263
+00:27:58,100 --> 00:28:04,400
+X هي R كوصين الزاوية تساوي واحد الكوصين قداش واحد
+
+264
+00:28:04,400 --> 00:28:11,040
+على second مظبوط اضرب كله في second تصير ال R
+
+265
+00:28:11,040 --> 00:28:17,580
+تساوي سك الثيتا في واحد لو سك الثيتا يبقى R ستتغير
+
+266
+00:28:17,580 --> 00:28:23,240
+من zero لغاية اي نقطة على هذا الخط الخط هذا معادلة
+
+267
+00:28:23,240 --> 00:28:31,400
+تسيك ثيتا يبقى وال Rأكبر من أو تساوي zero أقل من
+
+268
+00:28:31,400 --> 00:28:40,100
+أو يساوي 106 ثيتر نمر بيه من السؤال نمر بيه من
+
+269
+00:28:40,100 --> 00:28:45,040
+السؤال ماعطيني رسمة و الرسمة بالشكل هذا طلعوني
+
+270
+00:28:45,040 --> 00:28:51,120
+كويس هذا محور X وهذا محور Y وهذا نقطة الأصل اللي
+
+271
+00:28:51,120 --> 00:28:58,420
+هو Zero وماعطيني بوسك وقال هنا 1 هناو بعد هيك راح
+
+272
+00:28:58,420 --> 00:29:12,580
+اعملي مصطاطيل هيك او قلي المصطاطيل بهذا الشكل هذا
+
+273
+00:29:12,580 --> 00:29:23,180
+هنا قلي اتنين جالر تلت او هنا قلي اتنين
+
+274
+00:29:23,180 --> 00:29:26,420
+شكل عامل
+
+275
+00:29:29,710 --> 00:29:33,350
+هذه المعلومات اللي أعطاني هيك بقى فقط لغة، هي كل
+
+276
+00:29:33,350 --> 00:29:38,910
+المعلومات، وقال يعبر عن هذا بمين؟ بيه الاحداثية
+
+277
+00:29:38,910 --> 00:29:44,190
+القطبية، بقوله والله أستأنى هذا شكله غير شكل هذا،
+
+278
+00:29:44,190 --> 00:29:49,400
+مش طبيعي، مش زي اللي فوق، سهل دوريبقول له اه هذا
+
+279
+00:29:49,400 --> 00:29:54,620
+خط له معادلة و هذا خط له معادلة تانية اذا الوضع
+
+280
+00:29:54,620 --> 00:30:00,820
+مختلف تماما اذا هضطر اجباري اروح اجزء المنطقة الى
+
+281
+00:30:00,820 --> 00:30:06,460
+منطقة تانية فباقي بقول بتاخد المنطقة الأولى هذه
+
+282
+00:30:06,460 --> 00:30:13,040
+الشكل اللي عامله هذا كويس و الباقي هو المنطقة
+
+283
+00:30:13,040 --> 00:30:19,460
+الثانية طب المنطقة هذهأريد أن أعرف C تتغير لمنطقة
+
+284
+00:30:19,460 --> 00:30:24,500
+هذا المنطقة السوداء هذه المظلة باللون الأسود بس
+
+285
+00:30:24,500 --> 00:30:28,480
+نخلصها و نذهب لمين للمنطقة الثانية اللي عندنا هنا
+
+286
+00:30:28,480 --> 00:30:33,960
+أريد أن أعرف C تجدش هنا و أريد أن أعرف C تجدش هنا
+
+287
+00:30:33,960 --> 00:30:39,440
+الخط هذا لو دل مستمر على ما هو و بعد ذلك أريد أن
+
+288
+00:30:39,440 --> 00:30:45,500
+أعرف R اللي سيتغير من أين إلى أين من عند النقطة
+
+289
+00:30:45,500 --> 00:30:53,230
+هذهلغاية النقطة اللي عندنا و لما نخلصها بنروح
+
+290
+00:30:53,230 --> 00:30:57,510
+للمنطقة التانية إذا خلّينا مع θ في الأول من ويل
+
+291
+00:30:57,510 --> 00:31:02,590
+لويل ثيتا تساوي زيرو أظن فاش مشكلة يبقى هذه ثيتا
+
+292
+00:31:02,590 --> 00:31:08,330
+تساوي زيرو خط هذا طب بدنا الخط التاني هذا قداش
+
+293
+00:31:08,330 --> 00:31:17,710
+ثيتابسيطة خالص هذه المسافة قداش كلها هنا يبقى
+
+294
+00:31:17,710 --> 00:31:23,450
+هذه كلها من هنا لهنا هذين باثنين إذا بقدر أجيب له
+
+295
+00:31:23,450 --> 00:31:28,870
+الزاوية هذه اللي هي ثيتا ثم اقل يساوي المقابل على
+
+296
+00:31:28,870 --> 00:31:36,050
+المجاور بقدر أروح بقوله هنا ثان ثيتا يساوي المقابل
+
+297
+00:31:36,140 --> 00:31:41,120
+بمقابل اتنين على اتنين جذر تلاتة يسوى واحد على جذر
+
+298
+00:31:41,120 --> 00:31:45,200
+تلاتة يبقى هذا بيعطيك ان تيتا كداش تساوي ابنها
+
+299
+00:31:45,200 --> 00:31:53,440
+كداش؟ باي على ستة صحيح ولا لا؟ يبقى صار الخط هذا
+
+300
+00:31:53,440 --> 00:32:00,630
+تيتا تساوي باي على ستةإذا قصتنا صارت محلولة هذا
+
+301
+00:32:00,630 --> 00:32:06,410
+بالنسبة لمين لا ثيتا نجي ل R هنا R اللي هي معادلة
+
+302
+00:32:06,410 --> 00:32:10,610
+الدائرة اللي عندها لل R بواحد نضال عندنا هنا مين؟
+
+303
+00:32:10,610 --> 00:32:15,690
+R تبعت الخط الرأسي اللي عندنا هناإذا بدي أروح أجيب
+
+304
+00:32:15,690 --> 00:32:21,810
+له هذا قداش يساوي باجي بقوله هنا عندنا بنت ميم ال
+
+305
+00:32:21,810 --> 00:32:27,690
+X يساوي 2 جذر 3 يعني معادلة الخط الرأس الأزرق هذا
+
+306
+00:32:27,690 --> 00:32:38,860
+X يساوي 2 جذر 3 طيب ال X بقداشR Cos Zeta يساوي 2
+
+307
+00:32:38,860 --> 00:32:46,900
+جذر 3 Cos 1 على سك وضرب كله في سك بصير الـ R يساوي
+
+308
+00:32:46,900 --> 00:32:55,380
+2 جذر 3 سك ثيتا إذا الجزء الأول هذا المظلل بدأ
+
+309
+00:32:55,380 --> 00:33:02,000
+تبقى معادلته أو معادلتيه كتالةثيتا يا بنات بدت
+
+310
+00:33:02,000 --> 00:33:08,440
+تتغير من عند ال zero لغاية pi على ستة وال R بدها
+
+311
+00:33:08,440 --> 00:33:16,760
+تتغير من وين من عند ال واحد لغاية اتنين جذر تلاتة
+
+312
+00:33:16,760 --> 00:33:23,560
+في سك الزاوية خلصنا المنطقة المضللة السوداء بدنا
+
+313
+00:33:23,560 --> 00:33:30,510
+نجي للمنطقة المضللة الزرقاء هذهوهي غيرت كل كوتة
+
+314
+00:33:30,510 --> 00:33:36,230
+ضيقة عشان نعرف انها منطقتين اظن واضح ان θ تتغير من
+
+315
+00:33:36,230 --> 00:33:42,900
+وين لوين نخليله الرسممن باية ستة لغاية باية اثنان
+
+316
+00:33:42,900 --> 00:33:48,740
+يبقى جاهزين يبقى ضالة الار يبقى بالداخل الار و
+
+317
+00:33:48,740 --> 00:33:54,420
+ارسم خط من انه يبدأ من نقطة الاصل و يقطع منطقة
+
+318
+00:33:54,420 --> 00:33:58,380
+التكامل يبقى خطوة في النقطة هذه و النقطة هذه
+
+319
+00:33:58,380 --> 00:34:03,400
+النقطة هذه معروفة ار تساوي واحد لكن هذه النقطة مش
+
+320
+00:34:03,400 --> 00:34:09,520
+معروفة هذه النقطةاللي هو ال Y قداشه ساوية بنات؟
+
+321
+00:34:09,520 --> 00:34:12,580
+اتنين خاطر المستخدم اللي هو فوق يعني ال Y يساوي
+
+322
+00:34:12,580 --> 00:34:18,520
+اتنين ال Y بقداش ال R ساينس زاوية تيتا بده يساوي
+
+323
+00:34:18,520 --> 00:34:23,730
+اتنينالـ sine هي مقلوب مين؟ مقلوب الـ cosecant
+
+324
+00:34:23,730 --> 00:34:28,310
+يبقى هذه باعتبار R على cosecant يساوي اتنين يعني R
+
+325
+00:34:28,310 --> 00:34:33,610
+تساوي اتنين cosecant ثيتا، تمام؟ إذا هذه معناها إن
+
+326
+00:34:33,610 --> 00:34:39,970
+R تساوي اتنين cosecant، اللي همين؟ cosecant ثيتا،
+
+327
+00:34:39,970 --> 00:34:45,070
+يبقى صارت النقطة اللي عندنا هذه، اللي هي اتنين
+
+328
+00:34:45,070 --> 00:34:50,520
+cosecant ثيتا، اللي تساوي أرض الخط هذا كلهيبقى
+
+329
+00:34:50,520 --> 00:34:55,980
+بناء عليه المنطقة الزرقية هذه المناطق هقول ان ال
+
+330
+00:34:55,980 --> 00:35:02,920
+theta ستتغير من πي على ستة الى بي على اتنين وال R
+
+331
+00:35:02,920 --> 00:35:13,820
+ستتغير من الواحد الى اتنين كوسيكا ثيتا واضحة؟
+
+332
+00:35:13,820 --> 00:35:21,660
+هي استطعت كتابةاللي هو حدود هذه المنطقة صار مش
+
+333
+00:35:21,660 --> 00:35:24,620
+إمكانية إلا نجزئها إلى جزئين
+
+334
+00:35:28,470 --> 00:35:36,630
+أجزئيني وكتبنا حدود كل جزر من هذين الجزئين هذا نوع
+
+335
+00:35:36,630 --> 00:35:41,290
+من أنواع المسائل طبعا في الكتاب حاطس عندك بيجي خمس
+
+336
+00:35:41,290 --> 00:35:46,610
+رسمات اعتقد او ستة هيتن تان منهم وانت بنفس الطريقة
+
+337
+00:35:46,610 --> 00:35:49,530
+بتقدر تروح تجيب مين الباقي
+
+338
+00:36:03,490 --> 00:36:09,490
+Cartesian integral حول
+
+339
+00:36:09,490 --> 00:36:17,890
+التكامن في الإحداثية الكارتيزية into an equivalent
+
+340
+00:36:17,890 --> 00:36:21,730
+polar
+
+341
+00:36:21,730 --> 00:36:22,410
+integral
+
+342
+00:36:34,040 --> 00:36:47,720
+then evaluate the polar integral نمرأ
+
+343
+00:36:47,720 --> 00:36:56,080
+أيه من المثلة؟ بيقول تكامل من 0 ل 2 تكاملمن Zero
+
+344
+00:36:56,080 --> 00:37:03,260
+للجدري التربيعي للأربع ناقص Y تربيع لمين؟ لل X
+
+345
+00:37:03,260 --> 00:37:16,400
+تربيع زائد Y تربيع DXDY نمسح
+
+346
+00:37:16,400 --> 00:37:22,410
+الشجادي خلاص يا بنات؟ شجادي، طيببقول it changed
+
+347
+00:37:22,410 --> 00:37:26,330
+the cartesian integral حول التكامل في الإحداثات
+
+348
+00:37:26,330 --> 00:37:30,770
+الكارتيزية إلى التكامل المكافئ له في الإحداثيات
+
+349
+00:37:30,770 --> 00:37:36,750
+القطبية ومن ثم احسب ليه التكامل في الإحداثيات
+
+350
+00:37:36,750 --> 00:37:42,110
+القطبية بقوله كويس هي التكامل كارتيزيا بدي احوله
+
+351
+00:37:42,110 --> 00:37:46,710
+إلى قطبى عشان احوله إلى قطبى بروح ارسم منطقة
+
+352
+00:37:46,710 --> 00:37:52,190
+التكامل في الأولومنها بقدر أحول إلى تكمل في
+
+353
+00:37:52,190 --> 00:37:59,150
+الأحداثية القطبية بقول كويسة المحاول وهذا محور X
+
+354
+00:37:59,150 --> 00:38:04,650
+وهذا محور Y اللي هو في القطبية تيتا تساوي زيرو وهي
+
+355
+00:38:04,650 --> 00:38:10,470
+تيتا تساوي كده؟ باي على اتنين بدا يجي الحدود في ال
+
+356
+00:38:10,470 --> 00:38:16,130
+كارتيزيا اللي هو التكمل بالنسبة لما يبقى عند X
+
+357
+00:38:16,130 --> 00:38:23,010
+تساوي زيروأحوال Y يبقى هذا هو ال X يساوي Zero
+
+358
+00:38:23,010 --> 00:38:30,410
+التاني X يساوي الجدر بقوله X يساوي الجدر التربية
+
+359
+00:38:30,410 --> 00:38:36,830
+للأربعة ناقص Y تربية لو ربعت و نجلت ال Y على الشجر
+
+360
+00:38:36,830 --> 00:38:41,390
+تانية بس ال X تربية زاد Y تربية تساوي أربعة معانلة
+
+361
+00:38:41,390 --> 00:38:47,930
+إيش دائرة بس يقولها هل هي كل الدائرةوالله جزء من
+
+362
+00:38:47,930 --> 00:38:53,590
+الدائرة بيحدده main بيحدده ال y ستتغير من where ل
+
+363
+00:38:53,590 --> 00:38:59,150
+where يبقى ال y بس فتتغير من zero ل عند اتنين من
+
+364
+00:38:59,150 --> 00:39:04,570
+عند ال zero لغاية كدهش لغاية اتنين يبقى هذا ال
+
+365
+00:39:04,570 --> 00:39:12,640
+zero و هذا اتنينكل دائرة الإجابة لا هل هو نص
+
+366
+00:39:12,640 --> 00:39:17,920
+الدائرة ولا ربع الدائرة يبقى ربع الدائرة وليس نصف
+
+367
+00:39:17,920 --> 00:39:22,880
+الدائرة يبقى لو جيتي قلت هذا ربع الدائرة اللي
+
+368
+00:39:22,880 --> 00:39:28,640
+عندنا هذا ربع الدائرة اللي عندنا والأصل باقية
+
+369
+00:39:28,640 --> 00:39:33,500
+الدائرة هي لو روحنا نكملها بالشكل اللي عندنا هذا
+
+370
+00:39:33,500 --> 00:39:39,770
+هيك المنقط مش موجوديبقى احنا مقيلين فقط بالميلاد
+
+371
+00:39:39,770 --> 00:39:45,690
+من عند X يساوي Zero لغاية X يساوي 100 اللي هو
+
+372
+00:39:45,690 --> 00:39:49,690
+الدائرة اللي عندنا هذا و ال Y من عند الصفر لغاية
+
+373
+00:39:49,690 --> 00:39:53,210
+اتنين يبقى احنا باس الربع الأول
+
+374
+00:39:56,470 --> 00:40:02,530
+طيب ممتاز جدا يبقى بدنا نيجي نشوف θ بدت تتغير من
+
+375
+00:40:02,530 --> 00:40:07,090
+وين لوين وR بدت تتغير من وين لوين اظن واضحة θ من
+
+376
+00:40:07,090 --> 00:40:13,650
+وين لوين ضلت ال R ال R بدت تبدأ من نقطة الأصل و
+
+377
+00:40:13,650 --> 00:40:16,290
+لغاية محيط الدائر
+
+378
+00:40:28,360 --> 00:40:33,470
+نصف القطر اتنين مش اربعيبقى الدائرة هذه اللي هي
+
+379
+00:40:33,470 --> 00:40:38,610
+معادلتها R تساوي 2 في الإحداثيات القطبى لما رجعنا
+
+380
+00:40:38,610 --> 00:40:42,630
+في الcalculus يقولنا R تساوي رقم و الرقم إذا كان
+
+381
+00:40:42,630 --> 00:40:45,890
+سلب ولا موجب خديله ال absolute value يطلع رقم موجب
+
+382
+00:40:45,890 --> 00:40:50,710
+يبقى هذا يمثل دائما أبدا معادلة مين معادلة دائرة
+
+383
+00:40:50,710 --> 00:40:57,840
+في الإحداثيات القطبىيبقى الار ستتغير من عند الـ
+
+384
+00:40:57,840 --> 00:41:03,600
+zero لغاية الاتنين هو ده هيتغير من عن اللي هو ال
+
+385
+00:41:03,600 --> 00:41:08,640
+zero لغاية باي على اتنين يبقى هذا التكامل بيصير
+
+386
+00:41:08,640 --> 00:41:12,740
+هاي تكاملين X تلبية و Z و Y تلبية و هم في قدر
+
+387
+00:41:28,090 --> 00:41:32,810
+يبقى هذا الكلام لتساوي تكامل من Zero لغاية Pi على
+
+388
+00:41:32,810 --> 00:41:33,050
+اتنين
+
+389
+00:41:46,370 --> 00:41:49,690
+بنعمل بالقيمة اللى فوق بنقص الدخل اللى تحت طبعا
+
+390
+00:41:49,690 --> 00:41:55,250
+بزيرو و بضلي اتنين اقصى اربعة يوم ست عشر على اربعة
+
+391
+00:41:55,250 --> 00:42:02,330
+باربعة يبقى هذا اللي هو بيصير اربعة تكامل من zero
+
+392
+00:42:02,330 --> 00:42:03,530
+ن buy على اتنين
+
+393
+00:42:06,370 --> 00:42:11,890
+يبقى أربعة ثيتا من Zero لغاية Pi على اتنين يبقى
+
+394
+00:42:11,890 --> 00:42:18,730
+أربعة في Pi على اتنين ناقص Zero يبقى اتنين Pi فقط
+
+395
+00:42:18,730 --> 00:42:26,790
+لا غير ناخد
+
+396
+00:42:26,790 --> 00:42:37,480
+كمان نمرة B نمرة B بيقول بيبدو تكاملمن Zero لغاية
+
+397
+00:42:37,480 --> 00:42:49,080
+ستة وتكامل من Zero لغاية Y لل X DX DY بدي
+
+398
+00:42:49,080 --> 00:42:53,020
+أحاول هذا إلى Polar Coordinates علشان أحاوله إلى
+
+399
+00:42:53,020 --> 00:42:57,340
+Polar Coordinates بدي أروح و أرسم منطقة التكامل
+
+400
+00:42:57,340 --> 00:43:03,720
+والله يا شرايكوا يا كده على السكR cos θ و R dr d θ
+
+401
+00:43:03,720 --> 00:43:12,900
+و R sin θ و 006 زي مهمة اللي
+
+402
+00:43:12,900 --> 00:43:16,660
+كلمته هنا صح بس اللي كلمته على قدوت مش صحيح الـ
+
+403
+00:43:16,660 --> 00:43:20,980
+006 هذه الإحداثيات الكفزية مش هم هم المناطق اللي
+
+404
+00:43:20,980 --> 00:43:27,220
+هي الإحداثيات القطبية لذلك إجباري نروح نرسم منطقة
+
+405
+00:43:27,220 --> 00:43:33,190
+التكاملبقول له كويسة دي منطقة التكامل هي المحاول
+
+406
+00:43:33,190 --> 00:43:39,290
+هذا محور X وهذا محور Y أول حاجة بدها تكمل بالنسبة
+
+407
+00:43:39,290 --> 00:43:44,990
+ل X هي X تساوي Zero هو محور Y هذا هو X تساوي Zero
+
+408
+00:43:44,990 --> 00:43:51,410
+اللي بعد هو X يساوي قداشريعني y تساوي x اللي هو
+
+409
+00:43:51,410 --> 00:43:57,090
+الخط المنصف للربع الأول بالشكل هذا و بيبقى على
+
+410
+00:43:57,090 --> 00:44:03,390
+انتداله هذا الخط اللي هو y يساوي مين؟ يساوي x بعد
+
+411
+00:44:03,390 --> 00:44:08,530
+هيك ال y بدأ تتغير من هنا إلى هنامن zero لغاية ستة
+
+412
+00:44:08,530 --> 00:44:12,830
+يبقى لو روحت قولت هذه ال zero وهذه النقطة اللي هي
+
+413
+00:44:12,830 --> 00:44:18,970
+ستة يبقى بتصير عند الخط اللي هو y تساوي ستة إذا
+
+414
+00:44:18,970 --> 00:44:23,570
+المنطقة اللي بينهم هي المنطقة المظللة اللي عندها
+
+415
+00:44:23,570 --> 00:44:32,820
+طيب لما أقولك الخط y تساوي x تحوله لقط بيه؟و Y
+
+416
+00:44:32,820 --> 00:44:38,500
+تساوي X كده شو بيعمل في الزاوية 45 إذا الخط Y
+
+417
+00:44:38,500 --> 00:44:45,640
+تساوي X في القطب بدي قابله θ تساوي Y على 4 مباشرة
+
+418
+00:44:47,040 --> 00:44:51,860
+طيب قول رأسي ما هو معروف باي على اتنين يبقى هذا
+
+419
+00:44:51,860 --> 00:44:58,080
+ثيتا تساوي باي على اتنين اذا ثيتا محددة بقيت مين
+
+420
+00:44:58,080 --> 00:45:04,540
+بقيت ا ر بدا تبدأ من هنا ال zero ههه ونبقى المشيل
+
+421
+00:45:04,540 --> 00:45:09,060
+لغاية ما نقابل الخط اللي عندنا هناالخطة ده شو
+
+422
+00:45:09,060 --> 00:45:16,400
+معادلته Y تساوي ستة إذا لما أجي أقول يا بنات هنا Y
+
+423
+00:45:16,400 --> 00:45:23,380
+تساوي ستة ال Y اللي هي قداش R Sin Theta يبقى R Sin
+
+424
+00:45:23,380 --> 00:45:32,420
+Theta تساوي ستة يعني R تساوي ستة Cos Thetaيبقى أي
+
+425
+00:45:32,420 --> 00:45:37,740
+نقطة على الخط الأفقي هذا المعادلة القطبية له R
+
+426
+00:45:37,740 --> 00:45:44,160
+تسوية ستة كثيرة ثيتا إذا بناء عليه بيصبح التكاملين
+
+427
+00:45:44,160 --> 00:45:51,980
+اللي عندنا هذول كالتالي هاي تكامل وهي التاني ودالة
+
+428
+00:45:51,980 --> 00:46:01,550
+اللي عندنا X اللي هي 100R cos θ وDx Dy R Dr Dθ نجل
+
+429
+00:46:01,550 --> 00:46:10,410
+ال R ال R ستتغير من Zero لغاية ستة كوسيكا ثتا طب و
+
+430
+00:46:10,410 --> 00:46:17,450
+الثتا ستتغير من باي على أربعة إلى باي على اتنين
+
+431
+00:46:18,350 --> 00:46:21,530
+يبقى هذا العمود الفقري تبع المثل اجيب ناس اللي
+
+432
+00:46:21,530 --> 00:46:26,950
+مائة بالمائة ضلت عملية من عملية التكامل يبقى هذا
+
+433
+00:46:26,950 --> 00:46:32,810
+يا بنات يصير تكامل من πاي على اربعة لغاية باي على
+
+434
+00:46:32,810 --> 00:46:40,680
+اتنين بالشكل اللي انا ار في ارR تربية تكاملها R
+
+435
+00:46:40,680 --> 00:46:48,600
+تكييب على ثلاثة و الحاكم من Zero لغاية ستة كوسيكا
+
+436
+00:46:48,600 --> 00:46:56,480
+تيتا و أي كوسايم تيتا و أي ديتا واضح اظن طيب هذا
+
+437
+00:46:56,480 --> 00:47:03,920
+الكلام بده يساوي هذا يا بناتي ستة تكييبستة فى ستة
+
+438
+00:47:03,920 --> 00:47:08,140
+فى ستة لكن مجسوم على جداش على تلاتة يعني ستة فى
+
+439
+00:47:08,140 --> 00:47:14,440
+ستة فى اتنين ستة فى ستة ستة و تلاتين فى اتنين فى
+
+440
+00:47:14,440 --> 00:47:21,100
+اتنين و سبعين اذا هذه بدها تصير سبعين و اتنين وهي
+
+441
+00:47:21,100 --> 00:47:27,440
+تكامل من باى على اربع لغاية باى على اتنين لمين
+
+442
+00:47:27,440 --> 00:47:37,950
+لكسيكا تكيب ثيتاكوصين فيتا دي فيتا هذا
+
+443
+00:47:37,950 --> 00:47:45,390
+الكلام بالنسبة 72 تكامل من πاية على أربعة لباية
+
+444
+00:47:45,390 --> 00:47:49,170
+على اتنين شو رايكوا كامل الكامل هذه كوسيكا تكامل
+
+445
+00:47:49,170 --> 00:47:53,530
+كوصين تكامل كوسيكا تكامل كوسيكا تكامل كوسيكا تكامل
+
+446
+00:47:53,530 --> 00:47:56,230
+كوسيكا تكامل كوسيكا تكامل كوسيكا تكامل كوسيكا
+
+447
+00:47:56,230 --> 00:47:56,730
+كوسيكا تكامل كوسيكا تكامل كوسيكا تكامل كوسيكا
+
+448
+00:47:56,730 --> 00:47:57,390
+تكامل كوسيكا تكامل كوسيكا تكامل كوسيكا تكامواحد
+
+449
+00:47:57,390 --> 00:48:03,610
+على الـ sine يعني كأن المسألة صارت كوسيكا تربيع
+
+450
+00:48:03,610 --> 00:48:12,290
+ثيتا على مين؟ على الصين الزاوية ثيتا في كوسين
+
+451
+00:48:12,290 --> 00:48:16,790
+الزاوية ثيتا في دي ثيتا كوسيكا تقريبا أخدنا واحدة
+
+452
+00:48:16,790 --> 00:48:19,790
+صارت واحد على الصين صار عندي كوسين على الصين اللي
+
+453
+00:48:19,790 --> 00:48:26,500
+هو مين؟ كتال ممتاز جدايبقى هاي 72 تكامل من باي على
+
+454
+00:48:26,500 --> 00:48:32,260
+أربعة إلى باي على اتنين لكوسيكن تربيه تيتا كتان
+
+455
+00:48:32,260 --> 00:48:40,000
+تيتا دي تيتا هو تفضل كتان بجداش بس بإشارة يبقى هذه
+
+456
+00:48:40,000 --> 00:48:46,840
+بقدر اكتبها بالشكل التالف سالب 72 تكامل من باي على
+
+457
+00:48:46,840 --> 00:48:54,500
+أربعة إلى باي على اتنينلا كتان ثيتا مشتقت كتان
+
+458
+00:48:54,500 --> 00:48:59,760
+الثيتا يعني شيلت ال D ثيتا مع كوسيكا التربية ثيتا
+
+459
+00:48:59,760 --> 00:49:05,680
+و كتبت عليها D كتان لو اشتقتش بيطلع سالب كوسيكا
+
+460
+00:49:05,680 --> 00:49:09,580
+التربية هاي السالب موجود والكوسيكا التربية كتبنا
+
+461
+00:49:09,580 --> 00:49:14,180
+بدلها مين كتان ثيتا علموكوا هذه الشغله في ال class
+
+462
+00:49:14,180 --> 00:49:21,790
+base لها ناقصبال U ؟ طيب هذه هي ال U تبعتك هذه
+
+463
+00:49:21,790 --> 00:49:29,110
+المسألة تبعتنا هذه بقول pot cot θ تساوي U يبقى إذن
+
+464
+00:49:29,110 --> 00:49:34,510
+ال DU سالب كوسيكا تربيه ثيتا دي ثيتا يبقى شو يصير
+
+465
+00:49:34,510 --> 00:49:41,770
+المسألة تكامل ل U DU بإشارة سالب هي ال U و هي ال
+
+466
+00:49:41,770 --> 00:49:46,160
+DU و هي اشارة السالبيبقى ياه ولا لا؟ إذا بتعرف إيه
+
+467
+00:49:46,160 --> 00:49:53,120
+على طول ماشي الحال بتعرف إيش خلاص و بطلع تكامل يو
+
+468
+00:49:53,120 --> 00:49:57,620
+دي و بإشارة سالف هيبقى برا يبقى هذه والله هذه نفس
+
+469
+00:49:57,620 --> 00:50:00,740
+الشيء و لا .. انتوا طبعا درستوا في شعب مختلفة ولا
+
+470
+00:50:00,740 --> 00:50:07,700
+واحد قالكوا هالشغل هذي؟ كل كوا؟ طيب ما علينا بس في
+
+471
+00:50:07,700 --> 00:50:11,760
+في الكتاب جايلها الكتاب دي ربالك طبعة اتناش جايلها
+
+472
+00:50:11,760 --> 00:50:13,060
+أنا شوفتها بعيني
+
+473
+00:50:16,330 --> 00:50:20,330
+أه مظبوط لكن أنا دراس كتابة اللي يكتب الكتاب لكن
+
+474
+00:50:20,330 --> 00:50:25,280
+في الكتاب موجودة line كمانطب علينا ما علينا سواء
+
+475
+00:50:25,280 --> 00:50:28,660
+هذه والله هذه هي اتنين نفس الشيء ماساوي نفس الشيء
+
+476
+00:50:28,660 --> 00:50:35,320
+يبقى هذا الكلام يبقى يساوي نقص 72 وهذه كتان تربية
+
+477
+00:50:35,320 --> 00:50:42,840
+ثيتا على اتنين U DU يبقى U تربية على اتنين والحكي
+
+478
+00:50:42,840 --> 00:50:50,940
+هذا من باي على اربعة الى باي على اتنين ويساويسالف
+
+479
+00:50:50,940 --> 00:50:57,740
+ستة و تلاتين خلّيك برا 72 على 2 ب 36 يبقى هذا بصير
+
+480
+00:50:57,740 --> 00:51:04,400
+مين بصير كتان تربية في باي على اتنين باي على اتنين
+
+481
+00:51:04,400 --> 00:51:12,380
+ناقص كتان تربية اللي هو باي على اربع والجواب هو
+
+482
+00:51:12,380 --> 00:51:19,510
+ناقص ستة و تلاتين فيه كده كتان باي على اتنينيعني
+
+483
+00:51:19,510 --> 00:51:25,130
+كوصين بيع اتنين على صين بيع على اتنين صفر على واحد
+
+484
+00:51:25,130 --> 00:51:29,270
+ولا غير على القلة الحاسبة تحسبوها I am here is
+
+485
+00:51:29,270 --> 00:51:34,490
+zero وكتان بيع على اربعة مقلوب تان بيع على اربعة و
+
+486
+00:51:34,490 --> 00:51:37,770
+تان ال بيع على اربعة بواحد واحد على واحد يبقى
+
+487
+00:51:37,770 --> 00:51:44,030
+بواحد تربيع قداش بواحد يبقى الجواب ستة وتلاتين
+
+488
+00:51:44,030 --> 00:52:12,100
+بالمؤجب فقط لا غيرهل بتحب تسأل اي سؤال هنا؟ طيب
+
+489
+00:52:12,100 --> 00:52:13,880
+نمرى C من السؤال
+
+490
+00:52:20,930 --> 00:52:30,930
+من 0 للجدري التربيهي ل2 x ناقص x تربيه ومن 1 لغاية
+
+491
+00:52:30,930 --> 00:52:39,250
+2 لمن؟ ل1 عالى اللي هو x تربيه زاد y تربيه يعني كل
+
+492
+00:52:39,250 --> 00:52:43,150
+تربيه dy dx
+
+493
+00:53:14,440 --> 00:53:18,540
+أكف مباشرة لك المشكلة في اللي وين في الحدود إذا ما
+
+494
+00:53:18,540 --> 00:53:23,340
+تروح ترسم منطقة تتكمل من أول ومن ثم تروح للحدود
+
+495
+00:53:23,340 --> 00:53:30,620
+بقول مصير هذا من هذا محور X و هذا محور Y و هذا
+
+496
+00:53:30,620 --> 00:53:35,580
+نقطة الأصل اللي هي Zero المتغير الأولاني اللي همين
+
+497
+00:53:35,580 --> 00:53:40,960
+Y تساوي Zero اللي همين بلعب محور X يبقى هذا Y
+
+498
+00:53:40,960 --> 00:53:46,050
+تساوي Zeroبعدها y تساوي الجدرى اللى عندنا هذا بس
+
+499
+00:53:46,050 --> 00:53:50,050
+معادلة دي الشيء اللى أنا مش عارفه مظبوط بيبقى
+
+500
+00:53:50,050 --> 00:53:55,430
+بسيطة بيقولوا دبل حالك راح قال لي y تساوي الجدرى
+
+501
+00:53:55,430 --> 00:54:02,470
+التربية لإتنين x ناقص x تربية قولوا ماشي شوية
+
+502
+00:54:02,470 --> 00:54:07,450
+تتربعها يمكن الله يحل حلها هيك شويةيبقى لو جينا
+
+503
+00:54:07,450 --> 00:54:13,390
+ربعناها إيش بيصير؟ بيصير عندي Y تربية يساوي اتنين
+
+504
+00:54:13,390 --> 00:54:21,030
+X ناقص X تربية نطلع عليكم شغلة تانية شو رايك لمين
+
+505
+00:54:21,030 --> 00:54:25,850
+يعمله اكمل المربع؟ يبقى هذا إيش بيصير عندي؟ Y
+
+506
+00:54:25,850 --> 00:54:31,190
+تربية يساوي واحد ناقص واحد زائد اتنين X ناقص X
+
+507
+00:54:31,190 --> 00:54:37,600
+تربية يعني هذه عبارة عن مين؟ عبارة عن واحدتربية
+
+508
+00:54:37,600 --> 00:54:42,340
+ناقص اتنين X زي واحد هذول التلاتة خدت منهم ناقص
+
+509
+00:54:42,340 --> 00:54:48,340
+عامل مشترك يبقى صارت المسألة Y تربيه يسوى واحد X
+
+510
+00:54:48,340 --> 00:54:54,200
+ناقص واحد لكل تربيه بالشكل اللي عنده هذا او بمعنى
+
+511
+00:54:54,200 --> 00:54:59,360
+اخر صار عند ال X ناقص واحد لكل تربيه زي Y تربيه
+
+512
+00:54:59,360 --> 00:55:01,660
+يسوى واحد معنى نتيجة
+
+513
+00:55:09,370 --> 00:55:18,290
+يبقى هذه circle with center اللي هو main واحد
+
+514
+00:55:18,290 --> 00:55:27,690
+وزيرو and radius واحدة طب تعالى نوصل للمدرسة جالي
+
+515
+00:55:27,690 --> 00:55:32,110
+المركز واحد وزيرو اين الواحد والزيرو هاي النقطة
+
+516
+00:55:32,110 --> 00:55:39,550
+اللي هي واحد وزيرووبعدين نصف القطر تبعها كده؟ واحد
+
+517
+00:55:39,550 --> 00:55:45,850
+يبقى بده يجيك هنا كمان هذا بيصير كده؟ اتنين لأنه
+
+518
+00:55:45,850 --> 00:55:51,610
+هذه واحد وبده يطلع فوق واحد وبده ينزل كمان تحت
+
+519
+00:55:51,610 --> 00:55:57,230
+واحد بالشكل اللي عنه هذا لكن هل هذه هي كل دائرة
+
+520
+00:55:57,230 --> 00:56:02,210
+ولا ربعة ولا نصة ولا تلتة الله أعلم لكن احنا بيقول
+
+521
+00:56:04,500 --> 00:56:09,240
+هذه الدائرة بيصير الدائرة بالشكل اللي عندها يعني
+
+522
+00:56:09,240 --> 00:56:13,300
+طبعا
+
+523
+00:56:13,300 --> 00:56:17,400
+يبقى هذه الدائرة بالشكل اللي عندها الآن هذه
+
+524
+00:56:17,400 --> 00:56:23,960
+الدائرة بدي أشوف هل هي كل
+
+525
+00:56:23,960 --> 00:56:30,150
+دائرة ولا جزء منها تعالى أشوفأحنا حددنا y تساوي
+
+526
+00:56:30,150 --> 00:56:34,350
+zero وحددنا y تساوي الجذر يبقى خلطة هذي عبارة عن
+
+527
+00:56:34,350 --> 00:56:40,030
+الدرع كل x من عند الواحد لغاية اتنين من عند الواحد
+
+528
+00:56:40,030 --> 00:56:46,610
+لغاية اتنين يعني x لغاية هنا من هنا لغاية هنا يبقى
+
+529
+00:56:46,610 --> 00:56:51,030
+لما تيجي تقولي بترفع هك رأسي وهذا يكون
+
+530
+00:56:55,230 --> 00:57:01,630
+يبقى رب عيد دائرة فقط ماريا تمام؟ يبقى هاي
+
+531
+00:57:01,630 --> 00:57:05,370
+البوباجي الدائرة كله مالوش لزوم يبقى هذه يا بنات
+
+532
+00:57:05,370 --> 00:57:12,530
+بتغمجها يبقى هذه غمجناها يعني دائرة من الواحد
+
+533
+00:57:12,530 --> 00:57:18,140
+لغاية اتنين الشكل اللي عندهاإذا بدي أشوف فيتس
+
+534
+00:57:18,140 --> 00:57:24,300
+تتغير من وين لوين و R تتغير من وين لوين لو جيت
+
+535
+00:57:24,300 --> 00:57:31,040
+رسمت هنا من نقطة الأصل لغاية ما جيت على وين على
+
+536
+00:57:31,040 --> 00:57:36,920
+النقطة هذه يبقى فيتس تستخدم قداشر مش عارفينها لابد
+
+537
+00:57:36,920 --> 00:57:43,200
+انك تعرف كيف بدي أعرف بسيطة جدا هذا الخيار
+
+538
+00:57:50,310 --> 00:57:56,490
+هذا النقطة أحدثيها واحد و واحد صح ولا لا نقطة فوق
+
+539
+00:57:56,490 --> 00:58:01,050
+أحدثيها واحدة اتنين هذه النقطة تقع على الدائرة
+
+540
+00:58:01,050 --> 00:58:06,990
+وتقع على الخط المستقيم صح ولا لا إذا نقطة التقاط
+
+541
+00:58:06,990 --> 00:58:12,150
+ما بين الاتنين بتكون هي النقطة المطلوبة طب واحد
+
+542
+00:58:12,150 --> 00:58:16,890
+تاني قالتلي لا أستنى شوية بقولكقال هي نقطة تقاطة
+
+543
+00:58:16,890 --> 00:58:22,510
+الدائرة مع الخط هذا الرأس له X تساوي واحد يعني بدي
+
+544
+00:58:22,510 --> 00:58:26,470
+أحل ال X تساوي واحد مع معادلة الدائرة وشوف إيش بدي
+
+545
+00:58:26,470 --> 00:58:32,810
+يطلع عني وإيه معادلة الدائرة هي X يساوي واحد تساوي
+
+546
+00:58:32,810 --> 00:58:38,410
+واحد يعني أعطيتنا نقطة هذه واحد أه طبعا أعطيتك
+
+547
+00:58:38,410 --> 00:58:43,720
+نقطة هذه واحد و بس واحد واحد كارتيزيايبقى هذه اللي
+
+548
+00:58:43,720 --> 00:58:50,080
+هو واحد واحد ممتاز جدا يبقى هذا واحد وهذا واحد
+
+549
+00:58:50,080 --> 00:58:54,820
+والزاوية هذه قائمة متلث متساوى الساقين يبقى كل
+
+550
+00:58:54,820 --> 00:59:00,720
+زاوية قدام 45 درجة إذا صارت الزاوية هذه Pi على 4
+
+551
+00:59:01,180 --> 00:59:05,580
+وهذه صارت باية على أربعة كذلك إذا قطها ده ثيتا
+
+552
+00:59:05,580 --> 00:59:09,800
+تساوي قد إيه؟ باية على أربعة، إذا الثيتا ستتغير من
+
+553
+00:59:09,800 --> 00:59:14,700
+وين لوين، من Zero لباية على أربعة، حلنا قصة ثيتا،
+
+554
+00:59:14,700 --> 00:59:20,920
+تبقى لقصة مين؟ أخرج، بقى أجي برسم خط من نقطة الأصل
+
+555
+00:59:20,920 --> 00:59:27,240
+وخلّيه يقطع منطقة التكامل، يبقى هي النقطة الأولى
+
+556
+00:59:27,240 --> 00:59:34,730
+وهي النقطة الثانيةبقول الله كويس بدي اشوف R قداش
+
+557
+00:59:34,730 --> 00:59:39,830
+هنا و بدي اشوف قداش R هنا تمام تفضل كيف بدي اجيب
+
+558
+00:59:39,830 --> 00:59:43,690
+هذه يا ربنا بقوله بسيطة هذا الخط الراسي شوفوا
+
+559
+00:59:43,690 --> 00:59:49,270
+عادلته X يساوي واحد يعني R Cos θ يساوي واحد يبقى R
+
+560
+00:59:49,270 --> 00:59:54,190
+سكتين لإن هذا قضية بسيطة يبقى هذا بروح بقوله هنا
+
+561
+00:59:54,190 --> 00:59:55,510
+ال X
+
+562
+00:59:58,860 --> 01:00:03,640
+قصارى تيتا يساوي واحد يبقى الارض ساوي السك الزاوية
+
+563
+01:00:03,640 --> 01:00:09,040
+تيتا ضالمين عندى ضال المعادلة اللى عندنا دى معادلة
+
+564
+01:00:09,040 --> 01:00:13,620
+الدائرة وين معادلة الدائرة هاي معادلة الدائرة
+
+565
+01:00:13,620 --> 01:00:19,420
+بقوله اه وين هاي هاي معادلة الدائرة بقوله طب انا
+
+566
+01:00:19,420 --> 01:00:24,760
+باخد هادي احسنلي احسنلي فى الشغل كيف احسنلك قال لي
+
+567
+01:00:24,760 --> 01:00:28,600
+بس احسنلي بكيستر بيه على الشجرة تانيةيبقى بطبق
+
+568
+01:00:28,600 --> 01:00:37,780
+ولكن و X تربيع زائد Y تربيع يساوي 2X صح؟ طيب كداش
+
+569
+01:00:37,780 --> 01:00:45,520
+X تربيع زائد Y تربيع؟ و التانية 2R Cos زاوية ثيتا
+
+570
+01:00:45,520 --> 01:00:50,420
+صحيح ولا لا؟لو جبتها على الشجة التانية و أخدت R
+
+571
+01:00:50,420 --> 01:00:56,660
+عامل مشترك بيبقى عندي R ناقص اتنين Cos θ بده يسوى
+
+572
+01:00:56,660 --> 01:01:02,180
+قداش Zero يبقى الـ R تسوى Zero ماليش علاقة فيها
+
+573
+01:01:02,180 --> 01:01:09,980
+بيبقى عندي R تسوى اتنين Cos زاوية θ يبقى هذه
+
+574
+01:01:09,980 --> 01:01:17,840
+الدائرة عدلتها R يسوى اتنين Cos زاوية θخلّيني
+
+575
+01:01:17,840 --> 01:01:25,060
+اذاكركم يا ناسيين لما
+
+576
+01:01:25,060 --> 01:01:31,550
+جيتوا في احداثيات القطبين جيبتوا معادلة دائرةاللي
+
+577
+01:01:31,550 --> 01:01:37,290
+بتمر بنقطة الأصل ومركزها على محور X الموجة أو على
+
+578
+01:01:37,290 --> 01:01:41,970
+X السالق أو على Y الموجة وقال هو على Y السالق وقلت
+
+579
+01:01:41,970 --> 01:01:46,630
+انه إذا كان والله مركزها على محور X وتمر بنقطة
+
+580
+01:01:46,630 --> 01:01:51,670
+الأصل يجب ان اقع عليها R يسوى 2A Cos زاوية Tوإذا
+
+581
+01:01:51,670 --> 01:01:56,250
+عليك تسالق تسالق اتنين اكو صين تيتا إذا على واقع
+
+582
+01:01:56,250 --> 01:02:01,710
+الموجة باتنين ا صين تيتا ولا اتنين ا صين تيتا بس
+
+583
+01:02:01,710 --> 01:02:07,710
+بإشارة سالق أسألكم ماذا ذكريش شمس هذا القرآن قال
+
+584
+01:02:07,710 --> 01:02:13,010
+اللهم اجعله يرقد يفتذكرنا ماشي فبيبقى هذا إيه هاي
+
+585
+01:02:13,010 --> 01:02:16,670
+هطلق نفس المعادلة لاحبيتش أقوللكم من الأول حبيت
+
+586
+01:02:16,670 --> 01:02:22,220
+أصلبكمحزباً دقيقاً لأن هذه الدائرة بتمر بنقطة
+
+587
+01:02:22,220 --> 01:02:25,380
+الأصل ومركزها على الاتجاه الموجب لل exactly are
+
+588
+01:02:25,380 --> 01:02:32,260
+يسوى اتنين a sin θ حيث a نصف القطر نصف القطر عند
+
+589
+01:02:32,260 --> 01:02:35,220
+الحمد لله بواحد يبقى طرأ تلاته اتنين في واحد
+
+590
+01:02:35,220 --> 01:02:42,280
+cosine طلعت اتنين cosine ثم خلصنا كل الحاجات
+
+591
+01:02:42,280 --> 01:02:46,490
+الصعبة خلصنا هذا عملية show routineيبقى الشغل
+
+592
+01:02:46,490 --> 01:02:53,150
+الروتيني كالتالي بيصير المسألة هي تكاملين وهي واحد
+
+593
+01:02:53,150 --> 01:02:58,450
+على X تربيع زاد و تربيع تربيع تربيع تربيع تربيع
+
+594
+01:02:58,450 --> 01:03:02,410
+تربيع تربيع تربيع تربيع تربيع تربيع تربيع تربيع
+
+595
+01:03:02,410 --> 01:03:02,710
+تربيع تربيع تربيع تربيع تربيع تربيع تربيع تربيع
+
+596
+01:03:02,710 --> 01:03:13,450
+تربيع تربيع تربيع تربيع تربيع تربيع تربيع تربيع
+
+597
+01:03:13,670 --> 01:03:21,310
+للي اتنين كوفاين الثيتا وثيتا هذه من Zero لغاية Pi
+
+598
+01:03:21,310 --> 01:03:27,370
+على أربع يبقى هذا الكلام بدي اصلحه تكامل من Zero
+
+599
+01:03:27,370 --> 01:03:36,090
+لغاية Pi على أربع أربع أرقص أربع مقدر يعني كأنه
+
+600
+01:03:36,090 --> 01:03:43,910
+احنا بدنا نكاملمن sic θ إلى اتنين cosine θ للار
+
+601
+01:03:43,910 --> 01:03:51,810
+السالب تلاتة dr dtمظبوط ايه؟ يبقى بنضيف لنقص واحدة
+
+602
+01:03:51,810 --> 01:03:57,830
+بنقسم على القص الجديد يبقى هذا الكلام تكامل من
+
+603
+01:03:57,830 --> 01:04:04,950
+Zero لغاية Pi على أربعة لمين؟ لأ الارقص ناقص اتنين
+
+604
+01:04:04,950 --> 01:04:10,790
+على ناقص اتنين والحكي هذا من سك ثيتا للي اتنين
+
+605
+01:04:10,790 --> 01:04:21,540
+قصين الزاوية ثيتا لمين؟ لادى ثيتاوهذا حاضن وضوح
+
+606
+01:04:21,540 --> 01:04:27,550
+الشمس في رابعة النهارطيب هذا الكلام يجب ان يساوي
+
+607
+01:04:27,550 --> 01:04:33,570
+ناقص نص خلّيك برا وهي تكمل من zero ل πاي على أربعة
+
+608
+01:04:33,570 --> 01:04:38,990
+هذه يا بنات قداشر ليه واحد على R تربيع صح يبقى
+
+609
+01:04:38,990 --> 01:04:45,450
+بصير عندي مين بصير عندي واحد على أربعة كوصين تربيع
+
+610
+01:04:45,450 --> 01:04:53,570
+زاوية ثيتا ناقص واحدعلى سكتر بيه ثيتر كله بالنسبة
+
+611
+01:04:53,570 --> 01:05:00,470
+لدي ثيتر أو إن شئتوا فقلنا ناقص نصف تكمل من zero
+
+612
+01:05:00,470 --> 01:05:09,960
+لغاية pi على أربع لربع cosine مقلب منين؟يبقى سك
+
+613
+01:05:09,960 --> 01:05:18,500
+تربيع ثيتا وناقص cos تربيع ثيتا كله بالنسبة الي دي
+
+614
+01:05:18,500 --> 01:05:26,460
+ثيتا مظبوط هيك؟ طيب قدش تكمل سك تربيع؟ بتان يبقى
+
+615
+01:05:26,460 --> 01:05:34,170
+وسيطة هذه ناقص تمن تان ثيتاوالحكي من Zero لغاية Pi
+
+616
+01:05:34,170 --> 01:05:40,650
+على أربعة ناقص فناقص يتزاد هذه النص وهذه بيجيلك
+
+617
+01:05:40,650 --> 01:05:47,810
+كمان نص ومن Zero لغاية Pi على أربعة لمن لواحد زائد
+
+618
+01:05:47,810 --> 01:05:54,410
+cosine اتنين ثيتا D ثيتا يبقى هذا الكلام بيستوي
+
+619
+01:05:54,410 --> 01:06:03,900
+لناقص تون فيه وظل ال 45 وظل ال Zeroوهنا زائد رابع
+
+620
+01:06:03,900 --> 01:06:10,240
+في ثيتا زائد sin اتنين ثيتا على اتنين من Zero
+
+621
+01:06:10,240 --> 01:06:18,200
+لغاية Pi على اربع يبقى النتيجة ناقص تمن زائد رابع
+
+622
+01:06:18,200 --> 01:06:29,320
+في Pi على اربع وهنا زائد تمن تمينأفتح يوسف واضغط
+
+623
+01:06:29,320 --> 01:06:32,640
+هنا و اضغط باي على أربع و يصبح صين باي على اتنين
+
+624
+01:06:32,640 --> 01:06:42,800
+ناقص صين زيرو يبقى ناقص زيرو اظن زائد ثمن و ناقص
+
+625
+01:06:42,800 --> 01:06:52,960
+ثمن مع السلامة والجواب يسوى باي على ستة عشر حلوة
+
+626
+01:06:52,960 --> 01:06:53,840
+فكرة السؤال
+
+627
+01:07:11,130 --> 01:07:17,050
+خد بالمثال رقم ثلاثة
+
+628
+01:07:17,050 --> 01:07:23,070
+ثلاثة
+
+629
+01:07:23,070 --> 01:07:33,510
+find the area of the region find the area of the
+
+630
+01:07:33,510 --> 01:07:35,010
+region
+
+631
+01:07:44,730 --> 01:07:53,930
+to the interiors of
+
+632
+01:07:53,930 --> 01:08:00,870
+the cardioids of the
+
+633
+01:08:00,870 --> 01:08:08,290
+cardioids R تساوي واحد cosine الزاوية تيتا and ال
+
+634
+01:08:08,290 --> 01:08:13,770
+R يساوي واحد ناقص cosine الزاوية تيتا
+
+635
+01:08:43,000 --> 01:08:47,620
+يقول لهذه مسافة المنطقة المشتركة المنطقة الداخلية
+
+636
+01:08:47,620 --> 01:08:51,020
+المشتركة ما بين ال two cardoids اذا احنا عندنا
+
+637
+01:08:51,020 --> 01:08:57,140
+منحنية للقلب ودرسناهم في calculus دي بصبوط لو
+
+638
+01:08:57,140 --> 01:09:02,600
+قعدنا رسمهم بيكون على الشكل التالي هذا الوثيطة
+
+639
+01:09:02,600 --> 01:09:08,860
+تساوي zero او هذا الوثيطة تساوي by على اتنين ال
+
+640
+01:09:08,860 --> 01:09:12,780
+cardoid الأول الشكل اللي عندنا هذا هيك
+
+641
+01:09:17,210 --> 01:09:20,970
+والكاردويلي التاني على الناحية .. هذا مين هو؟ شو
+
+642
+01:09:20,970 --> 01:09:26,550
+اسمه هذا يا بنات؟ أبو الزائد ولا اللاقس؟ زائد يبقى
+
+643
+01:09:26,550 --> 01:09:32,650
+هذا أبو سام اللي هو واحد زائد كوصاين زامية كتيرة
+
+644
+01:09:32,650 --> 01:09:37,050
+وانحنى القلب التاني على الناحية التانية اللي هو
+
+645
+01:09:37,050 --> 01:09:39,830
+بيجيكي بالشكل هذا هيك
+
+646
+01:09:45,000 --> 01:09:51,660
+وهذا بيجي من ناحية التانية شكل هذا وين المنطقة
+
+647
+01:09:51,660 --> 01:09:57,320
+المشتركة فيما بينهما؟ في المنطقة تلعني و تل اتنين
+
+648
+01:09:57,320 --> 01:10:02,880
+هذول وكان ليها تقداش مساحة في المنطقة المشتركة ما
+
+649
+01:10:02,880 --> 01:10:07,300
+بين الاتنين بقوله بسيطة هل الوان حاليا في تمثل
+
+650
+01:10:07,300 --> 01:10:13,680
+بالنسبة لمحوري الإحداثية محور X ومحور Y؟اللي جابها
+
+651
+01:10:13,680 --> 01:10:18,420
+نعم يبقى هدول كام منطقة باعتبرهم اربع مناطق يبقى
+
+652
+01:10:18,420 --> 01:10:22,160
+لو جيبت منطقة وضربتها فيها اربعة بيقول اه خلصنا من
+
+653
+01:10:22,160 --> 01:10:26,260
+الشغل هذي يبقى يا بنات احنا بنأيجي ناخد المنطقة
+
+654
+01:10:26,260 --> 01:10:32,320
+المبلنة اللي عيدناها يعني لو روحت رسمتها على
+
+655
+01:10:32,320 --> 01:10:37,040
+الطبيعة من جديد بتقول المنطقة هيها هيك
+
+656
+01:10:41,020 --> 01:10:48,760
+هذه المنطقة المظللة هذا يكون θ تساوي y على 2 وهذا
+
+657
+01:10:48,760 --> 01:10:56,200
+يكون θ تساوي 0 تمام ؟ طيب إذا الخط الأزرق تبع
+
+658
+01:10:56,200 --> 01:11:01,400
+المنخنامين R يساوي 1 ناقص في صين الزاوية
+
+659
+01:11:04,410 --> 01:11:10,810
+لما بدنا نيجي نحسب مساحة هذه المنطقة يبقى بدي أخده
+
+660
+01:11:10,810 --> 01:11:18,490
+من نقطة الأصل لغاية مين؟ لغاية أي نقطة تقع على
+
+661
+01:11:18,490 --> 01:11:26,250
+محيط المنطقة هنا أرض كده شبنات؟ Zero وهنا أرض تسوى
+
+662
+01:11:26,250 --> 01:11:33,460
+كده؟ واحد ناقص كصين الزاوية ثتابقول له الـ Area
+
+663
+01:11:33,460 --> 01:11:41,940
+المطلوبة يسوى تكوينه لRDRD فيتا الـR ستتغير من
+
+664
+01:11:41,940 --> 01:11:48,640
+Zero إلى مين؟ واحد ناقص كوصين الزاوية فيتا طبعاً
+
+665
+01:11:48,640 --> 01:11:54,940
+تظل الفيتا ستتغير من أين إلى أين من Zero لضيعة نين
+
+666
+01:11:54,940 --> 01:12:01,700
+بكون جزء المنحنى هذايبقى من zero لغاية I على 2 هذا
+
+667
+01:12:01,700 --> 01:12:07,660
+بيعطيني فقط المنطقة المظلة للي عندنا هذه يبقى لو
+
+668
+01:12:07,660 --> 01:12:12,980
+ضربتها في أربعة بيعطيني ال mailكل المنطقة اللي
+
+669
+01:12:12,980 --> 01:12:29,920
+بدوها يبقى هذا الكلام
+
+670
+01:12:29,920 --> 01:12:36,100
+يبدو يساوي 2تكامل من Zero لغاية Pi على اتنين من
+
+671
+01:12:36,100 --> 01:12:40,780
+Zero لغاية Pi على اتنين للأرثر اللي هو واحد ناقص
+
+672
+01:12:40,780 --> 01:12:46,960
+Cos Theta الكل ترميه ناقص Zero كله في قدر في D
+
+673
+01:12:46,960 --> 01:12:53,420
+Theta او انشرتهم فاقولواإتنين تكامل من Zero لPi
+
+674
+01:12:53,420 --> 01:13:00,860
+على اتنين لواحد نقص اتنين Cos θ زائد Cos تربيع θ
+
+675
+01:13:00,860 --> 01:13:09,720
+كله بالنسبة الى Dθ هذا ما هو اتنين تكامل من Zero
+
+676
+01:13:09,720 --> 01:13:14,680
+لغاية Pi على اتنين واحد نقص اتنين Cos θ مافي مشكلة
+
+677
+01:13:14,680 --> 01:13:21,230
+هذه Cos تربيع بقدر اكتبها بدلالةكوصيني ضعف الزاوية
+
+678
+01:13:21,230 --> 01:13:31,270
+نص زائد نص كوصيني اتنين ثيتا كله في دي ثيتا طيب
+
+679
+01:13:31,270 --> 01:13:37,710
+تطلعيلي هذا واحد صحيح وهذا نصك كده؟ تلاتة على
+
+680
+01:13:37,710 --> 01:13:44,690
+اتنين يبقى هذا الكلام اتنين تلاتة على اتنين ثيتا
+
+681
+01:13:44,690 --> 01:13:47,530
+ناقص اتنين
+
+682
+01:14:04,130 --> 01:14:13,130
+وإليك الجواب الجواب يطلع يساوي تلاتة by على اتنين
+
+683
+01:14:13,130 --> 01:14:20,030
+ناقص اربع او ان شئتي فاقولي تلاتة by ناقص تمانية
+
+684
+01:14:20,030 --> 01:14:25,490
+كله على اتنين هذا بيعطينا اللي همين المساحة
+
+685
+01:14:25,490 --> 01:14:38,080
+المطلوب example اربع بقولي findthe area بدنا مساحة
+
+686
+01:14:38,080 --> 01:14:43,240
+enclosed والمغلقة
+
+687
+01:14:43,240 --> 01:14:56,800
+by one leaf by one leaf of the rose of the rose دي
+
+688
+01:14:56,800 --> 01:14:59,500
+الزهرة اللي هي من
+
+689
+01:15:03,240 --> 01:15:19,120
+للزهرة اللي A تساوى 12 Cos 3 Theta
+
+690
+01:15:19,120 --> 01:15:22,300
+هذه
+
+691
+01:15:22,300 --> 01:15:28,020
+رسمناها
+
+692
+01:15:28,020 --> 01:15:32,860
+في Calculus Bطبعا نطلع على الرقم اللى مضروب فى
+
+693
+01:15:32,860 --> 01:15:35,840
+الزاوية والله إذا الرقم مضروب فى الزاوية الفردي
+
+694
+01:15:35,840 --> 01:15:41,260
+يبقى عندي تلت ورقات لإن الرقم عندي تلت إذا خمسة
+
+695
+01:15:41,260 --> 01:15:44,500
+يبقى خمس ورقات إذا سبعة سبعة ورقات لكن إذا كان رقم
+
+696
+01:15:44,500 --> 01:15:48,820
+زوجى فعدد الورقات بره ثالث رقم يعني لو قلت لك
+
+697
+01:15:48,820 --> 01:15:52,330
+cosine اتنين ثتر بيطلع أربع ورقاتوصلت الاربع تيتا
+
+698
+01:15:52,330 --> 01:15:56,410
+تطلع تمانية و هكذا فدول تلاتة يبقى ماعنديش الا
+
+699
+01:15:56,410 --> 01:16:01,070
+تلاتة يبقى لو روحت قسمتها بنات بذكركوا تذكر برسم
+
+700
+01:16:01,070 --> 01:16:06,350
+باس تيتا تساوي زيرو وهي تيتا تساوي باي على اتنين
+
+701
+01:16:06,350 --> 01:16:12,170
+فكلت الرسم بالشكل اللي أديك و بتجيلك الورق اللي
+
+702
+01:16:12,170 --> 01:16:18,170
+بعدك و اللي بعدكيبقى هذا منحنى الزهرة دول ثلاث
+
+703
+01:16:18,170 --> 01:16:22,810
+ورقات اللي بديش مساحة الثلاث ورقات اللي بس بدي مان
+
+704
+01:16:22,810 --> 01:16:27,430
+ورقة واحدة يبقى يكفينا يا بنات احنا الورقة اللي
+
+705
+01:16:27,430 --> 01:16:32,910
+على اليمين ان جيه بدوش مساحتها بكون ايه حصلنا على
+
+706
+01:16:32,910 --> 01:16:37,050
+المطلوب يجيبوا زي هيك و بس هذه الورقة المتمثلة او
+
+707
+01:16:37,050 --> 01:16:42,230
+المنحنة المتمثلة بالنسبة لمحور X يبقى تكفيني النص
+
+708
+01:16:42,230 --> 01:16:47,300
+اللي فوق هذا و بضربه في جديرفى اتنين بيعطيني مساحة
+
+709
+01:16:47,300 --> 01:16:52,880
+الورقة الواحدة طب مشان هيك بدي اشوف θ تتغير من وين
+
+710
+01:16:52,880 --> 01:16:59,220
+لوين اها بدي θ تتغير من وين لوين المنحنى اللى
+
+711
+01:16:59,220 --> 01:17:06,130
+عندنا هذا هيك بدي θ اعرف من وين لوين وبعد هيكبدي
+
+712
+01:17:06,130 --> 01:17:11,790
+اعرف R من وين لوين R من وين لوين سهل وظلت بس تحديد
+
+713
+01:17:11,790 --> 01:17:17,750
+ثيتا هذه يا بنات لو روحت رسمتيها بدك تعمليلها جدول
+
+714
+01:17:17,750 --> 01:17:23,630
+الجدول لو رجعنا الى Calculus B بلاقي هذه ثيتا
+
+715
+01:17:23,630 --> 01:17:30,050
+تساوي Pi على ستة تلاتين درجة و هذه ثيتا تساوي اللي
+
+716
+01:17:30,050 --> 01:17:37,400
+هو من زيروإذاً الـ Area المطلوبة يسوى تكاملها للـ
+
+717
+01:17:37,400 --> 01:17:43,640
+RDRDθ بإننا نيجي لـ R ، الـ R بتبدأ من نقطة الأصل
+
+718
+01:17:43,640 --> 01:17:48,860
+بنقطة منطقة التكامل لبعياد المنص اللي وراه لحدود
+
+719
+01:17:48,860 --> 01:17:54,660
+المنحنى إذا R هتبدأ من الـ Zero المنحنى هي مقطع
+
+720
+01:17:54,660 --> 01:18:03,220
+عندنا اللي هو اتناشر كساين تلاتة ثيتاو θ من Zero
+
+721
+01:18:03,220 --> 01:18:10,660
+لغاية Pi على ستة يبقى هذا الكلام بدل ساوي تكامل من
+
+722
+01:18:10,660 --> 01:18:16,140
+Zero لغاية Pi على ستة للأرض تربيه على اتنين من
+
+723
+01:18:16,140 --> 01:18:23,840
+Zero لغاية اتناشر Cos ثلاثة ثيتا وهذه هنا من خدية
+
+724
+01:18:24,870 --> 01:18:29,530
+أظن لو عوضنا بيطلع مية وأربعة واربعين كوساين تربيع
+
+725
+01:18:29,530 --> 01:18:35,350
+مية وأربعة وأربعين على اتنين باتنين وسبعين اذا
+
+726
+01:18:35,350 --> 01:18:40,570
+دغري اتنين وسبعين تكمن من زيرو لداي على ستة
+
+727
+01:18:40,570 --> 01:18:48,470
+لكوساين تربيع تلاتة فيتا دي فيتا برضه هذه لازم
+
+728
+01:18:48,470 --> 01:18:54,070
+نحولها بدلالات ضعف الزاوية يبقى اتنين وسبعين
+
+729
+01:18:57,550 --> 01:19:02,690
+فاهمين فيتا كامل من Zero لغاية Pi على ستة لواحد
+
+730
+01:19:02,690 --> 01:19:10,550
+زائد كوساين قد هذه مرتين قداش بطلع دي فيتا يبقى
+
+731
+01:19:10,550 --> 01:19:17,010
+هذه ستة وتلاتين وهذا التكامل تبعها فيتا زائد ساين
+
+732
+01:19:17,010 --> 01:19:24,490
+ستة فيتا على فيتا من Zero لغاية Pi على ستة والجواب
+
+733
+01:19:24,490 --> 01:19:29,600
+دغري مباشرة اتناشر بعديبقى هذا الكلام متساوي
+
+734
+01:19:29,600 --> 01:19:38,780
+اتناشر واحد المثال رقم خمسة مثال رقم خمسة بيقول
+
+735
+01:19:38,780 --> 01:19:48,220
+ايش بيقول ال region that lies that region that
+
+736
+01:19:48,220 --> 01:19:58,880
+lies المنطقة التي تقع inside ديكاردوينinside the
+
+737
+01:19:58,880 --> 01:20:01,920
+cardioid
+
+738
+01:20:01,920 --> 01:20:09,760
+داخل ال cardioid الـR يساوي واحد زائد cosine ثيتا
+
+739
+01:20:09,760 --> 01:20:14,360
+and outside
+
+740
+01:20:14,360 --> 01:20:21,500
+the circle وخارج الدائرة R تساوي واحد
+
+741
+01:20:23,820 --> 01:20:32,800
+is the base of a solid is the base of a solid
+
+742
+01:20:32,800 --> 01:20:45,960
+right cylinder of a solid right cylinder
+
+743
+01:20:45,960 --> 01:20:50,320
+ونادأ ليها قائمة cylinder
+
+744
+01:20:53,650 --> 01:21:00,950
+الأعلى من السليندر ، الأعلى من
+
+745
+01:21:00,950 --> 01:21:04,330
+السليندر
+
+746
+01:21:04,330 --> 01:21:14,190
+، الأعلى من السليندر موجود في الطائرة ، موجود في
+
+747
+01:21:14,190 --> 01:21:17,370
+الطائرة
+
+748
+01:21:17,370 --> 01:21:37,340
+في المستوى Z بصميم Xfind the cylinders volume بده
+
+749
+01:21:37,340 --> 01:21:40,560
+كده حجم السيلندر اللي عندها
+
+750
+01:21:54,640 --> 01:22:03,140
+مافي مشكلة بيصير هذه ال R بيصير هيك من 0 ل 1 زي
+
+751
+01:22:03,140 --> 01:22:07,700
+cos θ صحيح مختلفات
+
+752
+01:22:07,700 --> 01:22:13,060
+الدالة و بدأت ضمية في أربعة نفس الشيء و لو أخدت
+
+753
+01:22:13,060 --> 01:22:17,220
+هذه اللي تحت كمان أو هذه سيية نفس الشيء والله ال
+
+754
+01:22:17,220 --> 01:22:23,020
+area بتتمهامش هي نفسها ثابتة لإن خدت أي واحدة من
+
+755
+01:22:23,020 --> 01:22:31,660
+الأربعة وضربتها في الأربعة خدتها سؤال
+
+756
+01:22:31,660 --> 01:22:46,720
+بيقول ليه الشيطان بيقول لي في عندي ايوة اتنين
+
+757
+01:22:46,720 --> 01:22:51,900
+كتبناها اتنين قبللأ لأ ما كتبناهاش يبقى الارى يا
+
+758
+01:22:51,900 --> 01:22:59,700
+بنات بدنا نلاقي اتنين التكامل وهنا بده يصير اتنين
+
+759
+01:22:59,700 --> 01:23:05,560
+التكامل وهذا بيصير هنا اتنين بتروح مع اتنين بيظل
+
+760
+01:23:05,560 --> 01:23:12,300
+مية واربع واربعين مظبوط اي مية واربع واربعين وهذه
+
+761
+01:23:12,300 --> 01:23:19,510
+بدها تصير اتنين وسبعين بدون نص دوريوهذه بدها صير
+
+762
+01:23:19,510 --> 01:23:25,110
+اتنين والسبعين اتنين والسبعين وانت تيجي تسيبها
+
+763
+01:23:25,110 --> 01:23:31,310
+بعدين ماشي كلام صحيح طيب يعني بحث نسينا نضغط في
+
+764
+01:23:31,310 --> 01:23:34,510
+التاني وانت نضغط في الأول لإن احنا خدنا نص المنطقة
+
+765
+01:23:34,510 --> 01:23:38,790
+طيب نيجي بعض الكتابة قولي the region that lies
+
+766
+01:23:38,790 --> 01:23:42,990
+inside the cardoid and الدائرة اللي عندنا هذه
+
+767
+01:23:42,990 --> 01:23:47,370
+تعالى نشوف الكاردويد والدائرة فين الكاردويد؟
+
+768
+01:23:51,400 --> 01:23:58,660
+Y ثيتا تساوي باي على اتنين الإشارة بالذلك بكل جهة
+
+769
+01:23:58,660 --> 01:24:03,740
+اليامين يبقى هذا الـCardioid بالشكل اللي عندنا
+
+770
+01:24:03,740 --> 01:24:08,040
+طبعا؟
+
+771
+01:24:08,040 --> 01:24:12,360
+طيب لو يبقى هنا تقول ثيتا تساوي Zero او واقف
+
+772
+01:24:12,360 --> 01:24:14,180
+معادلة الـCardioid
+
+773
+01:24:22,670 --> 01:24:29,970
+لكن الدائرة معدلتها جداش R تساوي واحد اذا هتمر
+
+774
+01:24:29,970 --> 01:24:35,770
+بالنقطة هذه اللي هي R تساوي واحد او تجيكي الدائرة
+
+775
+01:24:35,770 --> 01:24:38,650
+بالشكل اللي عندنا نصف قطرة واحد
+
+776
+01:24:42,440 --> 01:24:46,560
+هيبقى هاي الدائرة اللي عندنا هرسمها باللون الأزرق
+
+777
+01:24:46,560 --> 01:24:55,020
+لكي نميز ما بين الاتنين هاي الدائرة الشكل
+
+778
+01:24:55,020 --> 01:25:04,380
+اللي عندنا كويس؟
+
+779
+01:25:05,580 --> 01:25:11,860
+قال ايش؟ قال ال region داخل ال cardwell يبقى جوا
+
+780
+01:25:11,860 --> 01:25:17,220
+ال cardwell وفي نفس الوقت برا مين الدائرة يبقى وين
+
+781
+01:25:17,220 --> 01:25:22,400
+المنطقة هي اللي برا الدائرة وداخل ال cardwell
+
+782
+01:25:22,400 --> 01:25:28,690
+مالها؟اعتبرتها قاعدة وعملت عليها أسطوانة دائرية
+
+783
+01:25:28,690 --> 01:25:34,690
+قائمة يبقى هذه المظلة هي القاعدة تبع من الأسطوانة
+
+784
+01:25:34,690 --> 01:25:39,330
+الأسطوانة صارت من تحت لغاية فوق تمام؟ مين هي
+
+785
+01:25:39,330 --> 01:25:44,930
+الأسطوانة؟ يبقى للأسطوانة اللي هي Z تساوي Xطبعا
+
+786
+01:25:44,930 --> 01:25:48,170
+يبقى في مستوى المستوى الموجود في المستوى في
+
+787
+01:25:48,170 --> 01:25:52,850
+المستوى الموجود في المستوى الموجود في المستوى
+
+788
+01:25:52,850 --> 01:25:53,450
+الموجود في المستوى الموجود في المستوى الموجود في
+
+789
+01:25:53,450 --> 01:25:53,670
+المستوى الموجود في المستوى الموجود في المستوى
+
+790
+01:25:53,670 --> 01:25:57,570
+الموجود في المستوى الموجود في المستوى الموجود في
+
+791
+01:25:57,570 --> 01:25:58,910
+المستوى الموجود في المستوى الموجود في المستوى
+
+792
+01:25:58,910 --> 01:25:58,950
+المستوى الموجود في المستوى الموجود في المستوى
+
+793
+01:25:58,950 --> 01:25:59,010
+المستوى الموجود في المستوى الموجود في المستوى
+
+794
+01:25:59,010 --> 01:26:11,670
+الموجود في المستوى الموجود في المستوى
+
+795
+01:26:11,670 --> 01:26:17,970
+الموجوضربته فى اتنين كملت عليه كله وضربته فى اتنين
+
+796
+01:26:17,970 --> 01:26:23,330
+مش هفتقل انه هذا مقل المنخلة متمثل بالنسبة لمحور X
+
+797
+01:26:23,330 --> 01:26:29,590
+يبقى بدي اقوله اتنين المنطقة
+
+798
+01:26:29,590 --> 01:26:39,030
+دى ر دي تي تا ر دي تي تا صحيح؟ لأ مصحش مش صحيح
+
+799
+01:26:39,030 --> 01:26:45,660
+بتاكى تحط زيت جداش تساوييبقى بني بقوله هذه هيك
+
+800
+01:26:45,660 --> 01:26:53,980
+ومنطقة Z و هذه منطقة R و هذه DF و تعالي اكتب
+
+801
+01:26:53,980 --> 01:26:59,780
+التفاصيل تبعك الآن Z دي عندك ال top من فوق جداش X
+
+802
+01:26:59,780 --> 01:27:10,590
+يبقى هذه X تمامبس احنا بنشتغل في ال code ب R Cos θ
+
+803
+01:27:10,590 --> 01:27:17,690
+يعني كأن ال X دي A على المنطقة R يعني كأنه اتنين
+
+804
+01:27:17,690 --> 01:27:28,190
+تكاملين لل R Cos θ والدي A ل R دي R دي θ نيجي ال R
+
+805
+01:27:28,190 --> 01:27:34,580
+هتتغير من وين ل وينفدي برسم خط يقطع منطقة التكامل
+
+806
+01:27:34,580 --> 01:27:40,540
+النقطة هذه والنقطة هذه هنا أرض كده؟ في واحد و هنا
+
+807
+01:27:40,540 --> 01:27:47,790
+أرض ساعة كده؟ واحد زائد فصين الزاوية تيتاالارث
+
+808
+01:27:47,790 --> 01:27:52,790
+ستتغير من واحد إلى واحد زائد كوسايم الزاوية ثيتا
+
+809
+01:27:52,790 --> 01:27:58,770
+وثيتا ستتغير من عند ال zero لغاية كده؟ لغاية pi
+
+810
+01:27:58,770 --> 01:28:02,050
+على اتنين من zero لغاية pi على اتنين
+
+811
+01:28:17,720 --> 01:28:24,060
+ارتكيب على تلاتة من واحد لغاية واحد زائد كوصين
+
+812
+01:28:24,060 --> 01:28:29,920
+الزاوية ثيتا وهذا يظهر عند من كوصين الزاوية ثيتا
+
+813
+01:28:29,920 --> 01:28:36,580
+في دي ثيتا إذا هذا الكلام سيكون تلتين خلّيك برا
+
+814
+01:28:36,580 --> 01:28:43,190
+وهي تكامل من zero ل by باي على اتنينمن Zero لغاية
+
+815
+01:28:43,190 --> 01:28:51,650
+Pi على اتنين لواحد زائد Cos θ الكل تكيب ناقص
+
+816
+01:28:51,650 --> 01:28:56,330
+القيمة اللي هو ناقص واحد تكيب اللي هو واحد كله
+
+817
+01:28:56,330 --> 01:29:05,450
+مضروب في Cos θ d θ طيب يا تلتان خلّيك برا و اتكامل
+
+818
+01:29:05,450 --> 01:29:07,190
+من Zero لغاية Pi على اتنين
+
+819
+01:29:12,710 --> 01:29:18,010
+تلاتة cosine ثيتا زائد تلاتة cosine تربيع ثيتا
+
+820
+01:29:18,010 --> 01:29:24,390
+زائد cosine تكييب ثيتا ناقص واحد كله في مين؟ في
+
+821
+01:29:24,390 --> 01:29:33,350
+cosine ثيتا في d ثيتا اضل ناقص واحد وزاد واحد الله
+
+822
+01:29:33,350 --> 01:29:39,930
+يسهل عليكم مش زعلانين عليكم وهذا يتصير تلتين تكمل
+
+823
+01:29:39,930 --> 01:29:45,930
+من zero till pi على اتنينلي تلاتة cosine تربيع
+
+824
+01:29:45,930 --> 01:29:52,390
+زاوية ثيتا زائد تلاتة cosine تكييب زاوية ثيتا زائد
+
+825
+01:29:52,390 --> 01:30:01,190
+cosine أربعة ثيتا كله دي ثيتا يبقى ضالة مسألة بس
+
+826
+01:30:01,190 --> 01:30:05,430
+تكامل هذا المقدرة تعرفوا تكملوا و الله كله كلام
+
+827
+01:30:05,430 --> 01:30:18,070
+يدرسين Calculus B تعرفوايعني نسيبه ؟
+
+828
+01:30:18,070 --> 01:30:25,030
+طيب نخلقلكم بس نحاول نفتح لكم المجال هذه يا بنات
+
+829
+01:30:25,030 --> 01:30:30,370
+بتاجي اخد الأولى تلاتة مع تلاتة بيظلي اتنين هو
+
+830
+01:30:30,370 --> 01:30:35,070
+عندك هنا تكامل تلاتة مع تلاتة بيظلي اتنين من Zero
+
+831
+01:30:35,070 --> 01:30:40,730
+لPi على اتنين و Cos تربيعيبقى نص في واحد زائد
+
+832
+01:30:40,730 --> 01:30:48,410
+كوصين اتنين ثيتا في دي ثيتا طبعا اللي بعدها تلتين
+
+833
+01:30:48,410 --> 01:30:55,190
+بتروح يبقى زائد اتنين في تكامل من Zero لغاية Y على
+
+834
+01:30:55,190 --> 01:31:01,990
+اتنين Zero لغاية Y على اتنين لمين اتنين تلت من
+
+835
+01:31:01,990 --> 01:31:04,350
+اتنين لكوصين
+
+836
+01:31:13,360 --> 01:31:19,300
+وهي تكمل من Zero لغاية Pi على اتنين كوصين أوصى
+
+837
+01:31:19,300 --> 01:31:23,440
+اربعة اللي هي كوصين تربيه في كوصين تربيه وكوصين
+
+838
+01:31:23,440 --> 01:31:29,480
+تربيه اللي هي النص في واحد زائد كوصين اتنين ثيتا
+
+839
+01:31:29,480 --> 01:31:37,210
+لكل تربيه دي ثيتاهذه نص مع اتنين الله يسهل عليها
+
+840
+01:31:37,210 --> 01:31:44,650
+يبقى بظل تكامل من zero لغاية pi على اتنين لواحد
+
+841
+01:31:44,650 --> 01:31:49,590
+زائد cosine اتنين theta كله في d theta يبقى هذا
+
+842
+01:31:49,590 --> 01:31:58,810
+فرق طيب هذا مناسب زائد اتنين تكامل من zero لغاية
+
+843
+01:31:58,810 --> 01:32:06,290
+pi على اتنين شو رأيك هذا؟مش هذه مشتقة الـSin وهذه
+
+844
+01:32:06,290 --> 01:32:10,030
+مشتقة الـSin تربية أي واحد ناقص Sin تربية يبقى
+
+845
+01:32:10,030 --> 01:32:19,490
+واحد ناقص Sin تربية ثيتا مشتقة Sin الثيتا ضالمين
+
+846
+01:32:19,490 --> 01:32:26,870
+عندنا ال term الأخير هذا نص تربية بيظل كده؟ ربع
+
+847
+01:32:26,870 --> 01:32:30,210
+ربع مع هذا بيظل كده؟ سُدس
+
+848
+01:32:34,780 --> 01:32:40,640
+تكامل من Zero لغاية Pi على أربع بدي أفك هذا بلد
+
+849
+01:32:40,640 --> 01:32:46,780
+بيصير واحد زائد اتنين Cos اتنين ثيتا زائد Cos
+
+850
+01:32:46,780 --> 01:32:53,980
+ثالابية اتنين ثيتا كله بالنسبة الى D ثيتا يبقى هذا
+
+851
+01:32:53,980 --> 01:32:58,820
+الكلام مثل الاول ان هي جاهزةيبقى ثيتا زائد sin
+
+852
+01:32:58,820 --> 01:33:04,480
+اتنين ثيتا على اتنين من Zero لغاية Pi على اتنين
+
+853
+01:33:04,480 --> 01:33:11,720
+اللي بعدها هذه كمان زائد اتنين في sin الزاوية ثيتا
+
+854
+01:33:11,720 --> 01:33:17,740
+ناقص sin تكيب الزاوية ثيتا على تلاتة من Zero لغاية
+
+855
+01:33:17,740 --> 01:33:26,640
+Pi على اتنين خلصنا منها، دا للاخيرة زائد ستهه
+
+856
+01:33:26,640 --> 01:33:34,580
+فاهمين في theta في theta زائد اتنين sin اتنين
+
+857
+01:33:34,580 --> 01:33:39,400
+theta اتنين بتروح وكل هذا الكلام من عند ال zero
+
+858
+01:33:39,400 --> 01:33:46,970
+لغاية ال pi على اربع و هنا زائد سُدس في تكاملمن
+
+859
+01:33:46,970 --> 01:33:52,890
+Zero لغاية الـ Pi على أربع كوصين تربيع اللي عبارة
+
+860
+01:33:52,890 --> 01:34:03,690
+عن من نص بواحد زائد كوصين أربعة ثيتا كل دي U7
+
+861
+01:34:03,690 --> 01:34:11,050
+Pi على اتنين زائد حطي هذا بيصير Pi ب Zero ناقص
+
+862
+01:34:11,050 --> 01:34:16,350
+Zero ناقص Zero خلصنا التر من الأول اللي بعدزاية
+
+863
+01:34:16,350 --> 01:34:21,350
+اتنين باي على اتنين مقدرش بواحد و sign باي على
+
+864
+01:34:21,350 --> 01:34:27,090
+اتنين بواحد يبقى ناقص طول واللي بعده ناقص زيرو
+
+865
+01:34:27,090 --> 01:34:33,730
+زائد زيرو خلاصنا ليش اللي بعده هذا زائد سادس هذا
+
+866
+01:34:33,730 --> 01:34:41,530
+السادس فيه باي على اربعة باي على اتنين كلها باي
+
+867
+01:34:41,530 --> 01:34:42,650
+على اتنين
+
+868
+01:34:45,420 --> 01:34:49,340
+كله باي على اتنين يبقى plus thirds في باي على
+
+869
+01:34:49,340 --> 01:34:54,880
+اتنين زائد باي على اتنين بزيرو ومش باقي بزيرو كله
+
+870
+01:34:54,880 --> 01:35:02,740
+بزيرو وصل لهذا زائد واحد على اتناشر في ثيتا زائد
+
+871
+01:35:02,740 --> 01:35:10,100
+صين اربعة ثيتا على اربع والكلام من زيرو لغاية باي
+
+872
+01:35:10,100 --> 01:35:16,320
+على اتنين يبقى الجواب باي على اتنينوهنا واحد ناقص
+
+873
+01:35:16,320 --> 01:35:22,520
+تلت بضل قداش تلتين في اتنين يبقى زائد اربع على
+
+874
+01:35:22,520 --> 01:35:30,040
+تلاتة واللي بعده زائد باي على اتناشر واللي بعده
+
+875
+01:35:30,040 --> 01:35:39,260
+زائد واحد على اتناشر في اللي في أمين زائد واحد على
+
+876
+01:35:39,260 --> 01:35:43,000
+اتناشر في باي على اتنين
+
+877
+01:35:45,950 --> 01:35:51,870
+زائد باي على اتنين ويبقى الاتنين باي بزيرو وهنا
+
+878
+01:35:51,870 --> 01:35:58,570
+زائد الباقى كلهم زيكي خلصت من هنا تطلع هي خلصناها
+
+879
+01:35:58,570 --> 01:36:07,290
+لك للاخر تقريبا طيب
+
+880
+01:36:07,290 --> 01:36:14,170
+بدنا منكم الآن المسائل التالية نبقى
+
+881
+01:36:14,170 --> 01:36:22,290
+exercisesاللي هي تلتاشر اربع مسائل تالية من واحد
+
+882
+01:36:22,290 --> 01:36:26,970
+دبي التسعة وتلاتين القادة.
+
+883
+01:36:34,890 --> 01:36:37,430
+حد عنده ايه التساؤل؟
+
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/ismnVpIzntA_raw.json b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/ismnVpIzntA_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..706a9b7a760f572f811879270e7a0c62b379c4df
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/ismnVpIzntA_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 268, "start": 0.0, "end": 2.68, "text": "موسيقى", "tokens": [2304, 41779, 1829, 4587, 7578], "avg_logprob": -0.3717447817325592, "compression_ratio": 0.5714285714285714, "no_speech_prob": 0.0029888153076171875, "words": [{"start": 0.0, "end": 2.68, "word": "موسيقى", "probability": 0.7351318359375}], "temperature": 1.0}, {"id": 2, "seek": 3176, "start": 13.4, "end": 31.76, "text": "بسم الله الرحمن الرحيم نرجع الان نكمل ال section تبع المرة الماضية أخدنا مجموعة من الأمثلة وضع لنا مثال أخير يقول مثال اللي قدامنا على اللي هو حدث المثال بيقول ما يأتي by the volume of the solid in the first octant bounded by", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 8717, 47341, 3615, 2423, 7649, 8717, 24793, 1211, 2423, 3541, 6055, 3555, 3615, 9673, 25720, 9673, 46958, 10632, 5551, 9778, 3215, 8315, 3714, 7435, 2304, 2407, 27884, 9154, 16247, 2304, 12984, 37977, 4032, 11242, 3615, 5296, 8315, 50113, 6027, 5551, 9778, 13546, 7251, 39648, 50113, 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هاي هاي معادلة الدائرة بقوله طب انا باخد هادي احسنلي احسنلي فى الشغل كيف احسنلك قال لي بس احسنلي بكيستر بيه على الشجرة تانية", "tokens": [4587, 9381, 9640, 7578, 6055, 36081, 995, 7251, 3794, 995, 45865, 36764, 24401, 7251, 3555, 4587, 7578, 2423, 9640, 11242, 8608, 995, 45865, 21136, 4117, 6024, 110, 995, 2407, 10632, 6055, 36081, 995, 48812, 45340, 9957, 43242, 7578, 48812, 6027, 9673, 3615, 18513, 37977, 13672, 7578, 43242, 8315, 11778, 7578, 20449, 18513, 37977, 32748, 16373, 25720, 4032, 9957, 20449, 18513, 37977, 32748, 16373, 25720, 8032, 47302, 20449, 18513, 37977, 32748, 16373, 25720, 4724, 39648, 3224, 1975, 3224, 4032, 9957, 8032, 47302, 8032, 47302, 20449, 18513, 37977, 32748, 16373, 25720, 4724, 39648, 3224, 23032, 3555, 1975, 8315, 4724, 47283, 3215, 8032, 995, 16254, 1975, 5016, 3794, 1863, 20292, 1975, 5016, 3794, 1863, 20292, 6156, 7578, 25124, 17082, 1211, 9122, 33911, 1975, 5016, 3794, 1863, 23275, 50239, 32239, 4724, 3794, 1975, 5016, 3794, 1863, 20292, 4724, 4117, 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"text": "خلّيني اذاكركم يا ناسيين لما جيتوا في احداثيات القطبين جيبتوا معادلة دائرة", "tokens": [9778, 1211, 11703, 9957, 1829, 1975, 15730, 37983, 24793, 35186, 8717, 32277, 1829, 9957, 5296, 15042, 10874, 36081, 14407, 8978, 1975, 24401, 5718, 104, 1829, 9307, 25062, 9566, 3555, 9957, 10874, 1829, 3555, 2655, 14407, 20449, 18513, 37977, 11778, 16373, 25720], "avg_logprob": -0.3028273830811183, "compression_ratio": 1.3979591836734695, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 3677.08, "end": 3677.84, "word": "خلّيني", "probability": 0.772021484375}, {"start": 3677.84, "end": 3678.74, "word": " اذاكركم", "probability": 0.7178955078125}, {"start": 3678.74, "end": 3678.86, "word": " يا", "probability": 0.89404296875}, {"start": 3678.86, "end": 3679.58, "word": " ناسيين", "probability": 0.69842529296875}, {"start": 3679.58, "end": 3685.06, "word": " لما", "probability": 0.58575439453125}, {"start": 3685.06, "end": 3685.82, "word": " جيتوا", "probability": 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المنطقة المظللة هذا يكون θ تساوي y على 2 وهذا يكون θ تساوي 0 تمام ؟ طيب إذا الخط الأزرق تبع المنخنامين R يساوي 1 ناقص في صين الزاوية", "tokens": [3224, 24192, 9673, 1863, 9566, 28671, 9673, 19913, 1211, 37977, 23758, 7251, 30544, 12622, 6055, 3794, 995, 45865, 288, 15844, 568, 37037, 15730, 7251, 30544, 12622, 6055, 3794, 995, 45865, 1958, 46811, 10943, 45520, 23032, 1829, 3555, 11933, 15730, 33962, 9566, 16247, 11622, 2288, 4587, 6055, 3555, 3615, 9673, 1863, 9778, 8315, 2304, 9957, 497, 7251, 3794, 995, 45865, 502, 8717, 995, 4587, 9381, 8978, 20328, 9957, 6024, 110, 995, 2407, 10632], "avg_logprob": -0.34332193087225094, "compression_ratio": 1.6413793103448275, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 4241.02, "end": 4241.38, "word": "هذه", "probability": 0.693603515625}, {"start": 4241.38, "end": 4242.26, "word": " المنطقة", "probability": 0.9666748046875}, {"start": 4242.26, "end": 4243.72, "word": " المظللة", "probability": 0.749755859375}, {"start": 4243.72, 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5797.43, "text": "اللي هي تلتاشر اربع مسائل تالية من واحد دبي التسعة وتلاتين القادة. حد عنده ايه التساؤل؟", "tokens": [6027, 20292, 39896, 6055, 1211, 2655, 33599, 2288, 1975, 25513, 3615, 47524, 16373, 1211, 6055, 6027, 10632, 9154, 36764, 24401, 11778, 21292, 16712, 3794, 27884, 34683, 1211, 9307, 9957, 25062, 18513, 3660, 13, 11331, 3215, 43242, 3224, 1975, 1829, 3224, 16712, 3794, 5718, 97, 1211, 22807], "avg_logprob": -0.3111702114977735, "compression_ratio": 1.4363636363636363, "no_speech_prob": 0.0, "words": [{"start": 5776.83, "end": 5777.29, "word": "اللي", "probability": 0.970947265625}, {"start": 5777.29, "end": 5777.55, "word": " هي", "probability": 0.96630859375}, {"start": 5777.55, "end": 5778.87, "word": " تلتاشر", "probability": 0.8767578125}, {"start": 5778.87, "end": 5779.59, "word": " اربع", "probability": 0.783447265625}, {"start": 5779.59, "end": 5780.41, "word": " مسائل", "probability": 0.8689778645833334}, {"start": 5780.41, "end": 5781.13, "word": " تالية", 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/ismnVpIzntA_raw.srt b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/ismnVpIzntA_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..80a718583fade5b20262f41a0f2623ac3dc6bae6
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/ismnVpIzntA_raw.srt
@@ -0,0 +1,3552 @@
+1
+00:00:00,000 --> 00:00:02,680
+موسيقى
+
+2
+00:00:13,400 --> 00:00:17,700
+بسم الله الرحمن الرحيم نرجع الان نكمل ال section
+
+3
+00:00:17,700 --> 00:00:21,120
+تبع المرة الماضية أخدنا مجموعة من الأمثلة وضع لنا
+
+4
+00:00:21,120 --> 00:00:24,640
+مثال أخير يقول مثال اللي قدامنا على اللي هو حدث
+
+5
+00:00:24,640 --> 00:00:29,420
+المثال بيقول ما يأتي by the volume of the solid in
+
+6
+00:00:29,420 --> 00:00:33,660
+the first octant bounded bythe coordinate planes
+
+7
+00:00:33,660 --> 00:00:37,720
+the cylinder x تربية زائد y تربية يساوي أربعة and
+
+8
+00:00:37,720 --> 00:00:42,760
+the plane z زائد y يساوي تلاتة إذن احنا في عندنا
+
+9
+00:00:42,760 --> 00:00:48,880
+مجسم هذا المجسم ده محدود
+
+10
+00:00:48,880 --> 00:00:54,340
+من أعلى و كذلك محدود من أسفل كيف؟ قاللي هذا المجسم
+
+11
+00:00:54,340 --> 00:01:01,290
+موجود في الثمني الأولو محاط بمستويات الاحداثيات
+
+12
+00:01:01,290 --> 00:01:06,130
+bounded by the coordinate planes يبقى هاي مستويات
+
+13
+00:01:06,130 --> 00:01:11,790
+الاحداثيات اللي عندنا والسيلندر والاسطوانة X تربيه
+
+14
+00:01:11,790 --> 00:01:16,930
+زاد Y تربيه تسوى أربعة and the plane Y زائد Z بده
+
+15
+00:01:16,930 --> 00:01:22,330
+يسوى كده تلاتة طيب احنا بيمكن اروح نرسم هذه
+
+16
+00:01:22,330 --> 00:01:25,930
+المنطقة ولو انه ليس بالضرورة لأن المرة اللي فاتت
+
+17
+00:01:25,930 --> 00:01:31,130
+أخدنا ال volumeتكاملين عالمين على ال z لل function
+
+18
+00:01:31,130 --> 00:01:36,430
+دي اكس دي واي او دي واي دي اكس بجيب الحجب لكن اذا
+
+19
+00:01:36,430 --> 00:01:40,010
+حاببنا نستزيد و نعرف ما هو الشكل بنقول الشكل
+
+20
+00:01:40,010 --> 00:01:45,550
+كالتالي خلّي بالكم معناه الان لو جيت كنت هذا محور
+
+21
+00:01:45,550 --> 00:01:54,790
+X وهذا محور Y وهذا محور Z الشكل يعني هذا Y كبرناه
+
+22
+00:01:54,790 --> 00:02:04,440
+شويةهذا محور Y وهذا محور Z يقل المجسم محاض
+
+23
+00:02:04,440 --> 00:02:09,780
+بمستويات الإحداثية يبقى المستوى XY منشجع المستوى
+
+24
+00:02:09,780 --> 00:02:14,280
+YZ منشجع المستوى XY منشجع ليش انه يقل في الثمن
+
+25
+00:02:14,280 --> 00:02:19,820
+الأول يبقى في الثمن اللي جهتنا هذاقال لي هو في
+
+26
+00:02:19,820 --> 00:02:23,580
+عندي أسطوانة يبقى الأسطوانة يا بنات لو روحنا و
+
+27
+00:02:23,580 --> 00:02:28,240
+قولنا هذه هي مين هذه هي الأسطوانة اللي عندنا هذا
+
+28
+00:02:28,240 --> 00:02:32,440
+جزء منها اللي في الثمن اللي جهتنا بقيتها بتكون
+
+29
+00:02:32,440 --> 00:02:36,100
+وين؟ في الشجرة التانية ماعناش علاقة فيها احنا إنا
+
+30
+00:02:36,100 --> 00:02:40,720
+علاقة وين؟ في اللي جهتنا كويس يبقى بدأ فيجي جزء من
+
+31
+00:02:40,720 --> 00:02:45,280
+الأسطوانة يجي لي هنا كمان بالشكل اللي عندها دايما
+
+32
+00:02:46,230 --> 00:02:51,350
+واضح كويس لأن الأسطوان لسه لها جزء باقي ها جوز زي
+
+33
+00:02:51,350 --> 00:02:55,630
+هيك ترسمش استني شوية بس بدي أريك إياها و بعد هيك
+
+34
+00:02:55,630 --> 00:02:59,850
+همسحها لإنه بدنا نجيب المستوى يبقى فاق الأسطوان
+
+35
+00:02:59,850 --> 00:03:04,290
+هتيجيك زي هيك بالشكل اللي عندنا هذايبقى بده يجيكي
+
+36
+00:03:04,290 --> 00:03:08,410
+هذا الجزء بالشكل هذا يبقى هذا الجزء من الوصوان
+
+37
+00:03:08,410 --> 00:03:13,070
+اللي وين لجهتنا لكن في عندنا شغلة تانية ايش الشغلة
+
+38
+00:03:13,070 --> 00:03:18,350
+التانية اللي محطة من اعلى بالمستوى y زائد z يسوى
+
+39
+00:03:18,350 --> 00:03:22,330
+كدهش يسوى تلاتة اللي فوق هذا مستوى افق اللي احنا
+
+40
+00:03:22,330 --> 00:03:29,430
+رسمينه هذا مستوى موازي لهذابنروح نرسم هذا المستوى
+
+41
+00:03:29,430 --> 00:03:34,190
+لما قالي المستوى y زائد z يساوي تلاتة بجي بقوله لو
+
+42
+00:03:34,190 --> 00:03:39,910
+كانت z ب zero يبقى y بتجيني تلاتة إذا في عندي نقطة
+
+43
+00:03:39,910 --> 00:03:43,370
+عن هذه اللي هو الأسطولة نصف قطرة الدفعة تبعها
+
+44
+00:03:43,370 --> 00:03:49,730
+قداشر اتنين يبقى تلاتة بتجيني هنا مصبوط إذا
+
+45
+00:03:49,730 --> 00:03:57,470
+المستوى هيمر بنقطة zero وتلاتة وزيدز بزيرو و X في
+
+46
+00:03:57,470 --> 00:04:01,590
+الاصل مش موجودة يعني بزيرو بضل انمين و Y تساوي
+
+47
+00:04:01,590 --> 00:04:06,890
+تلاتة طيب بدي اجيب التقطع مع محور Z من فوق يبقى
+
+48
+00:04:06,890 --> 00:04:13,310
+بحط Y عندي بقداش بزيرو تصير Z بقداش تلاتة يبقى بده
+
+49
+00:04:13,310 --> 00:04:18,950
+يجينا عنها هاتف لو جيتك و افترض جدلا ان هذه النقطة
+
+50
+00:04:18,950 --> 00:04:25,950
+هي زيرو و زيرو و تلاتةيبقى بيننا نرسم هذا المستوى
+
+51
+00:04:25,950 --> 00:04:33,390
+بلون أخر يبقى
+
+52
+00:04:33,390 --> 00:04:36,710
+بيجي بقول أنا عندي مستوى بالشكل اللي عندي هذا
+
+53
+00:04:42,450 --> 00:04:49,370
+و يجينا من هنا على اللي هو هذا بالضبط و ايه بجيته
+
+54
+00:04:49,370 --> 00:04:54,470
+هك بهذا الشكل و بدي جيك المستوى بالشكل اللي عندها
+
+55
+00:04:54,470 --> 00:05:02,010
+لأن الأزرق هو المستوى من y زائد z سوى قداش تلاتة
+
+56
+00:05:02,010 --> 00:05:08,210
+إذا هذا الأزرق هو اللي يخلين z زائد y سوى قداش
+
+57
+00:05:08,210 --> 00:05:14,280
+تلاتةإذا يا بنات هذا المستوى هيقص الأسطوان الجزء
+
+58
+00:05:14,280 --> 00:05:19,140
+هذا اللي فوق مش هيظهر ايوة يبقى هتظهر وين نقطة
+
+59
+00:05:19,140 --> 00:05:24,500
+عندنا زي مين زي النقطة اللي عندنا هذه تمام ويصير
+
+60
+00:05:24,500 --> 00:05:31,580
+عندي قوس قوس موخود بهذا الشكل يبقى الخط الأسود هذا
+
+61
+00:05:31,580 --> 00:05:37,280
+هما هذا كله هينقص ويروح بصير مالوش وجودة
+
+62
+00:05:39,720 --> 00:05:47,040
+يبقى بصير ان هذا المستوى المائل من فوق هذا هو
+
+63
+00:05:47,040 --> 00:05:51,420
+المستوى الأزرق اللى موجود عندنا فوق اللى هو مين هو
+
+64
+00:05:51,420 --> 00:05:57,180
+y زائد z يساوي تلاتة ليش انه جزء من المستوى الأزرق
+
+65
+00:05:57,180 --> 00:06:01,160
+اللى احنا شايفه انه يبقى هذا اللى فوق هو كمان z
+
+66
+00:06:01,160 --> 00:06:05,580
+زائد y يساوي تلاتة نفس المستوى اللى احنا بنحكي
+
+67
+00:06:05,580 --> 00:06:13,210
+عليه طيبيبقى لان بدنا نروح نجيب قداش مقدار الحجم
+
+68
+00:06:13,210 --> 00:06:16,790
+اللي عندنا هذا ماخديني بقى كويس يبقى اللي تحت هذه
+
+69
+00:06:16,790 --> 00:06:23,550
+عبارة عن دائرة او جزء من دائرة ربعي الدائرة وهي
+
+70
+00:06:23,550 --> 00:06:27,870
+على الطبيعة لو حبيت اوريهالك بقولك هذا اللي هو
+
+71
+00:06:27,870 --> 00:06:32,710
+محور X وهذا محور Y حسب ما هو موجود على الطبيعة على
+
+72
+00:06:32,710 --> 00:06:36,510
+الرسمة وهي الدائرة اللي عندنا بالشكل اللي عندنا
+
+73
+00:06:36,510 --> 00:06:41,870
+هذايبقى هذه المنطقة المظللة هي المنطقة المظللة
+
+74
+00:06:41,870 --> 00:06:47,770
+اللى تحت الأدنى طبعا يجب ان اقوله بدي ال volume V
+
+75
+00:06:47,770 --> 00:06:56,290
+solution بدي ال volume V إذا بدي سوى تكامل على
+
+76
+00:06:56,290 --> 00:07:04,570
+مين؟ على Z دي ايه على المنطقة A مش هكذا المرة اللى
+
+77
+00:07:04,570 --> 00:07:09,070
+فاتت؟الـ Volume المحصور بين مجسم بين سطح فوق
+
+78
+00:07:09,070 --> 00:07:13,190
+ومستوى الـ XY plane هو بالشكل اللي عندنا هذا
+
+79
+00:07:13,190 --> 00:07:17,330
+واطلنا اكوا على ذلك مثالين هذا هو المثال الرقم
+
+80
+00:07:17,330 --> 00:07:21,910
+تلاتة يبقى هذا الكلام بديه يسوي تكاملين بدي اشيل
+
+81
+00:07:21,910 --> 00:07:27,550
+ال Z و احط قيمتها كده كم تزد هنا بنات تلاتة ناقص Y
+
+82
+00:07:27,550 --> 00:07:34,100
+يبقى تلاتة ناقص Y هي قيمة ال Zبدي اتكامل بالنسبة
+
+83
+00:07:34,100 --> 00:07:38,660
+الى X بمشي الحال في الاول او بدي اتكامل بالنسبة
+
+84
+00:07:38,660 --> 00:07:41,800
+الى Y بمشي الحال سواء كان هذه او تلك الاتنين
+
+85
+00:07:41,800 --> 00:07:47,020
+بيهدئي لنفس النتيجة اذا بروح اشوف X بدها تتغير من
+
+86
+00:07:47,020 --> 00:07:53,160
+وين لوين فبجي على المنطقة التكامل و برسم خط يقطع
+
+87
+00:07:53,160 --> 00:08:00,160
+منطقة التكامل وموازن لمحور X كده ايش قيمة X عند
+
+88
+00:08:00,160 --> 00:08:00,760
+هذه النقطة
+
+89
+00:08:04,210 --> 00:08:10,270
+هنا لم يكن هناك قيمة x على محور واحد قيمة x هو 0
+
+90
+00:08:10,270 --> 00:08:14,910
+من هنا مش هي نقطة الأصل يبقى على محور واحد قيمة x
+
+91
+00:08:14,910 --> 00:08:20,170
+بزيرو أنا ارسل خط مودي لمحور x أيه في أصل التوضيع
+
+92
+00:08:20,170 --> 00:08:26,430
+تمام يبقى هنا x تساوي 0 الخط اللي عندي هذا الجثة
+
+93
+00:08:26,430 --> 00:08:32,830
+ده معادلة مين؟مقادرة الأسطوانة أو قاعدة الأسطوانة
+
+94
+00:08:32,830 --> 00:08:37,750
+وهي عبارة عن دائرة إذا بدّر أجيب قداش X تساوي من
+
+95
+00:08:37,750 --> 00:08:43,530
+هنا قداش X تساوي أربعة ناقص Y تربيع تحت الجدر
+
+96
+00:08:43,530 --> 00:08:49,110
+التربيع إذا إن هنا بيكون ال X بتساوي الجدر التربيع
+
+97
+00:08:49,110 --> 00:08:54,710
+لأربعة ناقص Y تربيعاللي هي معادلة مين؟ معادلة
+
+98
+00:08:54,710 --> 00:09:01,510
+الدائرة اللي عندها إذا ال X ستتغير من Zero لغاية
+
+99
+00:09:01,510 --> 00:09:08,430
+كدهش لغاية الجذري التربيعي لأربعة ناقص Y تربيع بلت
+
+100
+00:09:08,430 --> 00:09:13,310
+عندي Y ده تتغير من وين و وين بناها من صفر لغاية
+
+101
+00:09:13,310 --> 00:09:17,450
+اتنين لأن نصف قطر القاعدة اللي هو كدهش باتنين هذا
+
+102
+00:09:17,450 --> 00:09:22,870
+النقطة اللي هي اتنينيبقى من 0 ل 2 إذا كتبنا
+
+103
+00:09:22,870 --> 00:09:27,210
+المعادلة صحيحة صارت مسألتنا بسيطة جدا خلاص شغل
+
+104
+00:09:27,210 --> 00:09:30,950
+روتيني ضال بنكامل ونطلع كمية ال volume اللي عندنا
+
+105
+00:09:30,950 --> 00:09:35,730
+كويس فبعدين بكمل بقول هذا الكلام بدى يساوي
+
+106
+00:09:35,730 --> 00:09:41,100
+integration من 0 ل 2لتلاتة ناقص y مالكش دعوة كله
+
+107
+00:09:41,100 --> 00:09:45,960
+constant و تكامله نسبة ل dx اللي هو ب X و الكلام
+
+108
+00:09:45,960 --> 00:09:52,040
+هذا من zero لجدري التربيع لاربع ناقص y تربيع dy أو
+
+109
+00:09:52,040 --> 00:09:57,880
+ان شئتولنا فقولنا تكامل من صفر للإتنين لتلاتة ناقص
+
+110
+00:09:57,880 --> 00:10:04,240
+y الجدري التربيع لاربع ناقص y تربيع ناقص zero بروح
+
+111
+00:10:04,240 --> 00:10:06,000
+و كل هذا ب 100
+
+112
+00:10:12,140 --> 00:10:17,180
+ما بيكونش إذا بدنا نروح نكامل الدالة اللي عندنا
+
+113
+00:10:17,180 --> 00:10:25,180
+هذه و نشوف كيف بدنا نكاملها تمام؟ قدامك بدل الخيار
+
+114
+00:10:25,180 --> 00:10:31,680
+اتنين لو جيت طلعت فصلت إلى جزين قلت تلاتة في الجذر
+
+115
+00:10:31,680 --> 00:10:35,640
+ناقص واي في الجذر ناقص واي في الجذر بصير اللي برا
+
+116
+00:10:35,640 --> 00:10:40,500
+الجذر هومش تقت ما تحت الجذر بيصير سهل لكن تلاتة في
+
+117
+00:10:40,500 --> 00:10:45,700
+الجذر ماليش إلا Trigonometric Substitution يبقى
+
+118
+00:10:45,700 --> 00:10:49,440
+مدام هيك خليها كلها على بعضها Trigonometric
+
+119
+00:10:49,440 --> 00:10:55,560
+Substitution يعني التعويض بدالة مثلثية أيوة نرجع ل
+
+120
+00:10:55,560 --> 00:11:01,980
+Calculus B Calculus B أخدنا section فيه في التكامل
+
+121
+00:11:01,980 --> 00:11:07,580
+اللي هو التعويض بدالة مثلثيةولا لو كان عندى جذر
+
+122
+00:11:07,580 --> 00:11:12,620
+بقدر اطيّر هذا الجذر بالتعويضة المثلثية بس بده
+
+123
+00:11:12,620 --> 00:11:18,320
+تعويضة مثلثية مناسبة مش اي تعويضة بطل على القيمة
+
+124
+00:11:18,320 --> 00:11:22,240
+اللى تحت الجذر والله إذا الإشارة بالموجة بين
+
+125
+00:11:22,240 --> 00:11:27,580
+القمسات بتعويضة بدلالي الطاقة وإذا كان ناقص بطل عن
+
+126
+00:11:27,580 --> 00:11:32,820
+ناقص هل هو للمتغير والله المقدار الثامنإذا للمقدار
+
+127
+00:11:32,820 --> 00:11:37,400
+الثابت التعويضة بدلالة سيك ثيتا وإذا كان الإشارة
+
+128
+00:11:37,400 --> 00:11:42,460
+السلبية المتغيرة يبقى التعويضة بدلالة ساين الزاوية
+
+129
+00:11:42,460 --> 00:11:48,080
+ثيتا إذا تعوضتنا هنا كم ستكون تلقاه اتنين ساين
+
+130
+00:11:48,080 --> 00:11:48,780
+ثيتا
+
+131
+00:11:55,920 --> 00:12:01,540
+Y تساوي اتنين في صين الزاوية تيتا وطبعا تيتا
+
+132
+00:12:01,540 --> 00:12:07,100
+مخصورة بين سالب باي على اتنين و باي على اتنين يبقى
+
+133
+00:12:07,100 --> 00:12:14,900
+DY تساوي اتنين Cos θ Dθ إذا انقلت المسألة إلى
+
+134
+00:12:14,900 --> 00:12:21,860
+الشكل التالي تساوي تكامل و هنا تلاتة ناقص اتنين
+
+135
+00:12:21,860 --> 00:12:28,060
+صين الزاوية تيتا اتنينصين الزاوية ثيتا في الجذر
+
+136
+00:12:28,060 --> 00:12:35,580
+التربيهي ليه؟ مين؟ أربعة ناقص أربعة في صين تربية
+
+137
+00:12:35,580 --> 00:12:41,360
+الزاوية ثيتا في دي اكس اللي هو باتنين قصين ثيتا في
+
+138
+00:12:41,360 --> 00:12:49,130
+دي ثيتا مين ضايق عندي يا بنات؟ حدود التكاملبعدين
+
+139
+00:12:49,130 --> 00:12:53,670
+بقوله لما نكون ال Y ب 2 يبقى بده أشيل Y و أحط
+
+140
+00:12:53,670 --> 00:12:58,630
+مكانها 2 معناته sine theta كده تساوي واحد مين
+
+141
+00:12:58,630 --> 00:13:02,550
+الزاوية اللي جيبها تساوي واحد باي على اتنين يبقى
+
+142
+00:13:02,550 --> 00:13:08,830
+بده يصير هنا باي على اتنين بعد هيك لو كانت ال Y ب
+
+143
+00:13:08,830 --> 00:13:13,950
+Zero حط Zero بصير sine theta تساوي Zero يبقى ب
+
+144
+00:13:13,950 --> 00:13:20,910
+Zero إذاحدود التكامل المكافئة لـ0 و 2 لما كان
+
+145
+00:13:20,910 --> 00:13:27,210
+المتغير Y هي 0 و باية 2 لما صار المتغير بدلالة θ
+
+146
+00:13:27,210 --> 00:13:32,250
+يبقى صار عندنا التكامل هذا طيب نجرّط بمثلتنا هك و
+
+147
+00:13:32,250 --> 00:13:38,450
+نشوف قداش ماتطلع هذه قداش بتطلع يا بناتأربعة واحد
+
+148
+00:13:38,450 --> 00:13:41,670
+نقص sin تربيع اللي هو cos تربيع تطلع من تحت الجانب
+
+149
+00:13:41,670 --> 00:13:46,810
+باتنين cosine وعندي اتنين cosine يبقى أربعة خليها
+
+150
+00:13:46,810 --> 00:13:51,310
+برا وضل عندي cosine تربيع يبقى الأربعة بتطلع برا
+
+151
+00:13:51,310 --> 00:13:56,450
+هنا ههه و باجي بقول تكامل من zero to pi على اتنين
+
+152
+00:13:56,450 --> 00:14:02,830
+لتلاتة نقص اتنين sin زاوية ثيتا في cosine تربيع
+
+153
+00:14:02,830 --> 00:14:10,740
+ثيتا في d ثيتاطب بدأ افك هذه يبقى هذه بدها تساوي
+
+154
+00:14:10,740 --> 00:14:23,360
+اللي همين 3×4 ب12 تكامل من 0 لغاية Pi على 4 لcos²θ
+
+155
+00:14:23,360 --> 00:14:31,850
+dθ ناقصهندك أربعة في اتنين بتمانية وهيتكاول من صفر
+
+156
+00:14:31,850 --> 00:14:38,070
+لغاية باي على اتنين لمين؟ لـ sin θ cos تربيع θ sin
+
+157
+00:14:38,070 --> 00:14:42,190
+θ cos تربيع θ في dθ
+
+158
+00:14:44,700 --> 00:14:49,400
+فكت الأقواص ووزعت التكامل لكل واحدة منهم طبعا
+
+159
+00:14:49,400 --> 00:14:53,960
+الأولين ماقدرش أكملها إلا أحولها بدلالة ضعف
+
+160
+00:14:53,960 --> 00:14:59,280
+الزاوية Cos تربيع نص في واحد زائد Cos اتنين فيها
+
+161
+00:14:59,280 --> 00:15:04,320
+يبقى هذه يا بنات بدأت تصير اتناشر مضروبة في نص في
+
+162
+00:15:04,320 --> 00:15:08,180
+تكامل من Zero لغاية Pi باي على اتنين
+
+163
+00:15:13,480 --> 00:15:18,580
+يبقى من zero ل πاى على اتنين لواحد زائد كوصين
+
+164
+00:15:18,580 --> 00:15:22,900
+اتنين في ده كله في دي دي ده
+
+165
+00:15:30,180 --> 00:15:38,440
+8 تكامل من 0 لπ على 2 ل cos تربية فيتا شو رايك sin
+
+166
+00:15:38,440 --> 00:15:45,680
+فيتا بفيتا أليست هي مشتقة cos فيتا صح ولا لا يبقى
+
+167
+00:15:45,680 --> 00:15:53,220
+بقدر اتبع هذه هي D لفو sin فيتا بس مشتقة ال cosine
+
+168
+00:15:53,220 --> 00:15:59,760
+ابسالب sin يبقى هذه لو خلتها موجة بقي ماسويتش شيء
+
+169
+00:16:00,510 --> 00:16:06,790
+يبقى أبدًا شيلت sin θ cos θ و كتبها دالها d cos θ
+
+170
+00:16:06,790 --> 00:16:11,330
+تمام يبقى صارت المثلة بالشكل اللي قدامنا هذا طيب
+
+171
+00:16:11,330 --> 00:16:16,890
+اتناشر في نص القداش بستة وهذه عبارة عن ثيتا زائد
+
+172
+00:16:16,890 --> 00:16:21,910
+sin اتنين ثيتا على اتنين الكلام من zero لغاية pi
+
+173
+00:16:21,910 --> 00:16:28,900
+على اتنينوهذه زائد تمانية على تلاتة كوصين تكييب
+
+174
+00:16:28,900 --> 00:16:35,340
+ثيتا من zero لغاية كده؟ باي على اتنين هذا الكلام
+
+175
+00:16:35,340 --> 00:16:42,540
+يسوى ستة في باي على اتنين زائد بدا اشيل ثيتا و احط
+
+176
+00:16:42,540 --> 00:16:45,260
+باي على اتنين و اتروح اتنين مع اتنين و يبقى sign
+
+177
+00:16:45,260 --> 00:16:46,360
+باي كده؟
+
+178
+00:16:54,070 --> 00:17:12,250
+زائد تمانية على تلاتة في نقص
+
+179
+00:17:12,250 --> 00:17:15,110
+نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص
+
+180
+00:17:15,110 --> 00:17:18,730
+نقص نقص نقص نقص نقص نقص نقص نقص نقصناقص تمانية على
+
+181
+00:17:18,730 --> 00:17:24,690
+تلاتة يعني قداش كله على تلاتة تسعة بايت ناقص
+
+182
+00:17:24,690 --> 00:17:30,490
+تمانية كله على تلاتة مقدار الحجم المطلوب
+
+183
+00:17:57,700 --> 00:17:58,600
+امسحها بنات
+
+184
+00:18:21,480 --> 00:18:24,720
+طب الحكي اللى اتحاكناه من اول ما بدأنا هذا ال
+
+185
+00:18:24,720 --> 00:18:28,460
+chapter و الى يومنا هذا حتى هذه اللحظة كان على ال
+
+186
+00:18:28,460 --> 00:18:32,220
+double integral in cartesian coordinates كان
+
+187
+00:18:32,220 --> 00:18:37,060
+المتغيرات x y لكن احنا روحنا في كل كلاص بيدرسنا
+
+188
+00:18:37,060 --> 00:18:41,380
+احداثيات جديدة سميناها ال polar coordinates فماهي
+
+189
+00:18:41,380 --> 00:18:44,780
+اخبار ال double integral in polar coordinates هذا
+
+190
+00:18:44,780 --> 00:18:47,760
+موضوع ال section 15-4
+
+191
+00:19:15,060 --> 00:19:20,940
+يبقى التكاملات الثنائية في الإحداثيات القطبية
+
+192
+00:19:23,230 --> 00:19:26,650
+نعطي تعريف وبناء على هذا التعريف نبدأ نشتغل
+
+193
+00:19:26,650 --> 00:19:35,030
+Definition بيقول ما يأتي definition f ال function
+
+194
+00:19:35,030 --> 00:19:40,090
+f كانت دالة في r و theta بدل ما كنا نقول x و y
+
+195
+00:19:40,090 --> 00:19:50,660
+هنقول r و theta is defined function دالة معرفةover
+
+196
+00:19:50,660 --> 00:20:02,920
+a region a over a region a bounded bounded by the
+
+197
+00:20:02,920 --> 00:20:13,040
+rays by the rays بالشعيني theta تساوي alpha و
+
+198
+00:20:13,040 --> 00:20:24,150
+theta تساوي beta and by the continuousand by the
+
+199
+00:20:24,150 --> 00:20:36,470
+continuous curves بالمنحنيات المتصلة R تساوي G1 of
+
+200
+00:20:36,470 --> 00:20:48,450
+theta وR تساوي G2 of theta G2 of theta with
+
+201
+00:20:50,370 --> 00:20:55,390
+الـ zero أقل من أو يساوي g1 of theta أقل من أو
+
+202
+00:20:55,390 --> 00:21:04,010
+يساوي g2 of theta نحن ندفع الانتجار نحن ندفع
+
+203
+00:21:04,010 --> 00:21:07,650
+الانتجار
+
+204
+00:21:07,650 --> 00:21:13,330
+of
+
+205
+00:21:13,330 --> 00:21:22,400
+ال function f of r و theta overالـ Region R by
+
+206
+00:21:22,400 --> 00:21:32,760
+تكاملين على الـ R لمين؟ للـ F of R وثيتا D A يسوى
+
+207
+00:21:32,760 --> 00:21:44,720
+تكاملين للـ F of R وثيتا في الـ R D R D ثيتاوهنا r
+
+208
+00:21:44,720 --> 00:21:51,840
+تساوي g1 of theta وهنا r تساوي g2 of theta وهنا
+
+209
+00:21:51,840 --> 00:21:59,940
+theta تساوي alpha وهنا theta تساوي beta command
+
+210
+00:21:59,940 --> 00:22:08,020
+definition تاني the area the
+
+211
+00:22:08,020 --> 00:22:15,210
+area of a closed bounded region of aبقرة مغلقة
+
+212
+00:22:15,210 --> 00:22:20,090
+بقرة
+
+213
+00:22:20,090 --> 00:22:37,210
+مغلقة بقرة مغلقة بقرة مغلقة بقرة مغلقة بقرة مغلقة
+
+214
+00:22:42,790 --> 00:22:55,290
+احداثيات القطبية الـ
+
+215
+00:22:55,290 --> 00:23:03,990
+A تساوي تكاملين على R لـ D A والرمز يساوي تكاملين
+
+216
+00:23:03,990 --> 00:23:07,730
+على R لـ R DR D
+
+217
+00:23:16,120 --> 00:23:21,420
+أيه اللي بتحكي؟ ولا
+
+218
+00:23:21,420 --> 00:23:27,520
+يهمك بسيطة
+
+219
+00:23:27,520 --> 00:23:32,160
+ايه
+
+220
+00:23:32,160 --> 00:23:41,820
+هو جمال public exercises عشر اتنين مثال من تسعة
+
+221
+00:23:41,820 --> 00:23:52,930
+لغاية أربعة تمثيلmultiple of three مباعظة تلاتة
+
+222
+00:23:52,930 --> 00:24:00,790
+ومن سبعة وخمسين لغاية خمسة وستين في العالم
+
+223
+00:24:15,470 --> 00:24:20,090
+نرجع الكلام اللي احنا كاتبينه و نحاول نفهم كل نقطة
+
+224
+00:24:20,090 --> 00:24:25,110
+احنا كاتبينها وسنحاول نرسم حتى نوضح الكلام اللي
+
+225
+00:24:25,110 --> 00:24:29,970
+بين ايدنا هذا لذلك لو روحت اخدت محاور يبقى من هذا
+
+226
+00:24:29,970 --> 00:24:34,230
+الشكل و روحت قلت هذا θ تساوي zero
+
+227
+00:24:38,330 --> 00:24:42,290
+اللي هو الاحداثيات القطبية او المحاور في الاحداث
+
+228
+00:24:42,290 --> 00:24:46,150
+القطبية المكتوب تقول x و y بقول θ تساوي zero و θ
+
+229
+00:24:46,150 --> 00:24:52,410
+تساوي باي على اتنى جيت رسمت اللي هو المنحليين
+
+230
+00:25:04,030 --> 00:25:12,550
+يبقى اتنين دوال موجبة يبقى وتنتين واحدة منهم اكبر
+
+231
+00:25:12,550 --> 00:25:17,530
+من التانية فمثلا لو روحت قلت على سبيل المثال هذا
+
+232
+00:25:17,530 --> 00:25:24,560
+المنحنى R تساوي G one of thetaو جينا يقولنا فيها
+
+233
+00:25:24,560 --> 00:25:34,020
+المنحنة تاني كان بالشكل هذا R تساوي G E2 of θ قال
+
+234
+00:25:34,020 --> 00:25:41,060
+لي θ هذه اتغيرت من θ تساوي Alpha قلت هذا الخط θ
+
+235
+00:25:41,060 --> 00:25:48,500
+تساوي Alpha إلى الخط التاني θ تساوي Beta اذا ما
+
+236
+00:25:48,500 --> 00:25:52,280
+بدت بقول
+
+237
+00:25:52,280 --> 00:25:57,350
+مرة تانيةمن خلال الـ definition هذا بدنا نحدد
+
+238
+00:25:57,350 --> 00:26:03,010
+منطقة التكامل اللي عندنا طبعا هي يصير θ تتغير من θ
+
+239
+00:26:03,010 --> 00:26:07,630
+تسوى Alpha إلى θ تسوى Beta يعني عند الخط θ تسوى
+
+240
+00:26:07,630 --> 00:26:12,570
+Alpha إلى الخط θ تسوى Beta لكن R اتغيرت من G1 of θ
+
+241
+00:26:12,570 --> 00:26:18,580
+لمين ل G2 of θ فصالي مينبالشكل اللي عندنا هذا بقيت
+
+242
+00:26:18,580 --> 00:26:23,780
+المشكلة اولا عن R من اين جاء بعد ما اعطينا جزء
+
+243
+00:26:23,780 --> 00:26:26,500
+النظر التابع اللي هو ال polar coordinates او ال
+
+244
+00:26:26,500 --> 00:26:29,800
+double integral ال polar coordinates نبدأ في اخذ
+
+245
+00:26:29,800 --> 00:26:34,200
+بعض اللامثلة قال لي اوصفلي المنطقة المرسومة يعني
+
+246
+00:26:34,200 --> 00:26:38,600
+هو اعطاني هذه الرسمة كويس الرسمة موجودة في الكتابة
+
+247
+00:26:38,600 --> 00:26:43,690
+السؤال في الكتابةهو قال لي عبر عن هذه الرسمة وهي
+
+248
+00:26:43,690 --> 00:26:49,070
+ضللتك إياها بمين بالإحداثيات القطبية، أعطاني هذا
+
+249
+00:26:49,070 --> 00:26:53,230
+واحد و أعطاني هنا جدر ثلاثة، بهذا الطول جدر ثلاثة،
+
+250
+00:26:53,230 --> 00:26:58,510
+بحسب فيثة غورفالضلة التانية كم؟ اتنين يبقى احنا
+
+251
+00:26:58,510 --> 00:27:03,830
+امام مثلة تلاتين ستين واحد وجذر تلاتة واثنين من
+
+252
+00:27:03,830 --> 00:27:06,950
+خواص المثلة التلاتين الستين الدولة المقابلة زوج
+
+253
+00:27:06,950 --> 00:27:12,990
+تلاتين يساوي نص الوتر يبقى هيوم يساوي كم نص الوتر
+
+254
+00:27:12,990 --> 00:27:17,600
+يبقى هذا زوج تلاتين درجة وهذا زوج الإيمان60 درجة
+
+255
+00:27:17,600 --> 00:27:22,000
+باي على تلاتة وديك باي على ستة إذا بدنا نعبر عن
+
+256
+00:27:22,000 --> 00:27:26,160
+هذه هه بمين بالإحداثية القطبية بقوله المنطقة
+
+257
+00:27:26,160 --> 00:27:31,020
+المضللة محصورة بين theta تساوي zero و theta تساوي
+
+258
+00:27:31,020 --> 00:27:36,080
+قداش باي على تلاتة ضايل عندنا R بدنا نعرف من وين
+
+259
+00:27:36,080 --> 00:27:40,660
+لوين يفجأر يا بنات بده يبدأ من النقطة الأصل اللي
+
+260
+00:27:40,660 --> 00:27:45,100
+عنده ويظل رايح لغاية ما يجيب الميمما يقابل الخط
+
+261
+00:27:45,100 --> 00:27:49,960
+اللى عندنا هذا اللى هو الرأسي طب هذا معطى كارتيزيا
+
+262
+00:27:49,960 --> 00:27:55,040
+انا بديه polar بقول هذا الخط اللى هو مين
+
+263
+00:27:58,100 --> 00:28:04,400
+X هي R كوصين الزاوية تساوي واحد الكوصين قداش واحد
+
+264
+00:28:04,400 --> 00:28:11,040
+على second مظبوط اضرب كله في second تصير ال R
+
+265
+00:28:11,040 --> 00:28:17,580
+تساوي سك الثيتا في واحد لو سك الثيتا يبقى R ستتغير
+
+266
+00:28:17,580 --> 00:28:23,240
+من zero لغاية اي نقطة على هذا الخط الخط هذا معادلة
+
+267
+00:28:23,240 --> 00:28:31,400
+تسيك ثيتا يبقى وال Rأكبر من أو تساوي zero أقل من
+
+268
+00:28:31,400 --> 00:28:40,100
+أو يساوي 106 ثيتر نمر بيه من السؤال نمر بيه من
+
+269
+00:28:40,100 --> 00:28:45,040
+السؤال ماعطيني رسمة و الرسمة بالشكل هذا طلعوني
+
+270
+00:28:45,040 --> 00:28:51,120
+كويس هذا محور X وهذا محور Y وهذا نقطة الأصل اللي
+
+271
+00:28:51,120 --> 00:28:58,420
+هو Zero وماعطيني بوسك وقال هنا 1 هناو بعد هيك راح
+
+272
+00:28:58,420 --> 00:29:12,580
+اعملي مصطاطيل هيك او قلي المصطاطيل بهذا الشكل هذا
+
+273
+00:29:12,580 --> 00:29:23,180
+هنا قلي اتنين جالر تلت او هنا قلي اتنين
+
+274
+00:29:23,180 --> 00:29:26,420
+شكل عامل
+
+275
+00:29:29,710 --> 00:29:33,350
+هذه المعلومات اللي أعطاني هيك بقى فقط لغة، هي كل
+
+276
+00:29:33,350 --> 00:29:38,910
+المعلومات، وقال يعبر عن هذا بمين؟ بيه الاحداثية
+
+277
+00:29:38,910 --> 00:29:44,190
+القطبية، بقوله والله أستأنى هذا شكله غير شكل هذا،
+
+278
+00:29:44,190 --> 00:29:49,400
+مش طبيعي، مش زي اللي فوق، سهل دوريبقول له اه هذا
+
+279
+00:29:49,400 --> 00:29:54,620
+خط له معادلة و هذا خط له معادلة تانية اذا الوضع
+
+280
+00:29:54,620 --> 00:30:00,820
+مختلف تماما اذا هضطر اجباري اروح اجزء المنطقة الى
+
+281
+00:30:00,820 --> 00:30:06,460
+منطقة تانية فباقي بقول بتاخد المنطقة الأولى هذه
+
+282
+00:30:06,460 --> 00:30:13,040
+الشكل اللي عامله هذا كويس و الباقي هو المنطقة
+
+283
+00:30:13,040 --> 00:30:19,460
+الثانية طب المنطقة هذهأريد أن أعرف C تتغير لمنطقة
+
+284
+00:30:19,460 --> 00:30:24,500
+هذا المنطقة السوداء هذه المظلة باللون الأسود بس
+
+285
+00:30:24,500 --> 00:30:28,480
+نخلصها و نذهب لمين للمنطقة الثانية اللي عندنا هنا
+
+286
+00:30:28,480 --> 00:30:33,960
+أريد أن أعرف C تجدش هنا و أريد أن أعرف C تجدش هنا
+
+287
+00:30:33,960 --> 00:30:39,440
+الخط هذا لو دل مستمر على ما هو و بعد ذلك أريد أن
+
+288
+00:30:39,440 --> 00:30:45,500
+أعرف R اللي سيتغير من أين إلى أين من عند النقطة
+
+289
+00:30:45,500 --> 00:30:53,230
+هذهلغاية النقطة اللي عندنا و لما نخلصها بنروح
+
+290
+00:30:53,230 --> 00:30:57,510
+للمنطقة التانية إذا خلّينا مع θ في الأول من ويل
+
+291
+00:30:57,510 --> 00:31:02,590
+لويل ثيتا تساوي زيرو أظن فاش مشكلة يبقى هذه ثيتا
+
+292
+00:31:02,590 --> 00:31:08,330
+تساوي زيرو خط هذا طب بدنا الخط التاني هذا قداش
+
+293
+00:31:08,330 --> 00:31:17,710
+ثيتابسيطة خالص هذه المسافة قداش كلها هنا يبقى
+
+294
+00:31:17,710 --> 00:31:23,450
+هذه كلها من هنا لهنا هذين باثنين إذا بقدر أجيب له
+
+295
+00:31:23,450 --> 00:31:28,870
+الزاوية هذه اللي هي ثيتا ثم اقل يساوي المقابل على
+
+296
+00:31:28,870 --> 00:31:36,050
+المجاور بقدر أروح بقوله هنا ثان ثيتا يساوي المقابل
+
+297
+00:31:36,140 --> 00:31:41,120
+بمقابل اتنين على اتنين جذر تلاتة يسوى واحد على جذر
+
+298
+00:31:41,120 --> 00:31:45,200
+تلاتة يبقى هذا بيعطيك ان تيتا كداش تساوي ابنها
+
+299
+00:31:45,200 --> 00:31:53,440
+كداش؟ باي على ستة صحيح ولا لا؟ يبقى صار الخط هذا
+
+300
+00:31:53,440 --> 00:32:00,630
+تيتا تساوي باي على ستةإذا قصتنا صارت محلولة هذا
+
+301
+00:32:00,630 --> 00:32:06,410
+بالنسبة لمين لا ثيتا نجي ل R هنا R اللي هي معادلة
+
+302
+00:32:06,410 --> 00:32:10,610
+الدائرة اللي عندها لل R بواحد نضال عندنا هنا مين؟
+
+303
+00:32:10,610 --> 00:32:15,690
+R تبعت الخط الرأسي اللي عندنا هناإذا بدي أروح أجيب
+
+304
+00:32:15,690 --> 00:32:21,810
+له هذا قداش يساوي باجي بقوله هنا عندنا بنت ميم ال
+
+305
+00:32:21,810 --> 00:32:27,690
+X يساوي 2 جذر 3 يعني معادلة الخط الرأس الأزرق هذا
+
+306
+00:32:27,690 --> 00:32:38,860
+X يساوي 2 جذر 3 طيب ال X بقداشR Cos Zeta يساوي 2
+
+307
+00:32:38,860 --> 00:32:46,900
+جذر 3 Cos 1 على سك وضرب كله في سك بصير الـ R يساوي
+
+308
+00:32:46,900 --> 00:32:55,380
+2 جذر 3 سك ثيتا إذا الجزء الأول هذا المظلل بدأ
+
+309
+00:32:55,380 --> 00:33:02,000
+تبقى معادلته أو معادلتيه كتالةثيتا يا بنات بدت
+
+310
+00:33:02,000 --> 00:33:08,440
+تتغير من عند ال zero لغاية pi على ستة وال R بدها
+
+311
+00:33:08,440 --> 00:33:16,760
+تتغير من وين من عند ال واحد لغاية اتنين جذر تلاتة
+
+312
+00:33:16,760 --> 00:33:23,560
+في سك الزاوية خلصنا المنطقة المضللة السوداء بدنا
+
+313
+00:33:23,560 --> 00:33:30,510
+نجي للمنطقة المضللة الزرقاء هذهوهي غيرت كل كوتة
+
+314
+00:33:30,510 --> 00:33:36,230
+ضيقة عشان نعرف انها منطقتين اظن واضح ان θ تتغير من
+
+315
+00:33:36,230 --> 00:33:42,900
+وين لوين نخليله الرسممن باية ستة لغاية باية اثنان
+
+316
+00:33:42,900 --> 00:33:48,740
+يبقى جاهزين يبقى ضالة الار يبقى بالداخل الار و
+
+317
+00:33:48,740 --> 00:33:54,420
+ارسم خط من انه يبدأ من نقطة الاصل و يقطع منطقة
+
+318
+00:33:54,420 --> 00:33:58,380
+التكامل يبقى خطوة في النقطة هذه و النقطة هذه
+
+319
+00:33:58,380 --> 00:34:03,400
+النقطة هذه معروفة ار تساوي واحد لكن هذه النقطة مش
+
+320
+00:34:03,400 --> 00:34:09,520
+معروفة هذه النقطةاللي هو ال Y قداشه ساوية بنات؟
+
+321
+00:34:09,520 --> 00:34:12,580
+اتنين خاطر المستخدم اللي هو فوق يعني ال Y يساوي
+
+322
+00:34:12,580 --> 00:34:18,520
+اتنين ال Y بقداش ال R ساينس زاوية تيتا بده يساوي
+
+323
+00:34:18,520 --> 00:34:23,730
+اتنينالـ sine هي مقلوب مين؟ مقلوب الـ cosecant
+
+324
+00:34:23,730 --> 00:34:28,310
+يبقى هذه باعتبار R على cosecant يساوي اتنين يعني R
+
+325
+00:34:28,310 --> 00:34:33,610
+تساوي اتنين cosecant ثيتا، تمام؟ إذا هذه معناها إن
+
+326
+00:34:33,610 --> 00:34:39,970
+R تساوي اتنين cosecant، اللي همين؟ cosecant ثيتا،
+
+327
+00:34:39,970 --> 00:34:45,070
+يبقى صارت النقطة اللي عندنا هذه، اللي هي اتنين
+
+328
+00:34:45,070 --> 00:34:50,520
+cosecant ثيتا، اللي تساوي أرض الخط هذا كلهيبقى
+
+329
+00:34:50,520 --> 00:34:55,980
+بناء عليه المنطقة الزرقية هذه المناطق هقول ان ال
+
+330
+00:34:55,980 --> 00:35:02,920
+theta ستتغير من πي على ستة الى بي على اتنين وال R
+
+331
+00:35:02,920 --> 00:35:13,820
+ستتغير من الواحد الى اتنين كوسيكا ثيتا واضحة؟
+
+332
+00:35:13,820 --> 00:35:21,660
+هي استطعت كتابةاللي هو حدود هذه المنطقة صار مش
+
+333
+00:35:21,660 --> 00:35:24,620
+إمكانية إلا نجزئها إلى جزئين
+
+334
+00:35:28,470 --> 00:35:36,630
+أجزئيني وكتبنا حدود كل جزر من هذين الجزئين هذا نوع
+
+335
+00:35:36,630 --> 00:35:41,290
+من أنواع المسائل طبعا في الكتاب حاطس عندك بيجي خمس
+
+336
+00:35:41,290 --> 00:35:46,610
+رسمات اعتقد او ستة هيتن تان منهم وانت بنفس الطريقة
+
+337
+00:35:46,610 --> 00:35:49,530
+بتقدر تروح تجيب مين الباقي
+
+338
+00:36:03,490 --> 00:36:09,490
+Cartesian integral حول
+
+339
+00:36:09,490 --> 00:36:17,890
+التكامن في الإحداثية الكارتيزية into an equivalent
+
+340
+00:36:17,890 --> 00:36:21,730
+polar
+
+341
+00:36:21,730 --> 00:36:22,410
+integral
+
+342
+00:36:34,040 --> 00:36:47,720
+then evaluate the polar integral نمرأ
+
+343
+00:36:47,720 --> 00:36:56,080
+أيه من المثلة؟ بيقول تكامل من 0 ل 2 تكاملمن Zero
+
+344
+00:36:56,080 --> 00:37:03,260
+للجدري التربيعي للأربع ناقص Y تربيع لمين؟ لل X
+
+345
+00:37:03,260 --> 00:37:16,400
+تربيع زائد Y تربيع DXDY نمسح
+
+346
+00:37:16,400 --> 00:37:22,410
+الشجادي خلاص يا بنات؟ شجادي، طيببقول it changed
+
+347
+00:37:22,410 --> 00:37:26,330
+the cartesian integral حول التكامل في الإحداثات
+
+348
+00:37:26,330 --> 00:37:30,770
+الكارتيزية إلى التكامل المكافئ له في الإحداثيات
+
+349
+00:37:30,770 --> 00:37:36,750
+القطبية ومن ثم احسب ليه التكامل في الإحداثيات
+
+350
+00:37:36,750 --> 00:37:42,110
+القطبية بقوله كويس هي التكامل كارتيزيا بدي احوله
+
+351
+00:37:42,110 --> 00:37:46,710
+إلى قطبى عشان احوله إلى قطبى بروح ارسم منطقة
+
+352
+00:37:46,710 --> 00:37:52,190
+التكامل في الأولومنها بقدر أحول إلى تكمل في
+
+353
+00:37:52,190 --> 00:37:59,150
+الأحداثية القطبية بقول كويسة المحاول وهذا محور X
+
+354
+00:37:59,150 --> 00:38:04,650
+وهذا محور Y اللي هو في القطبية تيتا تساوي زيرو وهي
+
+355
+00:38:04,650 --> 00:38:10,470
+تيتا تساوي كده؟ باي على اتنين بدا يجي الحدود في ال
+
+356
+00:38:10,470 --> 00:38:16,130
+كارتيزيا اللي هو التكمل بالنسبة لما يبقى عند X
+
+357
+00:38:16,130 --> 00:38:23,010
+تساوي زيروأحوال Y يبقى هذا هو ال X يساوي Zero
+
+358
+00:38:23,010 --> 00:38:30,410
+التاني X يساوي الجدر بقوله X يساوي الجدر التربية
+
+359
+00:38:30,410 --> 00:38:36,830
+للأربعة ناقص Y تربية لو ربعت و نجلت ال Y على الشجر
+
+360
+00:38:36,830 --> 00:38:41,390
+تانية بس ال X تربية زاد Y تربية تساوي أربعة معانلة
+
+361
+00:38:41,390 --> 00:38:47,930
+إيش دائرة بس يقولها هل هي كل الدائرةوالله جزء من
+
+362
+00:38:47,930 --> 00:38:53,590
+الدائرة بيحدده main بيحدده ال y ستتغير من where ل
+
+363
+00:38:53,590 --> 00:38:59,150
+where يبقى ال y بس فتتغير من zero ل عند اتنين من
+
+364
+00:38:59,150 --> 00:39:04,570
+عند ال zero لغاية كدهش لغاية اتنين يبقى هذا ال
+
+365
+00:39:04,570 --> 00:39:12,640
+zero و هذا اتنينكل دائرة الإجابة لا هل هو نص
+
+366
+00:39:12,640 --> 00:39:17,920
+الدائرة ولا ربع الدائرة يبقى ربع الدائرة وليس نصف
+
+367
+00:39:17,920 --> 00:39:22,880
+الدائرة يبقى لو جيتي قلت هذا ربع الدائرة اللي
+
+368
+00:39:22,880 --> 00:39:28,640
+عندنا هذا ربع الدائرة اللي عندنا والأصل باقية
+
+369
+00:39:28,640 --> 00:39:33,500
+الدائرة هي لو روحنا نكملها بالشكل اللي عندنا هذا
+
+370
+00:39:33,500 --> 00:39:39,770
+هيك المنقط مش موجوديبقى احنا مقيلين فقط بالميلاد
+
+371
+00:39:39,770 --> 00:39:45,690
+من عند X يساوي Zero لغاية X يساوي 100 اللي هو
+
+372
+00:39:45,690 --> 00:39:49,690
+الدائرة اللي عندنا هذا و ال Y من عند الصفر لغاية
+
+373
+00:39:49,690 --> 00:39:53,210
+اتنين يبقى احنا باس الربع الأول
+
+374
+00:39:56,470 --> 00:40:02,530
+طيب ممتاز جدا يبقى بدنا نيجي نشوف θ بدت تتغير من
+
+375
+00:40:02,530 --> 00:40:07,090
+وين لوين وR بدت تتغير من وين لوين اظن واضحة θ من
+
+376
+00:40:07,090 --> 00:40:13,650
+وين لوين ضلت ال R ال R بدت تبدأ من نقطة الأصل و
+
+377
+00:40:13,650 --> 00:40:16,290
+لغاية محيط الدائر
+
+378
+00:40:28,360 --> 00:40:33,470
+نصف القطر اتنين مش اربعيبقى الدائرة هذه اللي هي
+
+379
+00:40:33,470 --> 00:40:38,610
+معادلتها R تساوي 2 في الإحداثيات القطبى لما رجعنا
+
+380
+00:40:38,610 --> 00:40:42,630
+في الcalculus يقولنا R تساوي رقم و الرقم إذا كان
+
+381
+00:40:42,630 --> 00:40:45,890
+سلب ولا موجب خديله ال absolute value يطلع رقم موجب
+
+382
+00:40:45,890 --> 00:40:50,710
+يبقى هذا يمثل دائما أبدا معادلة مين معادلة دائرة
+
+383
+00:40:50,710 --> 00:40:57,840
+في الإحداثيات القطبىيبقى الار ستتغير من عند الـ
+
+384
+00:40:57,840 --> 00:41:03,600
+zero لغاية الاتنين هو ده هيتغير من عن اللي هو ال
+
+385
+00:41:03,600 --> 00:41:08,640
+zero لغاية باي على اتنين يبقى هذا التكامل بيصير
+
+386
+00:41:08,640 --> 00:41:12,740
+هاي تكاملين X تلبية و Z و Y تلبية و هم في قدر
+
+387
+00:41:28,090 --> 00:41:32,810
+يبقى هذا الكلام لتساوي تكامل من Zero لغاية Pi على
+
+388
+00:41:32,810 --> 00:41:33,050
+اتنين
+
+389
+00:41:46,370 --> 00:41:49,690
+بنعمل بالقيمة اللى فوق بنقص الدخل اللى تحت طبعا
+
+390
+00:41:49,690 --> 00:41:55,250
+بزيرو و بضلي اتنين اقصى اربعة يوم ست عشر على اربعة
+
+391
+00:41:55,250 --> 00:42:02,330
+باربعة يبقى هذا اللي هو بيصير اربعة تكامل من zero
+
+392
+00:42:02,330 --> 00:42:03,530
+ن buy على اتنين
+
+393
+00:42:06,370 --> 00:42:11,890
+يبقى أربعة ثيتا من Zero لغاية Pi على اتنين يبقى
+
+394
+00:42:11,890 --> 00:42:18,730
+أربعة في Pi على اتنين ناقص Zero يبقى اتنين Pi فقط
+
+395
+00:42:18,730 --> 00:42:26,790
+لا غير ناخد
+
+396
+00:42:26,790 --> 00:42:37,480
+كمان نمرة B نمرة B بيقول بيبدو تكاملمن Zero لغاية
+
+397
+00:42:37,480 --> 00:42:49,080
+ستة وتكامل من Zero لغاية Y لل X DX DY بدي
+
+398
+00:42:49,080 --> 00:42:53,020
+أحاول هذا إلى Polar Coordinates علشان أحاوله إلى
+
+399
+00:42:53,020 --> 00:42:57,340
+Polar Coordinates بدي أروح و أرسم منطقة التكامل
+
+400
+00:42:57,340 --> 00:43:03,720
+والله يا شرايكوا يا كده على السكR cos θ و R dr d θ
+
+401
+00:43:03,720 --> 00:43:12,900
+و R sin θ و 006 زي مهمة اللي
+
+402
+00:43:12,900 --> 00:43:16,660
+كلمته هنا صح بس اللي كلمته على قدوت مش صحيح الـ
+
+403
+00:43:16,660 --> 00:43:20,980
+006 هذه الإحداثيات الكفزية مش هم هم المناطق اللي
+
+404
+00:43:20,980 --> 00:43:27,220
+هي الإحداثيات القطبية لذلك إجباري نروح نرسم منطقة
+
+405
+00:43:27,220 --> 00:43:33,190
+التكاملبقول له كويسة دي منطقة التكامل هي المحاول
+
+406
+00:43:33,190 --> 00:43:39,290
+هذا محور X وهذا محور Y أول حاجة بدها تكمل بالنسبة
+
+407
+00:43:39,290 --> 00:43:44,990
+ل X هي X تساوي Zero هو محور Y هذا هو X تساوي Zero
+
+408
+00:43:44,990 --> 00:43:51,410
+اللي بعد هو X يساوي قداشريعني y تساوي x اللي هو
+
+409
+00:43:51,410 --> 00:43:57,090
+الخط المنصف للربع الأول بالشكل هذا و بيبقى على
+
+410
+00:43:57,090 --> 00:44:03,390
+انتداله هذا الخط اللي هو y يساوي مين؟ يساوي x بعد
+
+411
+00:44:03,390 --> 00:44:08,530
+هيك ال y بدأ تتغير من هنا إلى هنامن zero لغاية ستة
+
+412
+00:44:08,530 --> 00:44:12,830
+يبقى لو روحت قولت هذه ال zero وهذه النقطة اللي هي
+
+413
+00:44:12,830 --> 00:44:18,970
+ستة يبقى بتصير عند الخط اللي هو y تساوي ستة إذا
+
+414
+00:44:18,970 --> 00:44:23,570
+المنطقة اللي بينهم هي المنطقة المظللة اللي عندها
+
+415
+00:44:23,570 --> 00:44:32,820
+طيب لما أقولك الخط y تساوي x تحوله لقط بيه؟و Y
+
+416
+00:44:32,820 --> 00:44:38,500
+تساوي X كده شو بيعمل في الزاوية 45 إذا الخط Y
+
+417
+00:44:38,500 --> 00:44:45,640
+تساوي X في القطب بدي قابله θ تساوي Y على 4 مباشرة
+
+418
+00:44:47,040 --> 00:44:51,860
+طيب قول رأسي ما هو معروف باي على اتنين يبقى هذا
+
+419
+00:44:51,860 --> 00:44:58,080
+ثيتا تساوي باي على اتنين اذا ثيتا محددة بقيت مين
+
+420
+00:44:58,080 --> 00:45:04,540
+بقيت ا ر بدا تبدأ من هنا ال zero ههه ونبقى المشيل
+
+421
+00:45:04,540 --> 00:45:09,060
+لغاية ما نقابل الخط اللي عندنا هناالخطة ده شو
+
+422
+00:45:09,060 --> 00:45:16,400
+معادلته Y تساوي ستة إذا لما أجي أقول يا بنات هنا Y
+
+423
+00:45:16,400 --> 00:45:23,380
+تساوي ستة ال Y اللي هي قداش R Sin Theta يبقى R Sin
+
+424
+00:45:23,380 --> 00:45:32,420
+Theta تساوي ستة يعني R تساوي ستة Cos Thetaيبقى أي
+
+425
+00:45:32,420 --> 00:45:37,740
+نقطة على الخط الأفقي هذا المعادلة القطبية له R
+
+426
+00:45:37,740 --> 00:45:44,160
+تسوية ستة كثيرة ثيتا إذا بناء عليه بيصبح التكاملين
+
+427
+00:45:44,160 --> 00:45:51,980
+اللي عندنا هذول كالتالي هاي تكامل وهي التاني ودالة
+
+428
+00:45:51,980 --> 00:46:01,550
+اللي عندنا X اللي هي 100R cos θ وDx Dy R Dr Dθ نجل
+
+429
+00:46:01,550 --> 00:46:10,410
+ال R ال R ستتغير من Zero لغاية ستة كوسيكا ثتا طب و
+
+430
+00:46:10,410 --> 00:46:17,450
+الثتا ستتغير من باي على أربعة إلى باي على اتنين
+
+431
+00:46:18,350 --> 00:46:21,530
+يبقى هذا العمود الفقري تبع المثل اجيب ناس اللي
+
+432
+00:46:21,530 --> 00:46:26,950
+مائة بالمائة ضلت عملية من عملية التكامل يبقى هذا
+
+433
+00:46:26,950 --> 00:46:32,810
+يا بنات يصير تكامل من πاي على اربعة لغاية باي على
+
+434
+00:46:32,810 --> 00:46:40,680
+اتنين بالشكل اللي انا ار في ارR تربية تكاملها R
+
+435
+00:46:40,680 --> 00:46:48,600
+تكييب على ثلاثة و الحاكم من Zero لغاية ستة كوسيكا
+
+436
+00:46:48,600 --> 00:46:56,480
+تيتا و أي كوسايم تيتا و أي ديتا واضح اظن طيب هذا
+
+437
+00:46:56,480 --> 00:47:03,920
+الكلام بده يساوي هذا يا بناتي ستة تكييبستة فى ستة
+
+438
+00:47:03,920 --> 00:47:08,140
+فى ستة لكن مجسوم على جداش على تلاتة يعني ستة فى
+
+439
+00:47:08,140 --> 00:47:14,440
+ستة فى اتنين ستة فى ستة ستة و تلاتين فى اتنين فى
+
+440
+00:47:14,440 --> 00:47:21,100
+اتنين و سبعين اذا هذه بدها تصير سبعين و اتنين وهي
+
+441
+00:47:21,100 --> 00:47:27,440
+تكامل من باى على اربع لغاية باى على اتنين لمين
+
+442
+00:47:27,440 --> 00:47:37,950
+لكسيكا تكيب ثيتاكوصين فيتا دي فيتا هذا
+
+443
+00:47:37,950 --> 00:47:45,390
+الكلام بالنسبة 72 تكامل من πاية على أربعة لباية
+
+444
+00:47:45,390 --> 00:47:49,170
+على اتنين شو رايكوا كامل الكامل هذه كوسيكا تكامل
+
+445
+00:47:49,170 --> 00:47:53,530
+كوصين تكامل كوسيكا تكامل كوسيكا تكامل كوسيكا تكامل
+
+446
+00:47:53,530 --> 00:47:56,230
+كوسيكا تكامل كوسيكا تكامل كوسيكا تكامل كوسيكا
+
+447
+00:47:56,230 --> 00:47:56,230
+تكامل كوسيكا تكامل كوسيكا تكامل كوسيكا تكامل
+
+448
+00:47:56,230 --> 00:47:56,730
+كوسيكا تكامل كوسيكا تكامل كوسيكا تكامل كوسيكا
+
+449
+00:47:56,730 --> 00:47:57,390
+تكامل كوسيكا تكامل كوسيكا تكامل كوسيكا تكامواحد
+
+450
+00:47:57,390 --> 00:48:03,610
+على الـ sine يعني كأن المسألة صارت كوسيكا تربيع
+
+451
+00:48:03,610 --> 00:48:12,290
+ثيتا على مين؟ على الصين الزاوية ثيتا في كوسين
+
+452
+00:48:12,290 --> 00:48:16,790
+الزاوية ثيتا في دي ثيتا كوسيكا تقريبا أخدنا واحدة
+
+453
+00:48:16,790 --> 00:48:19,790
+صارت واحد على الصين صار عندي كوسين على الصين اللي
+
+454
+00:48:19,790 --> 00:48:26,500
+هو مين؟ كتال ممتاز جدايبقى هاي 72 تكامل من باي على
+
+455
+00:48:26,500 --> 00:48:32,260
+أربعة إلى باي على اتنين لكوسيكن تربيه تيتا كتان
+
+456
+00:48:32,260 --> 00:48:40,000
+تيتا دي تيتا هو تفضل كتان بجداش بس بإشارة يبقى هذه
+
+457
+00:48:40,000 --> 00:48:46,840
+بقدر اكتبها بالشكل التالف سالب 72 تكامل من باي على
+
+458
+00:48:46,840 --> 00:48:54,500
+أربعة إلى باي على اتنينلا كتان ثيتا مشتقت كتان
+
+459
+00:48:54,500 --> 00:48:59,760
+الثيتا يعني شيلت ال D ثيتا مع كوسيكا التربية ثيتا
+
+460
+00:48:59,760 --> 00:49:05,680
+و كتبت عليها D كتان لو اشتقتش بيطلع سالب كوسيكا
+
+461
+00:49:05,680 --> 00:49:09,580
+التربية هاي السالب موجود والكوسيكا التربية كتبنا
+
+462
+00:49:09,580 --> 00:49:14,180
+بدلها مين كتان ثيتا علموكوا هذه الشغله في ال class
+
+463
+00:49:14,180 --> 00:49:21,790
+base لها ناقصبال U ؟ طيب هذه هي ال U تبعتك هذه
+
+464
+00:49:21,790 --> 00:49:29,110
+المسألة تبعتنا هذه بقول pot cot θ تساوي U يبقى إذن
+
+465
+00:49:29,110 --> 00:49:34,510
+ال DU سالب كوسيكا تربيه ثيتا دي ثيتا يبقى شو يصير
+
+466
+00:49:34,510 --> 00:49:41,770
+المسألة تكامل ل U DU بإشارة سالب هي ال U و هي ال
+
+467
+00:49:41,770 --> 00:49:46,160
+DU و هي اشارة السالبيبقى ياه ولا لا؟ إذا بتعرف إيه
+
+468
+00:49:46,160 --> 00:49:53,120
+على طول ماشي الحال بتعرف إيش خلاص و بطلع تكامل يو
+
+469
+00:49:53,120 --> 00:49:57,620
+دي و بإشارة سالف هيبقى برا يبقى هذه والله هذه نفس
+
+470
+00:49:57,620 --> 00:50:00,740
+الشيء و لا .. انتوا طبعا درستوا في شعب مختلفة ولا
+
+471
+00:50:00,740 --> 00:50:07,700
+واحد قالكوا هالشغل هذي؟ كل كوا؟ طيب ما علينا بس في
+
+472
+00:50:07,700 --> 00:50:11,760
+في الكتاب جايلها الكتاب دي ربالك طبعة اتناش جايلها
+
+473
+00:50:11,760 --> 00:50:13,060
+أنا شوفتها بعيني
+
+474
+00:50:16,330 --> 00:50:20,330
+أه مظبوط لكن أنا دراس كتابة اللي يكتب الكتاب لكن
+
+475
+00:50:20,330 --> 00:50:25,280
+في الكتاب موجودة line كمانطب علينا ما علينا سواء
+
+476
+00:50:25,280 --> 00:50:28,660
+هذه والله هذه هي اتنين نفس الشيء ماساوي نفس الشيء
+
+477
+00:50:28,660 --> 00:50:35,320
+يبقى هذا الكلام يبقى يساوي نقص 72 وهذه كتان تربية
+
+478
+00:50:35,320 --> 00:50:42,840
+ثيتا على اتنين U DU يبقى U تربية على اتنين والحكي
+
+479
+00:50:42,840 --> 00:50:50,940
+هذا من باي على اربعة الى باي على اتنين ويساويسالف
+
+480
+00:50:50,940 --> 00:50:57,740
+ستة و تلاتين خلّيك برا 72 على 2 ب 36 يبقى هذا بصير
+
+481
+00:50:57,740 --> 00:51:04,400
+مين بصير كتان تربية في باي على اتنين باي على اتنين
+
+482
+00:51:04,400 --> 00:51:12,380
+ناقص كتان تربية اللي هو باي على اربع والجواب هو
+
+483
+00:51:12,380 --> 00:51:19,510
+ناقص ستة و تلاتين فيه كده كتان باي على اتنينيعني
+
+484
+00:51:19,510 --> 00:51:25,130
+كوصين بيع اتنين على صين بيع على اتنين صفر على واحد
+
+485
+00:51:25,130 --> 00:51:29,270
+ولا غير على القلة الحاسبة تحسبوها I am here is
+
+486
+00:51:29,270 --> 00:51:34,490
+zero وكتان بيع على اربعة مقلوب تان بيع على اربعة و
+
+487
+00:51:34,490 --> 00:51:37,770
+تان ال بيع على اربعة بواحد واحد على واحد يبقى
+
+488
+00:51:37,770 --> 00:51:44,030
+بواحد تربيع قداش بواحد يبقى الجواب ستة وتلاتين
+
+489
+00:51:44,030 --> 00:52:12,100
+بالمؤجب فقط لا غيرهل بتحب تسأل اي سؤال هنا؟ طيب
+
+490
+00:52:12,100 --> 00:52:13,880
+نمرى C من السؤال
+
+491
+00:52:20,930 --> 00:52:30,930
+من 0 للجدري التربيهي ل2 x ناقص x تربيه ومن 1 لغاية
+
+492
+00:52:30,930 --> 00:52:39,250
+2 لمن؟ ل1 عالى اللي هو x تربيه زاد y تربيه يعني كل
+
+493
+00:52:39,250 --> 00:52:43,150
+تربيه dy dx
+
+494
+00:53:14,440 --> 00:53:18,540
+أكف مباشرة لك المشكلة في اللي وين في الحدود إذا ما
+
+495
+00:53:18,540 --> 00:53:23,340
+تروح ترسم منطقة تتكمل من أول ومن ثم تروح للحدود
+
+496
+00:53:23,340 --> 00:53:30,620
+بقول مصير هذا من هذا محور X و هذا محور Y و هذا
+
+497
+00:53:30,620 --> 00:53:35,580
+نقطة الأصل اللي هي Zero المتغير الأولاني اللي همين
+
+498
+00:53:35,580 --> 00:53:40,960
+Y تساوي Zero اللي همين بلعب محور X يبقى هذا Y
+
+499
+00:53:40,960 --> 00:53:46,050
+تساوي Zeroبعدها y تساوي الجدرى اللى عندنا هذا بس
+
+500
+00:53:46,050 --> 00:53:50,050
+معادلة دي الشيء اللى أنا مش عارفه مظبوط بيبقى
+
+501
+00:53:50,050 --> 00:53:55,430
+بسيطة بيقولوا دبل حالك راح قال لي y تساوي الجدرى
+
+502
+00:53:55,430 --> 00:54:02,470
+التربية لإتنين x ناقص x تربية قولوا ماشي شوية
+
+503
+00:54:02,470 --> 00:54:07,450
+تتربعها يمكن الله يحل حلها هيك شويةيبقى لو جينا
+
+504
+00:54:07,450 --> 00:54:13,390
+ربعناها إيش بيصير؟ بيصير عندي Y تربية يساوي اتنين
+
+505
+00:54:13,390 --> 00:54:21,030
+X ناقص X تربية نطلع عليكم شغلة تانية شو رايك لمين
+
+506
+00:54:21,030 --> 00:54:25,850
+يعمله اكمل المربع؟ يبقى هذا إيش بيصير عندي؟ Y
+
+507
+00:54:25,850 --> 00:54:31,190
+تربية يساوي واحد ناقص واحد زائد اتنين X ناقص X
+
+508
+00:54:31,190 --> 00:54:37,600
+تربية يعني هذه عبارة عن مين؟ عبارة عن واحدتربية
+
+509
+00:54:37,600 --> 00:54:42,340
+ناقص اتنين X زي واحد هذول التلاتة خدت منهم ناقص
+
+510
+00:54:42,340 --> 00:54:48,340
+عامل مشترك يبقى صارت المسألة Y تربيه يسوى واحد X
+
+511
+00:54:48,340 --> 00:54:54,200
+ناقص واحد لكل تربيه بالشكل اللي عنده هذا او بمعنى
+
+512
+00:54:54,200 --> 00:54:59,360
+اخر صار عند ال X ناقص واحد لكل تربيه زي Y تربيه
+
+513
+00:54:59,360 --> 00:55:01,660
+يسوى واحد معنى نتيجة
+
+514
+00:55:09,370 --> 00:55:18,290
+يبقى هذه circle with center اللي هو main واحد
+
+515
+00:55:18,290 --> 00:55:27,690
+وزيرو and radius واحدة طب تعالى نوصل للمدرسة جالي
+
+516
+00:55:27,690 --> 00:55:32,110
+المركز واحد وزيرو اين الواحد والزيرو هاي النقطة
+
+517
+00:55:32,110 --> 00:55:39,550
+اللي هي واحد وزيرووبعدين نصف القطر تبعها كده؟ واحد
+
+518
+00:55:39,550 --> 00:55:45,850
+يبقى بده يجيك هنا كمان هذا بيصير كده؟ اتنين لأنه
+
+519
+00:55:45,850 --> 00:55:51,610
+هذه واحد وبده يطلع فوق واحد وبده ينزل كمان تحت
+
+520
+00:55:51,610 --> 00:55:57,230
+واحد بالشكل اللي عنه هذا لكن هل هذه هي كل دائرة
+
+521
+00:55:57,230 --> 00:56:02,210
+ولا ربعة ولا نصة ولا تلتة الله أعلم لكن احنا بيقول
+
+522
+00:56:04,500 --> 00:56:09,240
+هذه الدائرة بيصير الدائرة بالشكل اللي عندها يعني
+
+523
+00:56:09,240 --> 00:56:13,300
+طبعا
+
+524
+00:56:13,300 --> 00:56:17,400
+يبقى هذه الدائرة بالشكل اللي عندها الآن هذه
+
+525
+00:56:17,400 --> 00:56:23,960
+الدائرة بدي أشوف هل هي كل
+
+526
+00:56:23,960 --> 00:56:30,150
+دائرة ولا جزء منها تعالى أشوفأحنا حددنا y تساوي
+
+527
+00:56:30,150 --> 00:56:34,350
+zero وحددنا y تساوي الجذر يبقى خلطة هذي عبارة عن
+
+528
+00:56:34,350 --> 00:56:40,030
+الدرع كل x من عند الواحد لغاية اتنين من عند الواحد
+
+529
+00:56:40,030 --> 00:56:46,610
+لغاية اتنين يعني x لغاية هنا من هنا لغاية هنا يبقى
+
+530
+00:56:46,610 --> 00:56:51,030
+لما تيجي تقولي بترفع هك رأسي وهذا يكون
+
+531
+00:56:55,230 --> 00:57:01,630
+يبقى رب عيد دائرة فقط ماريا تمام؟ يبقى هاي
+
+532
+00:57:01,630 --> 00:57:05,370
+البوباجي الدائرة كله مالوش لزوم يبقى هذه يا بنات
+
+533
+00:57:05,370 --> 00:57:12,530
+بتغمجها يبقى هذه غمجناها يعني دائرة من الواحد
+
+534
+00:57:12,530 --> 00:57:18,140
+لغاية اتنين الشكل اللي عندهاإذا بدي أشوف فيتس
+
+535
+00:57:18,140 --> 00:57:24,300
+تتغير من وين لوين و R تتغير من وين لوين لو جيت
+
+536
+00:57:24,300 --> 00:57:31,040
+رسمت هنا من نقطة الأصل لغاية ما جيت على وين على
+
+537
+00:57:31,040 --> 00:57:36,920
+النقطة هذه يبقى فيتس تستخدم قداشر مش عارفينها لابد
+
+538
+00:57:36,920 --> 00:57:43,200
+انك تعرف كيف بدي أعرف بسيطة جدا هذا الخيار
+
+539
+00:57:50,310 --> 00:57:56,490
+هذا النقطة أحدثيها واحد و واحد صح ولا لا نقطة فوق
+
+540
+00:57:56,490 --> 00:58:01,050
+أحدثيها واحدة اتنين هذه النقطة تقع على الدائرة
+
+541
+00:58:01,050 --> 00:58:06,990
+وتقع على الخط المستقيم صح ولا لا إذا نقطة التقاط
+
+542
+00:58:06,990 --> 00:58:12,150
+ما بين الاتنين بتكون هي النقطة المطلوبة طب واحد
+
+543
+00:58:12,150 --> 00:58:16,890
+تاني قالتلي لا أستنى شوية بقولكقال هي نقطة تقاطة
+
+544
+00:58:16,890 --> 00:58:22,510
+الدائرة مع الخط هذا الرأس له X تساوي واحد يعني بدي
+
+545
+00:58:22,510 --> 00:58:26,470
+أحل ال X تساوي واحد مع معادلة الدائرة وشوف إيش بدي
+
+546
+00:58:26,470 --> 00:58:32,810
+يطلع عني وإيه معادلة الدائرة هي X يساوي واحد تساوي
+
+547
+00:58:32,810 --> 00:58:38,410
+واحد يعني أعطيتنا نقطة هذه واحد أه طبعا أعطيتك
+
+548
+00:58:38,410 --> 00:58:43,720
+نقطة هذه واحد و بس واحد واحد كارتيزيايبقى هذه اللي
+
+549
+00:58:43,720 --> 00:58:50,080
+هو واحد واحد ممتاز جدا يبقى هذا واحد وهذا واحد
+
+550
+00:58:50,080 --> 00:58:54,820
+والزاوية هذه قائمة متلث متساوى الساقين يبقى كل
+
+551
+00:58:54,820 --> 00:59:00,720
+زاوية قدام 45 درجة إذا صارت الزاوية هذه Pi على 4
+
+552
+00:59:01,180 --> 00:59:05,580
+وهذه صارت باية على أربعة كذلك إذا قطها ده ثيتا
+
+553
+00:59:05,580 --> 00:59:09,800
+تساوي قد إيه؟ باية على أربعة، إذا الثيتا ستتغير من
+
+554
+00:59:09,800 --> 00:59:14,700
+وين لوين، من Zero لباية على أربعة، حلنا قصة ثيتا،
+
+555
+00:59:14,700 --> 00:59:20,920
+تبقى لقصة مين؟ أخرج، بقى أجي برسم خط من نقطة الأصل
+
+556
+00:59:20,920 --> 00:59:27,240
+وخلّيه يقطع منطقة التكامل، يبقى هي النقطة الأولى
+
+557
+00:59:27,240 --> 00:59:34,730
+وهي النقطة الثانيةبقول الله كويس بدي اشوف R قداش
+
+558
+00:59:34,730 --> 00:59:39,830
+هنا و بدي اشوف قداش R هنا تمام تفضل كيف بدي اجيب
+
+559
+00:59:39,830 --> 00:59:43,690
+هذه يا ربنا بقوله بسيطة هذا الخط الراسي شوفوا
+
+560
+00:59:43,690 --> 00:59:49,270
+عادلته X يساوي واحد يعني R Cos θ يساوي واحد يبقى R
+
+561
+00:59:49,270 --> 00:59:54,190
+سكتين لإن هذا قضية بسيطة يبقى هذا بروح بقوله هنا
+
+562
+00:59:54,190 --> 00:59:55,510
+ال X
+
+563
+00:59:58,860 --> 01:00:03,640
+قصارى تيتا يساوي واحد يبقى الارض ساوي السك الزاوية
+
+564
+01:00:03,640 --> 01:00:09,040
+تيتا ضالمين عندى ضال المعادلة اللى عندنا دى معادلة
+
+565
+01:00:09,040 --> 01:00:13,620
+الدائرة وين معادلة الدائرة هاي معادلة الدائرة
+
+566
+01:00:13,620 --> 01:00:19,420
+بقوله اه وين هاي هاي معادلة الدائرة بقوله طب انا
+
+567
+01:00:19,420 --> 01:00:24,760
+باخد هادي احسنلي احسنلي فى الشغل كيف احسنلك قال لي
+
+568
+01:00:24,760 --> 01:00:28,600
+بس احسنلي بكيستر بيه على الشجرة تانيةيبقى بطبق
+
+569
+01:00:28,600 --> 01:00:37,780
+ولكن و X تربيع زائد Y تربيع يساوي 2X صح؟ طيب كداش
+
+570
+01:00:37,780 --> 01:00:45,520
+X تربيع زائد Y تربيع؟ و التانية 2R Cos زاوية ثيتا
+
+571
+01:00:45,520 --> 01:00:50,420
+صحيح ولا لا؟لو جبتها على الشجة التانية و أخدت R
+
+572
+01:00:50,420 --> 01:00:56,660
+عامل مشترك بيبقى عندي R ناقص اتنين Cos θ بده يسوى
+
+573
+01:00:56,660 --> 01:01:02,180
+قداش Zero يبقى الـ R تسوى Zero ماليش علاقة فيها
+
+574
+01:01:02,180 --> 01:01:09,980
+بيبقى عندي R تسوى اتنين Cos زاوية θ يبقى هذه
+
+575
+01:01:09,980 --> 01:01:17,840
+الدائرة عدلتها R يسوى اتنين Cos زاوية θخلّيني
+
+576
+01:01:17,840 --> 01:01:25,060
+اذاكركم يا ناسيين لما
+
+577
+01:01:25,060 --> 01:01:31,550
+جيتوا في احداثيات القطبين جيبتوا معادلة دائرةاللي
+
+578
+01:01:31,550 --> 01:01:37,290
+بتمر بنقطة الأصل ومركزها على محور X الموجة أو على
+
+579
+01:01:37,290 --> 01:01:41,970
+X السالق أو على Y الموجة وقال هو على Y السالق وقلت
+
+580
+01:01:41,970 --> 01:01:46,630
+انه إذا كان والله مركزها على محور X وتمر بنقطة
+
+581
+01:01:46,630 --> 01:01:51,670
+الأصل يجب ان اقع عليها R يسوى 2A Cos زاوية Tوإذا
+
+582
+01:01:51,670 --> 01:01:56,250
+عليك تسالق تسالق اتنين اكو صين تيتا إذا على واقع
+
+583
+01:01:56,250 --> 01:02:01,710
+الموجة باتنين ا صين تيتا ولا اتنين ا صين تيتا بس
+
+584
+01:02:01,710 --> 01:02:07,710
+بإشارة سالق أسألكم ماذا ذكريش شمس هذا القرآن قال
+
+585
+01:02:07,710 --> 01:02:13,010
+اللهم اجعله يرقد يفتذكرنا ماشي فبيبقى هذا إيه هاي
+
+586
+01:02:13,010 --> 01:02:16,670
+هطلق نفس المعادلة لاحبيتش أقوللكم من الأول حبيت
+
+587
+01:02:16,670 --> 01:02:22,220
+أصلبكمحزباً دقيقاً لأن هذه الدائرة بتمر بنقطة
+
+588
+01:02:22,220 --> 01:02:25,380
+الأصل ومركزها على الاتجاه الموجب لل exactly are
+
+589
+01:02:25,380 --> 01:02:32,260
+يسوى اتنين a sin θ حيث a نصف القطر نصف القطر عند
+
+590
+01:02:32,260 --> 01:02:35,220
+الحمد لله بواحد يبقى طرأ تلاته اتنين في واحد
+
+591
+01:02:35,220 --> 01:02:42,280
+cosine طلعت اتنين cosine ثم خلصنا كل الحاجات
+
+592
+01:02:42,280 --> 01:02:46,490
+الصعبة خلصنا هذا عملية show routineيبقى الشغل
+
+593
+01:02:46,490 --> 01:02:53,150
+الروتيني كالتالي بيصير المسألة هي تكاملين وهي واحد
+
+594
+01:02:53,150 --> 01:02:58,450
+على X تربيع زاد و تربيع تربيع تربيع تربيع تربيع
+
+595
+01:02:58,450 --> 01:03:02,410
+تربيع تربيع تربيع تربيع تربيع تربيع تربيع تربيع
+
+596
+01:03:02,410 --> 01:03:02,710
+تربيع تربيع تربيع تربيع تربيع تربيع تربيع تربيع
+
+597
+01:03:02,710 --> 01:03:02,710
+تربيع تربيع تربيع تربيع تربيع تربيع تربيع تربيع
+
+598
+01:03:02,710 --> 01:03:02,710
+تربيع تربيع تربيع تربيع تربيع تربيع تربيع تربيع
+
+599
+01:03:02,710 --> 01:03:13,450
+تربيع تربيع تربيع تربيع تربيع تربيع تربيع تربيع
+
+600
+01:03:13,670 --> 01:03:21,310
+للي اتنين كوفاين الثيتا وثيتا هذه من Zero لغاية Pi
+
+601
+01:03:21,310 --> 01:03:27,370
+على أربع يبقى هذا الكلام بدي اصلحه تكامل من Zero
+
+602
+01:03:27,370 --> 01:03:36,090
+لغاية Pi على أربع أربع أرقص أربع مقدر يعني كأنه
+
+603
+01:03:36,090 --> 01:03:43,910
+احنا بدنا نكاملمن sic θ إلى اتنين cosine θ للار
+
+604
+01:03:43,910 --> 01:03:51,810
+السالب تلاتة dr dtمظبوط ايه؟ يبقى بنضيف لنقص واحدة
+
+605
+01:03:51,810 --> 01:03:57,830
+بنقسم على القص الجديد يبقى هذا الكلام تكامل من
+
+606
+01:03:57,830 --> 01:04:04,950
+Zero لغاية Pi على أربعة لمين؟ لأ الارقص ناقص اتنين
+
+607
+01:04:04,950 --> 01:04:10,790
+على ناقص اتنين والحكي هذا من سك ثيتا للي اتنين
+
+608
+01:04:10,790 --> 01:04:21,540
+قصين الزاوية ثيتا لمين؟ لادى ثيتاوهذا حاضن وضوح
+
+609
+01:04:21,540 --> 01:04:27,550
+الشمس في رابعة النهارطيب هذا الكلام يجب ان يساوي
+
+610
+01:04:27,550 --> 01:04:33,570
+ناقص نص خلّيك برا وهي تكمل من zero ل πاي على أربعة
+
+611
+01:04:33,570 --> 01:04:38,990
+هذه يا بنات قداشر ليه واحد على R تربيع صح يبقى
+
+612
+01:04:38,990 --> 01:04:45,450
+بصير عندي مين بصير عندي واحد على أربعة كوصين تربيع
+
+613
+01:04:45,450 --> 01:04:53,570
+زاوية ثيتا ناقص واحدعلى سكتر بيه ثيتر كله بالنسبة
+
+614
+01:04:53,570 --> 01:05:00,470
+لدي ثيتر أو إن شئتوا فقلنا ناقص نصف تكمل من zero
+
+615
+01:05:00,470 --> 01:05:09,960
+لغاية pi على أربع لربع cosine مقلب منين؟يبقى سك
+
+616
+01:05:09,960 --> 01:05:18,500
+تربيع ثيتا وناقص cos تربيع ثيتا كله بالنسبة الي دي
+
+617
+01:05:18,500 --> 01:05:26,460
+ثيتا مظبوط هيك؟ طيب قدش تكمل سك تربيع؟ بتان يبقى
+
+618
+01:05:26,460 --> 01:05:34,170
+وسيطة هذه ناقص تمن تان ثيتاوالحكي من Zero لغاية Pi
+
+619
+01:05:34,170 --> 01:05:40,650
+على أربعة ناقص فناقص يتزاد هذه النص وهذه بيجيلك
+
+620
+01:05:40,650 --> 01:05:47,810
+كمان نص ومن Zero لغاية Pi على أربعة لمن لواحد زائد
+
+621
+01:05:47,810 --> 01:05:54,410
+cosine اتنين ثيتا D ثيتا يبقى هذا الكلام بيستوي
+
+622
+01:05:54,410 --> 01:06:03,900
+لناقص تون فيه وظل ال 45 وظل ال Zeroوهنا زائد رابع
+
+623
+01:06:03,900 --> 01:06:10,240
+في ثيتا زائد sin اتنين ثيتا على اتنين من Zero
+
+624
+01:06:10,240 --> 01:06:18,200
+لغاية Pi على اربع يبقى النتيجة ناقص تمن زائد رابع
+
+625
+01:06:18,200 --> 01:06:29,320
+في Pi على اربع وهنا زائد تمن تمينأفتح يوسف واضغط
+
+626
+01:06:29,320 --> 01:06:32,640
+هنا و اضغط باي على أربع و يصبح صين باي على اتنين
+
+627
+01:06:32,640 --> 01:06:42,800
+ناقص صين زيرو يبقى ناقص زيرو اظن زائد ثمن و ناقص
+
+628
+01:06:42,800 --> 01:06:52,960
+ثمن مع السلامة والجواب يسوى باي على ستة عشر حلوة
+
+629
+01:06:52,960 --> 01:06:53,840
+فكرة السؤال
+
+630
+01:07:11,130 --> 01:07:17,050
+خد بالمثال رقم ثلاثة
+
+631
+01:07:17,050 --> 01:07:23,070
+ثلاثة
+
+632
+01:07:23,070 --> 01:07:33,510
+find the area of the region find the area of the
+
+633
+01:07:33,510 --> 01:07:35,010
+region
+
+634
+01:07:44,730 --> 01:07:53,930
+to the interiors of
+
+635
+01:07:53,930 --> 01:08:00,870
+the cardioids of the
+
+636
+01:08:00,870 --> 01:08:08,290
+cardioids R تساوي واحد cosine الزاوية تيتا and ال
+
+637
+01:08:08,290 --> 01:08:13,770
+R يساوي واحد ناقص cosine الزاوية تيتا
+
+638
+01:08:43,000 --> 01:08:47,620
+يقول لهذه مسافة المنطقة المشتركة المنطقة الداخلية
+
+639
+01:08:47,620 --> 01:08:51,020
+المشتركة ما بين ال two cardoids اذا احنا عندنا
+
+640
+01:08:51,020 --> 01:08:57,140
+منحنية للقلب ودرسناهم في calculus دي بصبوط لو
+
+641
+01:08:57,140 --> 01:09:02,600
+قعدنا رسمهم بيكون على الشكل التالي هذا الوثيطة
+
+642
+01:09:02,600 --> 01:09:08,860
+تساوي zero او هذا الوثيطة تساوي by على اتنين ال
+
+643
+01:09:08,860 --> 01:09:12,780
+cardoid الأول الشكل اللي عندنا هذا هيك
+
+644
+01:09:17,210 --> 01:09:20,970
+والكاردويلي التاني على الناحية .. هذا مين هو؟ شو
+
+645
+01:09:20,970 --> 01:09:26,550
+اسمه هذا يا بنات؟ أبو الزائد ولا اللاقس؟ زائد يبقى
+
+646
+01:09:26,550 --> 01:09:32,650
+هذا أبو سام اللي هو واحد زائد كوصاين زامية كتيرة
+
+647
+01:09:32,650 --> 01:09:37,050
+وانحنى القلب التاني على الناحية التانية اللي هو
+
+648
+01:09:37,050 --> 01:09:39,830
+بيجيكي بالشكل هذا هيك
+
+649
+01:09:45,000 --> 01:09:51,660
+وهذا بيجي من ناحية التانية شكل هذا وين المنطقة
+
+650
+01:09:51,660 --> 01:09:57,320
+المشتركة فيما بينهما؟ في المنطقة تلعني و تل اتنين
+
+651
+01:09:57,320 --> 01:10:02,880
+هذول وكان ليها تقداش مساحة في المنطقة المشتركة ما
+
+652
+01:10:02,880 --> 01:10:07,300
+بين الاتنين بقوله بسيطة هل الوان حاليا في تمثل
+
+653
+01:10:07,300 --> 01:10:13,680
+بالنسبة لمحوري الإحداثية محور X ومحور Y؟اللي جابها
+
+654
+01:10:13,680 --> 01:10:18,420
+نعم يبقى هدول كام منطقة باعتبرهم اربع مناطق يبقى
+
+655
+01:10:18,420 --> 01:10:22,160
+لو جيبت منطقة وضربتها فيها اربعة بيقول اه خلصنا من
+
+656
+01:10:22,160 --> 01:10:26,260
+الشغل هذي يبقى يا بنات احنا بنأيجي ناخد المنطقة
+
+657
+01:10:26,260 --> 01:10:32,320
+المبلنة اللي عيدناها يعني لو روحت رسمتها على
+
+658
+01:10:32,320 --> 01:10:37,040
+الطبيعة من جديد بتقول المنطقة هيها هيك
+
+659
+01:10:41,020 --> 01:10:48,760
+هذه المنطقة المظللة هذا يكون θ تساوي y على 2 وهذا
+
+660
+01:10:48,760 --> 01:10:56,200
+يكون θ تساوي 0 تمام ؟ طيب إذا الخط الأزرق تبع
+
+661
+01:10:56,200 --> 01:11:01,400
+المنخنامين R يساوي 1 ناقص في صين الزاوية
+
+662
+01:11:04,410 --> 01:11:10,810
+لما بدنا نيجي نحسب مساحة هذه المنطقة يبقى بدي أخده
+
+663
+01:11:10,810 --> 01:11:18,490
+من نقطة الأصل لغاية مين؟ لغاية أي نقطة تقع على
+
+664
+01:11:18,490 --> 01:11:26,250
+محيط المنطقة هنا أرض كده شبنات؟ Zero وهنا أرض تسوى
+
+665
+01:11:26,250 --> 01:11:33,460
+كده؟ واحد ناقص كصين الزاوية ثتابقول له الـ Area
+
+666
+01:11:33,460 --> 01:11:41,940
+المطلوبة يسوى تكوينه لRDRD فيتا الـR ستتغير من
+
+667
+01:11:41,940 --> 01:11:48,640
+Zero إلى مين؟ واحد ناقص كوصين الزاوية فيتا طبعاً
+
+668
+01:11:48,640 --> 01:11:54,940
+تظل الفيتا ستتغير من أين إلى أين من Zero لضيعة نين
+
+669
+01:11:54,940 --> 01:12:01,700
+بكون جزء المنحنى هذايبقى من zero لغاية I على 2 هذا
+
+670
+01:12:01,700 --> 01:12:07,660
+بيعطيني فقط المنطقة المظلة للي عندنا هذه يبقى لو
+
+671
+01:12:07,660 --> 01:12:12,980
+ضربتها في أربعة بيعطيني ال mailكل المنطقة اللي
+
+672
+01:12:12,980 --> 01:12:29,920
+بدوها يبقى هذا الكلام
+
+673
+01:12:29,920 --> 01:12:36,100
+يبدو يساوي 2تكامل من Zero لغاية Pi على اتنين من
+
+674
+01:12:36,100 --> 01:12:40,780
+Zero لغاية Pi على اتنين للأرثر اللي هو واحد ناقص
+
+675
+01:12:40,780 --> 01:12:46,960
+Cos Theta الكل ترميه ناقص Zero كله في قدر في D
+
+676
+01:12:46,960 --> 01:12:53,420
+Theta او انشرتهم فاقولواإتنين تكامل من Zero لPi
+
+677
+01:12:53,420 --> 01:13:00,860
+على اتنين لواحد نقص اتنين Cos θ زائد Cos تربيع θ
+
+678
+01:13:00,860 --> 01:13:09,720
+كله بالنسبة الى Dθ هذا ما هو اتنين تكامل من Zero
+
+679
+01:13:09,720 --> 01:13:14,680
+لغاية Pi على اتنين واحد نقص اتنين Cos θ مافي مشكلة
+
+680
+01:13:14,680 --> 01:13:21,230
+هذه Cos تربيع بقدر اكتبها بدلالةكوصيني ضعف الزاوية
+
+681
+01:13:21,230 --> 01:13:31,270
+نص زائد نص كوصيني اتنين ثيتا كله في دي ثيتا طيب
+
+682
+01:13:31,270 --> 01:13:37,710
+تطلعيلي هذا واحد صحيح وهذا نصك كده؟ تلاتة على
+
+683
+01:13:37,710 --> 01:13:44,690
+اتنين يبقى هذا الكلام اتنين تلاتة على اتنين ثيتا
+
+684
+01:13:44,690 --> 01:13:47,530
+ناقص اتنين
+
+685
+01:14:04,130 --> 01:14:13,130
+وإليك الجواب الجواب يطلع يساوي تلاتة by على اتنين
+
+686
+01:14:13,130 --> 01:14:20,030
+ناقص اربع او ان شئتي فاقولي تلاتة by ناقص تمانية
+
+687
+01:14:20,030 --> 01:14:25,490
+كله على اتنين هذا بيعطينا اللي همين المساحة
+
+688
+01:14:25,490 --> 01:14:38,080
+المطلوب example اربع بقولي findthe area بدنا مساحة
+
+689
+01:14:38,080 --> 01:14:43,240
+enclosed والمغلقة
+
+690
+01:14:43,240 --> 01:14:56,800
+by one leaf by one leaf of the rose of the rose دي
+
+691
+01:14:56,800 --> 01:14:59,500
+الزهرة اللي هي من
+
+692
+01:15:03,240 --> 01:15:19,120
+للزهرة اللي A تساوى 12 Cos 3 Theta
+
+693
+01:15:19,120 --> 01:15:22,300
+هذه
+
+694
+01:15:22,300 --> 01:15:28,020
+رسمناها
+
+695
+01:15:28,020 --> 01:15:32,860
+في Calculus Bطبعا نطلع على الرقم اللى مضروب فى
+
+696
+01:15:32,860 --> 01:15:35,840
+الزاوية والله إذا الرقم مضروب فى الزاوية الفردي
+
+697
+01:15:35,840 --> 01:15:41,260
+يبقى عندي تلت ورقات لإن الرقم عندي تلت إذا خمسة
+
+698
+01:15:41,260 --> 01:15:44,500
+يبقى خمس ورقات إذا سبعة سبعة ورقات لكن إذا كان رقم
+
+699
+01:15:44,500 --> 01:15:48,820
+زوجى فعدد الورقات بره ثالث رقم يعني لو قلت لك
+
+700
+01:15:48,820 --> 01:15:52,330
+cosine اتنين ثتر بيطلع أربع ورقاتوصلت الاربع تيتا
+
+701
+01:15:52,330 --> 01:15:56,410
+تطلع تمانية و هكذا فدول تلاتة يبقى ماعنديش الا
+
+702
+01:15:56,410 --> 01:16:01,070
+تلاتة يبقى لو روحت قسمتها بنات بذكركوا تذكر برسم
+
+703
+01:16:01,070 --> 01:16:06,350
+باس تيتا تساوي زيرو وهي تيتا تساوي باي على اتنين
+
+704
+01:16:06,350 --> 01:16:12,170
+فكلت الرسم بالشكل اللي أديك و بتجيلك الورق اللي
+
+705
+01:16:12,170 --> 01:16:18,170
+بعدك و اللي بعدكيبقى هذا منحنى الزهرة دول ثلاث
+
+706
+01:16:18,170 --> 01:16:22,810
+ورقات اللي بديش مساحة الثلاث ورقات اللي بس بدي مان
+
+707
+01:16:22,810 --> 01:16:27,430
+ورقة واحدة يبقى يكفينا يا بنات احنا الورقة اللي
+
+708
+01:16:27,430 --> 01:16:32,910
+على اليمين ان جيه بدوش مساحتها بكون ايه حصلنا على
+
+709
+01:16:32,910 --> 01:16:37,050
+المطلوب يجيبوا زي هيك و بس هذه الورقة المتمثلة او
+
+710
+01:16:37,050 --> 01:16:42,230
+المنحنة المتمثلة بالنسبة لمحور X يبقى تكفيني النص
+
+711
+01:16:42,230 --> 01:16:47,300
+اللي فوق هذا و بضربه في جديرفى اتنين بيعطيني مساحة
+
+712
+01:16:47,300 --> 01:16:52,880
+الورقة الواحدة طب مشان هيك بدي اشوف θ تتغير من وين
+
+713
+01:16:52,880 --> 01:16:59,220
+لوين اها بدي θ تتغير من وين لوين المنحنى اللى
+
+714
+01:16:59,220 --> 01:17:06,130
+عندنا هذا هيك بدي θ اعرف من وين لوين وبعد هيكبدي
+
+715
+01:17:06,130 --> 01:17:11,790
+اعرف R من وين لوين R من وين لوين سهل وظلت بس تحديد
+
+716
+01:17:11,790 --> 01:17:17,750
+ثيتا هذه يا بنات لو روحت رسمتيها بدك تعمليلها جدول
+
+717
+01:17:17,750 --> 01:17:23,630
+الجدول لو رجعنا الى Calculus B بلاقي هذه ثيتا
+
+718
+01:17:23,630 --> 01:17:30,050
+تساوي Pi على ستة تلاتين درجة و هذه ثيتا تساوي اللي
+
+719
+01:17:30,050 --> 01:17:37,400
+هو من زيروإذاً الـ Area المطلوبة يسوى تكاملها للـ
+
+720
+01:17:37,400 --> 01:17:43,640
+RDRDθ بإننا نيجي لـ R ، الـ R بتبدأ من نقطة الأصل
+
+721
+01:17:43,640 --> 01:17:48,860
+بنقطة منطقة التكامل لبعياد المنص اللي وراه لحدود
+
+722
+01:17:48,860 --> 01:17:54,660
+المنحنى إذا R هتبدأ من الـ Zero المنحنى هي مقطع
+
+723
+01:17:54,660 --> 01:18:03,220
+عندنا اللي هو اتناشر كساين تلاتة ثيتاو θ من Zero
+
+724
+01:18:03,220 --> 01:18:10,660
+لغاية Pi على ستة يبقى هذا الكلام بدل ساوي تكامل من
+
+725
+01:18:10,660 --> 01:18:16,140
+Zero لغاية Pi على ستة للأرض تربيه على اتنين من
+
+726
+01:18:16,140 --> 01:18:23,840
+Zero لغاية اتناشر Cos ثلاثة ثيتا وهذه هنا من خدية
+
+727
+01:18:24,870 --> 01:18:29,530
+أظن لو عوضنا بيطلع مية وأربعة واربعين كوساين تربيع
+
+728
+01:18:29,530 --> 01:18:35,350
+مية وأربعة وأربعين على اتنين باتنين وسبعين اذا
+
+729
+01:18:35,350 --> 01:18:40,570
+دغري اتنين وسبعين تكمن من زيرو لداي على ستة
+
+730
+01:18:40,570 --> 01:18:48,470
+لكوساين تربيع تلاتة فيتا دي فيتا برضه هذه لازم
+
+731
+01:18:48,470 --> 01:18:54,070
+نحولها بدلالات ضعف الزاوية يبقى اتنين وسبعين
+
+732
+01:18:57,550 --> 01:19:02,690
+فاهمين فيتا كامل من Zero لغاية Pi على ستة لواحد
+
+733
+01:19:02,690 --> 01:19:10,550
+زائد كوساين قد هذه مرتين قداش بطلع دي فيتا يبقى
+
+734
+01:19:10,550 --> 01:19:17,010
+هذه ستة وتلاتين وهذا التكامل تبعها فيتا زائد ساين
+
+735
+01:19:17,010 --> 01:19:24,490
+ستة فيتا على فيتا من Zero لغاية Pi على ستة والجواب
+
+736
+01:19:24,490 --> 01:19:29,600
+دغري مباشرة اتناشر بعديبقى هذا الكلام متساوي
+
+737
+01:19:29,600 --> 01:19:38,780
+اتناشر واحد المثال رقم خمسة مثال رقم خمسة بيقول
+
+738
+01:19:38,780 --> 01:19:48,220
+ايش بيقول ال region that lies that region that
+
+739
+01:19:48,220 --> 01:19:58,880
+lies المنطقة التي تقع inside ديكاردوينinside the
+
+740
+01:19:58,880 --> 01:20:01,920
+cardioid
+
+741
+01:20:01,920 --> 01:20:09,760
+داخل ال cardioid الـR يساوي واحد زائد cosine ثيتا
+
+742
+01:20:09,760 --> 01:20:14,360
+and outside
+
+743
+01:20:14,360 --> 01:20:21,500
+the circle وخارج الدائرة R تساوي واحد
+
+744
+01:20:23,820 --> 01:20:32,800
+is the base of a solid is the base of a solid
+
+745
+01:20:32,800 --> 01:20:45,960
+right cylinder of a solid right cylinder
+
+746
+01:20:45,960 --> 01:20:50,320
+ونادأ ليها قائمة cylinder
+
+747
+01:20:53,650 --> 01:21:00,950
+الأعلى من السليندر ، الأعلى من
+
+748
+01:21:00,950 --> 01:21:04,330
+السليندر
+
+749
+01:21:04,330 --> 01:21:14,190
+، الأعلى من السليندر موجود في الطائرة ، موجود في
+
+750
+01:21:14,190 --> 01:21:17,370
+الطائرة
+
+751
+01:21:17,370 --> 01:21:37,340
+في المستوى Z بصميم Xfind the cylinders volume بده
+
+752
+01:21:37,340 --> 01:21:40,560
+كده حجم السيلندر اللي عندها
+
+753
+01:21:54,640 --> 01:22:03,140
+مافي مشكلة بيصير هذه ال R بيصير هيك من 0 ل 1 زي
+
+754
+01:22:03,140 --> 01:22:07,700
+cos θ صحيح مختلفات
+
+755
+01:22:07,700 --> 01:22:13,060
+الدالة و بدأت ضمية في أربعة نفس الشيء و لو أخدت
+
+756
+01:22:13,060 --> 01:22:17,220
+هذه اللي تحت كمان أو هذه سيية نفس الشيء والله ال
+
+757
+01:22:17,220 --> 01:22:23,020
+area بتتمهامش هي نفسها ثابتة لإن خدت أي واحدة من
+
+758
+01:22:23,020 --> 01:22:31,660
+الأربعة وضربتها في الأربعة خدتها سؤال
+
+759
+01:22:31,660 --> 01:22:46,720
+بيقول ليه الشيطان بيقول لي في عندي ايوة اتنين
+
+760
+01:22:46,720 --> 01:22:51,900
+كتبناها اتنين قبللأ لأ ما كتبناهاش يبقى الارى يا
+
+761
+01:22:51,900 --> 01:22:59,700
+بنات بدنا نلاقي اتنين التكامل وهنا بده يصير اتنين
+
+762
+01:22:59,700 --> 01:23:05,560
+التكامل وهذا بيصير هنا اتنين بتروح مع اتنين بيظل
+
+763
+01:23:05,560 --> 01:23:12,300
+مية واربع واربعين مظبوط اي مية واربع واربعين وهذه
+
+764
+01:23:12,300 --> 01:23:19,510
+بدها تصير اتنين وسبعين بدون نص دوريوهذه بدها صير
+
+765
+01:23:19,510 --> 01:23:25,110
+اتنين والسبعين اتنين والسبعين وانت تيجي تسيبها
+
+766
+01:23:25,110 --> 01:23:31,310
+بعدين ماشي كلام صحيح طيب يعني بحث نسينا نضغط في
+
+767
+01:23:31,310 --> 01:23:34,510
+التاني وانت نضغط في الأول لإن احنا خدنا نص المنطقة
+
+768
+01:23:34,510 --> 01:23:38,790
+طيب نيجي بعض الكتابة قولي the region that lies
+
+769
+01:23:38,790 --> 01:23:42,990
+inside the cardoid and الدائرة اللي عندنا هذه
+
+770
+01:23:42,990 --> 01:23:47,370
+تعالى نشوف الكاردويد والدائرة فين الكاردويد؟
+
+771
+01:23:51,400 --> 01:23:58,660
+Y ثيتا تساوي باي على اتنين الإشارة بالذلك بكل جهة
+
+772
+01:23:58,660 --> 01:24:03,740
+اليامين يبقى هذا الـCardioid بالشكل اللي عندنا
+
+773
+01:24:03,740 --> 01:24:08,040
+طبعا؟
+
+774
+01:24:08,040 --> 01:24:12,360
+طيب لو يبقى هنا تقول ثيتا تساوي Zero او واقف
+
+775
+01:24:12,360 --> 01:24:14,180
+معادلة الـCardioid
+
+776
+01:24:22,670 --> 01:24:29,970
+لكن الدائرة معدلتها جداش R تساوي واحد اذا هتمر
+
+777
+01:24:29,970 --> 01:24:35,770
+بالنقطة هذه اللي هي R تساوي واحد او تجيكي الدائرة
+
+778
+01:24:35,770 --> 01:24:38,650
+بالشكل اللي عندنا نصف قطرة واحد
+
+779
+01:24:42,440 --> 01:24:46,560
+هيبقى هاي الدائرة اللي عندنا هرسمها باللون الأزرق
+
+780
+01:24:46,560 --> 01:24:55,020
+لكي نميز ما بين الاتنين هاي الدائرة الشكل
+
+781
+01:24:55,020 --> 01:25:04,380
+اللي عندنا كويس؟
+
+782
+01:25:05,580 --> 01:25:11,860
+قال ايش؟ قال ال region داخل ال cardwell يبقى جوا
+
+783
+01:25:11,860 --> 01:25:17,220
+ال cardwell وفي نفس الوقت برا مين الدائرة يبقى وين
+
+784
+01:25:17,220 --> 01:25:22,400
+المنطقة هي اللي برا الدائرة وداخل ال cardwell
+
+785
+01:25:22,400 --> 01:25:28,690
+مالها؟اعتبرتها قاعدة وعملت عليها أسطوانة دائرية
+
+786
+01:25:28,690 --> 01:25:34,690
+قائمة يبقى هذه المظلة هي القاعدة تبع من الأسطوانة
+
+787
+01:25:34,690 --> 01:25:39,330
+الأسطوانة صارت من تحت لغاية فوق تمام؟ مين هي
+
+788
+01:25:39,330 --> 01:25:44,930
+الأسطوانة؟ يبقى للأسطوانة اللي هي Z تساوي Xطبعا
+
+789
+01:25:44,930 --> 01:25:48,170
+يبقى في مستوى المستوى الموجود في المستوى في
+
+790
+01:25:48,170 --> 01:25:52,850
+المستوى الموجود في المستوى الموجود في المستوى
+
+791
+01:25:52,850 --> 01:25:53,450
+الموجود في المستوى الموجود في المستوى الموجود في
+
+792
+01:25:53,450 --> 01:25:53,670
+المستوى الموجود في المستوى الموجود في المستوى
+
+793
+01:25:53,670 --> 01:25:57,570
+الموجود في المستوى الموجود في المستوى الموجود في
+
+794
+01:25:57,570 --> 01:25:58,910
+المستوى الموجود في المستوى الموجود في المستوى
+
+795
+01:25:58,910 --> 01:25:58,910
+الموجود في المستوى الموجود في المستوى الموجود في
+
+796
+01:25:58,910 --> 01:25:58,950
+المستوى الموجود في المستوى الموجود في المستوى
+
+797
+01:25:58,950 --> 01:25:58,950
+الموجود في المستوى الموجود في المستوى الموجود في
+
+798
+01:25:58,950 --> 01:25:59,010
+المستوى الموجود في المستوى الموجود في المستوى
+
+799
+01:25:59,010 --> 01:26:11,670
+الموجود في المستوى الموجود في المستوى
+
+800
+01:26:11,670 --> 01:26:17,970
+الموجوضربته فى اتنين كملت عليه كله وضربته فى اتنين
+
+801
+01:26:17,970 --> 01:26:23,330
+مش هفتقل انه هذا مقل المنخلة متمثل بالنسبة لمحور X
+
+802
+01:26:23,330 --> 01:26:29,590
+يبقى بدي اقوله اتنين المنطقة
+
+803
+01:26:29,590 --> 01:26:39,030
+دى ر دي تي تا ر دي تي تا صحيح؟ لأ مصحش مش صحيح
+
+804
+01:26:39,030 --> 01:26:45,660
+بتاكى تحط زيت جداش تساوييبقى بني بقوله هذه هيك
+
+805
+01:26:45,660 --> 01:26:53,980
+ومنطقة Z و هذه منطقة R و هذه DF و تعالي اكتب
+
+806
+01:26:53,980 --> 01:26:59,780
+التفاصيل تبعك الآن Z دي عندك ال top من فوق جداش X
+
+807
+01:26:59,780 --> 01:27:10,590
+يبقى هذه X تمامبس احنا بنشتغل في ال code ب R Cos θ
+
+808
+01:27:10,590 --> 01:27:17,690
+يعني كأن ال X دي A على المنطقة R يعني كأنه اتنين
+
+809
+01:27:17,690 --> 01:27:28,190
+تكاملين لل R Cos θ والدي A ل R دي R دي θ نيجي ال R
+
+810
+01:27:28,190 --> 01:27:34,580
+هتتغير من وين ل وينفدي برسم خط يقطع منطقة التكامل
+
+811
+01:27:34,580 --> 01:27:40,540
+النقطة هذه والنقطة هذه هنا أرض كده؟ في واحد و هنا
+
+812
+01:27:40,540 --> 01:27:47,790
+أرض ساعة كده؟ واحد زائد فصين الزاوية تيتاالارث
+
+813
+01:27:47,790 --> 01:27:52,790
+ستتغير من واحد إلى واحد زائد كوسايم الزاوية ثيتا
+
+814
+01:27:52,790 --> 01:27:58,770
+وثيتا ستتغير من عند ال zero لغاية كده؟ لغاية pi
+
+815
+01:27:58,770 --> 01:28:02,050
+على اتنين من zero لغاية pi على اتنين
+
+816
+01:28:17,720 --> 01:28:24,060
+ارتكيب على تلاتة من واحد لغاية واحد زائد كوصين
+
+817
+01:28:24,060 --> 01:28:29,920
+الزاوية ثيتا وهذا يظهر عند من كوصين الزاوية ثيتا
+
+818
+01:28:29,920 --> 01:28:36,580
+في دي ثيتا إذا هذا الكلام سيكون تلتين خلّيك برا
+
+819
+01:28:36,580 --> 01:28:43,190
+وهي تكامل من zero ل by باي على اتنينمن Zero لغاية
+
+820
+01:28:43,190 --> 01:28:51,650
+Pi على اتنين لواحد زائد Cos θ الكل تكيب ناقص
+
+821
+01:28:51,650 --> 01:28:56,330
+القيمة اللي هو ناقص واحد تكيب اللي هو واحد كله
+
+822
+01:28:56,330 --> 01:29:05,450
+مضروب في Cos θ d θ طيب يا تلتان خلّيك برا و اتكامل
+
+823
+01:29:05,450 --> 01:29:07,190
+من Zero لغاية Pi على اتنين
+
+824
+01:29:12,710 --> 01:29:18,010
+تلاتة cosine ثيتا زائد تلاتة cosine تربيع ثيتا
+
+825
+01:29:18,010 --> 01:29:24,390
+زائد cosine تكييب ثيتا ناقص واحد كله في مين؟ في
+
+826
+01:29:24,390 --> 01:29:33,350
+cosine ثيتا في d ثيتا اضل ناقص واحد وزاد واحد الله
+
+827
+01:29:33,350 --> 01:29:39,930
+يسهل عليكم مش زعلانين عليكم وهذا يتصير تلتين تكمل
+
+828
+01:29:39,930 --> 01:29:45,930
+من zero till pi على اتنينلي تلاتة cosine تربيع
+
+829
+01:29:45,930 --> 01:29:52,390
+زاوية ثيتا زائد تلاتة cosine تكييب زاوية ثيتا زائد
+
+830
+01:29:52,390 --> 01:30:01,190
+cosine أربعة ثيتا كله دي ثيتا يبقى ضالة مسألة بس
+
+831
+01:30:01,190 --> 01:30:05,430
+تكامل هذا المقدرة تعرفوا تكملوا و الله كله كلام
+
+832
+01:30:05,430 --> 01:30:18,070
+يدرسين Calculus B تعرفوايعني نسيبه ؟
+
+833
+01:30:18,070 --> 01:30:25,030
+طيب نخلقلكم بس نحاول نفتح لكم المجال هذه يا بنات
+
+834
+01:30:25,030 --> 01:30:30,370
+بتاجي اخد الأولى تلاتة مع تلاتة بيظلي اتنين هو
+
+835
+01:30:30,370 --> 01:30:35,070
+عندك هنا تكامل تلاتة مع تلاتة بيظلي اتنين من Zero
+
+836
+01:30:35,070 --> 01:30:40,730
+لPi على اتنين و Cos تربيعيبقى نص في واحد زائد
+
+837
+01:30:40,730 --> 01:30:48,410
+كوصين اتنين ثيتا في دي ثيتا طبعا اللي بعدها تلتين
+
+838
+01:30:48,410 --> 01:30:55,190
+بتروح يبقى زائد اتنين في تكامل من Zero لغاية Y على
+
+839
+01:30:55,190 --> 01:31:01,990
+اتنين Zero لغاية Y على اتنين لمين اتنين تلت من
+
+840
+01:31:01,990 --> 01:31:04,350
+اتنين لكوصين
+
+841
+01:31:13,360 --> 01:31:19,300
+وهي تكمل من Zero لغاية Pi على اتنين كوصين أوصى
+
+842
+01:31:19,300 --> 01:31:23,440
+اربعة اللي هي كوصين تربيه في كوصين تربيه وكوصين
+
+843
+01:31:23,440 --> 01:31:29,480
+تربيه اللي هي النص في واحد زائد كوصين اتنين ثيتا
+
+844
+01:31:29,480 --> 01:31:37,210
+لكل تربيه دي ثيتاهذه نص مع اتنين الله يسهل عليها
+
+845
+01:31:37,210 --> 01:31:44,650
+يبقى بظل تكامل من zero لغاية pi على اتنين لواحد
+
+846
+01:31:44,650 --> 01:31:49,590
+زائد cosine اتنين theta كله في d theta يبقى هذا
+
+847
+01:31:49,590 --> 01:31:58,810
+فرق طيب هذا مناسب زائد اتنين تكامل من zero لغاية
+
+848
+01:31:58,810 --> 01:32:06,290
+pi على اتنين شو رأيك هذا؟مش هذه مشتقة الـSin وهذه
+
+849
+01:32:06,290 --> 01:32:10,030
+مشتقة الـSin تربية أي واحد ناقص Sin تربية يبقى
+
+850
+01:32:10,030 --> 01:32:19,490
+واحد ناقص Sin تربية ثيتا مشتقة Sin الثيتا ضالمين
+
+851
+01:32:19,490 --> 01:32:26,870
+عندنا ال term الأخير هذا نص تربية بيظل كده؟ ربع
+
+852
+01:32:26,870 --> 01:32:30,210
+ربع مع هذا بيظل كده؟ سُدس
+
+853
+01:32:34,780 --> 01:32:40,640
+تكامل من Zero لغاية Pi على أربع بدي أفك هذا بلد
+
+854
+01:32:40,640 --> 01:32:46,780
+بيصير واحد زائد اتنين Cos اتنين ثيتا زائد Cos
+
+855
+01:32:46,780 --> 01:32:53,980
+ثالابية اتنين ثيتا كله بالنسبة الى D ثيتا يبقى هذا
+
+856
+01:32:53,980 --> 01:32:58,820
+الكلام مثل الاول ان هي جاهزةيبقى ثيتا زائد sin
+
+857
+01:32:58,820 --> 01:33:04,480
+اتنين ثيتا على اتنين من Zero لغاية Pi على اتنين
+
+858
+01:33:04,480 --> 01:33:11,720
+اللي بعدها هذه كمان زائد اتنين في sin الزاوية ثيتا
+
+859
+01:33:11,720 --> 01:33:17,740
+ناقص sin تكيب الزاوية ثيتا على تلاتة من Zero لغاية
+
+860
+01:33:17,740 --> 01:33:26,640
+Pi على اتنين خلصنا منها، دا للاخيرة زائد ستهه
+
+861
+01:33:26,640 --> 01:33:34,580
+فاهمين في theta في theta زائد اتنين sin اتنين
+
+862
+01:33:34,580 --> 01:33:39,400
+theta اتنين بتروح وكل هذا الكلام من عند ال zero
+
+863
+01:33:39,400 --> 01:33:46,970
+لغاية ال pi على اربع و هنا زائد سُدس في تكاملمن
+
+864
+01:33:46,970 --> 01:33:52,890
+Zero لغاية الـ Pi على أربع كوصين تربيع اللي عبارة
+
+865
+01:33:52,890 --> 01:34:03,690
+عن من نص بواحد زائد كوصين أربعة ثيتا كل دي U7
+
+866
+01:34:03,690 --> 01:34:11,050
+Pi على اتنين زائد حطي هذا بيصير Pi ب Zero ناقص
+
+867
+01:34:11,050 --> 01:34:16,350
+Zero ناقص Zero خلصنا التر من الأول اللي بعدزاية
+
+868
+01:34:16,350 --> 01:34:21,350
+اتنين باي على اتنين مقدرش بواحد و sign باي على
+
+869
+01:34:21,350 --> 01:34:27,090
+اتنين بواحد يبقى ناقص طول واللي بعده ناقص زيرو
+
+870
+01:34:27,090 --> 01:34:33,730
+زائد زيرو خلاصنا ليش اللي بعده هذا زائد سادس هذا
+
+871
+01:34:33,730 --> 01:34:41,530
+السادس فيه باي على اربعة باي على اتنين كلها باي
+
+872
+01:34:41,530 --> 01:34:42,650
+على اتنين
+
+873
+01:34:45,420 --> 01:34:49,340
+كله باي على اتنين يبقى plus thirds في باي على
+
+874
+01:34:49,340 --> 01:34:54,880
+اتنين زائد باي على اتنين بزيرو ومش باقي بزيرو كله
+
+875
+01:34:54,880 --> 01:35:02,740
+بزيرو وصل لهذا زائد واحد على اتناشر في ثيتا زائد
+
+876
+01:35:02,740 --> 01:35:10,100
+صين اربعة ثيتا على اربع والكلام من زيرو لغاية باي
+
+877
+01:35:10,100 --> 01:35:16,320
+على اتنين يبقى الجواب باي على اتنينوهنا واحد ناقص
+
+878
+01:35:16,320 --> 01:35:22,520
+تلت بضل قداش تلتين في اتنين يبقى زائد اربع على
+
+879
+01:35:22,520 --> 01:35:30,040
+تلاتة واللي بعده زائد باي على اتناشر واللي بعده
+
+880
+01:35:30,040 --> 01:35:39,260
+زائد واحد على اتناشر في اللي في أمين زائد واحد على
+
+881
+01:35:39,260 --> 01:35:43,000
+اتناشر في باي على اتنين
+
+882
+01:35:45,950 --> 01:35:51,870
+زائد باي على اتنين ويبقى الاتنين باي بزيرو وهنا
+
+883
+01:35:51,870 --> 01:35:58,570
+زائد الباقى كلهم زيكي خلصت من هنا تطلع هي خلصناها
+
+884
+01:35:58,570 --> 01:36:07,290
+لك للاخر تقريبا طيب
+
+885
+01:36:07,290 --> 01:36:14,170
+بدنا منكم الآن المسائل التالية نبقى
+
+886
+01:36:14,170 --> 01:36:22,290
+exercisesاللي هي تلتاشر اربع مسائل تالية من واحد
+
+887
+01:36:22,290 --> 01:36:26,970
+دبي التسعة وتلاتين القادة.
+
+888
+01:36:34,890 --> 01:36:37,430
+حد عنده ايه التساؤل؟
+
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/r80EmZhKdwI.srt b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/r80EmZhKdwI.srt
new file mode 100644
index 0000000000000000000000000000000000000000..1493dc11f1851174804279bd50e03d31844ca946
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/r80EmZhKdwI.srt
@@ -0,0 +1,2753 @@
+1
+00:00:12,920 --> 00:00:18,010
+السلام عليكم ورحمة الله وبركاته بسم الله الرحمن
+
+2
+00:00:18,010 --> 00:00:21,310
+الرحيم اليوم إن شاء الله هنبدأ في section 13-5
+
+3
+00:00:21,310 --> 00:00:26,510
+الذي يتحدث عن tangential and the component of
+
+4
+00:00:26,510 --> 00:00:31,350
+acceleration المركبة المماسية والمركبة العمودية
+
+5
+00:00:31,350 --> 00:00:37,550
+للعجلة يبقى tangential مماسية و normal عمودية و
+
+6
+00:00:37,550 --> 00:00:42,010
+component مركبات العجلة يبقى مركبات العجلة المركبة
+
+7
+00:00:42,010 --> 00:00:45,270
+المماسية والمركبة العمودية عليها
+
+8
+00:00:52,370 --> 00:00:59,070
+درسناها قبل ذلك  الذي هو V تساوي dR على dT  الـdR
+
+9
+00:00:59,070 --> 00:01:04,590
+على dT بدأ يدخل الـ arc length parameter S  فبسيطة عندك
+
+10
+00:01:04,590 --> 00:01:10,790
+dR على dS في dS على dT طبعا الـdR على dS درسناها
+
+11
+00:01:10,790 --> 00:01:12,450
+سابقا، اليوم  كانت من
+
+12
+00:01:16,210 --> 00:01:22,170
+يبقى ثانية، وأنا هشيلها وأكتب بدلا منها d وهذا يصير
+
+13
+00:01:22,170 --> 00:01:29,600
+dS على dT في unit tangent vector T إذا كتبنا الـ
+
+14
+00:01:29,600 --> 00:01:34,900
+Velocity V بدلا من الـ Unit Tangent T وكمية الـ
+
+15
+00:01:34,900 --> 00:01:40,540
+Scalar dS على dT سابقا تحدثنا وقلنا إن اتجاه
+
+16
+00:01:40,540 --> 00:01:46,420
+الحركة تبع الجسم هو نفس اتجاه السرعة ونفس اتجاه
+
+17
+00:01:46,420 --> 00:01:51,540
+Unit Tangent يبقى Tangent و Velocity في نفس
+
+18
+00:01:51,540 --> 00:01:56,440
+الاتجاه يبقى الاثنين بيكونوا في نفس الاتجاه لحظة
+
+19
+00:01:56,440 --> 00:02:02,200
+هي ال Velocity V تساوي  الـ dS على dT مضروبا في
+
+20
+00:02:02,200 --> 00:02:07,560
+الـ T يبقى الـ T والـ V متوازيان، الاثنين ما لهم
+
+21
+00:02:07,560 --> 00:02:15,120
+بيكونوا متوازيين لأن أحدهما مضاعف من الآخر، طيب
+
+22
+00:02:15,120 --> 00:02:19,620
+ما علينا، بنروح نجيب الـ acceleration اللي هو موضوع
+
+23
+00:02:19,620 --> 00:02:20,440
+هذا الـ section
+
+24
+00:02:27,890 --> 00:02:32,990
+معناته إننا نشتق المقدار اللي عندنا هذا يبقى d
+
+25
+00:02:32,990 --> 00:02:43,350
+على dT لـ dS على dT في اتجاه الـ T هذا يعتبر مشتق
+
+26
+00:02:43,350 --> 00:02:48,270
+حاصل ضرب دالة، يبقى هذا derivative للـ product of
+
+27
+00:02:48,270 --> 00:02:49,290
+two functions
+
+28
+00:03:00,380 --> 00:03:11,300
+d²S على dT² في T زائد dS على dT في dT على dT
+
+29
+00:03:11,300 --> 00:03:18,160
+يبقى مشتقة الأولى في الثانية كما هي زائد الأولى
+
+30
+00:03:18,160 --> 00:03:24,840
+كما هي في مشتقة الثانية بالشكل اللي عندنا هذا هنا
+
+31
+00:03:24,840 --> 00:03:29,840
+يوجد dS على dT وهنا يوجد dS على dT كذلك
+
+32
+00:03:29,840 --> 00:03:35,000
+الـ T هي عبارة عن function في الـ arc length parameter S
+
+33
+00:03:45,330 --> 00:03:56,770
+زائد dS على dT في dT على dS في dS على dT هذا
+
+34
+00:03:56,770 --> 00:04:03,030
+الكلام بيختصر، يصبح d²S على dT²
+
+35
+00:04:03,030 --> 00:04:11,750
+المشتقة الثانية في اتجاه T زائد dS على dT  ليه؟
+
+36
+00:04:16,550 --> 00:04:23,770
+في الـ principal normal unit vector N في dS على
+
+37
+00:04:23,770 --> 00:04:31,390
+dT إذا نروح نقول الـ acceleration a بدها تساوي اللي
+
+38
+00:04:31,390 --> 00:04:39,250
+هو d²S على dT² في اتجاه الـ T طبعا هذه scalar في
+
+39
+00:04:39,250 --> 00:04:44,110
+اتجاه الـ T زائد  انظر لهذا
+
+40
+00:04:46,720 --> 00:04:52,080
+والـ dS على dT والـ dS على dT يبقى dS
+
+41
+00:05:00,270 --> 00:05:06,430
+بالضبط كأننا حللنا الـ acceleration a إلى مركبتين
+
+42
+00:05:06,430 --> 00:05:11,790
+في اتجاهين متعامدين، المركبة الأولى في اتجاه الـ T
+
+43
+00:05:11,790 --> 00:05:15,430
+والمركبة الثانية في الاتجاه العمودي عليه الذي هو
+
+44
+00:05:15,430 --> 00:05:19,370
+الـ principal unit vector N، الـ principal unit
+
+45
+00:05:19,370 --> 00:05:24,300
+normal vector الذي هو N، تمام، تمام، يبقى الذي في
+
+46
+00:05:24,300 --> 00:05:27,540
+اتجاه T نسميه tangential component of
+
+47
+00:05:27,540 --> 00:05:31,560
+acceleration والذي في اتجاه الـ N نسميه normal
+
+48
+00:05:31,560 --> 00:05:35,860
+component of acceleration وكل واحدة فيهم is scalar
+
+49
+00:05:35,860 --> 00:05:41,880
+يعني هذه ليست كمية اتجاهية وإنما كمية قياسية وكذلك
+
+50
+00:05:41,880 --> 00:05:47,620
+هذه كمية قياسية، لكل واحدة منهما رمز، هذا الرمز المناسب
+
+51
+00:05:47,620 --> 00:05:54,440
+بالنسبة للـ tangential نرمز له بالرمز a<sub>T</sub> يبقى a<sub>T</sub> هي
+
+52
+00:05:54,440 --> 00:06:03,480
+عبارة عن d²S على dT²،  أو إن شئتم فقولوا
+
+53
+00:06:03,480 --> 00:06:13,120
+d على dT لـdS على dT، سؤال: هل هذه لها علاقة بـ
+
+54
+00:06:13,120 --> 00:06:17,980
+الـ speed يا بنات؟ طول الـ V، يعني مشتقة الـ speed يبقى
+
+55
+00:06:17,980 --> 00:06:26,430
+هذه d على dT لمين؟ لمشتقة الـ V، ممتاز جدا، يبقى 1000
+
+56
+00:06:26,430 --> 00:06:31,590
+ثانية، scalar tangential component of acceleration
+
+57
+00:06:31,590 --> 00:06:40,510
+يبقى هذه هي الـ scalar tangential
+
+58
+00:06:40,510 --> 00:06:44,590
+component
+
+59
+00:06:49,960 --> 00:06:56,460
+of acceleration يبقى
+
+60
+00:06:56,460 --> 00:07:00,740
+هذه المركبة المماسية للعجلة التي في اتجاه الـ unit
+
+61
+00:07:00,740 --> 00:07:05,460
+tangent T، لو أقرأها بصورة أخرى
+
+62
+00:07:10,280 --> 00:07:16,420
+معدل تغير مقدار السرعة،  ليست هي المشتقة
+
+63
+00:07:16,420 --> 00:07:20,580
+الأولى، هي معدل التغير وهي المشتقة الأولى وهي
+
+64
+00:07:20,580 --> 00:07:25,340
+الـمعامل التفاضلي الأول وهي ميل المماس للمنحنى،  ليس
+
+65
+00:07:25,340 --> 00:07:30,160
+كل هذه تعابير لها نفس المعنى، إذن هذه أقدر أقول
+
+66
+00:07:30,160 --> 00:07:36,120
+هي معدل تغير الـ speed أو الطول الذي لدينا تبع
+
+67
+00:07:36,120 --> 00:07:42,490
+الذي هو الـ V، طيب نجي للثانية، الثانية نرمز لها بالرمز
+
+68
+00:07:42,490 --> 00:07:50,270
+a<sub>N</sub> لأنها في اتجاه الـ N يبقى الـ a<sub>N</sub> بدها تساوي كابا في
+
+69
+00:07:50,270 --> 00:07:57,430
+dS على dT تربيع والذي بدوره يساوي curvature كابا
+
+70
+00:07:57,430 --> 00:08:05,590
+في طول الـ V تربيع، يبقى هذه التي في الاتجاه العمودي
+
+71
+00:08:05,590 --> 00:08:08,270
+الـ N، يبقى هذه التي نسميها الـ scalar
+
+72
+00:08:11,090 --> 00:08:18,010
+the scalar normal
+
+73
+00:08:18,010 --> 00:08:21,730
+component
+
+74
+00:08:21,730 --> 00:08:37,850
+of acceleration، طيب
+
+75
+00:08:37,850 --> 00:08:45,560
+يا بنات، في علاقة تربط العجلة الأساسية بالمركبتين
+
+76
+00:08:45,560 --> 00:08:51,840
+بدنا نعرف ما هي هذه العلاقة، عشان نعرف هذه العلاقة
+
+77
+00:08:51,840 --> 00:08:58,240
+بأجي بقول، كويس، لو عملنا ضرب نقطي بين العجلة مع نفسها
+
+78
+00:08:58,240 --> 00:09:04,460
+يبقى بأجي بقول الـ a هذا، حأعطيكم في صورة ملاحظة بسيطة
+
+79
+00:09:08,890 --> 00:09:14,210
+لو قلت لك الـ a ضرب a، تقولي لي ماذا؟ طول الـ a
+
+80
+00:09:14,210 --> 00:09:19,470
+تربيع، طيب الآن الـ a<sub>T</sub> سهل أجدها بسهولة، هذه التي
+
+81
+00:09:19,470 --> 00:09:24,850
+لديك بفضل الـ R وP، أحصل عليه، أجيب الطول أكون جبته
+
+82
+00:09:24,850 --> 00:09:29,070
+مشتقته، فأجيبه بسهولة، كما الـ curvature في الـ dS
+
+83
+00:09:29,070 --> 00:09:34,100
+على dT، بدأ طولها شوية، فهنا طريقة أقصد منها، إذا
+
+84
+00:09:34,100 --> 00:09:37,960
+جبت الـ acceleration، أعملها ضرب نقطي مع نفسها يبقى
+
+85
+00:09:37,960 --> 00:09:45,500
+يُعطيني طول الـ a تربيع، الآن لدينا الـ a<sub>T</sub> تربيع لـ
+
+86
+00:09:45,500 --> 00:09:53,020
+a ضرب a زائد الـ a<sub>N</sub> تربيع بدها تساوي من الذي هو
+
+87
+00:09:53,020 --> 00:09:57,840
+الـ a ضرب الـ a الذي بدوره يساوي طول الـ a تربيع
+
+88
+00:09:57,840 --> 00:10:05,020
+يبقى من هذه العبارة، وأقدر أحسب الـ a<sub>N</sub> التي
+
+89
+00:10:05,020 --> 00:10:13,760
+تساوي الـ square root لطول الـ A تربيع ناقص الـ a<sub>T</sub> تربيع، يبقى
+
+90
+00:10:13,760 --> 00:10:18,240
+هذه وسيلة عملية بسيطة للحصول على المركبة الثانية
+
+91
+00:10:18,240 --> 00:10:23,200
+للعجلة بدون ما نروح نحسب لا الـ curvature ولا الـ
+
+92
+00:10:23,200 --> 0:10:28,290
+الـ T ولا الأمر الثاني وما إلى ذلك، طيب، كويس يبقى
+
+93
+00:10:28,290 --> 00:10:32,210
+هذا يعني هذا الذي هو الجزء النظري تبع الـ
+
+94
+00:10:32,210 --> 00:10:36,710
+tangential و normal، لو حبينا نعرف الاتجاه، يعني كيف
+
+95
+00:10:36,710 --> 00:10:41,150
+بيكون بالضبط، فأجي بقول لو أخذت smooth curve على
+
+96
+00:10:41,150 --> 00:10:47,250
+سبيل المثال بهذا الشكل، وقلت هذه الـ base point P<sub>0</sub>
+
+97
+00:10:47,250 --> 00:10:52,810
+يبقى هذا الخط كله بيكون  arc length
+
+98
+00:10:52,810 --> 00:11:00,750
+parameter S  لو رحت عند نقطة مثل هذه النقطة و
+
+99
+00:11:00,750 --> 00:11:05,590
+رحت أخدت الذي هو الـ tangent عندها، يبقى الـ tangent
+
+100
+00:11:05,590 --> 00:11:11,170
+يكون بالشكل الذي لدينا هذا، يبقى
+
+101
+00:11:11,170 --> 00:11:16,490
+هذا الـ tangent للمماس عند هذه النقطة، هذا الذي هو
+
+102
+00:11:16,490 --> 00:11:18,310
+الـ tangent T
+
+103
+00:11:20,890 --> 00:11:25,590
+للـ principal normal بدي أكون أين؟ للداخل، الذي هو
+
+104
+00:11:25,590 --> 00:11:32,230
+عمودي عليه، هذا الذي هو N، يبقى الـ acceleration لها
+
+105
+00:11:32,230 --> 00:11:37,210
+مركبتان؟ المركبة الأولى في اتجاه الـ T التي
+
+106
+00:11:37,210 --> 00:11:46,290
+سميتها a<sub>T</sub>، من هي؟ هي d²S على dT²، المركبة الثانية
+
+107
+00:11:46,290 --> 00:11:53,330
+هنا a<sub>N</sub> التي هي الـ curvature كابا في من؟ في الذي هو
+
+108
+00:11:53,330 --> 00:11:58,470
+طول الـ V تربيع،  طيب السؤال أين الـ
+
+109
+00:11:58,470 --> 00:12:04,810
+acceleration؟ تقول لك، كامل المستطيل الذي لديك بهذا
+
+110
+00:12:04,810 --> 00:12:11,230
+الشكل، يبقى القطر تبع هذا المستطيل يمثل الـ
+
+111
+00:12:11,230 --> 00:12:17,400
+acceleration A التي حللناها إلى مركبتين، المركبة
+
+112
+00:12:17,400 --> 00:12:20,440
+الأولى هي الـ tangential component والمركبة
+
+113
+00:12:20,440 --> 00:12:25,040
+الثانية هي الـ normal component of acceleration
+
+114
+00:12:25,040 --> 00:12:32,780
+نعطي مثالا توضيحيا على هذا الكلام، هذا
+
+115
+00:12:32,780 --> 00:12:36,140
+مثال بسيط جدا
+
+116
+00:13:06,540 --> 00:13:15,180
+بقول الآن الـ A of T بدها تساوي الذي هو T زائد واحد
+
+117
+00:13:15,180 --> 00:13:20,760
+في اتجاه الـ i زائد اثنين T في اتجاه الـ j
+
+118
+00:13:32,620 --> 00:13:43,740
+The acceleration، طول العجلة A، يُعطى
+
+119
+00:13:43,740 --> 00:13:50,240
+على الشكل A يُعطى
+
+120
+00:13:50,240 --> 00:13:53,900
+على
+
+121
+00:13:53,900 --> 00:13:54,420
+الشكل
+
+122
+00:13:57,770 --> 00:14:08,850
+a<sub>T</sub> عند T تساوي واحد without finding .. without finding
+
+123
+00:14:08,850 --> 00:14:17,190
+بدون حساب أو بدون إيجاد T و الـ
+
+124
+00:14:30,480 --> 00:14:35,380
+نقرأ السؤال مرة ثانية، نحدد شو اللي مطلوب في السؤال
+
+125
+00:14:35,380 --> 00:14:41,680
+وبالتالي نقدر نحسب المطلوب حسابا دقيقا
+
+126
+00:14:41,680 --> 00:14:47,640
+يُعطيني الـ position vector لجسم يتحرك، وقال
+
+127
+00:14:47,640 --> 00:14:51,000
+لجسم، المعادلة تبعته، الـ vector value function، يُعطى
+
+128
+00:14:51,000 --> 00:14:55,440
+T في اتجاه i زائد اثنين T في اتجاه j زائد T
+
+129
+00:14:55,440 --> 00:15:02,460
+تربيع في اتجاه k، الذي يكتب لي العجلة على شكل مركبتيه
+
+130
+00:15:02,460 --> 00:15:06,700
+الـ tangential component و الـ normal component
+
+131
+00:15:06,700 --> 00:15:11,520
+احسب لي هذا الكلام عندما T تساوي 1 بدون ما تحسب لا T
+
+132
+00:15:11,520 --> 00:15:18,930
+ولا N، يبقى مش لازم نحسب لا T ولا N، لكن يجب أن تخلّي
+
+133
+00:15:18,930 --> 00:15:24,350
+T و N كما هما، يعني كأن المعادلة مكتوبة بدلالة T و N
+
+134
+00:15:24,350 --> 00:15:27,470
+لذلك يجب أن أحصل على tangential component
+
+135
+00:15:27,470 --> 00:15:32,150
+التانجينشال كومبوننت شرحناها قبل قليل، فكانت هي
+
+136
+00:15:32,150 --> 00:15:36,730
+عبارة عن مشتقة الـ speed، معناته الكلام بده يروح
+
+137
+00:15:36,730 --> 00:15:40,150
+إلى مشتقة الـ speed يبقى بدنا نروح ونجلب الـ
+
+138
+00:15:40,150 --> 00:15:44,530
+velocity ثم الـ speed ثم نشتقها، يبقى بعدين أقول له
+
+139
+00:15:44,530 --> 00:15:50,990
+solution بدي الـ V as a function of T يبقى التي هي
+
+140
+00:15:50,990 --> 00:16:01,090
+dR على dT ويساوي i زائد 2T زائد 2T<sup>2</sup>k
+
+141
+00:16:05,600 --> 00:16:11,140
+طول الـ vector V يساوي الجذر التربيعي لواحد زائد
+
+142
+00:16:11,140 --> 00:16:16,340
+أربعة زائد أربعة T تربيع ويساوي الـ square root
+
+143
+00:16:16,340 --> 00:16:26,560
+لخمسة زائد أربعة T تربيع، بعد هيك بدنا الـ a<sub>T</sub> يبقى
+
+144
+00:16:26,560 --> 00:16:33,260
+الـ a<sub>T</sub> هي عبارة عن d على dT لطول الـ V، يبقى معناته
+
+145
+00:16:33,260 --> 00:16:39,590
+بنشتق هذا الجذر، أخذناه في Calculus A، ليس نفس
+
+146
+00:16:39,590 --> 00:16:44,130
+الجذر، واحد على اثنين الجذر، هذا ليس نفس ما بداخل
+
+147
+00:16:59,670 --> 00:17:05,470
+يبقى النتيجة النهائية بعد الاختصار بتصير أربعة T
+
+148
+00:17:05,470 --> 00:17:11,970
+على الجذر التربيعي لخمسة زائد أربعة T تربيع، تمام
+
+149
+00:17:11,970 --> 00:17:19,670
+قال لي احسب لي هذا الكلام عند T تساوي واحد، يبقى عند T
+
+150
+00:17:19,670 --> 00:17:25,910
+تساوي واحد، هذا يصير أربعة على جذر خمسة زائد أربعة
+
+151
+00:17:25,910 --> 00:17:31,530
+في واحد تربيع، باربعة، أربعة وخمسة تسعة تحت الجذر
+
+152
+00:17:31,530 --> 00:17:36,750
+ثلاثة، يبقى النتيجة تساوي أربعة على ثلاثة، هذا
+
+153
+00:17:36,750 --> 00:17:41,710
+مقدار  a<sub>T</sub> component، وزي ما أنت شايف scalar، زي
+
+154
+00:17:41,710 --> 00:17:46,150
+ما قلنا لكم أن هذه النتيجة scalar قبل ذلك، المركبة
+
+155
+00:17:46,150 --> 00:17:51,650
+الأولى، بنروح نجيب المركبة الثانية، عشان نجيب
+
+156
+00:17:51,650 --> 00:17:56,450
+المركبة الثانية، بنروح
+
+157
+00:17:56,450 --> 00:18:01,150
+نجيب المركبة الثانية، عشان نجيب المركبة الأولى
+
+158
+00:18:01,150 --> 00:18:01,610
+بنروح نجيب المركبة الأولى، بنروح نجيب المركبة
+
+159
+00:18:01,610 --> 00:18:01,630
+الأولى، بنروح نجيب المركبة الأولى، بنروح
+
+160
+00:18:01,630 --> 00:18:01,930
+نجيب المركبة الأولى، بنروح نجيب المركبة الأولى
+
+161
+00:18:01,930 --> 00:18:02,410
+الأولى، بنروح نجيب المركبة الأولى، بنروح نجيب
+
+162
+00:18:02,410 --> 00:18:05,470
+المركبة الأولى، بنروح نجي
+
+163
+00:18:21,900 --> 00:18:27,860
+اثنين فقط متوازيين يبقى الآن لو جئت يا بنات أنتِ
+
+164
+00:18:27,860 --> 00:18:37,760
+قلت لكِ بدي الـ a ضرب a كده، بطلع لي طول الـ a
+
+165
+00:18:37,760 --> 00:18:44,820
+تربيعه، متجه في نفسه، بطلع كده، هذا بطلع أربعة، إذن
+
+166
+00:18:44,820 --> 00:18:49,440
+سهل إيجاد الذي هو الـ normal component of
+
+167
+00:18:49,440 --> 00:18:53,460
+acceleration فأروح بقول له normal component of
+
+168
+00:18:53,460 --> 00:18:58,600
+acceleration a<sub>N</sub> يساوي الجذر التربيعي لطول الـ A
+
+169
+00:18:58,600 --> 00:19:06,560
+تربيع ناقص الـ a<sub>T</sub> تربيع ويساوي الـ square root لـ A تربيع
+
+170
+00:19:10,730 --> 00:19:18,350
+ناقص أربعة على ثلاثة تربيع، يبقى هذا أربعة على ثلاثة الكل تربيع
+
+171
+00:19:18,350 --> 00:19:24,610
+يبقى الـ square root لأربعة ناقص ستة عشر على تسعة
+
+172
+00:19:33,590 --> 00:19:40,330
+العشرين، أربعة في خمسة يعني اثنين جذر خمسة على
+
+173
+00:19:40,330 --> 00:19:44,910
+ثلاثة، هذا مقدار ما هو الـ normal component of
+
+174
+00:19:44,910 --> 00:19:49,170
+acceleration، إذن أصبحت الـ acceleration التي
+
+175
+00:19:49,170 --> 00
+
+223
+00:24:56,660 --> 00:25:01,560
+من الـ cross product which is a vector سؤالنا هو هل
+
+224
+00:25:01,560 --> 00:25:02,960
+هذا unit vector؟
+
+225
+00:25:09,720 --> 00:25:13,860
+لو عملت cross product بين two vectors أن يكون
+
+226
+00:25:13,860 --> 00:25:19,520
+الناتج هو unit vector قد يكون وقد لا يكون لكن في
+
+227
+00:25:19,520 --> 00:25:23,160
+موضوع هنا الـ by normal vector الـ by normal vector
+
+228
+00:25:23,160 --> 00:25:28,620
+is a unit vector تمام بس in general الكلام هذا
+
+229
+00:25:28,620 --> 00:25:30,860
+معروف ليس صحيحًا
+
+230
+00:25:45,200 --> 00:25:50,960
+هذا المثال يُظهر أن هذا المعنى ليس صحيحًا
+
+231
+00:25:56,310 --> 00:26:01,250
+هه، كلفت نظرِكم الآن، بدنا نرجع لموضوعنا، الموضوع
+
+232
+00:26:01,250 --> 00:26:06,410
+الـ BINORMAL VECTOR، شو رأيكم يا بنات؟ لو روحنا
+
+233
+00:26:06,410 --> 00:26:09,970
+اشتقيناها، شوفوا لوين بدنا نوصل فيها الدنيا،
+
+234
+00:26:09,970 --> 00:26:18,410
+كويس؟ يبقى بدنا نأخذ مثلًا الـ derivative of
+
+235
+00:26:18,410 --> 00:26:29,830
+the bi- أو بي تساوي... الآن بدي أعمل اشتقاق و
+
+236
+00:26:29,830 --> 00:26:35,930
+أشوف إيش بده يكون، يعني لو روحت أخذت دي دي على دي
+
+237
+00:26:35,930 --> 00:26:38,510
+أس، أشوف إيش بده يكون
+
+238
+00:26:41,940 --> 00:26:47,660
+بنشتق، ويبقى كل واحد في مكانه لأن عملية cross
+
+239
+00:26:47,660 --> 00:26:52,740
+product not commutative، يبقى بيفضل كل واحد في مكانه
+
+240
+00:26:52,740 --> 00:27:03,040
+يبقى مجموعة DT على DS cross الـ N زائد T cross الـ
+
+241
+00:27:03,040 --> 00:27:06,040
+DN على D
+
+242
+00:27:09,250 --> 00:27:16,870
+طب كويس، طيب يا بنات، لو رجعنا شوية، قبل شوية كتبناها، و
+
+243
+00:27:16,870 --> 00:27:20,750
+احنا بنحكي في الـ tangential، لو روحنا لـ principal
+
+244
+00:27:20,750 --> 00:27:27,750
+unit normal N، قد إيش بساوي؟ واحد على كذا في مين؟ في DT
+
+245
+00:27:27,750 --> 00:27:34,750
+على DS، يعني الـ principal unit normal، و DT على DS
+
+246
+00:27:34,750 --> 00:27:42,030
+لاثنين are parallel، واحد فيهم مضاعفات الثانية، يبقى
+
+247
+00:27:42,030 --> 00:27:47,230
+ما اللي بقول sense فيما أن الـ principle unit
+
+248
+00:27:47,230 --> 00:27:53,630
+normal N بدها تساوي واحد على كذا دي تي على دي اس
+
+249
+00:27:53,630 --> 00:28:00,130
+يبقى إثنين هدول ما هم parallel لأن هذا هو scalar
+
+250
+00:28:00,130 --> 00:28:05,390
+وهذا هو vector، يبقى صار هذا مضاعف من الـ vector
+
+251
+00:28:05,390 --> 00:28:15,010
+الثاني، يبقى هذا يعطينا أن الـ N والـ DT على DT
+
+252
+00:28:15,010 --> 00:28:22,410
+are parallel، مدام إثنين متوازيين يبقى cross product
+
+253
+00:28:22,410 --> 00:28:33,240
+فيما بينهم، DT على DS يا بنات، DT على DS، يبقى
+
+254
+00:28:33,240 --> 00:28:36,560
+معنا إثنين هذول parallel، مدام parallel يبقى الـ
+
+255
+00:28:36,560 --> 00:28:42,140
+cross product لهم قد إيش؟ متوازيين، cross product
+
+256
+00:28:42,140 --> 00:28:49,160
+zero، يبقى هذا بده يعطينا أنه الآن والله زي ما هي
+
+257
+00:28:49,160 --> 00:28:57,060
+دي ت على دي اس cross الان بتساوي قد ايش؟ Zero، مدام
+
+258
+00:28:57,060 --> 00:29:01,300
+Zero، إذًا المعادلة دي أخذت شكل جديد
+
+259
+00:29:26,900 --> 00:29:35,720
+ماذا نفهم من هذه الجملة؟ إيش تفسيرها عندك؟ أنه DB
+
+260
+00:29:35,720 --> 00:29:42,380
+على DS يساوي عمليًا T cross DN على DS، شو العلاقة بين
+
+261
+00:29:42,380 --> 00:29:48,040
+هذا المتجه والمتجهين هذول؟ عمودي على الإثنين
+
+262
+00:29:48,040 --> 00:29:55,680
+يبقى ممتاز جدًا، يبقى هذا معناته أن DB على DS is
+
+263
+00:29:55,680 --> 00:30:10,040
+orthogonal to both لكل من T و DN على DS، يُعتبر
+
+264
+00:30:10,040 --> 00:30:15,420
+هذه المعادلة رقم واحد، نرجع
+
+265
+00:30:15,420 --> 00:30:21,180
+بالذاكرة إلى الوراء قليلًا، التعريف اللي فوق بيقول B
+
+266
+00:30:21,180 --> 00:30:26,340
+is a unit vector، يعني
+
+267
+00:30:26,340 --> 00:30:31,390
+vector with constant length، صحيح ولا لأ؟ لو أعمل
+
+268
+00:30:31,390 --> 00:30:38,570
+dot product ما بين الـ B ومشتقتها، كذا؟ Zero، كذلك،
+
+269
+00:30:38,570 --> 00:30:46,070
+خاصية أخذناها قبل ذلك، يبقى باجي بقوله since
+
+270
+00:30:46,070 --> 00:30:55,050
+بما أن الـ B is a constant vector,
+
+271
+00:30:56,510 --> 00:30:57,110
+we have
+
+272
+00:30:59,890 --> 00:31:11,590
+أن الـ B dot DB على DS بدها تساوي Zero، هذا إيش بيعطينا؟
+
+273
+00:31:11,590 --> 00:31:23,130
+هذا بيعطينا أن DB على DS is orthogonal لمن؟
+
+274
+00:31:23,130 --> 00:31:27,310
+is orthogonal to B
+
+275
+00:31:30,170 --> 00:31:36,190
+وهذه العلاقة رقم اثنين، تعالوا نتطلع في واحد واثنين
+
+276
+00:31:36,190 --> 00:31:43,890
+بيقول هنا DB على DS عمودي على T وعلى DN على DS
+
+277
+00:31:43,890 --> 00:31:49,430
+وهنا بيقول أن الـ DB على DS نفسها عمودي على مين؟
+
+278
+00:31:49,430 --> 00:31:54,210
+على B، إذًا معنى هذا الكلام أن الـ DB على DS عمودي
+
+279
+00:31:54,210 --> 00:32:01,420
+على كل من T وB، صحيح ولا لأ؟ يبقى هنا بقول له so
+
+280
+00:32:01,420 --> 00:32:12,640
+والله from واحد واثنين، الـ DB على دي اس is
+
+281
+00:32:12,640 --> 00:32:18,020
+orthogonal to
+
+282
+00:32:18,020 --> 00:32:22,220
+اللي هو الأولاني T والـ B
+
+283
+00:32:26,190 --> 00:32:48,830
+طيب، هذا سيولد لنا السؤال التالي، التعريف
+
+284
+00:32:48,830 --> 00:32:53,390
+اللي كتبناه، الـ BINORMAL، بيقول إن B عمودي على كل من
+
+285
+00:32:53,390 --> 00:33:01,200
+T و N، إذًا لو كان هذا T يا بنات، هذا T، هذا بيكون مين؟
+
+286
+00:33:01,200 --> 00:33:06,740
+N، يبقى العمودي على الإثنين مين بيكون؟ اللي هو B
+
+287
+00:33:06,740 --> 00:33:09,860
+هذا
+
+288
+00:33:09,860 --> 00:33:17,000
+يا بنات، المحاور صارت كإنها ثلاثة محاور، زي محور X وY وZ
+
+289
+00:33:17,000 --> 00:33:23,330
+بس هدول بيلتقوا وين؟ بيلتقوا عند نقطة، والتَقَطُع هذه
+
+290
+00:33:23,330 --> 00:33:28,160
+النقطة P، النقطة هذه تقع على المنحنى اللي رسمناها
+
+291
+00:33:28,160 --> 00:33:32,700
+قبل شوية، يعني على المنحنى وليست نقطة الأصل، يعني
+
+292
+00:33:32,700 --> 00:33:35,600
+عند أي نقطة موجودة على المنحنى اللي رسمناها، عندها
+
+293
+00:33:35,600 --> 00:33:38,440
+الـ unit tangent والـ principle normal وبعدها
+
+294
+00:33:38,440 --> 00:33:41,320
+رسمنا، العذر، الـ unit tangent والـ principle
+
+295
+00:33:41,320 --> 00:33:46,100
+normal والـ by normal، هاي هم عندنا، هذول بيعملوا لي
+
+296
+00:33:46,100 --> 00:33:53,870
+ثلاثة مستويات، المستوى الأول اللي بيجمع T وN بسميه
+
+297
+00:33:53,870 --> 00:34:03,430
+oscillating plane، يبقى هذا بسميه oscillating plane
+
+298
+00:34:03,430 --> 00:34:06,570
+طيب
+
+299
+00:34:06,570 --> 00:34:12,030
+واللي بيجمع B وN، هذا عمودي على الـ oscillating
+
+300
+00:34:12,030 --> 00:34:19,630
+plane، بسميه normal plane، يبقى هذا هو normal
+
+301
+00:34:19,630 --> 00:34:21,070
+plane
+
+302
+00:34:23,710 --> 00:34:33,330
+والمستوى اللي بعده هذا بسميه rectifying plane، يبقى
+
+303
+00:34:33,330 --> 00:34:36,510
+rectifying
+
+304
+00:34:36,510 --> 00:34:42,190
+plane، يبقى
+
+305
+00:34:42,190 --> 00:34:47,970
+الثلاثة هذول بيعملوا لي ثلاثة مستويات متعامدة، تعالوا نشوف
+
+306
+00:34:47,970 --> 00:34:52,490
+من خلال العبارة الأخيرة اللي كتبناها، هذه، إيش بيحصل
+
+307
+00:34:52,490 --> 00:34:57,780
+عندنا؟ بيقول من المعادلة 1 و2، الـ DB على DS is
+
+308
+00:34:57,780 --> 00:35:05,160
+orthogonal to both T and B، يبقى DB على DS عمودي
+
+309
+00:35:05,160 --> 00:35:11,260
+على كل من T وB، طب مين عمودي على T وB عندنا في
+
+310
+00:35:11,260 --> 00:35:17,820
+الرسم؟ N، إذًا ما هي العلاقة بين N و DB و DB على DS؟
+
+311
+00:35:17,820 --> 00:35:26,400
+إثنين are parallel، تمام، يبقى هذا معناه أن الـ DB
+
+312
+00:35:26,400 --> 00:35:43,340
+على DS ماله؟ is parallel to the normal vector N
+
+313
+00:35:43,340 --> 00:35:49,260
+عمودي عليه، مدام عمودي عليه إذًا هذا بيعطينا إيش؟
+
+314
+00:35:49,260 --> 00:35:59,160
+مضاعفاته، يعني جده مرات عديدة، يبقى بناء عليه DB على
+
+315
+00:35:59,160 --> 00:36:10,220
+DS بدها تساوي ناقص τ في N، τ scalar، الرقم يعني،
+
+316
+00:36:10,220 --> 00:36:10,920
+كويس؟
+
+317
+00:36:16,410 --> 00:36:21,770
+الكتاب بيقول أن الإشارة السالبة تقليدية، تقليدية
+
+318
+00:36:21,770 --> 00:36:26,910
+تقليدية، التباعه إن ماكسويل وده كتاب السبب، وضلت
+
+319
+00:36:26,910 --> 00:36:32,210
+ماشية مع الكل بنفس الطريقة، يبقى بيصير عندنا دي بي على
+
+320
+00:36:32,210 --> 00:36:38,890
+دي اس يساوي سالب تاو في N، طيب أنا بقدر أجيب الـ تاو
+
+321
+00:36:38,890 --> 00:36:44,850
+هذه ولا لا؟ بنقدر... بنقدر ما بكذبش، لو تخلصنا من الـ
+
+322
+00:36:44,850 --> 00:36:52,210
+N، طب كيف نتخلص من الـ N؟ نضرب المعادلة من اليمين اللي
+
+323
+00:36:52,210 --> 00:36:57,530
+عندي هذه بسالبها فقط بدون الـ N طبعًا، الـ N هنا الـ
+
+324
+00:36:57,530 --> 00:37:06,980
+vector، يبقى إيش بنعمل؟ بنعمل dot product بالـ N مع
+
+325
+00:37:06,980 --> 00:37:13,820
+نفسه، يبقى بناء عليه يا بنات بقدر أقول هنا الـ DB على
+
+326
+00:37:13,820 --> 00:37:22,840
+DS dot الـ N بدها تساوي ناقص τ في مين؟ في الـ N dot
+
+327
+00:37:22,840 --> 00:37:23,640
+الـ N
+
+328
+00:37:29,220 --> 00:37:37,560
+مدام واحد، يبقى بناء عليه τ تساوي سالب DB على DS
+
+329
+00:37:37,560 --> 00:37:45,520
+dot N، شكل اللي عندنا هذا الـ τ يا بنات إله اسم في
+
+330
+00:37:45,520 --> 00:37:53,260
+علمنا، اسمه Torsion Function، عزم الالتواء، كويس؟ يبقى...
+
+331
+00:37:53,260 --> 00:37:58,460
+هنعطيه الـ definition التالي، يبقى definition
+
+332
+00:38:01,280 --> 00:38:06,360
+التورشن فانكشن، التورشن
+
+333
+00:38:06,360 --> 00:38:11,000
+فانكشن
+
+334
+00:38:11,000 --> 00:38:24,680
+of a smooth curve، of a smooth curve is
+
+335
+00:38:24,680 --> 00:38:33,780
+τ دو يساوي... السالب DB على...  الوضع الذي تم وضعه فيه
+
+336
+00:38:33,780 --> 00:38:36,820
+حيث
+
+337
+00:38:36,820 --> 00:38:46,200
+τ هو قيمة... التي هي قيمة...
+
+338
+00:38:46,200 --> 00:38:51,500
+التي هي قيمة... التي هي قيمة... التي هي قيمة... التي هي
+
+339
+00:38:51,500 --> 00:38:55,300
+قيمة اللي هي...
+
+340
+00:38:55,300 --> 00:38:55,320
+قيمة اللي هي... قيمة اللي هي... قيمة اللي هي... قيمة اللي
+
+341
+00:38:55,320 --> 00:38:55,600
+هي قيمة اللي هي... قيمة...
+
+342
+00:39:07,560 --> 00:39:24,760
+there's there's about اللي هو الـ unit angularity، إذًا
+
+343
+00:39:25,400 --> 00:39:29,600
+كل الفكرة في الموضوع، إنك تأخذ الـ derivative تبع
+
+344
+00:39:29,600 --> 00:39:34,600
+الـ B، الهدف من ذلك أن أوصل لمين؟ للمعادلة اللي عندنا
+
+345
+00:39:34,600 --> 00:39:39,280
+وأوصل لتعريف جديد، اللي هو تعريف torsion function
+
+346
+00:39:39,280 --> 00:39:45,020
+تمام، بيقول إن التعريف هذا، torsion function، الـ
+
+347
+00:39:45,020 --> 00:39:50,060
+smooth curve هي τ تساوي d تربيع B على DS تربيع dot N، حيث
+
+348
+00:39:50,060 --> 00:39:54,560
+τ is the rate at which هو المعدل
+
+349
+00:39:58,020 --> 00:40:04,240
+اللي بيحاول يعمل دوران حول محور T، طبعًا هذا الـ
+
+350
+00:40:04,240 --> 00:40:09,040
+oscillating plane وهذا المحور T، يعني كأنه بده
+
+351
+00:40:09,040 --> 00:40:14,380
+يعمل شغلة بالشكل اللي عندها زي دوران بهذا الشكل
+
+352
+00:40:14,380 --> 00:40:21,940
+طيب، لو جيبنا سؤال وطلبنا إرشاد، وقلنا لك بالله
+
+353
+00:40:21,940 --> 00:40:26,680
+أسمعيني، يعني إذا بدك تجيبي عليه المعادلة هذه وجيبي لي
+
+354
+00:40:26,680 --> 00:40:36,120
+principal normal، يبقى نروح نجيب الـ V ونشتقها
+
+355
+00:40:36,120 --> 00:40:40,820
+بالنسبة للـ S ونحسب طولها ونقسم ونقول جبنا
+
+356
+00:40:40,820 --> 00:40:44,060
+reference بالنور، بقى زي ما سويت المرة اللي فاتت
+
+357
+00:40:44,060 --> 00:40:49,970
+قصة طويلة، صحيح ولا لأ؟ ويرتكن أديكم، سوبن... نرجع نجيب
+
+358
+00:40:49,970 --> 00:40:54,690
+cross product بين الـ T والـ N ونروح نشتقها بالنسبة
+
+359
+00:40:54,690 --> 00:40:56,950
+للـ S، ونجيب علاقة تربط الأصلها
+
+360
+00:40:59,970 --> 00:41:05,110
+لكن في مادة الـ advanced calculus اللي بيدرسوها
+
+361
+00:41:05,110 --> 00:41:09,950
+طلاب العلوم، اللي هو التفاضل والتكامل المتقدم، مادة
+
+362
+00:41:09,950 --> 00:41:15,990
+في سنة رابعة، حسب ذلك عمليًا، وبنستخدم هذا في حل
+
+363
+00:41:15,990 --> 00:41:21,190
+المسائل، أشهر من هذه العلاقة، يبقى بدي أحطها لكم في
+
+364
+00:41:21,190 --> 00:41:21,730
+الصيغة
+
+365
+00:41:34,300 --> 00:41:42,300
+advanced calculus، نحن
+
+366
+00:41:42,300 --> 00:41:47,620
+لدينا نقطة
+
+367
+00:41:47,620 --> 00:41:52,360
+الأولى، كيرفتشا
+
+368
+00:41:52,360 --> 00:42:04,820
+كذا، عرفنا سابقًا، على أنه... على DS، لكن عمليًا يا بنات
+
+369
+00:42:04,820 --> 00:42:09,320
+هو طول الـ cross product ما بين الـ velocity والـ
+
+370
+00:42:09,320 --> 00:42:15,360
+acceleration على طول الـ V تربيع، هذه العلاقة الأولى،
+
+371
+00:42:15,360 --> 00:42:17,940
+العلاقة الثانية
+
+372
+00:42:37,370 --> 00:42:48,850
+محدد X dot Y dot Z dot X double dot Y double dot Z
+
+373
+00:42:48,850 --> 00:42:50,210
+double dot
+
+374
+00:42:53,660 --> 00:43:02,120
+Y triple dot Z triple dot، كله مقسومًا على طول V
+
+375
+00:43:02,120 --> 00:43:12,720
+cross A الكل تربيع، بشرط أن V cross A هذا لا يساوي
+
+376
+00:43:12,720 --> 00:43:18,120
+Zero، V cross A لا يساوي Zero
+
+377
+00:43:22,040 --> 00:43:26,440
+نيجي نفسر الكلام اللي احنا كاتبينه هذا، لأننا بدنا
+
+378
+00:43:26,440 --> 00:43:29,400
+نستخدمه عمليًا في الشغل
+
+379
+00:43:58,580 --> 00:44:05,660
+الـ كيرفتشا كذا هي طول الـ DT على DS، أو DT ضربناها
+
+380
+00:44:05,660 --> 00:44:11,560
+على DT في DT على DS، وقلنا واحد على طول الـ V في طول
+
+381
+00:44:11,560 --> 00:44:16,220
+الـ DT على DT، هذا السابق، لكن هنا عشان أقول إن احنا
+
+382
+00:44:16,220 --> 00:44:17,420
+جبنا الـ velocity V
+
+383
+00:44:35,490 --> 00:44:41,330
+مشتقة كل من الـ X والـ Y والـ Z
+
+384
+00:44:45,640 --> 00:44:49,800
+عشان أنا بقول R of T، بقول X of T في اتجاه الـ I، و Y
+
+385
+00:44:49,800 --> 00:44:52,780
+of T في اتجاه الـ J، و Z of T في اتجاه الـ K، جيب لي
+
+386
+00:44:52,780 --> 00:44:55,920
+فيها، يبقى جيب لي المشتقة الأولى، إذًا هدول السطر
+
+387
+00:44:55,920 --> 00:45:02,320
+الأول في المحدد هي مركبات السرعة، بعد هيك هذه
+
+388
+00:45:02,320 --> 00:45:07,460
+double dot مركبات مين؟ العجلة، الـ acceleration
+
+389
+00:45:07,460 --> 00:45:13,810
+، المشتقة الثانية لـ R of T، طب هذه مشتقة العجلة،
+
+390
+00:45:13,810 --> 00:45:18,050
+مشتقة مركبات العجلة، إذًا الصف الأول هو مركبات
+
+391
+00:45:18,050 --> 00:45:22,390
+السرعة، الصف الثاني هو مركبات العجلة، الصف الثالث
+
+392
+00:45:22,390 --> 00:45:27,570
+مركبات مشتقة العجلة، المقام V cross A هو اللي
+
+393
+00:45:27,570 --> 00:45:33,080
+اتكلمنا عليه، الكل تربيع، وهذه وسيلة عملية أسهل
+
+394
+00:45:33,080 --> 00:45:38,480
+عمليًا في الحساب من الحالة الأولى اللي أوجدناها قبل
+
+395
+00:45:38,480 --> 00:45:44,640
+قليل، نعطي مثال على كل هذا الكلام، الـ T والـ N والـ
+
+396
+00:45:44,640 --> 00:45:48,140
+curvature والـ torsion كله نحسبه، والـ by normal
+
+397
+00:45:48,140 --> 00:45:57,700
+كمان نحسبه، كله بمثال، example بيقول
+
+398
+00:45:57,700 --> 00:46:05,
+
+445
+00:51:56,320 --> 00:52:07,400
+Dt على طول الـ Dt على Dt ويوسع كيف؟ من وين؟ الـ
+
+446
+00:52:07,400 --> 00:52:10,600
+Dt على طول الـ Dt مش بناخد عامة مشترك منها اللي هي
+
+447
+00:52:10,600 --> 00:52:15,400
+sin تربيع زائد و sin تربيع مش .. في مشكلة في هذه؟
+
+448
+00:52:15,400 --> 00:52:22,100
+في هذه إيش المشكلة فيها؟ ربعي هذه وهذه
+
+449
+00:52:24,730 --> 00:52:36,410
+سنة .. سنة .. سنة .. إصابة إبراهيم وأخطاء عمار هذه
+
+450
+00:52:36,410 --> 00:52:46,770
+نجيب الطول تبعها يبقى square root 9 كيف؟ بس بس
+
+451
+00:52:46,770 --> 00:52:47,950
+كيف؟
+
+452
+00:52:53,700 --> 00:52:59,060
+إحنا نطقنا صح وكتبنا خطأ، ولذلك بنقول لك لما تحلل
+
+453
+00:52:59,060 --> 00:53:03,220
+في الامتحان للآخر، خلي آخر خمس دقائق إجراح عليك
+
+454
+00:53:03,220 --> 00:53:07,280
+لازم تلاقي غلطة يعني حين هو هنكتب، نكتب الكلمة
+
+455
+00:53:07,280 --> 00:53:11,100
+مرتين وراء بعض، لما تلاقي مجهول، وراجع، بنلاقيها يبقى
+
+456
+00:53:11,100 --> 00:53:14,900
+تدير بالك تطلع بتقول والله أنا ألف ألف حلّ، تجيب
+
+457
+00:53:14,900 --> 00:53:18,840
+إنها ناقصة عليك شغلات فيها غلط، يبقى دائما هو ده
+
+458
+00:53:18,840 --> 00:53:24,460
+إحنا بشر، بنخطئ وبننسى وما إلى ذلك، لكن هذا
+
+459
+00:53:24,460 --> 00:53:28,500
+مرفوع عندنا عند الله، بس عندنا إحنا البشر لا نحسبه
+
+460
+00:53:28,500 --> 00:53:31,980
+الغلطة، بنحسبها عليك طبعا، القولين صلى الله عليه
+
+461
+00:53:31,980 --> 00:53:38,660
+وسلم رفع عن أمتي الخطأ والنسيان وما استُكرهوا عليه
+
+462
+00:53:38,660 --> 00:53:44,100
+يبقى دي روابط كويسة، يبقى المربع الأولاني تسعة أخماس
+
+463
+00:53:47,930 --> 00:53:54,210
+اللي بعده زائد تسعة على خمسة وعشرين، كتابنا صح ولم
+
+464
+00:53:54,210 --> 00:53:59,970
+أتأكد من غلطة، يبقى تسعة على خمسة وعشرين، كوساين
+
+465
+00:53:59,970 --> 00:54:04,530
+تربيع T، يبقى تلك اللي بناخد تسعة على خمسة وعشرين
+
+466
+00:54:04,530 --> 00:54:07,450
+بيبقى تسعة تربيع زائد كوساين تربيع الواحد يبقى
+
+467
+00:54:07,450 --> 00:54:15,430
+النتيجة فقط تلت أخماس، طيب إذا نجيب الـ N اللي هو DT
+
+468
+00:54:15,430 --> 00:54:20,000
+على DT، على طول الـ DT على DT، يبقى بدنا نقسم هذا كله
+
+469
+00:54:20,000 --> 00:54:25,980
+على مين؟ أمانا على تلت أخماس، بصير ناقص sin t في
+
+470
+00:54:25,980 --> 00:54:31,560
+اتجاه الـ I ناقص cos t في اتجاه مين؟ في اتجاه الـ J
+
+471
+00:54:31,560 --> 00:54:38,420
+بالمرة نحسبه عند الـ I على 2، إن عند الـ I على 2
+
+472
+00:54:38,420 --> 00:54:46,150
+تساوي ناقص I جا تسعين، واحد جا تسعين، اثنين أو صفر
+
+473
+00:54:46,150 --> 00:54:50,710
+إذا ماقدر أجيب الـ by normal vector، يبقى هذا كل
+
+474
+00:54:50,710 --> 00:54:56,350
+الحكي، لازم ضمن المطلوب الأول من المسألة، المطلوب
+
+475
+00:54:56,350 --> 00:55:03,250
+رقم A، يبقى دلوقتي بيقولوا هنا لسه ماخلصناش، بدنا B
+
+476
+00:55:03,250 --> 00:55:10,690
+بيساوي T cross الـ M، يبقى على طول الخط باخد المحدد
+
+477
+00:55:10,690 --> 00:55:20,330
+I J، الـ T عند الـ Pi على 2 هنا بـ 0، وهنا بسادة تلت
+
+478
+00:55:20,330 --> 00:55:27,270
+أخماس، وهنا بأربعة أخماس، لأن نيجي للـ end
+
+479
+00:55:32,190 --> 00:55:38,250
+by yourself، بتفكير محدد باستخدام عناصر الصف الثالث
+
+480
+00:55:38,250 --> 00:55:46,330
+يبقى هي ناقص واحد، فيه عشق بصفه وعموده، بصير أربعة
+
+481
+00:55:46,330 --> 00:55:56,410
+أخماس J، أربعة أخماس J، ناقص مع ناقص بصير زائد تلت
+
+482
+00:55:56,410 --> 00:56:00,430
+أخماس اللي هو K
+
+483
+00:56:03,240 --> 00:56:09,000
+يبقى صارت النتيجة ناقص أربعة أخماس في اتجاه I، ناقص
+
+484
+00:56:09,000 --> 00:56:14,800
+تلت أخماس في الجهة والتاني K، يبقى هذا الشكل اللي
+
+485
+00:56:14,800 --> 00:56:21,960
+عندنا مرة ثانية، بقول يا بنات P يساوي T cross الـ N
+
+486
+00:56:21,960 --> 00:56:27,800
+شيلنا T وحطينا مركبات عند البيعتين، ناقص تلت أخماس
+
+487
+00:56:27,800 --> 00:56:33,420
+وأربعة أخماس، لجل الـ L، للـ N اللي هو بسالب واحد، والباقي
+
+488
+00:56:33,420 --> 00:56:38,520
+بأصفار، بنفكر باستخدام عناصر العمود، الصف الثالث، ليش؟
+
+489
+00:56:38,520 --> 00:56:42,440
+إن فيه أصفار بسهل، يبقى بصير ناقص واحد، إشترط
+
+490
+00:56:42,440 --> 00:56:47,880
+وعموده بصير أربعة أخماس J، ناقص مع ناقص بصير زائد
+
+491
+00:56:47,880 --> 00:56:53,980
+تلت أخماس K، دخلنا الناقص، إذا انتهينا من المطلوب
+
+492
+00:56:53,980 --> 00:57:00,400
+الأول، بنجد المطلوب الثاني، تبع من؟ تبع المسألة
+
+493
+00:57:03,260 --> 00:57:08,920
+المطلوب الثاني قالوا بدي معادلة مين؟ الـ normal
+
+494
+00:57:08,920 --> 00:57:15,500
+plane، نرجع بالذاكرة إلى الوراق، يبقى هذا من المحاور
+
+495
+00:57:15,500 --> 00:57:23,580
+الثلاثة، هذا T، هذا M، وهذا B، هذا هو الـ normal plane
+
+496
+00:57:23,580 --> 00:57:30,920
+مظبوط؟ يبقى هذا هو الـ normal plane
+
+497
+00:57:32,560 --> 00:57:38,940
+مش هنجيب معادلة مستوى، شو بيلزم؟ نعملها عمودي عليه، و
+
+498
+00:57:38,940 --> 00:57:43,320
+نقطة تقع فيه، تمام؟ الحمد لله، العمودي عليه مين هو
+
+499
+00:57:43,320 --> 00:57:49,660
+هنا؟ T موجود عندي؟ اه موجود، دي بتبدي نقطة يبقى
+
+500
+00:57:49,660 --> 00:57:57,640
+بتبدي نقطة تقع وين؟ في الـ plane، صح ولا لا؟ طيب كويس
+
+501
+00:57:57,640 --> 00:58:04,490
+الـ T والـ N والـ B، مش هادئ الطاقة، عندها نقطة ونقطة
+
+502
+00:58:04,490 --> 00:58:08,790
+موجودة على الملحانة، يعني في الفراغ، إذا ماقدر أجيب
+
+503
+00:58:08,790 --> 00:58:16,670
+إحداثيات هذه النقطة، الـMid، الـNormal Plane يمر بها
+
+504
+00:58:16,670 --> 00:58:23,390
+النقطة اللي عندنا، هذه النقطة P، بتجيبها من وين؟
+
+505
+00:58:23,390 --> 00:58:27,770
+بتجيبها من رأس المسألة، يبقى إحنا عندنا الـ X
+
+506
+00:58:33,610 --> 00:58:38,410
+كان ليحسب الشغلات هذه وين؟ عند T تساويها، طيب هذه X
+
+507
+00:58:38,410 --> 00:58:43,470
+وهذه Y، وهذه Z، لأن هشيل كل T وأحط مكانها قيمها، يرجع
+
+508
+00:58:43,470 --> 00:58:51,990
+تصير ثلاثة Sin باي على اتنين، وثلاثة Cos باي على
+
+509
+00:58:51,990 --> 00:58:57,090
+اتنين، وأربعة في باي على اتنين، بالشكل اللي عندنا
+
+510
+00:58:57,090 --> 00:59:01,130
+هذا أربعة، تيجا تمام، يرجع تصير
+
+511
+00:59:06,450 --> 00:59:14,950
+يبقى هذه النقطة التي يمر بها الكلب هي نقطة P، يبقى
+
+512
+00:59:14,950 --> 00:59:23,210
+هذه هي نقطة P بالضبط تماما، طيب P موجودة، وT هو الـ
+
+513
+00:59:23,210 --> 00:59:33,470
+normal vector، الـ T عند الـ Pi على 2 is the normal
+
+514
+00:59:33,470 --> 00:59:34,370
+vector
+
+515
+00:59:46,570 --> 00:59:52,750
+إذا من خلال هذا باجي بقول الـ X راحة عندنا في زير
+
+516
+01:00:25,100 --> 01:00:32,940
+النتيجة ناقص ثلاثة أخماس Y زائد أربعة أخماس Z، هذا مع
+
+517
+01:00:32,940 --> 01:00:40,760
+السلامة ثمانية Y على خمسة، بعد ذلك اضرب بكله في خمسة
+
+518
+01:00:40,760 --> 01:00:42,000
+تخلص من الكسور
+
+519
+01:01:02,710 --> 01:01:08,730
+المطلوب الثاني، نمرّي هنا في المثل، قال هذه الـ
+
+520
+01:01:08,730 --> 01:01:12,410
+equation of the normal plane، المطلوب الثالث يحتاج
+
+521
+01:01:12,410 --> 01:01:18,550
+إلى كيرفتشار كابا، وتورشن تاو، هذه قيمة عندي، هذه
+
+522
+01:01:18,550 --> 01:01:26,230
+قيمة V موجودة، V موجودة، حسبناها يا بنات؟ ما حسبناش
+
+523
+01:01:26,230 --> 01:01:32,050
+الـ A، يبقى بدنا نروح نحسب الـ A عند الـ Y على 2، وناخد
+
+524
+01:01:32,050 --> 01:01:40,770
+cross product ما بين الـ 2، وقول الـ V، حسبناها؟
+
+525
+01:01:40,770 --> 01:01:40,950
+V
+
+526
+01:01:59,770 --> 01:02:07,990
+على دي P، وين الـ V؟ هاي سالب ثلاثة Sin T، سالب
+
+527
+01:02:07,990 --> 01:02:15,570
+ثلاثة Sin T في اتجاه الـ I، وبعدها ناقص ثلاثة و
+
+528
+01:02:15,570 --> 01:02:20,550
+Sin T في اتجاه الـ J، وهدي فجر الفتحة على روحك، و
+
+529
+01:02:20,550 --> 01:02:26,690
+نصلا مش تكتب Zero، بدنا نحسب الـ A عند الـ Pi على
+
+530
+01:02:26,690 --> 01:02:27,270
+اثنين
+
+531
+01:02:32,310 --> 01:02:36,590
+يبقى صار الـ A موجود، والـ V موجود، فتعمل cross
+
+532
+01:02:36,590 --> 01:02:41,530
+product لهم، وشوف قداش قوته تبعه هيكون، يبقى ناخده
+
+533
+01:02:41,530 --> 01:02:52,150
+الـ V cross الـ A يساوي I J K، الـ V، V هي سالب
+
+534
+01:02:52,150 --> 01:02:58,570
+ثلاثة وأربعة، يبقى Zero، سالب ثلاثة وأربعة، لأنه
+
+535
+01:02:58,570 --> 01:02:59,370
+ماعندش I
+
+536
+01:03:14,110 --> 01:03:21,150
+مرة واحدة، لأن فيها أصفار كتيرة، ناقص ثلاثة وشطر صفه
+
+537
+01:03:21,150 --> 01:03:30,950
+وعموده 4G، زائد ثلاثة K، أول
+
+538
+01:03:30,950 --> 01:03:40,830
+شهدتم، فقولوا ناقص ثلاثة ناقص تسعة كيلو، إحنا بنقدر
+
+539
+01:03:40,830 --> 01:04:01,150
+نجيب الكيرفتشار بسهولة بدون مشاكل، طيب
+
+540
+01:04:01,150 --> 01:04:08,470
+بدنا نجيب الكيرفتشار كذا، اللي هو طول الـ V cross الـ A
+
+541
+01:04:08,470 --> 01:04:15,470
+مقسوما على طول الـ V تكعيب، هذا الكلام، وإيه، ويساوي
+
+542
+01:04:15,470 --> 01:04:21,070
+الآن بدأ نجي لطول المتجه هذا، يبقى اللي هو مين
+
+543
+01:04:21,070 --> 01:04:27,830
+التربيعي، 12 في 12، مئة وأربعة وأربعين
+
+544
+01:04:27,830 --> 01:04:37,180
+زائد 9 في 9، و1، و80، كل هذا مقسوما وين؟ طول الـ V؟ طول
+
+545
+01:04:37,180 --> 01:04:39,260
+الـ V هي خمسة
+
+546
+01:05:02,160 --> 01:05:04,960
+مقدار الكيرفتشار
+
+547
+01:05:09,080 --> 01:05:14,560
+الـ X dot والـ Y dot والـ Z dot هي .. مظبوط؟ الـ A
+
+548
+01:05:14,560 --> 01:05:21,000
+الـ acceleration هي عند الـ Y على 2 هي جاذبة،
+
+549
+01:05:21,000 --> 01:05:29,920
+ضالمين إن الـ X double dot، يعني بدنا نشتغل الـ D
+
+550
+01:05:29,920 --> 01:05:39,060
+A على D T يساوي، هي الـ A اللي هو ناقص 3 Sin T في
+
+551
+01:05:39,060 --> 01:05:46,720
+اتجاه I زائد ثلاثة Sin T في اتجاه الـ J، هذا معناه
+
+552
+01:05:46,720 --> 01:05:56,440
+إن الـ DA على DT عند من؟ عند الـ PI على اتنين يساوي
+
+553
+01:05:56,440 --> 01:06:07,820
+هذه Zero، وهذه ثلاثة J، إذا بقدر أحسب لهاللي هو main
+
+554
+01:06:07,820 --> 01:06:13,740
+اللي هو torsion tower، قول
+
+555
+01:06:13,740 --> 01:06:24,300
+الـ V مش لازم طبعا، خلصنا منه، وهذا مش لازم، والـ
+
+556
+01:06:24,300 --> 01:06:32,940
+normal مش لازم، هاي
+
+557
+01:06:32,940 --> 01:06:42,540
+نيجي الآن للـtorsion tau، بدي أساوي المحدد X dot Y dot Z
+
+558
+01:06:42,540 --> 01:06:49,080
+dot، X double dot Y double dot Z double dot X
+
+559
+01:06:49,080 --> 01:06:54,960
+triple dot Y triple dot Z triple dot، كله مقسوما
+
+560
+01:06:54,960 --> 01:07:01,060
+على طول الـ V cross الـ A، أظن تربيع، هيك يا بنات صح؟
+
+561
+01:07:01,060 --> 01:07:06,820
+تمام، يبقى هذا الكلام بدي أساوي المحدد، مركبات
+
+562
+01:07:06,820 --> 01:07:14,400
+السرعة هي، يبقى Zero، وسالب ثلاثة، وأربعة، مركبات
+
+563
+01:07:14,400 --> 01:07:25,160
+العجلة الـ A، الـ A عند الـ Y على الـ 2، وناقص
+
+564
+01:07:25,160 --> 01:07:33,620
+ثلاثة I ناقص ثلاثة Zero Zero، مركبات المشتقة هي
+
+565
+01:07:34,010 --> 01:07:41,030
+ثلاثة J، يبقى Zero، ثلاثة Zero، بالشكل هذا، بيكروس
+
+566
+01:07:41,030 --> 01:07:45,830
+الـ A طوله تبعها، بيكروس الـ A، اللي بيبقى خمسة عشر
+
+567
+01:07:45,830 --> 01:07:52,270
+مظبوط، على خمسة عشر الكل تربيع، يبقى هذا الكلام بده
+
+568
+01:07:52,270 --> 01:07:56,190
+يساوي إيش رأيك؟ قبل أن أتفككه، باستخدام عناصر
+
+569
+01:07:56,190 --> 01:08:00,870
+العمود الثالث، يبقى هي R
+
+570
+01:08:08,340 --> 01:08:15,820
+مظبوط، على قداش؟ على خمسة عشر تربيع، يبقى هذا الكلام
+
+571
+01:08:15,820 --> 01:08:22,900
+يصير ناقص، فهنا أربعة على هذه ثلاثة في خمسة، وثلاثة
+
+572
+01:08:22,900 --> 01:08:27,140
+في خمسة، ثلاثة في ثلاثة، تسعة، من الخمسة تربيع، ناقص
+
+573
+01:08:27,140 --> 01:08:32,520
+أربعة على خمسة وعشرين، هذا مقدار الـ torsion اللي
+
+574
+01:08:32,520 --> 01:08:32,760
+عادي
+
+575
+01:08:36,620 --> 01:08:41,480
+اللي عندنا هنا، stop، انتهى الـ section، وإلى يكون أرقام
+
+576
+01:08:41,480 --> 01:08:50,700
+المسائل، exercises، اللي هو تلاتاشر، خمسة، المسائل من
+
+577
+01:08:50,700 --> 01:08:57,340
+واحد إلى ستة عشر، الـ odd، بالإضافة إلى سؤال
+
+578
+01:09:15,480 --> 01:09:22,360
+إيش معناها partial؟ يبقى partial derivatives، المشتقات
+
+579
+01:09:22,360 --> 01:09:30,740
+الجزئية، إحنا اللي درسناها قبل ذلك، where في
+
+580
+01:09:30,740 --> 01:09:37,420
+calculus A و B، ولغاية اليوم في Z، كان كله بناخد الـ
+
+581
+01:09:37,420 --> 01:09:43,960
+function ده اللي في متغير واحد، يبقى ناخد الـ
+
+582
+01:09:43,960 --> 01:09:49,600
+function لو كانت ده اللي أكتر من متغير، يبقى بنجي
+
+583
+01:09:49,600 --> 01:09:55,480
+لأول section اللي هو أربعة عشر واحد، اللي هو
+
+584
+01:09:55,480 --> 01:10:00,120
+functions of
+
+585
+01:10:00,120 --> 01:10:04,260
+several variables
+
+586
+01:10:09,720 --> 01:10:16,640
+الدوال في عدة متغيرات، يبقى من الآن فصاعدا، الشطر
+
+587
+01:10:16,640 --> 01:10:21,100
+هذا أربعة عشر، واللي جاي تبع التكامل هيكون عندي
+
+588
+01:10:21,100 --> 01:10:28,200
+متغيرين أو ثلاثة أو أربعة أو n من المتغيرات، يبقى
+
+589
+01:10:28,200 --> 01:10:32,620
+بهذه بقول these functions
+
+590
+01:10:45,580 --> 01:10:54,320
+ممكن أقول يا بنات Z function في X و Y، إذا صارت
+
+591
+01:10:54,320 --> 01:11:01,280
+الاقتران Z أو الدالة Z، دالة فيه متغيرين X و Y، ممكن
+
+592
+01:11:01,280 --> 01:11:05,080
+يكون الـ W function في X
+
+593
+01:11:08,210 --> 01:11:15,230
+يبقى الأولى دالة في متغيرين، الثانية دالة في ثلاثة
+
+594
+01:11:15,230 --> 01:11:21,330
+متغيرات، مش هأحدد لكم، بس ممكن يكون دالة في N من
+
+595
+01:11:21,330 --> 01:11:29,370
+المتغيرات، كيف؟ لو كان يقول لنا مثلا Y تساوي F of X1
+
+596
+01:11:29,370 --> 01:11:34,790
+X2 X3 وظلّينا ماشيين لغاية الـ X
+
+597
+01:11:39,950 --> 01:11:47,390
+يعني الحالة هذه بقول F دالة في N من المتغيرات، تمام
+
+598
+01:11:47,390 --> 01:11:53,690
+طب الآن بدنا نعرف شو الـ domain تبع هذه الدوال، والـ
+
+599
+01:11:53,690 --> 01:11:58,590
+range تبع هذه الدوال، هل هو زي تبع calculus A و
+
+600
+01:11:58,590 --> 01:12:03,230
+B؟ مختلف عنه نوعا ما، طبعا في calculus A كنا
+
+601
+01:12:03,230 --> 01:12:08,910
+ناخد الـ domain هو interval، والـ range هو كذلك main
+
+602
+01:12:09,230 --> 01:12:15,530
+Interval، صح ولا لأ؟ هل هذا الكلام لازال كما هو؟
+
+603
+01:12:15,530 --> 01:12:19,610
+والله صار فيه بعض الخلافات بالنسبة للـ functions of
+
+604
+01:12:19,610 --> 01:12:26,050
+several variables، مش هنغير، هبدأ بأمثلة على ذلك
+
+605
+01:12:26,050 --> 01:12:29,810
+أول مثال
+
+606
+01:12:40,210 --> 01:12:45,310
+أول مثال، بروزي F الـ
+
+607
+01:12:45,310 --> 01:12:57,530
+F of XY يساوي لن، F تعني لن، XY زائد Y ناقص واحد
+
+608
+01:13:20,110 --> 01:13:32,190
+يبقى بالتعويض، لن لمن؟ الـ X بي E، والـ Y واحد، في E ذات
+
+609
+01:13:32,190 --> 01:13:40,870
+Y، يبقى واحد ناقص واحد، يبقى بضل قداش؟ لن للـ E، لن للـ
+
+610
+01:13:40,870 --> 01:13:48,920
+E، قداش؟ ممتاز جداً، قيمة الدالة عند النقطة اللي إحداثياتها
+
+611
+01:13:48,920 --> 01:13:54,240
+هي E وواحد، هيقدر قيمة واحدة، اللي
+
+667
+01:20:00,790 --> 01:20:09,180
+ثلاثة في الجذر التربيعي لأربعة ناقص X تربيع ناقص Y
+
+668
+01:20:09,180 --> 01:20:15,080
+تربيع ناقص Y ناقص Y تربيع ناقص Y تربيع
+
+669
+01:20:15,080 --> 01:20:19,640
+ناقص Y تربيع ناقص Y تربيع ناقص Y تربيع ناقص Y
+
+670
+01:20:19,640 --> 01:20:19,720
+ناقص Y تربيع ناقص Y تربيع ناقص Y تربيع ناقص Y
+
+671
+01:20:19,720 --> 01:20:27,220
+تربيع ناقص Y تربيع ناقص Y تربيع ناقص
+
+672
+01:20:27,220 --> 01:20:30,100
+Y تربيع ناقص Y
+
+673
+01:20:33,280 --> 01:20:38,940
+الجذر هذا لكي يكون معرف يريد القيمة التي تحته أكبر
+
+674
+01:20:38,940 --> 01:20:45,280
+من أو تساوي صفر تمام يبقى يريد أن يكون  الأربعة ناقص x
+
+675
+01:20:45,280 --> 01:20:49,460
+تربيع ناقص y تربيع greater than or equal to zero
+
+676
+01:20:49,460 --> 01:20:53,820
+أو إن شئتم فاقولوا أنه بليلة هداية على الشجرة
+
+677
+01:20:53,820 --> 01:20:59,020
+الثانية بس ال x تربيع زائد y تربيع أقل من أو يساوي
+
+678
+01:20:59,020 --> 01:21:05,110
+100 الأربعة ماعدلتش هذه يساوي أربعة دائرة بس احنا
+
+679
+01:21:05,110 --> 01:21:09,530
+هنا لما نقول أقل من أو يساوي بس مش على المحيط وبس
+
+680
+01:21:09,530 --> 01:21:16,430
+وجوا ليه باشي بتكون عندي disk قرص مصمت يعني كله
+
+681
+01:21:16,430 --> 01:21:21,270
+المحيط والنقاط التي في داخله يبقى هذا لو روحته
+
+682
+01:21:21,270 --> 01:21:27,110
+رسمته بياخد الشكل التالي هقول هذا محور X هذا محور
+
+683
+01:21:27,110 --> 01:21:31,630
+Y هذه نقطة الأصل التي هي صفر عندي disk على شكل
+
+684
+01:21:31,630 --> 01:21:37,550
+دائرة، الشكل هذا نصف
+
+685
+01:21:37,550 --> 01:21:43,270
+قطرها يساوي كم؟ يساوي اثنين يبقى كل المنطقة
+
+686
+01:21:43,270 --> 01:21:48,170
+المظللة هذه يبقى
+
+687
+01:21:48,170 --> 01:21:49,210
+هذه disk
+
+688
+01:21:51,680 --> 01:22:03,040
+with center at the origin and
+
+689
+01:22:03,040 --> 01:22:08,000
+radius اثنين
+
+690
+01:22:16,480 --> 01:22:24,040
+من سالب اثنين للاثنين، وجهة نظر قد تكون صحيحة وقد
+
+691
+01:22:24,040 --> 01:22:32,260
+تكون خاطئة في ثلاثة في الجذر تخفيها من الحساب؟
+
+692
+01:22:32,260 --> 01:22:36,760
+لا يبقى من ناقص ستة لستة زي ما بتقولين من ناقص ستة
+
+693
+01:22:36,760 --> 01:22:42,220
+لستة صح؟ نقول من ثلاثة فيها طبعا إجابة خاطئة، بدنا
+
+694
+01:22:42,220 --> 01:22:49,410
+إجابة صحيحة، مصححة يعني هل القيمة التي تحت الجذر هذه
+
+695
+01:22:49,410 --> 01:22:54,330
+ممكن تطلع قيمة سالبة؟ لا لا مش ممكنة يبقى الكلام
+
+696
+01:22:54,330 --> 01:22:58,010
+الذي قلتموه غلط يعني من صفر لستة، من صفر لستة، من صفر
+
+697
+01:22:58,010 --> 01:23:06,710
+في تأكيد من صفر لستة وجهة نظر يبقى من Zero لغاية
+
+698
+01:23:06,710 --> 01:23:12,470
+ستة شكليا،  أن نشوف هل هذا الكلام صحيح كيف؟
+
+699
+01:23:28,350 --> 01:23:36,690
+عند أقل قيمة لما يهدى ال X Y التي هي صفر التي هي
+
+700
+01:23:36,690 --> 01:23:41,830
+عند المركز في ال domain طلع الناتج يساوي ستة، طب
+
+701
+01:23:41,830 --> 01:23:44,930
+بدنا نشوف عند أكبر قيمة ل X و Y
+
+702
+01:23:49,340 --> 01:23:55,960
+لو تساوي مجموع ال X تربيع و Y تربيع مع الأربعة، لو
+
+703
+01:23:55,960 --> 01:24:01,280
+كان X بجذر اثنين و Y بجذر اثنين وربعنا يصير أربعة
+
+704
+01:24:01,280 --> 01:24:07,860
+ناقص أربعة يساوي كم؟ صفر، صفر معناته ثلاثة في
+
+705
+01:24:07,860 --> 01:24:10,000
+أقل من صفر
+
+706
+01:24:13,100 --> 01:24:17,960
+بشمكالية يستحيل أن أقل قيمة آخذها ال range هي
+
+707
+01:24:17,960 --> 01:24:23,620
+صفر، أكبر قيمة آخذها الستة فقط لا غير، كلام صحيح
+
+708
+01:24:23,620 --> 01:24:29,600
+طيب نأخذ نمرة C، نمرة
+
+709
+01:24:29,600 --> 01:24:37,780
+ثلاثة نأخذ ال F X Y و7  الذي هو الجذر التربيعي ل X
+
+710
+01:24:37,780 --> 01:24:40,880
+تربيع زائد Y تربيع، نقطة
+
+711
+01:24:46,980 --> 01:24:55,420
+بدي أعرف ال domain موافق
+
+712
+01:24:55,420 --> 01:25:01,720
+موافق يبقى هنا بدنا ال X تربيع زائد Y تربيع ناقص 9
+
+713
+01:25:01,720 --> 01:25:07,800
+تكون greater than or equal to 0، وإيش كمان؟ بدي ال
+
+714
+01:25:07,800 --> 01:25:14,020
+X ناقص ال Y ممنوع تساوي 0،  وقول والله كويس، طب بدنا
+
+715
+01:25:14,020 --> 01:25:19,980
+نصيغها صياغة أخرى، يبقى شباجي بيقول ال X تربيع زائد
+
+716
+01:25:19,980 --> 01:25:25,800
+Y تربيع أكبر من أو يساوي تسعة، وال Y ممنوع تساوي ال
+
+717
+01:25:25,800 --> 01:25:30,380
+X، مظبوط
+
+718
+01:25:30,380 --> 01:25:36,180
+وال Y ممنوع تساوي ال X، نشوف الحكي هنا شو شكله على
+
+719
+01:25:36,180 --> 01:25:40,720
+الطبيعة، نحاول نفهم، فبقى يقول هذه معادلة إيش أصلاً؟
+
+720
+01:25:40,720 --> 01:25:45,960
+معادلة إنقلتية يبقى دائرة، يبقى لو رحت رسمت وقول
+
+721
+01:25:45,960 --> 01:25:51,900
+هذا الملحوظة اللي عندنا هذا محور X هذا محور Y فهذه
+
+722
+01:25:51,900 --> 01:25:57,920
+نقطة الأصل صفر وهي الدائرة طيب تمام إيش قال لي؟
+
+723
+01:25:57,920 --> 01:26:06,260
+قال لي أكبر من أو يساوي تسعة يبقى وين؟ برا الدائرة
+
+724
+01:26:06,700 --> 01:26:14,200
+برا يبقى المنطقة هذه، المنطقة المظللة بالأزرق، طب
+
+725
+01:26:14,200 --> 01:26:20,620
+الخط Y تساوي X يبقى هذا الخط الذي علناه في التراث
+
+726
+01:26:20,620 --> 01:26:27,460
+المانيكة من القرن هذا الخط
+
+727
+01:26:27,460 --> 01:26:34,220
+Y تساوي X يبقى
+
+728
+01:26:34,950 --> 01:26:40,990
+كل نقطة تقع على هذا الخط لازم تكون برا من؟ برا
+
+729
+01:26:40,990 --> 01:26:45,770
+الـdomain، ممنوع يحصل تساوي، كويس؟ يعني طلع لما نقول
+
+730
+01:26:45,770 --> 01:26:50,270
+في كل المنطقة التي برا الدائرة، هنا نقاط هي موجودة
+
+731
+01:26:50,270 --> 01:26:53,950
+برا الدائرة، مظبوط ولا لا؟ نقاط التي بيبقى ممنوع
+
+732
+01:26:53,950 --> 01:26:59,160
+هذه تكون من ضمن الـdomain؟ يبقى المنطقة المظللة خارج
+
+733
+01:26:59,160 --> 01:27:05,320
+الدائرة والتي لا تقع على الخط الذي هو Y تساوي X
+
+734
+01:27:05,320 --> 01:27:14,520
+طيب بدنا الـ range يا الله أشوف اللي فوق أظن موجبة
+
+735
+01:27:14,520 --> 01:27:21,180
+الذي فوق البسط على طول الخط بقى تبني قيمة موجبة بعد
+
+736
+01:27:21,180 --> 01:27:28,440
+الصفر من عندي، الثلاثة ما يمكن أن يكون سالبة بالمرة
+
+737
+01:27:28,440 --> 01:27:36,960
+طب لو قلت لك خذي ال X باثنين و Y بثلاثة، X باثنين و
+
+738
+01:27:36,960 --> 01:27:45,540
+Y بثلاثة، مقلوب عندها ولا لا؟ يبقى مقلوب الشيء صح؟
+
+739
+01:27:46,430 --> 01:27:50,810
+يعني المقام يبقى ممكن يكون موجب وممكن يكون سالب إن
+
+740
+01:27:50,810 --> 01:27:55,630
+استبعدت الصفر بس المساواة بين X وY يبقى ممكن يكون
+
+741
+01:27:55,630 --> 01:28:02,680
+سالب وممكن يكون موجب، تأخذ السالب كله والموجبات كله
+
+742
+01:28:02,680 --> 01:28:07,180
+معقول تأخذ السالب كله؟ معقول كيف؟ مش معقول، كل ال bus
+
+743
+01:28:07,180 --> 01:28:12,360
+كل متى ال bus خمسين على سبيل المثال وجئت أنا جئت
+
+744
+01:28:12,360 --> 01:28:18,220
+الفرق بين x و y واحد من ألف، واحد من الألف تبقى بصير
+
+745
+01:28:18,220 --> 01:28:22,780
+واحد على الألف، الألف تطلع وين؟ فوق وخمسين تصير خمسين
+
+746
+01:28:22,780 --> 01:28:28,700
+الألف، طب لو كان سالب في سالب خمسين التي يبقى هذا رايح
+
+747
+01:28:28,700 --> 01:28:31,840
+على المال النهائي وهذا رايح نحو سالب infinity
+
+748
+01:28:31,840 --> 01:28:37,400
+كل ال real line يبقى ال range هنا كل ال real line
+
+749
+01:28:37,400 --> 01:28:42,520
+بالاستثناء من سالب infinity إلى infinity، طيب أعطيك
+
+750
+01:28:42,520 --> 01:28:48,840
+الآن ثلاثة أمثلة وكلها زي ما أنت شايفة area وال
+
+751
+01:28:48,840 --> 01:28:52,320
+range هو interval، طب خذ لي لمرة أربعة
+
+752
+01:29:00,150 --> 01:29:07,690
+بتساوي الجذر التربيعي لواحد ناقص X تربيع ناقص Y
+
+753
+01:29:07,690 --> 01:29:14,190
+تربيع على أربعة ناقص Z تربيع على تسعة
+
+754
+01:29:21,210 --> 01:29:27,050
+السؤال وجهي، بتقول زميلتكم ممكن ال domain يطلع صفر
+
+755
+01:29:27,050 --> 01:29:33,850
+ولا لا يمكن، ال range ممكن ال range يطلع صفر ولا لا؟ نعم
+
+756
+01:29:33,850 --> 01:29:42,230
+ممكن، وقتي تدرس المقام أكبر ما يمكن طيب
+
+757
+01:29:42,230 --> 01:29:46,830
+الآن بدنا نجي لل domain تبع ال F بدي كل الكمية
+
+758
+01:29:46,830 --> 01:29:50,450
+التي تحت الجذر أكبر
+
+759
+01:29:51,360 --> 01:29:56,340
+من أو تساوي صفر، صحيح ولا لا؟ يبقى بالدنيا أقوله
+
+760
+01:29:56,340 --> 01:30:02,500
+الآن الذي هو بدي الواحد ناقص x تربيع ناقص y تربيع
+
+761
+01:30:02,500 --> 01:30:07,140
+على أربعة ناقص z تربيع على تسعة تكون أكبر من أو
+
+762
+01:30:07,140 --> 01:30:10,220
+تساوي صفر، أو أنشرته وانفقه
+
+763
+01:30:13,160 --> 01:30:19,040
+زي تربيع على أربعة، زي زد تربيع على تسعة ما له يكون
+
+764
+01:30:19,040 --> 01:30:24,560
+أقل من أو يساوي الواحد، طب هذه لو قلت يساوي واحد
+
+765
+01:30:24,560 --> 01:30:29,720
+معادلة إيش يا بنات؟ ellipsoid، طب الاستطالة في
+
+766
+01:30:29,720 --> 01:30:35,780
+اتجاه من؟ زد،  الذي تحته أكبر مايمكن، إذا لو
+
+767
+01:30:35,780 --> 01:30:41,840
+روحت أخذت محاولة بالشكل الذي عندها ذلك وقلت هذا
+
+768
+01:30:41,840 --> 01:30:48,640
+محور X هذا Y وهذا Z ومديت هذا على سيقانته و روحت
+
+769
+01:30:48,640 --> 01:30:54,700
+رسم ال ellipsoid فكان ال ellipsoid الشكل الذي
+
+770
+01:30:54,700 --> 01:31:02,780
+عندنا وهنا شكل هذا، هذا مش هيضايقني وهذا نقطة الأصل
+
+771
+01:31:02,780 --> 01:31:07,500
+وزيرة، يبقى هذا ال ellipsoid الذي عندنا يبقى هذا
+
+772
+01:31:07,500 --> 01:31:13,820
+من؟ الـ interior تبع الـ ellipsoid زي الـ boundary
+
+773
+01:31:13,820 --> 01:31:22,440
+كل الشكل الخارجي يبقى هنا بسميه الـ interior and
+
+774
+01:31:22,440 --> 01:31:28,680
+الـ boundary of
+
+775
+01:31:28,680 --> 01:31:37,280
+the ellipsoid، طيب
+
+776
+01:31:39,170 --> 01:31:43,350
+الـ Range، يلا
+
+777
+01:31:43,350 --> 01:31:53,710
+نشوف الـ Range، أيوة
+
+778
+01:31:53,710 --> 01:31:56,810
+يلا
+
+779
+01:31:56,810 --> 01:32:03,110
+أولى شوفي الصفر كم يطلع، موافق يلا بدي كمان يبقى
+
+780
+01:32:03,110 --> 01:32:08,050
+عند 0000 تطلع قيمة ال function هي واحد، غيره
+
+781
+01:32:12,450 --> 01:32:18,070
+هذه أكبر قيمة ولا أقل قيمة؟ أقل قيمة، أقل قيمة
+
+782
+01:32:18,070 --> 01:32:21,350
+التي هي الواحد، يعني بدرجة أكبر منها، تقدر تجيب لي
+
+783
+01:32:21,350 --> 01:32:26,690
+ولو قيمة واحدة تكون أكبر منها؟ إذا بتجيب لي كمان
+
+784
+01:32:26,690 --> 01:32:33,750
+قيمة تكون وأنتوا... جيب لي قيمة واحدة بس تكون
+
+785
+01:32:33,750 --> 01:32:38,150
+أكبر من الواحدة؟ الذي يجيبها يأخذها والله غير
+
+786
+01:32:38,150 --> 01:32:41,330
+أحط لها أربعين من أربعين في أعمال الفصل من دول
+
+787
+01:32:41,330 --> 01:32:45,930
+ما تقدمش امتحان، بس جيب لي الذي هو قيمة يأخذها
+
+788
+01:32:45,930 --> 01:32:49,510
+الدالة دي أكبر من واحد عشان لا تقولي واحد وواحد
+
+789
+01:32:49,510 --> 01:32:54,550
+من عشرة، أكبر مايمكن يبقى هذه ال maximum value لل
+
+790
+01:32:54,550 --> 01:33:01,490
+function، بزيدي شوية عن الواحد، طيب وأقل قيمة؟ قدر؟
+
+791
+01:33:01,490 --> 01:33:08,590
+سالمة؟ معقول كمية من تحت الجذر سالبة والجذر معرف
+
+792
+01:33:08,590 --> 01:33:14,310
+لكمية سالبة؟ يبقى
+
+793
+01:33:14,310 --> 01:33:20,310
+أكبر قيمة هي واحد وأصغر قيمة واحد برضه يعني يعني
+
+794
+01:33:20,310 --> 01:33:27,060
+بصير range نقطة، يعني مهما تغيرت X وY وZ، بدي يطلع
+
+795
+01:33:27,060 --> 01:33:30,860
+ناتج نفس القيمة؟ يعني كل النقط التي خلقها ربنا
+
+796
+01:33:30,860 --> 01:33:39,600
+داخل الـEllipsoid صورتها نقطة واحدة؟  لا
+
+797
+01:33:39,600 --> 01:33:45,680
+احتمال يكون مجموع هذه وهذه وهذه يطلع واحد، صحيح؟
+
+798
+01:33:46,210 --> 01:33:49,630
+وإذا طلع واحد صحيح بالسالب وعندك واحد يبقى يصير
+
+799
+01:33:49,630 --> 01:33:54,090
+صفر، مرضوه، يبقى دائماً من ال range بين الصفر
+
+800
+01:33:54,090 --> 01:34:01,770
+والواحد، يبقى هذا ال range من صفر لغاية واحد as
+
+801
+01:34:01,770 --> 01:34:04,130
+any closed interval
+
+802
+01:34:24,080 --> 01:34:32,560
+طيب خلوني أقول كمان هذه الدالة هذه نمرة أربعة، نمرة
+
+803
+01:34:32,560 --> 01:34:45,760
+خمسة، نمرة خمسة، خذ لي F X Y Z يساوي L X زائد اثنين
+
+804
+01:34:45,760 --> 01:34:51,480
+Y زائد اثنين زائد ناقص اثنين زائد اثنين زائد ناقص اثنين
+
+805
+01:34:51,480 --> 01:34:55,640
+زائد
+
+806
+01:34:55,640 --> 01:34:57,480
+اثنين زائد اثنين زائد اثنين زائد اثنين زائد اثنين
+
+807
+01:34:57,480 --> 01:34:57,520
+زائد اثنين زائد اثنين زائد اثنين زائد اثنين زائد
+
+808
+01:35:18,560 --> 01:35:28,600
+فكل النقاط X و Y و Z بحيث أن X زائد 2Y زائد 2Z ناقص
+
+809
+01:35:28,600 --> 01:35:37,040
+2 تبقى أكبر من 0 أو تساوي، يبقى كل النقاط X Y و Z
+
+810
+01:35:37,040 --> 01:35:47,430
+بحيث أن X زائد 2Y زائد 2Z تبقى أكبر من قداش،  احذف هذا
+
+811
+01:35:47,430 --> 01:35:52,890
+لو كانت تساوي اثنين، معادلة إيش؟ لو كانت بدل الأكبر
+
+812
+01:35:52,890 --> 01:36:03,550
+من كانت تساوي، معادلة إيش؟ مستوى
+
+813
+01:36:03,550 --> 01:36:08,650
+اثنين، يا أخسار، نعوذ بالله، نقرأ الفاتحة على من حرم
+
+814
+01:36:08,650 --> 01:36:13,970
+النبات على المسلمين، أخذنا فيه وحلينا بدل المثال خمسة،
+
+815
+01:36:13,970 --> 01:36:18,930
+ستة أمثلة على الموضوع، يبقى هنا إيه؟ يبقى هذه لو كانت
+
+816
+01:36:18,930 --> 01:36:24,110
+تساوي اثنين، معادلة plane، طب أكبر من هذا يبقى كل
+
+817
+01:36:24,110 --> 01:36:30,430
+الفضاء كل space الذي أعلى هذا ال plane، طبعاً، طيب لو
+
+818
+01:36:30,430 --> 01:36:35,370
+حبيت أتعرف عليه شو شكله أقول آه تفضلي أقول هذا
+
+819
+01:36:35,370 --> 01:36:43,310
+الشكل هذا، محور X وهذا Y وهذا Z بدي أجيب نقاط تقاطع
+
+820
+01:36:43,310 --> 01:36:48,150
+مع المحاور، النقاط، تفضل مع محور X يبقى Y و Z بقداش؟
+
+821
+01:36:48,150 --> 01:36:55,870
+صفر، يبقى X بقداش؟ 2، يبقى لو جئت قلت النقطة هذه 2 و
+
+822
+01:36:55,870 --> 01:37:02,120
+صفر وصفر، تقاطع مع محور Y يبقى X و Z بصفر و يبقى Y
+
+823
+01:37:02,120 --> 01:37:07,540
+يبقى بواحد يبقى النقطة التي عندنا هذه التي هي صفر
+
+824
+01:37:07,540 --> 01:37:12,900
+وواحد وصفر، تقاطع مع محور Z يبقى النقطة التي
+
+825
+01:37:12,900 --> 01:37:18,780
+عندنا هذه صفر وصفر وواحد، يبقى لو أصل بهذا
+
+826
+01:37:18,780 --> 01:37:24,720
+الشكل يبقى هذا الـ Infinity طبعاً، بيمتد كله من سالب
+
+827
+01:37:24,720 --> 01:37:29,060
+Infinity لـ Infinity بس احنا جيبنا لكم نقاط تقاطع ال
+
+828
+01:37:29,060 --> 01:37:35,760
+plane هذا ما له مع محاور الإحداثيات، يبقى لما أقول
+
+829
+01:37:35,760 --> 01:37:45,940
+أكبر من اثنين، كل ال space الذي أعلى من ال plane
+
+830
+01:37:45,940 --> 01:37:56,890
+هنا يبقى ال space هذا كله above that plane
+
+831
+01:37:56,890 --> 01:38:03,070
+الذي هو X زائد اثنين Y زائد اثنين Z بده يساوي
+
+832
+01:38:03,070 --> 01:38:08,190
+اثنين يبقى كل الفراغ الذي أعلى من هذا، طب ال range
+
+833
+01:38:08,190 --> 01:38:17,210
+كل ال... range الذي... R، كل ال R، وال range هنا ال
+
+834
+01:38:17,210 --> 01:38:17,910
+range
+
+835
+01:38:22,720 --> 01:38:29,180
+آخر حاجة نمرتها ستة وفكروا لي فيها كويس F of X وY
+
+836
+01:38:29,180 --> 01:38:38,760
+وZ، F of X وY وZ يساوي X زائد Y زائد Z على absolute
+
+837
+01:38:38,760 --> 01:38:43,680
+value ل X زائد Y ز
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/r80EmZhKdwI_postprocess.srt b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/r80EmZhKdwI_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..b58860ad32542f606787cd7113589eed04c52409
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/r80EmZhKdwI_postprocess.srt
@@ -0,0 +1,3520 @@
+1
+00:00:12,920 --> 00:00:18,010
+السلام عليكم ورحمة الله وبركاتهبسم الله الرحمن
+
+2
+00:00:18,010 --> 00:00:21,310
+الرحيم اليوم ان شاء الله هنبدأ في section 13-5
+
+3
+00:00:21,310 --> 00:00:26,510
+اللى بتحدث عن tangential and component of
+
+4
+00:00:26,510 --> 00:00:31,350
+acceleration المركبة الممسية والمركبة العمودية
+
+5
+00:00:31,350 --> 00:00:37,550
+لمهن للعجلة يبقى tangential ممسي و norm عمودي و
+
+6
+00:00:37,550 --> 00:00:42,010
+component مركبات العجلة يبقى مركبات العجلة المركبة
+
+7
+00:00:42,010 --> 00:00:45,270
+الممسية والمركبة العمودية عليها
+
+8
+00:00:52,370 --> 00:00:59,070
+درسناها قبل ذلك اللي هو V تساوي DR على DT الـDR
+
+9
+00:00:59,070 --> 00:01:04,590
+على DDT بدأ يدخل الاركليك parameter S فبسيطة عندك
+
+10
+00:01:04,590 --> 00:01:10,790
+DR على DS في DS على DD طبعا الـDR على DS درسناها
+
+11
+00:01:10,790 --> 00:01:12,450
+سابقا اليوم كانت من
+
+12
+00:01:16,210 --> 00:01:22,170
+يبقى ثاني و انا هشيلها و اكتب بدالها D و هذا بيصير
+
+13
+00:01:22,170 --> 00:01:29,600
+DS على DT في unit tangent vector Tإذا كتبنا الـ
+
+14
+00:01:29,600 --> 00:01:34,900
+Velocity V بدلة الـ Unit Tangent T وكمية الـ
+
+15
+00:01:34,900 --> 00:01:40,540
+Scalar EDS على DT سابقا تحدثنا و قلنا إن اتجاه
+
+16
+00:01:40,540 --> 00:01:46,420
+الحركة تبع الجسم هو نفس اتجاه السرعة و نفس اتجاه
+
+17
+00:01:46,420 --> 00:01:51,540
+Unit Tangent يبقى Tangent و Velocity 2 in the same
+
+18
+00:01:51,540 --> 00:01:56,440
+directionيبقى الاتنين بيكونوا في نفس الاتجاه لحظة
+
+19
+00:01:56,440 --> 00:02:02,200
+هي ال Velocity V تساوي الرقم الو DS على DT مضروف
+
+20
+00:02:02,200 --> 00:02:07,560
+Main T يبقى ال T و ال VR Parallel اتنين ما لهم
+
+21
+00:02:07,560 --> 00:02:15,120
+بيكونوا متوازين لأن أحدهم هو مضعفات من الآخر طيب
+
+22
+00:02:15,120 --> 00:02:19,620
+ما علينا بناروح نجيب ال acceleration اللي هو موضوع
+
+23
+00:02:19,620 --> 00:02:20,440
+هذا ال section
+
+24
+00:02:27,890 --> 00:02:32,990
+معناته باننا نشتغل المقدار اللي عندنا هذا يبقى D
+
+25
+00:02:32,990 --> 00:02:43,350
+على DT ل DS على DT في اتجاه الـ T هذا يعتبر مشتبط
+
+26
+00:02:43,350 --> 00:02:48,270
+حاصل ضغط دليل D يبقى هذا derivative لل product of
+
+27
+00:02:48,270 --> 00:02:49,290
+two functions
+
+28
+00:03:00,380 --> 00:03:11,300
+DS على DT في ميل زائد DS على DT في مشتقة DT على DT
+
+29
+00:03:11,300 --> 00:03:18,160
+يبقى مشتقة الأولى في الثانية كما هي زائد الأولى
+
+30
+00:03:18,160 --> 00:03:24,840
+كما هي في مشتقة التانية بالشكل اللي عندنا هذاهنا
+
+31
+00:03:24,840 --> 00:03:29,840
+يوجد دي S على دي T وهنا يوجد دي S على دي T كذلك
+
+32
+00:03:29,840 --> 00:03:35,000
+الـ T هي عبارة عن function في الـ arc parameter S
+
+33
+00:03:45,330 --> 00:03:56,770
+زائد DS على DT في DT على DS في DS على DT هذا
+
+34
+00:03:56,770 --> 00:04:03,030
+الكلام بدرساوي مركّبلونة كما هي D²S على DT²
+
+35
+00:04:03,030 --> 00:04:11,750
+المشتقة الثانية في اتجاه D زائد DS على DT ليه؟
+
+36
+00:04:16,550 --> 00:04:23,770
+8 في ال principle normal unit vector n في ds على
+
+37
+00:04:23,770 --> 00:04:31,390
+dt إذا نروح نقول ال acceleration a بدها تساوي اللي
+
+38
+00:04:31,390 --> 00:04:39,250
+هو d2s على dt2 في اتجاه ال T طبعا هذه scalar في
+
+39
+00:04:39,250 --> 00:04:44,110
+اتجاه ال T زائد اتطلعي ليه هذه الكلمة
+
+40
+00:04:46,720 --> 00:04:52,080
+و ال DS على DT و ال DS على DT يبقى DS
+
+41
+00:05:00,270 --> 00:05:06,430
+بالضبط كأننا حللنا الـ acceleration a إلى مركبتين
+
+42
+00:05:06,430 --> 00:05:11,790
+في اتجاهين متعمدين المركبة الأولى في اتجاه الـ T
+
+43
+00:05:11,790 --> 00:05:15,430
+والمركبة التانية في الاتجاه العمودي عليه اللي هو
+
+44
+00:05:15,430 --> 00:05:19,370
+ال principle unit vector N ال principle unit
+
+45
+00:05:19,370 --> 00:05:24,300
+normal vector اللي هو N تمام تماميبقى اللي في
+
+46
+00:05:24,300 --> 00:05:27,540
+اتجاه T بيسميها tangential component of
+
+47
+00:05:27,540 --> 00:05:31,560
+acceleration واللي في اتجاه ال N بيسميها normal
+
+48
+00:05:31,560 --> 00:05:35,860
+component of acceleration وكل واحدة فيهم is scalar
+
+49
+00:05:35,860 --> 00:05:41,880
+يعني هذه ليست كمية اتجاهية وانما كمية قياسية وكذلك
+
+50
+00:05:41,880 --> 00:05:47,620
+هذه كمية قياسية كل واحدة حد رموز هذا الرمز المناسب
+
+51
+00:05:47,620 --> 00:05:54,440
+بالنسبة له ال tangential حديها الرمز ATيبقى AT هي
+
+52
+00:05:54,440 --> 00:06:03,480
+عبارة عن D²S على DT² شكل العنادر أو إن شئتم فقولوا
+
+53
+00:06:03,480 --> 00:06:13,120
+D على DT لـDS على DT سؤال هل هذه لها علاقة بـ
+
+54
+00:06:13,120 --> 00:06:17,980
+Speed يا بنات؟ طول الـ V يعني مصدر الـ Speed يبقى
+
+55
+00:06:17,980 --> 00:06:26,430
+هذهD على DT لمين؟ لقول ال V ممتاز جدا يبقى 1000
+
+56
+00:06:26,430 --> 00:06:31,590
+ثانية scalar tangential component of acceleration
+
+57
+00:06:31,590 --> 00:06:40,510
+يبقى 80 هذه as the scalar tangential
+
+58
+00:06:40,510 --> 00:06:44,590
+component
+
+59
+00:06:49,960 --> 00:06:56,460
+of acceleration يبقى
+
+60
+00:06:56,460 --> 00:07:00,740
+هذه المراكبة الممسية للعجلة اللي في اتجاره ال unit
+
+61
+00:07:00,740 --> 00:07:05,460
+tangent T لو ده أقرأها بصورة أخرى
+
+62
+00:07:10,280 --> 00:07:16,420
+معدل تغيير مقدار السرعة مش هي بقولها مش المشتقة
+
+63
+00:07:16,420 --> 00:07:20,580
+الأولى هي معدل التغيير و هي المشتقة الأولى و هي
+
+64
+00:07:20,580 --> 00:07:25,340
+المعاملة التفاضل الأول و هي ميل المماثل المنحنة مش
+
+65
+00:07:25,340 --> 00:07:30,160
+كل هذه تعابيرات لها نفس المعنى إذا هذه بقدر أقول
+
+66
+00:07:30,160 --> 00:07:36,120
+هي معدل تغيير ال speed أو الطول اللي عندنا تبع
+
+67
+00:07:36,120 --> 00:07:42,490
+اللي هو ال V طيب نجي للثانيةالتانية هذه حموظها رمز
+
+68
+00:07:42,490 --> 00:07:50,270
+AN لأنها في اتجاه ال N يبقى ال AN بدر ساوي كابا في
+
+69
+00:07:50,270 --> 00:07:57,430
+DS على DT Square و اللي هو بدر ساوي كيرفيتشر كابا
+
+70
+00:07:57,430 --> 00:08:05,590
+في طول ال V لكل تربية يبقى هذه اللي في اتجاه عمودي
+
+71
+00:08:05,590 --> 00:08:08,270
+E يبقى هذه اللي بسميها ال scalar
+
+72
+00:08:11,090 --> 00:08:18,010
+the scalar normal
+
+73
+00:08:18,010 --> 00:08:21,730
+component
+
+74
+00:08:21,730 --> 00:08:37,850
+of acceleration طيب
+
+75
+00:08:37,850 --> 00:08:45,560
+يا بناتفي علاقة بتربط العجلة الأساسية بالمركبتين
+
+76
+00:08:45,560 --> 00:08:51,840
+بدنا نعرف ما هي هذه العلاقة عشان نعرف هذه العلاقة
+
+77
+00:08:51,840 --> 00:08:58,240
+باجي بقول كويس لو عامل ضغط ما بين العجلة مع نفسها
+
+78
+00:08:58,240 --> 00:09:04,460
+يبقى باجي بقول ال a هذا حطالك في صورة ملاحظة بسيطة
+
+79
+00:09:08,890 --> 00:09:14,210
+لو قلت لك ال a ضد ال a تقولي لي كده؟ طول ال a
+
+80
+00:09:14,210 --> 00:09:19,470
+ترميع طيب الآن ال at سهل أجدها بسهولة هذه اللي
+
+81
+00:09:19,470 --> 00:09:24,850
+عندك بفضل ال R و P بحصل عليه بجيب الطول بكون جبته
+
+82
+00:09:24,850 --> 00:09:29,070
+مشتاق فبجيبه على فول بس كما ال kermitian في ال D S
+
+83
+00:09:29,070 --> 00:09:34,100
+على D T بدأ طول عليها شوية فهنا طريقة أقصد منهاإذا
+
+84
+00:09:34,100 --> 00:09:37,960
+جبت ال acceleration اعملها ضوط مع نفسها يبقى
+
+85
+00:09:37,960 --> 00:09:45,500
+بيعطيني طول ال a تربيع الان عندنا ال a t square ل
+
+86
+00:09:45,500 --> 00:09:53,020
+a ضوط a زائد ال a n square بده يساوي مين اللي هو
+
+87
+00:09:53,020 --> 00:09:57,840
+ال a ضوط ال a اللي هو بده يساوي طول ال a تربيع
+
+88
+00:09:57,840 --> 00:10:05,020
+يبقى من هذه العبارةو بقدر احسب له من ال AM اللي
+
+89
+00:10:05,020 --> 00:10:13,760
+بتساوي ال square root لطول ال A² مقص ال AT² يبقى
+
+90
+00:10:13,760 --> 00:10:18,240
+هذه وسيلة عملية بسيطة للحصول على المركبة الثانية
+
+91
+00:10:18,240 --> 00:10:23,200
+للعجلة بدون ما نروح نحسب لا ال curvature ولا ال
+
+92
+00:10:23,200 --> 00:10:28,290
+main ولا الأمر التاني و ما إلى ذلكطيب كويس يبقى
+
+93
+00:10:28,290 --> 00:10:32,210
+هذا يعني هذا اللي هو الجزء النظري تبع ال
+
+94
+00:10:32,210 --> 00:10:36,710
+tangential normal لو حبنا نعرف الاتجاه يعني كيف
+
+95
+00:10:36,710 --> 00:10:41,150
+بيكون بالضبط فبجي بقول لو أخدت smooth curve على
+
+96
+00:10:41,150 --> 00:10:47,250
+سبيل المثال بهذا الشكل وقلت هذه ال base point P0
+
+97
+00:10:47,250 --> 00:10:52,810
+يبقى هذا الخط كله بيكون main ال arc length
+
+98
+00:10:52,810 --> 00:11:00,750
+parameter S of Tلو روحت عنده نقطة مثل هذه النقطة و
+
+99
+00:11:00,750 --> 00:11:05,590
+روحت أخدت اللي هو ال tangent عندها يبقى ال tangent
+
+100
+00:11:05,590 --> 00:11:11,170
+يكون بالشكل اللي عندنا هذا يبقى
+
+101
+00:11:11,170 --> 00:11:16,490
+هذا ال tangent للمماس عند هذه النقطة هذا اللي هو
+
+102
+00:11:16,490 --> 00:11:18,310
+ال tangent T
+
+103
+00:11:20,890 --> 00:11:25,590
+لـ Principal Normal بدي أكون وين؟ للداخل اللي هو
+
+104
+00:11:25,590 --> 00:11:32,230
+عمودي عليه هذا اليومين N يبقى الـ Acceleration إيه
+
+105
+00:11:32,230 --> 00:11:37,210
+لها مُركّبتين؟ المُركّبة الأولى في اتجاه الـT اللي
+
+106
+00:11:37,210 --> 00:11:46,290
+سميتها AT مين هي؟ هي D²S على DT² المُركّبة التانية
+
+107
+00:11:46,290 --> 00:11:53,330
+هنا AN اللي هي الـCurvature كابةفي مين؟ في اللي هو
+
+108
+00:11:53,330 --> 00:11:58,470
+طول ال V لكل ترابيع طب السؤال هو أين ال
+
+109
+00:11:58,470 --> 00:12:04,810
+acceleration؟ بتقولك كامل المستاطيل اللي عندك بهذا
+
+110
+00:12:04,810 --> 00:12:11,230
+الشكل يبقى القطر تبع هذا المستاطيل يمثل ال
+
+111
+00:12:11,230 --> 00:12:17,400
+acceleration A اللي حللناها إلى مركبتينالمُركّبة
+
+112
+00:12:17,400 --> 00:12:20,440
+الأولى هي الـ tangential component والمُركّبة
+
+113
+00:12:20,440 --> 00:12:25,040
+التانية هي الـ normal component of acceleration
+
+114
+00:12:25,040 --> 00:12:32,780
+نعطي مثال توضيح على هذا الكلام هذا
+
+115
+00:12:32,780 --> 00:12:36,140
+بده الشجرة دي سحاني
+
+116
+00:13:06,540 --> 00:13:15,180
+بقول الان ال A of T بده ساوي اللي هو T زائد واحد
+
+117
+00:13:15,180 --> 00:13:20,760
+في اتجاه ال I زائد اتنين T في اتجاه ال J
+
+118
+00:13:32,620 --> 00:13:43,740
+The acceleration طول العجلة A تنتجر
+
+119
+00:13:43,740 --> 00:13:50,240
+على الشكل A تنتجر
+
+120
+00:13:50,240 --> 00:13:53,900
+على
+
+121
+00:13:53,900 --> 00:13:54,420
+الشكل
+
+122
+00:13:57,770 --> 00:14:08,850
+at T تساوي واحد without finding .. without finding
+
+123
+00:14:08,850 --> 00:14:17,190
+.. بدون حساب أو بدون إيجاد T and الـ
+
+124
+00:14:30,480 --> 00:14:35,380
+نقرأ السؤال مرة ثانية نحدد شو اللي مطلوب في السؤال
+
+125
+00:14:35,380 --> 00:14:41,680
+وبالتالي بنقدر نحسب الشغل اللي بدناه حسابا دقيقة
+
+126
+00:14:41,680 --> 00:14:47,640
+ميعطيني ال position vector لجسم يتحرك معه وقال
+
+127
+00:14:47,640 --> 00:14:51,000
+لجسم المعادلة تبعته ال vector volume function يقرب
+
+128
+00:14:51,000 --> 00:14:55,440
+T T زي دوعة في اتجاه I زي اتنية T في اتجاه J زي T
+
+129
+00:14:55,440 --> 00:15:02,460
+تربية في اتجاه Kاللي يكتبلي العجلة على شكل مركبتيه
+
+130
+00:15:02,460 --> 00:15:06,700
+ال tangential component و ال normal component
+
+131
+00:15:06,700 --> 00:15:11,520
+احسبلي هذا الكلام عندما E تسوى 1 بدون ما تحسب لا T
+
+132
+00:15:11,520 --> 00:15:18,930
+ولا N يبقى مش لازم نحسب لا T ولا Nلكن يجب أن تخلّي
+
+133
+00:15:18,930 --> 00:15:24,350
+T و N كما هو يعني كأن المعادلة تكتب بدلالة T و N
+
+134
+00:15:24,350 --> 00:15:27,470
+لذلك يجب أن أحصل عليه tangential component
+
+135
+00:15:27,470 --> 00:15:32,150
+التانجينشال كومبوننت مسحناها قبل قليل فكانت هي
+
+136
+00:15:32,150 --> 00:15:36,730
+عبارة عن مشتقة ال velocity معناه الكلام بده يروح
+
+137
+00:15:36,730 --> 00:15:40,150
+أما مشتقة ال speed يبقى بدنا نروح و نجلب ال
+
+138
+00:15:40,150 --> 00:15:44,530
+velocity ثم ال speed ثم نشتقها يبقى بعدين أقول له
+
+139
+00:15:44,530 --> 00:15:50,990
+solutionبدي ال V as a function of T يبقى اللي هي
+
+140
+00:15:50,990 --> 00:16:01,090
+DR على DT و يساوي مشتقتها I زائد 2D زائد 2TK
+
+141
+00:16:05,600 --> 00:16:11,140
+طول الـ vector V يسوى الجذري التربيع يلي واحد زائد
+
+142
+00:16:11,140 --> 00:16:16,340
+أربعة زائد أربعة D تربيع ويسوى ال square root
+
+143
+00:16:16,340 --> 00:16:26,560
+للخمسة زائد أربعة D تربيع بعد هيك بدنا ال A T يبقى
+
+144
+00:16:26,560 --> 00:16:33,260
+ال A T هي عبارة عن D على DT لطول ال V يبقى معناته
+
+145
+00:16:33,260 --> 00:16:39,590
+بنشتغل منالجدر هذا خدناه في Calculus A مش نفس
+
+146
+00:16:39,590 --> 00:16:44,130
+الجدر واحد على تاني الجدر ده مش نفس ما داخل
+
+147
+00:16:59,670 --> 00:17:05,470
+يبقى النتيجة النهائية بعد الاختصار بتصير اربعة تي
+
+148
+00:17:05,470 --> 00:17:11,970
+على الجدرى التربية لخمسة زائد اربعة تي تربية تمام
+
+149
+00:17:11,970 --> 00:17:19,670
+جالي احسبلي هذا الكلامعند T تساوي واحد يبقى عند T
+
+150
+00:17:19,670 --> 00:17:25,910
+تساوي واحد هذا بيصير اربعة على جدر خمسة زائد اربعة
+
+151
+00:17:25,910 --> 00:17:31,530
+في واحد تربيع باربعة اربعة وخمسة تسعة تحت الجدر
+
+152
+00:17:31,530 --> 00:17:36,750
+بتلاتة يبقى النتيجة تساوي قدر اربعة تلاتة هذا
+
+153
+00:17:36,750 --> 00:17:41,710
+مقدار تجيش ال component وزي ما انت شايف اسكلف زي
+
+154
+00:17:41,710 --> 00:17:46,150
+ما قلنا لكوا ان هذا النتيجة اسكلف قبل ذلكالمركبة
+
+155
+00:17:46,150 --> 00:17:51,650
+الأولى بناروح نجيب المركبة الثانية عشان نجيب
+
+156
+00:17:51,650 --> 00:17:56,450
+المركبة الأولى بناروح
+
+157
+00:17:56,450 --> 00:18:01,150
+نجيب المركبة الثانية عشان نجيب المركبة الأولى
+
+158
+00:18:01,150 --> 00:18:01,610
+بناروح نجيب المركبة الأولى بناروح نجيب المركبة
+
+159
+00:18:01,610 --> 00:18:01,630
+المركبة الأولى بناروح نجيب المركبة الأولى بناروح
+
+160
+00:18:01,630 --> 00:18:01,930
+نجيب المركبة الأولى بناروح نجيب المركبة الأولى
+
+161
+00:18:01,930 --> 00:18:02,410
+الأولى بناروح نجيب المركبة الأولى بناروح نجيب
+
+162
+00:18:02,410 --> 00:18:05,470
+المركبة الأولى بناروح نجي
+
+163
+00:18:21,900 --> 00:18:27,860
+أتنين كيف فقط مغلق يبقى الأن لو جيت يا بنا أنت
+
+164
+00:18:27,860 --> 00:18:37,760
+قلتلك بدي ال a بطل a كده بطل عنه اللي هو طول ال a
+
+165
+00:18:37,760 --> 00:18:44,820
+تربعه اللي متجه فيه نفسه بطل كده هذا بطل أربعة إذا
+
+166
+00:18:44,820 --> 00:18:49,440
+سهل إيجاد اللي هو ال normal component of
+
+167
+00:18:49,440 --> 00:18:53,460
+accelerationفبروح بقوله normal component of
+
+168
+00:18:53,460 --> 00:18:58,600
+acceleration An يساوي الجدرح التربية لطول ال A
+
+169
+00:18:58,600 --> 00:19:06,560
+تربية ناقص ال AT² ويساوي ال square root A تربية
+
+170
+00:19:10,730 --> 00:19:18,350
+أربعة على تلاتة يبقى هذه أربعة على تلاتة كل تربيع
+
+171
+00:19:18,350 --> 00:19:24,610
+يبقى ال square root للأربعة نقص ستاشر على تسعة
+
+172
+00:19:33,590 --> 00:19:40,330
+العشرين اربعة في خمسة يعني اتنين جدر خمسة على
+
+173
+00:19:40,330 --> 00:19:44,910
+تلاتة هذا مقدار ماهو ال normal component of
+
+174
+00:19:44,910 --> 00:19:49,170
+acceleration اذا اصبحت ال acceleration اللي
+
+175
+00:19:49,170 --> 00:19:51,190
+بدوياها هي
+
+176
+00:20:03,860 --> 00:20:09,240
+بتجاه ال principle normal N يبقى هي حط نر العجلة
+
+177
+00:20:09,240 --> 00:20:13,480
+على صيغة ال component الواضحة الواضحة الواضحة
+
+178
+00:20:13,480 --> 00:20:16,560
+الواضحة الواضحة الواضحة الواضحة الواضحة الواضحة
+
+179
+00:20:16,560 --> 00:20:23,080
+الواضحة الواضحة الواضحة
+
+180
+00:20:23,080 --> 00:20:25,820
+الواضحة
+
+181
+00:20:28,350 --> 00:20:38,210
+نعود الآن لتعريف الـ BINORMAL VECTOR الـ BINORMAL
+
+182
+00:20:38,210 --> 00:20:44,310
+VECTOR يا بنات هو unit vector عمودي على كل ال manT
+
+183
+00:20:44,310 --> 00:20:49,330
+و N يبقى لو قلنا T و N اللي هو ال unit tangent
+
+184
+00:20:49,330 --> 00:20:53,410
+vector التانجنت والنورمال إذا هذا بدي يكون وين
+
+185
+00:20:53,410 --> 00:20:58,430
+عمودي عليهم عمودي على اتنين معناته بدي أعمل cross
+
+186
+00:20:58,430 --> 00:21:03,410
+product يبقى بنعرفه هو ال cross product لمين لل T
+
+187
+00:21:03,410 --> 00:21:10,350
+و ال N مع بعض يبقى مضاجي لل definition كالثالث ال
+
+188
+00:21:10,350 --> 00:21:19,690
+binomial vector Vباينرمال فيكتور of
+
+189
+00:21:19,690 --> 00:21:30,090
+a space curve of a space curve المنحنة في الفرقات
+
+190
+00:21:30,090 --> 00:21:41,290
+as P باينرمال تسوى تي كروس ال N as a unit vector
+
+191
+00:21:41,290 --> 00:21:55,380
+asأي unit vector orthogonal to
+
+192
+00:21:55,380 --> 00:22:04,960
+both عمودي على كل من T and N
+
+193
+00:22:11,790 --> 00:22:16,650
+نرجع نقرأ ال definition تاني و طرأ على هذه السؤال
+
+194
+00:22:16,650 --> 00:22:21,560
+الآنبنواجهكم من خلال الكلام اللي مكتوب على الصورة
+
+195
+00:22:21,560 --> 00:22:25,820
+اللي قدامنا Definition تججوا معايا كويس حتى نسمع
+
+196
+00:22:25,820 --> 00:22:30,720
+السؤال و نعرف كيف بنا نجاوب على هذا السؤال بيقول
+
+197
+00:22:30,720 --> 00:22:37,160
+دي by normal vector of A space curve S بنعرفه على
+
+198
+00:22:37,160 --> 00:22:42,820
+انه B يسوى T cross ال N يبقى ال B عمودي على كل من
+
+199
+00:22:42,820 --> 00:22:45,040
+ال main وطوله كده
+
+200
+00:22:49,490 --> 00:22:52,110
+T هو عبارة عن unit vector
+
+201
+00:22:56,310 --> 00:23:00,930
+و ال M عبارة عن unit vector عملت لهم cross product
+
+202
+00:23:00,930 --> 00:23:07,230
+طالع بيه هو unit vector بطرح السؤال التالي هل لو
+
+203
+00:23:07,230 --> 00:23:13,950
+عملت cross product بين two units vector إيه ناتج؟
+
+204
+00:23:13,950 --> 00:23:16,850
+هو unit vector؟ بالتأكيد
+
+205
+00:23:18,680 --> 00:23:24,960
+ما رأيكم؟ صحيح هذا الكلام؟ لا مش صحيح، يعني قد
+
+206
+00:23:24,960 --> 00:23:31,260
+يكونوا صحيحا و قد لا يكون، وبالتالي هذا كلام حتى
+
+207
+00:23:31,260 --> 00:23:35,280
+لو حصل مرتين، تلاتة، مية، لكن in general، لا مش
+
+208
+00:23:35,280 --> 00:23:40,840
+صحيح، كيف يعني؟ بجي بقولك بسيطة، في الهامش بنفكر،
+
+209
+00:23:40,840 --> 00:23:44,080
+ماعرفش ده عاجلة في بالنا سؤال و بدنا نجاوب عليهلو
+
+210
+00:23:44,080 --> 00:23:48,020
+جيت في الهام الشكل انا و قلت بدي اخد two unit
+
+211
+00:23:48,020 --> 00:23:51,740
+vectors و اعمل لهم cross product مع بعض و اشوف شو
+
+212
+00:23:51,740 --> 00:23:56,420
+اللي بده يحصل ايش زمين المتجهين لو جيت في المتجه
+
+213
+00:23:56,420 --> 00:24:00,860
+الأول واحد على جدر تلاتة في اتجاه ال I واحد على
+
+214
+00:24:00,860 --> 00:24:04,500
+جدر تلاتة في اتجاه ال J واحد على جدر تلاتة في
+
+215
+00:24:04,500 --> 00:24:09,420
+اتجاه ال Kمش هذا unit vector ربع المركبات وجمعها
+
+216
+00:24:09,420 --> 00:24:14,640
+بطلع كده واحد صحيح الان بدي اعمله cross product مع
+
+217
+00:24:14,640 --> 00:24:20,900
+ال I مش ال I unit vector مظبوط يبقى بداجي اخد U
+
+218
+00:24:20,900 --> 00:24:28,360
+cross ال I يبقى I و J و K واحد على جدر تلاتة واحد
+
+219
+00:24:28,360 --> 00:24:32,540
+على جدر تلاتة واحد على جدر تلاتة واحد و Zero Zero
+
+220
+00:24:34,780 --> 00:24:43,360
+بتفكر محدد باستخدام عناصر صف التالت يبقى هذا
+
+221
+00:24:43,360 --> 00:24:50,340
+الواحد فيه اشط بصفه عموده واحد على جذر تلاتة J نقص
+
+222
+00:24:50,340 --> 00:24:56,660
+واحد على جذر تلاتة K والباقي بقى أصفر هذا الناتج
+
+223
+00:24:56,660 --> 00:25:01,560
+من ال cross product which is a vector سؤالنا هو هل
+
+224
+00:25:01,560 --> 00:25:02,960
+هذا unit vector؟
+
+225
+00:25:09,720 --> 00:25:13,860
+لو عملت cross product بين two vectors أن يكون
+
+226
+00:25:13,860 --> 00:25:19,520
+الناتج هو unit vector قد يكون و قد لا يكون لكن في
+
+227
+00:25:19,520 --> 00:25:23,160
+موضوع هنا ال by normal vector ال by normal vector
+
+228
+00:25:23,160 --> 00:25:28,620
+is a unit vector تمام بس in general الكلام هذا
+
+229
+00:25:28,620 --> 00:25:30,860
+معروف ليس صحيحا
+
+230
+00:25:45,200 --> 00:25:50,960
+هذه المثال عامل يظهر أن هذا المعنى ليس صحيح
+
+231
+00:25:56,310 --> 00:26:01,250
+هه كلفت نظر لكم الان بدنا نرجع لموضوعنا الموضوع
+
+232
+00:26:01,250 --> 00:26:06,410
+الـ BINORMAL VECTORAL شو رايحة يا بنات؟ لو روحنا
+
+233
+00:26:06,410 --> 00:26:09,970
+اشتقناها، شوفوا لو اين بدنا نوصل فيها الدنيا،
+
+234
+00:26:09,970 --> 00:26:18,410
+كويس؟ يبقى بدنا ناخد مثلا الـ derivative of
+
+235
+00:26:18,410 --> 00:26:29,830
+the biأو بي تساوي ت برص الان بدي اعمل اشتقاق و
+
+236
+00:26:29,830 --> 00:26:35,930
+اشوف ايش بده يقين يعني لو روحت اخدت دي دي على دي
+
+237
+00:26:35,930 --> 00:26:38,510
+اس اشوف ايش بده يقين
+
+238
+00:26:41,940 --> 00:26:47,660
+بنشتق ويبقى كل واحد في مكانه لإن عملية cross
+
+239
+00:26:47,660 --> 00:26:52,740
+product not commutative يبقى بفضل كل واحد في مكانه
+
+240
+00:26:52,740 --> 00:27:03,040
+يبقى مجموعة DT على DS cross ال N زائد T cross ال
+
+241
+00:27:03,040 --> 00:27:06,040
+DN على D
+
+242
+00:27:09,250 --> 00:27:16,870
+طب كويس طيب ابنات لو رجعنا تاو قبل شوية كتبناها و
+
+243
+00:27:16,870 --> 00:27:20,750
+احنا بنحكي في ال tangential لو روحنا ل principal
+
+244
+00:27:20,750 --> 00:27:27,750
+unit normal N قدش بساوي واحد على كبه في مين في DT
+
+245
+00:27:27,750 --> 00:27:34,750
+على DS يعني ال principal unit normal و DT على DS
+
+246
+00:27:34,750 --> 00:27:42,030
+لاثنين are parallelواحد فيهم مضاعفات الثانية يبقى
+
+247
+00:27:42,030 --> 00:27:47,230
+ما اللي بقول sense فيما ان ال principle unit
+
+248
+00:27:47,230 --> 00:27:53,630
+normal M بدي ساوي واحد على كبر دي تي على دي اس
+
+249
+00:27:53,630 --> 00:28:00,130
+يبقى اتنين هدول ما لهمR Parallel لأن هذا هو Scalar
+
+250
+00:28:00,130 --> 00:28:05,390
+وهذا هو Vector يبقى صار هذا مضاعفا من ال vector
+
+251
+00:28:05,390 --> 00:28:15,010
+الثاني يبقى هذا يعطينا ان ال N and ال DT على DT
+
+252
+00:28:15,010 --> 00:28:22,410
+are parallel مدام اتنين توازين يبقى cross product
+
+253
+00:28:22,410 --> 00:28:33,240
+فيما بينهم DT على DS يا بناتDT على DS يبقى
+
+254
+00:28:33,240 --> 00:28:36,560
+معنا اتنين هذول parallel مادام parallel يبقى ال
+
+255
+00:28:36,560 --> 00:28:42,140
+cross product لهم جداش نه متوازن cross product
+
+256
+00:28:42,140 --> 00:28:49,160
+zero يبقى هذا بده يعطينا انهالان و الله زي ما هي
+
+257
+00:28:49,160 --> 00:28:57,060
+دي ت على دي اس cross الان بتسوى كده؟ Zero مدام
+
+258
+00:28:57,060 --> 00:29:01,300
+Zero إذا المعادلة دي أخدت شكل جديد
+
+259
+00:29:26,900 --> 00:29:35,720
+ماذا تفهمينا من هذه الجملةإيش تفسيرها عندك انه DB
+
+260
+00:29:35,720 --> 00:29:42,380
+على DS يسوى عمليا T cross DN على DS شو الولاقة بين
+
+261
+00:29:42,380 --> 00:29:48,040
+هذا المحتج والمحتجين الأثنين دول عبودي على الأثنين
+
+262
+00:29:48,040 --> 00:29:55,680
+يبقى ممتاز جدا يبقى هذا معناته ان DB على DS is
+
+263
+00:29:55,680 --> 00:30:10,040
+orthogonal to bothلكل من T and D N على D S يعتبر
+
+264
+00:30:10,040 --> 00:30:15,420
+هذه المعادلة رقم واحد نرجع
+
+265
+00:30:15,420 --> 00:30:21,180
+بالذاكرة إلى الوراء قليلا التعريف اللي فوق بيقول B
+
+266
+00:30:21,180 --> 00:30:26,340
+is a unit vector يعني
+
+267
+00:30:26,340 --> 00:30:31,390
+vector with constant length صحيح ولا لأ؟لو أعمل
+
+268
+00:30:31,390 --> 00:30:38,570
+dot product ما بين ال B ومشتقته، كده؟ Zero كذلك،
+
+269
+00:30:38,570 --> 00:30:46,070
+خاصية أخدناها قبل ذلك يبقى باجي بقوله since
+
+270
+00:30:46,070 --> 00:30:55,050
+بما أن ال B is a constant vector,
+
+271
+00:30:56,510 --> 00:30:57,110
+we have
+
+272
+00:30:59,890 --> 00:31:11,590
+إن ال B بط DB على DS بده يساوي Z هذا إيش بيعطينا؟
+
+273
+00:31:11,590 --> 00:31:23,130
+هذا بيعطينا إن DB على DS is orthogonal لمن؟
+
+274
+00:31:23,130 --> 00:31:27,310
+is orthogonal to B
+
+275
+00:31:30,170 --> 00:31:36,190
+وهذه العلاقة رقم اتنين تعالى نتطلع في واحد واتنين
+
+276
+00:31:36,190 --> 00:31:43,890
+بيقول هنا DBA على DS عمودي على T و على DN على DS
+
+277
+00:31:43,890 --> 00:31:49,430
+وهنا بيقول ان ال DBA على DS نفسها عمودي على مين
+
+278
+00:31:49,430 --> 00:31:54,210
+على B إذا معنى هذا الكلام ان ال DBA على DS عمودي
+
+279
+00:31:54,210 --> 00:32:01,420
+على كل من T وB صحيح ولا لأيبقى هنا بقول له so
+
+280
+00:32:01,420 --> 00:32:12,640
+والله from واحد and اثنين ال D بي على دي اس is
+
+281
+00:32:12,640 --> 00:32:18,020
+orthogonal to
+
+282
+00:32:18,020 --> 00:32:22,220
+اللي هو الأولاني T and ال B
+
+283
+00:32:26,190 --> 00:32:48,830
+طيب، هذا سيولّد لنا السؤال التالي التعريف
+
+284
+00:32:48,830 --> 00:32:53,390
+اللي كتبناه الـ BINORMAL يقول إن B عمودي على كل من
+
+285
+00:32:53,390 --> 00:33:01,200
+T و Nإذا لو كان هذا T يا بنات هذا T هذا بيكون مين؟
+
+286
+00:33:01,200 --> 00:33:06,740
+10 يبقى العمودي على الإتنين مين بيكون؟ اللي هو P
+
+287
+00:33:06,740 --> 00:33:09,860
+هذا
+
+288
+00:33:09,860 --> 00:33:17,000
+بنات المحاور صارت كإنها تلت محاور زي محور X وY وZ
+
+289
+00:33:17,000 --> 00:33:23,330
+بس هدول بيلتقوا وين؟بالتقوى عند نقطة و التكن هذه
+
+290
+00:33:23,330 --> 00:33:28,160
+النقطة Pالنقطة هذه تقع على المنحنى اللى رسمناها
+
+291
+00:33:28,160 --> 00:33:32,700
+قبل شوية يعني على المنحنى وليست نقطة الاصل يعني
+
+292
+00:33:32,700 --> 00:33:35,600
+عند اى نقطة موجودة على المنحنى اللى رسمناها عندها
+
+293
+00:33:35,600 --> 00:33:38,440
+ال unit tangent و ال principle normal و بعدها
+
+294
+00:33:38,440 --> 00:33:41,320
+رسمنا العجلة لأ ال unit tangent و ال principle
+
+295
+00:33:41,320 --> 00:33:46,100
+normal و ال by normal هاي هم عندنا هذول بيعملولى
+
+296
+00:33:46,100 --> 00:33:53,870
+تلت مستويات المستوى الاول اللى يجمع T و Nبسميه
+
+297
+00:33:53,870 --> 00:34:03,430
+oscillating plane يبقى هذا بسميه oscillating plane
+
+298
+00:34:03,430 --> 00:34:06,570
+طيب
+
+299
+00:34:06,570 --> 00:34:12,030
+و اللي بيجمع بيه و ان هذا عمودي على ال oscillating
+
+300
+00:34:12,030 --> 00:34:19,630
+plane بسميه normally plane يبقى هذا هو normally
+
+301
+00:34:19,630 --> 00:34:21,070
+plane
+
+302
+00:34:23,710 --> 00:34:33,330
+والمستوى اللي بعده هذا بسميه rectifying plane يبقى
+
+303
+00:34:33,330 --> 00:34:36,510
+rectifying
+
+304
+00:34:36,510 --> 00:34:42,190
+plane يبقى
+
+305
+00:34:42,190 --> 00:34:47,970
+التان هذول بيعملولي تلت مستويات متعامدة تعالى نشوف
+
+306
+00:34:47,970 --> 00:34:52,490
+من خلال العبارة الأخيرة اللي كتبناها هذه إيش بيحصل
+
+307
+00:34:52,490 --> 00:34:57,780
+عندنابيقول من المعادلة 1 و 2 الـ Db على Ds is
+
+308
+00:34:57,780 --> 00:35:05,160
+orthogonal to both T and B يبقى Db على Ds عمودي
+
+309
+00:35:05,160 --> 00:35:11,260
+على كل المن T و B طب مين عمودي على T و B عنده في
+
+310
+00:35:11,260 --> 00:35:17,820
+الرسم N إذا ما هي العلاقة بين N و Dbi و Db على Ds
+
+311
+00:35:17,820 --> 00:35:26,400
+اتنين are parallel تمام يبقى هذا معناهإن الـ DB
+
+312
+00:35:26,400 --> 00:35:43,340
+على DS ماله is parallel to the normal vector N
+
+313
+00:35:43,340 --> 00:35:49,260
+عمودي عليهمدام عمودي عليه إذا هذا بيعطينا إيش
+
+314
+00:35:49,260 --> 00:35:59,160
+مضاعفاته يعني جده عدت مرات يبقى بناء عليه DB على
+
+315
+00:35:59,160 --> 00:36:10,220
+DS بدي ساوي ناقص TAU في M TAU scalar الرقم يعني،
+
+316
+00:36:10,220 --> 00:36:10,920
+كويس؟
+
+317
+00:36:16,410 --> 00:36:21,770
+الكتاب يقول ان الإشارة السالبة تقليدية تقليدية
+
+318
+00:36:21,770 --> 00:36:26,910
+تقليدية التباعت ان ماكسيشن وده كتاب السلب وضلت
+
+319
+00:36:26,910 --> 00:36:32,210
+ماشية مع الكل بنفس الطريقة يبقى بصير عند دي بي على
+
+320
+00:36:32,210 --> 00:36:38,890
+دي اس يسوي سالب تاو في ان طيب انا بقدر اجيب التاو
+
+321
+00:36:38,890 --> 00:36:44,850
+هذي ولا بقدربنقدر .. بنقدر مابكتش لو تخلصنا من ال
+
+322
+00:36:44,850 --> 00:36:52,210
+N طب كيف نتخلص من ال N؟ تخلص الشجة اليمين اللي
+
+323
+00:36:52,210 --> 00:36:57,530
+عندي هذه سالبته فقط بدون ال N طبعا ال N هنا ال
+
+324
+00:36:57,530 --> 00:37:06,980
+vector يبقاش عمال ايش نسوي؟بتعمل dot product بمعين
+
+325
+00:37:06,980 --> 00:37:13,820
+نفسه يبقى بناء عليها بنات بقدر اقول هنا ال DB على
+
+326
+00:37:13,820 --> 00:37:22,840
+DS بط ال N بدي ساوي الناقص TAU في مين؟ في ال N بط
+
+327
+00:37:22,840 --> 00:37:23,640
+ال N
+
+328
+00:37:29,220 --> 00:37:37,560
+مدام واحد يبقى بناء عليه Tab تساوي سالب DB على DS
+
+329
+00:37:37,560 --> 00:37:45,520
+بطل N شكل اللي عندنا هذا التو يا بنات إله اسم في
+
+330
+00:37:45,520 --> 00:37:53,260
+علمنا اسمه Torsion Function عزم الله كويس؟ يبقى ..
+
+331
+00:37:53,260 --> 00:37:58,460
+هنعطيله ال definition التالي يبقى definition
+
+332
+00:38:01,280 --> 00:38:06,360
+التورشن فانكشن التورشن
+
+333
+00:38:06,360 --> 00:38:11,000
+فانكشن
+
+334
+00:38:11,000 --> 00:38:24,680
+of a smooth curve of a smooth curve is
+
+335
+00:38:24,680 --> 00:38:33,780
+تاو دو يساوي السالق DBعلى الارض التي تم وضعها فيها
+
+336
+00:38:33,780 --> 00:38:36,820
+حيث
+
+337
+00:38:36,820 --> 00:38:46,200
+تاو هو قيمة التي هي قيمة
+
+338
+00:38:46,200 --> 00:38:51,500
+التي هي قيمة التي هي قيمة التي هي قيمة التي هي
+
+339
+00:38:51,500 --> 00:38:55,300
+قيمة اللي هي
+
+340
+00:38:55,300 --> 00:38:55,320
+قيمة اللي هي قيمة اللي هي قيمة اللي هي قيمة اللي
+
+341
+00:38:55,320 --> 00:38:55,600
+هي قيمة اللي هي قيمة
+
+342
+00:39:07,560 --> 00:39:24,760
+there's there's about اللي هو ال unit angelity إذن
+
+343
+00:39:25,400 --> 00:39:29,600
+كل الفكرة في الموضوع اللى تاخد ال derivative تبع
+
+344
+00:39:29,600 --> 00:39:34,600
+ال P الهدف من ذلك ان اوصل لمين للمعادل اللى عندنا
+
+345
+00:39:34,600 --> 00:39:39,280
+و اوصل لتعريف جديد اللى هو تعريف torsion function
+
+346
+00:39:39,280 --> 00:39:45,020
+تمام بيقول اللى التعريف هذا torsion function ال
+
+347
+00:39:45,020 --> 00:39:50,060
+small curve هي تاو تساوية ثانية ترتيب P على DS بطل
+
+348
+00:39:50,060 --> 00:39:54,560
+ان حيث T is the rate at which هو المعدل
+
+349
+00:39:58,020 --> 00:40:04,240
+هو يحاول يعمل دوران حول محور T طبعا هذا الـ
+
+350
+00:40:04,240 --> 00:40:09,040
+oscillating plane و هذا المحور T يعني كأنه بده
+
+351
+00:40:09,040 --> 00:40:14,380
+يعمل شغلة بالشكل اللي عندها زي دوران بهذا الشكل
+
+352
+00:40:14,380 --> 00:40:21,940
+طيب لو جيبنا سؤال و طلبنا ترشد وقلنا لك بالله
+
+353
+00:40:21,940 --> 00:40:26,680
+أسمينا يعني إذا بدك تجي عليها المعادلة هذه و جيبلي
+
+354
+00:40:26,680 --> 00:40:36,120
+principal normيبقى نروح نجيب ال V و نجتقها
+
+355
+00:40:36,120 --> 00:40:40,820
+بالنسبالتي و نحسب قولها و نقسم و نقول جيبنا
+
+356
+00:40:40,820 --> 00:40:44,060
+reference بالنور بقى زي ما سويت المرة اللى فاترة
+
+357
+00:40:44,060 --> 00:40:49,970
+قصة طويلة صحيح ولا لأ؟ و يرتك أديكم بسوبنرجع نجيب
+
+358
+00:40:49,970 --> 00:40:54,690
+cross product بين ال T والL ونروح نشتقها بالنسبة
+
+359
+00:40:54,690 --> 00:40:56,950
+لل S ونجيب علاقة تربط أصلها
+
+360
+00:40:59,970 --> 00:41:05,110
+لكن في مادة ال advanced calculus اللي بيدرسوها
+
+361
+00:41:05,110 --> 00:41:09,950
+طلاب العلوم اللي هو التفاضل و التكمل المتقدم مادة
+
+362
+00:41:09,950 --> 00:41:15,990
+في سنة رابعة حسب ذلك عمليا و بنستخدم هذا في حل
+
+363
+00:41:15,990 --> 00:41:21,190
+المسائل أشهر من هذه العلاقة يبقى بدي أحطها لكم في
+
+364
+00:41:21,190 --> 00:41:21,730
+الصيغة
+
+365
+00:41:34,300 --> 00:41:42,300
+advanced calculus نحن
+
+366
+00:41:42,300 --> 00:41:47,620
+لدينا نقطة
+
+367
+00:41:47,620 --> 00:41:52,360
+الأولى كيرفيتشا
+
+368
+00:41:52,360 --> 00:42:04,820
+كذا عرفنا سابقا على انهعلى DSL لكن عمليا يا بنات
+
+369
+00:42:04,820 --> 00:42:09,320
+هو طول ال cross product ما بين ال velocity و ال
+
+370
+00:42:09,320 --> 00:42:15,360
+acceleration على طول ال VTK هذه العلاقة الأولى
+
+371
+00:42:15,360 --> 00:42:17,940
+العلاقة الثانية
+
+372
+00:42:37,370 --> 00:42:48,850
+محدد x dot y dot z dot x double dot y double dot z
+
+373
+00:42:48,850 --> 00:42:50,210
+double dot
+
+374
+00:42:53,660 --> 00:43:02,120
+Y triple dot Z triple dot كله مقسوما على طول V
+
+375
+00:43:02,120 --> 00:43:12,720
+cross A كل تربيع بس بشرط ان D cross هذا لايساوي
+
+376
+00:43:12,720 --> 00:43:18,120
+Zero V cross A لايساوي Zero
+
+377
+00:43:22,040 --> 00:43:26,440
+نيجي نفسر الكلام اللي احنا كاتبينه هذا لإننا بدنا
+
+378
+00:43:26,440 --> 00:43:29,400
+نستخدمه عمليا في الشغل
+
+379
+00:43:58,580 --> 00:44:05,660
+الكيربتشار كدا هي طول الـ DT على DS أو DT ضربناها
+
+380
+00:44:05,660 --> 00:44:11,560
+على DT في DT على DS وقلنا واحد على طول ال V في طول
+
+381
+00:44:11,560 --> 00:44:16,220
+ال DT على DT هذا السابق لكن هنا عشان اقول ان احنا
+
+382
+00:44:16,220 --> 00:44:17,420
+جيبنا ال velocity V
+
+383
+00:44:35,490 --> 00:44:41,330
+مشتقت كل من ال X و Y و Z
+
+384
+00:44:45,640 --> 00:44:49,800
+عشان انا بقول R of T بقول X of T في اتجاه ال I و I
+
+385
+00:44:49,800 --> 00:44:52,780
+of T في اتجاه ال Z و Z of T في اتجاه ال K جيبلي
+
+386
+00:44:52,780 --> 00:44:55,920
+فيه يبقى جيبلي المشتقة الأولى إذا هدولة السطر
+
+387
+00:44:55,920 --> 00:45:02,320
+الأول في المحدد هي مراكبات الصراع بعد هيك هذه
+
+388
+00:45:02,320 --> 00:45:07,460
+double dot مراكبات مين العجلة ال accelerator
+
+389
+00:45:07,460 --> 00:45:13,810
+المشتقة الثانية ل R of T طب هذهمشتقت من العجلة،
+
+390
+00:45:13,810 --> 00:45:18,050
+مشتقت مراكبات العجلة، إذا الصف الأول هو مراكبات
+
+391
+00:45:18,050 --> 00:45:22,390
+السرعة، الصف الثاني هو مراكبات العجلة، الصف الثالث
+
+392
+00:45:22,390 --> 00:45:27,570
+مراكبات مشتقة العجلة، المقام V cross V هو اللي
+
+393
+00:45:27,570 --> 00:45:33,080
+اتكلمنا عليه فهمالكل تربيع وهذه وسيلة عملية أسهل
+
+394
+00:45:33,080 --> 00:45:38,480
+عمليا في الحساب من الحالة الأولى اللى أوجدناها قبل
+
+395
+00:45:38,480 --> 00:45:44,640
+قليل نعطي مثال على كل هذا الكلام ال T و ال N و ال
+
+396
+00:45:44,640 --> 00:45:48,140
+curvature و ال torsion كله نحسب و ال by normal
+
+397
+00:45:48,140 --> 00:45:57,700
+كمان نحسب كله بمثال example بيقول
+
+398
+00:45:57,700 --> 00:46:05,600
+ال headالـ R of T بدها السبب تلاتة Sin T في اتجاه
+
+399
+00:46:05,600 --> 00:46:16,280
+I زائد تلاتة Cos T في اتجاه J زائد أربعة T كله في
+
+400
+00:46:16,280 --> 00:46:31,270
+اتجاه K المقبض الأول نمر A أو قبل A باجي بقولهAt T
+
+401
+00:46:31,270 --> 00:46:45,310
+تساوي Pi على 2 Find نمرة A الـ T والـ M and الـ B
+
+402
+00:46:45,310 --> 00:46:50,390
+نمرة B The
+
+403
+00:46:50,390 --> 00:47:06,800
+equation The equation ofThe Norman Plague مرسي The
+
+404
+00:47:06,800 --> 00:47:15,540
+curvature The
+
+405
+00:47:15,540 --> 00:47:21,900
+curvature اللي هو كابا and the torsion
+
+406
+00:47:38,970 --> 00:47:44,330
+هذا طلب كل الشغلات اللي اتعرضنا لها اليوم ايش
+
+407
+00:47:44,330 --> 00:47:49,490
+بيقوللي هاتلي اول شيء ال T و ال N و ال B يفجأة بدي
+
+408
+00:47:49,490 --> 00:47:55,750
+اقوله بدي اخدله ال V اللي هي DR على DTرح نشتق هذه
+
+409
+00:47:55,750 --> 00:48:00,670
+الدالة ثم ثلاثة cosine T في اتجاه I ناقص ثلاثة
+
+410
+00:48:00,670 --> 00:48:07,590
+sine T في اتجاه J زائد أربعة في اتجاه M في اتجاه K
+
+411
+00:48:07,590 --> 00:48:13,970
+لكي أحصل على T سوف أحصل عليه قدر اللي هو Velocity
+
+412
+00:48:13,970 --> 00:48:19,710
+V يبقى هذا قدر 4K في اتجاه K مظهر طيب يبقى يجب أن
+
+413
+00:48:19,710 --> 00:48:21,290
+أحصل عليه قول V
+
+414
+00:48:25,220 --> 00:48:33,440
+لتسعة cosine تربية T زائد تسعة sin تربية T زائد
+
+415
+00:48:33,440 --> 00:48:38,680
+ستة عشر ويساوي الجدر التربية يعني لو أخدنا تسعة
+
+416
+00:48:38,680 --> 00:48:43,000
+عامل مشترك ويظل sin تربية زائد وcos تربية واحد
+
+417
+00:48:43,000 --> 00:48:49,340
+يفجأ تسعة زائد ستة عشر يفجأ تسعة خمسة إذا بدي ال
+
+418
+00:48:49,340 --> 00:48:55,500
+unit tangent vector اللي طالبهفباجي بقوله T بدها
+
+419
+00:48:55,500 --> 00:49:01,140
+تساوي ال V على طول ال V ويرساوى الآن بدنا نقسم على
+
+420
+00:49:01,140 --> 00:49:07,560
+خمسة يبقى تلت أخمس cosine T في اتجاه ال I نقص تلت
+
+421
+00:49:07,560 --> 00:49:14,700
+أخمس sine T في اتجاه ال J زائد أربع أخمس في اتجاه
+
+422
+00:49:14,700 --> 00:49:21,510
+ال Kقال احسبلي هالشغلات هذه كلها عند T تساوي باي
+
+423
+00:49:21,510 --> 00:49:27,270
+على اتنين يبقى بقدر اقوله T عند ال باي على اتنين
+
+424
+00:49:27,270 --> 00:49:32,790
+بدها تساوي Cos باي على اتنين Zero مع السلامة غير
+
+425
+00:49:32,790 --> 00:49:37,490
+مقصوف عليها Sin باي على اتنين بواحد في ناقص تلت
+
+426
+00:49:37,490 --> 00:49:43,690
+أخمس في ناقص تلت أخمس في اتجاه ال J
+
+427
+00:49:52,620 --> 00:49:59,500
+بتجاه الـ K مافيش رأيك لو جربتي و حسبتي ال V عند
+
+428
+00:49:59,500 --> 00:50:07,820
+ال Y على 2 V عند ال Y على 2 هذا كم؟ Zero مع السلمة
+
+429
+00:50:07,820 --> 00:50:16,560
+وهذه واحد يبقى ناقص تلاتة جيب زائد أربعة Kجيبناله
+
+430
+00:50:16,560 --> 00:50:22,460
+T بده يقول ال principle normal vector يبقى ال N
+
+431
+00:50:22,460 --> 00:50:31,940
+بده يساوي يالا بره بدنا ال N يبقى نروح نشتغله T
+
+432
+00:50:31,940 --> 00:50:38,780
+يبقى قبل تجيب ال N بدك تجيب مشتقتي ال T لازم أقوله
+
+433
+00:50:38,780 --> 00:50:41,900
+هاي ال DT على DT
+
+434
+00:50:47,890 --> 00:50:53,690
+سين تي في اتجاه ال I ناقص ثلاث اشمس و سين تي في
+
+435
+00:50:53,690 --> 00:51:01,290
+اتجاه ال جيه و هدف كدهش بزيرو نخسب طوله لبنات يبقى
+
+436
+00:51:01,830 --> 00:51:08,770
+قول الـ Dt على Dt وساعة الجدر التنبيهي لمربع
+
+437
+00:51:08,770 --> 00:51:16,030
+المركبات يبقى هنا تسعة على خمسة وعشرين تسعة على
+
+438
+00:51:16,030 --> 00:51:25,430
+خمسة وعشرين زائد تسعة على خمسة وعشرين طبعا يبقى
+
+439
+00:51:25,430 --> 00:51:26,630
+كداش
+
+440
+00:51:28,790 --> 00:51:34,950
+بتلاتة على خمسة في جدري اتنين طبعا بصير تسعة على
+
+441
+00:51:34,950 --> 00:51:39,050
+خمسة وعشرين في اتنين تسعة على خمسة وعشرين مربع
+
+442
+00:51:39,050 --> 00:51:44,890
+جدرها تلاتة اخمس بيظل جدري اتنين هذا من هذا اللي
+
+443
+00:51:44,890 --> 00:51:48,570
+هو طول ال DT على DT إذا انت قادر تعطيه ال
+
+444
+00:51:48,570 --> 00:51:56,320
+principle your normal N اللي هو مناللي هو Dt على
+
+445
+00:51:56,320 --> 00:52:07,400
+Dt على طول الـ Dt على Dt و يوسعى كيف؟ من وين؟ الـ
+
+446
+00:52:07,400 --> 00:52:10,600
+Dt على طول الـ Dt مش بناخد عامة مشترك منها اللي هي
+
+447
+00:52:10,600 --> 00:52:15,400
+sin تربيع زاد و sin تربيع مش .. في مشكلة في هذه؟
+
+448
+00:52:15,400 --> 00:52:22,100
+في هذه إيش المشكلة فيها؟ ربعي هذه و هذه
+
+449
+00:52:24,730 --> 00:52:36,410
+سنة .. سنة .. سنة .. أصابة ابراهيم وأخطاء عمار هذه
+
+450
+00:52:36,410 --> 00:52:46,770
+نجيب الطول تبعها يبقى square root 9 كيف؟ بس بس
+
+451
+00:52:46,770 --> 00:52:47,950
+كيف؟
+
+452
+00:52:53,700 --> 00:52:59,060
+أحنا نطقنا صح و كتبنا خطأ و لذلك بنقولك لما تحلل
+
+453
+00:52:59,060 --> 00:53:03,220
+في الامتحان للآخر خلي آخر خمس دقايق إجراح عليك
+
+454
+00:53:03,220 --> 00:53:07,280
+لازم تلاقي غلطة يعني حين هو هنكتب نكتب الكلمة
+
+455
+00:53:07,280 --> 00:53:11,100
+مرتين ورا بعض لما تلاقي مجه و راجع بنلاقيها يبقى
+
+456
+00:53:11,100 --> 00:53:14,900
+تدير بالك تطلع بتقول والله أنا ألف ألف حلت تجيب
+
+457
+00:53:14,900 --> 00:53:18,840
+انها ناقص عليك شغلات فيها غلط يبقى دائما هو ده
+
+458
+00:53:18,840 --> 00:53:24,460
+احنا بشروكنا بشرا بنخطأ وبننسى وما إلى ذلك لكن هذا
+
+459
+00:53:24,460 --> 00:53:28,500
+مرفوع عندنا عند الله بس عندنا احنا البشر لا بنحسبه
+
+460
+00:53:28,500 --> 00:53:31,980
+الغلطة بنحسبها عليكي طبعا القولين صلى الله عليه
+
+461
+00:53:31,980 --> 00:53:38,660
+وسلم رفع ان أمتي الخطأ والنسيان وما استكرهوا عليه
+
+462
+00:53:38,660 --> 00:53:44,100
+يبقى دي روابط كويس يبقى المربع الأولاني تسعة أخماس
+
+463
+00:53:47,930 --> 00:53:54,210
+اللي بعده زائد تسعة على خمسة وعشرين كتابنا صح ولم
+
+464
+00:53:54,210 --> 00:53:59,970
+أتأكد من غلطة يبقى تسعة على خمسة وعشرين كوصاين
+
+465
+00:53:59,970 --> 00:54:04,530
+تربيع T يبقى تلك اللي بناخد تسعة على خمسة وعشرين
+
+466
+00:54:04,530 --> 00:54:07,450
+بيبقى تسعة تربيع زائد كوصاين تربيع الواحد يبقى
+
+467
+00:54:07,450 --> 00:54:15,430
+النتيجة فقط تلت أخمس طيب إذا نجيب ال N اللي هو DT
+
+468
+00:54:15,430 --> 00:54:20,000
+على DT على طول ال DT على DTيبقى بدنا نقسم هذا كله
+
+469
+00:54:20,000 --> 00:54:25,980
+على مين أمانا على تلت أخماس بصير ناقص sin t في
+
+470
+00:54:25,980 --> 00:54:31,560
+اتجاه ال I ناقص cos t في اتجاه مين؟ في اتجاه ال J
+
+471
+00:54:31,560 --> 00:54:38,420
+بالمرة نحسبه عند ال I على 2 ان عند ال I على 2
+
+472
+00:54:38,420 --> 00:54:46,150
+تساوي ناقص Iجا تسعين واحد جا تسعين اثنين او صفر
+
+473
+00:54:46,150 --> 00:54:50,710
+اذا ماقدر اجيب ال by normal vector يبقى هذا كل
+
+474
+00:54:50,710 --> 00:54:56,350
+الحكي لازم ضمن المطلوب الاول من المسألة المطلوب
+
+475
+00:54:56,350 --> 00:55:03,250
+رقم A يبقى دلوقتي بيقولوا هنا لسه مخلصناش بدنا B
+
+476
+00:55:03,250 --> 00:55:10,690
+بيساوي T cross ال M يبقى على طول الخط باخد المحدد
+
+477
+00:55:10,690 --> 00:55:20,330
+I Jالـ T عند الـ Pi على 2 هنا بـ 0 و هنا بسادة تلت
+
+478
+00:55:20,330 --> 00:55:27,270
+أخمس و هنا بأربع أخمس لان نيجي لل end
+
+479
+00:55:32,190 --> 00:55:38,250
+by yourself بتفكير محدد باستخدام عناصر الصف التالت
+
+480
+00:55:38,250 --> 00:55:46,330
+يبقى هي ناقص واحد فيه عشق بصفه و عموده بصير أربع
+
+481
+00:55:46,330 --> 00:55:56,410
+أخماس J أربع أخماس J ناقص مع ناقص بصير زائد تلت
+
+482
+00:55:56,410 --> 00:56:00,430
+أخماس اللي هو K
+
+483
+00:56:03,240 --> 00:56:09,000
+يبقى صارت النتيجة ناقص أربع أخمس في اتجاه I ناقص
+
+484
+00:56:09,000 --> 00:56:14,800
+تلت أخمس في الجهة و التاني K يبقى هذا الشكل اللي
+
+485
+00:56:14,800 --> 00:56:21,960
+عندنا مرة تانية بقول يا بنات P يساوي T cross ال N
+
+486
+00:56:21,960 --> 00:56:27,800
+شيلنا T و حطينا مركبات عند البيعتين ناقص تلت أخمس
+
+487
+00:56:27,800 --> 00:56:33,420
+و أربع أخمس لجل L لل Nاللي هو بسالب واحد والباقي
+
+488
+00:56:33,420 --> 00:56:38,520
+بأسطار بنفكر باستخدام عناصر العموق الصف التالت ليش
+
+489
+00:56:38,520 --> 00:56:42,440
+انه فيه أسفار بسهل يبقى بصير ناقص واحد اشتر طف
+
+490
+00:56:42,440 --> 00:56:47,880
+وعموده بصير أربع أخماس J ناقص مع ناقص بصير زائد
+
+491
+00:56:47,880 --> 00:56:53,980
+تلت أخماس K دخلنا الناقص إذا انتهينا من المطلوب
+
+492
+00:56:53,980 --> 00:57:00,400
+الأول بنجد المطلوب التاني تبع من؟ تبع المسألة
+
+493
+00:57:03,260 --> 00:57:08,920
+المطلوب التاني قالوا بدي معادلة مين؟ ال normal
+
+494
+00:57:08,920 --> 00:57:15,500
+plane نرجع بالذاكرة إلى الوراق يبقى هذا من المحاور
+
+495
+00:57:15,500 --> 00:57:23,580
+التلاتة هذا T هذا M وهذا B هذا هو ال normal plane
+
+496
+00:57:23,580 --> 00:57:30,920
+مظبوط؟ يبقى هذا هو ال normal plane
+
+497
+00:57:32,560 --> 00:57:38,940
+مش هنجيب معادلة مستوى شو بيلزم نقمنها عمودي عليه و
+
+498
+00:57:38,940 --> 00:57:43,320
+نقطة تقع فيه تمام؟ الحمد لله العمودي عليه مين هو
+
+499
+00:57:43,320 --> 00:57:49,660
+هنا؟ T موجود عندي؟ اه موجود دي بيبدي نقطة يبقى
+
+500
+00:57:49,660 --> 00:57:57,640
+بيبدي نقطة تقع وين؟ في ال plane صح ولا لا طيب كويس
+
+501
+00:57:57,640 --> 00:58:04,490
+ال T و ال N و ال B مش هادئبالتاقة عندها نقطة ونقطة
+
+502
+00:58:04,490 --> 00:58:08,790
+موجودة على الملحانة يعني في الفرار إذا ماقدر أجيب
+
+503
+00:58:08,790 --> 00:58:16,670
+إحداثيات هذه النقطة الـMid الـNormal Plane يمر بها
+
+504
+00:58:16,670 --> 00:58:23,390
+النقطة اللي عندنا هذه النقطة P بتجيبها من وين؟
+
+505
+00:58:23,390 --> 00:58:27,770
+بتجيبها من راس المسألة يبقى احنا عندنا ال X
+
+506
+00:58:33,610 --> 00:58:38,410
+كان ليحسب الشغلات هذه وين عند T تسويقها طيب هذه X
+
+507
+00:58:38,410 --> 00:58:43,470
+و هذه Y و هذه Z لأن هشيل كل T و أحط مكانها يرجع
+
+508
+00:58:43,470 --> 00:58:51,990
+تصير تلاتة Sin باي على اتنين و تلاتة Cos باي على
+
+509
+00:58:51,990 --> 00:58:57,090
+اتنين و اربع في باي على اتنين بالشكل اللي عندنا
+
+510
+00:58:57,090 --> 00:59:01,130
+هذا اربعة تيجا تمام يرجع تصير
+
+511
+00:59:06,450 --> 00:59:14,950
+يبقى هذه النقطة التي يمر بها الكلب هي نقطة P يبقى
+
+512
+00:59:14,950 --> 00:59:23,210
+هذه هي نقطة P بالضبط تماما طيب P موجودة و T هو ال
+
+513
+00:59:23,210 --> 00:59:33,470
+normal vector ال T عند ال Pi على 2 is the normal
+
+514
+00:59:33,470 --> 00:59:34,370
+vector
+
+515
+00:59:46,570 --> 00:59:52,750
+إذا من خلال هذا باجي بقول ال X راحة عندنا في زير
+
+516
+01:00:25,100 --> 01:00:32,940
+النتيجة ناقص ثلاث أخماس Y زائد أربع أخماس Z هذا مع
+
+517
+01:00:32,940 --> 01:00:40,760
+السلامة تمنية Y على خمسة بعد ذلك اضغط بكله في خمسة
+
+518
+01:00:40,760 --> 01:00:42,000
+تخلص من القصور
+
+519
+01:01:02,710 --> 01:01:08,730
+المطموب الثاني نمربي هنا في المثل قال هذه ال
+
+520
+01:01:08,730 --> 01:01:12,410
+equation of the normal plane المطموب التالت يحتاج
+
+521
+01:01:12,410 --> 01:01:18,550
+إلى كيرفتشار كابا و تورشن تارهذه كامة عندي هذه
+
+522
+01:01:18,550 --> 01:01:26,230
+كامة V موجودة V موجودة حسبناها يا بنات؟ ماحسبناش
+
+523
+01:01:26,230 --> 01:01:32,050
+ال A يبقى بدنا نروح نحسب ال A عند ال Y على 2 وناخد
+
+524
+01:01:32,050 --> 01:01:40,770
+cross product ما بين ال 2 وقول ال V حسبناها؟
+
+525
+01:01:40,770 --> 01:01:40,950
+V
+
+526
+01:01:59,770 --> 01:02:07,990
+على دي P وين ال V؟ هاي سالب تلاتة sign T سالب
+
+527
+01:02:07,990 --> 01:02:15,570
+تلاتة sign T في اتجاه ال I و بعدها ناقص تلاتة و
+
+528
+01:02:15,570 --> 01:02:20,550
+sign T في اتجاه ال J و هدي فجر الفتحة على روحك و
+
+529
+01:02:20,550 --> 01:02:26,690
+نصلا مش تكتب Zero بدنا نحسب ال A عند ال Pi على
+
+530
+01:02:26,690 --> 01:02:27,270
+اتنين
+
+531
+01:02:32,310 --> 01:02:36,590
+يبقى صار الـ A موجود والـ V موجود فتعمل cross
+
+532
+01:02:36,590 --> 01:02:41,530
+product لهم وشوف قداشة قوة تبعه هيكون يبقى ناخده
+
+533
+01:02:41,530 --> 01:02:52,150
+الـ V cross الـ A يساوي I J K الـ V V هي سالب
+
+534
+01:02:52,150 --> 01:02:58,570
+تلاتة وأربعة يبقى Zero سالب تلاتة وأربعة لأنه
+
+535
+01:02:58,570 --> 01:02:59,370
+ماعندش I
+
+536
+01:03:14,110 --> 01:03:21,150
+مرة واحدة لأن فيها أسفار كتير ناقص تلاتة وشطر صفه
+
+537
+01:03:21,150 --> 01:03:30,950
+وعموده 4G زائد تلاتة K أول
+
+538
+01:03:30,950 --> 01:03:40,830
+شهدتم فقولوا ناقص تلاتةنقص تسعة كيلو أحنا بنقدر
+
+539
+01:03:40,830 --> 01:04:01,150
+نجيب الكيربتشا بسهولة بدون مشاكل طيب
+
+540
+01:04:01,150 --> 01:04:08,470
+بدنا نجيب الكيربتشاكذا اللي هو طول ال V cross ال A
+
+541
+01:04:08,470 --> 01:04:15,470
+مقسوما على طول ال V تكعيب هذا الكلام وايه و ساوي
+
+542
+01:04:15,470 --> 01:04:21,070
+الآن بدأ نجي لطول المتجه هذا يبقى اللي هو مين
+
+543
+01:04:21,070 --> 01:04:27,830
+الجدري الترفيهي ل 12 في 12 مية و أربعة و أربعين
+
+544
+01:04:27,830 --> 01:04:37,180
+زاد 9 في 9 و 1 و 80كل هذا مقصودا وين طول ال V؟ طول
+
+545
+01:04:37,180 --> 01:04:39,260
+ال V هي خمسة
+
+546
+01:05:02,160 --> 01:05:04,960
+مقدار الكيروفيتشار
+
+547
+01:05:09,080 --> 01:05:14,560
+الـ X dot والـ Y dot والـ Z dot هي .. مظبوط؟ الـ A
+
+548
+01:05:14,560 --> 01:05:21,000
+الـ acceleration هي عند الـ Y على 2 هي جاذب،
+
+549
+01:05:21,000 --> 01:05:29,920
+ضالمين أنه الـ X double dot يعني بدنا نشتغل الـ D
+
+550
+01:05:29,920 --> 01:05:39,060
+A على D T يساوي، هي الـ A اللي هو ناقص 3وSin T في
+
+551
+01:05:39,060 --> 01:05:46,720
+اتجاه I زائد تلاتة Sin T في اتجاه الـ J هذا معناه
+
+552
+01:05:46,720 --> 01:05:56,440
+ان ال DA على DT عند من عند ال PI على اتنين يساوي
+
+553
+01:05:56,440 --> 01:06:07,820
+هذه Zero وهذه تلاتة J إذا بقدر احسب لهاللي هو main
+
+554
+01:06:07,820 --> 01:06:13,740
+اللي هو torsion tower قول
+
+555
+01:06:13,740 --> 01:06:24,300
+ال V مش لازم طبعا خلصنا منه و هذا مش لازم و ال
+
+556
+01:06:24,300 --> 01:06:32,940
+normal مش لازم هاي
+
+557
+01:06:32,940 --> 01:06:42,540
+نيجي الآنطورشين تاب بدي ساوي المحدد X dot Y dot Z
+
+558
+01:06:42,540 --> 01:06:49,080
+dot X double dot Y double dot Z double dot X
+
+559
+01:06:49,080 --> 01:06:54,960
+triple dot Y triple dot Z triple dot كله مقسوما
+
+560
+01:06:54,960 --> 01:07:01,060
+على قول ال V cross ال A أظن تربيه هيك يا بنات صح؟
+
+561
+01:07:01,060 --> 01:07:06,820
+تمام يبقى هذا الكلام بدي ساوي المحددمُركّبات
+
+562
+01:07:06,820 --> 01:07:14,400
+السرعة هي يبقى Zero و سالم تلاتة و أربعة مُركّبات
+
+563
+01:07:14,400 --> 01:07:25,160
+العجلة الـ A الـ A عند الـ Y على الـ N و ناقص
+
+564
+01:07:25,160 --> 01:07:33,620
+تلاتة I ناقص تلاتة Zero Zero مُركّبات المشتقة هي
+
+565
+01:07:34,010 --> 01:07:41,030
+تلاتة جيه يبقى Zero تلاتة Zero بالشكل هذا بيكروس
+
+566
+01:07:41,030 --> 01:07:45,830
+ال A طوله تبعها بيكروس ال A اللي بيبقى خمستاشر
+
+567
+01:07:45,830 --> 01:07:52,270
+مضبوط على خمستاشر الكوال تربيت يبقى هذا الكلام بده
+
+568
+01:07:52,270 --> 01:07:56,190
+يساوي ايش رأيك قبل ان اتفككوا باستخدام عناصر
+
+569
+01:07:56,190 --> 01:08:00,870
+العمود التالت يبقى هى R
+
+570
+01:08:08,340 --> 01:08:15,820
+مظبوط على كداش على خمس عشر تربية يبقى هذا الكلام
+
+571
+01:08:15,820 --> 01:08:22,900
+يصير ناقص فهنا أربعة على هذه تلاتة في خمسة و تلاتة
+
+572
+01:08:22,900 --> 01:08:27,140
+في خمسة تلاتة في تلاتة تسعة من الخمسة تربية ناقص
+
+573
+01:08:27,140 --> 01:08:32,520
+أربعة على خمسة وعشرين هذا مقدار ال torsion اللي
+
+574
+01:08:32,520 --> 01:08:32,760
+عادي
+
+575
+01:08:36,620 --> 01:08:41,480
+اللي عند هنا stop انتهى ال section وإلى يكون أرقام
+
+576
+01:08:41,480 --> 01:08:50,700
+المسائل exercises اللي هو تلتاشر كامسة المسائل من
+
+577
+01:08:50,700 --> 01:08:57,340
+واحد إلى ستاشر ال odd بالإضافة إلى سؤال
+
+578
+01:09:15,480 --> 01:09:22,360
+أيش مانا partial يبقى partial derivatives المشتقات
+
+579
+01:09:22,360 --> 01:09:30,740
+الجزدية احنا اللي درسناها قبل ذلك where في
+
+580
+01:09:30,740 --> 01:09:37,420
+calculus a و b و لغاية اليوم في z كان كله بناخد ال
+
+581
+01:09:37,420 --> 01:09:43,960
+function ده اللي في متغير واحديبقى ناخد ال
+
+582
+01:09:43,960 --> 01:09:49,600
+function لو كانت ده اللي أكتر من متغير يبقى بنجي
+
+583
+01:09:49,600 --> 01:09:55,480
+لأول section اللي هو اربعة عشر واحد اللي هو
+
+584
+01:09:55,480 --> 01:10:00,120
+functions of
+
+585
+01:10:00,120 --> 01:10:04,260
+several variables
+
+586
+01:10:09,720 --> 01:10:16,640
+الدوال في عدة متغيرات يبقى من الآن فصاعدا الشبطر
+
+587
+01:10:16,640 --> 01:10:21,100
+هذا اربعتاشر واللي جاي تبع التكامل هيكون عندي
+
+588
+01:10:21,100 --> 01:10:28,200
+متغيرين او تلاتة او اربعة او ان من المتغيرات يبقى
+
+589
+01:10:28,200 --> 01:10:32,620
+بهجة بقول these functions
+
+590
+01:10:45,580 --> 01:10:54,320
+ممكن أقول يا بنات z function في x و y إذا صارت
+
+591
+01:10:54,320 --> 01:11:01,280
+الاقتران z أو الدالة z دالة فيه متغيرين x و y ممكن
+
+592
+01:11:01,280 --> 01:11:05,080
+يكون ال w function في x
+
+593
+01:11:08,210 --> 01:11:15,230
+يبقى الأولى دالة في متغيرين التانية دالة في تلاتة
+
+594
+01:11:15,230 --> 01:11:21,330
+متغيرات مش هاجدكوا بس ممكن يكون دالة في N من
+
+595
+01:11:21,330 --> 01:11:29,370
+المتغيرات كيف؟ لو كان يقولنا مثلا Y تساوي F of X1
+
+596
+01:11:29,370 --> 01:11:34,790
+X2 X3 وظلينا ماشيين لغاية ال X
+
+597
+01:11:39,950 --> 01:11:47,390
+يعني الحالة هذه بقول F دالة في N من المتغيرات تمام
+
+598
+01:11:47,390 --> 01:11:53,690
+طب الآن بدنا نعرف شو ال domain تبع هذه الدوال و ال
+
+599
+01:11:53,690 --> 01:11:58,590
+range تبع هذه الدوال هل هو زي تبع calculus A و
+
+600
+01:11:58,590 --> 01:12:03,230
+الله مختلف عنه نوعا ما طبعا في calculus A بجينا
+
+601
+01:12:03,230 --> 01:12:08,910
+ناخد ال domain هو interval و ال range هو كذلك main
+
+602
+01:12:09,230 --> 01:12:15,530
+Interval صح ولا لأ؟ هل هذا الكلام ليزال كما هو؟
+
+603
+01:12:15,530 --> 01:12:19,610
+والله صار فيه بعض الخلافات بالنسبة لل functions of
+
+604
+01:12:19,610 --> 01:12:26,050
+several variables مش هنغير، هبدأ بأمثلة على ذلك
+
+605
+01:12:26,050 --> 01:12:29,810
+أول مثال
+
+606
+01:12:40,210 --> 01:12:45,310
+أول مثال بروزي F الـ
+
+607
+01:12:45,310 --> 01:12:57,530
+F of XY يساوي لان F تعيقظ XY زائد Y ناقص واحد
+
+608
+01:13:20,110 --> 01:13:32,190
+يبقى بالصين لن لمن؟ ال X بي E و ال Y واحد في E ذات
+
+609
+01:13:32,190 --> 01:13:40,870
+Y يبقى واحد ناقص واحد يبقى بضال قداش لن لل E لن لل
+
+610
+01:13:40,870 --> 01:13:48,920
+E قداش ممتاز جداقيمة الدالة عند النقطة اللي احدث
+
+611
+01:13:48,920 --> 01:13:54,240
+إيها E و واحد هيقدر قيمة واحدة اللي هي واحد و
+
+612
+01:13:54,240 --> 01:13:58,060
+أقيسي على ذلك نخش على ال domain أو ال range
+
+613
+01:13:58,060 --> 01:14:11,380
+example two you will find the domain and range
+
+614
+01:14:18,090 --> 01:14:24,590
+of the following functions
+
+615
+01:14:24,590 --> 01:14:28,770
+f
+
+616
+01:14:28,770 --> 01:14:32,510
+of
+
+617
+01:14:32,510 --> 01:14:40,910
+x و f of y يبدو يساوي len نقص
+
+618
+01:14:40,910 --> 01:14:43,710
+y زائد واحد
+
+619
+01:14:51,780 --> 01:15:00,180
+هو يحاول أن يحسب الـ Range لـ F جدكي
+
+620
+01:15:11,020 --> 01:15:16,000
+هو علاقة دلوقت باجي بقولك كويس f of x y هي ال len
+
+621
+01:15:16,000 --> 01:15:22,100
+دي شغلة الكميات مجموعة مع بعضها و قداش ال domain
+
+622
+01:15:22,100 --> 01:15:29,160
+أو ال len و قداش بتكون معرفة إذا كانكل اللي جوا لن
+
+623
+01:15:29,160 --> 01:15:33,880
+عدد و العدد ده أكبر من Zero إذا لن غير معرفة لكمية
+
+624
+01:15:33,880 --> 01:15:38,260
+سالبة و غير معرفة Little يبقى بد المقدار بين
+
+625
+01:15:38,260 --> 01:15:46,020
+القوسين يكون ماله أكبر من Zero كويس يبقى بد 2X
+
+626
+01:15:46,020 --> 01:15:54,040
+ناقص Y زائد واحد greater than Zero أو ممكن اكتبها
+
+627
+01:15:54,040 --> 01:15:55,320
+بشكل آخر
+
+628
+01:16:01,410 --> 01:16:09,930
+أقل من اتنين X زاوية واحدة طب ويه تساوي اتنين X
+
+629
+01:16:09,930 --> 01:16:15,450
+زاوية واحدة؟ ماعرفتش يا بناتي مستقيم اذا لو حبيت
+
+630
+01:16:15,450 --> 01:16:20,790
+ارسمها على الطريقة دي ماكان برسم ال domain مارسمش
+
+631
+01:16:20,790 --> 01:16:25,360
+الدالة الأصلية اللي عندي هذاهذه بدلا من قرص رسمها
+
+632
+01:16:25,360 --> 01:16:29,880
+هذه غير على جهاز الكمبيوتر برسمها انها شكل مجسمات
+
+633
+01:16:29,880 --> 01:16:35,300
+بصيفة فرحة يبقى انا برسم ال domain فقط فاجي بيقول
+
+634
+01:16:35,300 --> 01:16:40,360
+لو جيت هنا خدت محاول الشكل اللي قلنا هذا وقولت هذا
+
+635
+01:16:40,360 --> 01:16:48,720
+محور X وهذا محور Y وهذه نقطة الأصل اللي هي Z الخط
+
+636
+01:16:48,720 --> 01:16:56,160
+Y تسوي Xمنصف من الرابع الأول والرابع الثالث اتنين
+
+637
+01:16:56,160 --> 01:17:02,440
+اكس يبقى تقريب على مين؟ على محور Y زائد واحد شفت
+
+638
+01:17:02,440 --> 01:17:07,900
+إلى أعلى بمقدار واحد إذا لو كانت هذه النقطة هي
+
+639
+01:17:07,900 --> 01:17:15,020
+Zero و واحد، سيأتي الخط اللي بنقطها دبنات بالشكل
+
+640
+01:17:15,020 --> 01:17:15,580
+اللي عندنا
+
+641
+01:17:19,140 --> 01:17:25,800
+طب ليش رسمته مُنَقَر؟ ماعنديش يساوي طب why أقل من
+
+642
+01:17:25,800 --> 01:17:33,180
+هذا الخط؟ يبقى كل المساحة المظللة اللي عندنا لأسفل
+
+643
+01:17:33,180 --> 01:17:39,000
+هذا الخط يبقى يا بناتي ال domain هنا هي ال area
+
+644
+01:17:39,000 --> 01:17:47,380
+اللي بين لأسفل هذا الخط يبقى هذه هي ال area down
+
+645
+01:17:58,320 --> 01:18:04,140
+هل النقاط اللي على الخط من ضمن هذا ال domain لأ
+
+646
+01:18:04,140 --> 01:18:09,940
+لأنه أقل منماعنديش يساوي لو كان فيه يساوي كرسمتك
+
+647
+01:18:09,940 --> 01:18:15,560
+الخط هذا متواصل يبقى نظرا لإن نقاط الخط ليست من
+
+648
+01:18:15,560 --> 01:18:21,480
+ضمن ال domain رسمتلك نقطة يبقى كل المساحة المضللة
+
+649
+01:18:21,480 --> 01:18:25,700
+لأسفل هذا الخط تعتبر هي ال domain إذا انت خلف عن
+
+650
+01:18:25,700 --> 01:18:30,200
+Calculus A Calculus A كان Interval هنا طلعت ايش
+
+651
+01:18:30,200 --> 01:18:34,400
+مساحة و يمكن تطلع حجم كمان يا بنات ال domain مش
+
+652
+01:18:34,400 --> 01:18:39,890
+هاجد المساحةكما سنرى من خلال الأمثلة يبقى هذا هو
+
+653
+01:18:39,890 --> 01:18:47,510
+المثال الأول اروح للمثال الثاني ال range اه طيب ال
+
+654
+01:18:47,510 --> 01:18:52,190
+len لو رجعتي لمنحنى ال len تبع calculus B ال len
+
+655
+01:18:52,190 --> 01:18:57,930
+من وين لوين مش ذاكرين منحنى .. تبع calculus A كان
+
+656
+01:18:57,930 --> 01:19:03,610
+منحنى ال len في الشكل اللي عندك هذا ايه كان هذا
+
+657
+01:19:03,610 --> 01:19:03,970
+محور
+
+658
+01:19:06,700 --> 01:19:12,480
+وهذا Y تساوي لن X وهذا النقطة هي واحد وزيرو تمام
+
+659
+01:19:12,480 --> 01:19:18,540
+بعد الواحد قيمة موجبة قبل الواحد لزيرو كل كمية
+
+660
+01:19:18,540 --> 01:19:24,600
+سالب لأسفل مخر X لكن بعد زيرو هي القيمة الأعلى مخر
+
+661
+01:19:24,600 --> 01:19:29,060
+X فكان ال range قداش من سالب infinity لإنفنيت يعني
+
+662
+01:19:29,060 --> 01:19:35,730
+كل ال real life هل اتغير عندنا هنا ولا هويبقى هنا
+
+663
+01:19:35,730 --> 01:19:41,650
+بظل كل set of real numbers يابتكت بيها set R
+
+664
+01:19:41,650 --> 01:19:47,970
+يابتكت بيها من سالب infinity لغة ال infinity as an
+
+665
+01:19:47,970 --> 01:19:53,690
+open interval بهذا الشكل سنصل إلى السؤال التاني
+
+666
+01:19:53,690 --> 01:20:00,790
+السؤال التاني ميعطيني f of x و y تساوي اللي هي
+
+667
+01:20:00,790 --> 01:20:09,180
+تلاتةفى الجدرى التربيعى لأربعة ناقص X تربيع ناقص Y
+
+668
+01:20:09,180 --> 01:20:15,080
+تربيع ناقص Y ناقص Y تربيع ناقص Y تربيع
+
+669
+01:20:15,080 --> 01:20:19,640
+ناقص Y تربيع ناقص Y تربيع ناقص Y تربيع ناقص Y
+
+670
+01:20:19,640 --> 01:20:19,720
+ناقص Y تربيع ناقص Y تربيع ناقص Y تربيع ناقص Y
+
+671
+01:20:19,720 --> 01:20:27,220
+تربيع ناقص Y تربيع ناقص Y تربيع ناقص
+
+672
+01:20:27,220 --> 01:20:30,100
+Y تربيع ناقص Y ت
+
+673
+01:20:33,280 --> 01:20:38,940
+الجدر هذا لكي يكون معرف يريد القيمة التي تحته أكبر
+
+674
+01:20:38,940 --> 01:20:45,280
+من أو تساوي zero تمام يبقى يريد كل الأربعة ناقص x
+
+675
+01:20:45,280 --> 01:20:49,460
+تربية ناقص y تربية greater than or equal to zero
+
+676
+01:20:49,460 --> 01:20:53,820
+او إن شئتوا فاقولوا انه بلي هدالة على الشجرة
+
+677
+01:20:53,820 --> 01:20:59,020
+التانية بس ال x تربية زائد y تربية أقل من أو يساوي
+
+678
+01:20:59,020 --> 01:21:05,110
+100الاربعة ماعادلتش هذه يساوي اربعة دائرة بس احنا
+
+679
+01:21:05,110 --> 01:21:09,530
+هنا لما نقول اقل من او يساوي بس مش على المحيط و بس
+
+680
+01:21:09,530 --> 01:21:16,430
+و جوا ليه باشي بتكون عندي disk قرص مصمت يعني كله
+
+681
+01:21:16,430 --> 01:21:21,270
+المحيط و النقاط اللي في داخليبقى هذا لو روحته
+
+682
+01:21:21,270 --> 01:21:27,110
+رسمته بياخد الشكل التالي هقول هذا محور X هذا محور
+
+683
+01:21:27,110 --> 01:21:31,630
+Y هذا نقطة الأصل اللي هو Zero عندي desk على شكل
+
+684
+01:21:31,630 --> 01:21:37,550
+دائرة الشكل هذا نصف
+
+685
+01:21:37,550 --> 01:21:43,270
+قطرها يساوي كم؟ يساوي اتنين يبقى كل المنطقة
+
+686
+01:21:43,270 --> 01:21:48,170
+المظللة هذه يبقى
+
+687
+01:21:48,170 --> 01:21:49,210
+هذه desk
+
+688
+01:21:51,680 --> 01:22:03,040
+with center at the origin and
+
+689
+01:22:03,040 --> 01:22:08,000
+radius اتنين
+
+690
+01:22:16,480 --> 01:22:24,040
+من سلب اتنين لاتنين وجهة نظر قد تكون صحيحة وقد
+
+691
+01:22:24,040 --> 01:22:32,260
+تقول خاطئة في تلاتة برا الجدرد تخفيها من الحساب؟
+
+692
+01:22:32,260 --> 01:22:36,760
+لأ يبقى من ناقص ستة لستة زي ما بتقولين من ناقص ستة
+
+693
+01:22:36,760 --> 01:22:42,220
+لستة صح؟ نقول من تلاتة فيها طبعا إجابة خاطئة بدنا
+
+694
+01:22:42,220 --> 01:22:49,410
+إجابة صحيةمصححة يعني هل القيمة اللى متحت الجدر هذه
+
+695
+01:22:49,410 --> 01:22:54,330
+ممكن تطلع قيمة سالمة؟ لأ لأ مش ممكنين يبقى السلم
+
+696
+01:22:54,330 --> 01:22:58,010
+اللى قولتيه غلط يعني من صفر لست من صفر لست من صفر
+
+697
+01:22:58,010 --> 01:23:06,710
+في تأكيد من صفر لست وجهة نظر يبقى من Zero لغاية
+
+698
+01:23:06,710 --> 01:23:12,470
+ستة شكليا انها نشوف هل هذا الكلام صحيح كيف؟
+
+699
+01:23:28,350 --> 01:23:36,690
+عند أقل قيمةلما يهدى ال X Y اللي هي Zero اللي هي
+
+700
+01:23:36,690 --> 01:23:41,830
+عند المركز في ال domain طلع النتج يساوي ستة طب
+
+701
+01:23:41,830 --> 01:23:44,930
+بدها يشوف عند أكبر قيمة ل X و Y
+
+702
+01:23:49,340 --> 01:23:55,960
+لو تساوى مجموع ال X تربية و Y تربية مع الأربعة لو
+
+703
+01:23:55,960 --> 01:24:01,280
+كان X بجدر اتنين و Y بجدر اتنين وربعنا يصير اربعة
+
+704
+01:24:01,280 --> 01:24:07,860
+ناقص اربعة يساوي كم؟ Zero Zero معناته في تلاتة في
+
+705
+01:24:07,860 --> 01:24:10,000
+أقل من Zero
+
+706
+01:24:13,100 --> 01:24:17,960
+بالشمكالية يستحيل ان اقل قيمة باخدها ال range هي
+
+707
+01:24:17,960 --> 01:24:23,620
+zero اكبر قيمة باخدها ال six فقط لا غير كلام صحيح
+
+708
+01:24:23,620 --> 01:24:29,600
+طيب ناخد نمرة C نمرة
+
+709
+01:24:29,600 --> 01:24:37,780
+تلاتة ناخد ال F X Y و7 اللي هو الجدري التربيعي ل X
+
+710
+01:24:37,780 --> 01:24:40,880
+تربيع زائد Y تربيع نقطة
+
+711
+01:24:46,980 --> 01:24:55,420
+بدي أعرف ال domain موافق
+
+712
+01:24:55,420 --> 01:25:01,720
+موافق يبقى هنا بدنا ال X تربيه زاد Y تربيه نقص 9
+
+713
+01:25:01,720 --> 01:25:07,800
+تكون greater than or equal to 0 وإيش كمان؟ بدي ال
+
+714
+01:25:07,800 --> 01:25:14,020
+X نقص ال Y ممنوع تساوي 0 وقول والله كويس طب بدنا
+
+715
+01:25:14,020 --> 01:25:19,980
+نصيغها صياغة أخرىيبقى شباجي بيقول ال X تربيه زائد
+
+716
+01:25:19,980 --> 01:25:25,800
+Y تربيه أكبر من أو يسوى تسعة وال Y ممنوع تساوي ال
+
+717
+01:25:25,800 --> 01:25:30,380
+X مظبوط
+
+718
+01:25:30,380 --> 01:25:36,180
+وال Y ممنوع تساوي ال X نشوف الحكي هنا شو شكله على
+
+719
+01:25:36,180 --> 01:25:40,720
+الطبيعة حاول نفهمفبقى يقول هذه معادلة ايش اصلا
+
+720
+01:25:40,720 --> 01:25:45,960
+جاملة الانقلتية يبقى دائرة يبقى لو روحت رسام و قول
+
+721
+01:25:45,960 --> 01:25:51,900
+هذا الملحونة اللي عندنا هذا محور X هذا محور Y فهذا
+
+722
+01:25:51,900 --> 01:25:57,920
+نقطة أصلي Zero وهي الدائرة طيب تمام ايش قال لي؟
+
+723
+01:25:57,920 --> 01:26:06,260
+قال لي أكبر من أو يساوي تسعة يبقى وين؟ برا الدائرة
+
+724
+01:26:06,700 --> 01:26:14,200
+برا يبقى المنطقة هذه المنطقة المضللة بالأدرى طب
+
+725
+01:26:14,200 --> 01:26:20,620
+الخط Y تساوي X يبقى هذا الخط اللي علناه في التراث
+
+726
+01:26:20,620 --> 01:26:27,460
+مانيكا من القرن هذا الخط
+
+727
+01:26:27,460 --> 01:26:34,220
+Y تساوي X يبقى
+
+728
+01:26:34,950 --> 01:26:40,990
+كل نقطة تقع على هذا الخط لازم تكون برا من؟ برا
+
+729
+01:26:40,990 --> 01:26:45,770
+الدمان، ممنوع يحصل تساوي، كويس؟ يعني طلع لما نقول
+
+730
+01:26:45,770 --> 01:26:50,270
+في كل المنطقة اللي برا الدائرة، هنا نقاط هي موجودة
+
+731
+01:26:50,270 --> 01:26:53,950
+برا الدائرة، مظبوط ولا لا؟ نقاط ليه بيبقى ممنوع
+
+732
+01:26:53,950 --> 01:26:59,160
+هاد تكون من ضمن الدمان؟يبقى المنطقة المظللة خارج
+
+733
+01:26:59,160 --> 01:27:05,320
+الدائرة والتي لا تقع على الخط اللي هو Y تساوي X
+
+734
+01:27:05,320 --> 01:27:14,520
+طيب بدنا ال range يا الله أشوف اللي فوق أظن موجة
+
+735
+01:27:14,520 --> 01:27:21,180
+اللي فوق البسط على طول الخط بقى تبني قيمة موجة بعد
+
+736
+01:27:21,180 --> 01:27:28,440
+الصفرمن عندى التلاتة ما يمكن أن يكون سالم بالمرة
+
+737
+01:27:28,440 --> 01:27:36,960
+طب لو قلتلك خدي ال X باتنين و Y بتلاتة X باتنين و
+
+738
+01:27:36,960 --> 01:27:45,540
+Y بتلاتة مقرف عنده ولا لا؟ يبقى مخمطات الشيء صح؟
+
+739
+01:27:46,430 --> 01:27:50,810
+يعني المقام يبقى ممكن يكون موجة وممكن يكون سالب إن
+
+740
+01:27:50,810 --> 01:27:55,630
+استبعدت الصفر بس المساواة بين X وY يبقى ممكن يكون
+
+741
+01:27:55,630 --> 01:28:02,680
+سالب وممكن يكون موجةتاخد السالب كله و الموجات كله
+
+742
+01:28:02,680 --> 01:28:07,180
+معقول تاخد السالب كله معقول كيف مش معقول كل ال bus
+
+743
+01:28:07,180 --> 01:28:12,360
+كل متى ال bus خمسين على سبيل المثال و جيت انا لجيت
+
+744
+01:28:12,360 --> 01:28:18,220
+الفرق بين x و y واحد من مين واحد من الف تبقى بصير
+
+745
+01:28:18,220 --> 01:28:22,780
+واحد على الف الف اطلع وين فوق و خمسين تصير خمسين
+
+746
+01:28:22,780 --> 01:28:28,700
+الفطب لو كان سالب في سالب خمسين اللي يبقى هذا رايح
+
+747
+01:28:28,700 --> 01:28:31,840
+على المال النهائي و هذا رايح نويل لسالب infinity
+
+748
+01:28:31,840 --> 01:28:37,400
+كل ال real line يبقى ال range هنا كل ال real line
+
+749
+01:28:37,400 --> 01:28:42,520
+بالاستثناء من سالب infinity إلى infinity طيب اعطنك
+
+750
+01:28:42,520 --> 01:28:48,840
+الآن ثلاثة أمثلة و كلها زي ما انت شايفة area و ال
+
+751
+01:28:48,840 --> 01:28:52,320
+range هو interval طب خدلي لمرة أربع
+
+752
+01:29:00,150 --> 01:29:07,690
+بتساوي الجدري التربيعي لواحد ناقص X تربيع ناقص Y
+
+753
+01:29:07,690 --> 01:29:14,190
+تربيع على أربعة ناقص Z تربيع على تسعة
+
+754
+01:29:21,210 --> 01:29:27,050
+السؤال وجهي بتقول زميلتكوا ممكن ال domain يطلع صفر
+
+755
+01:29:27,050 --> 01:29:33,850
+ولا لا يمكن الرجع ممكن الرجع يطلع صفر ولا لا نعم
+
+756
+01:29:33,850 --> 01:29:42,230
+ممكن وقتى تدرسر المقام اكبر ما يمكن طيب
+
+757
+01:29:42,230 --> 01:29:46,830
+الان بدنا نيجي لل domain تبع ال F بدي كل الكمية
+
+758
+01:29:46,830 --> 01:29:50,450
+اللى تحت الجدر اكبر
+
+759
+01:29:51,360 --> 01:29:56,340
+من أو تساوي zero صحيح ولا لأ يبقى بالدنيا أقوله
+
+760
+01:29:56,340 --> 01:30:02,500
+الآن اللي هو بدي الواحد ناقص x تربيه ناقص y تربيه
+
+761
+01:30:02,500 --> 01:30:07,140
+على أربع ناقص z تربيه على تسعة تكون أكبر من أو
+
+762
+01:30:07,140 --> 01:30:10,220
+تساوي zero أو انشرته وانفقه
+
+763
+01:30:13,160 --> 01:30:19,040
+زي تربيع على اربعة زي زد تربيع على تسعة ماله يكون
+
+764
+01:30:19,040 --> 01:30:24,560
+اقل من او يساوي الواحد طب هذه لو قلت يساوي واحد
+
+765
+01:30:24,560 --> 01:30:29,720
+معادلة ايش يا بنات؟ ellipsoid طب الاستطالة في
+
+766
+01:30:29,720 --> 01:30:35,780
+اتجاه مين؟ زد زي اللي تحتيه اكبر مايمكن اذا لو
+
+767
+01:30:35,780 --> 01:30:41,840
+روحت اخدت محاولة بالشكل اللي عندها ذلك وقلتهذا
+
+768
+01:30:41,840 --> 01:30:48,640
+محور X هذا Y وهذا Z ومديت هذا على سيقانته وروحت
+
+769
+01:30:48,640 --> 01:30:54,700
+رسم ال ellipsoid فكان ال ellipsoid الشكل اللي
+
+770
+01:30:54,700 --> 01:31:02,780
+عندنا وهنا شكل هذا هذا مش هيضغرني وهذا نقطة أصلي
+
+771
+01:31:02,780 --> 01:31:07,500
+وزيرة يبقى هذا ال ellipsoid اللي عندنا يبقى هذا
+
+772
+01:31:07,500 --> 01:31:13,820
+مين؟الـ interior تبع الـ ellipsoid زي الـ boundary
+
+773
+01:31:13,820 --> 01:31:22,440
+كل الشكل الخارجي يبقى هنا بسميه الـ interior and
+
+774
+01:31:22,440 --> 01:31:28,680
+ال boundary of
+
+775
+01:31:28,680 --> 01:31:37,280
+the ellipsoid طيب
+
+776
+01:31:39,170 --> 01:31:43,350
+الـ Range يلّا
+
+777
+01:31:43,350 --> 01:31:53,710
+نشوف الـ Range أيوة
+
+778
+01:31:53,710 --> 01:31:56,810
+يلّا
+
+779
+01:31:56,810 --> 01:32:03,110
+أولى شوفي السفر كم يطلع موافق يلّا بدي كمان يبقى
+
+780
+01:32:03,110 --> 01:32:08,050
+عند 0000 تطلع القيمة ال function هي واحدة غيره
+
+781
+01:32:12,450 --> 01:32:18,070
+هذه أكبر قيمة ولا أقل قيمة؟ أقل قيمة. أقل قيمة
+
+782
+01:32:18,070 --> 01:32:21,350
+اللي هي الواحد، يعني بدرجة أكبر منها. تقدر تجيبولي
+
+783
+01:32:21,350 --> 01:32:26,690
+و لو قيمة واحدة تكون أكبر منها؟ إذا بتجيبولي كمان
+
+784
+01:32:26,690 --> 01:32:33,750
+قيمة بتكون و أنتوا .. جيبولي قيمة واحدة بس تكون
+
+785
+01:32:33,750 --> 01:32:38,150
+أكبر من الواحدة؟اللي جيبها تاخدها و الله غير
+
+786
+01:32:38,150 --> 01:32:41,330
+احطلها اربعين من اربعين في اعمال الفصل من دول
+
+787
+01:32:41,330 --> 01:32:45,930
+ماتقدمش امتحان بس جيبلي اللي هو قيمة بياخدها
+
+788
+01:32:45,930 --> 01:32:49,510
+الدالة دي اكبر من واحد عشان لا تقولي واحد و واحد
+
+789
+01:32:49,510 --> 01:32:54,550
+من عشرة اكبر مايمكن يبقى هذه ال maximum value لل
+
+790
+01:32:54,550 --> 01:33:01,490
+function بزيدي شعن الواحد طيب و اقل قيمة؟ قدر؟
+
+791
+01:33:01,490 --> 01:33:08,590
+سالم؟معقول كمية من تحت الجدر سالبة و الجدر مُعرف
+
+792
+01:33:08,590 --> 01:33:14,310
+لكمية سالبة؟ يبقى
+
+793
+01:33:14,310 --> 01:33:20,310
+أكبر قيمة هي واحد و أصغر قيمة واحد برضه يعني يعني
+
+794
+01:33:20,310 --> 01:33:27,060
+بصير لينج نقطةيعني مهما تغيرت X وY وZ، بدي يطلع
+
+795
+01:33:27,060 --> 01:33:30,860
+ناتج نفس القيمة؟ يعني كل النقطة اللي خلّجها ربنا
+
+796
+01:33:30,860 --> 01:33:39,600
+داخل الـEllipsoid صورتها نقطة واحدة؟ فيش
+
+797
+01:33:39,600 --> 01:33:45,680
+احتمال يكون مجموع هذه و هذه و هذه يطلع واحد صحيح؟
+
+798
+01:33:46,210 --> 01:33:49,630
+وإذا طلع واحد صحيح بالسالب و عندك واحد يبقى مصير
+
+799
+01:33:49,630 --> 01:33:54,090
+زيرو مرضوه يبقى دائما من ال range بين الصفر
+
+800
+01:33:54,090 --> 01:34:01,770
+والواحد يبقى هذا ال range من zero لغاية واحد as
+
+801
+01:34:01,770 --> 01:34:04,130
+any closed interval
+
+802
+01:34:24,080 --> 01:34:32,560
+طيب خلوني أقول كمان هالدالة هذه نمرة أربعة نمرة
+
+803
+01:34:32,560 --> 01:34:45,760
+خمسة نمرة خمسة خديني F X Y Z يساوي L X زيدي اتنين
+
+804
+01:34:45,760 --> 01:34:51,480
+Yزائد اتنين زاد نقص اتنين زائد اتنين زاد نقص اتنين
+
+805
+01:34:51,480 --> 01:34:55,640
+زائد
+
+806
+01:34:55,640 --> 01:34:57,480
+اتنين زائد اتنين زائد اتنين زائد اتنين زائد اتنين
+
+807
+01:34:57,480 --> 01:34:57,520
+زائد اتنين زائد اتنين زائد اتنين زائد اتنين زائد
+
+808
+01:35:18,560 --> 01:35:28,600
+فكل النقاط X و Y و Z بحيث أن X زائد 2Y زائد 2Z نقص
+
+809
+01:35:28,600 --> 01:35:37,040
+2 تبقى أكبر من 0 ولا تساوي يبقى كل النقاط X Y و Z
+
+810
+01:35:37,040 --> 01:35:47,430
+بحيث أن X زائد 2Y زائد 2Z تبقى أكبر من قداشطب هذا
+
+811
+01:35:47,430 --> 01:35:52,890
+لو كانت تساوي اتنين معادلة إيش؟ لو كانت بدل الأكبر
+
+812
+01:35:52,890 --> 01:36:03,550
+من كانت تساوي معادلة إيش؟ مستوى
+
+813
+01:36:03,550 --> 01:36:08,650
+اتنين يا أخسار بعوض الله نقرأ الفاتعة على من حرم
+
+814
+01:36:08,650 --> 01:36:13,970
+النباتي المسلمين نخدت فيه وحلينا بدل المثال خمس،
+
+815
+01:36:13,970 --> 01:36:18,930
+ست أمثل على الموضوعيبقى هنا إيه؟ يبقى هذه لو كانت
+
+816
+01:36:18,930 --> 01:36:24,110
+تساوي إتنين وعادلة plane طب أكبر من هذا يبقى كل
+
+817
+01:36:24,110 --> 01:36:30,430
+الفرق كل space اللي أعلى هذا ال plane طبعا طيب لو
+
+818
+01:36:30,430 --> 01:36:35,370
+حبيت أتعرف عليه شو شكله أقول آه تفضلي أقول هاي
+
+819
+01:36:35,370 --> 01:36:43,310
+الشكل هذا محور X وهذا Y وهذا Z بدي أجيب نقاط تقاطع
+
+820
+01:36:43,310 --> 01:36:48,150
+مع المحاولالنقاط تفضل مع محور X يبقى Y و Z بقداش
+
+821
+01:36:48,150 --> 01:36:55,870
+Zero يبقى X بقداش 2 يبقى لو جيت قلت النقطة هذه 2 و
+
+822
+01:36:55,870 --> 01:37:02,120
+Zero و Zeroتقاطع مع محور Y يبقى X و Z بـ0 و يبقى Y
+
+823
+01:37:02,120 --> 01:37:07,540
+يبقى D بـ1 يبقى النقطة اللي عندنا هذه اللي هي Zero
+
+824
+01:37:07,540 --> 01:37:12,900
+و واحد و Zero تقاطع مع محور Z يبقى النقطة اللي
+
+825
+01:37:12,900 --> 01:37:18,780
+عندنا هذه Zero و Zero و واحد يبقى لو أصل بهذا
+
+826
+01:37:18,780 --> 01:37:24,720
+الشكل يبقى هذا الـ Infinity طبعا بمتاد كله من سالب
+
+827
+01:37:24,720 --> 01:37:29,060
+Infinity ل Infinityبس احنا جيبنالكم نقاط تقاطع ال
+
+828
+01:37:29,060 --> 01:37:35,760
+plane هذا ماله مع محاور الإحداثية يبقى لما أقول
+
+829
+01:37:35,760 --> 01:37:45,940
+أكبر من اتنين كل ال space اللي أعلى من ال plane
+
+830
+01:37:45,940 --> 01:37:56,890
+هنا يبقى ال space هذا كله above thatأيه الـ Plane
+
+831
+01:37:56,890 --> 01:38:03,070
+اللي هو X زيدي اتنين Y زيدي اتنين Z بده يساوي
+
+832
+01:38:03,070 --> 01:38:08,190
+اتنين يبقى كل الفراخ اللي أعلى من هذا طب ال range
+
+833
+01:38:08,190 --> 01:38:17,210
+كل ال .. range اللي .. R كل ال R و ال range هنا ال
+
+834
+01:38:17,210 --> 01:38:17,910
+range
+
+835
+01:38:22,720 --> 01:38:29,180
+أخر حاجة نمرها ستة وفكروا لي فيها كويس F of X وY
+
+836
+01:38:29,180 --> 01:38:38,760
+وZ F of X وY وZ يساوي X زائد Y زائد Z على absolute
+
+837
+01:38:38,760 --> 01:38:43,680
+value ل X زائد Y زائد Z
+
+838
+01:38:53,330 --> 01:39:03,390
+بدي الدمين يالا شوف هارمع دمين معناه Zero طيب و
+
+839
+01:39:03,390 --> 01:39:07,810
+جهدنا لها يعني أنا بدي أشيل بس من ال plane نقطة
+
+840
+01:39:07,810 --> 01:39:15,930
+الأصل مش هيك؟ طيب موافقين؟ طيب أنا بدي أجيبلك نقطة
+
+841
+01:39:15,930 --> 01:39:22,490
+ماهياش نقطة الأصل و أشوف معرفة عنده ولا لاخد لي X
+
+842
+01:39:22,490 --> 01:39:32,570
+بواحد و Y بواحد و Z بثاني باتنين Zero Undefined
+
+843
+01:39:32,570 --> 01:39:39,710
+هذه ماهياش نقطة في الأصل صح؟
+
+844
+01:39:39,710 --> 01:39:46,590
+يبقى كل ال X و Y و Z المجموعة بصير Zero ممنوع
+
+845
+01:39:46,590 --> 01:39:53,840
+يكونوا في ال domainيبقى كل الفرار ما على النقاط
+
+846
+01:39:53,840 --> 01:39:59,700
+اللتي تقع على الـ plate X زي Y زي Z تساوي 0 صح ولا
+
+847
+01:39:59,700 --> 01:40:07,200
+لا؟ يبقى هنا ال domain تبع ال F ال domain تبع ال F
+
+848
+01:40:07,200 --> 01:40:16,060
+بده يساوي all the points in the space
+
+849
+01:40:44,270 --> 01:40:47,070
+بالنسبة للمجموعات الموجودة في المجموعات الموجودة
+
+850
+01:40:47,070 --> 01:40:48,210
+المجموعات الموجودة في المجموعاتأبصري عشان اطلع
+
+851
+01:40:48,210 --> 01:40:55,350
+عندنا هنا يالا يا عزيزي نمشي ارمى على زيرو ارمى
+
+852
+01:40:55,350 --> 01:41:01,070
+على زيرو وجهة نظر وليست وجاها في النظر يالا غيرها
+
+853
+01:41:01,070 --> 01:41:06,310
+همشي قول يا بنت هو لو غلط تعود احكي انت تقولي غلط
+
+854
+01:41:06,310 --> 01:41:10,510
+كل مرة تقولي غلط و بعدها تقولي صح فسيدي فكري مخي
+
+855
+01:41:10,510 --> 01:41:13,830
+يالا
+
+856
+01:41:13,830 --> 01:41:14,250
+غيرها
+
+857
+01:41:17,020 --> 01:41:21,560
+أرمى عدسة يعني نفس الكلام اللي جالس في زميلتي ها
+
+858
+01:41:21,560 --> 01:41:31,740
+غيره طب هل النقطة 2 تقع على ال Ray؟
+
+859
+01:41:31,740 --> 01:41:38,540
+القيمة 2 هي من ضمن قيمة ال Ray؟ واحد منافق طب
+
+860
+01:41:38,540 --> 01:41:44,600
+اتنين ألف طب
+
+861
+01:41:44,600 --> 01:41:49,740
+شو قال؟هل هناك قيم بياخدها الرئيس غير الواحد
+
+862
+01:41:49,740 --> 01:41:55,540
+والسالي بواحد؟ بس القيمتين هدول، في غيرهم؟ هو
+
+863
+01:41:55,540 --> 01:41:57,020
+تعريف ال absolute value
+
+864
+01:41:59,390 --> 01:42:03,410
+وحد و سالب واحد هذا نفس الفيديو صحيح و لا لأ تختصر
+
+865
+01:42:03,410 --> 01:42:06,550
+ال bus و لا تقفش و تبقى الهندين بس واحد و سالب
+
+866
+01:42:06,550 --> 01:42:11,290
+واحد في الشميرو يبقى ال range تبع هذه الدنيا بس
+
+867
+01:42:11,290 --> 01:42:15,670
+نقطتين مش internal من سالب واحد إلى واحد بس سالب
+
+868
+01:42:15,670 --> 01:42:19,310
+واحد واحد يبقى ال range لل F
+
+869
+01:42:27,630 --> 01:42:33,130
+من قيمتين لواحد وسالم واحد تقدروا تجيبولي قيمة
+
+870
+01:42:33,130 --> 01:42:36,750
+غيرهم يللا اللي جيب قيمة غيرهم برضه تاخد ال full
+
+871
+01:42:36,750 --> 01:42:44,990
+mark يللا و ترتاحأه خلاص يبقى لا حد هنا انت هنا
+
+872
+01:42:44,990 --> 01:42:49,010
+لكن لسه ال section احنا في بدايته يعني في المحاضرة
+
+873
+01:42:49,010 --> 01:42:53,530
+القادمة يدوب نخلص هذا ال section يعني كلام كتير
+
+874
+01:42:53,530 --> 01:42:59,470
+لسه بدنا نتكلم عن ال functions اللي عندنا هذه
+
+875
+01:42:59,470 --> 01:43:05,370
+المختلفةو ال function بنا نعرف حاجة اسمها ال
+
+876
+01:43:05,370 --> 01:43:12,290
+bounded و ال unbounded و ما إلى ذلك كل الشغلات و
+
+877
+01:43:12,290 --> 01:43:15,330
+ناخد اللي في الحالة الأولى في ال plane و بعدين
+
+878
+01:43:15,330 --> 01:43:19,130
+نروح في الفراد و في level curve و في level
+
+879
+01:43:19,130 --> 01:43:23,950
+surfaces و ما إلى ذلك كله الموضوع المحاضرة القادمة
+
+880
+01:43:23,950 --> 01:43:26,450
+ان شاء الله تعالى يعطيكوا العافية
+
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/r80EmZhKdwI_raw.json b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/r80EmZhKdwI_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..7d1f964295da96b874df6213ed9276b4eef1cffd
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/r80EmZhKdwI_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 1498, "start": 12.92, "end": 14.98, "text": "السلام عليكم ورحمة الله وبركاته", "tokens": [6027, 3794, 37440, 25894, 24793, 4032, 2288, 35571, 3660, 21984, 46599, 31747, 9307, 3224], "avg_logprob": -0.5145833174387614, "compression_ratio": 0.9666666666666667, "no_speech_prob": 4.291534423828125e-06, "words": [{"start": 12.92, "end": 13.82, "word": "السلام", "probability": 0.50885009765625}, {"start": 13.82, "end": 13.82, "word": " عليكم", "probability": 0.92578125}, {"start": 13.82, "end": 14.36, "word": " ورحمة", "probability": 0.8553466796875}, {"start": 14.36, "end": 14.62, "word": " الله", "probability": 0.9609375}, {"start": 14.62, "end": 14.98, "word": " وبركاته", "probability": 0.6006927490234375}], "temperature": 1.0}, {"id": 2, "seek": 4527, "start": 17.03, "end": 45.27, "text": "بسم الله الرحمن الرحيم اليوم ان شاء الله هنبدأ في section 13-5 اللى بتحدث عن tangential and component of acceleration المركبة الممسية والمركبة العمودية لمهن للعجلة يبقى tangential ممسي و norm عمودي و component مركبات العجلة يبقى مركبات العجلة المركبة الممسية والمركبة العمودية عليها", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 45595, 20498, 16472, 13412, 16606, 21984, 8032, 1863, 44510, 10721, 8978, 3541, 3705, 12, 20, 13672, 7578, 39894, 24401, 12984, 18871, 10266, 2549, 293, 6542, 295, 17162, 9673, 31747, 49401, 9673, 2304, 3794, 10632, 16070, 29973, 4117, 49401, 18863, 2304, 2407, 16254, 3660, 32767, 3224, 1863, 24976, 3615, 7435, 37977, 7251, 3555, 4587, 7578, 10266, 2549, 3714, 2304, 3794, 1829, 4032, 2026, 6225, 2304, 2407, 16254, 4032, 6542, 3714, 31747, 3555, 9307, 18863, 7435, 37977, 7251, 3555, 4587, 7578, 3714, 31747, 3555, 9307, 18863, 7435, 37977, 9673, 31747, 49401, 9673, 2304, 3794, 10632, 16070, 29973, 4117, 49401, 18863, 2304, 2407, 16254, 3660, 25894, 11296], "avg_logprob": -0.18928180059842897, "compression_ratio": 2.1578947368421053, "no_speech_prob": 4.291534423828125e-06, "words": [{"start": 17.03, 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"word": " T", "probability": 0.97216796875}, {"start": 280.41, "end": 281.85, "word": " زائد", "probability": 0.8798828125}, {"start": 281.85, "end": 283.19, "word": " اتطلعي", "probability": 0.7440999348958334}, {"start": 283.19, "end": 283.41, "word": " ليه", "probability": 0.73779296875}, {"start": 283.41, "end": 283.63, "word": " هذه", "probability": 0.55419921875}, {"start": 283.63, "end": 284.11, "word": " الكلمة", "probability": 0.9464518229166666}], "temperature": 1.0}, {"id": 12, "seek": 29208, "start": 286.72, "end": 292.08, "text": "و ال DS على DT و ال DS على DT يبقى DS", "tokens": [2407, 2423, 15816, 15844, 413, 51, 4032, 2423, 15816, 15844, 413, 51, 7251, 3555, 4587, 7578, 15816], "avg_logprob": -0.284505201710595, "compression_ratio": 1.2926829268292683, "no_speech_prob": 0.0, "words": [{"start": 286.72, "end": 287.54, "word": "و", "probability": 0.6767578125}, {"start": 287.54, "end": 287.72, "word": " ال", "probability": 0.5400390625}, {"start": 287.72, "end": 288.0, 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unit vector N ال principle unit normal vector اللي هو N تمام تمام", "tokens": [3555, 6027, 11242, 3555, 9566, 9122, 33456, 8315, 11331, 1211, 1211, 8315, 2423, 39184, 17162, 257, 30731, 3714, 31747, 3555, 2655, 9957, 8978, 1975, 2655, 7435, 40294, 9957, 44650, 25957, 3215, 9957, 9673, 31747, 49401, 16247, 12610, 7578, 8978, 1975, 2655, 7435, 40294, 2423, 39184, 314, 16070, 29973, 4117, 49401, 16712, 7649, 10632, 8978, 2423, 9307, 7435, 40294, 18863, 2304, 2407, 16254, 47356, 13672, 1829, 31439, 2423, 8665, 4985, 8062, 426, 2423, 8665, 4985, 2710, 8062, 13672, 1829, 31439, 426, 46811, 10943, 46811, 10943], "avg_logprob": -0.18952205742106717, "compression_ratio": 1.8578947368421053, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 300.27, "end": 301.19, "word": "بالضبط", "probability": 0.91728515625}, {"start": 301.19, "end": 301.95, "word": " كأننا", "probability": 0.9542643229166666}, {"start": 301.95, "end": 302.65, "word": " حللنا", "probability": 0.906494140625}, 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{"start": 1496.96, "end": 1497.24, "word": " cross", "probability": 0.51318359375}, {"start": 1497.24, "end": 1497.76, "word": " product", "probability": 0.96142578125}, {"start": 1497.76, "end": 1498.1, "word": " which", "probability": 0.759765625}, {"start": 1498.1, "end": 1498.52, "word": " is", "probability": 0.96728515625}, {"start": 1498.52, "end": 1498.86, "word": " a", "probability": 0.92919921875}, {"start": 1498.86, "end": 1499.3, "word": " vector", "probability": 0.958984375}, {"start": 1499.3, "end": 1500.52, "word": " سؤالنا", "probability": 0.8294677734375}, {"start": 1500.52, "end": 1500.9, "word": " هو", "probability": 0.951171875}, {"start": 1500.9, "end": 1501.56, "word": " هل", "probability": 0.924072265625}, {"start": 1501.56, "end": 1501.86, "word": " هذا", "probability": 0.9072265625}, {"start": 1501.86, "end": 1502.16, "word": " unit", "probability": 0.95556640625}, {"start": 1502.16, "end": 1502.96, "word": " vector؟", "probability": 0.834228515625}], "temperature": 1.0}, {"id": 59, "seek": 153086, "start": 1509.72, "end": 1530.86, "text": "لو عملت cross product بين two vectors أن يكون الناتج هو unit vector قد يكون و قد لا يكون لكن في موضوع هنا ال by normal vector ال by normal vector is a unit vector تمام بس in general الكلام هذا معروف ليس صحيحا", "tokens": [1211, 2407, 6225, 42213, 2655, 3278, 1674, 49374, 732, 18875, 14739, 7251, 30544, 28239, 9307, 7435, 31439, 4985, 8062, 12174, 3215, 7251, 30544, 4032, 12174, 3215, 20193, 7251, 30544, 44381, 8978, 3714, 2407, 11242, 45367, 34105, 2423, 538, 2710, 8062, 2423, 538, 2710, 8062, 307, 257, 4985, 8062, 46811, 10943, 4724, 3794, 294, 2674, 2423, 28820, 10943, 23758, 20449, 32887, 5172, 32239, 3794, 20328, 5016, 1829, 5016, 995], "avg_logprob": -0.3245018236878989, "compression_ratio": 1.564516129032258, "no_speech_prob": 0.0, "words": [{"start": 1509.7199999999998, "end": 1510.6, "word": "لو", "probability": 0.17822265625}, {"start": 1510.6, "end": 1511.04, "word": " عملت", 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1527.08, "end": 1527.74, "word": " general", "probability": 0.92822265625}, {"start": 1527.74, "end": 1528.42, "word": " الكلام", "probability": 0.8186848958333334}, {"start": 1528.42, "end": 1528.62, "word": " هذا", "probability": 0.92041015625}, {"start": 1528.62, "end": 1529.16, "word": " معروف", "probability": 0.7469075520833334}, {"start": 1529.16, "end": 1529.88, "word": " ليس", "probability": 0.96533203125}, {"start": 1529.88, "end": 1530.86, "word": " صحيحا", "probability": 0.96279296875}], "temperature": 1.0}, {"id": 60, "seek": 155096, "start": 1545.2, "end": 1550.96, "text": "هذه المثال عامل يظهر أن هذا المعنى ليس صحيح", "tokens": [3224, 24192, 9673, 12984, 6027, 6225, 10943, 1211, 7251, 19913, 3224, 2288, 14739, 23758, 9673, 3615, 1863, 7578, 32239, 3794, 20328, 5016, 1829, 5016], "avg_logprob": -0.60375, "compression_ratio": 1.1142857142857143, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 1545.2000000000003, "end": 1546.3200000000002, "word": "هذه", "probability": 0.471435546875}, {"start": 1546.3200000000002, "end": 1547.44, "word": " المثال", "probability": 0.7148844401041666}, {"start": 1547.44, "end": 1547.98, "word": " عامل", "probability": 0.4754231770833333}, {"start": 1547.98, "end": 1548.6, "word": " يظهر", "probability": 0.65765380859375}, {"start": 1548.6, "end": 1548.84, "word": " أن", "probability": 0.25146484375}, {"start": 1548.84, "end": 1549.42, "word": " هذا", "probability": 0.468017578125}, {"start": 1549.42, "end": 1549.86, "word": " المعنى", "probability": 0.6435546875}, {"start": 1549.86, "end": 1550.4, "word": " ليس", "probability": 0.7880859375}, {"start": 1550.4, "end": 1550.96, "word": " صحيح", "probability": 0.9298095703125}], "temperature": 1.0}, {"id": 61, "seek": 158209, "start": 1556.31, "end": 1582.09, "text": "هه كلفت نظر لكم الان بدنا نرجع لموضوعنا الموضوع الـ BINORMAL VECTORAL شو رايحة يا بنات؟ لو روحنا اشتقناها، شوفوا لو اين بدنا نوصل فيها الدنيا، كويس؟ يبقى بدنا ناخد مثلا الـ derivative of the bi", "tokens": [3224, 3224, 9122, 46538, 2655, 8717, 19913, 2288, 5296, 24793, 2423, 7649, 47525, 8315, 8717, 47341, 3615, 32767, 2407, 11242, 45367, 8315, 9673, 2407, 11242, 45367, 2423, 39184, 363, 1464, 2483, 44, 3427, 691, 8140, 36400, 3427, 13412, 2407, 12602, 47302, 5016, 3660, 35186, 4724, 8315, 2655, 22807, 45164, 12602, 2407, 5016, 8315, 1975, 8592, 2655, 4587, 8315, 11296, 12399, 13412, 38688, 14407, 45164, 1975, 9957, 47525, 8315, 8717, 2407, 36520, 8978, 11296, 32748, 22653, 995, 12399, 9122, 45865, 3794, 22807, 7251, 3555, 4587, 7578, 47525, 8315, 8717, 47283, 3215, 50113, 15040, 2423, 39184, 13760, 295, 264, 3228], "avg_logprob": -0.3693181679706381, "compression_ratio": 1.5, "no_speech_prob": 0.0, "words": [{"start": 1556.31, "end": 1556.77, "word": "هه", "probability": 0.234466552734375}, {"start": 1556.77, "end": 1557.43, "word": " كلفت", "probability": 0.7506510416666666}, {"start": 1557.43, "end": 1557.81, "word": " نظر", "probability": 0.966796875}, {"start": 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"word": " length", "probability": 0.84130859375}, {"start": 1829.18, "end": 1829.9, "word": " صحيح", "probability": 0.97314453125}, {"start": 1829.9, "end": 1830.06, "word": " ولا", "probability": 0.7412109375}, {"start": 1830.06, "end": 1830.46, "word": " لأ؟", "probability": 0.830078125}], "temperature": 1.0}, {"id": 72, "seek": 185711, "start": 1830.73, "end": 1857.11, "text": "لو أعمل dot product ما بين ال B ومشتقته، كده؟ Zero كذلك، خاصية أخدناها قبل ذلك يبقى باجي بقوله since بما أن ال B is a constant vector, we have", "tokens": [1211, 2407, 5551, 25957, 1211, 5893, 1674, 19446, 49374, 2423, 363, 4032, 2304, 8592, 2655, 38149, 3224, 12399, 9122, 3215, 3224, 22807, 17182, 9122, 8848, 23275, 12399, 16490, 33546, 10632, 5551, 9778, 3215, 8315, 11296, 12174, 36150, 29910, 23275, 7251, 3555, 4587, 7578, 4724, 26108, 1829, 4724, 39648, 3224, 1670, 4724, 15042, 14739, 2423, 363, 307, 257, 5754, 8062, 11, 321, 362], "avg_logprob": -0.3834325406286452, "compression_ratio": 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{"start": 1837.67, "end": 1838.57, "word": " كذلك،", "probability": 0.70819091796875}, {"start": 1838.57, "end": 1839.05, "word": " خاصية", "probability": 0.6985677083333334}, {"start": 1839.05, "end": 1839.65, "word": " أخدناها", "probability": 0.812841796875}, {"start": 1839.65, "end": 1840.27, "word": " قبل", "probability": 0.98974609375}, {"start": 1840.27, "end": 1840.73, "word": " ذلك", "probability": 0.96240234375}, {"start": 1840.73, "end": 1841.37, "word": " يبقى", "probability": 0.8231201171875}, {"start": 1841.37, "end": 1841.73, "word": " باجي", "probability": 0.7010091145833334}, {"start": 1841.73, "end": 1842.91, "word": " بقوله", "probability": 0.6193033854166666}, {"start": 1842.91, "end": 1846.07, "word": " since", "probability": 0.243896484375}, {"start": 1846.07, "end": 1846.75, "word": " بما", "probability": 0.942138671875}, {"start": 1846.75, "end": 1847.21, "word": " أن", "probability": 0.90087890625}, {"start": 1847.21, "end": 1848.19, "word": " ال", "probability": 0.91943359375}, {"start": 1848.19, "end": 1848.55, "word": " B", "probability": 0.86474609375}, {"start": 1848.55, "end": 1849.59, "word": " is", "probability": 0.8193359375}, {"start": 1849.59, "end": 1851.25, "word": " a", "probability": 0.95947265625}, {"start": 1851.25, "end": 1852.49, "word": " constant", "probability": 0.9072265625}, {"start": 1852.49, "end": 1855.05, "word": " vector,", "probability": 0.9443359375}, {"start": 1856.51, "end": 1856.63, "word": " we", "probability": 0.9111328125}, {"start": 1856.63, "end": 1857.11, "word": " have", "probability": 0.96484375}], "temperature": 1.0}, {"id": 73, "seek": 188731, "start": 1859.89, "end": 1887.31, "text": "إن ال B بط DB على DS بده يساوي Z هذا إيش بيعطينا؟ هذا بيعطينا إن DB على DS is orthogonal لمن؟ is orthogonal to B", "tokens": [28814, 1863, 2423, 363, 4724, 9566, 26754, 15844, 15816, 47525, 3224, 7251, 3794, 995, 45865, 1176, 23758, 11933, 1829, 8592, 4724, 40228, 9566, 1829, 8315, 22807, 23758, 4724, 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" Z", "probability": 0.5546875}, {"start": 1867.27, "end": 1869.07, "word": " هذا", "probability": 0.8232421875}, {"start": 1869.07, "end": 1869.39, "word": " إيش", "probability": 0.7967122395833334}, {"start": 1869.39, "end": 1871.59, "word": " بيعطينا؟", "probability": 0.8604736328125}, {"start": 1871.59, "end": 1872.01, "word": " هذا", "probability": 0.876953125}, {"start": 1872.01, "end": 1873.13, "word": " بيعطينا", "probability": 0.98525390625}, {"start": 1873.13, "end": 1873.89, "word": " إن", "probability": 0.552734375}, {"start": 1873.89, "end": 1874.85, "word": " DB", "probability": 0.6435546875}, {"start": 1874.85, "end": 1876.37, "word": " على", "probability": 0.8583984375}, {"start": 1876.37, "end": 1877.25, "word": " DS", "probability": 0.986328125}, {"start": 1877.25, "end": 1878.27, "word": " is", "probability": 0.66552734375}, {"start": 1878.27, "end": 1880.11, "word": " orthogonal", "probability": 0.8115234375}, {"start": 1880.11, "end": 1883.13, "word": " لمن؟", 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1895.11, "word": " في", "probability": 0.6806640625}, {"start": 1895.11, "end": 1895.53, "word": " واحد", "probability": 0.90087890625}, {"start": 1895.53, "end": 1896.19, "word": " واتنين", "probability": 0.8385009765625}, {"start": 1896.19, "end": 1897.73, "word": " بيقول", "probability": 0.7959798177083334}, {"start": 1897.73, "end": 1898.09, "word": " هنا", "probability": 0.8994140625}, {"start": 1898.09, "end": 1898.79, "word": " DBA", "probability": 0.4862060546875}, {"start": 1898.79, "end": 1899.41, "word": " على", "probability": 0.63037109375}, {"start": 1899.41, "end": 1899.99, "word": " DS", "probability": 0.92529296875}, {"start": 1899.99, "end": 1901.01, "word": " عمودي", "probability": 0.9844970703125}, {"start": 1901.01, "end": 1901.39, "word": " على", "probability": 0.90966796875}, {"start": 1901.39, "end": 1901.97, "word": " T", "probability": 0.9345703125}, {"start": 1901.97, "end": 1902.43, "word": " و", "probability": 0.955078125}, {"start": 1902.43, "end": 1902.67, "word": " على", "probability": 0.361572265625}, {"start": 1902.67, "end": 1903.07, "word": " DN", "probability": 0.87939453125}, {"start": 1903.07, "end": 1903.35, "word": " على", "probability": 0.8388671875}, {"start": 1903.35, "end": 1903.89, "word": " DS", "probability": 0.97900390625}, {"start": 1903.89, "end": 1904.87, "word": " وهنا", "probability": 0.79638671875}, {"start": 1904.87, "end": 1905.35, "word": " بيقول", "probability": 0.9471028645833334}, {"start": 1905.35, "end": 1905.61, "word": " ان", "probability": 0.4775390625}, {"start": 1905.61, "end": 1905.81, "word": " ال", "probability": 0.483642578125}, {"start": 1905.81, "end": 1906.23, "word": " DBA", "probability": 0.44757080078125}, {"start": 1906.23, "end": 1906.47, "word": " على", "probability": 0.83740234375}, {"start": 1906.47, "end": 1906.87, "word": " DS", "probability": 0.96044921875}, {"start": 1906.87, "end": 1907.99, "word": " نفسها", "probability": 0.9576822916666666}, {"start": 1907.99, "end": 1908.69, 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"probability": 0.88623046875}, {"start": 1913.35, "end": 1913.69, "word": " DS", "probability": 0.939453125}, {"start": 1913.69, "end": 1914.21, "word": " عمودي", "probability": 0.98486328125}, {"start": 1914.21, "end": 1914.47, "word": " على", "probability": 0.92626953125}, {"start": 1914.47, "end": 1915.01, "word": " كل", "probability": 0.962890625}, {"start": 1915.01, "end": 1915.59, "word": " من", "probability": 0.9326171875}, {"start": 1915.59, "end": 1916.85, "word": " T", "probability": 0.82080078125}, {"start": 1916.85, "end": 1917.63, "word": " وB", "probability": 0.778564453125}, {"start": 1917.63, "end": 1918.39, "word": " صحيح", "probability": 0.984130859375}, {"start": 1918.39, "end": 1918.57, "word": " ولا", "probability": 0.94970703125}, {"start": 1918.57, "end": 1918.91, "word": " لأ", "probability": 0.77734375}], "temperature": 1.0}, {"id": 75, "seek": 194222, "start": 1919.24, "end": 1942.22, "text": "يبقى هنا بقول له so والله from واحد and اثنين ال D بي على دي اس is orthogonal to اللي هو الأولاني T and ال B", "tokens": [1829, 3555, 4587, 7578, 34105, 4724, 39648, 46740, 370, 16070, 43761, 490, 36764, 24401, 293, 1975, 12984, 1863, 9957, 2423, 413, 4724, 1829, 15844, 11778, 1829, 24525, 307, 41488, 281, 13672, 1829, 31439, 16247, 12610, 7649, 1829, 314, 293, 2423, 363], "avg_logprob": -0.34728423683416276, "compression_ratio": 1.2755905511811023, "no_speech_prob": 0.0, "words": [{"start": 1919.24, "end": 1919.78, "word": "يبقى", "probability": 0.9132080078125}, {"start": 1919.78, "end": 1920.04, "word": " هنا", "probability": 0.96728515625}, {"start": 1920.04, "end": 1920.62, "word": " بقول", "probability": 0.914306640625}, {"start": 1920.62, "end": 1920.96, "word": " له", "probability": 0.341064453125}, {"start": 1920.96, "end": 1921.42, "word": " so", "probability": 0.10394287109375}, {"start": 1921.42, "end": 1922.0, "word": " والله", "probability": 0.6201171875}, {"start": 1922.0, "end": 1922.58, "word": " from", "probability": 0.94287109375}, {"start": 1922.58, "end": 1925.3, "word": " واحد", "probability": 0.7978515625}, {"start": 1925.3, "end": 1925.94, "word": " and", "probability": 0.8466796875}, {"start": 1925.94, "end": 1927.68, "word": " اثنين", "probability": 0.841796875}, {"start": 1927.68, "end": 1928.42, "word": " ال", "probability": 0.92333984375}, {"start": 1928.42, "end": 1928.9, "word": " D", "probability": 0.673828125}, {"start": 1928.9, "end": 1930.06, "word": " بي", "probability": 0.6768798828125}, {"start": 1930.06, "end": 1930.66, "word": " على", "probability": 0.66455078125}, {"start": 1930.66, "end": 1931.18, "word": " دي", "probability": 0.748291015625}, {"start": 1931.18, "end": 1931.58, "word": " اس", "probability": 0.54736328125}, {"start": 1931.58, "end": 1932.64, "word": " is", "probability": 0.73486328125}, {"start": 1932.64, "end": 1934.52, "word": " orthogonal", "probability": 0.8447265625}, {"start": 1934.52, "end": 1938.02, "word": " to", "probability": 0.86181640625}, {"start": 1938.02, "end": 1939.22, "word": " اللي", "probability": 0.5911865234375}, {"start": 1939.22, "end": 1939.4, "word": " هو", "probability": 0.92919921875}, {"start": 1939.4, "end": 1940.08, "word": " الأولاني", "probability": 0.73065185546875}, {"start": 1940.08, "end": 1940.58, "word": " T", "probability": 0.67041015625}, {"start": 1940.58, "end": 1941.58, "word": " and", "probability": 0.92822265625}, {"start": 1941.58, "end": 1941.9, "word": " ال", "probability": 0.904296875}, {"start": 1941.9, "end": 1942.22, "word": " B", "probability": 0.55126953125}], "temperature": 1.0}, {"id": 76, "seek": 197453, "start": 1946.19, "end": 1974.53, "text": "طيب، هذا سيولّد لنا السؤال التالي التعريف اللي كتبناه الـ BINORMAL يقول إن B عمودي على كل من T و N", "tokens": [9566, 1829, 3555, 12399, 23758, 8608, 1829, 12610, 11703, 3215, 5296, 8315, 21136, 33604, 6027, 16712, 6027, 1829, 16712, 3615, 16572, 5172, 13672, 1829, 9122, 2655, 3555, 8315, 3224, 2423, 39184, 363, 1464, 2483, 44, 3427, 7251, 39648, 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"word": " مايمكن", "probability": 0.8040364583333334}, {"start": 5434.86, "end": 5435.5, "word": " اذا", "probability": 0.695556640625}, {"start": 5435.5, "end": 5435.78, "word": " لو", "probability": 0.98388671875}, {"start": 5435.78, "end": 5436.18, "word": " روحت", "probability": 0.8870442708333334}, {"start": 5436.18, "end": 5436.84, "word": " اخدت", "probability": 0.6650390625}, {"start": 5436.84, "end": 5437.8, "word": " محاولة", "probability": 0.8970703125}, {"start": 5437.8, "end": 5438.58, "word": " بالشكل", "probability": 0.91357421875}, {"start": 5438.58, "end": 5438.78, "word": " اللي", "probability": 0.975341796875}, {"start": 5438.78, "end": 5439.24, "word": " عندها", "probability": 0.863525390625}, {"start": 5439.24, "end": 5439.82, "word": " ذلك", "probability": 0.342529296875}, {"start": 5439.82, "end": 5441.28, "word": " وقلت", "probability": 0.796875}], "temperature": 1.0}, {"id": 203, "seek": 546812, "start": 5441.36, "end": 5468.12, "text": "هذا محور X هذا Y وهذا Z ومديت هذا على سيقانته وروحت رسم ال ellipsoid فكان ال ellipsoid الشكل اللي عندنا وهنا شكل هذا هذا مش هيضغرني وهذا نقطة أصلي وزيرة يبقى هذا ال ellipsoid اللي عندنا يبقى هذا مين؟", "tokens": [3224, 15730, 3714, 5016, 13063, 1783, 23758, 398, 37037, 15730, 1176, 4032, 2304, 3215, 36081, 23758, 15844, 8608, 1829, 4587, 7649, 47395, 4032, 32887, 33753, 12602, 38251, 2423, 8284, 647, 539, 327, 6156, 41361, 2423, 8284, 647, 539, 327, 25124, 28820, 13672, 1829, 43242, 8315, 4032, 3224, 8315, 13412, 28820, 23758, 23758, 37893, 39896, 11242, 17082, 2288, 22653, 37037, 15730, 8717, 47432, 3660, 5551, 9381, 20292, 4032, 11622, 1829, 25720, 7251, 3555, 4587, 7578, 23758, 2423, 8284, 647, 539, 327, 13672, 1829, 43242, 8315, 7251, 3555, 4587, 7578, 23758, 3714, 9957, 22807], "avg_logprob": -0.2693212506591633, "compression_ratio": 1.8379888268156424, "no_speech_prob": 0.0, "words": [{"start": 5441.36, "end": 5441.84, "word": "هذا", "probability": 0.838134765625}, {"start": 5441.84, "end": 5442.32, 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ال", "probability": 0.92333984375}, {"start": 5449.98, "end": 5451.2, "word": " ellipsoid", "probability": 0.78668212890625}, {"start": 5451.2, "end": 5452.14, "word": " فكان", "probability": 0.924560546875}, {"start": 5452.14, "end": 5452.38, "word": " ال", "probability": 0.81884765625}, {"start": 5452.38, "end": 5453.5, "word": " ellipsoid", "probability": 0.9755859375}, {"start": 5453.5, "end": 5454.48, "word": " الشكل", "probability": 0.825439453125}, {"start": 5454.48, "end": 5454.7, "word": " اللي", "probability": 0.923828125}, {"start": 5454.7, "end": 5455.1, "word": " عندنا", "probability": 0.81298828125}, {"start": 5455.1, "end": 5456.3, "word": " وهنا", "probability": 0.5690511067708334}, {"start": 5456.3, "end": 5458.2, "word": " شكل", "probability": 0.6258544921875}, {"start": 5458.2, "end": 5458.54, "word": " هذا", "probability": 0.8623046875}, {"start": 5458.54, "end": 5459.66, "word": " هذا", "probability": 0.256103515625}, {"start": 5459.66, "end": 5460.3, "word": " مش", "probability": 0.9189453125}, {"start": 5460.3, "end": 5461.2, "word": " هيضغرني", "probability": 0.4056640625}, {"start": 5461.2, "end": 5461.96, "word": " وهذا", "probability": 0.70361328125}, {"start": 5461.96, "end": 5462.34, "word": " نقطة", "probability": 0.9514973958333334}, {"start": 5462.34, "end": 5462.78, "word": " أصلي", "probability": 0.7998046875}, {"start": 5462.78, "end": 5463.36, "word": " وزيرة", "probability": 0.68212890625}, {"start": 5463.36, "end": 5464.22, "word": " يبقى", "probability": 0.9368896484375}, {"start": 5464.22, "end": 5464.54, "word": " هذا", "probability": 0.9189453125}, {"start": 5464.54, "end": 5464.7, "word": " ال", "probability": 0.89794921875}, {"start": 5464.7, "end": 5465.66, "word": " ellipsoid", "probability": 0.973876953125}, {"start": 5465.66, "end": 5465.88, "word": " اللي", "probability": 0.982177734375}, {"start": 5465.88, "end": 5466.56, "word": " عندنا", "probability": 0.970947265625}, {"start": 5466.56, "end": 5467.26, "word": " يبقى", "probability": 0.9686279296875}, {"start": 5467.26, "end": 5467.5, "word": " هذا", "probability": 0.96435546875}, {"start": 5467.5, "end": 5468.12, "word": " مين؟", "probability": 0.8243815104166666}], "temperature": 1.0}, {"id": 204, "seek": 549728, "start": 5468.38, "end": 5497.28, "text": "الـ interior تبع الـ ellipsoid زي الـ boundary كل الشكل الخارجي يبقى هنا بسميه الـ interior and ال boundary of the ellipsoid طيب", "tokens": [6027, 39184, 10636, 6055, 3555, 3615, 2423, 39184, 8284, 647, 539, 327, 30767, 1829, 2423, 39184, 12866, 28242, 25124, 28820, 33962, 9640, 7435, 1829, 7251, 3555, 4587, 7578, 34105, 4724, 38251, 1829, 3224, 2423, 39184, 10636, 293, 2423, 12866, 295, 264, 8284, 647, 539, 327, 23032, 1829, 3555], "avg_logprob": -0.287149224962507, "compression_ratio": 1.408, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 5468.38, "end": 5468.98, "word": "الـ", "probability": 0.4605712890625}, {"start": 5468.98, "end": 5469.64, "word": " interior", "probability": 0.1292724609375}, {"start": 5469.64, "end": 5470.78, "word": " تبع", "probability": 0.8250325520833334}, {"start": 5470.78, "end": 5471.08, "word": " الـ", "probability": 0.74951171875}, {"start": 5471.08, "end": 5472.16, "word": " ellipsoid", "probability": 0.822998046875}, {"start": 5472.16, "end": 5472.78, "word": " زي", "probability": 0.582763671875}, {"start": 5472.78, "end": 5473.14, "word": " الـ", "probability": 0.58935546875}, {"start": 5473.14, "end": 5473.82, "word": " boundary", "probability": 0.9462890625}, {"start": 5473.82, "end": 5474.66, "word": " كل", "probability": 0.74755859375}, {"start": 5474.66, "end": 5475.26, "word": " الشكل", "probability": 0.97216796875}, {"start": 5475.26, "end": 5476.02, "word": " الخارجي", "probability": 0.9923095703125}, {"start": 5476.02, "end": 5476.96, "word": " يبقى", "probability": 0.6566162109375}, {"start": 5476.96, "end": 5477.34, "word": " هنا", "probability": 0.923828125}, {"start": 5477.34, "end": 5478.58, "word": " بسميه", "probability": 0.72637939453125}, {"start": 5478.58, "end": 5478.86, "word": " الـ", "probability": 0.82421875}, {"start": 5478.86, "end": 5479.74, "word": " interior", "probability": 0.5712890625}, {"start": 5479.74, "end": 5482.44, "word": " and", "probability": 0.89599609375}, {"start": 5482.44, "end": 5484.36, "word": " ال", "probability": 0.61669921875}, {"start": 5484.36, "end": 5485.34, "word": " boundary", "probability": 0.74267578125}, {"start": 5485.34, "end": 5488.68, "word": " of", "probability": 0.96484375}, {"start": 5488.68, "end": 5490.26, "word": " the", "probability": 0.826171875}, {"start": 5490.26, "end": 5491.9, "word": " ellipsoid", "probability": 0.953369140625}, {"start": 5491.9, "end": 5497.28, "word": " طيب", "probability": 0.955078125}], "temperature": 1.0}, {"id": 205, "seek": 552805, "start": 5499.17, "end": 5528.05, "text": "الـ Range يلّا نشوف الـ Range أيوة يلّا أولى شوفي السفر كم يطلع موافق يلّا بدي كمان يبقى عند 0000 تطلع القيمة ال function هي واحدة غيره", "tokens": [6027, 39184, 33778, 7251, 1211, 11703, 995, 8717, 8592, 38688, 2423, 39184, 33778, 36632, 2407, 3660, 7251, 1211, 11703, 995, 5551, 12610, 7578, 13412, 38688, 1829, 21136, 5172, 2288, 9122, 2304, 7251, 9566, 1211, 3615, 3714, 14407, 5172, 4587, 7251, 1211, 11703, 995, 4724, 16254, 9122, 2304, 7649, 7251, 3555, 4587, 7578, 43242, 1958, 1360, 6055, 9566, 1211, 3615, 25062, 32640, 3660, 2423, 2445, 39896, 36764, 24401, 3660, 32771, 13546, 3224], "avg_logprob": -0.4079860966238711, "compression_ratio": 1.4509803921568627, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 5499.17, "end": 5499.55, "word": "الـ", "probability": 0.445068359375}, {"start": 5499.55, "end": 5500.25, "word": " Range", "probability": 0.86376953125}, {"start": 5500.25, "end": 5503.35, "word": " يلّا", "probability": 0.4958648681640625}, {"start": 5503.35, "end": 5503.89, "word": " نشوف", "probability": 0.5906575520833334}, {"start": 5503.89, "end": 5506.15, "word": " 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قيمة ولا أقل قيمة؟ أقل قيمة. أقل قيمة اللي هي الواحد، يعني بدرجة أكبر منها. تقدر تجيبولي و لو قيمة واحدة تكون أكبر منها؟ إذا بتجيبولي كمان قيمة بتكون و أنتوا .. جيبولي قيمة واحدة بس تكون أكبر من الواحدة؟", "tokens": [3224, 24192, 5551, 4117, 26890, 12174, 32640, 3660, 49429, 5551, 4587, 1211, 12174, 32640, 3660, 22807, 5551, 4587, 1211, 12174, 32640, 3660, 13, 5551, 4587, 1211, 12174, 32640, 3660, 13672, 1829, 39896, 2423, 14407, 24401, 12399, 37495, 22653, 47525, 47341, 3660, 5551, 4117, 26890, 9154, 11296, 13, 6055, 28543, 2288, 6055, 7435, 1829, 3555, 12610, 1829, 4032, 45164, 12174, 32640, 3660, 36764, 24401, 3660, 6055, 30544, 5551, 4117, 26890, 9154, 11296, 22807, 11933, 15730, 39894, 7435, 1829, 3555, 12610, 1829, 9122, 2304, 7649, 12174, 32640, 3660, 39894, 30544, 4032, 14739, 2655, 14407, 4386, 10874, 1829, 3555, 12610, 1829, 12174, 32640, 3660, 36764, 24401, 3660, 4724, 3794, 6055, 30544, 5551, 4117, 26890, 9154, 2423, 14407, 24401, 3660, 22807], "avg_logprob": 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0.83349609375}, {"start": 6165.83, "end": 6166.01, "word": " section", "probability": 0.5966796875}, {"start": 6166.01, "end": 6166.31, "word": " احنا", "probability": 0.9202473958333334}, {"start": 6166.31, "end": 6166.45, "word": " في", "probability": 0.70458984375}, {"start": 6166.45, "end": 6167.19, "word": " بدايته", "probability": 0.919921875}, {"start": 6167.19, "end": 6168.11, "word": " يعني", "probability": 0.776123046875}, {"start": 6168.11, "end": 6168.31, "word": " في", "probability": 0.361083984375}, {"start": 6168.31, "end": 6169.01, "word": " المحاضرة", "probability": 0.9844970703125}, {"start": 6169.01, "end": 6169.83, "word": " القادمة", "probability": 0.9923502604166666}, {"start": 6169.83, "end": 6170.91, "word": " يدوب", "probability": 0.5582682291666666}, {"start": 6170.91, "end": 6171.53, "word": " نخلص", "probability": 0.8359375}, {"start": 6171.53, "end": 6171.77, "word": " هذا", "probability": 0.332275390625}, {"start": 6171.77, "end": 6171.91, "word": " ال", "probability": 0.974609375}, {"start": 6171.91, "end": 6172.13, "word": " section", "probability": 0.8125}, {"start": 6172.13, "end": 6172.61, "word": " يعني", "probability": 0.664794921875}, {"start": 6172.61, "end": 6173.01, "word": " كلام", "probability": 0.951416015625}, {"start": 6173.01, "end": 6173.53, "word": " كتير", "probability": 0.970703125}, {"start": 6173.53, "end": 6174.29, "word": " لسه", "probability": 0.9768880208333334}, {"start": 6174.29, "end": 6174.53, "word": " بدنا", "probability": 0.42919921875}, {"start": 6174.53, "end": 6175.11, "word": " نتكلم", "probability": 0.9921875}, {"start": 6175.11, "end": 6176.01, "word": " عن", "probability": 0.99365234375}, {"start": 6176.01, "end": 6177.79, "word": " ال", "probability": 0.96142578125}, {"start": 6177.79, "end": 6178.29, "word": " functions", "probability": 0.93212890625}, {"start": 6178.29, "end": 6178.67, "word": " اللي", "probability": 0.859130859375}, {"start": 6178.67, "end": 6179.07, "word": " عندنا", "probability": 0.989501953125}, {"start": 6179.07, "end": 6179.47, "word": " هذه", "probability": 0.73828125}, {"start": 6179.47, "end": 6181.17, "word": " المختلفة", "probability": 0.9915771484375}], "temperature": 1.0}, {"id": 231, "seek": 620645, "start": 6181.51, "end": 6206.45, "text": "و ال function بنا نعرف حاجة اسمها ال bounded و ال unbounded و ما إلى ذلك كل الشغلات و ناخد اللي في الحالة الأولى في ال plane و بعدين نروح في الفراد و في level curve و في level surfaces و ما إلى ذلك كله الموضوع المحاضرة القادمة ان شاء الله تعالى يعطيكوا العافية", "tokens": [2407, 2423, 2445, 4724, 8315, 8717, 3615, 28480, 11331, 26108, 3660, 24525, 2304, 11296, 2423, 37498, 4032, 2423, 517, 18767, 292, 4032, 19446, 30731, 29910, 23275, 28242, 25124, 17082, 1211, 9307, 4032, 8717, 47283, 3215, 13672, 1829, 8978, 21542, 6027, 3660, 16247, 12610, 7578, 8978, 2423, 5720, 4032, 39182, 9957, 8717, 32887, 5016, 8978, 27188, 2288, 18513, 4032, 8978, 1496, 7605, 4032, 8978, 1496, 16130, 4032, 19446, 30731, 29910, 23275, 28242, 3224, 9673, 2407, 11242, 45367, 9673, 5016, 46958, 25720, 25062, 18513, 46007, 16472, 13412, 16606, 21984, 37279, 6027, 7578, 37495, 9566, 1829, 4117, 14407, 18863, 31845, 10632], "avg_logprob": -0.17140151454944802, "compression_ratio": 1.7584745762711864, "no_speech_prob": 7.152557373046875e-07, "words": [{"start": 6181.51, "end": 6182.07, "word": "و", "probability": 0.8828125}, {"start": 6182.07, "end": 6183.13, "word": " ال", "probability": 0.58056640625}, {"start": 6183.13, "end": 6183.43, "word": " function", "probability": 0.059478759765625}, {"start": 6183.43, "end": 6183.73, "word": " بنا", "probability": 0.4298095703125}, {"start": 6183.73, "end": 6184.19, "word": " نعرف", "probability": 0.99267578125}, {"start": 6184.19, "end": 6184.79, "word": " حاجة", "probability": 0.9537760416666666}, {"start": 6184.79, "end": 6185.21, "word": " اسمها", "probability": 0.91943359375}, {"start": 6185.21, "end": 6185.37, "word": " ال", "probability": 0.7490234375}, {"start": 6185.37, "end": 6185.95, "word": " bounded", "probability": 0.90185546875}, {"start": 6185.95, "end": 6186.69, "word": " و", "probability": 0.87451171875}, {"start": 6186.69, "end": 6186.83, "word": " ال", "probability": 0.90869140625}, {"start": 6186.83, "end": 6188.33, "word": " unbounded", "probability": 0.9296875}, {"start": 6188.33, "end": 6188.81, "word": " و", "probability": 0.98486328125}, {"start": 6188.81, "end": 6189.83, "word": " ما", "probability": 0.338623046875}, {"start": 6189.83, "end": 6190.05, "word": " إلى", "probability": 0.91015625}, {"start": 6190.05, "end": 6190.59, "word": " ذلك", "probability": 0.994873046875}, {"start": 6190.59, "end": 6191.19, "word": " كل", "probability": 0.65771484375}, {"start": 6191.19, "end": 6191.89, "word": " الشغلات", "probability": 0.97314453125}, {"start": 6191.89, "end": 6192.29, "word": " و", "probability": 0.9375}, {"start": 6192.29, "end": 6192.73, "word": " ناخد", "probability": 0.9873046875}, {"start": 6192.73, "end": 6192.89, "word": " اللي", "probability": 0.87451171875}, {"start": 6192.89, "end": 6192.99, "word": " في", "probability": 0.8544921875}, {"start": 6192.99, "end": 6193.41, "word": " الحالة", "probability": 0.9415690104166666}, {"start": 6193.41, "end": 6193.77, "word": " الأولى", "probability": 0.9736328125}, {"start": 6193.77, "end": 6193.93, "word": " في", "probability": 0.6982421875}, {"start": 6193.93, "end": 6194.03, "word": " ال", "probability": 0.9697265625}, {"start": 6194.03, "end": 6194.49, "word": " plane", "probability": 0.64990234375}, {"start": 6194.49, "end": 6194.97, "word": " و", "probability": 0.94482421875}, {"start": 6194.97, "end": 6195.33, "word": " بعدين", "probability": 0.79638671875}, {"start": 6195.33, "end": 6195.71, "word": " نروح", "probability": 0.9270833333333334}, {"start": 6195.71, "end": 6195.85, "word": " في", "probability": 0.81494140625}, {"start": 6195.85, "end": 6196.45, "word": " الفراد", "probability": 0.779296875}, {"start": 6196.45, "end": 6196.87, "word": " و", "probability": 0.884765625}, {"start": 6196.87, "end": 6197.01, "word": " في", "probability": 0.7724609375}, {"start": 6197.01, "end": 6197.29, "word": " level", "probability": 0.42724609375}, {"start": 6197.29, "end": 6197.91, "word": " curve", "probability": 0.72314453125}, {"start": 6197.91, "end": 6198.67, "word": " و", "probability": 0.994140625}, {"start": 6198.67, "end": 6198.81, "word": " في", "probability": 0.75390625}, {"start": 6198.81, "end": 6199.13, "word": " level", "probability": 0.9609375}, {"start": 6199.13, "end": 6200.13, "word": " surfaces", "probability": 0.87255859375}, {"start": 6200.13, "end": 6200.65, "word": " و", "probability": 0.99462890625}, {"start": 6200.65, "end": 6200.83, "word": " ما", "probability": 0.931640625}, {"start": 6200.83, "end": 6201.09, "word": " إلى", "probability": 0.9814453125}, {"start": 6201.09, "end": 6201.43, "word": " ذلك", "probability": 0.99609375}, {"start": 6201.43, "end": 6201.79, "word": " كله", "probability": 0.709716796875}, {"start": 6201.79, "end": 6202.45, "word": " الموضوع", "probability": 0.8831787109375}, {"start": 6202.45, "end": 6203.39, "word": " المحاضرة", "probability": 0.971435546875}, {"start": 6203.39, "end": 6203.95, "word": " القادمة", "probability": 0.9947916666666666}, {"start": 6203.95, "end": 6204.21, "word": " ان", "probability": 0.7607421875}, {"start": 6204.21, "end": 6204.47, "word": " شاء", "probability": 0.982421875}, {"start": 6204.47, "end": 6204.65, "word": " الله", "probability": 0.9521484375}, {"start": 6204.65, "end": 6205.19, "word": " تعالى", "probability": 0.9814453125}, {"start": 6205.19, "end": 6206.07, "word": " يعطيكوا", "probability": 0.8568359375}, {"start": 6206.07, "end": 6206.45, "word": " العافية", "probability": 0.90576171875}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 6206.9725, "duration_after_vad": 5640.939718750033}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/r80EmZhKdwI_raw.srt b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/r80EmZhKdwI_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..89a77bf46a218ac1c8dbb65825d1d54b315bb97d
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/r80EmZhKdwI_raw.srt
@@ -0,0 +1,3584 @@
+1
+00:00:12,920 --> 00:00:18,010
+السلام عليكم ورحمة الله وبركاتهبسم الله الرحمن
+
+2
+00:00:18,010 --> 00:00:21,310
+الرحيم اليوم ان شاء الله هنبدأ في section 13-5
+
+3
+00:00:21,310 --> 00:00:26,510
+اللى بتحدث عن tangential and component of
+
+4
+00:00:26,510 --> 00:00:31,350
+acceleration المركبة الممسية والمركبة العمودية
+
+5
+00:00:31,350 --> 00:00:37,550
+لمهن للعجلة يبقى tangential ممسي و norm عمودي و
+
+6
+00:00:37,550 --> 00:00:42,010
+component مركبات العجلة يبقى مركبات العجلة المركبة
+
+7
+00:00:42,010 --> 00:00:45,270
+الممسية والمركبة العمودية عليها
+
+8
+00:00:52,370 --> 00:00:59,070
+درسناها قبل ذلك اللي هو V تساوي DR على DT الـDR
+
+9
+00:00:59,070 --> 00:01:04,590
+على DDT بدأ يدخل الاركليك parameter S فبسيطة عندك
+
+10
+00:01:04,590 --> 00:01:10,790
+DR على DS في DS على DD طبعا الـDR على DS درسناها
+
+11
+00:01:10,790 --> 00:01:12,450
+سابقا اليوم كانت من
+
+12
+00:01:16,210 --> 00:01:22,170
+يبقى ثاني و انا هشيلها و اكتب بدالها D و هذا بيصير
+
+13
+00:01:22,170 --> 00:01:29,600
+DS على DT في unit tangent vector Tإذا كتبنا الـ
+
+14
+00:01:29,600 --> 00:01:34,900
+Velocity V بدلة الـ Unit Tangent T وكمية الـ
+
+15
+00:01:34,900 --> 00:01:40,540
+Scalar EDS على DT سابقا تحدثنا و قلنا إن اتجاه
+
+16
+00:01:40,540 --> 00:01:46,420
+الحركة تبع الجسم هو نفس اتجاه السرعة و نفس اتجاه
+
+17
+00:01:46,420 --> 00:01:51,540
+Unit Tangent يبقى Tangent و Velocity 2 in the same
+
+18
+00:01:51,540 --> 00:01:56,440
+directionيبقى الاتنين بيكونوا في نفس الاتجاه لحظة
+
+19
+00:01:56,440 --> 00:02:02,200
+هي ال Velocity V تساوي الرقم الو DS على DT مضروف
+
+20
+00:02:02,200 --> 00:02:07,560
+Main T يبقى ال T و ال VR Parallel اتنين ما لهم
+
+21
+00:02:07,560 --> 00:02:15,120
+بيكونوا متوازين لأن أحدهم هو مضعفات من الآخر طيب
+
+22
+00:02:15,120 --> 00:02:19,620
+ما علينا بناروح نجيب ال acceleration اللي هو موضوع
+
+23
+00:02:19,620 --> 00:02:20,440
+هذا ال section
+
+24
+00:02:27,890 --> 00:02:32,990
+معناته باننا نشتغل المقدار اللي عندنا هذا يبقى D
+
+25
+00:02:32,990 --> 00:02:43,350
+على DT ل DS على DT في اتجاه الـ T هذا يعتبر مشتبط
+
+26
+00:02:43,350 --> 00:02:48,270
+حاصل ضغط دليل D يبقى هذا derivative لل product of
+
+27
+00:02:48,270 --> 00:02:49,290
+two functions
+
+28
+00:03:00,380 --> 00:03:11,300
+DS على DT في ميل زائد DS على DT في مشتقة DT على DT
+
+29
+00:03:11,300 --> 00:03:18,160
+يبقى مشتقة الأولى في الثانية كما هي زائد الأولى
+
+30
+00:03:18,160 --> 00:03:24,840
+كما هي في مشتقة التانية بالشكل اللي عندنا هذاهنا
+
+31
+00:03:24,840 --> 00:03:29,840
+يوجد دي S على دي T وهنا يوجد دي S على دي T كذلك
+
+32
+00:03:29,840 --> 00:03:35,000
+الـ T هي عبارة عن function في الـ arc parameter S
+
+33
+00:03:45,330 --> 00:03:56,770
+زائد DS على DT في DT على DS في DS على DT هذا
+
+34
+00:03:56,770 --> 00:04:03,030
+الكلام بدرساوي مركّبلونة كما هي D²S على DT²
+
+35
+00:04:03,030 --> 00:04:11,750
+المشتقة الثانية في اتجاه D زائد DS على DT ليه؟
+
+36
+00:04:16,550 --> 00:04:23,770
+8 في ال principle normal unit vector n في ds على
+
+37
+00:04:23,770 --> 00:04:31,390
+dt إذا نروح نقول ال acceleration a بدها تساوي اللي
+
+38
+00:04:31,390 --> 00:04:39,250
+هو d2s على dt2 في اتجاه ال T طبعا هذه scalar في
+
+39
+00:04:39,250 --> 00:04:44,110
+اتجاه ال T زائد اتطلعي ليه هذه الكلمة
+
+40
+00:04:46,720 --> 00:04:52,080
+و ال DS على DT و ال DS على DT يبقى DS
+
+41
+00:05:00,270 --> 00:05:06,430
+بالضبط كأننا حللنا الـ acceleration a إلى مركبتين
+
+42
+00:05:06,430 --> 00:05:11,790
+في اتجاهين متعمدين المركبة الأولى في اتجاه الـ T
+
+43
+00:05:11,790 --> 00:05:15,430
+والمركبة التانية في الاتجاه العمودي عليه اللي هو
+
+44
+00:05:15,430 --> 00:05:19,370
+ال principle unit vector N ال principle unit
+
+45
+00:05:19,370 --> 00:05:24,300
+normal vector اللي هو N تمام تماميبقى اللي في
+
+46
+00:05:24,300 --> 00:05:27,540
+اتجاه T بيسميها tangential component of
+
+47
+00:05:27,540 --> 00:05:31,560
+acceleration واللي في اتجاه ال N بيسميها normal
+
+48
+00:05:31,560 --> 00:05:35,860
+component of acceleration وكل واحدة فيهم is scalar
+
+49
+00:05:35,860 --> 00:05:41,880
+يعني هذه ليست كمية اتجاهية وانما كمية قياسية وكذلك
+
+50
+00:05:41,880 --> 00:05:47,620
+هذه كمية قياسية كل واحدة حد رموز هذا الرمز المناسب
+
+51
+00:05:47,620 --> 00:05:54,440
+بالنسبة له ال tangential حديها الرمز ATيبقى AT هي
+
+52
+00:05:54,440 --> 00:06:03,480
+عبارة عن D²S على DT² شكل العنادر أو إن شئتم فقولوا
+
+53
+00:06:03,480 --> 00:06:13,120
+D على DT لـDS على DT سؤال هل هذه لها علاقة بـ
+
+54
+00:06:13,120 --> 00:06:17,980
+Speed يا بنات؟ طول الـ V يعني مصدر الـ Speed يبقى
+
+55
+00:06:17,980 --> 00:06:26,430
+هذهD على DT لمين؟ لقول ال V ممتاز جدا يبقى 1000
+
+56
+00:06:26,430 --> 00:06:31,590
+ثانية scalar tangential component of acceleration
+
+57
+00:06:31,590 --> 00:06:40,510
+يبقى 80 هذه as the scalar tangential
+
+58
+00:06:40,510 --> 00:06:44,590
+component
+
+59
+00:06:49,960 --> 00:06:56,460
+of acceleration يبقى
+
+60
+00:06:56,460 --> 00:07:00,740
+هذه المراكبة الممسية للعجلة اللي في اتجاره ال unit
+
+61
+00:07:00,740 --> 00:07:05,460
+tangent T لو ده أقرأها بصورة أخرى
+
+62
+00:07:10,280 --> 00:07:16,420
+معدل تغيير مقدار السرعة مش هي بقولها مش المشتقة
+
+63
+00:07:16,420 --> 00:07:20,580
+الأولى هي معدل التغيير و هي المشتقة الأولى و هي
+
+64
+00:07:20,580 --> 00:07:25,340
+المعاملة التفاضل الأول و هي ميل المماثل المنحنة مش
+
+65
+00:07:25,340 --> 00:07:30,160
+كل هذه تعابيرات لها نفس المعنى إذا هذه بقدر أقول
+
+66
+00:07:30,160 --> 00:07:36,120
+هي معدل تغيير ال speed أو الطول اللي عندنا تبع
+
+67
+00:07:36,120 --> 00:07:42,490
+اللي هو ال V طيب نجي للثانيةالتانية هذه حموظها رمز
+
+68
+00:07:42,490 --> 00:07:50,270
+AN لأنها في اتجاه ال N يبقى ال AN بدر ساوي كابا في
+
+69
+00:07:50,270 --> 00:07:57,430
+DS على DT Square و اللي هو بدر ساوي كيرفيتشر كابا
+
+70
+00:07:57,430 --> 00:08:05,590
+في طول ال V لكل تربية يبقى هذه اللي في اتجاه عمودي
+
+71
+00:08:05,590 --> 00:08:08,270
+E يبقى هذه اللي بسميها ال scalar
+
+72
+00:08:11,090 --> 00:08:18,010
+the scalar normal
+
+73
+00:08:18,010 --> 00:08:21,730
+component
+
+74
+00:08:21,730 --> 00:08:37,850
+of acceleration طيب
+
+75
+00:08:37,850 --> 00:08:45,560
+يا بناتفي علاقة بتربط العجلة الأساسية بالمركبتين
+
+76
+00:08:45,560 --> 00:08:51,840
+بدنا نعرف ما هي هذه العلاقة عشان نعرف هذه العلاقة
+
+77
+00:08:51,840 --> 00:08:58,240
+باجي بقول كويس لو عامل ضغط ما بين العجلة مع نفسها
+
+78
+00:08:58,240 --> 00:09:04,460
+يبقى باجي بقول ال a هذا حطالك في صورة ملاحظة بسيطة
+
+79
+00:09:08,890 --> 00:09:14,210
+لو قلت لك ال a ضد ال a تقولي لي كده؟ طول ال a
+
+80
+00:09:14,210 --> 00:09:19,470
+ترميع طيب الآن ال at سهل أجدها بسهولة هذه اللي
+
+81
+00:09:19,470 --> 00:09:24,850
+عندك بفضل ال R و P بحصل عليه بجيب الطول بكون جبته
+
+82
+00:09:24,850 --> 00:09:29,070
+مشتاق فبجيبه على فول بس كما ال kermitian في ال D S
+
+83
+00:09:29,070 --> 00:09:34,100
+على D T بدأ طول عليها شوية فهنا طريقة أقصد منهاإذا
+
+84
+00:09:34,100 --> 00:09:37,960
+جبت ال acceleration اعملها ضوط مع نفسها يبقى
+
+85
+00:09:37,960 --> 00:09:45,500
+بيعطيني طول ال a تربيع الان عندنا ال a t square ل
+
+86
+00:09:45,500 --> 00:09:53,020
+a ضوط a زائد ال a n square بده يساوي مين اللي هو
+
+87
+00:09:53,020 --> 00:09:57,840
+ال a ضوط ال a اللي هو بده يساوي طول ال a تربيع
+
+88
+00:09:57,840 --> 00:10:05,020
+يبقى من هذه العبارةو بقدر احسب له من ال AM اللي
+
+89
+00:10:05,020 --> 00:10:13,760
+بتساوي ال square root لطول ال A² مقص ال AT² يبقى
+
+90
+00:10:13,760 --> 00:10:18,240
+هذه وسيلة عملية بسيطة للحصول على المركبة الثانية
+
+91
+00:10:18,240 --> 00:10:23,200
+للعجلة بدون ما نروح نحسب لا ال curvature ولا ال
+
+92
+00:10:23,200 --> 00:10:28,290
+main ولا الأمر التاني و ما إلى ذلكطيب كويس يبقى
+
+93
+00:10:28,290 --> 00:10:32,210
+هذا يعني هذا اللي هو الجزء النظري تبع ال
+
+94
+00:10:32,210 --> 00:10:36,710
+tangential normal لو حبنا نعرف الاتجاه يعني كيف
+
+95
+00:10:36,710 --> 00:10:41,150
+بيكون بالضبط فبجي بقول لو أخدت smooth curve على
+
+96
+00:10:41,150 --> 00:10:47,250
+سبيل المثال بهذا الشكل وقلت هذه ال base point P0
+
+97
+00:10:47,250 --> 00:10:52,810
+يبقى هذا الخط كله بيكون main ال arc length
+
+98
+00:10:52,810 --> 00:11:00,750
+parameter S of Tلو روحت عنده نقطة مثل هذه النقطة و
+
+99
+00:11:00,750 --> 00:11:05,590
+روحت أخدت اللي هو ال tangent عندها يبقى ال tangent
+
+100
+00:11:05,590 --> 00:11:11,170
+يكون بالشكل اللي عندنا هذا يبقى
+
+101
+00:11:11,170 --> 00:11:16,490
+هذا ال tangent للمماس عند هذه النقطة هذا اللي هو
+
+102
+00:11:16,490 --> 00:11:18,310
+ال tangent T
+
+103
+00:11:20,890 --> 00:11:25,590
+لـ Principal Normal بدي أكون وين؟ للداخل اللي هو
+
+104
+00:11:25,590 --> 00:11:32,230
+عمودي عليه هذا اليومين N يبقى الـ Acceleration إيه
+
+105
+00:11:32,230 --> 00:11:37,210
+لها مُركّبتين؟ المُركّبة الأولى في اتجاه الـT اللي
+
+106
+00:11:37,210 --> 00:11:46,290
+سميتها AT مين هي؟ هي D²S على DT² المُركّبة التانية
+
+107
+00:11:46,290 --> 00:11:53,330
+هنا AN اللي هي الـCurvature كابةفي مين؟ في اللي هو
+
+108
+00:11:53,330 --> 00:11:58,470
+طول ال V لكل ترابيع طب السؤال هو أين ال
+
+109
+00:11:58,470 --> 00:12:04,810
+acceleration؟ بتقولك كامل المستاطيل اللي عندك بهذا
+
+110
+00:12:04,810 --> 00:12:11,230
+الشكل يبقى القطر تبع هذا المستاطيل يمثل ال
+
+111
+00:12:11,230 --> 00:12:17,400
+acceleration A اللي حللناها إلى مركبتينالمُركّبة
+
+112
+00:12:17,400 --> 00:12:20,440
+الأولى هي الـ tangential component والمُركّبة
+
+113
+00:12:20,440 --> 00:12:25,040
+التانية هي الـ normal component of acceleration
+
+114
+00:12:25,040 --> 00:12:32,780
+نعطي مثال توضيح على هذا الكلام هذا
+
+115
+00:12:32,780 --> 00:12:36,140
+بده الشجرة دي سحاني
+
+116
+00:13:06,540 --> 00:13:15,180
+بقول الان ال A of T بده ساوي اللي هو T زائد واحد
+
+117
+00:13:15,180 --> 00:13:20,760
+في اتجاه ال I زائد اتنين T في اتجاه ال J
+
+118
+00:13:32,620 --> 00:13:43,740
+The acceleration طول العجلة A تنتجر
+
+119
+00:13:43,740 --> 00:13:50,240
+على الشكل A تنتجر
+
+120
+00:13:50,240 --> 00:13:53,900
+على
+
+121
+00:13:53,900 --> 00:13:54,420
+الشكل
+
+122
+00:13:57,770 --> 00:14:08,850
+at T تساوي واحد without finding .. without finding
+
+123
+00:14:08,850 --> 00:14:17,190
+.. بدون حساب أو بدون إيجاد T and الـ
+
+124
+00:14:30,480 --> 00:14:35,380
+نقرأ السؤال مرة ثانية نحدد شو اللي مطلوب في السؤال
+
+125
+00:14:35,380 --> 00:14:41,680
+وبالتالي بنقدر نحسب الشغل اللي بدناه حسابا دقيقة
+
+126
+00:14:41,680 --> 00:14:47,640
+ميعطيني ال position vector لجسم يتحرك معه وقال
+
+127
+00:14:47,640 --> 00:14:51,000
+لجسم المعادلة تبعته ال vector volume function يقرب
+
+128
+00:14:51,000 --> 00:14:55,440
+T T زي دوعة في اتجاه I زي اتنية T في اتجاه J زي T
+
+129
+00:14:55,440 --> 00:15:02,460
+تربية في اتجاه Kاللي يكتبلي العجلة على شكل مركبتيه
+
+130
+00:15:02,460 --> 00:15:06,700
+ال tangential component و ال normal component
+
+131
+00:15:06,700 --> 00:15:11,520
+احسبلي هذا الكلام عندما E تسوى 1 بدون ما تحسب لا T
+
+132
+00:15:11,520 --> 00:15:18,930
+ولا N يبقى مش لازم نحسب لا T ولا Nلكن يجب أن تخلّي
+
+133
+00:15:18,930 --> 00:15:24,350
+T و N كما هو يعني كأن المعادلة تكتب بدلالة T و N
+
+134
+00:15:24,350 --> 00:15:27,470
+لذلك يجب أن أحصل عليه tangential component
+
+135
+00:15:27,470 --> 00:15:32,150
+التانجينشال كومبوننت مسحناها قبل قليل فكانت هي
+
+136
+00:15:32,150 --> 00:15:36,730
+عبارة عن مشتقة ال velocity معناه الكلام بده يروح
+
+137
+00:15:36,730 --> 00:15:40,150
+أما مشتقة ال speed يبقى بدنا نروح و نجلب ال
+
+138
+00:15:40,150 --> 00:15:44,530
+velocity ثم ال speed ثم نشتقها يبقى بعدين أقول له
+
+139
+00:15:44,530 --> 00:15:50,990
+solutionبدي ال V as a function of T يبقى اللي هي
+
+140
+00:15:50,990 --> 00:16:01,090
+DR على DT و يساوي مشتقتها I زائد 2D زائد 2TK
+
+141
+00:16:05,600 --> 00:16:11,140
+طول الـ vector V يسوى الجذري التربيع يلي واحد زائد
+
+142
+00:16:11,140 --> 00:16:16,340
+أربعة زائد أربعة D تربيع ويسوى ال square root
+
+143
+00:16:16,340 --> 00:16:26,560
+للخمسة زائد أربعة D تربيع بعد هيك بدنا ال A T يبقى
+
+144
+00:16:26,560 --> 00:16:33,260
+ال A T هي عبارة عن D على DT لطول ال V يبقى معناته
+
+145
+00:16:33,260 --> 00:16:39,590
+بنشتغل منالجدر هذا خدناه في Calculus A مش نفس
+
+146
+00:16:39,590 --> 00:16:44,130
+الجدر واحد على تاني الجدر ده مش نفس ما داخل
+
+147
+00:16:59,670 --> 00:17:05,470
+يبقى النتيجة النهائية بعد الاختصار بتصير اربعة تي
+
+148
+00:17:05,470 --> 00:17:11,970
+على الجدرى التربية لخمسة زائد اربعة تي تربية تمام
+
+149
+00:17:11,970 --> 00:17:19,670
+جالي احسبلي هذا الكلامعند T تساوي واحد يبقى عند T
+
+150
+00:17:19,670 --> 00:17:25,910
+تساوي واحد هذا بيصير اربعة على جدر خمسة زائد اربعة
+
+151
+00:17:25,910 --> 00:17:31,530
+في واحد تربيع باربعة اربعة وخمسة تسعة تحت الجدر
+
+152
+00:17:31,530 --> 00:17:36,750
+بتلاتة يبقى النتيجة تساوي قدر اربعة تلاتة هذا
+
+153
+00:17:36,750 --> 00:17:41,710
+مقدار تجيش ال component وزي ما انت شايف اسكلف زي
+
+154
+00:17:41,710 --> 00:17:46,150
+ما قلنا لكوا ان هذا النتيجة اسكلف قبل ذلكالمركبة
+
+155
+00:17:46,150 --> 00:17:51,650
+الأولى بناروح نجيب المركبة الثانية عشان نجيب
+
+156
+00:17:51,650 --> 00:17:56,450
+المركبة الأولى بناروح
+
+157
+00:17:56,450 --> 00:18:01,150
+نجيب المركبة الثانية عشان نجيب المركبة الأولى
+
+158
+00:18:01,150 --> 00:18:01,610
+بناروح نجيب المركبة الأولى بناروح نجيب المركبة
+
+159
+00:18:01,610 --> 00:18:01,610
+الأولى بناروح نجيب المركبة الأولى بناروح نجيب
+
+160
+00:18:01,610 --> 00:18:01,630
+المركبة الأولى بناروح نجيب المركبة الأولى بناروح
+
+161
+00:18:01,630 --> 00:18:01,930
+نجيب المركبة الأولى بناروح نجيب المركبة الأولى
+
+162
+00:18:01,930 --> 00:18:01,930
+بناروح نجيب المركبة الأولى بناروح نجيب المركبة
+
+163
+00:18:01,930 --> 00:18:02,410
+الأولى بناروح نجيب المركبة الأولى بناروح نجيب
+
+164
+00:18:02,410 --> 00:18:05,470
+المركبة الأولى بناروح نجي
+
+165
+00:18:21,900 --> 00:18:27,860
+أتنين كيف فقط مغلق يبقى الأن لو جيت يا بنا أنت
+
+166
+00:18:27,860 --> 00:18:37,760
+قلتلك بدي ال a بطل a كده بطل عنه اللي هو طول ال a
+
+167
+00:18:37,760 --> 00:18:44,820
+تربعه اللي متجه فيه نفسه بطل كده هذا بطل أربعة إذا
+
+168
+00:18:44,820 --> 00:18:49,440
+سهل إيجاد اللي هو ال normal component of
+
+169
+00:18:49,440 --> 00:18:53,460
+accelerationفبروح بقوله normal component of
+
+170
+00:18:53,460 --> 00:18:58,600
+acceleration An يساوي الجدرح التربية لطول ال A
+
+171
+00:18:58,600 --> 00:19:06,560
+تربية ناقص ال AT² ويساوي ال square root A تربية
+
+172
+00:19:10,730 --> 00:19:18,350
+أربعة على تلاتة يبقى هذه أربعة على تلاتة كل تربيع
+
+173
+00:19:18,350 --> 00:19:24,610
+يبقى ال square root للأربعة نقص ستاشر على تسعة
+
+174
+00:19:33,590 --> 00:19:40,330
+العشرين اربعة في خمسة يعني اتنين جدر خمسة على
+
+175
+00:19:40,330 --> 00:19:44,910
+تلاتة هذا مقدار ماهو ال normal component of
+
+176
+00:19:44,910 --> 00:19:49,170
+acceleration اذا اصبحت ال acceleration اللي
+
+177
+00:19:49,170 --> 00:19:51,190
+بدوياها هي
+
+178
+00:20:03,860 --> 00:20:09,240
+بتجاه ال principle normal N يبقى هي حط نر العجلة
+
+179
+00:20:09,240 --> 00:20:13,480
+على صيغة ال component الواضحة الواضحة الواضحة
+
+180
+00:20:13,480 --> 00:20:16,560
+الواضحة الواضحة الواضحة الواضحة الواضحة الواضحة
+
+181
+00:20:16,560 --> 00:20:23,080
+الواضحة الواضحة الواضحة
+
+182
+00:20:23,080 --> 00:20:25,820
+الواضحة
+
+183
+00:20:28,350 --> 00:20:38,210
+نعود الآن لتعريف الـ BINORMAL VECTOR الـ BINORMAL
+
+184
+00:20:38,210 --> 00:20:44,310
+VECTOR يا بنات هو unit vector عمودي على كل ال manT
+
+185
+00:20:44,310 --> 00:20:49,330
+و N يبقى لو قلنا T و N اللي هو ال unit tangent
+
+186
+00:20:49,330 --> 00:20:53,410
+vector التانجنت والنورمال إذا هذا بدي يكون وين
+
+187
+00:20:53,410 --> 00:20:58,430
+عمودي عليهم عمودي على اتنين معناته بدي أعمل cross
+
+188
+00:20:58,430 --> 00:21:03,410
+product يبقى بنعرفه هو ال cross product لمين لل T
+
+189
+00:21:03,410 --> 00:21:10,350
+و ال N مع بعض يبقى مضاجي لل definition كالثالث ال
+
+190
+00:21:10,350 --> 00:21:19,690
+binomial vector Vباينرمال فيكتور of
+
+191
+00:21:19,690 --> 00:21:30,090
+a space curve of a space curve المنحنة في الفرقات
+
+192
+00:21:30,090 --> 00:21:41,290
+as P باينرمال تسوى تي كروس ال N as a unit vector
+
+193
+00:21:41,290 --> 00:21:55,380
+asأي unit vector orthogonal to
+
+194
+00:21:55,380 --> 00:22:04,960
+both عمودي على كل من T and N
+
+195
+00:22:11,790 --> 00:22:16,650
+نرجع نقرأ ال definition تاني و طرأ على هذه السؤال
+
+196
+00:22:16,650 --> 00:22:21,560
+الآنبنواجهكم من خلال الكلام اللي مكتوب على الصورة
+
+197
+00:22:21,560 --> 00:22:25,820
+اللي قدامنا Definition تججوا معايا كويس حتى نسمع
+
+198
+00:22:25,820 --> 00:22:30,720
+السؤال و نعرف كيف بنا نجاوب على هذا السؤال بيقول
+
+199
+00:22:30,720 --> 00:22:37,160
+دي by normal vector of A space curve S بنعرفه على
+
+200
+00:22:37,160 --> 00:22:42,820
+انه B يسوى T cross ال N يبقى ال B عمودي على كل من
+
+201
+00:22:42,820 --> 00:22:45,040
+ال main وطوله كده
+
+202
+00:22:49,490 --> 00:22:52,110
+T هو عبارة عن unit vector
+
+203
+00:22:56,310 --> 00:23:00,930
+و ال M عبارة عن unit vector عملت لهم cross product
+
+204
+00:23:00,930 --> 00:23:07,230
+طالع بيه هو unit vector بطرح السؤال التالي هل لو
+
+205
+00:23:07,230 --> 00:23:13,950
+عملت cross product بين two units vector إيه ناتج؟
+
+206
+00:23:13,950 --> 00:23:16,850
+هو unit vector؟ بالتأكيد
+
+207
+00:23:18,680 --> 00:23:24,960
+ما رأيكم؟ صحيح هذا الكلام؟ لا مش صحيح، يعني قد
+
+208
+00:23:24,960 --> 00:23:31,260
+يكونوا صحيحا و قد لا يكون، وبالتالي هذا كلام حتى
+
+209
+00:23:31,260 --> 00:23:35,280
+لو حصل مرتين، تلاتة، مية، لكن in general، لا مش
+
+210
+00:23:35,280 --> 00:23:40,840
+صحيح، كيف يعني؟ بجي بقولك بسيطة، في الهامش بنفكر،
+
+211
+00:23:40,840 --> 00:23:44,080
+ماعرفش ده عاجلة في بالنا سؤال و بدنا نجاوب عليهلو
+
+212
+00:23:44,080 --> 00:23:48,020
+جيت في الهام الشكل انا و قلت بدي اخد two unit
+
+213
+00:23:48,020 --> 00:23:51,740
+vectors و اعمل لهم cross product مع بعض و اشوف شو
+
+214
+00:23:51,740 --> 00:23:56,420
+اللي بده يحصل ايش زمين المتجهين لو جيت في المتجه
+
+215
+00:23:56,420 --> 00:24:00,860
+الأول واحد على جدر تلاتة في اتجاه ال I واحد على
+
+216
+00:24:00,860 --> 00:24:04,500
+جدر تلاتة في اتجاه ال J واحد على جدر تلاتة في
+
+217
+00:24:04,500 --> 00:24:09,420
+اتجاه ال Kمش هذا unit vector ربع المركبات وجمعها
+
+218
+00:24:09,420 --> 00:24:14,640
+بطلع كده واحد صحيح الان بدي اعمله cross product مع
+
+219
+00:24:14,640 --> 00:24:20,900
+ال I مش ال I unit vector مظبوط يبقى بداجي اخد U
+
+220
+00:24:20,900 --> 00:24:28,360
+cross ال I يبقى I و J و K واحد على جدر تلاتة واحد
+
+221
+00:24:28,360 --> 00:24:32,540
+على جدر تلاتة واحد على جدر تلاتة واحد و Zero Zero
+
+222
+00:24:34,780 --> 00:24:43,360
+بتفكر محدد باستخدام عناصر صف التالت يبقى هذا
+
+223
+00:24:43,360 --> 00:24:50,340
+الواحد فيه اشط بصفه عموده واحد على جذر تلاتة J نقص
+
+224
+00:24:50,340 --> 00:24:56,660
+واحد على جذر تلاتة K والباقي بقى أصفر هذا الناتج
+
+225
+00:24:56,660 --> 00:25:01,560
+من ال cross product which is a vector سؤالنا هو هل
+
+226
+00:25:01,560 --> 00:25:02,960
+هذا unit vector؟
+
+227
+00:25:09,720 --> 00:25:13,860
+لو عملت cross product بين two vectors أن يكون
+
+228
+00:25:13,860 --> 00:25:19,520
+الناتج هو unit vector قد يكون و قد لا يكون لكن في
+
+229
+00:25:19,520 --> 00:25:23,160
+موضوع هنا ال by normal vector ال by normal vector
+
+230
+00:25:23,160 --> 00:25:28,620
+is a unit vector تمام بس in general الكلام هذا
+
+231
+00:25:28,620 --> 00:25:30,860
+معروف ليس صحيحا
+
+232
+00:25:45,200 --> 00:25:50,960
+هذه المثال عامل يظهر أن هذا المعنى ليس صحيح
+
+233
+00:25:56,310 --> 00:26:01,250
+هه كلفت نظر لكم الان بدنا نرجع لموضوعنا الموضوع
+
+234
+00:26:01,250 --> 00:26:06,410
+الـ BINORMAL VECTORAL شو رايحة يا بنات؟ لو روحنا
+
+235
+00:26:06,410 --> 00:26:09,970
+اشتقناها، شوفوا لو اين بدنا نوصل فيها الدنيا،
+
+236
+00:26:09,970 --> 00:26:18,410
+كويس؟ يبقى بدنا ناخد مثلا الـ derivative of
+
+237
+00:26:18,410 --> 00:26:29,830
+the biأو بي تساوي ت برص الان بدي اعمل اشتقاق و
+
+238
+00:26:29,830 --> 00:26:35,930
+اشوف ايش بده يقين يعني لو روحت اخدت دي دي على دي
+
+239
+00:26:35,930 --> 00:26:38,510
+اس اشوف ايش بده يقين
+
+240
+00:26:41,940 --> 00:26:47,660
+بنشتق ويبقى كل واحد في مكانه لإن عملية cross
+
+241
+00:26:47,660 --> 00:26:52,740
+product not commutative يبقى بفضل كل واحد في مكانه
+
+242
+00:26:52,740 --> 00:27:03,040
+يبقى مجموعة DT على DS cross ال N زائد T cross ال
+
+243
+00:27:03,040 --> 00:27:06,040
+DN على D
+
+244
+00:27:09,250 --> 00:27:16,870
+طب كويس طيب ابنات لو رجعنا تاو قبل شوية كتبناها و
+
+245
+00:27:16,870 --> 00:27:20,750
+احنا بنحكي في ال tangential لو روحنا ل principal
+
+246
+00:27:20,750 --> 00:27:27,750
+unit normal N قدش بساوي واحد على كبه في مين في DT
+
+247
+00:27:27,750 --> 00:27:34,750
+على DS يعني ال principal unit normal و DT على DS
+
+248
+00:27:34,750 --> 00:27:42,030
+لاثنين are parallelواحد فيهم مضاعفات الثانية يبقى
+
+249
+00:27:42,030 --> 00:27:47,230
+ما اللي بقول sense فيما ان ال principle unit
+
+250
+00:27:47,230 --> 00:27:53,630
+normal M بدي ساوي واحد على كبر دي تي على دي اس
+
+251
+00:27:53,630 --> 00:28:00,130
+يبقى اتنين هدول ما لهمR Parallel لأن هذا هو Scalar
+
+252
+00:28:00,130 --> 00:28:05,390
+وهذا هو Vector يبقى صار هذا مضاعفا من ال vector
+
+253
+00:28:05,390 --> 00:28:15,010
+الثاني يبقى هذا يعطينا ان ال N and ال DT على DT
+
+254
+00:28:15,010 --> 00:28:22,410
+are parallel مدام اتنين توازين يبقى cross product
+
+255
+00:28:22,410 --> 00:28:33,240
+فيما بينهم DT على DS يا بناتDT على DS يبقى
+
+256
+00:28:33,240 --> 00:28:36,560
+معنا اتنين هذول parallel مادام parallel يبقى ال
+
+257
+00:28:36,560 --> 00:28:42,140
+cross product لهم جداش نه متوازن cross product
+
+258
+00:28:42,140 --> 00:28:49,160
+zero يبقى هذا بده يعطينا انهالان و الله زي ما هي
+
+259
+00:28:49,160 --> 00:28:57,060
+دي ت على دي اس cross الان بتسوى كده؟ Zero مدام
+
+260
+00:28:57,060 --> 00:29:01,300
+Zero إذا المعادلة دي أخدت شكل جديد
+
+261
+00:29:26,900 --> 00:29:35,720
+ماذا تفهمينا من هذه الجملةإيش تفسيرها عندك انه DB
+
+262
+00:29:35,720 --> 00:29:42,380
+على DS يسوى عمليا T cross DN على DS شو الولاقة بين
+
+263
+00:29:42,380 --> 00:29:48,040
+هذا المحتج والمحتجين الأثنين دول عبودي على الأثنين
+
+264
+00:29:48,040 --> 00:29:55,680
+يبقى ممتاز جدا يبقى هذا معناته ان DB على DS is
+
+265
+00:29:55,680 --> 00:30:10,040
+orthogonal to bothلكل من T and D N على D S يعتبر
+
+266
+00:30:10,040 --> 00:30:15,420
+هذه المعادلة رقم واحد نرجع
+
+267
+00:30:15,420 --> 00:30:21,180
+بالذاكرة إلى الوراء قليلا التعريف اللي فوق بيقول B
+
+268
+00:30:21,180 --> 00:30:26,340
+is a unit vector يعني
+
+269
+00:30:26,340 --> 00:30:31,390
+vector with constant length صحيح ولا لأ؟لو أعمل
+
+270
+00:30:31,390 --> 00:30:38,570
+dot product ما بين ال B ومشتقته، كده؟ Zero كذلك،
+
+271
+00:30:38,570 --> 00:30:46,070
+خاصية أخدناها قبل ذلك يبقى باجي بقوله since
+
+272
+00:30:46,070 --> 00:30:55,050
+بما أن ال B is a constant vector,
+
+273
+00:30:56,510 --> 00:30:57,110
+we have
+
+274
+00:30:59,890 --> 00:31:11,590
+إن ال B بط DB على DS بده يساوي Z هذا إيش بيعطينا؟
+
+275
+00:31:11,590 --> 00:31:23,130
+هذا بيعطينا إن DB على DS is orthogonal لمن؟
+
+276
+00:31:23,130 --> 00:31:27,310
+is orthogonal to B
+
+277
+00:31:30,170 --> 00:31:36,190
+وهذه العلاقة رقم اتنين تعالى نتطلع في واحد واتنين
+
+278
+00:31:36,190 --> 00:31:43,890
+بيقول هنا DBA على DS عمودي على T و على DN على DS
+
+279
+00:31:43,890 --> 00:31:49,430
+وهنا بيقول ان ال DBA على DS نفسها عمودي على مين
+
+280
+00:31:49,430 --> 00:31:54,210
+على B إذا معنى هذا الكلام ان ال DBA على DS عمودي
+
+281
+00:31:54,210 --> 00:32:01,420
+على كل من T وB صحيح ولا لأيبقى هنا بقول له so
+
+282
+00:32:01,420 --> 00:32:12,640
+والله from واحد and اثنين ال D بي على دي اس is
+
+283
+00:32:12,640 --> 00:32:18,020
+orthogonal to
+
+284
+00:32:18,020 --> 00:32:22,220
+اللي هو الأولاني T and ال B
+
+285
+00:32:26,190 --> 00:32:48,830
+طيب، هذا سيولّد لنا السؤال التالي التعريف
+
+286
+00:32:48,830 --> 00:32:53,390
+اللي كتبناه الـ BINORMAL يقول إن B عمودي على كل من
+
+287
+00:32:53,390 --> 00:33:01,200
+T و Nإذا لو كان هذا T يا بنات هذا T هذا بيكون مين؟
+
+288
+00:33:01,200 --> 00:33:06,740
+10 يبقى العمودي على الإتنين مين بيكون؟ اللي هو P
+
+289
+00:33:06,740 --> 00:33:09,860
+هذا
+
+290
+00:33:09,860 --> 00:33:17,000
+بنات المحاور صارت كإنها تلت محاور زي محور X وY وZ
+
+291
+00:33:17,000 --> 00:33:23,330
+بس هدول بيلتقوا وين؟بالتقوى عند نقطة و التكن هذه
+
+292
+00:33:23,330 --> 00:33:28,160
+النقطة Pالنقطة هذه تقع على المنحنى اللى رسمناها
+
+293
+00:33:28,160 --> 00:33:32,700
+قبل شوية يعني على المنحنى وليست نقطة الاصل يعني
+
+294
+00:33:32,700 --> 00:33:35,600
+عند اى نقطة موجودة على المنحنى اللى رسمناها عندها
+
+295
+00:33:35,600 --> 00:33:38,440
+ال unit tangent و ال principle normal و بعدها
+
+296
+00:33:38,440 --> 00:33:41,320
+رسمنا العجلة لأ ال unit tangent و ال principle
+
+297
+00:33:41,320 --> 00:33:46,100
+normal و ال by normal هاي هم عندنا هذول بيعملولى
+
+298
+00:33:46,100 --> 00:33:53,870
+تلت مستويات المستوى الاول اللى يجمع T و Nبسميه
+
+299
+00:33:53,870 --> 00:34:03,430
+oscillating plane يبقى هذا بسميه oscillating plane
+
+300
+00:34:03,430 --> 00:34:06,570
+طيب
+
+301
+00:34:06,570 --> 00:34:12,030
+و اللي بيجمع بيه و ان هذا عمودي على ال oscillating
+
+302
+00:34:12,030 --> 00:34:19,630
+plane بسميه normally plane يبقى هذا هو normally
+
+303
+00:34:19,630 --> 00:34:21,070
+plane
+
+304
+00:34:23,710 --> 00:34:33,330
+والمستوى اللي بعده هذا بسميه rectifying plane يبقى
+
+305
+00:34:33,330 --> 00:34:36,510
+rectifying
+
+306
+00:34:36,510 --> 00:34:42,190
+plane يبقى
+
+307
+00:34:42,190 --> 00:34:47,970
+التان هذول بيعملولي تلت مستويات متعامدة تعالى نشوف
+
+308
+00:34:47,970 --> 00:34:52,490
+من خلال العبارة الأخيرة اللي كتبناها هذه إيش بيحصل
+
+309
+00:34:52,490 --> 00:34:57,780
+عندنابيقول من المعادلة 1 و 2 الـ Db على Ds is
+
+310
+00:34:57,780 --> 00:35:05,160
+orthogonal to both T and B يبقى Db على Ds عمودي
+
+311
+00:35:05,160 --> 00:35:11,260
+على كل المن T و B طب مين عمودي على T و B عنده في
+
+312
+00:35:11,260 --> 00:35:17,820
+الرسم N إذا ما هي العلاقة بين N و Dbi و Db على Ds
+
+313
+00:35:17,820 --> 00:35:26,400
+اتنين are parallel تمام يبقى هذا معناهإن الـ DB
+
+314
+00:35:26,400 --> 00:35:43,340
+على DS ماله is parallel to the normal vector N
+
+315
+00:35:43,340 --> 00:35:49,260
+عمودي عليهمدام عمودي عليه إذا هذا بيعطينا إيش
+
+316
+00:35:49,260 --> 00:35:59,160
+مضاعفاته يعني جده عدت مرات يبقى بناء عليه DB على
+
+317
+00:35:59,160 --> 00:36:10,220
+DS بدي ساوي ناقص TAU في M TAU scalar الرقم يعني،
+
+318
+00:36:10,220 --> 00:36:10,920
+كويس؟
+
+319
+00:36:16,410 --> 00:36:21,770
+الكتاب يقول ان الإشارة السالبة تقليدية تقليدية
+
+320
+00:36:21,770 --> 00:36:26,910
+تقليدية التباعت ان ماكسيشن وده كتاب السلب وضلت
+
+321
+00:36:26,910 --> 00:36:32,210
+ماشية مع الكل بنفس الطريقة يبقى بصير عند دي بي على
+
+322
+00:36:32,210 --> 00:36:38,890
+دي اس يسوي سالب تاو في ان طيب انا بقدر اجيب التاو
+
+323
+00:36:38,890 --> 00:36:44,850
+هذي ولا بقدربنقدر .. بنقدر مابكتش لو تخلصنا من ال
+
+324
+00:36:44,850 --> 00:36:52,210
+N طب كيف نتخلص من ال N؟ تخلص الشجة اليمين اللي
+
+325
+00:36:52,210 --> 00:36:57,530
+عندي هذه سالبته فقط بدون ال N طبعا ال N هنا ال
+
+326
+00:36:57,530 --> 00:37:06,980
+vector يبقاش عمال ايش نسوي؟بتعمل dot product بمعين
+
+327
+00:37:06,980 --> 00:37:13,820
+نفسه يبقى بناء عليها بنات بقدر اقول هنا ال DB على
+
+328
+00:37:13,820 --> 00:37:22,840
+DS بط ال N بدي ساوي الناقص TAU في مين؟ في ال N بط
+
+329
+00:37:22,840 --> 00:37:23,640
+ال N
+
+330
+00:37:29,220 --> 00:37:37,560
+مدام واحد يبقى بناء عليه Tab تساوي سالب DB على DS
+
+331
+00:37:37,560 --> 00:37:45,520
+بطل N شكل اللي عندنا هذا التو يا بنات إله اسم في
+
+332
+00:37:45,520 --> 00:37:53,260
+علمنا اسمه Torsion Function عزم الله كويس؟ يبقى ..
+
+333
+00:37:53,260 --> 00:37:58,460
+هنعطيله ال definition التالي يبقى definition
+
+334
+00:38:01,280 --> 00:38:06,360
+التورشن فانكشن التورشن
+
+335
+00:38:06,360 --> 00:38:11,000
+فانكشن
+
+336
+00:38:11,000 --> 00:38:24,680
+of a smooth curve of a smooth curve is
+
+337
+00:38:24,680 --> 00:38:33,780
+تاو دو يساوي السالق DBعلى الارض التي تم وضعها فيها
+
+338
+00:38:33,780 --> 00:38:36,820
+حيث
+
+339
+00:38:36,820 --> 00:38:46,200
+تاو هو قيمة التي هي قيمة
+
+340
+00:38:46,200 --> 00:38:51,500
+التي هي قيمة التي هي قيمة التي هي قيمة التي هي
+
+341
+00:38:51,500 --> 00:38:55,300
+قيمة اللي هي
+
+342
+00:38:55,300 --> 00:38:55,300
+قيمة اللي هي قيمة اللي هي قيمة اللي هي قيمة اللي
+
+343
+00:38:55,300 --> 00:38:55,300
+هي قيمة اللي هي قيمة اللي هي قيمة اللي هي قيمة
+
+344
+00:38:55,300 --> 00:38:55,300
+اللي هي قيمة اللي هي قيمة اللي هي قيمة اللي هي
+
+345
+00:38:55,300 --> 00:38:55,320
+قيمة اللي هي قيمة اللي هي قيمة اللي هي قيمة اللي
+
+346
+00:38:55,320 --> 00:38:55,320
+هي قيمة اللي هي قيمة اللي هي قيمة اللي هي قيمة
+
+347
+00:38:55,320 --> 00:38:55,320
+اللي هي قيمة اللي هي قيمة اللي هي قيمة اللي هي
+
+348
+00:38:55,320 --> 00:38:55,320
+قيمة اللي هي قيمة اللي هي قيمة اللي هي قيمة اللي
+
+349
+00:38:55,320 --> 00:38:55,600
+هي قيمة اللي هي قيمة
+
+350
+00:39:07,560 --> 00:39:24,760
+there's there's about اللي هو ال unit angelity إذن
+
+351
+00:39:25,400 --> 00:39:29,600
+كل الفكرة في الموضوع اللى تاخد ال derivative تبع
+
+352
+00:39:29,600 --> 00:39:34,600
+ال P الهدف من ذلك ان اوصل لمين للمعادل اللى عندنا
+
+353
+00:39:34,600 --> 00:39:39,280
+و اوصل لتعريف جديد اللى هو تعريف torsion function
+
+354
+00:39:39,280 --> 00:39:45,020
+تمام بيقول اللى التعريف هذا torsion function ال
+
+355
+00:39:45,020 --> 00:39:50,060
+small curve هي تاو تساوية ثانية ترتيب P على DS بطل
+
+356
+00:39:50,060 --> 00:39:54,560
+ان حيث T is the rate at which هو المعدل
+
+357
+00:39:58,020 --> 00:40:04,240
+هو يحاول يعمل دوران حول محور T طبعا هذا الـ
+
+358
+00:40:04,240 --> 00:40:09,040
+oscillating plane و هذا المحور T يعني كأنه بده
+
+359
+00:40:09,040 --> 00:40:14,380
+يعمل شغلة بالشكل اللي عندها زي دوران بهذا الشكل
+
+360
+00:40:14,380 --> 00:40:21,940
+طيب لو جيبنا سؤال و طلبنا ترشد وقلنا لك بالله
+
+361
+00:40:21,940 --> 00:40:26,680
+أسمينا يعني إذا بدك تجي عليها المعادلة هذه و جيبلي
+
+362
+00:40:26,680 --> 00:40:36,120
+principal normيبقى نروح نجيب ال V و نجتقها
+
+363
+00:40:36,120 --> 00:40:40,820
+بالنسبالتي و نحسب قولها و نقسم و نقول جيبنا
+
+364
+00:40:40,820 --> 00:40:44,060
+reference بالنور بقى زي ما سويت المرة اللى فاترة
+
+365
+00:40:44,060 --> 00:40:49,970
+قصة طويلة صحيح ولا لأ؟ و يرتك أديكم بسوبنرجع نجيب
+
+366
+00:40:49,970 --> 00:40:54,690
+cross product بين ال T والL ونروح نشتقها بالنسبة
+
+367
+00:40:54,690 --> 00:40:56,950
+لل S ونجيب علاقة تربط أصلها
+
+368
+00:40:59,970 --> 00:41:05,110
+لكن في مادة ال advanced calculus اللي بيدرسوها
+
+369
+00:41:05,110 --> 00:41:09,950
+طلاب العلوم اللي هو التفاضل و التكمل المتقدم مادة
+
+370
+00:41:09,950 --> 00:41:15,990
+في سنة رابعة حسب ذلك عمليا و بنستخدم هذا في حل
+
+371
+00:41:15,990 --> 00:41:21,190
+المسائل أشهر من هذه العلاقة يبقى بدي أحطها لكم في
+
+372
+00:41:21,190 --> 00:41:21,730
+الصيغة
+
+373
+00:41:34,300 --> 00:41:42,300
+advanced calculus نحن
+
+374
+00:41:42,300 --> 00:41:47,620
+لدينا نقطة
+
+375
+00:41:47,620 --> 00:41:52,360
+الأولى كيرفيتشا
+
+376
+00:41:52,360 --> 00:42:04,820
+كذا عرفنا سابقا على انهعلى DSL لكن عمليا يا بنات
+
+377
+00:42:04,820 --> 00:42:09,320
+هو طول ال cross product ما بين ال velocity و ال
+
+378
+00:42:09,320 --> 00:42:15,360
+acceleration على طول ال VTK هذه العلاقة الأولى
+
+379
+00:42:15,360 --> 00:42:17,940
+العلاقة الثانية
+
+380
+00:42:37,370 --> 00:42:48,850
+محدد x dot y dot z dot x double dot y double dot z
+
+381
+00:42:48,850 --> 00:42:50,210
+double dot
+
+382
+00:42:53,660 --> 00:43:02,120
+Y triple dot Z triple dot كله مقسوما على طول V
+
+383
+00:43:02,120 --> 00:43:12,720
+cross A كل تربيع بس بشرط ان D cross هذا لايساوي
+
+384
+00:43:12,720 --> 00:43:18,120
+Zero V cross A لايساوي Zero
+
+385
+00:43:22,040 --> 00:43:26,440
+نيجي نفسر الكلام اللي احنا كاتبينه هذا لإننا بدنا
+
+386
+00:43:26,440 --> 00:43:29,400
+نستخدمه عمليا في الشغل
+
+387
+00:43:58,580 --> 00:44:05,660
+الكيربتشار كدا هي طول الـ DT على DS أو DT ضربناها
+
+388
+00:44:05,660 --> 00:44:11,560
+على DT في DT على DS وقلنا واحد على طول ال V في طول
+
+389
+00:44:11,560 --> 00:44:16,220
+ال DT على DT هذا السابق لكن هنا عشان اقول ان احنا
+
+390
+00:44:16,220 --> 00:44:17,420
+جيبنا ال velocity V
+
+391
+00:44:35,490 --> 00:44:41,330
+مشتقت كل من ال X و Y و Z
+
+392
+00:44:45,640 --> 00:44:49,800
+عشان انا بقول R of T بقول X of T في اتجاه ال I و I
+
+393
+00:44:49,800 --> 00:44:52,780
+of T في اتجاه ال Z و Z of T في اتجاه ال K جيبلي
+
+394
+00:44:52,780 --> 00:44:55,920
+فيه يبقى جيبلي المشتقة الأولى إذا هدولة السطر
+
+395
+00:44:55,920 --> 00:45:02,320
+الأول في المحدد هي مراكبات الصراع بعد هيك هذه
+
+396
+00:45:02,320 --> 00:45:07,460
+double dot مراكبات مين العجلة ال accelerator
+
+397
+00:45:07,460 --> 00:45:13,810
+المشتقة الثانية ل R of T طب هذهمشتقت من العجلة،
+
+398
+00:45:13,810 --> 00:45:18,050
+مشتقت مراكبات العجلة، إذا الصف الأول هو مراكبات
+
+399
+00:45:18,050 --> 00:45:22,390
+السرعة، الصف الثاني هو مراكبات العجلة، الصف الثالث
+
+400
+00:45:22,390 --> 00:45:27,570
+مراكبات مشتقة العجلة، المقام V cross V هو اللي
+
+401
+00:45:27,570 --> 00:45:33,080
+اتكلمنا عليه فهمالكل تربيع وهذه وسيلة عملية أسهل
+
+402
+00:45:33,080 --> 00:45:38,480
+عمليا في الحساب من الحالة الأولى اللى أوجدناها قبل
+
+403
+00:45:38,480 --> 00:45:44,640
+قليل نعطي مثال على كل هذا الكلام ال T و ال N و ال
+
+404
+00:45:44,640 --> 00:45:48,140
+curvature و ال torsion كله نحسب و ال by normal
+
+405
+00:45:48,140 --> 00:45:57,700
+كمان نحسب كله بمثال example بيقول
+
+406
+00:45:57,700 --> 00:46:05,600
+ال headالـ R of T بدها السبب تلاتة Sin T في اتجاه
+
+407
+00:46:05,600 --> 00:46:16,280
+I زائد تلاتة Cos T في اتجاه J زائد أربعة T كله في
+
+408
+00:46:16,280 --> 00:46:31,270
+اتجاه K المقبض الأول نمر A أو قبل A باجي بقولهAt T
+
+409
+00:46:31,270 --> 00:46:45,310
+تساوي Pi على 2 Find نمرة A الـ T والـ M and الـ B
+
+410
+00:46:45,310 --> 00:46:50,390
+نمرة B The
+
+411
+00:46:50,390 --> 00:47:06,800
+equation The equation ofThe Norman Plague مرسي The
+
+412
+00:47:06,800 --> 00:47:15,540
+curvature The
+
+413
+00:47:15,540 --> 00:47:21,900
+curvature اللي هو كابا and the torsion
+
+414
+00:47:38,970 --> 00:47:44,330
+هذا طلب كل الشغلات اللي اتعرضنا لها اليوم ايش
+
+415
+00:47:44,330 --> 00:47:49,490
+بيقوللي هاتلي اول شيء ال T و ال N و ال B يفجأة بدي
+
+416
+00:47:49,490 --> 00:47:55,750
+اقوله بدي اخدله ال V اللي هي DR على DTرح نشتق هذه
+
+417
+00:47:55,750 --> 00:48:00,670
+الدالة ثم ثلاثة cosine T في اتجاه I ناقص ثلاثة
+
+418
+00:48:00,670 --> 00:48:07,590
+sine T في اتجاه J زائد أربعة في اتجاه M في اتجاه K
+
+419
+00:48:07,590 --> 00:48:13,970
+لكي أحصل على T سوف أحصل عليه قدر اللي هو Velocity
+
+420
+00:48:13,970 --> 00:48:19,710
+V يبقى هذا قدر 4K في اتجاه K مظهر طيب يبقى يجب أن
+
+421
+00:48:19,710 --> 00:48:21,290
+أحصل عليه قول V
+
+422
+00:48:25,220 --> 00:48:33,440
+لتسعة cosine تربية T زائد تسعة sin تربية T زائد
+
+423
+00:48:33,440 --> 00:48:38,680
+ستة عشر ويساوي الجدر التربية يعني لو أخدنا تسعة
+
+424
+00:48:38,680 --> 00:48:43,000
+عامل مشترك ويظل sin تربية زائد وcos تربية واحد
+
+425
+00:48:43,000 --> 00:48:49,340
+يفجأ تسعة زائد ستة عشر يفجأ تسعة خمسة إذا بدي ال
+
+426
+00:48:49,340 --> 00:48:55,500
+unit tangent vector اللي طالبهفباجي بقوله T بدها
+
+427
+00:48:55,500 --> 00:49:01,140
+تساوي ال V على طول ال V ويرساوى الآن بدنا نقسم على
+
+428
+00:49:01,140 --> 00:49:07,560
+خمسة يبقى تلت أخمس cosine T في اتجاه ال I نقص تلت
+
+429
+00:49:07,560 --> 00:49:14,700
+أخمس sine T في اتجاه ال J زائد أربع أخمس في اتجاه
+
+430
+00:49:14,700 --> 00:49:21,510
+ال Kقال احسبلي هالشغلات هذه كلها عند T تساوي باي
+
+431
+00:49:21,510 --> 00:49:27,270
+على اتنين يبقى بقدر اقوله T عند ال باي على اتنين
+
+432
+00:49:27,270 --> 00:49:32,790
+بدها تساوي Cos باي على اتنين Zero مع السلامة غير
+
+433
+00:49:32,790 --> 00:49:37,490
+مقصوف عليها Sin باي على اتنين بواحد في ناقص تلت
+
+434
+00:49:37,490 --> 00:49:43,690
+أخمس في ناقص تلت أخمس في اتجاه ال J
+
+435
+00:49:52,620 --> 00:49:59,500
+بتجاه الـ K مافيش رأيك لو جربتي و حسبتي ال V عند
+
+436
+00:49:59,500 --> 00:50:07,820
+ال Y على 2 V عند ال Y على 2 هذا كم؟ Zero مع السلمة
+
+437
+00:50:07,820 --> 00:50:16,560
+وهذه واحد يبقى ناقص تلاتة جيب زائد أربعة Kجيبناله
+
+438
+00:50:16,560 --> 00:50:22,460
+T بده يقول ال principle normal vector يبقى ال N
+
+439
+00:50:22,460 --> 00:50:31,940
+بده يساوي يالا بره بدنا ال N يبقى نروح نشتغله T
+
+440
+00:50:31,940 --> 00:50:38,780
+يبقى قبل تجيب ال N بدك تجيب مشتقتي ال T لازم أقوله
+
+441
+00:50:38,780 --> 00:50:41,900
+هاي ال DT على DT
+
+442
+00:50:47,890 --> 00:50:53,690
+سين تي في اتجاه ال I ناقص ثلاث اشمس و سين تي في
+
+443
+00:50:53,690 --> 00:51:01,290
+اتجاه ال جيه و هدف كدهش بزيرو نخسب طوله لبنات يبقى
+
+444
+00:51:01,830 --> 00:51:08,770
+قول الـ Dt على Dt وساعة الجدر التنبيهي لمربع
+
+445
+00:51:08,770 --> 00:51:16,030
+المركبات يبقى هنا تسعة على خمسة وعشرين تسعة على
+
+446
+00:51:16,030 --> 00:51:25,430
+خمسة وعشرين زائد تسعة على خمسة وعشرين طبعا يبقى
+
+447
+00:51:25,430 --> 00:51:26,630
+كداش
+
+448
+00:51:28,790 --> 00:51:34,950
+بتلاتة على خمسة في جدري اتنين طبعا بصير تسعة على
+
+449
+00:51:34,950 --> 00:51:39,050
+خمسة وعشرين في اتنين تسعة على خمسة وعشرين مربع
+
+450
+00:51:39,050 --> 00:51:44,890
+جدرها تلاتة اخمس بيظل جدري اتنين هذا من هذا اللي
+
+451
+00:51:44,890 --> 00:51:48,570
+هو طول ال DT على DT إذا انت قادر تعطيه ال
+
+452
+00:51:48,570 --> 00:51:56,320
+principle your normal N اللي هو مناللي هو Dt على
+
+453
+00:51:56,320 --> 00:52:07,400
+Dt على طول الـ Dt على Dt و يوسعى كيف؟ من وين؟ الـ
+
+454
+00:52:07,400 --> 00:52:10,600
+Dt على طول الـ Dt مش بناخد عامة مشترك منها اللي هي
+
+455
+00:52:10,600 --> 00:52:15,400
+sin تربيع زاد و sin تربيع مش .. في مشكلة في هذه؟
+
+456
+00:52:15,400 --> 00:52:22,100
+في هذه إيش المشكلة فيها؟ ربعي هذه و هذه
+
+457
+00:52:24,730 --> 00:52:36,410
+سنة .. سنة .. سنة .. أصابة ابراهيم وأخطاء عمار هذه
+
+458
+00:52:36,410 --> 00:52:46,770
+نجيب الطول تبعها يبقى square root 9 كيف؟ بس بس
+
+459
+00:52:46,770 --> 00:52:47,950
+كيف؟
+
+460
+00:52:53,700 --> 00:52:59,060
+أحنا نطقنا صح و كتبنا خطأ و لذلك بنقولك لما تحلل
+
+461
+00:52:59,060 --> 00:53:03,220
+في الامتحان للآخر خلي آخر خمس دقايق إجراح عليك
+
+462
+00:53:03,220 --> 00:53:07,280
+لازم تلاقي غلطة يعني حين هو هنكتب نكتب الكلمة
+
+463
+00:53:07,280 --> 00:53:11,100
+مرتين ورا بعض لما تلاقي مجه و راجع بنلاقيها يبقى
+
+464
+00:53:11,100 --> 00:53:14,900
+تدير بالك تطلع بتقول والله أنا ألف ألف حلت تجيب
+
+465
+00:53:14,900 --> 00:53:18,840
+انها ناقص عليك شغلات فيها غلط يبقى دائما هو ده
+
+466
+00:53:18,840 --> 00:53:24,460
+احنا بشروكنا بشرا بنخطأ وبننسى وما إلى ذلك لكن هذا
+
+467
+00:53:24,460 --> 00:53:28,500
+مرفوع عندنا عند الله بس عندنا احنا البشر لا بنحسبه
+
+468
+00:53:28,500 --> 00:53:31,980
+الغلطة بنحسبها عليكي طبعا القولين صلى الله عليه
+
+469
+00:53:31,980 --> 00:53:38,660
+وسلم رفع ان أمتي الخطأ والنسيان وما استكرهوا عليه
+
+470
+00:53:38,660 --> 00:53:44,100
+يبقى دي روابط كويس يبقى المربع الأولاني تسعة أخماس
+
+471
+00:53:47,930 --> 00:53:54,210
+اللي بعده زائد تسعة على خمسة وعشرين كتابنا صح ولم
+
+472
+00:53:54,210 --> 00:53:59,970
+أتأكد من غلطة يبقى تسعة على خمسة وعشرين كوصاين
+
+473
+00:53:59,970 --> 00:54:04,530
+تربيع T يبقى تلك اللي بناخد تسعة على خمسة وعشرين
+
+474
+00:54:04,530 --> 00:54:07,450
+بيبقى تسعة تربيع زائد كوصاين تربيع الواحد يبقى
+
+475
+00:54:07,450 --> 00:54:15,430
+النتيجة فقط تلت أخمس طيب إذا نجيب ال N اللي هو DT
+
+476
+00:54:15,430 --> 00:54:20,000
+على DT على طول ال DT على DTيبقى بدنا نقسم هذا كله
+
+477
+00:54:20,000 --> 00:54:25,980
+على مين أمانا على تلت أخماس بصير ناقص sin t في
+
+478
+00:54:25,980 --> 00:54:31,560
+اتجاه ال I ناقص cos t في اتجاه مين؟ في اتجاه ال J
+
+479
+00:54:31,560 --> 00:54:38,420
+بالمرة نحسبه عند ال I على 2 ان عند ال I على 2
+
+480
+00:54:38,420 --> 00:54:46,150
+تساوي ناقص Iجا تسعين واحد جا تسعين اثنين او صفر
+
+481
+00:54:46,150 --> 00:54:50,710
+اذا ماقدر اجيب ال by normal vector يبقى هذا كل
+
+482
+00:54:50,710 --> 00:54:56,350
+الحكي لازم ضمن المطلوب الاول من المسألة المطلوب
+
+483
+00:54:56,350 --> 00:55:03,250
+رقم A يبقى دلوقتي بيقولوا هنا لسه مخلصناش بدنا B
+
+484
+00:55:03,250 --> 00:55:10,690
+بيساوي T cross ال M يبقى على طول الخط باخد المحدد
+
+485
+00:55:10,690 --> 00:55:20,330
+I Jالـ T عند الـ Pi على 2 هنا بـ 0 و هنا بسادة تلت
+
+486
+00:55:20,330 --> 00:55:27,270
+أخمس و هنا بأربع أخمس لان نيجي لل end
+
+487
+00:55:32,190 --> 00:55:38,250
+by yourself بتفكير محدد باستخدام عناصر الصف التالت
+
+488
+00:55:38,250 --> 00:55:46,330
+يبقى هي ناقص واحد فيه عشق بصفه و عموده بصير أربع
+
+489
+00:55:46,330 --> 00:55:56,410
+أخماس J أربع أخماس J ناقص مع ناقص بصير زائد تلت
+
+490
+00:55:56,410 --> 00:56:00,430
+أخماس اللي هو K
+
+491
+00:56:03,240 --> 00:56:09,000
+يبقى صارت النتيجة ناقص أربع أخمس في اتجاه I ناقص
+
+492
+00:56:09,000 --> 00:56:14,800
+تلت أخمس في الجهة و التاني K يبقى هذا الشكل اللي
+
+493
+00:56:14,800 --> 00:56:21,960
+عندنا مرة تانية بقول يا بنات P يساوي T cross ال N
+
+494
+00:56:21,960 --> 00:56:27,800
+شيلنا T و حطينا مركبات عند البيعتين ناقص تلت أخمس
+
+495
+00:56:27,800 --> 00:56:33,420
+و أربع أخمس لجل L لل Nاللي هو بسالب واحد والباقي
+
+496
+00:56:33,420 --> 00:56:38,520
+بأسطار بنفكر باستخدام عناصر العموق الصف التالت ليش
+
+497
+00:56:38,520 --> 00:56:42,440
+انه فيه أسفار بسهل يبقى بصير ناقص واحد اشتر طف
+
+498
+00:56:42,440 --> 00:56:47,880
+وعموده بصير أربع أخماس J ناقص مع ناقص بصير زائد
+
+499
+00:56:47,880 --> 00:56:53,980
+تلت أخماس K دخلنا الناقص إذا انتهينا من المطلوب
+
+500
+00:56:53,980 --> 00:57:00,400
+الأول بنجد المطلوب التاني تبع من؟ تبع المسألة
+
+501
+00:57:03,260 --> 00:57:08,920
+المطلوب التاني قالوا بدي معادلة مين؟ ال normal
+
+502
+00:57:08,920 --> 00:57:15,500
+plane نرجع بالذاكرة إلى الوراق يبقى هذا من المحاور
+
+503
+00:57:15,500 --> 00:57:23,580
+التلاتة هذا T هذا M وهذا B هذا هو ال normal plane
+
+504
+00:57:23,580 --> 00:57:30,920
+مظبوط؟ يبقى هذا هو ال normal plane
+
+505
+00:57:32,560 --> 00:57:38,940
+مش هنجيب معادلة مستوى شو بيلزم نقمنها عمودي عليه و
+
+506
+00:57:38,940 --> 00:57:43,320
+نقطة تقع فيه تمام؟ الحمد لله العمودي عليه مين هو
+
+507
+00:57:43,320 --> 00:57:49,660
+هنا؟ T موجود عندي؟ اه موجود دي بيبدي نقطة يبقى
+
+508
+00:57:49,660 --> 00:57:57,640
+بيبدي نقطة تقع وين؟ في ال plane صح ولا لا طيب كويس
+
+509
+00:57:57,640 --> 00:58:04,490
+ال T و ال N و ال B مش هادئبالتاقة عندها نقطة ونقطة
+
+510
+00:58:04,490 --> 00:58:08,790
+موجودة على الملحانة يعني في الفرار إذا ماقدر أجيب
+
+511
+00:58:08,790 --> 00:58:16,670
+إحداثيات هذه النقطة الـMid الـNormal Plane يمر بها
+
+512
+00:58:16,670 --> 00:58:23,390
+النقطة اللي عندنا هذه النقطة P بتجيبها من وين؟
+
+513
+00:58:23,390 --> 00:58:27,770
+بتجيبها من راس المسألة يبقى احنا عندنا ال X
+
+514
+00:58:33,610 --> 00:58:38,410
+كان ليحسب الشغلات هذه وين عند T تسويقها طيب هذه X
+
+515
+00:58:38,410 --> 00:58:43,470
+و هذه Y و هذه Z لأن هشيل كل T و أحط مكانها يرجع
+
+516
+00:58:43,470 --> 00:58:51,990
+تصير تلاتة Sin باي على اتنين و تلاتة Cos باي على
+
+517
+00:58:51,990 --> 00:58:57,090
+اتنين و اربع في باي على اتنين بالشكل اللي عندنا
+
+518
+00:58:57,090 --> 00:59:01,130
+هذا اربعة تيجا تمام يرجع تصير
+
+519
+00:59:06,450 --> 00:59:14,950
+يبقى هذه النقطة التي يمر بها الكلب هي نقطة P يبقى
+
+520
+00:59:14,950 --> 00:59:23,210
+هذه هي نقطة P بالضبط تماما طيب P موجودة و T هو ال
+
+521
+00:59:23,210 --> 00:59:33,470
+normal vector ال T عند ال Pi على 2 is the normal
+
+522
+00:59:33,470 --> 00:59:34,370
+vector
+
+523
+00:59:46,570 --> 00:59:52,750
+إذا من خلال هذا باجي بقول ال X راحة عندنا في زير
+
+524
+01:00:25,100 --> 01:00:32,940
+النتيجة ناقص ثلاث أخماس Y زائد أربع أخماس Z هذا مع
+
+525
+01:00:32,940 --> 01:00:40,760
+السلامة تمنية Y على خمسة بعد ذلك اضغط بكله في خمسة
+
+526
+01:00:40,760 --> 01:00:42,000
+تخلص من القصور
+
+527
+01:01:02,710 --> 01:01:08,730
+المطموب الثاني نمربي هنا في المثل قال هذه ال
+
+528
+01:01:08,730 --> 01:01:12,410
+equation of the normal plane المطموب التالت يحتاج
+
+529
+01:01:12,410 --> 01:01:18,550
+إلى كيرفتشار كابا و تورشن تارهذه كامة عندي هذه
+
+530
+01:01:18,550 --> 01:01:26,230
+كامة V موجودة V موجودة حسبناها يا بنات؟ ماحسبناش
+
+531
+01:01:26,230 --> 01:01:32,050
+ال A يبقى بدنا نروح نحسب ال A عند ال Y على 2 وناخد
+
+532
+01:01:32,050 --> 01:01:40,770
+cross product ما بين ال 2 وقول ال V حسبناها؟
+
+533
+01:01:40,770 --> 01:01:40,950
+V
+
+534
+01:01:59,770 --> 01:02:07,990
+على دي P وين ال V؟ هاي سالب تلاتة sign T سالب
+
+535
+01:02:07,990 --> 01:02:15,570
+تلاتة sign T في اتجاه ال I و بعدها ناقص تلاتة و
+
+536
+01:02:15,570 --> 01:02:20,550
+sign T في اتجاه ال J و هدي فجر الفتحة على روحك و
+
+537
+01:02:20,550 --> 01:02:26,690
+نصلا مش تكتب Zero بدنا نحسب ال A عند ال Pi على
+
+538
+01:02:26,690 --> 01:02:27,270
+اتنين
+
+539
+01:02:32,310 --> 01:02:36,590
+يبقى صار الـ A موجود والـ V موجود فتعمل cross
+
+540
+01:02:36,590 --> 01:02:41,530
+product لهم وشوف قداشة قوة تبعه هيكون يبقى ناخده
+
+541
+01:02:41,530 --> 01:02:52,150
+الـ V cross الـ A يساوي I J K الـ V V هي سالب
+
+542
+01:02:52,150 --> 01:02:58,570
+تلاتة وأربعة يبقى Zero سالب تلاتة وأربعة لأنه
+
+543
+01:02:58,570 --> 01:02:59,370
+ماعندش I
+
+544
+01:03:14,110 --> 01:03:21,150
+مرة واحدة لأن فيها أسفار كتير ناقص تلاتة وشطر صفه
+
+545
+01:03:21,150 --> 01:03:30,950
+وعموده 4G زائد تلاتة K أول
+
+546
+01:03:30,950 --> 01:03:40,830
+شهدتم فقولوا ناقص تلاتةنقص تسعة كيلو أحنا بنقدر
+
+547
+01:03:40,830 --> 01:04:01,150
+نجيب الكيربتشا بسهولة بدون مشاكل طيب
+
+548
+01:04:01,150 --> 01:04:08,470
+بدنا نجيب الكيربتشاكذا اللي هو طول ال V cross ال A
+
+549
+01:04:08,470 --> 01:04:15,470
+مقسوما على طول ال V تكعيب هذا الكلام وايه و ساوي
+
+550
+01:04:15,470 --> 01:04:21,070
+الآن بدأ نجي لطول المتجه هذا يبقى اللي هو مين
+
+551
+01:04:21,070 --> 01:04:27,830
+الجدري الترفيهي ل 12 في 12 مية و أربعة و أربعين
+
+552
+01:04:27,830 --> 01:04:37,180
+زاد 9 في 9 و 1 و 80كل هذا مقصودا وين طول ال V؟ طول
+
+553
+01:04:37,180 --> 01:04:39,260
+ال V هي خمسة
+
+554
+01:05:02,160 --> 01:05:04,960
+مقدار الكيروفيتشار
+
+555
+01:05:09,080 --> 01:05:14,560
+الـ X dot والـ Y dot والـ Z dot هي .. مظبوط؟ الـ A
+
+556
+01:05:14,560 --> 01:05:21,000
+الـ acceleration هي عند الـ Y على 2 هي جاذب،
+
+557
+01:05:21,000 --> 01:05:29,920
+ضالمين أنه الـ X double dot يعني بدنا نشتغل الـ D
+
+558
+01:05:29,920 --> 01:05:39,060
+A على D T يساوي، هي الـ A اللي هو ناقص 3وSin T في
+
+559
+01:05:39,060 --> 01:05:46,720
+اتجاه I زائد تلاتة Sin T في اتجاه الـ J هذا معناه
+
+560
+01:05:46,720 --> 01:05:56,440
+ان ال DA على DT عند من عند ال PI على اتنين يساوي
+
+561
+01:05:56,440 --> 01:06:07,820
+هذه Zero وهذه تلاتة J إذا بقدر احسب لهاللي هو main
+
+562
+01:06:07,820 --> 01:06:13,740
+اللي هو torsion tower قول
+
+563
+01:06:13,740 --> 01:06:24,300
+ال V مش لازم طبعا خلصنا منه و هذا مش لازم و ال
+
+564
+01:06:24,300 --> 01:06:32,940
+normal مش لازم هاي
+
+565
+01:06:32,940 --> 01:06:42,540
+نيجي الآنطورشين تاب بدي ساوي المحدد X dot Y dot Z
+
+566
+01:06:42,540 --> 01:06:49,080
+dot X double dot Y double dot Z double dot X
+
+567
+01:06:49,080 --> 01:06:54,960
+triple dot Y triple dot Z triple dot كله مقسوما
+
+568
+01:06:54,960 --> 01:07:01,060
+على قول ال V cross ال A أظن تربيه هيك يا بنات صح؟
+
+569
+01:07:01,060 --> 01:07:06,820
+تمام يبقى هذا الكلام بدي ساوي المحددمُركّبات
+
+570
+01:07:06,820 --> 01:07:14,400
+السرعة هي يبقى Zero و سالم تلاتة و أربعة مُركّبات
+
+571
+01:07:14,400 --> 01:07:25,160
+العجلة الـ A الـ A عند الـ Y على الـ N و ناقص
+
+572
+01:07:25,160 --> 01:07:33,620
+تلاتة I ناقص تلاتة Zero Zero مُركّبات المشتقة هي
+
+573
+01:07:34,010 --> 01:07:41,030
+تلاتة جيه يبقى Zero تلاتة Zero بالشكل هذا بيكروس
+
+574
+01:07:41,030 --> 01:07:45,830
+ال A طوله تبعها بيكروس ال A اللي بيبقى خمستاشر
+
+575
+01:07:45,830 --> 01:07:52,270
+مضبوط على خمستاشر الكوال تربيت يبقى هذا الكلام بده
+
+576
+01:07:52,270 --> 01:07:56,190
+يساوي ايش رأيك قبل ان اتفككوا باستخدام عناصر
+
+577
+01:07:56,190 --> 01:08:00,870
+العمود التالت يبقى هى R
+
+578
+01:08:08,340 --> 01:08:15,820
+مظبوط على كداش على خمس عشر تربية يبقى هذا الكلام
+
+579
+01:08:15,820 --> 01:08:22,900
+يصير ناقص فهنا أربعة على هذه تلاتة في خمسة و تلاتة
+
+580
+01:08:22,900 --> 01:08:27,140
+في خمسة تلاتة في تلاتة تسعة من الخمسة تربية ناقص
+
+581
+01:08:27,140 --> 01:08:32,520
+أربعة على خمسة وعشرين هذا مقدار ال torsion اللي
+
+582
+01:08:32,520 --> 01:08:32,760
+عادي
+
+583
+01:08:36,620 --> 01:08:41,480
+اللي عند هنا stop انتهى ال section وإلى يكون أرقام
+
+584
+01:08:41,480 --> 01:08:50,700
+المسائل exercises اللي هو تلتاشر كامسة المسائل من
+
+585
+01:08:50,700 --> 01:08:57,340
+واحد إلى ستاشر ال odd بالإضافة إلى سؤال
+
+586
+01:09:15,480 --> 01:09:22,360
+أيش مانا partial يبقى partial derivatives المشتقات
+
+587
+01:09:22,360 --> 01:09:30,740
+الجزدية احنا اللي درسناها قبل ذلك where في
+
+588
+01:09:30,740 --> 01:09:37,420
+calculus a و b و لغاية اليوم في z كان كله بناخد ال
+
+589
+01:09:37,420 --> 01:09:43,960
+function ده اللي في متغير واحديبقى ناخد ال
+
+590
+01:09:43,960 --> 01:09:49,600
+function لو كانت ده اللي أكتر من متغير يبقى بنجي
+
+591
+01:09:49,600 --> 01:09:55,480
+لأول section اللي هو اربعة عشر واحد اللي هو
+
+592
+01:09:55,480 --> 01:10:00,120
+functions of
+
+593
+01:10:00,120 --> 01:10:04,260
+several variables
+
+594
+01:10:09,720 --> 01:10:16,640
+الدوال في عدة متغيرات يبقى من الآن فصاعدا الشبطر
+
+595
+01:10:16,640 --> 01:10:21,100
+هذا اربعتاشر واللي جاي تبع التكامل هيكون عندي
+
+596
+01:10:21,100 --> 01:10:28,200
+متغيرين او تلاتة او اربعة او ان من المتغيرات يبقى
+
+597
+01:10:28,200 --> 01:10:32,620
+بهجة بقول these functions
+
+598
+01:10:45,580 --> 01:10:54,320
+ممكن أقول يا بنات z function في x و y إذا صارت
+
+599
+01:10:54,320 --> 01:11:01,280
+الاقتران z أو الدالة z دالة فيه متغيرين x و y ممكن
+
+600
+01:11:01,280 --> 01:11:05,080
+يكون ال w function في x
+
+601
+01:11:08,210 --> 01:11:15,230
+يبقى الأولى دالة في متغيرين التانية دالة في تلاتة
+
+602
+01:11:15,230 --> 01:11:21,330
+متغيرات مش هاجدكوا بس ممكن يكون دالة في N من
+
+603
+01:11:21,330 --> 01:11:29,370
+المتغيرات كيف؟ لو كان يقولنا مثلا Y تساوي F of X1
+
+604
+01:11:29,370 --> 01:11:34,790
+X2 X3 وظلينا ماشيين لغاية ال X
+
+605
+01:11:39,950 --> 01:11:47,390
+يعني الحالة هذه بقول F دالة في N من المتغيرات تمام
+
+606
+01:11:47,390 --> 01:11:53,690
+طب الآن بدنا نعرف شو ال domain تبع هذه الدوال و ال
+
+607
+01:11:53,690 --> 01:11:58,590
+range تبع هذه الدوال هل هو زي تبع calculus A و
+
+608
+01:11:58,590 --> 01:12:03,230
+الله مختلف عنه نوعا ما طبعا في calculus A بجينا
+
+609
+01:12:03,230 --> 01:12:08,910
+ناخد ال domain هو interval و ال range هو كذلك main
+
+610
+01:12:09,230 --> 01:12:15,530
+Interval صح ولا لأ؟ هل هذا الكلام ليزال كما هو؟
+
+611
+01:12:15,530 --> 01:12:19,610
+والله صار فيه بعض الخلافات بالنسبة لل functions of
+
+612
+01:12:19,610 --> 01:12:26,050
+several variables مش هنغير، هبدأ بأمثلة على ذلك
+
+613
+01:12:26,050 --> 01:12:29,810
+أول مثال
+
+614
+01:12:40,210 --> 01:12:45,310
+أول مثال بروزي F الـ
+
+615
+01:12:45,310 --> 01:12:57,530
+F of XY يساوي لان F تعيقظ XY زائد Y ناقص واحد
+
+616
+01:13:20,110 --> 01:13:32,190
+يبقى بالصين لن لمن؟ ال X بي E و ال Y واحد في E ذات
+
+617
+01:13:32,190 --> 01:13:40,870
+Y يبقى واحد ناقص واحد يبقى بضال قداش لن لل E لن لل
+
+618
+01:13:40,870 --> 01:13:48,920
+E قداش ممتاز جداقيمة الدالة عند النقطة اللي احدث
+
+619
+01:13:48,920 --> 01:13:54,240
+إيها E و واحد هيقدر قيمة واحدة اللي هي واحد و
+
+620
+01:13:54,240 --> 01:13:58,060
+أقيسي على ذلك نخش على ال domain أو ال range
+
+621
+01:13:58,060 --> 01:14:11,380
+example two you will find the domain and range
+
+622
+01:14:18,090 --> 01:14:24,590
+of the following functions
+
+623
+01:14:24,590 --> 01:14:28,770
+f
+
+624
+01:14:28,770 --> 01:14:32,510
+of
+
+625
+01:14:32,510 --> 01:14:40,910
+x و f of y يبدو يساوي len نقص
+
+626
+01:14:40,910 --> 01:14:43,710
+y زائد واحد
+
+627
+01:14:51,780 --> 01:15:00,180
+هو يحاول أن يحسب الـ Range لـ F جدكي
+
+628
+01:15:11,020 --> 01:15:16,000
+هو علاقة دلوقت باجي بقولك كويس f of x y هي ال len
+
+629
+01:15:16,000 --> 01:15:22,100
+دي شغلة الكميات مجموعة مع بعضها و قداش ال domain
+
+630
+01:15:22,100 --> 01:15:29,160
+أو ال len و قداش بتكون معرفة إذا كانكل اللي جوا لن
+
+631
+01:15:29,160 --> 01:15:33,880
+عدد و العدد ده أكبر من Zero إذا لن غير معرفة لكمية
+
+632
+01:15:33,880 --> 01:15:38,260
+سالبة و غير معرفة Little يبقى بد المقدار بين
+
+633
+01:15:38,260 --> 01:15:46,020
+القوسين يكون ماله أكبر من Zero كويس يبقى بد 2X
+
+634
+01:15:46,020 --> 01:15:54,040
+ناقص Y زائد واحد greater than Zero أو ممكن اكتبها
+
+635
+01:15:54,040 --> 01:15:55,320
+بشكل آخر
+
+636
+01:16:01,410 --> 01:16:09,930
+أقل من اتنين X زاوية واحدة طب ويه تساوي اتنين X
+
+637
+01:16:09,930 --> 01:16:15,450
+زاوية واحدة؟ ماعرفتش يا بناتي مستقيم اذا لو حبيت
+
+638
+01:16:15,450 --> 01:16:20,790
+ارسمها على الطريقة دي ماكان برسم ال domain مارسمش
+
+639
+01:16:20,790 --> 01:16:25,360
+الدالة الأصلية اللي عندي هذاهذه بدلا من قرص رسمها
+
+640
+01:16:25,360 --> 01:16:29,880
+هذه غير على جهاز الكمبيوتر برسمها انها شكل مجسمات
+
+641
+01:16:29,880 --> 01:16:35,300
+بصيفة فرحة يبقى انا برسم ال domain فقط فاجي بيقول
+
+642
+01:16:35,300 --> 01:16:40,360
+لو جيت هنا خدت محاول الشكل اللي قلنا هذا وقولت هذا
+
+643
+01:16:40,360 --> 01:16:48,720
+محور X وهذا محور Y وهذه نقطة الأصل اللي هي Z الخط
+
+644
+01:16:48,720 --> 01:16:56,160
+Y تسوي Xمنصف من الرابع الأول والرابع الثالث اتنين
+
+645
+01:16:56,160 --> 01:17:02,440
+اكس يبقى تقريب على مين؟ على محور Y زائد واحد شفت
+
+646
+01:17:02,440 --> 01:17:07,900
+إلى أعلى بمقدار واحد إذا لو كانت هذه النقطة هي
+
+647
+01:17:07,900 --> 01:17:15,020
+Zero و واحد، سيأتي الخط اللي بنقطها دبنات بالشكل
+
+648
+01:17:15,020 --> 01:17:15,580
+اللي عندنا
+
+649
+01:17:19,140 --> 01:17:25,800
+طب ليش رسمته مُنَقَر؟ ماعنديش يساوي طب why أقل من
+
+650
+01:17:25,800 --> 01:17:33,180
+هذا الخط؟ يبقى كل المساحة المظللة اللي عندنا لأسفل
+
+651
+01:17:33,180 --> 01:17:39,000
+هذا الخط يبقى يا بناتي ال domain هنا هي ال area
+
+652
+01:17:39,000 --> 01:17:47,380
+اللي بين لأسفل هذا الخط يبقى هذه هي ال area down
+
+653
+01:17:58,320 --> 01:18:04,140
+هل النقاط اللي على الخط من ضمن هذا ال domain لأ
+
+654
+01:18:04,140 --> 01:18:09,940
+لأنه أقل منماعنديش يساوي لو كان فيه يساوي كرسمتك
+
+655
+01:18:09,940 --> 01:18:15,560
+الخط هذا متواصل يبقى نظرا لإن نقاط الخط ليست من
+
+656
+01:18:15,560 --> 01:18:21,480
+ضمن ال domain رسمتلك نقطة يبقى كل المساحة المضللة
+
+657
+01:18:21,480 --> 01:18:25,700
+لأسفل هذا الخط تعتبر هي ال domain إذا انت خلف عن
+
+658
+01:18:25,700 --> 01:18:30,200
+Calculus A Calculus A كان Interval هنا طلعت ايش
+
+659
+01:18:30,200 --> 01:18:34,400
+مساحة و يمكن تطلع حجم كمان يا بنات ال domain مش
+
+660
+01:18:34,400 --> 01:18:39,890
+هاجد المساحةكما سنرى من خلال الأمثلة يبقى هذا هو
+
+661
+01:18:39,890 --> 01:18:47,510
+المثال الأول اروح للمثال الثاني ال range اه طيب ال
+
+662
+01:18:47,510 --> 01:18:52,190
+len لو رجعتي لمنحنى ال len تبع calculus B ال len
+
+663
+01:18:52,190 --> 01:18:57,930
+من وين لوين مش ذاكرين منحنى .. تبع calculus A كان
+
+664
+01:18:57,930 --> 01:19:03,610
+منحنى ال len في الشكل اللي عندك هذا ايه كان هذا
+
+665
+01:19:03,610 --> 01:19:03,970
+محور
+
+666
+01:19:06,700 --> 01:19:12,480
+وهذا Y تساوي لن X وهذا النقطة هي واحد وزيرو تمام
+
+667
+01:19:12,480 --> 01:19:18,540
+بعد الواحد قيمة موجبة قبل الواحد لزيرو كل كمية
+
+668
+01:19:18,540 --> 01:19:24,600
+سالب لأسفل مخر X لكن بعد زيرو هي القيمة الأعلى مخر
+
+669
+01:19:24,600 --> 01:19:29,060
+X فكان ال range قداش من سالب infinity لإنفنيت يعني
+
+670
+01:19:29,060 --> 01:19:35,730
+كل ال real life هل اتغير عندنا هنا ولا هويبقى هنا
+
+671
+01:19:35,730 --> 01:19:41,650
+بظل كل set of real numbers يابتكت بيها set R
+
+672
+01:19:41,650 --> 01:19:47,970
+يابتكت بيها من سالب infinity لغة ال infinity as an
+
+673
+01:19:47,970 --> 01:19:53,690
+open interval بهذا الشكل سنصل إلى السؤال التاني
+
+674
+01:19:53,690 --> 01:20:00,790
+السؤال التاني ميعطيني f of x و y تساوي اللي هي
+
+675
+01:20:00,790 --> 01:20:09,180
+تلاتةفى الجدرى التربيعى لأربعة ناقص X تربيع ناقص Y
+
+676
+01:20:09,180 --> 01:20:15,080
+تربيع ناقص Y ناقص Y تربيع ناقص Y تربيع
+
+677
+01:20:15,080 --> 01:20:19,640
+ناقص Y تربيع ناقص Y تربيع ناقص Y تربيع ناقص Y
+
+678
+01:20:19,640 --> 01:20:19,640
+تربيع ناقص Y تربيع ناقص Y تربيع ناقص Y تربيع ناقص
+
+679
+01:20:19,640 --> 01:20:19,640
+Y تربيع ناقص Y تربيع ناقص Y تربيع ناقص Y تربيع
+
+680
+01:20:19,640 --> 01:20:19,720
+ناقص Y تربيع ناقص Y تربيع ناقص Y تربيع ناقص Y
+
+681
+01:20:19,720 --> 01:20:27,220
+تربيع ناقص Y تربيع ناقص Y تربيع ناقص
+
+682
+01:20:27,220 --> 01:20:30,100
+Y تربيع ناقص Y ت
+
+683
+01:20:33,280 --> 01:20:38,940
+الجدر هذا لكي يكون معرف يريد القيمة التي تحته أكبر
+
+684
+01:20:38,940 --> 01:20:45,280
+من أو تساوي zero تمام يبقى يريد كل الأربعة ناقص x
+
+685
+01:20:45,280 --> 01:20:49,460
+تربية ناقص y تربية greater than or equal to zero
+
+686
+01:20:49,460 --> 01:20:53,820
+او إن شئتوا فاقولوا انه بلي هدالة على الشجرة
+
+687
+01:20:53,820 --> 01:20:59,020
+التانية بس ال x تربية زائد y تربية أقل من أو يساوي
+
+688
+01:20:59,020 --> 01:21:05,110
+100الاربعة ماعادلتش هذه يساوي اربعة دائرة بس احنا
+
+689
+01:21:05,110 --> 01:21:09,530
+هنا لما نقول اقل من او يساوي بس مش على المحيط و بس
+
+690
+01:21:09,530 --> 01:21:16,430
+و جوا ليه باشي بتكون عندي disk قرص مصمت يعني كله
+
+691
+01:21:16,430 --> 01:21:21,270
+المحيط و النقاط اللي في داخليبقى هذا لو روحته
+
+692
+01:21:21,270 --> 01:21:27,110
+رسمته بياخد الشكل التالي هقول هذا محور X هذا محور
+
+693
+01:21:27,110 --> 01:21:31,630
+Y هذا نقطة الأصل اللي هو Zero عندي desk على شكل
+
+694
+01:21:31,630 --> 01:21:37,550
+دائرة الشكل هذا نصف
+
+695
+01:21:37,550 --> 01:21:43,270
+قطرها يساوي كم؟ يساوي اتنين يبقى كل المنطقة
+
+696
+01:21:43,270 --> 01:21:48,170
+المظللة هذه يبقى
+
+697
+01:21:48,170 --> 01:21:49,210
+هذه desk
+
+698
+01:21:51,680 --> 01:22:03,040
+with center at the origin and
+
+699
+01:22:03,040 --> 01:22:08,000
+radius اتنين
+
+700
+01:22:16,480 --> 01:22:24,040
+من سلب اتنين لاتنين وجهة نظر قد تكون صحيحة وقد
+
+701
+01:22:24,040 --> 01:22:32,260
+تقول خاطئة في تلاتة برا الجدرد تخفيها من الحساب؟
+
+702
+01:22:32,260 --> 01:22:36,760
+لأ يبقى من ناقص ستة لستة زي ما بتقولين من ناقص ستة
+
+703
+01:22:36,760 --> 01:22:42,220
+لستة صح؟ نقول من تلاتة فيها طبعا إجابة خاطئة بدنا
+
+704
+01:22:42,220 --> 01:22:49,410
+إجابة صحيةمصححة يعني هل القيمة اللى متحت الجدر هذه
+
+705
+01:22:49,410 --> 01:22:54,330
+ممكن تطلع قيمة سالمة؟ لأ لأ مش ممكنين يبقى السلم
+
+706
+01:22:54,330 --> 01:22:58,010
+اللى قولتيه غلط يعني من صفر لست من صفر لست من صفر
+
+707
+01:22:58,010 --> 01:23:06,710
+في تأكيد من صفر لست وجهة نظر يبقى من Zero لغاية
+
+708
+01:23:06,710 --> 01:23:12,470
+ستة شكليا انها نشوف هل هذا الكلام صحيح كيف؟
+
+709
+01:23:28,350 --> 01:23:36,690
+عند أقل قيمةلما يهدى ال X Y اللي هي Zero اللي هي
+
+710
+01:23:36,690 --> 01:23:41,830
+عند المركز في ال domain طلع النتج يساوي ستة طب
+
+711
+01:23:41,830 --> 01:23:44,930
+بدها يشوف عند أكبر قيمة ل X و Y
+
+712
+01:23:49,340 --> 01:23:55,960
+لو تساوى مجموع ال X تربية و Y تربية مع الأربعة لو
+
+713
+01:23:55,960 --> 01:24:01,280
+كان X بجدر اتنين و Y بجدر اتنين وربعنا يصير اربعة
+
+714
+01:24:01,280 --> 01:24:07,860
+ناقص اربعة يساوي كم؟ Zero Zero معناته في تلاتة في
+
+715
+01:24:07,860 --> 01:24:10,000
+أقل من Zero
+
+716
+01:24:13,100 --> 01:24:17,960
+بالشمكالية يستحيل ان اقل قيمة باخدها ال range هي
+
+717
+01:24:17,960 --> 01:24:23,620
+zero اكبر قيمة باخدها ال six فقط لا غير كلام صحيح
+
+718
+01:24:23,620 --> 01:24:29,600
+طيب ناخد نمرة C نمرة
+
+719
+01:24:29,600 --> 01:24:37,780
+تلاتة ناخد ال F X Y و7 اللي هو الجدري التربيعي ل X
+
+720
+01:24:37,780 --> 01:24:40,880
+تربيع زائد Y تربيع نقطة
+
+721
+01:24:46,980 --> 01:24:55,420
+بدي أعرف ال domain موافق
+
+722
+01:24:55,420 --> 01:25:01,720
+موافق يبقى هنا بدنا ال X تربيه زاد Y تربيه نقص 9
+
+723
+01:25:01,720 --> 01:25:07,800
+تكون greater than or equal to 0 وإيش كمان؟ بدي ال
+
+724
+01:25:07,800 --> 01:25:14,020
+X نقص ال Y ممنوع تساوي 0 وقول والله كويس طب بدنا
+
+725
+01:25:14,020 --> 01:25:19,980
+نصيغها صياغة أخرىيبقى شباجي بيقول ال X تربيه زائد
+
+726
+01:25:19,980 --> 01:25:25,800
+Y تربيه أكبر من أو يسوى تسعة وال Y ممنوع تساوي ال
+
+727
+01:25:25,800 --> 01:25:30,380
+X مظبوط
+
+728
+01:25:30,380 --> 01:25:36,180
+وال Y ممنوع تساوي ال X نشوف الحكي هنا شو شكله على
+
+729
+01:25:36,180 --> 01:25:40,720
+الطبيعة حاول نفهمفبقى يقول هذه معادلة ايش اصلا
+
+730
+01:25:40,720 --> 01:25:45,960
+جاملة الانقلتية يبقى دائرة يبقى لو روحت رسام و قول
+
+731
+01:25:45,960 --> 01:25:51,900
+هذا الملحونة اللي عندنا هذا محور X هذا محور Y فهذا
+
+732
+01:25:51,900 --> 01:25:57,920
+نقطة أصلي Zero وهي الدائرة طيب تمام ايش قال لي؟
+
+733
+01:25:57,920 --> 01:26:06,260
+قال لي أكبر من أو يساوي تسعة يبقى وين؟ برا الدائرة
+
+734
+01:26:06,700 --> 01:26:14,200
+برا يبقى المنطقة هذه المنطقة المضللة بالأدرى طب
+
+735
+01:26:14,200 --> 01:26:20,620
+الخط Y تساوي X يبقى هذا الخط اللي علناه في التراث
+
+736
+01:26:20,620 --> 01:26:27,460
+مانيكا من القرن هذا الخط
+
+737
+01:26:27,460 --> 01:26:34,220
+Y تساوي X يبقى
+
+738
+01:26:34,950 --> 01:26:40,990
+كل نقطة تقع على هذا الخط لازم تكون برا من؟ برا
+
+739
+01:26:40,990 --> 01:26:45,770
+الدمان، ممنوع يحصل تساوي، كويس؟ يعني طلع لما نقول
+
+740
+01:26:45,770 --> 01:26:50,270
+في كل المنطقة اللي برا الدائرة، هنا نقاط هي موجودة
+
+741
+01:26:50,270 --> 01:26:53,950
+برا الدائرة، مظبوط ولا لا؟ نقاط ليه بيبقى ممنوع
+
+742
+01:26:53,950 --> 01:26:59,160
+هاد تكون من ضمن الدمان؟يبقى المنطقة المظللة خارج
+
+743
+01:26:59,160 --> 01:27:05,320
+الدائرة والتي لا تقع على الخط اللي هو Y تساوي X
+
+744
+01:27:05,320 --> 01:27:14,520
+طيب بدنا ال range يا الله أشوف اللي فوق أظن موجة
+
+745
+01:27:14,520 --> 01:27:21,180
+اللي فوق البسط على طول الخط بقى تبني قيمة موجة بعد
+
+746
+01:27:21,180 --> 01:27:28,440
+الصفرمن عندى التلاتة ما يمكن أن يكون سالم بالمرة
+
+747
+01:27:28,440 --> 01:27:36,960
+طب لو قلتلك خدي ال X باتنين و Y بتلاتة X باتنين و
+
+748
+01:27:36,960 --> 01:27:45,540
+Y بتلاتة مقرف عنده ولا لا؟ يبقى مخمطات الشيء صح؟
+
+749
+01:27:46,430 --> 01:27:50,810
+يعني المقام يبقى ممكن يكون موجة وممكن يكون سالب إن
+
+750
+01:27:50,810 --> 01:27:55,630
+استبعدت الصفر بس المساواة بين X وY يبقى ممكن يكون
+
+751
+01:27:55,630 --> 01:28:02,680
+سالب وممكن يكون موجةتاخد السالب كله و الموجات كله
+
+752
+01:28:02,680 --> 01:28:07,180
+معقول تاخد السالب كله معقول كيف مش معقول كل ال bus
+
+753
+01:28:07,180 --> 01:28:12,360
+كل متى ال bus خمسين على سبيل المثال و جيت انا لجيت
+
+754
+01:28:12,360 --> 01:28:18,220
+الفرق بين x و y واحد من مين واحد من الف تبقى بصير
+
+755
+01:28:18,220 --> 01:28:22,780
+واحد على الف الف اطلع وين فوق و خمسين تصير خمسين
+
+756
+01:28:22,780 --> 01:28:28,700
+الفطب لو كان سالب في سالب خمسين اللي يبقى هذا رايح
+
+757
+01:28:28,700 --> 01:28:31,840
+على المال النهائي و هذا رايح نويل لسالب infinity
+
+758
+01:28:31,840 --> 01:28:37,400
+كل ال real line يبقى ال range هنا كل ال real line
+
+759
+01:28:37,400 --> 01:28:42,520
+بالاستثناء من سالب infinity إلى infinity طيب اعطنك
+
+760
+01:28:42,520 --> 01:28:48,840
+الآن ثلاثة أمثلة و كلها زي ما انت شايفة area و ال
+
+761
+01:28:48,840 --> 01:28:52,320
+range هو interval طب خدلي لمرة أربع
+
+762
+01:29:00,150 --> 01:29:07,690
+بتساوي الجدري التربيعي لواحد ناقص X تربيع ناقص Y
+
+763
+01:29:07,690 --> 01:29:14,190
+تربيع على أربعة ناقص Z تربيع على تسعة
+
+764
+01:29:21,210 --> 01:29:27,050
+السؤال وجهي بتقول زميلتكوا ممكن ال domain يطلع صفر
+
+765
+01:29:27,050 --> 01:29:33,850
+ولا لا يمكن الرجع ممكن الرجع يطلع صفر ولا لا نعم
+
+766
+01:29:33,850 --> 01:29:42,230
+ممكن وقتى تدرسر المقام اكبر ما يمكن طيب
+
+767
+01:29:42,230 --> 01:29:46,830
+الان بدنا نيجي لل domain تبع ال F بدي كل الكمية
+
+768
+01:29:46,830 --> 01:29:50,450
+اللى تحت الجدر اكبر
+
+769
+01:29:51,360 --> 01:29:56,340
+من أو تساوي zero صحيح ولا لأ يبقى بالدنيا أقوله
+
+770
+01:29:56,340 --> 01:30:02,500
+الآن اللي هو بدي الواحد ناقص x تربيه ناقص y تربيه
+
+771
+01:30:02,500 --> 01:30:07,140
+على أربع ناقص z تربيه على تسعة تكون أكبر من أو
+
+772
+01:30:07,140 --> 01:30:10,220
+تساوي zero أو انشرته وانفقه
+
+773
+01:30:13,160 --> 01:30:19,040
+زي تربيع على اربعة زي زد تربيع على تسعة ماله يكون
+
+774
+01:30:19,040 --> 01:30:24,560
+اقل من او يساوي الواحد طب هذه لو قلت يساوي واحد
+
+775
+01:30:24,560 --> 01:30:29,720
+معادلة ايش يا بنات؟ ellipsoid طب الاستطالة في
+
+776
+01:30:29,720 --> 01:30:35,780
+اتجاه مين؟ زد زي اللي تحتيه اكبر مايمكن اذا لو
+
+777
+01:30:35,780 --> 01:30:41,840
+روحت اخدت محاولة بالشكل اللي عندها ذلك وقلتهذا
+
+778
+01:30:41,840 --> 01:30:48,640
+محور X هذا Y وهذا Z ومديت هذا على سيقانته وروحت
+
+779
+01:30:48,640 --> 01:30:54,700
+رسم ال ellipsoid فكان ال ellipsoid الشكل اللي
+
+780
+01:30:54,700 --> 01:31:02,780
+عندنا وهنا شكل هذا هذا مش هيضغرني وهذا نقطة أصلي
+
+781
+01:31:02,780 --> 01:31:07,500
+وزيرة يبقى هذا ال ellipsoid اللي عندنا يبقى هذا
+
+782
+01:31:07,500 --> 01:31:13,820
+مين؟الـ interior تبع الـ ellipsoid زي الـ boundary
+
+783
+01:31:13,820 --> 01:31:22,440
+كل الشكل الخارجي يبقى هنا بسميه الـ interior and
+
+784
+01:31:22,440 --> 01:31:28,680
+ال boundary of
+
+785
+01:31:28,680 --> 01:31:37,280
+the ellipsoid طيب
+
+786
+01:31:39,170 --> 01:31:43,350
+الـ Range يلّا
+
+787
+01:31:43,350 --> 01:31:53,710
+نشوف الـ Range أيوة
+
+788
+01:31:53,710 --> 01:31:56,810
+يلّا
+
+789
+01:31:56,810 --> 01:32:03,110
+أولى شوفي السفر كم يطلع موافق يلّا بدي كمان يبقى
+
+790
+01:32:03,110 --> 01:32:08,050
+عند 0000 تطلع القيمة ال function هي واحدة غيره
+
+791
+01:32:12,450 --> 01:32:18,070
+هذه أكبر قيمة ولا أقل قيمة؟ أقل قيمة. أقل قيمة
+
+792
+01:32:18,070 --> 01:32:21,350
+اللي هي الواحد، يعني بدرجة أكبر منها. تقدر تجيبولي
+
+793
+01:32:21,350 --> 01:32:26,690
+و لو قيمة واحدة تكون أكبر منها؟ إذا بتجيبولي كمان
+
+794
+01:32:26,690 --> 01:32:33,750
+قيمة بتكون و أنتوا .. جيبولي قيمة واحدة بس تكون
+
+795
+01:32:33,750 --> 01:32:38,150
+أكبر من الواحدة؟اللي جيبها تاخدها و الله غير
+
+796
+01:32:38,150 --> 01:32:41,330
+احطلها اربعين من اربعين في اعمال الفصل من دول
+
+797
+01:32:41,330 --> 01:32:45,930
+ماتقدمش امتحان بس جيبلي اللي هو قيمة بياخدها
+
+798
+01:32:45,930 --> 01:32:49,510
+الدالة دي اكبر من واحد عشان لا تقولي واحد و واحد
+
+799
+01:32:49,510 --> 01:32:54,550
+من عشرة اكبر مايمكن يبقى هذه ال maximum value لل
+
+800
+01:32:54,550 --> 01:33:01,490
+function بزيدي شعن الواحد طيب و اقل قيمة؟ قدر؟
+
+801
+01:33:01,490 --> 01:33:08,590
+سالم؟معقول كمية من تحت الجدر سالبة و الجدر مُعرف
+
+802
+01:33:08,590 --> 01:33:14,310
+لكمية سالبة؟ يبقى
+
+803
+01:33:14,310 --> 01:33:20,310
+أكبر قيمة هي واحد و أصغر قيمة واحد برضه يعني يعني
+
+804
+01:33:20,310 --> 01:33:27,060
+بصير لينج نقطةيعني مهما تغيرت X وY وZ، بدي يطلع
+
+805
+01:33:27,060 --> 01:33:30,860
+ناتج نفس القيمة؟ يعني كل النقطة اللي خلّجها ربنا
+
+806
+01:33:30,860 --> 01:33:39,600
+داخل الـEllipsoid صورتها نقطة واحدة؟ فيش
+
+807
+01:33:39,600 --> 01:33:45,680
+احتمال يكون مجموع هذه و هذه و هذه يطلع واحد صحيح؟
+
+808
+01:33:46,210 --> 01:33:49,630
+وإذا طلع واحد صحيح بالسالب و عندك واحد يبقى مصير
+
+809
+01:33:49,630 --> 01:33:54,090
+زيرو مرضوه يبقى دائما من ال range بين الصفر
+
+810
+01:33:54,090 --> 01:34:01,770
+والواحد يبقى هذا ال range من zero لغاية واحد as
+
+811
+01:34:01,770 --> 01:34:04,130
+any closed interval
+
+812
+01:34:24,080 --> 01:34:32,560
+طيب خلوني أقول كمان هالدالة هذه نمرة أربعة نمرة
+
+813
+01:34:32,560 --> 01:34:45,760
+خمسة نمرة خمسة خديني F X Y Z يساوي L X زيدي اتنين
+
+814
+01:34:45,760 --> 01:34:51,480
+Yزائد اتنين زاد نقص اتنين زائد اتنين زاد نقص اتنين
+
+815
+01:34:51,480 --> 01:34:55,640
+زائد
+
+816
+01:34:55,640 --> 01:34:57,480
+اتنين زائد اتنين زائد اتنين زائد اتنين زائد اتنين
+
+817
+01:34:57,480 --> 01:34:57,520
+زائد اتنين زائد اتنين زائد اتنين زائد اتنين زائد
+
+818
+01:34:57,520 --> 01:34:57,520
+اتنين زائد اتنين زائد اتنين زائد اتنين زائد اتنين
+
+819
+01:34:57,520 --> 01:34:57,520
+زائد اتنين زائد اتنين زائد اتنين زائد اتنين زائد
+
+820
+01:34:57,520 --> 01:34:57,520
+اتنين زائد اتنين زائد اتنين زائد اتنين زائد اتنين
+
+821
+01:34:57,520 --> 01:34:57,520
+زائد اتنين زائد اتn
+
+822
+01:35:18,560 --> 01:35:28,600
+فكل النقاط X و Y و Z بحيث أن X زائد 2Y زائد 2Z نقص
+
+823
+01:35:28,600 --> 01:35:37,040
+2 تبقى أكبر من 0 ولا تساوي يبقى كل النقاط X Y و Z
+
+824
+01:35:37,040 --> 01:35:47,430
+بحيث أن X زائد 2Y زائد 2Z تبقى أكبر من قداشطب هذا
+
+825
+01:35:47,430 --> 01:35:52,890
+لو كانت تساوي اتنين معادلة إيش؟ لو كانت بدل الأكبر
+
+826
+01:35:52,890 --> 01:36:03,550
+من كانت تساوي معادلة إيش؟ مستوى
+
+827
+01:36:03,550 --> 01:36:08,650
+اتنين يا أخسار بعوض الله نقرأ الفاتعة على من حرم
+
+828
+01:36:08,650 --> 01:36:13,970
+النباتي المسلمين نخدت فيه وحلينا بدل المثال خمس،
+
+829
+01:36:13,970 --> 01:36:18,930
+ست أمثل على الموضوعيبقى هنا إيه؟ يبقى هذه لو كانت
+
+830
+01:36:18,930 --> 01:36:24,110
+تساوي إتنين وعادلة plane طب أكبر من هذا يبقى كل
+
+831
+01:36:24,110 --> 01:36:30,430
+الفرق كل space اللي أعلى هذا ال plane طبعا طيب لو
+
+832
+01:36:30,430 --> 01:36:35,370
+حبيت أتعرف عليه شو شكله أقول آه تفضلي أقول هاي
+
+833
+01:36:35,370 --> 01:36:43,310
+الشكل هذا محور X وهذا Y وهذا Z بدي أجيب نقاط تقاطع
+
+834
+01:36:43,310 --> 01:36:48,150
+مع المحاولالنقاط تفضل مع محور X يبقى Y و Z بقداش
+
+835
+01:36:48,150 --> 01:36:55,870
+Zero يبقى X بقداش 2 يبقى لو جيت قلت النقطة هذه 2 و
+
+836
+01:36:55,870 --> 01:37:02,120
+Zero و Zeroتقاطع مع محور Y يبقى X و Z بـ0 و يبقى Y
+
+837
+01:37:02,120 --> 01:37:07,540
+يبقى D بـ1 يبقى النقطة اللي عندنا هذه اللي هي Zero
+
+838
+01:37:07,540 --> 01:37:12,900
+و واحد و Zero تقاطع مع محور Z يبقى النقطة اللي
+
+839
+01:37:12,900 --> 01:37:18,780
+عندنا هذه Zero و Zero و واحد يبقى لو أصل بهذا
+
+840
+01:37:18,780 --> 01:37:24,720
+الشكل يبقى هذا الـ Infinity طبعا بمتاد كله من سالب
+
+841
+01:37:24,720 --> 01:37:29,060
+Infinity ل Infinityبس احنا جيبنالكم نقاط تقاطع ال
+
+842
+01:37:29,060 --> 01:37:35,760
+plane هذا ماله مع محاور الإحداثية يبقى لما أقول
+
+843
+01:37:35,760 --> 01:37:45,940
+أكبر من اتنين كل ال space اللي أعلى من ال plane
+
+844
+01:37:45,940 --> 01:37:56,890
+هنا يبقى ال space هذا كله above thatأيه الـ Plane
+
+845
+01:37:56,890 --> 01:38:03,070
+اللي هو X زيدي اتنين Y زيدي اتنين Z بده يساوي
+
+846
+01:38:03,070 --> 01:38:08,190
+اتنين يبقى كل الفراخ اللي أعلى من هذا طب ال range
+
+847
+01:38:08,190 --> 01:38:17,210
+كل ال .. range اللي .. R كل ال R و ال range هنا ال
+
+848
+01:38:17,210 --> 01:38:17,910
+range
+
+849
+01:38:22,720 --> 01:38:29,180
+أخر حاجة نمرها ستة وفكروا لي فيها كويس F of X وY
+
+850
+01:38:29,180 --> 01:38:38,760
+وZ F of X وY وZ يساوي X زائد Y زائد Z على absolute
+
+851
+01:38:38,760 --> 01:38:43,680
+value ل X زائد Y زائد Z
+
+852
+01:38:53,330 --> 01:39:03,390
+بدي الدمين يالا شوف هارمع دمين معناه Zero طيب و
+
+853
+01:39:03,390 --> 01:39:07,810
+جهدنا لها يعني أنا بدي أشيل بس من ال plane نقطة
+
+854
+01:39:07,810 --> 01:39:15,930
+الأصل مش هيك؟ طيب موافقين؟ طيب أنا بدي أجيبلك نقطة
+
+855
+01:39:15,930 --> 01:39:22,490
+ماهياش نقطة الأصل و أشوف معرفة عنده ولا لاخد لي X
+
+856
+01:39:22,490 --> 01:39:32,570
+بواحد و Y بواحد و Z بثاني باتنين Zero Undefined
+
+857
+01:39:32,570 --> 01:39:39,710
+هذه ماهياش نقطة في الأصل صح؟
+
+858
+01:39:39,710 --> 01:39:46,590
+يبقى كل ال X و Y و Z المجموعة بصير Zero ممنوع
+
+859
+01:39:46,590 --> 01:39:53,840
+يكونوا في ال domainيبقى كل الفرار ما على النقاط
+
+860
+01:39:53,840 --> 01:39:59,700
+اللتي تقع على الـ plate X زي Y زي Z تساوي 0 صح ولا
+
+861
+01:39:59,700 --> 01:40:07,200
+لا؟ يبقى هنا ال domain تبع ال F ال domain تبع ال F
+
+862
+01:40:07,200 --> 01:40:16,060
+بده يساوي all the points in the space
+
+863
+01:40:44,270 --> 01:40:47,070
+بالنسبة للمجموعات الموجودة في المجموعات الموجودة
+
+864
+01:40:47,070 --> 01:40:47,070
+في المجموعات الموجودة في المجموعات الموجودة في
+
+865
+01:40:47,070 --> 01:40:47,070
+المجموعات الموجودة في المجموعات الموجودة في
+
+866
+01:40:47,070 --> 01:40:48,210
+المجموعات الموجودة في المجموعاتأبصري عشان اطلع
+
+867
+01:40:48,210 --> 01:40:55,350
+عندنا هنا يالا يا عزيزي نمشي ارمى على زيرو ارمى
+
+868
+01:40:55,350 --> 01:41:01,070
+على زيرو وجهة نظر وليست وجاها في النظر يالا غيرها
+
+869
+01:41:01,070 --> 01:41:06,310
+همشي قول يا بنت هو لو غلط تعود احكي انت تقولي غلط
+
+870
+01:41:06,310 --> 01:41:10,510
+كل مرة تقولي غلط و بعدها تقولي صح فسيدي فكري مخي
+
+871
+01:41:10,510 --> 01:41:13,830
+يالا
+
+872
+01:41:13,830 --> 01:41:14,250
+غيرها
+
+873
+01:41:17,020 --> 01:41:21,560
+أرمى عدسة يعني نفس الكلام اللي جالس في زميلتي ها
+
+874
+01:41:21,560 --> 01:41:31,740
+غيره طب هل النقطة 2 تقع على ال Ray؟
+
+875
+01:41:31,740 --> 01:41:38,540
+القيمة 2 هي من ضمن قيمة ال Ray؟ واحد منافق طب
+
+876
+01:41:38,540 --> 01:41:44,600
+اتنين ألف طب
+
+877
+01:41:44,600 --> 01:41:49,740
+شو قال؟هل هناك قيم بياخدها الرئيس غير الواحد
+
+878
+01:41:49,740 --> 01:41:55,540
+والسالي بواحد؟ بس القيمتين هدول، في غيرهم؟ هو
+
+879
+01:41:55,540 --> 01:41:57,020
+تعريف ال absolute value
+
+880
+01:41:59,390 --> 01:42:03,410
+وحد و سالب واحد هذا نفس الفيديو صحيح و لا لأ تختصر
+
+881
+01:42:03,410 --> 01:42:06,550
+ال bus و لا تقفش و تبقى الهندين بس واحد و سالب
+
+882
+01:42:06,550 --> 01:42:11,290
+واحد في الشميرو يبقى ال range تبع هذه الدنيا بس
+
+883
+01:42:11,290 --> 01:42:15,670
+نقطتين مش internal من سالب واحد إلى واحد بس سالب
+
+884
+01:42:15,670 --> 01:42:19,310
+واحد واحد يبقى ال range لل F
+
+885
+01:42:27,630 --> 01:42:33,130
+من قيمتين لواحد وسالم واحد تقدروا تجيبولي قيمة
+
+886
+01:42:33,130 --> 01:42:36,750
+غيرهم يللا اللي جيب قيمة غيرهم برضه تاخد ال full
+
+887
+01:42:36,750 --> 01:42:44,990
+mark يللا و ترتاحأه خلاص يبقى لا حد هنا انت هنا
+
+888
+01:42:44,990 --> 01:42:49,010
+لكن لسه ال section احنا في بدايته يعني في المحاضرة
+
+889
+01:42:49,010 --> 01:42:53,530
+القادمة يدوب نخلص هذا ال section يعني كلام كتير
+
+890
+01:42:53,530 --> 01:42:59,470
+لسه بدنا نتكلم عن ال functions اللي عندنا هذه
+
+891
+01:42:59,470 --> 01:43:05,370
+المختلفةو ال function بنا نعرف حاجة اسمها ال
+
+892
+01:43:05,370 --> 01:43:12,290
+bounded و ال unbounded و ما إلى ذلك كل الشغلات و
+
+893
+01:43:12,290 --> 01:43:15,330
+ناخد اللي في الحالة الأولى في ال plane و بعدين
+
+894
+01:43:15,330 --> 01:43:19,130
+نروح في الفراد و في level curve و في level
+
+895
+01:43:19,130 --> 01:43:23,950
+surfaces و ما إلى ذلك كله الموضوع المحاضرة القادمة
+
+896
+01:43:23,950 --> 01:43:26,450
+ان شاء الله تعالى يعطيكوا العافية
+
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/tT-7ILSFEbI.srt b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/tT-7ILSFEbI.srt
new file mode 100644
index 0000000000000000000000000000000000000000..35450ecb0df655c5e2ad4e62145b1560f67e8288
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/tT-7ILSFEbI.srt
@@ -0,0 +1,2364 @@
+1
+00:00:11,040 --> 00:00:15,920
+بسم الله الرحمن الرحيم. انتهينا في المحاضرة الماضية
+
+2
+00:00:15,920 --> 00:00:20,300
+من الـ section 12-1، والآن نبدأ من الـ section 12-2
+
+3
+00:00:20,750 --> 00:00:24,910
+أتناشر اتنين هو عبارة عن الـ vectors، طبعًا الـ
+
+4
+00:00:24,910 --> 00:00:32,570
+vectors هذه سبقت دراستها في فيزياء عامة B، وإحنا هنا
+
+5
+00:00:32,570 --> 00:00:37,030
+بنعطي الـ section هنا من جانب، وذكر فإن الذكرى تنفع
+
+6
+00:00:37,030 --> 00:00:42,330
+المؤمنين، ومن جانب آخر لأن دراستنا خلال Calculus C
+
+7
+00:00:42,330 --> 00:00:48,870
+ستكون مبنية على الـ vectors أو المتجهات، الكميات التي
+
+8
+00:00:48,870 --> 00:00:53,370
+رَدَّنا سبحانه وتعالى خلقها لنا نوعين، نقول في كميات
+
+9
+00:00:53,370 --> 00:00:58,950
+قياسية، وفي كميات متجهة. نعطي بعض الأمثلة للكميات
+
+10
+00:00:58,950 --> 00:01:05,550
+القياسية، وبعض الأمثلة للكميات الاتجاهية. فمثلاً لو
+
+11
+00:01:05,550 --> 00:01:09,270
+جِبنا بنت أي واحدة، دي يكو جِبنا جسم، الطول تبعها
+
+12
+00:01:09,270 --> 00:01:14,050
+لِجناه 170 سنتيمتر، الـ 170 سنتيمتر إيه؟
+
+13
+00:01:14,050 --> 00:01:19,690
+الاتجاه؟ والله، بس طول. بالطبع لا يوجد اتجاه، لا 170
+
+14
+00:01:19,690 --> 00:01:22,870
+متر في اتجاه الشرق ولا الغرب ولا الشمال ولا الجنوب
+
+15
+00:01:22,870 --> 00:01:27,110
+ولا الشمال الغربي ولا الجنوب، ولا حاجة. إذاً بناءً
+
+16
+00:01:27,110 --> 00:01:35,090
+عليه، الطول كمية قياسية. زي إيش كذلك؟ كتلة كمية
+
+17
+00:01:35,090 --> 00:01:39,330
+قياسية، زي المساحة، مساحة القاعة اللي إحنا فيها
+
+18
+00:01:39,330 --> 00:01:46,590
+مساحة، لو قُلت الطول 4 والعرض 3، يبقى 3
+
+19
+00:01:46,590 --> 00:01:51,390
+× 4 = 12 متر مربع. هذه مساحة، يبقى هذه كمية
+
+20
+00:01:51,390 --> 00:01:56,750
+قياسية. حجم الغرفة اللي إحنا فيها، متوازن والسقوف،
+
+21
+00:01:56,750 --> 00:02:01,190
+يبقى الطول × العرض × الارتفاع، يبقى الحجم كمية
+
+22
+00:02:01,190 --> 00:02:07,110
+قياسية. كذلك يبقى هذه الكميات بسميها كميات قياسية.
+
+23
+00:02:07,440 --> 00:02:12,280
+يبقى أول نوع من الكميات حاجة بسميها scalar
+
+24
+00:02:12,280 --> 00:02:22,360
+quantity، الكمية
+
+25
+00:02:22,360 --> 00:02:30,840
+القياسية. زي إيه؟ زي الـ length، زي
+
+26
+00:02:30,840 --> 00:02:44,700
+الـ mass، الكتلة، زي الـ area، زي الـ volume، وهكذا. نأتي
+
+27
+00:02:44,700 --> 00:02:51,740
+الآن نبحث عن الـ vector quantity، vector quantity
+
+28
+00:02:51,740 --> 00:02:56,580
+زي
+
+29
+00:02:56,580 --> 00:03:01,700
+إيش الـ vector quantity؟ آه، فيها حاجة هنا نميز بين
+
+30
+00:03:01,700 --> 00:03:06,920
+أمرين: في حاجة اسمها speed، وفي حاجة اسمها velocity.
+
+31
+00:03:07,630 --> 00:03:13,190
+Speed هي مقدار السرعة، لكن الـ velocity هي السرعة
+
+32
+00:03:13,190 --> 00:03:17,890
+ومقدار واتجاه. يعني وأنت راكب في السيارة، الصورة
+
+33
+00:03:17,890 --> 00:03:21,850
+وأنت حاسس السواق بيحكي مع مين؟ بيحكي مع اللي قاعد
+
+34
+00:03:21,850 --> 00:03:25,910
+جنبه، بيقول له والله كنت ماشي، والـ speed متر عندي
+
+35
+00:03:25,910 --> 00:03:30,770
+معلم كذا speed متر، يعني عداد السرعة هذا يعطيني قد إيش
+
+36
+00:03:30,770 --> 00:03:35,630
+مقدار السرعة، لكنه لا يعطيني اتجاه السرعة. إذاً كذلك هنا
+
+37
+00:03:35,630 --> 00:03:43,110
+لو قُلت الـ speed، الـ speed هذه مقدار السرعة، لكن جيت
+
+38
+00:03:43,110 --> 00:03:48,270
+قلت هنا velocity، هذه
+
+39
+00:03:48,270 --> 00:03:54,820
+مقدار السرعة والإزاحة. إزاحة جسم في اتجاه ما، يبقى
+
+40
+00:03:54,820 --> 00:04:02,180
+هذه بسميها displacement، الإزاحة.
+
+41
+00:04:02,180 --> 00:04:07,680
+زي إيش مثلاً كمان؟ زي الـ force، القوة. أثرت قوة على
+
+42
+00:04:07,680 --> 00:04:15,860
+جسم ما، القوة بعطيها مقداراً واتجاهًا. زي الـ force، وهكذا. هذه نوعين من الكميات، حاجة بسميها scalar
+
+43
+00:04:20,920 --> 00:04:24,680
+quantity، والنوع الثاني اللي هو الـ vector
+
+44
+00:04:24,680 --> 00:04:30,180
+quantity. الآن بدنا نعطي تعريف لمين؟ للـ vector، اللي
+
+45
+00:04:30,180 --> 00:04:36,500
+هو أساس دراستنا عليه خلال هذا الفصل. يبقى بدنا نجي لـ
+
+46
+00:04:36,500 --> 00:04:42,100
+definition: the vector is a directed line
+
+47
+00:04:42,100 --> 00:04:55,460
+segment.  The vector is a directed line
+
+48
+00:04:55,460 --> 00:04:58,740
+segment
+
+49
+00:04:58,740 --> 00:05:11,320
+وحد الرمز AB، وعليه سهم بهذا الشكل. from an initial
+
+50
+00:05:11,320 --> 00:05:28,010
+point A to a terminal point B. الـ
+
+51
+00:05:28,010 --> 00:05:32,490
+initial point، نقطة ابتدائية. Terminal point، نقطة
+
+52
+00:05:32,490 --> 00:05:38,470
+نهائية، التي ينتهي عندها هذا السهم. يبقى directed
+
+53
+00:05:38,470 --> 00:05:46,170
+line segment، يبدأ من النقطة A وينتهي في النقطة B.
+
+54
+00:05:46,480 --> 00:05:53,020
+وبنحط سهم عند نقطة النهاية، دليل على أن هذا الـ
+
+55
+00:05:53,020 --> 00:05:57,520
+vector يبدأ من النقطة A وينتهي في النقطة B، اللي
+
+56
+00:05:57,520 --> 00:06:03,020
+كنتوا في الابتدائي بتسموه الشعاع. الشعاع بيبدأ من
+
+57
+00:06:03,020 --> 00:06:08,860
+نقطة وبينتقل إلى نقطة أخرى. زي ما كنا نقول مثلاً
+
+58
+00:06:08,860 --> 00:06:15,280
+شعاع الشمس. مصدره وين؟ الشمس، ثم ينتقل إلى الكون في كل
+
+59
+00:06:15,280 --> 00:06:20,620
+الاتجاهات، تمام؟ يبقى هذا اللي هو بنسميه، بنسميه
+
+60
+00:06:20,620 --> 00:06:26,260
+vector. لو بدنا طول هذا، يبقى باجي بقول the
+
+61
+00:06:26,260 --> 00:06:32,660
+length، اللي هو الطول، أو بعض المؤلفين بيسموه الـ
+
+62
+00:06:32,660 --> 00:06:36,960
+magnitude، اللي
+
+63
+00:06:36,960 --> 00:06:48,300
+هو المقدار. magnitude أو الـ length of the vector A, B
+
+64
+00:06:48,300 --> 00:07:00,000
+is denoted by، بدي أعطيه رمز A, B، وبحطه بين خطين
+
+65
+00:07:00,000 --> 00:07:04,840
+بهذا الشكل. هذه ليست absolute value تبع الـ calculus
+
+66
+00:07:04,840 --> 00:07:11,320
+A، وإنما المقصود طول المتجه A, B، الـ length للـ
+
+67
+00:07:11,320 --> 00:07:17,440
+vector A, B. الآن بدنا نجي لتساوي two vectors.
+
+68
+00:07:17,440 --> 00:07:28,780
+Definition: Two vectors, two vectors are equal are
+
+69
+00:07:28,780 --> 00:07:44,960
+equal if they have the same length and direction.
+
+70
+00:07:44,960 --> 00:07:53,060
+يبقى
+
+71
+00:07:53,060 --> 00:07:57,080
+المتجهين متساويين
+
+72
+00:07:57,080 --> 00:08:03,200
+إذا كان لهم نفس المقدار ونفس الاتجاه. كيف يعني؟ لو
+
+73
+00:08:03,200 --> 00:08:12,170
+جاءت خط الـ coordinate axes، المحور X، محور Y، محور Z،
+
+74
+00:08:12,170 --> 00:08:15,670
+أنا
+
+75
+00:08:15,670 --> 00:08:18,930
+بقول في عندي متجهين، والمتجهين الاتنين هذول
+
+76
+00:08:18,930 --> 00:08:25,270
+متساويين. شرط التساوي: تساوي المقدار ونفس الاتجاه.
+
+77
+00:08:25,270 --> 00:08:30,810
+كيف يعني؟ لو جيت قُلت، افترض أن هذا بدأ من نقطة الأصل
+
+78
+00:08:30,810 --> 00:08:38,260
+وانتهى في النقطة هذه، يبقى هذا سميته V، vector.
+
+79
+00:08:38,260 --> 00:08:45,220
+كان ابتدأ من هذه النقطة، وفي اتجاه نفس المتجه اللي
+
+80
+00:08:45,220 --> 00:08:53,160
+عندنا هذا، نفس المتجه، وكان له نفس الطول، يبقى اتنين
+
+81
+00:08:53,160 --> 00:09:00,460
+هذول are equal. أو لو بدأ من هنا، من النقطة هذه، وفي
+
+82
+00:09:00,460 --> 00:09:05,800
+الاتجاه اللي عندنا هذا، وكان له نفس الطول، يبقى هذا
+
+83
+00:09:05,800 --> 00:09:12,110
+المتجه V، وهذا المتجه V كذلك. يبقى التلاتة هذول are
+
+84
+00:09:12,110 --> 00:09:14,690
+equal or are equivalent.
+
+85
+00:09:17,580 --> 00:09:24,140
+زي بعض، ولو إنهم ما انطلقوش من نفس النقطة، لكن لهم
+
+86
+00:09:24,140 --> 00:09:31,840
+نفس الطول ولهم كذلك نفس الاتجاه، يبقى هذول بقول
+
+87
+00:09:31,840 --> 00:09:38,940
+عنهم vectors متساوية، أو متجهات متساوية. كمان
+
+88
+00:09:38,940 --> 00:09:46,800
+definition مهم اللي هو the zero vector، الـ zero
+
+89
+00:09:46,800 --> 00:09:51,600
+vector. سأعطيه رمز 0، وقته مطول شوية لكي نتميزه
+
+90
+00:09:51,600 --> 00:09:58,000
+عن الـ zero العادي، تمام؟ يبقى the zero vector، اللي
+
+91
+00:09:58,000 --> 00:10:10,080
+هو، حد يقول، رمز 0 is a vector with length zero.
+
+92
+00:10:10,080 --> 00:10:20,170
+الطول تبعه يساوي الصفر، and no determined direction.
+
+93
+00:10:20,170 --> 00:10:23,990
+يعني
+
+94
+00:10:23,990 --> 00:10:28,670
+ممكن
+
+95
+00:10:28,670 --> 00:10:34,210
+أن يكون اتجاهه في أي اتجاه بدك إياه. يبقى الـ zero
+
+96
+00:10:34,210 --> 00:10:39,120
+vector هو عبارة عن متجه طوله يساوي الصفر، وممكن أن
+
+97
+00:10:39,120 --> 00:10:43,800
+يؤخذ في أي اتجاه بدك إياه. ومن هنا قلنا no
+
+98
+00:10:43,800 --> 00:10:48,840
+determined direction، ما لوش اتجاه محدد. يعني ممكن
+
+99
+00:10:48,840 --> 00:10:53,760
+أخذه في أي اتجاه بدون قيود، without restriction. بدي
+
+100
+00:10:53,760 --> 00:11:01,720
+أخذه في أي اتجاه بدي إياه. الآن بدنا نيجي إلى توازي
+
+101
+00:11:01,720 --> 00:11:15,580
+المتجهات. كذلك، definition: two nonzero vectors, two non
+
+102
+00:11:15,580 --> 00:11:24,080
+zero vectors U and V are said to be parallel are
+
+103
+00:11:24,080 --> 00:11:35,280
+said to be parallel، ممكن نقول عليهم متوازية.
+
+104
+00:11:37,020 --> 00:11:47,360
+if there is a real number, if there is a real number
+
+105
+00:11:47,360 --> 00:12:03,200
+alpha such that، بحيث أن الـ V تساوي Alpha U. For
+
+106
+00:12:03,200 --> 00:12:03,820
+example,
+
+107
+00:12:09,030 --> 00:12:24,910
+the vectors مثلًا V، و 3V، و -2V are parallel.
+
+108
+00:12:24,910 --> 00:12:29,330
+يبقى
+
+109
+00:12:29,330 --> 00:12:35,310
+هذه المتجهات بقول عنها متجهات متوازية، لأن كل واحد
+
+110
+00:12:35,310 --> 00:12:41,150
+هو عبارة عن مضاعفات الآخر، وليس بالضرورة أن تكون
+
+111
+00:12:41,150 --> 00:12:46,170
+alpha عدداً صحيحاً. يعني ممكن يكون هذا، هذا على 2
+
+112
+00:12:46,170 --> 00:12:51,230
+V، يعني ممكن يكون كسر. المهم واحد منهم مضاعفات
+
+113
+00:12:51,230 --> 00:12:57,550
+الآخر. فمثلاً لو جيت قُلت هذا هو الـ vector V، على سبيل
+
+114
+00:12:57,550 --> 00:13:03,290
+المثال، 3/2 V،  جد؟ جِدّ إيش؟ مرة ونصف، وفي
+
+115
+00:13:03,290 --> 00:13:09,050
+نفس الاتجاه، يبقى هذا يكون بالشكل اللي عنده هذا.
+
+116
+00:13:09,050 --> 00:13:16,970
+يبقى هذا 3/2 V. طب -2V، جدّ V مرتين، بس في عكس الاتجاه، يبقى هذا يكون بالشكل اللي
+
+117
+00:13:16,970 --> 00:13:23,570
+عنده هذا. -2V، التلاتة are parallel، لغاية إن
+
+118
+00:13:29,720 --> 00:13:35,680
+الاتجاهات مالها؟ متعاكسة مع بعض. هذا كله لا يوصل
+
+119
+00:13:35,680 --> 00:13:48,540
+نيجي الآن لنقطة جديدة، وهي remark: we
+
+120
+00:13:48,540 --> 00:13:49,780
+write any vector
+
+121
+00:13:57,840 --> 00:14:04,060
+any vector، يبقى بنقدر نكتب أي متجه algebraically
+
+122
+00:14:04,060 --> 00:14:24,240
+جبرِياً، جبرياً
+
+123
+00:14:24,240 --> 00:14:32,700
+algebraically by its components، by its components.
+
+124
+00:14:32,700 --> 00:14:36,780
+بالمركبات.
+
+125
+00:14:36,780 --> 00:14:44,960
+ابتدأناها as follows، مثلاً
+
+126
+00:14:44,960 --> 00:14:54,300
+في الـ plane، in the plane، الـ vector V، بقدر أكتبه
+
+127
+00:14:54,300 --> 00:15:02,560
+على الشكل التالي: V1، V2. في الـ space، in the space،
+
+128
+00:15:02,560 --> 00:15:17,240
+الـ V بده يساوي V1، V2، V3، where، حيث V1، V2، V3
+
+129
+00:15:17,240 --> 00:15:24,780
+are the components of
+
+130
+00:15:26,740 --> 00:15:42,660
+the vector، of the vector V، in the direction of the
+
+131
+00:15:42,660 --> 00:15:51,180
+coordinate axes.
+
+132
+00:15:51,180 --> 00:16:00,020
+كيف هذا الكلام؟ نحاول أن نضع الكلام اللي نقوله على
+
+133
+00:16:00,020 --> 00:16:04,660
+الرسم، لكي يكون واضح أمامنا تماماً.
+
+134
+00:16:45,590 --> 00:16:51,170
+تشوف؟ لو جينا تخيلنا عندي إن في vector V بهذا الشكل،
+
+135
+00:16:51,170 --> 00:16:58,390
+يبقى هذا هو الـ vector V. بنشوف وين المركبات تبعات
+
+136
+00:16:58,390 --> 00:17:03,830
+الـ vector V. يبقى لو جيت من هنا، نزلت عمودي بالشكل
+
+137
+00:17:03,830 --> 00:17:09,610
+على هذا لغاية ما قبل الـ XY plane، ورسمت من هنا
+
+138
+00:17:09,610 --> 00:17:19,710
+أفقي، ومن هنا موازي، بين، موازي للـ X، يبقى هذه الـ
+
+139
+00:17:19,710 --> 00:17:25,190
+Y، موازي للـ XY بالشكل هذا. هذا تعتبر المركب اللي
+
+140
+00:17:25,190 --> 00:17:31,070
+هي V1، هذه الموازية اللي هي V1. هذا V2، الموازية
+
+141
+00:17:31,070 --> 00:17:36,030
+للمحور Y. هذا اللي رأسي، الموازية لمحور Z، اللي هي
+
+142
+00:17:36,030 --> 00:17:43,710
+V3. يبقى V1 ستبدأ من نقطة الأصل لغاية هذه النقطة،
+
+143
+00:17:43,710 --> 00:17:50,270
+يعني كأن إحداثيات النقطة هذه V1، 0، 0، زي ما درسنا
+
+144
+00:17:50,270 --> 00:18:00,090
+في المحاضرة الماضية. هذه الـ V1، وV2، و0. هذه الآن V1،
+
+145
+00:18:00,090 --> 00:18:07,310
+وV2، وV3. يبقى هذه المركبات الثلاثة لمين؟ للـ
+
+146
+00:18:07,310 --> 00:18:15,950
+vector V in space. حد بيسأل؟ طيب.
+
+147
+00:18:15,950 --> 00:18:21,700
+يبقى هذه المركبات، من الآن فصاعداً سنحاول أن نكتب
+
+148
+00:18:21,700 --> 00:18:27,440
+دائماً وأبداً الـ vector V بدلالة المركبات الثلاثة
+
+149
+00:18:27,440 --> 00:18:35,420
+تبعته في الاتجاهات تبعات محور الإحداثيات X، وY، وZ.
+
+150
+00:18:35,420 --> 00:18:41,420
+ممكن
+
+151
+00:18:41,420 --> 00:18:50,270
+نعطي شكل عام لمين؟ للـ vector V.  تولة ما نقول إن two
+
+152
+00:18:50,270 --> 00:18:54,690
+vectors are parallel، لو رحت رسمت موازي لهذا الـ
+
+153
+00:18:54,690 --> 00:18:59,070
+vector، وليكن الموازي هو الـ vector اللي عندنا هذا
+
+154
+00:18:59,070 --> 00:19:06,030
+على سبيل المثال، موازي L وG بالضبط تماماً، وكانت هذه
+
+155
+00:19:06,030 --> 00:19:17,120
+النقطة P1، of X1، وY1، وZ1، وكانت النقطة هذه P2، لـ X2،
+
+156
+00:19:17,120 --> 00:19:22,520
+وY2، وZ2. إذاً الـ vector اللي عيني هذا، جد الـ vector
+
+157
+00:19:22,520 --> 00:19:30,560
+هذا بالضبط تماماً، مقداراً واتجاهاً. طيب، بناءً عليه الـ
+
+158
+00:19:30,560 --> 00:19:36,620
+vector V بدي أكتبه بدلالة المركبات تبعات هذه النقطة،
+
+159
+00:19:36,620 --> 00:19:43,180
+يبقى بناءً عليه، in general، بروح بقول هيك: in general
+
+160
+00:19:46,360 --> 00:19:52,380
+على وجه العموم، الـ vector V، اللي مركبته V1، وV2، و
+
+161
+00:19:52,380 --> 00:19:59,080
+V3، بقدر أكتبه بشكل جديد بواسطة النقاط اللي عندنا
+
+162
+00:19:59,080 --> 00:20:06,120
+هذا اللي تمثل الـ vector V بالضبط تماماً. يبقى X2 - X1،
+
+163
+00:20:06,120 --> 00:20:16,040
+Y2 - Y1، Z2 - Z1، بهذا الشكل. يبقى إن كتبنا الـ vector
+
+164
+00:20:16,040 --> 00:20:21,880
+بدلالة الـ terminal point، و نسبناه إلى النقطة الأصل،
+
+165
+00:20:21,880 --> 00:20:27,280
+أو كتبناه بدلالة النقطتين اللي عندنا، الاتنين
+
+166
+00:20:27,280 --> 00:20:32,820
+are the same. يبقى اتنين نفس الشيء. أثناء شغلنا في
+
+167
+00:20:32,820 --> 00:20:34,940
+الناحية الرياضية.
+
+168
+00:20:41,360 --> 00:20:47,860
+كويس. لو بدي أكتب تساوي متجهين بدلالة المركبات،
+
+169
+00:20:47,860 --> 00:20:54,000
+فباجي بقول ملاحظة: two
+
+170
+00:20:54,000 --> 00:20:58,580
+vectors U
+
+171
+00:20:58,580 --> 00:21:06,140
+اللي هو بده يساوي U1، U2، U3، and V
+
+172
+00:21:06,140 --> 00:21:13,140
+اللي هو بده يساوي V1، V2، V3.
+
+173
+00:21:13,140 --> 00:21:20,520
+(The numbers V4-V21 seem to be a mistake and are omitted)
+
+174
+00:21:20,520 --> 00:21
+
+223
+00:26:00,030 --> 00:26:02,190
+بالشكل اللي عندنا هذا
+
+224
+00:26:08,290 --> 00:26:12,390
+طيب الـ C اللي بدنا نضربها يا بنات يمكن تكون موجبة
+
+225
+00:26:12,390 --> 00:26:19,710
+ويمكن تكون سالبة، صح ولا لا؟ لو ضربت الـ C كرقم موجّه في
+
+226
+00:26:19,710 --> 00:26:24,570
+المتجه، بيطلع متجه في نفس الاتجاه تبع المتجه الأصلي
+
+227
+00:26:24,570 --> 00:26:30,010
+لو كانت الـ C سالبة، بيعكسوا على طول القطر. خلينا نكتب
+
+228
+00:26:30,010 --> 00:26:34,550
+هذه الملاحظة البسيطة، هذه لأنّ بدنا نبني عليها شغل
+
+229
+00:26:34,550 --> 00:26:37,170
+بعد ذلك إن شاء الله تعالى
+
+230
+00:26:39,780 --> 00:26:45,080
+يبقى بدّي أقول... بدي
+
+231
+00:26:45,080 --> 00:26:50,700
+أحطها زي ملاحظة بسيطة هيك: if C أكبر من الـ zero،
+
+232
+00:26:50,700 --> 00:27:04,340
+then C, V and L, V are in the same direction.
+
+233
+00:27:10,600 --> 00:27:19,040
+اللي بقى، لو كان الـ C أقل من الـ 0، يعني كمية
+
+234
+00:27:19,040 --> 00:27:32,640
+سالبة، then CV and V are of the opposite
+
+235
+00:27:32,640 --> 00:27:35,840
+directions.
+
+236
+00:27:37,580 --> 00:27:45,480
+في اتجاهين متعاكسين. طب لو حبيت النقطة الثالثة، أجيب
+
+237
+00:27:45,480 --> 00:27:51,940
+طول المتجه CV حسب
+
+238
+00:27:51,940 --> 00:27:58,940
+تعريفنا. طول المتجه بده يساوي الجذر التربيعي لـ CV1
+
+239
+00:27:58,940 --> 00:28:09,050
+لكل تربيع + CV2 لكل تربيع + CV3 لكل تربيع. هذا بقدر أقول
+
+240
+00:28:09,050 --> 00:28:16,230
+ويساوي لـ square root لـ C تربيع (بياخذ عامل مشترك)
+
+241
+00:28:16,230 --> 00:28:24,610
+بظل V1 تربيع + V2 تربيع + V3 تربيع. شكل اللي
+
+242
+00:28:24,610 --> 00:28:30,630
+عنده. طب الـ C تربيع بقدر أطلعها من تحت الجذر، تمام؟
+
+243
+00:28:31,110 --> 00:28:36,410
+لما نطلعها من تحت الجذر، بتطلع بـ Absolute Value، زي
+
+244
+00:28:36,410 --> 00:28:40,570
+ما اتعلمنا في Calculus A في أول محاضرة أخدتها في
+
+245
+00:28:40,570 --> 00:28:46,930
+Calculus A. يبقى هذا بيصير عندي Absolute Value للـ C
+
+246
+00:28:46,930 --> 00:28:55,970
+في الجذر التربيعي لـ: V1 تربيع + V2 تربيع + V3
+
+247
+00:28:55,970 --> 00:28:56,950
+تربيع.
+
+248
+00:28:59,710 --> 00:29:05,990
+يعني هذا بقدر أقول: absolute value للـ C في طول الـ V.
+
+249
+00:29:05,990 --> 00:29:15,390
+يبقى الأولى يا بنات، هذه تُقرأ: absolute value of C.
+
+250
+00:29:15,390 --> 00:29:19,710
+يعني إن كانت موجبة فهي موجبة، وإن كانت سالبة خذ الـ
+
+251
+00:29:19,710 --> 00:29:26,330
+absolute value، بصير موجبة. أما عن هذا فهو the
+
+252
+00:29:26,330 --> 00:29:37,850
+length of V. يبقى هذا طول المتجه V. هنا بنحاول نوقف
+
+253
+00:29:37,850 --> 00:29:43,470
+شوية بسيطة، وناخد بعض الأمثلة لتوضيح المفاهيم التي
+
+254
+00:29:43,470 --> 00:29:51,770
+ذكرناها قبل قليل. إذا بدنا نروح نحل بعض الأمثلة
+
+255
+00:29:51,770 --> 00:29:57,830
+العددية على ما ذكرنا قبل قليل.
+
+256
+00:30:12,320 --> 00:30:17,440
+نمسح هذا، خلاص. وأنا بشرحها لبنات، اللي ما تستمعش أي
+
+257
+00:30:17,440 --> 00:30:23,700
+نقطة، تقول: لو سمحت، استأذن وأسألي أي سؤال بدّك إياه من
+
+258
+00:30:23,700 --> 00:30:27,820
+خلال الأسئلة. بتثبت المعلومات عندكم، اللي بتكون فهمت
+
+259
+00:30:27,820 --> 00:30:36,360
+غلط، بتصير تفهم صح، وهكذا. نجي لأول مثال، example F
+
+260
+00:30:43,900 --> 00:30:54,920
+P1، F P1، النقطة وإحداثيات P1
+
+261
+00:30:54,920 --> 00:31:00,340
+F P1، F P1، F P1،
+
+262
+00:31:00,340 --> 00:31:04,920
+F P1، F P1، F P1، F P1، F P1، F P1، F P1، F P1، F P1،
+
+263
+00:31:04,920 --> 00:31:06,620
+F P1، F P1، F P1، F P1، F P1، F P1، F P1، F P1، F P1،
+
+264
+00:31:06,620 --> 00:31:10,240
+F P1، F P1، F P1، F P1، F P1، F P1، F P1، F P1، F P1،
+
+265
+00:31:10,240 --> 00:31:10,380
+F P1، F P1، F P1، F P1، F P1، F P1، F P1، F P1، F P1،
+
+266
+00:31:10,380 --> 00:31:10,420
+F P1، F P1، F P1، F P1، F P1، F P1، F P1، F P
+
+267
+00:31:21,050 --> 00:31:35,490
+2 points. نريد find طول جديدنا the length of
+
+268
+00:31:35,490 --> 00:31:49,510
+الضلع P1 P2، that is أي أننا نريد طول الضلع P1 P2
+
+269
+00:31:49,510 --> 00:31:59,860
+as a vector، b by the vector، or is the vector
+
+270
+00:31:59,860 --> 00:32:03,380
+is
+
+271
+00:32:03,380 --> 00:32:11,760
+the vector u، اللي هو بده يساوي تسعة، واثنا عشر، وصفر.
+
+272
+00:32:11,760 --> 00:32:16,620
+parallel to
+
+273
+00:32:16,620 --> 00:32:21,180
+P1 P2 أم لا.
+
+274
+00:32:28,630 --> 00:32:36,330
+Solution. نرجع لسؤالنا مرة ثانية، نقرأ السؤال، نترجم
+
+275
+00:32:36,330 --> 00:32:39,710
+المطلوب. شو اللي بدي أعطيه؟  الطلب، إذا حددنا شو اللي
+
+276
+00:32:39,710 --> 00:32:45,130
+بدنا إياه. إذا ما نقدر نحدد الإجابة تبعنا بدقة، ما عطينا
+
+277
+00:32:45,130 --> 00:32:52,680
+نقطتين P1 و P2، وقال لي: هات لي الطول تبع المتجه
+
+278
+00:32:52,680 --> 00:32:59,200
+4 P1 P2. يبقى بده يقول: المتجه 4 P1 P2، إذا
+
+279
+00:32:59,200 --> 00:33:04,500
+بده يجيب المتجه P1 P2، أربعة، يعني أربعة أمثال، و
+
+280
+00:33:04,500 --> 00:33:12,220
+بيصير، يعني كأنه طالب متجه موازٍ للمتجه P1 P2، بس طوله
+
+281
+00:33:12,220 --> 00:33:17,280
+أربعة مرات، تمام؟ كويس. يبقى خلينا نجيب المتجه
+
+282
+00:33:17,280 --> 00:33:24,470
+P1 P2 في الأول. يبقى باجي بقول له: نمرة A، بدي المتجه P1
+
+283
+00:33:24,470 --> 00:33:28,930
+P2، يبقى
+
+284
+00:33:28,930 --> 00:33:40,150
+هذا الكلام بدّه يساوي: X2 - X1، Y2 - Y1، Z2 - Z1، عشان أخذنا
+
+285
+00:33:40,150 --> 00:33:45,730
+التعريف قبل قليل. إذا بدي أطبّق هذا التعريف، يبقى بدي
+
+286
+00:33:45,730 --> 00:33:51,220
+أجي: 4 - 1، 4 - 1،
+
+287
+00:33:51,220 --> 00:33:58,560
+7 - 3، 2 - 2،
+
+288
+00:33:58,560 --> 00:34:04,160
+ناقص ناقص 2، زائد 2. يبقى صار عندي هذا
+
+289
+00:34:04,160 --> 00:34:11,660
+المتجه هو: 3، و 4، و 0، بهذا الشكل. يبقى هذا
+
+290
+00:34:11,660 --> 00:34:19,860
+المتجه P1 P2. أنا بدّي 4 P1
+
+291
+00:34:19,860 --> 00:34:25,380
+P2، المتجه اللي عندنا هذا. يبقى هذا الكلام بده
+
+292
+00:34:25,380 --> 00:34:31,880
+يساوي 4 × (3، 4، 0). يبقى هذا الكلام
+
+293
+00:34:31,880 --> 00:34:38,800
+بده يساوي: 12، 16، 0. كويس.
+
+294
+00:34:45,240 --> 00:34:50,960
+أخر حاجة أخذناها قبل قليل، كان طول المتجه C في V.
+
+295
+00:34:50,960 --> 00:34:57,680
+قلنا: absolute value للـ C في طول الـ V. احنا أخذنا
+
+296
+00:34:57,680 --> 00:35:04,500
+الـ CV، اللي هو بده يساوي absolute value للـ C في
+
+297
+00:35:04,500 --> 00:35:12,040
+طول الـ V. طيب الـ C عندنا هنا، ما كانتش بنات 4، يبقى
+
+298
+00:35:12,040 --> 00:35:17,640
+absolute value للـ 4، طول الـ V، الجذر التربيعي
+
+299
+00:35:17,640 --> 00:35:25,960
+للمركبات تبعها، هي: يبقى 3 تربيع + 4
+
+300
+00:35:25,960 --> 00:35:36,440
+تربيع + 0 تربيع، ويساوي 4 في (9 + 16) = 25، بخمسة. يبقى الطول تبعه جذر الـ
+
+301
+00:35:36,440 --> 00:35:43,260
+20. يبقى الطول تبعه 20، اللي هو
+
+302
+00:35:43,260 --> 00:35:44,100
+20
+
+303
+00:35:47,680 --> 00:35:51,520
+طب واحدة تقول: ليه؟ طب ما احنا جبنا هاي 4P و
+
+304
+00:35:51,520 --> 00:35:56,760
+طلعنا هذا، لو ربعنا هذا تحت الجذر، بيطلع 20.
+
+305
+00:35:56,760 --> 00:36:02,390
+بنقول: surely، بالتأكيد. كيف؟ 12 × 12 = 144، و
+
+306
+00:36:02,390 --> 00:36:06,150
+4 × 4 = 16. 16 × 16 = 256. 256 + 144 = 400. جذر الـ
+
+307
+00:36:06,150 --> 00:36:10,170
+400 = 20. وهو المطلوب. يعني إن عملتي زي... و
+
+308
+00:36:10,170 --> 00:36:14,890
+الله، روحتي أخدتِ الطول هذا مباشرة، بتنسي الاتنين، صح؟
+
+309
+00:36:14,890 --> 00:36:19,550
+وما أحدٍ يقدر يعترضها عالم كده. هذا هو المطلوب الأول.
+
+310
+00:36:19,550 --> 00:36:24,010
+المطلوب الثاني، نمرة B، بقول: إيه؟ هات لي هل الـ vector
+
+311
+00:36:24,010 --> 00:36:30,180
+هذا موازٍ للـ vector P1 P2 ولا لأ؟ قبل قليل قولنا
+
+312
+00:36:30,180 --> 00:36:36,640
+المتجهين المتوازيين، إذا كان واحد فيهم مضاعف للآخر.
+
+313
+00:36:36,640 --> 00:36:42,020
+قولنا: V موازٍ لـ 2V، موازٍ لـ -3V، وهكذا. إذا أنا بدّي أجي للـ
+
+314
+00:36:42,020 --> 00:36:49,220
+vector اللي عندنا هذا، اللي مضاعفينه، اللي هو قدّاش؟
+
+315
+00:36:49,220 --> 00:36:54,750
+الـ vector u اللي هو بده يساوي 9، و 12، و 0. بقدر آخذ
+
+316
+00:36:54,750 --> 00:37:02,630
+منه 3 برا من كل مركبة من هذه المركبات. بيظل
+
+317
+00:37:02,630 --> 00:37:09,190
+قدّاش عندنا هنا؟ 3، هنا 4، وهنا 0. من هو المتجه
+
+318
+00:37:09,190 --> 00:37:15,590
+اللي عندنا هذا؟ مش هو P1 P2. يبقى هذا الكلام بده
+
+319
+00:37:15,590 --> 00:37:22,030
+يساوي 3 P1 P2. صار الآن مضاعف للـ P1 P2، يبقى
+
+320
+00:37:22,030 --> 00:37:30,070
+الاثنين هذول مالهم؟ are parallel. زي ما طلع، هذول
+
+321
+00:37:30,070 --> 00:37:34,410
+متوازيين أم لا؟ يبقى إن أثبتنا إنهم متوازيين، يبقى so
+
+322
+00:37:34,410 --> 00:37:40,130
+the U and P1 P2 are parallel vectors. يبقى هذول
+
+323
+00:37:40,130 --> 00:37:51,910
+متجهات مالها؟ متوازية. نجي
+
+324
+00:37:51,910 --> 00:37:59,550
+لتعريف جديد، definition.
+
+325
+00:37:59,550 --> 00:38:05,210
+سمعتوا في الفيزياء بمتجه الوحدة؟ أحد فيكم بتذكرني، ولا بالبلدي يعني مش بتعرفوا متجه
+
+326
+00:38:05,210 --> 00:38:11,030
+الوحدة؟ طوله واحد صحيح، يعني طوله واحد. من واحدة
+
+327
+00:38:11,030 --> 00:38:14,410
+الطول. إن كان مثلاً بالمتر، بقول: متر، طول متر واحد.
+
+328
+00:38:14,410 --> 00:38:20,440
+إن كان بالأقدام، بقول: قدم واحد، أو بالسنتيمتر بقول
+
+329
+00:38:20,440 --> 00:38:26,980
+سنتيمتر واحد، ولا كده تمام؟ إذا متجه الوحدة هو
+
+330
+00:38:26,980 --> 00:38:31,340
+عبارة عن متجه with length، والطول تبعه واحد صحيح.
+
+331
+00:38:31,340 --> 00:38:36,400
+إبقى باجي بقول: that unit vector is a vector with
+
+332
+00:38:36,400 --> 00:38:43,240
+length one. يبقى
+
+333
+00:38:43,240 --> 00:38:54,670
+هو عبارة عن متجه، الطول تبعه يساوي الواحد الصحيح.
+
+334
+00:38:54,670 --> 00:39:03,070
+for example، مثلاً، four.
+
+335
+00:39:16,580 --> 00:39:27,400
+example. في عندنا حاجة اسمها: the standard unit
+
+336
+00:39:27,400 --> 00:39:36,020
+vectors. الـ vectors المتعارف عليهم في كل كتب
+
+337
+00:39:36,020 --> 00:39:41,700
+الرياضيات والفيزياء وما إلى ذلك، ثلاثة: الـ I، والـ
+
+338
+00:39:41,700 --> 00:39:47,650
+J، والـ K. هؤلاء المتعارف عليهم، تلك متجهات
+
+339
+00:39:47,650 --> 00:39:51,770
+وحدة في اتجاه الـ coordinate axes، وكل واحد طوله
+
+340
+00:39:51,770 --> 00:39:57,670
+يساوي قدّاش؟ يعني على الطبيعة، لو جينا كل هذه المحاور
+
+341
+00:39:57,670 --> 00:40:05,230
+شكلهم هذا: هذا محور X، هذا محور Y، هذا محور Z، فإن
+
+342
+00:40:05,230 --> 00:40:10,920
+المتجهات الثلاثة، المتجه الأول، هو خط طوله هنا يساوي
+
+343
+00:40:10,920 --> 00:40:17,640
+الوحدة. يبقى بيكون هذا المتجه I. هنا خط طوله كذلك
+
+344
+00:40:17,640 --> 00:40:23,740
+يساوي الوحدة. يبقى بيكون هذا هو المتجه J. هنا خط طوله
+
+345
+00:40:23,740 --> 00:40:29,620
+يساوي الوحدة كذلك، جذر الوحدة الثلاثة، يبقى هذا
+
+346
+00:40:29,620 --> 00:40:35,800
+المتجه K، بهذا الشكل. يبقى هذا الـ I، والـ J، والـ K
+
+347
+00:40:35,800 --> 00:40:43,960
+اللي هي الـ standard unit vector. ما بقى
+
+348
+00:40:43,960 --> 00:40:48,540
+رأيك يا بنات، أي vector بيجي في بالك، بقدر أكتبه
+
+349
+00:40:48,540 --> 00:40:52,300
+بإشارة الـ standard unit vectors، هذول؟  الدلالة
+
+350
+00:40:52,300 --> 00:41:02,230
+كيف؟ علاقة لمن؟ فهمت قصدي؟ قصدي، مكتوب لي أنه لو بدّي
+
+351
+00:41:02,230 --> 00:41:08,130
+أجيب متجه الوحدة لمتجه معيّن، بروح بقسم المتجه على
+
+352
+00:41:08,130 --> 00:41:12,850
+طول المتجه. مش هذا اللي قصدته عادة. اللي قصدته أنه
+
+353
+00:41:12,850 --> 00:41:19,150
+أي vector عندنا، بقدر أكتبه بدلالة الـ three: الـ I، والـ
+
+354
+00:41:19,150 --> 00:41:25,050
+J، والـ K، تمام؟ كيف يكون التالي؟ هكتب هالك remark
+
+355
+00:41:25,050 --> 00:41:25,650
+هذه.
+
+356
+00:41:30,950 --> 00:41:37,150
+أي vector V
+
+357
+00:41:37,150 --> 00:41:47,950
+بده يساوي V1، و V2، و V3، is written أو
+
+358
+00:41:47,950 --> 00:41:58,210
+is a linear combination of
+
+359
+00:41:58,210 --> 00:41:59,710
+the
+
+360
+00:42:02,440 --> 00:42:14,960
+Standard Unit Vectors. كيف أصفّه؟ كالتالي: طلع لي الـ
+
+361
+00:42:14,960 --> 00:42:23,400
+vector V، هاي مركباته V1، و V2، و V3. بقدر أكتب هذا الـ
+
+362
+00:42:23,400 --> 00:42:36,190
+vector على شكل مجموع ثلاثة متجهات. كيف؟ كالتالي: V1، V2،
+
+363
+00:42:36,190 --> 00:42:41,690
+V3،
+
+364
+00:42:41,690 --> 00:42:44,990
+V4،
+
+365
+00:42:44,990 --> 00:42:45,170
+V5 V6 V7 V8 V9 V10 V11 V12 V13 V12 V13 V13 V13 V13
+
+366
+00:42:45,170 --> 00:42:45,770
+V13 V13 V13 V13 V13 V13 V13 V13 V13 V13 V13 V13
+
+367
+00:42:45,770 --> 00:42:45,810
+V13 V13 V13 V13 V13 V13 V13 V13 V13 V13 V13 V13
+
+368
+00:42:45,810 --> 00:42:45,910
+V13 V13 V13 V13 V13 V13 V13 V13 V13 V13 V13 V13
+
+369
+00:42:45,910 --> 00:42:46,670
+V13 V13 V13 V13 V13 V13 V13 V13 V13 V13 V13 V13
+
+370
+00:42:46,670 --> 00:42:48,690
+V13 V13 V13 V13 V13 V13 V13 V13 V13 V13
+
+371
+00:42:52,760 --> 00:42:59,500
+اللي بعده هو: 0 + V2 + 0 في V2 + 0 + V3
+
+372
+00:42:59,500 --> 00:43:06,060
+في V3. طيب الآن بدّي أجي ضرب scalar في vector، يبقى
+
+373
+00:43:06,060 --> 00:43:09,300
+scalar إن ضربته في الداخل، ولا طلعته برا، الاثنين
+
+374
+00:43:09,300 --> 00:43:13,900
+are the same. يبقى بقدر أقول: هذا الكلام بده يصير
+
+375
+00:43:13,900 --> 00:43:27,550
+اللي هو V1 × (1، 0، 0)، تمام؟ زائد V2 (0، 1،
+
+376
+00:43:27,550 --> 00:43:40,770
+0) زائد V3 (0، 0، 1). شكلها يعني احنا
+
+377
+00:43:40,770 --> 00:43:44,430
+قولنا الـ standard unit vectors، وقولنا لك هاي الـ
+
+378
+00:43:44,430 --> 00:43:49,340
+standard unit vectors اللي هو I، و J، و K. لو جيت
+
+379
+00:43:49,340 --> 00:43:55,480
+بقول لك هنا الـ I بده يساوي هو (1، 0، 0)، صحيح
+
+380
+00:43:55,480 --> 00:44:01,340
+ولا لا؟ صحيح. ليش؟ لأن النقطة هذه إحداثياتها (1،
+
+381
+00:44:01,340 --> 00:44:09,280
+0، 0). وهذا النقطة (0، 1، 0). وهذا
+
+382
+00:44:09,280 --> 00:44:19,310
+النقطة (0، 0، 1). الـ J هيكون يساوي (0، 1، 0)،
+
+383
+00:44:19,310 --> 00:44:28,390
+والـ K اللي هو بده يساوي (0، 0، 1). إذا بناءً عليه،
+
+384
+00:44:28,390 --> 
+
+445
+00:50:42,390 --> 00:50:50,690
+أكمل معناه لو جاء المتجه V مضروبا في رقم
+
+446
+00:50:50,690 --> 00:50:56,620
+بنفس الرقم هل تتغير قيمة هذا المتجه
+
+447
+00:50:56,620 --> 00:51:01,400
+أو شكله؟ لأ، طب إيش رأيك؟ بدي أختار رقم محدد، الرقم
+
+448
+00:51:01,400 --> 00:51:07,900
+المحدد هو عبارة عن طول هذا المتجه، فبقدر أقول هذا
+
+449
+00:51:07,900 --> 00:51:17,380
+الكلام بيساوي طول الـ V في الـ V على طول الـ V، كأن
+
+450
+00:51:17,380 --> 00:51:20,680
+أنا أتكلم في جد يا شباب؟ في واحد صح يقول متجه كما هو
+
+451
+00:51:20,680 --> 00:51:27,080
+بدي أعيد الصياغة اللي أنا قلتها، يبقى طول الـ V ضربته
+
+452
+00:51:27,080 --> 00:51:32,740
+في الـ V على طول الـ V، قلت هذا على هذا وهذا زي ما هو
+
+453
+00:51:32,740 --> 00:51:41,100
+هذا مين؟ بنات، الجزء الأول طول الـ V، يبقى هذا الـ N
+
+454
+00:51:41,100 --> 00:51:50,400
+أو الـ V، هذا اتجاه الـ V، يعني متجه الوحدة في اتجاه الـ V
+
+455
+00:51:50,770 --> 00:51:58,550
+يبقى هذا الـ direction of v، إذا بنبني على الرمز و
+
+456
+00:51:58,550 --> 00:52:04,470
+تقولي أي non zero vector بقدر أكتبه بدلالة الـ length
+
+457
+00:52:04,470 --> 00:52:10,190
+تبعه والـ direction تبعه، يبقى هاي الـ direction of
+
+458
+00:52:10,190 --> 00:52:15,070
+v وهاي الـ length تبعه من تبع الـ v، يبقى أي متجهة بقدر
+
+459
+00:52:15,070 --> 00:52:19,350
+أكتبه بالشكل اللي قدامه، نيجي ناخد مثال، example
+
+460
+00:52:28,940 --> 00:52:33,140
+example one بيقول
+
+461
+00:52:33,140 --> 00:52:44,360
+let الـ U تساوي (2, 0, -3) and الـ V
+
+462
+00:52:44,360 --> 00:52:53,240
+بده يساوي (0, 1, -2)، fine، هو إيش
+
+463
+00:52:53,240 --> 00:53:06,160
+بدنا نمرة A: 2U - 3V، نمرة B: طول 2U - 3V،
+
+464
+00:53:06,160 --> 00:53:15,140
+نمرة C: write
+
+465
+00:53:15,140 --> 00:53:26,880
+the vector، write the vector 2U - 3V as
+
+466
+00:53:26,880 --> 00:53:34,880
+a product of
+
+467
+00:53:34,880 --> 00:53:50,200
+its length and direction. نمر دي
+
+468
+00:53:50,200 --> 00:53:54,560
+find
+
+469
+00:53:54,560 --> 00:54:07,640
+a vector of length 10، a vector of length 10 in
+
+470
+00:54:07,640 --> 00:54:15,240
+the opposite direction، in
+
+471
+00:54:15,240 --> 00:54:18,320
+the
+
+472
+00:54:18,320 --> 00:54:22,680
+opposite direction of U
+
+473
+00:54:59,060 --> 00:55:03,500
+نرجع للسؤال اللي كتبته مرة ثانية، نقرأ هذا السؤال
+
+474
+00:55:03,500 --> 00:55:09,700
+قراءة جيدة، ثم بعد ذلك أروح أشوف ما هو المطلوب في
+
+475
+00:55:09,700 --> 00:55:14,840
+كل نقطة من النقاط في المثال، السؤال مرة ثانية، عطيني
+
+476
+00:55:14,840 --> 00:55:20,320
+two vectors U و V، قال لي هاتلي 2U - 3
+
+477
+00:55:20,320 --> 00:55:27,860
+V، يعني أنا بدي أجيب مضاعفات 2U، و 3 أمثال V
+
+478
+00:55:28,240 --> 00:55:33,480
+وأطرح 2U من 3V يعني ثلاث عمليات بده يشتغل، مش
+
+479
+00:55:33,480 --> 00:55:37,900
+هي؟ المطلوب الثاني يعتمد على الأول، مطلوب المتجه
+
+480
+00:55:37,900 --> 00:55:42,440
+اللي بيطلع عندك، بده تجيب قد إيش طوله، المطلوب الثاني،
+
+481
+00:55:42,440 --> 00:55:48,440
+اللي بدك تكتب المتجه اللي طالع عندك بدلالة الطول
+
+482
+00:55:48,440 --> 00:55:54,800
+تبعه والاتجاه، يعني كان طلب قد إيش متجه الوحدة في
+
+483
+00:55:54,800 --> 00:56:01,500
+هذا الاتجاه بطريقة خفية، مقدار واتجاه، المطلوب الرابع
+
+484
+00:56:01,500 --> 00:56:07,840
+قال لي اه، بدك تجيب vector طوله 10 وحدات طول في
+
+485
+00:56:07,840 --> 00:56:13,780
+اتجاه معاكس للاتجاه اللي إنت جيبته، والله كويس
+
+486
+00:56:13,780 --> 00:56:17,240
+يعني شغل كثير بده هذه الشغلة، لكن تعالَ نشوف هل هو
+
+487
+00:56:17,240 --> 00:56:21,320
+كثير والله، يعني قال للمطلوب الأول هات الـ 2U
+
+488
+00:56:21,320 --> 00:56:26,230
++ 3V، هذه بسيطة، يبدأ يضرب الأول في 2 و
+
+489
+00:56:26,230 --> 00:56:30,090
+الثاني في 3، ويطرح 2 من بعض، يبقى
+
+490
+00:56:30,090 --> 00:56:36,930
+باقي بقوله هنا 2U - 3V تساوي، إذا إنت
+
+491
+00:56:36,930 --> 00:56:41,470
+حاجة على الـ U، اضربها في قد إيش؟ في 2، يبقى هاي
+
+492
+00:56:41,470 --> 00:56:51,350
+4، وهي 0، وهي -6، ناقص المتجه الثاني، أو
+
+493
+00:56:51,350 --> 00:56:56,490
+بقدر أكتب يا بنات، زائد وأدخل الـ -3 جوا،
+
+494
+00:56:56,490 --> 00:57:02,410
+مظبوط؟ يعني بقدر الناقص هذه أكتبها زائد واللي جوا
+
+495
+00:57:02,410 --> 00:57:07,470
+هنا أديره وين، فـ -3، يبقى 0 وهنا -
+
+496
+00:57:07,470 --> 00:57:13,190
+3 وهنا +6 بالشكل هذا، يبقى هذا
+
+497
+00:57:13,190 --> 00:57:17,930
+الكلام بده يساوي (4, 0, -3)، (0, -3, 6) يبقى جبت له
+
+498
+00:57:17,930 --> 00:57:22,610
+المطلوب الأول، يقول لي عليه ثلاث عمليات بسهولة
+
+499
+00:57:22,610 --> 00:57:26,390
+بخطوة واحدة، طيب، نبدأ في نمرة ب، نمرة ب قال لي
+
+500
+00:57:26,390 --> 00:57:33,770
+قد إيش طول المتجه هذا؟ إذا هاي حصلت عليه، إذا باجي
+
+501
+00:57:33,770 --> 00:57:39,120
+بقوله طول المتجه 2U - 3V اللي هو
+
+502
+00:57:39,120 --> 00:57:45,640
+الـ square root لـ 4 تربيع + (-3) تربيع
+
+503
+00:57:45,640 --> 00:57:51,980
+تربيع + 0 تربيع، لو جمعت التربيع 16 و 9 و
+
+504
+00:57:51,980 --> 00:57:57,160
+25 يبقى الجواب يساوي 5، نمر سي،
+
+505
+00:57:57,160 --> 00:58:05,020
+نمر سي بيقول لي اكتب المتجه كحاصل ضرب الطول تبعه في الـ
+
+506
+00:58:05,020 --> 00:58:12,260
+direction، الطول إحنا حصلنا عليه، هي 5
+
+507
+00:58:12,260 --> 00:58:18,160
+يبقى ضايل عندي الـ direction، يعني الـ direction of
+
+508
+00:58:18,160 --> 00:58:27,420
+v is the unit، unit الـ vector is the unit vector in
+
+509
+00:58:27,420 --> 00:58:39,980
+the direction of
+
+510
+00:58:39,980 --> 00:58:46,720
+V، that is الـ V على طول أو، مستحيل أقول الـ V على
+
+511
+00:58:55,640 --> 00:58:56,340
+طول الـ V
+
+512
+00:59:19,890 --> 00:59:27,710
+يبقى هنا w وهنا w، يبقى بالحق أقول in the
+
+513
+00:59:27,710 --> 00:59:34,940
+direction of w، that is اللي هو الـ w على طول
+
+514
+00:59:34,940 --> 00:59:42,900
+الـ w، الـ w اللي هو قد إيش؟ الـ w اللي هو عندي
+
+515
+00:59:42,900 --> 00:59:48,400
+على طول الخط اللي طالع فوق اللي هو (4, -3, 0) على قد إيش؟ على 5، اللي هو بده يساوي
+
+516
+00:59:55,120 --> 01:00:00,780
+(4/5, -3/5, 0)
+
+517
+01:00:03,710 --> 01:00:09,490
+هو بالسؤال، هو هل هذا يا ترى فعلاً unit vector؟ تعالَ
+
+518
+01:00:09,490 --> 01:00:18,610
+ربع 16/25 + 9/25 + 0 = 25/25 = 1
+
+519
+01:00:18,610 --> 01:00:24,990
+قد إيش؟ يبقى فعلاً هذا هو unit vector، بناء عليه بقدر
+
+520
+01:00:24,990 --> 01:00:32,830
+أقوله لـ 2U - 3V بده يساوي أقوله قد إيش؟
+
+521
+01:00:33,020 --> 01:00:41,740
+5 والـ unit vector تبعه في، في (4/5, -3/5, 0) بهذا الشكل
+
+522
+01:00:41,740 --> 01:00:49,640
+يبقى هذا الـ
+
+523
+01:00:49,640 --> 01:00:57,680
+length وهذا الـ direction يبقى
+
+524
+01:00:57,680 --> 01:01:03,120
+هذا المقدار جيد، انتهينا من المطلوب رقم C، كتبنا
+
+525
+01:01:03,120 --> 01:01:08,180
+الـ vector 2U - 3C as a product of length and
+
+526
+01:01:08,180 --> 01:01:18,540
+direction، هات لي متجه طوله 10 في عكس اتجاه 2U - 3V
+
+527
+01:01:18,540 --> 01:01:27,540
+الـ unit vector في اتجاه 2U - 3V
+
+528
+01:01:30,830 --> 01:01:35,630
+مظبوط؟ يعني هذا هو الـ unit vector، عكسه بدي أحط
+
+529
+01:01:35,630 --> 01:01:42,110
+إشارة سالبة، وجد عشرة مرات بدي أضرب في 10، تمام؟ يبقى
+
+530
+01:01:42,110 --> 01:01:53,970
+باجي بقول هنا the، نمر دي، the unit vector in the
+
+531
+01:01:53,970 --> 01:02:00,290
+direction، in the opposite direction in the
+
+532
+01:02:00,800 --> 01:02:07,960
+opposite direction of
+
+533
+01:02:07,960 --> 01:02:21,950
+2U - 3V اللي هو -4/5، -3/5، يبقى الآن نيجي للمطلوب الرابع والأخير
+
+534
+01:02:29,090 --> 01:02:32,090
+هو الـ vector of length 10 in the opposite
+
+535
+01:02:32,090 --> 01:02:36,750
+direction of 2U - 3، عكس هذا
+
+536
+01:02:36,750 --> 01:02:39,650
+الاتجاه هو المتجه اللي قدامنا هذا اللي هو المتجه
+
+537
+01:02:39,650 --> 01:02:44,800
+الوحدة هذا، يبقى أبدأ أضرب -5 في 10، يبقى الآن
+
+538
+01:02:44,800 --> 01:02:54,080
+10 في (-4/5، 3/5، 0) واللي
+
+539
+01:02:54,080 --> 01:02:58,860
+هو بده يساوي متجه جديد، هدخل 10 على كل component
+
+540
+01:02:58,860 --> 01:03:03,360
+من هذه الـ components، يبقى هنا إيش بيصير -8
+
+541
+01:03:03,360 --> 01:03:08,040
+10/5 = 2، والمركبة الثانية بيصير
+
+542
+01:03:08,040 --> 01:03:08,740
+6
+
+543
+01:03:11,290 --> 01:03:15,950
+يبقى يا إخوة، والكلام للسامعين، لو حبينا نجيب طول
+
+544
+01:03:15,950 --> 01:03:19,510
+هذا الـ vector بنقول الجذر التربيعي لـ -8
+
+545
+01:03:19,510 --> 01:03:24,950
+تربيع = 64 + 6 تربيع = 36
+
+546
+01:03:24,950 --> 01:03:29,210
++ 0 = 100، قد إيش جذر الـ 100؟ 10 وهو
+
+547
+01:03:29,210 --> 01:03:36,660
+المطلوب، يبقى هذا يثبت صحة ما ذكرناه قبل قليل، حظي
+
+548
+01:03:36,660 --> 01:03:39,880
+الهي استفسار هنا في هذا المثال قبل أن نذهب إلى
+
+549
+01:03:39,880 --> 01:03:46,400
+المثال الثاني، طيب الآن نمسح هذا المثال ونروح
+
+550
+01:03:46,400 --> 01:03:51,600
+للمثال رقم 2 على هذا الموضوع
+
+551
+01:04:17,320 --> 01:04:28,440
+بنيجي لـ Example 2 بيقول
+
+552
+01:04:28,440 --> 01:04:32,880
+F المتجه
+
+553
+01:04:32,880 --> 01:04:44,880
+AB يجب أن يساوي -7i + 3j + 8k، and
+
+554
+01:04:46,720 --> 01:04:56,900
+الـ A is the point هي عبارة عن النقطة اللي هو -
+
+555
+01:04:56,900 --> 01:05:09,080
+2 و -3 و 6، find the point B
+
+556
+01:05:19,500 --> 01:05:26,120
+نرجع لسؤالنا مرة ثانية، معطيني متجه AB = -7i
+
+557
+01:05:26,120 --> 01:05:32,780
++ 3j + 8k ومعطيني إحداثيات النقطة A، وطلب
+
+558
+01:05:32,780 --> 01:05:39,700
+مني قد إيش إحداثيات النقطة B، بقوله كويس المتجه هذا
+
+559
+01:05:39,700 --> 01:05:44,100
+هو عبارة عن المتجه AB
+
+560
+01:05:47,130 --> 01:05:53,450
+هذه النقطة A على سبيل المثال هي ما طال، هي -
+
+561
+01:05:53,450 --> 01:06:01,310
+2 و -3 و 6، وهذه النقطة B اللي مش
+
+562
+01:06:01,310 --> 01:06:07,690
+عارفينها، تمام؟ إذا لو حطيت لها رموز وليكن على سبيل
+
+563
+01:06:07,690 --> 01:06:13,150
+المثال X، Y، و Z، إذن
+
+564
+01:06:13,550 --> 01:06:17,630
+بدي أكوّن المتجه اللي عندي وأسويه بالمتجه هذا
+
+565
+01:06:17,630 --> 01:06:23,890
+يبقى بناء عليها بيكون المتجه عندي AB هو المتجه
+
+566
+01:06:23,890 --> 01:06:30,910
+التالي، (X - (-2))i + (Y - (-3))j + (Z - 6)k = -7i + 3j + 8k
+
+567
+01:06:30,910 --> 01:06:40,490
+بده يساوي -7i + 3j + 8k، يبقى x + 2 في اتجاه الـ
+
+568
+01:06:40,490 --> 01:06:50,100
+i + y + 3 في اتجاه الـ j + z - 6 في اتجاه الـ
+
+569
+01:06:50,100 --> 01:06:56,780
+k، هذول المتجهين متساويين، أخذنا قبل قليل متجهين
+
+570
+01:06:56,780 --> 01:07:02,500
+متساويين إذا كانت المركبات المتناظرة متساوية، بناء
+
+571
+01:07:02,500 --> 01:07:09,080
+عليه، بصير عندي x + 2 = -7، هذا بده
+
+572
+01:07:09,080 --> 01:07:16,140
+يعطيك أن x = -9، بعدها y + 3
+
+573
+01:07:16,140 --> 01:07:22,060
+بده يساوي 3، هذا معناه أن y =
+
+574
+01:07:22,060 --> 01:07:30,160
+0، اللي بعدها z - 6 بده يساوي 8، هذا
+
+575
+01:07:30,160 --> 01:07:37,840
+معناته أن z = 14، من هذا الكلام بيطلع أن
+
+576
+01:07:37,840 --> 01:07:46,020
+الـ point B إحداثياتها الأول -9، الإحداثي
+
+577
+01:07:46,020 --> 01:07:51,340
+الثاني 0، الإحداثي الثالث اللي هو 14، و
+
+578
+01:07:51,340 --> 01:07:59,820
+هكذا، نيجي لبعض الخواص على الـ vector، يبقى بالدالي أن
+
+579
+01:07:59,820 --> 01:08:13,720
+الـ properties of vector operations، بعض
+
+580
+01:08:13,720 --> 01:08:19,820
+الخواص البسيطة على العمليات على الـ vector، نيجي بقول
+
+581
+01:08:19,820 --> 01:08:30,590
+إذا الـ U، والـ V، والـ W are vectors، and
+
+582
+01:08:30,590 --> 01:08:42,230
+الـ A، والـ B are scalars، يبقى كميات قياسية، ذاتية
+
+583
+01:08:42,230 --> 01:08:51,560
+النقطة الأولى، U + V = V + U، النقطة الثانية U + V + W =
+
+584
+01:08:51,560 --> 01:09:00,680
+U + (V + W)، النقطة الثالثة U + 0 = U، النقطة الرابعة U + (-U) =
+
+585
+01:09:00,680 --> 01:09:09,000
+0، النقطة الخامسة 0 + U = 0، النقطة
+
+586
+01:09:09,000 --> 01:09:19,460
+السادسة 1 × U = U، النقطة السابعة A × (B × U) = (A × B)
+
+587
+01:09:19,460 --> 01:09:29,700
+× U، الثامنة A × (U + V) = A × U + A × V، التاسعة
+
+588
+01:09:29,700 --> 01:09:37,820
+والأخيرة A + B × U = A × U + B × U، بدي
+
+589
+01:09:37,820 --> 01:09:44,360
+أحاول أرجع الآن لمعنى كل خاصية من هذه الخواص حتى
+
+590
+01:09:44,360 --> 01:09:54,910
+نفهم فهماً صحيحاً، مش أكتب وأمشي، شوفوا يا بنات الآن
+
+591
+01:09:54,910 --> 01:10:02,670
+بيقول لو عندي ثلاث vectors U، V، و W
+
+592
+01:10:02,670 --> 01:10:09,670
+وعندي two scalars A و B، يبقى في عندي U + V
+
+593
+01:10:09,670 --> 01:10:15,650
+= V + U، إيش العملية هذه؟ الإبدالية، يبقى
+
+594
+01:10:15,650 --> 01:10:25,950
+عملية الجمع عن المتجهات عملية إبدالية، الـ addition of two vectors is a commutative operation، عملية
+
+595
+01:10:25,950 --> 01:10:31,690
+الجمع عن الـ vectors عملية إبدالية، لو جمعت الـ U والـ
+
+596
+01:10:31,690 --> 01:10:38,330
+V أولاً، وأضفت الناتج للـ W، تماماً كما لو جمعت الـ V والـ
+
+597
+01:10:38,330 --> 01:10:44,110
+W أولاً، ثم أضفت لهم من الـ U، يبقى هذه بسميها
+
+598
+01:10:44,110 --> 01:10:50,650
+associative، عملية إدماجية أو تجميعية، associative
+
+599
+01:10:50,650 --> 01:10:51,250
+property
+
+600
+01:12:03,540 --> 01:12:07,020
+الـ 0 هذا يا بنات scalar ولا vector؟
+
+601
+01:12:10,360 --> 01:12:16,400
+إحنا أخذنا عملية جمع vector مع scalar؟ لأ، أخذنا ضرب
+
+602
+01:12:16,400 --> 01:12:20,620
+scalar في vector، لكن جمع لأ، يبقى الـ 0 بعمله
+
+603
+01:12:20,620 --> 01:12:25,100
+دائرة كبيرة، بنات، zero vector، الـ scalar بعمله دائرة
+
+604
+01:12:25,100 --> 01:12:32,040
+صغيرة، يبقى هذا هو zero vector، يبقى الـ U vector +
+
+605
+01:12:32,040 --> 01:12:39,050
+الـ zero vector يساوي الـ U vector، هنا الـ U +
+
+606
+01:12:39,050 --> 01:12:45,370
+-U، يعني المتجه والمتجه المعاكس إله تماماً،
+
+607
+01:12:45,370 --> 01:12:51,010
+مجموعهم قد إيش؟ 0، scalar ولا vector؟ يعني
+
+608
+01:12:51,010 --> 01:12:54,550
+مجموع أي two vectors بده يعطيني vector، حتى وإن
+
+609
+01:12:54,550 --> 01:12:59,470
+كان الـ 0 يبقى هذا الـ zero vector، طيب الـ 0 × U
+
+610
+01:12:59,470 --> 01:13:05,540
+scalar الـ 0 هذا ولا vector؟ scalar، لأن ضرب
+
+611
+01:13:05,540 --> 01:13:07,560
+الـ vectors في عالمنا لا يوجد جمع، لا يوجد
+
+612
+01:13:07,560 --> 01:13:09,780
+جمع لا يوجد جمع لا يوجد جمع لا يوجد جمع لا يوجد
+
+613
+01:13
+
+667
+01:19:01,510 --> 01:19:06,090
+الصيغة هذه الاثنين قوسين إذا أنا بدي أروح أجيب له
+
+668
+01:19:06,090 --> 01:19:14,240
+متجه P1 P2 يساوي بدي أكتب  دبري يا بنات يبقى هذا كأنه
+
+669
+01:19:14,240 --> 01:19:17,260
+يبدأ كتابة يابا كتابة دلالة الاثنين المقرنين
+
+670
+01:19:17,260 --> 01:19:20,680
+القوسين المقرنين هما دلالة الـ I و الـ J و الـ K سيان
+
+671
+01:19:20,680 --> 01:19:26,700
+كل واحد إذا لو جاي تقول أربعة ناقص واحد في اتجاه
+
+672
+01:19:26,700 --> 01:19:33,340
+الـ I زائد  ثلاثة ناقص اثنين ناقص أربعة في اتجاه
+
+673
+01:19:33,340 --> 01:19:35,200
+الـ J زائد
+
+674
+01:19:40,290 --> 01:19:47,810
+يبقى هذا عبارة عن ثلاثة I وهنا ناقص ستة J وهنا
+
+675
+01:19:47,810 --> 01:19:56,990
+زائد اثنين K بدي أجيب قيمة  P1 P2 اللي
+
+676
+01:19:56,990 --> 01:20:05,900
+هو بده يساوي جذر التربيع لتسعة زائد ستة وثلاثين زائد
+
+677
+01:20:05,900 --> 01:20:12,400
+أربعة ويساوي جذر تسعة وأربعين تحت
+
+678
+01:20:12,400 --> 01:20:21,840
+الجذر تسعة وأربعين سبعة يبقى باجي بقول له the direction of
+
+679
+01:20:21,840 --> 01:20:35,120
+P1 P2 اللي هو P1 P2 على طول الـ P1 P2 واللي هو بده
+
+680
+01:20:35,120 --> 01:20:43,240
+يساوي 7 كله على سبعة يبقى ثلاثة أسباع في اتجاه الـ I ناقص ستة
+
+681
+01:20:43,240 --> 01:20:50,480
+أسباع في اتجاه الـ J زائد سبعة أسباع في اتجاه الـ K  نمرة
+
+682
+01:20:50,480 --> 01:20:57,030
+B قال لي هاتلي الـ midpoint ما بين النقطتين الاثنين
+
+683
+01:20:57,030 --> 01:21:03,270
+هدول يبقى الـ M تساوي مباشرة يبقى بده أجمع أربعة
+
+684
+01:21:03,270 --> 01:21:09,310
+زائد واحد على اثنين أربعة زائد واحد على اثنين اللي
+
+685
+01:21:09,310 --> 01:21:15,910
+بعدها ناقص اثنين زائد أربعة على اثنين
+
+686
+01:21:19,710 --> 01:21:26,650
+اللي بعدها سبعة زائد خمسة على اثنين سبعة زائد خمسة
+
+687
+01:21:26,650 --> 01:21:33,010
+كله على اثنين واللي هي بدها تساوي خمسة على
+
+688
+01:21:33,010 --> 01:21:38,810
+اثنين تبقى كما هي وهنا اثنين على اثنين واحد
+
+689
+01:21:38,810 --> 01:21:43,690
+واحد وعشرة على اثنين اللي هو بقد ايش ستة هذه النقطة
+
+690
+01:21:43,690 --> 01:21:50,960
+المتوسطة آخر مثال في محاضرة اليوم بيقول ما يأتي له
+
+691
+01:21:50,960 --> 01:21:58,980
+سؤال 14 من الكتاب بيقول find a unit vector find
+
+692
+01:21:58,980 --> 01:22:13,660
+the unit vector that makes an angle that makes an
+
+693
+01:22:13,660 --> 01:22:16,080
+angle
+
+694
+01:22:19,550 --> 01:22:29,030
+ثيتا تساوي سالب ثلاثة باي على أربعة with the
+
+695
+01:22:29,030 --> 01:22:38,950
+positive with the positive اللي هو x أكسي x axis
+
+696
+01:23:00,440 --> 01:23:04,160
+خلّي بالك معانا هنا والله شوية السؤال مرة ثانية
+
+697
+01:23:04,160 --> 01:23:08,560
+جاء لي هات لي متجه الوحدة اللي يصنع زاوية مقدارها
+
+698
+01:23:08,560 --> 01:23:15,200
+سالب ثلاثة باي على أربعة من اتجاه الموجب لمين للـ X
+
+699
+01:23:15,200 --> 01:23:19,980
+axis الزاوية هذه زي ما أنت شايفها زاوية سالبة وإحنا
+
+700
+01:23:19,980 --> 01:23:23,840
+أخذنا في الـ polar coordinates إنهم أول كلمة
+
+701
+01:23:23,840 --> 01:23:27,260
+أخذناهم في الـ polar coordinates ممكن الزاوية تكون
+
+702
+01:23:27,260 --> 01:23:32,460
+positive angle وممكن تكون negative angle إذا مشينا
+
+703
+01:23:32,460 --> 01:23:39,000
+counter clockwise ضد عقل الساعة وإذا مشينا مع عقل
+
+704
+01:23:39,000 --> 01:23:43,590
+الساعة فالزاوية مالها سالبة طيب إذا إحنا لو روحنا
+
+705
+01:23:43,590 --> 01:23:49,750
+مشينا مع عقارب الساعة أو لو جيت تصورت إنه في دائرة
+
+706
+01:23:49,750 --> 01:23:54,630
+عندي نصف قطر هيساوي الواحد الصحيح يبقى الدائرة
+
+707
+01:23:54,630 --> 01:24:10,310
+هتأخذ الشكل التالي الشكل اللي عندنا هذا تمام؟
+
+708
+01:24:10,650 --> 01:24:17,290
+يبقى هذه الدرجة طيب بتساوي قد ايش 135 درجة بس وين
+
+709
+01:24:17,290 --> 01:24:24,110
+بالسالب يبقى هذه 90 مع عقارب الساعة هذه 90 وبدي
+
+710
+01:24:24,110 --> 01:24:30,970
+كمان 45 يبقى بالدرجات الخاطئة اللي عندنا تمام يبقى
+
+711
+01:24:30,970 --> 01:24:39,790
+الزاوية هذه سالب ثلاثة باي على أربعة طيب
+
+712
+01:24:40,640 --> 01:24:45,880
+لو جيت اعتبرت أن هذا متجه وطوله يساوي الواحد
+
+713
+01:24:45,880 --> 01:24:51,000
+الصحيح إذا ايش مركبه في اتجاه محور X واِيش مركبه في
+
+714
+01:24:51,000 --> 01:24:57,440
+اتجاه محور Y؟ يعني لو اعتبرت أن هذا متجه وطوله
+
+715
+01:24:57,440 --> 01:25:01,760
+واحد صحيح، لماذا؟ لأنه قال لي هذا unit vector،
+
+716
+01:25:01,760 --> 01:25:08,200
+تمام؟ إذا بناء عليه بدي يكون الـ unit vector u بدي
+
+717
+01:25:08,200 --> 01:25:14,580
+يساوي واحد في cosine اللي هو سالب ثلاثة باي على
+
+718
+01:25:14,580 --> 01:25:21,120
+أربعة في اتجاه الـ I زائد واحد sin ثلاثة باي على
+
+719
+01:25:21,120 --> 01:25:27,940
+أربعة، مين السالب؟ سالب في اتجاه مين؟ في اتجاه الـ
+
+720
+01:25:27,940 --> 01:25:34,970
+J okay ماعنديش طيب، هذا الكلام بدي يساوي الـ cosine
+
+721
+01:25:34,970 --> 01:25:40,250
+even والله odd يبقى السالب هذا معه السلامة يبقاش
+
+722
+01:25:40,250 --> 01:25:46,150
+بيصير هنا cosine ثلاثة باي على أربعة في اتجاه الـ I
+
+723
+01:25:46,150 --> 01:25:54,270
+زائد الـ sine، odd يبقى السالب أطلع بره، الـ sine ثلاثة باي على
+
+724
+01:25:54,270 --> 01:26:00,540
+أربعة في اتجاه الـ J نجي لجيب تمام
+
+725
+01:26:00,540 --> 01:26:07,240
+الزاوية اللي 135 درجة جيب تمام أي زاوية يساوي جيب
+
+726
+01:26:07,240 --> 01:26:11,660
+تمام الزاوية المكملة لها مع مراعات قاعدة الإشارات
+
+727
+01:26:11,660 --> 01:26:20,380
+جيب 135 هي جيب 45 جيب 45 واحد على جذر اثنين بس
+
+728
+01:26:20,380 --> 01:26:23,420
+هذه في الربع الثاني في الربع الثاني بالسالب
+
+729
+01:26:23,420 --> 01:26:28,700
+بالسالب لإنه درسوكوا الـ formula وحفظوكوها هذه
+
+730
+01:26:28,700 --> 01:26:36,700
+الأنشودة في الثانوية كل جيل جاء له جاء جاهز وأنا
+
+731
+01:26:36,700 --> 01:26:40,300
+جاءت في اللي ايش تمام؟ الـ English و الأمريكان عندهم
+
+732
+01:26:40,300 --> 01:26:48,000
+صيغة مناظرة All students learn calculus كل الطلاب
+
+733
+01:26:48,000 --> 01:26:51,000
+في العلم والهندسة والتدريب والتكنولوجيا
+
+734
+01:26:51,000 --> 01:26:54,660
+المعلومات بياخذوا تكامل يبقى all في الربع
+
+735
+01:26:54,660 --> 01:26:59,440
+الأول كل حرف  students الحرف الأول كل كلمة sign يعني
+
+736
+01:26:59,440 --> 01:27:07,080
+الـ j ترك الحرف الأول كل كلمة تان اللي هو غلط ترك
+
+737
+01:27:07,080 --> 01:27:11,720
+calculus الحرف الأول منه sign يبقى من هنا بقول هذه
+
+738
+01:27:11,720 --> 01:27:17,300
+في الربع اللي هو الثاني يبقى بالسالب يبقى سالب واحد
+
+739
+01:27:17,300 --> 01:27:23,420
+على جذر اثنين في اتجاه الـ I وهذه ناقص وهذه في
+
+740
+01:27:23,420 --> 01:27:27,160
+الربع الثاني والـ J في الربع الثاني موجب جيب
+
+741
+01:27:27,160 --> 01:27:32,220
+الخمسة والأربعين كذلك بواحد على جذر اثنين في اتجاه
+
+742
+01:27:32,220 --> 01:27:40,140
+الـ J طب السؤال هل هذا فعلاً unit vector؟ كيف لا؟
+
+743
+01:27:40,140 --> 01:27:44,140
+على ربع كل واحدة فيه فهذه بواحدة على جذر اثنين
+
+744
+01:27:44,140 --> 01:27:46,280
+وربعها بالنص زائد نص
+
+745
+01:27:49,220 --> 01:27:54,440
+يبقى هذا اللي طلعه unit vector في .. that makes
+
+746
+01:27:54,440 --> 01:27:59,080
+اللي عامله زاوية 135 مع الاتجاه الموجب لمحور x
+
+747
+01:27:59,080 --> 01:28:03,600
+لحد هنا stop انتهاء الـ section إلى يكون أرقام
+
+748
+01:28:03,600 --> 01:28:09,420
+المسائل المطلوب حلها في البيت إن شاء الله يبقى
+
+749
+01:28:09,420 --> 01:28:20,150
+exercises أرقام اثنين واحد ثلاثة خمسة سبعة أحد عشر
+
+750
+01:28:20,150 --> 01:28:29,550
+ثلاثة عشر سبعة عشر تسعة عشر واحد وعشرون خمسة وعشرون سبعة
+
+751
+01:28:29,550 --> 01:28:37,890
+وعشرون خمسة وعشرون سبعة وعشرون تسعة وعشرون واحد
+
+752
+01:28:37,890 --> 01:28:44,450
+وثلاثين ثلاثة وثلاثين خمسة وثلاثين سبعة وثلاثين
+
+753
+01:28:44,450 --> 01:28:46,270
+تسعة وثلاثين
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/tT-7ILSFEbI_postprocess.srt b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/tT-7ILSFEbI_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..8db64ac7d60076a99514e7dac2959e0e187a6e1f
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/tT-7ILSFEbI_postprocess.srt
@@ -0,0 +1,3012 @@
+1
+00:00:11,040 --> 00:00:15,920
+بسم الله الرحمن الرحيم انتهينا في المحاضرة الماضية
+
+2
+00:00:15,920 --> 00:00:20,300
+من ال section 12-1 والان نبدأ من section 12-2
+
+3
+00:00:20,750 --> 00:00:24,910
+أتناشر اتنين هو عبارة عن ال vectors طبعا ال
+
+4
+00:00:24,910 --> 00:00:32,570
+vectors هذه سبقت دراستها في فيزيا عامة B واحنا هنا
+
+5
+00:00:32,570 --> 00:00:37,030
+بنعطي ال section هنا من جانب وذكر فإن الذكرة تنفع
+
+6
+00:00:37,030 --> 00:00:42,330
+المؤمنين ومن جانب آخر لإن دراستنا خلال Calculus C
+
+7
+00:00:42,330 --> 00:00:48,870
+ستكون مبنية على ال vectors أو المتجهاتالكميات اللى
+
+8
+00:00:48,870 --> 00:00:53,370
+ردنا سبحانه وتعالى خلقها لنا نوعين نقول في كميات
+
+9
+00:00:53,370 --> 00:00:58,950
+قياسية وفي كميات متجهة نعطي بعض الأمثل للكميات
+
+10
+00:00:58,950 --> 00:01:05,550
+القياسية وبعض الأمثل للكميات الاتجاهية فمثلا لو
+
+11
+00:01:05,550 --> 00:01:09,270
+جيبنا بنت اي واحدة دي يكو جيبنا جسم الطول تبعها
+
+12
+00:01:09,270 --> 00:01:14,050
+لجناه مية وسبعين سنتمتر المية وسبعين سنتمتر إيه
+
+13
+00:01:14,050 --> 00:01:19,690
+الاتجاه والله بس طولبالطبع لا يوجد اتجاه لا 170
+
+14
+00:01:19,690 --> 00:01:22,870
+متر في اتجاه الشرق ولا الغرب ولا الشمال ولا الجنوب
+
+15
+00:01:22,870 --> 00:01:27,110
+ولا الشمال الغربي ولا الجنوب ولا حاجة إذا بناء
+
+16
+00:01:27,110 --> 00:01:35,090
+عليه الطول وكمية قياسية زي ايش كذلك كتلة كمية
+
+17
+00:01:35,090 --> 00:01:39,330
+قياسية زي المساحة مساحة القاعة اللي احنا فيها
+
+18
+00:01:39,330 --> 00:01:46,590
+مساحة لو قلتالطول أربعة والعرض ثلاثة يبقى ثلاثة
+
+19
+00:01:46,590 --> 00:01:51,390
+أربعة ومعاشر متر مربع هذه مساحة يبقى هذه كمية
+
+20
+00:01:51,390 --> 00:01:56,750
+قياسية حجم الغرفة اللي احنا فيها متوازن والسطيلات
+
+21
+00:01:56,750 --> 00:02:01,190
+يبقى الطول في العرض في الارتفاع يبقى الحجم كمية
+
+22
+00:02:01,190 --> 00:02:07,110
+قياسية كذلك يبقى هذه الكميات بسميها كميات قياسية
+
+23
+00:02:07,440 --> 00:02:12,280
+يبقى أول نوع من الكميات حاجة بسميها scalar
+
+24
+00:02:12,280 --> 00:02:22,360
+quantity الكمية
+
+25
+00:02:22,360 --> 00:02:30,840
+القياسية زي ايه؟ زي ال length زي
+
+26
+00:02:30,840 --> 00:02:44,700
+ال mass الكتلة زي ال areaزي الـ volume و هكذا نأتي
+
+27
+00:02:44,700 --> 00:02:51,740
+الآن نبحث عن الـ vector quantity vector quantity
+
+28
+00:02:51,740 --> 00:02:56,580
+زي
+
+29
+00:02:56,580 --> 00:03:01,700
+ايش ال vector quantity؟ اه فيها حاجة هنا نميز بين
+
+30
+00:03:01,700 --> 00:03:06,920
+امرين في حاجة اسمها speed و في حاجة اسمها velocity
+
+31
+00:03:07,630 --> 00:03:13,190
+Speed هي مقدار السرعة، لكن ال velocity هي السرعة
+
+32
+00:03:13,190 --> 00:03:17,890
+مقدار المهتجان، يعني وانت راكبه في السيارة الصورة
+
+33
+00:03:17,890 --> 00:03:21,850
+و حاسس السواك بيحكي مع مين، بيحكي مع اللي قاعد
+
+34
+00:03:21,850 --> 00:03:25,910
+جنبه، بيقوله والله كنت ماشي و ال speed و متر عندي
+
+35
+00:03:25,910 --> 00:03:30,770
+معلم كذاSpeedومتر يعني عداد السرعة هذا يعطيني قداش
+
+36
+00:03:30,770 --> 00:03:35,630
+قمت السرعة لكنه لايعطيني اتجاه السرعة اذا كذلك هنا
+
+37
+00:03:35,630 --> 00:03:43,110
+لو قلت ال speed ال speed هذه مقدار السرعة لكن جيت
+
+38
+00:03:43,110 --> 00:03:48,270
+قلت هنا velocity هذه
+
+39
+00:03:48,270 --> 00:03:54,820
+مقدار السرعة الإزاحة ازاحنا جسم في اتجاه مايبقى
+
+40
+00:03:54,820 --> 00:04:02,180
+هذه بسميها displacement الإزاحة
+
+41
+00:04:02,180 --> 00:04:07,680
+زي ايش مثلا كمان زي ال force القوة أثرت قوة على
+
+42
+00:04:07,680 --> 00:04:15,860
+جسم ما القوة بعطيها مقدرا واتجاها زي ال force و
+
+43
+00:04:15,860 --> 00:04:20,920
+هكذاهذه نوعين من الكميات حاجة بسميها scalar
+
+44
+00:04:20,920 --> 00:04:24,680
+quantity والنوع الثاني اللي هو ال vector a
+
+45
+00:04:24,680 --> 00:04:30,180
+quantity الآن بدنا نعطي تعريف لمين لل vector اللي
+
+46
+00:04:30,180 --> 00:04:36,500
+هو حسن ابني دراستنا عليه خلال هذا الفصل يبقى بداجي
+
+47
+00:04:36,500 --> 00:04:42,100
+إلى definition the vector is the direct line
+
+48
+00:04:42,100 --> 00:04:55,460
+segment of the vectoris the directed line
+
+49
+00:04:55,460 --> 00:04:58,740
+segment
+
+50
+00:04:58,740 --> 00:05:11,320
+وحد الرمز AB وعليه سهم بهذا الشكل from an initial
+
+51
+00:05:11,320 --> 00:05:28,010
+point A toA Terminal Point B الـ
+
+52
+00:05:28,010 --> 00:05:32,490
+initial point نقطة ابتدائية Terminal point نقطة
+
+53
+00:05:32,490 --> 00:05:38,470
+نهيئة التي ينتهي عندها هذا السهم يبقى directed
+
+54
+00:05:38,470 --> 00:05:46,170
+line segment يبدأ من النقطة A وينتهي في النقطة B
+
+55
+00:05:46,480 --> 00:05:53,020
+وبنحط سهم عند نقطة النهاية دليل على أن هذا ال
+
+56
+00:05:53,020 --> 00:05:57,520
+vector يبدأ من النقطة A وينتهي في النقطة B اللي
+
+57
+00:05:57,520 --> 00:06:03,020
+كنتوا في الإبتدائي بتسموه الشعاع الشعاع بيبدأ من
+
+58
+00:06:03,020 --> 00:06:08,860
+نقطة وبينتقل إلى نقطة أخرى زي ما كنا نقول مثلا
+
+59
+00:06:08,860 --> 00:06:15,280
+شعاع الشمس مصدر وين؟ الشمسثم ينتقل إلى الكون في كل
+
+60
+00:06:15,280 --> 00:06:20,620
+الاتجاهات تمام؟ يبقى هذا اللي هو بنسميه air بنسميه
+
+61
+00:06:20,620 --> 00:06:26,260
+virtual لأ لو بدنا الطول التالع يبقى باجي بقول the
+
+62
+00:06:26,260 --> 00:06:32,660
+length اللي هو الطول أو بعض المؤلفين بيسموه ال
+
+63
+00:06:32,660 --> 00:06:36,960
+magnitude اللي
+
+64
+00:06:36,960 --> 00:06:48,300
+هو المقدار magnitude أو ال lengthof the vector a,b
+
+65
+00:06:48,300 --> 00:07:00,000
+is denoted by بدي أعطيه رمز a,b وبحطه بين خطين
+
+66
+00:07:00,000 --> 00:07:04,840
+بهذا الشكل هذا ليست absolute value تبع ال calculus
+
+67
+00:07:04,840 --> 00:07:11,320
+a وإنما المقصود طول المتجه a,bالـ Length للـ
+
+68
+00:07:11,320 --> 00:07:17,440
+Vector A, B الأن بدأ نجي لتساوي Two Vectors
+
+69
+00:07:17,440 --> 00:07:28,780
+Definition Two Vectors Two Vectors Are Equal Are
+
+70
+00:07:28,780 --> 00:07:44,960
+Equal If They Have The Samelength and direction
+
+71
+00:07:44,960 --> 00:07:53,060
+يبقى
+
+72
+00:07:53,060 --> 00:07:57,080
+المتجهين متساوين
+
+73
+00:07:57,080 --> 00:08:03,200
+إذا كان لهم نفس المقدار و نفس الاتجاه كيف يعني؟ لو
+
+74
+00:08:03,200 --> 00:08:12,170
+جاءت خط ال coordinate axes المحور Xمحور Y محور Z
+
+75
+00:08:12,170 --> 00:08:15,670
+انا
+
+76
+00:08:15,670 --> 00:08:18,930
+بقول في يويندي متجهين والمتجهين اتنين هذول
+
+77
+00:08:18,930 --> 00:08:25,270
+متساويين شرط التساوي تساوي المقدار ونفس الاتجاه
+
+78
+00:08:25,270 --> 00:08:30,810
+كيف يعني لو جيت قلت افترق ان هذا بدأ من نقطة الاصل
+
+79
+00:08:30,810 --> 00:08:38,260
+وانتهى في النقطة هذه يبقى هذا سميته Vأجى vector
+
+80
+00:08:38,260 --> 00:08:45,220
+كان ابتدأ من هذه النقطة وفي اتجاه نفس المتجه اللي
+
+81
+00:08:45,220 --> 00:08:53,160
+عندنا هذا نفس المتجه وكان له نفس الطول يبقى اتنين
+
+82
+00:08:53,160 --> 00:09:00,460
+هذول are equal او لو بدأ من هنا من النقطة هذه وفي
+
+83
+00:09:00,460 --> 00:09:05,800
+الاتجاه اللي عندنا هذا وكان له نفس الطول يبقى هذا
+
+84
+00:09:05,800 --> 00:09:12,110
+المتجه Vوهذا المتجه V كذلك يبقى التلاتة هذول are
+
+85
+00:09:12,110 --> 00:09:14,690
+equal or are equivalent
+
+86
+00:09:17,580 --> 00:09:24,140
+زي بعض ولو انهم ما انطلقوش من نفس النقطة لكن لهم
+
+87
+00:09:24,140 --> 00:09:31,840
+نفس الطول ولهم كذلك نفس الاتجاه يبقى هذول بقول
+
+88
+00:09:31,840 --> 00:09:38,940
+عنهم vectors متساوية او متجهات متساوية كمان
+
+89
+00:09:38,940 --> 00:09:46,800
+definition مهم اللي هو the zero vectorالـ zero
+
+90
+00:09:46,800 --> 00:09:51,600
+vector سأعطيه run zero وقته مطول شوية لكي نتميزه
+
+91
+00:09:51,600 --> 00:09:58,000
+عن ال zero العادي تمام يبقى the zero vector اللي
+
+92
+00:09:58,000 --> 00:10:10,080
+هو حد يقول run zero is a vector with length zero
+
+93
+00:10:10,080 --> 00:10:20,170
+الطول تبعه يسوى الصفر andNo determined direction
+
+94
+00:10:20,170 --> 00:10:23,990
+يعني
+
+95
+00:10:23,990 --> 00:10:28,670
+ممكن
+
+96
+00:10:28,670 --> 00:10:34,210
+أن يكون اتجاهه في أي اتجاه بدكية يبقى الـ zero
+
+97
+00:10:34,210 --> 00:10:39,120
+vector هو عبارة عن اتجاه طوله يساوي الصفرو ممكن أن
+
+98
+00:10:39,120 --> 00:10:43,800
+يُأخذ في أي اتجاه بدنيا و من هنا قلنا no
+
+99
+00:10:43,800 --> 00:10:48,840
+determined direction مالوش اتجاه محدد يعني ممكن
+
+100
+00:10:48,840 --> 00:10:53,760
+أخذه في أي اتجاه بدون قيود without restriction بدي
+
+101
+00:10:53,760 --> 00:11:01,720
+أخذه في أي اتجاه بدية الان بدي نيجي إلى توازي
+
+102
+00:11:01,720 --> 00:11:15,580
+المتجهات كذلك definitionto non zero vectors to non
+
+103
+00:11:15,580 --> 00:11:24,080
+zero vectors u and lv are said to be parallel are
+
+104
+00:11:24,080 --> 00:11:35,280
+said to be parallel ممكن نقول عليهم متوازية
+
+105
+00:11:37,020 --> 00:11:47,360
+there is a real number if there is a real number
+
+106
+00:11:47,360 --> 00:12:03,200
+alpha such that بحيث أن ال V تساوي Alpha U for
+
+107
+00:12:03,200 --> 00:12:03,820
+example
+
+108
+00:12:09,030 --> 00:12:24,910
+The vectors مثلًا V و 3V and ناقص 2V are parallel
+
+109
+00:12:24,910 --> 00:12:29,330
+يبقى
+
+110
+00:12:29,330 --> 00:12:35,310
+هذه المتجهاتبقول عنها متجهات متساوية لأن كل واحد
+
+111
+00:12:35,310 --> 00:12:41,150
+هو عبارة عن مضاعفات الآخر وليس بالضرورة أن تكون
+
+112
+00:12:41,150 --> 00:12:46,170
+Alpha عددا صحيحا يعني ممكن يكون هذا تلك على اتنين
+
+113
+00:12:46,170 --> 00:12:51,230
+V يعني ممكن يكون كاسرك المهم واحد منهم مضاعفات
+
+114
+00:12:51,230 --> 00:12:57,550
+الآخر فمثلا لو جيت قلت هذا هو ال vector V على سبيل
+
+115
+00:12:57,550 --> 00:13:03,290
+المثالتلاتة على اتنين V جد و جداش مرة و نص و في
+
+116
+00:13:03,290 --> 00:13:09,050
+نفس الاتجاه يبقى هذا يكون بالشكل اللي عنده هذا
+
+117
+00:13:09,050 --> 00:13:16,970
+يبقى هذا تلاتة على اتنين V طب ناقص اتنين V جد V
+
+118
+00:13:16,970 --> 00:13:23,570
+مرتين بس في عكس الاتجاه يبقى هذا يكون بالشكل اللي
+
+119
+00:13:23,570 --> 00:13:29,720
+عنده هذا ناقص اتنين Vالتلاتة are parallel لغاية أن
+
+120
+00:13:29,720 --> 00:13:35,680
+الاتجاهات مالها متعاكسة مع البعض هذا كله لا يوصل
+
+121
+00:13:35,680 --> 00:13:48,540
+نجي الآن لنقطة جديدة وهي remark we
+
+122
+00:13:48,540 --> 00:13:49,780
+write any vector
+
+123
+00:13:57,840 --> 00:14:04,060
+Any vector يبقى بنقدر نكتب أي متجه algebraically
+
+124
+00:14:04,060 --> 00:14:24,240
+جابريا جابريا
+
+125
+00:14:24,240 --> 00:14:32,700
+algebraically by its componentsby its components
+
+126
+00:14:32,700 --> 00:14:36,780
+بالمركبات
+
+127
+00:14:36,780 --> 00:14:44,960
+ابتدعتها as follows مثلا
+
+128
+00:14:44,960 --> 00:14:54,300
+في ال plane and the plane ال vector v بقدر اكتبه
+
+129
+00:14:54,300 --> 00:15:02,560
+على الشكل التالي v1و V2 في الـ space in the space
+
+130
+00:15:02,560 --> 00:15:17,240
+ال V بده ساوي V1 و V2 و V3 where حيث V1 و V2 و V3
+
+131
+00:15:17,240 --> 00:15:24,780
+are the components of
+
+132
+00:15:26,740 --> 00:15:42,660
+the vector of the vector v in the direction of the
+
+133
+00:15:42,660 --> 00:15:51,180
+coordinate axes
+
+134
+00:15:51,180 --> 00:16:00,020
+كيف هذا الكلامنحاول أن نضع الكلام اللي نقوله على
+
+135
+00:16:00,020 --> 00:16:04,660
+الرسم، لكي يكون واضح أمامنا تماما
+
+136
+00:16:45,590 --> 00:16:51,170
+تشوف؟ لو جاء تخيلتي عندى ان في vector V بهذا الشكل
+
+137
+00:16:51,170 --> 00:16:58,390
+يبقى هذا هو ال vector Vبنشوف وين المُركّبات تبعات
+
+138
+00:16:58,390 --> 00:17:03,830
+الـ vector V يبقى لو جيت من هنا نزلت عموض بالشكل
+
+139
+00:17:03,830 --> 00:17:09,610
+على هذا لغاية ما قبل الـ X Y plane و رسمت من هنا
+
+140
+00:17:09,610 --> 00:17:19,710
+أفقي و من هنا موازي لبين موازي لل X Y يبقى هذه ال
+
+141
+00:17:19,710 --> 00:17:25,190
+Y موازي لل X Y بالشكل هذاهذا تعتبر المُركّب اللي
+
+142
+00:17:25,190 --> 00:17:31,070
+هي V1 هذه الموازية اللي هي V1 هذا V2 الموازية
+
+143
+00:17:31,070 --> 00:17:36,030
+لمحور Y هذا اللي رأسي الموازية لمحور Z اللي همين
+
+144
+00:17:36,030 --> 00:17:43,710
+V3 يبقى V1 ستبدأ من نقطة الأصل لغاية هذه النقطة
+
+145
+00:17:43,710 --> 00:17:50,270
+يعني كأن إحداث النقطة هذه V1 و 0 و 0 زي ما درسنا
+
+146
+00:17:50,270 --> 00:18:00,090
+في المحاضرة الماضيةهذه الـ V1 و V2 و 0 هذه الان V1
+
+147
+00:18:00,090 --> 00:18:07,310
+و V2 و V3 يبقى هذه المراكبات الثلاثة لمين للـ
+
+148
+00:18:07,310 --> 00:18:15,950
+vector V in space حد بيتسأل؟ طيب
+
+149
+00:18:15,950 --> 00:18:21,700
+يبقى هذه المراكبات من الأن فصاعداسنحاول أن نكتب
+
+150
+00:18:21,700 --> 00:18:27,440
+دائما و أبدا الـ vector V بدلالة المركبات التلاتة
+
+151
+00:18:27,440 --> 00:18:35,420
+تبعته في الإتجاهات تبعت محور الإحداثيات X و Y و Z
+
+152
+00:18:35,420 --> 00:18:41,420
+ممكن
+
+153
+00:18:41,420 --> 00:18:50,270
+نعطي شكل عام لمين لل vector Vتاولة ما نقول ان two
+
+154
+00:18:50,270 --> 00:18:54,690
+vectors are parallel لو روحت رسمت موازي لهذا ال
+
+155
+00:18:54,690 --> 00:18:59,070
+vector وليكن الموازي هو ال vector اللي عندنا هذا
+
+156
+00:18:59,070 --> 00:19:06,030
+على سبيل المثال موازي L وG بالضغط تماما وكانت هذه
+
+157
+00:19:06,030 --> 00:19:17,120
+النقطة P1 of X1 وY1 وZ1 وكانت النقطة هذه P2 لX2و
+
+158
+00:19:17,120 --> 00:19:22,520
+Y2 و Z2 إذا ال vector اللي عيني هذا جد ال vector
+
+159
+00:19:22,520 --> 00:19:30,560
+هذا بالضبط تماما مقدارا و اتجاها طيب بناء عليه ال
+
+160
+00:19:30,560 --> 00:19:36,620
+vector V بدي أكتبه بدللة المركبات تبعات هذه النقطة
+
+161
+00:19:36,620 --> 00:19:43,180
+يبقى بناء عليه in general بروح بقول هيك in general
+
+162
+00:19:46,360 --> 00:19:52,380
+على وجه العموم الـ vector V اللي مركبته V1 و V2 و
+
+163
+00:19:52,380 --> 00:19:59,080
+V3 بقدر أكتبه بشكل جديد بواسطة النقاط اللي عندنا
+
+164
+00:19:59,080 --> 00:20:06,120
+هذا اللي تمثل ال vector V بالضبط تماماً يبقى X2-X1
+
+165
+00:20:06,120 --> 00:20:16,040
+Y2-Y1 Z2-Z1بهذا الشكل يبقى إن كتبنا ال vector
+
+166
+00:20:16,040 --> 00:20:21,880
+بدلالة ال terminal point و نسبناه إلى النقطة الأصل
+
+167
+00:20:21,880 --> 00:20:27,280
+أو كتبناه بدلالة النقطة اللي اتنين عندنا الاتنين
+
+168
+00:20:27,280 --> 00:20:32,820
+are the same يبقى اتنين نفس الشيء أثناء شغلنا في
+
+169
+00:20:32,820 --> 00:20:34,940
+الناحية الرياضية
+
+170
+00:20:41,360 --> 00:20:47,860
+كويس لو بدى اكتب تساوي متجهين بدلالة المراكبات
+
+171
+00:20:47,860 --> 00:20:54,000
+فباجي بقول ملاحظة two
+
+172
+00:20:54,000 --> 00:20:58,580
+vectors u
+
+173
+00:20:58,580 --> 00:21:06,140
+اللى هو بدى يساوي u واحد و u اتنين و u تلاتة and v
+
+174
+00:21:06,140 --> 00:21:13,140
+اللى هو بدى يساوي v واحدV1 V2 V3 V4 V5 V6 V7 V8 V9
+
+175
+00:21:13,140 --> 00:21:20,520
+V10 V11 V12 V13 V14 V15 V16 V17 V18 V19 V20
+
+176
+00:21:20,520 --> 00:21:26,660
+V21 V21 V21 V21 V21 V21 V21 V21 V21 V21 V21 V21
+
+177
+00:21:26,660 --> 00:21:27,300
+V21 V21 V21 V21 V21 V21 V21 V21 V21 V21 V21 V21
+
+178
+00:21:27,300 --> 00:21:29,320
+V21 V21 V21 V21 V21 V21 V21 V21 V21 V21 V21 V21
+
+179
+00:21:29,320 --> 00:21:30,100
+V21 V21 V21 V21 V21 V21 V21 V21 V21 V21 V21 V21
+
+180
+00:21:30,100 --> 00:21:30,400
+V21 V21 V21 V21 V21 V21 V21 V21 V21 V21 V21 V21
+
+181
+00:21:30,400 --> 00:21:30,600
+V21 V21 V21 V21 V21 V21 V21 V21 V21 V21 V21 V21
+
+182
+00:21:35,660 --> 00:21:41,120
+إذا تساوة المُركّبات المُتنظرة في كل منهم
+
+183
+00:21:41,120 --> 00:21:44,680
+المُركّبة الأولى في المُتجه الأول هي نفس المُركّبة
+
+184
+00:21:44,680 --> 00:21:47,620
+الأولى في المُتجه الثاني المُركّبة الثانية في
+
+185
+00:21:47,620 --> 00:21:50,340
+المُتجه الأول هي المُركّبة الثانية في المُتجه
+
+186
+00:21:50,340 --> 00:21:53,720
+الثاني المُركّبة التالتة في المُتجه الأول هي
+
+187
+00:21:53,720 --> 00:21:59,200
+المُركّبة التالتة في المُتجه الثاني وهكذا يبقى من
+
+188
+00:21:59,200 --> 00:22:06,670
+هنا بقول المُتجهين الاتنين متساوينطب لو بدى أجيب
+
+189
+00:22:06,670 --> 00:22:13,090
+طول ال vector جبريا كيف بدها أسبوع فبعدى بقول هذا
+
+190
+00:22:13,090 --> 00:22:17,950
+الملاحظة الأولى الملاحظة الثانية اللى هو the
+
+191
+00:22:17,950 --> 00:22:30,050
+length of the vector v you said ال squareإذا بدأت
+
+192
+00:22:30,050 --> 00:22:33,430
+أكتب دلات المُركّبات ده بقولي بقى باجي بقول V1
+
+193
+00:22:33,430 --> 00:22:40,690
+تربيع زائد V2 تربيع زائد V3 تربيع او إذا بدأت أكتب
+
+194
+00:22:40,690 --> 00:22:45,730
+بواسطة ال general form اللي يقول عليه ال X وما إلى
+
+195
+00:22:45,730 --> 00:22:52,750
+ذلك باجي بقول يبقى هو X2 ناقص X1 لكل تربيع اللي هي
+
+196
+00:22:52,750 --> 00:23:05,390
+قيمة main اللي هي V1 زائدy2-y1 كل تربيع y2-y1
+
+197
+00:23:05,390 --> 00:23:06,490
+كل تربيع y2-y1 كل تربيع y2-y1 كل تربيع y2-y1 كل
+
+198
+00:23:06,490 --> 00:23:09,850
+تربيع y2-y1 كل تربيع y2-y1 كل تربيع y2-y2 كل تربيع
+
+199
+00:23:09,850 --> 00:23:10,250
+y2-y2 كل تربيع y2-y2 كل تربيع y2-y2 كل تربيع y2-y2
+
+200
+00:23:10,250 --> 00:23:17,290
+y2-y2 كل تربيع y2-y2 كل تربيع y2-y2 كل تربيع y2-y2
+
+201
+00:23:17,290 --> 00:23:24,560
+كل تربيع y2-yمش absolute value ل V وإنما طول ال
+
+202
+00:23:24,560 --> 00:23:30,540
+vector V اللي عندنا هذا بدنا
+
+203
+00:23:30,540 --> 00:23:35,240
+نيجي هنا نقطة بسيطة قبل أن نبدأ في أخذ بعض الأمثلة
+
+204
+00:23:35,240 --> 00:23:40,660
+النقطة دي كيف بدنا نجمع two vectors أو نترحهم أو
+
+205
+00:23:40,660 --> 00:23:46,020
+نضرب ال vector في scalar هحطه على شكل التعريف
+
+206
+00:23:46,020 --> 00:23:48,380
+التالي definition
+
+207
+00:23:53,530 --> 00:24:05,730
+let U تساوي U واحد و U اتنين و U تلاتة بدلالة
+
+208
+00:24:05,730 --> 00:24:14,210
+المراكبات تبعها and V تساوي V واحد و V اتنين و V
+
+209
+00:24:14,210 --> 00:24:20,470
+تلاتة بي two vectors
+
+210
+00:24:22,820 --> 00:24:30,840
+عبارة عن متجهين and c is scalar scalar يعني يا
+
+211
+00:24:30,840 --> 00:24:37,780
+بنات كمية قياسية يعني عدد حقيقي then النقطة الأولى
+
+212
+00:24:37,780 --> 00:24:44,180
+لو ده جاخد u زائد ال V يبقى بجمع ال components
+
+213
+00:24:44,180 --> 00:24:50,540
+المتناظرة مع بعضها إيش بصير عندي u واحد زائد v
+
+214
+00:24:50,540 --> 00:25:00,710
+واحدU2 زائد V2 U3 زائد V3 يبقى بجمع ال components
+
+215
+00:25:00,710 --> 00:25:07,230
+المتنظرة مع بعض بالمثل لو طرحت U ناقص V يبقى U1
+
+216
+00:25:07,230 --> 00:25:16,470
+ناقص V1 U2 ناقص V2 U3 ناقص V3 يعني أنا كونت متجه
+
+217
+00:25:16,470 --> 00:25:22,270
+جديد من المتجهين الاتنين اللي موجودات عندككمان؟
+
+218
+00:25:22,270 --> 00:25:27,910
+كوانت متجهدية اسمه محاصلة المتجهين الموجودين سواء
+
+219
+00:25:27,910 --> 00:25:33,190
+كان بالجامعة أو بالطارقة النقطة الثانية لو بدي
+
+220
+00:25:33,190 --> 00:25:43,030
+اضرب C في ال V يبقى C هادى حتى نضرب8 في V1 و V2 و
+
+221
+00:25:43,030 --> 00:25:48,750
+V3 اللي هي هتساوي ال C ستضرب في كل مركبة من
+
+222
+00:25:48,750 --> 00:26:00,030
+المركبات الثلاث اللي هو C V1 C V2 C في V3 C V3
+
+223
+00:26:00,030 --> 00:26:02,190
+بالشكل اللي عندنا هذا
+
+224
+00:26:08,290 --> 00:26:12,390
+طيب C اللي بدنا نضربها يا بنات يمكن تكون موجبة
+
+225
+00:26:12,390 --> 00:26:19,710
+ويمكن تكون سالبة صح ولا لا؟ لو ضربت C كرقم موجة في
+
+226
+00:26:19,710 --> 00:26:24,570
+البيت بطلع مدتجة في نفس الاتجاه تبع المدتجة الأصلي
+
+227
+00:26:24,570 --> 00:26:30,010
+لو كانت C سالبة يعكسوا على طول القطر خلينا نكتب
+
+228
+00:26:30,010 --> 00:26:34,550
+هذه الملاحظة البسيطة هذه لأنه بدنا نبني عليها شغل
+
+229
+00:26:34,550 --> 00:26:37,170
+بعد ذلك ان شاء الله تعالى
+
+230
+00:26:39,780 --> 00:26:45,080
+يبقى بدأجي أقول .. بدي
+
+231
+00:26:45,080 --> 00:26:50,700
+أحطها زي ملاحظة بسيطة هيك if c أكبر من ال zero
+
+232
+00:26:50,700 --> 00:27:04,340
+then c, v and l, v are in the same direction
+
+233
+00:27:10,600 --> 00:27:19,040
+اللي بقى، لو كان الـC أقل من الـ0، يعني كمية
+
+234
+00:27:19,040 --> 00:27:32,640
+سالبة، then CV and V are of the opposite
+
+235
+00:27:32,640 --> 00:27:35,840
+directions
+
+236
+00:27:37,580 --> 00:27:45,480
+في اتجاهين متعاكسين طب لو حبيت النقطة التالتة اجيب
+
+237
+00:27:45,480 --> 00:27:51,940
+طول المتجه CV بحسب
+
+238
+00:27:51,940 --> 00:27:58,940
+تعريفنا طول المتجه بده يسوى الجذر التربيعي ل CV1
+
+239
+00:27:58,940 --> 00:28:09,050
+لكل تربيع CV2 لكل تربيع CV3 لكل تربيعهذا بقدر اقول
+
+240
+00:28:09,050 --> 00:28:16,230
+ويساوي لـ square root لـ C تربيع بياخد عامل مشترك
+
+241
+00:28:16,230 --> 00:28:24,610
+بظل V1 تربيع زائد V2 تربيع زائد V3 تربيع شكل اللي
+
+242
+00:28:24,610 --> 00:28:30,630
+عناه طب الـ C تربيع بقدر اطلعها من تحت الجدر تمام
+
+243
+00:28:31,110 --> 00:28:36,410
+لما نطلعها من تحت الجذر تطلع بـ Absolute Value زي
+
+244
+00:28:36,410 --> 00:28:40,570
+ما اتعلمنا في Calculus A في أول محاضرة أخدتها في
+
+245
+00:28:40,570 --> 00:28:46,930
+Calculus A يبقى هذا بيصير عندي Absolute Value لـ C
+
+246
+00:28:46,930 --> 00:28:55,970
+في الجذر التربيعي لمن؟ لـ V1 تربيع V2 تربيع V3
+
+247
+00:28:55,970 --> 00:28:56,950
+تربيع
+
+248
+00:28:59,710 --> 00:29:05,990
+يعني هذه بقدر اقول absolute value ل C في طول ال V
+
+249
+00:29:05,990 --> 00:29:15,390
+يبقى الأولى يا بنات هذه تقرأ absolute value of C
+
+250
+00:29:15,390 --> 00:29:19,710
+يعني إن كانت موجبة فهي موجبة وإن كانت سالبة خد ال
+
+251
+00:29:19,710 --> 00:29:26,330
+absolute value بالصير موجبة أما عن هذا فهو the
+
+252
+00:29:26,330 --> 00:29:37,850
+length ofV يبقى هذا طول المتجة V هنا بنحاول نوقف
+
+253
+00:29:37,850 --> 00:29:43,470
+شوية بسيطة و ناخد بعض الأمثلة لتوضيح المفاهيم التي
+
+254
+00:29:43,470 --> 00:29:51,770
+ذكرناها قبل قليل إذا بدنا نروح لانحل بعض الأمثلة
+
+255
+00:29:51,770 --> 00:29:57,830
+العددية على ما ذكرناهم قبل قليل
+
+256
+00:30:12,320 --> 00:30:17,440
+نمسح هذا خلاص وانا بشرحها لابنات اللي ماتستمعش اي
+
+257
+00:30:17,440 --> 00:30:23,700
+نقطة تقول لو سمحت استهلنا واسألي اي سؤال بدكيه من
+
+258
+00:30:23,700 --> 00:30:27,820
+خلال اسئلة بتثبت المعلومات عندكوا اللي بتكون فهمت
+
+259
+00:30:27,820 --> 00:30:36,360
+غلط بتصير تفهم صح و هكذا نجي لأول مثال example F
+
+260
+00:30:43,900 --> 00:30:54,920
+P1 F P1 النقطة الأحدثيات P1
+
+261
+00:30:54,920 --> 00:31:00,340
+F P1 F P1 F P1
+
+262
+00:31:00,340 --> 00:31:04,920
+F P1 F P1 F P1 F P1 F P1 F P1 F P1 F P1 F P1 F P1
+
+263
+00:31:04,920 --> 00:31:06,620
+F P1 F P1 F P1 F P1 F P1 F P1 F P1 F P1 F P1 F P1
+
+264
+00:31:06,620 --> 00:31:10,240
+F P1 F P1 F P1 F P1 F P1 F P1 F P1 F P1 F P1 F P1
+
+265
+00:31:10,240 --> 00:31:10,380
+F P1 F P1 F P1 F P1 F P1 F P1 F P1 F P1 F P1 F P1
+
+266
+00:31:10,380 --> 00:31:10,420
+F P1 F P1 F P1 F P1 F P1 F P1 F P
+
+267
+00:31:21,050 --> 00:31:35,490
+2 points نمرأة find طول جديدنا the length of
+
+268
+00:31:35,490 --> 00:31:49,510
+الأربع P1 P2 that is أي أننا بدنا طول الأربع P1 P2
+
+269
+00:31:49,510 --> 00:31:59,860
+as a vectoremra b by the vector او is the vector
+
+270
+00:31:59,860 --> 00:32:03,380
+is
+
+271
+00:32:03,380 --> 00:32:11,760
+the vector u اللي هو بده يساوي تسعة واطناشر وزيرا
+
+272
+00:32:11,760 --> 00:32:16,620
+parallel to
+
+273
+00:32:16,620 --> 00:32:21,180
+p1 p2 ام لا
+
+274
+00:32:28,630 --> 00:32:36,330
+Solution نرجع لسؤالنا مرة ثانية نقرأ السؤال نتكج
+
+275
+00:32:36,330 --> 00:32:39,710
+المرطب شو اللي بدي اعطاه الطب إذا حددنا شو اللي
+
+276
+00:32:39,710 --> 00:32:45,130
+بدناه إذا ما نقدر نحدد الإجابة تبعتنا بدقة ماعطينا
+
+277
+00:32:45,130 --> 00:32:52,680
+نقطتين P1 و P2 و قال لي هاتلي الطولتبع المتجة
+
+278
+00:32:52,680 --> 00:32:59,200
+اربعة P1 P2 يبقى بده يقول المتجة اربعة P1 P2 اذا
+
+279
+00:32:59,200 --> 00:33:04,500
+بده يجيب المتجة P1 P2 اربعة يعني اربعة امثال و
+
+280
+00:33:04,500 --> 00:33:12,220
+بصير يعني كأنه طالب متجة موازي للمتجة P1 P2 بس جد
+
+281
+00:33:12,220 --> 00:33:17,280
+واش اربعة مرات تمام؟ كويس يبقى خلينا نجيب المتجة
+
+282
+00:33:17,280 --> 00:33:24,470
+P1 P2 في الأوليبقى باجي بقوله نمرة A بدي المتجه P1
+
+283
+00:33:24,470 --> 00:33:28,930
+P2 يبقى
+
+284
+00:33:28,930 --> 00:33:40,150
+هذا الكلام بدي يساوي X2-X1 Y2-Y1 Z2-Z1 عشان أخدنا
+
+285
+00:33:40,150 --> 00:33:45,730
+التعريف قبل قليل إذا بدي أطبق هذا التعريف يبقى بدي
+
+286
+00:33:45,730 --> 00:33:51,220
+أجي نميماللي هو أربعة ناقص واحد أربعة ناقص واحد
+
+287
+00:33:51,220 --> 00:33:58,560
+سبعة ناقص تلاتة ناقص اتنين زائد اتنين ناقص اتنين
+
+288
+00:33:58,560 --> 00:34:04,160
+ناقص ناقص اتنين زائد اتنين يبقى صار عندى هذا
+
+289
+00:34:04,160 --> 00:34:11,660
+المتجه هو تلاتة واربعة و Zero بهذا الشكل يبقى هذا
+
+290
+00:34:11,660 --> 00:34:19,860
+المتجه P واحد P اتنين أنا بديأربعة اللي هو P واحد
+
+291
+00:34:19,860 --> 00:34:25,380
+P اتنين متجه اللي عندنا هذا يبقى هذا الكلام بده
+
+292
+00:34:25,380 --> 00:34:31,880
+يساوي أربعة في تلاتة أربعة زيرو يبقى هذا الكلام
+
+293
+00:34:31,880 --> 00:34:38,800
+بده يساوي تلاتة في أربعة باطناش وأربعة في أربعة
+
+294
+00:34:38,800 --> 00:34:43,440
+بستاشر أوزي كويس
+
+295
+00:34:45,240 --> 00:34:50,960
+أخر حاجة أخدناها قبل قليل كان طول المتجه C في V
+
+296
+00:34:50,960 --> 00:34:57,680
+قلنا absolute value للـC في طول الـV أحنا أخدنا
+
+297
+00:34:57,680 --> 00:35:04,500
+all اللي هو C V بده يساوي absolute value للـC في
+
+298
+00:35:04,500 --> 00:35:12,040
+طول الـV طيب الـC عنا هنا ماكنتاش بنات أربع يبقى
+
+299
+00:35:12,040 --> 00:35:17,640
+absolute value للأربعطول الـ V الجدري التربية
+
+300
+00:35:17,640 --> 00:35:25,960
+للمُركّبات تبعها هي يبقى تلاتة تربية زائد أربعة
+
+301
+00:35:25,960 --> 00:35:36,440
+تربية زائد Zero تربية ويساوي أربعة في تسعة وست عشر
+
+302
+00:35:36,440 --> 00:35:43,260
+خمسة وعشرين بخمسة يبقى الطول تبعه جدير اللي هو
+
+303
+00:35:43,260 --> 00:35:44,100
+عشرين
+
+304
+00:35:47,680 --> 00:35:51,520
+طب واحدة تقول ليه؟ طب ما احنا جيبنا هاي أربعة P و
+
+305
+00:35:51,520 --> 00:35:56,760
+طلعنا هذا، لو ربعنا هذا تحت الجدر بطلع عشرين،
+
+306
+00:35:56,760 --> 00:36:02,390
+بنقولاش surely، بالتأكيد، كيف؟ اتناش في اتناشمية و
+
+307
+00:36:02,390 --> 00:36:06,150
+أربعة و أربعين ستة عشر في ستة عشر ميتين و ستة و
+
+308
+00:36:06,150 --> 00:36:10,170
+خمسين و مية و أربعة و أربعين أربع مية جداش جدرال
+
+309
+00:36:10,170 --> 00:36:14,890
+أربع مية عشرين و هو المطلوب يعني إن عملتي زي .. و
+
+310
+00:36:14,890 --> 00:36:19,550
+الله روحتي أخدت الطول هذا مباشرة تنسيان لاتنين صح
+
+311
+00:36:19,550 --> 00:36:24,010
+و ماحدش مقدر يعطرها عالم كده هذا هو المطلوب الأول
+
+312
+00:36:24,010 --> 00:36:30,180
+المطلوب التاني نمرابيد بقول إيه هاتليهل ال vector
+
+313
+00:36:30,180 --> 00:36:36,640
+هذا موازي ال vector P1 P2 ولا لأ قبل قليل قولنا
+
+314
+00:36:36,640 --> 00:36:42,020
+المتجهين المتوازين إذا كان واحد فيهم مضاعفة الآخر
+
+315
+00:36:42,020 --> 00:36:49,220
+قولنا V موازي ل 2V موازي ل-3V و هكذا إذا أنا بداجي
+
+316
+00:36:49,220 --> 00:36:54,750
+لل vector اللي عندنا هذا اللي مضينيااللي هو قداش
+
+317
+00:36:54,750 --> 00:37:02,630
+ال vector u اللي هو بده يساوي 9 و 12 و 0 بقدر أخد
+
+318
+00:37:02,630 --> 00:37:09,190
+منه تلاتة برا من كل مركبة من هذه المركبات بيظل
+
+319
+00:37:09,190 --> 00:37:15,590
+قداش عند هنا تلاتة هنا أربع وهنا Zero من هو المتجه
+
+320
+00:37:15,590 --> 00:37:22,030
+اللي عندنا هذا مش هو P1 P2 يبقى هذا الكلام بده
+
+321
+00:37:22,030 --> 00:37:30,070
+يساوي تلاتةP1 P2 صار اليوم مضاعفة ال P1 P2 يبقى
+
+322
+00:37:30,070 --> 00:37:34,410
+اتنين هذول مالهم are parallel زي ما طلقالي هذول
+
+323
+00:37:34,410 --> 00:37:40,130
+متوازين ام لا يبقى ان اثبتلوا انهم متوازين يبقى so
+
+324
+00:37:40,130 --> 00:37:51,910
+ال U and P1 P2 are parallel vectors يبقى هذول
+
+325
+00:37:51,910 --> 00:37:59,550
+متجهات مالهامتوازن نجي
+
+326
+00:37:59,550 --> 00:38:05,210
+لتعريف جديد definition
+
+327
+00:38:05,210 --> 00:38:11,030
+سمعتوا في ال فيزيا بيه بمتج هالوحدة؟ حد فيكم بتجرى
+
+328
+00:38:11,030 --> 00:38:14,410
+تذكرني و لا و بالبلد يعني مش بتعرف ع المتج
+
+329
+00:38:14,410 --> 00:38:20,440
+هالوحدة؟طوله واحد صحيح يعني طوله واحد من واحدة
+
+330
+00:38:20,440 --> 00:38:26,980
+الطول ان كان مثلا بالمتر بقول المتر طول متر واحد
+
+331
+00:38:26,980 --> 00:38:31,340
+ان كان بالأقدام بقول قدم واحد او بالسانتيمتر بقول
+
+332
+00:38:31,340 --> 00:38:36,400
+سانتيمتر واحد و لا كده تمام؟ إذا منتجة الواحدة هو
+
+333
+00:38:36,400 --> 00:38:43,240
+عبارة عن منتجة with length والطول تبعه واحد صحيح
+
+334
+00:38:43,240 --> 00:38:54,670
+ابقى باجي بقول thatunit vector is a vector with
+
+335
+00:38:54,670 --> 00:39:03,070
+length one يبقى
+
+336
+00:39:03,070 --> 00:39:09,690
+هو عبارة عن متجة الطول تبعه يساوي الواحد الصحيحة
+
+337
+00:39:09,690 --> 00:39:14,530
+for example مثلا four
+
+338
+00:39:16,580 --> 00:39:27,400
+example في عندنا حاجة اسمها the standard unit
+
+339
+00:39:27,400 --> 00:39:36,020
+vectors ال vectors المتعارف عليهم في كل كتب
+
+340
+00:39:36,020 --> 00:39:41,700
+الرياضيات و الفيزيا و ما إلى ذلك تلاتة ال I و مي
+
+341
+00:39:41,700 --> 00:39:47,650
+كمانالـJ والـK هؤلاء الفلسفة المتعارفة تلك متجهات
+
+342
+00:39:47,650 --> 00:39:51,770
+واحدة في اتجاه ال coordinate axes وكل واحد طوله
+
+343
+00:39:51,770 --> 00:39:57,670
+يساوي جداش يعني على الطبيعة لو جينا كل هذه المحاور
+
+344
+00:39:57,670 --> 00:40:05,230
+شكلا هذا هذا محور X هذا محور Y هذا محور Z فإن
+
+345
+00:40:05,230 --> 00:40:10,920
+المتجهات التلاتةالمتجه الأول هو خط طول هنا يساوي
+
+346
+00:40:10,920 --> 00:40:17,640
+الوحدة يبقى بيكون هذا المتجه I هنا خط الطول كذلك
+
+347
+00:40:17,640 --> 00:40:23,740
+يساوي الوحدة يبقى بيكون هذا هو المتجه J هنا خط طول
+
+348
+00:40:23,740 --> 00:40:29,620
+يساوي الوحدة كذلك جد بعض الأطوال التلاتة يبقى هذا
+
+349
+00:40:29,620 --> 00:40:35,800
+المتجه K بهذا الشكليبقى هذا ال I و ال J و ال K
+
+350
+00:40:35,800 --> 00:40:43,960
+اللي ال standard unit vector مابقاش
+
+351
+00:40:43,960 --> 00:40:48,540
+رأيك يا بنات أي vector ييجي في بالك بقدر اكتبه
+
+352
+00:40:48,540 --> 00:40:52,300
+بالذلالة ال standard unit vectors هدول الدلالة
+
+353
+00:40:52,300 --> 00:41:02,230
+كيف؟ علاقه لمن؟ فهمتش قصتي، قصتي كتبوليإنه لو بدى
+
+354
+00:41:02,230 --> 00:41:08,130
+أجيب متجه الوحدة لمتجه الماء بروح بقسم المتجه على
+
+355
+00:41:08,130 --> 00:41:12,850
+طول المتجه مش هذا اللي قصدته عادة اللي قصدته أنه
+
+356
+00:41:12,850 --> 00:41:19,150
+أي فكتر علنا بقدر اكتبه بدلالة ال three و ال I و
+
+357
+00:41:19,150 --> 00:41:25,050
+ال J و ال K تمام؟ كيف كان التالي؟ هكتب هالك remark
+
+358
+00:41:25,050 --> 00:41:25,650
+هذه
+
+359
+00:41:30,950 --> 00:41:37,150
+اني vector V
+
+360
+00:41:37,150 --> 00:41:47,950
+بدي يساوي V واحد و V اتنين و V تلاتة is written أو
+
+361
+00:41:47,950 --> 00:41:58,210
+is a linear combination of
+
+362
+00:41:58,210 --> 00:41:59,710
+the
+
+363
+00:42:02,440 --> 00:42:14,960
+Standard Unit Vectors كيف أزفله؟ كالتالي طلعلي ال
+
+364
+00:42:14,960 --> 00:42:23,400
+vector V هاي مركبته V1 و V2 و V3 بقدر أكتب هذا ال
+
+365
+00:42:23,400 --> 00:42:36,190
+vector على شكل مجموع تلت متجهات كيف؟ كالتاليV1 V2
+
+366
+00:42:36,190 --> 00:42:41,690
+V3
+
+367
+00:42:41,690 --> 00:42:44,990
+V4
+
+368
+00:42:44,990 --> 00:42:45,170
+V5 V6 V7 V8 V9 V10 V11 V12 V13 V12 V13 V13 V13 V13
+
+369
+00:42:45,170 --> 00:42:45,770
+V13 V13 V13 V13 V13 V13 V13 V13 V13 V13 V13 V13
+
+370
+00:42:45,770 --> 00:42:45,810
+V13 V13 V13 V13 V13 V13 V13 V13 V13 V13 V13 V13
+
+371
+00:42:45,810 --> 00:42:45,910
+V13 V13 V13 V13 V13 V13 V13 V13 V13 V13 V13 V13
+
+372
+00:42:45,910 --> 00:42:46,670
+V13 V13 V13 V13 V13 V13 V13 V13 V13 V13 V13 V13
+
+373
+00:42:46,670 --> 00:42:48,690
+V13 V13 V13 V13 V13 V13 V13 V13 V13 V13
+
+374
+00:42:52,760 --> 00:42:59,500
+اللي بعد هو 0 زائد v2 زائد 0 في v2 زائد 0 زائد v3
+
+375
+00:42:59,500 --> 00:43:06,060
+في v3 طيب الآن بداجي ضرب scalar في vector يبقى
+
+376
+00:43:06,060 --> 00:43:09,300
+scalar ان ضربته في الداخل ولا طلعته برا الاتنين
+
+377
+00:43:09,300 --> 00:43:13,900
+are the same يبقى مقدر اقول هذا الكلام بده ساعة
+
+378
+00:43:13,900 --> 00:43:27,550
+اللي هو v1 في 1 و 0 و 0 تمام؟زائد V2 Zero و واحد و
+
+379
+00:43:27,550 --> 00:43:40,770
+Zero زائد V3 Zero و Zero و واحد شكل يعني انا احنا
+
+380
+00:43:40,770 --> 00:43:44,430
+قولنا ال standard unit vectors و قولنا لك هاي ال
+
+381
+00:43:44,430 --> 00:43:49,340
+standard unit vectors اللي هو I و J و Kلو جهت
+
+382
+00:43:49,340 --> 00:43:55,480
+بقولتلك هنا ال I بده يساوي هو واحد وزير وزير صحيح
+
+383
+00:43:55,480 --> 00:44:01,340
+ولا لا؟ صحيح ليش؟ لأن النقطة هذه أحداثيها واحد
+
+384
+00:44:01,340 --> 00:44:09,280
+وزير وزير وزير وهذا النقطة زير وواحد وزير وهذا
+
+385
+00:44:09,280 --> 00:44:19,310
+النقطة زير وزير وواحدالـ J هيكون يساوي 0 و 1 و 0
+
+386
+00:44:19,310 --> 00:44:28,390
+والـ K اللي هو بده يساوي 0 و 0 و 1 إذا بناء عليه
+
+387
+00:44:28,390 --> 00:44:36,010
+هذا بيصير V1 في اتجاه الـ I زائد V2 في اتجاه الـ J
+
+388
+00:44:36,010 --> 00:44:42,190
+زائد V3 في اتجاه الـ Kيبقى أي vector من الـ M
+
+389
+00:44:42,190 --> 00:44:47,390
+فصاعدا، يا بنكتبه على الصيغة اللي عندناها دي، ع
+
+390
+00:44:47,390 --> 00:44:53,890
+شكل غسين مجرنات، يا إما بدلالة ال standard vectors
+
+391
+00:44:53,890 --> 00:45:01,620
+اللي هو I وJ وK طبعاً V1 وV2 وV3 اس colorsوالـ I و
+
+392
+00:45:01,620 --> 00:45:06,240
+G و K هما الـ Main Vectors يبقى هذا مضاعفات الـ I
+
+393
+00:45:06,240 --> 00:45:10,200
+وهذا مضاعفات الـ G وهذا مضاعفات الـ Main مضاعفات
+
+394
+00:45:10,200 --> 00:45:15,920
+الـ K يبقى من الأن فساعدا أي Vector نقدر نكتبه
+
+395
+00:45:15,920 --> 00:45:21,710
+بهذه الطريقةطب يا بنات لو كانت V1 هذه الفرق ما بين
+
+396
+00:45:21,710 --> 00:45:28,850
+X2-X1 زي ما كتبناها قبل شوية مسحناها يعني بقدر
+
+397
+00:45:28,850 --> 00:45:39,190
+أقول هذه كمان بالضبط هي X2-X1 في اتجاه I وهذه Y2
+
+398
+00:45:39,190 --> 00:45:49,060
+-Y1 في اتجاه J وهذه Z2-Z1 في اتجاه Mفي اتجاه الـ K
+
+399
+00:45:49,060 --> 00:45:54,080
+زي ما انت شايفها إذا يا بكتب المتجهة بالشكل هذا
+
+400
+00:45:54,080 --> 00:46:00,140
+تمام يا بقدر أكتب بالشكل اللي عندنا هذا يا بقدر
+
+401
+00:46:00,140 --> 00:46:05,040
+أكتب بالشكل هذا إن كنت عارف نقطة البداية ونقطة
+
+402
+00:46:05,040 --> 00:46:11,540
+النهاية لهذا المتجه طيب نجد الكلام اللي قالته
+
+403
+00:46:11,540 --> 00:46:16,900
+الأخت شو اسمك انتي classroom classroomالوقت خلاص
+
+404
+00:46:16,900 --> 00:46:22,360
+كورالته قبل قليل بتقول متجه الوحدة هو عبارة عن
+
+405
+00:46:22,360 --> 00:46:29,360
+خارج قسم المتجه على قوله نقولها كلامك صحيح و
+
+406
+00:46:29,360 --> 00:46:38,100
+هنحطها في صيغة محددة الأن و نشتغل عليها بعد ذلك
+
+407
+00:46:38,100 --> 00:46:47,460
+يبقى الصيغة هذه كالتالي لو جيت قولتلك Vعلى طول ال
+
+408
+00:46:47,460 --> 00:46:54,660
+V هذا انطلع طوله يسوى واحد صحيح إذا هو unit vector
+
+409
+00:46:54,660 --> 00:47:08,380
+مظبوط يبقى هذا as a unit vector in the direction
+
+410
+00:47:10,640 --> 00:47:17,360
+of V يبقى هذا متجه الوحدة في اتجاه ال V السبب ليش؟
+
+411
+00:47:17,360 --> 00:47:22,560
+because لو بدى اجيب الطول تبع ال V على طول ال V
+
+412
+00:47:22,560 --> 00:47:26,400
+حسب ما احنا معرفين ال unit vector ان طلع طوله
+
+413
+00:47:26,400 --> 00:47:31,740
+يساوي واحد صحيح اذا فهو unit vector مظبوط؟ يبقى
+
+414
+00:47:31,740 --> 00:47:38,260
+هذا الكلام بدى يساوي واحد على طول طول ال V ما هو
+
+415
+00:47:38,260 --> 00:47:43,610
+طول ال Vبيظل اللي فوق هذا اللي هو طول ال V هذا
+
+416
+00:47:43,610 --> 00:47:48,070
+الكلام لو اختصرت اللي فوق مع اللي تحت المقدار اللي
+
+417
+00:47:48,070 --> 00:47:53,550
+عندنا هذا مع المقدار هذا بيظل جدير واحد صحيح بس
+
+418
+00:47:53,550 --> 00:47:58,250
+ديلو بالك في شغلة ممكن تفهميها غلط مافيش حاجة
+
+419
+00:47:58,250 --> 00:48:03,490
+اسمها اسم المتجه على المتجهات لايوجد عندنا في
+
+420
+00:48:03,490 --> 00:48:09,570
+الرياضية حاجة اسمها اسم المتجهات زي المصففاتفي
+
+421
+00:48:09,570 --> 00:48:13,190
+الجابرة الخاطئ، مافيش حاجة يسمى قسم المصرفات على
+
+422
+00:48:13,190 --> 00:48:17,430
+الإطلاق، عمرك لما انضرفت مصرفات في الثانوية،
+
+423
+00:48:17,430 --> 00:48:22,620
+قسمتهم اصفين على بعض، ماحصلش، مهالييعني ليه قسمة
+
+424
+00:48:22,620 --> 00:48:28,080
+مصوفات و كذلك ليه يوجد حاجة اسمها قسمة متجات لما
+
+425
+00:48:28,080 --> 00:48:33,100
+أقول قسمت المتجة على طوله يعني كان ضربت في سكلة
+
+426
+00:48:33,100 --> 00:48:37,940
+واحد على طول المتجة هذا سكلة ضربته في المتجة إذا
+
+427
+00:48:37,940 --> 00:48:42,660
+بضال المتجة من هو هذا المتجة هو متجة الوحدة في
+
+428
+00:48:42,660 --> 00:48:47,880
+اتجاه من المتجة إذا لو جبتلك سؤال و قلت لك أعطيتك
+
+429
+00:48:47,880 --> 00:48:51,660
+vectorأو قلت لك بالله هاتيلي قداش طول ال vector
+
+430
+00:48:51,660 --> 00:48:56,920
+هذا أو هاتيلي متجهي الوحدة في اتجاه هذا ال vector
+
+431
+00:48:56,920 --> 00:49:02,820
+بروح بشوف قداش طول هذا المتجه و بقسم كل مراكبة من
+
+432
+00:49:02,820 --> 00:49:07,960
+مراكبات المتجه المُعطَى على هذا الطول بيعطيني متجه
+
+433
+00:49:07,960 --> 00:49:12,560
+الوحدة في اتجاه المتجه الأصلي طب لو قلت لك في
+
+434
+00:49:12,560 --> 00:49:17,640
+اتجاه معكس للمتجه الأصلي لماذا؟ بقسم على هذا الرقم
+
+435
+00:49:17,640 --> 00:49:23,000
+بإشارةالسالب بيكون حصلت علامين على المتجه في عكس
+
+436
+00:49:23,000 --> 00:49:29,820
+الاتجاه اللي هو موجود عندنا طيب
+
+437
+00:49:29,820 --> 00:49:36,440
+ممكن اكتب يا بنات اي متجه في الدنيا بدلاله طوله
+
+438
+00:49:36,440 --> 00:49:41,300
+واتجاهه كيف؟ كالتالي احفظلك بصيغة ال remark
+
+439
+00:49:41,300 --> 00:49:43,160
+التالية remark
+
+440
+00:49:54,250 --> 00:50:07,950
+is a non-zero vector متجه غير الصفر we can write
+
+441
+00:50:07,950 --> 00:50:15,590
+نستطيع كتابة V in
+
+442
+00:50:15,590 --> 00:50:22,430
+terms of its length
+
+443
+00:50:25,790 --> 00:50:34,870
+الطول تبعه undirection as
+
+444
+00:50:34,870 --> 00:50:42,390
+follow دعوني
+
+445
+00:50:42,390 --> 00:50:50,690
+أكمل معناه لو جاءت مجلسك المتجه V بذرساه بدي أضربه
+
+446
+00:50:50,690 --> 00:50:56,620
+في رقم واسمه على نفس الرقمهل تتغير قيمة هذا المتجه
+
+447
+00:50:56,620 --> 00:51:01,400
+أو شكله؟ لأ طب إيش رأيته؟ بدي أختار رقم محدد الرقم
+
+448
+00:51:01,400 --> 00:51:07,900
+المحدد هو عبارة عن طول هذا المتجه فبقدر أقول هذا
+
+449
+00:51:07,900 --> 00:51:17,380
+الكلام بيساوي طول ال V في ال V على طول ال V كأن
+
+450
+00:51:17,380 --> 00:51:20,680
+أنا أتعرف في جد ياش؟ في واحد صح يقول متجه كما هو
+
+451
+00:51:20,680 --> 00:51:27,080
+بدي أعيد الصياغة اللي أنا قلتهايبقى طول ال V ضربته
+
+452
+00:51:27,080 --> 00:51:32,740
+في V على طول ال V قلت هذا على هذا و هذا زي ما هو
+
+453
+00:51:32,740 --> 00:51:41,100
+هذا مين أبنات الجزء الأول طول ال V يبقى هذا ال N
+
+454
+00:51:41,100 --> 00:51:50,400
+أر V هذا اتجاه ال V يعني متجه الوحدة في اتجاه ال V
+
+455
+00:51:50,770 --> 00:51:58,550
+يبقى هذا الـdirection of v إذا بناني علي الرمج و
+
+456
+00:51:58,550 --> 00:52:04,470
+تقولي أي non zero vector بقدر أكتبه بدلالة ال lens
+
+457
+00:52:04,470 --> 00:52:10,190
+تبعه و ال direction تبعه يبقى هاي ال direction of
+
+458
+00:52:10,190 --> 00:52:15,070
+v و هاي ال lens تبع من تبع ال v يبقى أي متجهة بقدر
+
+459
+00:52:15,070 --> 00:52:19,350
+أكتبه بالشكل اللي قدامها نجي ناخد مثال example
+
+460
+00:52:28,940 --> 00:52:33,140
+example one بيقول
+
+461
+00:52:33,140 --> 00:52:44,360
+let ال U تساوي اتنين وزيره و سالب تلاته and ال V
+
+462
+00:52:44,360 --> 00:52:53,240
+بده يساوي زيره و واحد و سالب اتنين fine هو ايش
+
+463
+00:52:53,240 --> 00:53:06,160
+دولنا نمرة Aاتنين U ناقص تلاتة V نمرة B طول اتنين
+
+464
+00:53:06,160 --> 00:53:15,140
+U ناقص تلاتة V نمرة C write
+
+465
+00:53:15,140 --> 00:53:26,880
+the vector write the vector اتنين U ناقص تلاتة Vas
+
+466
+00:53:26,880 --> 00:53:34,880
+a product of
+
+467
+00:53:34,880 --> 00:53:50,200
+its length and direction.Nimredi
+
+468
+00:53:50,200 --> 00:53:54,560
+find
+
+469
+00:53:54,560 --> 00:54:07,640
+a vector of length عشرة5 a vector of لن عشرة in
+
+470
+00:54:07,640 --> 00:54:15,240
+the opposite direction in
+
+471
+00:54:15,240 --> 00:54:18,320
+the
+
+472
+00:54:18,320 --> 00:54:22,680
+opposite direction of لن U
+
+473
+00:54:59,060 --> 00:55:03,500
+نرجع للسؤال اللي كتبته مرة ثانية نقرأ هذا السؤال
+
+474
+00:55:03,500 --> 00:55:09,700
+قراءة جيدة ثم بعد ذلك أروح أشوف ما هو المطلوب في
+
+475
+00:55:09,700 --> 00:55:14,840
+كل نقطة من النقاط في المثل السؤال مرة ثانية ماتيني
+
+476
+00:55:14,840 --> 00:55:20,320
+two vectors U و V قال لي هاتلي اتنين U ناقص ثلاثة
+
+477
+00:55:20,320 --> 00:55:27,860
+V يعني أنا بدي أجيب مضاعفات لوليو ثلاثة أمثال V
+
+478
+00:55:28,240 --> 00:55:33,480
+وأطلع اتنين من بعض يعني تلت عمليات بده يشتغل، مش
+
+479
+00:55:33,480 --> 00:55:37,900
+هي؟ مطلوب التاني يعتمد على الأول، مطلوب المتجه
+
+480
+00:55:37,900 --> 00:55:42,440
+اللي بطلع عندك بده تجيب قداش طول، مطلوب التاني،
+
+481
+00:55:42,440 --> 00:55:48,440
+اللي بدك تكتب المتجه اللي طالع عندك بدلالة الطول
+
+482
+00:55:48,440 --> 00:55:54,800
+تبعه والاتجاه، يعني كان طلب قداش متجه الواحدة في
+
+483
+00:55:54,800 --> 00:56:01,500
+هذا الاتجاه بطريقة خفيةنقدار واتجاه المطلوب الرابع
+
+484
+00:56:01,500 --> 00:56:07,840
+قال لي اه بدك تجيب vector طوله عشر وحدات طول في
+
+485
+00:56:07,840 --> 00:56:13,780
+اتجاه معاكس للاتجاه اللي انت جيبته و الله كويس
+
+486
+00:56:13,780 --> 00:56:17,240
+يعني شغل كتير بده هذه الشغلة لكن تعالى نشوف هل هو
+
+487
+00:56:17,240 --> 00:56:21,320
+كتير و الله يعني قال للمطلوب الأول هات الأثنين U
+
+488
+00:56:21,320 --> 00:56:26,230
+زائد تلاتة V هذه بسيطةيبدأ يضرب الأول في اتنين و
+
+489
+00:56:26,230 --> 00:56:30,090
+الثاني في ثلاثة و الظاهر على اتنين من بعض يبقى
+
+490
+00:56:30,090 --> 00:56:36,930
+باقي بقوله هنا اتنين U ناقص تلاتة V تساوي اذا انت
+
+491
+00:56:36,930 --> 00:56:41,470
+حاجة على ال U اضربها في قداش؟ في اتنين يبقى هاي
+
+492
+00:56:41,470 --> 00:56:51,350
+أربعة وهي Zero وهي ناقص ستة ناقص المتجه التانيأو
+
+493
+00:56:51,350 --> 00:56:56,490
+بقدر أكتب يا بناتي زائد و أدخل الناقص تلاتة جوا،
+
+494
+00:56:56,490 --> 00:57:02,410
+مظبوط؟ يعني بقدر الناقص هذه أكتبها زائد و اللي جوا
+
+495
+00:57:02,410 --> 00:57:07,470
+هنا أدره وين فناقص تلاتة، يبقى zero و هنا ناقص
+
+496
+00:57:07,470 --> 00:57:13,190
+تلاتة و هنا زائد ستة بالشكل اللي عنهايبقى هذا
+
+497
+00:57:13,190 --> 00:57:17,930
+الكلام بده يساوي أربعة و Zero له بأربعة Zero سالف
+
+498
+00:57:17,930 --> 00:57:22,610
+تلاتة Zero سالف تلاتة و هنا Zero يبقى جبتله
+
+499
+00:57:22,610 --> 00:57:26,390
+المطلوب الأول يقولني عليها تلاتة عمليات بسهولة
+
+500
+00:57:26,390 --> 00:57:33,770
+بخطوة واحدة طيب، بدأي إلى نمربيه، نمربيه قال لي
+
+501
+00:57:33,770 --> 00:57:39,120
+قداش طول المتجه هذاإذا هايو حصلت عليه إذا باجي
+
+502
+00:57:39,120 --> 00:57:45,640
+بقوله طول المتجة اتنين يوم ناقص تلاتة بيه اللي هو
+
+503
+00:57:45,640 --> 00:57:51,980
+ال square root للأربعة تربية زائد ناقص تلاتة لكل
+
+504
+00:57:51,980 --> 00:57:57,160
+تربية زائد zero تربية لو زاد التربية ستات و تسعة و
+
+505
+00:57:57,160 --> 00:58:05,020
+خمسة و عشرين يبقى الجواب يساوي خمس نمرسينمرسي
+
+506
+00:58:05,020 --> 00:58:12,260
+بيقول لي اكتب المتجه كحاصل ضرب الطول تبعه في ال
+
+507
+00:58:12,260 --> 00:58:18,160
+direction الطول اظن حصلت عليه هي و جايه الخمسة
+
+508
+00:58:18,160 --> 00:58:27,420
+يبقاش ضال عندي ال direction يعني ال direction of
+
+509
+00:58:27,420 --> 00:58:39,980
+v is the unit unitالـ vector is the unit vector in
+
+510
+00:58:39,980 --> 00:58:46,720
+the direction of
+
+511
+00:58:46,720 --> 00:58:55,640
+V that is I N ال V على طول أو مستحيل أقول ال V على
+
+512
+00:58:55,640 --> 00:58:56,340
+طول ال V
+
+513
+00:59:19,890 --> 00:59:27,710
+يبقى هنا w و هنا w يبقى بالدرجة اقول in the
+
+514
+00:59:27,710 --> 00:59:34,940
+direction of w that is اللي هو mainالـ W على طول
+
+515
+00:59:34,940 --> 00:59:42,900
+الـ W الـ W اللي هو جداش اتنين الـ W اللي هو عندي
+
+516
+00:59:42,900 --> 00:59:48,400
+على طول الخط اللي طالع فوق اللي هو أربعة وسالب
+
+517
+00:59:48,400 --> 00:59:55,120
+تلاتة و Zero على جداش على خمسة اللي هو بده يساوي
+
+518
+00:59:55,120 --> 01:00:00,780
+أربعة أخمس سالب تلت أخمس و Zero
+
+519
+01:00:03,710 --> 01:00:09,490
+هو بالسؤال هو هل هذا يا ترى فعلا unit vector تعالى
+
+520
+01:00:09,490 --> 01:00:18,610
+ربعي 16 على 25 زائد 9 على 25 زائد 0 25 على 25
+
+521
+01:00:18,610 --> 01:00:24,990
+مقداش يبقى فعلا هذا هو unit vector بناء عليه بقدر
+
+522
+01:00:24,990 --> 01:00:32,830
+أقوله لإتنين يون ناقص تلاتة V بده يسامر قوله مقداش
+
+523
+01:00:33,020 --> 01:00:41,740
+خمسة و ال unit vector تبعه في main في أربع أخماس
+
+524
+01:00:41,740 --> 01:00:49,640
+سالب تلت أخماس و كذلك zero بهذا الشكل يبقى هذا ال
+
+525
+01:00:49,640 --> 01:00:57,680
+length و هذا main ال direction يبقى
+
+526
+01:00:57,680 --> 01:01:03,120
+هذا المقدرات جيدا انتهينامن المطلوب برقم C كتبنا
+
+527
+01:01:03,120 --> 01:01:08,180
+ال vector 2U-3C as a product of length and
+
+528
+01:01:08,180 --> 01:01:18,540
+direction هاتبي متجه طوله عشرة في عكس اتجاه 2U-3V
+
+529
+01:01:18,540 --> 01:01:27,540
+ال unit vector في اتجاه 2U-3V
+
+530
+01:01:30,830 --> 01:01:35,630
+مظبوط؟ يعني هذا هو ال unit vector عكسه بدي أحط
+
+531
+01:01:35,630 --> 01:01:42,110
+إشارة سالم جده عشر مرات بدي أضرب في عشر تمام؟ يبقى
+
+532
+01:01:42,110 --> 01:01:53,970
+باجي بقول هنا the .. نمر دي the unit vector in the
+
+533
+01:01:53,970 --> 01:02:00,290
+direction .. in the opposite direction in the ..
+
+534
+01:02:00,800 --> 01:02:07,960
+opposite direction of
+
+535
+01:02:07,960 --> 01:02:21,950
+اتنين يو ناقص تلاتة في الـ z اللي هونقص أربع أخماس
+
+536
+01:02:21,950 --> 01:02:29,090
+و تلت أخماس يبقى الأن نجي للمطلوب الرابع والأخير
+
+537
+01:02:29,090 --> 01:02:32,090
+هو ال vector of length عشرة in the opposite
+
+538
+01:02:32,090 --> 01:02:36,750
+direction of اتنين يو ناقص تلت أمين عكس هذا
+
+539
+01:02:36,750 --> 01:02:39,650
+الاتجاه هو المتجه اللي قدامنا هذا اللي هو المتجه
+
+540
+01:02:39,650 --> 01:02:44,800
+الواحدة هذا يبقى بدأ أضرب أثوين في عشرةيبقى الآن
+
+541
+01:02:44,800 --> 01:02:54,080
+عشرة في ناقص أربع أخماس و تلت أخماس و Zero و اللي
+
+542
+01:02:54,080 --> 01:02:58,860
+هو بده يساوي متنهج جديد هدخل عشر على كل component
+
+543
+01:02:58,860 --> 01:03:03,360
+من هذه ال components يبقى هنا إيش بيصير تمانية
+
+544
+01:03:03,360 --> 01:03:08,040
+عشرة على خمسة تانية اتنية و المركبة التانية بيصير
+
+545
+01:03:08,040 --> 01:03:08,740
+ستة
+
+546
+01:03:11,290 --> 01:03:15,950
+يبقى يا إخلاص و الكلام للسامعين لو حبنا نجيب طول
+
+547
+01:03:15,950 --> 01:03:19,510
+هذا ال vector بنقول الجدر التربية إلى سلب تمانية
+
+548
+01:03:19,510 --> 01:03:24,950
+تربية لأربعة و ستين زائد ستة تربية لستة و تلاتين
+
+549
+01:03:24,950 --> 01:03:29,210
+زائد زيرول هو مية، جداش جدر المية؟ بعشرة و هو
+
+550
+01:03:29,210 --> 01:03:36,660
+المطلوب، يبقى هذا يثبت صحة ما ذكرناه قبل قليلحظي
+
+551
+01:03:36,660 --> 01:03:39,880
+الهي استفسار هنا في هذا المثال قبل أن نذهب إلى
+
+552
+01:03:39,880 --> 01:03:46,400
+المثال الثاني طيب الآن نمسح هذا المثال ونروح
+
+553
+01:03:46,400 --> 01:03:51,600
+للمثال رقم 2 على هذا الموضوع
+
+554
+01:04:17,320 --> 01:04:28,440
+بنجي لـ Example 2 بقول
+
+555
+01:04:28,440 --> 01:04:32,880
+F المتجه
+
+556
+01:04:32,880 --> 01:04:44,880
+A B يجب أن يسوى ناقص 7I زائد 3J زائد 8K and
+
+557
+01:04:46,720 --> 01:04:56,900
+الـ A is the point هي عبارة عن النقطة اللي هو ناقص
+
+558
+01:04:56,900 --> 01:05:09,080
+اتنين وناقص ثلاثة وستة find the point B
+
+559
+01:05:19,500 --> 01:05:26,120
+نرجع لسؤالنا مرة ثانية ميعطيني متجه a,b ناقص 7i
+
+560
+01:05:26,120 --> 01:05:32,780
+زائد 3j زائد 8k وميعطيني إحداثيات النقطة a وطلب
+
+561
+01:05:32,780 --> 01:05:39,700
+مني قداش إحداثيات النقطة b بقوله كويس المتجه هذا
+
+562
+01:05:39,700 --> 01:05:44,100
+هو عبارة عن المتجه التالف
+
+563
+01:05:47,130 --> 01:05:53,450
+هذه النقطة A على سبيل المثال هي ما طال هي ناقص
+
+564
+01:05:53,450 --> 01:06:01,310
+اتنين وناقص تلاتة وستة وهذه النقطة B اللي مش
+
+565
+01:06:01,310 --> 01:06:07,690
+عارفينها تمام؟ إذا لو حطيتيلها رموز وليكن على سبيل
+
+566
+01:06:07,690 --> 01:06:13,150
+المثال X Y و Z إذن
+
+567
+01:06:13,550 --> 01:06:17,630
+بدي أكوّن المتجه اللي عندي و أسويه بالمتجه هذا
+
+568
+01:06:17,630 --> 01:06:23,890
+يبقى بناء عليها بيكون المتجه عندي a,b هو المتجه
+
+569
+01:06:23,890 --> 01:06:30,910
+التالي الماضي و ناقص سبعة i زائد تلاتة j زائد
+
+570
+01:06:30,910 --> 01:06:40,490
+تمانية k بده 7 على الرسم يبقى x زائد 2 في اتجاه ال
+
+571
+01:06:40,490 --> 01:06:50,100
+Iزائد Y زائد 3 في اتجاه ال J زائد Z نقص 6 في اتجاه
+
+572
+01:06:50,100 --> 01:06:56,780
+ال K هذول المتجهين متساويين أخدنا قبل قليل متجهين
+
+573
+01:06:56,780 --> 01:07:02,500
+متساويين إذا كانت المركبات المتناظرة متساوية بناء
+
+574
+01:07:02,500 --> 01:07:09,080
+عليهبصير عندي x زائد اتنين يساوي ناقص سبعة هذا بده
+
+575
+01:07:09,080 --> 01:07:16,140
+يعطيك ان x يساوي قداش ناقص تسعة بعدها y زائد تلاتة
+
+576
+01:07:16,140 --> 01:07:22,060
+بده يساوي قداش اللي هو تلاتة هذا معناه ان y تساوي
+
+577
+01:07:22,060 --> 01:07:30,160
+قداش zeroاللي بعدها z ناقص ستة بده ساوي تمانية هذا
+
+578
+01:07:30,160 --> 01:07:37,840
+معناته ان z تساوي 14 من هذا الكلام بدرست انتج ان
+
+579
+01:07:37,840 --> 01:07:46,020
+ال point بي از الاحدات الاول لها ناقص تسعة الاحدات
+
+580
+01:07:46,020 --> 01:07:51,340
+التانية زيرو الاحدات التالتة اللي همين اربعتاش و
+
+581
+01:07:51,340 --> 01:07:59,820
+هكذانجي لبعض الخواص على ال vector يبقى بالدالي ان
+
+582
+01:07:59,820 --> 01:08:13,720
+ال properties of vector operations بعض
+
+583
+01:08:13,720 --> 01:08:19,820
+الخواص البسيطة على العمليات على ال vector نجي بقول
+
+584
+01:08:19,820 --> 01:08:30,590
+Fالـ U و الـ V و الـ W are vectors and
+
+585
+01:08:30,590 --> 01:08:42,230
+الـ A و الـ B are scalars يبقى كميات قياسية ذاتية
+
+586
+01:08:42,230 --> 01:08:51,560
+النقطة الأولى الـ U زائد الـ V بدها ساوي Vزائد الـ
+
+587
+01:08:51,560 --> 01:09:00,680
+U النقطة الثانية الـ U زائد ال V زائد ال W بدها
+
+588
+01:09:00,680 --> 01:09:09,000
+تساوي ال U زائد ال V زائد ال W النقطة التالتة الـ
+
+589
+01:09:09,000 --> 01:09:19,460
+U زائد ال Zero بدها تساوي ال U النقطة الرابعة الـ
+
+590
+01:09:19,460 --> 01:09:29,700
+Uزائر نقص اليوم بدها تساوي zero النقطة الخامسة ال
+
+591
+01:09:29,700 --> 01:09:37,820
+zero في اليوم بده يساوي ال zero النقطة
+
+592
+01:09:37,820 --> 01:09:44,360
+السادسة ال واحد مضروب في اليوم بده يساوي ال you
+
+593
+01:09:44,360 --> 01:09:54,910
+السابع ال aأضربها في الـ B في الـ U بده ساوي الـ A
+
+594
+01:09:54,910 --> 01:10:06,050
+B في الـ U التامنة الـ A في الـ U زائد الـ V بده
+
+595
+01:10:06,050 --> 01:10:14,410
+تساوي A في الـ U زائد A في الـ V التاسعة
+
+596
+01:10:14,410 --> 01:10:22,950
+والأخيرة اللي هو الـ Aزائد ال B في ال U بده يساوي
+
+597
+01:10:22,950 --> 01:10:43,550
+A في ال U زائد B في ال U بدي
+
+598
+01:10:43,550 --> 01:10:50,350
+أحاول أرجع الأن لمعنىكل خاصية من هذه القواسم حتى
+
+599
+01:10:50,350 --> 01:10:58,550
+نفهم فهما صحيحا مش اكتب وامشي شوف يا بنات الان
+
+600
+01:10:58,550 --> 01:11:02,670
+بيقول لو عندي تلاتة vectors ال U و ال V و ال W
+
+601
+01:11:02,670 --> 01:11:09,670
+وعندي two scalars A و B يبقى في عندي U زائد ال V
+
+602
+01:11:09,670 --> 01:11:15,650
+تساوي V زائد ال U ايش العملية هذه بالابدالية؟يبقى
+
+603
+01:11:15,650 --> 01:11:25,950
+عملية الجمع عن المتجهات عملية إبدالية الـ positive
+
+604
+01:11:25,950 --> 01:11:31,690
+of two vectors is a commutative operation عملية
+
+605
+01:11:31,690 --> 01:11:38,330
+الجمع عن ال vectors عملية إبداليةلو جمعت ال U و ال
+
+606
+01:11:38,330 --> 01:11:45,110
+V أولا و أضفت الناتج لل W تماما كما لو جمعت ال V و
+
+607
+01:11:45,110 --> 01:11:49,650
+ال W أولا ثم أضفت لهم من ال U يبقى هذه بسميها
+
+608
+01:11:49,650 --> 01:11:56,910
+associative عملية إدماجية أو تجميعية associative
+
+609
+01:11:56,910 --> 01:11:57,510
+property
+
+610
+01:12:03,540 --> 01:12:07,020
+الزيرو هد يا بناتي scalar ولا vector؟
+
+611
+01:12:10,360 --> 01:12:16,400
+أحنا أخدنا عملية جمع vector مع scalar لأ أخدنا ضرب
+
+612
+01:12:16,400 --> 01:12:20,620
+scalar في vector لكن جماعة لأ يبقى ال zero بعمله
+
+613
+01:12:20,620 --> 01:12:25,100
+طاول طويل بنات zero vector ال scalar بعمله دائرة
+
+614
+01:12:25,100 --> 01:12:32,040
+صغيرة يبقى هذا هو zero vector يبقى ال u vector زي
+
+615
+01:12:32,040 --> 01:12:39,050
+ال zero vector يسوى من ال u vectorهنا الـ U زائد
+
+616
+01:12:39,050 --> 01:12:45,370
+ناقص الـ U يعني المتجه والمتجه المعاكس إله تماماً
+
+617
+01:12:45,370 --> 01:12:51,010
+مجموع اتنين قداش؟ Zero scalar ولا vector؟ يعني
+
+618
+01:12:51,010 --> 01:12:54,550
+مجموع any two vectors بدي يعطيني vector حتى وإن
+
+619
+01:12:54,550 --> 01:12:59,470
+كان الـ zero يبقى هذا ال zero vector طيب ال zero
+
+620
+01:12:59,470 --> 01:13:05,540
+في U scalar ال zero هذا ولا vector؟ scalarلأن ضارب
+
+621
+01:13:05,540 --> 01:13:07,560
+ال vectors في أنمي العالم لا يوجد ضارب لا يوجد
+
+622
+01:13:07,560 --> 01:13:09,780
+ضارب لايوجد ضارب لايوجد ضارب لايوجد ضارب لايوجد
+
+623
+01:13:09,780 --> 01:13:15,920
+ضارب لايوجد ضارب لايوجد ضارب لايوجد ضارب لايوجد
+
+624
+01:13:15,920 --> 01:13:20,360
+ضارب لايوجد ضارب لايوجد ضارب لايوجد ضارب لايوجد
+
+625
+01:13:20,360 --> 01:13:21,260
+ضارب لايوجد ضارب لايوجد ضارب لايوجد ضارب لايوجد
+
+626
+01:13:21,260 --> 01:13:28,880
+ضارب لايوجد ضارب لايوجد ضارب
+
+627
+01:13:28,880 --> 01:13:34,140
+لايوجد ضارب لايوجد ضارب لايوجد ضارب لايوجد ضارب
+
+628
+01:13:34,140 --> 01:13:36,870
+لايوجد ضارب لايوجد ضارب لادربت في الـ scalar B و
+
+629
+01:13:36,870 --> 01:13:41,550
+النتج دربت في الـ scalar A تماما كما لو دربت ال
+
+630
+01:13:41,550 --> 01:13:45,410
+two scalars بعضهم A و B في بعض و النتج دربته في
+
+631
+01:13:45,410 --> 01:13:49,640
+مين في مين فمثلا لو قلت لك اتنين يوموبعد ذلك
+
+632
+01:13:49,640 --> 01:13:53,920
+اتضارب تلاتة في اتنين U كما لو ضربت اتنين في تلاتة
+
+633
+01:13:53,920 --> 01:13:58,540
+ام ستة في U نفس النتيجة هنا ال A في U زائد V
+
+634
+01:13:58,540 --> 01:14:05,080
+Distributive Law قانون التوزيع يبقى هنا بدوزع ال A
+
+635
+01:14:05,080 --> 01:14:09,920
+على مجموع ال two vectors فبعدين بقول A U زائد A V
+
+636
+01:14:10,610 --> 01:14:16,370
+نمر 9 الـ A زائد B فلو الـ Distributive ما بين two
+
+637
+01:14:16,370 --> 01:14:22,570
+scalars مع ال vector V ب A U زائد B U و هكذا
+
+638
+01:14:22,570 --> 01:14:28,110
+بايلغن آخر definition في هذا ال section بيقول ما
+
+639
+01:14:28,110 --> 01:14:34,470
+يأتي definition ده
+
+640
+01:14:34,470 --> 01:14:36,930
+midpoint
+
+641
+01:14:38,790 --> 01:14:46,710
+نقطة المنتصف الـ midpoint حديها الرمز M of the
+
+642
+01:14:46,710 --> 01:14:58,610
+line segment the line segment joining
+
+643
+01:14:58,610 --> 01:15:08,720
+the points joining the pointsوالذي يجمع النقطتين
+
+644
+01:15:08,720 --> 01:15:27,560
+P1 of X1 و Y1 و Z1 and P2 of X2 و Y2 و Z2 as the
+
+645
+01:15:27,560 --> 01:15:38,730
+point هي عبارة عن النقطة MR X1 زائد X2 على 2 Y1
+
+646
+01:15:38,730 --> 01:15:50,210
+زائد Y2 على 2 Z1 زائد Z2 على 2 يعني
+
+647
+01:15:50,210 --> 01:15:56,610
+لو قلت هذه المحاور على سبيل المثال قلت هذا X وهذا
+
+648
+01:15:56,610 --> 01:16:04,440
+Y وهذا Z هذا نقطة الأصل اللي هو Zeroو رسمت نقطتين
+
+649
+01:16:04,440 --> 01:16:12,000
+و وصلت بينهم بخط مستقيم فجيت قول هذه النقطة الأولى
+
+650
+01:16:12,000 --> 01:16:27,580
+P1 X1 Y1 Z1 وهذه النقطة P2 X2 Y2 Z2 بين النقطة
+
+651
+01:16:27,580 --> 01:16:33,570
+المنقصرة فيما بينهميبقى نقطة المنتصف لو قلت هذه
+
+652
+01:16:33,570 --> 01:16:39,370
+اللي هي النقطة M يبقى
+
+653
+01:16:39,370 --> 01:16:45,090
+النقطة M بدأ تيجي في منتصف المسافة بين النقطتين
+
+654
+01:16:45,090 --> 01:16:50,930
+إحداث هذه النقطة هو الإحداث اللي احنا كاتبينه هنا
+
+655
+01:16:50,930 --> 01:16:55,630
+الأن نعطي مثال توضيحي على ذلك example
+
+656
+01:17:01,340 --> 01:17:08,100
+Example one اللي هو سؤال ستة وتلاتين من الكتاب
+
+657
+01:17:08,100 --> 01:17:18,520
+بيقولت P1 اللي هي عبارة عن واحد واربعة وخمسة and
+
+658
+01:17:18,520 --> 01:17:27,580
+P2 هي عبارة عن النقطة اربعة وناقص اتنين وسبعة
+
+659
+01:17:27,580 --> 01:17:40,270
+المطلوب الأول نمر ايه؟Find the direction of
+
+660
+01:17:40,270 --> 01:17:42,770
+P1,
+
+661
+01:17:43,370 --> 01:17:47,330
+P2 نمر
+
+662
+01:17:47,330 --> 01:17:50,830
+بـ Find the midpoint
+
+663
+01:17:57,570 --> 01:18:08,890
+نقطة المنصفة of the line segment P1 P2
+
+664
+01:18:43,530 --> 01:18:49,010
+سؤال مرة تانية قلت لي هاتلي ال direction تبع
+
+665
+01:18:49,010 --> 01:18:54,970
+المتجه P1 P2 إذا هو إيش قصد يقول ليهاتلي متجهي
+
+666
+01:18:54,970 --> 01:19:01,510
+الوحدة في اتجاه P1 P2 سواء صيغة الصيغة هذه أو
+
+667
+01:19:01,510 --> 01:19:06,090
+الصيغة هذه الأثنين أرزسين إذا أنا بدي أروح أجيب له
+
+668
+01:19:06,090 --> 01:19:14,240
+متجه P1 P2 يسار بدي أكتب دبري يا بناتيبقى هذا كأنه
+
+669
+01:19:14,240 --> 01:19:17,260
+يبدأ كتابة يابا كتابة دلالة الاتنين المقرنين
+
+670
+01:19:17,260 --> 01:19:20,680
+القوسين المقرنين اما دلالة ال I و ال J و ال K سيان
+
+671
+01:19:20,680 --> 01:19:26,700
+كل واحد اذا لو جاي تقول اربعة ناقص واحد في اتجاه
+
+672
+01:19:26,700 --> 01:19:33,340
+ال I زائد ال همين ناقص اتنين ناقص اربعة في اتجاه
+
+673
+01:19:33,340 --> 01:19:35,200
+ال J زائد
+
+674
+01:19:40,290 --> 01:19:47,810
+يبقى هذا عبارة عن تلاتة I وهنا ناقص ستة J وهنا
+
+675
+01:19:47,810 --> 01:19:56,990
+زائد اتنين K بدي اجيب قول تبعه قول ال P1 P2 اللي
+
+676
+01:19:56,990 --> 01:20:05,900
+هو بده يساوي جدر التربيع لتسعة زائد ستة وتلاتينزاد
+
+677
+01:20:05,900 --> 01:20:12,400
+اربع و يسوى انا ابعين و تسعة جو تسعة و اربعين تحت
+
+678
+01:20:12,400 --> 01:20:21,840
+الجدر الجدد سبعة يبقى باجي بقوله the direction of
+
+679
+01:20:21,840 --> 01:20:35,120
+P1 P2 Sاللي هو P1 P2 على طول ال P1 P2 واللي هو بده
+
+680
+01:20:35,120 --> 01:20:43,240
+7 كله على سبعة يبقى تلت أسباع في اتجاه ال I نقص ست
+
+681
+01:20:43,240 --> 01:20:50,480
+أسباع في اتجاه ال J زائد سبعين في اتجاه ال K نمرى
+
+682
+01:20:50,480 --> 01:20:57,030
+B قال لي هدل ال midpointما بين النقطتين الاتنين
+
+683
+01:20:57,030 --> 01:21:03,270
+هدول يبقى ال M تساوى مباشرة يبقى بده أجمع أربعة
+
+684
+01:21:03,270 --> 01:21:09,310
+زائد واحد على اتنين أربعة زائد واحد على اتنين اللي
+
+685
+01:21:09,310 --> 01:21:15,910
+بعدها ناقص اتنين زائد أربعة على اتنين
+
+686
+01:21:19,710 --> 01:21:26,650
+اللي بعدها سبعة زائد خمسة على اتنين سبعة زائد خمسة
+
+687
+01:21:26,650 --> 01:21:33,010
+كله على اتنين واللي هي بدها تساوي مين خمسة على
+
+688
+01:21:33,010 --> 01:21:38,810
+اتنين تبقى كما هي وهنا مضال اتنين على اتنين بواحد
+
+689
+01:21:38,810 --> 01:21:43,690
+واطن عشر على اتنين اللي هو بقداش ستة هذه النقطات
+
+690
+01:21:43,690 --> 01:21:50,960
+المتوسطة اخر مثال في محاضرة اليومبيقول ما يأتي له
+
+691
+01:21:50,960 --> 01:21:58,980
+سؤال 14 من الكتاب بيقول find a unit vector find
+
+692
+01:21:58,980 --> 01:22:13,660
+the unit vector that makes an angle that makes an
+
+693
+01:22:13,660 --> 01:22:16,080
+angle
+
+694
+01:22:19,550 --> 01:22:29,030
+فيتا تساوي السالف تلاتة y على أربع with the
+
+695
+01:22:29,030 --> 01:22:38,950
+positive with the positive اللي هو x أكسي x axis
+
+696
+01:23:00,440 --> 01:23:04,160
+خلّي بالك معانا هنا و الله شوية السؤال مرة تانية
+
+697
+01:23:04,160 --> 01:23:08,560
+جالي هاتلي متجه الوحدة اللي يصنع زاوية مقدارها
+
+698
+01:23:08,560 --> 01:23:15,200
+سالب تلاتة باي على أربع من اتجاه الموجب لمين لل X
+
+699
+01:23:15,200 --> 01:23:19,980
+axis الزاوية هذه زي ما انت شايفها زاوية سالبةواحنا
+
+700
+01:23:19,980 --> 01:23:23,840
+أخدنا في ال polar coordinates إنهم أول كلمتي
+
+701
+01:23:23,840 --> 01:23:27,260
+أخدناهم في ال polar coordinates ممكن الزاوية تكون
+
+702
+01:23:27,260 --> 01:23:32,460
+positive angle وممكن تكون negative angle إذا مشينا
+
+703
+01:23:32,460 --> 01:23:39,000
+counter clockwise ضد عقل الساعة وإذا مشينا مع عقل
+
+704
+01:23:39,000 --> 01:23:43,590
+الساعة فالزاوية مالها سالبةطب إذا إحنا لو روحنا
+
+705
+01:23:43,590 --> 01:23:49,750
+مشينا مع قريب الساعة أو لو جيت تصورت إنه في دائرة
+
+706
+01:23:49,750 --> 01:23:54,630
+عندي نصف قطر هيساوي الواحد الصحيح يبقى الدائرة
+
+707
+01:23:54,630 --> 01:24:10,310
+هتاخد الشكل التالي الشكل اللي عندنا هذا تمام؟
+
+708
+01:24:10,650 --> 01:24:17,290
+يبقى هذه الدرجة طب بتدامش قداش 135 درجة بس وين
+
+709
+01:24:17,290 --> 01:24:24,110
+بالسالح يبقى هذه 90 مع قارب الساعة هذه 90 و بدي
+
+710
+01:24:24,110 --> 01:24:30,970
+كمان 45 يبقى بالدرجين الخاطة اللي عندنا تمام يبقى
+
+711
+01:24:30,970 --> 01:24:39,790
+الزاوية هذه سالف تلاتة بال على أربع طيب
+
+712
+01:24:40,640 --> 01:24:45,880
+لو جيت اعتبرت أن هذا متجه وطوله يساوي الواحد
+
+713
+01:24:45,880 --> 01:24:51,000
+الصحيح إذا إيه مركب في اتجاه محور X وإيه مركب في
+
+714
+01:24:51,000 --> 01:24:57,440
+اتجاه محور Y؟ يعني لو اعتبرت أن هذا متجه وطوله
+
+715
+01:24:57,440 --> 01:25:01,760
+واحد صحيح، لماذا؟ لأنه قال لي هذه اليونة Vector،
+
+716
+01:25:01,760 --> 01:25:08,200
+تمام؟ إذا بناء عليهبدي يكون ال unit vector u بدي
+
+717
+01:25:08,200 --> 01:25:14,580
+يساوي واحد في cosine اللي هو سالب تلاتة باية على
+
+718
+01:25:14,580 --> 01:25:21,120
+أربعة في اتجاه ال I زائد واحد sin تلاتة باية على
+
+719
+01:25:21,120 --> 01:25:27,940
+أربعة، مين السالب؟ سالب في اتجاه مين؟ في اتجاه ال
+
+720
+01:25:27,940 --> 01:25:34,970
+G okay ماعنديش طيب، هذا الكلام بدي يساويالـ cosine
+
+721
+01:25:34,970 --> 01:25:40,250
+even والله odd يبقى السلف هذا معه السلامة يبقاش
+
+722
+01:25:40,250 --> 01:25:46,150
+بصير هنا cosine تلاتة by على أربعة في اتجاه ال I
+
+723
+01:25:46,150 --> 01:25:54,270
+زائد ال sine، odd يبقى السلف أطلع برا، ال sine له
+
+724
+01:25:54,270 --> 01:26:00,540
+تلاتة by على أربعة في اتجاه ال Gنجي لجيب تمام
+
+725
+01:26:00,540 --> 01:26:07,240
+الزاوية اللي 135 درجة جيب تمام أي زاوية ساوية جيب
+
+726
+01:26:07,240 --> 01:26:11,660
+تمام الزاوية المكملة لها معبرعات قاعدة الإشارات
+
+727
+01:26:11,660 --> 01:26:20,380
+جتل 135 هي جتل 45 جتل 45 بواحد على جذر اتنين بس
+
+728
+01:26:20,380 --> 01:26:23,420
+هذه في الربع التاني في الربع التاني بالسالب
+
+729
+01:26:23,420 --> 01:26:28,700
+بالسالب لإنه درسوكوا ال formula وحفظوكواهذه
+
+730
+01:26:28,700 --> 01:26:36,700
+الأنشودة في التانوية كل جاية غالب جاتوا جاهية وانا
+
+731
+01:26:36,700 --> 01:26:40,300
+جات في اللي إيه تمام؟ ال English و الأمريكان عندهم
+
+732
+01:26:40,300 --> 01:26:48,000
+صيغة مناظرة All students learn calculus كل الطلاب
+
+733
+01:26:48,000 --> 01:26:51,000
+في العلم و الهندسة و التدريب و التكنولوجيا
+
+734
+01:26:51,000 --> 01:26:54,660
+المعلومات بياخدوا تفضل و تكامل يبقى all في الرابع
+
+735
+01:26:54,660 --> 01:26:59,440
+الأول كل موجةstudents الحرف الأول مكلمة sign يعني
+
+736
+01:26:59,440 --> 01:27:07,080
+ال j ترك الحرف الأول مكلمة تان اللي هو غلط ترك
+
+737
+01:27:07,080 --> 01:27:11,720
+كاركورس الحرف الأول منه sign يبقى من هنا بقول هذه
+
+738
+01:27:11,720 --> 01:27:17,300
+فالربع اللي هو الثاني يبقى بالسالب يبقى سالب واحد
+
+739
+01:27:17,300 --> 01:27:23,420
+على جدر اتنينفي اتجاه الـ I وهذه ناقص وهذه في
+
+740
+01:27:23,420 --> 01:27:27,160
+الربع الثاني والـ J في الربع التاني موجب جيب
+
+741
+01:27:27,160 --> 01:27:32,220
+الخمسة واربعين كذلك بواحد على جدر اتنين في اتجاه
+
+742
+01:27:32,220 --> 01:27:40,140
+الـ G طب السؤال هل هذا فعلا unit vector؟ كيف لا؟
+
+743
+01:27:40,140 --> 01:27:44,140
+على ربع كل واحدة فيه فهذه بواحدة على جدر اتنين
+
+744
+01:27:44,140 --> 01:27:46,280
+وربعها بالنص زائد نص
+
+745
+01:27:49,220 --> 01:27:54,440
+يبقى هاي اللي طلعه unit vector في .. that makes
+
+746
+01:27:54,440 --> 01:27:59,080
+اللي عامله زاوية 145 مع الاتجاه الموجب لمح وراكز
+
+747
+01:27:59,080 --> 01:28:03,600
+لحد هنا stop انتهاء ال section إلى يكون أرقام
+
+748
+01:28:03,600 --> 01:28:09,420
+المسائل المطلوب حلها في البيت ان شاء الله يبقى
+
+749
+01:28:09,420 --> 01:28:20,150
+exercises أتناش اتنين واحد تلاتة خمسة سبعةأحد عشر
+
+750
+01:28:20,150 --> 01:28:29,550
+تلتاش سبعتاش تسعة عشر واحد وعشرين خمسة وعشرين سبعة
+
+751
+01:28:29,550 --> 01:28:37,890
+وعشرين خمسة وعشرين سبعة وعشرين تسعة وعشرين واحد
+
+752
+01:28:37,890 --> 01:28:44,450
+وتلاتين تلاتة وتلاتين خمسة وتلاتين سبعة وتلاتين
+
+753
+01:28:44,450 --> 01:28:46,270
+تسعة وتلاتين
+
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/tT-7ILSFEbI_raw.json b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/tT-7ILSFEbI_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..88e121a899a1894b33fe79e528a47cabeb9ccd20
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/tT-7ILSFEbI_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 2030, "start": 11.04, "end": 20.3, "text": "بسم الله الرحمن الرحيم انتهينا في المحاضرة الماضية من ال section 12-1 والان نبدأ من section 12-2", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 16472, 47395, 1829, 8315, 8978, 9673, 5016, 46958, 25720, 9673, 46958, 10632, 9154, 2423, 3541, 2272, 12, 16, 16070, 7649, 8717, 44510, 10721, 9154, 3541, 2272, 12, 17], "avg_logprob": -0.21299342105263158, "compression_ratio": 1.4128440366972477, "no_speech_prob": 6.616115570068359e-06, "words": [{"start": 11.039999999999997, "end": 11.92, "word": "بسم", "probability": 0.755859375}, {"start": 11.92, "end": 12.12, "word": " الله", "probability": 0.97119140625}, {"start": 12.12, "end": 12.56, "word": " الرحمن", "probability": 0.9720052083333334}, {"start": 12.56, "end": 13.08, "word": " الرحيم", "probability": 0.9938151041666666}, {"start": 13.08, "end": 14.78, "word": " انتهينا", "probability": 0.8685302734375}, {"start": 14.78, "end": 14.94, 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" وفي", "probability": 0.8701171875}, {"start": 522.06, "end": 523.14, "word": " اتجاه", "probability": 0.9881591796875}, {"start": 523.14, "end": 524.28, "word": " نفس", "probability": 0.986083984375}, {"start": 524.28, "end": 525.02, "word": " المتجه", "probability": 0.98193359375}, {"start": 525.02, "end": 525.22, "word": " اللي", "probability": 0.737060546875}, {"start": 525.22, "end": 525.76, "word": " عندنا", "probability": 0.823486328125}, {"start": 525.76, "end": 525.92, "word": " هذا", "probability": 0.5439453125}, {"start": 525.92, "end": 526.88, "word": " نفس", "probability": 0.864501953125}, {"start": 526.88, "end": 527.7, "word": " المتجه", "probability": 0.9937744140625}, {"start": 527.7, "end": 529.1, "word": " وكان", "probability": 0.765869140625}, {"start": 529.1, "end": 529.62, "word": " له", "probability": 0.92919921875}, {"start": 529.62, "end": 530.74, "word": " نفس", "probability": 0.99853515625}, {"start": 530.74, "end": 531.36, "word": " الطول", "probability": 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"probability": 0.9884033203125}, {"start": 546.5, "end": 546.76, "word": " V", "probability": 0.72900390625}], "temperature": 1.0}, {"id": 21, "seek": 55469, "start": 547.09, "end": 554.69, "text": "وهذا المتجه V كذلك يبقى التلاتة هذول are equal or are equivalent", "tokens": [2407, 3224, 15730, 9673, 2655, 7435, 3224, 691, 9122, 8848, 23275, 7251, 3555, 4587, 7578, 16712, 1211, 9307, 3660, 8032, 8848, 12610, 366, 2681, 420, 366, 10344], "avg_logprob": -0.23228237086108752, "compression_ratio": 1.0449438202247192, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 547.09, "end": 547.69, "word": "وهذا", "probability": 0.7029622395833334}, {"start": 547.69, "end": 548.43, "word": " المتجه", "probability": 0.903564453125}, {"start": 548.43, "end": 548.85, "word": " V", "probability": 0.6767578125}, {"start": 548.85, "end": 549.61, "word": " كذلك", "probability": 0.865234375}, {"start": 549.61, "end": 550.57, "word": " يبقى", "probability": 0.90478515625}, {"start": 550.57, "end": 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"probability": 0.8916015625}, {"start": 612.46, "end": 613.78, "word": " and", "probability": 0.8662109375}], "temperature": 1.0}, {"id": 24, "seek": 63792, "start": 614.55, "end": 637.93, "text": "No determined direction يعني ممكن أن يكون اتجاهه في أي اتجاه بدكية يبقى الـ zero vector هو عبارة عن اتجاه طوله يساوي الصفر", "tokens": [4540, 9540, 3513, 37495, 22653, 3714, 43020, 14739, 7251, 30544, 1975, 2655, 7435, 40294, 3224, 8978, 36632, 1975, 2655, 7435, 40294, 47525, 4117, 10632, 7251, 3555, 4587, 7578, 2423, 39184, 4018, 8062, 31439, 6225, 3555, 9640, 3660, 18871, 1975, 2655, 7435, 40294, 23032, 12610, 3224, 7251, 3794, 995, 45865, 31767, 5172, 2288], "avg_logprob": -0.2933372574032478, "compression_ratio": 1.3082191780821917, "no_speech_prob": 0.0, "words": [{"start": 614.55, "end": 615.43, "word": "No", "probability": 0.03021240234375}, {"start": 615.43, "end": 617.73, "word": " determined", "probability": 0.40380859375}, {"start": 617.73, "end": 620.17, "word": " direction", "probability": 0.931640625}, {"start": 620.17, "end": 623.99, "word": " يعني", "probability": 0.720947265625}, {"start": 623.99, "end": 628.67, "word": " ممكن", "probability": 0.5185546875}, {"start": 628.67, "end": 629.05, "word": " أن", "probability": 0.6494140625}, {"start": 629.05, "end": 629.67, "word": " يكون", "probability": 0.99072265625}, {"start": 629.67, "end": 630.53, "word": " اتجاهه", "probability": 0.94306640625}, {"start": 630.53, "end": 630.79, "word": " في", "probability": 0.97509765625}, {"start": 630.79, "end": 631.25, "word": " أي", "probability": 0.64990234375}, {"start": 631.25, "end": 631.87, "word": " اتجاه", "probability": 0.9913330078125}, {"start": 631.87, "end": 632.63, "word": " بدكية", "probability": 0.5065104166666666}, {"start": 632.63, "end": 633.83, "word": " يبقى", "probability": 0.834716796875}, {"start": 633.83, "end": 634.03, "word": " الـ", "probability": 0.4881591796875}, {"start": 634.03, "end": 634.21, "word": " zero", "probability": 0.41845703125}, {"start": 634.21, "end": 634.73, "word": " vector", "probability": 0.9208984375}, {"start": 634.73, "end": 635.37, "word": " هو", "probability": 0.85986328125}, {"start": 635.37, "end": 635.75, "word": " عبارة", "probability": 0.9818115234375}, {"start": 635.75, "end": 635.97, "word": " عن", "probability": 0.99755859375}, {"start": 635.97, "end": 636.45, "word": " اتجاه", "probability": 0.962158203125}, {"start": 636.45, "end": 636.89, "word": " طوله", "probability": 0.9812825520833334}, {"start": 636.89, "end": 637.25, "word": " يساوي", "probability": 0.784912109375}, {"start": 637.25, "end": 637.93, "word": " الصفر", "probability": 0.8214518229166666}], "temperature": 1.0}, {"id": 25, "seek": 66564, "start": 638.18, "end": 665.64, "text": "و ممكن أن يُأخذ في أي اتجاه بدنيا و من هنا قلنا no determined direction مالوش اتجاه محدد يعني ممكن أخذه في أي اتجاه بدون قيود without restriction بدي أخذه في أي اتجاه بدية الان بدي نيجي إلى توازي المتجهات كذلك definition", "tokens": [2407, 3714, 43020, 14739, 7251, 10859, 10721, 9778, 8848, 8978, 36632, 1975, 2655, 7435, 40294, 47525, 22653, 995, 4032, 9154, 34105, 12174, 1211, 8315, 572, 9540, 3513, 3714, 6027, 2407, 8592, 1975, 2655, 7435, 40294, 3714, 24401, 3215, 37495, 22653, 3714, 43020, 5551, 9778, 24192, 8978, 36632, 1975, 2655, 7435, 40294, 47525, 11536, 12174, 1829, 23328, 1553, 29529, 4724, 16254, 5551, 9778, 24192, 8978, 36632, 1975, 2655, 7435, 40294, 47525, 10632, 2423, 7649, 4724, 16254, 8717, 1829, 7435, 1829, 30731, 33427, 31377, 1829, 9673, 2655, 7435, 3224, 9307, 9122, 8848, 23275, 7123], "avg_logprob": -0.22731855223255773, "compression_ratio": 1.7857142857142858, "no_speech_prob": 0.0, "words": [{"start": 638.18, "end": 638.44, "word": "و", "probability": 0.341552734375}, {"start": 638.44, "end": 638.86, "word": " ممكن", "probability": 0.739501953125}, {"start": 638.86, "end": 639.12, "word": " أن", "probability": 0.5107421875}, {"start": 639.12, "end": 639.72, "word": " يُأخذ", "probability": 0.82333984375}, {"start": 639.72, "end": 639.96, "word": " في", "probability": 0.966796875}, {"start": 639.96, "end": 640.46, "word": " أي", "probability": 0.88037109375}, {"start": 640.46, "end": 641.16, "word": " اتجاه", "probability": 0.9676513671875}, {"start": 641.16, "end": 641.96, "word": " بدنيا", "probability": 0.7062174479166666}, {"start": 641.96, "end": 642.38, "word": " و", "probability": 0.7490234375}, {"start": 642.38, "end": 642.6, "word": " من", "probability": 0.64501953125}, {"start": 642.6, "end": 642.82, "word": " هنا", "probability": 0.9873046875}, {"start": 642.82, "end": 643.34, "word": " قلنا", "probability": 0.8792317708333334}, {"start": 643.34, "end": 643.8, "word": " no", "probability": 0.2001953125}, {"start": 643.8, "end": 644.7, "word": " determined", "probability": 0.7802734375}, {"start": 644.7, "end": 645.52, "word": " direction", "probability": 0.9560546875}, {"start": 645.52, "end": 646.46, "word": " مالوش", "probability": 0.8089599609375}, {"start": 646.46, "end": 647.12, "word": " اتجاه", "probability": 0.987548828125}, {"start": 647.12, "end": 647.86, "word": " محدد", "probability": 0.99365234375}, {"start": 647.86, "end": 648.42, "word": " يعني", "probability": 0.884033203125}, {"start": 648.42, "end": 648.84, "word": " ممكن", "probability": 0.98876953125}, {"start": 648.84, "end": 649.34, "word": " أخذه", "probability": 0.591796875}, {"start": 649.34, "end": 649.56, "word": " في", "probability": 0.97412109375}, {"start": 649.56, "end": 649.86, "word": " أي", "probability": 0.72216796875}, {"start": 649.86, "end": 650.46, "word": " اتجاه", "probability": 0.990966796875}, {"start": 650.46, "end": 651.38, "word": " بدون", "probability": 0.982666015625}, {"start": 651.38, "end": 651.84, "word": " قيود", "probability": 0.9860026041666666}, {"start": 651.84, "end": 652.14, "word": " without", "probability": 0.74658203125}, {"start": 652.14, "end": 653.12, "word": " restriction", "probability": 0.845703125}, {"start": 653.12, "end": 653.76, "word": " بدي", "probability": 0.4483642578125}, {"start": 653.76, "end": 654.0, "word": " أخذه", "probability": 0.9220377604166666}, {"start": 654.0, "end": 654.22, "word": " في", "probability": 0.98291015625}, {"start": 654.22, "end": 654.58, "word": " أي", "probability": 0.7958984375}, {"start": 654.58, "end": 655.38, "word": " اتجاه", "probability": 0.9908447265625}, {"start": 655.38, "end": 656.52, "word": " بدية", "probability": 0.5518798828125}, {"start": 656.52, "end": 658.92, "word": " الان", "probability": 0.6234130859375}, {"start": 658.92, "end": 659.18, "word": " بدي", "probability": 0.7294921875}, {"start": 659.18, "end": 659.7, "word": " نيجي", "probability": 0.846923828125}, {"start": 659.7, "end": 660.2, "word": " إلى", "probability": 0.7314453125}, {"start": 660.2, "end": 661.72, "word": " توازي", "probability": 0.8681640625}, {"start": 661.72, "end": 663.64, "word": " المتجهات", "probability": 0.94697265625}, {"start": 663.64, "end": 665.06, "word": " كذلك", "probability": 0.7732747395833334}, {"start": 665.06, "end": 665.64, "word": " definition", "probability": 0.3984375}], "temperature": 1.0}, {"id": 26, "seek": 69528, "start": 667.42, "end": 695.28, "text": "to non zero vectors to non zero vectors u and lv are said to be parallel are said to be parallel ممكن نقول عليهم متوازية", "tokens": [1353, 2107, 4018, 18875, 281, 2107, 4018, 18875, 344, 293, 287, 85, 366, 848, 281, 312, 8952, 366, 848, 281, 312, 8952, 3714, 43020, 8717, 39648, 25894, 16095, 44650, 2407, 31377, 10632], "avg_logprob": -0.28361742424242425, "compression_ratio": 1.3725490196078431, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 667.42, "end": 667.9, "word": "to", "probability": 0.385498046875}, {"start": 667.9, "end": 670.36, "word": " non", "probability": 0.71630859375}, {"start": 670.36, "end": 672.04, "word": " zero", "probability": 0.296630859375}, {"start": 672.04, "end": 674.26, "word": " vectors", "probability": 0.94677734375}, {"start": 674.26, "end": 675.34, "word": " to", "probability": 0.14990234375}, {"start": 675.34, "end": 675.58, "word": " non", "probability": 0.95751953125}, {"start": 675.58, "end": 676.0, "word": " zero", "probability": 0.80712890625}, {"start": 676.0, "end": 676.88, "word": " vectors", "probability": 0.9619140625}, {"start": 676.88, "end": 678.08, "word": " u", "probability": 0.470703125}, {"start": 678.08, "end": 679.38, "word": " and", "probability": 0.9521484375}, {"start": 679.38, "end": 680.82, "word": " lv", "probability": 0.60595703125}, {"start": 680.82, "end": 681.84, "word": " are", "probability": 0.8681640625}, {"start": 681.84, "end": 682.1, "word": " said", "probability": 0.94873046875}, {"start": 682.1, "end": 682.3, "word": " to", "probability": 0.98291015625}, {"start": 682.3, "end": 682.5, "word": " be", "probability": 0.9072265625}, {"start": 682.5, "end": 683.14, "word": " parallel", "probability": 0.9052734375}, {"start": 683.14, "end": 684.08, "word": " are", "probability": 0.77001953125}, {"start": 684.08, "end": 685.42, "word": " said", "probability": 0.95263671875}, {"start": 685.42, "end": 687.12, "word": " to", "probability": 0.9853515625}, {"start": 687.12, "end": 689.2, "word": " be", "probability": 0.951171875}, {"start": 689.2, "end": 690.7, "word": " parallel", "probability": 0.92236328125}, {"start": 690.7, "end": 692.68, "word": " ممكن", "probability": 0.89990234375}, {"start": 692.68, "end": 692.98, "word": " نقول", "probability": 0.807861328125}, {"start": 692.98, "end": 693.46, "word": " عليهم", "probability": 0.963134765625}, {"start": 693.46, "end": 695.28, "word": " متوازية", "probability": 0.8663330078125}], "temperature": 1.0}, {"id": 27, "seek": 72382, "start": 697.02, "end": 723.82, "text": "there is a real number if there is a real number alpha such that بحيث أن ال V تساوي Alpha U for example", "tokens": [15456, 307, 257, 957, 1230, 498, 456, 307, 257, 957, 1230, 8961, 1270, 300, 4724, 5016, 1829, 12984, 14739, 2423, 691, 6055, 3794, 995, 45865, 20588, 624, 337, 1365], "avg_logprob": -0.2464843809604645, "compression_ratio": 1.16, "no_speech_prob": 0.0, "words": [{"start": 697.02, "end": 697.46, "word": "there", "probability": 0.06964111328125}, {"start": 697.46, "end": 698.24, "word": " is", "probability": 0.9560546875}, {"start": 698.24, "end": 700.16, "word": " a", "probability": 0.9443359375}, {"start": 700.16, "end": 700.74, "word": " real", "probability": 0.96826171875}, {"start": 700.74, "end": 702.98, "word": " number", "probability": 0.9697265625}, {"start": 702.98, "end": 704.52, "word": " if", "probability": 0.48486328125}, {"start": 704.52, "end": 704.82, "word": " there", "probability": 0.94482421875}, {"start": 704.82, "end": 705.08, "word": " is", "probability": 0.947265625}, {"start": 705.08, "end": 705.36, "word": " a", "probability": 0.98193359375}, {"start": 705.36, "end": 705.82, "word": " real", "probability": 0.95556640625}, {"start": 705.82, "end": 707.36, "word": " number", "probability": 0.9580078125}, {"start": 707.36, "end": 708.76, "word": " alpha", "probability": 0.5185546875}, {"start": 708.76, "end": 710.7, "word": " such", "probability": 0.92919921875}, {"start": 710.7, "end": 711.36, "word": " that", "probability": 0.95947265625}, {"start": 711.36, "end": 713.6, "word": " بحيث", "probability": 0.8790283203125}, {"start": 713.6, "end": 714.02, "word": " أن", "probability": 0.63330078125}, {"start": 714.02, "end": 715.12, "word": " ال", "probability": 0.884765625}, {"start": 715.12, "end": 715.56, "word": " V", "probability": 0.74462890625}, {"start": 715.56, "end": 716.88, "word": " تساوي", "probability": 0.875}, {"start": 716.88, "end": 718.16, "word": " Alpha", "probability": 0.352783203125}, {"start": 718.16, "end": 718.86, "word": " U", "probability": 0.9541015625}, {"start": 718.86, "end": 723.2, "word": " for", "probability": 0.86083984375}, {"start": 723.2, "end": 723.82, "word": " example", "probability": 0.97509765625}], "temperature": 1.0}, {"id": 28, "seek": 75045, "start": 729.03, "end": 750.45, "text": "The vectors مثلًا V و 3V and ناقص 2V are parallel يبقى هذه المتجهات", "tokens": [2278, 18875, 50113, 1211, 14111, 995, 691, 4032, 805, 53, 293, 8717, 995, 4587, 9381, 568, 53, 366, 8952, 7251, 3555, 4587, 7578, 29538, 9673, 2655, 7435, 3224, 9307], "avg_logprob": -0.21770834028720856, "compression_ratio": 0.9484536082474226, "no_speech_prob": 0.0, "words": [{"start": 729.03, "end": 729.61, "word": "The", "probability": 0.2353515625}, {"start": 729.61, "end": 731.63, "word": " vectors", "probability": 0.9443359375}, {"start": 731.63, "end": 733.63, "word": " مثلًا", "probability": 0.8375244140625}, {"start": 733.63, "end": 734.29, "word": " V", "probability": 0.490234375}, {"start": 734.29, "end": 735.53, "word": " و", "probability": 0.84130859375}, {"start": 735.53, "end": 737.87, "word": " 3V", "probability": 0.6685791015625}, {"start": 737.87, "end": 739.17, "word": " and", "probability": 0.73095703125}, {"start": 739.17, "end": 740.89, "word": " ناقص", "probability": 0.6674346923828125}, {"start": 740.89, "end": 742.59, "word": " 2V", "probability": 0.898193359375}, {"start": 742.59, "end": 743.69, "word": " are", "probability": 0.83984375}, {"start": 743.69, "end": 744.91, "word": " parallel", "probability": 0.84912109375}, {"start": 744.91, "end": 749.33, "word": " يبقى", "probability": 0.9521484375}, {"start": 749.33, "end": 749.59, "word": " هذه", "probability": 0.9365234375}, {"start": 749.59, "end": 750.45, "word": " المتجهات", "probability": 0.97353515625}], "temperature": 1.0}, {"id": 29, "seek": 77811, "start": 750.73, "end": 778.11, "text": "بقول عنها متجهات متساوية لأن كل واحد هو عبارة عن مضاعفات الآخر وليس بالضرورة أن تكون Alpha عددا صحيحا يعني ممكن يكون هذا تلك على اتنين V يعني ممكن يكون كاسرك المهم واحد منهم مضاعفات الآخر فمثلا لو جيت قلت هذا هو ال vector V على سبيل المثال", "tokens": [3555, 39648, 18871, 11296, 44650, 7435, 3224, 9307, 44650, 3794, 995, 2407, 10632, 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"word": " V1", "probability": 0.905029296875}, {"start": 1067.39, "end": 1067.97, "word": " و", "probability": 0.59033203125}, {"start": 1067.97, "end": 1068.33, "word": " 0", "probability": 0.389892578125}, {"start": 1068.33, "end": 1068.55, "word": " و", "probability": 0.82763671875}, {"start": 1068.55, "end": 1068.95, "word": " 0", "probability": 0.908203125}, {"start": 1068.95, "end": 1069.67, "word": " زي", "probability": 0.935302734375}, {"start": 1069.67, "end": 1069.83, "word": " ما", "probability": 0.978515625}, {"start": 1069.83, "end": 1070.27, "word": " درسنا", "probability": 0.9141845703125}, {"start": 1070.27, "end": 1070.41, "word": " في", "probability": 0.9755859375}, {"start": 1070.41, "end": 1071.03, "word": " المحاضرة", "probability": 0.9671630859375}, {"start": 1071.03, "end": 1071.55, "word": " الماضية", "probability": 0.91943359375}], "temperature": 1.0}, {"id": 40, "seek": 109999, "start": 1072.49, "end": 1099.99, "text": "هذه الـ V1 و V2 و 0 هذه الان V1 و V2 و V3 يبقى هذه المراكبات الثلاثة لمين للـ vector V in space حد بيتسأل؟ طيب يبقى هذه المراكبات من الأن فصاعدا", "tokens": [3224, 24192, 2423, 39184, 691, 16, 4032, 691, 17, 4032, 1958, 29538, 2423, 7649, 691, 16, 4032, 691, 17, 4032, 691, 18, 7251, 3555, 4587, 7578, 29538, 9673, 23557, 4117, 3555, 9307, 6024, 104, 1211, 5718, 104, 3660, 32767, 9957, 24976, 39184, 8062, 691, 294, 1901, 11331, 3215, 4724, 36081, 3794, 10721, 1211, 22807, 23032, 1829, 3555, 7251, 3555, 4587, 7578, 29538, 9673, 23557, 4117, 3555, 9307, 9154, 16247, 1863, 6156, 9381, 995, 22488, 995], "avg_logprob": -0.27014803337423426, "compression_ratio": 1.582191780821918, "no_speech_prob": 0.0, "words": [{"start": 1072.49, "end": 1073.15, "word": "هذه", "probability": 0.62744140625}, {"start": 1073.15, "end": 1073.75, "word": " الـ", "probability": 0.3109130859375}, {"start": 1073.75, "end": 1074.63, "word": " V1", "probability": 0.7176513671875}, {"start": 1074.63, "end": 1075.25, "word": " و", "probability": 0.67431640625}, {"start": 1075.25, "end": 1076.09, "word": " V2", "probability": 0.960693359375}, {"start": 1076.09, "end": 1076.65, "word": " و", "probability": 0.96142578125}, {"start": 1076.65, "end": 1077.11, "word": " 0", "probability": 0.4208984375}, {"start": 1077.11, "end": 1078.49, "word": " هذه", "probability": 0.47509765625}, {"start": 1078.49, "end": 1079.05, "word": " الان", "probability": 0.681396484375}, {"start": 1079.05, "end": 1080.09, "word": " V1", "probability": 0.958984375}, {"start": 1080.09, "end": 1080.59, "word": " و", "probability": 0.89208984375}, {"start": 1080.59, "end": 1081.35, "word": " V2", "probability": 0.973388671875}, {"start": 1081.35, "end": 1082.01, "word": " و", "probability": 0.994140625}, {"start": 1082.01, "end": 1083.19, "word": " V3", "probability": 0.936279296875}, {"start": 1083.19, "end": 1084.13, "word": " يبقى", "probability": 0.8839111328125}, {"start": 1084.13, "end": 1084.45, "word": " هذه", "probability": 0.94921875}, {"start": 1084.45, "end": 1085.37, "word": " المراكبات", "probability": 0.8330810546875}, {"start": 1085.37, "end": 1086.17, "word": " الثلاثة", "probability": 0.9220377604166666}, {"start": 1086.17, "end": 1086.59, "word": " لمين", "probability": 0.792236328125}, {"start": 1086.59, "end": 1087.31, "word": " للـ", "probability": 0.478271484375}, {"start": 1087.31, "end": 1087.63, "word": " vector", "probability": 0.62548828125}, {"start": 1087.63, "end": 1088.15, "word": " V", "probability": 0.82763671875}, {"start": 1088.15, "end": 1088.61, "word": " in", "probability": 0.6787109375}, {"start": 1088.61, "end": 1089.15, "word": " space", "probability": 0.7392578125}, {"start": 1089.15, "end": 1089.65, "word": " حد", "probability": 0.464111328125}, {"start": 1089.65, "end": 1092.19, "word": " بيتسأل؟", "probability": 0.8358561197916666}, {"start": 1092.19, "end": 1095.95, "word": " طيب", "probability": 0.7841796875}, {"start": 1095.95, "end": 1096.41, "word": " يبقى", "probability": 0.88427734375}, {"start": 1096.41, "end": 1096.65, "word": " هذه", "probability": 0.958984375}, {"start": 1096.65, "end": 1097.47, "word": " المراكبات", "probability": 0.9853515625}, {"start": 1097.47, "end": 1098.03, "word": " من", "probability": 0.4072265625}, {"start": 1098.03, "end": 1099.01, "word": " الأن", "probability": 0.714111328125}, {"start": 1099.01, "end": 1099.99, "word": " فصاعدا", "probability": 0.90078125}], "temperature": 1.0}, {"id": 41, "seek": 112808, "start": 1100.32, "end": 1128.08, "text": "سنحاول أن نكتب دائما و أبدا الـ vector V بدلالة المركبات التلاتة تبعته في الإتجاهات تبعت محور الإحداثيات X و Y و Z ممكن نعطي شكل عام لمين لل vector V", "tokens": [3794, 1863, 5016, 995, 12610, 14739, 8717, 4117, 2655, 3555, 11778, 16373, 15042, 4032, 5551, 3555, 28259, 2423, 39184, 8062, 691, 47525, 1211, 6027, 3660, 9673, 31747, 3555, 9307, 16712, 1211, 9307, 3660, 6055, 3555, 34268, 3224, 8978, 33688, 2655, 7435, 40294, 9307, 6055, 3555, 34268, 3714, 5016, 13063, 33688, 24401, 5718, 104, 1829, 9307, 1783, 4032, 398, 4032, 1176, 3714, 43020, 8717, 3615, 9566, 1829, 13412, 28820, 6225, 10943, 32767, 9957, 24976, 8062, 691], "avg_logprob": -0.21278783188838707, "compression_ratio": 1.5493827160493827, "no_speech_prob": 0.0, "words": [{"start": 1100.32, "end": 1101.1, "word": "سنحاول", "probability": 0.8751953125}, {"start": 1101.1, "end": 1101.34, "word": " أن", "probability": 0.493408203125}, {"start": 1101.34, "end": 1101.7, "word": " نكتب", "probability": 0.9833984375}, {"start": 1101.7, "end": 1102.2, "word": " دائما", "probability": 0.9404296875}, {"start": 1102.2, "end": 1102.42, "word": " و", "probability": 0.6376953125}, {"start": 1102.42, "end": 1102.9, "word": " أبدا", "probability": 0.8011067708333334}, {"start": 1102.9, "end": 1103.66, "word": " الـ", "probability": 0.6253662109375}, {"start": 1103.66, "end": 1104.0, "word": " vector", "probability": 0.638671875}, {"start": 1104.0, "end": 1104.36, "word": " V", "probability": 0.423583984375}, {"start": 1104.36, "end": 1105.14, "word": " بدلالة", "probability": 0.8145751953125}, {"start": 1105.14, "end": 1106.42, "word": " المركبات", "probability": 0.80462646484375}, {"start": 1106.42, "end": 1107.44, "word": " التلاتة", "probability": 0.927490234375}, {"start": 1107.44, "end": 1108.44, "word": " تبعته", "probability": 0.7535400390625}, {"start": 1108.44, "end": 1108.86, "word": " في", "probability": 0.9033203125}, {"start": 1108.86, "end": 1109.92, "word": " الإتجاهات", "probability": 0.831640625}, {"start": 1109.92, "end": 1110.32, "word": " تبعت", "probability": 0.7898763020833334}, {"start": 1110.32, "end": 1110.78, "word": " محور", "probability": 0.92138671875}, {"start": 1110.78, "end": 1111.82, "word": " الإحداثيات", "probability": 0.9339192708333334}, {"start": 1111.82, "end": 1112.84, "word": " X", "probability": 0.404296875}, {"start": 1112.84, "end": 1113.34, "word": " و", "probability": 0.6123046875}, {"start": 1113.34, "end": 1113.88, "word": " Y", "probability": 0.451171875}, {"start": 1113.88, "end": 1114.7, "word": " و", "probability": 0.98681640625}, {"start": 1114.7, "end": 1115.42, "word": " Z", "probability": 0.9326171875}, {"start": 1115.42, "end": 1121.42, "word": " ممكن", "probability": 0.917724609375}, {"start": 1121.42, "end": 1124.36, "word": " نعطي", "probability": 0.921875}, {"start": 1124.36, "end": 1125.2, "word": " شكل", "probability": 0.939697265625}, {"start": 1125.2, "end": 1126.1, "word": " عام", "probability": 0.9970703125}, {"start": 1126.1, "end": 1126.88, "word": " لمين", "probability": 0.7008056640625}, {"start": 1126.88, "end": 1127.32, "word": " لل", "probability": 0.81201171875}, {"start": 1127.32, "end": 1127.72, "word": " vector", "probability": 0.595703125}, {"start": 1127.72, "end": 1128.08, "word": " V", "probability": 0.94091796875}], "temperature": 1.0}, {"id": 42, "seek": 115651, "start": 1128.63, "end": 1156.51, "text": "تاولة ما نقول ان two vectors are parallel لو روحت رسمت موازي لهذا ال vector وليكن الموازي هو ال vector اللي عندنا هذا على سبيل المثال موازي L وG بالضغط تماما وكانت هذه النقطة P1 of X1 وY1 وZ1 وكانت النقطة هذه P2 لX2", "tokens": [2655, 995, 12610, 3660, 19446, 8717, 39648, 16472, 732, 18875, 366, 8952, 45164, 12602, 2407, 33753, 12602, 38251, 2655, 3714, 2407, 31377, 1829, 46740, 15730, 2423, 8062, 4032, 20292, 19452, 9673, 2407, 31377, 1829, 31439, 2423, 8062, 13672, 1829, 43242, 8315, 23758, 15844, 8608, 21292, 1211, 9673, 12984, 6027, 3714, 2407, 31377, 1829, 441, 4032, 38, 20666, 11242, 17082, 9566, 46811, 10943, 995, 4032, 41361, 2655, 29538, 28239, 47432, 3660, 430, 16, 295, 1783, 16, 4032, 56, 16, 4032, 57, 16, 4032, 41361, 2655, 28239, 47432, 3660, 29538, 430, 17, 5296, 55, 17], "avg_logprob": -0.2257313888440741, "compression_ratio": 1.6328502415458936, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1128.63, "end": 1129.15, "word": "تاولة", "probability": 0.494049072265625}, {"start": 1129.15, "end": 1129.23, "word": " ما", "probability": 0.347900390625}, {"start": 1129.23, "end": 1129.53, "word": " نقول", "probability": 0.898193359375}, {"start": 1129.53, "end": 1129.91, "word": " ان", "probability": 0.4248046875}, {"start": 1129.91, "end": 1130.27, "word": " two", "probability": 0.1673583984375}, {"start": 1130.27, "end": 1130.85, "word": " vectors", "probability": 0.9375}, {"start": 1130.85, "end": 1131.33, "word": " are", "probability": 0.91748046875}, {"start": 1131.33, "end": 1132.01, "word": " parallel", "probability": 0.89306640625}, {"start": 1132.01, "end": 1132.45, "word": " لو", "probability": 0.78857421875}, {"start": 1132.45, "end": 1132.81, "word": " روحت", "probability": 0.7411295572916666}, {"start": 1132.81, "end": 1133.43, "word": " رسمت", "probability": 0.9231770833333334}, {"start": 1133.43, "end": 1134.01, "word": " موازي", "probability": 0.90771484375}, {"start": 1134.01, "end": 1134.49, "word": " لهذا", "probability": 0.94580078125}, {"start": 1134.49, "end": 1134.69, "word": " ال", "probability": 0.939453125}, {"start": 1134.69, "end": 1135.07, "word": " vector", "probability": 0.86474609375}, {"start": 1135.07, "end": 1136.33, "word": " وليكن", "probability": 0.8006184895833334}, {"start": 1136.33, "end": 1137.15, "word": " الموازي", "probability": 0.965087890625}, {"start": 1137.15, "end": 1137.41, "word": " هو", "probability": 0.98828125}, {"start": 1137.41, "end": 1137.61, "word": " ال", "probability": 0.9052734375}, {"start": 1137.61, "end": 1137.97, "word": " vector", "probability": 0.97216796875}, {"start": 1137.97, "end": 1138.27, "word": " اللي", "probability": 0.8701171875}, {"start": 1138.27, "end": 1138.73, "word": " عندنا", "probability": 0.97314453125}, {"start": 1138.73, "end": 1139.07, "word": " هذا", "probability": 0.8466796875}, {"start": 1139.07, "end": 1139.43, "word": " على", "probability": 0.83544921875}, {"start": 1139.43, "end": 1140.01, "word": " سبيل", "probability": 0.9879557291666666}, {"start": 1140.01, "end": 1140.63, "word": " المثال", "probability": 0.98681640625}, {"start": 1140.63, "end": 1141.75, "word": " موازي", "probability": 0.929931640625}, {"start": 1141.75, "end": 1141.95, "word": " L", "probability": 0.32421875}, {"start": 1141.95, "end": 1142.37, "word": " وG", "probability": 0.46917724609375}, {"start": 1142.37, "end": 1143.47, "word": " بالضغط", "probability": 0.91162109375}, {"start": 1143.47, "end": 1144.45, "word": " تماما", "probability": 0.9930013020833334}, {"start": 1144.45, "end": 1145.55, "word": " وكانت", "probability": 0.8919270833333334}, {"start": 1145.55, "end": 1146.03, "word": " هذه", "probability": 0.97802734375}, {"start": 1146.03, "end": 1147.23, "word": " النقطة", "probability": 0.9820963541666666}, {"start": 1147.23, "end": 1148.53, "word": " P1", "probability": 0.779296875}, {"start": 1148.53, "end": 1148.95, "word": " of", "probability": 0.44384765625}, {"start": 1148.95, "end": 1149.85, "word": " X1", "probability": 0.918701171875}, {"start": 1149.85, "end": 1150.75, "word": " وY1", "probability": 0.7835286458333334}, {"start": 1150.75, "end": 1151.67, "word": " وZ1", "probability": 0.8828125}, {"start": 1151.67, "end": 1153.03, "word": " وكانت", "probability": 0.9685872395833334}, {"start": 1153.03, "end": 1153.77, "word": " النقطة", "probability": 0.95556640625}, {"start": 1153.77, "end": 1154.21, "word": " هذه", "probability": 0.43310546875}, {"start": 1154.21, "end": 1155.29, "word": " P2", "probability": 0.980224609375}, {"start": 1155.29, "end": 1156.51, "word": " لX2", "probability": 0.687744140625}], "temperature": 1.0}, {"id": 43, "seek": 118318, "start": 1156.86, "end": 1183.18, "text": "و Y2 و Z2 إذا ال vector اللي عيني هذا جد ال vector هذا بالضبط تماما مقدارا و اتجاها طيب بناء عليه ال vector V بدي أكتبه بدللة المركبات تبعات هذه النقطة يبقى بناء عليه in general بروح بقول هيك in general", "tokens": [2407, 398, 17, 4032, 1176, 17, 11933, 15730, 2423, 8062, 13672, 1829, 6225, 9957, 1829, 23758, 10874, 3215, 2423, 8062, 23758, 20666, 11242, 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"word": " vector", "probability": 0.693359375}, {"start": 1404.96, "end": 1405.6, "word": " V", "probability": 0.8544921875}, {"start": 1405.6, "end": 1406.02, "word": " اللي", "probability": 0.86767578125}, {"start": 1406.02, "end": 1406.56, "word": " عندنا", "probability": 0.8271484375}, {"start": 1406.56, "end": 1407.04, "word": " هذا", "probability": 0.7900390625}, {"start": 1407.04, "end": 1410.54, "word": " بدنا", "probability": 0.6356201171875}, {"start": 1410.54, "end": 1410.78, "word": " نيجي", "probability": 0.91259765625}, {"start": 1410.78, "end": 1410.96, "word": " هنا", "probability": 0.8662109375}, {"start": 1410.96, "end": 1411.52, "word": " نقطة", "probability": 0.9801432291666666}, {"start": 1411.52, "end": 1412.7, "word": " بسيطة", "probability": 0.9900390625}, {"start": 1412.7, "end": 1413.1, "word": " قبل", "probability": 0.99169921875}, {"start": 1413.1, "end": 1413.34, "word": " أن", "probability": 0.85400390625}, {"start": 1413.34, "end": 1413.74, "word": " نبدأ", "probability": 0.9537760416666666}, {"start": 1413.74, "end": 1413.94, "word": " في", "probability": 0.9111328125}, {"start": 1413.94, "end": 1414.24, "word": " أخذ", "probability": 0.8331705729166666}, {"start": 1414.24, "end": 1414.56, "word": " بعض", "probability": 0.982177734375}, {"start": 1414.56, "end": 1415.24, "word": " الأمثلة", "probability": 0.984375}, {"start": 1415.24, "end": 1416.1, "word": " النقطة", "probability": 0.9632161458333334}, {"start": 1416.1, "end": 1416.32, "word": " دي", "probability": 0.6676025390625}, {"start": 1416.32, "end": 1416.68, "word": " كيف", "probability": 0.938720703125}, {"start": 1416.68, "end": 1416.98, "word": " بدنا", "probability": 0.83251953125}, {"start": 1416.98, "end": 1417.4, "word": " نجمع", "probability": 0.957763671875}, {"start": 1417.4, "end": 1417.74, "word": " two", "probability": 0.66845703125}, {"start": 1417.74, "end": 1418.38, "word": " vectors", "probability": 0.96826171875}, {"start": 1418.38, "end": 1419.14, "word": " أو", "probability": 0.8984375}, {"start": 1419.14, "end": 1420.0, "word": " نترحهم", "probability": 0.83857421875}, {"start": 1420.0, "end": 1420.66, "word": " أو", "probability": 0.95654296875}, {"start": 1420.66, "end": 1421.12, "word": " نضرب", "probability": 0.9873046875}, {"start": 1421.12, "end": 1421.28, "word": " ال", "probability": 0.974609375}, {"start": 1421.28, "end": 1421.64, "word": " vector", "probability": 0.95361328125}, {"start": 1421.64, "end": 1422.12, "word": " في", "probability": 0.978515625}, {"start": 1422.12, "end": 1423.0, "word": " scalar", "probability": 0.4482421875}, {"start": 1423.0, "end": 1424.38, "word": " هحطه", "probability": 0.7194366455078125}, {"start": 1424.38, "end": 1424.64, "word": " على", "probability": 0.93212890625}, {"start": 1424.64, "end": 1425.08, "word": " شكل", "probability": 0.974609375}, {"start": 1425.08, "end": 1426.02, "word": " التعريف", "probability": 0.990234375}, {"start": 1426.02, "end": 1427.1, "word": " التالي", "probability": 0.91796875}, {"start": 1427.1, "end": 1428.38, "word": " definition", "probability": 0.59765625}], "temperature": 1.0}, {"id": 53, "seek": 146047, "start": 1433.53, "end": 1460.47, "text": "let U تساوي U واحد و U اتنين و U تلاتة بدلالة المراكبات تبعها and V تساوي V واحد و V اتنين و V تلاتة بي two vectors", "tokens": [2631, 624, 6055, 3794, 995, 45865, 624, 36764, 24401, 4032, 624, 1975, 2655, 1863, 9957, 4032, 624, 6055, 1211, 9307, 3660, 4724, 3215, 1211, 6027, 3660, 9673, 23557, 4117, 3555, 9307, 6055, 3555, 3615, 11296, 293, 691, 6055, 3794, 995, 45865, 691, 36764, 24401, 4032, 691, 1975, 2655, 1863, 9957, 4032, 691, 6055, 1211, 9307, 3660, 4724, 1829, 732, 18875], "avg_logprob": -0.2197745930953104, "compression_ratio": 1.4916666666666667, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1433.53, "end": 1434.11, "word": "let", "probability": 0.26953125}, {"start": 1434.11, "end": 1436.09, "word": " U", "probability": 0.3837890625}, {"start": 1436.09, "end": 1436.93, "word": " تساوي", "probability": 0.7006378173828125}, {"start": 1436.93, "end": 1437.37, "word": " U", "probability": 0.7890625}, {"start": 1437.37, "end": 1437.97, "word": " واحد", "probability": 0.660888671875}, {"start": 1437.97, "end": 1438.53, "word": " و", "probability": 0.91650390625}, {"start": 1438.53, "end": 1438.71, "word": " U", "probability": 0.68359375}, {"start": 1438.71, "end": 1439.35, "word": " اتنين", "probability": 0.8670654296875}, {"start": 1439.35, "end": 1439.93, "word": " و", "probability": 0.98388671875}, {"start": 1439.93, "end": 1440.27, "word": " U", "probability": 0.9267578125}, {"start": 1440.27, "end": 1442.01, "word": " تلاتة", "probability": 0.8935546875}, {"start": 1442.01, "end": 1445.73, "word": " بدلالة", "probability": 0.764599609375}, {"start": 1445.73, "end": 1446.71, "word": " المراكبات", "probability": 0.88662109375}, {"start": 1446.71, "end": 1447.53, "word": " تبعها", "probability": 0.6817626953125}, {"start": 1447.53, "end": 1448.47, "word": " and", "probability": 0.634765625}, {"start": 1448.47, "end": 1450.01, "word": " V", "probability": 0.50732421875}, {"start": 1450.01, "end": 1451.07, "word": " تساوي", "probability": 0.96484375}, {"start": 1451.07, "end": 1451.33, "word": " V", "probability": 0.96337890625}, {"start": 1451.33, "end": 1451.95, "word": " واحد", "probability": 0.99169921875}, {"start": 1451.95, "end": 1452.37, "word": " و", "probability": 0.978515625}, {"start": 1452.37, "end": 1452.59, "word": " V", "probability": 0.92822265625}, {"start": 1452.59, "end": 1453.31, "word": " اتنين", "probability": 0.97119140625}, {"start": 1453.31, "end": 1453.89, "word": " و", "probability": 0.99755859375}, {"start": 1453.89, "end": 1454.21, "word": " V", "probability": 0.96044921875}, {"start": 1454.21, "end": 1455.73, "word": " تلاتة", "probability": 0.988037109375}, {"start": 1455.73, "end": 1457.35, "word": " بي", "probability": 0.66064453125}, {"start": 1457.35, "end": 1459.09, "word": " two", "probability": 0.4248046875}, {"start": 1459.09, "end": 1460.47, "word": " vectors", "probability": 0.94189453125}], "temperature": 1.0}, {"id": 54, "seek": 149096, "start": 1462.82, "end": 1490.96, "text": "عبارة عن متجهين and c is scalar scalar يعني يا بنات كمية قياسية يعني عدد حقيقي then النقطة الأولى لو ده جاخد u زائد ال V يبقى بجمع ال components المتناظرة مع بعضها إيش بصير عندي u واحد زائد v واحد", "tokens": [3615, 3555, 9640, 3660, 18871, 44650, 7435, 3224, 9957, 293, 269, 307, 39684, 39684, 37495, 22653, 35186, 4724, 8315, 2655, 9122, 2304, 10632, 12174, 25528, 3794, 10632, 37495, 22653, 6225, 3215, 3215, 11331, 38436, 38436, 550, 28239, 47432, 3660, 16247, 12610, 7578, 45164, 11778, 3224, 10874, 47283, 3215, 344, 30767, 16373, 3215, 2423, 691, 7251, 3555, 4587, 7578, 4724, 7435, 2304, 3615, 2423, 6677, 9673, 2655, 1863, 5718, 116, 25720, 20449, 45030, 11242, 11296, 11933, 1829, 8592, 4724, 9381, 13546, 18871, 16254, 344, 36764, 24401, 30767, 16373, 3215, 371, 36764, 24401], "avg_logprob": -0.19276494613808134, "compression_ratio": 1.5566502463054188, "no_speech_prob": 0.0, "words": [{"start": 1462.82, "end": 1463.4, "word": "عبارة", "probability": 0.81103515625}, {"start": 1463.4, "end": 1463.6, "word": " عن", "probability": 0.943359375}, {"start": 1463.6, "end": 1464.6, "word": " متجهين", "probability": 0.8826904296875}, {"start": 1464.6, "end": 1465.8, "word": " and", "probability": 0.68310546875}, {"start": 1465.8, "end": 1467.62, "word": " c", "probability": 0.385009765625}, {"start": 1467.62, "end": 1468.44, "word": " is", "probability": 0.884765625}, {"start": 1468.44, "end": 1469.18, "word": " scalar", "probability": 0.841796875}, {"start": 1469.18, "end": 1470.22, "word": " scalar", "probability": 0.1376953125}, {"start": 1470.22, "end": 1470.68, "word": " يعني", "probability": 0.951416015625}, {"start": 1470.68, "end": 1470.84, "word": " يا", "probability": 0.93310546875}, {"start": 1470.84, "end": 1471.22, "word": " بنات", "probability": 0.8450520833333334}, {"start": 1471.22, "end": 1471.68, "word": " كمية", "probability": 0.95556640625}, {"start": 1471.68, "end": 1472.22, "word": " قياسية", "probability": 0.9599609375}, {"start": 1472.22, "end": 1472.44, "word": " يعني", "probability": 0.88525390625}, {"start": 1472.44, "end": 1473.0, "word": " عدد", "probability": 0.9775390625}, {"start": 1473.0, "end": 1474.3, "word": " حقيقي", "probability": 0.9905598958333334}, {"start": 1474.3, "end": 1475.54, "word": " then", "probability": 0.71337890625}, {"start": 1475.54, "end": 1477.3, "word": " النقطة", "probability": 0.87353515625}, {"start": 1477.3, "end": 1477.78, "word": " الأولى", "probability": 0.9405924479166666}, {"start": 1477.78, "end": 1478.56, "word": " لو", "probability": 0.56591796875}, {"start": 1478.56, "end": 1478.88, "word": " ده", "probability": 0.631103515625}, {"start": 1478.88, "end": 1479.48, "word": " جاخد", "probability": 0.8365885416666666}, {"start": 1479.48, "end": 1479.9, "word": " u", "probability": 0.7421875}, {"start": 1479.9, "end": 1480.76, "word": " زائد", "probability": 0.9230143229166666}, {"start": 1480.76, "end": 1481.02, "word": " ال", "probability": 0.5810546875}, {"start": 1481.02, "end": 1481.26, "word": " V", "probability": 0.5908203125}, {"start": 1481.26, "end": 1482.6, "word": " يبقى", "probability": 0.965576171875}, {"start": 1482.6, "end": 1483.26, "word": " بجمع", "probability": 0.889892578125}, {"start": 1483.26, "end": 1483.42, "word": " ال", "probability": 0.95849609375}, {"start": 1483.42, "end": 1484.18, "word": " components", "probability": 0.94482421875}, {"start": 1484.18, "end": 1485.38, "word": " المتناظرة", "probability": 0.8602701822916666}, {"start": 1485.38, "end": 1485.74, "word": " مع", "probability": 0.994140625}, {"start": 1485.74, "end": 1486.58, "word": " بعضها", "probability": 0.9983723958333334}, {"start": 1486.58, "end": 1487.28, "word": " إيش", "probability": 0.7445475260416666}, {"start": 1487.28, "end": 1487.7, "word": " بصير", "probability": 0.8330078125}, {"start": 1487.7, "end": 1488.16, "word": " عندي", "probability": 0.804443359375}, {"start": 1488.16, "end": 1488.74, "word": " u", "probability": 0.2734375}, {"start": 1488.74, "end": 1489.4, "word": " واحد", "probability": 0.756591796875}, {"start": 1489.4, "end": 1490.32, "word": " زائد", "probability": 0.98095703125}, {"start": 1490.32, "end": 1490.54, "word": " v", "probability": 0.73583984375}, {"start": 1490.54, "end": 1490.96, "word": " واحد", "probability": 0.992919921875}], "temperature": 1.0}, {"id": 55, "seek": 152117, "start": 1491.33, "end": 1521.17, "text": "U2 زائد V2 U3 زائد V3 يبقى بجمع ال components المتنظرة مع بعض بالمثل لو طرحت U ناقص V يبقى U1 ناقص V1 U2 ناقص V2 U3 ناقص V3 يعني أنا كونت متجه جديد من المتجهين الاتنين اللي موجودات عندك", "tokens": [52, 17, 30767, 16373, 3215, 691, 17, 624, 18, 30767, 16373, 3215, 691, 18, 7251, 3555, 4587, 7578, 4724, 7435, 2304, 3615, 2423, 6677, 9673, 2655, 1863, 19913, 25720, 20449, 45030, 11242, 20666, 2304, 12984, 1211, 45164, 23032, 2288, 33753, 624, 8717, 995, 4587, 9381, 691, 7251, 3555, 4587, 7578, 624, 16, 8717, 995, 4587, 9381, 691, 16, 624, 17, 8717, 995, 4587, 9381, 691, 17, 624, 18, 8717, 995, 4587, 9381, 691, 18, 37495, 22653, 41850, 9122, 11536, 2655, 44650, 7435, 3224, 10874, 16254, 3215, 9154, 9673, 2655, 7435, 3224, 9957, 2423, 9307, 1863, 9957, 13672, 1829, 3714, 29245, 23328, 9307, 43242, 4117], "avg_logprob": -0.13318452267419725, "compression_ratio": 1.670391061452514, "no_speech_prob": 0.0, "words": [{"start": 1491.33, "end": 1492.21, "word": "U2", "probability": 0.6947021484375}, {"start": 1492.21, "end": 1493.15, "word": " زائد", "probability": 0.6067466735839844}, {"start": 1493.15, "end": 1493.87, "word": " V2", "probability": 0.935302734375}, {"start": 1493.87, "end": 1495.19, "word": " U3", "probability": 0.77587890625}, {"start": 1495.19, "end": 1496.57, "word": " زائد", "probability": 0.94970703125}, {"start": 1496.57, "end": 1497.69, "word": " V3", "probability": 0.994140625}, {"start": 1497.69, "end": 1498.95, "word": " يبقى", "probability": 0.923583984375}, {"start": 1498.95, "end": 1499.65, "word": " بجمع", "probability": 0.8062744140625}, {"start": 1499.65, "end": 1500.17, "word": " ال", "probability": 0.8818359375}, {"start": 1500.17, "end": 1500.71, "word": " components", "probability": 0.77685546875}, {"start": 1500.71, "end": 1501.55, "word": " المتنظرة", "probability": 0.76240234375}, {"start": 1501.55, "end": 1501.75, "word": " مع", "probability": 0.96630859375}, {"start": 1501.75, "end": 1501.95, "word": " بعض", "probability": 0.98388671875}, {"start": 1501.95, "end": 1502.73, "word": " بالمثل", "probability": 0.937255859375}, {"start": 1502.73, "end": 1503.03, "word": " لو", "probability": 0.93896484375}, {"start": 1503.03, "end": 1503.63, "word": " طرحت", "probability": 0.8307291666666666}, {"start": 1503.63, "end": 1504.63, "word": " U", "probability": 0.8837890625}, {"start": 1504.63, "end": 1505.37, "word": 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عند هنا تلاتة هنا أربع وهنا Zero من هو المتجه اللي عندنا هذا مش هو P1 P2 يبقى هذا الكلام بده يساوي تلاتة", "tokens": [6027, 20292, 31439, 12174, 3215, 33599, 2423, 8062, 344, 13672, 1829, 31439, 47525, 3224, 7251, 3794, 995, 45865, 1722, 4032, 2272, 4032, 1958, 4724, 28543, 2288, 5551, 9778, 3215, 9154, 3224, 6055, 1211, 9307, 3660, 4724, 23557, 9154, 28242, 3714, 31747, 49401, 9154, 29538, 9673, 31747, 3555, 9307, 4724, 1829, 19913, 1211, 12174, 3215, 33599, 43242, 34105, 6055, 1211, 9307, 3660, 34105, 5551, 25513, 3615, 37037, 8315, 17182, 9154, 31439, 9673, 2655, 7435, 3224, 13672, 1829, 43242, 8315, 23758, 37893, 31439, 430, 16, 430, 17, 7251, 3555, 4587, 7578, 23758, 2423, 28820, 10943, 47525, 3224, 7251, 3794, 995, 45865, 6055, 1211, 9307, 3660], "avg_logprob": -0.22611177855959305, "compression_ratio": 1.835820895522388, "no_speech_prob": 1.430511474609375e-06, "words": [{"start": 2213.69, "end": 2213.99, "word": "اللي", "probability": 0.3365478515625}, {"start": 2213.99, "end": 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"word": " V13", "probability": 0.9775390625}, {"start": 2566.67, "end": 2566.67, "word": " V13", "probability": 0.977783203125}, {"start": 2566.67, "end": 2566.67, "word": " V13", "probability": 0.978271484375}, {"start": 2566.67, "end": 2566.67, "word": " V13", "probability": 0.978759765625}, {"start": 2566.67, "end": 2567.07, "word": " V13", "probability": 0.977294921875}, {"start": 2567.07, "end": 2568.69, "word": " V13", "probability": 0.97509765625}], "temperature": 1.0}, {"id": 93, "seek": 260188, "start": 2572.76, "end": 2601.88, "text": "اللي بعد هو 0 زائد v2 زائد 0 في v2 زائد 0 زائد v3 في v3 طيب الآن بداجي ضرب scalar في vector يبقى scalar ان ضربته في الداخل ولا طلعته برا الاتنين are the same يبقى مقدر اقول هذا الكلام بده ساعة اللي هو v1 في 1 و 0 و 0 تمام؟", "tokens": [6027, 20292, 39182, 31439, 1958, 30767, 16373, 3215, 371, 17, 30767, 16373, 3215, 1958, 8978, 371, 17, 30767, 16373, 3215, 1958, 30767, 16373, 3215, 371, 18, 8978, 371, 18, 23032, 1829, 3555, 6024, 48506, 47525, 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"end": 2628.25, "text": "زائد V2 Zero و واحد و Zero زائد V3 Zero و Zero و واحد شكل يعني انا احنا قولنا ال standard unit vectors و قولنا لك هاي ال standard unit vectors اللي هو I و J و K", "tokens": [11622, 16373, 3215, 691, 17, 17182, 4032, 36764, 24401, 4032, 17182, 30767, 16373, 3215, 691, 18, 17182, 4032, 17182, 4032, 36764, 24401, 13412, 28820, 37495, 22653, 1975, 8315, 1975, 5016, 8315, 12174, 12610, 8315, 2423, 3832, 4985, 18875, 4032, 12174, 12610, 8315, 5296, 4117, 8032, 47302, 2423, 3832, 4985, 18875, 13672, 1829, 31439, 286, 4032, 508, 4032, 591], "avg_logprob": -0.36811440374891635, "compression_ratio": 1.6323529411764706, "no_speech_prob": 0.0, "words": [{"start": 2602.29, "end": 2603.11, "word": "زائد", "probability": 0.663818359375}, {"start": 2603.11, "end": 2605.01, "word": " V2", "probability": 0.640380859375}, {"start": 2605.01, "end": 2606.03, "word": " Zero", "probability": 0.0310211181640625}, {"start": 2606.03, "end": 2606.55, "word": " و", "probability": 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النقطة هذه أحداثيها واحد وزير وزير وزير وهذا النقطة زير وواحد وزير وهذا النقطة زير وزير وواحد", "tokens": [1211, 2407, 10874, 3224, 2655, 4724, 39648, 2655, 23275, 34105, 2423, 286, 47525, 3224, 7251, 3794, 995, 45865, 31439, 36764, 24401, 4032, 11622, 13546, 4032, 11622, 13546, 20328, 5016, 1829, 5016, 49429, 20193, 22807, 20328, 5016, 1829, 5016, 32239, 8592, 22807, 5296, 33456, 28239, 47432, 3660, 29538, 5551, 24401, 5718, 104, 1829, 11296, 36764, 24401, 4032, 11622, 13546, 4032, 11622, 13546, 4032, 11622, 13546, 37037, 15730, 28239, 47432, 3660, 30767, 13546, 4032, 14407, 24401, 4032, 11622, 13546, 37037, 15730, 28239, 47432, 3660, 30767, 13546, 4032, 11622, 13546, 4032, 14407, 24401], "avg_logprob": -0.2501716980567345, "compression_ratio": 2.2071428571428573, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2628.62, "end": 2629.0, "word": "لو", "probability": 0.749267578125}, {"start": 2629.0, "end": 2629.34, "word": " جهت", "probability": 0.7945963541666666}, 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الصفر we can write نستطيع كتابة V in terms of its length", "tokens": [271, 257, 2107, 12, 32226, 8062, 44650, 7435, 3224, 32771, 13546, 31767, 5172, 2288, 321, 393, 2464, 8717, 14851, 9566, 40228, 9122, 2655, 16758, 3660, 691, 294, 2115, 295, 1080, 4641], "avg_logprob": -0.19128417409956455, "compression_ratio": 0.9732142857142857, "no_speech_prob": 0.0, "words": [{"start": 2994.25, "end": 2994.75, "word": "is", "probability": 0.4736328125}, {"start": 2994.75, "end": 2995.81, "word": " a", "probability": 0.958984375}, {"start": 2995.81, "end": 2996.37, "word": " non", "probability": 0.923828125}, {"start": 2996.37, "end": 2998.11, "word": "-zero", "probability": 0.6650390625}, {"start": 2998.11, "end": 2999.01, "word": " vector", "probability": 0.96630859375}, {"start": 2999.01, "end": 3000.45, "word": " متجه", "probability": 0.78857421875}, {"start": 3000.45, "end": 3000.73, "word": " غير", "probability": 0.994140625}, {"start": 3000.73, "end": 3001.35, "word": " الصفر", 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تلاتة لكل تربية زائد zero تربية لو زاد التربية ستات و تسعة و خمسة و عشرين يبقى الجواب يساوي خمس نمرسي", "tokens": [28814, 15730, 8032, 47302, 2407, 11331, 36520, 2655, 47356, 11933, 15730, 4724, 26108, 1829, 4724, 39648, 3224, 23032, 12610, 9673, 2655, 7435, 3660, 1975, 2655, 1863, 9957, 7251, 20498, 8717, 995, 4587, 9381, 6055, 1211, 9307, 3660, 4724, 1829, 3224, 13672, 1829, 31439, 2423, 3732, 5593, 24976, 10721, 25513, 27884, 6055, 25513, 10632, 30767, 16373, 3215, 8717, 995, 4587, 9381, 6055, 1211, 9307, 3660, 5296, 28820, 6055, 25513, 10632, 30767, 16373, 3215, 4018, 6055, 25513, 10632, 5296, 2407, 30767, 18513, 16712, 25513, 10632, 8608, 2655, 9307, 4032, 6055, 3794, 27884, 4032, 16490, 2304, 3794, 3660, 4032, 6225, 46309, 9957, 7251, 3555, 4587, 7578, 25724, 14407, 3555, 7251, 3794, 995, 45865, 16490, 2304, 3794, 8717, 29973, 3794, 1829], "avg_logprob": -0.2018008538979595, "compression_ratio": 1.857843137254902, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 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يعني لو قلت هذه المحاور على سبيل المثال قلت هذا X وهذا Y وهذا Z هذا نقطة الأصل اللي هو Zero", "tokens": [49, 1783, 16, 30767, 16373, 3215, 1783, 17, 15844, 568, 398, 16, 30767, 16373, 3215, 398, 17, 15844, 568, 1176, 16, 30767, 16373, 3215, 1176, 17, 15844, 568, 37495, 22653, 45164, 12174, 1211, 2655, 29538, 9673, 5016, 995, 13063, 15844, 8608, 21292, 1211, 9673, 12984, 6027, 12174, 1211, 2655, 23758, 1783, 37037, 15730, 398, 37037, 15730, 1176, 23758, 8717, 47432, 3660, 16247, 36520, 13672, 1829, 31439, 17182], "avg_logprob": -0.17555146357592413, "compression_ratio": 1.6962962962962962, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 4532.71, "end": 4533.25, "word": "R", "probability": 0.42138671875}, {"start": 4533.25, "end": 4534.81, "word": " X1", "probability": 0.705810546875}, {"start": 4534.81, "end": 4535.81, "word": " زائد", "probability": 0.399993896484375}, {"start": 4535.81, "end": 4536.55, "word": " X2", "probability": 0.961181640625}, {"start": 4536.55, 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"probability": 0.99365234375}, {"start": 4557.07, "end": 4558.13, "word": " وهذا", "probability": 0.89990234375}, {"start": 4558.13, "end": 4558.71, "word": " Z", "probability": 0.97607421875}, {"start": 4558.71, "end": 4559.43, "word": " هذا", "probability": 0.50244140625}, {"start": 4559.43, "end": 4559.89, "word": " نقطة", "probability": 0.9684244791666666}, {"start": 4559.89, "end": 4560.27, "word": " الأصل", "probability": 0.822998046875}, {"start": 4560.27, "end": 4560.43, "word": " اللي", "probability": 0.6510009765625}, {"start": 4560.43, "end": 4560.59, "word": " هو", "probability": 0.72607421875}, {"start": 4560.59, "end": 4560.85, "word": " Zero", "probability": 0.6708984375}], "temperature": 1.0}, {"id": 165, "seek": 458978, "start": 4561.78, "end": 4589.78, "text": "و رسمت نقطتين و وصلت بينهم بخط مستقيم فجيت قول هذه النقطة الأولى P1 X1 Y1 Z1 وهذه النقطة P2 X2 Y2 Z2 بين النقطة المنقصرة فيما بينهم", "tokens": [2407, 12602, 38251, 2655, 8717, 47432, 2655, 9957, 4032, 4032, 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بخط", "probability": 0.953125}, {"start": 4566.92, "end": 4568.42, "word": " مستقيم", "probability": 0.9464111328125}, {"start": 4568.42, "end": 4569.38, "word": " فجيت", "probability": 0.8409830729166666}, {"start": 4569.38, "end": 4569.82, "word": " قول", "probability": 0.435546875}, {"start": 4569.82, "end": 4570.58, "word": " هذه", "probability": 0.462158203125}, {"start": 4570.58, "end": 4571.22, "word": " النقطة", "probability": 0.9612630208333334}, {"start": 4571.22, "end": 4572.0, "word": " الأولى", "probability": 0.89794921875}, {"start": 4572.0, "end": 4573.76, "word": " P1", "probability": 0.661376953125}, {"start": 4573.76, "end": 4575.38, "word": " X1", "probability": 0.7041015625}, {"start": 4575.38, "end": 4576.74, "word": " Y1", "probability": 0.90966796875}, {"start": 4576.74, "end": 4577.88, "word": " Z1", "probability": 0.72314453125}, {"start": 4577.88, "end": 4578.8, "word": " وهذه", "probability": 0.606201171875}, {"start": 4578.8, "end": 4579.42, "word": " النقطة", "probability": 0.94873046875}, {"start": 4579.42, "end": 4580.84, "word": " P2", "probability": 0.971435546875}, {"start": 4580.84, "end": 4582.32, "word": " X2", "probability": 0.94140625}, {"start": 4582.32, "end": 4583.98, "word": " Y2", "probability": 0.96240234375}, {"start": 4583.98, "end": 4585.36, "word": " Z2", "probability": 0.939208984375}, {"start": 4585.36, "end": 4586.84, "word": " بين", "probability": 0.2166748046875}, {"start": 4586.84, "end": 4587.58, "word": " النقطة", "probability": 0.9396158854166666}, {"start": 4587.58, "end": 4588.5, "word": " المنقصرة", "probability": 0.8615234375}, {"start": 4588.5, "end": 4589.02, "word": " فيما", "probability": 0.641357421875}, {"start": 4589.02, "end": 4589.78, "word": " بينهم", "probability": 0.7425537109375}], "temperature": 1.0}, {"id": 166, "seek": 461563, "start": 4590.47, "end": 4615.63, "text": "يبقى نقطة المنتصف لو قلت هذه اللي هي النقطة M يبقى النقطة M بدأ تيجي في منتصف المسافة بين النقطتين إحداث هذه النقطة هو الإحداث اللي احنا كاتبينه هنا الأن نعطي مثال توضيحي على ذلك example", "tokens": [1829, 3555, 4587, 7578, 8717, 47432, 3660, 9673, 29399, 9381, 5172, 45164, 12174, 1211, 2655, 29538, 13672, 1829, 39896, 28239, 47432, 3660, 376, 7251, 3555, 4587, 7578, 28239, 47432, 3660, 376, 47525, 10721, 6055, 1829, 7435, 1829, 8978, 9154, 2655, 9381, 5172, 9673, 3794, 31845, 3660, 49374, 28239, 47432, 2655, 9957, 11933, 24401, 5718, 104, 29538, 28239, 47432, 3660, 31439, 33688, 24401, 5718, 104, 13672, 1829, 1975, 5016, 8315, 9122, 9307, 3555, 9957, 3224, 34105, 16247, 1863, 8717, 3615, 9566, 1829, 50113, 6027, 33427, 11242, 1829, 5016, 1829, 15844, 29910, 23275, 1365], "avg_logprob": -0.1785954326711675, "compression_ratio": 1.8324022346368716, "no_speech_prob": 0.0, "words": [{"start": 4590.47, "end": 4591.03, "word": "يبقى", "probability": 0.86572265625}, {"start": 4591.03, "end": 4591.61, "word": " نقطة", "probability": 0.9314778645833334}, {"start": 4591.61, "end": 4592.43, "word": " 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النقطة اربعة وناقص اتنين وسبعة المطلوب الأول نمر ايه؟", "tokens": [11149, 335, 781, 472, 13672, 1829, 31439, 8608, 33604, 6027, 8608, 2655, 3660, 34683, 1211, 9307, 9957, 9154, 33251, 2655, 16758, 4724, 1829, 39648, 2655, 430, 16, 13672, 1829, 39896, 6225, 3555, 9640, 3660, 18871, 36764, 24401, 4032, 9640, 3555, 27884, 4032, 9778, 2304, 3794, 3660, 293, 430, 17, 39896, 6225, 3555, 9640, 3660, 18871, 28239, 47432, 3660, 1975, 25513, 27884, 4032, 8315, 4587, 9381, 1975, 2655, 1863, 9957, 4032, 35457, 27884, 9673, 9566, 1211, 37746, 16247, 12610, 8717, 29973, 1975, 1829, 3224, 22807], "avg_logprob": -0.18511029481887817, "compression_ratio": 1.6091954022988506, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 4621.34, "end": 4622.02, "word": "Example", "probability": 0.723388671875}, {"start": 4622.02, "end": 4622.5, "word": " one", "probability": 0.340576171875}, {"start": 4622.5, "end": 4625.3, "word": " اللي", "probability": 0.54779052734375}, {"start": 4625.3, "end": 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0.7957356770833334}, {"start": 5265.82, "end": 5266.28, "word": " نص", "probability": 0.9814453125}], "temperature": 1.0}, {"id": 190, "seek": 529788, "start": 5269.22, "end": 5297.88, "text": "يبقى هاي اللي طلعه unit vector في .. that makes اللي عامله زاوية 145 مع الاتجاه الموجب لمح وراكز لحد هنا stop انتهاء ال section إلى يكون أرقام المسائل المطلوب حلها في البيت ان شاء الله يبقى exercises أتناش اتنين واحد تلاتة خمسة سبعة", "tokens": [1829, 3555, 4587, 7578, 8032, 47302, 13672, 1829, 23032, 1211, 3615, 3224, 4985, 8062, 8978, 4386, 300, 1669, 13672, 1829, 6225, 10943, 43761, 30767, 995, 2407, 10632, 3499, 20, 20449, 2423, 9307, 7435, 40294, 9673, 29245, 3555, 32767, 5016, 4032, 23557, 4117, 11622, 5296, 24401, 34105, 1590, 16472, 47395, 16606, 2423, 3541, 30731, 7251, 30544, 5551, 2288, 4587, 10943, 9673, 3794, 16373, 1211, 9673, 9566, 1211, 37746, 11331, 1211, 11296, 8978, 2423, 21292, 2655, 16472, 13412, 16606, 21984, 7251, 3555, 4587, 7578, 11900, 5551, 2655, 1863, 33599, 1975, 2655, 1863, 9957, 36764, 24401, 6055, 1211, 9307, 3660, 16490, 2304, 3794, 3660, 8608, 3555, 27884], "avg_logprob": -0.24687500454130626, "compression_ratio": 1.5450819672131149, "no_speech_prob": 0.0, "words": [{"start": 5269.22, "end": 5269.98, "word": "يبقى", "probability": 0.78363037109375}, {"start": 5269.98, "end": 5270.22, "word": " هاي", "probability": 0.46240234375}, {"start": 5270.22, "end": 5270.32, "word": " اللي", "probability": 0.739990234375}, {"start": 5270.32, "end": 5270.62, "word": " طلعه", "probability": 0.631591796875}, {"start": 5270.62, "end": 5270.82, "word": " unit", "probability": 0.91259765625}, {"start": 5270.82, "end": 5271.38, "word": " vector", "probability": 0.9521484375}, {"start": 5271.38, "end": 5272.22, "word": " في", "probability": 0.7666015625}, {"start": 5272.22, "end": 5272.96, "word": " ..", "probability": 0.2088623046875}, {"start": 5272.96, "end": 5274.08, "word": " that", "probability": 0.491455078125}, {"start": 5274.08, "end": 5274.44, "word": " makes", "probability": 0.7666015625}, {"start": 5274.44, "end": 5274.6, "word": " اللي", "probability": 0.928955078125}, {"start": 5274.6, "end": 5274.9, "word": " عامله", "probability": 0.4510904947916667}, {"start": 5274.9, "end": 5275.32, "word": " زاوية", "probability": 0.9212646484375}, {"start": 5275.32, "end": 5276.56, "word": " 145", "probability": 0.918212890625}, {"start": 5276.56, "end": 5277.1, "word": " مع", "probability": 0.955078125}, {"start": 5277.1, "end": 5277.6, "word": " الاتجاه", "probability": 0.80078125}, {"start": 5277.6, "end": 5278.06, "word": " الموجب", "probability": 0.7549641927083334}, {"start": 5278.06, "end": 5278.42, "word": " لمح", "probability": 0.640380859375}, {"start": 5278.42, "end": 5279.08, "word": " وراكز", "probability": 0.67974853515625}, {"start": 5279.08, "end": 5279.78, "word": " لحد", "probability": 0.936767578125}, {"start": 5279.78, "end": 5280.04, "word": " هنا", "probability": 0.978515625}, {"start": 5280.04, "end": 5280.4, "word": " stop", "probability": 0.7744140625}, {"start": 5280.4, "end": 5280.86, "word": " انتهاء", "probability": 0.5958658854166666}, {"start": 5280.86, "end": 5281.0, "word": " ال", "probability": 0.8681640625}, {"start": 5281.0, "end": 5281.36, "word": " section", "probability": 0.859375}, {"start": 5281.36, "end": 5282.06, "word": " إلى", "probability": 0.56884765625}, {"start": 5282.06, "end": 5282.58, "word": " يكون", "probability": 0.974853515625}, {"start": 5282.58, "end": 5283.6, "word": " أرقام", "probability": 0.9173583984375}, {"start": 5283.6, "end": 5284.84, "word": " المسائل", "probability": 0.9515380859375}, {"start": 5284.84, "end": 5286.34, "word": " المطلوب", "probability": 0.987548828125}, {"start": 5286.34, "end": 5287.08, "word": " حلها", "probability": 0.8855794270833334}, {"start": 5287.08, "end": 5287.34, "word": " في", "probability": 0.91357421875}, {"start": 5287.34, "end": 5287.74, "word": " البيت", "probability": 0.9755859375}, {"start": 5287.74, "end": 5287.94, "word": " ان", "probability": 0.60205078125}, {"start": 5287.94, "end": 5288.2, "word": " شاء", "probability": 0.979248046875}, {"start": 5288.2, "end": 5288.5, "word": " الله", "probability": 0.95751953125}, {"start": 5288.5, "end": 5289.42, "word": " يبقى", "probability": 0.9791259765625}, {"start": 5289.42, "end": 5290.52, "word": " exercises", "probability": 0.93603515625}, {"start": 5290.52, "end": 5291.94, "word": " أتناش", "probability": 0.70111083984375}, {"start": 5291.94, "end": 5293.54, "word": " اتنين", "probability": 0.9315185546875}, {"start": 5293.54, "end": 5294.92, "word": " واحد", "probability": 0.926025390625}, {"start": 5294.92, "end": 5295.98, "word": " تلاتة", "probability": 0.8135986328125}, {"start": 5295.98, "end": 5297.1, "word": " خمسة", "probability": 0.940185546875}, {"start": 5297.1, "end": 5297.88, "word": " سبعة", "probability": 0.9425455729166666}], "temperature": 1.0}, {"id": 191, "seek": 532627, "start": 5298.55, "end": 5326.27, "text": "أحد عشر تلتاش سبعتاش تسعة عشر واحد وعشرين خمسة وعشرين سبعة وعشرين خمسة وعشرين سبعة وعشرين تسعة وعشرين واحد وتلاتين تلاتة وتلاتين خمسة وتلاتين سبعة وتلاتين تسعة وتلاتين", "tokens": [10721, 24401, 6225, 46309, 6055, 1211, 2655, 33599, 8608, 3555, 34268, 33599, 6055, 3794, 27884, 6225, 46309, 36764, 24401, 4032, 3615, 46309, 9957, 16490, 2304, 3794, 3660, 4032, 3615, 46309, 9957, 8608, 3555, 27884, 4032, 3615, 46309, 9957, 16490, 2304, 3794, 3660, 4032, 3615, 46309, 9957, 8608, 3555, 27884, 4032, 3615, 46309, 9957, 6055, 3794, 27884, 4032, 3615, 46309, 9957, 36764, 24401, 4032, 2655, 1211, 9307, 9957, 6055, 1211, 9307, 3660, 4032, 2655, 1211, 9307, 9957, 16490, 2304, 3794, 3660, 4032, 2655, 1211, 9307, 9957, 8608, 3555, 27884, 4032, 2655, 1211, 9307, 9957, 6055, 3794, 27884, 4032, 2655, 1211, 9307, 9957], "avg_logprob": -0.10140931116891842, "compression_ratio": 2.8425925925925926, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 5298.55, "end": 5299.61, "word": "أحد", "probability": 0.55413818359375}, {"start": 5299.61, "end": 5300.15, "word": " عشر", "probability": 0.877685546875}, {"start": 5300.15, "end": 5301.31, "word": " تلتاش", "probability": 0.75726318359375}, {"start": 5301.31, "end": 5302.91, "word": " سبعتاش", "probability": 0.8760986328125}, {"start": 5302.91, "end": 5304.59, "word": " تسعة", "probability": 0.8772786458333334}, {"start": 5304.59, "end": 5305.17, "word": " عشر", "probability": 0.5966796875}, {"start": 5305.17, "end": 5305.71, "word": " واحد", "probability": 0.928466796875}, {"start": 5305.71, "end": 5306.83, "word": " وعشرين", "probability": 0.8931884765625}, {"start": 5306.83, "end": 5307.99, "word": " خمسة", "probability": 0.9658203125}, {"start": 5307.99, "end": 5308.95, "word": " وعشرين", "probability": 0.9610595703125}, {"start": 5308.95, "end": 5309.55, "word": " سبعة", "probability": 0.966796875}, {"start": 5309.55, "end": 5310.65, "word": " وعشرين", "probability": 0.9549560546875}, {"start": 5310.65, "end": 5311.79, "word": " خمسة", "probability": 0.976318359375}, {"start": 5311.79, "end": 5312.55, "word": " وعشرين", "probability": 0.9564208984375}, {"start": 5312.55, "end": 5313.41, "word": " سبعة", "probability": 0.9860026041666666}, {"start": 5313.41, "end": 5314.65, "word": " وعشرين", "probability": 0.9542236328125}, {"start": 5314.65, "end": 5315.31, "word": " تسعة", "probability": 0.9933268229166666}, {"start": 5315.31, "end": 5316.55, "word": " وعشرين", "probability": 0.9591064453125}, {"start": 5316.55, "end": 5317.89, "word": " واحد", "probability": 0.986572265625}, {"start": 5317.89, "end": 5318.99, "word": " وتلاتين", "probability": 0.7458984375}, {"start": 5318.99, "end": 5319.67, "word": " تلاتة", "probability": 0.9718017578125}, {"start": 5319.67, "end": 5320.57, "word": " وتلاتين", "probability": 0.93935546875}, {"start": 5320.57, "end": 5321.25, "word": " خمسة", "probability": 0.9927978515625}, {"start": 5321.25, "end": 5322.21, "word": " وتلاتين", "probability": 0.97626953125}, {"start": 5322.21, "end": 5323.21, "word": " سبعة", "probability": 0.9913736979166666}, {"start": 5323.21, "end": 5324.45, "word": " وتلاتين", "probability": 0.98017578125}, {"start": 5324.45, "end": 5325.43, "word": " تسعة", "probability": 0.9949544270833334}, {"start": 5325.43, "end": 5326.27, "word": " وتلاتين", "probability": 0.94033203125}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 5332.4395, "duration_after_vad": 5003.936593750015}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/tT-7ILSFEbI_raw.srt b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/tT-7ILSFEbI_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..10ac5e2076f4db0fca621ff8cf2f4f14b34cd68b
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/tT-7ILSFEbI_raw.srt
@@ -0,0 +1,3052 @@
+1
+00:00:11,040 --> 00:00:15,920
+بسم الله الرحمن الرحيم انتهينا في المحاضرة الماضية
+
+2
+00:00:15,920 --> 00:00:20,300
+من ال section 12-1 والان نبدأ من section 12-2
+
+3
+00:00:20,750 --> 00:00:24,910
+أتناشر اتنين هو عبارة عن ال vectors طبعا ال
+
+4
+00:00:24,910 --> 00:00:32,570
+vectors هذه سبقت دراستها في فيزيا عامة B واحنا هنا
+
+5
+00:00:32,570 --> 00:00:37,030
+بنعطي ال section هنا من جانب وذكر فإن الذكرة تنفع
+
+6
+00:00:37,030 --> 00:00:42,330
+المؤمنين ومن جانب آخر لإن دراستنا خلال Calculus C
+
+7
+00:00:42,330 --> 00:00:48,870
+ستكون مبنية على ال vectors أو المتجهاتالكميات اللى
+
+8
+00:00:48,870 --> 00:00:53,370
+ردنا سبحانه وتعالى خلقها لنا نوعين نقول في كميات
+
+9
+00:00:53,370 --> 00:00:58,950
+قياسية وفي كميات متجهة نعطي بعض الأمثل للكميات
+
+10
+00:00:58,950 --> 00:01:05,550
+القياسية وبعض الأمثل للكميات الاتجاهية فمثلا لو
+
+11
+00:01:05,550 --> 00:01:09,270
+جيبنا بنت اي واحدة دي يكو جيبنا جسم الطول تبعها
+
+12
+00:01:09,270 --> 00:01:14,050
+لجناه مية وسبعين سنتمتر المية وسبعين سنتمتر إيه
+
+13
+00:01:14,050 --> 00:01:19,690
+الاتجاه والله بس طولبالطبع لا يوجد اتجاه لا 170
+
+14
+00:01:19,690 --> 00:01:22,870
+متر في اتجاه الشرق ولا الغرب ولا الشمال ولا الجنوب
+
+15
+00:01:22,870 --> 00:01:27,110
+ولا الشمال الغربي ولا الجنوب ولا حاجة إذا بناء
+
+16
+00:01:27,110 --> 00:01:35,090
+عليه الطول وكمية قياسية زي ايش كذلك كتلة كمية
+
+17
+00:01:35,090 --> 00:01:39,330
+قياسية زي المساحة مساحة القاعة اللي احنا فيها
+
+18
+00:01:39,330 --> 00:01:46,590
+مساحة لو قلتالطول أربعة والعرض ثلاثة يبقى ثلاثة
+
+19
+00:01:46,590 --> 00:01:51,390
+أربعة ومعاشر متر مربع هذه مساحة يبقى هذه كمية
+
+20
+00:01:51,390 --> 00:01:56,750
+قياسية حجم الغرفة اللي احنا فيها متوازن والسطيلات
+
+21
+00:01:56,750 --> 00:02:01,190
+يبقى الطول في العرض في الارتفاع يبقى الحجم كمية
+
+22
+00:02:01,190 --> 00:02:07,110
+قياسية كذلك يبقى هذه الكميات بسميها كميات قياسية
+
+23
+00:02:07,440 --> 00:02:12,280
+يبقى أول نوع من الكميات حاجة بسميها scalar
+
+24
+00:02:12,280 --> 00:02:22,360
+quantity الكمية
+
+25
+00:02:22,360 --> 00:02:30,840
+القياسية زي ايه؟ زي ال length زي
+
+26
+00:02:30,840 --> 00:02:44,700
+ال mass الكتلة زي ال areaزي الـ volume و هكذا نأتي
+
+27
+00:02:44,700 --> 00:02:51,740
+الآن نبحث عن الـ vector quantity vector quantity
+
+28
+00:02:51,740 --> 00:02:56,580
+زي
+
+29
+00:02:56,580 --> 00:03:01,700
+ايش ال vector quantity؟ اه فيها حاجة هنا نميز بين
+
+30
+00:03:01,700 --> 00:03:06,920
+امرين في حاجة اسمها speed و في حاجة اسمها velocity
+
+31
+00:03:07,630 --> 00:03:13,190
+Speed هي مقدار السرعة، لكن ال velocity هي السرعة
+
+32
+00:03:13,190 --> 00:03:17,890
+مقدار المهتجان، يعني وانت راكبه في السيارة الصورة
+
+33
+00:03:17,890 --> 00:03:21,850
+و حاسس السواك بيحكي مع مين، بيحكي مع اللي قاعد
+
+34
+00:03:21,850 --> 00:03:25,910
+جنبه، بيقوله والله كنت ماشي و ال speed و متر عندي
+
+35
+00:03:25,910 --> 00:03:30,770
+معلم كذاSpeedومتر يعني عداد السرعة هذا يعطيني قداش
+
+36
+00:03:30,770 --> 00:03:35,630
+قمت السرعة لكنه لايعطيني اتجاه السرعة اذا كذلك هنا
+
+37
+00:03:35,630 --> 00:03:43,110
+لو قلت ال speed ال speed هذه مقدار السرعة لكن جيت
+
+38
+00:03:43,110 --> 00:03:48,270
+قلت هنا velocity هذه
+
+39
+00:03:48,270 --> 00:03:54,820
+مقدار السرعة الإزاحة ازاحنا جسم في اتجاه مايبقى
+
+40
+00:03:54,820 --> 00:04:02,180
+هذه بسميها displacement الإزاحة
+
+41
+00:04:02,180 --> 00:04:07,680
+زي ايش مثلا كمان زي ال force القوة أثرت قوة على
+
+42
+00:04:07,680 --> 00:04:15,860
+جسم ما القوة بعطيها مقدرا واتجاها زي ال force و
+
+43
+00:04:15,860 --> 00:04:20,920
+هكذاهذه نوعين من الكميات حاجة بسميها scalar
+
+44
+00:04:20,920 --> 00:04:24,680
+quantity والنوع الثاني اللي هو ال vector a
+
+45
+00:04:24,680 --> 00:04:30,180
+quantity الآن بدنا نعطي تعريف لمين لل vector اللي
+
+46
+00:04:30,180 --> 00:04:36,500
+هو حسن ابني دراستنا عليه خلال هذا الفصل يبقى بداجي
+
+47
+00:04:36,500 --> 00:04:42,100
+إلى definition the vector is the direct line
+
+48
+00:04:42,100 --> 00:04:55,460
+segment of the vectoris the directed line
+
+49
+00:04:55,460 --> 00:04:58,740
+segment
+
+50
+00:04:58,740 --> 00:05:11,320
+وحد الرمز AB وعليه سهم بهذا الشكل from an initial
+
+51
+00:05:11,320 --> 00:05:28,010
+point A toA Terminal Point B الـ
+
+52
+00:05:28,010 --> 00:05:32,490
+initial point نقطة ابتدائية Terminal point نقطة
+
+53
+00:05:32,490 --> 00:05:38,470
+نهيئة التي ينتهي عندها هذا السهم يبقى directed
+
+54
+00:05:38,470 --> 00:05:46,170
+line segment يبدأ من النقطة A وينتهي في النقطة B
+
+55
+00:05:46,480 --> 00:05:53,020
+وبنحط سهم عند نقطة النهاية دليل على أن هذا ال
+
+56
+00:05:53,020 --> 00:05:57,520
+vector يبدأ من النقطة A وينتهي في النقطة B اللي
+
+57
+00:05:57,520 --> 00:06:03,020
+كنتوا في الإبتدائي بتسموه الشعاع الشعاع بيبدأ من
+
+58
+00:06:03,020 --> 00:06:08,860
+نقطة وبينتقل إلى نقطة أخرى زي ما كنا نقول مثلا
+
+59
+00:06:08,860 --> 00:06:15,280
+شعاع الشمس مصدر وين؟ الشمسثم ينتقل إلى الكون في كل
+
+60
+00:06:15,280 --> 00:06:20,620
+الاتجاهات تمام؟ يبقى هذا اللي هو بنسميه air بنسميه
+
+61
+00:06:20,620 --> 00:06:26,260
+virtual لأ لو بدنا الطول التالع يبقى باجي بقول the
+
+62
+00:06:26,260 --> 00:06:32,660
+length اللي هو الطول أو بعض المؤلفين بيسموه ال
+
+63
+00:06:32,660 --> 00:06:36,960
+magnitude اللي
+
+64
+00:06:36,960 --> 00:06:48,300
+هو المقدار magnitude أو ال lengthof the vector a,b
+
+65
+00:06:48,300 --> 00:07:00,000
+is denoted by بدي أعطيه رمز a,b وبحطه بين خطين
+
+66
+00:07:00,000 --> 00:07:04,840
+بهذا الشكل هذا ليست absolute value تبع ال calculus
+
+67
+00:07:04,840 --> 00:07:11,320
+a وإنما المقصود طول المتجه a,bالـ Length للـ
+
+68
+00:07:11,320 --> 00:07:17,440
+Vector A, B الأن بدأ نجي لتساوي Two Vectors
+
+69
+00:07:17,440 --> 00:07:28,780
+Definition Two Vectors Two Vectors Are Equal Are
+
+70
+00:07:28,780 --> 00:07:44,960
+Equal If They Have The Samelength and direction
+
+71
+00:07:44,960 --> 00:07:53,060
+يبقى
+
+72
+00:07:53,060 --> 00:07:57,080
+المتجهين متساوين
+
+73
+00:07:57,080 --> 00:08:03,200
+إذا كان لهم نفس المقدار و نفس الاتجاه كيف يعني؟ لو
+
+74
+00:08:03,200 --> 00:08:12,170
+جاءت خط ال coordinate axes المحور Xمحور Y محور Z
+
+75
+00:08:12,170 --> 00:08:15,670
+انا
+
+76
+00:08:15,670 --> 00:08:18,930
+بقول في يويندي متجهين والمتجهين اتنين هذول
+
+77
+00:08:18,930 --> 00:08:25,270
+متساويين شرط التساوي تساوي المقدار ونفس الاتجاه
+
+78
+00:08:25,270 --> 00:08:30,810
+كيف يعني لو جيت قلت افترق ان هذا بدأ من نقطة الاصل
+
+79
+00:08:30,810 --> 00:08:38,260
+وانتهى في النقطة هذه يبقى هذا سميته Vأجى vector
+
+80
+00:08:38,260 --> 00:08:45,220
+كان ابتدأ من هذه النقطة وفي اتجاه نفس المتجه اللي
+
+81
+00:08:45,220 --> 00:08:53,160
+عندنا هذا نفس المتجه وكان له نفس الطول يبقى اتنين
+
+82
+00:08:53,160 --> 00:09:00,460
+هذول are equal او لو بدأ من هنا من النقطة هذه وفي
+
+83
+00:09:00,460 --> 00:09:05,800
+الاتجاه اللي عندنا هذا وكان له نفس الطول يبقى هذا
+
+84
+00:09:05,800 --> 00:09:12,110
+المتجه Vوهذا المتجه V كذلك يبقى التلاتة هذول are
+
+85
+00:09:12,110 --> 00:09:14,690
+equal or are equivalent
+
+86
+00:09:17,580 --> 00:09:24,140
+زي بعض ولو انهم ما انطلقوش من نفس النقطة لكن لهم
+
+87
+00:09:24,140 --> 00:09:31,840
+نفس الطول ولهم كذلك نفس الاتجاه يبقى هذول بقول
+
+88
+00:09:31,840 --> 00:09:38,940
+عنهم vectors متساوية او متجهات متساوية كمان
+
+89
+00:09:38,940 --> 00:09:46,800
+definition مهم اللي هو the zero vectorالـ zero
+
+90
+00:09:46,800 --> 00:09:51,600
+vector سأعطيه run zero وقته مطول شوية لكي نتميزه
+
+91
+00:09:51,600 --> 00:09:58,000
+عن ال zero العادي تمام يبقى the zero vector اللي
+
+92
+00:09:58,000 --> 00:10:10,080
+هو حد يقول run zero is a vector with length zero
+
+93
+00:10:10,080 --> 00:10:20,170
+الطول تبعه يسوى الصفر andNo determined direction
+
+94
+00:10:20,170 --> 00:10:23,990
+يعني
+
+95
+00:10:23,990 --> 00:10:28,670
+ممكن
+
+96
+00:10:28,670 --> 00:10:34,210
+أن يكون اتجاهه في أي اتجاه بدكية يبقى الـ zero
+
+97
+00:10:34,210 --> 00:10:39,120
+vector هو عبارة عن اتجاه طوله يساوي الصفرو ممكن أن
+
+98
+00:10:39,120 --> 00:10:43,800
+يُأخذ في أي اتجاه بدنيا و من هنا قلنا no
+
+99
+00:10:43,800 --> 00:10:48,840
+determined direction مالوش اتجاه محدد يعني ممكن
+
+100
+00:10:48,840 --> 00:10:53,760
+أخذه في أي اتجاه بدون قيود without restriction بدي
+
+101
+00:10:53,760 --> 00:11:01,720
+أخذه في أي اتجاه بدية الان بدي نيجي إلى توازي
+
+102
+00:11:01,720 --> 00:11:15,580
+المتجهات كذلك definitionto non zero vectors to non
+
+103
+00:11:15,580 --> 00:11:24,080
+zero vectors u and lv are said to be parallel are
+
+104
+00:11:24,080 --> 00:11:35,280
+said to be parallel ممكن نقول عليهم متوازية
+
+105
+00:11:37,020 --> 00:11:47,360
+there is a real number if there is a real number
+
+106
+00:11:47,360 --> 00:12:03,200
+alpha such that بحيث أن ال V تساوي Alpha U for
+
+107
+00:12:03,200 --> 00:12:03,820
+example
+
+108
+00:12:09,030 --> 00:12:24,910
+The vectors مثلًا V و 3V and ناقص 2V are parallel
+
+109
+00:12:24,910 --> 00:12:29,330
+يبقى
+
+110
+00:12:29,330 --> 00:12:35,310
+هذه المتجهاتبقول عنها متجهات متساوية لأن كل واحد
+
+111
+00:12:35,310 --> 00:12:41,150
+هو عبارة عن مضاعفات الآخر وليس بالضرورة أن تكون
+
+112
+00:12:41,150 --> 00:12:46,170
+Alpha عددا صحيحا يعني ممكن يكون هذا تلك على اتنين
+
+113
+00:12:46,170 --> 00:12:51,230
+V يعني ممكن يكون كاسرك المهم واحد منهم مضاعفات
+
+114
+00:12:51,230 --> 00:12:57,550
+الآخر فمثلا لو جيت قلت هذا هو ال vector V على سبيل
+
+115
+00:12:57,550 --> 00:13:03,290
+المثالتلاتة على اتنين V جد و جداش مرة و نص و في
+
+116
+00:13:03,290 --> 00:13:09,050
+نفس الاتجاه يبقى هذا يكون بالشكل اللي عنده هذا
+
+117
+00:13:09,050 --> 00:13:16,970
+يبقى هذا تلاتة على اتنين V طب ناقص اتنين V جد V
+
+118
+00:13:16,970 --> 00:13:23,570
+مرتين بس في عكس الاتجاه يبقى هذا يكون بالشكل اللي
+
+119
+00:13:23,570 --> 00:13:29,720
+عنده هذا ناقص اتنين Vالتلاتة are parallel لغاية أن
+
+120
+00:13:29,720 --> 00:13:35,680
+الاتجاهات مالها متعاكسة مع البعض هذا كله لا يوصل
+
+121
+00:13:35,680 --> 00:13:48,540
+نجي الآن لنقطة جديدة وهي remark we
+
+122
+00:13:48,540 --> 00:13:49,780
+write any vector
+
+123
+00:13:57,840 --> 00:14:04,060
+Any vector يبقى بنقدر نكتب أي متجه algebraically
+
+124
+00:14:04,060 --> 00:14:24,240
+جابريا جابريا
+
+125
+00:14:24,240 --> 00:14:32,700
+algebraically by its componentsby its components
+
+126
+00:14:32,700 --> 00:14:36,780
+بالمركبات
+
+127
+00:14:36,780 --> 00:14:44,960
+ابتدعتها as follows مثلا
+
+128
+00:14:44,960 --> 00:14:54,300
+في ال plane and the plane ال vector v بقدر اكتبه
+
+129
+00:14:54,300 --> 00:15:02,560
+على الشكل التالي v1و V2 في الـ space in the space
+
+130
+00:15:02,560 --> 00:15:17,240
+ال V بده ساوي V1 و V2 و V3 where حيث V1 و V2 و V3
+
+131
+00:15:17,240 --> 00:15:24,780
+are the components of
+
+132
+00:15:26,740 --> 00:15:42,660
+the vector of the vector v in the direction of the
+
+133
+00:15:42,660 --> 00:15:51,180
+coordinate axes
+
+134
+00:15:51,180 --> 00:16:00,020
+كيف هذا الكلامنحاول أن نضع الكلام اللي نقوله على
+
+135
+00:16:00,020 --> 00:16:04,660
+الرسم، لكي يكون واضح أمامنا تماما
+
+136
+00:16:45,590 --> 00:16:51,170
+تشوف؟ لو جاء تخيلتي عندى ان في vector V بهذا الشكل
+
+137
+00:16:51,170 --> 00:16:58,390
+يبقى هذا هو ال vector Vبنشوف وين المُركّبات تبعات
+
+138
+00:16:58,390 --> 00:17:03,830
+الـ vector V يبقى لو جيت من هنا نزلت عموض بالشكل
+
+139
+00:17:03,830 --> 00:17:09,610
+على هذا لغاية ما قبل الـ X Y plane و رسمت من هنا
+
+140
+00:17:09,610 --> 00:17:19,710
+أفقي و من هنا موازي لبين موازي لل X Y يبقى هذه ال
+
+141
+00:17:19,710 --> 00:17:25,190
+Y موازي لل X Y بالشكل هذاهذا تعتبر المُركّب اللي
+
+142
+00:17:25,190 --> 00:17:31,070
+هي V1 هذه الموازية اللي هي V1 هذا V2 الموازية
+
+143
+00:17:31,070 --> 00:17:36,030
+لمحور Y هذا اللي رأسي الموازية لمحور Z اللي همين
+
+144
+00:17:36,030 --> 00:17:43,710
+V3 يبقى V1 ستبدأ من نقطة الأصل لغاية هذه النقطة
+
+145
+00:17:43,710 --> 00:17:50,270
+يعني كأن إحداث النقطة هذه V1 و 0 و 0 زي ما درسنا
+
+146
+00:17:50,270 --> 00:18:00,090
+في المحاضرة الماضيةهذه الـ V1 و V2 و 0 هذه الان V1
+
+147
+00:18:00,090 --> 00:18:07,310
+و V2 و V3 يبقى هذه المراكبات الثلاثة لمين للـ
+
+148
+00:18:07,310 --> 00:18:15,950
+vector V in space حد بيتسأل؟ طيب
+
+149
+00:18:15,950 --> 00:18:21,700
+يبقى هذه المراكبات من الأن فصاعداسنحاول أن نكتب
+
+150
+00:18:21,700 --> 00:18:27,440
+دائما و أبدا الـ vector V بدلالة المركبات التلاتة
+
+151
+00:18:27,440 --> 00:18:35,420
+تبعته في الإتجاهات تبعت محور الإحداثيات X و Y و Z
+
+152
+00:18:35,420 --> 00:18:41,420
+ممكن
+
+153
+00:18:41,420 --> 00:18:50,270
+نعطي شكل عام لمين لل vector Vتاولة ما نقول ان two
+
+154
+00:18:50,270 --> 00:18:54,690
+vectors are parallel لو روحت رسمت موازي لهذا ال
+
+155
+00:18:54,690 --> 00:18:59,070
+vector وليكن الموازي هو ال vector اللي عندنا هذا
+
+156
+00:18:59,070 --> 00:19:06,030
+على سبيل المثال موازي L وG بالضغط تماما وكانت هذه
+
+157
+00:19:06,030 --> 00:19:17,120
+النقطة P1 of X1 وY1 وZ1 وكانت النقطة هذه P2 لX2و
+
+158
+00:19:17,120 --> 00:19:22,520
+Y2 و Z2 إذا ال vector اللي عيني هذا جد ال vector
+
+159
+00:19:22,520 --> 00:19:30,560
+هذا بالضبط تماما مقدارا و اتجاها طيب بناء عليه ال
+
+160
+00:19:30,560 --> 00:19:36,620
+vector V بدي أكتبه بدللة المركبات تبعات هذه النقطة
+
+161
+00:19:36,620 --> 00:19:43,180
+يبقى بناء عليه in general بروح بقول هيك in general
+
+162
+00:19:46,360 --> 00:19:52,380
+على وجه العموم الـ vector V اللي مركبته V1 و V2 و
+
+163
+00:19:52,380 --> 00:19:59,080
+V3 بقدر أكتبه بشكل جديد بواسطة النقاط اللي عندنا
+
+164
+00:19:59,080 --> 00:20:06,120
+هذا اللي تمثل ال vector V بالضبط تماماً يبقى X2-X1
+
+165
+00:20:06,120 --> 00:20:16,040
+Y2-Y1 Z2-Z1بهذا الشكل يبقى إن كتبنا ال vector
+
+166
+00:20:16,040 --> 00:20:21,880
+بدلالة ال terminal point و نسبناه إلى النقطة الأصل
+
+167
+00:20:21,880 --> 00:20:27,280
+أو كتبناه بدلالة النقطة اللي اتنين عندنا الاتنين
+
+168
+00:20:27,280 --> 00:20:32,820
+are the same يبقى اتنين نفس الشيء أثناء شغلنا في
+
+169
+00:20:32,820 --> 00:20:34,940
+الناحية الرياضية
+
+170
+00:20:41,360 --> 00:20:47,860
+كويس لو بدى اكتب تساوي متجهين بدلالة المراكبات
+
+171
+00:20:47,860 --> 00:20:54,000
+فباجي بقول ملاحظة two
+
+172
+00:20:54,000 --> 00:20:58,580
+vectors u
+
+173
+00:20:58,580 --> 00:21:06,140
+اللى هو بدى يساوي u واحد و u اتنين و u تلاتة and v
+
+174
+00:21:06,140 --> 00:21:13,140
+اللى هو بدى يساوي v واحدV1 V2 V3 V4 V5 V6 V7 V8 V9
+
+175
+00:21:13,140 --> 00:21:20,520
+V10 V11 V12 V13 V14 V15 V16 V17 V18 V19 V20
+
+176
+00:21:20,520 --> 00:21:26,660
+V21 V21 V21 V21 V21 V21 V21 V21 V21 V21 V21 V21
+
+177
+00:21:26,660 --> 00:21:27,300
+V21 V21 V21 V21 V21 V21 V21 V21 V21 V21 V21 V21
+
+178
+00:21:27,300 --> 00:21:29,320
+V21 V21 V21 V21 V21 V21 V21 V21 V21 V21 V21 V21
+
+179
+00:21:29,320 --> 00:21:30,100
+V21 V21 V21 V21 V21 V21 V21 V21 V21 V21 V21 V21
+
+180
+00:21:30,100 --> 00:21:30,400
+V21 V21 V21 V21 V21 V21 V21 V21 V21 V21 V21 V21
+
+181
+00:21:30,400 --> 00:21:30,600
+V21 V21 V21 V21 V21 V21 V21 V21 V21 V21 V21 V21
+
+182
+00:21:30,600 --> 00:21:30,600
+V21 V21 V21 V21 V21 V21 V21 V21 V21 V21 V21 V21
+
+183
+00:21:30,600 --> 00:21:30,600
+V21 V21 V21 V21 V21 V21 V21 V21
+
+184
+00:21:35,660 --> 00:21:41,120
+إذا تساوة المُركّبات المُتنظرة في كل منهم
+
+185
+00:21:41,120 --> 00:21:44,680
+المُركّبة الأولى في المُتجه الأول هي نفس المُركّبة
+
+186
+00:21:44,680 --> 00:21:47,620
+الأولى في المُتجه الثاني المُركّبة الثانية في
+
+187
+00:21:47,620 --> 00:21:50,340
+المُتجه الأول هي المُركّبة الثانية في المُتجه
+
+188
+00:21:50,340 --> 00:21:53,720
+الثاني المُركّبة التالتة في المُتجه الأول هي
+
+189
+00:21:53,720 --> 00:21:59,200
+المُركّبة التالتة في المُتجه الثاني وهكذا يبقى من
+
+190
+00:21:59,200 --> 00:22:06,670
+هنا بقول المُتجهين الاتنين متساوينطب لو بدى أجيب
+
+191
+00:22:06,670 --> 00:22:13,090
+طول ال vector جبريا كيف بدها أسبوع فبعدى بقول هذا
+
+192
+00:22:13,090 --> 00:22:17,950
+الملاحظة الأولى الملاحظة الثانية اللى هو the
+
+193
+00:22:17,950 --> 00:22:30,050
+length of the vector v you said ال squareإذا بدأت
+
+194
+00:22:30,050 --> 00:22:33,430
+أكتب دلات المُركّبات ده بقولي بقى باجي بقول V1
+
+195
+00:22:33,430 --> 00:22:40,690
+تربيع زائد V2 تربيع زائد V3 تربيع او إذا بدأت أكتب
+
+196
+00:22:40,690 --> 00:22:45,730
+بواسطة ال general form اللي يقول عليه ال X وما إلى
+
+197
+00:22:45,730 --> 00:22:52,750
+ذلك باجي بقول يبقى هو X2 ناقص X1 لكل تربيع اللي هي
+
+198
+00:22:52,750 --> 00:23:05,390
+قيمة main اللي هي V1 زائدy2-y1 كل تربيع y2-y1
+
+199
+00:23:05,390 --> 00:23:06,490
+كل تربيع y2-y1 كل تربيع y2-y1 كل تربيع y2-y1 كل
+
+200
+00:23:06,490 --> 00:23:09,850
+تربيع y2-y1 كل تربيع y2-y1 كل تربيع y2-y2 كل تربيع
+
+201
+00:23:09,850 --> 00:23:10,250
+y2-y2 كل تربيع y2-y2 كل تربيع y2-y2 كل تربيع y2-y2
+
+202
+00:23:10,250 --> 00:23:10,250
+كل تربيع y2-y2 كل تربيع y2-y2 كل تربيع y2-y2 كل
+
+203
+00:23:10,250 --> 00:23:10,250
+تربيع y2-y2 كل تربيع y2-y2 كل تربيع y2-y2 كل تربيع
+
+204
+00:23:10,250 --> 00:23:17,290
+y2-y2 كل تربيع y2-y2 كل تربيع y2-y2 كل تربيع y2-y2
+
+205
+00:23:17,290 --> 00:23:24,560
+كل تربيع y2-yمش absolute value ل V وإنما طول ال
+
+206
+00:23:24,560 --> 00:23:30,540
+vector V اللي عندنا هذا بدنا
+
+207
+00:23:30,540 --> 00:23:35,240
+نيجي هنا نقطة بسيطة قبل أن نبدأ في أخذ بعض الأمثلة
+
+208
+00:23:35,240 --> 00:23:40,660
+النقطة دي كيف بدنا نجمع two vectors أو نترحهم أو
+
+209
+00:23:40,660 --> 00:23:46,020
+نضرب ال vector في scalar هحطه على شكل التعريف
+
+210
+00:23:46,020 --> 00:23:48,380
+التالي definition
+
+211
+00:23:53,530 --> 00:24:05,730
+let U تساوي U واحد و U اتنين و U تلاتة بدلالة
+
+212
+00:24:05,730 --> 00:24:14,210
+المراكبات تبعها and V تساوي V واحد و V اتنين و V
+
+213
+00:24:14,210 --> 00:24:20,470
+تلاتة بي two vectors
+
+214
+00:24:22,820 --> 00:24:30,840
+عبارة عن متجهين and c is scalar scalar يعني يا
+
+215
+00:24:30,840 --> 00:24:37,780
+بنات كمية قياسية يعني عدد حقيقي then النقطة الأولى
+
+216
+00:24:37,780 --> 00:24:44,180
+لو ده جاخد u زائد ال V يبقى بجمع ال components
+
+217
+00:24:44,180 --> 00:24:50,540
+المتناظرة مع بعضها إيش بصير عندي u واحد زائد v
+
+218
+00:24:50,540 --> 00:25:00,710
+واحدU2 زائد V2 U3 زائد V3 يبقى بجمع ال components
+
+219
+00:25:00,710 --> 00:25:07,230
+المتنظرة مع بعض بالمثل لو طرحت U ناقص V يبقى U1
+
+220
+00:25:07,230 --> 00:25:16,470
+ناقص V1 U2 ناقص V2 U3 ناقص V3 يعني أنا كونت متجه
+
+221
+00:25:16,470 --> 00:25:22,270
+جديد من المتجهين الاتنين اللي موجودات عندككمان؟
+
+222
+00:25:22,270 --> 00:25:27,910
+كوانت متجهدية اسمه محاصلة المتجهين الموجودين سواء
+
+223
+00:25:27,910 --> 00:25:33,190
+كان بالجامعة أو بالطارقة النقطة الثانية لو بدي
+
+224
+00:25:33,190 --> 00:25:43,030
+اضرب C في ال V يبقى C هادى حتى نضرب8 في V1 و V2 و
+
+225
+00:25:43,030 --> 00:25:48,750
+V3 اللي هي هتساوي ال C ستضرب في كل مركبة من
+
+226
+00:25:48,750 --> 00:26:00,030
+المركبات الثلاث اللي هو C V1 C V2 C في V3 C V3
+
+227
+00:26:00,030 --> 00:26:02,190
+بالشكل اللي عندنا هذا
+
+228
+00:26:08,290 --> 00:26:12,390
+طيب C اللي بدنا نضربها يا بنات يمكن تكون موجبة
+
+229
+00:26:12,390 --> 00:26:19,710
+ويمكن تكون سالبة صح ولا لا؟ لو ضربت C كرقم موجة في
+
+230
+00:26:19,710 --> 00:26:24,570
+البيت بطلع مدتجة في نفس الاتجاه تبع المدتجة الأصلي
+
+231
+00:26:24,570 --> 00:26:30,010
+لو كانت C سالبة يعكسوا على طول القطر خلينا نكتب
+
+232
+00:26:30,010 --> 00:26:34,550
+هذه الملاحظة البسيطة هذه لأنه بدنا نبني عليها شغل
+
+233
+00:26:34,550 --> 00:26:37,170
+بعد ذلك ان شاء الله تعالى
+
+234
+00:26:39,780 --> 00:26:45,080
+يبقى بدأجي أقول .. بدي
+
+235
+00:26:45,080 --> 00:26:50,700
+أحطها زي ملاحظة بسيطة هيك if c أكبر من ال zero
+
+236
+00:26:50,700 --> 00:27:04,340
+then c, v and l, v are in the same direction
+
+237
+00:27:10,600 --> 00:27:19,040
+اللي بقى، لو كان الـC أقل من الـ0، يعني كمية
+
+238
+00:27:19,040 --> 00:27:32,640
+سالبة، then CV and V are of the opposite
+
+239
+00:27:32,640 --> 00:27:35,840
+directions
+
+240
+00:27:37,580 --> 00:27:45,480
+في اتجاهين متعاكسين طب لو حبيت النقطة التالتة اجيب
+
+241
+00:27:45,480 --> 00:27:51,940
+طول المتجه CV بحسب
+
+242
+00:27:51,940 --> 00:27:58,940
+تعريفنا طول المتجه بده يسوى الجذر التربيعي ل CV1
+
+243
+00:27:58,940 --> 00:28:09,050
+لكل تربيع CV2 لكل تربيع CV3 لكل تربيعهذا بقدر اقول
+
+244
+00:28:09,050 --> 00:28:16,230
+ويساوي لـ square root لـ C تربيع بياخد عامل مشترك
+
+245
+00:28:16,230 --> 00:28:24,610
+بظل V1 تربيع زائد V2 تربيع زائد V3 تربيع شكل اللي
+
+246
+00:28:24,610 --> 00:28:30,630
+عناه طب الـ C تربيع بقدر اطلعها من تحت الجدر تمام
+
+247
+00:28:31,110 --> 00:28:36,410
+لما نطلعها من تحت الجذر تطلع بـ Absolute Value زي
+
+248
+00:28:36,410 --> 00:28:40,570
+ما اتعلمنا في Calculus A في أول محاضرة أخدتها في
+
+249
+00:28:40,570 --> 00:28:46,930
+Calculus A يبقى هذا بيصير عندي Absolute Value لـ C
+
+250
+00:28:46,930 --> 00:28:55,970
+في الجذر التربيعي لمن؟ لـ V1 تربيع V2 تربيع V3
+
+251
+00:28:55,970 --> 00:28:56,950
+تربيع
+
+252
+00:28:59,710 --> 00:29:05,990
+يعني هذه بقدر اقول absolute value ل C في طول ال V
+
+253
+00:29:05,990 --> 00:29:15,390
+يبقى الأولى يا بنات هذه تقرأ absolute value of C
+
+254
+00:29:15,390 --> 00:29:19,710
+يعني إن كانت موجبة فهي موجبة وإن كانت سالبة خد ال
+
+255
+00:29:19,710 --> 00:29:26,330
+absolute value بالصير موجبة أما عن هذا فهو the
+
+256
+00:29:26,330 --> 00:29:37,850
+length ofV يبقى هذا طول المتجة V هنا بنحاول نوقف
+
+257
+00:29:37,850 --> 00:29:43,470
+شوية بسيطة و ناخد بعض الأمثلة لتوضيح المفاهيم التي
+
+258
+00:29:43,470 --> 00:29:51,770
+ذكرناها قبل قليل إذا بدنا نروح لانحل بعض الأمثلة
+
+259
+00:29:51,770 --> 00:29:57,830
+العددية على ما ذكرناهم قبل قليل
+
+260
+00:30:12,320 --> 00:30:17,440
+نمسح هذا خلاص وانا بشرحها لابنات اللي ماتستمعش اي
+
+261
+00:30:17,440 --> 00:30:23,700
+نقطة تقول لو سمحت استهلنا واسألي اي سؤال بدكيه من
+
+262
+00:30:23,700 --> 00:30:27,820
+خلال اسئلة بتثبت المعلومات عندكوا اللي بتكون فهمت
+
+263
+00:30:27,820 --> 00:30:36,360
+غلط بتصير تفهم صح و هكذا نجي لأول مثال example F
+
+264
+00:30:43,900 --> 00:30:54,920
+P1 F P1 النقطة الأحدثيات P1
+
+265
+00:30:54,920 --> 00:31:00,340
+F P1 F P1 F P1
+
+266
+00:31:00,340 --> 00:31:04,920
+F P1 F P1 F P1 F P1 F P1 F P1 F P1 F P1 F P1 F P1
+
+267
+00:31:04,920 --> 00:31:06,620
+F P1 F P1 F P1 F P1 F P1 F P1 F P1 F P1 F P1 F P1
+
+268
+00:31:06,620 --> 00:31:10,240
+F P1 F P1 F P1 F P1 F P1 F P1 F P1 F P1 F P1 F P1
+
+269
+00:31:10,240 --> 00:31:10,380
+F P1 F P1 F P1 F P1 F P1 F P1 F P1 F P1 F P1 F P1
+
+270
+00:31:10,380 --> 00:31:10,380
+F P1 F P1 F P1 F P1 F P1 F P1 F P1 F P1 F P1 F P1
+
+271
+00:31:10,380 --> 00:31:10,380
+F P1 F P1 F P1 F P1 F P1 F P1 F P1 F P1 F P1 F P1
+
+272
+00:31:10,380 --> 00:31:10,420
+F P1 F P1 F P1 F P1 F P1 F P1 F P
+
+273
+00:31:21,050 --> 00:31:35,490
+2 points نمرأة find طول جديدنا the length of
+
+274
+00:31:35,490 --> 00:31:49,510
+الأربع P1 P2 that is أي أننا بدنا طول الأربع P1 P2
+
+275
+00:31:49,510 --> 00:31:59,860
+as a vectoremra b by the vector او is the vector
+
+276
+00:31:59,860 --> 00:32:03,380
+is
+
+277
+00:32:03,380 --> 00:32:11,760
+the vector u اللي هو بده يساوي تسعة واطناشر وزيرا
+
+278
+00:32:11,760 --> 00:32:16,620
+parallel to
+
+279
+00:32:16,620 --> 00:32:21,180
+p1 p2 ام لا
+
+280
+00:32:28,630 --> 00:32:36,330
+Solution نرجع لسؤالنا مرة ثانية نقرأ السؤال نتكج
+
+281
+00:32:36,330 --> 00:32:39,710
+المرطب شو اللي بدي اعطاه الطب إذا حددنا شو اللي
+
+282
+00:32:39,710 --> 00:32:45,130
+بدناه إذا ما نقدر نحدد الإجابة تبعتنا بدقة ماعطينا
+
+283
+00:32:45,130 --> 00:32:52,680
+نقطتين P1 و P2 و قال لي هاتلي الطولتبع المتجة
+
+284
+00:32:52,680 --> 00:32:59,200
+اربعة P1 P2 يبقى بده يقول المتجة اربعة P1 P2 اذا
+
+285
+00:32:59,200 --> 00:33:04,500
+بده يجيب المتجة P1 P2 اربعة يعني اربعة امثال و
+
+286
+00:33:04,500 --> 00:33:12,220
+بصير يعني كأنه طالب متجة موازي للمتجة P1 P2 بس جد
+
+287
+00:33:12,220 --> 00:33:17,280
+واش اربعة مرات تمام؟ كويس يبقى خلينا نجيب المتجة
+
+288
+00:33:17,280 --> 00:33:24,470
+P1 P2 في الأوليبقى باجي بقوله نمرة A بدي المتجه P1
+
+289
+00:33:24,470 --> 00:33:28,930
+P2 يبقى
+
+290
+00:33:28,930 --> 00:33:40,150
+هذا الكلام بدي يساوي X2-X1 Y2-Y1 Z2-Z1 عشان أخدنا
+
+291
+00:33:40,150 --> 00:33:45,730
+التعريف قبل قليل إذا بدي أطبق هذا التعريف يبقى بدي
+
+292
+00:33:45,730 --> 00:33:51,220
+أجي نميماللي هو أربعة ناقص واحد أربعة ناقص واحد
+
+293
+00:33:51,220 --> 00:33:58,560
+سبعة ناقص تلاتة ناقص اتنين زائد اتنين ناقص اتنين
+
+294
+00:33:58,560 --> 00:34:04,160
+ناقص ناقص اتنين زائد اتنين يبقى صار عندى هذا
+
+295
+00:34:04,160 --> 00:34:11,660
+المتجه هو تلاتة واربعة و Zero بهذا الشكل يبقى هذا
+
+296
+00:34:11,660 --> 00:34:19,860
+المتجه P واحد P اتنين أنا بديأربعة اللي هو P واحد
+
+297
+00:34:19,860 --> 00:34:25,380
+P اتنين متجه اللي عندنا هذا يبقى هذا الكلام بده
+
+298
+00:34:25,380 --> 00:34:31,880
+يساوي أربعة في تلاتة أربعة زيرو يبقى هذا الكلام
+
+299
+00:34:31,880 --> 00:34:38,800
+بده يساوي تلاتة في أربعة باطناش وأربعة في أربعة
+
+300
+00:34:38,800 --> 00:34:43,440
+بستاشر أوزي كويس
+
+301
+00:34:45,240 --> 00:34:50,960
+أخر حاجة أخدناها قبل قليل كان طول المتجه C في V
+
+302
+00:34:50,960 --> 00:34:57,680
+قلنا absolute value للـC في طول الـV أحنا أخدنا
+
+303
+00:34:57,680 --> 00:35:04,500
+all اللي هو C V بده يساوي absolute value للـC في
+
+304
+00:35:04,500 --> 00:35:12,040
+طول الـV طيب الـC عنا هنا ماكنتاش بنات أربع يبقى
+
+305
+00:35:12,040 --> 00:35:17,640
+absolute value للأربعطول الـ V الجدري التربية
+
+306
+00:35:17,640 --> 00:35:25,960
+للمُركّبات تبعها هي يبقى تلاتة تربية زائد أربعة
+
+307
+00:35:25,960 --> 00:35:36,440
+تربية زائد Zero تربية ويساوي أربعة في تسعة وست عشر
+
+308
+00:35:36,440 --> 00:35:43,260
+خمسة وعشرين بخمسة يبقى الطول تبعه جدير اللي هو
+
+309
+00:35:43,260 --> 00:35:44,100
+عشرين
+
+310
+00:35:47,680 --> 00:35:51,520
+طب واحدة تقول ليه؟ طب ما احنا جيبنا هاي أربعة P و
+
+311
+00:35:51,520 --> 00:35:56,760
+طلعنا هذا، لو ربعنا هذا تحت الجدر بطلع عشرين،
+
+312
+00:35:56,760 --> 00:36:02,390
+بنقولاش surely، بالتأكيد، كيف؟ اتناش في اتناشمية و
+
+313
+00:36:02,390 --> 00:36:06,150
+أربعة و أربعين ستة عشر في ستة عشر ميتين و ستة و
+
+314
+00:36:06,150 --> 00:36:10,170
+خمسين و مية و أربعة و أربعين أربع مية جداش جدرال
+
+315
+00:36:10,170 --> 00:36:14,890
+أربع مية عشرين و هو المطلوب يعني إن عملتي زي .. و
+
+316
+00:36:14,890 --> 00:36:19,550
+الله روحتي أخدت الطول هذا مباشرة تنسيان لاتنين صح
+
+317
+00:36:19,550 --> 00:36:24,010
+و ماحدش مقدر يعطرها عالم كده هذا هو المطلوب الأول
+
+318
+00:36:24,010 --> 00:36:30,180
+المطلوب التاني نمرابيد بقول إيه هاتليهل ال vector
+
+319
+00:36:30,180 --> 00:36:36,640
+هذا موازي ال vector P1 P2 ولا لأ قبل قليل قولنا
+
+320
+00:36:36,640 --> 00:36:42,020
+المتجهين المتوازين إذا كان واحد فيهم مضاعفة الآخر
+
+321
+00:36:42,020 --> 00:36:49,220
+قولنا V موازي ل 2V موازي ل-3V و هكذا إذا أنا بداجي
+
+322
+00:36:49,220 --> 00:36:54,750
+لل vector اللي عندنا هذا اللي مضينيااللي هو قداش
+
+323
+00:36:54,750 --> 00:37:02,630
+ال vector u اللي هو بده يساوي 9 و 12 و 0 بقدر أخد
+
+324
+00:37:02,630 --> 00:37:09,190
+منه تلاتة برا من كل مركبة من هذه المركبات بيظل
+
+325
+00:37:09,190 --> 00:37:15,590
+قداش عند هنا تلاتة هنا أربع وهنا Zero من هو المتجه
+
+326
+00:37:15,590 --> 00:37:22,030
+اللي عندنا هذا مش هو P1 P2 يبقى هذا الكلام بده
+
+327
+00:37:22,030 --> 00:37:30,070
+يساوي تلاتةP1 P2 صار اليوم مضاعفة ال P1 P2 يبقى
+
+328
+00:37:30,070 --> 00:37:34,410
+اتنين هذول مالهم are parallel زي ما طلقالي هذول
+
+329
+00:37:34,410 --> 00:37:40,130
+متوازين ام لا يبقى ان اثبتلوا انهم متوازين يبقى so
+
+330
+00:37:40,130 --> 00:37:51,910
+ال U and P1 P2 are parallel vectors يبقى هذول
+
+331
+00:37:51,910 --> 00:37:59,550
+متجهات مالهامتوازن نجي
+
+332
+00:37:59,550 --> 00:38:05,210
+لتعريف جديد definition
+
+333
+00:38:05,210 --> 00:38:11,030
+سمعتوا في ال فيزيا بيه بمتج هالوحدة؟ حد فيكم بتجرى
+
+334
+00:38:11,030 --> 00:38:14,410
+تذكرني و لا و بالبلد يعني مش بتعرف ع المتج
+
+335
+00:38:14,410 --> 00:38:20,440
+هالوحدة؟طوله واحد صحيح يعني طوله واحد من واحدة
+
+336
+00:38:20,440 --> 00:38:26,980
+الطول ان كان مثلا بالمتر بقول المتر طول متر واحد
+
+337
+00:38:26,980 --> 00:38:31,340
+ان كان بالأقدام بقول قدم واحد او بالسانتيمتر بقول
+
+338
+00:38:31,340 --> 00:38:36,400
+سانتيمتر واحد و لا كده تمام؟ إذا منتجة الواحدة هو
+
+339
+00:38:36,400 --> 00:38:43,240
+عبارة عن منتجة with length والطول تبعه واحد صحيح
+
+340
+00:38:43,240 --> 00:38:54,670
+ابقى باجي بقول thatunit vector is a vector with
+
+341
+00:38:54,670 --> 00:39:03,070
+length one يبقى
+
+342
+00:39:03,070 --> 00:39:09,690
+هو عبارة عن متجة الطول تبعه يساوي الواحد الصحيحة
+
+343
+00:39:09,690 --> 00:39:14,530
+for example مثلا four
+
+344
+00:39:16,580 --> 00:39:27,400
+example في عندنا حاجة اسمها the standard unit
+
+345
+00:39:27,400 --> 00:39:36,020
+vectors ال vectors المتعارف عليهم في كل كتب
+
+346
+00:39:36,020 --> 00:39:41,700
+الرياضيات و الفيزيا و ما إلى ذلك تلاتة ال I و مي
+
+347
+00:39:41,700 --> 00:39:47,650
+كمانالـJ والـK هؤلاء الفلسفة المتعارفة تلك متجهات
+
+348
+00:39:47,650 --> 00:39:51,770
+واحدة في اتجاه ال coordinate axes وكل واحد طوله
+
+349
+00:39:51,770 --> 00:39:57,670
+يساوي جداش يعني على الطبيعة لو جينا كل هذه المحاور
+
+350
+00:39:57,670 --> 00:40:05,230
+شكلا هذا هذا محور X هذا محور Y هذا محور Z فإن
+
+351
+00:40:05,230 --> 00:40:10,920
+المتجهات التلاتةالمتجه الأول هو خط طول هنا يساوي
+
+352
+00:40:10,920 --> 00:40:17,640
+الوحدة يبقى بيكون هذا المتجه I هنا خط الطول كذلك
+
+353
+00:40:17,640 --> 00:40:23,740
+يساوي الوحدة يبقى بيكون هذا هو المتجه J هنا خط طول
+
+354
+00:40:23,740 --> 00:40:29,620
+يساوي الوحدة كذلك جد بعض الأطوال التلاتة يبقى هذا
+
+355
+00:40:29,620 --> 00:40:35,800
+المتجه K بهذا الشكليبقى هذا ال I و ال J و ال K
+
+356
+00:40:35,800 --> 00:40:43,960
+اللي ال standard unit vector مابقاش
+
+357
+00:40:43,960 --> 00:40:48,540
+رأيك يا بنات أي vector ييجي في بالك بقدر اكتبه
+
+358
+00:40:48,540 --> 00:40:52,300
+بالذلالة ال standard unit vectors هدول الدلالة
+
+359
+00:40:52,300 --> 00:41:02,230
+كيف؟ علاقه لمن؟ فهمتش قصتي، قصتي كتبوليإنه لو بدى
+
+360
+00:41:02,230 --> 00:41:08,130
+أجيب متجه الوحدة لمتجه الماء بروح بقسم المتجه على
+
+361
+00:41:08,130 --> 00:41:12,850
+طول المتجه مش هذا اللي قصدته عادة اللي قصدته أنه
+
+362
+00:41:12,850 --> 00:41:19,150
+أي فكتر علنا بقدر اكتبه بدلالة ال three و ال I و
+
+363
+00:41:19,150 --> 00:41:25,050
+ال J و ال K تمام؟ كيف كان التالي؟ هكتب هالك remark
+
+364
+00:41:25,050 --> 00:41:25,650
+هذه
+
+365
+00:41:30,950 --> 00:41:37,150
+اني vector V
+
+366
+00:41:37,150 --> 00:41:47,950
+بدي يساوي V واحد و V اتنين و V تلاتة is written أو
+
+367
+00:41:47,950 --> 00:41:58,210
+is a linear combination of
+
+368
+00:41:58,210 --> 00:41:59,710
+the
+
+369
+00:42:02,440 --> 00:42:14,960
+Standard Unit Vectors كيف أزفله؟ كالتالي طلعلي ال
+
+370
+00:42:14,960 --> 00:42:23,400
+vector V هاي مركبته V1 و V2 و V3 بقدر أكتب هذا ال
+
+371
+00:42:23,400 --> 00:42:36,190
+vector على شكل مجموع تلت متجهات كيف؟ كالتاليV1 V2
+
+372
+00:42:36,190 --> 00:42:41,690
+V3
+
+373
+00:42:41,690 --> 00:42:44,990
+V4
+
+374
+00:42:44,990 --> 00:42:45,170
+V5 V6 V7 V8 V9 V10 V11 V12 V13 V12 V13 V13 V13 V13
+
+375
+00:42:45,170 --> 00:42:45,770
+V13 V13 V13 V13 V13 V13 V13 V13 V13 V13 V13 V13
+
+376
+00:42:45,770 --> 00:42:45,770
+V13 V13 V13 V13 V13 V13 V13 V13 V13 V13 V13 V13
+
+377
+00:42:45,770 --> 00:42:45,770
+V13 V13 V13 V13 V13 V13 V13 V13 V13 V13 V13 V13
+
+378
+00:42:45,770 --> 00:42:45,810
+V13 V13 V13 V13 V13 V13 V13 V13 V13 V13 V13 V13
+
+379
+00:42:45,810 --> 00:42:45,910
+V13 V13 V13 V13 V13 V13 V13 V13 V13 V13 V13 V13
+
+380
+00:42:45,910 --> 00:42:45,910
+V13 V13 V13 V13 V13 V13 V13 V13 V13 V13 V13 V13
+
+381
+00:42:45,910 --> 00:42:46,670
+V13 V13 V13 V13 V13 V13 V13 V13 V13 V13 V13 V13
+
+382
+00:42:46,670 --> 00:42:48,690
+V13 V13 V13 V13 V13 V13 V13 V13 V13 V13
+
+383
+00:42:52,760 --> 00:42:59,500
+اللي بعد هو 0 زائد v2 زائد 0 في v2 زائد 0 زائد v3
+
+384
+00:42:59,500 --> 00:43:06,060
+في v3 طيب الآن بداجي ضرب scalar في vector يبقى
+
+385
+00:43:06,060 --> 00:43:09,300
+scalar ان ضربته في الداخل ولا طلعته برا الاتنين
+
+386
+00:43:09,300 --> 00:43:13,900
+are the same يبقى مقدر اقول هذا الكلام بده ساعة
+
+387
+00:43:13,900 --> 00:43:27,550
+اللي هو v1 في 1 و 0 و 0 تمام؟زائد V2 Zero و واحد و
+
+388
+00:43:27,550 --> 00:43:40,770
+Zero زائد V3 Zero و Zero و واحد شكل يعني انا احنا
+
+389
+00:43:40,770 --> 00:43:44,430
+قولنا ال standard unit vectors و قولنا لك هاي ال
+
+390
+00:43:44,430 --> 00:43:49,340
+standard unit vectors اللي هو I و J و Kلو جهت
+
+391
+00:43:49,340 --> 00:43:55,480
+بقولتلك هنا ال I بده يساوي هو واحد وزير وزير صحيح
+
+392
+00:43:55,480 --> 00:44:01,340
+ولا لا؟ صحيح ليش؟ لأن النقطة هذه أحداثيها واحد
+
+393
+00:44:01,340 --> 00:44:09,280
+وزير وزير وزير وهذا النقطة زير وواحد وزير وهذا
+
+394
+00:44:09,280 --> 00:44:19,310
+النقطة زير وزير وواحدالـ J هيكون يساوي 0 و 1 و 0
+
+395
+00:44:19,310 --> 00:44:28,390
+والـ K اللي هو بده يساوي 0 و 0 و 1 إذا بناء عليه
+
+396
+00:44:28,390 --> 00:44:36,010
+هذا بيصير V1 في اتجاه الـ I زائد V2 في اتجاه الـ J
+
+397
+00:44:36,010 --> 00:44:42,190
+زائد V3 في اتجاه الـ Kيبقى أي vector من الـ M
+
+398
+00:44:42,190 --> 00:44:47,390
+فصاعدا، يا بنكتبه على الصيغة اللي عندناها دي، ع
+
+399
+00:44:47,390 --> 00:44:53,890
+شكل غسين مجرنات، يا إما بدلالة ال standard vectors
+
+400
+00:44:53,890 --> 00:45:01,620
+اللي هو I وJ وK طبعاً V1 وV2 وV3 اس colorsوالـ I و
+
+401
+00:45:01,620 --> 00:45:06,240
+G و K هما الـ Main Vectors يبقى هذا مضاعفات الـ I
+
+402
+00:45:06,240 --> 00:45:10,200
+وهذا مضاعفات الـ G وهذا مضاعفات الـ Main مضاعفات
+
+403
+00:45:10,200 --> 00:45:15,920
+الـ K يبقى من الأن فساعدا أي Vector نقدر نكتبه
+
+404
+00:45:15,920 --> 00:45:21,710
+بهذه الطريقةطب يا بنات لو كانت V1 هذه الفرق ما بين
+
+405
+00:45:21,710 --> 00:45:28,850
+X2-X1 زي ما كتبناها قبل شوية مسحناها يعني بقدر
+
+406
+00:45:28,850 --> 00:45:39,190
+أقول هذه كمان بالضبط هي X2-X1 في اتجاه I وهذه Y2
+
+407
+00:45:39,190 --> 00:45:49,060
+-Y1 في اتجاه J وهذه Z2-Z1 في اتجاه Mفي اتجاه الـ K
+
+408
+00:45:49,060 --> 00:45:54,080
+زي ما انت شايفها إذا يا بكتب المتجهة بالشكل هذا
+
+409
+00:45:54,080 --> 00:46:00,140
+تمام يا بقدر أكتب بالشكل اللي عندنا هذا يا بقدر
+
+410
+00:46:00,140 --> 00:46:05,040
+أكتب بالشكل هذا إن كنت عارف نقطة البداية ونقطة
+
+411
+00:46:05,040 --> 00:46:11,540
+النهاية لهذا المتجه طيب نجد الكلام اللي قالته
+
+412
+00:46:11,540 --> 00:46:16,900
+الأخت شو اسمك انتي classroom classroomالوقت خلاص
+
+413
+00:46:16,900 --> 00:46:22,360
+كورالته قبل قليل بتقول متجه الوحدة هو عبارة عن
+
+414
+00:46:22,360 --> 00:46:29,360
+خارج قسم المتجه على قوله نقولها كلامك صحيح و
+
+415
+00:46:29,360 --> 00:46:38,100
+هنحطها في صيغة محددة الأن و نشتغل عليها بعد ذلك
+
+416
+00:46:38,100 --> 00:46:47,460
+يبقى الصيغة هذه كالتالي لو جيت قولتلك Vعلى طول ال
+
+417
+00:46:47,460 --> 00:46:54,660
+V هذا انطلع طوله يسوى واحد صحيح إذا هو unit vector
+
+418
+00:46:54,660 --> 00:47:08,380
+مظبوط يبقى هذا as a unit vector in the direction
+
+419
+00:47:10,640 --> 00:47:17,360
+of V يبقى هذا متجه الوحدة في اتجاه ال V السبب ليش؟
+
+420
+00:47:17,360 --> 00:47:22,560
+because لو بدى اجيب الطول تبع ال V على طول ال V
+
+421
+00:47:22,560 --> 00:47:26,400
+حسب ما احنا معرفين ال unit vector ان طلع طوله
+
+422
+00:47:26,400 --> 00:47:31,740
+يساوي واحد صحيح اذا فهو unit vector مظبوط؟ يبقى
+
+423
+00:47:31,740 --> 00:47:38,260
+هذا الكلام بدى يساوي واحد على طول طول ال V ما هو
+
+424
+00:47:38,260 --> 00:47:43,610
+طول ال Vبيظل اللي فوق هذا اللي هو طول ال V هذا
+
+425
+00:47:43,610 --> 00:47:48,070
+الكلام لو اختصرت اللي فوق مع اللي تحت المقدار اللي
+
+426
+00:47:48,070 --> 00:47:53,550
+عندنا هذا مع المقدار هذا بيظل جدير واحد صحيح بس
+
+427
+00:47:53,550 --> 00:47:58,250
+ديلو بالك في شغلة ممكن تفهميها غلط مافيش حاجة
+
+428
+00:47:58,250 --> 00:48:03,490
+اسمها اسم المتجه على المتجهات لايوجد عندنا في
+
+429
+00:48:03,490 --> 00:48:09,570
+الرياضية حاجة اسمها اسم المتجهات زي المصففاتفي
+
+430
+00:48:09,570 --> 00:48:13,190
+الجابرة الخاطئ، مافيش حاجة يسمى قسم المصرفات على
+
+431
+00:48:13,190 --> 00:48:17,430
+الإطلاق، عمرك لما انضرفت مصرفات في الثانوية،
+
+432
+00:48:17,430 --> 00:48:22,620
+قسمتهم اصفين على بعض، ماحصلش، مهالييعني ليه قسمة
+
+433
+00:48:22,620 --> 00:48:28,080
+مصوفات و كذلك ليه يوجد حاجة اسمها قسمة متجات لما
+
+434
+00:48:28,080 --> 00:48:33,100
+أقول قسمت المتجة على طوله يعني كان ضربت في سكلة
+
+435
+00:48:33,100 --> 00:48:37,940
+واحد على طول المتجة هذا سكلة ضربته في المتجة إذا
+
+436
+00:48:37,940 --> 00:48:42,660
+بضال المتجة من هو هذا المتجة هو متجة الوحدة في
+
+437
+00:48:42,660 --> 00:48:47,880
+اتجاه من المتجة إذا لو جبتلك سؤال و قلت لك أعطيتك
+
+438
+00:48:47,880 --> 00:48:51,660
+vectorأو قلت لك بالله هاتيلي قداش طول ال vector
+
+439
+00:48:51,660 --> 00:48:56,920
+هذا أو هاتيلي متجهي الوحدة في اتجاه هذا ال vector
+
+440
+00:48:56,920 --> 00:49:02,820
+بروح بشوف قداش طول هذا المتجه و بقسم كل مراكبة من
+
+441
+00:49:02,820 --> 00:49:07,960
+مراكبات المتجه المُعطَى على هذا الطول بيعطيني متجه
+
+442
+00:49:07,960 --> 00:49:12,560
+الوحدة في اتجاه المتجه الأصلي طب لو قلت لك في
+
+443
+00:49:12,560 --> 00:49:17,640
+اتجاه معكس للمتجه الأصلي لماذا؟ بقسم على هذا الرقم
+
+444
+00:49:17,640 --> 00:49:23,000
+بإشارةالسالب بيكون حصلت علامين على المتجه في عكس
+
+445
+00:49:23,000 --> 00:49:29,820
+الاتجاه اللي هو موجود عندنا طيب
+
+446
+00:49:29,820 --> 00:49:36,440
+ممكن اكتب يا بنات اي متجه في الدنيا بدلاله طوله
+
+447
+00:49:36,440 --> 00:49:41,300
+واتجاهه كيف؟ كالتالي احفظلك بصيغة ال remark
+
+448
+00:49:41,300 --> 00:49:43,160
+التالية remark
+
+449
+00:49:54,250 --> 00:50:07,950
+is a non-zero vector متجه غير الصفر we can write
+
+450
+00:50:07,950 --> 00:50:15,590
+نستطيع كتابة V in
+
+451
+00:50:15,590 --> 00:50:22,430
+terms of its length
+
+452
+00:50:25,790 --> 00:50:34,870
+الطول تبعه undirection as
+
+453
+00:50:34,870 --> 00:50:42,390
+follow دعوني
+
+454
+00:50:42,390 --> 00:50:50,690
+أكمل معناه لو جاءت مجلسك المتجه V بذرساه بدي أضربه
+
+455
+00:50:50,690 --> 00:50:56,620
+في رقم واسمه على نفس الرقمهل تتغير قيمة هذا المتجه
+
+456
+00:50:56,620 --> 00:51:01,400
+أو شكله؟ لأ طب إيش رأيته؟ بدي أختار رقم محدد الرقم
+
+457
+00:51:01,400 --> 00:51:07,900
+المحدد هو عبارة عن طول هذا المتجه فبقدر أقول هذا
+
+458
+00:51:07,900 --> 00:51:17,380
+الكلام بيساوي طول ال V في ال V على طول ال V كأن
+
+459
+00:51:17,380 --> 00:51:20,680
+أنا أتعرف في جد ياش؟ في واحد صح يقول متجه كما هو
+
+460
+00:51:20,680 --> 00:51:27,080
+بدي أعيد الصياغة اللي أنا قلتهايبقى طول ال V ضربته
+
+461
+00:51:27,080 --> 00:51:32,740
+في V على طول ال V قلت هذا على هذا و هذا زي ما هو
+
+462
+00:51:32,740 --> 00:51:41,100
+هذا مين أبنات الجزء الأول طول ال V يبقى هذا ال N
+
+463
+00:51:41,100 --> 00:51:50,400
+أر V هذا اتجاه ال V يعني متجه الوحدة في اتجاه ال V
+
+464
+00:51:50,770 --> 00:51:58,550
+يبقى هذا الـdirection of v إذا بناني علي الرمج و
+
+465
+00:51:58,550 --> 00:52:04,470
+تقولي أي non zero vector بقدر أكتبه بدلالة ال lens
+
+466
+00:52:04,470 --> 00:52:10,190
+تبعه و ال direction تبعه يبقى هاي ال direction of
+
+467
+00:52:10,190 --> 00:52:15,070
+v و هاي ال lens تبع من تبع ال v يبقى أي متجهة بقدر
+
+468
+00:52:15,070 --> 00:52:19,350
+أكتبه بالشكل اللي قدامها نجي ناخد مثال example
+
+469
+00:52:28,940 --> 00:52:33,140
+example one بيقول
+
+470
+00:52:33,140 --> 00:52:44,360
+let ال U تساوي اتنين وزيره و سالب تلاته and ال V
+
+471
+00:52:44,360 --> 00:52:53,240
+بده يساوي زيره و واحد و سالب اتنين fine هو ايش
+
+472
+00:52:53,240 --> 00:53:06,160
+دولنا نمرة Aاتنين U ناقص تلاتة V نمرة B طول اتنين
+
+473
+00:53:06,160 --> 00:53:15,140
+U ناقص تلاتة V نمرة C write
+
+474
+00:53:15,140 --> 00:53:26,880
+the vector write the vector اتنين U ناقص تلاتة Vas
+
+475
+00:53:26,880 --> 00:53:34,880
+a product of
+
+476
+00:53:34,880 --> 00:53:50,200
+its length and direction.Nimredi
+
+477
+00:53:50,200 --> 00:53:54,560
+find
+
+478
+00:53:54,560 --> 00:54:07,640
+a vector of length عشرة5 a vector of لن عشرة in
+
+479
+00:54:07,640 --> 00:54:15,240
+the opposite direction in
+
+480
+00:54:15,240 --> 00:54:18,320
+the
+
+481
+00:54:18,320 --> 00:54:22,680
+opposite direction of لن U
+
+482
+00:54:59,060 --> 00:55:03,500
+نرجع للسؤال اللي كتبته مرة ثانية نقرأ هذا السؤال
+
+483
+00:55:03,500 --> 00:55:09,700
+قراءة جيدة ثم بعد ذلك أروح أشوف ما هو المطلوب في
+
+484
+00:55:09,700 --> 00:55:14,840
+كل نقطة من النقاط في المثل السؤال مرة ثانية ماتيني
+
+485
+00:55:14,840 --> 00:55:20,320
+two vectors U و V قال لي هاتلي اتنين U ناقص ثلاثة
+
+486
+00:55:20,320 --> 00:55:27,860
+V يعني أنا بدي أجيب مضاعفات لوليو ثلاثة أمثال V
+
+487
+00:55:28,240 --> 00:55:33,480
+وأطلع اتنين من بعض يعني تلت عمليات بده يشتغل، مش
+
+488
+00:55:33,480 --> 00:55:37,900
+هي؟ مطلوب التاني يعتمد على الأول، مطلوب المتجه
+
+489
+00:55:37,900 --> 00:55:42,440
+اللي بطلع عندك بده تجيب قداش طول، مطلوب التاني،
+
+490
+00:55:42,440 --> 00:55:48,440
+اللي بدك تكتب المتجه اللي طالع عندك بدلالة الطول
+
+491
+00:55:48,440 --> 00:55:54,800
+تبعه والاتجاه، يعني كان طلب قداش متجه الواحدة في
+
+492
+00:55:54,800 --> 00:56:01,500
+هذا الاتجاه بطريقة خفيةنقدار واتجاه المطلوب الرابع
+
+493
+00:56:01,500 --> 00:56:07,840
+قال لي اه بدك تجيب vector طوله عشر وحدات طول في
+
+494
+00:56:07,840 --> 00:56:13,780
+اتجاه معاكس للاتجاه اللي انت جيبته و الله كويس
+
+495
+00:56:13,780 --> 00:56:17,240
+يعني شغل كتير بده هذه الشغلة لكن تعالى نشوف هل هو
+
+496
+00:56:17,240 --> 00:56:21,320
+كتير و الله يعني قال للمطلوب الأول هات الأثنين U
+
+497
+00:56:21,320 --> 00:56:26,230
+زائد تلاتة V هذه بسيطةيبدأ يضرب الأول في اتنين و
+
+498
+00:56:26,230 --> 00:56:30,090
+الثاني في ثلاثة و الظاهر على اتنين من بعض يبقى
+
+499
+00:56:30,090 --> 00:56:36,930
+باقي بقوله هنا اتنين U ناقص تلاتة V تساوي اذا انت
+
+500
+00:56:36,930 --> 00:56:41,470
+حاجة على ال U اضربها في قداش؟ في اتنين يبقى هاي
+
+501
+00:56:41,470 --> 00:56:51,350
+أربعة وهي Zero وهي ناقص ستة ناقص المتجه التانيأو
+
+502
+00:56:51,350 --> 00:56:56,490
+بقدر أكتب يا بناتي زائد و أدخل الناقص تلاتة جوا،
+
+503
+00:56:56,490 --> 00:57:02,410
+مظبوط؟ يعني بقدر الناقص هذه أكتبها زائد و اللي جوا
+
+504
+00:57:02,410 --> 00:57:07,470
+هنا أدره وين فناقص تلاتة، يبقى zero و هنا ناقص
+
+505
+00:57:07,470 --> 00:57:13,190
+تلاتة و هنا زائد ستة بالشكل اللي عنهايبقى هذا
+
+506
+00:57:13,190 --> 00:57:17,930
+الكلام بده يساوي أربعة و Zero له بأربعة Zero سالف
+
+507
+00:57:17,930 --> 00:57:22,610
+تلاتة Zero سالف تلاتة و هنا Zero يبقى جبتله
+
+508
+00:57:22,610 --> 00:57:26,390
+المطلوب الأول يقولني عليها تلاتة عمليات بسهولة
+
+509
+00:57:26,390 --> 00:57:33,770
+بخطوة واحدة طيب، بدأي إلى نمربيه، نمربيه قال لي
+
+510
+00:57:33,770 --> 00:57:39,120
+قداش طول المتجه هذاإذا هايو حصلت عليه إذا باجي
+
+511
+00:57:39,120 --> 00:57:45,640
+بقوله طول المتجة اتنين يوم ناقص تلاتة بيه اللي هو
+
+512
+00:57:45,640 --> 00:57:51,980
+ال square root للأربعة تربية زائد ناقص تلاتة لكل
+
+513
+00:57:51,980 --> 00:57:57,160
+تربية زائد zero تربية لو زاد التربية ستات و تسعة و
+
+514
+00:57:57,160 --> 00:58:05,020
+خمسة و عشرين يبقى الجواب يساوي خمس نمرسينمرسي
+
+515
+00:58:05,020 --> 00:58:12,260
+بيقول لي اكتب المتجه كحاصل ضرب الطول تبعه في ال
+
+516
+00:58:12,260 --> 00:58:18,160
+direction الطول اظن حصلت عليه هي و جايه الخمسة
+
+517
+00:58:18,160 --> 00:58:27,420
+يبقاش ضال عندي ال direction يعني ال direction of
+
+518
+00:58:27,420 --> 00:58:39,980
+v is the unit unitالـ vector is the unit vector in
+
+519
+00:58:39,980 --> 00:58:46,720
+the direction of
+
+520
+00:58:46,720 --> 00:58:55,640
+V that is I N ال V على طول أو مستحيل أقول ال V على
+
+521
+00:58:55,640 --> 00:58:56,340
+طول ال V
+
+522
+00:59:19,890 --> 00:59:27,710
+يبقى هنا w و هنا w يبقى بالدرجة اقول in the
+
+523
+00:59:27,710 --> 00:59:34,940
+direction of w that is اللي هو mainالـ W على طول
+
+524
+00:59:34,940 --> 00:59:42,900
+الـ W الـ W اللي هو جداش اتنين الـ W اللي هو عندي
+
+525
+00:59:42,900 --> 00:59:48,400
+على طول الخط اللي طالع فوق اللي هو أربعة وسالب
+
+526
+00:59:48,400 --> 00:59:55,120
+تلاتة و Zero على جداش على خمسة اللي هو بده يساوي
+
+527
+00:59:55,120 --> 01:00:00,780
+أربعة أخمس سالب تلت أخمس و Zero
+
+528
+01:00:03,710 --> 01:00:09,490
+هو بالسؤال هو هل هذا يا ترى فعلا unit vector تعالى
+
+529
+01:00:09,490 --> 01:00:18,610
+ربعي 16 على 25 زائد 9 على 25 زائد 0 25 على 25
+
+530
+01:00:18,610 --> 01:00:24,990
+مقداش يبقى فعلا هذا هو unit vector بناء عليه بقدر
+
+531
+01:00:24,990 --> 01:00:32,830
+أقوله لإتنين يون ناقص تلاتة V بده يسامر قوله مقداش
+
+532
+01:00:33,020 --> 01:00:41,740
+خمسة و ال unit vector تبعه في main في أربع أخماس
+
+533
+01:00:41,740 --> 01:00:49,640
+سالب تلت أخماس و كذلك zero بهذا الشكل يبقى هذا ال
+
+534
+01:00:49,640 --> 01:00:57,680
+length و هذا main ال direction يبقى
+
+535
+01:00:57,680 --> 01:01:03,120
+هذا المقدرات جيدا انتهينامن المطلوب برقم C كتبنا
+
+536
+01:01:03,120 --> 01:01:08,180
+ال vector 2U-3C as a product of length and
+
+537
+01:01:08,180 --> 01:01:18,540
+direction هاتبي متجه طوله عشرة في عكس اتجاه 2U-3V
+
+538
+01:01:18,540 --> 01:01:27,540
+ال unit vector في اتجاه 2U-3V
+
+539
+01:01:30,830 --> 01:01:35,630
+مظبوط؟ يعني هذا هو ال unit vector عكسه بدي أحط
+
+540
+01:01:35,630 --> 01:01:42,110
+إشارة سالم جده عشر مرات بدي أضرب في عشر تمام؟ يبقى
+
+541
+01:01:42,110 --> 01:01:53,970
+باجي بقول هنا the .. نمر دي the unit vector in the
+
+542
+01:01:53,970 --> 01:02:00,290
+direction .. in the opposite direction in the ..
+
+543
+01:02:00,800 --> 01:02:07,960
+opposite direction of
+
+544
+01:02:07,960 --> 01:02:21,950
+اتنين يو ناقص تلاتة في الـ z اللي هونقص أربع أخماس
+
+545
+01:02:21,950 --> 01:02:29,090
+و تلت أخماس يبقى الأن نجي للمطلوب الرابع والأخير
+
+546
+01:02:29,090 --> 01:02:32,090
+هو ال vector of length عشرة in the opposite
+
+547
+01:02:32,090 --> 01:02:36,750
+direction of اتنين يو ناقص تلت أمين عكس هذا
+
+548
+01:02:36,750 --> 01:02:39,650
+الاتجاه هو المتجه اللي قدامنا هذا اللي هو المتجه
+
+549
+01:02:39,650 --> 01:02:44,800
+الواحدة هذا يبقى بدأ أضرب أثوين في عشرةيبقى الآن
+
+550
+01:02:44,800 --> 01:02:54,080
+عشرة في ناقص أربع أخماس و تلت أخماس و Zero و اللي
+
+551
+01:02:54,080 --> 01:02:58,860
+هو بده يساوي متنهج جديد هدخل عشر على كل component
+
+552
+01:02:58,860 --> 01:03:03,360
+من هذه ال components يبقى هنا إيش بيصير تمانية
+
+553
+01:03:03,360 --> 01:03:08,040
+عشرة على خمسة تانية اتنية و المركبة التانية بيصير
+
+554
+01:03:08,040 --> 01:03:08,740
+ستة
+
+555
+01:03:11,290 --> 01:03:15,950
+يبقى يا إخلاص و الكلام للسامعين لو حبنا نجيب طول
+
+556
+01:03:15,950 --> 01:03:19,510
+هذا ال vector بنقول الجدر التربية إلى سلب تمانية
+
+557
+01:03:19,510 --> 01:03:24,950
+تربية لأربعة و ستين زائد ستة تربية لستة و تلاتين
+
+558
+01:03:24,950 --> 01:03:29,210
+زائد زيرول هو مية، جداش جدر المية؟ بعشرة و هو
+
+559
+01:03:29,210 --> 01:03:36,660
+المطلوب، يبقى هذا يثبت صحة ما ذكرناه قبل قليلحظي
+
+560
+01:03:36,660 --> 01:03:39,880
+الهي استفسار هنا في هذا المثال قبل أن نذهب إلى
+
+561
+01:03:39,880 --> 01:03:46,400
+المثال الثاني طيب الآن نمسح هذا المثال ونروح
+
+562
+01:03:46,400 --> 01:03:51,600
+للمثال رقم 2 على هذا الموضوع
+
+563
+01:04:17,320 --> 01:04:28,440
+بنجي لـ Example 2 بقول
+
+564
+01:04:28,440 --> 01:04:32,880
+F المتجه
+
+565
+01:04:32,880 --> 01:04:44,880
+A B يجب أن يسوى ناقص 7I زائد 3J زائد 8K and
+
+566
+01:04:46,720 --> 01:04:56,900
+الـ A is the point هي عبارة عن النقطة اللي هو ناقص
+
+567
+01:04:56,900 --> 01:05:09,080
+اتنين وناقص ثلاثة وستة find the point B
+
+568
+01:05:19,500 --> 01:05:26,120
+نرجع لسؤالنا مرة ثانية ميعطيني متجه a,b ناقص 7i
+
+569
+01:05:26,120 --> 01:05:32,780
+زائد 3j زائد 8k وميعطيني إحداثيات النقطة a وطلب
+
+570
+01:05:32,780 --> 01:05:39,700
+مني قداش إحداثيات النقطة b بقوله كويس المتجه هذا
+
+571
+01:05:39,700 --> 01:05:44,100
+هو عبارة عن المتجه التالف
+
+572
+01:05:47,130 --> 01:05:53,450
+هذه النقطة A على سبيل المثال هي ما طال هي ناقص
+
+573
+01:05:53,450 --> 01:06:01,310
+اتنين وناقص تلاتة وستة وهذه النقطة B اللي مش
+
+574
+01:06:01,310 --> 01:06:07,690
+عارفينها تمام؟ إذا لو حطيتيلها رموز وليكن على سبيل
+
+575
+01:06:07,690 --> 01:06:13,150
+المثال X Y و Z إذن
+
+576
+01:06:13,550 --> 01:06:17,630
+بدي أكوّن المتجه اللي عندي و أسويه بالمتجه هذا
+
+577
+01:06:17,630 --> 01:06:23,890
+يبقى بناء عليها بيكون المتجه عندي a,b هو المتجه
+
+578
+01:06:23,890 --> 01:06:30,910
+التالي الماضي و ناقص سبعة i زائد تلاتة j زائد
+
+579
+01:06:30,910 --> 01:06:40,490
+تمانية k بده 7 على الرسم يبقى x زائد 2 في اتجاه ال
+
+580
+01:06:40,490 --> 01:06:50,100
+Iزائد Y زائد 3 في اتجاه ال J زائد Z نقص 6 في اتجاه
+
+581
+01:06:50,100 --> 01:06:56,780
+ال K هذول المتجهين متساويين أخدنا قبل قليل متجهين
+
+582
+01:06:56,780 --> 01:07:02,500
+متساويين إذا كانت المركبات المتناظرة متساوية بناء
+
+583
+01:07:02,500 --> 01:07:09,080
+عليهبصير عندي x زائد اتنين يساوي ناقص سبعة هذا بده
+
+584
+01:07:09,080 --> 01:07:16,140
+يعطيك ان x يساوي قداش ناقص تسعة بعدها y زائد تلاتة
+
+585
+01:07:16,140 --> 01:07:22,060
+بده يساوي قداش اللي هو تلاتة هذا معناه ان y تساوي
+
+586
+01:07:22,060 --> 01:07:30,160
+قداش zeroاللي بعدها z ناقص ستة بده ساوي تمانية هذا
+
+587
+01:07:30,160 --> 01:07:37,840
+معناته ان z تساوي 14 من هذا الكلام بدرست انتج ان
+
+588
+01:07:37,840 --> 01:07:46,020
+ال point بي از الاحدات الاول لها ناقص تسعة الاحدات
+
+589
+01:07:46,020 --> 01:07:51,340
+التانية زيرو الاحدات التالتة اللي همين اربعتاش و
+
+590
+01:07:51,340 --> 01:07:59,820
+هكذانجي لبعض الخواص على ال vector يبقى بالدالي ان
+
+591
+01:07:59,820 --> 01:08:13,720
+ال properties of vector operations بعض
+
+592
+01:08:13,720 --> 01:08:19,820
+الخواص البسيطة على العمليات على ال vector نجي بقول
+
+593
+01:08:19,820 --> 01:08:30,590
+Fالـ U و الـ V و الـ W are vectors and
+
+594
+01:08:30,590 --> 01:08:42,230
+الـ A و الـ B are scalars يبقى كميات قياسية ذاتية
+
+595
+01:08:42,230 --> 01:08:51,560
+النقطة الأولى الـ U زائد الـ V بدها ساوي Vزائد الـ
+
+596
+01:08:51,560 --> 01:09:00,680
+U النقطة الثانية الـ U زائد ال V زائد ال W بدها
+
+597
+01:09:00,680 --> 01:09:09,000
+تساوي ال U زائد ال V زائد ال W النقطة التالتة الـ
+
+598
+01:09:09,000 --> 01:09:19,460
+U زائد ال Zero بدها تساوي ال U النقطة الرابعة الـ
+
+599
+01:09:19,460 --> 01:09:29,700
+Uزائر نقص اليوم بدها تساوي zero النقطة الخامسة ال
+
+600
+01:09:29,700 --> 01:09:37,820
+zero في اليوم بده يساوي ال zero النقطة
+
+601
+01:09:37,820 --> 01:09:44,360
+السادسة ال واحد مضروب في اليوم بده يساوي ال you
+
+602
+01:09:44,360 --> 01:09:54,910
+السابع ال aأضربها في الـ B في الـ U بده ساوي الـ A
+
+603
+01:09:54,910 --> 01:10:06,050
+B في الـ U التامنة الـ A في الـ U زائد الـ V بده
+
+604
+01:10:06,050 --> 01:10:14,410
+تساوي A في الـ U زائد A في الـ V التاسعة
+
+605
+01:10:14,410 --> 01:10:22,950
+والأخيرة اللي هو الـ Aزائد ال B في ال U بده يساوي
+
+606
+01:10:22,950 --> 01:10:43,550
+A في ال U زائد B في ال U بدي
+
+607
+01:10:43,550 --> 01:10:50,350
+أحاول أرجع الأن لمعنىكل خاصية من هذه القواسم حتى
+
+608
+01:10:50,350 --> 01:10:58,550
+نفهم فهما صحيحا مش اكتب وامشي شوف يا بنات الان
+
+609
+01:10:58,550 --> 01:11:02,670
+بيقول لو عندي تلاتة vectors ال U و ال V و ال W
+
+610
+01:11:02,670 --> 01:11:09,670
+وعندي two scalars A و B يبقى في عندي U زائد ال V
+
+611
+01:11:09,670 --> 01:11:15,650
+تساوي V زائد ال U ايش العملية هذه بالابدالية؟يبقى
+
+612
+01:11:15,650 --> 01:11:25,950
+عملية الجمع عن المتجهات عملية إبدالية الـ positive
+
+613
+01:11:25,950 --> 01:11:31,690
+of two vectors is a commutative operation عملية
+
+614
+01:11:31,690 --> 01:11:38,330
+الجمع عن ال vectors عملية إبداليةلو جمعت ال U و ال
+
+615
+01:11:38,330 --> 01:11:45,110
+V أولا و أضفت الناتج لل W تماما كما لو جمعت ال V و
+
+616
+01:11:45,110 --> 01:11:49,650
+ال W أولا ثم أضفت لهم من ال U يبقى هذه بسميها
+
+617
+01:11:49,650 --> 01:11:56,910
+associative عملية إدماجية أو تجميعية associative
+
+618
+01:11:56,910 --> 01:11:57,510
+property
+
+619
+01:12:03,540 --> 01:12:07,020
+الزيرو هد يا بناتي scalar ولا vector؟
+
+620
+01:12:10,360 --> 01:12:16,400
+أحنا أخدنا عملية جمع vector مع scalar لأ أخدنا ضرب
+
+621
+01:12:16,400 --> 01:12:20,620
+scalar في vector لكن جماعة لأ يبقى ال zero بعمله
+
+622
+01:12:20,620 --> 01:12:25,100
+طاول طويل بنات zero vector ال scalar بعمله دائرة
+
+623
+01:12:25,100 --> 01:12:32,040
+صغيرة يبقى هذا هو zero vector يبقى ال u vector زي
+
+624
+01:12:32,040 --> 01:12:39,050
+ال zero vector يسوى من ال u vectorهنا الـ U زائد
+
+625
+01:12:39,050 --> 01:12:45,370
+ناقص الـ U يعني المتجه والمتجه المعاكس إله تماماً
+
+626
+01:12:45,370 --> 01:12:51,010
+مجموع اتنين قداش؟ Zero scalar ولا vector؟ يعني
+
+627
+01:12:51,010 --> 01:12:54,550
+مجموع any two vectors بدي يعطيني vector حتى وإن
+
+628
+01:12:54,550 --> 01:12:59,470
+كان الـ zero يبقى هذا ال zero vector طيب ال zero
+
+629
+01:12:59,470 --> 01:13:05,540
+في U scalar ال zero هذا ولا vector؟ scalarلأن ضارب
+
+630
+01:13:05,540 --> 01:13:07,560
+ال vectors في أنمي العالم لا يوجد ضارب لا يوجد
+
+631
+01:13:07,560 --> 01:13:09,780
+ضارب لايوجد ضارب لايوجد ضارب لايوجد ضارب لايوجد
+
+632
+01:13:09,780 --> 01:13:15,920
+ضارب لايوجد ضارب لايوجد ضارب لايوجد ضارب لايوجد
+
+633
+01:13:15,920 --> 01:13:20,360
+ضارب لايوجد ضارب لايوجد ضارب لايوجد ضارب لايوجد
+
+634
+01:13:20,360 --> 01:13:20,360
+ضارب لايوجد ضارب لايوجد ضارب لايوجد ضارب لايوجد
+
+635
+01:13:20,360 --> 01:13:21,260
+ضارب لايوجد ضارب لايوجد ضارب لايوجد ضارب لايوجد
+
+636
+01:13:21,260 --> 01:13:28,880
+ضارب لايوجد ضارب لايوجد ضارب
+
+637
+01:13:28,880 --> 01:13:34,140
+لايوجد ضارب لايوجد ضارب لايوجد ضارب لايوجد ضارب
+
+638
+01:13:34,140 --> 01:13:36,870
+لايوجد ضارب لايوجد ضارب لادربت في الـ scalar B و
+
+639
+01:13:36,870 --> 01:13:41,550
+النتج دربت في الـ scalar A تماما كما لو دربت ال
+
+640
+01:13:41,550 --> 01:13:45,410
+two scalars بعضهم A و B في بعض و النتج دربته في
+
+641
+01:13:45,410 --> 01:13:49,640
+مين في مين فمثلا لو قلت لك اتنين يوموبعد ذلك
+
+642
+01:13:49,640 --> 01:13:53,920
+اتضارب تلاتة في اتنين U كما لو ضربت اتنين في تلاتة
+
+643
+01:13:53,920 --> 01:13:58,540
+ام ستة في U نفس النتيجة هنا ال A في U زائد V
+
+644
+01:13:58,540 --> 01:14:05,080
+Distributive Law قانون التوزيع يبقى هنا بدوزع ال A
+
+645
+01:14:05,080 --> 01:14:09,920
+على مجموع ال two vectors فبعدين بقول A U زائد A V
+
+646
+01:14:10,610 --> 01:14:16,370
+نمر 9 الـ A زائد B فلو الـ Distributive ما بين two
+
+647
+01:14:16,370 --> 01:14:22,570
+scalars مع ال vector V ب A U زائد B U و هكذا
+
+648
+01:14:22,570 --> 01:14:28,110
+بايلغن آخر definition في هذا ال section بيقول ما
+
+649
+01:14:28,110 --> 01:14:34,470
+يأتي definition ده
+
+650
+01:14:34,470 --> 01:14:36,930
+midpoint
+
+651
+01:14:38,790 --> 01:14:46,710
+نقطة المنتصف الـ midpoint حديها الرمز M of the
+
+652
+01:14:46,710 --> 01:14:58,610
+line segment the line segment joining
+
+653
+01:14:58,610 --> 01:15:08,720
+the points joining the pointsوالذي يجمع النقطتين
+
+654
+01:15:08,720 --> 01:15:27,560
+P1 of X1 و Y1 و Z1 and P2 of X2 و Y2 و Z2 as the
+
+655
+01:15:27,560 --> 01:15:38,730
+point هي عبارة عن النقطة MR X1 زائد X2 على 2 Y1
+
+656
+01:15:38,730 --> 01:15:50,210
+زائد Y2 على 2 Z1 زائد Z2 على 2 يعني
+
+657
+01:15:50,210 --> 01:15:56,610
+لو قلت هذه المحاور على سبيل المثال قلت هذا X وهذا
+
+658
+01:15:56,610 --> 01:16:04,440
+Y وهذا Z هذا نقطة الأصل اللي هو Zeroو رسمت نقطتين
+
+659
+01:16:04,440 --> 01:16:12,000
+و وصلت بينهم بخط مستقيم فجيت قول هذه النقطة الأولى
+
+660
+01:16:12,000 --> 01:16:27,580
+P1 X1 Y1 Z1 وهذه النقطة P2 X2 Y2 Z2 بين النقطة
+
+661
+01:16:27,580 --> 01:16:33,570
+المنقصرة فيما بينهميبقى نقطة المنتصف لو قلت هذه
+
+662
+01:16:33,570 --> 01:16:39,370
+اللي هي النقطة M يبقى
+
+663
+01:16:39,370 --> 01:16:45,090
+النقطة M بدأ تيجي في منتصف المسافة بين النقطتين
+
+664
+01:16:45,090 --> 01:16:50,930
+إحداث هذه النقطة هو الإحداث اللي احنا كاتبينه هنا
+
+665
+01:16:50,930 --> 01:16:55,630
+الأن نعطي مثال توضيحي على ذلك example
+
+666
+01:17:01,340 --> 01:17:08,100
+Example one اللي هو سؤال ستة وتلاتين من الكتاب
+
+667
+01:17:08,100 --> 01:17:18,520
+بيقولت P1 اللي هي عبارة عن واحد واربعة وخمسة and
+
+668
+01:17:18,520 --> 01:17:27,580
+P2 هي عبارة عن النقطة اربعة وناقص اتنين وسبعة
+
+669
+01:17:27,580 --> 01:17:40,270
+المطلوب الأول نمر ايه؟Find the direction of
+
+670
+01:17:40,270 --> 01:17:42,770
+P1,
+
+671
+01:17:43,370 --> 01:17:47,330
+P2 نمر
+
+672
+01:17:47,330 --> 01:17:50,830
+بـ Find the midpoint
+
+673
+01:17:57,570 --> 01:18:08,890
+نقطة المنصفة of the line segment P1 P2
+
+674
+01:18:43,530 --> 01:18:49,010
+سؤال مرة تانية قلت لي هاتلي ال direction تبع
+
+675
+01:18:49,010 --> 01:18:54,970
+المتجه P1 P2 إذا هو إيش قصد يقول ليهاتلي متجهي
+
+676
+01:18:54,970 --> 01:19:01,510
+الوحدة في اتجاه P1 P2 سواء صيغة الصيغة هذه أو
+
+677
+01:19:01,510 --> 01:19:06,090
+الصيغة هذه الأثنين أرزسين إذا أنا بدي أروح أجيب له
+
+678
+01:19:06,090 --> 01:19:14,240
+متجه P1 P2 يسار بدي أكتب دبري يا بناتيبقى هذا كأنه
+
+679
+01:19:14,240 --> 01:19:17,260
+يبدأ كتابة يابا كتابة دلالة الاتنين المقرنين
+
+680
+01:19:17,260 --> 01:19:20,680
+القوسين المقرنين اما دلالة ال I و ال J و ال K سيان
+
+681
+01:19:20,680 --> 01:19:26,700
+كل واحد اذا لو جاي تقول اربعة ناقص واحد في اتجاه
+
+682
+01:19:26,700 --> 01:19:33,340
+ال I زائد ال همين ناقص اتنين ناقص اربعة في اتجاه
+
+683
+01:19:33,340 --> 01:19:35,200
+ال J زائد
+
+684
+01:19:40,290 --> 01:19:47,810
+يبقى هذا عبارة عن تلاتة I وهنا ناقص ستة J وهنا
+
+685
+01:19:47,810 --> 01:19:56,990
+زائد اتنين K بدي اجيب قول تبعه قول ال P1 P2 اللي
+
+686
+01:19:56,990 --> 01:20:05,900
+هو بده يساوي جدر التربيع لتسعة زائد ستة وتلاتينزاد
+
+687
+01:20:05,900 --> 01:20:12,400
+اربع و يسوى انا ابعين و تسعة جو تسعة و اربعين تحت
+
+688
+01:20:12,400 --> 01:20:21,840
+الجدر الجدد سبعة يبقى باجي بقوله the direction of
+
+689
+01:20:21,840 --> 01:20:35,120
+P1 P2 Sاللي هو P1 P2 على طول ال P1 P2 واللي هو بده
+
+690
+01:20:35,120 --> 01:20:43,240
+7 كله على سبعة يبقى تلت أسباع في اتجاه ال I نقص ست
+
+691
+01:20:43,240 --> 01:20:50,480
+أسباع في اتجاه ال J زائد سبعين في اتجاه ال K نمرى
+
+692
+01:20:50,480 --> 01:20:57,030
+B قال لي هدل ال midpointما بين النقطتين الاتنين
+
+693
+01:20:57,030 --> 01:21:03,270
+هدول يبقى ال M تساوى مباشرة يبقى بده أجمع أربعة
+
+694
+01:21:03,270 --> 01:21:09,310
+زائد واحد على اتنين أربعة زائد واحد على اتنين اللي
+
+695
+01:21:09,310 --> 01:21:15,910
+بعدها ناقص اتنين زائد أربعة على اتنين
+
+696
+01:21:19,710 --> 01:21:26,650
+اللي بعدها سبعة زائد خمسة على اتنين سبعة زائد خمسة
+
+697
+01:21:26,650 --> 01:21:33,010
+كله على اتنين واللي هي بدها تساوي مين خمسة على
+
+698
+01:21:33,010 --> 01:21:38,810
+اتنين تبقى كما هي وهنا مضال اتنين على اتنين بواحد
+
+699
+01:21:38,810 --> 01:21:43,690
+واطن عشر على اتنين اللي هو بقداش ستة هذه النقطات
+
+700
+01:21:43,690 --> 01:21:50,960
+المتوسطة اخر مثال في محاضرة اليومبيقول ما يأتي له
+
+701
+01:21:50,960 --> 01:21:58,980
+سؤال 14 من الكتاب بيقول find a unit vector find
+
+702
+01:21:58,980 --> 01:22:13,660
+the unit vector that makes an angle that makes an
+
+703
+01:22:13,660 --> 01:22:16,080
+angle
+
+704
+01:22:19,550 --> 01:22:29,030
+فيتا تساوي السالف تلاتة y على أربع with the
+
+705
+01:22:29,030 --> 01:22:38,950
+positive with the positive اللي هو x أكسي x axis
+
+706
+01:23:00,440 --> 01:23:04,160
+خلّي بالك معانا هنا و الله شوية السؤال مرة تانية
+
+707
+01:23:04,160 --> 01:23:08,560
+جالي هاتلي متجه الوحدة اللي يصنع زاوية مقدارها
+
+708
+01:23:08,560 --> 01:23:15,200
+سالب تلاتة باي على أربع من اتجاه الموجب لمين لل X
+
+709
+01:23:15,200 --> 01:23:19,980
+axis الزاوية هذه زي ما انت شايفها زاوية سالبةواحنا
+
+710
+01:23:19,980 --> 01:23:23,840
+أخدنا في ال polar coordinates إنهم أول كلمتي
+
+711
+01:23:23,840 --> 01:23:27,260
+أخدناهم في ال polar coordinates ممكن الزاوية تكون
+
+712
+01:23:27,260 --> 01:23:32,460
+positive angle وممكن تكون negative angle إذا مشينا
+
+713
+01:23:32,460 --> 01:23:39,000
+counter clockwise ضد عقل الساعة وإذا مشينا مع عقل
+
+714
+01:23:39,000 --> 01:23:43,590
+الساعة فالزاوية مالها سالبةطب إذا إحنا لو روحنا
+
+715
+01:23:43,590 --> 01:23:49,750
+مشينا مع قريب الساعة أو لو جيت تصورت إنه في دائرة
+
+716
+01:23:49,750 --> 01:23:54,630
+عندي نصف قطر هيساوي الواحد الصحيح يبقى الدائرة
+
+717
+01:23:54,630 --> 01:24:10,310
+هتاخد الشكل التالي الشكل اللي عندنا هذا تمام؟
+
+718
+01:24:10,650 --> 01:24:17,290
+يبقى هذه الدرجة طب بتدامش قداش 135 درجة بس وين
+
+719
+01:24:17,290 --> 01:24:24,110
+بالسالح يبقى هذه 90 مع قارب الساعة هذه 90 و بدي
+
+720
+01:24:24,110 --> 01:24:30,970
+كمان 45 يبقى بالدرجين الخاطة اللي عندنا تمام يبقى
+
+721
+01:24:30,970 --> 01:24:39,790
+الزاوية هذه سالف تلاتة بال على أربع طيب
+
+722
+01:24:40,640 --> 01:24:45,880
+لو جيت اعتبرت أن هذا متجه وطوله يساوي الواحد
+
+723
+01:24:45,880 --> 01:24:51,000
+الصحيح إذا إيه مركب في اتجاه محور X وإيه مركب في
+
+724
+01:24:51,000 --> 01:24:57,440
+اتجاه محور Y؟ يعني لو اعتبرت أن هذا متجه وطوله
+
+725
+01:24:57,440 --> 01:25:01,760
+واحد صحيح، لماذا؟ لأنه قال لي هذه اليونة Vector،
+
+726
+01:25:01,760 --> 01:25:08,200
+تمام؟ إذا بناء عليهبدي يكون ال unit vector u بدي
+
+727
+01:25:08,200 --> 01:25:14,580
+يساوي واحد في cosine اللي هو سالب تلاتة باية على
+
+728
+01:25:14,580 --> 01:25:21,120
+أربعة في اتجاه ال I زائد واحد sin تلاتة باية على
+
+729
+01:25:21,120 --> 01:25:27,940
+أربعة، مين السالب؟ سالب في اتجاه مين؟ في اتجاه ال
+
+730
+01:25:27,940 --> 01:25:34,970
+G okay ماعنديش طيب، هذا الكلام بدي يساويالـ cosine
+
+731
+01:25:34,970 --> 01:25:40,250
+even والله odd يبقى السلف هذا معه السلامة يبقاش
+
+732
+01:25:40,250 --> 01:25:46,150
+بصير هنا cosine تلاتة by على أربعة في اتجاه ال I
+
+733
+01:25:46,150 --> 01:25:54,270
+زائد ال sine، odd يبقى السلف أطلع برا، ال sine له
+
+734
+01:25:54,270 --> 01:26:00,540
+تلاتة by على أربعة في اتجاه ال Gنجي لجيب تمام
+
+735
+01:26:00,540 --> 01:26:07,240
+الزاوية اللي 135 درجة جيب تمام أي زاوية ساوية جيب
+
+736
+01:26:07,240 --> 01:26:11,660
+تمام الزاوية المكملة لها معبرعات قاعدة الإشارات
+
+737
+01:26:11,660 --> 01:26:20,380
+جتل 135 هي جتل 45 جتل 45 بواحد على جذر اتنين بس
+
+738
+01:26:20,380 --> 01:26:23,420
+هذه في الربع التاني في الربع التاني بالسالب
+
+739
+01:26:23,420 --> 01:26:28,700
+بالسالب لإنه درسوكوا ال formula وحفظوكواهذه
+
+740
+01:26:28,700 --> 01:26:36,700
+الأنشودة في التانوية كل جاية غالب جاتوا جاهية وانا
+
+741
+01:26:36,700 --> 01:26:40,300
+جات في اللي إيه تمام؟ ال English و الأمريكان عندهم
+
+742
+01:26:40,300 --> 01:26:48,000
+صيغة مناظرة All students learn calculus كل الطلاب
+
+743
+01:26:48,000 --> 01:26:51,000
+في العلم و الهندسة و التدريب و التكنولوجيا
+
+744
+01:26:51,000 --> 01:26:54,660
+المعلومات بياخدوا تفضل و تكامل يبقى all في الرابع
+
+745
+01:26:54,660 --> 01:26:59,440
+الأول كل موجةstudents الحرف الأول مكلمة sign يعني
+
+746
+01:26:59,440 --> 01:27:07,080
+ال j ترك الحرف الأول مكلمة تان اللي هو غلط ترك
+
+747
+01:27:07,080 --> 01:27:11,720
+كاركورس الحرف الأول منه sign يبقى من هنا بقول هذه
+
+748
+01:27:11,720 --> 01:27:17,300
+فالربع اللي هو الثاني يبقى بالسالب يبقى سالب واحد
+
+749
+01:27:17,300 --> 01:27:23,420
+على جدر اتنينفي اتجاه الـ I وهذه ناقص وهذه في
+
+750
+01:27:23,420 --> 01:27:27,160
+الربع الثاني والـ J في الربع التاني موجب جيب
+
+751
+01:27:27,160 --> 01:27:32,220
+الخمسة واربعين كذلك بواحد على جدر اتنين في اتجاه
+
+752
+01:27:32,220 --> 01:27:40,140
+الـ G طب السؤال هل هذا فعلا unit vector؟ كيف لا؟
+
+753
+01:27:40,140 --> 01:27:44,140
+على ربع كل واحدة فيه فهذه بواحدة على جدر اتنين
+
+754
+01:27:44,140 --> 01:27:46,280
+وربعها بالنص زائد نص
+
+755
+01:27:49,220 --> 01:27:54,440
+يبقى هاي اللي طلعه unit vector في .. that makes
+
+756
+01:27:54,440 --> 01:27:59,080
+اللي عامله زاوية 145 مع الاتجاه الموجب لمح وراكز
+
+757
+01:27:59,080 --> 01:28:03,600
+لحد هنا stop انتهاء ال section إلى يكون أرقام
+
+758
+01:28:03,600 --> 01:28:09,420
+المسائل المطلوب حلها في البيت ان شاء الله يبقى
+
+759
+01:28:09,420 --> 01:28:20,150
+exercises أتناش اتنين واحد تلاتة خمسة سبعةأحد عشر
+
+760
+01:28:20,150 --> 01:28:29,550
+تلتاش سبعتاش تسعة عشر واحد وعشرين خمسة وعشرين سبعة
+
+761
+01:28:29,550 --> 01:28:37,890
+وعشرين خمسة وعشرين سبعة وعشرين تسعة وعشرين واحد
+
+762
+01:28:37,890 --> 01:28:44,450
+وتلاتين تلاتة وتلاتين خمسة وتلاتين سبعة وتلاتين
+
+763
+01:28:44,450 --> 01:28:46,270
+تسعة وتلاتين
+
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/vNBEf-x0cGk.srt b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/vNBEf-x0cGk.srt
new file mode 100644
index 0000000000000000000000000000000000000000..7cf78f182825b50bdb377cdbe68b248ba9441f81
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/vNBEf-x0cGk.srt
@@ -0,0 +1,2842 @@
+1
+00:00:15,420 --> 00:00:20,910
+بسم الله الرحمن الرحيم، الآن نكمل الـ section الذي 
+
+2
+00:00:20,910 --> 00:00:25,550
+بدأنَاهُ المرة الماضية،  منهُ الذي كان، وهو tangent
+
+3
+00:00:25,550 --> 00:00:29,430
+planes and differential. طبعاً عرفنا المرة التي فاتت
+
+4
+00:00:29,430 --> 00:00:33,950
+tangent plane، وقلنا المعادلة بتاعتُه هي المستوية
+
+5
+00:00:33,950 --> 00:00:38,620
+المستوية بالنسبة لـ F أو بالنسبة لـ X عند النقطة X<sub>0</sub>
+
+6
+00:00:38,620 --> 00:00:43,880
+و Y<sub>0</sub> في X - X<sub>0</sub> زائد المشتقة عندها نفس
+
+7
+00:00:43,880 --> 00:00:48,940
+النقطة في Y - Y<sub>0</sub> زائد مشتقة F بالنسبة لـ Z عند
+
+8
+00:00:48,940 --> 00:00:53,860
+نفس النقطة في Z - Z<sub>0</sub> يساوي صفر، ومن هنا
+
+9
+00:00:53,860 --> 00:00:55,220
+روحنا، وطلعنا كمان من
+
+10
+00:01:02,140 --> 00:01:07,020
+هذه النقطة هي حالة خاصة من الحالة الماضية، تابعة
+
+11
+00:01:07,020 --> 00:01:11,000
+للمرة الماضية.
+
+12
+00:01:11,000 --> 00:01:11,300
+(repeated phrase removed)
+
+13
+00:01:11,300 --> 00:01:11,520
+(repeated phrase removed)
+
+14
+00:01:11,520 --> 00:01:13,260
+(repeated phrase removed)
+
+15
+00:01:13,260 --> 00:01:14,480
+(repeated phrase removed)
+
+16
+00:01:14,480 --> 00:01:15,380
+(repeated phrase removed)
+
+17
+00:01:15,380 --> 00:01:16,880
+(repeated phrase removed)
+
+18
+00:01:16,880 --> 00:01:20,120
+للمرة الماضية، تابعة المرة الماضية. إذن، إحنا
+
+19
+00:01:20,120 --> 00:01:26,260
+عندنا surface حيث z دالة  f  لـ x و y، بدي
+
+20
+00:01:26,260 --> 00:01:31,120
+أحاول من خلال هذا الـ surface الوصول إلى معادلة
+
+21
+00:01:31,120 --> 00:01:35,540
+مشابهة للمعادلة التي كنا أثبتناها المرة الماضية، مع
+
+22
+00:01:35,540 --> 00:01:40,100
+فارق بسيط جداً. الآن بدنا نشوف ما هو هذا الفارق
+
+23
+00:01:40,100 --> 00:01:46,460
+البسيط. لنوجد معادلة للـ plane الذي يكون مماثلاً
+
+24
+00:01:46,460 --> 00:01:53,960
+للسطح z = f(x, y) عند النقطة P<sub>0</sub> (x<sub>0</sub>, y<sub>0</sub>, z<sub>0</sub>). الـ
+
+25
+00:01:53,960 --> 00:01:58,520
+right f(x, y) - z = صفر. يعني
+
+26
+00:01:58,520 --> 00:02:02,080
+المعادلة هذه، هنجيب z وين؟ على الجهة الثانية، بس
+
+27
+00:02:02,080 --> 00:02:06,040
+ينبغي بشَكلٍ مخالف. فـ f(x, y) - z = صفر.
+
+28
+00:02:06,040 --> 00:02:09,920
+صفر. المعادلة التي عندنا، هذا الطرف الأيسر صار
+
+29
+00:02:09,920 --> 00:02:11,040
+function في
+
+30
+00:02:39,830 --> 00:02:44,800
+في ثلاثة متغيرات. إذن، كأنه أنا عندي دالة جديدة
+
+31
+00:02:44,800 --> 00:02:52,800
+سميتها F(X, Y, Z). بدأتُ بـ F(X, Y)
+
+32
+00:02:52,800 --> 00:02:57,580
+نقصدها كأنها هذه الدالة الأصلية، ولما سويتها بـ
+
+33
+00:02:57,580 --> 00:03:04,820
+صفر، كان هذا هو zero level surface بالنسبة لها. الآن
+
+34
+00:03:04,820 --> 00:03:10,420
+بنجيب الـ equation للـ tangent لهذا الـ level surface، بقول
+
+35
+00:03:10,420 --> 00:03:14,200
+بسيطة جداً، نشتقّ الدالة بالنسبة لـ X، بالنسبة
+
+36
+00:03:14,200 --> 00:03:19,620
+لـ Y، وبالنسبة لـ Z، ونعوّض في معادلة المرة الماضية.
+
+37
+00:03:19,620 --> 00:03:24,760
+يبقى بدلاً من F<sub>x</sub>، يعني بدي اشتغل الدالة
+
+38
+00:03:24,760 --> 00:03:32,420
+الجديدة بالنسبة لـ X. هذه المشتقة، دلالياً على اليمين
+
+39
+00:03:32,420 --> 00:03:37,440
+بالنسبة لهذه الـ function في x و y، يبقى مشتقتها بتكون
+
+40
+00:03:37,440 --> 00:03:45,840
+f (أف صغيرة)، تمام. والـ z يبقى كم؟ صفر. يبقى ناقص صفر.
+
+41
+00:03:45,840 --> 00:03:51,540
+يبقى تصبح المشتقة بتاعة F(x, y) هي نفس
+
+42
+00:03:51,540 --> 00:03:56,470
+المشتقة بتاعة الـ function التي عندنا. In
+
+43
+00:03:56,470 --> 00:04:03,310
+general، بدي أقول بدي أجيب f<sub>x</sub> عند النقطة x<sub>0</sub> و
+
+44
+00:04:03,310 --> 00:04:09,730
+y<sub>0</sub> و z<sub>0</sub>. هذا الكلام، بدي أسوي f<sub>x</sub> عند النقطة
+
+45
+00:04:09,730 --> 00:04:18,270
+x<sub>0</sub> و y<sub>0</sub> و z<sub>0</sub>. طيب، بدي أجيب f<sub>y</sub>. هذا
+
+46
+00:04:18,270 --> 00:04:23,200
+الكلام، بدي أسوي. وباختصار، بدي أخليها نفس عند
+
+47
+00:04:23,200 --> 00:04:27,840
+النقطة x<sub>0</sub> و y<sub>0</sub> و z<sub>0</sub>. معناته، بدل ما اشتقّ
+
+48
+00:04:27,840 --> 00:04:32,020
+دالة، لأن هذه بالنسبة لمين؟ لو z، يبقى مشتقة الـ z
+
+49
+00:04:32,020 --> 00:04:38,120
+صفر. يبقى هذه، يبقى تساوي f<sub>x</sub> عند النقطة f<sub>y</sub>
+
+50
+00:04:38,120 --> 00:04:44,960
+عند النقطة x<sub>0</sub> و y<sub>0</sub> و z<sub>0</sub> ناقص الصفر. طيب،
+
+51
+00:04:44,960 --> 00:04:47,100
+كويس.  بدأ نروح نجيب F<sub>z</sub>
+
+52
+00:04:49,850 --> 00:04:54,890
+عند النقطة التي هي x<sub>0</sub> و y<sub>0</sub> و z<sub>0</sub>، يبقى
+
+53
+00:04:54,890 --> 00:04:59,010
+هذا السبب بده صفر. طبعاً، هذه كلها في x و y،
+
+54
+00:04:59,010 --> 00:05:02,750
+ونحن نشتقّ بالنسبة لـ z، يبقى مشتقتها بصفر.
+
+55
+00:05:22,200 --> 00:05:29,500
+هل اختلفت F<sub>x</sub> عن F<sub>x</sub> الماضية؟ يبقى زي ما هي.
+
+56
+00:05:44,450 --> 00:05:49,790
+عند الـ x<sub>0</sub> والـ y<sub>0</sub> والـ z<sub>0</sub> في  مين؟ في الـ y
+
+57
+00:05:49,790 --> 00:05:54,590
+ناقص y<sub>0</sub>. نجي للـ z، اللي يبقى كده هنا؟
+
+58
+00:05:54,590 --> 00:06:02,050
+بواحد. يبقى هنا  هاي سالب واحد في مين؟ في z - z
+
+59
+00:06:02,050 --> 00:06:09,230
+<sub>0</sub>. كل هذا الكلام بده يساوي صفر. إذن، الفرق البسيط
+
+60
+00:06:09,230 --> 00:06:15,430
+بين هذه المعادلة ومعادلة المرة الماضية أن الـ F<sub>z</sub>
+
+61
+00:06:15,430 --> 00:06:20,170
+عنها طلعت بقد إيش؟ بسالب واحد. وهذا هو الفرق بين
+
+62
+00:06:20,170 --> 00:06:26,410
+المعادلة هذه ومعادلة المرة الماضية. كإني وليّ خاطر
+
+63
+00:06:26,410 --> 00:06:32,630
+أسألك هكذا: هذه
+
+64
+00:06:32,630 --> 00:06:36,450
+سالب واحد صحيح، وهي سالب واحد موجود. تمام، صحيح.
+
+65
+00:06:40,000 --> 00:06:44,720
+طبعاً، المدرّس الناجح الذي يكون لديه حسٌّ بِطلابه، يعني
+
+66
+00:06:44,720 --> 00:06:48,460
+بدي أحس أنه شو اللي بيفهمه وشو اللي ما بيفهموش، و
+
+67
+00:06:48,460 --> 00:06:51,500
+أنا من النوع الذي يقرأ هذا في وجوه الطلاب الذين
+
+68
+00:06:51,500 --> 00:06:55,040
+أنا أُدرّسهم، يعني إذا في شغلة مش واضحة، بقرأها في
+
+69
+00:06:55,040 --> 00:07:00,300
+وجههم. تمام. لذلك، الطالب بعرف متابعني، مش متابعني،
+
+70
+00:07:00,300 --> 00:07:03,080
+فاهم، مش فاهم، من خلال المحاضرة، حتى لو كانت القاعة
+
+71
+00:07:03,080 --> 00:07:06,080
+فيها مئة طالبة، واحد واحد، المئة والعشرين
+
+72
+00:07:06,080 --> 00:07:09,500
+بالنسبة لي سهل، لأنّي متعود على اللي هو العدد
+
+73
+00:07:09,500 --> 00:07:12,520
+الكبير أو العدد الصغير، ما تفرقش عندي بالنسبة لي،
+
+74
+00:07:12,520 --> 00:07:19,140
+فلذلك بتلاقيني دقيق الملاحظة في هذه الأمور. نبدأ
+
+75
+00:07:19,140 --> 00:07:21,220
+بأخذ مثال على ذلك، example.
+
+76
+00:07:28,520 --> 00:07:37,860
+يقول: الـ final equation، five and equation for the
+
+77
+00:07:37,860 --> 00:07:41,900
+plane that
+
+78
+00:07:41,900 --> 00:07:45,900
+is tangent
+
+79
+00:07:45,900 --> 00:07:47,240
+to the surface
+
+80
+00:07:58,100 --> 00:08:08,300
+والذي يكون هو مثل سطح Z تساوي لـ X
+
+81
+00:08:08,300 --> 00:08:15,460
+ناقص اثنين Y، at the
+
+82
+00:08:15,460 --> 00:08:16,120
+point
+
+83
+00:08:31,820 --> 00:08:36,420
+السؤال مرة ثانية، بيقول: هذه معادلة المستوى الذي
+
+84
+00:08:36,420 --> 00:08:42,340
+يكون ممثلاً في سطح z تساوي لـ x ناقص اثنين y عند
+
+85
+00:08:42,340 --> 00:08:47,940
+النقطة (3, 1, 1). لو جئتُ نظرتُ لهذه المعادلة،
+
+86
+00:08:47,940 --> 00:08:54,290
+ألاحظ أن z  ممثلة كـ function تمام، في المتغيرين x و y.
+
+87
+00:08:54,290 --> 00:09:01,590
+إذن، أنا بقدر أكتب هذه المعادلة بطريقة أخرى. لو نقلتُ
+
+88
+00:09:01,590 --> 00:09:08,840
+الـ z على الجهة الثانية. لو جئت كتبت أن الـ F أو الـ
+
+89
+00:09:08,840 --> 00:09:21,140
+x - 2y - z بدها تساوي صفر. يبقى حصلت
+
+90
+00:09:21,140 --> 00:09:25,060
+على معادلة جديدة. الطرف الأيسر صار function في
+
+91
+00:09:25,060 --> 00:09:30,400
+ثلاثة متغيرات، اللي هي x و y و z. يبقى بناءً على
+
+92
+00:09:30,400 --> 00:09:33,300
+عليها هذا الكلام، دي تساوي كونستانْت، و إذن هذا
+
+93
+00:09:33,300 --> 00:09:44,800
+يمثل level surface لدالة ما. يبقى this is a أو this
+
+94
+00:09:44,800 --> 00:09:55,980
+is the zero level surface for
+
+95
+00:10:13,770 --> 00:10:23,050
+F<sub>x</sub>، يبقى F<sub>x</sub> نشتقّ واحد على اللي داخل القوس بالنسبة لـ X
+
+96
+00:10:23,050 --> 00:10:29,110
+ناقص اثنين Y. فمشتقة ما داخل القوس بالنسبة لـ X
+
+97
+00:10:29,110 --> 00:10:35,850
+اللي هو بواحد. صحيح. بدنا نروح نحسب قد إيش الـ F<sub>x</sub> عند
+
+98
+00:10:35,850 --> 00:10:42,200
+النقطة المعطاة (3, 1, 0). بدل ما نعملها، نشيل كل X
+
+99
+00:10:42,200 --> 00:10:46,820
+ونحط مكانه ثلاثة، ونشيل كل Y ونحط مكانه واحد، ويصير
+
+100
+00:10:46,820 --> 00:10:53,390
+واحد على ثلاثة ناقص اثنين، ويساوي واحد. بنروح نجيب
+
+101
+00:10:53,390 --> 00:11:00,190
+الـ F<sub>y</sub> كذلك. يبقى واحد على X ناقص اثنين Y في مشتقّة
+
+102
+00:11:00,190 --> 00:11:06,410
+ما داخل القوس بالنسبة لـ Y، اللي هو سالب اثنين. إذن،
+
+103
+00:11:06,410 --> 00:11:12,290
+النتيجة هذه بتعطيني الـ F<sub>y</sub> عند النقطة (3, 1,
+
+104
+00:11:12,290 --> 00:11:19,610
+0)، بتساوي ناقص اثنين على ثلاثة ناقص اثنين، وهي سالب
+
+105
+00:11:19,610 --> 00:11:26,540
+اثنين. F<sub>z</sub> معروفة مباشرة كده يا فنان؟ سالب
+
+106
+00:11:26,540 --> 00:11:32,920
+واحد. تمام. لأنّ الكلّ مقدار ثابت بالنسبة لـ z، يبقى
+
+107
+00:11:32,920 --> 00:11:38,180
+مشتقته يساوي سالب واحد. معناته أن الـ F<sub>z</sub> عند
+
+108
+00:11:38,180 --> 00:11:43,700
+الثلاثة، واحد، و صفر، أو عند أي نقطة أخرى بدها تساوي
+
+109
+00:11:43,700 --> 00:11:49,140
+كذلك سالب واحد. الآن النقطة موجودة، مشتقاتها الثلاثة موجودة،
+
+110
+00:11:49,140 --> 00:11:51,360
+إذن أتوماتيكياً سهل أجيب
+
+111
+00:11:55,140 --> 00:12:00,940
+معادلة هذه. نسميها star، وبدنا نعوّض في معادلة رقم
+
+112
+00:12:00,940 --> 00:12:05,500
+star. إذن، بدي أشيل الـ F<sub>x</sub> وأضعه بـ واحد، يبقى هاي واحد
+
+113
+00:12:05,500 --> 00:12:13,100
+في x - 3. اللي بعدها الـ
+
+114
+00:12:13,100 --> 00:12:17,040
+F<sub>y</sub> ناقص اثنين في y
+
+115
+00:12:20,540 --> 00:12:29,920
+بعدها ناقص واحد في z - 1، بيصير زائد واحد. كل هذا
+
+116
+00:12:29,920 --> 00:12:32,440
+الكلام بده يساوي صفر.
+
+117
+00:12:38,460 --> 00:12:45,760
+z فقط لـ غير  اللي ناقص صفر، بده يساوي صفر. فبفكّ
+
+118
+00:12:45,760 --> 00:12:51,400
+المعادلة هذه، يبقى بيصير x - 3 ناقص اثنين y
+
+119
+00:12:51,400 --> 00:12:58,180
+زائد اثنين ناقص z كلّه بده يساوي صفر. أو بمعنى آخر،
+
+120
+00:12:58,180 --> 00:13:07,230
+شكلها بده ياخد الشكل التالي: x - 2y - z + 7  عندك هنا
+
+121
+00:13:07,230 --> 00:13:12,810
+(repeated numbers removed)
+
+122
+00:13:12,810 --> 00:13:16,910
+(repeated numbers removed)
+
+123
+00:13:16,910 --> 00:13:17,010
+(repeated numbers removed)
+
+124
+00:13:17,010 --> 00:13:17,030
+(repeated numbers removed)
+
+125
+00:13:17,030 --> 00:13:20,790
+(repeated numbers removed)
+
+126
+00:13:32,830 --> 00:13:38,290
+هل تذكروا موضوع الـ linearization في Calculus A؟
+
+127
+00:13:52,630 --> 00:13:56,590
+ثم functions of three variables. هنجيب الـ
+
+128
+00:13:56,590 --> 00:14:00,630
+linearization في الحالتين. طيب، حد منكم يتذكر، يعني
+
+129
+00:14:00,630 --> 00:14:05,670
+بالبلدي، شو يعني المقصود بالـ linearization عندها
+
+130
+00:14:05,670 --> 00:14:11,970
+نقطة؟ أيوة. كلمة linearization جايه من كلمة إيه؟
+
+131
+00:14:11,970 --> 00:14:18,930
+من كلمة line، تمام؟ أيوة. يبقى المثل في الحالة اللي
+
+132
+00:14:18,930 --> 00:14:22,090
+عندنا... أنا عندي function مُعقّدة، وبكون الـ
+
+133
+00:14:22,090 --> 00:14:28,940
+function صعبة التعامل معاها، كويس؟ بنجيب دالة أخرى
+
+134
+00:14:28,940 --> 00:14:35,220
+تكافئ هذه الدالة. وهذه الدالة بيكون دالة خطية، يعني
+
+135
+00:14:35,220 --> 00:14:40,080
+بيكون الفرق بينها وبين الدالة الأصليّة بسيط جداً،
+
+136
+00:14:40,080 --> 00:14:45,300
+يمكن الاستغناء عنه. هذا معنى كلمة
+
+137
+00:14:45,300 --> 00:14:49,880
+linearization. يعني أنا بدي أحوّل الدالة التي عندنا
+
+138
+00:14:50,150 --> 00:14:55,050
+إلى دالة خطية عند نقطة. بيصير قيمة الدالة الخطية
+
+139
+00:14:55,050 --> 00:14:59,810
+وقيمة الـ function عند هذه النقطة، قريبتين جداً، مع
+
+140
+00:14:59,810 --> 00:15:05,430
+فارق بسيط جداً، أقل من عشرة، أقل من مئة، أقل من ألف.
+
+141
+00:15:05,430 --> 00:15:09,330
+وبالتالي يمكن الاستغناء عن الـ function الأصلية،
+
+142
+00:15:09,330 --> 00:15:14,790
+والإكتفاء بالـ function الخطية التي عندنا. هذا
+
+143
+00:15:14,790 --> 00:15:20,220
+بالبلدي هيك. لكن إحنا بنشتغل شغل رياضي، مشان شغل رياضي،
+
+144
+00:15:20,220 --> 00:15:24,200
+بنروح نحط تعريف للـ linearization في الـ functions
+
+145
+00:15:24,200 --> 00:15:29,300
+of two variables، ثم نستخدم هذا التعريف في حساب الـ
+
+146
+00:15:29,300 --> 00:15:33,060
+linearization لدالة ما. يبقى definition
+
+147
+00:15:45,400 --> 00:15:50,300
+of a function f
+
+148
+00:15:50,300 --> 00:16:01,740
+of x و y at a point عند النقطة x<sub>0</sub> و y<sub>0</sub>
+
+149
+00:16:01,740 --> 00:16:12,860
+where الـ f is differentiable function is
+
+150
+00:16:15,850 --> 00:16:25,370
+عندنا رمز f(x, y) عملياً يساوي f(x<sub>0</sub>, y<sub>0</sub>) زائد f<sub>x</sub> عند النقطة x<sub>0</sub> و y
+
+151
+00:16:25,370 --> 00:16:32,870
+<sub>0</sub> في الـ x - x<sub>0</sub> زائد f<sub>y</sub> عند
+
+152
+00:16:32,870 --> 00:16:41,190
+النقطة x<sub>0</sub> و y<sub>0</sub> في الـ y - y<sub>0</sub>
+
+153
+00:16:41,190 --> 00:16:47,700
+يبقى
+
+154
+00:16:47,700 --> 00:16:52,080
+هذا الـ linearization بتاعة الدالة. هو هذا التعريف
+
+155
+00:16:52,080 --> 00:16:56,300
+الأول. التعريف الثاني: approximation function
+
+156
+00:16:56,300 --> 00:17:01,800
+approximation
+
+157
+00:17:01,800 --> 00:17:05,820
+function
+
+158
+00:17:05,820 --> 00:17:09,860
+يعني الدالة التقريبية. الـ F(x, y) التي تساوي تقريباً L
+
+159
+00:17:09,860 --> 00:17:19,380
+(x, y) is called the
+
+160
+00:17:19,380 --> 00:17:28,600
+standard linear
+
+161
+00:17:28,600 --> 00:17:38,560
+approximation
+
+162
+00:17:38,560 --> 00:17:39,280
+.
+
+163
+00:17:49,720 --> 00:17:58,520
+Linear Approximation of F at
+
+164
+00:17:58,520 --> 00:18:05,520
+point
+
+165
+00:18:05,520 --> 00:18:08,760
+x<sub>0</sub>, y<sub>0</sub>
+
+166
+00:18:59,840 --> 00:19:03,700
+نرجع للتعريف اللي إحنا كاتبينه هذا مرة ثانية.
+
+167
+00:19:05,050 --> 00:19:08,670
+يبقى باجي بقول: الـ linearization للدالة f(x, y)
+
+168
+00:19:08,670 --> 00:19:12,690
+عند النقطة x<sub>0</sub>, y<sub>0</sub> حيث الـ f دالة قابلة
+
+169
+00:19:12,690 --> 00:19:20,790
+للإشتقاق، نسميها L(x, y). قيمة الدالة
+
+170
+00:19:20,790 --> 00:19:25,570
+الأصلية عند النقطة المعطاة f(x<sub>0</sub>, y<sub>0</sub>)
+
+171
+00:19:25,570 --> 00:19:31,150
+مضافة إليها مشتقة الدالة بالنسبة لـ x عند تلك النقطة
+
+172
+00:19:31,150 --> 00:19:33,670
+مضروبة في x - x<sub>0</sub>
+
+173
+00:19:
+
+223
+00:26:04,070 --> 00:26:12,390
+ناقص عشرة زائد عشرة Y ناقص عشرين يبقى هذا الكلام
+
+224
+00:26:12,390 --> 00:26:15,090
+بده يساوي عشرة X
+
+225
+00:26:19,130 --> 00:26:26,950
+يبقى ناقص خمسة وزائد خمسة وعشرين يبقى ناقص خمسة
+
+226
+00:26:38,870 --> 00:26:44,670
+خطية في معادلة من الدرجة الأولى في كل من X وY إذا
+
+227
+00:26:44,670 --> 00:26:50,490
+هي معادلة خطية ومن ثم هذا الـ linearization للدالة
+
+228
+00:26:50,490 --> 00:26:58,450
+الأصلية التي موجودة عندنا فوق طيب احنا تاول الساعة
+
+229
+00:26:58,450 --> 00:27:03,330
+بنقول إيش؟ بنقول أنه لما نستبدل الدالة بالـ
+
+230
+00:27:03,330 --> 00:27:09,310
+linearization تبعها بيكون هناك فيه خطأ بسيط تمام؟
+
+231
+00:27:09,310 --> 00:27:15,430
+الآن بنحاول نحسب قديش قيمة هذا الخطأ الذي احنا
+
+232
+00:27:15,430 --> 00:27:19,490
+افترضناه من الأصل  لما سوينا الدالة بالـ
+
+233
+00:27:19,490 --> 00:27:24,690
+linearization تبعها طيب مشان هيك بنروح نحط القاعدة
+
+234
+00:27:24,690 --> 00:27:29,750
+تبعنا ونروح نبدأ نشتغل عليها، القاعدة التالية في
+
+235
+00:27:29,750 --> 00:27:43,110
+صيغة الـ remark التالية: if الـ
+
+236
+00:27:43,110 --> 00:27:55,230
+if f has continuous first and second
+
+237
+00:27:55,230 --> 00:28:06,440
+partial derivatives
+
+238
+00:28:06,440 --> 00:28:09,720
+partial derivatives
+
+239
+00:28:09,720 --> 00:28:13,400
+مشتقات
+
+240
+00:28:13,400 --> 00:28:19,380
+الأولى والثانية through an open set containing
+
+241
+00:28:36,850 --> 00:28:44,510
+a rectangle
+
+242
+00:28:44,510 --> 00:28:47,890
+مستطيل
+
+243
+00:28:47,890 --> 00:28:54,630
+centered at
+
+244
+00:28:55,460 --> 00:29:03,560
+النقطة X نوت و Y نوت، و
+
+245
+00:29:03,560 --> 00:29:07,920
+إذا
+
+246
+00:29:07,920 --> 00:29:17,320
+كان الـ M is any upper bound
+
+247
+00:29:22,490 --> 00:29:33,590
+for the values of
+
+248
+00:29:33,590 --> 00:29:45,150
+the absolute value of Fxx, the absolute value of Fyy, and
+
+249
+00:29:45,150 --> 00:29:56,250
+the absolute value of Fxy on the rectangle R, then
+
+250
+00:29:56,250 --> 00:30:04,590
+the error, مقدار الخطأ الذي تحصل عليه،
+
+251
+00:30:04,590 --> 00:30:15,090
+الرمز E, as a function of replacing
+
+252
+00:30:15,090 --> 00:30:27,350
+f of x y on R by
+
+253
+00:30:27,350 --> 00:30:31,550
+its
+
+254
+00:30:31,550 --> 00:30:34,850
+linearization
+
+255
+00:30:34,850 --> 00:30:40,630
+الذي
+
+256
+00:30:40,630 --> 00:30:54,140
+هو L of x y = f of x0 وy0 + Fx عند النقطة x0 وy0
+
+257
+00:30:54,140 --> 00:31:03,760
+(x - x0) + Fy عند الـ x0 وy0 (y -
+
+258
+00:31:03,760 --> 00:31:04,680
+y0)
+
+259
+00:31:13,560 --> 00:31:21,260
+باستخدام المتباينة نحقق
+
+260
+00:31:21,260 --> 00:31:33,000
+المتباينة، قيمة أكبر للخطأ، كمشكلة x وy أقل من أو
+
+261
+00:31:33,000 --> 00:31:41,500
+يساوي نصف M  |x - x0|
+
+262
+00:31:41,500 --> 00:31:48,060
++ |y - y0| الكل تربيع
+
+263
+00:32:36,010 --> 00:32:40,910
+مرة ثانية، بنتكلم عن الـ error، اللي هو مقدار الخطأ
+
+264
+00:32:40,910 --> 00:32:46,550
+بين الدالة f of x وy و linearization لهذه الدالة
+
+265
+00:32:46,550 --> 00:32:52,270
+التي نرمز لها بالرمز L of x وy. فبأجي بقول لو كانت
+
+266
+00:32:52,270 --> 00:32:57,570
+الدالة f دالة متصلة، if f has continuous
+
+267
+00:32:57,570 --> 00:33:01,290
+first and second partial derivatives، المشتقات
+
+268
+00:33:01,290 --> 00:33:06,660
+الأولى والثانية لهذه الدالة دوال متصلة على
+
+269
+00:33:06,660 --> 00:33:12,740
+فترة مفتوحة تحتوي على مستطيل centered at x naught y
+
+270
+00:33:12,740 --> 00:33:17,380
+naught. إيش يعني؟ يعني لو راحت قلت هذا مثلا على سبيل
+
+271
+00:33:17,380 --> 00:33:23,080
+المثال محور x وهذا محور y وهذه النقطة في الأصل
+
+272
+00:33:30,810 --> 00:33:36,690
+مركزه نقطة x naught و y naught. الشكل الذي عندنا
+
+273
+00:33:36,690 --> 00:33:45,530
+هنا كويس، في عندي هنا هذا الطول الذي عندنا
+
+274
+00:33:45,530 --> 00:33:51,690
+هذا أو الطول هذا، الاثنان are the same، يبقى هذا
+
+275
+00:33:51,690 --> 00:33:59,990
+الطول لو سميته H وهذا سميته K على سبيل المثال
+
+276
+00:34:04,630 --> 00:34:08,930
+المشتقات الأولى والثانية لهذه الدالة دوال متصلة
+
+277
+00:34:08,930 --> 00:34:16,490
+على منطقة R ضمن مستطيل مركز النقطة التي عندنا هذا
+
+278
+00:34:17,130 --> 00:34:22,510
+بقول: لأن  وإذا كان الـ M is any upper bound for
+
+279
+00:34:22,510 --> 00:34:26,350
+the values of، يبقى جبنا المشتقة الثانية بالنسبة
+
+280
+00:34:26,350 --> 00:34:30,190
+لـ X، جبنا المشتقة الثانية بالنسبة إلى Y، جبنا
+
+281
+00:34:30,190 --> 00:34:33,970
+المشتقة الثانية Fxy، وأخذنا الـ absolute value
+
+282
+00:34:33,970 --> 00:34:41,490
+للاثلاث عند نفس النقطة x naught وy naught. أيوة، يمكن
+
+283
+00:34:41,490 --> 00:34:45,050
+واحدة تقول لي: طب وين الرابع؟ فأقول لها: وين
+
+284
+00:34:45,050 --> 00:34:50,610
+الرابع؟ تقول لي: FYX الـ absolute value. فما أخذنا FXX,
+
+285
+00:34:50,610 --> 00:34:58,590
+FYY, FXY، لكن FYX مالها؟ ما جبنا سيرتها. طب يكون هذا
+
+286
+00:34:58,590 --> 00:35:06,570
+غلط؟ لا، يعني FXY وFYX يتساووا.  اشترطنا، أخذنا نظرية
+
+287
+00:35:06,570 --> 00:35:13,430
+قبل ذلك: إذا كان، إذا لو مشتقاتها دوال متصلة عند من؟
+
+288
+00:35:13,430 --> 00:35:18,910
+عند النقطة التي نحسب عندها هذه المشتقات. إذا لو
+
+289
+00:35:18,910 --> 00:35:24,990
+روحنا كتبنا يا بنات ما هؤلاء، كتبنا FYX، معناته كررنا
+
+290
+00:35:24,990 --> 00:35:29,690
+القيمة التي عندنا هذه، تكرار، وهذا لا داعي له لأن
+
+291
+00:35:29,690 --> 00:35:34,990
+مشترط لدينا الـ continuity هنا، وبالتالي أزلنا من هي؟
+
+292
+00:35:34,990 --> 00:35:39,650
+النقطة الثالثة. نرجع ثانية إلى M، يبقى احنا في عندنا ثلاث
+
+293
+00:35:39,650 --> 00:35:44,850
+مقادير: |Fxx|, |Fyy|,
+
+294
+00:35:44,850 --> 00:35:49,490
+|Fxy|، يبقى ثلاث قيم. ناخذ الـ
+
+295
+00:35:49,490 --> 00:35:52,870
+absolute value، فتصبح قيم موجبة، يعني أنا
+
+296
+00:35:52,870 --> 00:35:55,790
+أقول القيم الموجبة، وأخذنا الـ absolute value للصين،
+
+297
+00:35:55,790 --> 00:36:00,910
+إذا صار عندنا ثلاث قيم موجبة وقد تكون إحداها بصفر،
+
+298
+00:36:00,910 --> 00:36:04,270
+معنى المشكلة، موجبة أو بصفر، أخذنا الـ absolute
+
+299
+00:36:04,270 --> 00:36:10,010
+value لثلاث قيم، أكبر رقم فيهم، نعتبر هذا upper
+
+300
+00:36:10,010 --> 00:36:17,260
+bound، حد علوي للثلاث. أنا آخذ أكبر رقم من الأرقام
+
+301
+00:36:17,260 --> 00:36:23,900
+الثلاث التي تسمى الـ least upper bound، أقل حد علوي
+
+302
+00:36:23,900 --> 00:36:30,480
+لمن؟ للثلاث التي عندنا. نقول: within the error، مقدار
+
+303
+00:36:30,480 --> 00:36:34,740
+الخطأ الذي حصل عندك نتيجة استبدال الدالة بالـ
+
+304
+00:36:34,740 --> 00:36:40,300
+linearization تبعها، قديش مقدار يخضع لهذه الـ
+
+305
+00:36:40,300 --> 00:36:43,440
+inequality: |E| أقل من أو
+
+306
+00:36:43,440 --> 00:36:47,760
+يساوي نصف في الـ upper bound في |x - x
+
+307
+00:36:47,760 --> 00:36:55,380
+naught| + |y - y naught| الكل تربيع. طبعاً يبقى هذا
+
+308
+00:36:55,380 --> 00:37:02,280
+المصطلح بنات الذي اسمه R، عادي عشان نروح ناخذ الكلام
+
+309
+00:37:02,280 --> 00:37:06,640
+هذا، عامل لأنه شكله ياكد زي المكاملة كبير شوية هو
+
+310
+00:37:06,640 --> 00:37:11,760
+لا مكاملة ولا حاجة، بسيطة هذه، سهل حساب هذين
+
+311
+00:37:11,760 --> 00:37:15,360
+سهل حسابهم، سهل أخذ نفس الـ value، سهل أخذ الكبيرة
+
+312
+00:37:15,360 --> 00:37:20,580
+فيهم. إذا صار النص قيمته جاهز هنا، x - x economic
+
+313
+00:37:20,580 --> 00:37:25,940
+في الغالب هو بيعطيها لي، يعني 99.9 زي
+
+314
+00:37:25,940 --> 00:37:29,060
+الانتخابات العربية، بيكون أعطانا القيمة هذه و
+
+315
+00:37:29,060 --> 00:37:32,260
+أعطانا القيمة هذه مباشرة، يبقى ما علي إلا أجمعهم
+
+316
+00:37:32,260 --> 00:37:37,240
+بس وربع، وكلنا بنعرف نجمع 2.25، بس قضيتنا إيه
+
+317
+00:37:37,240 --> 00:37:41,340
+سهلة شوية، ناخذ مثال تطبيق زي ما بنكرره في
+
+318
+00:37:41,340 --> 00:37:45,800
+الامتحانات هنا، يعني يتكرر، بدل المرة ثلاث مرات في
+
+319
+00:37:45,800 --> 00:37:50,870
+الامتحانات، لكن أنا السنة الماضية ما جبتش، طيب فإجب
+
+320
+00:37:50,870 --> 00:37:56,350
+أقول هنا، نعطي مثال، الله أعلم، اللي شريك اللي مات
+
+321
+00:37:56,350 --> 00:38:00,930
+وبالتالي نجيب، ما يجيبوا، ما يقدروش، أقوله، يبقى هنا
+
+322
+00:38:00,930 --> 00:38:13,290
+مثال A: find the linearization
+
+323
+00:38:13,290 --> 00:38:26,210
+L of x y of the function، للدالة
+
+324
+00:38:26,210 --> 00:38:37,670
+f of x y تساوي، اللي هو x y تربيع + y cos
+
+325
+00:38:37,670 --> 00:38:47,090
+x - 1، at، عند النقطة التي هي 1 و2، كذا
+
+326
+00:38:47,090 --> 00:38:56,200
+نمر بـ B: find an
+
+327
+00:38:56,200 --> 00:39:03,420
+upper bound for
+
+328
+00:39:03,420 --> 00:39:17,460
+the magnitude of the absolute
+
+329
+00:39:17,460 --> 00:39:28,620
+value للـ error  في الـ x وy، magnitude
+
+330
+00:39:28,620 --> 00:39:33,600
+of the
+
+331
+00:39:33,600 --> 00:39:39,320
+error in
+
+332
+00:39:39,320 --> 00:39:47,000
+approximating the function، in approximating
+
+333
+00:39:54,060 --> 00:40:11,400
+f of x y بـ L of x y over the rectangle R
+
+334
+00:40:15,960 --> 00:40:23,760
+حيث |x - 1| أقل من أو تساوي 0.1،
+
+335
+00:40:23,760 --> 00:40:31,080
+و |y - 2| أقل من أو تساوي
+
+336
+00:40:31,080 --> 00:40:33,520
+0.1
+
+337
+00:40:55,850 --> 00:41:01,650
+مرة ثانية، قال في المثال مطلبين، وكأنه هذا هو المثال
+
+338
+00:41:01,650 --> 00:41:06,330
+الرقم 2، على إيجاد الـ linearization لذلك، وبعدها
+
+339
+00:41:06,330 --> 00:41:12,810
+نحصل نفس الجدار، أعلى قيمة موجودة للخطأ، نتيجة
+
+340
+00:41:12,810 --> 00:41:17,660
+لاستبدال الدالة f of x بـ linearization تبعها. إذا
+
+341
+00:41:17,660 --> 00:41:20,760
+تخلينا مع الـ function الأولى، طبعاً واضح أنه ما
+
+342
+00:41:20,760 --> 00:41:24,460
+أعطينا نقطة (1، 2). إذا بدي أحسب الدالة
+
+343
+00:41:24,460 --> 00:41:30,300
+ومشتقاتها عند النقطة (1، 2)، فبأجي بقول: بدي آخذ
+
+344
+00:41:30,300 --> 00:41:38,460
+الجزء A، بدي آخذ f of x y التي تساوي x
+
+345
+00:41:38,460 --> 00:41:42,240
+y تربيع +
+
+346
+00:41:48,440 --> 00:41:57,730
+نحسب f of (1، 2) = 1 × 2 تربيع
+
+347
+00:41:57,730 --> 00:42:06,690
++ 2 cos 0 = 1 × 4 + 2 × 1 = 6
+
+348
+00:42:06,690 --> 00:42:14,850
+يبقى الناتج يساوي 6. بعدين بدنا نروح نجيب Fx
+
+349
+00:42:14,850 --> 00:42:23,440
+يبقى هذا الكلام يساوي y تربيع، لـ y مالكش دعوة. تفضل
+
+350
+00:42:23,440 --> 00:42:29,200
+الـ cos بسالب sin (x - 1) × مشتقة الزاوية
+
+351
+00:42:29,200 --> 00:42:37,640
+= 1. نحسب هذه الـ Fx عند النقطة (1، 2): y
+
+352
+00:42:37,640 --> 00:42:45,040
+تربيع - 2 sin 0 = 4 - 0 = 4
+
+353
+00:42:45,040 --> 00:42:46,100
+sin 0 = 0
+
+354
+00:42:56,270 --> 00:43:06,250
+2xy + cos (x - 1)، لأن cos (x - 1)
+
+355
+00:43:06,250 --> 00:43:11,130
+كلها تعتبر constant إذا اشتغلنا بالنسبة لمن؟ إلى y
+
+356
+00:43:11,130 --> 00:43:18,770
+نحصل قديش Fy عند النقطة (1، 2) = 2 ×
+
+357
+00:43:18,770 --> 00:43:23,510
+1 × 2 + cos 0 = 5
+
+358
+00:43:27,760 --> 00:43:33,500
+= 5. يبقى بناء عليه، بعدها
+
+359
+00:43:33,500 --> 00:43:39,820
+نجيب له الـ linearization  لـ x و y، يبقى هنا f
+
+360
+00:43:39,820 --> 00:43:46,480
+of (1، 2) + Fx عند النقطة (1،
+
+361
+00:43:46,480 --> 00:43:52,560
+2) (x - 1) + Fy عند النقطة
+
+362
+00:43:52,560 --> 00:43:59,740
+(1، 2) (y - 2). نعوض فيها بـ (1، 2) التي هي 6، Fx = 4، (x -
+
+363
+00:43:59,740 --> 00:44:06,680
+1)، Fy = 5 (y - 2). إذاً هذا
+
+364
+00:44:06,680 --> 00:44:14,540
+الكلام = 6 + 4x - 4 + 5y - 10. إذاً
+
+365
+00:44:14,540 --> 00:44:20,120
+هذا الكلام = 6 + 4x - 4 + 5y - 10 = 4x +
+
+366
+00:44:20,120 --> 00:44:27,780
+5y - 8. هذا الكلام عندك هنا
+
+367
+00:44:27,780 --> 00:44:35,580
+4x + 5y - 8. يبقى هذا الـ linear function
+
+368
+00:44:35,580 --> 00:44:43,620
+أو الـ linearization للـ function الأصلية، وهو
+
+369
+00:44:43,620 --> 00:44:48,020
+المطلوب الأول من المسألة. نجي للمطلوب الثاني نجيب
+
+370
+00:44:54,040 --> 00:44:54,900
+الجزء B
+
+372
+00:44:58,830 --> 00:45:03,390
+يبقى هذا زي السؤال، المثال السابق،  تماماً زيه
+
+373
+00:45:03,390 --> 00:45:09,850
+وكان يعتبر المثال رقم 2، فأجي أتعامل معه، بأجي
+
+374
+00:45:09,850 --> 00:45:13,370
+أروح أجيب له الـ error التي عندنا، مشان هيك هذه
+
+375
+00:45:13,370 --> 00:45:19,880
+جاهزة، وهذه جاهزة، وقال علينا من؟ بس الـ M، الـ M بدي
+
+376
+00:45:19,880 --> 00:45:28,260
+أعمل مقارنة بين الـ absolute value لـ Fxx, Fyy, Fxy، و
+
+377
+00:45:28,260 --> 00:45:35,420
+هكذا. طيب الـ Fx الحمد لله جاهزة. إذاً إحنا بدنا الـ Fxx
+
+378
+00:45:35,420 --> 00:45:42,340
+الذي هو ∂/∂x للـ Fx، يعني ∂/∂x  لـ Fx. هي جاهزة فوق: y تربيع - y
+
+379
+00:45:42,340 --> 00:45:49,240
+sin (x - 1). ولهذا، تبقى الدالة هذه
+
+380
+00:45:49,240 --> 00:45:55,360
+بالنسبة لـ x، يبقى y تربيع مع السلامة، الـ y هذه مقدر
+
+381
+00:45:55,360 --> 00:46:00,400
+تعتبر ثابتة، تفضل الـ sin، يبقى -y cos (x -
+
+382
+00:46:00,400 --> 00:46:08,420
+1) × مشتقة الزاوية التي هي 1.  نحسبها مرة ثانية
+
+384
+00:46:22,160 --> 00:46:27,860
+عند النقطة (1، 2) = -2 cos 0 = -2
+
+386
+00:46:27,860 --> 00:46:39,400
+cos 0 = 1
+
+394
+00:46:51,910 --> 00:46:59,790
+بدنا نروح لـ Fyy، يعني ∂/∂y للـ Fy،
+
+395
+00:46:59,790 --> 00:47:05,610
+يعني ∂/∂y للـ Fy. وين الـ Fy؟ هي فوق
+
+396
+00:47:05,610 --> 00:47:10,130
+التي هي 2xy + cos 0
+
+397
+00:47:13,650 --> 00:47:18,390
+إن مشتقتها بالنسبة لمن؟ إلى y، يبقى الـ cos كله بـ
+
+398
+00:47:18,390 --> 00:47:26,110
+0، يبقى فقط كده عنده 2x. يبقى هذا معناته أن
+
+399
+00:47:26,110 --> 00:47:34,770
+الـ Fyy كده تساوي عند النقطة 1، عند النقطة (1،
+
+400
+00:47:34,770 --> 00:47:38,870
+2)، عند النقطة (1، 2) تساوي كده يا بنات
+
+401
+00:47:38,870 --> 00:47:46,490
+2. لأن بدي أشيل x، وقتها... طيب 2 أختي
+
+402
+00:47:46,490 --> 00:47:51,330
+لها الـ absolute value، و الله ما أختيها، هي 2
+
+403
+00:47:51,330 --> 00:47:56,710
+يبقى بدنا نبرزها، وكمان نرجع لها بعد قليل. يبقى
+
+404
+00:47:56,710 --> 00:48:02,290
+بدنا نروح نجيب له كمان من؟ الـ Fxy، يعني ∂/∂y
+
+405
+00:48:02,290 --> 00:48:09,730
+لـ Fx، هذا الكلام بده يساوي ∂/∂y
+
+406
+00:48:09,730 --> 00:48:10,630
+لـ
+
+407
+00:48:16,980 --> 00:48:
+
+445
+00:52:58,590 --> 00:53:08,050
+نقول الـ L of x و y و z يساوي الـ F عند النقطة P
+
+446
+00:53:08,050 --> 00:53:16,790
+مضافاً إليها F<sub>x</sub> عند النقطة P في الـ X مضروبة الـ
+
+447
+00:53:16,790 --> 00:53:24,150
+X مضافاً إليها F<sub>y</sub> عند النقطة P في الـ Y
+
+448
+00:53:32,360 --> 00:53:38,760
+يبقى هنا الشكل
+
+449
+00:53:38,760 --> 00:53:46,600
+الـ linearization فيه فرقين أو اثنين من الفروق
+
+450
+00:53:46,600 --> 00:53:50,300
+بين الـ function وبين الـ linearization في حالة الـ
+
+451
+00:53:50,300 --> 00:53:55,960
+الفرق الأول، بعد ما كنا بنحسب عند نقطة
+
+452
+00:53:55,960 --> 00:54:02,340
+بإحداثيين أو بإحداثيين، أصبحنا نحسب عند نقطة بثلاث
+
+453
+00:54:02,340 --> 00:54:07,720
+إحداثيات، فهذا الفرق الأول. الفرق الثاني بأن نضيف الـ
+
+454
+00:54:07,720 --> 00:54:12,340
+term الزيادة، اللي هو عند هذا المشتقة الجزئية
+
+455
+00:54:12,340 --> 00:54:17,480
+بالنسبة إلى z عند نفس النقطة مضروبة في Δz
+
+456
+00:54:17,480 --> 00:54:18,620
+ناقص
+
+457
+00:54:23,560 --> 00:54:28,100
+للـ error بسرعتنا، الـ linearization جديد، إذا في
+
+458
+00:54:28,100 --> 00:54:33,480
+error جديد، بدنا نعرف إيش الـ error هذا، يبقى  نبرة
+
+459
+00:54:33,480 --> 00:54:38,600
+اثنين نقول
+
+460
+00:54:38,600 --> 00:54:46,400
+نفترض أن الـ R هي منطقة مغلقة، نفترض أن
+
+461
+00:54:46,400 --> 00:55:07,710
+الـ R، أو إيش رأيكم نعاود الكلام هذا كله أو
+
+462
+00:55:07,710 --> 00:55:12,330
+في
+
+463
+00:55:12,330 --> 00:55:13,210
+هذه الحالة
+
+464
+00:55:18,860 --> 00:55:32,360
+في حالة الدوال ذات المتغيرات الثلاثة، فإن الـ
+
+465
+00:55:32,360 --> 00:55:43,300
+error  له رمز E، و X، و Y، و Z،  و القيمة المطلقة
+
+466
+00:55:43,300 --> 00:55:52,710
+أقل من أو تساوي  M، و القيمة المطلقة لـ X
+
+467
+00:55:52,710 --> 00:56:00,510
+ناقص X<sub>0</sub> زائد Y ناقص Y<sub>0</sub> زائد القيمة المطلقة
+
+468
+00:56:00,510 --> 00:56:11,910
+لـ Z ناقص Z<sub>0</sub> الكل تربيع، حيث أن الـ M هي
+
+469
+00:56:11,910 --> 00:56:17,650
+الحد الأعلى
+
+470
+00:56:18,880 --> 00:56:27,820
+للقيمة المطلقة لـ F<sub>xx</sub>، القيمة المطلقة لـ F<sub>yy</sub>،
+
+471
+00:56:27,820 --> 00:56:36,940
+القيمة المطلقة لـ F<sub>zz</sub>، القيمة المطلقة لـ F<sub>xy</sub>،
+
+472
+00:56:36,940 --> 00:56:48,000
+القيمة المطلقة لـ F<sub>xz</sub> و القيمة المطلقة لـ F<sub>yz</sub>
+
+473
+00:57:35,750 --> 00:57:40,990
+نفس الصيغة اللي قبل، اللهم إلا زدنا لها term  ثالث
+
+474
+00:57:40,990 --> 00:57:45,640
+اللي عندنا، و الـ M هذه اللي هي الحد الأعلى
+
+475
+00:57:45,640 --> 00:57:52,840
+لستة المقادير اللي عندنا F<sub>xx</sub>، F<sub>yy</sub>، F<sub>zz</sub>، طبعاً بـ
+
+476
+00:57:52,840 --> 00:57:58,140
+القيمة المطلقة، F<sub>xy</sub>، F<sub>yx</sub>، طبعاً استبعدناها  مِن أجل الـ
+
+477
+00:57:58,140 --> 00:58:03,120
+استمرارية، F<sub>xz</sub>، واستبعدنا F<sub>zx</sub> من أجل الاستمرارية،
+
+478
+00:58:03,120 --> 00:58:08,740
+F<sub>yz</sub>، واستبعدنا F<sub>zy</sub> كذلك بسبب؟ بسبب الـ
+
+479
+00:58:08,740 --> 00:58:13,460
+استمرارية، مش هنخليكم تايهين، بنعطيكم مثال أوضح
+
+480
+00:58:13,460 --> 00:58:21,100
+على ذلك. مثال: أوجد
+
+481
+00:58:21,100 --> 00:58:31,100
+الـ linearization
+
+482
+00:58:31,100 --> 00:58:34,560
+اللي
+
+483
+00:58:34,560 --> 00:58:50,020
+هو L of X, Y, و Z للدالة f
+
+484
+00:58:50,020 --> 00:59:02,500
+of x, y, و z يساوي جذر 2 cos x sin y
+
+485
+00:59:02,500 --> 00:59:18,180
+زائد z عند النقطة P<sub>0</sub>
+
+486
+00:59:18,180 --> 00:59:18,560
+P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub>
+
+487
+00:59:18,560 --> 00:59:19,720
+P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub>
+
+488
+00:59:19,720 --> 00:59:22,860
+P<sub>0</sub>
+
+489
+00:59:22,860 --> 00:59:24,320
+P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub>
+
+490
+00:59:24,320 --> 00:59:27,740
+P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub> P<sub>0</sub>
+
+491
+00:59:27,740 --> 00:59:30,360
+P<sub>0</sub>
+
+492
+00:59:38,380 --> 00:59:48,960
+لقيمة
+
+493
+00:59:48,960 --> 01:00:01,540
+اللي عندنا هذا للخطأ في التقريب و
+
+494
+01:00:01,540 --> 01:00:05,100
+التقريب
+
+495
+01:00:15,150 --> 01:00:19,930
+F of X, Y, و
+
+496
+01:00:19,930 --> 01:00:27,690
+Z, F
+
+497
+01:00:27,690 --> 01:00:37,130
+of X, Y, و Z, بدأ الـ sound، L of X, Y, و Z على
+
+498
+01:00:37,130 --> 01:00:43,550
+المنطقة، على المنطقة
+
+499
+01:00:45,400 --> 01:00:56,280
+محددة كالتالي، A حيث أن قيمة X أقل
+
+500
+01:00:56,280 --> 01:01:06,530
+من أو تساوي 0.1، وقيمة Y أقل من أو
+
+501
+01:01:06,530 --> 01:01:12,310
+تساوي كذلك بنفس الطريقة 0.1، وهكذا
+
+502
+01:01:12,310 --> 01:01:19,590
+ننتقل إلى Z ناقص π/4 أقل من أو تساوي 0.1
+
+503
+01:01:19,590 --> 01:01:21,410
+0.1
+
+504
+01:01:40,040 --> 01:01:45,660
+السؤال شبيه بالسؤال الماضي، لكن مع الفارق الذي
+
+505
+01:01:45,660 --> 01:01:50,820
+يناسب طبيعة دالة المتغيرات الثلاثة المطروحة.
+
+506
+01:01:50,820 --> 01:01:54,940
+الأول،  الذي يطلب  الـ linearization، وين عنده
+
+507
+01:01:54,940 --> 01:01:58,260
+النقطة، إذاً خلينا نروح نحسب له الـ linearization
+
+508
+01:01:58,260 --> 01:02:05,180
+الذي يطلبه، يبقى نبدأ أول شيء بالدالة F of X, Y, و Z
+
+509
+01:02:05,180 --> 01:02:14,050
+التي تساوي جذر 2 cos X sin Y
+
+510
+01:02:14,050 --> 01:02:22,490
+زائد Z، نحسب قيمة الدالة عند الـ 0, 0, و
+
+511
+01:02:22,490 --> 01:02:29,030
+π/4، نجد أن الإجابة هي جذر 2 cos 0
+
+512
+01:02:29,030 --> 01:02:32,650
+بمقدار 1، يبقى في 1
+
+513
+01:02:42,100 --> 01:02:47,920
+يبقى الجواب كده؟ 1، فالناتج 1. لماذا؟
+
+514
+01:02:47,920 --> 01:02:54,160
+الآن F<sub>xy</sub>، سبق أن اشتقينا الدالة بالنسبة إلى X،
+
+515
+01:02:54,160 --> 01:03:01,700
+cos، سالب جذر 2 sin x، والباقي كل مصطلح
+
+516
+01:03:01,700 --> 01:03:09,600
+لا علاقة له، يبقى هنا sin Y زائد Z. بدنا نحسب الآن
+
+517
+01:03:09,600 --> 01:03:14,700
+F<sub>x</sub> عند الـ 0، 0، و π/4، ما
+
+518
+01:03:14,700 --> 01:03:22,720
+يساوي؟ إذن سالب جذر 2، و sin 0 بصفر. F
+
+519
+01:03:22,720 --> 01:03:28,100
+0، و sin π/4 = 1/جذر 2، يبقى
+
+520
+01:03:28,100 --> 01:03:35,860
+كده؟ 0، ذهب، طيب إذاً ننتقل إلى F<sub>y</sub> يساوي
+
+521
+01:03:35,860 --> 01:03:41,200
+نشتق، لو اشتقينا، سنجد جذر 2 cos X، لا علاقة له
+
+522
+01:03:41,200 --> 01:03:49,800
+بنا، ننتقل للباقي، cos Y زائد Z في
+
+523
+01:03:49,800 --> 01:03:55,790
+مشتقة Y التي تساوي 1، نروح نحسب الآن
+
+524
+01:03:55,790 --> 01:04:04,730
+F<sub>y</sub> عند النقطة 0، 0، π/4، هو يساوي جذر 2، و
+
+525
+01:04:04,730 --> 01:04:15,450
+cos 0 بـ 1، و cos π/4 أيضاً = 1/جذر 2
+
+526
+01:04:15,450 --> 01:04:18,250
+يبقى أيضاً يساوي 1
+
+527
+01:04:22,890 --> 01:04:26,490
+يبقى F<sub>z</sub> يبقى 1
+
+528
+01:04:30,940 --> 01:04:37,080
+تبقى sin Y زائد Z في مشتقة Z
+
+529
+01:04:37,080 --> 01:04:41,760
+التي هي 1، يبقى مشتقة Z = 1
+
+530
+01:04:41,760 --> 01:04:48,480
+F<sub>y</sub>، F<sub>z</sub> متشابهتان، إذاً بنحسب  F<sub>z</sub> عند الـ 0،
+
+531
+01:04:48,480 --> 01:04:52,280
+0، و π/4، كلها أيضاً تساوي جذر 2،
+
+532
+01:04:52,280 --> 01:04:59,450
+تساوي 1، إذاً أقدر أجيب له الـ linearization، L كـ
+
+533
+01:04:59,450 --> 01:05:04,170
+دالة في x, y,
+
+534
+01:05:04,330 --> 01:05:15,390
+z، لدينا ثلاثة لأنها ثلاثة متغيرات،  f of 0, 0, π/4،
+
+535
+01:05:15,390 --> 01:05:23,550
+اللي هو 1، F<sub>x</sub> الذي مقداره 0
+
+536
+01:05:31,980 --> 01:05:38,560
+زائد F<sub>y</sub> اللي هي بواحد في y ناقص الـ 0
+
+537
+01:05:38,560 --> 01:05:45,760
+F<sub>z</sub> أيضاً 1، في z ناقص π/4
+
+538
+01:05:45,760 --> 01:05:50,720
+يبقى بناءً على ذلك، الـ linearization يجب أن يكون
+
+539
+01:05:50,720 --> 01:05:55,280
+x + y + z
+
+540
+01:05:59,300 --> 01:06:05,640
+يبقى هذا 0 في أي رقم في 0، هو يصبح صحيح، وهذا
+
+541
+01:06:05,640 --> 01:06:10,760
+شيء مميز جداً، يبقى وصوله على ماذا؟ هذه النقطة، يبقى
+
+542
+01:06:10,760 --> 01:06:18,520
+y + z - π/4 + 1، كل هذا الـ
+
+543
+01:06:18,520 --> 01:06:26,220
+linearization لـ X, Y, و Z، شكراً، يبقى هذا  نهاية
+
+544
+01:06:26,220 --> 01:06:27,700
+ماذا من المسألة؟
+
+545
+01:06:30,040 --> 01:06:34,320
+الآن  لحساب الـ M، بدنا نروح نحسب ستة
+
+546
+01:06:34,320 --> 01:06:40,080
+شغلات، تمام، إذاً بدنا نروح للستة شغلات نحسبها، وهي
+
+547
+01:06:40,080 --> 01:06:42,700
+القيمة المطلقة لـ F<sub>xx</sub>، القيمة المطلقة لـ
+
+548
+01:06:42,700 --> 01:06:47,620
+F<sub>yy</sub>،  F<sub>zz</sub> إلى آخره
+
+549
+01:06:47,620 --> 01:06:55,040
+لغاية ما نكمل، إذاً بدنا نروح إلى ماذا؟  F<sub>xx</sub>
+
+550
+01:06:55,040 --> 01:07:00,350
+يبقى  نشتقها مرة أخرى بالنسبة إلى X، يبقى
+
+551
+01:07:00,350 --> 01:07:09,570
+سالب جذر 2 cos X، وهنا sin Y زائد Z، لا علاقة له
+
+552
+01:07:09,570 --> 01:07:16,570
+بالمرة نحسبها، يبقى هذا يعطينا  F<sub>xx</sub>
+
+553
+01:07:16,570 --> 01:07:25,150
+عند النقطة 0، 0، π/4، cos 0 = 1، يبقى سالب
+
+554
+01:07:25,150 --> 01:07:32,600
+جذر 2 في 1، و sin π/4 = 1/جذر
+
+555
+01:07:32,600 --> 01:07:37,460
+2، يبقى النتيجة ماذا؟ سالب 1، يبقى
+
+556
+01:07:37,460 --> 01:07:44,640
+F<sub>x</sub> كانت بـ 0، لكن F<sub>xx</sub>  مقدارها بسالب 1
+
+557
+01:07:44,640 --> 01:07:53,660
+بدنا نيجي إلى ماذا؟ القيمة المطلقة لـ F<sub>xx</sub>، بدنا نسيب
+
+558
+01:07:53,660 --> 01:07:56,400
+القيمة المطلقة لسالب 1، = 1
+
+559
+01:08:00,450 --> 01:08:05,670
+يجب أن نشتق بالنسبة إلى Y، يبقى جذر 2 في
+
+560
+01:08:05,670 --> 01:08:12,610
+cos X، لا علاقة له، ويبقى cos  سالب sin Y
+
+561
+01:08:12,610 --> 01:08:18,190
+زائد Z في مشتقة Y، تساوي 1، يجب أن
+
+562
+01:08:18,190 --> 01:08:26,410
+أحسب F<sub>yy</sub> عند النقطة 0، 0، و π/4،
+
+563
+01:08:26,410 --> 01:08:34,520
+تساوي جذر 2، سالب جذر 2 في 1 في
+
+564
+01:08:34,520 --> 01:08:42,820
+ماذا؟ في 1/جذر 2، وكذلك تساوي ماذا؟ سالب
+
+565
+01:08:42,820 --> 01:08:48,280
+1، يبقى القيمة المطلقة لـ F<sub>yy</sub>،
+
+566
+01:08:48,280 --> 01:08:51,160
+القيمة المطلقة لسالب 1، = 1
+
+567
+01:08:59,690 --> 01:09:08,710
+جذر 2 و sin X sin Y زائد Z، مشتقتها
+
+568
+01:09:08,710 --> 01:09:15,910
+بالنسبة إلى Z،  وضعنا السالب خارجاً، نحسب الآن المشتقة F<sub>zz</sub>
+
+569
+01:09:15,910 --> 01:09:24,590
+عند النقطة 0، 0، π/4، يساوي سالب
+
+570
+01:09:24,590 --> 01:09:32,330
+جذر 2 في 1 في sin،  هنا أيضاً جذر 2،
+
+571
+01:09:32,330 --> 01:09:39,210
+اللي هو سالب 1، يبقى القيمة المطلقة لـ F<sub>zz</sub> =
+
+572
+01:09:39,210 --> 01:09:44,470
+القيمة المطلقة لسالب 1 أيضاً، =
+
+573
+01:09:44,470 --> 01:09:46,770
+الذي هو 1
+
+574
+01:10:19,560 --> 01:10:34,600
+F<sub>xy</sub>، هي المشتقة الجزئية بالنسبة إلى Y، لـ F<sub>x</sub>، سالب
+
+575
+01:10:34,600 --> 01:10:37,340
+جذر 2 sin X
+
+576
+01:10:46,690 --> 01:10:50,830
+cos Y
+
+577
+01:10:50,830 --> 01:10:59,110
+زائد Z،  نحسب F<sub>xy</sub> عند النقطة 0، 0، π/4،
+
+578
+01:10:59,110 --> 01:11:09,930
+ويساوي سالب جذر 2 في 0 في 1/جذر 2، ويساوي 0،
+
+579
+01:11:09,930 --> 01:11:14,030
+بعد ذلك،  يبقى القيمة المطلقة لها = 0، نحتاج الـ
+
+580
+01:11:14,030 --> 01:11:22,880
+F<sub>xz</sub>،  اللي هي المشتقة الجزئية بالنسبة إلى Z، لـ
+
+581
+01:11:22,880 --> 01:11:28,960
+F<sub>x</sub>، نشتق F<sub>x</sub> من جديد،  سالب جذر
+
+582
+01:11:28,960 --> 01:11:38,960
+2 cos X، لا علاقة له، وهذه cos Y زائد Z، يبقى
+
+583
+01:11:38,960 --> 01:11:44,420
+F<sub>xz</sub>، نفس النتيجة،  = 0
+
+584
+01:11:44,420 --> 01:11:49,440
+تساوي 0،  أوجدنا F<sub>xy</sub>، F<sub>xz</sub>، نحتاج الـ
+
+585
+01:11:49,440 --> 01:11:57,280
+F<sub>yz</sub>، المشتقة الجزئية بالنسبة إلى Z، لـ F<sub>y</sub>،
+
+586
+01:11:57,280 --> 01:12:04,900
+بدنا نيجي إلى F<sub>y</sub>، جذر 2 cos X، لا علاقة له،
+
+587
+01:12:06,090 --> 01:12:14,310
+يبقى سالب sin Y زائد Z
+
+588
+01:12:36,260 --> 01:12:46,600
+F<sub>yz</sub>،  القيمة المطلقة  = 1، و مقداره
+
+589
+01:12:46,600 --> 01:12:55,760
+بـ 1، لدينا قيمة، اثنان، ثلاثة، وهي الرابعة، وهذه
+
+590
+01:12:55,760 --> 01:13:00,320
+الخامسة، وهذه السادسة
+
+591
+01:13:12,920 --> 01:13:22,060
+Y و Z أقل من أو تساوي M،  X ناقص X<sub>0</sub> كقيمة مطلقة،
+
+592
+01:13:22,060 --> 01:13:29,880
+و Y ناقص Y<sub>0</sub> كقيمة مطلقة، و Z
+
+593
+01:13:29,880 --> 01:13:38,190
+ناقص Z<sub>0</sub> كقيمة مطلقة، الكل تربيع، يبقى الـ Error
+
+594
+01:13:38,190 --> 01:13:43,830
+الذي لدينا هذا لـ X، Y، و Z أقل من أو تساوي نصف M،
+
+595
+01:13:43,830 --> 01:13:52,630
+بمقدار 1، 1، 1، مجرد أن كل واحدة منهم 1
+
+596
+01:13:52,630 --> 01:13:59,810
+من مئة، يبقى 0.1، 0.1،
+
+597
+01:13:59,810 --> 01:14:07,320
+0.1، 0.1، بشكل عام، يبقى هذه
+
+598
+01:14:07,320 --> 01:14:15,940
+الصيغة، نصف في ماذا؟ 0.3،
+
+599
+01:14:15,940 --> 01:14:23,600
+لكل تربيع، يبقى هذا الكلام يساوي نصف في 0.3
+
+600
+01:14:23,600 --> 01:14:29,580
+لكل تربيع = 0.09، من عشرة آلاف
+
+601
+01:14:29,580 --> 01:14:35,060
+عشرة آلاف، رقمين بعد الفاصلة، يبقى هذا الـ 0.
+
+602
+01:14:38,350 --> 01:14:48,370
+00009، تمام،  إن شئتم نقول 0.00045
+
+603
+01:14:48,370 --> 01:14:51,530
+نصف
+
+604
+01:14:51,530 --> 01:14:59,930
+يبقى  45 من 100000، كسر  كما تشاهدون متناهي
+
+605
+01:14:59,930 --> 01:15:05,190
+في الصغر، إلى هنا،  توقفنا، انتهينا من هذا الجزء
+
+606
+01:15:05,760 --> 01:15:13,460
+نقوم بحل التمارين 11، 6،  المسائل من 3 إلى
+
+607
+01:15:13,460 --> 01:15:20,540
+21،  وكذلك من 25
+
+608
+01:15:20,540 --> 01:15:27,360
+إلى 45، أيضاً
+
+609
+01:15:30,240 --> 01:15:36,880
+الجزء الأخير الذي سنأخذه في هذا الفصل، هو
+
+610
+01:15
+
+667
+01:23:18,730 --> 01:23:23,370
+في شبه كثير جدا، الدالة f of x, y المعرفة على ال
+
+668
+01:23:23,370 --> 01:23:27,710
+region R، التي تحتوي على النقطة a وb
+
+669
+01:23:27,710 --> 01:23:31,650
+يبقى الـ f of a, b  بسميها local maximum إذا كان
+
+670
+01:23:31,650 --> 01:23:37,990
+قيمة الدالة هذه أكبر من أي قيمة أخرى للدالة بحيث
+
+671
+01:23:37,990 --> 01:23:41,090
+تكون موجودة في الـ domain تبعها، هذا في الـ
+
+672
+01:23:41,090 --> 01:23:45,310
+local maximum، و الـ local minimum بتكون أقل من أي
+
+673
+01:23:45,310 --> 01:23:49,550
+قيمة أخرى للدالة على الـ domain تبعها. هل اختلف هذا
+
+674
+01:23:49,550 --> 01:23:53,630
+التعريف عن تعريف Calculus؟ أيه، اللهم إلَّه بس الـ
+
+675
+01:23:53,630 --> 01:23:57,710
+function في two variables، بقى نقول معرفة على
+
+676
+01:23:57,710 --> 01:24:02,960
+open disk، تمام. طيب، الكلام هذا
+
+677
+01:24:02,960 --> 01:24:09,420
+بدنا نروح نرسمه بالرسم حتى يظهر معنى كل واحد من
+
+678
+01:24:09,420 --> 01:24:14,900
+التعريفين الاثنين اللي عندنا. فبنروح ناخد محاور X، Y
+
+679
+01:24:14,900 --> 01:24:19,760
+و Z، لأن احنا بنتكلم على وين؟ على الفراغ. إذا
+
+680
+01:24:19,760 --> 01:24:24,200
+احنا لو روحنا أخدنا المحاور بالشكل اللي على هذا
+
+681
+01:24:24,200 --> 01:24:27,940
+يبقى
+
+682
+01:24:27,940 --> 01:24:36,640
+هذا محور X، هذا محور Y، وهذا محور Z. لما أقول أن عندي
+
+683
+01:24:36,640 --> 01:24:43,340
+function في X و Y، يعني كأن Z as a function of X و Y
+
+684
+01:24:43,340 --> 01:24:44,780
+لما أقول أن عندي function في X و Y، يعني كأن Z as a
+
+685
+01:24:44,780 --> 01:24:47,280
+function of X و Y. لما أقول أن عندي function في X و Y
+
+686
+01:24:47,280 --> 01:24:51,180
+يعني كأن Z as
+
+687
+01:24:51,180 --> 01:24:52,120
+a function
+
+688
+01:24:57,350 --> 01:25:02,010
+أيش ما يكون، يكون كويس. مكان الـ service على الشكل
+
+689
+01:25:02,010 --> 01:25:08,850
+اللي عندنا الآن. بدي آجي للـ domain تبعه، يبقى الـ
+
+690
+01:25:08,850 --> 01:25:16,430
+domain تبعه بقي كأنه بسقط هذا كله على المستوى x, y
+
+691
+01:25:16,430 --> 01:25:21,930
+plane، بيصير عند مين يا بنات؟ هنا اللي هو disk بالشكل
+
+692
+01:25:21,930 --> 01:25:25,850
+اللي عندنا. طيب،
+
+693
+01:25:25,850 --> 01:25:33,260
+كويس. الآن، لو جيت للنقطة اللي عندنا هذه فوق، وجيت
+
+694
+01:25:33,260 --> 01:25:40,540
+أسقطها هنا، يبقى بتجيني وين؟ على مركز الـ disk
+
+695
+01:25:40,540 --> 01:25:47,340
+مركز الدائرة هو النقطة A و B، يبقى هذه النقطة اللي
+
+696
+01:25:47,340 --> 01:25:49,160
+عندنا A و B
+
+697
+01:25:51,820 --> 01:25:57,180
+يبقى يا بنات، كأنه domain الدالة هو الدائرة الزرقاء
+
+698
+01:25:57,180 --> 01:26:01,120
+اللي عندنا، هذا هو الـ domain للدالة، و الدالة وين هي؟
+
+699
+01:26:01,120 --> 01:26:05,920
+رسميتها فوق، لكن الـ domain تبعها وين؟ في المستوى xy
+
+700
+01:26:05,920 --> 01:26:10,380
+فلان أندي f of x, y، تمام. يبقى الـ domain تبعها في الـ
+
+701
+01:26:10,380 --> 01:26:17,250
+xy plane. طيب، نرجع للتعريف اللي احنا جايينه، ونمشي
+
+702
+01:26:17,250 --> 01:26:21,630
+معاه خطوة بخطوة، ونحاول نسقط هذا التعريف على الرسمة
+
+703
+01:26:21,630 --> 01:26:25,310
+اللي عندنا هنا، عشان تثبت هذه المعلومة في دماغنا
+
+704
+01:26:25,310 --> 01:26:30,410
+كويس. فإيش بيقول هنا؟ بيقول:  f of x, y، معرفة
+
+705
+01:26:30,410 --> 01:26:35,810
+على region R containing the point A و B، يبقى معرفة
+
+706
+01:26:35,810 --> 01:26:41,840
+على region R. بدي أفترض أن هذه كلها هي الـ region R
+
+707
+01:26:41,840 --> 01:26:44,960
+اللي هي الـ function المعرفة، لأن أنا أخذت جزء منها
+
+708
+01:26:44,960 --> 01:26:48,300
+هذا جزء من الـ surface، أيًّا ما يكون هذا الـ surface
+
+709
+01:26:48,300 --> 01:26:52,500
+يكون. تمام. يبقى هذا الـ region R. الـ region R جاي وين
+
+710
+01:26:52,500 --> 01:26:58,660
+يا بنات؟ في المستوى XY plane، اه، أوعى تنسى طيب.
+
+711
+01:26:58,660 --> 01:27:05,580
+بقول: في هذه الحالة، F of A, B is a local maximum. وين
+
+712
+01:27:05,580 --> 01:27:11,280
+الـ f of a, b؟ يبقى النقطة اللي عندها دي، يبقى a, b
+
+713
+01:27:11,280 --> 01:27:16,880
+و f of a, b، الخط الأزرق المنقط هذا، هذا الطول كله
+
+714
+01:27:16,880 --> 01:27:21,480
+يعتبر f of a, b. ليش؟ لأن النقطة اللي عندها دي في
+
+715
+01:27:21,480 --> 01:27:29,200
+الفراغ هنا. لو جيت حددتها، بتبدأ يكون a, b، و f of
+
+716
+01:27:29,200 --> 01:27:34,190
+a, b. صحيح ولا لأ؟ يجب أن أُعطي إحداثيات النقطة اللي
+
+717
+01:27:34,190 --> 01:27:38,110
+في الـ top تبع الـ surface اللي عندها. طيب، عشان أقول
+
+718
+01:27:38,110 --> 01:27:43,510
+لك: النقطة هذه بسميها local maximum إذا كانت
+
+719
+01:27:43,510 --> 01:27:49,750
+قيمة الدالة أكبر من أو تساوي عند هذه النقطة، أكبر من
+
+720
+01:27:49,750 --> 01:27:55,890
+أو تساوي أي قيمة أخرى موجودة في domain x, y، اللي
+
+721
+01:27:55,890 --> 01:28:00,750
+موجودة في الـ open disk اللي مركزه a, b، اللي هو a, b
+
+722
+01:28:00,750 --> 01:28:05,730
+يبقى هذا اللي هو الـ open disk اللي مركزه في A, B
+
+723
+01:28:05,730 --> 01:28:11,470
+طيب، بدي آجي أشوف كيف بدي آخد أي نقطة موجودة في الـ
+
+724
+01:28:11,470 --> 01:28:17,390
+open disk. لو جيت أخذت أي نقطة زي النقطة هذه موجودة
+
+725
+01:28:17,390 --> 01:28:20,870
+في الـ open disk، بدي أشوف قيمة الدالة عندها، يبقى
+
+726
+01:28:20,870 --> 01:28:25,530
+بطلع لغاية ما أجاوب مين؟ ما أجاوب السطح. يعني لو جيت
+
+727
+01:28:25,530 --> 01:28:30,130
+بدي أجاوب السطح بالشكل اللي عندنا، يمشي يمشي أجابته
+
+728
+01:28:30,130 --> 01:28:34,390
+مثلًا عند النقطة هذه، إذا
+
+729
+01:28:36,110 --> 01:28:39,150
+البعد اللي عندك هذا الأسود، ولا البعد الأزرق؟ من
+
+730
+01:28:39,150 --> 01:28:44,130
+اللي أكبر؟ الأزرق أكبر. يبقى بناء عليه، قيمة الدالة
+
+731
+01:28:44,130 --> 01:28:48,570
+صارت أقل من قيمة الدالة عند النقطة A, B. أو بمعنى
+
+732
+01:28:48,570 --> 01:28:54,690
+آخر، قيمة الدالة عند A, B أكبر من أي قيمة على الـ
+
+733
+01:28:54,690 --> 01:28:58,410
+open disk. طبعًا هناخد نقطة عشوائية، وبالتالي دي
+
+734
+01:28:58,410 --> 01:29:03,470
+ممكن تكون أي نقطة أخرى. يبقى هذه النقطة الإحداثية
+
+735
+01:29:03,470 --> 01:29:10,030
+اللي هي x, y.  إذا، قيمة الدالة عند نقطة x, y، دائمًا
+
+736
+01:29:10,030 --> 01:29:17,450
+وأبدًا أقل من مين؟ من قيمة الدالة عند مين؟ عند A, B.
+
+737
+01:29:17,450 --> 01:29:21,270
+إذا حدث ذلك، يبقى النقطة اللي فوق بتقول عنها مين؟
+
+738
+01:29:21,270 --> 01:29:27,870
+local maximum. طيب، استنى شوية، نرجع بالذاكرة إلى
+
+739
+01:29:27,870 --> 01:29:32,070
+الدرس اللي في Calculus A. بقى أقول فيه: في Calculus A، عند
+
+740
+01:29:32,070 --> 01:29:37,840
+local maximum، في عندي المشتقة بتكون zero، و
+
+741
+01:29:37,840 --> 01:29:43,980
+لو رسمت tangent line بيصير مين؟ أفقي، صحيح؟ طب، أكرر،
+
+742
+01:29:43,980 --> 01:29:48,120
+tangent line بقدر أرسم عند النقطة اللي فوق بس واحد
+
+743
+01:29:48,120 --> 01:29:54,430
+tangent line. ماذا يعني؟ يبقى هذه الـ tangents بيجمعهم
+
+744
+01:29:54,430 --> 01:29:59,330
+في مستوى واحد اسمه الـ tangent plane. يبقى الـ
+
+745
+01:29:59,330 --> 01:30:05,150
+tangent plane في هذه الحالة يكون أفقيًا. يعني لو
+
+746
+01:30:05,150 --> 01:30:10,070
+جيت رسمت هذا الـ tangent plane، على سبيل المثال، يبقى
+
+747
+01:30:10,070 --> 01:30:15,350
+الـ tangent plane بيصير بالشكل اللي عندنا هذا. هي الـ
+
+748
+01:30:15,350 --> 01:30:22,410
+tangent plane اللي هو المضلل بالأزرق هذا. مَسّ مين؟
+
+749
+01:30:22,410 --> 01:30:27,890
+مَسّ الـ surface عند مين؟ عند النقطة هذه. يبقى هذه هي
+
+750
+01:30:27,890 --> 01:30:33,510
+نقطة التماس، وهذا الـ plane يكون أفقيًا، وبالتالي
+
+751
+01:30:33,510 --> 01:30:40,960
+معادلته z تساوي z naught، يعني Z تساوي ثلاثة، أربعة،
+
+752
+01:30:40,960 --> 01:30:46,460
+خمسة حسب البعد بينه وبين المستوى XY. لأن الـ XY
+
+753
+01:30:46,460 --> 01:30:51,520
+معادلة Z تساوي كم؟ zero. يعني لو قلنا مستوى الغرفة
+
+754
+01:30:51,520 --> 01:30:55,760
+اللي عندنا هذه، معادلة Z تساوي zero. لو ارتفعنا
+
+755
+01:30:55,760 --> 01:31:00,000
+مستوى السقف، بيساوي جدًّا، شي المسافة بينه وبين السقف ثلاثة
+
+756
+01:31:00,000 --> 01:31:05,300
+متر، إذا السقف معادلته Z تساوي ثلاثة، يعني Z naught مثلًا
+
+757
+01:31:05,300 --> 01:31:10,500
+عندنا بتلاتة، اتنين، واحد، عشرة، قد ما يكون. مستوى الآن
+
+758
+01:31:10,500 --> 01:31:17,440
+المستوى الأزرق يكون أفقيًا، وبالتالي هذه الملاحظة
+
+759
+01:31:17,440 --> 01:31:22,240
+اللي كتبناها هنا، لما
+
+760
+01:31:22,240 --> 01:31:25,240
+أقول local extrema، يعني جبت الـ local maximum و الـ
+
+761
+01:31:25,240 --> 01:31:28,380
+local minimum، يعني جمعتهم كلهم بـ local
+
+762
+01:31:28,380 --> 01:31:33,520
+extrema، الـ tangent plane بيكون horizontal، وبالتالي
+
+763
+01:31:33,520 --> 01:31:40,410
+المعادلة تكون… اللي اتكلمنا عليه على الـ local
+
+764
+01:31:40,410 --> 01:31:43,850
+maximum ده، بيروح يتكرر على الـ local minimum
+
+765
+01:31:43,850 --> 01:31:49,510
+يبقى نفس الصيغة، بس قلنا: الـ f of A, B يكون أقل من f
+
+766
+01:31:49,510 --> 01:31:54,030
+of X, Y في جميع القيم على الإطلاق في الـ open disk
+
+767
+01:31:54,030 --> 01:31:57,950
+اللي يمثل جزء من الـ domain. يبقى يا بنات، لو روحت أخذت
+
+768
+01:31:57,950 --> 01:32:03,510
+المحاور مرة ثانية، في هذا الشكل، وقلت: هذا محور X،
+
+769
+01:32:03,510 --> 01:32:09,310
+وهذا محور Y، وهذا محور Z، يبقى النقطة هذه يا بنات،
+
+770
+01:32:09,310 --> 01:32:15,750
+تعتبر f of a, b، القيمة القصوى، الـ local maximum. لو خلّقت
+
+771
+01:32:15,750 --> 01:32:24,470
+أسئلة، هذه تمثل الـ local maximum point. طيب، لو جيت
+
+772
+01:32:24,470 --> 01:32:30,280
+تخيل أن عندي surface، surface بالشكل هذا، ومن هنا
+
+773
+01:32:30,280 --> 01:32:37,000
+كان شكله بالشكل اللي عندنا، وجيت أسقطه هذا على
+
+774
+01:32:37,000 --> 01:32:45,140
+مين؟ على المستوى XY plane، بهذا الشكل، صار عنده
+
+775
+01:32:45,140 --> 01:32:51,800
+إيش؟ الـ disk بالشكل هذا. جيت، ان النقطة هذه إيش؟ أَجَتْ
+
+776
+01:32:51,800 --> 01:32:55,160
+وين؟ في المركز اللي هو A, B.
+
+777
+01:32:57,840 --> 01:33:02,660
+خُذ أي نقطة في الـ open disk في المستوى XY،  وتكون
+
+778
+01:33:02,660 --> 01:33:08,240
+النقطة لمين؟ عندنا نقطة هذه. يبقى النقطة هذه الـ  x, y.
+
+779
+01:33:08,240 --> 01:33:15,040
+جاء الطالب، توكل على الله، وجاء الطالب، يقابل في
+
+780
+01:33:15,040 --> 01:33:21,240
+الـ surface وين؟ عند النقطة اللي عندنا هذه. إذا أَجَتْ
+
+781
+01:33:21,240 --> 01:33:25,500
+النقطة هذه أعلى من النقطة اللي عندنا هنا، وبالتالي
+
+782
+01:33:25,860 --> 01:33:32,700
+قيمة الدالة عند A, B كانت أقل من أي قيمة أخرى
+
+783
+01:33:32,700 --> 01:33:36,780
+في الـ domain تبع مين؟ تبع الدالة اللي عندنا هذه.
+
+784
+01:33:36,780 --> 01:33:41,700
+يبقى هذه النقطة إيش بسميها؟ local minimum. يبقى هذه
+
+785
+01:33:41,700 --> 01:33:46,800
+اللي عندنا بتصير هنا local minimum.
+
+786
+01:33:49,080 --> 01:33:53,700
+وبالتالي، لو رسمت tangent plane، بدي يكون كمان مين؟
+
+787
+01:33:53,700 --> 01:33:58,800
+كمان أفقيًا، وبدي يمسّ وين؟ عند النقطة اللي عندنا
+
+788
+01:33:58,800 --> 01:34:05,160
+يا بنات. لو روحت رسمته، هرسمه باللون الأزرق كذلك، زي
+
+789
+01:34:05,160 --> 01:34:09,700
+ما رسمنا هذا باللون الأزرق. بدي يكون عندك مماسّ طبعًا
+
+790
+01:34:09,700 --> 01:34:15,440
+هنا مش هيظهر، هيظل ماشي هيك، ويجيك المستوى بالشكل
+
+791
+01:34:15,440 --> 01:34:22,940
+اللي عندنا هذا هيك. يبقى هذا المستوى المضلل بالأزرق
+
+792
+01:34:22,940 --> 01:34:30,670
+حصل تماس بينه وبين المنحنى عند النقطة. إلا أن هذا
+
+793
+01:34:30,670 --> 01:34:37,130
+يبقى هذا معادلته z كذلك تساوي z naught، جدًّا ما تطلع
+
+794
+01:34:37,130 --> 01:34:41,010
+تطلع. يبقى عرفنا شو الفرق بين الـ local maximum و
+
+795
+01:34:41,010 --> 01:34:45,980
+الـ local minimum من خلال الرسم. الـ domain تبعه
+
+796
+01:34:45,980 --> 01:34:51,660
+بيكون في المستوى XY، لكن الرسم بتكون فوق الـ
+
+797
+01:34:51,660 --> 01:34:55,120
+local maximum و الـ local minimum. بعتبر عندي disk
+
+798
+01:34:55,120 --> 01:35:00,440
+مركزه النقطة اللي هي تعتبر local maximum أو local
+
+799
+01:35:00,440 --> 01:35:05,060
+minimum. لو جيت لأي قيمة للدالة خلال أي نقطة
+
+800
+01:35:05,060 --> 01:35:09,300
+موجودة في هذا الـ domain، إذا والله لقيتها أقل من
+
+801
+01:35:09,300 --> 01:35:13,740
+قيمة الدالة، يبقى local maximum. أكبر، يبقى local
+
+802
+01:35:13,740 --> 01:35:18,850
+minimum، وانتهينا من هنا من القصة اللي عندنا. طيب،
+
+803
+01:35:18,850 --> 01:35:22,750
+الآن، مذاكرين بقى، بيقولوا: في عندي critical points،
+
+804
+01:35:22,750 --> 01:35:28,870
+نقاط حرجة. وكيف كنا نحصل عليهم؟ بنروح نجيب المشتقة
+
+805
+01:35:28,870 --> 01:35:33,370
+الأولى، ونسويها بالـ zero. القيم اللي بتحققها بس
+
+806
+01:35:33,370 --> 01:35:38,890
+هي critical points. بس هذه والله هي كمان شغلة، آه،
+
+807
+01:35:38,890 --> 01:35:44,620
+لو كانت المشتقة غير معرفة عند نقطة، بقول: هذه كمان
+
+808
+01:35:44,620 --> 01:35:48,680
+critical point. طيب، بدي أسألك كمان سؤال إجباري،
+
+809
+01:35:48,680 --> 01:35:52,060
+عندي critical points، بتكون عندي local maximum و
+
+810
+01:35:52,060 --> 01:35:57,180
+local minimum؟ لأ، ليس بالضرورة. يعني مش كل critical
+
+811
+01:35:57,180 --> 01:36:02,760
+point بتكون هي local maximum أو local minimum. وهذا
+
+812
+01:36:02,760 --> 01:36:08,800
+الكلام ينطبق على الوضع عندنا تمامًا. إذا بدنا
+
+813
+01:36:08,800 --> 01:36:13,350
+نيجي لحاجة يا بنات اسمها الـ first derivative test،
+
+814
+01:36:13,350 --> 01:36:19,810
+for local extreme values. بنحط عنوان بعد هذا تمامًا،
+
+815
+01:36:19,810 --> 01:36:24,790
+و بنقول: الـ first derivative
+
+816
+01:36:24,790 --> 01:36:28,510
+test
+
+817
+01:36:28,510 --> 01:36:38,930
+for local extreme values. for local extreme values.
+
+818
+01:36:40,910 --> 01:36:51,650
+إيش بيقول هذا؟ بيقول: f of x, y has
+
+819
+01:36:51,650 --> 01:37:02,970
+a local maximum
+
+820
+01:37:02,970 --> 01:37:14,300
+or minimum value. or minimum value at an interior
+
+821
+01:37:14,300 --> 01:37:25,080
+point of
+
+822
+01:37:25,080 --> 01:37:29,740
+its
+
+823
+01:37:29,740 --> 01:37:35,900
+domain، المجال
+
+824
+01:37:35,900 --> 01:37:36,680
+تبعها.
+
+825
+01:37:40,130 --> 01:37:52,430
+إذا كانت المشتقة الأولى، المشتقة الأولى، المشتقة الأولى
+
+826
+01:37:52,430 --> 01:37:57,770
+مشتقة
+
+827
+01:37:57,770 --> 01:38:01,590
+مشتقة موجودة،
+
+828
+01:38:01,590 --> 01:38:04,630
+هناك
+
+829
+01:38:04,630 --> 01:38:06,550
+ثم
+
+830
+01:38:09,470 --> 01:38:17,510
+الـ Fx عند الـ A و الـ B بدها تساوي zero، و الـ
+
+831
+01:38:17,510 --> 01:38:24,050
+Fy عند الـ A و الـ B كذلك بدها تساوي zero.
+
+832
+01:38:24,050 --> 01:38:30,950
+Definition
+
+833
+01:38:30,950 --> 01:38:37,470
+كمان ثاني، بيقول:
+
+834
+01:38:37,470 --> 01:38:46,840
+Any interior point،  a
+
+835
+01:38:46,840 --> 01:38:50,760
+و b of
+
+836
+01:38:50,760 --> 01:39:03,260
+the domain، of the domain of a function f of x, y
+
+837
+01:39:03,260 --> 01:39:06,900
+is
+
+838
+01:39:06,900 --> 01:39:16,200
+called a critical point، is called a critical point.
+
+83
+
+889
+01:45:44,090 --> 01:45:47,570
+X يساوي صفر إذا المشتقة الأولى بالنسبة ل Y تساوي
+
+890
+01:45:47,570 --> 01:45:51,590
+صفر هذا الأمر الأول، الأمر الثاني لو كانت إحدى
+
+891
+01:45:51,590 --> 01:45:59,770
+المشتقتين أو كلاهما تساوي صفراً، طيب وين بدنا نروح؟
+
+892
+01:45:59,770 --> 01:46:04,590
+ندور على مواضع النهايات العظمى والصغرى؟ بنقول في
+
+893
+01:46:04,590 --> 01:46:09,510
+ثلاثة أماكن، إذا كنت تريد أن تدور وتشوف عند هذه  في
+
+894
+01:46:09,510 --> 01:46:14,050
+local maximum و local minimum،  الآن، المكان الأول
+
+895
+01:46:14,050 --> 01:46:18,890
+النقاط الداخلية، أيه للمشتقة بالنسبة لـ X تساوي
+
+896
+01:46:18,890 --> 01:46:20,530
+المشتقة الأولى بالنسبة لها؟
+
+897
+01:46:28,800 --> 01:46:35,560
+النقاط التي إحدى قيمتها أو كلاهما غير معرفة.
+
+898
+01:46:35,560 --> 01:46:41,000
+الأمر الثالث، على الـ boundary، يبقى  بقي لنا أن نقول احنا
+
+899
+01:46:41,000 --> 01:46:46,250
+في الحالة الكلاسيكية، أول الفترة وآخر الفترة،  بنجي
+
+900
+01:46:46,250 --> 01:46:50,130
+ندور ونقول هذه  ممكن يكون عندها اللي هو local
+
+901
+01:46:50,130 --> 01:46:54,810
+maximum قد يكون وقد لا يكون، تمام، يبقى بروح على
+
+902
+01:46:54,810 --> 01:46:58,930
+المناطق التي هي، اللي هو الـ boundary عندنا، تبع مين؟
+
+903
+01:46:58,930 --> 01:47:03,390
+تبع الـ domain، تبع الدالة، طبعاً لو درسنا الـ boundary
+
+904
+01:47:03,390 --> 01:47:08,140
+في أول section اللي هو أربعة عشر، واحد، مضبوط، يبقى
+
+905
+01:47:08,140 --> 01:47:12,700
+هذا كلام ليس جديداً علينا، المرة القادمة إن شاء الله
+
+906
+01:47:12,700 --> 01:47:18,320
+بنبدأ ناخذ مثال على هذا الشغل ونكمل عليه فيه
+
+907
+01:47:18,320 --> 01:47:23,200
+كمان، يبقى عندي absolute maximum و absolute minimum
+
+908
+01:47:23,200 --> 01:47:27,500
+ونشوف كيف بندور على الـ boundary كمان، مين مين يكون
+
+909
+01:47:27,500 --> 01:47:30,400
+على الـ boundary، في عندي local maximum أو local
+
+910
+01:47:30,400 --> 01:47:35,280
+minimum إن شاء الله، وتعالى طبعاً اليوم السبت بصير
+
+911
+01:47:35,280 --> 01:47:39,910
+خير إن شاء الله، حاولوا تجروا السكين ولو زي قناة
+
+912
+01:47:39,910 --> 01:47:43,490
+جريدة قبل أن تجيء المرة القادمة، عشان احنا نمشيها
+
+913
+01:47:43,490 --> 01:47:46,590
+بالكلمة البيضاء، المعلومة اللي عشانها.
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/vNBEf-x0cGk_postprocess.srt b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/vNBEf-x0cGk_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..87037f90a112b65ecda9b4b63591edef90a87ed9
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/vNBEf-x0cGk_postprocess.srt
@@ -0,0 +1,3652 @@
+1
+00:00:15,420 --> 00:00:20,910
+بسم الله الرحمن الرحيمالان بنكمل ال section اللى
+
+2
+00:00:20,910 --> 00:00:25,550
+بدناه المرة الماضية منها اللى كان اللى هو tangent
+
+3
+00:00:25,550 --> 00:00:29,430
+planes and differential طبعا عرفنا المرة اللى فاتة
+
+4
+00:00:29,430 --> 00:00:33,950
+tangent plane وقلنا المعادلة بتابعة هو هي المستقلة
+
+5
+00:00:33,950 --> 00:00:38,620
+تتدلة بالنسبة ل Fأو بالنسبة ل X عند النقطة X node
+
+6
+00:00:38,620 --> 00:00:43,880
+وY node في X نقص X node زائد المشتقة عندها نفس
+
+7
+00:00:43,880 --> 00:00:48,940
+النقطة في Y نقص Y node زائد مشتقة F بالنسبة لZ عند
+
+8
+00:00:48,940 --> 00:00:53,860
+نفس النقطة في Z نقص Z node يساوي Zero ومن هنا
+
+9
+00:00:53,860 --> 00:00:55,220
+روحنا و طلعنا كمان من
+
+10
+00:01:02,140 --> 00:01:07,020
+هذه النقطة هي حالة خاصة من الحالة الماضية تابعة
+
+11
+00:01:07,020 --> 00:01:11,000
+المرة الماضية تابعة المرة الماضية تابعة المرة
+
+12
+00:01:11,000 --> 00:01:11,300
+الماضية تابعة المرة الماضية تابعة المرة الماضية
+
+13
+00:01:11,300 --> 00:01:11,520
+تابعة المرة الماضية تابعة المرة الماضية تابعة
+
+14
+00:01:11,520 --> 00:01:13,260
+المرة الماضية تابعة المرة الماضية تابعة المرة
+
+15
+00:01:13,260 --> 00:01:14,480
+الماضية تابعة المرة الماضية تابعة المرة الماضية
+
+16
+00:01:14,480 --> 00:01:15,380
+تابعة المرة الماضية تابعة المرة الماضية تابعة
+
+17
+00:01:15,380 --> 00:01:16,880
+المرة الماضية تابعة المرة الماضية تابعة المرة
+
+18
+00:01:16,880 --> 00:01:20,120
+الماضية تابعة المرة الماضية تابزت نول إذا إحنا
+
+19
+00:01:20,120 --> 00:01:26,260
+عندنا surface مواطئ z as a function f of x و y بدي
+
+20
+00:01:26,260 --> 00:01:31,120
+أحاول من خلال هذا ال surface أوصل إلى معادلة
+
+21
+00:01:31,120 --> 00:01:35,540
+مشابهة للمعادلة اللي كنا تثبناها المرة الماضية مع
+
+22
+00:01:35,540 --> 00:01:40,100
+فارق بسيط جدا الآن بدنا نشوف ما هو هذا الفارق
+
+23
+00:01:40,100 --> 00:01:46,460
+البسيطمش هنوجد معادلة للـ plane الذي يكون مماثن
+
+24
+00:01:46,460 --> 00:01:53,960
+للسطح z of x of y عند النقطة vp0 x0 و y0 و z0 ال
+
+25
+00:01:53,960 --> 00:01:58,520
+right f of x of y نقص z يسوى منين؟ Zero يعني
+
+26
+00:01:58,520 --> 00:02:02,080
+المعادلة هذه هنجيب z وين؟ على الشجرة التانية بس
+
+27
+00:02:02,080 --> 00:02:06,040
+ينبسط بشرة مخالفة فال f of x of y نقص z يسوى منين؟
+
+28
+00:02:06,040 --> 00:02:09,920
+Zero المعادلة اللي عندنا هذه الطرف الشمالي صار
+
+29
+00:02:09,920 --> 00:02:11,040
+function في منين؟
+
+30
+00:02:39,830 --> 00:02:44,800
+في تلاثة متغيراتأذا كأنه أنا عندي دالة جديدة
+
+31
+00:02:44,800 --> 00:02:52,800
+سميتها capital F of X و Y و Z بدأت سوية F of X و Y
+
+32
+00:02:52,800 --> 00:02:57,580
+نقصدها كأنها هذه الدالة الأصلية و لما سويتها بال
+
+33
+00:02:57,580 --> 00:03:04,820
+zero كان هذا هو zero level surface بالنسبة لهاالان
+
+34
+00:03:04,820 --> 00:03:10,420
+بنجيب ال equation لتنجل لهذا ال level surface بقول
+
+35
+00:03:10,420 --> 00:03:14,200
+بسيطة جدا، بنشتغل ال function بالنسبة ل X بالنسبة
+
+36
+00:03:14,200 --> 00:03:19,620
+ل Y و بالنسبة ل Z و نعوض في معادلة المرة الماضية
+
+37
+00:03:19,620 --> 00:03:24,760
+يبقى بنات بدالي capital F X يعني بدي اشتغل الدالة
+
+38
+00:03:24,760 --> 00:03:32,420
+الجديدة بالنسبة ل Xهذه المشتقة دلالي على اليمين
+
+39
+00:03:32,420 --> 00:03:37,440
+بالنسبالك هذه function في x و y يبقى مشتقتها بتكون
+
+40
+00:03:37,440 --> 00:03:45,840
+f small f تمام والزد يبقى كم؟ Zero يبقى ناقص Zero
+
+41
+00:03:45,840 --> 00:03:51,540
+يبقى تصبح المشتقة تبعت capital F of x و y هي نفس
+
+42
+00:03:51,540 --> 00:03:56,470
+المشتقة تبعت من تبعت ال function اللي عندناIn
+
+43
+00:03:56,470 --> 00:04:03,310
+general بدي أقوله بدي أجيب f x عند النقطة x node و
+
+44
+00:04:03,310 --> 00:04:09,730
+y node و z node هذا الكلام بدي أسوي f x عند النقطة
+
+45
+00:04:09,730 --> 00:04:18,270
+x node و y node و z node طيب بدي أجيب fy هذا
+
+46
+00:04:18,270 --> 00:04:23,200
+الكلام بدي أسوي و باختصارة بدي أخليها نفسيعند
+
+47
+00:04:23,200 --> 00:04:27,840
+النقطة x نوت و y نوت و z نوت معناته بدلا اشتقت
+
+48
+00:04:27,840 --> 00:04:32,020
+دالة لان هذه بالنسبة لمين لو ايه يبقى مشتقة الـ z
+
+49
+00:04:32,020 --> 00:04:38,120
+جزيرو يبقى هذه يبقى سوية f small x عند النقطة fy
+
+50
+00:04:38,120 --> 00:04:44,960
+عند النقطة x نوت و y نوت و z نوت ناقص الـ zero طيب
+
+51
+00:04:44,960 --> 00:04:47,100
+كويس بدأ أروح أجيب كامة
+
+52
+00:04:49,850 --> 00:04:54,890
+عند النقطة التي هي x node و y node و z node يبقى
+
+53
+00:04:54,890 --> 00:04:59,010
+هذا السبب بده zero طبعا هذه ده اللي كلها في x و y
+
+54
+00:04:59,010 --> 00:05:02,750
+و احنا بنفضل بالنسبة إلى z يبقى مشتقتها ب zero
+
+55
+00:05:22,200 --> 00:05:29,500
+هل اختلفت Fx عن Fx الماضية يبقى زي ما هي
+
+56
+00:05:44,450 --> 00:05:49,790
+عند ال X نوت و ال Y نوت و ال Z نوت في مين؟ في ال Y
+
+57
+00:05:49,790 --> 00:05:54,590
+ناقص Y نوت نجي اللي في Z اللي يبقى كده شعلة هنا؟
+
+58
+00:05:54,590 --> 00:06:02,050
+بواحد يبقى هنا هاي سالب واحد في مين؟ في Z ناقص Z
+
+59
+00:06:02,050 --> 00:06:09,230
+نوت كل هذا الكلام بده يساوي Zeroإذا الفرق البسيط
+
+60
+00:06:09,230 --> 00:06:15,430
+بين هذه المعادلة ومعادلة المرة الماضية ان ال F زد
+
+61
+00:06:15,430 --> 00:06:20,170
+عنها طلعت بقداش بسالب واحد وهذا هو الفرق بين
+
+62
+00:06:20,170 --> 00:06:26,410
+المعادلة هذه ومعادلة المرة الماضية كإني ولي خطر
+
+63
+00:06:26,410 --> 00:06:32,630
+تسألي هكذا هذي
+
+64
+00:06:32,630 --> 00:06:36,450
+سالب واحد صحيح وهي سالب واحد موجود تمام صحيح
+
+65
+00:06:40,000 --> 00:06:44,720
+طبعا المدرس الناجح اللي بكون عند حس طلابه، يعني
+
+66
+00:06:44,720 --> 00:06:48,460
+بدي أحس أنه شو اللي بيفهمه و شو اللي بيفهموش، و
+
+67
+00:06:48,460 --> 00:06:51,500
+أنا من النوع اللي بيقرأ هذا في وجوه الطلاب اللي
+
+68
+00:06:51,500 --> 00:06:55,040
+أنا بدرسهم، يعني إذا في شغلة مش واضحة بقرأها في
+
+69
+00:06:55,040 --> 00:07:00,300
+وجههم تمامالذلك الطالب بعرف امتابعني، مش امتابعني،
+
+70
+00:07:00,300 --> 00:07:03,080
+فاهم، مش فاهم من خلال المحاضرة، حتى لو كان القاعة
+
+71
+00:07:03,080 --> 00:07:06,080
+فيها مية طالبة، واحد واحد، المية والعشرين
+
+72
+00:07:06,080 --> 00:07:09,500
+بالنسبالي سيجان، لأنه متعود على اللي هو العدد
+
+73
+00:07:09,500 --> 00:07:12,520
+الكبير أو العدد الصغير، ماتفرقش عندي بالنسبالي،
+
+74
+00:07:12,520 --> 00:07:19,140
+فلذلك بتلاقيني دقيق الملاحظة في هذه الأمور نبدأ
+
+75
+00:07:19,140 --> 00:07:21,220
+ناخد مثال على ذلك example
+
+76
+00:07:28,520 --> 00:07:37,860
+يقول الـ final equation five and equation for the
+
+77
+00:07:37,860 --> 00:07:41,900
+plane that
+
+78
+00:07:41,900 --> 00:07:45,900
+is tangent
+
+79
+00:07:45,900 --> 00:07:47,240
+to the surface
+
+80
+00:07:58,100 --> 00:08:08,300
+والذي يكون هو مثل سطح Z تساوي لل X
+
+81
+00:08:08,300 --> 00:08:15,460
+نقص اتنين Y at the
+
+82
+00:08:15,460 --> 00:08:16,120
+point
+
+83
+00:08:31,820 --> 00:08:36,420
+السؤال مرة ثانية بيقول هذه المعادلة المستوى الذي
+
+84
+00:08:36,420 --> 00:08:42,340
+يكون ممثل في سطح z تساوي لل x ناقص اتنين y عند
+
+85
+00:08:42,340 --> 00:08:47,940
+النقطة تلاتة واحد وزير لو جيت نظرتي هذه المعادلة
+
+86
+00:08:47,940 --> 00:08:54,290
+بلاحظ ان z مواطع ك function تمامفي المتغيرين x و y
+
+87
+00:08:54,290 --> 00:09:01,590
+اذا انا بقدر اكتب هذه المعادلة بطريقة اخرى لو نجلت
+
+88
+00:09:01,590 --> 00:09:08,840
+ال z على الشجرة التانيةلو جيت كتبت ان ال F أو ال
+
+89
+00:09:08,840 --> 00:09:21,140
+LEN LEN ال X ناقص 2Y ناقص Z بدها تساوي Z يبقى حصلت
+
+90
+00:09:21,140 --> 00:09:25,060
+على معادلة جديدة الطرف الشمال صار function في
+
+91
+00:09:25,060 --> 00:09:30,400
+ثلاثة متغيراتاللي ال X و ال Y و ال Z يبقى بناء ان
+
+92
+00:09:30,400 --> 00:09:33,300
+عليها هذا الكلام دي يساوي الكون و الصدر إذا هذا
+
+93
+00:09:33,300 --> 00:09:44,800
+يمثل level surface لدالة ما يبقى this is a أو this
+
+94
+00:09:44,800 --> 00:09:55,980
+is the zero level surface for
+
+95
+00:10:13,770 --> 00:10:23,050
+Fx يبقى Fx نشتقل لين واحدعلى اللى داخل الليل و X
+
+96
+00:10:23,050 --> 00:10:29,110
+نقص اتنين Y فمشتقت ما داخل الليل بالنسبة الى X
+
+97
+00:10:29,110 --> 00:10:35,850
+اللى هو بواحد صحيح بدنا نروح نحسب قداش ال F X عند
+
+98
+00:10:35,850 --> 00:10:42,200
+النقطة المعطاعة تلاتة واحد و Zero بدل سنةهشيل كل X
+
+99
+00:10:42,200 --> 00:10:46,820
+وحط مكانه تلاتة وشيل كل Y وحط مكانه واحد ويصير
+
+100
+00:10:46,820 --> 00:10:53,390
+واحد على تلاتة نقص اتنين ويسوء جدير واحدبنروح نجيب
+
+101
+00:10:53,390 --> 00:11:00,190
+ال Fy كذلك يبقى واحد على X نقص اتنين Y في مستقل
+
+102
+00:11:00,190 --> 00:11:06,410
+مداخل الليمب بالنسبة الى Y اللي هو سالم اتنين يتجه
+
+103
+00:11:06,410 --> 00:11:12,290
+النتيجة هذه بتعطيني ال Fy عند النقطة تلاتة واحد
+
+104
+00:11:12,290 --> 00:11:19,610
+وزيره بتسوي نقص اتنين على تلاتة نقص اتنين وهي سامة
+
+105
+00:11:19,610 --> 00:11:26,540
+الدرج نقص اتنينفز معروفة مباشرة كده يا فنان؟ سالب
+
+106
+00:11:26,540 --> 00:11:32,920
+واحد تمام لأن الان كلها مقدار ثابت بالنسبة لز يبقى
+
+107
+00:11:32,920 --> 00:11:38,180
+مع السلامة ويبقى سالب واحد معناته ان الفز عند
+
+108
+00:11:38,180 --> 00:11:43,700
+التلاتة او واحد وزي او عند اي نقطة اخرى بدل سواء
+
+109
+00:11:43,700 --> 00:11:49,140
+كده واحد الان النقطة موجودة مشتقات التلاتة موجودة
+
+110
+00:11:49,140 --> 00:11:51,360
+اذا اتوماتيك سهل اجيب
+
+111
+00:11:55,140 --> 00:12:00,940
+معادلة هذي سميها ال star و بدنا نعوض في معادلة رقم
+
+112
+00:12:00,940 --> 00:12:05,500
+ال star إذا بدي أشيل ال fx و أضعه في درجة دي ال
+
+113
+00:12:05,500 --> 00:12:13,100
+واحد يبقى هاي واحد دقيق ناقص تلاتة اللي بعدها ال
+
+114
+00:12:13,100 --> 00:12:17,040
+fy ناقص اتنين في ال y
+
+115
+00:12:20,540 --> 00:12:29,920
+بعدها ناقص واحد في زد ناقص بيصير زائد واحد كل هذا
+
+116
+00:12:29,920 --> 00:12:32,440
+الكلام بده يساوي Zero
+
+117
+00:12:38,460 --> 00:12:45,760
+زد فقط لغير اللي نقص Zero بدر يساوي Zero فالفك
+
+118
+00:12:45,760 --> 00:12:51,400
+المعادلة هذه يبقى بصير X نقص تلاتة نقص اتنين Y
+
+119
+00:12:51,400 --> 00:12:58,180
+زائدي اتنين نقص Z كله بدر يساوي Zero او بمعنى اخر
+
+120
+00:12:58,180 --> 00:13:07,230
+شكل تبعها بدر ياخد الشكل التالفX-2Y-Z و7 عندك هنا
+
+121
+00:13:07,230 --> 00:13:12,810
+2 وهنا 3 و3 و3 و3 و3 و3 و3 و3 و3 و3 و1 و1 و1 و1 و1
+
+122
+00:13:12,810 --> 00:13:16,910
+و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1
+
+123
+00:13:16,910 --> 00:13:17,010
+و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1
+
+124
+00:13:17,010 --> 00:13:17,030
+و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1
+
+125
+00:13:17,030 --> 00:13:20,790
+و1 و1 و1 و1 و1 و
+
+126
+00:13:32,830 --> 00:13:38,290
+هل تذكروا موضوع ال linearization في calculus A؟
+
+127
+00:13:52,630 --> 00:13:56,590
+ثم functions of a three variables هنجيب ال
+
+128
+00:13:56,590 --> 00:14:00,630
+linearization في الحالتين طب حد من الذكرة يعني
+
+129
+00:14:00,630 --> 00:14:05,670
+بالبلدين شو يعني مقصود ال linearization؟ عندها
+
+130
+00:14:05,670 --> 00:14:11,970
+نقطة؟ أيوةهو كلمة linearization جاي من كلمة ايه؟
+
+131
+00:14:11,970 --> 00:14:18,930
+من كلمة line تمام؟ ايوة يبقى المثل في الحالة اللي
+
+132
+00:14:18,930 --> 00:14:22,090
+عندنا .. انا عندي function ابنان و بكون ال
+
+133
+00:14:22,090 --> 00:14:28,940
+function صعب التعامل معاها، كويس؟ بجيبدالة أخرى
+
+134
+00:14:28,940 --> 00:14:35,220
+تكافئ هذه الدالة وهذه الدالة بيكون دالة خاطية يعني
+
+135
+00:14:35,220 --> 00:14:40,080
+بيكون الفرق بينها وبين الدالة لأن الفرق بسيط جدا
+
+136
+00:14:40,080 --> 00:14:45,300
+يمكن يمكن الاستغناء عنه هذا معناه كلمة
+
+137
+00:14:45,300 --> 00:14:49,880
+linearization يعني أنا بدي أحول الدالة اللي عندنا
+
+138
+00:14:50,150 --> 00:14:55,050
+الى دالة خطية على نقطة بيصير قيمة الدالة الخطية
+
+139
+00:14:55,050 --> 00:14:59,810
+وقيمة ال function عند هذه النقطة اتنين اردسين مع
+
+140
+00:14:59,810 --> 00:15:05,430
+ثانث بسيط جدا كثر من عشرة كثر من مية كثر من الف
+
+141
+00:15:05,430 --> 00:15:09,330
+وبالتالي يمكن الاستغناء عن ال function الأصلية
+
+142
+00:15:09,330 --> 00:15:14,790
+والتعامل مع ال function الخطية اللي عندنا هذا
+
+143
+00:15:14,790 --> 00:15:20,220
+بالبلد هيكلكن احنا بنشتغل شغل رياضي مشان شغل رياضي
+
+144
+00:15:20,220 --> 00:15:24,200
+بنروح نحط تعريف لل linearization في ال functions
+
+145
+00:15:24,200 --> 00:15:29,300
+of two variables ثم نستخدم هذا التعريف في حساب ال
+
+146
+00:15:29,300 --> 00:15:33,060
+linearization لدالة ما يبقى definition
+
+147
+00:15:45,400 --> 00:15:50,300
+of a function f
+
+148
+00:15:50,300 --> 00:16:01,740
+of x و y at a point عند النقطة x naught و y naught
+
+149
+00:16:01,740 --> 00:16:12,860
+where ال f is differentiable function is
+
+150
+00:16:15,850 --> 00:16:25,370
+عندنا رمز f as a function of x y عمليا يسوى f of x
+
+151
+00:16:25,370 --> 00:16:32,870
+naught و y naught زائد f x عند النقطة x naught و y
+
+152
+00:16:32,870 --> 00:16:41,190
+naught في ال x ناقص ال x naught زائد f y عند
+
+153
+00:16:41,190 --> 00:16:47,700
+النقطة x naught و y naughtفى الـ y ما قصد why not
+
+154
+00:16:47,700 --> 00:16:52,080
+يبقى
+
+155
+00:16:52,080 --> 00:16:56,300
+هذا ال linearization تبع الدلة هو هذا التعريف
+
+156
+00:16:56,300 --> 00:17:01,800
+الأول التعريف الثاني approximation function
+
+157
+00:17:01,800 --> 00:17:05,820
+approximation
+
+158
+00:17:05,820 --> 00:17:09,860
+function
+
+159
+00:17:09,860 --> 00:17:19,380
+يعني الدلة التقريبيةالـ F of XY التي تسوى تقريبا L
+
+160
+00:17:19,380 --> 00:17:28,600
+of XY is called the
+
+161
+00:17:28,600 --> 00:17:38,560
+standard linear
+
+162
+00:17:38,560 --> 00:17:39,280
+approximation
+
+163
+00:17:49,720 --> 00:17:58,520
+Linear Approximation of F at
+
+164
+00:17:58,520 --> 00:18:05,520
+point
+
+165
+00:18:05,520 --> 00:18:08,760
+X0 وY0
+
+166
+00:18:59,840 --> 00:19:03,700
+نرجع للتعريف اللي احنا كاتبينه في هذا مرة ثانية
+
+167
+00:19:05,050 --> 00:19:08,670
+يبقى باجي بقول ال linearization للدالة f of x و y
+
+168
+00:19:08,670 --> 00:19:12,690
+عند النقطة x نقطة و y نقطة حيث ال f دالة قابلة
+
+169
+00:19:12,690 --> 00:19:20,790
+للاشتقاقية هديها الرمز L of x و y قيمة الدالة
+
+170
+00:19:20,790 --> 00:19:25,570
+الأصلية عند النقطة المعطاة f of x نقطة و y نقطة
+
+171
+00:19:25,570 --> 00:19:31,150
+مضافة إليها مشتقة الدالة بالنسبة لx عند تلك النقطة
+
+172
+00:19:31,150 --> 00:19:33,670
+مضروب في x نقص ال x نقطة
+
+173
+00:19:42,420 --> 00:19:49,740
+السؤال هو هل هذه دالة خطية في X و Y أم لا
+
+174
+00:19:54,410 --> 00:20:00,030
+صح ولا لأ؟ وهذا كمان رقم و X نود رقم يبقى بقية X
+
+175
+00:20:00,030 --> 00:20:06,010
+مضروبة في رقم هذا كمان رقم وهذا رقم Y يبقى دالة ما
+
+176
+00:20:06,010 --> 00:20:10,490
+بين X وY كلهم من X وY من الدرجة الأولى إذا معادلة
+
+177
+00:20:10,490 --> 00:20:17,050
+خط مستقيم ومن هنا سمنها دالة خطية Linearization
+
+178
+00:20:17,050 --> 00:20:21,630
+Linearization دالة خطية هذه حصل عليها من مين؟من
+
+179
+00:20:21,630 --> 00:20:27,210
+الدالة الأصلية عند نقطة تقع عالمين على الدالة
+
+180
+00:20:27,210 --> 00:20:34,670
+الأصلية يبقى عمليا هذه القيمة للدالة الخطية عند
+
+181
+00:20:34,670 --> 00:20:40,210
+تلك النقطة تساوي قيمة الدالة الخطية عند تلك النقطة
+
+182
+00:20:40,210 --> 00:20:45,990
+طبعا يكون فارق بسيط جدا من هنا روحنا للتعريف
+
+183
+00:20:45,990 --> 00:20:51,860
+الثاني فقولنا approximation function f of x yتساوي
+
+184
+00:20:51,860 --> 00:20:57,180
+تقريبا ال
+
+185
+00:20:57,180 --> 00:21:04,200
+L of X Y فسميناها الدالة التقريبية للدالة F of X Y
+
+186
+00:21:04,200 --> 00:21:08,700
+هي مين؟ هي L of X Y يبقى هذه اللي بسميها ال
+
+187
+00:21:08,700 --> 00:21:13,120
+standard linear approximation للدالة F عند النقطة
+
+188
+00:21:13,120 --> 00:21:17,750
+اللي عندنا هذهعلى أي حال بنبدأ ناخد مثال عملي
+
+189
+00:21:17,750 --> 00:21:22,170
+تطبيقه أه اللي مذكرة شوية في calculus A هل اختلفت
+
+190
+00:21:22,170 --> 00:21:26,370
+عن تبع ال calculus A؟ أبدا بيجي نقول اللي نغضب لو
+
+191
+00:21:26,370 --> 00:21:33,110
+كانت y دالة في x يوجه y تساوي f of x بدليها فبنروح
+
+192
+00:21:33,110 --> 00:21:37,970
+نحسب قيمة الدالة عند النقطة x non مضافة إليها
+
+193
+00:21:37,970 --> 00:21:43,150
+مشتقة الدالة لf بالنسبة لx عند تلك النقطة مضروب في
+
+194
+00:21:43,150 --> 00:21:48,220
+x نقص x nonبنعمل من الذنب قطيب اضافنا له احنا من
+
+195
+00:21:48,220 --> 00:21:52,480
+اضافنا له ال term اللي عندنا هذا لأنه صارت دالة في
+
+196
+00:21:52,480 --> 00:21:57,180
+two variables الان على اي حال نبدأ ناخد مثال
+
+197
+00:21:57,180 --> 00:22:08,860
+تطبيقي على ذلك ناخد example why
+
+198
+00:22:08,860 --> 00:22:12,780
+the linearization عين لا
+
+199
+00:22:18,120 --> 00:22:25,480
+Linearization of a function L
+
+200
+00:22:25,480 --> 00:22:43,820
+of X Y of the function R of the function F of X YX
+
+201
+00:22:43,820 --> 00:22:53,760
+زائد Y زائد Z الكل تربيع A عند النقطة واحد واثنين
+
+202
+00:23:06,550 --> 00:23:11,690
+مش هنحسب اللي نرزقه تروح أحسب تلت شغلات شغلة
+
+203
+00:23:11,690 --> 00:23:15,990
+الأولى بدي قيمة الدلة عند النقطة بتشتق الدلة
+
+204
+00:23:15,990 --> 00:23:20,030
+بالنسبة ل X و أحسبها عند نفس النقطة تشتق الدلة
+
+205
+00:23:20,030 --> 00:23:24,790
+بالنسبة ل Y و أحسبها عند نفس النقطة يبقى لو جيت
+
+206
+00:23:24,790 --> 00:23:30,470
+هنا قلت ال F of واحد واثنينيبقى هذا الكلام عملي
+
+207
+00:23:30,470 --> 00:23:36,070
+يبدو ساوي و F of X هي زائد اتنين يا بنات وليس زائد
+
+208
+00:23:36,070 --> 00:23:39,090
+Z X زائد Y زائد اتنين
+
+209
+00:23:48,250 --> 00:23:54,890
+بإثنين لكل تاربيع كم ساعة بدأت؟ خمس ساعة وعشرين
+
+210
+00:23:54,890 --> 00:24:03,050
+تمام بدنا نحسب Fx يبقى هذا قص مرفوع لقص يبقى بروح
+
+211
+00:24:03,050 --> 00:24:10,650
+بقوله القص في القص مرفوع لنفس القص مضروح منه واحد
+
+212
+00:24:10,650 --> 00:24:15,950
+مضروح في مشتقة مداخل القص بالنسبة
+
+213
+00:24:26,430 --> 00:24:36,390
+يبدأ تساوي 2 في 1 زائدي 2 زائدي 2 ويساوي كتير عشرة
+
+214
+00:24:36,390 --> 00:24:48,530
+بعدين لنجيب fy اللي يبدأ تساوي الأس في الجزء مرفوع
+
+215
+00:24:48,530 --> 00:24:49,410
+لنفس الأس
+
+216
+00:25:10,980 --> 00:25:18,980
+يساوي F of واحد واتنين F of واحد واتنين
+
+217
+00:25:23,570 --> 00:25:30,550
+8 في ال X ناقص واحد زائد ال FY عندنا نقطة واحد
+
+218
+00:25:30,550 --> 00:25:37,270
+واتنين في Y ناقص اتنين شكل عنها يبقى هذا الكلام
+
+219
+00:25:37,270 --> 00:25:42,230
+يبقى يساوي ال realization تبع الدالة F of واحد
+
+220
+00:25:42,230 --> 00:25:49,490
+واتنين هي خمس وعشرين و ال FX عندنا عشرة يبقى عشرة
+
+221
+00:25:49,490 --> 00:25:51,190
+في X ناقص واحد
+
+222
+00:25:57,610 --> 00:26:04,070
+يبقى هذا الكلام بده يساوي خمسة وعشرين زائد عشرة X
+
+223
+00:26:04,070 --> 00:26:12,390
+ناقص عشرة زائد عشرة Y ناقص عشرين يبقى هذا الكلام
+
+224
+00:26:12,390 --> 00:26:15,090
+بده يساوي عشرة X
+
+225
+00:26:19,130 --> 00:26:26,950
+يبقى ناقص خمسة وزائد خمسة وعشرين يبقى ناقص خمسة
+
+226
+00:26:38,870 --> 00:26:44,670
+خطية في معادلة من الدرجة الأولى في كل من X وY إذا
+
+227
+00:26:44,670 --> 00:26:50,490
+هي معادلة خطية ومن ثم هذا ال linearization للدالة
+
+228
+00:26:50,490 --> 00:26:58,450
+الأصلية اللى موجودة عندنا فوق طيب احنا تاول الساعة
+
+229
+00:26:58,450 --> 00:27:03,330
+بنقول إيش؟بنقول انه لما نستبدل الدالة بال
+
+230
+00:27:03,330 --> 00:27:09,310
+linearization تبعها بيكون هناك فيه خطأ بسيط تمام؟
+
+231
+00:27:09,310 --> 00:27:15,430
+الآن بنحاول نحسب جديش قيمة هذا الخطأ اللي احنا
+
+232
+00:27:15,430 --> 00:27:19,490
+افترضناه من الأصل إلى سوين الدالة بال
+
+233
+00:27:19,490 --> 00:27:24,690
+linearization تبعه طيب مشان هيك بنروح نحط القاعدة
+
+234
+00:27:24,690 --> 00:27:29,750
+تبعنا ونروح نبدأ نشتغل عليهاالقاعدة حوالطالية في
+
+235
+00:27:29,750 --> 00:27:43,110
+صيغة ال remark التالية if ال
+
+236
+00:27:43,110 --> 00:27:55,230
+if has continuous has continuous first and second
+
+237
+00:27:55,230 --> 00:28:06,440
+firstand seeking partial derivatives partial
+
+238
+00:28:06,440 --> 00:28:09,720
+derivatives
+
+239
+00:28:09,720 --> 00:28:13,400
+مشتقات
+
+240
+00:28:13,400 --> 00:28:19,380
+الأولى والثانى through an open set from and
+
+241
+00:28:36,850 --> 00:28:44,510
+containing a rectangle a
+
+242
+00:28:44,510 --> 00:28:47,890
+مستطيل
+
+243
+00:28:47,890 --> 00:28:54,630
+a centered at
+
+244
+00:28:55,460 --> 00:29:03,560
+النقطة اكس نوت او Y نوت و
+
+245
+00:29:03,560 --> 00:29:07,920
+اذا
+
+246
+00:29:07,920 --> 00:29:17,320
+كان ال M is any upper bound
+
+247
+00:29:22,490 --> 00:29:33,590
+upper bound for the values of for the values of
+
+248
+00:29:33,590 --> 00:29:45,150
+absolute value لل Fxx absolute value لل Fyy and
+
+249
+00:29:45,150 --> 00:29:56,250
+absolute value لل Fxy علىالمستقيل اللي هو R then
+
+250
+00:29:56,250 --> 00:30:04,590
+the error then the error مقدار الخطأ اللي حتيله
+
+251
+00:30:04,590 --> 00:30:15,090
+الرمز E as a function of Y of replacing of
+
+252
+00:30:15,090 --> 00:30:27,350
+replacing FL of XY on R by
+
+253
+00:30:27,350 --> 00:30:31,550
+its
+
+254
+00:30:31,550 --> 00:30:34,850
+linearization
+
+255
+00:30:34,850 --> 00:30:40,630
+اللي
+
+256
+00:30:40,630 --> 00:30:54,140
+هو L of XYF of X0 وY0 زي ال Fx عند النقطة X0 وY0
+
+257
+00:30:54,140 --> 00:31:03,760
+ال X نقص ال X0 زي ال Fy عند ال X0 وY0 ال Y نقص ال
+
+258
+00:31:03,760 --> 00:31:04,680
+Y0
+
+259
+00:31:13,560 --> 00:31:21,260
+استثمار الإنكولاتية لحقق
+
+260
+00:31:21,260 --> 00:31:33,000
+المتباينة قيمة أكتر للخطأ كمشكلة X وYأقل من أو
+
+261
+00:31:33,000 --> 00:31:41,500
+يساوي نص M بال X نقص ال X node ك absolute value
+
+262
+00:31:41,500 --> 00:31:48,060
+زائد absolute value لل Y نقص Y node لكل ترابيع
+
+263
+00:32:36,010 --> 00:32:40,910
+مرة ثانية بنتكلم عن ال error اللي هو مقدار الخطأ
+
+264
+00:32:40,910 --> 00:32:46,550
+بين الدالة F of X وY وlinearization لهذه الدالة
+
+265
+00:32:46,550 --> 00:32:52,270
+اللي دي ناله رمز L of X وY فباجي بقول لو كانت
+
+266
+00:32:52,270 --> 00:32:57,570
+الدالة F دالة مفتاصلة if and if has continuous
+
+267
+00:32:57,570 --> 00:33:01,290
+first and second partially derivatives المشتقات
+
+268
+00:33:01,290 --> 00:33:06,660
+الأولى والمشتقات الثانيةلهذه الدالة دوال متصلة على
+
+269
+00:33:06,660 --> 00:33:12,740
+فترة مفتوحة تحتوي على مستطيل centered at x not y
+
+270
+00:33:12,740 --> 00:33:17,380
+not ايش يعني؟ يعني لو روحتي قلت هذا مثلا على سبيل
+
+271
+00:33:17,380 --> 00:33:23,080
+المثال محور X وهذا محور Y وهذا نقطة في الأصل
+
+272
+00:33:30,810 --> 00:33:36,690
+مركزه نقطة x naught و y naught الشكل اللي عندنا
+
+273
+00:33:36,690 --> 00:33:45,530
+هنا كويس فى عندى هنا ساعة اللى هو الطول اللى عندنا
+
+274
+00:33:45,530 --> 00:33:51,690
+هذا او الطول هذا الاتنين are the same يبقى هذا
+
+275
+00:33:51,690 --> 00:33:59,990
+الطول لو سميته H و هذا سميته K على سبيل المثال
+
+276
+00:34:04,630 --> 00:34:08,930
+المستقلات الأولى والثانية لهذه الدالة دوال محتاصلة
+
+277
+00:34:08,930 --> 00:34:16,490
+على منطقة R تحت مستطيل مركز النقطة اللى عندنا هذا
+
+278
+00:34:17,130 --> 00:34:22,510
+بقول لأن Fm وإذا كان ال M is any upper bound for
+
+279
+00:34:22,510 --> 00:34:26,350
+the values of يبقى جيبنا المشتاقة الثانية بالنسبة
+
+280
+00:34:26,350 --> 00:34:30,190
+ل X جيبنا المشتاقة الثانية بالنسبة إلى Y جيبنا
+
+281
+00:34:30,190 --> 00:34:33,970
+المشتاقة التانية Fxy واخدنا ال absolute value
+
+282
+00:34:33,970 --> 00:34:41,490
+للتلاتة عند نفس النقطة X node وY nodeأيوة يمكن
+
+283
+00:34:41,490 --> 00:34:45,050
+واحدة تقولي طب وين الرابع؟ قلت لها بقولها وين
+
+284
+00:34:45,050 --> 00:34:50,610
+الرابع؟ تقولي FYX ال absolute value فما أخد FXX
+
+285
+00:34:50,610 --> 00:34:58,590
+FYY FXY لكن FYX مالها؟ ماجيبناش سيرتها طب يكون هذا
+
+286
+00:34:58,590 --> 00:35:06,570
+غلط؟ لأ يعني FXY و FYX بيتساووا اشترطنا خدنا نظرية
+
+287
+00:35:06,570 --> 00:35:13,430
+قبل ذلكإذا كان إذا لو مشتقاتها دوال متصلة عند مين
+
+288
+00:35:13,430 --> 00:35:18,910
+عند النقطة اللى بنحسب عندها هذه المشتقات إذا لو
+
+289
+00:35:18,910 --> 00:35:24,990
+روحنا كتبنا يا بنات ما هدول كتبنا FYX معناته كررنا
+
+290
+00:35:24,990 --> 00:35:29,690
+القيمة اللى عندنا هذه تكرار وهذا لا داعي له لأن
+
+291
+00:35:29,690 --> 00:35:34,990
+مشتركنا ال continuity هناوبالتالي زيحنا مين هي
+
+292
+00:35:34,990 --> 00:35:39,650
+النقطة التالتة نرجع تاني ل M يبقى احنا فيه انا تلت
+
+293
+00:35:39,650 --> 00:35:44,850
+مقادير Absolute value ل Fxx Absolute value ل Fyy
+
+294
+00:35:44,850 --> 00:35:49,490
+Absolute value ل Fxy يبقى تلات قيمباخدوا ال
+
+295
+00:35:49,490 --> 00:35:52,870
+absolute value بيبطل يصير فيهم قيم سالمة، يعني انا
+
+296
+00:35:52,870 --> 00:35:55,790
+اقولها السالمة واخدنا ال absolute value بالصين،
+
+297
+00:35:55,790 --> 00:36:00,910
+إذا صار عندنا تلت قيم موجبة وقد تكون أحدهم بصفر،
+
+298
+00:36:00,910 --> 00:36:04,270
+معنى مشكلة، موجبة و الله بصفر، أخدنا ال absolute
+
+299
+00:36:04,270 --> 00:36:10,010
+value بتلات قيم، أكبر رقم فيهم، باعتبر هذا upper
+
+300
+00:36:10,010 --> 00:36:17,260
+bound حد علوي للتلاتأنا باخد أكبر رقم من الأرقام
+
+301
+00:36:17,260 --> 00:36:23,900
+التلاتة اللى يسمى ال base upper bound أقل حد علوي
+
+302
+00:36:23,900 --> 00:36:30,480
+لمين للتلاتة اللى عندنابقول within the error مقدار
+
+303
+00:36:30,480 --> 00:36:34,740
+الخطأ اللى حصل عندك نتيجة استبدال الدالة بال
+
+304
+00:36:34,740 --> 00:36:40,300
+linearization تابعها جداش مقدار يخضع لهذه ال
+
+305
+00:36:40,300 --> 00:36:43,440
+inequality absolute value of the error أقل من أو
+
+306
+00:36:43,440 --> 00:36:47,760
+يسوى النص في ال upper bound في ال X نقص ال X
+
+307
+00:36:47,760 --> 00:36:55,380
+naught وY نقص Y naught لكل تربيع طبعا يبقى هذا
+
+308
+00:36:55,380 --> 00:37:02,280
+المصطلح بنات اللى اسمه Rعادي عشان نروح ناخد الكلام
+
+309
+00:37:02,280 --> 00:37:06,640
+هذا عاملي لأنه شكله ياكد زي المكالكة كبير شوية هو
+
+310
+00:37:06,640 --> 00:37:11,760
+لا مكالكة ولا حاجة بسيطة هذه سهل حسابة كنتين هذولك
+
+311
+00:37:11,760 --> 00:37:15,360
+سهل حسابهم سهل أخد نفس ال value سهل أخد الكبيرة
+
+312
+00:37:15,360 --> 00:37:20,580
+فيهم إذا صار النص قيمته جاهز هنا X نقص ال economic
+
+313
+00:37:20,580 --> 00:37:25,940
+في الغالب هو بيعطيها لييعني تسعة وتسعين وشلة تسعة
+
+314
+00:37:25,940 --> 00:37:29,060
+زي الانتخابات العربية بيكون أعطانا القيمة هذه و
+
+315
+00:37:29,060 --> 00:37:32,260
+أعطانا القيمة هذه مباشرة يبقى ما علي اللي أجمعهم
+
+316
+00:37:32,260 --> 00:37:37,240
+بس وربع وكلنا بنعرف نجمع اتنين وربع بس قضيتنا ايه
+
+317
+00:37:37,240 --> 00:37:41,340
+سهلة شوية ناخد مثال تطبيق ذي بالك بنكرره في
+
+318
+00:37:41,340 --> 00:37:45,800
+الامتحانات هنا يعني اتكرر بدل المرة تلاتة في
+
+319
+00:37:45,800 --> 00:37:50,870
+الامتحانات لكن انا السنة الماضية ماجبتشطيب فاجب
+
+320
+00:37:50,870 --> 00:37:56,350
+اقول هنا نعطي مثال الله أعلم اللي شريك اللي مات
+
+321
+00:37:56,350 --> 00:38:00,930
+وبالتالي نجيبه مايجيبوش مايقدرش اقوله يبقى هنا
+
+322
+00:38:00,930 --> 00:38:13,290
+امرا A find the linearization find
+
+323
+00:38:13,290 --> 00:38:26,210
+the linearization L of X Yof the function لدالة
+
+324
+00:38:26,210 --> 00:38:37,670
+f of x y تساوي اللي هو x y تربيع زائد y في cosine
+
+325
+00:38:37,670 --> 00:38:47,090
+x ناقص واحد at عند النقطة اللي هو واحد واثنين كذا
+
+326
+00:38:47,090 --> 00:38:56,200
+نمر بيهFind an
+
+327
+00:38:56,200 --> 00:39:03,420
+upper bound for
+
+328
+00:39:03,420 --> 00:39:17,460
+the magnitude of absolute
+
+329
+00:39:17,460 --> 00:39:28,620
+valueللـ error تبع ال X وY magnitude
+
+330
+00:39:28,620 --> 00:39:33,600
+of the
+
+331
+00:39:33,600 --> 00:39:39,320
+error in
+
+332
+00:39:39,320 --> 00:39:47,000
+the approximating function in the approximating
+
+333
+00:39:54,060 --> 00:40:11,400
+f of x of y تساوي L of x of y over the rectangle R
+
+334
+00:40:15,960 --> 00:40:23,760
+الـ X ناقص الواحد أقل من أو تساوي واحد من عشرة
+
+335
+00:40:23,760 --> 00:40:31,080
+والـ Y ناقص اتنين absolute value أقل من أو تساوي
+
+336
+00:40:31,080 --> 00:40:33,520
+واحد من عشرة
+
+337
+00:40:55,850 --> 00:41:01,650
+مرة تانية قال في المثال مطلبين وكأنه هذا هو المثال
+
+338
+00:41:01,650 --> 00:41:06,330
+الرقم اتنين على إيجار ال linearization لذلك وبعدها
+
+339
+00:41:06,330 --> 00:41:12,810
+نحصل نفس الجدار أعلى قيمة موجودة للخطأ اللي نتيجة
+
+340
+00:41:12,810 --> 00:41:17,660
+لمسواتالدالة F of X بالـ Linearization تبعها إذا
+
+341
+00:41:17,660 --> 00:41:20,760
+تخلينا مع الـ Function الأولى طبعا واضح أنه ما
+
+342
+00:41:20,760 --> 00:41:24,460
+أعطينا نقطة واحد واثنين إذا بدي أحسب الدالة
+
+343
+00:41:24,460 --> 00:41:30,300
+ومشتقتها عند النقطة واحد واثنين فبجي بقوله بدي أخد
+
+344
+00:41:30,300 --> 00:41:38,460
+دمرة A بدي أخد F of X Y اللي هي تساوي condition X
+
+345
+00:41:38,460 --> 00:41:42,240
+Y تربيع زاد
+
+346
+00:41:48,440 --> 00:41:57,730
+يحسب f of 1 و 2 و 7طبعاً واحد و هنا اتنين ترابيع
+
+347
+00:41:57,730 --> 00:42:06,690
+زائد اتنين cosine صفر و واحد يبقى مضل اتنين واربعة
+
+348
+00:42:06,690 --> 00:42:14,850
+ستة يبقى الناتج يساوي ستة بعدين بدنا نروح نجيب Fx
+
+349
+00:42:14,850 --> 00:42:23,440
+يبقى هذا الكلام يساوي Y ترابيعY مالكيش دعوة تفضل
+
+350
+00:42:23,440 --> 00:42:29,200
+الـ Cos بسالب Sine X ناقص واحد ضرب مشتقة الزاوية
+
+351
+00:42:29,200 --> 00:42:37,640
+لواحد صحيح نحسب هذه ال Fx عند النقطة واحد واثنين Y
+
+352
+00:42:37,640 --> 00:42:45,040
+شاوي اتنين ترابية ناقص اتنين في Sine Zero Sine
+
+353
+00:42:45,040 --> 00:42:46,100
+Zero ب Zero
+
+354
+00:42:56,270 --> 00:43:06,250
+Y يبقى 2XY زائد Cos X نقص واحد لأن Cos X نقص واحد
+
+355
+00:43:06,250 --> 00:43:11,130
+كلها تعتبر constant إذا اشتغلنا بالنسبة لمين إلى Y
+
+356
+00:43:11,130 --> 00:43:18,770
+نحصل قديش FY عند النقطة واحد واتنين هو يساوي 2 في
+
+357
+00:43:18,770 --> 00:43:23,510
+واحد في كمان اتنين زائد Cos
+
+358
+00:43:27,760 --> 00:43:33,500
+بصير صفر اف واحد وقداش خمسة يبقى بناء عليه بعدها
+
+359
+00:43:33,500 --> 00:43:39,820
+اجيب له ال linearization تبع ال X و Y يبقى هنا F
+
+360
+00:43:39,820 --> 00:43:46,480
+اف واحد و اتنين زائد ال F X عند النقطة واحد و
+
+361
+00:43:46,480 --> 00:43:52,560
+اتنين في ال X ناقص ال واحد زائد F Y عند النقطة
+
+362
+00:43:52,560 --> 00:43:59,740
+واحد و اتنين في ال Y ناقص اتنينالعوض فيها بف بواحد
+
+363
+00:43:59,740 --> 00:44:06,680
+و اتنين اللي هم قداش بستة ال Fx باربعة في ال X
+
+364
+00:44:06,680 --> 00:44:14,540
+ناقص واحد وال Fy بخمسة في ال Y ناقص اتنين اذا ان
+
+365
+00:44:14,540 --> 00:44:20,120
+هذه فيديو يتساوي ستة زائد اربعة X ناقص اربعة زائد
+
+366
+00:44:20,120 --> 00:44:27,780
+خمسة Y ناقص عشرة هذا الكلام بالدول الساعةعندك هنا
+
+367
+00:44:27,780 --> 00:44:35,580
+اربع X زائد خمسة Y يبقى لدينا ناقص أربعة عشر نقص
+
+368
+00:44:35,580 --> 00:44:43,620
+تمنية يبقى ناقص تمنية يبقى هذا ال linear function
+
+369
+00:44:43,620 --> 00:44:48,020
+أو ال linearization لل function الأصلية وهو
+
+370
+00:44:48,020 --> 00:44:54,040
+المطلوب الأول من المسألة نجي للمطلوب التاني نجيه
+
+371
+00:44:54,040 --> 00:44:54,900
+نملة V
+
+372
+00:44:58,830 --> 00:45:03,390
+يبقى هذا زي السؤال المثال السابق هيعلنها تماما زيه
+
+373
+00:45:03,390 --> 00:45:09,850
+وكان يعتبر المثال رقم اتنين بدأجي ألمع بيه، بدأ
+
+374
+00:45:09,850 --> 00:45:13,370
+أروح أجيبله ال error اللي عندنا، مشان هيك هذه
+
+375
+00:45:13,370 --> 00:45:19,880
+جاهزةوهذه جاهزة وقال علينا مين؟ بس ال M ال M بدي
+
+376
+00:45:19,880 --> 00:45:28,260
+أعقد مقارنة بين ال absolute value ل Fxx, Yy, Fxy و
+
+377
+00:45:28,260 --> 00:45:35,420
+هكذا طب ال Fx الحمد لله جازة إذا إحنا بدنا ال Fxx
+
+378
+00:45:35,420 --> 00:45:42,340
+اللي هو partial على partial X لل Fxيعني partial
+
+379
+00:45:42,340 --> 00:45:49,240
+على partial X لل F X هي جهزة فوق ال Y تربية ناقص Y
+
+380
+00:45:49,240 --> 00:45:55,360
+في صين X ناقص واحد وله بدوسةدش تبقى الدلة هذه
+
+381
+00:45:55,360 --> 00:46:00,400
+بالاسم ال X يبقى Y تربيع مع السلامة ال Y هذى مقدر
+
+382
+00:46:00,400 --> 00:46:08,420
+ثابت تفضل ال sign بيكو ساين يبقى ناقص Y كو ساين X
+
+383
+00:46:08,420 --> 00:46:13,900
+ناقص واحد ضرب مشتقة الزاوية اللى هو واحد صحيح
+
+384
+00:46:13,900 --> 00:46:15,700
+بالمرة نحسبها عيد مال
+
+385
+00:46:22,160 --> 00:46:27,860
+بندل نقطة واحد واثنين بيكون ساوي سالي باتنين في
+
+386
+00:46:27,860 --> 00:46:39,400
+كوساين زير بيكون سالي باتنين في كوساين
+
+387
+00:46:39,400 --> 00:46:42,580
+زير بيكون سالي باتنين في كوساين زير بيكون سالي
+
+388
+00:46:42,580 --> 00:46:43,500
+باتنين في كوساين زير بيكون سالي باتنين في كوساين
+
+389
+00:46:43,500 --> 00:46:43,580
+زير بيكون سالي باتنين في كوساين زير بيكون سالي
+
+390
+00:46:43,580 --> 00:46:44,540
+باتنين في كوساين زير بيكون سالي باتنين في كوساين
+
+391
+00:46:44,540 --> 00:46:45,940
+زير بيكون سالي باتنين في كوساين زير بيكون سالي
+
+392
+00:46:45,940 --> 00:46:48,660
+باتنين في كوساين زير بيكون سالي باتنين في كوساين
+
+393
+00:46:48,660 --> 00:46:51,910
+زير بيكون سالي باتنين في كوساين زير بيكون سبعد هيك
+
+394
+00:46:51,910 --> 00:46:59,790
+بدنا نروح لل FYY يعني partial على partial Y لل FY
+
+395
+00:46:59,790 --> 00:47:05,610
+يعني partial على partial Y لل FY وين ال FY هي فوق
+
+396
+00:47:05,610 --> 00:47:10,130
+اللي هو 2XY زائد قصارى
+
+397
+00:47:13,650 --> 00:47:18,390
+إن الفاضلها بالنسبة لمن إلى Y يبقى ال cosine كله ب
+
+398
+00:47:18,390 --> 00:47:26,110
+Zero بظل فقط كده عنده اتنين X يبقى هذا معناته ان
+
+399
+00:47:26,110 --> 00:47:34,770
+ال FYY كده تساوي عند النقطة واحدة عند النقطة واحدة
+
+400
+00:47:34,770 --> 00:47:38,870
+و اتنين عند النقطة واحدة و اتنين تساوي كده يا بنات
+
+401
+00:47:38,870 --> 00:47:46,490
+اتنين لإن بدي اشيل ال X وقت ما كانطيب اتنين اختي
+
+402
+00:47:46,490 --> 00:47:51,330
+لها ال absolute value و الله مااختيها هي اتنين
+
+403
+00:47:51,330 --> 00:47:56,710
+يبقى بدنا نبروزها و كمان نرجعلها بعد قليل يبقى
+
+404
+00:47:56,710 --> 00:48:02,290
+بدنا نروح اجيبله كمان مين ال Fxy يعني partial على
+
+405
+00:48:02,290 --> 00:48:09,730
+partial y لل Fx هذا الكلام بده يساوي partial على
+
+406
+00:48:09,730 --> 00:48:10,630
+partial y
+
+407
+00:48:16,980 --> 00:48:24,920
+نقص y في sin x نقص واحد ويسار تفاضلها بالنسبة ل y
+
+408
+00:48:24,920 --> 00:48:34,820
+اتنين y نقص sin x نقص واحد والsin تعتبر هنا
+
+409
+00:48:42,500 --> 00:48:47,940
+Y عند نقطة واحد و اتنين بيبقى اتساوي اتنين في
+
+410
+00:48:47,940 --> 00:48:54,520
+اتنين مقص صيني زيرو صيني زيرو مقداش يا بنات يبقى
+
+411
+00:48:54,520 --> 00:48:59,980
+بضال مقداش عندنا اربعة ممتاز اتطلع في اللي
+
+412
+00:48:59,980 --> 00:49:05,140
+بروزناهم واحد اللي و اتنين و التالتة هذي يبقى
+
+413
+00:49:05,140 --> 00:49:10,440
+اتنين و اتنين و اربعة وين اكبر رقم منهم يبقى ال M
+
+414
+00:49:10,440 --> 00:49:20,410
+تبع تلكأربعة يبقى بروح بقوله هنا sum تساوي أربعة
+
+415
+00:49:20,410 --> 00:49:26,470
+هذه اللي هو من ال upper bound لل values تبعتي
+
+416
+00:49:26,470 --> 00:49:30,790
+التلاتة اللي عندنا يبقى احنا جاهزين مش ضايل عندنا
+
+417
+00:49:30,790 --> 00:49:36,560
+إلا نفسي بالأرور عن طريقة تعويض وينفي ال equality
+
+418
+00:49:36,560 --> 00:49:41,280
+اللى قدامنا هذه بقوله بسيطة جدا يبقى بدنا نمسح
+
+419
+00:49:41,280 --> 00:49:46,280
+اللي قوم كله هذا ونخل ال equality لإن ال equality
+
+420
+00:49:46,280 --> 00:49:53,680
+هذه بدنا نعوض فيها هذه سميها يا بنات سمينا قبل
+
+421
+00:49:53,680 --> 00:50:00,020
+شوية star سميها W star يبقى بنيجي نقوله هنا
+
+422
+00:50:00,020 --> 00:50:00,740
+substitute
+
+423
+00:50:05,750 --> 00:50:11,970
+تانى الانكواليتي اللى بابلس تار بنحصل على ما يتى
+
+424
+00:50:11,970 --> 00:50:18,570
+absolute value للera as a function of x و y أقل من
+
+425
+00:50:18,570 --> 00:50:25,830
+نص الام بقدرش أربع افتح يوسط x ماتس اكس نوت مواطع
+
+426
+00:50:25,830 --> 00:50:32,130
+اللى واحد من عشرةيبقى هاي Zero و واحد من عشرة
+
+427
+00:50:32,130 --> 00:50:38,410
+والتانية Zero و واحد من عشرة الكل تربية يبقى هذه
+
+428
+00:50:38,410 --> 00:50:45,410
+لو جينا حسبناها فصير عندي قداش اتنين في Zero اتنين
+
+429
+00:50:45,410 --> 00:50:50,890
+من عشرة الكل تربية فبتنين من عشرة الكل تربية قداش
+
+430
+00:50:50,890 --> 00:50:56,750
+تطلع اربعة من مية ممتازة يبقى Zero Zero
+
+431
+00:51:01,020 --> 00:51:08,380
+0 0 8 من 100 يبقى نسبة الخطأ أو مقدار الخطأ يا
+
+432
+00:51:08,380 --> 00:51:13,240
+بنات دائما و أبدا في المثال هذا عنده نقطة واحد و
+
+433
+00:51:13,240 --> 00:51:18,120
+اتنين إذا استبدلنا الدالة بال linearization تبعها
+
+434
+00:51:18,120 --> 00:51:24,600
+عند هذه النقطة بيكون مقدار الخطأ أقل من 8 من 100
+
+435
+00:51:24,600 --> 00:51:32,920
+وبالتالي ماعنا مشكلة في هذه الحالةالان بنقول لو
+
+436
+00:51:32,920 --> 00:51:37,240
+بدنا نعمم هذا الكلام ل functions of three
+
+437
+00:51:37,240 --> 00:51:43,080
+variables فإيش اللي بده يصير هذا الكلام اللي آخر
+
+438
+00:51:43,080 --> 00:51:47,320
+النقطة في هذا ال section اللي بدنا نعمم هذا ل
+
+439
+00:51:47,320 --> 00:51:50,100
+functions of three variables
+
+440
+00:52:02,550 --> 00:52:09,230
+هيبقى حطيه لعنوان صغير هيك functions of
+
+441
+00:52:09,230 --> 00:52:20,390
+more than more than two
+
+442
+00:52:35,290 --> 00:52:40,370
+the linearization of
+
+443
+00:52:40,370 --> 00:52:49,830
+الـ function f of x و y و z at أي ند النقطة p نوت
+
+444
+00:52:49,830 --> 00:52:58,590
+و x نوت و y نوت و z نوت as نجي
+
+445
+00:52:58,590 --> 00:53:08,050
+نقول ال L of x و y و zبدي ساوى ال F عند النقطة P
+
+446
+00:53:08,050 --> 00:53:16,790
+non مضافا اليها Fx عند النقطة P non بال X معقص ال
+
+447
+00:53:16,790 --> 00:53:24,150
+X non زائد ال Fy عند النقطة P non بالY
+
+448
+00:53:32,360 --> 00:53:38,760
+يبقى هنا شكل
+
+449
+00:53:38,760 --> 00:53:46,600
+ال linearization يبقى فيه فرقين او اثنين من الفروق
+
+450
+00:53:46,600 --> 00:53:50,300
+بين و بين ال linearization في حالة ال function on
+
+451
+00:53:50,300 --> 00:53:55,960
+to mario الفرق الاولبعد ما كنا بنحسب عند نقطة
+
+452
+00:53:55,960 --> 00:54:02,340
+بمركبين أو بإحداثين بصير نحسب عند نقطة بثلاث
+
+453
+00:54:02,340 --> 00:54:07,720
+إحداثين فهذا الفرق الأول الفرق الثاني بانضيف ال
+
+454
+00:54:07,720 --> 00:54:12,340
+term الزيادة اللي هو عند هذا man مشتقة يتدلة
+
+455
+00:54:12,340 --> 00:54:17,480
+بالنسبة إلى z عند نفس النقطة مضروبة في man في z
+
+456
+00:54:17,480 --> 00:54:18,620
+ناقص
+
+457
+00:54:23,560 --> 00:54:28,100
+للـ error بسرعاتنا ال linearization جديد إذا في
+
+458
+00:54:28,100 --> 00:54:33,480
+error جديد بدنا نعرف إيش ال error هذا يبقى نبرة
+
+459
+00:54:33,480 --> 00:54:38,600
+اتنين اقول
+
+460
+00:54:38,600 --> 00:54:46,400
+suppose that ال R is a closed suppose that
+
+461
+00:54:46,400 --> 00:55:07,710
+ال Rاو ايش رايك بناشي نعيد الكلام هذا كله او
+
+462
+00:55:07,710 --> 00:55:12,330
+in
+
+463
+00:55:12,330 --> 00:55:13,210
+this case
+
+464
+00:55:18,860 --> 00:55:32,360
+the case of functions of a three variables of the
+
+465
+00:55:32,360 --> 00:55:43,300
+error S هدى الرمز E, X, Y, Z وايه ال absolute
+
+466
+00:55:43,300 --> 00:55:52,710
+value أقل من أو يسوى مصف ال M فيهabsolute value x
+
+467
+00:55:52,710 --> 00:56:00,510
+نقص ال x node زائد y نقص ال y node زائد absolute
+
+468
+00:56:00,510 --> 00:56:11,910
+value z نقص ال z node لكل ترابيع where حيث ال M is
+
+469
+00:56:11,910 --> 00:56:17,650
+the upper bound
+
+470
+00:56:18,880 --> 00:56:27,820
+of absolute value لل Fxx absolute value لل Fyy
+
+471
+00:56:27,820 --> 00:56:36,940
+absolute value لل Fzz absolute value لل Fxy
+
+472
+00:56:36,940 --> 00:56:48,000
+absolute value لل Fxz and absolute value لل Fyz
+
+473
+00:57:35,750 --> 00:57:40,990
+نفس الصيغة اللي قبل اللهم إلا زدنا لها term التالت
+
+474
+00:57:40,990 --> 00:57:45,640
+اللي عندنا هذهوالـ M هذه اللي هي ال upper bound
+
+475
+00:57:45,640 --> 00:57:52,840
+لمين لستة مقادير اللي عندنا Fxx Fyy Fzz طبعا ب
+
+476
+00:57:52,840 --> 00:57:58,140
+absolute value Fxy Fyx طبعا استبعدناها مشان ال
+
+477
+00:57:58,140 --> 00:58:03,120
+continuity Fxz واستبعدنا Fzx مشان ال continuity
+
+478
+00:58:03,120 --> 00:58:08,740
+Fyz وااستبعدنا Fzy كذلك بسبب مين؟ بسبب ال
+
+479
+00:58:08,740 --> 00:58:13,460
+continuity مش هنخليكوا تايهينبنعطيكم مثال أوضحي
+
+480
+00:58:13,460 --> 00:58:21,100
+على ذلك example find
+
+481
+00:58:21,100 --> 00:58:31,100
+the linearization
+
+482
+00:58:31,100 --> 00:58:34,560
+اللي
+
+483
+00:58:34,560 --> 00:58:50,020
+هو L of X Y و Zof the function مدالة f
+
+484
+00:58:50,020 --> 00:59:02,500
+of x y و z يسوى جدري اتنين T cosine of x في صين y
+
+485
+00:59:02,500 --> 00:59:18,180
+زائد z at the pointعند النقطة اليمين P0 P0 P0 P0
+
+486
+00:59:18,180 --> 00:59:18,560
+P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0
+
+487
+00:59:18,560 --> 00:59:19,720
+P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0
+
+488
+00:59:19,720 --> 00:59:22,860
+P0
+
+489
+00:59:22,860 --> 00:59:24,320
+P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0
+
+490
+00:59:24,320 --> 00:59:27,740
+P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0
+
+491
+00:59:27,740 --> 00:59:30,360
+P0
+
+492
+00:59:38,380 --> 00:59:48,960
+for the magnitude للقرار
+
+493
+00:59:48,960 --> 01:00:01,540
+اللي عندنا هذا of the error the approximation and
+
+494
+01:00:01,540 --> 01:00:05,100
+the approximation
+
+495
+01:00:15,150 --> 01:00:19,930
+F of X و Y و
+
+496
+01:00:19,930 --> 01:00:27,690
+Z F
+
+497
+01:00:27,690 --> 01:00:37,130
+of X و Y و Z بدأ ال sound L of X و Y و Z over the
+
+498
+01:00:37,130 --> 01:00:43,550
+region over the region
+
+499
+01:00:45,400 --> 01:00:56,280
+محطان كده فوق هي A ان هي عبارة عن value من X اقل
+
+500
+01:00:56,280 --> 01:01:06,530
+من او تسوى 00 1 من 10 و ال value من Yأقل من أو
+
+501
+01:01:06,530 --> 01:01:12,310
+تساوي كمان بنفس الطريقة Zero واحد من عشرة وهكذا
+
+502
+01:01:12,310 --> 01:01:19,590
+نتقل إلى Z ناقص Pi على أربعة أقل من أو تساوي Zero
+
+503
+01:01:19,590 --> 01:01:21,410
+Zero واحدة
+
+504
+01:01:40,040 --> 01:01:45,660
+السؤال شبيه بالسؤال الماضي لكن مع الفارق اللذي
+
+505
+01:01:45,660 --> 01:01:50,820
+يناسب طبيعة ال function of three variables المطموع
+
+506
+01:01:50,820 --> 01:01:54,940
+الأول اللي مراهية طلب ال linearization وين عنده
+
+507
+01:01:54,940 --> 01:01:58,260
+النقطة، إذا خلّيني أروح نحسب له ال linearization
+
+508
+01:01:58,260 --> 01:02:05,180
+اللي عنها، يبقى نبدأ أول شيء بالدالة F of X وY وZ
+
+509
+01:02:05,180 --> 01:02:14,050
+اللي يتسببقداش الدالة جدري اتنين في Cos X في Sin Y
+
+510
+01:02:14,050 --> 01:02:22,490
+زائد Z نحسب قداش قيمة الدالة على الـ Zero و Zero و
+
+511
+01:02:22,490 --> 01:02:29,030
+Pi على أربع نجي الامنات هي جدري اتنين Cos صفر
+
+512
+01:02:29,030 --> 01:02:32,650
+بقداش واحد يبقى في واحد
+
+513
+01:02:42,100 --> 01:02:47,920
+يبقى الجواهر كده؟ واحد صحيح فاللي علي شجهه ليه
+
+514
+01:02:47,920 --> 01:02:54,160
+دلوقتي لل Fxy سبق أن اشتقت الدالة بالنسبة لإستفادة
+
+515
+01:02:54,160 --> 01:03:01,700
+Cos سالف جزير اتنين ساين ال X والباقي كل مصطلح
+
+516
+01:03:01,700 --> 01:03:09,600
+مانوش دعوةيبقى هنا في Sine Y زاقة Z. بدنا نحسب كده
+
+517
+01:03:09,600 --> 01:03:14,700
+ال Fx عند ال zero و ال zero و ال Pi على أربعة ما
+
+518
+01:03:14,700 --> 01:03:22,720
+يساوي. إذن سادي سالب جدر اتنين و Sine Zero بناه. F
+
+519
+01:03:22,720 --> 01:03:28,100
+Zero و Sine Pi على أربعة واحد على جدر اتنين يبقى
+
+520
+01:03:28,100 --> 01:03:35,860
+كده؟ Zero راح مع السلامة.طيب إذا نجي ل ال fy يساوي
+
+521
+01:03:35,860 --> 01:03:41,200
+نشتغل نسمة لو هيبقى جدري اتنين cosine ال X مالكش
+
+522
+01:03:41,200 --> 01:03:49,800
+داعو نجي لل أخرى نفضلها بين f cosine y زائد z في
+
+523
+01:03:49,800 --> 01:03:55,790
+مشتقة ال y اللي هيبقى داشر واحد صحيحتروح نحسب كدهش
+
+524
+01:03:55,790 --> 01:04:04,730
+ال FY أن النقطة 00Y على 4 هو يساوي هي جدرين 2 و
+
+525
+01:04:04,730 --> 01:04:15,450
+Cos 0 ب1 و Cos 0 زي 4 جتها 45 كذلك ب1 على جدرين 2
+
+526
+01:04:15,450 --> 01:04:18,250
+يبقى كمان يساوي 1
+
+527
+01:04:22,890 --> 01:04:26,490
+يبقى 5z يبقى January 2
+
+528
+01:04:30,940 --> 01:04:37,080
+تفضل الـ Sine بيكو ساين Y زائد Z في مشتقة الـ Z
+
+529
+01:04:37,080 --> 01:04:41,760
+اللي هي ودرجة واحدة يبقى طالع المشتقة اللي اتنين
+
+530
+01:04:41,760 --> 01:04:48,480
+زي بعض FY زي FZ إذا بنان عليه ال FZ عند ال zero و
+
+531
+01:04:48,480 --> 01:04:52,280
+ال zero و ال Y على أربع كله بده ساوي كدرجة بده
+
+532
+01:04:52,280 --> 01:04:59,450
+ساوي واحد إذا بقدر أجيب له ال linearizationL as a
+
+533
+01:04:59,450 --> 01:05:04,170
+function of x, y,
+
+534
+01:05:04,330 --> 01:05:15,390
+z لدي تلاتة لأنها ثلاثة متغيرات يجيلي f of 0,0 بقى
+
+535
+01:05:15,390 --> 01:05:23,550
+الاربع اللي يبقى واحد اللي بعده fx اللي مقدش 0
+
+536
+01:05:31,980 --> 01:05:38,560
+زائد الـ fy اللي هي بواحد في ال y ناقص ال zero
+
+537
+01:05:38,560 --> 01:05:45,760
+اللي بعده fz كذلك واحد في ال z ناقص y على اربع
+
+538
+01:05:45,760 --> 01:05:50,720
+يبقى بناء ان عليه صفر ال linearization يجب ان يكون
+
+539
+01:05:50,720 --> 01:05:55,280
+x زائد y زائد z
+
+540
+01:05:59,300 --> 01:06:05,640
+يبقى هذا zero في أي رقم في zero هو يصبح صحيح وهذا
+
+541
+01:06:05,640 --> 01:06:10,760
+شيء مميز جدا يبقى وصوله على مين؟ هذه الطاقة يبقى
+
+542
+01:06:10,760 --> 01:06:18,520
+ال Y زائد Z ناقص Y على أربعة زائد واحد كل هذا ال
+
+543
+01:06:18,520 --> 01:06:26,220
+linearization لل X Y وZ شكل العالم يبقى هذا نمرأة
+
+544
+01:06:26,220 --> 01:06:27,700
+ايه من المسألة؟
+
+545
+01:06:30,040 --> 01:06:34,320
+المرة بي بشان نجيب المرة بي بدنا نروح نحسب ست
+
+546
+01:06:34,320 --> 01:06:40,080
+شغلات تمام إذا بدنا نروح للست شغلات نحسبها اللي هي
+
+547
+01:06:40,080 --> 01:06:42,700
+absolute value للألا absolute value لل Fxx
+
+548
+01:06:42,700 --> 01:06:47,620
+absolute value Fyy absolute value Fzz إلى آخرى
+
+549
+01:06:47,620 --> 01:06:55,040
+لغاية ما نكمل إذا بدنا نروح لمين بدات لل FxxY7
+
+550
+01:06:55,040 --> 01:07:00,350
+يبقى بده اشتقها دي كمان مرة بنسبة لمين إلى Xيبقى
+
+551
+01:07:00,350 --> 01:07:09,570
+سالب جدري اتنين Cos X وهنا Sine Y زائد Z ملاش دعوة
+
+552
+01:07:09,570 --> 01:07:16,570
+بالمرة نحسبها يبقى هذا بدي يعطينا مين ان ال F XX
+
+553
+01:07:16,570 --> 01:07:25,150
+عند النقطة 00Y على أربع يسام Cos 0 بواحد يبقى ناقص
+
+554
+01:07:25,150 --> 01:07:32,600
+جدري اتنين في واحدوSin Pi على 4 بواحد عالى جدري
+
+555
+01:07:32,600 --> 01:07:37,460
+اتنين يبقى النتيجة قداشنا بنات سالب واحد يبقى ال
+
+556
+01:07:37,460 --> 01:07:44,640
+Fx كانت بزيرو لكن ال Fx اكثر من قدرين بسالب واحد
+
+557
+01:07:44,640 --> 01:07:53,660
+بدنا نيجي لمين لل absolute value لل Fx X بدنا نسيب
+
+558
+01:07:53,660 --> 01:07:56,400
+ال absolute value لسالب واحد لو قدرين
+
+559
+01:08:00,450 --> 01:08:05,670
+يجب ان اشتغل بالنسبة للوان يبقى جذري اتنين في
+
+560
+01:08:05,670 --> 01:08:12,610
+كوصين ال X مالكش دعوة وتفضل كوصين بسالف ساين Y
+
+561
+01:08:12,610 --> 01:08:18,190
+زائد Z في مستقبل ال Y يبقى داشر ات واحد يجب ان
+
+562
+01:08:18,190 --> 01:08:26,410
+احسب F Y Y عند النقطة Zero و Zero و باي على اربع
+
+563
+01:08:26,410 --> 01:08:34,520
+تسامهي جدري اتنين والله سالب جدري اتنين في واحد في
+
+564
+01:08:34,520 --> 01:08:42,820
+مين؟ في واحد على جدري اتنين وكذلك تساوي مين؟ سالب
+
+565
+01:08:42,820 --> 01:08:48,280
+واحد يبقى سالب absolute value لل FYY absolute
+
+566
+01:08:48,280 --> 01:08:51,160
+value للسالب واحد للمقدس واحد
+
+567
+01:08:59,690 --> 01:09:08,710
+جدري اتنين وصين ال X في صين Y زائد Z مشتقتها
+
+568
+01:09:08,710 --> 01:09:15,910
+بالنسبة للسالب حطت السالب برا نحسب كده المشتقة FZZ
+
+569
+01:09:15,910 --> 01:09:24,590
+عند النقطة Zero و Zero و Y على اربعة يساوي ناقص
+
+570
+01:09:24,590 --> 01:09:32,330
+جدري اتنين في واحد في صين واحدهنا جائري اتنين كذلك
+
+571
+01:09:32,330 --> 01:09:39,210
+اللي هو سالم واحد يبقى absolute value لل FZZ بدي
+
+572
+01:09:39,210 --> 01:09:44,470
+ساوي absolute value لسالم واحد كمان اللي هو مقدش
+
+573
+01:09:44,470 --> 01:09:46,770
+اللي هو واحد
+
+574
+01:10:19,560 --> 01:10:34,600
+يبقى ال Fxy هي partial على partial Y لل Fxy سالف
+
+575
+01:10:34,600 --> 01:10:37,340
+جذري اتنين في Sine X
+
+576
+01:10:46,690 --> 01:10:50,830
+يبقى Cos y
+
+577
+01:10:50,830 --> 01:10:59,110
+زائد z يلّا بالمرة نحسب ال Fxy عن النقطة 00Y على 4
+
+578
+01:10:59,110 --> 01:11:09,930
+ويساوي سالب جدر 2 في 0 في 1 على جدر 2 ويساوي 0 بعد
+
+579
+01:11:09,930 --> 01:11:14,030
+ذلك يبقى خلاص ال absolute value لها في 0 بدنا ال
+
+580
+01:11:14,030 --> 01:11:22,880
+Fxzيبقى هنا اللي هي partial على partial z لمين لل
+
+581
+01:11:22,880 --> 01:11:28,960
+Fx يالا نشتق ال Fx من اسمه لزي دي يبقى سالف جدري
+
+582
+01:11:28,960 --> 01:11:38,960
+اتنين كصين ال X مالهاش دعوة وهذه كصينY زائد Z يبقى
+
+583
+01:11:38,960 --> 01:11:44,420
+ال F X Z عظيم نفس النتيجة اللي بقى بناها بدها
+
+584
+01:11:44,420 --> 01:11:49,440
+تساوي Zero طيب جيبنا ال F X Y F X Z بقى اللي عندنا
+
+585
+01:11:49,440 --> 01:11:57,280
+main F Y Z يبقى partial على partial Z لل F Y و لZ
+
+586
+01:11:57,280 --> 01:12:04,900
+بدنا نيجي لل F Y يبقى جذري اتنين Cos X مالهاش دعوة
+
+587
+01:12:06,090 --> 01:12:14,310
+يبقى فضل هدف سالب ساين يبقى سالب ساين Y زائد Z
+
+588
+01:12:36,260 --> 01:12:46,600
+أصبح fy fyz كabsolute value لسالة بواحدة وقدراش
+
+589
+01:12:46,600 --> 01:12:55,760
+بواحدة عندنا قيمة اتن تان ثلاثة وهي الرابعة وهذه
+
+590
+01:12:55,760 --> 01:13:00,320
+الخامسة وهذه السادسة
+
+591
+01:13:12,920 --> 01:13:22,060
+Y و Z أقل من أو يساوي مُص M X ناقص X نوت كأبسوليوت
+
+592
+01:13:22,060 --> 01:13:29,880
+Value وهنا Y ناقص Y نوت كأبسوليوت Value وهنا Z
+
+593
+01:13:29,880 --> 01:13:38,190
+ناقص Z نوت كأبسوليوت Value لكل تربيةيبقى الـ Error
+
+594
+01:13:38,190 --> 01:13:43,830
+اللي عندنا هذا X وY وZ أقل من أو يسوى نص الـ M
+
+595
+01:13:43,830 --> 01:13:52,630
+بقدرش واحد صحيح تمين مجرد هذا كل واحدة فيهم واحد
+
+596
+01:13:52,630 --> 01:13:59,810
+من مية يبقى Zero Zero Point Zero واحد Zero Point
+
+597
+01:13:59,810 --> 01:14:07,320
+Zero واحد Zero Point Zero واحد بشكل عاميبقى هذه
+
+598
+01:14:07,320 --> 01:14:15,940
+الصحرة نص في كتاش ولا بنات Zero Zero تلاتة من مية
+
+599
+01:14:15,940 --> 01:14:23,600
+لكل تربيع يبقى هذا الكلام بده يساوي نص فيه تلاتة
+
+600
+01:14:23,600 --> 01:14:29,580
+من مية لكل تربيع تسعة من الف و الله من عشرة آلاف
+
+601
+01:14:29,580 --> 01:14:35,060
+عشرة آلاف رقامين بعد الفاصلة يبقى هذا ال zero
+
+602
+01:14:38,350 --> 01:14:48,370
+.00009 تمام ان شئتم تقولنا 000045
+
+603
+01:14:48,370 --> 01:14:51,530
+نص
+
+604
+01:14:51,530 --> 01:14:59,930
+يبقى بيصير 45 من 100000 كسر زي ما تشايفين متناهي
+
+605
+01:14:59,930 --> 01:15:05,190
+في الصغر لحد هنا stop انتهينا من هذا ال section
+
+606
+01:15:05,760 --> 01:15:13,460
+بنقول exercises أحداشر ستة المسائل من تلاتة لغاية
+
+607
+01:15:13,460 --> 01:15:20,540
+واحد وعشرين اللي هي الأد وكذلك من خمسة وعشرين
+
+608
+01:15:20,540 --> 01:15:27,360
+لغاية اللي هو خمسة واربعين الأد كذلك
+
+609
+01:15:30,240 --> 01:15:36,880
+بالآخر section سنأخذه في هذا ال chapter وهو ال
+
+610
+01:15:36,880 --> 01:15:41,740
+extreme values and saddle points يبقى بني إلى
+
+611
+01:15:41,740 --> 01:15:51,200
+section 14.7 14.7 اللي هو بتتكلم عن ال extreme
+
+612
+01:15:51,200 --> 01:15:54,680
+values
+
+613
+01:15:54,680 --> 01:16:00,020
+and saddle points
+
+614
+01:16:02,850 --> 01:16:03,250
+Oy.
+
+615
+01:16:16,990 --> 01:16:21,510
+قبل أن نبدأ في هذا ال section نحاول نفسر اللي هو
+
+616
+01:16:21,510 --> 01:16:26,130
+العنوان اللي احنا كاتبينه هذا مكتوب ب Extreme
+
+617
+01:16:26,130 --> 01:16:29,810
+Values كلمة Extreme مرت معانا قبل ايه في كل كلاسية
+
+618
+01:16:29,810 --> 01:16:34,690
+كتير مظبوط؟ ايش بقيت تسموها؟ القيم القصوى أو القيم
+
+619
+01:16:34,690 --> 01:16:40,070
+المتطرفة العمال القيم المتطرف يعني القيم الإرهابية
+
+620
+01:16:40,070 --> 01:16:46,070
+يبقى هذه نسميها القيم القصوى and setting pointإيش
+
+621
+01:16:46,070 --> 01:16:51,950
+سدل؟ كيف؟
+
+622
+01:16:51,950 --> 01:16:57,430
+يعني لا حرجة لا مش صحيحة مش ذاكرينيكم أقول نقطة
+
+623
+01:16:57,430 --> 01:17:02,730
+الإنقلاب للمنحنة دي شو نسميها؟ انعطاف أو
+
+624
+01:17:02,730 --> 01:17:08,170
+inflection point تمام؟ هذه بنسميها نقطة الركاب
+
+625
+01:17:08,170 --> 01:17:13,970
+المناظرة لنقطة الانعطاف أو نقطة الإنقلاب تبعت
+
+626
+01:17:13,970 --> 01:17:17,740
+المنحنةتبقى reflection point نقطة انقلابها نقطة
+
+627
+01:17:17,740 --> 01:17:22,760
+اقافية للمنحنة بقابلها هنا settle point اللي هي
+
+628
+01:17:22,760 --> 01:17:27,520
+نقطة الركاب لإن احنا عندنا مجسم مش خط منحنى وانما
+
+629
+01:17:27,520 --> 01:17:34,320
+عندنا على شكل ا مجسم سير في السطعيبقى هنا نقول
+
+630
+01:17:34,320 --> 01:17:38,880
+settle point نقطة recap يبقى هنا هنا في هذا ال
+
+631
+01:17:38,880 --> 01:17:44,820
+section حمارة على ال local maximum و local minimum
+
+632
+01:17:44,820 --> 01:17:48,740
+طبعا points و كذلك settle points يبقى هذول التلاتة
+
+633
+01:17:48,740 --> 01:17:52,740
+الأساسية في ال section اللي قلناها هنا يبقى نروح
+
+634
+01:17:52,740 --> 01:17:56,880
+نعطي تعريف ل local maximum و local minimum points
+
+635
+01:17:56,880 --> 01:18:01,780
+و بعد هيك نروح لمينبنروح ل ال settle points ل main
+
+636
+01:18:01,780 --> 01:18:08,860
+لل functions of two or more variables تمام نعطي
+
+637
+01:18:08,860 --> 01:18:14,120
+تعريف الأول و بعد هيك بنشوف كيف بدنا نشتغل الشغل
+
+638
+01:18:14,120 --> 01:18:25,500
+يبقى باجي بقول definition let f of x y be a
+
+639
+01:18:25,500 --> 01:18:32,060
+functiondefine on
+
+640
+01:18:32,060 --> 01:18:40,580
+a region R on a region R containing the point
+
+641
+01:18:40,580 --> 01:18:46,100
+containing the
+
+642
+01:18:46,100 --> 01:18:51,200
+point UA
+
+643
+01:18:51,200 --> 01:18:52,240
+وB
+
+644
+01:18:56,830 --> 01:19:06,330
+مقا الأولى بقول F of A وB is a local maximum value
+
+645
+01:19:06,330 --> 01:19:20,370
+is a local maximum value local maximum value of F
+
+646
+01:19:20,370 --> 01:19:26,290
+إذا كان ال F of A وB
+
+647
+01:19:33,780 --> 01:19:41,160
+for all domain points for all
+
+648
+01:19:41,160 --> 01:19:57,380
+domain points for all domain points x y x y in
+
+649
+01:19:57,380 --> 01:20:02,940
+an open disk in an open
+
+650
+01:20:13,130 --> 01:20:20,130
+النقطة A وB الـ
+
+651
+01:20:20,130 --> 01:20:28,630
+F من A وB هي قيمة
+
+652
+01:20:28,630 --> 01:20:41,930
+أقل محلية محلية أقل محليةF إذا كان of F إذا كان ال
+
+653
+01:20:41,930 --> 01:20:51,490
+F of A و B أقل من أو يساوي F of X و Y for all
+
+654
+01:20:51,490 --> 01:21:01,570
+domain points for all domain points for all domain
+
+655
+01:21:01,570 --> 01:21:19,060
+pointsxy in an open disk centered at
+
+656
+01:21:19,060 --> 01:21:23,300
+point a1
+
+657
+01:21:39,120 --> 01:21:46,100
+في موقع الـ Local
+
+658
+01:21:46,100 --> 01:21:55,560
+Extrema الـ
+
+659
+01:21:55,560 --> 01:22:04,160
+Tangent Appliance الـ
+
+660
+01:22:04,160 --> 01:22:12,900
+Tangent Applianceار هوريزونتال ر
+
+661
+01:22:12,900 --> 01:22:30,340
+هوريزونتال هذا يعني ان اكتشف اكتشف اكتشف اكتشف
+
+662
+01:22:53,820 --> 01:22:58,220
+نرجع ل two definitions مرة ثانية نقرأ ال two
+
+663
+01:22:58,220 --> 01:23:03,480
+definitions نقارنهم ب calculus ايه نحاول نعرفهم
+
+664
+01:23:03,480 --> 01:23:09,040
+برسل شو معنى هذا ال definition طبعا لو رجعنا لكلام
+
+665
+01:23:09,040 --> 01:23:13,260
+اللي احنا كاتبينه و رجعنا الى calculus ايه بلاقي
+
+666
+01:23:13,260 --> 01:23:18,730
+ال two definitions are similarأتنين مالهم متشابهين
+
+667
+01:23:18,730 --> 01:23:23,370
+في شبه كثير جدا الدالة f of x y المعرفة على ال
+
+668
+01:23:23,370 --> 01:23:27,710
+region R يبقى الcontaining بتحتوي على النقطة a وb
+
+669
+01:23:27,710 --> 01:23:31,650
+يبقى ال f of a وb بسميها local maximum إذا كان
+
+670
+01:23:31,650 --> 01:23:37,990
+قيمة الدالة هذه أكبرمن أي قيمة أخرى للدالة بحيث
+
+671
+01:23:37,990 --> 01:23:41,090
+تكون موجودة ويعني في ال domain تبعها هذا في ال
+
+672
+01:23:41,090 --> 01:23:45,310
+local maximum و ال local minimum بتكون أقل من أي
+
+673
+01:23:45,310 --> 01:23:49,550
+قيمة أخرى للدالة على ال domain تبعها هل اختلف هذا
+
+674
+01:23:49,550 --> 01:23:53,630
+تعريف عن تعريف Calculus ايه اللهم يلّه بس ال
+
+675
+01:23:53,630 --> 01:23:57,710
+function في two variables بقى نقول معرفة على
+
+676
+01:23:57,710 --> 01:24:02,960
+intervals ما نقول على open diskتمام طيب الكلام هذا
+
+677
+01:24:02,960 --> 01:24:09,420
+بدنا نروح أرسمه بالرسم حتى يظهر معنى كل واحد من
+
+678
+01:24:09,420 --> 01:24:14,900
+التعريفين الإثنين اللي عندنا فبنروح أاخد محاور X Y
+
+679
+01:24:14,900 --> 01:24:19,760
+و Z لإن احنا بتكلم ال L على وين؟ على الفرار إذا
+
+680
+01:24:19,760 --> 01:24:24,200
+احنا لو روحنا أخدنا المحاور بالشكل اللي على هذا
+
+681
+01:24:24,200 --> 01:24:27,940
+يبقى
+
+682
+01:24:27,940 --> 01:24:36,640
+هذا محور Xهذا محور Y وهذا محور Z لما اقول ان عندي
+
+683
+01:24:36,640 --> 01:24:43,340
+function في X وY يعني كأن Z as a function of X وY
+
+684
+01:24:43,340 --> 01:24:44,780
+لما اقول ان عندي function في X وY يعني كأن Z as a
+
+685
+01:24:44,780 --> 01:24:47,280
+function of X وY لما اقول ان عندي function في X وY
+
+686
+01:24:47,280 --> 01:24:51,180
+يعني كأن Z as
+
+687
+01:24:51,180 --> 01:24:52,120
+a function
+
+688
+01:24:57,350 --> 01:25:02,010
+أيش ما يكون يكون كويس مكان ال service على الشكل
+
+689
+01:25:02,010 --> 01:25:08,850
+اللي عندناه الان بدي اجي لل domain تبعه يبقى ال
+
+690
+01:25:08,850 --> 01:25:16,430
+domain تبعه بقي كأنه بسقط هذا كله على المستوى x y
+
+691
+01:25:16,430 --> 01:25:21,930
+plane بصير عند مين يا بنات هنا اللي هو desk بالشكل
+
+692
+01:25:21,930 --> 01:25:25,850
+اللي عندناه طب
+
+693
+01:25:25,850 --> 01:25:33,260
+كويسالان لو جيت للنقطة اللى عندنا هذه فوق و جيت
+
+694
+01:25:33,260 --> 01:25:40,540
+أسقطة هنا يبقى بتجيني وين؟ على المركز جال للدسك
+
+695
+01:25:40,540 --> 01:25:47,340
+المركز سبعه هو النقطة A وB يبقى هذه النقطة اللى
+
+696
+01:25:47,340 --> 01:25:49,160
+عندنا A وB
+
+697
+01:25:51,820 --> 01:25:57,180
+يبقى أبنات كأنه domain الدالة هو الدائرة الزرقى
+
+698
+01:25:57,180 --> 01:26:01,120
+اللى عندنا هذا هو ال domain الدالة و الدالة وين هي
+
+699
+01:26:01,120 --> 01:26:05,920
+رسميتها فوق لكن ال domain تبعها وين في المستوى xy
+
+700
+01:26:05,920 --> 01:26:10,380
+فلان أندي f of x y تمام يبقى ال domain تبعها في ال
+
+701
+01:26:10,380 --> 01:26:17,250
+xy planeطيب نرجع للتعريف اللي احنا جايلينه ونمشي
+
+702
+01:26:17,250 --> 01:26:21,630
+معاه خطوة بخطوة ونحاول نسقط هذا التعريف على الرسمة
+
+703
+01:26:21,630 --> 01:26:25,310
+اللي عندنا هنا عشان تثبت هذه المعلومة في دماغنا
+
+704
+01:26:25,310 --> 01:26:30,410
+كويس فإيش بيقول هنا اختصر lithopics y دلنا معرفة
+
+705
+01:26:30,410 --> 01:26:35,810
+على region R containing the point A وB يبقى معرفة
+
+706
+01:26:35,810 --> 01:26:41,840
+على region Rبدي افترض ان هذه كلها هي ال region R
+
+707
+01:26:41,840 --> 01:26:44,960
+اللي هي ال function المعرفة لان انا خدتني جزء منها
+
+708
+01:26:44,960 --> 01:26:48,300
+هذا جزء من ال surface مين ما يكون ال surface هذا
+
+709
+01:26:48,300 --> 01:26:52,500
+يكون تمام يبقى هذا ال region R ال region R جاي وين
+
+710
+01:26:52,500 --> 01:26:58,660
+يا بنات في المستوى XY plane اه اديني بالكم طيب
+
+711
+01:26:58,660 --> 01:27:05,580
+بقول في هذه الحالة F of A وBis a local maximum وين
+
+712
+01:27:05,580 --> 01:27:11,280
+ال f of a و b يبقى النقطة اللى عندها دى يبقى a و b
+
+713
+01:27:11,280 --> 01:27:16,880
+و f of a و b الخط الأزرق المنقط هذا هذا الطول كله
+
+714
+01:27:16,880 --> 01:27:21,480
+يعتبر main a و b ليش لإن النقطة اللى عندها دى فى
+
+715
+01:27:21,480 --> 01:27:29,200
+الفراغ هنا لو جتلى يحدثيها تبدى يكون a و b و f of
+
+716
+01:27:29,200 --> 01:27:34,190
+a و bصحيح ولا لأ؟ يجب ان ادى احداثيات النقطة اللى
+
+717
+01:27:34,190 --> 01:27:38,110
+في ال top تبع ال surface اللى عندها طيب عشان اقول
+
+718
+01:27:38,110 --> 01:27:43,510
+لك النقطة هذه بسميها عليها local maximum اذا كانت
+
+719
+01:27:43,510 --> 01:27:49,750
+قيمة الدلة اكبر من او تساوي عند هذه النقطة اكبر من
+
+720
+01:27:49,750 --> 01:27:55,890
+او تساوي اي قيمة اخرى موجودة في domain x واي اللى
+
+721
+01:27:55,890 --> 01:28:00,750
+موجودة في ال open disk اللى مركزه mainاللي هو A وB
+
+722
+01:28:00,750 --> 01:28:05,730
+يبقى هذا اللي هو ال open disk اللي مركزه في A وB
+
+723
+01:28:05,730 --> 01:28:11,470
+طيب بدي أجي أشوف كيف بدي أاخد أي نقطة موجودة في ال
+
+724
+01:28:11,470 --> 01:28:17,390
+open disk لو جيت أخدت أي نقطة زي النقطة هذه موجودة
+
+725
+01:28:17,390 --> 01:28:20,870
+في ال open disk بدي أشوف قيمة الدالة عندها يبقى
+
+726
+01:28:20,870 --> 01:28:25,530
+بطلع لغاية ما جابل مين ما جابل السطح يعني لو جيت
+
+727
+01:28:25,530 --> 01:28:30,130
+بدي أجابل السطح بالشكل اللي عندنايمشي يمشي جابلته
+
+728
+01:28:30,130 --> 01:28:34,390
+مثلا عند النقطة هذه إذا
+
+729
+01:28:36,110 --> 01:28:39,150
+البعد اللي عندك هذا الأسود و لا البعد الأزرق من
+
+730
+01:28:39,150 --> 01:28:44,130
+اللي أكبر الأزرق أكبر يبقى بناء عليه قيمة الدالة
+
+731
+01:28:44,130 --> 01:28:48,570
+صارت أقل من قيمة الدالة عند النقطة A وB أو بمعنى
+
+732
+01:28:48,570 --> 01:28:54,690
+أخر قيمة الدالة عند A وB أكبر من أي قيمة على ال
+
+733
+01:28:54,690 --> 01:28:58,410
+open disk طبعا هناخد تالية عشوائية وبالتالية دي
+
+734
+01:28:58,410 --> 01:29:03,470
+ممكن تكون أي نقطة أخرى يبقى هذه النقطة الأحدثية
+
+735
+01:29:03,470 --> 01:29:10,030
+تالية يمينX هو إذا قيمة الدالة عند نقطة X وY دائما
+
+736
+01:29:10,030 --> 01:29:17,450
+و أبدا أقل من مين من قيمة الدالة عند مين عند A وB
+
+737
+01:29:17,450 --> 01:29:21,270
+إذا حدث ذلك يبقى النقطة اللي فوق بتقول عنها مين
+
+738
+01:29:21,270 --> 01:29:27,870
+local maximum طيب استنى شوية نرجع بالذكرة إلى
+
+739
+01:29:27,870 --> 01:29:32,070
+الورق لCalculus A بقين أقول فيه Calculus A عند
+
+740
+01:29:32,070 --> 01:29:37,840
+local maximumفي عندى فهمة المستقبلية بتكون zero و
+
+741
+01:29:37,840 --> 01:29:43,980
+لو رسمت tangent line بيصير مين؟ أفقي صحيح؟ طب أكرر
+
+742
+01:29:43,980 --> 01:29:48,120
+tangent line بقدر أرسم عند النقطة اللى فوق بس واحد
+
+743
+01:29:48,120 --> 01:29:54,430
+tangent lineماذا يعني؟ يبقى هؤلاء التنجين بيجمعهم
+
+744
+01:29:54,430 --> 01:29:59,330
+في مستوى واحد اسمه ال tangent plane يبقى ال
+
+745
+01:29:59,330 --> 01:30:05,150
+tangent plane في هذه الحالة يكون أفوقيا يعني لو
+
+746
+01:30:05,150 --> 01:30:10,070
+جيت رسمت هذا ال tangent plane على سبيل المثال يبقى
+
+747
+01:30:10,070 --> 01:30:15,350
+ال tangent plane بيصير بالشكل اللي عندنا هذا هي ال
+
+748
+01:30:15,350 --> 01:30:22,410
+tangent planeاللي هو المضلل بالأزرق هذا مَس مين؟
+
+749
+01:30:22,410 --> 01:30:27,890
+مَس ال surface عند مين؟ عند النقطة هذه يبقى هذه هي
+
+750
+01:30:27,890 --> 01:30:33,510
+نقطتي التماس وهذا ال plane يكون أفقيًا وبالتالي
+
+751
+01:30:33,510 --> 01:30:40,960
+معادلة z تساوي z naughtيعني Z تساوي تلاتة اربع
+
+752
+01:30:40,960 --> 01:30:46,460
+خمسة حسب البعد بينه بين المستوى XY لإن ال XY
+
+753
+01:30:46,460 --> 01:30:51,520
+معادلة Z تساوي كم؟ Zero يعني لو قلنا مستوى الغرفة
+
+754
+01:30:51,520 --> 01:30:55,760
+اللي عندنا هذه معادلة Z تساوي Zero لو ارتفعتنا
+
+755
+01:30:55,760 --> 01:31:00,000
+مستوى السجف بسيوف جداشي المسافة بينه بين سجف تلاتة
+
+756
+01:31:00,000 --> 01:31:05,300
+متر إذا السجف معادلة Z تساوي تلاتة يعني Z نُد مثلا
+
+757
+01:31:05,300 --> 01:31:10,500
+عندنا بتلاتة اتنين واحدعشرة قد ما يكون مستوى الان
+
+758
+01:31:10,500 --> 01:31:17,440
+المستوى الأزرق يكون أوفقيا وبالتالي هذه الملاحظة
+
+759
+01:31:17,440 --> 01:31:22,240
+اللي كتبناها هنا لما
+
+760
+01:31:22,240 --> 01:31:25,240
+اقول local extrema يعني جبت ال local maximum و ال
+
+761
+01:31:25,240 --> 01:31:28,380
+local minimum يعني جامعة جمعتهم كلهم ب local
+
+762
+01:31:28,380 --> 01:31:33,520
+extrema التانجين تبلز بيكون horizontal وبالتالي
+
+763
+01:31:33,520 --> 01:31:40,410
+المعادلة تكوناللي اتكلمنا عليه على ال local
+
+764
+01:31:40,410 --> 01:31:43,850
+maximum ده روح يتكرر عالميا على ال local minimum
+
+765
+01:31:43,850 --> 01:31:49,510
+يبقى نفس الصيغة بسقل ال F of A و B يكون أقل من F
+
+766
+01:31:49,510 --> 01:31:54,030
+of X و Y في جميع القيم على الإطلاق في ال open disk
+
+767
+01:31:54,030 --> 01:31:57,950
+اللي يمثل جزء من ال domain يبقى بنات لو روحت أخد
+
+768
+01:31:57,950 --> 01:32:03,510
+المحاور مرة ثانيةفي هذا الشكل و قلت هذا محور X
+
+769
+01:32:03,510 --> 01:32:09,310
+وهذا محور Y وهذا محور Z يبقى النقطة هذه يا بنات
+
+770
+01:32:09,310 --> 01:32:15,750
+تعتبر main القيمة القصوى ال local maximum لو خلقت
+
+771
+01:32:15,750 --> 01:32:24,470
+اسئلة هذه تمثل ال local maximum point طيب لو جيت
+
+772
+01:32:24,470 --> 01:32:30,280
+تخيل ان عندي surface Surface بالشكل هذاو من هنا
+
+773
+01:32:30,280 --> 01:32:37,000
+كان شكله بالشكل اللي عندنا و جيت أسقطه هذا على
+
+774
+01:32:37,000 --> 01:32:45,140
+مين؟ على المستوى XY في Lane بهذا الشكل صار عنده
+
+775
+01:32:45,140 --> 01:32:51,800
+ايش؟ ال disk بالشكل هذا جيت ان النقطة هذه ايه؟ اجت
+
+776
+01:32:51,800 --> 01:32:55,160
+وين؟ في المركز اللي هو A و B
+
+777
+01:32:57,840 --> 01:33:02,660
+خُد أي نقطة في ال open disk في المستوى XY وان تكون
+
+778
+01:33:02,660 --> 01:33:08,240
+النقطة لمين عندنا نقطة هذه يبقى النقطة هذه اليمين
+
+779
+01:33:08,240 --> 01:33:15,040
+XY جاء الطالب اتوكل على الله وجاء الطالب اقابل في
+
+780
+01:33:15,040 --> 01:33:21,240
+ال surface وين عند النقطة اللي عندنا هذه اذا اجت
+
+781
+01:33:21,240 --> 01:33:25,500
+النقطة هذه اعلى من النقطة اللي عندنا هنا وبالتالي
+
+782
+01:33:25,860 --> 01:33:32,700
+قيمة الدالة عند اي و بي كانت اقل من اي قيمة اخرى
+
+783
+01:33:32,700 --> 01:33:36,780
+في ال domain تبع من؟ تبع الدالة اللي عندنا هذه
+
+784
+01:33:36,780 --> 01:33:41,700
+يبقى هذه النقطة ايش بسميها؟ local minimum يبقى هذه
+
+785
+01:33:41,700 --> 01:33:46,800
+اللي عندنا بتصير هنا local minimum
+
+786
+01:33:49,080 --> 01:33:53,700
+وبالتالي لو رسمت tangent انا بدي يكون كمان مين؟
+
+787
+01:33:53,700 --> 01:33:58,800
+كمان أفقي و بدي بيمسى وين؟ عند النقطة اللى عندنا
+
+788
+01:33:58,800 --> 01:34:05,160
+يا بنات لو روحت رسمته هرسمه باللون الأزرق كذلك زى
+
+789
+01:34:05,160 --> 01:34:09,700
+ما رسمنا هذا باللون الأزرق بدي يكون عندك ممسك طبعا
+
+790
+01:34:09,700 --> 01:34:15,440
+هنا مش هيظهرهيظل ماشي هيك و يجيك المستوى بالشكل
+
+791
+01:34:15,440 --> 01:34:22,940
+اللي عندنا هذا هيك يبقى هذا المستوى المضلل بالأزرق
+
+792
+01:34:22,940 --> 01:34:30,670
+حصل تماث بينه وبين المنحنةعند النقطة 2 إلا إن هذا
+
+793
+01:34:30,670 --> 01:34:37,130
+يبقى هذا معادلته z كذلك تساوي z naught جد ما تطلع
+
+794
+01:34:37,130 --> 01:34:41,010
+تطلع يبقى عارفنا شو الفرق بين ال local maximum و
+
+795
+01:34:41,010 --> 01:34:45,980
+ال local minimum من خلال الرسمالـ domain تبعه
+
+796
+01:34:45,980 --> 01:34:51,660
+بيكون في المستويه XY لكن الراسم بتكون فوق الـ
+
+797
+01:34:51,660 --> 01:34:55,120
+local maximum و ال local minimum بعتبر عندي desk
+
+798
+01:34:55,120 --> 01:35:00,440
+مركزه النقطة اللي هي تعتبر local maximum او local
+
+799
+01:35:00,440 --> 01:35:05,060
+minimum لو جيتلي اي قيمة للدالة خلال اي نقطة
+
+800
+01:35:05,060 --> 01:35:09,300
+موجودة في هذا ال domain اذا والله لقيتهاأقل من
+
+801
+01:35:09,300 --> 01:35:13,740
+قيمة الدالة يبقى local maximum أكبر يبقى local
+
+802
+01:35:13,740 --> 01:35:18,850
+minimum وانتهينا من هنامن القصة اللي عندناها طيب
+
+803
+01:35:18,850 --> 01:35:22,750
+الان مذاكرين بقين يقولوا في عندي critical points
+
+804
+01:35:22,750 --> 01:35:28,870
+نقاط حرجة و كيف كنا نحصل عليهم؟ بقين نجيب المشتقة
+
+805
+01:35:28,870 --> 01:35:33,370
+الأولى و نسويها بال zero القيم اللي بتحققها بس
+
+806
+01:35:33,370 --> 01:35:38,890
+انها critical points بس هذه والله هي كمان شغلة اه
+
+807
+01:35:38,890 --> 01:35:44,620
+لو كانت المشتقة غير معرفة عنده نقطةبقول هذه كمان
+
+808
+01:35:44,620 --> 01:35:48,680
+ال critical point طب فدي اسألك كمان سؤال إجباري
+
+809
+01:35:48,680 --> 01:35:52,060
+عندي critical points بتكون عندي local maximum و
+
+810
+01:35:52,060 --> 01:35:57,180
+local minimum؟ لأ ليس بالضرورة يعني مش كل critical
+
+811
+01:35:57,180 --> 01:36:02,760
+point بتكون هي local maximum أو local minimum وهذا
+
+812
+01:36:02,760 --> 01:36:08,800
+نفس الكلاب ينطق على الوضع عندنا تماما إذا بدنا
+
+813
+01:36:08,800 --> 01:36:13,350
+نيجي لحاجة يا بنات اسمهاالـ first derivative test
+
+814
+01:36:13,350 --> 01:36:19,810
+for local extreme values بنحط عنوان بعد هذا تماما
+
+815
+01:36:19,810 --> 01:36:24,790
+و بنقول ال first derivative
+
+816
+01:36:24,790 --> 01:36:28,510
+test
+
+817
+01:36:28,510 --> 01:36:38,930
+for local extreme values for local extreme values
+
+818
+01:36:40,910 --> 01:36:51,650
+إيش بيقول هذا؟ بيقول F ال F of X و Y has
+
+819
+01:36:51,650 --> 01:37:02,970
+.. has a local maximum
+
+820
+01:37:02,970 --> 01:37:14,300
+or minimum value or minimumvalue at an interior
+
+821
+01:37:14,300 --> 01:37:25,080
+point of
+
+822
+01:37:25,080 --> 01:37:29,740
+its
+
+823
+01:37:29,740 --> 01:37:35,900
+domain المجال
+
+824
+01:37:35,900 --> 01:37:36,680
+سبعها
+
+825
+01:37:40,130 --> 01:37:52,430
+إذا كانت الأولى مبادرة مبادرة مبادرة
+
+826
+01:37:52,430 --> 01:37:57,770
+مبادرة
+
+827
+01:37:57,770 --> 01:38:01,590
+مبادرة موجودة
+
+828
+01:38:01,590 --> 01:38:04,630
+هناك
+
+829
+01:38:04,630 --> 01:38:06,550
+ثم
+
+830
+01:38:09,470 --> 01:38:17,510
+الـ Fx عند الـ A و الـ B بدها تساوي Zero and الـ
+
+831
+01:38:17,510 --> 01:38:24,050
+Fy عند الـ A و الـ B كذلك بدها تساوي Zero
+
+832
+01:38:24,050 --> 01:38:30,950
+Definition
+
+833
+01:38:30,950 --> 01:38:37,470
+كمان تاني مقلل
+
+834
+01:38:37,470 --> 01:38:46,840
+Any Interval Pointانترا point a
+
+835
+01:38:46,840 --> 01:38:50,760
+و b of
+
+836
+01:38:50,760 --> 01:39:03,260
+the domain of the domain of a function f of x y
+
+837
+01:39:03,260 --> 01:39:06,900
+it's
+
+838
+01:39:06,900 --> 01:39:16,200
+called a critical pointis all a critical point
+
+839
+01:39:16,200 --> 01:39:32,560
+نقطة حريجة if either اما اما واحد ال fx عند ال a و
+
+840
+01:39:32,560 --> 01:39:38,780
+ال b بدو يسوى zero or والله and
+
+841
+01:39:41,930 --> 01:39:51,270
+and fy عند النقطة a وb بسوى zero كذلك النقطة
+
+842
+01:39:51,270 --> 01:40:04,550
+الثانية one or both one or both of fx عند ال a و
+
+843
+01:40:04,550 --> 01:40:16,050
+ال b and fyعند الـ A will be .. عند ال A will be
+
+844
+01:40:16,050 --> 01:40:21,630
+does not exist
+
+845
+01:40:52,270 --> 01:41:01,890
+تكمل إله بطريقة مركز صغيرة قادمة الـ
+
+846
+01:41:01,890 --> 01:41:16,530
+function f of x y have extreme values
+
+847
+01:41:24,970 --> 01:41:34,670
+القيم المتواجدة في المواقع
+
+848
+01:41:34,670 --> 01:41:41,430
+المتواجدة في المواقع
+
+849
+01:41:41,430 --> 01:41:44,330
+المتواجدة
+
+850
+01:41:48,580 --> 01:41:56,100
+الـ Fx بيساوي الـ Fy ده بيساوي زيرو لإنها ده الـ
+
+851
+01:41:56,100 --> 01:42:13,040
+interim points where one or both of Fx and Fy does
+
+852
+01:42:13,040 --> 01:42:16,360
+not exist
+
+853
+01:42:18,040 --> 01:42:25,320
+المرة التلاتة الـ boundary points
+
+854
+01:42:25,320 --> 01:42:33,300
+ال boundary points of the functions domain
+
+855
+01:42:44,640 --> 01:42:50,620
+أحاول بس نقرأ كلام اللي كتبناه هذا، نفهم كل نقطة
+
+856
+01:42:50,620 --> 01:42:53,760
+فيه، و بيه نهي محاضرته
+
+857
+01:43:09,770 --> 01:43:12,670
+نرجع لـ first derivative test for local extreme
+
+858
+01:43:12,670 --> 01:43:16,190
+values وكان معناه فيه كالبقصة .. فيه كالبقصية
+
+859
+01:43:16,190 --> 01:43:20,910
+بنفسي تسوية لم تغير، بقول لو كانت ال F of X و Y
+
+860
+01:43:20,910 --> 01:43:26,220
+has a local maximum أو local minimumAt an interior
+
+861
+01:43:26,220 --> 01:43:30,080
+point a وb of x, the main and if the first partial
+
+862
+01:43:30,080 --> 01:43:33,880
+derivative exists، إذا بالتفاضل الدالة بالنسبة لX
+
+863
+01:43:33,880 --> 01:43:38,260
+والتفاضل الدالة بالنسبة لY exist، then ال Fx بدأ
+
+864
+01:43:38,260 --> 01:43:42,840
+تساوي Zero والFy تساوي Zero، شوفوا أنا قرأته، و
+
+865
+01:43:42,840 --> 01:43:46,650
+بدأ أقول إيش فهمت، شوفوا فهمي صح ولا غلطأقول بأجعل
+
+866
+01:43:46,650 --> 01:43:52,450
+دان F of X 1 إذا لقيت أنها نقطة F X زي الساوية 0 و
+
+867
+01:43:52,450 --> 01:43:55,690
+F Y زي الساوية 0 يبدأ معناته أن عندي local maximum
+
+868
+01:43:55,690 --> 01:43:57,290
+و local minimum
+
+869
+01:44:03,060 --> 01:44:07,200
+مرة تانية بقول جيت على الذنب استقلت من اسم ال X
+
+870
+01:44:07,200 --> 01:44:10,760
+استقلت من اسم ال Y جيت عنها نقطة ما لقيت هذا
+
+871
+01:44:10,760 --> 01:44:13,820
+الكلام يساوي Zero إذا هل عند هذا نقطة فيه عند لقه
+
+872
+01:44:13,820 --> 01:44:20,360
+ما؟ لأ إذا هذا فهم خاطر فهم مخلوق 180 درجة فإيش
+
+873
+01:44:20,360 --> 01:44:25,780
+الفهم المعدون اقرأه كويس يبقى هذي بقول لو كان عندك
+
+874
+01:44:25,780 --> 01:44:28,620
+local maximum و local minimum value
+
+875
+01:44:35,270 --> 01:44:41,630
+يبقى على عكس ما قلت في الأول تماما 180 درجة واضح
+
+876
+01:44:41,630 --> 01:44:45,770
+يبقى عند مواقع ال local maximum أو ال local
+
+877
+01:44:45,770 --> 01:44:49,790
+minimum بدا تبقى المشتقة بالنسبة ل X تسوى Zero
+
+878
+01:44:49,790 --> 01:44:53,630
+والمشتقة بالنسبة ل Y تسوى Zero هذه هي النقطة
+
+879
+01:44:53,630 --> 01:44:59,410
+الأولى نقطة ثانيةبقول ال point A و B اللي موجودة
+
+880
+01:44:59,410 --> 01:45:05,290
+في دمية دالة F بسميها critical point في حالتين
+
+881
+01:45:05,290 --> 01:45:10,170
+الحالة الأولى لو جبت ال F X عندها لقيتها زواو زيرو
+
+882
+01:45:10,170 --> 01:45:14,650
+وال F Y زواو زيرو والحالة الثانية لو كانت واحدة
+
+883
+01:45:14,650 --> 01:45:22,030
+منهمأو كلاهما غير معرفة عند تلك النقطة هل اختلف
+
+884
+01:45:22,030 --> 01:45:25,890
+تعريف ال critical point عنفي كالكلاسية نفس المفهوم
+
+885
+01:45:25,890 --> 01:45:30,950
+بالضبط تماما بس بدنا نعوض بقيمتين أو بالإحداثين
+
+886
+01:45:30,950 --> 01:45:36,250
+بدل إحداثي واحد إذا مرة تانية النقطة الداخلية هذه
+
+887
+01:45:36,250 --> 01:45:39,570
+اللي موجودة في domain الـ F بسميها critical point
+
+888
+01:45:39,570 --> 01:45:44,090
+النقطة حرجة في حالتينإذا المشتقة الأولى بالنسبة ل
+
+889
+01:45:44,090 --> 01:45:47,570
+X يسوى Zero إذا المشتقة الأولى بالنسبة ل Y سوى
+
+890
+01:45:47,570 --> 01:45:51,590
+Zero هذا الأمر الأول الأمر الثاني لو كانت إحدى
+
+891
+01:45:51,590 --> 01:45:59,770
+المشتقتين أو كلاهما اتنتل ب Zeroطيب وين بدنا نروح
+
+892
+01:45:59,770 --> 01:46:04,590
+ندور على مواضع نهايات العظمة والصغرة؟ بنقول في
+
+893
+01:46:04,590 --> 01:46:09,510
+ثلاثة أماكن، إذا كنت تروح تدوري تشوف عند هذه في
+
+894
+01:46:09,510 --> 01:46:14,050
+local maximum و local minimum و لا لا المكان الأول
+
+895
+01:46:14,050 --> 01:46:18,890
+النقاط الداخلية إيه للمشتقة بالنسبة لك؟ سوى
+
+896
+01:46:18,890 --> 01:46:20,530
+المشتقة الأولى بالنسبةها؟
+
+897
+01:46:28,800 --> 01:46:35,560
+النقاط اللي وحدة فيهم أو كلاهما تبقى غير معرفة
+
+898
+01:46:35,560 --> 01:46:41,000
+الأمر الثالث على ال boundary يبقى بقيانا نقول احنا
+
+899
+01:46:41,000 --> 01:46:46,250
+في الحكاية القلاصيةأول الفترة و آخر الفترة بجينا
+
+900
+01:46:46,250 --> 01:46:50,130
+ندور و نقول هذه ممكن يكون عندها اللي هو local
+
+901
+01:46:50,130 --> 01:46:54,810
+maximum قد يكون و قد لا يكون تمام يبقى بروح على
+
+902
+01:46:54,810 --> 01:46:58,930
+المناظر اللي هي اللي هو ال boundary عندنا تبع مين
+
+903
+01:46:58,930 --> 01:47:03,390
+تبع ال domain تبع الدولة طبعا لو درسنا ال boundary
+
+904
+01:47:03,390 --> 01:47:08,140
+في أول section اللي هو أربعة عشر واحدمظبوط يبقى
+
+905
+01:47:08,140 --> 01:47:12,700
+هذا كلام ليس جديدا علينا المرة القادمة ان شاء الله
+
+906
+01:47:12,700 --> 01:47:18,320
+بنبدأ ناخد مثال على هالشغل هذي ونكمل عليها فيه
+
+907
+01:47:18,320 --> 01:47:23,200
+كمان يبقى عندي absolute maximum و absolute minimum
+
+908
+01:47:23,200 --> 01:47:27,500
+وشوف كيف كان دور على ال boundary كمان مين مين يكون
+
+909
+01:47:27,500 --> 01:47:30,400
+على ال boundary في عندي local maximum او local
+
+910
+01:47:30,400 --> 01:47:35,280
+minimum ان شاء الله و تعالى طبعا اليوم السبت بصير
+
+911
+01:47:35,280 --> 01:47:39,910
+خير ان شاء اللهحاولوا تجروا السكين ولو زي قناة
+
+912
+01:47:39,910 --> 01:47:43,490
+جريدة قبل ان تجو المرة الجاية عشان احنا نمشيها
+
+913
+01:47:43,490 --> 01:47:46,590
+بالكلمة أبيض المعلومة اللي عشان عليها
+
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/vNBEf-x0cGk_raw.srt b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/vNBEf-x0cGk_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..272914f880d0e9254b418e714b02e8667fdfb3f0
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/vNBEf-x0cGk_raw.srt
@@ -0,0 +1,3712 @@
+1
+00:00:15,420 --> 00:00:20,910
+بسم الله الرحمن الرحيمالان بنكمل ال section اللى
+
+2
+00:00:20,910 --> 00:00:25,550
+بدناه المرة الماضية منها اللى كان اللى هو tangent
+
+3
+00:00:25,550 --> 00:00:29,430
+planes and differential طبعا عرفنا المرة اللى فاتة
+
+4
+00:00:29,430 --> 00:00:33,950
+tangent plane وقلنا المعادلة بتابعة هو هي المستقلة
+
+5
+00:00:33,950 --> 00:00:38,620
+تتدلة بالنسبة ل Fأو بالنسبة ل X عند النقطة X node
+
+6
+00:00:38,620 --> 00:00:43,880
+وY node في X نقص X node زائد المشتقة عندها نفس
+
+7
+00:00:43,880 --> 00:00:48,940
+النقطة في Y نقص Y node زائد مشتقة F بالنسبة لZ عند
+
+8
+00:00:48,940 --> 00:00:53,860
+نفس النقطة في Z نقص Z node يساوي Zero ومن هنا
+
+9
+00:00:53,860 --> 00:00:55,220
+روحنا و طلعنا كمان من
+
+10
+00:01:02,140 --> 00:01:07,020
+هذه النقطة هي حالة خاصة من الحالة الماضية تابعة
+
+11
+00:01:07,020 --> 00:01:11,000
+المرة الماضية تابعة المرة الماضية تابعة المرة
+
+12
+00:01:11,000 --> 00:01:11,000
+الماضية تابعة المرة الماضية تابعة المرة الماضية
+
+13
+00:01:11,000 --> 00:01:11,000
+تابعة المرة الماضية تابعة المرة الماضية تابعة
+
+14
+00:01:11,000 --> 00:01:11,000
+المرة الماضية تابعة المرة الماضية تابعة المرة
+
+15
+00:01:11,000 --> 00:01:11,300
+الماضية تابعة المرة الماضية تابعة المرة الماضية
+
+16
+00:01:11,300 --> 00:01:11,520
+تابعة المرة الماضية تابعة المرة الماضية تابعة
+
+17
+00:01:11,520 --> 00:01:13,260
+المرة الماضية تابعة المرة الماضية تابعة المرة
+
+18
+00:01:13,260 --> 00:01:14,480
+الماضية تابعة المرة الماضية تابعة المرة الماضية
+
+19
+00:01:14,480 --> 00:01:15,380
+تابعة المرة الماضية تابعة المرة الماضية تابعة
+
+20
+00:01:15,380 --> 00:01:16,880
+المرة الماضية تابعة المرة الماضية تابعة المرة
+
+21
+00:01:16,880 --> 00:01:20,120
+الماضية تابعة المرة الماضية تابزت نول إذا إحنا
+
+22
+00:01:20,120 --> 00:01:26,260
+عندنا surface مواطئ z as a function f of x و y بدي
+
+23
+00:01:26,260 --> 00:01:31,120
+أحاول من خلال هذا ال surface أوصل إلى معادلة
+
+24
+00:01:31,120 --> 00:01:35,540
+مشابهة للمعادلة اللي كنا تثبناها المرة الماضية مع
+
+25
+00:01:35,540 --> 00:01:40,100
+فارق بسيط جدا الآن بدنا نشوف ما هو هذا الفارق
+
+26
+00:01:40,100 --> 00:01:46,460
+البسيطمش هنوجد معادلة للـ plane الذي يكون مماثن
+
+27
+00:01:46,460 --> 00:01:53,960
+للسطح z of x of y عند النقطة vp0 x0 و y0 و z0 ال
+
+28
+00:01:53,960 --> 00:01:58,520
+right f of x of y نقص z يسوى منين؟ Zero يعني
+
+29
+00:01:58,520 --> 00:02:02,080
+المعادلة هذه هنجيب z وين؟ على الشجرة التانية بس
+
+30
+00:02:02,080 --> 00:02:06,040
+ينبسط بشرة مخالفة فال f of x of y نقص z يسوى منين؟
+
+31
+00:02:06,040 --> 00:02:09,920
+Zero المعادلة اللي عندنا هذه الطرف الشمالي صار
+
+32
+00:02:09,920 --> 00:02:11,040
+function في منين؟
+
+33
+00:02:39,830 --> 00:02:44,800
+في تلاثة متغيراتأذا كأنه أنا عندي دالة جديدة
+
+34
+00:02:44,800 --> 00:02:52,800
+سميتها capital F of X و Y و Z بدأت سوية F of X و Y
+
+35
+00:02:52,800 --> 00:02:57,580
+نقصدها كأنها هذه الدالة الأصلية و لما سويتها بال
+
+36
+00:02:57,580 --> 00:03:04,820
+zero كان هذا هو zero level surface بالنسبة لهاالان
+
+37
+00:03:04,820 --> 00:03:10,420
+بنجيب ال equation لتنجل لهذا ال level surface بقول
+
+38
+00:03:10,420 --> 00:03:14,200
+بسيطة جدا، بنشتغل ال function بالنسبة ل X بالنسبة
+
+39
+00:03:14,200 --> 00:03:19,620
+ل Y و بالنسبة ل Z و نعوض في معادلة المرة الماضية
+
+40
+00:03:19,620 --> 00:03:24,760
+يبقى بنات بدالي capital F X يعني بدي اشتغل الدالة
+
+41
+00:03:24,760 --> 00:03:32,420
+الجديدة بالنسبة ل Xهذه المشتقة دلالي على اليمين
+
+42
+00:03:32,420 --> 00:03:37,440
+بالنسبالك هذه function في x و y يبقى مشتقتها بتكون
+
+43
+00:03:37,440 --> 00:03:45,840
+f small f تمام والزد يبقى كم؟ Zero يبقى ناقص Zero
+
+44
+00:03:45,840 --> 00:03:51,540
+يبقى تصبح المشتقة تبعت capital F of x و y هي نفس
+
+45
+00:03:51,540 --> 00:03:56,470
+المشتقة تبعت من تبعت ال function اللي عندناIn
+
+46
+00:03:56,470 --> 00:04:03,310
+general بدي أقوله بدي أجيب f x عند النقطة x node و
+
+47
+00:04:03,310 --> 00:04:09,730
+y node و z node هذا الكلام بدي أسوي f x عند النقطة
+
+48
+00:04:09,730 --> 00:04:18,270
+x node و y node و z node طيب بدي أجيب fy هذا
+
+49
+00:04:18,270 --> 00:04:23,200
+الكلام بدي أسوي و باختصارة بدي أخليها نفسيعند
+
+50
+00:04:23,200 --> 00:04:27,840
+النقطة x نوت و y نوت و z نوت معناته بدلا اشتقت
+
+51
+00:04:27,840 --> 00:04:32,020
+دالة لان هذه بالنسبة لمين لو ايه يبقى مشتقة الـ z
+
+52
+00:04:32,020 --> 00:04:38,120
+جزيرو يبقى هذه يبقى سوية f small x عند النقطة fy
+
+53
+00:04:38,120 --> 00:04:44,960
+عند النقطة x نوت و y نوت و z نوت ناقص الـ zero طيب
+
+54
+00:04:44,960 --> 00:04:47,100
+كويس بدأ أروح أجيب كامة
+
+55
+00:04:49,850 --> 00:04:54,890
+عند النقطة التي هي x node و y node و z node يبقى
+
+56
+00:04:54,890 --> 00:04:59,010
+هذا السبب بده zero طبعا هذه ده اللي كلها في x و y
+
+57
+00:04:59,010 --> 00:05:02,750
+و احنا بنفضل بالنسبة إلى z يبقى مشتقتها ب zero
+
+58
+00:05:22,200 --> 00:05:29,500
+هل اختلفت Fx عن Fx الماضية يبقى زي ما هي
+
+59
+00:05:44,450 --> 00:05:49,790
+عند ال X نوت و ال Y نوت و ال Z نوت في مين؟ في ال Y
+
+60
+00:05:49,790 --> 00:05:54,590
+ناقص Y نوت نجي اللي في Z اللي يبقى كده شعلة هنا؟
+
+61
+00:05:54,590 --> 00:06:02,050
+بواحد يبقى هنا هاي سالب واحد في مين؟ في Z ناقص Z
+
+62
+00:06:02,050 --> 00:06:09,230
+نوت كل هذا الكلام بده يساوي Zeroإذا الفرق البسيط
+
+63
+00:06:09,230 --> 00:06:15,430
+بين هذه المعادلة ومعادلة المرة الماضية ان ال F زد
+
+64
+00:06:15,430 --> 00:06:20,170
+عنها طلعت بقداش بسالب واحد وهذا هو الفرق بين
+
+65
+00:06:20,170 --> 00:06:26,410
+المعادلة هذه ومعادلة المرة الماضية كإني ولي خطر
+
+66
+00:06:26,410 --> 00:06:32,630
+تسألي هكذا هذي
+
+67
+00:06:32,630 --> 00:06:36,450
+سالب واحد صحيح وهي سالب واحد موجود تمام صحيح
+
+68
+00:06:40,000 --> 00:06:44,720
+طبعا المدرس الناجح اللي بكون عند حس طلابه، يعني
+
+69
+00:06:44,720 --> 00:06:48,460
+بدي أحس أنه شو اللي بيفهمه و شو اللي بيفهموش، و
+
+70
+00:06:48,460 --> 00:06:51,500
+أنا من النوع اللي بيقرأ هذا في وجوه الطلاب اللي
+
+71
+00:06:51,500 --> 00:06:55,040
+أنا بدرسهم، يعني إذا في شغلة مش واضحة بقرأها في
+
+72
+00:06:55,040 --> 00:07:00,300
+وجههم تمامالذلك الطالب بعرف امتابعني، مش امتابعني،
+
+73
+00:07:00,300 --> 00:07:03,080
+فاهم، مش فاهم من خلال المحاضرة، حتى لو كان القاعة
+
+74
+00:07:03,080 --> 00:07:06,080
+فيها مية طالبة، واحد واحد، المية والعشرين
+
+75
+00:07:06,080 --> 00:07:09,500
+بالنسبالي سيجان، لأنه متعود على اللي هو العدد
+
+76
+00:07:09,500 --> 00:07:12,520
+الكبير أو العدد الصغير، ماتفرقش عندي بالنسبالي،
+
+77
+00:07:12,520 --> 00:07:19,140
+فلذلك بتلاقيني دقيق الملاحظة في هذه الأمور نبدأ
+
+78
+00:07:19,140 --> 00:07:21,220
+ناخد مثال على ذلك example
+
+79
+00:07:28,520 --> 00:07:37,860
+يقول الـ final equation five and equation for the
+
+80
+00:07:37,860 --> 00:07:41,900
+plane that
+
+81
+00:07:41,900 --> 00:07:45,900
+is tangent
+
+82
+00:07:45,900 --> 00:07:47,240
+to the surface
+
+83
+00:07:58,100 --> 00:08:08,300
+والذي يكون هو مثل سطح Z تساوي لل X
+
+84
+00:08:08,300 --> 00:08:15,460
+نقص اتنين Y at the
+
+85
+00:08:15,460 --> 00:08:16,120
+point
+
+86
+00:08:31,820 --> 00:08:36,420
+السؤال مرة ثانية بيقول هذه المعادلة المستوى الذي
+
+87
+00:08:36,420 --> 00:08:42,340
+يكون ممثل في سطح z تساوي لل x ناقص اتنين y عند
+
+88
+00:08:42,340 --> 00:08:47,940
+النقطة تلاتة واحد وزير لو جيت نظرتي هذه المعادلة
+
+89
+00:08:47,940 --> 00:08:54,290
+بلاحظ ان z مواطع ك function تمامفي المتغيرين x و y
+
+90
+00:08:54,290 --> 00:09:01,590
+اذا انا بقدر اكتب هذه المعادلة بطريقة اخرى لو نجلت
+
+91
+00:09:01,590 --> 00:09:08,840
+ال z على الشجرة التانيةلو جيت كتبت ان ال F أو ال
+
+92
+00:09:08,840 --> 00:09:21,140
+LEN LEN ال X ناقص 2Y ناقص Z بدها تساوي Z يبقى حصلت
+
+93
+00:09:21,140 --> 00:09:25,060
+على معادلة جديدة الطرف الشمال صار function في
+
+94
+00:09:25,060 --> 00:09:30,400
+ثلاثة متغيراتاللي ال X و ال Y و ال Z يبقى بناء ان
+
+95
+00:09:30,400 --> 00:09:33,300
+عليها هذا الكلام دي يساوي الكون و الصدر إذا هذا
+
+96
+00:09:33,300 --> 00:09:44,800
+يمثل level surface لدالة ما يبقى this is a أو this
+
+97
+00:09:44,800 --> 00:09:55,980
+is the zero level surface for
+
+98
+00:10:13,770 --> 00:10:23,050
+Fx يبقى Fx نشتقل لين واحدعلى اللى داخل الليل و X
+
+99
+00:10:23,050 --> 00:10:29,110
+نقص اتنين Y فمشتقت ما داخل الليل بالنسبة الى X
+
+100
+00:10:29,110 --> 00:10:35,850
+اللى هو بواحد صحيح بدنا نروح نحسب قداش ال F X عند
+
+101
+00:10:35,850 --> 00:10:42,200
+النقطة المعطاعة تلاتة واحد و Zero بدل سنةهشيل كل X
+
+102
+00:10:42,200 --> 00:10:46,820
+وحط مكانه تلاتة وشيل كل Y وحط مكانه واحد ويصير
+
+103
+00:10:46,820 --> 00:10:53,390
+واحد على تلاتة نقص اتنين ويسوء جدير واحدبنروح نجيب
+
+104
+00:10:53,390 --> 00:11:00,190
+ال Fy كذلك يبقى واحد على X نقص اتنين Y في مستقل
+
+105
+00:11:00,190 --> 00:11:06,410
+مداخل الليمب بالنسبة الى Y اللي هو سالم اتنين يتجه
+
+106
+00:11:06,410 --> 00:11:12,290
+النتيجة هذه بتعطيني ال Fy عند النقطة تلاتة واحد
+
+107
+00:11:12,290 --> 00:11:19,610
+وزيره بتسوي نقص اتنين على تلاتة نقص اتنين وهي سامة
+
+108
+00:11:19,610 --> 00:11:26,540
+الدرج نقص اتنينفز معروفة مباشرة كده يا فنان؟ سالب
+
+109
+00:11:26,540 --> 00:11:32,920
+واحد تمام لأن الان كلها مقدار ثابت بالنسبة لز يبقى
+
+110
+00:11:32,920 --> 00:11:38,180
+مع السلامة ويبقى سالب واحد معناته ان الفز عند
+
+111
+00:11:38,180 --> 00:11:43,700
+التلاتة او واحد وزي او عند اي نقطة اخرى بدل سواء
+
+112
+00:11:43,700 --> 00:11:49,140
+كده واحد الان النقطة موجودة مشتقات التلاتة موجودة
+
+113
+00:11:49,140 --> 00:11:51,360
+اذا اتوماتيك سهل اجيب
+
+114
+00:11:55,140 --> 00:12:00,940
+معادلة هذي سميها ال star و بدنا نعوض في معادلة رقم
+
+115
+00:12:00,940 --> 00:12:05,500
+ال star إذا بدي أشيل ال fx و أضعه في درجة دي ال
+
+116
+00:12:05,500 --> 00:12:13,100
+واحد يبقى هاي واحد دقيق ناقص تلاتة اللي بعدها ال
+
+117
+00:12:13,100 --> 00:12:17,040
+fy ناقص اتنين في ال y
+
+118
+00:12:20,540 --> 00:12:29,920
+بعدها ناقص واحد في زد ناقص بيصير زائد واحد كل هذا
+
+119
+00:12:29,920 --> 00:12:32,440
+الكلام بده يساوي Zero
+
+120
+00:12:38,460 --> 00:12:45,760
+زد فقط لغير اللي نقص Zero بدر يساوي Zero فالفك
+
+121
+00:12:45,760 --> 00:12:51,400
+المعادلة هذه يبقى بصير X نقص تلاتة نقص اتنين Y
+
+122
+00:12:51,400 --> 00:12:58,180
+زائدي اتنين نقص Z كله بدر يساوي Zero او بمعنى اخر
+
+123
+00:12:58,180 --> 00:13:07,230
+شكل تبعها بدر ياخد الشكل التالفX-2Y-Z و7 عندك هنا
+
+124
+00:13:07,230 --> 00:13:12,810
+2 وهنا 3 و3 و3 و3 و3 و3 و3 و3 و3 و3 و1 و1 و1 و1 و1
+
+125
+00:13:12,810 --> 00:13:16,910
+و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1
+
+126
+00:13:16,910 --> 00:13:17,010
+و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1
+
+127
+00:13:17,010 --> 00:13:17,010
+و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1
+
+128
+00:13:17,010 --> 00:13:17,010
+و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1
+
+129
+00:13:17,010 --> 00:13:17,030
+و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1 و1
+
+130
+00:13:17,030 --> 00:13:20,790
+و1 و1 و1 و1 و1 و
+
+131
+00:13:32,830 --> 00:13:38,290
+هل تذكروا موضوع ال linearization في calculus A؟
+
+132
+00:13:52,630 --> 00:13:56,590
+ثم functions of a three variables هنجيب ال
+
+133
+00:13:56,590 --> 00:14:00,630
+linearization في الحالتين طب حد من الذكرة يعني
+
+134
+00:14:00,630 --> 00:14:05,670
+بالبلدين شو يعني مقصود ال linearization؟ عندها
+
+135
+00:14:05,670 --> 00:14:11,970
+نقطة؟ أيوةهو كلمة linearization جاي من كلمة ايه؟
+
+136
+00:14:11,970 --> 00:14:18,930
+من كلمة line تمام؟ ايوة يبقى المثل في الحالة اللي
+
+137
+00:14:18,930 --> 00:14:22,090
+عندنا .. انا عندي function ابنان و بكون ال
+
+138
+00:14:22,090 --> 00:14:28,940
+function صعب التعامل معاها، كويس؟ بجيبدالة أخرى
+
+139
+00:14:28,940 --> 00:14:35,220
+تكافئ هذه الدالة وهذه الدالة بيكون دالة خاطية يعني
+
+140
+00:14:35,220 --> 00:14:40,080
+بيكون الفرق بينها وبين الدالة لأن الفرق بسيط جدا
+
+141
+00:14:40,080 --> 00:14:45,300
+يمكن يمكن الاستغناء عنه هذا معناه كلمة
+
+142
+00:14:45,300 --> 00:14:49,880
+linearization يعني أنا بدي أحول الدالة اللي عندنا
+
+143
+00:14:50,150 --> 00:14:55,050
+الى دالة خطية على نقطة بيصير قيمة الدالة الخطية
+
+144
+00:14:55,050 --> 00:14:59,810
+وقيمة ال function عند هذه النقطة اتنين اردسين مع
+
+145
+00:14:59,810 --> 00:15:05,430
+ثانث بسيط جدا كثر من عشرة كثر من مية كثر من الف
+
+146
+00:15:05,430 --> 00:15:09,330
+وبالتالي يمكن الاستغناء عن ال function الأصلية
+
+147
+00:15:09,330 --> 00:15:14,790
+والتعامل مع ال function الخطية اللي عندنا هذا
+
+148
+00:15:14,790 --> 00:15:20,220
+بالبلد هيكلكن احنا بنشتغل شغل رياضي مشان شغل رياضي
+
+149
+00:15:20,220 --> 00:15:24,200
+بنروح نحط تعريف لل linearization في ال functions
+
+150
+00:15:24,200 --> 00:15:29,300
+of two variables ثم نستخدم هذا التعريف في حساب ال
+
+151
+00:15:29,300 --> 00:15:33,060
+linearization لدالة ما يبقى definition
+
+152
+00:15:45,400 --> 00:15:50,300
+of a function f
+
+153
+00:15:50,300 --> 00:16:01,740
+of x و y at a point عند النقطة x naught و y naught
+
+154
+00:16:01,740 --> 00:16:12,860
+where ال f is differentiable function is
+
+155
+00:16:15,850 --> 00:16:25,370
+عندنا رمز f as a function of x y عمليا يسوى f of x
+
+156
+00:16:25,370 --> 00:16:32,870
+naught و y naught زائد f x عند النقطة x naught و y
+
+157
+00:16:32,870 --> 00:16:41,190
+naught في ال x ناقص ال x naught زائد f y عند
+
+158
+00:16:41,190 --> 00:16:47,700
+النقطة x naught و y naughtفى الـ y ما قصد why not
+
+159
+00:16:47,700 --> 00:16:52,080
+يبقى
+
+160
+00:16:52,080 --> 00:16:56,300
+هذا ال linearization تبع الدلة هو هذا التعريف
+
+161
+00:16:56,300 --> 00:17:01,800
+الأول التعريف الثاني approximation function
+
+162
+00:17:01,800 --> 00:17:05,820
+approximation
+
+163
+00:17:05,820 --> 00:17:09,860
+function
+
+164
+00:17:09,860 --> 00:17:19,380
+يعني الدلة التقريبيةالـ F of XY التي تسوى تقريبا L
+
+165
+00:17:19,380 --> 00:17:28,600
+of XY is called the
+
+166
+00:17:28,600 --> 00:17:38,560
+standard linear
+
+167
+00:17:38,560 --> 00:17:39,280
+approximation
+
+168
+00:17:49,720 --> 00:17:58,520
+Linear Approximation of F at
+
+169
+00:17:58,520 --> 00:18:05,520
+point
+
+170
+00:18:05,520 --> 00:18:08,760
+X0 وY0
+
+171
+00:18:59,840 --> 00:19:03,700
+نرجع للتعريف اللي احنا كاتبينه في هذا مرة ثانية
+
+172
+00:19:05,050 --> 00:19:08,670
+يبقى باجي بقول ال linearization للدالة f of x و y
+
+173
+00:19:08,670 --> 00:19:12,690
+عند النقطة x نقطة و y نقطة حيث ال f دالة قابلة
+
+174
+00:19:12,690 --> 00:19:20,790
+للاشتقاقية هديها الرمز L of x و y قيمة الدالة
+
+175
+00:19:20,790 --> 00:19:25,570
+الأصلية عند النقطة المعطاة f of x نقطة و y نقطة
+
+176
+00:19:25,570 --> 00:19:31,150
+مضافة إليها مشتقة الدالة بالنسبة لx عند تلك النقطة
+
+177
+00:19:31,150 --> 00:19:33,670
+مضروب في x نقص ال x نقطة
+
+178
+00:19:42,420 --> 00:19:49,740
+السؤال هو هل هذه دالة خطية في X و Y أم لا
+
+179
+00:19:54,410 --> 00:20:00,030
+صح ولا لأ؟ وهذا كمان رقم و X نود رقم يبقى بقية X
+
+180
+00:20:00,030 --> 00:20:06,010
+مضروبة في رقم هذا كمان رقم وهذا رقم Y يبقى دالة ما
+
+181
+00:20:06,010 --> 00:20:10,490
+بين X وY كلهم من X وY من الدرجة الأولى إذا معادلة
+
+182
+00:20:10,490 --> 00:20:17,050
+خط مستقيم ومن هنا سمنها دالة خطية Linearization
+
+183
+00:20:17,050 --> 00:20:21,630
+Linearization دالة خطية هذه حصل عليها من مين؟من
+
+184
+00:20:21,630 --> 00:20:27,210
+الدالة الأصلية عند نقطة تقع عالمين على الدالة
+
+185
+00:20:27,210 --> 00:20:34,670
+الأصلية يبقى عمليا هذه القيمة للدالة الخطية عند
+
+186
+00:20:34,670 --> 00:20:40,210
+تلك النقطة تساوي قيمة الدالة الخطية عند تلك النقطة
+
+187
+00:20:40,210 --> 00:20:45,990
+طبعا يكون فارق بسيط جدا من هنا روحنا للتعريف
+
+188
+00:20:45,990 --> 00:20:51,860
+الثاني فقولنا approximation function f of x yتساوي
+
+189
+00:20:51,860 --> 00:20:57,180
+تقريبا ال
+
+190
+00:20:57,180 --> 00:21:04,200
+L of X Y فسميناها الدالة التقريبية للدالة F of X Y
+
+191
+00:21:04,200 --> 00:21:08,700
+هي مين؟ هي L of X Y يبقى هذه اللي بسميها ال
+
+192
+00:21:08,700 --> 00:21:13,120
+standard linear approximation للدالة F عند النقطة
+
+193
+00:21:13,120 --> 00:21:17,750
+اللي عندنا هذهعلى أي حال بنبدأ ناخد مثال عملي
+
+194
+00:21:17,750 --> 00:21:22,170
+تطبيقه أه اللي مذكرة شوية في calculus A هل اختلفت
+
+195
+00:21:22,170 --> 00:21:26,370
+عن تبع ال calculus A؟ أبدا بيجي نقول اللي نغضب لو
+
+196
+00:21:26,370 --> 00:21:33,110
+كانت y دالة في x يوجه y تساوي f of x بدليها فبنروح
+
+197
+00:21:33,110 --> 00:21:37,970
+نحسب قيمة الدالة عند النقطة x non مضافة إليها
+
+198
+00:21:37,970 --> 00:21:43,150
+مشتقة الدالة لf بالنسبة لx عند تلك النقطة مضروب في
+
+199
+00:21:43,150 --> 00:21:48,220
+x نقص x nonبنعمل من الذنب قطيب اضافنا له احنا من
+
+200
+00:21:48,220 --> 00:21:52,480
+اضافنا له ال term اللي عندنا هذا لأنه صارت دالة في
+
+201
+00:21:52,480 --> 00:21:57,180
+two variables الان على اي حال نبدأ ناخد مثال
+
+202
+00:21:57,180 --> 00:22:08,860
+تطبيقي على ذلك ناخد example why
+
+203
+00:22:08,860 --> 00:22:12,780
+the linearization عين لا
+
+204
+00:22:18,120 --> 00:22:25,480
+Linearization of a function L
+
+205
+00:22:25,480 --> 00:22:43,820
+of X Y of the function R of the function F of X YX
+
+206
+00:22:43,820 --> 00:22:53,760
+زائد Y زائد Z الكل تربيع A عند النقطة واحد واثنين
+
+207
+00:23:06,550 --> 00:23:11,690
+مش هنحسب اللي نرزقه تروح أحسب تلت شغلات شغلة
+
+208
+00:23:11,690 --> 00:23:15,990
+الأولى بدي قيمة الدلة عند النقطة بتشتق الدلة
+
+209
+00:23:15,990 --> 00:23:20,030
+بالنسبة ل X و أحسبها عند نفس النقطة تشتق الدلة
+
+210
+00:23:20,030 --> 00:23:24,790
+بالنسبة ل Y و أحسبها عند نفس النقطة يبقى لو جيت
+
+211
+00:23:24,790 --> 00:23:30,470
+هنا قلت ال F of واحد واثنينيبقى هذا الكلام عملي
+
+212
+00:23:30,470 --> 00:23:36,070
+يبدو ساوي و F of X هي زائد اتنين يا بنات وليس زائد
+
+213
+00:23:36,070 --> 00:23:39,090
+Z X زائد Y زائد اتنين
+
+214
+00:23:48,250 --> 00:23:54,890
+بإثنين لكل تاربيع كم ساعة بدأت؟ خمس ساعة وعشرين
+
+215
+00:23:54,890 --> 00:24:03,050
+تمام بدنا نحسب Fx يبقى هذا قص مرفوع لقص يبقى بروح
+
+216
+00:24:03,050 --> 00:24:10,650
+بقوله القص في القص مرفوع لنفس القص مضروح منه واحد
+
+217
+00:24:10,650 --> 00:24:15,950
+مضروح في مشتقة مداخل القص بالنسبة
+
+218
+00:24:26,430 --> 00:24:36,390
+يبدأ تساوي 2 في 1 زائدي 2 زائدي 2 ويساوي كتير عشرة
+
+219
+00:24:36,390 --> 00:24:48,530
+بعدين لنجيب fy اللي يبدأ تساوي الأس في الجزء مرفوع
+
+220
+00:24:48,530 --> 00:24:49,410
+لنفس الأس
+
+221
+00:25:10,980 --> 00:25:18,980
+يساوي F of واحد واتنين F of واحد واتنين
+
+222
+00:25:23,570 --> 00:25:30,550
+8 في ال X ناقص واحد زائد ال FY عندنا نقطة واحد
+
+223
+00:25:30,550 --> 00:25:37,270
+واتنين في Y ناقص اتنين شكل عنها يبقى هذا الكلام
+
+224
+00:25:37,270 --> 00:25:42,230
+يبقى يساوي ال realization تبع الدالة F of واحد
+
+225
+00:25:42,230 --> 00:25:49,490
+واتنين هي خمس وعشرين و ال FX عندنا عشرة يبقى عشرة
+
+226
+00:25:49,490 --> 00:25:51,190
+في X ناقص واحد
+
+227
+00:25:57,610 --> 00:26:04,070
+يبقى هذا الكلام بده يساوي خمسة وعشرين زائد عشرة X
+
+228
+00:26:04,070 --> 00:26:12,390
+ناقص عشرة زائد عشرة Y ناقص عشرين يبقى هذا الكلام
+
+229
+00:26:12,390 --> 00:26:15,090
+بده يساوي عشرة X
+
+230
+00:26:19,130 --> 00:26:26,950
+يبقى ناقص خمسة وزائد خمسة وعشرين يبقى ناقص خمسة
+
+231
+00:26:38,870 --> 00:26:44,670
+خطية في معادلة من الدرجة الأولى في كل من X وY إذا
+
+232
+00:26:44,670 --> 00:26:50,490
+هي معادلة خطية ومن ثم هذا ال linearization للدالة
+
+233
+00:26:50,490 --> 00:26:58,450
+الأصلية اللى موجودة عندنا فوق طيب احنا تاول الساعة
+
+234
+00:26:58,450 --> 00:27:03,330
+بنقول إيش؟بنقول انه لما نستبدل الدالة بال
+
+235
+00:27:03,330 --> 00:27:09,310
+linearization تبعها بيكون هناك فيه خطأ بسيط تمام؟
+
+236
+00:27:09,310 --> 00:27:15,430
+الآن بنحاول نحسب جديش قيمة هذا الخطأ اللي احنا
+
+237
+00:27:15,430 --> 00:27:19,490
+افترضناه من الأصل إلى سوين الدالة بال
+
+238
+00:27:19,490 --> 00:27:24,690
+linearization تبعه طيب مشان هيك بنروح نحط القاعدة
+
+239
+00:27:24,690 --> 00:27:29,750
+تبعنا ونروح نبدأ نشتغل عليهاالقاعدة حوالطالية في
+
+240
+00:27:29,750 --> 00:27:43,110
+صيغة ال remark التالية if ال
+
+241
+00:27:43,110 --> 00:27:55,230
+if has continuous has continuous first and second
+
+242
+00:27:55,230 --> 00:28:06,440
+firstand seeking partial derivatives partial
+
+243
+00:28:06,440 --> 00:28:09,720
+derivatives
+
+244
+00:28:09,720 --> 00:28:13,400
+مشتقات
+
+245
+00:28:13,400 --> 00:28:19,380
+الأولى والثانى through an open set from and
+
+246
+00:28:36,850 --> 00:28:44,510
+containing a rectangle a
+
+247
+00:28:44,510 --> 00:28:47,890
+مستطيل
+
+248
+00:28:47,890 --> 00:28:54,630
+a centered at
+
+249
+00:28:55,460 --> 00:29:03,560
+النقطة اكس نوت او Y نوت و
+
+250
+00:29:03,560 --> 00:29:07,920
+اذا
+
+251
+00:29:07,920 --> 00:29:17,320
+كان ال M is any upper bound
+
+252
+00:29:22,490 --> 00:29:33,590
+upper bound for the values of for the values of
+
+253
+00:29:33,590 --> 00:29:45,150
+absolute value لل Fxx absolute value لل Fyy and
+
+254
+00:29:45,150 --> 00:29:56,250
+absolute value لل Fxy علىالمستقيل اللي هو R then
+
+255
+00:29:56,250 --> 00:30:04,590
+the error then the error مقدار الخطأ اللي حتيله
+
+256
+00:30:04,590 --> 00:30:15,090
+الرمز E as a function of Y of replacing of
+
+257
+00:30:15,090 --> 00:30:27,350
+replacing FL of XY on R by
+
+258
+00:30:27,350 --> 00:30:31,550
+its
+
+259
+00:30:31,550 --> 00:30:34,850
+linearization
+
+260
+00:30:34,850 --> 00:30:40,630
+اللي
+
+261
+00:30:40,630 --> 00:30:54,140
+هو L of XYF of X0 وY0 زي ال Fx عند النقطة X0 وY0
+
+262
+00:30:54,140 --> 00:31:03,760
+ال X نقص ال X0 زي ال Fy عند ال X0 وY0 ال Y نقص ال
+
+263
+00:31:03,760 --> 00:31:04,680
+Y0
+
+264
+00:31:13,560 --> 00:31:21,260
+استثمار الإنكولاتية لحقق
+
+265
+00:31:21,260 --> 00:31:33,000
+المتباينة قيمة أكتر للخطأ كمشكلة X وYأقل من أو
+
+266
+00:31:33,000 --> 00:31:41,500
+يساوي نص M بال X نقص ال X node ك absolute value
+
+267
+00:31:41,500 --> 00:31:48,060
+زائد absolute value لل Y نقص Y node لكل ترابيع
+
+268
+00:32:36,010 --> 00:32:40,910
+مرة ثانية بنتكلم عن ال error اللي هو مقدار الخطأ
+
+269
+00:32:40,910 --> 00:32:46,550
+بين الدالة F of X وY وlinearization لهذه الدالة
+
+270
+00:32:46,550 --> 00:32:52,270
+اللي دي ناله رمز L of X وY فباجي بقول لو كانت
+
+271
+00:32:52,270 --> 00:32:57,570
+الدالة F دالة مفتاصلة if and if has continuous
+
+272
+00:32:57,570 --> 00:33:01,290
+first and second partially derivatives المشتقات
+
+273
+00:33:01,290 --> 00:33:06,660
+الأولى والمشتقات الثانيةلهذه الدالة دوال متصلة على
+
+274
+00:33:06,660 --> 00:33:12,740
+فترة مفتوحة تحتوي على مستطيل centered at x not y
+
+275
+00:33:12,740 --> 00:33:17,380
+not ايش يعني؟ يعني لو روحتي قلت هذا مثلا على سبيل
+
+276
+00:33:17,380 --> 00:33:23,080
+المثال محور X وهذا محور Y وهذا نقطة في الأصل
+
+277
+00:33:30,810 --> 00:33:36,690
+مركزه نقطة x naught و y naught الشكل اللي عندنا
+
+278
+00:33:36,690 --> 00:33:45,530
+هنا كويس فى عندى هنا ساعة اللى هو الطول اللى عندنا
+
+279
+00:33:45,530 --> 00:33:51,690
+هذا او الطول هذا الاتنين are the same يبقى هذا
+
+280
+00:33:51,690 --> 00:33:59,990
+الطول لو سميته H و هذا سميته K على سبيل المثال
+
+281
+00:34:04,630 --> 00:34:08,930
+المستقلات الأولى والثانية لهذه الدالة دوال محتاصلة
+
+282
+00:34:08,930 --> 00:34:16,490
+على منطقة R تحت مستطيل مركز النقطة اللى عندنا هذا
+
+283
+00:34:17,130 --> 00:34:22,510
+بقول لأن Fm وإذا كان ال M is any upper bound for
+
+284
+00:34:22,510 --> 00:34:26,350
+the values of يبقى جيبنا المشتاقة الثانية بالنسبة
+
+285
+00:34:26,350 --> 00:34:30,190
+ل X جيبنا المشتاقة الثانية بالنسبة إلى Y جيبنا
+
+286
+00:34:30,190 --> 00:34:33,970
+المشتاقة التانية Fxy واخدنا ال absolute value
+
+287
+00:34:33,970 --> 00:34:41,490
+للتلاتة عند نفس النقطة X node وY nodeأيوة يمكن
+
+288
+00:34:41,490 --> 00:34:45,050
+واحدة تقولي طب وين الرابع؟ قلت لها بقولها وين
+
+289
+00:34:45,050 --> 00:34:50,610
+الرابع؟ تقولي FYX ال absolute value فما أخد FXX
+
+290
+00:34:50,610 --> 00:34:58,590
+FYY FXY لكن FYX مالها؟ ماجيبناش سيرتها طب يكون هذا
+
+291
+00:34:58,590 --> 00:35:06,570
+غلط؟ لأ يعني FXY و FYX بيتساووا اشترطنا خدنا نظرية
+
+292
+00:35:06,570 --> 00:35:13,430
+قبل ذلكإذا كان إذا لو مشتقاتها دوال متصلة عند مين
+
+293
+00:35:13,430 --> 00:35:18,910
+عند النقطة اللى بنحسب عندها هذه المشتقات إذا لو
+
+294
+00:35:18,910 --> 00:35:24,990
+روحنا كتبنا يا بنات ما هدول كتبنا FYX معناته كررنا
+
+295
+00:35:24,990 --> 00:35:29,690
+القيمة اللى عندنا هذه تكرار وهذا لا داعي له لأن
+
+296
+00:35:29,690 --> 00:35:34,990
+مشتركنا ال continuity هناوبالتالي زيحنا مين هي
+
+297
+00:35:34,990 --> 00:35:39,650
+النقطة التالتة نرجع تاني ل M يبقى احنا فيه انا تلت
+
+298
+00:35:39,650 --> 00:35:44,850
+مقادير Absolute value ل Fxx Absolute value ل Fyy
+
+299
+00:35:44,850 --> 00:35:49,490
+Absolute value ل Fxy يبقى تلات قيمباخدوا ال
+
+300
+00:35:49,490 --> 00:35:52,870
+absolute value بيبطل يصير فيهم قيم سالمة، يعني انا
+
+301
+00:35:52,870 --> 00:35:55,790
+اقولها السالمة واخدنا ال absolute value بالصين،
+
+302
+00:35:55,790 --> 00:36:00,910
+إذا صار عندنا تلت قيم موجبة وقد تكون أحدهم بصفر،
+
+303
+00:36:00,910 --> 00:36:04,270
+معنى مشكلة، موجبة و الله بصفر، أخدنا ال absolute
+
+304
+00:36:04,270 --> 00:36:10,010
+value بتلات قيم، أكبر رقم فيهم، باعتبر هذا upper
+
+305
+00:36:10,010 --> 00:36:17,260
+bound حد علوي للتلاتأنا باخد أكبر رقم من الأرقام
+
+306
+00:36:17,260 --> 00:36:23,900
+التلاتة اللى يسمى ال base upper bound أقل حد علوي
+
+307
+00:36:23,900 --> 00:36:30,480
+لمين للتلاتة اللى عندنابقول within the error مقدار
+
+308
+00:36:30,480 --> 00:36:34,740
+الخطأ اللى حصل عندك نتيجة استبدال الدالة بال
+
+309
+00:36:34,740 --> 00:36:40,300
+linearization تابعها جداش مقدار يخضع لهذه ال
+
+310
+00:36:40,300 --> 00:36:43,440
+inequality absolute value of the error أقل من أو
+
+311
+00:36:43,440 --> 00:36:47,760
+يسوى النص في ال upper bound في ال X نقص ال X
+
+312
+00:36:47,760 --> 00:36:55,380
+naught وY نقص Y naught لكل تربيع طبعا يبقى هذا
+
+313
+00:36:55,380 --> 00:37:02,280
+المصطلح بنات اللى اسمه Rعادي عشان نروح ناخد الكلام
+
+314
+00:37:02,280 --> 00:37:06,640
+هذا عاملي لأنه شكله ياكد زي المكالكة كبير شوية هو
+
+315
+00:37:06,640 --> 00:37:11,760
+لا مكالكة ولا حاجة بسيطة هذه سهل حسابة كنتين هذولك
+
+316
+00:37:11,760 --> 00:37:15,360
+سهل حسابهم سهل أخد نفس ال value سهل أخد الكبيرة
+
+317
+00:37:15,360 --> 00:37:20,580
+فيهم إذا صار النص قيمته جاهز هنا X نقص ال economic
+
+318
+00:37:20,580 --> 00:37:25,940
+في الغالب هو بيعطيها لييعني تسعة وتسعين وشلة تسعة
+
+319
+00:37:25,940 --> 00:37:29,060
+زي الانتخابات العربية بيكون أعطانا القيمة هذه و
+
+320
+00:37:29,060 --> 00:37:32,260
+أعطانا القيمة هذه مباشرة يبقى ما علي اللي أجمعهم
+
+321
+00:37:32,260 --> 00:37:37,240
+بس وربع وكلنا بنعرف نجمع اتنين وربع بس قضيتنا ايه
+
+322
+00:37:37,240 --> 00:37:41,340
+سهلة شوية ناخد مثال تطبيق ذي بالك بنكرره في
+
+323
+00:37:41,340 --> 00:37:45,800
+الامتحانات هنا يعني اتكرر بدل المرة تلاتة في
+
+324
+00:37:45,800 --> 00:37:50,870
+الامتحانات لكن انا السنة الماضية ماجبتشطيب فاجب
+
+325
+00:37:50,870 --> 00:37:56,350
+اقول هنا نعطي مثال الله أعلم اللي شريك اللي مات
+
+326
+00:37:56,350 --> 00:38:00,930
+وبالتالي نجيبه مايجيبوش مايقدرش اقوله يبقى هنا
+
+327
+00:38:00,930 --> 00:38:13,290
+امرا A find the linearization find
+
+328
+00:38:13,290 --> 00:38:26,210
+the linearization L of X Yof the function لدالة
+
+329
+00:38:26,210 --> 00:38:37,670
+f of x y تساوي اللي هو x y تربيع زائد y في cosine
+
+330
+00:38:37,670 --> 00:38:47,090
+x ناقص واحد at عند النقطة اللي هو واحد واثنين كذا
+
+331
+00:38:47,090 --> 00:38:56,200
+نمر بيهFind an
+
+332
+00:38:56,200 --> 00:39:03,420
+upper bound for
+
+333
+00:39:03,420 --> 00:39:17,460
+the magnitude of absolute
+
+334
+00:39:17,460 --> 00:39:28,620
+valueللـ error تبع ال X وY magnitude
+
+335
+00:39:28,620 --> 00:39:33,600
+of the
+
+336
+00:39:33,600 --> 00:39:39,320
+error in
+
+337
+00:39:39,320 --> 00:39:47,000
+the approximating function in the approximating
+
+338
+00:39:54,060 --> 00:40:11,400
+f of x of y تساوي L of x of y over the rectangle R
+
+339
+00:40:15,960 --> 00:40:23,760
+الـ X ناقص الواحد أقل من أو تساوي واحد من عشرة
+
+340
+00:40:23,760 --> 00:40:31,080
+والـ Y ناقص اتنين absolute value أقل من أو تساوي
+
+341
+00:40:31,080 --> 00:40:33,520
+واحد من عشرة
+
+342
+00:40:55,850 --> 00:41:01,650
+مرة تانية قال في المثال مطلبين وكأنه هذا هو المثال
+
+343
+00:41:01,650 --> 00:41:06,330
+الرقم اتنين على إيجار ال linearization لذلك وبعدها
+
+344
+00:41:06,330 --> 00:41:12,810
+نحصل نفس الجدار أعلى قيمة موجودة للخطأ اللي نتيجة
+
+345
+00:41:12,810 --> 00:41:17,660
+لمسواتالدالة F of X بالـ Linearization تبعها إذا
+
+346
+00:41:17,660 --> 00:41:20,760
+تخلينا مع الـ Function الأولى طبعا واضح أنه ما
+
+347
+00:41:20,760 --> 00:41:24,460
+أعطينا نقطة واحد واثنين إذا بدي أحسب الدالة
+
+348
+00:41:24,460 --> 00:41:30,300
+ومشتقتها عند النقطة واحد واثنين فبجي بقوله بدي أخد
+
+349
+00:41:30,300 --> 00:41:38,460
+دمرة A بدي أخد F of X Y اللي هي تساوي condition X
+
+350
+00:41:38,460 --> 00:41:42,240
+Y تربيع زاد
+
+351
+00:41:48,440 --> 00:41:57,730
+يحسب f of 1 و 2 و 7طبعاً واحد و هنا اتنين ترابيع
+
+352
+00:41:57,730 --> 00:42:06,690
+زائد اتنين cosine صفر و واحد يبقى مضل اتنين واربعة
+
+353
+00:42:06,690 --> 00:42:14,850
+ستة يبقى الناتج يساوي ستة بعدين بدنا نروح نجيب Fx
+
+354
+00:42:14,850 --> 00:42:23,440
+يبقى هذا الكلام يساوي Y ترابيعY مالكيش دعوة تفضل
+
+355
+00:42:23,440 --> 00:42:29,200
+الـ Cos بسالب Sine X ناقص واحد ضرب مشتقة الزاوية
+
+356
+00:42:29,200 --> 00:42:37,640
+لواحد صحيح نحسب هذه ال Fx عند النقطة واحد واثنين Y
+
+357
+00:42:37,640 --> 00:42:45,040
+شاوي اتنين ترابية ناقص اتنين في Sine Zero Sine
+
+358
+00:42:45,040 --> 00:42:46,100
+Zero ب Zero
+
+359
+00:42:56,270 --> 00:43:06,250
+Y يبقى 2XY زائد Cos X نقص واحد لأن Cos X نقص واحد
+
+360
+00:43:06,250 --> 00:43:11,130
+كلها تعتبر constant إذا اشتغلنا بالنسبة لمين إلى Y
+
+361
+00:43:11,130 --> 00:43:18,770
+نحصل قديش FY عند النقطة واحد واتنين هو يساوي 2 في
+
+362
+00:43:18,770 --> 00:43:23,510
+واحد في كمان اتنين زائد Cos
+
+363
+00:43:27,760 --> 00:43:33,500
+بصير صفر اف واحد وقداش خمسة يبقى بناء عليه بعدها
+
+364
+00:43:33,500 --> 00:43:39,820
+اجيب له ال linearization تبع ال X و Y يبقى هنا F
+
+365
+00:43:39,820 --> 00:43:46,480
+اف واحد و اتنين زائد ال F X عند النقطة واحد و
+
+366
+00:43:46,480 --> 00:43:52,560
+اتنين في ال X ناقص ال واحد زائد F Y عند النقطة
+
+367
+00:43:52,560 --> 00:43:59,740
+واحد و اتنين في ال Y ناقص اتنينالعوض فيها بف بواحد
+
+368
+00:43:59,740 --> 00:44:06,680
+و اتنين اللي هم قداش بستة ال Fx باربعة في ال X
+
+369
+00:44:06,680 --> 00:44:14,540
+ناقص واحد وال Fy بخمسة في ال Y ناقص اتنين اذا ان
+
+370
+00:44:14,540 --> 00:44:20,120
+هذه فيديو يتساوي ستة زائد اربعة X ناقص اربعة زائد
+
+371
+00:44:20,120 --> 00:44:27,780
+خمسة Y ناقص عشرة هذا الكلام بالدول الساعةعندك هنا
+
+372
+00:44:27,780 --> 00:44:35,580
+اربع X زائد خمسة Y يبقى لدينا ناقص أربعة عشر نقص
+
+373
+00:44:35,580 --> 00:44:43,620
+تمنية يبقى ناقص تمنية يبقى هذا ال linear function
+
+374
+00:44:43,620 --> 00:44:48,020
+أو ال linearization لل function الأصلية وهو
+
+375
+00:44:48,020 --> 00:44:54,040
+المطلوب الأول من المسألة نجي للمطلوب التاني نجيه
+
+376
+00:44:54,040 --> 00:44:54,900
+نملة V
+
+377
+00:44:58,830 --> 00:45:03,390
+يبقى هذا زي السؤال المثال السابق هيعلنها تماما زيه
+
+378
+00:45:03,390 --> 00:45:09,850
+وكان يعتبر المثال رقم اتنين بدأجي ألمع بيه، بدأ
+
+379
+00:45:09,850 --> 00:45:13,370
+أروح أجيبله ال error اللي عندنا، مشان هيك هذه
+
+380
+00:45:13,370 --> 00:45:19,880
+جاهزةوهذه جاهزة وقال علينا مين؟ بس ال M ال M بدي
+
+381
+00:45:19,880 --> 00:45:28,260
+أعقد مقارنة بين ال absolute value ل Fxx, Yy, Fxy و
+
+382
+00:45:28,260 --> 00:45:35,420
+هكذا طب ال Fx الحمد لله جازة إذا إحنا بدنا ال Fxx
+
+383
+00:45:35,420 --> 00:45:42,340
+اللي هو partial على partial X لل Fxيعني partial
+
+384
+00:45:42,340 --> 00:45:49,240
+على partial X لل F X هي جهزة فوق ال Y تربية ناقص Y
+
+385
+00:45:49,240 --> 00:45:55,360
+في صين X ناقص واحد وله بدوسةدش تبقى الدلة هذه
+
+386
+00:45:55,360 --> 00:46:00,400
+بالاسم ال X يبقى Y تربيع مع السلامة ال Y هذى مقدر
+
+387
+00:46:00,400 --> 00:46:08,420
+ثابت تفضل ال sign بيكو ساين يبقى ناقص Y كو ساين X
+
+388
+00:46:08,420 --> 00:46:13,900
+ناقص واحد ضرب مشتقة الزاوية اللى هو واحد صحيح
+
+389
+00:46:13,900 --> 00:46:15,700
+بالمرة نحسبها عيد مال
+
+390
+00:46:22,160 --> 00:46:27,860
+بندل نقطة واحد واثنين بيكون ساوي سالي باتنين في
+
+391
+00:46:27,860 --> 00:46:39,400
+كوساين زير بيكون سالي باتنين في كوساين
+
+392
+00:46:39,400 --> 00:46:42,580
+زير بيكون سالي باتنين في كوساين زير بيكون سالي
+
+393
+00:46:42,580 --> 00:46:43,500
+باتنين في كوساين زير بيكون سالي باتنين في كوساين
+
+394
+00:46:43,500 --> 00:46:43,580
+زير بيكون سالي باتنين في كوساين زير بيكون سالي
+
+395
+00:46:43,580 --> 00:46:44,540
+باتنين في كوساين زير بيكون سالي باتنين في كوساين
+
+396
+00:46:44,540 --> 00:46:45,940
+زير بيكون سالي باتنين في كوساين زير بيكون سالي
+
+397
+00:46:45,940 --> 00:46:48,660
+باتنين في كوساين زير بيكون سالي باتنين في كوساين
+
+398
+00:46:48,660 --> 00:46:51,910
+زير بيكون سالي باتنين في كوساين زير بيكون سبعد هيك
+
+399
+00:46:51,910 --> 00:46:59,790
+بدنا نروح لل FYY يعني partial على partial Y لل FY
+
+400
+00:46:59,790 --> 00:47:05,610
+يعني partial على partial Y لل FY وين ال FY هي فوق
+
+401
+00:47:05,610 --> 00:47:10,130
+اللي هو 2XY زائد قصارى
+
+402
+00:47:13,650 --> 00:47:18,390
+إن الفاضلها بالنسبة لمن إلى Y يبقى ال cosine كله ب
+
+403
+00:47:18,390 --> 00:47:26,110
+Zero بظل فقط كده عنده اتنين X يبقى هذا معناته ان
+
+404
+00:47:26,110 --> 00:47:34,770
+ال FYY كده تساوي عند النقطة واحدة عند النقطة واحدة
+
+405
+00:47:34,770 --> 00:47:38,870
+و اتنين عند النقطة واحدة و اتنين تساوي كده يا بنات
+
+406
+00:47:38,870 --> 00:47:46,490
+اتنين لإن بدي اشيل ال X وقت ما كانطيب اتنين اختي
+
+407
+00:47:46,490 --> 00:47:51,330
+لها ال absolute value و الله مااختيها هي اتنين
+
+408
+00:47:51,330 --> 00:47:56,710
+يبقى بدنا نبروزها و كمان نرجعلها بعد قليل يبقى
+
+409
+00:47:56,710 --> 00:48:02,290
+بدنا نروح اجيبله كمان مين ال Fxy يعني partial على
+
+410
+00:48:02,290 --> 00:48:09,730
+partial y لل Fx هذا الكلام بده يساوي partial على
+
+411
+00:48:09,730 --> 00:48:10,630
+partial y
+
+412
+00:48:16,980 --> 00:48:24,920
+نقص y في sin x نقص واحد ويسار تفاضلها بالنسبة ل y
+
+413
+00:48:24,920 --> 00:48:34,820
+اتنين y نقص sin x نقص واحد والsin تعتبر هنا
+
+414
+00:48:42,500 --> 00:48:47,940
+Y عند نقطة واحد و اتنين بيبقى اتساوي اتنين في
+
+415
+00:48:47,940 --> 00:48:54,520
+اتنين مقص صيني زيرو صيني زيرو مقداش يا بنات يبقى
+
+416
+00:48:54,520 --> 00:48:59,980
+بضال مقداش عندنا اربعة ممتاز اتطلع في اللي
+
+417
+00:48:59,980 --> 00:49:05,140
+بروزناهم واحد اللي و اتنين و التالتة هذي يبقى
+
+418
+00:49:05,140 --> 00:49:10,440
+اتنين و اتنين و اربعة وين اكبر رقم منهم يبقى ال M
+
+419
+00:49:10,440 --> 00:49:20,410
+تبع تلكأربعة يبقى بروح بقوله هنا sum تساوي أربعة
+
+420
+00:49:20,410 --> 00:49:26,470
+هذه اللي هو من ال upper bound لل values تبعتي
+
+421
+00:49:26,470 --> 00:49:30,790
+التلاتة اللي عندنا يبقى احنا جاهزين مش ضايل عندنا
+
+422
+00:49:30,790 --> 00:49:36,560
+إلا نفسي بالأرور عن طريقة تعويض وينفي ال equality
+
+423
+00:49:36,560 --> 00:49:41,280
+اللى قدامنا هذه بقوله بسيطة جدا يبقى بدنا نمسح
+
+424
+00:49:41,280 --> 00:49:46,280
+اللي قوم كله هذا ونخل ال equality لإن ال equality
+
+425
+00:49:46,280 --> 00:49:53,680
+هذه بدنا نعوض فيها هذه سميها يا بنات سمينا قبل
+
+426
+00:49:53,680 --> 00:50:00,020
+شوية star سميها W star يبقى بنيجي نقوله هنا
+
+427
+00:50:00,020 --> 00:50:00,740
+substitute
+
+428
+00:50:05,750 --> 00:50:11,970
+تانى الانكواليتي اللى بابلس تار بنحصل على ما يتى
+
+429
+00:50:11,970 --> 00:50:18,570
+absolute value للera as a function of x و y أقل من
+
+430
+00:50:18,570 --> 00:50:25,830
+نص الام بقدرش أربع افتح يوسط x ماتس اكس نوت مواطع
+
+431
+00:50:25,830 --> 00:50:32,130
+اللى واحد من عشرةيبقى هاي Zero و واحد من عشرة
+
+432
+00:50:32,130 --> 00:50:38,410
+والتانية Zero و واحد من عشرة الكل تربية يبقى هذه
+
+433
+00:50:38,410 --> 00:50:45,410
+لو جينا حسبناها فصير عندي قداش اتنين في Zero اتنين
+
+434
+00:50:45,410 --> 00:50:50,890
+من عشرة الكل تربية فبتنين من عشرة الكل تربية قداش
+
+435
+00:50:50,890 --> 00:50:56,750
+تطلع اربعة من مية ممتازة يبقى Zero Zero
+
+436
+00:51:01,020 --> 00:51:08,380
+0 0 8 من 100 يبقى نسبة الخطأ أو مقدار الخطأ يا
+
+437
+00:51:08,380 --> 00:51:13,240
+بنات دائما و أبدا في المثال هذا عنده نقطة واحد و
+
+438
+00:51:13,240 --> 00:51:18,120
+اتنين إذا استبدلنا الدالة بال linearization تبعها
+
+439
+00:51:18,120 --> 00:51:24,600
+عند هذه النقطة بيكون مقدار الخطأ أقل من 8 من 100
+
+440
+00:51:24,600 --> 00:51:32,920
+وبالتالي ماعنا مشكلة في هذه الحالةالان بنقول لو
+
+441
+00:51:32,920 --> 00:51:37,240
+بدنا نعمم هذا الكلام ل functions of three
+
+442
+00:51:37,240 --> 00:51:43,080
+variables فإيش اللي بده يصير هذا الكلام اللي آخر
+
+443
+00:51:43,080 --> 00:51:47,320
+النقطة في هذا ال section اللي بدنا نعمم هذا ل
+
+444
+00:51:47,320 --> 00:51:50,100
+functions of three variables
+
+445
+00:52:02,550 --> 00:52:09,230
+هيبقى حطيه لعنوان صغير هيك functions of
+
+446
+00:52:09,230 --> 00:52:20,390
+more than more than two
+
+447
+00:52:35,290 --> 00:52:40,370
+the linearization of
+
+448
+00:52:40,370 --> 00:52:49,830
+الـ function f of x و y و z at أي ند النقطة p نوت
+
+449
+00:52:49,830 --> 00:52:58,590
+و x نوت و y نوت و z نوت as نجي
+
+450
+00:52:58,590 --> 00:53:08,050
+نقول ال L of x و y و zبدي ساوى ال F عند النقطة P
+
+451
+00:53:08,050 --> 00:53:16,790
+non مضافا اليها Fx عند النقطة P non بال X معقص ال
+
+452
+00:53:16,790 --> 00:53:24,150
+X non زائد ال Fy عند النقطة P non بالY
+
+453
+00:53:32,360 --> 00:53:38,760
+يبقى هنا شكل
+
+454
+00:53:38,760 --> 00:53:46,600
+ال linearization يبقى فيه فرقين او اثنين من الفروق
+
+455
+00:53:46,600 --> 00:53:50,300
+بين و بين ال linearization في حالة ال function on
+
+456
+00:53:50,300 --> 00:53:55,960
+to mario الفرق الاولبعد ما كنا بنحسب عند نقطة
+
+457
+00:53:55,960 --> 00:54:02,340
+بمركبين أو بإحداثين بصير نحسب عند نقطة بثلاث
+
+458
+00:54:02,340 --> 00:54:07,720
+إحداثين فهذا الفرق الأول الفرق الثاني بانضيف ال
+
+459
+00:54:07,720 --> 00:54:12,340
+term الزيادة اللي هو عند هذا man مشتقة يتدلة
+
+460
+00:54:12,340 --> 00:54:17,480
+بالنسبة إلى z عند نفس النقطة مضروبة في man في z
+
+461
+00:54:17,480 --> 00:54:18,620
+ناقص
+
+462
+00:54:23,560 --> 00:54:28,100
+للـ error بسرعاتنا ال linearization جديد إذا في
+
+463
+00:54:28,100 --> 00:54:33,480
+error جديد بدنا نعرف إيش ال error هذا يبقى نبرة
+
+464
+00:54:33,480 --> 00:54:38,600
+اتنين اقول
+
+465
+00:54:38,600 --> 00:54:46,400
+suppose that ال R is a closed suppose that
+
+466
+00:54:46,400 --> 00:55:07,710
+ال Rاو ايش رايك بناشي نعيد الكلام هذا كله او
+
+467
+00:55:07,710 --> 00:55:12,330
+in
+
+468
+00:55:12,330 --> 00:55:13,210
+this case
+
+469
+00:55:18,860 --> 00:55:32,360
+the case of functions of a three variables of the
+
+470
+00:55:32,360 --> 00:55:43,300
+error S هدى الرمز E, X, Y, Z وايه ال absolute
+
+471
+00:55:43,300 --> 00:55:52,710
+value أقل من أو يسوى مصف ال M فيهabsolute value x
+
+472
+00:55:52,710 --> 00:56:00,510
+نقص ال x node زائد y نقص ال y node زائد absolute
+
+473
+00:56:00,510 --> 00:56:11,910
+value z نقص ال z node لكل ترابيع where حيث ال M is
+
+474
+00:56:11,910 --> 00:56:17,650
+the upper bound
+
+475
+00:56:18,880 --> 00:56:27,820
+of absolute value لل Fxx absolute value لل Fyy
+
+476
+00:56:27,820 --> 00:56:36,940
+absolute value لل Fzz absolute value لل Fxy
+
+477
+00:56:36,940 --> 00:56:48,000
+absolute value لل Fxz and absolute value لل Fyz
+
+478
+00:57:35,750 --> 00:57:40,990
+نفس الصيغة اللي قبل اللهم إلا زدنا لها term التالت
+
+479
+00:57:40,990 --> 00:57:45,640
+اللي عندنا هذهوالـ M هذه اللي هي ال upper bound
+
+480
+00:57:45,640 --> 00:57:52,840
+لمين لستة مقادير اللي عندنا Fxx Fyy Fzz طبعا ب
+
+481
+00:57:52,840 --> 00:57:58,140
+absolute value Fxy Fyx طبعا استبعدناها مشان ال
+
+482
+00:57:58,140 --> 00:58:03,120
+continuity Fxz واستبعدنا Fzx مشان ال continuity
+
+483
+00:58:03,120 --> 00:58:08,740
+Fyz وااستبعدنا Fzy كذلك بسبب مين؟ بسبب ال
+
+484
+00:58:08,740 --> 00:58:13,460
+continuity مش هنخليكوا تايهينبنعطيكم مثال أوضحي
+
+485
+00:58:13,460 --> 00:58:21,100
+على ذلك example find
+
+486
+00:58:21,100 --> 00:58:31,100
+the linearization
+
+487
+00:58:31,100 --> 00:58:34,560
+اللي
+
+488
+00:58:34,560 --> 00:58:50,020
+هو L of X Y و Zof the function مدالة f
+
+489
+00:58:50,020 --> 00:59:02,500
+of x y و z يسوى جدري اتنين T cosine of x في صين y
+
+490
+00:59:02,500 --> 00:59:18,180
+زائد z at the pointعند النقطة اليمين P0 P0 P0 P0
+
+491
+00:59:18,180 --> 00:59:18,180
+P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0
+
+492
+00:59:18,180 --> 00:59:18,560
+P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0
+
+493
+00:59:18,560 --> 00:59:19,720
+P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0
+
+494
+00:59:19,720 --> 00:59:22,860
+P0
+
+495
+00:59:22,860 --> 00:59:24,320
+P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0
+
+496
+00:59:24,320 --> 00:59:24,320
+P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0
+
+497
+00:59:24,320 --> 00:59:27,740
+P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0 P0
+
+498
+00:59:27,740 --> 00:59:30,360
+P0
+
+499
+00:59:38,380 --> 00:59:48,960
+for the magnitude للقرار
+
+500
+00:59:48,960 --> 01:00:01,540
+اللي عندنا هذا of the error the approximation and
+
+501
+01:00:01,540 --> 01:00:05,100
+the approximation
+
+502
+01:00:15,150 --> 01:00:19,930
+F of X و Y و
+
+503
+01:00:19,930 --> 01:00:27,690
+Z F
+
+504
+01:00:27,690 --> 01:00:37,130
+of X و Y و Z بدأ ال sound L of X و Y و Z over the
+
+505
+01:00:37,130 --> 01:00:43,550
+region over the region
+
+506
+01:00:45,400 --> 01:00:56,280
+محطان كده فوق هي A ان هي عبارة عن value من X اقل
+
+507
+01:00:56,280 --> 01:01:06,530
+من او تسوى 00 1 من 10 و ال value من Yأقل من أو
+
+508
+01:01:06,530 --> 01:01:12,310
+تساوي كمان بنفس الطريقة Zero واحد من عشرة وهكذا
+
+509
+01:01:12,310 --> 01:01:19,590
+نتقل إلى Z ناقص Pi على أربعة أقل من أو تساوي Zero
+
+510
+01:01:19,590 --> 01:01:21,410
+Zero واحدة
+
+511
+01:01:40,040 --> 01:01:45,660
+السؤال شبيه بالسؤال الماضي لكن مع الفارق اللذي
+
+512
+01:01:45,660 --> 01:01:50,820
+يناسب طبيعة ال function of three variables المطموع
+
+513
+01:01:50,820 --> 01:01:54,940
+الأول اللي مراهية طلب ال linearization وين عنده
+
+514
+01:01:54,940 --> 01:01:58,260
+النقطة، إذا خلّيني أروح نحسب له ال linearization
+
+515
+01:01:58,260 --> 01:02:05,180
+اللي عنها، يبقى نبدأ أول شيء بالدالة F of X وY وZ
+
+516
+01:02:05,180 --> 01:02:14,050
+اللي يتسببقداش الدالة جدري اتنين في Cos X في Sin Y
+
+517
+01:02:14,050 --> 01:02:22,490
+زائد Z نحسب قداش قيمة الدالة على الـ Zero و Zero و
+
+518
+01:02:22,490 --> 01:02:29,030
+Pi على أربع نجي الامنات هي جدري اتنين Cos صفر
+
+519
+01:02:29,030 --> 01:02:32,650
+بقداش واحد يبقى في واحد
+
+520
+01:02:42,100 --> 01:02:47,920
+يبقى الجواهر كده؟ واحد صحيح فاللي علي شجهه ليه
+
+521
+01:02:47,920 --> 01:02:54,160
+دلوقتي لل Fxy سبق أن اشتقت الدالة بالنسبة لإستفادة
+
+522
+01:02:54,160 --> 01:03:01,700
+Cos سالف جزير اتنين ساين ال X والباقي كل مصطلح
+
+523
+01:03:01,700 --> 01:03:09,600
+مانوش دعوةيبقى هنا في Sine Y زاقة Z. بدنا نحسب كده
+
+524
+01:03:09,600 --> 01:03:14,700
+ال Fx عند ال zero و ال zero و ال Pi على أربعة ما
+
+525
+01:03:14,700 --> 01:03:22,720
+يساوي. إذن سادي سالب جدر اتنين و Sine Zero بناه. F
+
+526
+01:03:22,720 --> 01:03:28,100
+Zero و Sine Pi على أربعة واحد على جدر اتنين يبقى
+
+527
+01:03:28,100 --> 01:03:35,860
+كده؟ Zero راح مع السلامة.طيب إذا نجي ل ال fy يساوي
+
+528
+01:03:35,860 --> 01:03:41,200
+نشتغل نسمة لو هيبقى جدري اتنين cosine ال X مالكش
+
+529
+01:03:41,200 --> 01:03:49,800
+داعو نجي لل أخرى نفضلها بين f cosine y زائد z في
+
+530
+01:03:49,800 --> 01:03:55,790
+مشتقة ال y اللي هيبقى داشر واحد صحيحتروح نحسب كدهش
+
+531
+01:03:55,790 --> 01:04:04,730
+ال FY أن النقطة 00Y على 4 هو يساوي هي جدرين 2 و
+
+532
+01:04:04,730 --> 01:04:15,450
+Cos 0 ب1 و Cos 0 زي 4 جتها 45 كذلك ب1 على جدرين 2
+
+533
+01:04:15,450 --> 01:04:18,250
+يبقى كمان يساوي 1
+
+534
+01:04:22,890 --> 01:04:26,490
+يبقى 5z يبقى January 2
+
+535
+01:04:30,940 --> 01:04:37,080
+تفضل الـ Sine بيكو ساين Y زائد Z في مشتقة الـ Z
+
+536
+01:04:37,080 --> 01:04:41,760
+اللي هي ودرجة واحدة يبقى طالع المشتقة اللي اتنين
+
+537
+01:04:41,760 --> 01:04:48,480
+زي بعض FY زي FZ إذا بنان عليه ال FZ عند ال zero و
+
+538
+01:04:48,480 --> 01:04:52,280
+ال zero و ال Y على أربع كله بده ساوي كدرجة بده
+
+539
+01:04:52,280 --> 01:04:59,450
+ساوي واحد إذا بقدر أجيب له ال linearizationL as a
+
+540
+01:04:59,450 --> 01:05:04,170
+function of x, y,
+
+541
+01:05:04,330 --> 01:05:15,390
+z لدي تلاتة لأنها ثلاثة متغيرات يجيلي f of 0,0 بقى
+
+542
+01:05:15,390 --> 01:05:23,550
+الاربع اللي يبقى واحد اللي بعده fx اللي مقدش 0
+
+543
+01:05:31,980 --> 01:05:38,560
+زائد الـ fy اللي هي بواحد في ال y ناقص ال zero
+
+544
+01:05:38,560 --> 01:05:45,760
+اللي بعده fz كذلك واحد في ال z ناقص y على اربع
+
+545
+01:05:45,760 --> 01:05:50,720
+يبقى بناء ان عليه صفر ال linearization يجب ان يكون
+
+546
+01:05:50,720 --> 01:05:55,280
+x زائد y زائد z
+
+547
+01:05:59,300 --> 01:06:05,640
+يبقى هذا zero في أي رقم في zero هو يصبح صحيح وهذا
+
+548
+01:06:05,640 --> 01:06:10,760
+شيء مميز جدا يبقى وصوله على مين؟ هذه الطاقة يبقى
+
+549
+01:06:10,760 --> 01:06:18,520
+ال Y زائد Z ناقص Y على أربعة زائد واحد كل هذا ال
+
+550
+01:06:18,520 --> 01:06:26,220
+linearization لل X Y وZ شكل العالم يبقى هذا نمرأة
+
+551
+01:06:26,220 --> 01:06:27,700
+ايه من المسألة؟
+
+552
+01:06:30,040 --> 01:06:34,320
+المرة بي بشان نجيب المرة بي بدنا نروح نحسب ست
+
+553
+01:06:34,320 --> 01:06:40,080
+شغلات تمام إذا بدنا نروح للست شغلات نحسبها اللي هي
+
+554
+01:06:40,080 --> 01:06:42,700
+absolute value للألا absolute value لل Fxx
+
+555
+01:06:42,700 --> 01:06:47,620
+absolute value Fyy absolute value Fzz إلى آخرى
+
+556
+01:06:47,620 --> 01:06:55,040
+لغاية ما نكمل إذا بدنا نروح لمين بدات لل FxxY7
+
+557
+01:06:55,040 --> 01:07:00,350
+يبقى بده اشتقها دي كمان مرة بنسبة لمين إلى Xيبقى
+
+558
+01:07:00,350 --> 01:07:09,570
+سالب جدري اتنين Cos X وهنا Sine Y زائد Z ملاش دعوة
+
+559
+01:07:09,570 --> 01:07:16,570
+بالمرة نحسبها يبقى هذا بدي يعطينا مين ان ال F XX
+
+560
+01:07:16,570 --> 01:07:25,150
+عند النقطة 00Y على أربع يسام Cos 0 بواحد يبقى ناقص
+
+561
+01:07:25,150 --> 01:07:32,600
+جدري اتنين في واحدوSin Pi على 4 بواحد عالى جدري
+
+562
+01:07:32,600 --> 01:07:37,460
+اتنين يبقى النتيجة قداشنا بنات سالب واحد يبقى ال
+
+563
+01:07:37,460 --> 01:07:44,640
+Fx كانت بزيرو لكن ال Fx اكثر من قدرين بسالب واحد
+
+564
+01:07:44,640 --> 01:07:53,660
+بدنا نيجي لمين لل absolute value لل Fx X بدنا نسيب
+
+565
+01:07:53,660 --> 01:07:56,400
+ال absolute value لسالب واحد لو قدرين
+
+566
+01:08:00,450 --> 01:08:05,670
+يجب ان اشتغل بالنسبة للوان يبقى جذري اتنين في
+
+567
+01:08:05,670 --> 01:08:12,610
+كوصين ال X مالكش دعوة وتفضل كوصين بسالف ساين Y
+
+568
+01:08:12,610 --> 01:08:18,190
+زائد Z في مستقبل ال Y يبقى داشر ات واحد يجب ان
+
+569
+01:08:18,190 --> 01:08:26,410
+احسب F Y Y عند النقطة Zero و Zero و باي على اربع
+
+570
+01:08:26,410 --> 01:08:34,520
+تسامهي جدري اتنين والله سالب جدري اتنين في واحد في
+
+571
+01:08:34,520 --> 01:08:42,820
+مين؟ في واحد على جدري اتنين وكذلك تساوي مين؟ سالب
+
+572
+01:08:42,820 --> 01:08:48,280
+واحد يبقى سالب absolute value لل FYY absolute
+
+573
+01:08:48,280 --> 01:08:51,160
+value للسالب واحد للمقدس واحد
+
+574
+01:08:59,690 --> 01:09:08,710
+جدري اتنين وصين ال X في صين Y زائد Z مشتقتها
+
+575
+01:09:08,710 --> 01:09:15,910
+بالنسبة للسالب حطت السالب برا نحسب كده المشتقة FZZ
+
+576
+01:09:15,910 --> 01:09:24,590
+عند النقطة Zero و Zero و Y على اربعة يساوي ناقص
+
+577
+01:09:24,590 --> 01:09:32,330
+جدري اتنين في واحد في صين واحدهنا جائري اتنين كذلك
+
+578
+01:09:32,330 --> 01:09:39,210
+اللي هو سالم واحد يبقى absolute value لل FZZ بدي
+
+579
+01:09:39,210 --> 01:09:44,470
+ساوي absolute value لسالم واحد كمان اللي هو مقدش
+
+580
+01:09:44,470 --> 01:09:46,770
+اللي هو واحد
+
+581
+01:10:19,560 --> 01:10:34,600
+يبقى ال Fxy هي partial على partial Y لل Fxy سالف
+
+582
+01:10:34,600 --> 01:10:37,340
+جذري اتنين في Sine X
+
+583
+01:10:46,690 --> 01:10:50,830
+يبقى Cos y
+
+584
+01:10:50,830 --> 01:10:59,110
+زائد z يلّا بالمرة نحسب ال Fxy عن النقطة 00Y على 4
+
+585
+01:10:59,110 --> 01:11:09,930
+ويساوي سالب جدر 2 في 0 في 1 على جدر 2 ويساوي 0 بعد
+
+586
+01:11:09,930 --> 01:11:14,030
+ذلك يبقى خلاص ال absolute value لها في 0 بدنا ال
+
+587
+01:11:14,030 --> 01:11:22,880
+Fxzيبقى هنا اللي هي partial على partial z لمين لل
+
+588
+01:11:22,880 --> 01:11:28,960
+Fx يالا نشتق ال Fx من اسمه لزي دي يبقى سالف جدري
+
+589
+01:11:28,960 --> 01:11:38,960
+اتنين كصين ال X مالهاش دعوة وهذه كصينY زائد Z يبقى
+
+590
+01:11:38,960 --> 01:11:44,420
+ال F X Z عظيم نفس النتيجة اللي بقى بناها بدها
+
+591
+01:11:44,420 --> 01:11:49,440
+تساوي Zero طيب جيبنا ال F X Y F X Z بقى اللي عندنا
+
+592
+01:11:49,440 --> 01:11:57,280
+main F Y Z يبقى partial على partial Z لل F Y و لZ
+
+593
+01:11:57,280 --> 01:12:04,900
+بدنا نيجي لل F Y يبقى جذري اتنين Cos X مالهاش دعوة
+
+594
+01:12:06,090 --> 01:12:14,310
+يبقى فضل هدف سالب ساين يبقى سالب ساين Y زائد Z
+
+595
+01:12:36,260 --> 01:12:46,600
+أصبح fy fyz كabsolute value لسالة بواحدة وقدراش
+
+596
+01:12:46,600 --> 01:12:55,760
+بواحدة عندنا قيمة اتن تان ثلاثة وهي الرابعة وهذه
+
+597
+01:12:55,760 --> 01:13:00,320
+الخامسة وهذه السادسة
+
+598
+01:13:12,920 --> 01:13:22,060
+Y و Z أقل من أو يساوي مُص M X ناقص X نوت كأبسوليوت
+
+599
+01:13:22,060 --> 01:13:29,880
+Value وهنا Y ناقص Y نوت كأبسوليوت Value وهنا Z
+
+600
+01:13:29,880 --> 01:13:38,190
+ناقص Z نوت كأبسوليوت Value لكل تربيةيبقى الـ Error
+
+601
+01:13:38,190 --> 01:13:43,830
+اللي عندنا هذا X وY وZ أقل من أو يسوى نص الـ M
+
+602
+01:13:43,830 --> 01:13:52,630
+بقدرش واحد صحيح تمين مجرد هذا كل واحدة فيهم واحد
+
+603
+01:13:52,630 --> 01:13:59,810
+من مية يبقى Zero Zero Point Zero واحد Zero Point
+
+604
+01:13:59,810 --> 01:14:07,320
+Zero واحد Zero Point Zero واحد بشكل عاميبقى هذه
+
+605
+01:14:07,320 --> 01:14:15,940
+الصحرة نص في كتاش ولا بنات Zero Zero تلاتة من مية
+
+606
+01:14:15,940 --> 01:14:23,600
+لكل تربيع يبقى هذا الكلام بده يساوي نص فيه تلاتة
+
+607
+01:14:23,600 --> 01:14:29,580
+من مية لكل تربيع تسعة من الف و الله من عشرة آلاف
+
+608
+01:14:29,580 --> 01:14:35,060
+عشرة آلاف رقامين بعد الفاصلة يبقى هذا ال zero
+
+609
+01:14:38,350 --> 01:14:48,370
+.00009 تمام ان شئتم تقولنا 000045
+
+610
+01:14:48,370 --> 01:14:51,530
+نص
+
+611
+01:14:51,530 --> 01:14:59,930
+يبقى بيصير 45 من 100000 كسر زي ما تشايفين متناهي
+
+612
+01:14:59,930 --> 01:15:05,190
+في الصغر لحد هنا stop انتهينا من هذا ال section
+
+613
+01:15:05,760 --> 01:15:13,460
+بنقول exercises أحداشر ستة المسائل من تلاتة لغاية
+
+614
+01:15:13,460 --> 01:15:20,540
+واحد وعشرين اللي هي الأد وكذلك من خمسة وعشرين
+
+615
+01:15:20,540 --> 01:15:27,360
+لغاية اللي هو خمسة واربعين الأد كذلك
+
+616
+01:15:30,240 --> 01:15:36,880
+بالآخر section سنأخذه في هذا ال chapter وهو ال
+
+617
+01:15:36,880 --> 01:15:41,740
+extreme values and saddle points يبقى بني إلى
+
+618
+01:15:41,740 --> 01:15:51,200
+section 14.7 14.7 اللي هو بتتكلم عن ال extreme
+
+619
+01:15:51,200 --> 01:15:54,680
+values
+
+620
+01:15:54,680 --> 01:16:00,020
+and saddle points
+
+621
+01:16:02,850 --> 01:16:03,250
+Oy.
+
+622
+01:16:16,990 --> 01:16:21,510
+قبل أن نبدأ في هذا ال section نحاول نفسر اللي هو
+
+623
+01:16:21,510 --> 01:16:26,130
+العنوان اللي احنا كاتبينه هذا مكتوب ب Extreme
+
+624
+01:16:26,130 --> 01:16:29,810
+Values كلمة Extreme مرت معانا قبل ايه في كل كلاسية
+
+625
+01:16:29,810 --> 01:16:34,690
+كتير مظبوط؟ ايش بقيت تسموها؟ القيم القصوى أو القيم
+
+626
+01:16:34,690 --> 01:16:40,070
+المتطرفة العمال القيم المتطرف يعني القيم الإرهابية
+
+627
+01:16:40,070 --> 01:16:46,070
+يبقى هذه نسميها القيم القصوى and setting pointإيش
+
+628
+01:16:46,070 --> 01:16:51,950
+سدل؟ كيف؟
+
+629
+01:16:51,950 --> 01:16:57,430
+يعني لا حرجة لا مش صحيحة مش ذاكرينيكم أقول نقطة
+
+630
+01:16:57,430 --> 01:17:02,730
+الإنقلاب للمنحنة دي شو نسميها؟ انعطاف أو
+
+631
+01:17:02,730 --> 01:17:08,170
+inflection point تمام؟ هذه بنسميها نقطة الركاب
+
+632
+01:17:08,170 --> 01:17:13,970
+المناظرة لنقطة الانعطاف أو نقطة الإنقلاب تبعت
+
+633
+01:17:13,970 --> 01:17:17,740
+المنحنةتبقى reflection point نقطة انقلابها نقطة
+
+634
+01:17:17,740 --> 01:17:22,760
+اقافية للمنحنة بقابلها هنا settle point اللي هي
+
+635
+01:17:22,760 --> 01:17:27,520
+نقطة الركاب لإن احنا عندنا مجسم مش خط منحنى وانما
+
+636
+01:17:27,520 --> 01:17:34,320
+عندنا على شكل ا مجسم سير في السطعيبقى هنا نقول
+
+637
+01:17:34,320 --> 01:17:38,880
+settle point نقطة recap يبقى هنا هنا في هذا ال
+
+638
+01:17:38,880 --> 01:17:44,820
+section حمارة على ال local maximum و local minimum
+
+639
+01:17:44,820 --> 01:17:48,740
+طبعا points و كذلك settle points يبقى هذول التلاتة
+
+640
+01:17:48,740 --> 01:17:52,740
+الأساسية في ال section اللي قلناها هنا يبقى نروح
+
+641
+01:17:52,740 --> 01:17:56,880
+نعطي تعريف ل local maximum و local minimum points
+
+642
+01:17:56,880 --> 01:18:01,780
+و بعد هيك نروح لمينبنروح ل ال settle points ل main
+
+643
+01:18:01,780 --> 01:18:08,860
+لل functions of two or more variables تمام نعطي
+
+644
+01:18:08,860 --> 01:18:14,120
+تعريف الأول و بعد هيك بنشوف كيف بدنا نشتغل الشغل
+
+645
+01:18:14,120 --> 01:18:25,500
+يبقى باجي بقول definition let f of x y be a
+
+646
+01:18:25,500 --> 01:18:32,060
+functiondefine on
+
+647
+01:18:32,060 --> 01:18:40,580
+a region R on a region R containing the point
+
+648
+01:18:40,580 --> 01:18:46,100
+containing the
+
+649
+01:18:46,100 --> 01:18:51,200
+point UA
+
+650
+01:18:51,200 --> 01:18:52,240
+وB
+
+651
+01:18:56,830 --> 01:19:06,330
+مقا الأولى بقول F of A وB is a local maximum value
+
+652
+01:19:06,330 --> 01:19:20,370
+is a local maximum value local maximum value of F
+
+653
+01:19:20,370 --> 01:19:26,290
+إذا كان ال F of A وB
+
+654
+01:19:33,780 --> 01:19:41,160
+for all domain points for all
+
+655
+01:19:41,160 --> 01:19:57,380
+domain points for all domain points x y x y in
+
+656
+01:19:57,380 --> 01:20:02,940
+an open disk in an open
+
+657
+01:20:13,130 --> 01:20:20,130
+النقطة A وB الـ
+
+658
+01:20:20,130 --> 01:20:28,630
+F من A وB هي قيمة
+
+659
+01:20:28,630 --> 01:20:41,930
+أقل محلية محلية أقل محليةF إذا كان of F إذا كان ال
+
+660
+01:20:41,930 --> 01:20:51,490
+F of A و B أقل من أو يساوي F of X و Y for all
+
+661
+01:20:51,490 --> 01:21:01,570
+domain points for all domain points for all domain
+
+662
+01:21:01,570 --> 01:21:19,060
+pointsxy in an open disk centered at
+
+663
+01:21:19,060 --> 01:21:23,300
+point a1
+
+664
+01:21:39,120 --> 01:21:46,100
+في موقع الـ Local
+
+665
+01:21:46,100 --> 01:21:55,560
+Extrema الـ
+
+666
+01:21:55,560 --> 01:22:04,160
+Tangent Appliance الـ
+
+667
+01:22:04,160 --> 01:22:12,900
+Tangent Applianceار هوريزونتال ر
+
+668
+01:22:12,900 --> 01:22:30,340
+هوريزونتال هذا يعني ان اكتشف اكتشف اكتشف اكتشف
+
+669
+01:22:53,820 --> 01:22:58,220
+نرجع ل two definitions مرة ثانية نقرأ ال two
+
+670
+01:22:58,220 --> 01:23:03,480
+definitions نقارنهم ب calculus ايه نحاول نعرفهم
+
+671
+01:23:03,480 --> 01:23:09,040
+برسل شو معنى هذا ال definition طبعا لو رجعنا لكلام
+
+672
+01:23:09,040 --> 01:23:13,260
+اللي احنا كاتبينه و رجعنا الى calculus ايه بلاقي
+
+673
+01:23:13,260 --> 01:23:18,730
+ال two definitions are similarأتنين مالهم متشابهين
+
+674
+01:23:18,730 --> 01:23:23,370
+في شبه كثير جدا الدالة f of x y المعرفة على ال
+
+675
+01:23:23,370 --> 01:23:27,710
+region R يبقى الcontaining بتحتوي على النقطة a وb
+
+676
+01:23:27,710 --> 01:23:31,650
+يبقى ال f of a وb بسميها local maximum إذا كان
+
+677
+01:23:31,650 --> 01:23:37,990
+قيمة الدالة هذه أكبرمن أي قيمة أخرى للدالة بحيث
+
+678
+01:23:37,990 --> 01:23:41,090
+تكون موجودة ويعني في ال domain تبعها هذا في ال
+
+679
+01:23:41,090 --> 01:23:45,310
+local maximum و ال local minimum بتكون أقل من أي
+
+680
+01:23:45,310 --> 01:23:49,550
+قيمة أخرى للدالة على ال domain تبعها هل اختلف هذا
+
+681
+01:23:49,550 --> 01:23:53,630
+تعريف عن تعريف Calculus ايه اللهم يلّه بس ال
+
+682
+01:23:53,630 --> 01:23:57,710
+function في two variables بقى نقول معرفة على
+
+683
+01:23:57,710 --> 01:24:02,960
+intervals ما نقول على open diskتمام طيب الكلام هذا
+
+684
+01:24:02,960 --> 01:24:09,420
+بدنا نروح أرسمه بالرسم حتى يظهر معنى كل واحد من
+
+685
+01:24:09,420 --> 01:24:14,900
+التعريفين الإثنين اللي عندنا فبنروح أاخد محاور X Y
+
+686
+01:24:14,900 --> 01:24:19,760
+و Z لإن احنا بتكلم ال L على وين؟ على الفرار إذا
+
+687
+01:24:19,760 --> 01:24:24,200
+احنا لو روحنا أخدنا المحاور بالشكل اللي على هذا
+
+688
+01:24:24,200 --> 01:24:27,940
+يبقى
+
+689
+01:24:27,940 --> 01:24:36,640
+هذا محور Xهذا محور Y وهذا محور Z لما اقول ان عندي
+
+690
+01:24:36,640 --> 01:24:43,340
+function في X وY يعني كأن Z as a function of X وY
+
+691
+01:24:43,340 --> 01:24:44,780
+لما اقول ان عندي function في X وY يعني كأن Z as a
+
+692
+01:24:44,780 --> 01:24:44,780
+function of X وY لما اقول ان عندي function في X وY
+
+693
+01:24:44,780 --> 01:24:44,780
+يعني كأن Z as a function of X وY لما اقول ان عندي
+
+694
+01:24:44,780 --> 01:24:44,780
+function في X وY يعني كأن Z as a function of X وY
+
+695
+01:24:44,780 --> 01:24:44,780
+لما اقول ان عندي function في X وY يعني كأن Z as a
+
+696
+01:24:44,780 --> 01:24:44,780
+function of X وY لما اقول ان عندي function في X وY
+
+697
+01:24:44,780 --> 01:24:44,780
+يعني كأن Z as a function of X وY لما اقول ان عندي
+
+698
+01:24:44,780 --> 01:24:44,780
+function في X وY يعني كأن Z as a function of X وY
+
+699
+01:24:44,780 --> 01:24:44,780
+لما اقول ان عندي function في X وY يعني كأن Z as a
+
+700
+01:24:44,780 --> 01:24:47,280
+function of X وY لما اقول ان عندي function في X وY
+
+701
+01:24:47,280 --> 01:24:51,180
+يعني كأن Z as
+
+702
+01:24:51,180 --> 01:24:52,120
+a function
+
+703
+01:24:57,350 --> 01:25:02,010
+أيش ما يكون يكون كويس مكان ال service على الشكل
+
+704
+01:25:02,010 --> 01:25:08,850
+اللي عندناه الان بدي اجي لل domain تبعه يبقى ال
+
+705
+01:25:08,850 --> 01:25:16,430
+domain تبعه بقي كأنه بسقط هذا كله على المستوى x y
+
+706
+01:25:16,430 --> 01:25:21,930
+plane بصير عند مين يا بنات هنا اللي هو desk بالشكل
+
+707
+01:25:21,930 --> 01:25:25,850
+اللي عندناه طب
+
+708
+01:25:25,850 --> 01:25:33,260
+كويسالان لو جيت للنقطة اللى عندنا هذه فوق و جيت
+
+709
+01:25:33,260 --> 01:25:40,540
+أسقطة هنا يبقى بتجيني وين؟ على المركز جال للدسك
+
+710
+01:25:40,540 --> 01:25:47,340
+المركز سبعه هو النقطة A وB يبقى هذه النقطة اللى
+
+711
+01:25:47,340 --> 01:25:49,160
+عندنا A وB
+
+712
+01:25:51,820 --> 01:25:57,180
+يبقى أبنات كأنه domain الدالة هو الدائرة الزرقى
+
+713
+01:25:57,180 --> 01:26:01,120
+اللى عندنا هذا هو ال domain الدالة و الدالة وين هي
+
+714
+01:26:01,120 --> 01:26:05,920
+رسميتها فوق لكن ال domain تبعها وين في المستوى xy
+
+715
+01:26:05,920 --> 01:26:10,380
+فلان أندي f of x y تمام يبقى ال domain تبعها في ال
+
+716
+01:26:10,380 --> 01:26:17,250
+xy planeطيب نرجع للتعريف اللي احنا جايلينه ونمشي
+
+717
+01:26:17,250 --> 01:26:21,630
+معاه خطوة بخطوة ونحاول نسقط هذا التعريف على الرسمة
+
+718
+01:26:21,630 --> 01:26:25,310
+اللي عندنا هنا عشان تثبت هذه المعلومة في دماغنا
+
+719
+01:26:25,310 --> 01:26:30,410
+كويس فإيش بيقول هنا اختصر lithopics y دلنا معرفة
+
+720
+01:26:30,410 --> 01:26:35,810
+على region R containing the point A وB يبقى معرفة
+
+721
+01:26:35,810 --> 01:26:41,840
+على region Rبدي افترض ان هذه كلها هي ال region R
+
+722
+01:26:41,840 --> 01:26:44,960
+اللي هي ال function المعرفة لان انا خدتني جزء منها
+
+723
+01:26:44,960 --> 01:26:48,300
+هذا جزء من ال surface مين ما يكون ال surface هذا
+
+724
+01:26:48,300 --> 01:26:52,500
+يكون تمام يبقى هذا ال region R ال region R جاي وين
+
+725
+01:26:52,500 --> 01:26:58,660
+يا بنات في المستوى XY plane اه اديني بالكم طيب
+
+726
+01:26:58,660 --> 01:27:05,580
+بقول في هذه الحالة F of A وBis a local maximum وين
+
+727
+01:27:05,580 --> 01:27:11,280
+ال f of a و b يبقى النقطة اللى عندها دى يبقى a و b
+
+728
+01:27:11,280 --> 01:27:16,880
+و f of a و b الخط الأزرق المنقط هذا هذا الطول كله
+
+729
+01:27:16,880 --> 01:27:21,480
+يعتبر main a و b ليش لإن النقطة اللى عندها دى فى
+
+730
+01:27:21,480 --> 01:27:29,200
+الفراغ هنا لو جتلى يحدثيها تبدى يكون a و b و f of
+
+731
+01:27:29,200 --> 01:27:34,190
+a و bصحيح ولا لأ؟ يجب ان ادى احداثيات النقطة اللى
+
+732
+01:27:34,190 --> 01:27:38,110
+في ال top تبع ال surface اللى عندها طيب عشان اقول
+
+733
+01:27:38,110 --> 01:27:43,510
+لك النقطة هذه بسميها عليها local maximum اذا كانت
+
+734
+01:27:43,510 --> 01:27:49,750
+قيمة الدلة اكبر من او تساوي عند هذه النقطة اكبر من
+
+735
+01:27:49,750 --> 01:27:55,890
+او تساوي اي قيمة اخرى موجودة في domain x واي اللى
+
+736
+01:27:55,890 --> 01:28:00,750
+موجودة في ال open disk اللى مركزه mainاللي هو A وB
+
+737
+01:28:00,750 --> 01:28:05,730
+يبقى هذا اللي هو ال open disk اللي مركزه في A وB
+
+738
+01:28:05,730 --> 01:28:11,470
+طيب بدي أجي أشوف كيف بدي أاخد أي نقطة موجودة في ال
+
+739
+01:28:11,470 --> 01:28:17,390
+open disk لو جيت أخدت أي نقطة زي النقطة هذه موجودة
+
+740
+01:28:17,390 --> 01:28:20,870
+في ال open disk بدي أشوف قيمة الدالة عندها يبقى
+
+741
+01:28:20,870 --> 01:28:25,530
+بطلع لغاية ما جابل مين ما جابل السطح يعني لو جيت
+
+742
+01:28:25,530 --> 01:28:30,130
+بدي أجابل السطح بالشكل اللي عندنايمشي يمشي جابلته
+
+743
+01:28:30,130 --> 01:28:34,390
+مثلا عند النقطة هذه إذا
+
+744
+01:28:36,110 --> 01:28:39,150
+البعد اللي عندك هذا الأسود و لا البعد الأزرق من
+
+745
+01:28:39,150 --> 01:28:44,130
+اللي أكبر الأزرق أكبر يبقى بناء عليه قيمة الدالة
+
+746
+01:28:44,130 --> 01:28:48,570
+صارت أقل من قيمة الدالة عند النقطة A وB أو بمعنى
+
+747
+01:28:48,570 --> 01:28:54,690
+أخر قيمة الدالة عند A وB أكبر من أي قيمة على ال
+
+748
+01:28:54,690 --> 01:28:58,410
+open disk طبعا هناخد تالية عشوائية وبالتالية دي
+
+749
+01:28:58,410 --> 01:29:03,470
+ممكن تكون أي نقطة أخرى يبقى هذه النقطة الأحدثية
+
+750
+01:29:03,470 --> 01:29:10,030
+تالية يمينX هو إذا قيمة الدالة عند نقطة X وY دائما
+
+751
+01:29:10,030 --> 01:29:17,450
+و أبدا أقل من مين من قيمة الدالة عند مين عند A وB
+
+752
+01:29:17,450 --> 01:29:21,270
+إذا حدث ذلك يبقى النقطة اللي فوق بتقول عنها مين
+
+753
+01:29:21,270 --> 01:29:27,870
+local maximum طيب استنى شوية نرجع بالذكرة إلى
+
+754
+01:29:27,870 --> 01:29:32,070
+الورق لCalculus A بقين أقول فيه Calculus A عند
+
+755
+01:29:32,070 --> 01:29:37,840
+local maximumفي عندى فهمة المستقبلية بتكون zero و
+
+756
+01:29:37,840 --> 01:29:43,980
+لو رسمت tangent line بيصير مين؟ أفقي صحيح؟ طب أكرر
+
+757
+01:29:43,980 --> 01:29:48,120
+tangent line بقدر أرسم عند النقطة اللى فوق بس واحد
+
+758
+01:29:48,120 --> 01:29:54,430
+tangent lineماذا يعني؟ يبقى هؤلاء التنجين بيجمعهم
+
+759
+01:29:54,430 --> 01:29:59,330
+في مستوى واحد اسمه ال tangent plane يبقى ال
+
+760
+01:29:59,330 --> 01:30:05,150
+tangent plane في هذه الحالة يكون أفوقيا يعني لو
+
+761
+01:30:05,150 --> 01:30:10,070
+جيت رسمت هذا ال tangent plane على سبيل المثال يبقى
+
+762
+01:30:10,070 --> 01:30:15,350
+ال tangent plane بيصير بالشكل اللي عندنا هذا هي ال
+
+763
+01:30:15,350 --> 01:30:22,410
+tangent planeاللي هو المضلل بالأزرق هذا مَس مين؟
+
+764
+01:30:22,410 --> 01:30:27,890
+مَس ال surface عند مين؟ عند النقطة هذه يبقى هذه هي
+
+765
+01:30:27,890 --> 01:30:33,510
+نقطتي التماس وهذا ال plane يكون أفقيًا وبالتالي
+
+766
+01:30:33,510 --> 01:30:40,960
+معادلة z تساوي z naughtيعني Z تساوي تلاتة اربع
+
+767
+01:30:40,960 --> 01:30:46,460
+خمسة حسب البعد بينه بين المستوى XY لإن ال XY
+
+768
+01:30:46,460 --> 01:30:51,520
+معادلة Z تساوي كم؟ Zero يعني لو قلنا مستوى الغرفة
+
+769
+01:30:51,520 --> 01:30:55,760
+اللي عندنا هذه معادلة Z تساوي Zero لو ارتفعتنا
+
+770
+01:30:55,760 --> 01:31:00,000
+مستوى السجف بسيوف جداشي المسافة بينه بين سجف تلاتة
+
+771
+01:31:00,000 --> 01:31:05,300
+متر إذا السجف معادلة Z تساوي تلاتة يعني Z نُد مثلا
+
+772
+01:31:05,300 --> 01:31:10,500
+عندنا بتلاتة اتنين واحدعشرة قد ما يكون مستوى الان
+
+773
+01:31:10,500 --> 01:31:17,440
+المستوى الأزرق يكون أوفقيا وبالتالي هذه الملاحظة
+
+774
+01:31:17,440 --> 01:31:22,240
+اللي كتبناها هنا لما
+
+775
+01:31:22,240 --> 01:31:25,240
+اقول local extrema يعني جبت ال local maximum و ال
+
+776
+01:31:25,240 --> 01:31:28,380
+local minimum يعني جامعة جمعتهم كلهم ب local
+
+777
+01:31:28,380 --> 01:31:33,520
+extrema التانجين تبلز بيكون horizontal وبالتالي
+
+778
+01:31:33,520 --> 01:31:40,410
+المعادلة تكوناللي اتكلمنا عليه على ال local
+
+779
+01:31:40,410 --> 01:31:43,850
+maximum ده روح يتكرر عالميا على ال local minimum
+
+780
+01:31:43,850 --> 01:31:49,510
+يبقى نفس الصيغة بسقل ال F of A و B يكون أقل من F
+
+781
+01:31:49,510 --> 01:31:54,030
+of X و Y في جميع القيم على الإطلاق في ال open disk
+
+782
+01:31:54,030 --> 01:31:57,950
+اللي يمثل جزء من ال domain يبقى بنات لو روحت أخد
+
+783
+01:31:57,950 --> 01:32:03,510
+المحاور مرة ثانيةفي هذا الشكل و قلت هذا محور X
+
+784
+01:32:03,510 --> 01:32:09,310
+وهذا محور Y وهذا محور Z يبقى النقطة هذه يا بنات
+
+785
+01:32:09,310 --> 01:32:15,750
+تعتبر main القيمة القصوى ال local maximum لو خلقت
+
+786
+01:32:15,750 --> 01:32:24,470
+اسئلة هذه تمثل ال local maximum point طيب لو جيت
+
+787
+01:32:24,470 --> 01:32:30,280
+تخيل ان عندي surface Surface بالشكل هذاو من هنا
+
+788
+01:32:30,280 --> 01:32:37,000
+كان شكله بالشكل اللي عندنا و جيت أسقطه هذا على
+
+789
+01:32:37,000 --> 01:32:45,140
+مين؟ على المستوى XY في Lane بهذا الشكل صار عنده
+
+790
+01:32:45,140 --> 01:32:51,800
+ايش؟ ال disk بالشكل هذا جيت ان النقطة هذه ايه؟ اجت
+
+791
+01:32:51,800 --> 01:32:55,160
+وين؟ في المركز اللي هو A و B
+
+792
+01:32:57,840 --> 01:33:02,660
+خُد أي نقطة في ال open disk في المستوى XY وان تكون
+
+793
+01:33:02,660 --> 01:33:08,240
+النقطة لمين عندنا نقطة هذه يبقى النقطة هذه اليمين
+
+794
+01:33:08,240 --> 01:33:15,040
+XY جاء الطالب اتوكل على الله وجاء الطالب اقابل في
+
+795
+01:33:15,040 --> 01:33:21,240
+ال surface وين عند النقطة اللي عندنا هذه اذا اجت
+
+796
+01:33:21,240 --> 01:33:25,500
+النقطة هذه اعلى من النقطة اللي عندنا هنا وبالتالي
+
+797
+01:33:25,860 --> 01:33:32,700
+قيمة الدالة عند اي و بي كانت اقل من اي قيمة اخرى
+
+798
+01:33:32,700 --> 01:33:36,780
+في ال domain تبع من؟ تبع الدالة اللي عندنا هذه
+
+799
+01:33:36,780 --> 01:33:41,700
+يبقى هذه النقطة ايش بسميها؟ local minimum يبقى هذه
+
+800
+01:33:41,700 --> 01:33:46,800
+اللي عندنا بتصير هنا local minimum
+
+801
+01:33:49,080 --> 01:33:53,700
+وبالتالي لو رسمت tangent انا بدي يكون كمان مين؟
+
+802
+01:33:53,700 --> 01:33:58,800
+كمان أفقي و بدي بيمسى وين؟ عند النقطة اللى عندنا
+
+803
+01:33:58,800 --> 01:34:05,160
+يا بنات لو روحت رسمته هرسمه باللون الأزرق كذلك زى
+
+804
+01:34:05,160 --> 01:34:09,700
+ما رسمنا هذا باللون الأزرق بدي يكون عندك ممسك طبعا
+
+805
+01:34:09,700 --> 01:34:15,440
+هنا مش هيظهرهيظل ماشي هيك و يجيك المستوى بالشكل
+
+806
+01:34:15,440 --> 01:34:22,940
+اللي عندنا هذا هيك يبقى هذا المستوى المضلل بالأزرق
+
+807
+01:34:22,940 --> 01:34:30,670
+حصل تماث بينه وبين المنحنةعند النقطة 2 إلا إن هذا
+
+808
+01:34:30,670 --> 01:34:37,130
+يبقى هذا معادلته z كذلك تساوي z naught جد ما تطلع
+
+809
+01:34:37,130 --> 01:34:41,010
+تطلع يبقى عارفنا شو الفرق بين ال local maximum و
+
+810
+01:34:41,010 --> 01:34:45,980
+ال local minimum من خلال الرسمالـ domain تبعه
+
+811
+01:34:45,980 --> 01:34:51,660
+بيكون في المستويه XY لكن الراسم بتكون فوق الـ
+
+812
+01:34:51,660 --> 01:34:55,120
+local maximum و ال local minimum بعتبر عندي desk
+
+813
+01:34:55,120 --> 01:35:00,440
+مركزه النقطة اللي هي تعتبر local maximum او local
+
+814
+01:35:00,440 --> 01:35:05,060
+minimum لو جيتلي اي قيمة للدالة خلال اي نقطة
+
+815
+01:35:05,060 --> 01:35:09,300
+موجودة في هذا ال domain اذا والله لقيتهاأقل من
+
+816
+01:35:09,300 --> 01:35:13,740
+قيمة الدالة يبقى local maximum أكبر يبقى local
+
+817
+01:35:13,740 --> 01:35:18,850
+minimum وانتهينا من هنامن القصة اللي عندناها طيب
+
+818
+01:35:18,850 --> 01:35:22,750
+الان مذاكرين بقين يقولوا في عندي critical points
+
+819
+01:35:22,750 --> 01:35:28,870
+نقاط حرجة و كيف كنا نحصل عليهم؟ بقين نجيب المشتقة
+
+820
+01:35:28,870 --> 01:35:33,370
+الأولى و نسويها بال zero القيم اللي بتحققها بس
+
+821
+01:35:33,370 --> 01:35:38,890
+انها critical points بس هذه والله هي كمان شغلة اه
+
+822
+01:35:38,890 --> 01:35:44,620
+لو كانت المشتقة غير معرفة عنده نقطةبقول هذه كمان
+
+823
+01:35:44,620 --> 01:35:48,680
+ال critical point طب فدي اسألك كمان سؤال إجباري
+
+824
+01:35:48,680 --> 01:35:52,060
+عندي critical points بتكون عندي local maximum و
+
+825
+01:35:52,060 --> 01:35:57,180
+local minimum؟ لأ ليس بالضرورة يعني مش كل critical
+
+826
+01:35:57,180 --> 01:36:02,760
+point بتكون هي local maximum أو local minimum وهذا
+
+827
+01:36:02,760 --> 01:36:08,800
+نفس الكلاب ينطق على الوضع عندنا تماما إذا بدنا
+
+828
+01:36:08,800 --> 01:36:13,350
+نيجي لحاجة يا بنات اسمهاالـ first derivative test
+
+829
+01:36:13,350 --> 01:36:19,810
+for local extreme values بنحط عنوان بعد هذا تماما
+
+830
+01:36:19,810 --> 01:36:24,790
+و بنقول ال first derivative
+
+831
+01:36:24,790 --> 01:36:28,510
+test
+
+832
+01:36:28,510 --> 01:36:38,930
+for local extreme values for local extreme values
+
+833
+01:36:40,910 --> 01:36:51,650
+إيش بيقول هذا؟ بيقول F ال F of X و Y has
+
+834
+01:36:51,650 --> 01:37:02,970
+.. has a local maximum
+
+835
+01:37:02,970 --> 01:37:14,300
+or minimum value or minimumvalue at an interior
+
+836
+01:37:14,300 --> 01:37:25,080
+point of
+
+837
+01:37:25,080 --> 01:37:29,740
+its
+
+838
+01:37:29,740 --> 01:37:35,900
+domain المجال
+
+839
+01:37:35,900 --> 01:37:36,680
+سبعها
+
+840
+01:37:40,130 --> 01:37:52,430
+إذا كانت الأولى مبادرة مبادرة مبادرة
+
+841
+01:37:52,430 --> 01:37:57,770
+مبادرة
+
+842
+01:37:57,770 --> 01:38:01,590
+مبادرة موجودة
+
+843
+01:38:01,590 --> 01:38:04,630
+هناك
+
+844
+01:38:04,630 --> 01:38:06,550
+ثم
+
+845
+01:38:09,470 --> 01:38:17,510
+الـ Fx عند الـ A و الـ B بدها تساوي Zero and الـ
+
+846
+01:38:17,510 --> 01:38:24,050
+Fy عند الـ A و الـ B كذلك بدها تساوي Zero
+
+847
+01:38:24,050 --> 01:38:30,950
+Definition
+
+848
+01:38:30,950 --> 01:38:37,470
+كمان تاني مقلل
+
+849
+01:38:37,470 --> 01:38:46,840
+Any Interval Pointانترا point a
+
+850
+01:38:46,840 --> 01:38:50,760
+و b of
+
+851
+01:38:50,760 --> 01:39:03,260
+the domain of the domain of a function f of x y
+
+852
+01:39:03,260 --> 01:39:06,900
+it's
+
+853
+01:39:06,900 --> 01:39:16,200
+called a critical pointis all a critical point
+
+854
+01:39:16,200 --> 01:39:32,560
+نقطة حريجة if either اما اما واحد ال fx عند ال a و
+
+855
+01:39:32,560 --> 01:39:38,780
+ال b بدو يسوى zero or والله and
+
+856
+01:39:41,930 --> 01:39:51,270
+and fy عند النقطة a وb بسوى zero كذلك النقطة
+
+857
+01:39:51,270 --> 01:40:04,550
+الثانية one or both one or both of fx عند ال a و
+
+858
+01:40:04,550 --> 01:40:16,050
+ال b and fyعند الـ A will be .. عند ال A will be
+
+859
+01:40:16,050 --> 01:40:21,630
+does not exist
+
+860
+01:40:52,270 --> 01:41:01,890
+تكمل إله بطريقة مركز صغيرة قادمة الـ
+
+861
+01:41:01,890 --> 01:41:16,530
+function f of x y have extreme values
+
+862
+01:41:24,970 --> 01:41:34,670
+القيم المتواجدة في المواقع
+
+863
+01:41:34,670 --> 01:41:41,430
+المتواجدة في المواقع
+
+864
+01:41:41,430 --> 01:41:44,330
+المتواجدة
+
+865
+01:41:48,580 --> 01:41:56,100
+الـ Fx بيساوي الـ Fy ده بيساوي زيرو لإنها ده الـ
+
+866
+01:41:56,100 --> 01:42:13,040
+interim points where one or both of Fx and Fy does
+
+867
+01:42:13,040 --> 01:42:16,360
+not exist
+
+868
+01:42:18,040 --> 01:42:25,320
+المرة التلاتة الـ boundary points
+
+869
+01:42:25,320 --> 01:42:33,300
+ال boundary points of the functions domain
+
+870
+01:42:44,640 --> 01:42:50,620
+أحاول بس نقرأ كلام اللي كتبناه هذا، نفهم كل نقطة
+
+871
+01:42:50,620 --> 01:42:53,760
+فيه، و بيه نهي محاضرته
+
+872
+01:43:09,770 --> 01:43:12,670
+نرجع لـ first derivative test for local extreme
+
+873
+01:43:12,670 --> 01:43:16,190
+values وكان معناه فيه كالبقصة .. فيه كالبقصية
+
+874
+01:43:16,190 --> 01:43:20,910
+بنفسي تسوية لم تغير، بقول لو كانت ال F of X و Y
+
+875
+01:43:20,910 --> 01:43:26,220
+has a local maximum أو local minimumAt an interior
+
+876
+01:43:26,220 --> 01:43:30,080
+point a وb of x, the main and if the first partial
+
+877
+01:43:30,080 --> 01:43:33,880
+derivative exists، إذا بالتفاضل الدالة بالنسبة لX
+
+878
+01:43:33,880 --> 01:43:38,260
+والتفاضل الدالة بالنسبة لY exist، then ال Fx بدأ
+
+879
+01:43:38,260 --> 01:43:42,840
+تساوي Zero والFy تساوي Zero، شوفوا أنا قرأته، و
+
+880
+01:43:42,840 --> 01:43:46,650
+بدأ أقول إيش فهمت، شوفوا فهمي صح ولا غلطأقول بأجعل
+
+881
+01:43:46,650 --> 01:43:52,450
+دان F of X 1 إذا لقيت أنها نقطة F X زي الساوية 0 و
+
+882
+01:43:52,450 --> 01:43:55,690
+F Y زي الساوية 0 يبدأ معناته أن عندي local maximum
+
+883
+01:43:55,690 --> 01:43:57,290
+و local minimum
+
+884
+01:44:03,060 --> 01:44:07,200
+مرة تانية بقول جيت على الذنب استقلت من اسم ال X
+
+885
+01:44:07,200 --> 01:44:10,760
+استقلت من اسم ال Y جيت عنها نقطة ما لقيت هذا
+
+886
+01:44:10,760 --> 01:44:13,820
+الكلام يساوي Zero إذا هل عند هذا نقطة فيه عند لقه
+
+887
+01:44:13,820 --> 01:44:20,360
+ما؟ لأ إذا هذا فهم خاطر فهم مخلوق 180 درجة فإيش
+
+888
+01:44:20,360 --> 01:44:25,780
+الفهم المعدون اقرأه كويس يبقى هذي بقول لو كان عندك
+
+889
+01:44:25,780 --> 01:44:28,620
+local maximum و local minimum value
+
+890
+01:44:35,270 --> 01:44:41,630
+يبقى على عكس ما قلت في الأول تماما 180 درجة واضح
+
+891
+01:44:41,630 --> 01:44:45,770
+يبقى عند مواقع ال local maximum أو ال local
+
+892
+01:44:45,770 --> 01:44:49,790
+minimum بدا تبقى المشتقة بالنسبة ل X تسوى Zero
+
+893
+01:44:49,790 --> 01:44:53,630
+والمشتقة بالنسبة ل Y تسوى Zero هذه هي النقطة
+
+894
+01:44:53,630 --> 01:44:59,410
+الأولى نقطة ثانيةبقول ال point A و B اللي موجودة
+
+895
+01:44:59,410 --> 01:45:05,290
+في دمية دالة F بسميها critical point في حالتين
+
+896
+01:45:05,290 --> 01:45:10,170
+الحالة الأولى لو جبت ال F X عندها لقيتها زواو زيرو
+
+897
+01:45:10,170 --> 01:45:14,650
+وال F Y زواو زيرو والحالة الثانية لو كانت واحدة
+
+898
+01:45:14,650 --> 01:45:22,030
+منهمأو كلاهما غير معرفة عند تلك النقطة هل اختلف
+
+899
+01:45:22,030 --> 01:45:25,890
+تعريف ال critical point عنفي كالكلاسية نفس المفهوم
+
+900
+01:45:25,890 --> 01:45:30,950
+بالضبط تماما بس بدنا نعوض بقيمتين أو بالإحداثين
+
+901
+01:45:30,950 --> 01:45:36,250
+بدل إحداثي واحد إذا مرة تانية النقطة الداخلية هذه
+
+902
+01:45:36,250 --> 01:45:39,570
+اللي موجودة في domain الـ F بسميها critical point
+
+903
+01:45:39,570 --> 01:45:44,090
+النقطة حرجة في حالتينإذا المشتقة الأولى بالنسبة ل
+
+904
+01:45:44,090 --> 01:45:47,570
+X يسوى Zero إذا المشتقة الأولى بالنسبة ل Y سوى
+
+905
+01:45:47,570 --> 01:45:51,590
+Zero هذا الأمر الأول الأمر الثاني لو كانت إحدى
+
+906
+01:45:51,590 --> 01:45:59,770
+المشتقتين أو كلاهما اتنتل ب Zeroطيب وين بدنا نروح
+
+907
+01:45:59,770 --> 01:46:04,590
+ندور على مواضع نهايات العظمة والصغرة؟ بنقول في
+
+908
+01:46:04,590 --> 01:46:09,510
+ثلاثة أماكن، إذا كنت تروح تدوري تشوف عند هذه في
+
+909
+01:46:09,510 --> 01:46:14,050
+local maximum و local minimum و لا لا المكان الأول
+
+910
+01:46:14,050 --> 01:46:18,890
+النقاط الداخلية إيه للمشتقة بالنسبة لك؟ سوى
+
+911
+01:46:18,890 --> 01:46:20,530
+المشتقة الأولى بالنسبةها؟
+
+912
+01:46:28,800 --> 01:46:35,560
+النقاط اللي وحدة فيهم أو كلاهما تبقى غير معرفة
+
+913
+01:46:35,560 --> 01:46:41,000
+الأمر الثالث على ال boundary يبقى بقيانا نقول احنا
+
+914
+01:46:41,000 --> 01:46:46,250
+في الحكاية القلاصيةأول الفترة و آخر الفترة بجينا
+
+915
+01:46:46,250 --> 01:46:50,130
+ندور و نقول هذه ممكن يكون عندها اللي هو local
+
+916
+01:46:50,130 --> 01:46:54,810
+maximum قد يكون و قد لا يكون تمام يبقى بروح على
+
+917
+01:46:54,810 --> 01:46:58,930
+المناظر اللي هي اللي هو ال boundary عندنا تبع مين
+
+918
+01:46:58,930 --> 01:47:03,390
+تبع ال domain تبع الدولة طبعا لو درسنا ال boundary
+
+919
+01:47:03,390 --> 01:47:08,140
+في أول section اللي هو أربعة عشر واحدمظبوط يبقى
+
+920
+01:47:08,140 --> 01:47:12,700
+هذا كلام ليس جديدا علينا المرة القادمة ان شاء الله
+
+921
+01:47:12,700 --> 01:47:18,320
+بنبدأ ناخد مثال على هالشغل هذي ونكمل عليها فيه
+
+922
+01:47:18,320 --> 01:47:23,200
+كمان يبقى عندي absolute maximum و absolute minimum
+
+923
+01:47:23,200 --> 01:47:27,500
+وشوف كيف كان دور على ال boundary كمان مين مين يكون
+
+924
+01:47:27,500 --> 01:47:30,400
+على ال boundary في عندي local maximum او local
+
+925
+01:47:30,400 --> 01:47:35,280
+minimum ان شاء الله و تعالى طبعا اليوم السبت بصير
+
+926
+01:47:35,280 --> 01:47:39,910
+خير ان شاء اللهحاولوا تجروا السكين ولو زي قناة
+
+927
+01:47:39,910 --> 01:47:43,490
+جريدة قبل ان تجو المرة الجاية عشان احنا نمشيها
+
+928
+01:47:43,490 --> 01:47:46,590
+بالكلمة أبيض المعلومة اللي عشان عليها
+
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/xMNKd8BQ9Wg.srt b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/xMNKd8BQ9Wg.srt
new file mode 100644
index 0000000000000000000000000000000000000000..a1fd7dc809618156a224a4ee93b3a7d5956f2d3c
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/xMNKd8BQ9Wg.srt
@@ -0,0 +1,2431 @@
+1
+00:00:14,640 --> 00:00:19,860
+بسم الله الرحمن الرحيم لأن بنرجع مرة ثانية لل
+
+2
+00:00:19,860 --> 00:00:23,910
+section اللي بدناها في نهاية المحاضرة الماضية، فكرنا
+
+3
+00:00:23,910 --> 00:00:30,690
+العنوان: extreme values and saddle points، طبعاً
+
+4
+00:00:30,690 --> 00:00:34,390
+أعطينا تعريف لل local maximum و local minimum
+
+5
+00:00:34,390 --> 00:00:38,750
+أو إن شئنا قلنا local extrema، لكن ال saddle
+
+6
+00:00:38,750 --> 00:00:43,030
+point لم نعطِ لها تعريفاً. وعرفنا في حالة ال local
+
+7
+00:00:43,030 --> 00:00:47,550
+maximum، النقطة بقول عنها local maximum إذا كانت
+
+8
+00:00:47,550 --> 00:00:51,830
+قيمة الدالة عند هذه النقطة أكبر من أي قيمة في
+
+9
+00:00:51,830 --> 00:00:56,130
+المنطقة المجاورة لهذه النقطة في ال domain تبعها.
+
+10
+00:00:56,130 --> 00:01:00,830
+وكذلك بالنسبة لل local minimum، بكون قيمتها
+
+11
+00:01:00,830 --> 00:01:06,170
+أقل من جميع قيم الدالة خلال المنطقة المُعرفة، دي أو
+
+12
+00:01:06,170 --> 00:01:11,310
+على open disk من جزء من ال domain تبع هذه الدالة.
+
+13
+00:01:11,310 --> 00:01:15,390
+طبعاً التعريف لاحظتُه المرة الماضية أنه في شبه كبير
+
+14
+00:01:15,390 --> 00:01:18,150
+جداً بينه وبين تعريف ال local maximum و local
+
+15
+00:01:18,150 --> 00:01:24,070
+minimum for the function of one variable. طيب وصلنا
+
+16
+00:01:24,070 --> 00:01:27,830
+الآن لما نيجي لتعريف ال saddle point، اللي هي النقطة
+
+17
+00:01:27,830 --> 00:01:34,990
+السرجية التي تُقابِل نقطة الانقلاب أو نقطة الانعطاف
+
+18
+00:01:34,990 --> 00:01:40,030
+في ال calculus  أو ال functions of one
+
+19
+00:01:40,030 --> 00:01:43,950
+variable. التعريف بيقول إيش؟ بيقول:  A differentiable
+
+20
+00:01:43,950 --> 00:01:50,360
+function f of x و y has a saddle point. يبقى بيكون
+
+21
+00:01:50,360 --> 00:01:55,600
+عند نقطة سرجية at a critical point a و b، عند
+
+22
+00:01:55,600 --> 00:02:01,000
+النقطة a و b، if in every open disk centered
+
+23
+00:02:01,000 --> 00:02:07,040
+at a و b، روحنا على جزء من ال domain للنقطة a و b،
+
+24
+00:02:07,040 --> 00:02:12,300
+أخذنا disk حولها، there are domain points x و y
+
+25
+00:02:12,300 --> 00:02:18,570
+where f of x و y أكبر من ال f of a و b. يعني في نقاط
+
+26
+00:02:18,570 --> 00:02:24,730
+في ال domain، قيمة الدالة عندها أكبر من قيمة الدالة
+
+27
+00:02:24,730 --> 00:02:29,490
+f of a و b، أو قيمة الدالة f of a و b، وكَذلك domain
+
+28
+00:02:29,490 --> 00:02:34,650
+points x و y حيث f of x و y أقل، على عكس اللي فوق،
+
+29
+00:02:34,650 --> 00:02:41,760
+أقل من f of a و b.  النقطة A و B و f of A و B
+
+30
+00:02:41,760 --> 00:02:48,140
+on the surface، لأن هذا اسمه point on the surface.
+
+31
+00:02:48,140 --> 00:02:53,800
+الآن، مش هنفهم هذا ال definition، تعالوا إلى إحدى أو
+
+32
+00:02:53,800 --> 00:02:58,660
+بعض ال surfaces اللي مرت علينا دراستها قبل ذلك في
+
+33
+00:02:58,660 --> 00:03:05,480
+هذا المقرر. فكان عندنا الشكل، لأن هذا الرسم رقم 6
+
+34
+00:03:05,480 --> 00:03:07,300
+من الرسومات.
+
+35
+00:03:11,110 --> 00:03:17,210
+هذا الشكل، اليوم رسمناه، يشبه السرج تبع الحصان، وزي
+
+36
+00:03:17,210 --> 00:03:21,830
+ما تشوفوا، فعلاً يشبه السرج تبع الحصان. الآن لو جئت
+
+37
+00:03:21,830 --> 00:03:26,830
+للنقطة اللي عندنا هذه، على سبيل المثال، يبقى النقطة
+
+38
+00:03:26,830 --> 00:03:31,870
+اللي عندنا هذه، زي ما أنتم شايفين، لو جئت أخذت نقطة
+
+39
+00:03:31,870 --> 00:03:37,120
+ثانية على السطح، زي النقطة اللي عندنا هذه. طبعاً هذه
+
+40
+00:03:37,120 --> 00:03:41,920
+لو جئت أسقطها على القاعدة هنا، بيكون f of A و B.
+
+41
+00:03:41,920 --> 00:03:46,720
+اليمين، النقطة اللي عندنا هذه، تمام. لو جئنا للنقطة
+
+42
+00:03:46,720 --> 00:03:53,480
+دي، قيمة الدالة أكبر من قيمة الدالة عند هذه النقطة.
+
+43
+00:03:53,480 --> 00:03:59,830
+تمام. طب لو جئت أخذت نقطة زي النقطة هذه على السطح،
+
+44
+00:03:59,830 --> 00:04:03,330
+اللي جهة اليمين، يا بنات، أخذتها، يبقى قيمة الدالة أنها
+
+45
+00:04:03,330 --> 00:04:09,910
+مالها؟ أقل من هذه النقطة. بل هنا كانت z بـ 0، هنا z
+
+46
+00:04:09,910 --> 00:04:15,170
+بقيمة سالبة، وبالتالي الإحداثي رقم ثلاثة بقيمة سالبة.
+
+47
+00:04:15,170 --> 00:04:20,610
+إذا هي عندي نقاط، قيمة الدالة عندها بتكون أكبر من
+
+48
+00:04:20,610 --> 00:04:25,810
+قيمة الدالة عند النقطة السرجية، وكذلك نقاط أخرى
+
+49
+00:04:25,810 --> 00:04:30,690
+قيمة الدالة عندها أقل من قيمة النقطة السرجية. إذا
+
+50
+00:04:30,690 --> 00:04:35,330
+حدث ذلك، يبقى بقول النقطة هذه saddle point، نقطة
+
+51
+00:04:35,330 --> 00:04:41,170
+سرجية. إذا يا بنات، النقطة هذه اللي هنا بقول saddle
+
+52
+00:04:41,170 --> 00:04:48,900
+point. يبقى هذه saddle point، اللي هي النقطة السرجية.
+
+53
+00:04:48,900 --> 00:04:55,000
+الآن، فهمنا هذا التعريف. إن قيمة الدالة عند أي
+
+54
+00:04:55,000 --> 00:05:01,040
+نقطة في domainها أكبر من قيمة الدالة اللي هو f of a
+
+55
+00:05:01,040 --> 00:05:05,240
+و b، وفي المقابل برضه قيمة عند نقطة أخرى
+
+56
+00:05:13,640 --> 00:05:17,880
+هذه العملية صعبة شوية، ونقعد نجيب نقاط وأحسب
+
+57
+00:05:17,880 --> 00:05:24,020
+عددها، لذلك بعد قليل هنحط قاعدة من خلالها نحدد ماهي
+
+58
+00:05:24,020 --> 00:05:27,540
+ال local maximum، وماهي ال local minimum، وماهي
+
+59
+00:05:27,540 --> 00:05:34,270
+النقاط السرجية. بس هاذي بنروح لمين؟ لاختبار المشتقة
+
+60
+00:05:34,270 --> 00:05:38,410
+الثانية. طبعاً في ال calculus،  بنجيب ال local
+
+61
+00:05:38,410 --> 00:05:41,030
+maximum و ال local minimum و ال inflection point
+
+62
+00:05:41,030 --> 00:05:45,730
+برضه بالاختبارين، وخاصة الاختبار الثاني. وهنا كذلك
+
+63
+00:05:45,970 --> 00:05:49,870
+بالاختبار الثاني. إذا، مشان نحسب ال saddle points
+
+64
+00:05:49,870 --> 00:05:53,450
+عملياً، وكَذلك ال local maximum و ال local minimum
+
+65
+00:05:53,450 --> 00:05:57,290
+اللي عرفناها المرة الماضية، بدنا نيجي نحط القاعدة
+
+66
+00:05:57,290 --> 00:06:03,350
+المُستَخدَمة ثانية، وبناءً عليها نشتغل. إذا بدنا نروح نحط
+
+67
+00:06:03,350 --> 00:06:08,330
+عنها، هنقول: second derivative test.
+
+68
+00:06:16,200 --> 00:06:23,960
+test for local
+
+69
+00:06:23,960 --> 00:06:32,720
+extreme values.
+
+70
+00:06:48,210 --> 00:07:00,910
+الطريقه was that: إن ال f of x و y and its first and
+
+71
+00:07:00,910 --> 00:07:15,790
+second partial
+
+72
+00:07:15,790 --> 00:07:16,450
+derivatives
+
+73
+00:07:26,290 --> 00:07:36,610
+partial derivatives are continuous through a
+
+74
+00:07:36,610 --> 00:07:44,690
+open
+
+75
+00:07:44,690 --> 00:07:45,630
+disc centered
+
+76
+00:07:59,480 --> 00:08:08,420
+centered at اللي هو النقطة A و B، and
+
+77
+00:08:08,420 --> 00:08:14,080
+that
+
+78
+00:08:14,080 --> 00:08:21,500
+f<sub>x</sub> عند النقطة A و B يساوي
+
+79
+00:08:21,500 --> 00:08:34,710
+f<sub>y</sub> عند النقطة A و B يساوي 0. ثم، امر واحد: ال f has
+
+80
+00:08:34,710 --> 00:08:47,970
+a local maximum. ال f has a local maximum at النقطة A و B
+
+81
+00:08:47,970 --> 00:08:58,000
+if f<sub>xx</sub>  أقل من ال 0، أقل من ال
+
+82
+00:08:58,000 --> 00:09:11,360
+0، and ال f<sub>xx</sub> مضروب في ال f<sub>yy</sub> ناقص f<sub>xy</sub>² كله
+
+83
+00:09:11,360 --> 00:09:15,720
+greater than 0.  عند النقطة A و B.
+
+84
+00:09:18,950 --> 00:09:25,590
+ال f has a local minimum عند النقطة a و b إذا كان
+
+85
+00:09:25,590 --> 00:09:38,090
+ال f<sub>xx</sub> greater than zero، and ال f<sub>xx</sub>f<sub>yy</sub> ناقص f<sub>xy</sub>²
+
+86
+00:09:38,090 --> 00:09:48,490
+برضه كان greater than zero عند النقطة a و b.
+
+87
+00:09:53,930 --> 00:10:07,250
+ال f has a saddle point، نقطة سرجية، at النقطة A و B
+
+88
+00:10:07,250 --> 00:10:11,930
+إذا كان ال f<sub>xx</sub>
+
+89
+00:10:18,300 --> 00:10:28,680
+أقل من ال 0 at النقطة A و B. النقطة الرابعة
+
+90
+00:10:28,680 --> 00:10:36,080
+والأخيرة من هذا الاختبار تقول: The test is
+
+91
+00:10:36,080 --> 00:10:42,420
+inconclusive at
+
+92
+00:10:42,420 --> 00:10:56,230
+A و B عند النقطة A و B إذا كان ال f<sub>xx</sub>f<sub>yy</sub> ناقص f<sub>xy</sub>²
+
+93
+00:10:56,230 --> 00:11:04,490
+بده يساوي 0 at اللي هو عند النقطة A و B.
+
+94
+00:11:38,880 --> 00:11:43,580
+بعدين نرجع لهذا الاختبار مرة ثانية، نحاول نقرأه
+
+95
+00:11:43,580 --> 00:11:48,300
+كويس، نفهم الشيء اللي موجود فيه. أقول: second
+
+96
+00:11:48,300 --> 00:11:52,920
+derivative test for local extreme values. اختبار
+
+97
+00:11:52,920 --> 00:11:58,620
+المشتقة الثانية لمعرفة ال local minimum و ال
+
+98
+00:11:58,620 --> 00:12:03,060
+local maximum و ال saddle point. الآن نفترض أن هذا
+
+99
+00:12:03,060 --> 00:12:07,020
+f of x و y and its first and second partial
+
+100
+00:12:07,020 --> 00:12:07,840
+derivatives
+
+101
+00:12:18,730 --> 00:12:20,130
+YYYYYYYYYYYYYYYYYYYYY
+
+102
+00:12:37,480 --> 00:12:42,340
+قال لي، وكذلك كان ال f<sub>x</sub> عند ال a و ال b بده يساوي
+
+103
+00:12:42,340 --> 00:12:47,300
+0، و ال f<sub>y</sub> عند ال a و ال b بده يساوي 0. طب ليش هذا
+
+104
+00:12:47,300 --> 00:12:52,360
+ال condition حطه؟ مش هنضمن إن في عندي critical
+
+105
+00:12:52,360 --> 00:12:56,970
+point. يبقى ال f<sub>x</sub> لما نساويها بالزيرو، و ال f<sub>y</sub> لما
+
+106
+00:12:56,970 --> 00:13:01,870
+نساويها بالزيرو، أو لو كانت إحداهما أو كلاهما is
+
+107
+00:13:01,870 --> 00:13:05,590
+undefined عندها، بنقول هنا هذه critical points
+
+108
+00:13:05,590 --> 00:13:10,570
+اللي ممكن يكون local maximum أو local minimum.
+
+109
+00:13:16,570 --> 00:13:21,250
+النقطة الأولى: ال f has a local maximum عند النقطة
+
+110
+00:13:21,250 --> 00:13:25,490
+الأولى إذا كان f<sub>xx</sub> أقل من ال 0،
+
+111
+00:13:28,870 --> 00:13:34,290
+ومقدار المُتباينة يجب أن يكون أكبر من ال 0. f<sub>xx</sub>
+
+112
+00:13:34,290 --> 00:13:42,970
+ضربتها في f<sub>yy</sub> ونقصتها أو طرحتها من ال f<sub>xy</sub> لكل
+
+113
+00:13:42,970 --> 00:13:43,550
+تربيع.
+
+114
+00:13:48,120 --> 00:13:54,880
+القيمة هذه قيمة موجبة، والقيمة هذه قيمة سالبة، يبقى
+
+115
+00:13:54,880 --> 00:13:59,500
+بقول إنّي local maximum. طب local minimum، القيمة هذه
+
+116
+00:13:59,500 --> 00:14:04,740
+بتبقى قيمة موجبة، اللي فوق سالبة، وهذه موجبة، لكن
+
+117
+00:14:04,740 --> 00:14:09,220
+القيمة هذه مالها؟ موجبة. المحدد أو المميز اللي عندنا
+
+118
+00:14:09,220 --> 00:14:14,200
+هذا في كل الأمرين بقيمة موجبة. طب مين بدي أفرّق مع
+
+119
+00:14:14,200 --> 00:14:18,590
+ال local maximum و ال local minimum؟ ال f<sub>xx</sub>. والله
+
+120
+00:14:18,590 --> 00:14:23,630
+إذا كان f<sub>xx</sub> سالبة يبقى لدي local maximum. f<sub>xx</sub> موجبة
+
+121
+00:14:23,630 --> 00:14:29,710
+يبقى local minimum. طب افترض إن المحدد، لأن هذا أو
+
+122
+00:14:29,710 --> 00:14:35,970
+المميز هذا كان أقل من ال 0، و ال f<sub>xx</sub> إيش ما كانت
+
+123
+00:14:35,970 --> 00:14:40,610
+تكون موجبة سالبة ما تفرقش معي، طلع القيمة إيش؟ قيمة
+
+124
+00:14:40,610 --> 00:14:46,730
+سالبة. إن حدث ذلك، يبقى بقول النقطة هنا saddle
+
+125
+00:14:46,730 --> 00:14:51,830
+point. طب لو كله يساوي 0، اختبارنا فشل، وبدنا
+
+126
+00:14:51,830 --> 00:14:55,390
+نرجع لمين؟ للاختبار الأول اللي اتكلمنا عليه المرة
+
+127
+00:14:55,390 --> 00:14:58,810
+الماضية، اللي هو ال first derivative test for
+
+128
+00:14:58,810 --> 00:15:03,070
+local extreme values. ما علينا، مرة ثانية بقول
+
+129
+00:15:03,070 --> 00:15:10,240
+باختصار، يبقى يا بنات المشتقة الأولى لل f،
+
+130
+00:15:10,240 --> 00:15:15,920
+والمشتقة الثانية f<sub>xx</sub> بتلعب دور كبير في تحديد هل
+
+131
+00:15:15,920 --> 00:15:20,180
+هي ال local maximum أو ال local minimum. هذه ال
+
+132
+00:15:20,180 --> 00:15:24,500
+inequality هنا أكبر من ال 0 في الحالتين، يبقى
+
+133
+00:15:24,500 --> 00:15:27,100
+بدأ الفرق من ال local maximum و ال local minimum
+
+134
+00:15:27,100 --> 00:15:32,400
+بطلع لل f<sub>xx</sub>. والله إذا كانت أكبر من ال 0، يبقى
+
+135
+00:15:32,400 --> 00:15:38,230
+local minimum. أقل من ال 0، يبقى local... افترض أنها
+
+136
+00:15:38,230 --> 00:15:41,970
+كانت أقل من ال 0، اللي هو اللي نقلت الثاني إلى
+
+137
+00:15:41,970 --> 00:15:45,770
+اليمين، و ال f<sub>xx</sub> إيش ما تكون، تكون موجبة والله سالبة
+
+138
+00:15:45,770 --> 00:15:49,890
+ما تفرقش معي، بهذه، إذا والله طلعت سالبة، يبقى
+
+139
+00:15:49,890 --> 00:15:55,450
+يبقى هذه ال saddle point. يبقى من هنا فرّقت ما بين
+
+140
+00:15:55,450 --> 00:15:58,370
+ال saddle point و ال local maximum و ال local
+
+141
+00:15:58,370 --> 00:16:00,830
+minimum. فرّقت ما بين ال local maximum و ال local
+
+142
+00:16:00,830 --> 00:16:06,900
+minimum بقيمة ال f<sub>xx</sub>. فرق بينهم وبين ال saddle point
+
+143
+00:16:06,900 --> 00:16:11,540
+بواسطة ال main inequality اللي عندنا. طب أطلع النتيجة
+
+144
+00:16:11,540 --> 00:16:16,560
+هذه تساوي 0، يبقى لا أستطيع الحكم على المسألة
+
+145
+00:16:16,560 --> 00:16:21,580
+اللي عندنا. عشان نثبت هذه المعلومات، ناخذ مثال نحسب
+
+146
+00:16:21,580 --> 00:16:25,000
+فيه ال local maximum و ال local minimum و ال
+
+147
+00:16:25,000 --> 00:16:27,700
+saddle point. طب نقول example
+
+148
+00:16:51,380 --> 00:17:01,720
+local extrema and saddle points
+
+149
+00:17:01,720 --> 00:17:11,600
+of the function: لدالة f of x y بده يساوي
+
+150
+00:17:11,600 --> 00:17:21,840
+اللي هو x<sup>3</sup> + y<sup>3</sup> + 3x<sup>2</sup> -
+
+151
+00:17:21,840 --> 00:17:31,280
+3y<sup>2</sup> - 8. solution
+
+152
+00:18:05,060 --> 00:18:08,880
+خليني أخبركم إني حقاً أقول هذه ال local extreme
+
+153
+00:18:08,880 --> 00:18:12,740
+values اللي عندك، وهذه ال saddle points للدالة اللي
+
+154
+00:18:12,740 --> 00:18:19,920
+عندنا هذا. يبقى بدي أرجع، لازم أحسب له f<sub>xx</sub>, f<sub>yy</sub>, f<sub>xy</sub>
+
+155
+00:18:19,920 --> 00:18:23,540
+يبقى هي دول التلاتة اللي هم بيلعبوا الدور الكبير
+
+156
+00:18:23,540 --> 00:18:27,080
+في معرفة ال local extreme أو saddle points لمين؟ لل
+
+157
+00:18:27,080 --> 00:18:32,790
+function اللي عندنا. إذا بدي أبدأ بال f<sub>x</sub> يساوي
+
+158
+00:18:32,790 --> 00:18:41,930
+3x<sup>2</sup> + 6x، والباقي بسيطة بالمرة، نحسب
+
+159
+00:18:41,930 --> 00:18:51,770
+f<sub>xx</sub>، فيساوي نشتق كمان مرة، يبقى 6x + 6.
+
+160
+00:18:51,770 --> 00:18:53,810
+فاهمين كويس؟
+
+161
+00:18:56,480 --> 00:19:01,440
+أنا لم أحصل على نقطة محددة في المثال، لذلك أنا
+
+162
+00:19:01,440 --> 00:19:08,280
+سأخرج النقطة لوحدي. النقطة لوحدي منين؟ من ال f<sub>x</sub>
+
+163
+00:19:08,280 --> 00:19:13,960
+يبقى شرطنا هنا إيش يا بنات؟ بدي إياها تقدر تساوي؟ تساوي
+
+164
+00:19:13,960 --> 00:19:19,660
+0. إذا بدي آخذ ال f<sub>x</sub> بده تساوي 0، وهذا بيعطينا
+
+165
+00:19:20,050 --> 00:19:25,910
+إنّه 3x<sup>2</sup> + 6x بده يساوي 0. هذا بدي
+
+166
+00:19:25,910 --> 00:19:35,170
+يعطينا، يعني إنّه 3x(x + 2) بضل
+
+167
+00:19:35,170 --> 00:19:42,180
+عندنا هنا، x + 2، كله بده يساوي 0. إذا
+
+168
+00:19:42,180 --> 00:19:48,840
+بنقل عليه هذا، بده يعطينا إن x بده تساوي 0، و x بده
+
+169
+00:19:48,840 --> 00:20:00,120
+يساوي سالب 2. طيب، نروح نجيب f<sub>y</sub> يساوي. يبقى f<sub>y</sub>
+
+170
+00:20:00,120 --> 00:20:07,860
+أنا بدأت مع السلامة، هذه 3y<sup>2</sup>، وهنا ناقص
+
+171
+00:20:07,860 --> 00:20:12,120
+6y، ونساويها بالزيرو مشان نجيب ال critical
+
+172
+00:20:12,120 --> 00:20:17,780
+points كلهم مرة واحدة. يبقى بناءً عليه هذا بدي يعطي
+
+173
+00:20:17,780 --> 00:20:24,910
+نعني، بناءً على 3y(y - 2) بده يساوي قداش؟
+
+174
+00:20:24,910 --> 00:20:30,110
+بده يساوي 0. هيك هذا بده يعطينا يعني إن
+
+223
+00:27:38,910 --> 00:27:46,490
+الثالثة يبقى بالداخل نأخذ الـ point النقطة
+
+224
+00:27:46,490 --> 00:27:54,070
+الثالثة اللي هو سالب اثنين وزيرو سالب اثنين وزيرو
+
+225
+00:27:54,070 --> 00:28:04,050
+طيب يبقى بدنا نجي نعود في الـ mean في المعادلة الأصلية
+
+226
+00:28:04,050 --> 00:28:04,670
+ونحسب
+
+227
+00:28:08,080 --> 00:28:12,720
+يبقى مثل ما بدأنا بالضبط تماماً في الأول بدي آخذ
+
+228
+00:28:12,720 --> 00:28:19,820
+fxx عند النقطة سالب اثنين وزيرو إذا بدي أشيل كل x
+
+229
+00:28:19,820 --> 00:28:27,480
+وأحط مكانها سالب اثنين يبقى ستة في سالب اثنين
+
+230
+00:28:27,480 --> 00:28:32,760
+يساوي ستة ويساوي سالب ستة وزي ما أنتم شايفين مالها
+
+231
+00:28:33,590 --> 00:28:41,970
+أقل من زيرو كمية سالبة يبقى مضطر آخذ كمان الـ FYY
+
+232
+00:28:41,970 --> 00:28:47,930
+اللي هو عند النقطة اللي هو سالب اثنين وزيرو يساوي
+
+233
+00:28:47,930 --> 00:28:54,850
+FYY فوق اللي هو عبارة عن زيرو سالب ستة ويساوي
+
+234
+00:28:54,850 --> 00:29:01,970
+سالب ستة والـ FXY هذه ثابتة ما هي إلا زيرو للكل
+
+235
+00:29:02,650 --> 00:29:04,870
+يبقى بتروح آخذ F
+
+236
+00:29:31,790 --> 00:29:40,090
+XX أقل من الـ Zero أقل من الـ Zero وهذه أكبر من 100
+
+237
+00:29:40,090 --> 00:29:44,170
+من الـ Zero في الـ Calculus Maximum إذا بدنا نروح
+
+238
+00:29:44,170 --> 00:29:52,810
+نحسب كده الـ F أو نقص اثنين وZero في الجسم بدنا نشيل
+
+239
+00:29:52,810 --> 00:29:57,930
+كل Y ونحط مكانها Zero ونشيل كل X ونحط مكانها
+
+240
+00:29:57,930 --> 00:29:58,090
+Zero
+
+241
+00:30:07,580 --> 00:30:15,640
+الكل ثمانية وهنا ناقص Zero ناقص ثمانية وهي ستة
+
+242
+00:30:15,640 --> 00:30:22,860
+طبعاً هنا ناقص ثمانية وهنا ناقص ثمانية تصير ناقص
+
+243
+00:30:22,860 --> 00:30:30,820
+ستة عشر وهنا اثنا عشر بضل قداش ناقص أربعة إذا بروح
+
+244
+00:30:30,820 --> 00:30:39,690
+بقول له if has local maximum اللي هو قداش؟ سالب
+
+245
+00:30:39,690 --> 00:30:45,050
+أربعة at the
+
+246
+00:30:45,050 --> 00:30:53,350
+point عند النقطة اللي هو سالب اثنين وزيرو إذا طلعت
+
+247
+00:30:53,350 --> 00:30:56,770
+واحدة سادسة الـ point واحدة local maximum واحدة
+
+248
+00:30:56,770 --> 00:31:01,850
+local minimum بقيت النقطة الأخيرة
+
+249
+00:31:28,870 --> 00:31:35,130
+يبقى النقطة الأخيرة يا بناتي اللي هي الـ point كده؟
+
+250
+00:31:35,130 --> 00:31:42,350
+سالب اثنين واثنين بدنا نروح نحسب اللي هو الـ f x
+
+251
+00:31:42,350 --> 00:31:48,750
+x عند النقطة سالب اثنين واثنين وقت السابق وين
+
+252
+00:31:48,750 --> 00:31:52,990
+الـ fxx؟ مسحناها يعني كان ستة x زي ستة،
+
+253
+00:31:52,990 --> 00:32:02,870
+مظبوط؟ يبقى ستة في ناقص اثنين زائد ستة ويساوي كده؟
+
+254
+00:32:02,870 --> 00:32:13,650
+ناقص ستة لما لها أقل من الـ zero فبنحسب FYY FYY عند
+
+255
+00:32:13,650 --> 00:32:20,190
+النقطة ناقص اثنين واثنين والـ FYY هيقول يبقى هنا
+
+256
+00:32:20,190 --> 00:32:29,850
+ستة في اثنين ناقص ستة ويساوي كده ستة ومعروف الـ Fxy
+
+257
+00:32:29,850 --> 00:32:34,350
+عند أي نقطة كلها تساوي Zero على طول الخط
+
+258
+00:32:53,910 --> 00:33:00,430
+اللي فوق بتهمنيش سالبة ولا موجبة يبقى النقطة هذه
+
+259
+00:33:00,430 --> 00:33:01,630
+تعتبر مين؟
+
+260
+00:33:31,710 --> 00:33:38,970
+ناقص ثمانية ناقص ثمانية يبقى هذا الكلام لو جيت فاكته
+
+261
+00:33:38,970 --> 00:33:45,110
+بيصير ناقص ثمانية وهنا زائد ثمانية وهنا زائد
+
+262
+00:33:45,110 --> 00:33:51,870
+اثنا عشر وهنا ناقص اثنا عشر وهنا ناقص ثمانية هذه و
+
+263
+00:33:51,870 --> 00:33:56,130
+هذه مع بعض وهذه وهذه مع السلامة يبقى الجواب
+
+264
+00:33:56,130 --> 00:34:04,030
+قداش؟ سالب ثمانية يبقى الـ F has saddle point
+
+265
+00:34:24,820 --> 00:34:28,840
+الأشياء اللي ليس بالضرورة ممكن تكون كل القيم موجبة
+
+266
+00:34:29,360 --> 00:34:35,260
+النسبة للمسألة اللي عندك يعني إحنا بدل سالب ثمانية
+
+267
+00:34:35,260 --> 0:34:40,180
+في المسألة لو حطينا زائد ثمانية هيجيك أحياناً صفر
+
+268
+00:34:40,180 --> 00:34:45,300
+وأحياناً رقم مش هتلاقي ولا رقم سالب صحيح ولا لا؟
+
+269
+00:34:47,800 --> 00:34:54,140
+لكن هناك موقع آخر وليس في نفس الموقع يعني نقطة
+
+270
+00:34:54,140 --> 00:34:57,560
+اتغيرت مش نفس النقطة وبالتالي انتقلنا مثلاً عند
+
+271
+00:34:57,560 --> 00:35:00,560
+النقطة هذه في local maximum عند النقطة هذه في
+
+272
+00:35:00,560 --> 00:35:03,340
+saddle point عند النقطة هذه في saddle point عند
+
+273
+00:35:03,340 --> 00:35:07,330
+النقطة الثالثة في local minimum وهكذا يعني طالع و
+
+274
+00:35:07,330 --> 00:35:11,450
+نازل الرسمة طبعاً لا يمكن نقل نقص من الرسمة لأنه
+
+275
+00:35:11,450 --> 00:35:15,470
+رسم كمبيوتر تمام كل الرسمة اللي بتشوفها في الكتاب
+
+276
+00:35:15,470 --> 00:35:22,690
+رسمت كمبيوتر وبالتالي بتلاقي مجسمات  أينها حد بتسأل
+
+277
+00:35:22,690 --> 00:35:28,870
+أي سؤال هنا كمان خلاص طيب الآن ننتقل إلى النقطة
+
+278
+00:35:28,870 --> 00:35:31,930
+الثانية من هذا الـ section وهي
+
+279
+00:35:37,450 --> 00:35:43,430
+وخاصة الامتحانات النهائية اللي هو بنجيبها بنات الـ
+
+280
+00:35:43,430 --> 00:35:49,210
+absolute maximum والـ absolute minimum للـ function
+
+281
+00:35:49,210 --> 00:35:53,470
+نفس تعريف الـ absolute maximum والـ absolute
+
+282
+00:35:53,470 --> 00:35:58,770
+minimum في حالة الـ function of one variable اللي
+
+283
+00:35:58,770 --> 00:36:03,430
+درسناه في Calculus A قبل ذلك
+
+284
+00:36:42,650 --> 00:36:46,490
+على منطقة مغلقة ومحدودة
+
+285
+00:36:59,820 --> 00:37:14,020
+maximum أو absolute minimum أو absolute minimum أو
+
+286
+00:37:14,020 --> 00:37:16,080
+absolute minimum أو absolute minimum أو absolute
+
+287
+00:37:16,080 --> 00:37:16,400
+minimum أو absolute minimum أو absolute minimum أو
+
+288
+00:37:16,400 --> 00:37:16,740
+absolute minimum أو absolute minimum أو absolute
+
+289
+00:37:16,740 --> 00:37:16,960
+minimum أو absolute minimum أو absolute minimum أو
+
+290
+00:37:16,960 --> 00:37:17,020
+absolute minimum أو absolute minimum أو absolute
+
+291
+00:37:17,020 --> 00:37:17,060
+minimum أو absolute minimum أو absolute minimum أو
+
+292
+00:37:17,060 --> 00:37:23,160
+absolute minimum أو absolute minimum
+
+293
+00:37:23,160 --> 00:37:28,140
+أو absolute minimum
+
+294
+00:37:39,160 --> 00:37:48,600
+النقطة الداخلية للمنطقة R where
+
+295
+00:37:48,600 --> 00:37:54,560
+الـ F may
+
+296
+00:37:54,560 --> 00:38:00,760
+have may have local maximum
+
+297
+00:38:03,860 --> 00:38:14,260
+local maximum or local minimum or local
+
+298
+00:38:14,260 --> 00:38:19,320
+minima and evaluate the function's value and
+
+299
+00:38:19,320 --> 00:38:31,930
+evaluate the function's value قيمة الدالة at this
+
+300
+00:38:31,930 --> 00:38:42,690
+point at this point عند هذه النقاط these
+
+301
+00:38:42,690 --> 00:38:46,210
+are
+
+302
+00:38:46,210 --> 00:38:51,990
+the points هذه
+
+303
+00:38:51,990 --> 00:39:02,970
+النقاط where الـ fx يتساوي الـ fy يتساوي الـ zero or
+
+304
+00:39:02,970 --> 00:39:09,270
+where
+
+305
+00:39:09,270 --> 00:39:22,330
+one or both of Fx
+
+306
+00:39:22,330 --> 00:39:27,850
+and Fy fail to exist
+
+307
+00:39:32,840 --> 00:39:43,220
+بعد ذلك هذه المقاومة الموجودة في
+
+308
+00:39:43,220 --> 00:39:47,440
+المقاومة هذه المقاومة
+
+309
+00:39:47,440 --> 00:39:53,100
+الموجودة في المقاومة الموجودة في المقاومة R إذا
+
+310
+00:39:53,100 --> 00:39:58,720
+F كان
+
+311
+00:39:58,720 --> 00:40:02,240
+لديه مقاومة
+
+312
+00:40:04,690 --> 00:40:20,110
+maximum هو local minimum and find the
+
+313
+00:40:20,110 --> 00:40:27,130
+function value
+
+314
+00:40:27,130 --> 00:40:38,870
+قيمة الدالة at these points
+
+315
+00:40:38,870 --> 00:40:50,450
+عند هذه اللحظة ثلاثة لـ maximum and
+
+316
+00:40:50,450 --> 00:40:55,390
+minimum values
+
+317
+00:41:02,670 --> 00:41:09,410
+أو إذا أنطقت
+
+318
+00:41:09,410 --> 00:41:17,990
+سيكون الـ Absolute سيكون الـ Absolute
+
+319
+00:41:17,990 --> 00:41:21,390
+maximum
+
+320
+00:41:21,390 --> 00:41:24,530
+و
+
+321
+00:41:24,530 --> 00:41:30,230
+Absolute minimum
+
+322
+00:41:31,830 --> 00:41:44,650
+respectively examples
+
+323
+00:41:44,650 --> 00:41:50,410
+اتحول
+
+324
+00:41:50,410 --> 00:41:59,770
+لثالث by the absolute maximum by the absolute
+
+325
+00:42:02,720 --> 00:42:11,240
+maximum and minimum of
+
+326
+00:42:11,240 --> 00:42:16,600
+the function لدى
+
+327
+00:42:16,600 --> 00:42:22,780
+f of x و y يساوي
+
+328
+00:42:25,610 --> 00:42:37,390
+معكوس XY زائد Y تربيع زائد واحد on the closed
+
+329
+00:42:37,390 --> 00:42:49,310
+triangle closed triangle plate in
+
+330
+00:42:49,310 --> 00:42:50,130
+the first
+
+331
+00:42:54,840 --> 00:43:03,940
+الـ first quadrant أو
+
+332
+00:43:03,940 --> 00:43:13,060
+البيان العين أو
+
+333
+00:43:13,060 --> 00:43:22,220
+البيان العين X تساوي Zero وY تساوي أربعة and
+
+334
+00:43:24,440 --> 00:43:26,740
+Y مستوى S
+
+335
+00:44:28,050 --> 00:44:32,050
+نرجع للكلام اللي كتبناه على اللوح ثانية نقرأ كل
+
+336
+00:44:32,050 --> 00:44:37,150
+نقطة  وكل حيثية لك نفهم شو اللي مطلوب منه وبعد
+
+337
+00:44:37,150 --> 00:44:43,190
+ذلك نروح نحل المثال تبعه بيقول لي ده نجل الـ
+
+338
+00:44:43,190 --> 00:44:46,030
+absolute maximum والـ absolute minimum اللي يدال
+
+339
+00:44:46,030 --> 00:44:51,530
+على الـ domain تبعها بيات الـ domain كمنطقة محدودة و
+
+340
+00:44:51,530 --> 00:44:57,710
+كذلك منطقة مغلقة طبعاً بعد قليل هأقول لك ليش منطقة
+
+341
+00:44:57,710 --> 00:45:02,990
+مغلقة و ليش منطقة محدودة بقول to find the absolute
+
+342
+00:45:02,990 --> 00:45:06,750
+maximum أو absolute minimum make the following
+
+343
+00:45:06,750 --> 00:45:12,250
+steps بدنا نعمل خطوات ثانية الخطوة الأولى بقول
+
+344
+00:45:12,250 --> 00:45:15,410
+list the internal points قائمة بالنقاط
+
+345
+00:45:15,410 --> 00:45:21,330
+الداخلية للـ region R بحيث الدالة Fممكن تأخذ local
+
+346
+00:45:21,330 --> 00:45:26,070
+maximum أو local minimum على هذه المنطقة واحسب لي
+
+347
+00:45:26,070 --> 00:45:30,290
+قيمتي الدالة عند main، عند هذه النقاط، يبقى أنوش
+
+348
+00:45:30,290 --> 00:45:37,130
+بيقول لي اتلي كل نقاط الحرجة على المنطقة المعطاة،
+
+349
+00:45:37,130 --> 00:45:41,230
+بدنا إياها هدول وعندي النقاط اللي حالياً بدي أحسب مين
+
+350
+00:45:41,230 --> 00:45:46,530
+القيم تبعت هذه الدالة وأقولهم اطيعوا شوية بس نكمل
+
+351
+00:45:46,530 --> 00:45:51,810
+باقي الشغل وبعد هيك نروح لمين؟ List the boundary
+
+352
+00:45:51,810 --> 00:45:56,270
+points يبقى أول شغلة جبنا الـ internal points يبقى
+
+353
+00:45:56,270 --> 00:46:02,930
+إحنا داخل الـ open region يبقى ضل عندنا الـ
+
+354
+00:46:02,930 --> 00:46:07,170
+boundary اللي على الحدود يبقى بدنا نجيب list كمان
+
+355
+00:46:07,170 --> 00:46:12,010
+بالـ boundary region للدالة F اللي عندها ممكن تأخذ
+
+356
+00:46:12,010 --> 00:46:16,570
+local maximum و local minimum ونحسب قيم الدالة
+
+357
+00:46:16,570 --> 00:46:21,670
+عندها إذا صرت عندي الحمد لله قيم كثيرة قيم تبع
+
+358
+00:46:21,670 --> 00:46:24,470
+الـ interior points وقيم تبع الـ boundary points
+
+359
+00:46:24,470 --> 00:46:29,570
+باجي في الآخر خطوة ثالثة وأخيرة بطلع أكبر قيمة
+
+360
+00:46:29,570 --> 00:46:33,310
+بقول هذه الـ absolute maximum وأقل قيمة بقول main
+
+361
+00:46:33,310 --> 00:46:36,710
+هذه الـ absolute minimum  موفقين بالتوفيق
+
+362
+00:46:36,710 --> 00:46:41,010
+يبقى هذا باختصار اللي بدنا نعمله يبقى أول حاجة بده
+
+363
+00:46:41,010 --> 00:46:45,470
+أحسب الـ internal points اللي الدالة ممكن تأخذ
+
+364
+00:46:45,470 --> 00:46:50,500
+عندها local maximum أو local minimum بعد هيك بدي
+
+365
+00:46:50,500 --> 00:46:53,300
+آجي إلى الـ boundary points اللي ممكن الدالة تكون
+
+366
+00:46:53,300 --> 00:46:56,840
+عندها local maximum وlocal minimum عند هذه النقاط
+
+367
+00:46:56,840 --> 00:46:59,900
+في حالة الـ intro هو الـ boundary بدي أحسب قداش
+
+368
+00:46:59,900 --> 00:47:04,660
+القيم المختلفة لهذه الدالة بعدين بدي أقارن بين هذه
+
+369
+00:47:04,660 --> 00:47:08,940
+القيم القيم اللي عندها أكبر قيمة بقول هي absolute
+
+370
+00:47:08,940 --> 00:47:13,700
+maximum وأقل قيمة بقول هي main absolute minimum
+
+371
+00:47:13,700 --> 00:47:19,700
+لهذه الدالة أعظم موضوع احتلالي حد بتسأل أي سؤال قبل
+
+372
+00:47:19,700 --> 00:47:27,820
+أن نبدأ الآن؟ في أي تساؤل؟ طيب أنا بسأل،
+
+373
+00:47:27,820 --> 00:47:32,140
+مظبوط؟ ليش قال لي المنطقة  بدها تكون closed، ما كان
+
+374
+00:47:32,140 --> 00:47:33,580
+قال لي open وراح ينفعني؟
+
+375
+00:47:36,870 --> 00:47:42,270
+لا ممكن يكون، بس إيش؟ بصير اللي على الحدود هذه
+
+376
+00:47:42,270 --> 00:47:45,990
+البابرة بصير مغلق ليش علاقة فيها، يبقى كأنه لغيت
+
+377
+00:47:45,990 --> 00:47:51,050
+مين؟ لغيت الخطوة هذه تمام وإحنا دلوقت راجعنا لـ
+
+378
+00:47:51,050 --> 00:47:55,550
+Calculus إيه اللي بجيء ممكن يكون في absolute في
+
+379
+00:47:55,550 --> 00:47:59,750
+maximum أو minimum على مين؟ على الـ interval المعرف
+
+380
+00:47:59,750 --> 00:48:03,210
+عليها طالع عند أول الـ interval أو نهاية الـ interval
+
+381
+00:48:03,210 --> 00:48:07,630
+هو بالطبع ممكن يكون عند الـ boundary points عندنا
+
+382
+00:48:07,630 --> 00:48:12,170
+يكون في عند local maximum أو local minimum ومن هنا
+
+383
+00:48:12,170 --> 00:48:16,820
+اشتغلنا المنطقة بدون get lost region يعني الـ
+
+384
+00:48:16,820 --> 00:48:20,800
+boundary بدهم يدخلوا في الحساب عندك وهات الصورة
+
+385
+00:48:20,800 --> 00:48:26,960
+طيب نجي نسأل سؤالها وقول هات الـ absolute maximum و
+
+386
+00:48:26,960 --> 00:48:31,420
+الـ absolute minimum و لمين؟ للدالة f of x و y وأعطاني دالة و
+
+387
+00:48:31,420 --> 00:48:34,380
+أعطاني closed in triangle plate
+
+388
+00:48:40,880 --> 00:48:45,900
+يبقى لما أقول عند هنا على الـ close triangle plate
+
+389
+00:48:45,900 --> 00:48:51,580
+يعني مثلث مغلق زي ما نقول قرص في حالة الدائرة يبقى
+
+390
+00:48:51,580 --> 00:48:56,960
+هنا بقول close triangle plate مثلث مغلق يعني كل
+
+391
+00:48:56,960 --> 00:49:04,720
+نقاط المثلث مالها؟ هي نقاط الـ domain للدالة اللي عندنا
+
+392
+00:49:04,720 --> 00:49:09,440
+تمام مش بس على المحيط وبس على المحيط وداخل
+
+393
+00:49:09,440 --> 00:49:13,260
+المدالة هذا المقصود فيه هنا يبقى on a closed
+
+394
+00:49:13,260 --> 00:49:16,960
+triangular plane in the first quadrant في الربع
+
+395
+00:49:16,960 --> 00:49:22,520
+الأول والمحدود بالثلاثة خطوط اللي قدامنا X تساوي
+
+396
+00:49:26,490 --> 00:49:32,670
+محور y هو y تساوي 4 موازي لمحور x هو y تساوي x
+
+397
+00:49:32,670 --> 00:49:37,990
+الخط المنصف للربع الأول والربع الثالث لكن إحنا كنا
+
+398
+00:49:37,990 --> 00:49:41,830
+في الربع الأول يبقى مالنا علاقة بمين؟ بالربع الثالث
+
+399
+00:49:41,830 --> 00:49:47,610
+يُريد كبل نبدأ خلينا نرسم المنطقة تبعتنا طب المنطقة
+
+400
+00:49:47,610 --> 00:49:54,760
+بنات هذه هي domain الدالة والدالة نفسها domain
+
+401
+00:49:54,760 --> 00:49:59,000
+الدالة يعني الدالة بتبقى كأنها surface  فاضي
+
+402
+00:49:59,000 --> 00:50:03,620
+وعالمستوى XY plane المثلثة اللي إحنا رسمناها هذا
+
+403
+00:50:03,620 --> 00:50:07,620
+جزء من domain الدالة إحنا بنحسب على هذا الجزء من
+
+404
+00:50:07,620 --> 00:50:10,820
+الـ domain اللي هو local maximum وlocal absolute
+
+405
+00:50:10,820 --> 00:50:16,740
+maximum و absolute minimum بسيطة لذا لو روحنا
+
+406
+00:50:16,740 --> 00:50:22,560
+رسمنا روح نأخذ
+
+445
+00:54:44,420 --> 00:54:51,100
+الدالة عندها إذا يا بنات بتروح أجيب الـ F of 00
+
+446
+00:54:51,100 --> 00:54:57,020
+يبقى هذا الكلام بده يسوي بده يفوت يساوي قداش واحد
+
+447
+00:54:57,540 --> 00:55:03,520
+يبقى بنأجلها ونروح نخليها لأن لنا إليها عودة بعد
+
+448
+00:55:03,520 --> 00:55:08,340
+قليل إن شاء الله تعالى، يبقى خلاصنا النقطة الأولى
+
+449
+00:55:08,340 --> 00:55:11,280
+اللي هو الـ interior points وجينا نحسب الـ interior
+
+450
+00:55:11,280 --> 00:55:15,300
+طولها، عندنا main boundary يبقى ما عندناش مشكلة، يبقى
+
+451
+00:55:15,300 --> 00:55:18,380
+عندنا نحسبهم، الـ boundary بروحش أحسبها ثانية مرة
+
+452
+00:55:18,380 --> 00:55:22,440
+ثانية، لو حسبناها خلاصهم، يبقى بدأت على الـ main
+
+453
+00:55:22,440 --> 00:55:23,740
+boundary points
+
+454
+00:55:34,380 --> 00:55:40,360
+أنا بمشي على الحدود الإقليمية، يبقى بروح أسمي
+
+455
+00:55:40,360 --> 00:55:45,580
+المثلث، بالرواق السابع، بدي أقول هذه مثلاً النقطة A
+
+456
+00:55:45,580 --> 00:55:54,420
+وهذه النقطة B وهذه النقطة C، وبدي أبدأ هنا، بدي
+
+457
+00:55:54,420 --> 00:56:01,600
+أقول on the line على الخط AB
+
+458
+00:56:05,720 --> 00:56:14,220
+على الخط AB كم مقدار X؟ صفر، يبقى هنا الـ X بدها
+
+459
+00:56:14,220 --> 00:56:23,060
+تساوي صفر، هذا بده يعطيك أن الـ F هو صفر، يعني أنا
+
+460
+00:56:23,060 --> 00:56:27,420
+هشيل كل X وأحط مكانها صفر، ثم بقول ماذا يجب أن
+
+461
+00:56:27,420 --> 00:56:32,100
+يساوي هاي الدالة فوق الصفر، بصير عند اليمين بيبقى طبعاً
+
+462
+00:56:32,100 --> 00:56:38,260
+صفر، لأن عندي Y تربيع زائد واحد، والـ Y هتتغير من
+
+463
+00:56:38,260 --> 00:56:44,750
+وين لوين؟ من صفر لغاية أربعة، ممتاز جداً، يبقى من
+
+464
+00:56:44,750 --> 00:56:52,570
+صفر لغاية 4، سؤال هو: هل هذه صارت دالة في متغيرين ولا
+
+465
+00:56:52,570 --> 00:56:57,770
+متغير واحد؟ متغير واحد، يبقى بروح بقوله بدي أجيب له
+
+466
+00:56:57,770 --> 00:57:05,910
+الـ F prime يعني كأنه بده يجيب الـ point على الخط على
+
+467
+00:57:05,910 --> 00:57:11,270
+الـ interval من صفر لـ 4، يبقى هذا الكلام  دي يساوي كده؟
+
+468
+00:57:11,270 --> 00:57:19,070
+اثنين واحد، ويساوي مين؟ يبقى هذا بدي أعطيك أن واحد
+
+469
+00:57:19,070 --> 00:57:20,290
+يساوي صفر
+
+470
+00:57:22,940 --> 00:57:31,380
+تمام، طيب لما الـ Y تساوي صفر، إذا إذا لو عوضت هنا
+
+471
+00:57:31,380 --> 00:57:35,820
+بصير قيمة الدالة عندك كده واحد، يعني تطلع النقطة
+
+472
+00:57:35,820 --> 00:57:41,120
+اللي عندها هذه الأصلية كما كانت، تمام، يبقى هذا بدي
+
+473
+00:57:41,120 --> 00:57:46,980
+يعطيك نفس النقطة الأصلية، وبالتالي بنحسب F of صفر
+
+474
+00:57:46,980 --> 00:57:54,390
+وصفر، يبقى هذا بدي يعطيك الـ F of 00 هي الواحد
+
+475
+00:57:54,390 --> 00:57:59,410
+اللي حصلنا عليها من قبل قليل، يبقى لم نأتِ بمين
+
+476
+00:57:59,410 --> 00:58:07,230
+بأي جديد عندنا، تمام، طيب لازلنا مع الـ line AB اللي
+
+477
+00:58:07,230 --> 00:58:13,500
+عندنا هذا، وبالتالي بدي أحسب آخر الـ line يعني
+
+478
+00:58:13,500 --> 00:58:18,520
+ما لقيتش نقطة داخل الـ line ولا نقطة، أجيت عند الـ 00
+
+479
+00:58:18,520 --> 00:58:26,880
+ضل عند الـ main نقطة 04، يبقى بروح بحسبه F of 04
+
+480
+00:58:26,880 --> 00:58:32,140
+يبقى هذا الكلام ضل السبب، ارجع للدالة اللي فوق و
+
+481
+00:58:32,140 --> 00:58:38,050
+الله، هيها عندي جاهزة ومبسطة موجودة هي، يبقى ما أجِي
+
+482
+00:58:38,050 --> 00:58:43,870
+بيقول لي هذه بدها تساوي أربعة تربيع زائد واحد، يساوي قداش
+
+483
+00:58:43,870 --> 00:58:51,170
+17، هاي بأجلها وسنرجع لها بعد قليل، بعد هيك
+
+484
+00:58:51,170 --> 00:59:00,290
+بدي أجي أقول له on the line BC، على الـ BC، قيمة
+
+485
+00:59:00,290 --> 00:59:10,550
+قداش؟ أربعة، تمام، كويس، يبقى هنا الـ Y تساوي 4، معناته
+
+486
+00:59:10,550 --> 00:59:17,370
+هذه بدها تصير F of X و 4، الـ Y ساوت 4، يبقى بدنا نرجع
+
+487
+00:59:17,370 --> 00:59:24,990
+للدالة اللي عندنا هنا، بتصير X تربيع ناقص 4X زائد
+
+488
+00:59:24,990 --> 00:59:34,870
+16 زائد 1، يبقى صارت عندنا دالة F of X و 4 اللي
+
+489
+00:59:34,870 --> 00:59:43,220
+تساوي مين؟ X تربيع ناقص 4X زائد 17، بدي
+
+490
+00:59:43,220 --> 00:59:48,820
+أشوف على هذا الخط في عندي نقاط داخلية ولا لا، يمكنش
+
+491
+00:59:48,820 --> 01:00:00,220
+أعمل اشتقاق F prime of X و 4، يساوي 2X ناقص
+
+492
+01:00:00,220 --> 01:00:05,720
+4، ونساويه بمين يا بنات؟ بالصفر، لما نساويه بالصفر
+
+493
+01:00:05,980 --> 01:00:11,340
+بدي أطلع عندي 2X بدي أساويه بالـ 4، يبقى الـ X بدي
+
+494
+01:00:11,340 --> 01:00:16,900
+أساويه بكام؟ 2، يبقى إحداثيات النقطة مين؟ 2
+
+495
+01:00:16,900 --> 01:00:21,300
+و 4،  و أين النقطة 2 و 4؟ بتجيني هنا في
+
+496
+01:00:21,300 --> 01:00:26,860
+المنطقة، يعني مشيت 2 وطلعت 4، يبقى هذا
+
+497
+01:00:26,860 --> 01:00:32,120
+النقطة 2 و 4 اللي عندها قد يكون local
+
+498
+01:00:32,120 --> 01:00:37,260
+maximum أو local minimum، إذا بروح بحسبه النقطة F
+
+499
+01:00:37,260 --> 01:00:43,420
+2 و 4، تساوي، هيفضل جاهزة عندي، يعني هنا معوض
+
+500
+01:00:43,420 --> 01:00:49,900
+بـ 4، ضل بس عوض بمن؟ بـ 2، يبقى هذه 2 تربيع
+
+501
+01:00:50,110 --> 01:00:58,110
+ناقص 4 في 2 زائد 17، يساوي هنا 4 وهنا
+
+502
+01:00:58,110 --> 01:01:03,730
+سالب 8، بيظل سالب 4 من 17، بيظل
+
+503
+01:01:03,730 --> 01:01:12,090
+13، وهذه بأجلها، كذا ضلت مين عندي؟ 4
+
+504
+01:01:12,090 --> 01:01:12,730
+4 4 4 4 4 4 4 4
+
+505
+01:01:12,730 --> 01:01:17,990
+4 4 4 4 4 4 4
+
+506
+01:01:40,400 --> 01:01:48,280
+طبعاً هنا إحنا عندنا F of X و 4، يبقى هاي بأجلها، بده
+
+507
+01:01:48,280 --> 01:01:53,000
+أشيل كل X وأحط مكانها 4، يبقى هادي بده يتساوى
+
+508
+01:01:58,370 --> 01:02:05,030
+الـ 17 زائد 17 هو يساوي 17
+
+509
+01:02:05,030 --> 01:02:20,230
+17 17 17 17 17 17 17 17 17 17
+
+510
+01:02:20,710 --> 01:02:28,250
+طيب على هذا الـ line يا بنات، Y تساوي X، طبعاً Y تساوي
+
+511
+01:02:28,250 --> 01:02:36,170
+X، أنا بدي أقول لك أن F of X و X، يعني هشيل كل Y وأحط
+
+512
+01:02:36,170 --> 01:02:41,270
+مكانها X، أو العكس، هشيل كل X وأحط مكانها Y، واحدة من الاثنين
+
+513
+01:02:41,270 --> 01:02:45,490
+مش واحدة من الاثنين، يجي هنا بقول له هذا الكلام يساوي
+
+514
+01:02:45,490 --> 01:02:46,790
+برجع للمثال
+
+515
+01:03:10,760 --> 01:03:16,900
+يبقى هنا والـ X أكبر من أو تساوي صفر وأقل من أو
+
+516
+01:03:16,900 --> 01:03:21,600
+تساوي أربعة، يعني الخط هذا مش على طول وطالع فوقنا
+
+517
+01:03:21,600 --> 01:03:25,920
+لأ، بس أنا بدي الفتره من صفر لأربعة، من صفر
+
+518
+01:03:25,920 --> 01:03:29,400
+لغاية هذه هنا أربعة
+
+519
+01:03:38,420 --> 01:03:46,160
+يبقى X هو X، يبقى نقطة زي
+
+520
+01:03:46,160 --> 01:03:53,760
+نقطة زي نقطة نقطة نقطة نقطة نقطة نقطة نقطة
+
+521
+01:03:53,760 --> 01:04:00,580
+نقطة نقطة نقطة نقطة نقطة نقطة نقطة نقطة نقطة
+
+522
+01:04:00,580 --> 01:04:01,500
+نقطة نقطة نقطة نقطة نقطة نقطة نقطة نقطة
+
+523
+01:04:01,500 --> 01:04:05,780
+نقطة نقطة نقطة نقطة نقطة نقطة نقطة
+
+524
+01:04:05,780 --> 01:04:05,880
+نقط
+
+525
+01:04:18,690 --> 01:04:23,870
+النقطة على الـ 00 هي، فهي انتهينا، ليش؟ ولا نقطة في
+
+526
+01:04:23,870 --> 01:04:28,830
+الطريق، فـ 4 و 4 حسبناها مع اللي قبلها، بروحش أغيرها
+
+527
+01:04:28,830 --> 01:04:34,960
+ثاني، انتهينا الآن من الخطوات، من كل الـ boundary
+
+528
+01:04:34,960 --> 01:04:39,360
+points ومن كل الـ interior points، تمام؟ شو بدي
+
+529
+01:04:39,360 --> 01:04:44,120
+أعمل الآن؟ بدي أقوم بمقارنة، أكبر قيمة بقول هذا
+
+530
+01:04:44,120 --> 01:04:48,020
+absolute maximum، وأقل قيمة absolute minimum
+
+531
+01:04:48,020 --> 01:04:53,280
+باجي بطلع في المربعات اللي عندي أنا أجلتها هنا
+
+532
+01:04:53,280 --> 01:05:00,680
+يبقى أكبر قيمة جديدة وأقل قيمة، ممتازة، ده بروح
+
+533
+01:05:00,680 --> 01:05:12,690
+بقول له الـ F has absolute maximum 17 at the points
+
+534
+01:05:12,690 --> 01:05:18,770
+في موقعين، الموقع الأول يا بنات، له كده، شو؟ صفر و
+
+535
+01:05:18,770 --> 01:05:27,090
+أربعة، صفر و أربعة، والموقع الثاني and أربعة و
+
+536
+01:05:27,090 --> 01:05:27,550
+أربعة
+
+537
+01:05:53,020 --> 01:06:02,270
+طب افترض يا بنات كان مش مثلث مربع أو مستطيل، يبقى
+
+538
+01:06:02,270 --> 01:06:06,890
+نفس الشيء، نروح نديله الضلع الرابع وهكذا، طبعاً أنا بس
+
+539
+01:06:06,890 --> 01:06:11,870
+السؤال أنه كيف الكتاب مثال يبقى مستطيل، يبقى حاجة
+
+540
+01:06:11,870 --> 01:06:16,150
+زي المحاضرات، المثلث بالعلم، المستطيل بالضبط تماماً، بس
+
+541
+01:06:16,150 --> 01:06:20,910
+بضمين الضلع الرابع، لكن أنا لخاطر أعطيكم مثال غير
+
+542
+01:06:20,910 --> 01:06:26,750
+مستطيل، مش موجود زيه في الكتاب ومرة جئنا به في
+
+543
+01:06:26,750 --> 01:06:34,480
+إحدى الامتحانات، لذلك بدنا نروح نعطيك مثال ما هو لا
+
+544
+01:06:34,480 --> 01:06:44,040
+مستقيم ولا مُثلّث ولا حتى مُربّع. أيش المثال هذا؟
+
+545
+01:06:44,040 --> 01:06:52,080
+بقول لك ستراه الآن إن شاء الله تعالى، بعد أن نكمل
+
+546
+01:06:52,080 --> 01:06:54,220
+مسح اللوحين
+
+547
+01:07:10,870 --> 01:07:12,810
+مثال 2
+
+548
+01:07:30,490 --> 01:07:47,590
+and minimum values of the function للدالة F of X Y
+
+549
+01:07:47,590 --> 01:07:56,850
+تساوي واحد زائد X Y ناقص 3X on the closed
+
+550
+01:07:56,850 --> 01:08:08,850
+region، on a closed region bounded by
+
+551
+01:08:08,850 --> 01:08:22,070
+والمحدودة بـ the parabola بالقطع المكافئ Y تساوي X
+
+552
+01:08:22,070 --> 01:08:29,870
+تربيع and the line Y تساوي 4
+
+553
+01:08:46,910 --> 01:08:52,110
+أحد المدرسين كان يدرس صيفياً زي الصيف هذا، فقام جاب
+
+554
+01:08:52,110 --> 01:08:58,010
+السؤال للطلاب اللي بدرسهم، إحنا بنعطيكم إياه كمثال
+
+555
+01:08:58,010 --> 01:09:01,490
+إن شاء الله تعالى، بيقول: هات الـ absolute maximum والـ
+
+556
+01:09:01,490 --> 01:09:05,530
+absolute minimum للدالة اللي قدام هذه على المنطقة
+
+557
+01:09:05,530 --> 01:09:10,170
+المغلقة المحدودة بالقطع المكافئ Y تساوي X تربيع
+
+558
+01:09:10,170 --> 01:09:16,870
+و بخط Y تساوي 4، لو روحنا نتعرف على المنطقة اللي
+
+559
+01:09:16,870 --> 01:09:23,270
+عندنا هذه، بقول هي المحاور، وهذا محور X وهذا محور Y
+
+560
+01:09:23,270 --> 01:09:31,190
+وهذه نقطة الأصل، القطع اللي عندنا أبسط شيء مشهور
+
+561
+01:09:31,190 --> 01:09:35,490
+عندنا من الكورس الصحيح، كلنا بنعرف رسمته، يبقى
+
+562
+01:09:35,490 --> 01:09:37,390
+هذا Y تساوي X
+
+563
+01:09:40,430 --> 01:09:47,170
+Y تساوي 4، خط يوازي محور X، ويبقى عند مسافة
+
+564
+01:09:47,170 --> 01:09:53,470
+مقدارها 4، يبقى هذه 4، وهذا الخط يوازي محور
+
+565
+01:09:53,470 --> 01:09:54,130
+X، ويبقى هذه 4، وهذا الخط يوازي محور X، ويبقى هذه
+
+566
+01:09:54,130 --> 01:09:56,790
+4، وهذا الخط يوازي محور X، ويبقى هذه 4، وهذا
+
+567
+01:09:56,790 --> 01:09:57,410
+الخط يوازي محور X، ويبقى هذه 4، وهذا الخط يوازي
+
+568
+01:09:57,410 --> 01:10:00,510
+4، وهذا الخط يوازي محور X، ويبقى هذه 4، وهذا
+
+569
+01:10:00,510 --> 01:10:01,750
+الخط يوازي محور X، و
+
+570
+01:10:09,360 --> 01:10:16,020
+الـ interior points، النقاط الداخلية، وبعد ذلك بروح لمين
+
+571
+01:10:16,020 --> 01:10:21,040
+للنقاط الخارجية، إذا بدنا نروح ونجيب له مين يا بنات؟
+
+572
+01:10:21,040 --> 01:10:28,180
+F X، نشتغل بالنسبة لـ X، هي اللي قدامنا هنا، نشتقها، من Y
+
+573
+01:10:28,180 --> 01:10:35,700
+ناقص ثلاثة ونساويه بالصفر، إذا الـ Y تساوي كام؟ ثلاثة
+
+574
+01:10:35,700 --> 01:10:37,680
+بالمثل بدنا نجيب له F
+
+575
+01:10:43,690 --> 01:10:50,450
+بالنسبة لـ Y، تمام، ونساويه بالصفر، إذا الـ X بدها تساوي
+
+576
+01:10:50,450 --> 01:10:58,050
+قداش؟ صفر، يبقى الـ interior point اللي يبقى صفر و
+
+577
+01:10:58,050 --> 01:11:08,010
+ثلاثة is a
+
+578
+01:11:08,010 --> 01:11:10,430
+critical point
+
+579
+01:11:15,350 --> 01:11:22,270
+0.3 يعني وين بدها تيجي 0.3؟ هنا، هذه النقطة اللي هي صفر
+
+580
+01:11:22,270 --> 01:11:27,670
+و 3، بيبقى أجد داخل المنطقة، مش ده السؤال اللي قبل
+
+581
+01:11:27,670 --> 01:11:31,570
+ما لاجئناش، ولا نقطة داخل المنطقة، لاجئناها على الحد
+
+582
+01:11:31,570 --> 01:11:36,990
+ده هذه لاجئناها نقطة داخل المنطقة اللي عندنا، إذا
+
+583
+01:11:36,990 --> 01:11:39,250
+بدنا نروح نحسبه قداش
+
+584
+01:11:57,260 --> 01:12:01,700
+نأجلها، وسنرجع لها إن شاء الله، بعد هيك بدنا نروح
+
+585
+01:12:01,700 --> 01:12:10,600
+لمين؟ للـ boundary points، النقاط
+
+586
+01:12:10,600 --> 01:12:18,600
+الحدودية، إيش رأيك نبدأ بالـ parabola في الأول، يبقى
+
+587
+01:12:18,930 --> 01:12:23,890
+باجي بقول له، بقول: on the line، يبقى on the curve Y
+
+588
+01:12:23,890 --> 01:12:33,910
+تساوي X تربيع، أو on the parabola اللي
+
+589
+01:12:33,910 --> 01:12:42,870
+هو Y تساوي X تربيع، وهاد بدي يصير F of X ومين
+
+590
+01:12:42,870 --> 01:12:47,570
+بجنبه؟ وX تربيع، مش الـ Y بحط X تربيع، فبنحجي
+
+591
+01:12:47,570 --> 01:12:56,550
+عليها، بتصير تساوي واحد زائد تساوي
+
+592
+01:12:56,550 --> 01:12:59,990
+واحد
+
+593
+01:12:59,990 --> 01:13:01,770
+زائد تساوي واحد زائد تساوي واحد زائد تساوي واحد
+
+594
+01:13:01,770 --> 01:13:02,010
+زائد تساوي واحد زائد تساوي واحد زائد تساوي واحد
+
+595
+01:13:02,010 --> 01:13:03,770
+زائد تساوي واحد زائد تساوي واحد زائد تساوي واحد
+
+596
+01:13:03,770 --> 01:13:06,410
+زائد تساوي واحد زائد تساوي واحد زائد تساوي واحد
+
+597
+01:13:06,410 --> 01:13:08,150
+زائد تساوي واحد زائد تساوي واحد زائد تساوي واحد
+
+598
+01:13:08,150 --> 01:13:12,510
+زائد تساوي واحد زائد تساوي واحد زائد تساوي واحد
+
+599
+01:13:12,510 --> 01:13:17,770
+زائد تساوي واحد زائد تساوي و
+
+600
+01:13:21,120 --> 01:13:27,100
+ناقص ثلاثة، يعني ثلاثة في X تربيع ناقص واحد، يعني
+
+601
+01:13:27,100 --> 01:13:32,560
+ثلاثة في X ناقص واحد في X زائد واحد، ونساويه بالصفر
+
+602
+01:13:32,560 --> 01:13:41,440
+يبقى باجي بقول هذا بيعطي كذا critical points at
+
+603
+01:13:41,440 --> 01:13:52,400
+X تساوي واحد و X تساوي كده؟ سالب واحد، طبعاً إذا بدنا
+
+604
+01:13:52,400 --> 01:14:01,180
+نجيب F of واحد وواحد تربيع، في الثانوية شيلنا الـ
+
+605
+01:14:01,180 --> 01:14:07,320
+X وحطينا مكانها واحد، يبقى واحد زائد واحد ناقص
+
+606
+01:14:07,320 --> 01:14:14,970
+ثلاثة، ويساوي كذا؟ ناقص واحد، بعدها بدنا نجيب F of سالب
+
+607
+01:14:14,970 --> 01:14:21,610
+واحد وسالب واحد تربيع، هو يساوي واحد، سالب واحد
+
+608
+01:14:21,610 --> 01:14:28,190
+تربيع ناقص ثلاثة في ناقص واحد، يبقى أيش؟ ثلاثة، واحد
+
+609
+01:14:28,190 --> 01:14:35,910
+أربعة، شيل منهم واحد بالسالب، يظل كده؟ يظل ثلاثة، هذه
+
+610
+01:14:35,910 --> 01:14:45,510
+الأخرى، تمام؟ طيب، الآن جبنا اللي هو على الـ
+
+611
+01:14:45,510 --> 01:14:49,250
+boundary points،
+
+667
+01:22:24,060 --> 01:22:27,620
+X أقل من أو يساوي
+
+668
+01:22:32,680 --> 01:22:42,420
+وY أكبر من أو يساوي C أقل من أو يساوي D, then the
+
+669
+01:22:42,420 --> 01:22:55,700
+double integral over
+
+670
+01:22:55,700 --> 01:23:01,000
+double integral over R
+
+671
+01:23:03,280 --> 01:23:17,140
+R defined by  عرفت تكامليْن على R من F of X و Y
+
+672
+01:23:17,140 --> 01:23:28,220
+دي  تكامل من A إلى B، تكامل من C إلى D من F of X و
+
+673
+01:23:28,220 --> 01:23:37,480
+Y  dx dy
+
+674
+01:23:37,480 --> 01:23:49,160
+وطبعاً  dy dx تساوي تكامل من C إلى D، ومن A إلى B  لـ F of X وY
+
+675
+01:23:49,160 --> 01:23:56,100
+dx dy
+
+676
+01:24:07,790 --> 01:24:14,790
+أمثلة أو النساء اللاتي
+
+677
+01:24:14,790 --> 01:24:21,470
+تتبعون
+
+678
+01:24:34,130 --> 01:24:42,770
+متكامل من باي لغاية 2 باي، ومتكامل من صفر
+
+679
+01:24:42,770 --> 01:24:53,170
+لغاية باي. لمين؟ لقيم  X نفسها، وقيم Y كلها في
+
+680
+01:24:53,170 --> 01:24:55,710
+الـ dx في الـ dy
+
+681
+01:25:27,320 --> 01:25:31,260
+الشبكة الماضية كانت  عن partial derivatives كلها
+
+682
+01:25:31,260 --> 01:25:36,760
+بتلزم الاشتغالات من أوله إلى آخره، هذا إن شاء الله
+
+683
+01:25:36,760 --> 01:25:41,000
+كلها تكاملات، بس مش تكامل واحد زي ما درسنا بالـ
+
+684
+01:25:41,000 --> 01:25:45,340
+calculus a و b. ممكن يكون تكامليْن، ممكن يكون ثلاثة
+
+685
+01:25:45,340 --> 01:25:50,820
+تكاملات، ممكن يكون إحداثيات كارتزية، ممكن يكون
+
+686
+01:25:50,820 --> 01:25:56,480
+إحداثيات قطبية، وكيف يمكن التحويل من تكاملات في
+
+687
+01:25:56,480 --> 01:26:01,760
+الإحداثيات الكارتزية إلى الإحداثيات القطبية، وبالعكس
+
+688
+01:26:01,760 --> 01:26:07,640
+وممكن يكون في إحداثيات أسطوانية، وفي
+
+689
+01:26:07,640 --> 01:26:13,140
+إحداثيات كروية، وكيف نحسب التكاملات فيها يوم أن
+
+690
+01:26:13,140 --> 01:26:18,480
+نصلها إن شاء الله تعالى. لكن هنبدأ بأبسط الأشياء، هو
+
+691
+01:26:18,480 --> 01:26:22,550
+أول section، section 15،  راح نتطرق إلى integrant of a
+
+692
+01:26:22,550 --> 01:26:27,270
+rectangle. يبقى إحنا بدنا نحسب قيمة التكاملات
+
+693
+01:26:27,270 --> 01:26:31,890
+الثنائية على مستطيلات. لازم أقول قيمة التكامل
+
+694
+01:26:31,890 --> 01:26:36,950
+هذه عبارة عن مستطيل له طول وله عرض. إذاً x هتتغير
+
+695
+01:26:36,950 --> 01:26:41,370
+بين رقمين، والـ y هتتغير بين رقمين. يبقى
+
+696
+01:26:41,370 --> 01:26:47,590
+هذا تكامل على منطقة مستطيلة الشكل. تعريف تاني، خد
+
+697
+01:26:47,590 --> 01:26:54,630
+دالة f(x,y) متصلة خلال هذه المنطقة المستطيلة. x
+
+698
+01:26:54,630 --> 01:27:00,370
+محصورة بين A وB، وy محصورة بين C وD. يعني لو رحنا
+
+699
+01:27:00,370 --> 01:27:05,150
+ورسمنا، قلنا هذا المحور x، وهذا المحور y،
+
+700
+01:27:05,150 --> 01:27:10,270
+وهذه عندي نقاط، وجينا وصلنا النقاط بالشكل هذا، وقلنا هذه
+
+701
+01:27:10,270 --> 01:27:16,250
+المنطقة A، وهذه B، وهذه C، وهذه D. يبقى المنطقة
+
+702
+01:27:16,250 --> 01:27:21,370
+المظللة اللي عندنا هذه هي المحصورة بين A وB
+
+703
+01:27:21,370 --> 01:27:27,730
+و C وD. فده نحسب مقدار المساحة بتاعت المنطقة بتاعت هذه
+
+704
+01:27:27,730 --> 01:27:32,370
+المنطقة. فبقول double integral على المنطقة هذه
+
+705
+01:27:32,370 --> 01:27:38,250
+بعرفه كتالي: تكامليْن على المنطقة، أكرر f(x,y) dy
+
+706
+01:27:38,250 --> 01:27:50,940
+dx. يعني dy dx.  دي إيه؟ دي إيه؟ دي إيه؟ دي
+
+707
+01:27:50,940 --> 01:27:57,580
+إيه؟ دي إيه؟ دي إيه؟
+
+708
+01:27:57,580 --> 01:28:04,010
+دي إيه؟ دي إيه؟ dy dx. يبقى أول ما بدي أكامل بالنسبة
+
+709
+01:28:04,010 --> 01:28:08,970
+لـ y فبحط حدود الـ y من C إلى D. ثم اللي ينتج بدي
+
+710
+01:28:08,970 --> 01:28:14,430
+أكلمه بالنسبة إلى x، فبحط حدود الـ x من A إلى B. لو كنت
+
+711
+01:28:14,430 --> 01:28:18,950
+بدي أكامل بالنسبة لـ x في الأول، فبحط حدود الـ x من A إلى
+
+712
+01:28:18,950 --> 01:28:23,070
+B، ثم بدي أكامل لـ y، بحط حدود الـ y من C إلى D. الآن هذا كلام مضغوط، سنضعه على أرض الواقع ببعض
+
+713
+01:28:23,070 --> 01:28:29,430
+الأمثلة. سنأخذ بس مثال بسيط ومباشر إن شاء
+
+714
+01:28:29,430 --> 01:28:33,850
+الله، وسنكمل عليه. يبقى قال لي: أحسب لي قيمة التكامل
+
+715
+01:28:33,850 --> 01:28:38,430
+التالية، وعطاني أول تكامل، تكامل من صفر إلى باي،
+
+716
+01:28:38,430 --> 01:28:43,570
+ومن باي إلى 2 باي. فهذه منطقة مستطيلة، لأنه عطاني
+
+717
+01:28:43,570 --> 01:28:48,450
+أرقام لقيم x و  Cos y dx dy مخلينيش يعني محتار
+
+718
+01:28:48,450 --> 01:28:55,560
+لكنك تكامل بالنسبة لـ x من الأول، وبعدين تكامل
+
+719
+01:28:55,560 --> 01:28:59,460
+بالنسبة لـ y. زي حالات لما كنا بالنسبه لـ x بعتبر الـ y
+
+720
+01:28:59,460 --> 01:29:04,600
+ثابتة، وهنا لما أكامل بالنسبة لـ x بعتبر الـ y
+
+721
+01:29:04,600 --> 01:29:09,200
+ثابتة، وأكمل بالنسبة لـ y بعتبر الـ x ثابتة، و
+
+722
+01:29:09,200 --> 01:29:13,840
+هكذا. يبقى هذا الكلام،  بترتب التكامل من باي إلى 2
+
+723
+01:29:13,840 --> 01:29:20,680
+باي، تكامل من صفر إلى باي، يبقى تكامل الـ cos
+
+724
+01:29:20,680 --> 01:29:26,500
+y سالب cos x، يبقى سالب cos x. كوساين  يُعتبر
+
+725
+01:29:26,500 --> 01:29:33,280
+من صفر إلى باي،  يبقى سالب كوساين الباي كوساين الصفر
+
+726
+01:29:33,280 --> 01:29:36,900
+اللي هو بواحد.
+
+727
+01:29:49,800 --> 01:29:56,100
+يبقى هذا الكلام يبدو يساوي تكامل من باي
+
+728
+01:29:56,100 --> 01:30:01,520
+إلى 2 باي لـ: بضعّط بالقيمة اللي فوق، ناقص القيمة اللي تحت
+
+729
+01:30:01,520 --> 01:30:09,620
+اللي هي -1، يبقى معي -(-1) اللي هو بـ1
+
+730
+01:30:10,190 --> 01:30:13,370
+هذا يجب أن أضع x بدل y
+
+731
+01:30:16,810 --> 01:30:22,890
+يبقى باي × cos y. خلصنا القيم اللي فوق، نعود بالقيم
+
+732
+01:30:22,890 --> 01:30:28,850
+اللي تحت: ناقص مع ناقص بصير زائد، و cos صفر اللي
+
+733
+01:30:28,850 --> 01:30:35,950
+هو بواحد. وهنا ناقص صفر في cos y اللي هو بصفر
+
+734
+01:30:35,950 --> 01:30:42,650
+كلها بالنسبة إلى dy، يبقى صارت المسألة تكامل من
+
+735
+01:30:42,650 --> 01:30:49,660
+باي إلى 2 باي، لمين؟ لـ 2 – 1، وهي
+
+736
+01:30:49,660 --> 01:30:55,240
+زائد، فيه زائد يا بنت هنا.. أيوه، يبقى هنا واحد + 1
+
+737
+01:30:55,240 --> 01:31:03,300
+× 2 + باي × cos y dy، ويساوي
+
+738
+01:31:03,300 --> 01:31:09,460
+أنا بدأت أكامل بالنسبة لـ y، يبقى 2y + باي ×
+
+739
+01:31:09,460 --> 01:31:16,260
+sin y كلها من باي لغاية 2 باي. يبقى هذا
+
+740
+01:31:16,260 --> 01:31:25,190
+الكلام بده يساوي 2 × 2 باي + باي × sin
+
+741
+01:31:25,190 --> 01:31:32,730
+2 باي اللي هو بقد إيش؟ بصفر، ناقص 2 باي ناقص
+
+742
+01:31:32,730 --> 01:31:40,200
+باي × sin صفر اللي هو بصفر.  شكلها .. يبقى الجواب
+
+743
+01:31:40,200 --> 01:31:47,160
+4 باي – 2 باي، ويساوي قد إيش؟ 2 باي.
+
+744
+01:31:47,160 --> 01:31:52,260
+نتيجة التكامل. لا حد هنا stop. المرة
+
+745
+01:31:52,260 --> 01:31:57,280
+الجاية إن شاء الله بنكمل. آخر محاضرة يوم الأربعاء
+
+746
+01:31:57,280 --> 01:32:01,820
+القادم، الأربعاء اللي بعدها بيكون يوم 18
+
+747
+01:32:01,820 --> 01:32:07,040
+ثمانية، والامتحان أظن 25. أنا ماشي
+
+748
+01:32:07,040 --> 01:32:12,400
+يبقى شدوا حيلكم، وركزوا معلوماتكم، ذاكروا أول بأول
+
+749
+01:32:12,400 --> 01:32:15,640
+حتى تستفيدوا إن شاء الله
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/xMNKd8BQ9Wg_postprocess.srt b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/xMNKd8BQ9Wg_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f82410b33f9eee5a7b9f2cbfd9dd9481c02f7f8e
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/xMNKd8BQ9Wg_postprocess.srt
@@ -0,0 +1,2996 @@
+1
+00:00:14,640 --> 00:00:19,860
+بسم الله الرحمن الرحيم لان بنرجع مرة ثانية لل
+
+2
+00:00:19,860 --> 00:00:23,910
+section اللي بدناها في نهاية المحاضرة الماضيةفكرنا
+
+3
+00:00:23,910 --> 00:00:30,690
+العنوان ال extreme values and saddle points طبعا
+
+4
+00:00:30,690 --> 00:00:34,390
+أعطينا تعريف لل local maximum و ال local minimum
+
+5
+00:00:34,390 --> 00:00:38,750
+أو ان شئ تمقوله ال local extrema لكن ال saddle
+
+6
+00:00:38,750 --> 00:00:43,030
+point لم نعطي لها تعريفوعرفنا في حالة ال local
+
+7
+00:00:43,030 --> 00:00:47,550
+maximum النقطة بقول عنها local maximum إذا كانت
+
+8
+00:00:47,550 --> 00:00:51,830
+قيمة الدالة عند هذه النقطة أكبر من أي قيمة في
+
+9
+00:00:51,830 --> 00:00:56,130
+المنطقة المجاورة لهذه النقطة في ال domain تبعها
+
+10
+00:00:56,130 --> 00:01:00,830
+يعني وكذلك بالنسبة لمين لل local منما بكون قيمتها
+
+11
+00:01:00,830 --> 00:01:06,170
+أقلمن جميع قيم الدالة خلال المنطقة المعرفة دي أو
+
+12
+00:01:06,170 --> 00:01:11,310
+على open disk من جزء من ال domain تبع هذه الدالة
+
+13
+00:01:11,310 --> 00:01:15,390
+طبعا التعريف لاحظه المرة الماضية انه في شبه كبير
+
+14
+00:01:15,390 --> 00:01:18,150
+جدا بينه بين تعريف ال local maximum و local
+
+15
+00:01:18,150 --> 00:01:24,070
+minimum for the function ofone variable طيب وصلنا
+
+16
+00:01:24,070 --> 00:01:27,830
+الأن لماين لتعريف ال settle point اللي هي النقطة
+
+17
+00:01:27,830 --> 00:01:34,990
+السارجية التي تقابل نقطة الانقلاب أو نقطة الانعطاف
+
+18
+00:01:34,990 --> 00:01:40,030
+وين في ال calculus ايه او ال functions of one
+
+19
+00:01:40,030 --> 00:01:43,950
+variable التعريف بيقول ايش بيقول ال differentiable
+
+20
+00:01:43,950 --> 00:01:50,360
+function f of x و y has a settle pointيبقى بيكون
+
+21
+00:01:50,360 --> 00:01:55,600
+عندى نقطة سارجية at a critical point a و b عند
+
+22
+00:01:55,600 --> 00:02:01,000
+النقطة الحاجة a و b if in every open disk centered
+
+23
+00:02:01,000 --> 00:02:07,040
+at a و b روحنا على جزء من ال domain النقطة ل a و b
+
+24
+00:02:07,040 --> 00:02:12,300
+أخدنا disk حوالها there are domain points x و y
+
+25
+00:02:12,300 --> 00:02:18,570
+where f of x و y أكبر من ال f of a و bيعني في نقاط
+
+26
+00:02:18,570 --> 00:02:24,730
+في ال domain قيمة الدالة عندها أكبر من قيم الدالة
+
+27
+00:02:24,730 --> 00:02:29,490
+f of a و b أو قيمة الدالة f of a و b و كذلك domain
+
+28
+00:02:29,490 --> 00:02:34,650
+point x و y حيث f of x و y أقل على عكس اللي فوق
+
+29
+00:02:34,650 --> 00:02:41,760
+أقل من f of a و b ال pointالـA والـB والـF of A وB
+
+30
+00:02:41,760 --> 00:02:48,140
+on the surface لأن هذا اسمه point of the surface
+
+31
+00:02:48,140 --> 00:02:53,800
+الان مش هنفهم هذا ال definition تعالوا الى احدى أو
+
+32
+00:02:53,800 --> 00:02:58,660
+بعض ال surfaces اللي مرت علينا دراستها قبل ذلك في
+
+33
+00:02:58,660 --> 00:03:05,480
+هذا المقرر فكان عندنا الشكل لأن هذا الرسم الرقم 6
+
+34
+00:03:05,480 --> 00:03:07,300
+من الرسومات ال 6
+
+35
+00:03:11,110 --> 00:03:17,210
+هذا الشكل اليوم رسمناه يشبه السرج تبع الحصان وزي
+
+36
+00:03:17,210 --> 00:03:21,830
+ما تشوفين فعلا يشبه السرج تبع الحصان الان لو جيت
+
+37
+00:03:21,830 --> 00:03:26,830
+للنقطة اللي عندنا هذه على سبيل المثال يبقى النقطة
+
+38
+00:03:26,830 --> 00:03:31,870
+اللي عندنا هذه زي ما انتوا شايفين لو جيت أخدت نقطة
+
+39
+00:03:31,870 --> 00:03:37,120
+تانية على السطح زي النقطة اللي عندنا هذهطبعا هذه
+
+40
+00:03:37,120 --> 00:03:41,920
+لو جيت أسقطها على القاعدة هنا بيكون F of A وB
+
+41
+00:03:41,920 --> 00:03:46,720
+اليمين النقطة اللي عندنا هذه تمام لو جيتنا النقطة
+
+42
+00:03:46,720 --> 00:03:53,480
+دي قيمة الدالة أكبر من قيمة الدالة عند هذه النقطة
+
+43
+00:03:53,480 --> 00:03:59,830
+تمام طب لو جيت أخد نقطة زي النقطة هذهعلى السطح
+
+44
+00:03:59,830 --> 00:04:03,330
+اللي جهتنا يا بنات أخدتها يبقى قيمة الدالة أنها
+
+45
+00:04:03,330 --> 00:04:09,910
+مالها أقل من هذه النقطة بل هنا كانت Z ب Zero هنا Z
+
+46
+00:04:09,910 --> 00:04:15,170
+بقيمة سالبة وبالتالي الإحداث رقم تلاتة بقيمة سالبة
+
+47
+00:04:15,170 --> 00:04:20,610
+إذا هي عندي نقاطقيمة الدالة عندها بتكون أكبر من
+
+48
+00:04:20,610 --> 00:04:25,810
+قيمة الدالة عند النقطة السرجية وكذلك نقاط أخرى
+
+49
+00:04:25,810 --> 00:04:30,690
+قيمة الدالة عندها أقل من قيمة النقطة السرجية إذا
+
+50
+00:04:30,690 --> 00:04:35,330
+حدث ذلك يبقى بقول النقطة هذه settle point نقطة
+
+51
+00:04:35,330 --> 00:04:41,170
+سرجية إذا يا بنات النقطة هذه اللي هنا بقول settle
+
+52
+00:04:41,170 --> 00:04:48,900
+pointيبقى هذه سدل point اللى هى النقطة سرجى لعامة
+
+53
+00:04:48,900 --> 00:04:55,000
+الانفون فهمنا هذا التعريف ان قيمة الدالة عند اى
+
+54
+00:04:55,000 --> 00:05:01,040
+نقطة في دومينها اكبر من قيمة الدالة اللى هو f of a
+
+55
+00:05:01,040 --> 00:05:05,240
+وb وفي المقابل برضه قيمة عند نقطة اخرى
+
+56
+00:05:13,640 --> 00:05:17,880
+هذه العملية صعبة شوية و نقعد أجيب نقاط و أحسب
+
+57
+00:05:17,880 --> 00:05:24,020
+عددها لذلك بعد قليل هنحط قاعدة من خلالها نحدد ماهي
+
+58
+00:05:24,020 --> 00:05:27,540
+ال local maximum و ماهي ال local minimum و ماهي
+
+59
+00:05:27,540 --> 00:05:34,270
+النقاط السرجيةبس هاذي بروح لمين لاختبار المشتقة
+
+60
+00:05:34,270 --> 00:05:38,410
+الثانية طبعا في الcalculus ايه بجينا نجيب ال local
+
+61
+00:05:38,410 --> 00:05:41,030
+maximum و ال local minimum و ال reflection point
+
+62
+00:05:41,030 --> 00:05:45,730
+برضه بالاختبارين و خاصة الاختبار الثاني وهنا كذلك
+
+63
+00:05:45,970 --> 00:05:49,870
+بالاختبار الثاني إذا مشان نحسب ال settle points
+
+64
+00:05:49,870 --> 00:05:53,450
+عمليا و كذلك ال local maximum و ال local minimum
+
+65
+00:05:53,450 --> 00:05:57,290
+اللي عرفناها المرة الماضية بدنا نيجي نحط القاعدة
+
+66
+00:05:57,290 --> 00:06:03,350
+المستقبل ثانية وبناء عليها نشتغل إذا بدنا نروح نحط
+
+67
+00:06:03,350 --> 00:06:08,330
+عنها هنقول second derivative test
+
+68
+00:06:16,200 --> 00:06:23,960
+test for local
+
+69
+00:06:23,960 --> 00:06:32,720
+extreme values
+
+70
+00:06:48,210 --> 00:07:00,910
+طريقه was that ان ال f of x و y and its first and
+
+71
+00:07:00,910 --> 00:07:15,790
+its first and second partially
+
+72
+00:07:15,790 --> 00:07:16,450
+derivatives
+
+73
+00:07:26,290 --> 00:07:36,610
+partial derivatives are continuous a
+
+74
+00:07:36,610 --> 00:07:44,690
+throw a
+
+75
+00:07:44,690 --> 00:07:45,630
+disc center
+
+76
+00:07:59,480 --> 00:08:08,420
+centred at اللي هو النقطة A وB and
+
+77
+00:08:08,420 --> 00:08:14,080
+that ال
+
+78
+00:08:14,080 --> 00:08:21,500
+Fx عند النقطة A وB يساوي
+
+79
+00:08:21,500 --> 00:08:34,710
+ال Fy عند النقطة A وB يساوي 0ثم امرا واحد ال F has
+
+80
+00:08:34,710 --> 00:08:47,970
+local maximum ال F has local maximum at نقطة A و B
+
+81
+00:08:47,970 --> 00:08:58,000
+F إذا كان ال F XX أكبر من أقل من ال zeroأقل من الـ
+
+82
+00:08:58,000 --> 00:09:11,360
+0 and الـ Fxx مضروب في الـ Fyy ناقص F²xy كله
+
+83
+00:09:11,360 --> 00:09:15,720
+greater than 0 حتى النقطة A وD
+
+84
+00:09:18,950 --> 00:09:25,590
+الـ f has local minimum عند النقطة a و b إذا كان
+
+85
+00:09:25,590 --> 00:09:38,090
+ال fxx greater than zero and ال fxx fyy ناقص f²xy
+
+86
+00:09:38,090 --> 00:09:48,490
+f²xy برضه كان greater than zero عند النقطة a و b
+
+87
+00:09:53,930 --> 00:10:07,250
+فـ has a saddle point نقطة سرجية at النقطة A وB
+
+88
+00:10:07,250 --> 00:10:11,930
+فإذا كان الـ F XX
+
+89
+00:10:18,300 --> 00:10:28,680
+أقل من الـ zero at النقطة A وB النقطة الرابعة
+
+90
+00:10:28,680 --> 00:10:36,080
+والأخيرة من هذا الاختبار تقول The test is
+
+91
+00:10:36,080 --> 00:10:42,420
+inconclusive at
+
+92
+00:10:42,420 --> 00:10:56,230
+A وBعند النقطة A وB إذا كان الـ Fxx Fyy ناقص Fxy²
+
+93
+00:10:56,230 --> 00:11:04,490
+بده يساوي Zero at اللي هو من النقطة A وB
+
+94
+00:11:38,880 --> 00:11:43,580
+بعدين نرجع لهذا الاختبار مرة ثانية نحاول نقرأه
+
+95
+00:11:43,580 --> 00:11:48,300
+كويس نفهم الشيء اللي موجود فيه اقول second
+
+96
+00:11:48,300 --> 00:11:52,920
+derivative test for local extreme value اختبار
+
+97
+00:11:52,920 --> 00:11:58,620
+المشتق ايه الثاني لمعرفة ال local minimum و ال
+
+98
+00:11:58,620 --> 00:12:03,060
+local maximum و الsettled point الان نفترض ان هذا
+
+99
+00:12:03,060 --> 00:12:07,020
+f of x و y and is first and second partial
+
+100
+00:12:07,020 --> 00:12:07,840
+derivative
+
+101
+00:12:18,730 --> 00:12:20,130
+YYYYYYYYYYYYYYYYYYYYY
+
+102
+00:12:37,480 --> 00:12:42,340
+قال لي و كذلك كان ال fx عند ال a و ال b بده يساوي
+
+103
+00:12:42,340 --> 00:12:47,300
+0 و ال fy عند ال a و ال b بده يساوي 0 طب ليش هذا
+
+104
+00:12:47,300 --> 00:12:52,360
+ال condition حطه؟ مش هنضمن ان في عندي critical
+
+105
+00:12:52,360 --> 00:12:56,970
+pointيبقى ال Fx لما نسويها بالزيرو و ال Fy لما
+
+106
+00:12:56,970 --> 00:13:01,870
+نسويها بالزيرو أو لو كانت إحداهما أو كلاهما is
+
+107
+00:13:01,870 --> 00:13:05,590
+undefined عندها نقطة بقول هنا هذه critical points
+
+108
+00:13:05,590 --> 00:13:10,570
+اللي ممكن يكون local maximum أو local minimum
+
+109
+00:13:16,570 --> 00:13:21,250
+النقطة الأولى الـ f has local maximum عند النقطة
+
+110
+00:13:21,250 --> 00:13:25,490
+الأولى إذا كان fxx أقل من الـ zero
+
+111
+00:13:28,870 --> 00:13:34,290
+مقدار المتباين يجب أن يكون أكبر من الـ 0 FXX
+
+112
+00:13:34,290 --> 00:13:42,970
+ضربتها في FYY و نقصتها أو طرحتها من الـ FXY لكل
+
+113
+00:13:42,970 --> 00:13:43,550
+تربيع
+
+114
+00:13:48,120 --> 00:13:54,880
+القيمة هذه قيمة موجبة والقيمة هذه قيمة سالبة يبقى
+
+115
+00:13:54,880 --> 00:13:59,500
+بقول اني local maximum طب local minimum القيمة هذه
+
+116
+00:13:59,500 --> 00:14:04,740
+بتبقى قيمة سأق موجبة اللي فوق سالبة وهذه موجبة لكن
+
+117
+00:14:04,740 --> 00:14:09,220
+القيمة هذه مالها موجبة المحدد او المميز اللي عندنا
+
+118
+00:14:09,220 --> 00:14:14,200
+هذا في كل الأمرين بقيمة موجبة طب مين بدي افرق مع
+
+119
+00:14:14,200 --> 00:14:18,590
+ال local maximum و ال local minimum؟الـ FXX والله
+
+120
+00:14:18,590 --> 00:14:23,630
+إذا كان FXX سالبة يبقى لدي local maximum FXX موجبة
+
+121
+00:14:23,630 --> 00:14:29,710
+يبقى local minimum طب افترض إن المحدد لأن هذا أو
+
+122
+00:14:29,710 --> 00:14:35,970
+المميز هذا كان أقل من ال zero وال FXX إيش ما كانت
+
+123
+00:14:35,970 --> 00:14:40,610
+تكون موجبة سلمة ماتفرقش عني طلع القيمة إيش قيمة
+
+124
+00:14:40,610 --> 00:14:46,730
+سلمة إن حدث ذلكيبقى بقول النقطة الان هنا settle
+
+125
+00:14:46,730 --> 00:14:51,830
+point طب لو كله يسوي zero باختبارنا فشل و بدنا
+
+126
+00:14:51,830 --> 00:14:55,390
+نرجع لمين؟ للاختبار الأول اللي اتكلمنا عليه المرة
+
+127
+00:14:55,390 --> 00:14:58,810
+الماضية اللي هو ال first derivative test for four
+
+128
+00:14:58,810 --> 00:15:03,070
+local extreme values ما علينا مرة ثانية بقول
+
+129
+00:15:03,070 --> 00:15:10,240
+باختصاريبقى يا بنات المشتقة الأولى لدى ال F
+
+130
+00:15:10,240 --> 00:15:15,920
+والمشتقة التانية Fxx بتلعب دور كبير فيه تحديد هل
+
+131
+00:15:15,920 --> 00:15:20,180
+هي ال local maximum أو ال local minimum هذه ال
+
+132
+00:15:20,180 --> 00:15:24,500
+inequality هنا أكبر من ال zero في الحالتين يبقى
+
+133
+00:15:24,500 --> 00:15:27,100
+بدأ فرق من ال local maximum و ال local minimum
+
+134
+00:15:27,100 --> 00:15:32,400
+بتطلع لل Fxx والله إذا كانت أكبر من ال zero يبقى
+
+135
+00:15:32,400 --> 00:15:38,230
+local minimum أقل من ال zero يبقى localأفترض أنها
+
+136
+00:15:38,230 --> 00:15:41,970
+كانت أقل من الـ zero اللي هو اللي انقلت التاني إلى
+
+137
+00:15:41,970 --> 00:15:45,770
+اليمين و ال fxx ايش ما تكون تكون موجة و الله سالبة
+
+138
+00:15:45,770 --> 00:15:49,890
+ما تفرقش عني بهمنها دي إذا و الله طلعت سالبة يبقى
+
+139
+00:15:49,890 --> 00:15:55,450
+يبقى هذي ال settle point يبقى من هنا فرقت ما بين
+
+140
+00:15:55,450 --> 00:15:58,370
+ال settle point و ال local maximum و ال local
+
+141
+00:15:58,370 --> 00:16:00,830
+minimum فرقت ما بين ال local maximum و ال local
+
+142
+00:16:00,830 --> 00:16:06,900
+minimum بقيمة ال fxxفرق بينهم وبين ال settle point
+
+143
+00:16:06,900 --> 00:16:11,540
+بواسطة ال main inequality اللي عندنا طب أطلع النتج
+
+144
+00:16:11,540 --> 00:16:16,560
+هذا يساوي zero يبقى لا أستطيع الحكم على المسألة
+
+145
+00:16:16,560 --> 00:16:21,580
+اللي عندنا عشان نثبت هذه المعلومات ناخد مثال نحسب
+
+146
+00:16:21,580 --> 00:16:25,000
+فيه ال local maximum و ال local minimum و ال
+
+147
+00:16:25,000 --> 00:16:27,700
+settle point طب نقول example
+
+148
+00:16:51,380 --> 00:17:01,720
+local extremum and settled points and settled
+
+149
+00:17:01,720 --> 00:17:11,600
+points of the function لدالة f of x y بده ساوي
+
+150
+00:17:11,600 --> 00:17:21,840
+اللي هو x تكيب زائد y تكيب زائد تلاتة x ترابيعناقص
+
+151
+00:17:21,840 --> 00:17:31,280
+تلاتة وايت ربيع ناقص تماني solution
+
+152
+00:18:05,060 --> 00:18:08,880
+خلّيني أخبركم أني حقا أقول هذه الـ local extreme
+
+153
+00:18:08,880 --> 00:18:12,740
+values اللي عندك وهذه ال settle points للدالة اللي
+
+154
+00:18:12,740 --> 00:18:19,920
+عندنا هذا يبقى بدي أرجع لازم أحسب له FXX, FYY, FXY
+
+155
+00:18:19,920 --> 00:18:23,540
+يبقى هي دول التلاتة اللي هم بيلعبوا الدور الكبير
+
+156
+00:18:23,540 --> 00:18:27,080
+في معرفة ال local extreme أو settle points لميار
+
+157
+00:18:27,080 --> 00:18:32,790
+ال function اللي عندناإذا بدي أبدأ بال Fx يساوي
+
+158
+00:18:32,790 --> 00:18:41,930
+تلاتة X تربيع زائد ستة X والباقي بطيئة بالمرة نحسب
+
+159
+00:18:41,930 --> 00:18:51,770
+Fxx فيساوي نشتغل كمان مرة يبقى ستة X زائد ستة
+
+160
+00:18:51,770 --> 00:18:53,810
+فاهمين كويس؟
+
+161
+00:18:56,480 --> 00:19:01,440
+أنا لم أحصل على نقطة محددة في المثل ، لذلك انا
+
+162
+00:19:01,440 --> 00:19:08,280
+سأخرج النقطة لوحدي النقطة لوحدي من اين؟ من ال Fx
+
+163
+00:19:08,280 --> 00:19:13,960
+يبقى شرطنا هنا انوش يا بنات بديها قدر تساوي؟ تساوي
+
+164
+00:19:13,960 --> 00:19:19,660
+Zero إذا بدي أخد ال Fx بده تساوي Zero وهذا بتعطينا
+
+165
+00:19:20,050 --> 00:19:25,910
+إنه تلاتة X تربيه زائد ستة X بدي ساوي Zero هذا بدي
+
+166
+00:19:25,910 --> 00:19:35,170
+يعطينا ميم انه ستة X و الله كدهش تلاتة تلاتة X بضل
+
+167
+00:19:35,170 --> 00:19:42,180
+عند هنا X زائد اتنين كله بدي ساوي كدهش Zeroإذا
+
+168
+00:19:42,180 --> 00:19:48,840
+بنقل عليه هذا بده يعطينا ان X بدها تساوي 0 و X بده
+
+169
+00:19:48,840 --> 00:20:00,120
+يساوي كده؟ سالي 2 طيب اروح نجيب FY يساوييبقى fy
+
+170
+00:20:00,120 --> 00:20:07,860
+انا بدأت مع السلامة هذه تلاتة وي تربع و هنا ناقص
+
+171
+00:20:07,860 --> 00:20:12,120
+ستة وي و نسويها بالزيرو مشان نجيب ال critical
+
+172
+00:20:12,120 --> 00:20:17,780
+points كلهم مرة واحدة يبقى بناء عليه هذا بدي يعطي
+
+173
+00:20:17,780 --> 00:20:24,910
+نمينا بناء تلاتة ويفي Y ناقص اتنين بده يساوي قداش
+
+174
+00:20:24,910 --> 00:20:30,110
+بده يساوي زيرو يهجر هذا بده يعطينا ميم ان ال Y بده
+
+175
+00:20:30,110 --> 00:20:35,770
+يساوي زيرو وY تساوي ميم اتنين يبقى كام critical
+
+176
+00:20:35,770 --> 00:20:41,290
+point عندي انتين ولا اربعة اربعة اربعة critical
+
+177
+00:20:41,290 --> 00:20:49,170
+points يبقى باجي بقول هنا ده critical points
+
+178
+00:20:52,470 --> 00:21:03,430
+أه Zero و Zero و كذلك Zero و اتنين و نقص اتنين و
+
+179
+00:21:03,430 --> 00:21:11,120
+Zero و نقص اتنين و اتنينإذا بدنا نبحث كل نقطة من
+
+180
+00:21:11,120 --> 00:21:15,840
+هذه النقاط مين منهم settle point مين منهم local
+
+181
+00:21:15,840 --> 00:21:21,540
+maximum مين منهم local minimum لذلك بدنا نروح نجيب
+
+182
+00:21:21,540 --> 00:21:33,060
+من F Y Y إذا بدنا نرجع نجيب هنا F Y Y 7 نشتق هذه
+
+183
+00:21:33,060 --> 00:21:36,220
+كمان مرة إذا 6Y-6
+
+184
+00:21:51,580 --> 00:21:59,680
+يبدأ يتزاوي partial على partial Y لمن؟ لل Fx يبقى
+
+185
+00:21:59,680 --> 00:22:03,840
+partial على partial Y ليه؟ نرجع ل Fx اللي هي تلاتة
+
+186
+00:22:03,840 --> 00:22:09,880
+X تربية زائد ستة X اللي هي تلاتة X تربية زائد ستة
+
+187
+00:22:09,880 --> 00:22:11,860
+X بالمستقبل كده؟
+
+188
+00:22:30,130 --> 00:22:45,700
+النقطة الأولى 0 و 0 فنحسب F X Xعند النقطة 00 بيبقى
+
+189
+00:22:45,700 --> 00:22:50,600
+0 زائد
+
+190
+00:22:50,600 --> 00:22:52,280
+6 و لو بيبقى 6 بيبقى 6
+
+191
+00:23:02,300 --> 00:23:13,180
+يبقى ال FXY يبقى 0 على طول الخط جاهزين نبدأ من هنا
+
+192
+00:23:13,180 --> 00:23:24,060
+نحسب من الانقلة اللي عندنا يبقى بداخله FXX في FYY
+
+193
+00:23:24,060 --> 00:23:32,990
+نقص FXY2Y7 احنا ال FXX عندنا كده يا بنات هناقيمة
+
+194
+00:23:32,990 --> 00:23:37,970
+موجبة مظبوط او لا طيب يبقى انيش نشوف هذا اللي بدي
+
+195
+00:23:37,970 --> 00:23:43,910
+يعطينا يبقى هذا بدي يعطينا ستة و ال FYY عندنا
+
+196
+00:23:43,910 --> 00:23:50,990
+بقدرش اللي هو سالب ستة وهنا ناقص Zero لكل تربيع و
+
+197
+00:23:50,990 --> 00:23:55,570
+يساوي سالب ستة و تلاتين يبقى لين كلتي مالها
+
+198
+00:24:05,820 --> 00:24:13,140
+فبتعود بالنقاط اللي قالنا في المعادلة الأصلية اذا
+
+199
+00:24:13,140 --> 00:24:19,740
+بروح بقول الف زيرو وزيرو هذا سواء ان سالف تمانية
+
+200
+00:24:19,740 --> 00:24:30,160
+خلاصنا يبقى هنا هذا بدي يعطينا ان الف لديه
+
+201
+00:24:31,670 --> 00:24:38,410
+Settle point at
+
+202
+00:24:38,410 --> 00:24:44,530
+two zero و zero ايش السبب يا بنات ان ال link والتي
+
+203
+00:24:44,530 --> 00:24:51,490
+هذه طلعت قيمة سالبة اللي هو نقطة رقم تلاتة عندنا
+
+204
+00:24:51,490 --> 00:24:57,210
+تمام؟ خلصنا النقطة هذه بناروح للنقطة التانية
+
+205
+00:24:57,210 --> 00:24:59,790
+بنااخدها النقطة
+
+206
+00:25:17,970 --> 00:25:25,590
+يبقى برضه ستة و الستة مالها يا بنات أكبر من مين؟
+
+207
+00:25:25,590 --> 00:25:32,330
+أكبر من الزرع يجب أن أحسبله fyy فإن الـ zero و
+
+208
+00:25:32,330 --> 00:25:38,510
+اتنين هي فوق يبقى في قدرات؟ في ستة ولا في سلف ستة؟
+
+209
+00:25:38,510 --> 00:25:43,350
+ستة موجة اه ممتاز جدا هذه ماحطت اتنين ماعنديش X
+
+210
+00:25:43,350 --> 00:25:46,370
+يبقى بصير هنا ستة
+
+211
+00:25:52,350 --> 00:26:01,370
+هو الـ Fxy في أي نقطة كلها بـ 0 على طول القطع فانا
+
+212
+00:26:01,370 --> 00:26:11,550
+باخد الـ Fxx في الـ Fyy نقص Fxy² و يساوي
+
+213
+00:26:25,400 --> 00:26:28,800
+يبقى Fx6 أكبر من الـ Zero Fx6 أكبر من الـ Zero Fx6
+
+214
+00:26:28,800 --> 00:26:30,020
+أكبر من الـ Zero Fx6 أكبر من الـ Zero Fx6 أكبر من
+
+215
+00:26:30,020 --> 00:26:32,780
+الـ Zero Fx6 أكبر من الـ Zero Fx6 أكبر من الـ Zero
+
+216
+00:26:32,780 --> 00:26:40,000
+Fx6 أكبر من الـ Zero Fx6 أكبر من الـ Zero Fx6 أكبر
+
+217
+00:26:40,000 --> 00:26:42,870
+من الـ Zeroالـ F of 0 و 2
+
+218
+00:27:06,710 --> 00:27:13,250
+بنقص تمانية مع السلامة واربع في تلاتة بسالف اتناش
+
+219
+00:27:13,250 --> 00:27:21,310
+يبقى سالف اتناش فاروح بقول الفيه has local minimum
+
+220
+00:27:21,310 --> 00:27:29,210
+اللي هي سالف اتناش at the point عند النقطة اللي هو
+
+221
+00:27:29,210 --> 00:27:33,630
+main اللي موجودة في domainها اللي هي main zero و
+
+222
+00:27:33,630 --> 00:27:38,910
+اتنانخلصنا النقطة التانية بنروح لمين للنقطة
+
+223
+00:27:38,910 --> 00:27:46,490
+التالتة يبقى بالداخل ناخد ال point النقطة
+
+224
+00:27:46,490 --> 00:27:54,070
+التالتة اللي هو سالب اتنين و زيب سالب اتنين و زيب
+
+225
+00:27:54,070 --> 00:28:04,050
+طيب يبقى بدنا نجي نعود في mean في المعادلة الأصلية
+
+226
+00:28:04,050 --> 00:28:04,670
+و نحسب
+
+227
+00:28:08,080 --> 00:28:12,720
+يبقى مثل ما بدأنا بالضبط تماما في الأول بدي أخد
+
+228
+00:28:12,720 --> 00:28:19,820
+fxx عند النقطة سالب اتنين و زيه إذا بدي أشيل كل x
+
+229
+00:28:19,820 --> 00:28:27,480
+و أحط مكانها سالب في اتنين يبقى ستة في سالب اتنين
+
+230
+00:28:27,480 --> 00:28:32,760
+زي ستة و يسوي سالب ستة و زي ما انتوا شايفين مالها
+
+231
+00:28:33,590 --> 00:28:41,970
+أقل من زيرو كمية سالك يبقى مضاجي اخد كمان ال F Y Y
+
+232
+00:28:41,970 --> 00:28:47,930
+اللي هو عند النقطة اللي هو سالب اتنين وزيرو يساوي
+
+233
+00:28:47,930 --> 00:28:54,850
+F Y Y فوق اللي هو عبارة عن زيرو سالب ستة ويساوي
+
+234
+00:28:54,850 --> 00:29:01,970
+سالب ستة و ال F X Y هذه ثابتة ما هيبت زيرو للكل
+
+235
+00:29:02,650 --> 00:29:04,870
+يبقى بتروح اخد F
+
+236
+00:29:31,790 --> 00:29:40,090
+XX أقل من الـ Zero أقل من ال Zero وهذه أكبر من 100
+
+237
+00:29:40,090 --> 00:29:44,170
+من ال Zero في ال Calculus Maximum إذا بدنا نروح
+
+238
+00:29:44,170 --> 00:29:52,810
+نحسب كده ال F أو نقص 2 و Zero في الجسم بدنا نشيل
+
+239
+00:29:52,810 --> 00:29:57,930
+كل Y و نحط مكانها Zero و نشيل كل X و نحط مكانها
+
+240
+00:29:57,930 --> 00:29:58,090
+Zero
+
+241
+00:30:07,580 --> 00:30:15,640
+الكل تان ربيع وهنا ناقص Zero ناقص تمانية وهي ستة
+
+242
+00:30:15,640 --> 00:30:22,860
+طبعا هنا ناقص تمانية وهنا ناقص تمانية تصير ناقص
+
+243
+00:30:22,860 --> 00:30:30,820
+ستة عشر وهنا اتناش بضل قداش ناقص اربع اذا بروح
+
+244
+00:30:30,820 --> 00:30:39,690
+بقول له if has local maximumاللي هو قداش؟ سالف
+
+245
+00:30:39,690 --> 00:30:45,050
+أربع at the
+
+246
+00:30:45,050 --> 00:30:53,350
+point عند النقطة اللي هو سالف اتنين وزي اذا طلعت
+
+247
+00:30:53,350 --> 00:30:56,770
+واحدة سادي ال point واحدة local maximum واحدة
+
+248
+00:30:56,770 --> 00:31:01,850
+local minimum بقيت ال نقطة الأخيرة
+
+249
+00:31:28,870 --> 00:31:35,130
+يبقى النقطة الأخيرة يا بناتي اللي هي point كده؟
+
+250
+00:31:35,130 --> 00:31:42,350
+سالب اتنين و اتنين بدنا نروح نحسب اللي هو الف اكس
+
+251
+00:31:42,350 --> 00:31:48,750
+اكس عند النقطة سالب اتنين و اتنين وقت السابق وين
+
+252
+00:31:48,750 --> 00:31:52,990
+الف اكس اكس؟ مسحناها يعني كان ستة اكس زي ستة،
+
+253
+00:31:52,990 --> 00:32:02,870
+مظبوط؟ يبقى ستةفى ناقص اتنين ذائد ستة ويسوي كده؟
+
+254
+00:32:02,870 --> 00:32:13,650
+ناقص ستة لما لها اقل من ال zero فبنحسب FYY FYY عند
+
+255
+00:32:13,650 --> 00:32:20,190
+النقطة ناقص اتنين و اتنين و ال FYY هيقول يبقى هنا
+
+256
+00:32:20,190 --> 00:32:29,850
+ستةفى اتنين ناقص ستة ويسوي كدهش ستة ومعروف ال Fxy
+
+257
+00:32:29,850 --> 00:32:34,350
+عند اى نقطة كلها تساوي Zero على طول الخط
+
+258
+00:32:53,910 --> 00:33:00,430
+اللي فوق بتهمنيش سالبة ولا موجبة يبقى النقطة هذه
+
+259
+00:33:00,430 --> 00:33:01,630
+تعتبر مين
+
+260
+00:33:31,710 --> 00:33:38,970
+نقص تمانية نقص تمانيةيبقى هذا الكلام لو جيت فاكتهم
+
+261
+00:33:38,970 --> 00:33:45,110
+بصير ناقص تمانية و هنا زائد تمانية و هنا زائد
+
+262
+00:33:45,110 --> 00:33:51,870
+اتناشر و هنا ناقص اتناشر و هنا ناقص تمانية هذه و
+
+263
+00:33:51,870 --> 00:33:56,130
+هذه مع بعض و هذه و هذه مع السلامة يبقى الجواب
+
+264
+00:33:56,130 --> 00:34:04,030
+قداشر سالب تمانية يبقى ال F has saddle point
+
+265
+00:34:24,820 --> 00:34:28,840
+الأشياء اللي ليس بالضرورة ممكن تكون كل القيم موجبة
+
+266
+00:34:29,360 --> 00:34:35,260
+النسبة للمسألة اللى عندك يعني احنا بدل سالب تمانية
+
+267
+00:34:35,260 --> 00:34:40,180
+في المسألة لو حطينا زائد تمانية هيجيكي أحيانا صفر
+
+268
+00:34:40,180 --> 00:34:45,300
+و أحيانا رقم مش هتلاقي ولا رقم سالب صحيح ولا لا؟
+
+269
+00:34:47,800 --> 00:34:54,140
+لكن هناك موقع آخر و ليس في نفس الموقع يعني نقطة
+
+270
+00:34:54,140 --> 00:34:57,560
+اتغيرت مش نفس النقطة وبالتالي انتقلنا مثلا عند
+
+271
+00:34:57,560 --> 00:35:00,560
+النقطة هذه في local maximum عند النقطة هذه في
+
+272
+00:35:00,560 --> 00:35:03,340
+settle point عند النقطة هذه في settle point عند
+
+273
+00:35:03,340 --> 00:35:07,330
+النقطة تالتة في local minimum و هكذايعني طالع و
+
+274
+00:35:07,330 --> 00:35:11,450
+نازل الرسمة طبعا لا يمكن نقل نقص من الرسمة لأنه
+
+275
+00:35:11,450 --> 00:35:15,470
+رسم كمبيوتر تمام كل الرسمة اللي بتشوفها في الكتاب
+
+276
+00:35:15,470 --> 00:35:22,690
+رسمت كمبيوتر وبالتالي بتلاقي مجسمات أينها حد بتسأل
+
+277
+00:35:22,690 --> 00:35:28,870
+أي سؤال هنا كمان خلاص طيب فالان بننتقل إلى النقطة
+
+278
+00:35:28,870 --> 00:35:31,930
+الثانية من هذا ال section وهي
+
+279
+00:35:37,450 --> 00:35:43,430
+وخاصة الامتحانات النهائية اللي هو بنجيبها بنات ال
+
+280
+00:35:43,430 --> 00:35:49,210
+absolute maximum و ال absolute minimum لل function
+
+281
+00:35:49,210 --> 00:35:53,470
+نفس تعريف ال absolute maximum و ال absolute
+
+282
+00:35:53,470 --> 00:35:58,770
+minimum في حالة ال function of one variable اللي
+
+283
+00:35:58,770 --> 00:36:03,430
+درسناه في Calculus A قبل ذلك
+
+284
+00:36:42,650 --> 00:36:46,490
+على منطقة مغلفة ومحدودة
+
+285
+00:36:59,820 --> 00:37:14,020
+maximum او absolute minimum او absolute minimum او
+
+286
+00:37:14,020 --> 00:37:16,080
+absolute minimum او absolute minimum او absolute
+
+287
+00:37:16,080 --> 00:37:16,400
+minimum او absolute minimum او absolute minimum او
+
+288
+00:37:16,400 --> 00:37:16,740
+absolute minimum او absolute minimum او absolute
+
+289
+00:37:16,740 --> 00:37:16,960
+minimum او absolute minimum او absolute minimum او
+
+290
+00:37:16,960 --> 00:37:17,020
+absolute minimum او absolute minimum او absolute
+
+291
+00:37:17,020 --> 00:37:17,060
+minimum او absolute minimum او absolute minimum او
+
+292
+00:37:17,060 --> 00:37:23,160
+absolute minimum او absolute minimum
+
+293
+00:37:23,160 --> 00:37:28,140
+او absolute minimum
+
+294
+00:37:39,160 --> 00:37:48,600
+النقطة الداخلية للمنطقة R where
+
+295
+00:37:48,600 --> 00:37:54,560
+ال F may
+
+296
+00:37:54,560 --> 00:38:00,760
+have may have local maximum
+
+297
+00:38:03,860 --> 00:38:14,260
+local maximum or local minimum or local
+
+298
+00:38:14,260 --> 00:38:19,320
+minima and evaluate the function's value and
+
+299
+00:38:19,320 --> 00:38:31,930
+evaluate the function's value قيمة الدالةat this
+
+300
+00:38:31,930 --> 00:38:42,690
+point at this point عند هذه النقاط these
+
+301
+00:38:42,690 --> 00:38:46,210
+are
+
+302
+00:38:46,210 --> 00:38:51,990
+the points هذه
+
+303
+00:38:51,990 --> 00:39:02,970
+النقاط where ال fx يتساوي ال fy يتساوي ال zeroor
+
+304
+00:39:02,970 --> 00:39:09,270
+where
+
+305
+00:39:09,270 --> 00:39:22,330
+one or both of Fx
+
+306
+00:39:22,330 --> 00:39:27,850
+and Fy fail to exist
+
+307
+00:39:32,840 --> 00:39:43,220
+بعد ذلك هذه المقاومة الموجودة في
+
+308
+00:39:43,220 --> 00:39:47,440
+المقاومة هذه المقاومة
+
+309
+00:39:47,440 --> 00:39:53,100
+الموجودة في المقاومة الموجودة في المقاومة R اذا
+
+310
+00:39:53,100 --> 00:39:58,720
+F كان
+
+311
+00:39:58,720 --> 00:40:02,240
+لديه مقاومة
+
+312
+00:40:04,690 --> 00:40:20,110
+maximum هو local minimum and find the
+
+313
+00:40:20,110 --> 00:40:27,130
+function value
+
+314
+00:40:27,130 --> 00:40:38,870
+قيمة الدولةat these points
+
+315
+00:40:38,870 --> 00:40:50,450
+عند هذه اللحظة ثلاثة لـ maximum and
+
+316
+00:40:50,450 --> 00:40:55,390
+minimum ماليوز
+
+317
+00:41:02,670 --> 00:41:09,410
+او اذا انطقت
+
+318
+00:41:09,410 --> 00:41:17,990
+سيكون الـ Absolute سيكون الـ Absolute
+
+319
+00:41:17,990 --> 00:41:21,390
+maximum
+
+320
+00:41:21,390 --> 00:41:24,530
+و
+
+321
+00:41:24,530 --> 00:41:30,230
+Absolute minimum
+
+322
+00:41:31,830 --> 00:41:44,650
+respectively examples
+
+323
+00:41:44,650 --> 00:41:50,410
+اتحول
+
+324
+00:41:50,410 --> 00:41:59,770
+لثالث by the absolute maximum by the absolute
+
+325
+00:42:02,720 --> 00:42:11,240
+maximum and minimum of
+
+326
+00:42:11,240 --> 00:42:16,600
+the function لدى
+
+327
+00:42:16,600 --> 00:42:22,780
+f of x و y بساوية
+
+328
+00:42:25,610 --> 00:42:37,390
+معقس XY زائد Y تربيع زائد واحد on the closed
+
+329
+00:42:37,390 --> 00:42:49,310
+triangle closed triangle plate in
+
+330
+00:42:49,310 --> 00:42:50,130
+the first
+
+331
+00:42:54,840 --> 00:43:03,940
+الـ first quadrant او
+
+332
+00:43:03,940 --> 00:43:13,060
+البيان العين او
+
+333
+00:43:13,060 --> 00:43:22,220
+البيان العين X تساوي Zero وY تساوي أربعة and
+
+334
+00:43:24,440 --> 00:43:26,740
+Y مستوى S
+
+335
+00:44:28,050 --> 00:44:32,050
+نرجع الكلام اللي كتبناه على اللوح تاني نقرأ كل
+
+336
+00:44:32,050 --> 00:44:37,150
+نقطة ي و كل حيثية لك نفهم شو اللي مطلوب منه و بعد
+
+337
+00:44:37,150 --> 00:44:43,190
+ذلك بنروح نحل المثال تبعه بيقول لي ده نجل ال
+
+338
+00:44:43,190 --> 00:44:46,030
+absolute maximum و ال absolute minimum اللي يدال
+
+339
+00:44:46,030 --> 00:44:51,530
+على ال domain تبعها بيات ال domain كمنطقة محدودة و
+
+340
+00:44:51,530 --> 00:44:57,710
+كذلك منطقة محدودةطبعا بعد قليل هقولك ليش منطقة
+
+341
+00:44:57,710 --> 00:45:02,990
+مغلقة و ليش منطقة محدودة بقول to find the absolute
+
+342
+00:45:02,990 --> 00:45:06,750
+maximum او absolute minimum make the following
+
+343
+00:45:06,750 --> 00:45:12,250
+steps بدنا نعمل خطوات أتانية الخطوة الأولى بقول
+
+344
+00:45:12,250 --> 00:45:15,410
+less than internal constantly قائمة بالنقاط
+
+345
+00:45:15,410 --> 00:45:21,330
+الداخلية ل region R بحيث الدالة Fممكن تاخد local
+
+346
+00:45:21,330 --> 00:45:26,070
+maximum او local minimum على هذه المنطقة و احسبلي
+
+347
+00:45:26,070 --> 00:45:30,290
+قيمتي الدالة عند main، عند هذه النقاط، يبقى انوش
+
+348
+00:45:30,290 --> 00:45:37,130
+بيقولي اتلي كل نقاط الحريجة على المنطقة المعطالة،
+
+349
+00:45:37,130 --> 00:45:41,230
+بدناياهم هدولوعندي النقاط اللي حاليا بدي أحسب مين
+
+350
+00:45:41,230 --> 00:45:46,530
+القيم تبعت هذه الدالة و أقولهم اطيعوا شوية بس نكمل
+
+351
+00:45:46,530 --> 00:45:51,810
+باقى الشغل و بعد هيك بنروح لمين؟ List the boundary
+
+352
+00:45:51,810 --> 00:45:56,270
+points يبقى أول شغلة جيبنا ال internal points يبقى
+
+353
+00:45:56,270 --> 00:46:02,930
+احنا داخل ال open region يبقى مضل عندنا ال
+
+354
+00:46:02,930 --> 00:46:07,170
+boundary اللي على الحدوديبقى بدنا نجيب less كمان
+
+355
+00:46:07,170 --> 00:46:12,010
+بال boundary region للدالة F اللى عندها ممكن تاخد
+
+356
+00:46:12,010 --> 00:46:16,570
+local maximum و local minimum و نحصل قيم الدالة
+
+357
+00:46:16,570 --> 00:46:21,670
+عندنا هذا إذا صرت عندى الحمد لله قيم كتيرة قيم تبع
+
+358
+00:46:21,670 --> 00:46:24,470
+ال interior points و قيم تبع ال boundary points
+
+359
+00:46:24,470 --> 00:46:29,570
+باجي في الآخر خطوة تالتة و الأخيرةبطلع أكبر قيمة
+
+360
+00:46:29,570 --> 00:46:33,310
+بقول هذه ال absolute maximum و أقل قيمة بقول main
+
+361
+00:46:33,310 --> 00:46:36,710
+هذه ال absolute minimum مكافئة الله بالسرعليمة
+
+362
+00:46:36,710 --> 00:46:41,010
+يبقى هذا باختصار اللي بدنا نعمله يبقى أول حاجة بده
+
+363
+00:46:41,010 --> 00:46:45,470
+أحسب ال internal points اللي الدالة ممكن تاخد
+
+364
+00:46:45,470 --> 00:46:50,500
+عندها local maximum أو local minimum بعد هيكبدي
+
+365
+00:46:50,500 --> 00:46:53,300
+اجي الى ال boundary points اللي ممكن الذالة تكون
+
+366
+00:46:53,300 --> 00:46:56,840
+عندها local maximum و local minimum عند هذه النقاط
+
+367
+00:46:56,840 --> 00:46:59,900
+في حالة ال intro هو ال boundary بدي احسب قداش
+
+368
+00:46:59,900 --> 00:47:04,660
+القيم المختلفة لهذه الذالة بعدين بدي اقارن بين هذه
+
+369
+00:47:04,660 --> 00:47:08,940
+القيمة القيم اللي عندها اكبر قيمة بقول هي absolute
+
+370
+00:47:08,940 --> 00:47:13,700
+maximum واقل قيمة بقول هي main absolute minimum
+
+371
+00:47:13,700 --> 00:47:19,700
+لهذه الذالة اعظم موضوع احتلاليحد بتسأل اي سؤال قبل
+
+372
+00:47:19,700 --> 00:47:27,820
+ان نبدأ ان يكان؟ في اي تساؤل؟ طيب انا بنسأل،
+
+373
+00:47:27,820 --> 00:47:32,140
+مظبوط؟ ليش قاللي المنطقة بدأ تبقى closed، ماكان
+
+374
+00:47:32,140 --> 00:47:33,580
+قاللي open و رايحني؟
+
+375
+00:47:36,870 --> 00:47:42,270
+لا ممكن يكون، بس ايش؟ بصير اللي على الحدود هذه
+
+376
+00:47:42,270 --> 00:47:45,990
+البابرة بصير مغرب ليش علاقة فيها، يبقى كأنه لغيت
+
+377
+00:47:45,990 --> 00:47:51,050
+مين، لغيت الخطوة هذهتمام و احنا دلوقت راجعنا ل
+
+378
+00:47:51,050 --> 00:47:55,550
+Calculus ايه بجينا ممكن يكون في absolute في
+
+379
+00:47:55,550 --> 00:47:59,750
+maximum او minimum على مين على ال interval المعرف
+
+380
+00:47:59,750 --> 00:48:03,210
+عليها تالع عند اول interval او نهاية ال interval
+
+381
+00:48:03,210 --> 00:48:07,630
+هو بالتالع ممكن يكون عند ال boundary points عندنا
+
+382
+00:48:07,630 --> 00:48:12,170
+يكون في عند local maximum او local minimum ومن هنا
+
+383
+00:48:12,170 --> 00:48:16,820
+اشتغلنا المنطقة بدون get lost regionيعني ال
+
+384
+00:48:16,820 --> 00:48:20,800
+boundary بدهم يدخلوا في الأحساب عندك و هات الصورة
+
+385
+00:48:20,800 --> 00:48:26,960
+طيب نجي نسأل سؤالها وقول هات ال absolute maximum و
+
+386
+00:48:26,960 --> 00:48:31,420
+ال absolute من و لمين لدلة لإنها دي و أعطاني دلة و
+
+387
+00:48:31,420 --> 00:48:34,380
+أعطاني closed in triangle plate
+
+388
+00:48:40,880 --> 00:48:45,900
+يبقى لما أقول عند هنا على ال close triangle plate
+
+389
+00:48:45,900 --> 00:48:51,580
+يعني مثلث مصمد زي ما نقول قرص في حالة الدائرة يبقى
+
+390
+00:48:51,580 --> 00:48:56,960
+هنا بقول close triangle plate مثلث مصمد يعني كل
+
+391
+00:48:56,960 --> 00:49:04,720
+نقاط المثلثمالها هي نقاط ك domain للدل اللي عندنا
+
+392
+00:49:04,720 --> 00:49:09,440
+تمام مش بس على المحيط و بس على المحيط و داخل
+
+393
+00:49:09,440 --> 00:49:13,260
+المدلات هاي المقصود فيه هنا يبقى on a closed
+
+394
+00:49:13,260 --> 00:49:16,960
+triangular plane in the first quadrant في الرابع
+
+395
+00:49:16,960 --> 00:49:22,520
+الأول و المحدود بالثلاثة فطوط اللي قدامنا X تساوي
+
+396
+00:49:26,490 --> 00:49:32,670
+محور y هو y تساوي 4 موازي لمحور x هو y تساوي x
+
+397
+00:49:32,670 --> 00:49:37,990
+الخط المنصف للربع الأول والربع الثالث لكن احنا كنا
+
+398
+00:49:37,990 --> 00:49:41,830
+في الربع الأول يبقى مالنا علاقة بمين بالربع التالت
+
+399
+00:49:41,830 --> 00:49:47,610
+يريد كبل نبدأ خلينا نرسم المنطقة تبعتنا طب المنطقة
+
+400
+00:49:47,610 --> 00:49:54,760
+بنات هذه هي domain الدالة والدالة نفسهاdomain
+
+401
+00:49:54,760 --> 00:49:59,000
+الدالة يعني الدالة بتبقى كأنه surface فاض
+
+402
+00:49:59,000 --> 00:50:03,620
+وعالمستوى XY plane المثلثة اللي احنا رسمناها هذا
+
+403
+00:50:03,620 --> 00:50:07,620
+جزء من domain الدالة احنا بنحسب على هذا الجزء من
+
+404
+00:50:07,620 --> 00:50:10,820
+ال domain اللي هو local maximum و local absolute
+
+405
+00:50:10,820 --> 00:50:16,740
+maximum و absolute minimum بسيطة لذا لو روحنا
+
+406
+00:50:16,740 --> 00:50:22,560
+رسمنا روح ناخد المحاور اللي عندنا هذا محور X وهذا
+
+407
+00:50:22,560 --> 00:50:29,860
+اللي عندنا مالهاللي هو محور Y يبقى هذا اللي هو
+
+408
+00:50:29,860 --> 00:50:36,420
+محور Y لأنه هذه نقطة الاصل قال
+
+409
+00:50:36,420 --> 00:50:41,920
+لي الخط الأول هو X تساوي 0 اتفاجنا اللي هو محور Y
+
+410
+00:50:41,920 --> 00:50:48,960
+الخط التاني Y تساوي 4 وY تساوي 4 خط موازي لمحور X
+
+411
+00:50:48,960 --> 00:50:55,460
+بالشكل ان هذا يبقى هذا Y تساوي 4الخط التالت هو Y
+
+412
+00:50:55,460 --> 00:51:02,480
+تساوي X اللى بنصف الربع تماما بهذا الشكل يبقى هذا
+
+413
+00:51:02,480 --> 00:51:08,800
+الخط اللى هو Y تساوي X بدءا عليه أصبحت إحداثيات
+
+414
+00:51:08,800 --> 00:51:15,740
+النقطة هذه معلومة لـ 0 0 و النقطة هذه كده شبنات؟ 0
+
+415
+00:51:15,740 --> 00:51:23,530
+و 4 طب النقطة هذه كدهش؟أربعة وأربعة لإن Y تساوي X
+
+416
+00:51:23,530 --> 00:51:31,890
+فY هيها و X هيها يبقى هذا النقطة أربعة وكذلك أربعة
+
+417
+00:51:31,890 --> 00:51:39,750
+يبقى هذه المنطقة اللي تعتبر Domain الدالة طيب إذا
+
+418
+00:51:39,750 --> 00:51:43,710
+احنا بدنا نمشي حسب ما احنا كاتبين نروح واخد Domain
+
+419
+00:52:03,420 --> 00:52:11,560
+النقطة الأولى للـ interior points النقطة
+
+420
+00:52:11,560 --> 00:52:17,400
+الداخليةيقول ان انترال فورس بتجيبهم لما تجيب
+
+421
+00:52:17,400 --> 00:52:21,560
+المشتقة بالنسبة ل X مستويها بالزيرو و تجيب المشتقة
+
+422
+00:52:21,560 --> 00:52:25,920
+بالنسبة ل Y مستويها بالزيرو بمجرد ما بسيطة احنا
+
+423
+00:52:25,920 --> 00:52:32,540
+عندنا ان ال F of XY بده يساوي اللي هي امين X تربيع
+
+424
+00:52:32,540 --> 00:52:38,620
+ناقص XY زائد Y تربيع زائد واحد
+
+425
+00:52:44,450 --> 00:52:58,570
+2x-y ونسويها بالزيرو ونجيب له fy نشتقها كمان ناقص
+
+426
+00:52:58,570 --> 00:53:03,950
+x زائد 2y ونسوي بالزيرو
+
+427
+00:53:06,860 --> 00:53:12,580
+بدي أجيب النقاط الحرجة لهذه الدلالة في السؤال اللي
+
+428
+00:53:12,580 --> 00:53:17,120
+قبل شوية بنات طلعت المشتقة الأولى كلها بدلالة X
+
+429
+00:53:17,120 --> 00:53:21,500
+وطلعت المشتقة التانية كلها بدلالة Y مظبوط مثال
+
+430
+00:53:21,500 --> 00:53:24,580
+اللي قبل قليل لكن هذا لأ طلعت المشتقة الأولى
+
+431
+00:53:24,580 --> 00:53:27,860
+بدلالة X وY والمشتقة الأولى في الحالة التانية
+
+432
+00:53:27,860 --> 00:53:33,280
+بدلالة X وY بروح بحل المعادلتين مع بعض و بطلع قيمة
+
+433
+00:53:33,280 --> 00:53:36,400
+X وY بجي بقولك وايد
+
+434
+00:53:41,020 --> 00:53:45,380
+المعادلة الأولى في اتنين لو ضربنا اتنين ايش بيصير
+
+435
+00:53:45,380 --> 00:53:50,140
+عندى اربعة اكس ناقص اتنين Y بيكونوا سوى Zero
+
+436
+00:53:50,140 --> 00:53:56,630
+المعادلة التانية ناقص X زائد اتنين Y تسوى Zeroأيه
+
+437
+00:53:56,630 --> 00:54:01,030
+يا جماعة لو جميعنا بروح قعدل مع بعض بظل أهدي قداش
+
+438
+00:54:01,030 --> 00:54:06,610
+تلاتة X يساوي Zero هذا بدي يعطيلك ان X يساوي قداش
+
+439
+00:54:06,610 --> 00:54:12,790
+Zero لو X ساوي Zero يبقى Y قداش Zero يبقى هذا بدي
+
+440
+00:54:12,790 --> 00:54:19,690
+يعطيك ان Y يساوي Zero يبقى هذا بدي يعطيك ان Zero
+
+441
+00:54:19,690 --> 00:54:24,650
+Zero is a critical point
+
+442
+00:54:27,980 --> 00:54:33,160
+السؤال هو إيش رأيك في النقطة هذه interior ولا
+
+443
+00:54:33,160 --> 00:54:38,620
+boundary الحمد لله طالما ماعنديش ولا interior
+
+444
+00:54:38,620 --> 00:54:44,420
+point يبقى المدام حسبتها إذا خليني أجيب قيمة
+
+445
+00:54:44,420 --> 00:54:51,100
+الدالة عندها إذا يا بنات بتروح أجيب ال F on 00
+
+446
+00:54:51,100 --> 00:54:57,020
+يبقى هذا الكلام بده يسوي بده يفوت تسوي قداش واحد
+
+447
+00:54:57,540 --> 00:55:03,520
+يبقى بنوزيها وروح نخليها لإن لنا إليها عودة بعد
+
+448
+00:55:03,520 --> 00:55:08,340
+قليل ان شاء الله تعالى يبقى خلاصنا النقطة الأولى
+
+449
+00:55:08,340 --> 00:55:11,280
+اللى هو ال interior points و جينا نحسب ال interior
+
+450
+00:55:11,280 --> 00:55:15,300
+طولها فعنا main boundary يبقى ماعناش مشكلة يبقى
+
+451
+00:55:15,300 --> 00:55:18,380
+عندنا أحسبهم ال boundary بروحش أحسبها تانية مرة
+
+452
+00:55:18,380 --> 00:55:22,440
+تانية لو حسبناها خلاصهم يبقى بداني على main ال
+
+453
+00:55:22,440 --> 00:55:23,740
+boundary points
+
+454
+00:55:34,380 --> 00:55:40,360
+أنا بتمشي على الحدود الإقليمية يبقى بروح أسمي
+
+455
+00:55:40,360 --> 00:55:45,580
+المثلث بالروح السابعة بدي أقول هذه مثلا النقطة A
+
+456
+00:55:45,580 --> 00:55:54,420
+وهذه النقطة B وهذه النقطة C و بدي أبدأه هنا بدي
+
+457
+00:55:54,420 --> 00:56:01,600
+أقول on the line على الخط A B
+
+458
+00:56:05,720 --> 00:56:14,220
+على الخط AB كم مقدار X؟ Zero يبقى هنا ال X بدها
+
+459
+00:56:14,220 --> 00:56:23,060
+ساوي Zero هذا بده يعطيك ان ال F هو Zero Yيعني انا
+
+460
+00:56:23,060 --> 00:56:27,420
+هشيل كل X و احط مكانها Zero ثم بقول ماذا يجب ان
+
+461
+00:56:27,420 --> 00:56:32,100
+يسوي هاي الدالة فوق Zero بصير عن اليمين بيبقى طبعا
+
+462
+00:56:32,100 --> 00:56:38,260
+Zero لان عندي Y تربيع زائد واحد و ال Y هتتغير من
+
+463
+00:56:38,260 --> 00:56:44,750
+وين وين لبناء من صفر لغاية أربعة ممتاز جدايبقى من
+
+464
+00:56:44,750 --> 00:56:52,570
+0 لغاية 4 سؤال هو هل هذه صارت دالة في متغيرين ولا
+
+465
+00:56:52,570 --> 00:56:57,770
+متغير واحد؟ متغير واحد يبقى بروح بقوله بدي أجيب له
+
+466
+00:56:57,770 --> 00:57:05,910
+ال F primeيعني كأنه بده يجيب ال point على الخط على
+
+467
+00:57:05,910 --> 00:57:11,270
+ال interval من 0 ل 4 يبقى هذا الكلام دي ساوي كده؟
+
+468
+00:57:11,270 --> 00:57:19,070
+اتنين واحد و ساوي مين؟ يبقى هذا بدي اعطيك ان واحد
+
+469
+00:57:19,070 --> 00:57:20,290
+ساوي زيت
+
+470
+00:57:22,940 --> 00:57:31,380
+تمام طيب لما ال y تساوي zero إذا إذا لو عوضت هنا
+
+471
+00:57:31,380 --> 00:57:35,820
+بصير قيمة الدالة عندك كده واحد يعني تطلع النقطة
+
+472
+00:57:35,820 --> 00:57:41,120
+اللي عندها هذه الأصلية كما كانت تمام يبقى هذا بدي
+
+473
+00:57:41,120 --> 00:57:46,980
+يعطيك نفس النقطة الأصلية وبالتالي بنحسب f of zero
+
+474
+00:57:46,980 --> 00:57:54,390
+و zero يبقى هذا بدي يعطيكالـ F of 00 هي الواحد
+
+475
+00:57:54,390 --> 00:57:59,410
+اللي حصل عليها مالها قبل قليل يبقى لم نأتي بمين
+
+476
+00:57:59,410 --> 00:58:07,230
+بأي جديد عندنا تمام طيب لازلنا مع ال line AB اللي
+
+477
+00:58:07,230 --> 00:58:13,500
+عندنا هذا وبالتاليبدي احسب اخر ال line يعني
+
+478
+00:58:13,500 --> 00:58:18,520
+ملاقيتش نقطة داخل ال line ولا نقطة اجيت عند ال 00
+
+479
+00:58:18,520 --> 00:58:26,880
+مضلش عند ال main نقطة 04 يبقى بروح بحسبله F of 04
+
+480
+00:58:26,880 --> 00:58:32,140
+يبقى هذا الكلام مضي السبب ارجع للدلة اللى فوق و
+
+481
+00:58:32,140 --> 00:58:38,050
+الله هيها عندي جازة و مبسطة موجودة هييبقى ماجي
+
+482
+00:58:38,050 --> 00:58:43,870
+بيقوله هذه بدت سوى أربعة تربيه زائد واحد يسوى قداش
+
+483
+00:58:43,870 --> 00:58:51,170
+سبعتاش هاي بروزناها وسنرجع لها بعد قليل بعد هيك
+
+484
+00:58:51,170 --> 00:59:00,290
+بدت أجي أقوله on the line بي سي على ال بي سي وايف
+
+485
+00:59:00,290 --> 00:59:10,550
+قداش أربع تمام كويس يبقى هناالـ Y تساوي 4 معناته
+
+486
+00:59:10,550 --> 00:59:17,370
+هذه بدها تصير F of X و 4 Y ساوية يبقى بدنا نرجع
+
+487
+00:59:17,370 --> 00:59:24,990
+للدالة اللي عندنا هنا بتضالها X تربيع ناقص 4X زائد
+
+488
+00:59:24,990 --> 00:59:34,870
+16 زائد 1 يبقى صارت منها تدالة F of X و 4 اللي
+
+489
+00:59:34,870 --> 00:59:43,220
+تساوي مين؟x تربيع نقص اربعة x زائد سبعة عشر بدا
+
+490
+00:59:43,220 --> 00:59:48,820
+اشوف على هذا الخط في عندى نقاط داخلية ولا لا يمكنش
+
+491
+00:59:48,820 --> 01:00:00,220
+بعمل اشتق ف prime of x واربعة y سبعة اتنين x ناقص
+
+492
+01:00:00,220 --> 01:00:05,720
+اربعة و سوى بمين يا بنات بال zero لما سوى بال zero
+
+493
+01:00:05,980 --> 01:00:11,340
+بدي أطلع عندى 2X بدي أسوأ الاربعة يبقى ال X بدي
+
+494
+01:00:11,340 --> 01:00:16,900
+أسوأ كده؟ اتنين يبقى فاصيل النقطة مين؟ اتنين
+
+495
+01:00:16,900 --> 01:00:21,300
+واربعة و اين النقطة اتنين واربعة بتجيلي هنا في
+
+496
+01:00:21,300 --> 01:00:26,860
+النصتنين يعني مشيت اتنين وطلعت اربعة يبقى هذا
+
+497
+01:00:26,860 --> 01:00:32,120
+النقطة اتنين واربعة اللي عندها قد يكون local
+
+498
+01:00:32,120 --> 01:00:37,260
+maximum او local minimum اذا بروح بحسبله النقطة F
+
+499
+01:00:37,260 --> 01:00:43,420
+اتنين واربعة تسابر هيفضل جاهزة عندى يعني هنا معوض
+
+500
+01:00:43,420 --> 01:00:49,900
+باربعة ضل بس عوض بمن؟ باتنين يبقى هذه اتنين تربيع
+
+501
+01:00:50,110 --> 01:00:58,110
+نقص اربعة في اتنين زي سبعتاشر يسام هنا اربعة وهنا
+
+502
+01:00:58,110 --> 01:01:03,730
+سالب تمانية بيظل سالب اربعة من سبعتاشر بيظل
+
+503
+01:01:03,730 --> 01:01:12,090
+ثلاثاشر وهذه باروزناها كذا ضالت مين عندي اربعة
+
+504
+01:01:12,090 --> 01:01:12,730
+اربعة اربعة اربعة اربعة اربعة اربعة اربعة اربعة
+
+505
+01:01:12,730 --> 01:01:17,990
+اربعة اربعة اربعة اربعة اربعة اربعة اربعة
+
+506
+01:01:40,400 --> 01:01:48,280
+طبعا هنا احنا عندنا f of x و 4 يبقى هاي هجازة بده
+
+507
+01:01:48,280 --> 01:01:53,000
+اشيل كل x وحط مكانها 4 يبقى هادي بده يتسرب
+
+508
+01:01:58,370 --> 01:02:05,030
+العشرة عشر زائد سبعتاش هو يسوى السبعة عشرة عشرة
+
+509
+01:02:05,030 --> 01:02:20,230
+عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة
+
+510
+01:02:20,710 --> 01:02:28,250
+طيب على هذا ال line يا بناه Y تساوي X طبعا Y تساوي
+
+511
+01:02:28,250 --> 01:02:36,170
+X أنا بدي أقولك ان F of X و X يعني هشيل كل Y وحق
+
+512
+01:02:36,170 --> 01:02:41,270
+مكانها او العكس هشيل كل X وحق مكان Y واحدة متنتين
+
+513
+01:02:41,270 --> 01:02:45,490
+مش واحدتنتين يمجي هنا بقول له هذا الكلام يساوي
+
+514
+01:02:45,490 --> 01:02:46,790
+برجع لمثلة
+
+515
+01:03:10,760 --> 01:03:16,900
+يبقى هنا و ال X أكبر من أو تساوي Zero و أقل من أو
+
+516
+01:03:16,900 --> 01:03:21,600
+تساوي أربع يعني الخط هذا مش على طول و طالع فوقنا
+
+517
+01:03:21,600 --> 01:03:25,920
+لأ بس أنا بدي أغنى الفترة من Zero لأربع من Zero
+
+518
+01:03:25,920 --> 01:03:29,400
+لغاية هذه هنا أربعة
+
+519
+01:03:38,420 --> 01:03:46,160
+يبقى X هو X يبقى نقطة زي
+
+520
+01:03:46,160 --> 01:03:53,760
+نقطة زي نقطة نقطة نقطة نقطة نقطة نقطة نقطة نقطة
+
+521
+01:03:53,760 --> 01:04:00,580
+نقطة نقطة نقطة نقطة نقطة نقطة نقطة نقطة نقطة نقطة
+
+522
+01:04:00,580 --> 01:04:01,500
+نقطة نقطة نقطة نقطة نقطة نقطة نقطة نقطة نقطة نقطة
+
+523
+01:04:01,500 --> 01:04:05,780
+نقطة نقطة نقطة نقطة نقطة نقطة نقطة نقطة نقطة
+
+524
+01:04:05,780 --> 01:04:05,880
+نقط
+
+525
+01:04:18,690 --> 01:04:23,870
+النقطة على الـ 00 هي فهي اختلطت ليش ولا نقطة في
+
+526
+01:04:23,870 --> 01:04:28,830
+الطريق ف4 و 4 حسبناها مع اللي قبلها بروحش بتغيرها
+
+527
+01:04:28,830 --> 01:04:34,960
+تاني انتهينا الان من الخطواتمن كل الـ boundary
+
+528
+01:04:34,960 --> 01:04:39,360
+points و من كل ال interior points تمام؟ شو بدي
+
+529
+01:04:39,360 --> 01:04:44,120
+أعمل الآن؟ بدي أعقد مقارنة أكبر قيمة بقول هذا
+
+530
+01:04:44,120 --> 01:04:48,020
+absolute maximum و الأقل قيمة absolute minimum
+
+531
+01:04:48,020 --> 01:04:53,280
+باجي بطلع في المربعات اللي عندى أنا بروزتهم هنا
+
+532
+01:04:53,280 --> 01:05:00,680
+يبقى أكبر قيمة جديدة و أقل قيمة ممتازة ده بروح
+
+533
+01:05:00,680 --> 01:05:12,690
+بقولها ال Fhas absolute maximum 17 at the points
+
+534
+01:05:12,690 --> 01:05:18,770
+في موقعين الموقع الأول يا بناتله كدهش؟ Zero و
+
+535
+01:05:18,770 --> 01:05:27,090
+أربعة Zero و أربعة و الموقع التاني and أربعة و
+
+536
+01:05:27,090 --> 01:05:27,550
+أربعة
+
+537
+01:05:53,020 --> 01:06:02,270
+طب افترض يا بنات كان مش مثلت مربع او مستطيليبقى
+
+538
+01:06:02,270 --> 01:06:06,890
+نفسنا نروح نديله الضلع الرابع و هكذا طبعا انا بس
+
+539
+01:06:06,890 --> 01:06:11,870
+السؤال انه كيف الكتاب مثال تبقى مستطيل يبقى حاجة
+
+540
+01:06:11,870 --> 01:06:16,150
+زي المحلين المثلث بالعلم المستطيل بالضبط تماما بس
+
+541
+01:06:16,150 --> 01:06:20,910
+بضلمين الضلع الرابع لكن انا لخاطر اعطيكم مثال غير
+
+542
+01:06:20,910 --> 01:06:26,750
+مستطيل مش موجود زيه في الكتاب و مرة جئنا به في
+
+543
+01:06:26,750 --> 01:06:34,480
+احدى الامتحاناتلذلك بدنا نروح نعطيكي مثال ما هو لا
+
+544
+01:06:34,480 --> 01:06:44,040
+مستقيم ولا مُثلّد ولا حتى مُربّع. إيش المثال هذا؟
+
+545
+01:06:44,040 --> 01:06:52,080
+بقولك ستراهنه حالا ان شاء الله تعالى بعد ان نكمل
+
+546
+01:06:52,080 --> 01:06:54,220
+مسح اللوحيين
+
+547
+01:07:10,870 --> 01:07:12,810
+مثال 2
+
+548
+01:07:30,490 --> 01:07:47,590
+and minimum values of the function للدالة f of x y
+
+549
+01:07:47,590 --> 01:07:56,850
+تساوي واحد زي x y ناقص تلاتة x on the closed
+
+550
+01:07:56,850 --> 01:08:08,850
+region on theA closed region bounded by
+
+551
+01:08:08,850 --> 01:08:22,070
+والمحدودة ب The parabola بالقطع المكافئ Y تساوي X
+
+552
+01:08:22,070 --> 01:08:29,870
+تربيع and the line Y تساوي R
+
+553
+01:08:46,910 --> 01:08:52,110
+أحد المدرسين كان بدرس صيفي زي الصيف هذا فقام جاب
+
+554
+01:08:52,110 --> 01:08:58,010
+السؤال لأطلال اللي بدرسهم احنا بنعطيكوا ياه كمثال
+
+555
+01:08:58,010 --> 01:09:01,490
+ان شاء الله و تعالى بيقول هات الأبسلوت maximum و
+
+556
+01:09:01,490 --> 01:09:05,530
+الأبسلوت minimum للدالة اللي قدام هذه على المنطقة
+
+557
+01:09:05,530 --> 01:09:10,170
+المغنطة المحدودة بالقطع المكافئ Y تساوي X تربية
+
+558
+01:09:10,170 --> 01:09:16,870
+وكلك الخط Y تساوي Aلو روحنا نتعرف على المنطقة اللي
+
+559
+01:09:16,870 --> 01:09:23,270
+عندنا هذه بقول هي المحاول وهذا محور X وهذا محور Y
+
+560
+01:09:23,270 --> 01:09:31,190
+وهذه نقطة الاصل القرابل اللي عندنا أبعد مشهور
+
+561
+01:09:31,190 --> 01:09:35,490
+عندنا من الكاركورا الصحيح كلنا بنعرف رسمته يبقى
+
+562
+01:09:35,490 --> 01:09:37,390
+هذا Y تسوى X
+
+563
+01:09:40,430 --> 01:09:47,170
+Y تساوي أربعة خط يوازي محور X ويبقى عنده مسافة
+
+564
+01:09:47,170 --> 01:09:53,470
+مقدارها أربعة يبقى هذه أربعة وهذا الخط يوازي محور
+
+565
+01:09:53,470 --> 01:09:54,130
+X ويبقى هذه أربعة وهذا الخط يوازي محور X ويبقى هذه
+
+566
+01:09:54,130 --> 01:09:56,790
+أربعة وهذا الخط يوازي محور X ويبقى هذه أربعة وهذا
+
+567
+01:09:56,790 --> 01:09:57,410
+الخط يوازي محور X ويبقى هذه أربعة وهذا الخط يوازي
+
+568
+01:09:57,410 --> 01:10:00,510
+أربعة وهذا الخط يوازي محور X ويبقى هذه أربعة وهذا
+
+569
+01:10:00,510 --> 01:10:01,750
+الخط يوازي محور X و
+
+570
+01:10:09,360 --> 01:10:16,020
+الانترال قوائز النقاط الداخلية وبعد ذلك بروح لمين
+
+571
+01:10:16,020 --> 01:10:21,040
+للنقاط الخارجية إذا بدنا نروح ونجيب له مين يا بنات
+
+572
+01:10:21,040 --> 01:10:28,180
+F X نشتغل بالنسبة ل X هي اللي قدامنا هنا تظهر من Y
+
+573
+01:10:28,180 --> 01:10:35,700
+ناقص ثلاثة ونسوى بال Zero إذا ال Y تسوى كم؟ ثلاثة
+
+574
+01:10:35,700 --> 01:10:37,680
+بالمثل بدنا نجيب له F
+
+575
+01:10:43,690 --> 01:10:50,450
+فقط لغير تمام و نسوي بال zero إذا ال X بدي ساوي
+
+576
+01:10:50,450 --> 01:10:58,050
+قداش Zero يبقى ال interior point اللي يبقى Zero و
+
+577
+01:10:58,050 --> 01:11:08,010
+تلاتة is a
+
+578
+01:11:08,010 --> 01:11:10,430
+critical point
+
+579
+01:11:15,350 --> 01:11:22,270
+0.3 يعني وين بده تيجي 0.3 هنا هذا النقطة اللي هي 0
+
+580
+01:11:22,270 --> 01:11:27,670
+هو 3 بيبقى أجد داخل المنطقة مش ده السؤال اللي قبل
+
+581
+01:11:27,670 --> 01:11:31,570
+ما لاجيناش ولا نقطة داخل المنطقة لاجيناها على الحد
+
+582
+01:11:31,570 --> 01:11:36,990
+ده هذه لاجيناها نقطة داخل المنطقة اللي عندناها إذا
+
+583
+01:11:36,990 --> 01:11:39,250
+بدنا نروح نحسبله جديش
+
+584
+01:11:57,260 --> 01:12:01,700
+خليها وسنرجع لها ان شاء الله بعد هيك بدنا نروح
+
+585
+01:12:01,700 --> 01:12:10,600
+لمين لل boundary points النقاط
+
+586
+01:12:10,600 --> 01:12:18,600
+الحديد ايش رايك نبدأ في الفرابنة في الأول يبقى
+
+587
+01:12:18,930 --> 01:12:23,890
+باجي بقوله بقولش on the line يبقى on the curve Y
+
+588
+01:12:23,890 --> 01:12:33,910
+تساوي X تربيع او on the parabola اللي
+
+589
+01:12:33,910 --> 01:12:42,870
+هو Y تساوي X تربيع ويهاد بدي أصير F of X ومين
+
+590
+01:12:42,870 --> 01:12:47,570
+أبناده؟ و X تربيع مش ال Y بحط على X تربيع فبنجي
+
+591
+01:12:47,570 --> 01:12:56,550
+علي مثلتنابصير تساوي واحد زائد تساوي
+
+592
+01:12:56,550 --> 01:12:59,990
+واحد
+
+593
+01:12:59,990 --> 01:13:01,770
+زائد تساوي واحد زائد تساوي واحد زائد تساوي واحد
+
+594
+01:13:01,770 --> 01:13:02,010
+زائد تساوي واحد زائد تساوي واحد زائد تساوي واحد
+
+595
+01:13:02,010 --> 01:13:03,770
+زائد تساوي واحد زائد تساوي واحد زائد تساوي واحد
+
+596
+01:13:03,770 --> 01:13:06,410
+زائد تساوي واحد زائد تساوي واحد زائد تساوي واحد
+
+597
+01:13:06,410 --> 01:13:08,150
+زائد تساوي واحد زائد تساوي واحد زائد تساوي واحد
+
+598
+01:13:08,150 --> 01:13:12,510
+زائد تساوي واحد زائد تساوي واحد زائد تساوي واحد
+
+599
+01:13:12,510 --> 01:13:17,770
+زائد تساوي واحد زائد تساوي وا
+
+600
+01:13:21,120 --> 01:13:27,100
+نقص تلاتة يعني تلاتة في X تربيع ناقص واحد يعني
+
+601
+01:13:27,100 --> 01:13:32,560
+تلاتة في X ناقص واحد في X زاد واحد ونسوي بالزيرو
+
+602
+01:13:32,560 --> 01:13:41,440
+يبقى باجي بيقولوا هذا بيعطي كذا critical points at
+
+603
+01:13:41,440 --> 01:13:52,400
+X تساوي واحد و X تساوي كده؟ سالب واحدطبعا إذا بدنا
+
+604
+01:13:52,400 --> 01:14:01,180
+نجيب F of واحد وواحد تربيع في الثانوية شيلنا ال
+
+605
+01:14:01,180 --> 01:14:07,320
+Exo وحطينا مكانها واحد يبقى واحد زائد واحد ناقص
+
+606
+01:14:07,320 --> 01:14:14,970
+تلاتة ويسوي جدا ناقص واحدبعدها بدنا نجيب F أو سالب
+
+607
+01:14:14,970 --> 01:14:21,610
+واحد و سالب واحد تربيه هو تساوي واحد سالب واحد
+
+608
+01:14:21,610 --> 01:14:28,190
+تكيب ناقص تلاتة في ناقص واحد. يبقى ايه تلاتة؟ واحد
+
+609
+01:14:28,190 --> 01:14:35,910
+اربع. شيل منهم واحد بالسالب يظل كده؟ يظل تلاتة هذه
+
+610
+01:14:35,910 --> 01:14:45,510
+الوزنة. تمام؟ طيبالان جيبنا اللى هو على ال
+
+611
+01:14:45,510 --> 01:14:49,250
+boundary points جيبنا الحمد لله بدلا من قيمة انت
+
+612
+01:14:49,250 --> 01:14:55,090
+انت شو ضايل عندى نقطتين اللى هو النقطة اللى عندنا
+
+613
+01:14:55,090 --> 01:15:02,590
+هذه و النقطة اللى عندنا هذه هذه ها بدي اعرف كده
+
+614
+01:15:02,590 --> 01:15:09,570
+قيمة x عندها وهذه بدي اعرف كده قيمة x عندها تمام
+
+615
+01:15:09,570 --> 01:15:13,600
+طيب بدي اعرفها من وينهذه النقطة بتجي على الخط
+
+616
+01:15:13,600 --> 01:15:20,040
+المستقيم وبتيجي كمان على المنحلة يعني لو حلت
+
+617
+01:15:20,040 --> 01:15:25,800
+التنتين مع بعض بكون جيب احداثيات النقطة تل اتنين
+
+618
+01:15:25,800 --> 01:15:32,380
+هدوش احنا انا y تساوي x تربع وعندي y تساوي اربعة
+
+619
+01:15:32,380 --> 01:15:40,720
+يبقى x قديم يساوي او ناقص اتنينهذه تكون اتنين وهذه
+
+620
+01:15:40,720 --> 01:15:46,600
+كم؟ سالب اتنين يبقى النقطة هذه ايضا كم؟ سالب اتنين
+
+621
+01:15:46,600 --> 01:15:55,200
+واربع وهذه النقطة اتنين واربع اذا بدي اشتغل F of
+
+622
+01:15:55,200 --> 01:16:01,140
+سالب اتنين واربع وF of اتنين واربع يبقى بدي اشتغل
+
+623
+01:16:01,140 --> 01:16:09,350
+F of سالب اتنين واربع وY سالبأتدالة هيصرت فوق عنا
+
+624
+01:16:09,350 --> 01:16:14,750
+بالشكل هذا، يبقى الأربع هذه كأنها لا قيمة لها،
+
+625
+01:16:14,750 --> 01:16:16,750
+يبقى شو بتصير؟ واحد
+
+626
+01:16:19,390 --> 01:16:27,030
+-2-3-2-8
+
+627
+01:16:27,030 --> 01:16:30,070
+-6
+
+628
+01:16:30,070 --> 01:16:34,810
+-14
+
+629
+01:16:34,810 --> 01:16:45,550
+-6-1-7-8-1
+
+630
+01:16:46,910 --> 01:16:52,870
+بالمعنى فإننا نجيب له F of اتنين واربع واي وسبع
+
+631
+01:16:52,870 --> 01:17:00,190
+يبقى يصير واحد زائد اتنين لكل تكيب نقص تلاتة في
+
+632
+01:17:00,190 --> 01:17:07,150
+اتنين واي وسبع تمانية واحد تسعة هتشيله نوم ستة هضل
+
+633
+01:17:07,150 --> 01:17:16,090
+قداش تلاتة طب إيش رأيك؟لما حولنا هذه هيك يبقى
+
+634
+01:17:16,090 --> 01:17:22,590
+حصرنا X بين مين ومين إذا لو حطيت فاصلة وقلت ناقص
+
+635
+01:17:22,590 --> 01:17:28,190
+اتنين اقل من او يساوي X اقل من او يساوي اتنين يكون
+
+636
+01:17:28,190 --> 01:17:33,970
+افضل كتير فالان مين ضايل عندين على ال line الهن
+
+637
+01:17:33,970 --> 01:17:41,490
+هذا Y تساوي اربع يعني بدي أشيل كل Yوحق مكانها
+
+638
+01:17:41,490 --> 01:17:48,870
+اربعة وشوف ايش بصير اذا بدى اجي اقول ان ال I Y
+
+639
+01:17:48,870 --> 01:17:57,410
+تساوي اربعة يبقى بدى اصير عندى F of X واربعة حسبنا
+
+640
+01:17:57,410 --> 01:18:03,350
+قبل هيك F X واربعة طبعا لا تمام يبقى بدى ارجع على
+
+641
+01:18:03,350 --> 01:18:07,770
+المثل انا بدى اشيل كل Y واحق مكانها اربعة يبقى
+
+642
+01:18:07,770 --> 01:18:18,200
+اصير عندى واحدزائد اربعة X وناخذ تلاتة X بظبط يعني
+
+643
+01:18:18,200 --> 01:18:25,980
+بيقول اني جداش واحد زائد X وال X بتتغير ما بين
+
+644
+01:18:25,980 --> 01:18:33,600
+ثاني باتنين وما بين اتنين كذلك يبقى F prime of X
+
+645
+01:18:33,600 --> 01:18:38,000
+الجداش يا بناتبنسوي بال zero اه بدنا نسوي بال zero
+
+646
+01:18:38,000 --> 01:18:44,720
+ايش رأيك؟ مفقود؟ impossible غير ممكن يبقى
+
+647
+01:18:44,720 --> 01:18:52,860
+impossible يعني لا يمكن انه يجد نقطة على هذا ال
+
+648
+01:18:52,860 --> 01:18:59,020
+line تبقى a critical point يبقى بضلش الا ميم طرفين
+
+649
+01:18:59,020 --> 01:19:04,700
+الخط المستقيم طب احنا حسبناهم الطرفينرح نكرر تاني؟
+
+650
+01:19:04,700 --> 01:19:12,660
+لأ انتهينا منه إذا بدا أجي أقول لهم f has absolute
+
+651
+01:19:12,660 --> 01:19:19,520
+maximum أبصر قداشر دعنا ندور هاي واحد و سالف واحد
+
+652
+01:19:19,520 --> 01:19:25,560
+و تلاتة و سالف واحد و تلاتة يبقى تلاتة at the
+
+653
+01:19:25,560 --> 01:19:34,420
+pointsعند النقطتين اللي هو سالب واحد وواحد اللي هو
+
+654
+01:19:34,420 --> 01:19:39,040
+السالب واحد وواحد لما نضعها بصير هذي كتير واحد
+
+655
+01:19:39,040 --> 01:19:48,340
+واتنين واربع and اتنين واربع وقالك if هذا absolute
+
+656
+01:19:48,340 --> 01:19:58,490
+minimum سالب واحد هنا واحد راحوهنا سالب واحد عند
+
+657
+01:19:58,490 --> 01:20:07,670
+النقطة at the point عند النقطة تانية الواحد واحد
+
+658
+01:20:07,670 --> 01:20:13,790
+والتانية and سالبي اتنين اقل
+
+659
+01:20:21,950 --> 01:20:28,730
+طيب افنجوا الآن لل exercises exercises لمين؟
+
+660
+01:20:28,730 --> 01:20:37,690
+لاربعتاشر سبعة المسائلة هنا من تلاتة لغاية تلاتين
+
+661
+01:20:37,690 --> 01:20:48,730
+من تلاتة من واحد لتلاتين الو multiple of
+
+662
+01:20:48,730 --> 01:21:01,760
+threeوبعد ذلك من واحد و تلاتين لغاية اربعين القادة
+
+663
+01:21:01,760 --> 01:21:10,800
+و
+
+664
+01:21:10,800 --> 01:21:14,100
+اول section منه اللي هو double integrals
+
+665
+01:21:31,790 --> 01:21:36,710
+Power Integrals over rectangles
+
+666
+01:22:14,480 --> 01:22:24,060
+Rectangular Rectangular Region R
+
+667
+01:22:24,060 --> 01:22:27,620
+X أقل من أو يساوي
+
+668
+01:22:32,680 --> 01:22:42,420
+وY أكبر من أو يساوي C أقل من أو يساوي D then the
+
+669
+01:22:42,420 --> 01:22:55,700
+double integral over
+
+670
+01:22:55,700 --> 01:23:01,000
+double integral over R
+
+671
+01:23:03,280 --> 01:23:17,140
+R defined by عرفت تالي تكامنين على R من F of X و Y
+
+672
+01:23:17,140 --> 01:23:28,220
+دي A تكامن من A إلى B تكامن من C إلى D من F of X و
+
+673
+01:23:28,220 --> 01:23:37,480
+Y دي Xدي واي دي
+
+674
+01:23:37,480 --> 01:23:49,160
+واي طبعاً دي اكس تساوي تكامل من C إلى D ومن هنا من
+
+675
+01:23:49,160 --> 01:23:56,100
+A إلى B لل F of X وY دي اكس دي واي
+
+676
+01:24:07,790 --> 01:24:14,790
+مثالات أو النساء الذين
+
+677
+01:24:14,790 --> 01:24:21,470
+تتبعون
+
+678
+01:24:34,130 --> 01:24:42,770
+متتكامن من باقي لغاية اتنين باقي ومتكامن من Zero
+
+679
+01:24:42,770 --> 01:24:53,170
+لغاية باقي لمين؟ لصين ال X ذاته وصين ال Y كله في
+
+680
+01:24:53,170 --> 01:24:55,710
+ال D X في ال D Y
+
+681
+01:25:27,320 --> 01:25:31,260
+الشبكة الماضية كانت بنات partial derivatives كله
+
+682
+01:25:31,260 --> 01:25:36,760
+بتلزم الاشتغالات من أوله إلى آخره هذا ان شاء الله
+
+683
+01:25:36,760 --> 01:25:41,000
+كله تكاملات بس مش تكامل واحد زي ما درسنا بال
+
+684
+01:25:41,000 --> 01:25:45,340
+calculus a و b ممكن يكون تكاملين ممكن يكون تلت
+
+685
+01:25:45,340 --> 01:25:50,820
+تكاملات ممكن يكون إحداثيات كورتيزية ممكن يكون
+
+686
+01:25:50,820 --> 01:25:56,480
+إحداثياتقطبية وكيف يمكن التحويل من تكابلات في
+
+687
+01:25:56,480 --> 01:26:01,760
+الاحداثيات الكارتزية للاحداثيات القطبية وبالعكس
+
+688
+01:26:01,760 --> 01:26:07,640
+وممكن يكون في احداثيات الاحداثيات أسطوانية وفي
+
+689
+01:26:07,640 --> 01:26:13,140
+احداثيات كوروية كما هنحسب التكابلات فيها يوم أن
+
+690
+01:26:13,140 --> 01:26:18,480
+نصلها ان شاء الله تعالى لكن هنبدأ بأوسط الأشياء هو
+
+691
+01:26:18,480 --> 01:26:22,550
+أول section section 15 راحطب ال integrant of a
+
+692
+01:26:22,550 --> 01:26:27,270
+rectangle يبقى احنا بدنا نحسب قداش التكاملات
+
+693
+01:26:27,270 --> 01:26:31,890
+الثلائية على مستطيلات كده لازم اقول قاعة الغرفة
+
+694
+01:26:31,890 --> 01:26:36,950
+هذه عبارة عن مستطيل له طول وله عرض إذا نكس هتتغير
+
+695
+01:26:36,950 --> 01:26:41,370
+من بين الرقمين و ال Y هتتغير من بين الرقمين يبقى
+
+696
+01:26:41,370 --> 01:26:47,590
+داش متكاملة على منطقة مستطيلة الشكل تعريف كتاني خد
+
+697
+01:26:47,590 --> 01:26:54,630
+دلف و بكس دلة متصلةخلال هذه المنطقة المستقلة X
+
+698
+01:26:54,630 --> 01:27:00,370
+محصورة بين A وB وY محصورة بين C وD يعني لو رحنا
+
+699
+01:27:00,370 --> 01:27:05,150
+وقلنا هذه المحاولة وقلنا هذه محور X وهذه محور Y
+
+700
+01:27:05,150 --> 01:27:10,270
+وهذه عندي خاتين وجينا خاتين بالشكل هذا وقلنا هذه
+
+701
+01:27:10,270 --> 01:27:16,250
+المنطقة A وهذه B وهذه Cوهذه دي يبقى المنطقة
+
+702
+01:27:16,250 --> 01:27:21,370
+المظللة اللى عندنا هذه هي المحصوة بين ال A والD
+
+703
+01:27:21,370 --> 01:27:27,730
+والC والD فده نحسب مقدار المساحة تبع Game تبعت هذه
+
+704
+01:27:27,730 --> 01:27:32,370
+المنطقة فبقول double integral على المنطقة هذه
+
+705
+01:27:32,370 --> 01:27:38,250
+بعرفه كتالي تكاملين على المنطقة اقررن F of X وY دي
+
+706
+01:27:38,250 --> 01:27:50,940
+ايه يعني دي ايه الامندي ايه؟ دي ايه؟ دي ايه؟ دي
+
+707
+01:27:50,940 --> 01:27:57,580
+ايه؟ دي ايه؟ دي ايه؟
+
+708
+01:27:57,580 --> 01:28:04,010
+دي ايه؟ دي ايه؟DY DX يبقى أول ما بدي أكمل بالنسبة
+
+709
+01:28:04,010 --> 01:28:08,970
+ل Y فبحط حدود ال Y من C إلى D ثم اللي ينتج بدي
+
+710
+01:28:08,970 --> 01:28:14,430
+أكمله بالنسبة إلى X فبحط حدود ال X ل A و B لو كنت
+
+711
+01:28:14,430 --> 01:28:18,950
+بدي أكمل بالنسبة ل X في الأول فبحط حدود ال X ل A و
+
+712
+01:28:18,950 --> 01:28:23,070
+B ثم بدي أكمل ل Y بحط حدود الحدود اللي أكمل ليمين
+
+713
+01:28:23,070 --> 01:28:29,430
+C وDالآن هذا كلام مضغوط، سنضعه على أرض الواقع ببعض
+
+714
+01:28:29,430 --> 01:28:33,850
+الأمثلة، سنأخذ بس المثال البسيط والمواجهة ان شاء
+
+715
+01:28:33,850 --> 01:28:38,430
+الله سنكمل عليه يبقى قال لي أحسبني كل من التكاملة
+
+716
+01:28:38,430 --> 01:28:43,570
+التالية وعطاني لسه أول تكاملة تكاملة من zero ل باي
+
+717
+01:28:43,570 --> 01:28:48,450
+ومن باي لثانه باي، فهذه منطقة مستطيلة لأنه عطاني
+
+718
+01:28:48,450 --> 01:28:55,560
+أرقام لمين لصين ال X Cos YDXDYمخلنيش يعني حيران
+
+719
+01:28:55,560 --> 01:28:59,460
+لكنك تكمل بالنسبة ل X من الأول و بعدين تكمل
+
+720
+01:28:59,460 --> 01:29:04,600
+بالنسبة ل Y زي بلات لما كنا بالفضل ل X بعتبر ال Y
+
+721
+01:29:04,600 --> 01:29:09,200
+constant و هنا لما كمل بالنسبة ل X بتعتبر ال Y
+
+722
+01:29:09,200 --> 01:29:13,840
+constant كامل بالنسبة ل Y بعتبر ال X constant و
+
+723
+01:29:13,840 --> 01:29:20,680
+هكذا يبقى هذا الكلام بترسالتكامل من الـπي للإتنين
+
+724
+01:29:20,680 --> 01:29:26,500
+الـπي تكامل من السلمين للإكس يبقى تكامل الـPsi
+
+725
+01:29:26,500 --> 01:29:33,280
+سالب كوساين يبقى سالب كوساين للإكس كوساين هو يعتبر
+
+726
+01:29:33,280 --> 01:29:36,900
+من الضرر ثالث زي اتنين او تلاتة
+
+727
+01:29:49,800 --> 01:29:56,100
+يبقى هذا الكلام يبدو يساوي integration من بايت
+
+728
+01:29:56,100 --> 01:30:01,520
+لغاية اتنين بايت ليه؟ بضعوط بالقيمة اللي فوق مصطلح
+
+729
+01:30:01,520 --> 01:30:09,620
+الـ180 جدرس سالف واحد يبقى معه سالف سالف سالف واحد
+
+730
+01:30:10,190 --> 01:30:13,370
+هذا يجب أن أضع X أكثر من Y
+
+731
+01:30:16,810 --> 01:30:22,890
+يبقى باي في cos y خلصنا القيم اللى فوق نعود بالقيم
+
+732
+01:30:22,890 --> 01:30:28,850
+اللى اتحاد ناقص مع ناقص بالصير زاد وcos صفر اللى
+
+733
+01:30:28,850 --> 01:30:35,950
+هو بواحد و هنا ناقص zero في cos y اللى هو بقدر F
+
+734
+01:30:35,950 --> 01:30:42,650
+zero كله بالنسبة الى dy يبقى صارت المسألة تكامل من
+
+735
+01:30:42,650 --> 01:30:49,660
+باي الى اتنين باي لمينلالي اتنين هذه ناقص واحد وهي
+
+736
+01:30:49,660 --> 01:30:55,240
+زائد، في زائد يا بنت هناايوة يبقى هنا واحد هو واحد
+
+737
+01:30:55,240 --> 01:31:03,300
+في اتنين زائد باي في كوصين ال Y في ال D Y ويساوي
+
+738
+01:31:03,300 --> 01:31:09,460
+انا بدأ اكمل و اصل ال Y يبقى اتنين Y زائد باي في
+
+739
+01:31:09,460 --> 01:31:16,260
+صين ال Y كله من باي لغاية قداشر اتنين باي يبقى هذا
+
+740
+01:31:16,260 --> 01:31:25,190
+الكلام بده يساوي اتنينفي اتنين باى زائد باى في صين
+
+741
+01:31:25,190 --> 01:31:32,730
+اتنين باى اللي هو بقداش بزيرو ناقص اتنين باى ناقص
+
+742
+01:31:32,730 --> 01:31:40,200
+باى في صين الزيرو اللي هو بزيرو شكل انايبقى الجواب
+
+743
+01:31:40,200 --> 01:31:47,160
+اربعة باى ناقص اتنين باى و يسوي قداش اتنين باى
+
+744
+01:31:47,160 --> 01:31:52,260
+نتيجة تمين نتيجة التكامل لا حد هنا stop المرة
+
+745
+01:31:52,260 --> 01:31:57,280
+الجاية ان شاء الله بنكمل اخر محاضرة مش الأربعاء
+
+746
+01:31:57,280 --> 01:32:01,820
+القادم الأربعاء اللي بعدها بيكون يوم تمانتاشر
+
+747
+01:32:01,820 --> 01:32:07,040
+تمانية و الامتحان اظن انت خمسة و عشرين انا ماشي
+
+748
+01:32:07,040 --> 01:32:12,400
+يبقى شد حيالكواركزوا معلوماتكوا، ذاكروا أول بأول
+
+749
+01:32:12,400 --> 01:32:15,640
+حتى تستفيدوا ان شاء الله
+
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/xMNKd8BQ9Wg_raw.json b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/xMNKd8BQ9Wg_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..8bfe50b867c975ae16fe840a5fa69f1d2bec8fe8
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/xMNKd8BQ9Wg_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 2290, "start": 14.64, "end": 22.9, "text": "بسم الله الرحمن الرحيم لان بنرجع مرة ثانية لل section اللي بدناها في نهاية المحاضرة الماضية", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 5296, 7649, 44945, 47341, 3615, 3714, 25720, 38637, 7649, 10632, 24976, 3541, 13672, 1829, 47525, 8315, 11296, 8978, 8717, 11296, 10632, 9673, 5016, 46958, 25720, 9673, 46958, 10632], "avg_logprob": -0.17763157463387438, "compression_ratio": 1.4285714285714286, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 14.639999999999999, "end": 15.56, "word": "بسم", "probability": 0.752685546875}, {"start": 15.56, "end": 15.82, "word": " الله", "probability": 0.98046875}, {"start": 15.82, "end": 16.22, "word": " الرحمن", "probability": 0.9576822916666666}, {"start": 16.22, "end": 16.78, "word": " الرحيم", "probability": 0.9923502604166666}, {"start": 16.78, "end": 17.98, "word": " لان", "probability": 0.3448486328125}, {"start": 17.98, "end": 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" A", "probability": 0.420166015625}, {"start": 606.65, "end": 607.25, "word": " وB", "probability": 0.739013671875}, {"start": 607.25, "end": 609.11, "word": " فإذا", "probability": 0.695556640625}, {"start": 609.11, "end": 609.69, "word": " كان", "probability": 0.98974609375}, {"start": 609.69, "end": 610.87, "word": " الـ", "probability": 0.716796875}, {"start": 610.87, "end": 611.15, "word": " F", "probability": 0.650390625}, {"start": 611.15, "end": 611.93, "word": " XX", "probability": 0.6025390625}], "temperature": 1.0}, {"id": 25, "seek": 64528, "start": 618.3, "end": 645.28, "text": "أقل من الـ zero at النقطة A وB النقطة الرابعة والأخيرة من هذا الاختبار تقول The test is inconclusive at A وB", "tokens": [10721, 4587, 1211, 9154, 2423, 39184, 4018, 412, 28239, 47432, 3660, 316, 4032, 33, 28239, 47432, 3660, 34892, 16758, 27884, 16070, 10721, 9778, 48923, 9154, 23758, 2423, 47283, 2655, 3555, 9640, 6055, 39648, 440, 1500, 307, 20972, 66, 7233, 412, 316, 4032, 33], "avg_logprob": -0.303622150963003, "compression_ratio": 1.2366412213740459, "no_speech_prob": 0.0, "words": [{"start": 618.3, "end": 618.64, "word": "أقل", "probability": 0.8556315104166666}, {"start": 618.64, "end": 618.82, "word": " من", "probability": 0.98193359375}, {"start": 618.82, "end": 619.16, "word": " الـ", "probability": 0.70458984375}, {"start": 619.16, "end": 621.38, "word": " zero", "probability": 0.2080078125}, {"start": 621.38, "end": 623.14, "word": " at", "probability": 0.3818359375}, {"start": 623.14, "end": 625.58, "word": " النقطة", "probability": 0.7615559895833334}, {"start": 625.58, "end": 625.88, "word": " A", "probability": 0.51220703125}, {"start": 625.88, "end": 626.36, "word": " وB", "probability": 0.729736328125}, {"start": 626.36, "end": 628.26, "word": " النقطة", "probability": 0.8287760416666666}, {"start": 628.26, "end": 628.68, "word": " الرابعة", "probability": 0.8400065104166666}, {"start": 628.68, "end": 629.84, "word": " والأخيرة", "probability": 0.74853515625}, {"start": 629.84, "end": 630.1, "word": " من", "probability": 0.9697265625}, {"start": 630.1, "end": 630.4, "word": " هذا", "probability": 0.9150390625}, {"start": 630.4, "end": 631.22, "word": " الاختبار", "probability": 0.90400390625}, {"start": 631.22, "end": 632.5, "word": " تقول", "probability": 0.76611328125}, {"start": 632.5, "end": 633.06, "word": " The", "probability": 0.0938720703125}, {"start": 633.06, "end": 634.74, "word": " test", "probability": 0.7060546875}, {"start": 634.74, "end": 636.08, "word": " is", "probability": 0.93701171875}, {"start": 636.08, "end": 639.0, "word": " inconclusive", "probability": 0.9182942708333334}, {"start": 639.0, "end": 642.42, "word": " at", "probability": 0.95556640625}, {"start": 642.42, "end": 644.72, "word": " A", "probability": 0.9052734375}, {"start": 644.72, "end": 645.28, "word": " وB", "probability": 0.91845703125}], "temperature": 1.0}, {"id": 26, "seek": 66449, "start": 646.13, "end": 664.49, "text": "عند النقطة A وB إذا كان الـ Fxx Fyy ناقص Fxy² بده يساوي Zero at اللي هو من النقطة A وB", "tokens": [3615, 41260, 28239, 47432, 3660, 316, 4032, 33, 11933, 15730, 25961, 2423, 39184, 479, 30569, 479, 15630, 8717, 995, 4587, 9381, 479, 12876, 27643, 47525, 3224, 7251, 3794, 995, 45865, 17182, 412, 13672, 1829, 31439, 9154, 28239, 47432, 3660, 316, 4032, 33], "avg_logprob": -0.4026162860005401, "compression_ratio": 1.176991150442478, "no_speech_prob": 0.0, "words": [{"start": 646.13, "end": 646.59, "word": "عند", "probability": 0.594482421875}, {"start": 646.59, "end": 647.11, "word": " النقطة", "probability": 0.9513346354166666}, {"start": 647.11, "end": 647.27, "word": " A", "probability": 0.1513671875}, {"start": 647.27, "end": 647.57, "word": " وB", "probability": 0.754638671875}, {"start": 647.57, "end": 648.21, "word": " إذا", "probability": 0.84228515625}, {"start": 648.21, "end": 648.95, "word": " كان", "probability": 0.97412109375}, {"start": 648.95, "end": 650.03, "word": " الـ", "probability": 0.4345703125}, {"start": 650.03, "end": 650.95, "word": " Fxx", "probability": 0.460205078125}, {"start": 650.95, "end": 652.73, "word": " Fyy", "probability": 0.637939453125}, {"start": 652.73, "end": 654.23, "word": " ناقص", "probability": 0.7010498046875}, {"start": 654.23, "end": 656.23, "word": " Fxy²", "probability": 0.7000325520833334}, {"start": 656.23, "end": 656.99, "word": " بده", "probability": 0.173431396484375}, {"start": 656.99, "end": 657.55, "word": " يساوي", "probability": 0.86181640625}, {"start": 657.55, "end": 658.15, "word": " Zero", "probability": 0.292236328125}, {"start": 658.15, "end": 659.49, "word": " at", "probability": 0.365478515625}, {"start": 659.49, "end": 660.79, "word": " اللي", "probability": 0.786376953125}, {"start": 660.79, "end": 660.97, "word": " هو", "probability": 0.9052734375}, {"start": 660.97, "end": 661.37, "word": " من", "probability": 0.7236328125}, {"start": 661.37, "end": 663.05, "word": " النقطة", "probability": 0.9724934895833334}, {"start": 663.05, "end": 663.81, "word": " A", "probability": 0.95068359375}, {"start": 663.81, "end": 664.49, "word": " وB", "probability": 0.950439453125}], "temperature": 1.0}, {"id": 27, "seek": 72784, "start": 698.88, "end": 727.84, "text": "بعدين نرجع لهذا الاختبار مرة ثانية نحاول نقرأه كويس نفهم الشيء اللي موجود فيه اقول second derivative test for local extreme value اختبار المشتق ايه الثاني لمعرفة ال local minimum و ال local maximum و الsettled point الان نفترض ان هذا f of x و y and is first and second partial derivative", "tokens": [3555, 22488, 9957, 8717, 47341, 3615, 46740, 15730, 2423, 47283, 2655, 3555, 9640, 3714, 25720, 38637, 7649, 10632, 8717, 5016, 995, 12610, 8717, 4587, 2288, 10721, 3224, 9122, 45865, 3794, 8717, 5172, 16095, 25124, 1829, 38207, 13672, 1829, 3714, 29245, 23328, 8978, 3224, 1975, 39648, 1150, 13760, 1500, 337, 2654, 8084, 2158, 1975, 46456, 3555, 9640, 9673, 8592, 2655, 4587, 1975, 1829, 3224, 6024, 104, 7649, 1829, 32767, 3615, 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{"start": 703.58, "end": 704.08, "word": " كويس", "probability": 0.9249674479166666}, {"start": 704.08, "end": 704.96, "word": " نفهم", "probability": 0.8644205729166666}, {"start": 704.96, "end": 705.46, "word": " الشيء", "probability": 0.8611653645833334}, {"start": 705.46, "end": 705.64, "word": " اللي", "probability": 0.87451171875}, {"start": 705.64, "end": 706.3, "word": " موجود", "probability": 0.9881184895833334}, {"start": 706.3, "end": 707.44, "word": " فيه", "probability": 0.977783203125}, {"start": 707.44, "end": 707.88, "word": " اقول", "probability": 0.677734375}, {"start": 707.88, "end": 708.3, "word": " second", "probability": 0.454345703125}, {"start": 708.3, "end": 708.96, "word": " derivative", "probability": 0.9345703125}, {"start": 708.96, "end": 709.5, "word": " test", "probability": 0.75830078125}, {"start": 709.5, "end": 709.86, "word": " for", "probability": 0.91650390625}, {"start": 709.86, "end": 710.26, "word": " local", "probability": 0.75537109375}, {"start": 710.26, "end": 710.9, "word": " extreme", "probability": 0.88720703125}, {"start": 710.9, "end": 711.58, "word": " value", "probability": 0.77392578125}, {"start": 711.58, "end": 712.92, "word": " اختبار", "probability": 0.9541015625}, {"start": 712.92, "end": 713.96, "word": " المشتق", "probability": 0.7862548828125}, {"start": 713.96, "end": 714.76, "word": " ايه", "probability": 0.4798990885416667}, {"start": 714.76, "end": 715.44, "word": " الثاني", "probability": 0.80908203125}, {"start": 715.44, "end": 716.8, "word": " لمعرفة", "probability": 0.9698486328125}, {"start": 716.8, "end": 717.4, "word": " ال", "probability": 0.953125}, {"start": 717.4, "end": 717.82, "word": " local", "probability": 0.60791015625}, {"start": 717.82, "end": 718.3, "word": " minimum", "probability": 0.96484375}, {"start": 718.3, "end": 718.58, "word": " و", "probability": 0.74267578125}, {"start": 718.58, "end": 718.62, "word": " ال", "probability": 0.335205078125}, {"start": 718.62, "end": 718.86, "word": " local", "probability": 0.6533203125}, {"start": 718.86, "end": 719.42, "word": " maximum", "probability": 0.96240234375}, {"start": 719.42, "end": 719.72, "word": " و", "probability": 0.87744140625}, {"start": 719.72, "end": 720.2, "word": " الsettled", "probability": 0.41490936279296875}, {"start": 720.2, "end": 720.68, "word": " point", "probability": 0.43017578125}, {"start": 720.68, "end": 721.34, "word": " الان", "probability": 0.495361328125}, {"start": 721.34, "end": 722.64, "word": " نفترض", "probability": 0.754730224609375}, {"start": 722.64, "end": 722.84, "word": " ان", "probability": 0.80322265625}, {"start": 722.84, "end": 723.06, "word": " هذا", "probability": 0.453125}, {"start": 723.06, "end": 723.4, "word": " f", "probability": 0.224365234375}, {"start": 723.4, "end": 723.56, "word": " of", "probability": 0.66650390625}, {"start": 723.56, "end": 723.84, "word": " x", "probability": 0.90185546875}, {"start": 723.84, "end": 724.04, "word": " و", "probability": 0.35986328125}, {"start": 724.04, "end": 724.52, "word": " y", "probability": 0.76123046875}, {"start": 724.52, "end": 725.02, "word": " and", "probability": 0.2236328125}, {"start": 725.02, "end": 725.38, "word": " is", "probability": 0.36328125}, {"start": 725.38, "end": 725.7, "word": " first", "probability": 0.81396484375}, {"start": 725.7, "end": 725.96, "word": " and", "probability": 0.958984375}, {"start": 725.96, "end": 726.4, "word": " second", "probability": 0.9169921875}, {"start": 726.4, "end": 727.02, "word": " partial", "probability": 0.90234375}, {"start": 727.02, "end": 727.84, "word": " derivative", "probability": 0.54345703125}], "temperature": 1.0}, {"id": 28, "seek": 74013, "start": 738.73, "end": 740.13, "text": "YYYYYYYYYYYYYYYYYYYYY", "tokens": [56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56], "avg_logprob": -0.5419033901257948, "compression_ratio": 1.9090909090909092, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 738.73, "end": 740.13, "word": "YYYYYYYYYYYYYYYYYYYYY", "probability": 0.8417198544456845}], "temperature": 1.0}, {"id": 29, "seek": 77348, "start": 757.48, "end": 773.48, "text": "قال لي و كذلك كان ال fx عند ال a و ال b بده يساوي 0 و ال fy عند ال a و ال b بده يساوي 0 طب ليش هذا ال condition حطه؟ مش هنضمن ان في عندي critical point", "tokens": [4587, 6027, 32239, 4032, 9122, 8848, 23275, 25961, 2423, 283, 87, 43242, 2423, 257, 4032, 2423, 272, 47525, 3224, 7251, 3794, 995, 45865, 1958, 4032, 2423, 38777, 43242, 2423, 257, 4032, 2423, 272, 47525, 3224, 7251, 3794, 995, 45865, 1958, 23032, 3555, 32239, 8592, 23758, 2423, 4188, 11331, 9566, 3224, 22807, 37893, 8032, 1863, 11242, 27842, 16472, 8978, 43242, 1829, 4924, 935], "avg_logprob": -0.35391864322480704, "compression_ratio": 1.5972222222222223, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 757.48, "end": 757.94, "word": "قال", "probability": 0.53204345703125}, {"start": 757.94, "end": 758.08, "word": " لي", "probability": 0.63916015625}, {"start": 758.08, "end": 758.18, "word": " و", "probability": 0.7236328125}, {"start": 758.18, "end": 758.92, "word": " كذلك", "probability": 0.9363606770833334}, {"start": 758.92, "end": 759.22, "word": " كان", "probability": 0.8515625}, {"start": 759.22, "end": 759.4, "word": " ال", "probability": 0.7734375}, {"start": 759.4, "end": 760.12, "word": " fx", "probability": 0.49298095703125}, {"start": 760.12, "end": 760.4, "word": " عند", "probability": 0.947265625}, {"start": 760.4, "end": 760.64, "word": " ال", "probability": 0.7109375}, {"start": 760.64, "end": 760.86, "word": " a", "probability": 0.822265625}, {"start": 760.86, "end": 761.04, "word": " و", "probability": 0.49267578125}, {"start": 761.04, "end": 761.3, "word": " ال", "probability": 0.90185546875}, {"start": 761.3, "end": 761.58, "word": " b", "probability": 0.982421875}, {"start": 761.58, "end": 761.92, "word": " بده", "probability": 0.20220947265625}, {"start": 761.92, "end": 762.34, "word": " يساوي", "probability": 0.78228759765625}, {"start": 762.34, "end": 762.78, "word": " 0", "probability": 0.34375}, {"start": 762.78, "end": 763.34, "word": " و", "probability": 0.609375}, {"start": 763.34, "end": 763.5, "word": " ال", "probability": 0.84814453125}, {"start": 763.5, "end": 764.1, "word": " fy", "probability": 0.95068359375}, {"start": 764.1, "end": 764.62, "word": " عند", "probability": 0.9609375}, {"start": 764.62, "end": 764.84, "word": " ال", "probability": 0.94287109375}, {"start": 764.84, "end": 765.04, "word": " a", "probability": 0.9794921875}, {"start": 765.04, "end": 765.16, "word": " و", "probability": 0.98291015625}, {"start": 765.16, "end": 765.24, "word": " ال", "probability": 0.91357421875}, {"start": 765.24, "end": 765.38, "word": " b", "probability": 0.9931640625}, {"start": 765.38, "end": 765.62, "word": " بده", "probability": 0.9287109375}, {"start": 765.62, "end": 765.94, "word": " يساوي", "probability": 0.9844970703125}, {"start": 765.94, "end": 766.38, "word": " 0", "probability": 0.9033203125}, {"start": 766.38, "end": 766.9, "word": " طب", "probability": 0.7939453125}, {"start": 766.9, "end": 767.14, "word": " ليش", "probability": 0.92724609375}, {"start": 767.14, "end": 767.3, "word": " هذا", "probability": 0.456298828125}, {"start": 767.3, "end": 767.44, "word": " ال", "probability": 0.9541015625}, {"start": 767.44, "end": 767.76, "word": " condition", "probability": 0.982421875}, {"start": 767.76, "end": 768.72, "word": " حطه؟", "probability": 0.56048583984375}, {"start": 768.72, "end": 769.12, "word": " مش", "probability": 0.397216796875}, {"start": 769.12, "end": 769.98, "word": " هنضمن", "probability": 0.7891845703125}, {"start": 769.98, "end": 770.4, "word": " ان", "probability": 0.496826171875}, {"start": 770.4, "end": 770.72, "word": " في", "probability": 0.7314453125}, {"start": 770.72, "end": 771.54, "word": " عندي", "probability": 0.6162109375}, {"start": 771.54, "end": 772.36, "word": " critical", "probability": 0.8447265625}, {"start": 772.36, "end": 773.48, "word": " point", "probability": 0.916015625}], "temperature": 1.0}, {"id": 30, "seek": 79057, "start": 773.83, "end": 790.57, "text": "يبقى ال Fx لما نسويها بالزيرو و ال Fy لما نسويها بالزيرو أو لو كانت إحداهما أو كلاهما is undefined عندها نقطة بقول هنا هذه critical points اللي ممكن يكون local maximum أو local minimum", "tokens": [1829, 3555, 4587, 7578, 2423, 479, 87, 5296, 15042, 8717, 3794, 45865, 11296, 20666, 11622, 13546, 2407, 4032, 2423, 479, 88, 5296, 15042, 8717, 3794, 45865, 11296, 20666, 11622, 13546, 2407, 34051, 45164, 25961, 2655, 11933, 24401, 40294, 15042, 34051, 9122, 15040, 3224, 15042, 307, 674, 5666, 2001, 43242, 11296, 8717, 47432, 3660, 4724, 39648, 34105, 29538, 4924, 2793, 13672, 1829, 3714, 43020, 7251, 30544, 2654, 6674, 34051, 2654, 7285], "avg_logprob": -0.20653608819128763, "compression_ratio": 1.5698324022346368, "no_speech_prob": 0.0, "words": [{"start": 773.83, "end": 774.45, "word": "يبقى", "probability": 0.83843994140625}, {"start": 774.45, "end": 774.57, "word": " ال", "probability": 0.580078125}, {"start": 774.57, "end": 775.23, "word": " Fx", "probability": 0.5770263671875}, {"start": 775.23, "end": 775.47, "word": " لما", "probability": 0.798828125}, {"start": 775.47, "end": 775.83, "word": " نسويها", "probability": 0.911376953125}, {"start": 775.83, "end": 776.23, "word": " بالزيرو", "probability": 0.6126708984375}, {"start": 776.23, "end": 776.33, "word": " و", "probability": 0.54296875}, {"start": 776.33, "end": 776.39, "word": " ال", "probability": 0.67529296875}, {"start": 776.39, "end": 776.75, "word": " Fy", "probability": 0.82958984375}, {"start": 776.75, "end": 776.97, "word": " لما", "probability": 0.987060546875}, {"start": 776.97, "end": 777.49, "word": " نسويها", "probability": 0.97216796875}, {"start": 777.49, "end": 778.23, "word": " بالزيرو", "probability": 0.9786376953125}, {"start": 778.23, "end": 778.69, "word": " أو", "probability": 0.5986328125}, {"start": 778.69, "end": 778.95, "word": " لو", "probability": 0.95166015625}, {"start": 778.95, "end": 779.35, "word": " كانت", "probability": 0.949462890625}, {"start": 779.35, "end": 780.07, "word": " إحداهما", "probability": 0.8109130859375}, {"start": 780.07, "end": 780.45, "word": " أو", "probability": 0.8779296875}, {"start": 780.45, "end": 781.37, "word": " كلاهما", "probability": 0.8487548828125}, {"start": 781.37, "end": 781.87, "word": " is", "probability": 0.81787109375}, {"start": 781.87, "end": 782.85, "word": " undefined", "probability": 0.8338216145833334}, {"start": 782.85, "end": 783.27, "word": " عندها", "probability": 0.870849609375}, {"start": 783.27, "end": 783.61, "word": " نقطة", "probability": 0.95263671875}, {"start": 783.61, "end": 783.95, "word": " بقول", "probability": 0.6942138671875}, {"start": 783.95, "end": 784.23, "word": " هنا", "probability": 0.85107421875}, {"start": 784.23, "end": 784.57, "word": " هذه", "probability": 0.69091796875}, {"start": 784.57, "end": 785.01, "word": " critical", "probability": 0.495849609375}, {"start": 785.01, "end": 785.59, "word": " points", "probability": 0.91162109375}, {"start": 785.59, "end": 786.23, "word": " اللي", "probability": 0.935302734375}, {"start": 786.23, "end": 786.67, "word": " ممكن", "probability": 0.990478515625}, {"start": 786.67, "end": 787.15, "word": " يكون", "probability": 0.7353515625}, {"start": 787.15, "end": 787.51, "word": " local", "probability": 0.7724609375}, {"start": 787.51, "end": 788.25, "word": " maximum", "probability": 0.9609375}, {"start": 788.25, "end": 789.03, "word": " أو", "probability": 0.8134765625}, {"start": 789.03, "end": 789.85, "word": " local", "probability": 0.92822265625}, {"start": 789.85, "end": 790.57, "word": " minimum", "probability": 0.97265625}], "temperature": 1.0}, {"id": 31, "seek": 80549, "start": 796.57, "end": 805.49, "text": "النقطة الأولى الـ f has local maximum عند النقطة الأولى إذا كان fxx أقل من الـ zero", "tokens": [6027, 1863, 47432, 3660, 16247, 12610, 7578, 2423, 39184, 283, 575, 2654, 6674, 43242, 28239, 47432, 3660, 16247, 12610, 7578, 11933, 15730, 25961, 283, 30569, 5551, 4587, 1211, 9154, 2423, 39184, 4018], "avg_logprob": -0.5658143939393939, "compression_ratio": 1.27, "no_speech_prob": 0.0, "words": [{"start": 796.57, "end": 797.45, "word": "النقطة", "probability": 0.700531005859375}, {"start": 797.45, "end": 797.93, "word": " الأولى", "probability": 0.9508463541666666}, {"start": 797.93, "end": 798.25, "word": " الـ", "probability": 0.225830078125}, {"start": 798.25, "end": 798.41, "word": " f", "probability": 0.2626953125}, {"start": 798.41, "end": 798.69, "word": " has", "probability": 0.427978515625}, {"start": 798.69, "end": 799.21, "word": " local", "probability": 0.70751953125}, {"start": 799.21, "end": 799.95, "word": " maximum", "probability": 0.943359375}, {"start": 799.95, "end": 800.75, "word": " عند", "probability": 0.9228515625}, {"start": 800.75, "end": 801.25, "word": " النقطة", "probability": 0.9348958333333334}, {"start": 801.25, "end": 801.59, "word": " الأولى", "probability": 0.6009928385416666}, {"start": 801.59, "end": 802.03, "word": " إذا", "probability": 0.67236328125}, {"start": 802.03, "end": 802.39, "word": " كان", "probability": 0.9599609375}, {"start": 802.39, "end": 803.51, "word": " fxx", "probability": 0.5638427734375}, {"start": 803.51, "end": 804.69, "word": " أقل", "probability": 0.8972981770833334}, {"start": 804.69, "end": 804.93, "word": " من", "probability": 0.98779296875}, {"start": 804.93, "end": 805.21, "word": " الـ", "probability": 0.48388671875}, {"start": 805.21, "end": 805.49, "word": " zero", "probability": 0.357177734375}], "temperature": 1.0}, {"id": 32, "seek": 82355, "start": 808.87, "end": 823.55, "text": "مقدار المتباين يجب أن يكون أكبر من الـ 0 FXX ضربتها في FYY و نقصتها أو طرحتها من الـ FXY لكل تربيع", "tokens": [2304, 28543, 9640, 9673, 2655, 3555, 995, 9957, 7251, 7435, 3555, 14739, 7251, 30544, 5551, 4117, 26890, 9154, 2423, 39184, 1958, 479, 55, 55, 48812, 25513, 2655, 11296, 8978, 42730, 56, 4032, 8717, 4587, 9381, 2655, 11296, 34051, 23032, 2288, 33753, 11296, 9154, 2423, 39184, 479, 55, 56, 5296, 28820, 6055, 2288, 21292, 3615], "avg_logprob": -0.4568181948228316, "compression_ratio": 1.3865546218487395, "no_speech_prob": 2.980232238769531e-07, "words": [{"start": 808.87, "end": 809.59, "word": "مقدار", "probability": 0.6985677083333334}, {"start": 809.59, "end": 810.65, "word": " المتباين", "probability": 0.784228515625}, {"start": 810.65, "end": 811.83, "word": " يجب", "probability": 0.4543050130208333}, {"start": 811.83, "end": 811.83, "word": " أن", "probability": 0.64013671875}, {"start": 811.83, "end": 812.03, "word": " يكون", "probability": 0.95849609375}, {"start": 812.03, "end": 812.51, "word": " أكبر", "probability": 0.8577473958333334}, {"start": 812.51, "end": 812.71, "word": " من", "probability": 0.9755859375}, {"start": 812.71, "end": 812.93, "word": " الـ", "probability": 0.5010986328125}, {"start": 812.93, "end": 813.11, "word": " 0", "probability": 0.263671875}, {"start": 813.11, "end": 814.29, "word": " FXX", "probability": 0.395263671875}, {"start": 814.29, "end": 815.35, "word": " ضربتها", "probability": 0.652069091796875}, {"start": 815.35, "end": 815.53, "word": " في", "probability": 0.92578125}, {"start": 815.53, "end": 816.67, "word": " FYY", "probability": 0.7025146484375}, {"start": 816.67, "end": 817.03, "word": " و", "probability": 0.8408203125}, {"start": 817.03, "end": 817.93, "word": " نقصتها", "probability": 0.752685546875}, {"start": 817.93, "end": 818.15, "word": " أو", "probability": 0.6279296875}, {"start": 818.15, "end": 819.29, "word": " طرحتها", "probability": 0.9195556640625}, {"start": 819.29, "end": 819.53, "word": " من", "probability": 0.95654296875}, {"start": 819.53, "end": 820.79, "word": " الـ", "probability": 0.462890625}, {"start": 820.79, "end": 822.51, "word": " FXY", "probability": 0.85546875}, {"start": 822.51, "end": 822.97, "word": " لكل", "probability": 0.78125}, {"start": 822.97, "end": 823.55, "word": " تربيع", "probability": 0.8568115234375}], "temperature": 1.0}, {"id": 33, "seek": 85636, "start": 828.12, "end": 856.36, "text": "القيمة هذه قيمة موجبة والقيمة هذه قيمة سالبة يبقى بقول اني local maximum طب local minimum القيمة هذه بتبقى قيمة سأق موجبة اللي فوق سالبة وهذه موجبة لكن القيمة هذه مالها موجبة المحدد او المميز اللي عندنا هذا في كل الأمرين بقيمة موجبة طب مين بدي افرق مع ال local maximum و ال local minimum؟", "tokens": [6027, 4587, 32640, 3660, 29538, 12174, 32640, 3660, 3714, 29245, 49401, 16070, 4587, 32640, 3660, 29538, 12174, 32640, 3660, 8608, 6027, 49401, 7251, 3555, 4587, 7578, 4724, 39648, 16472, 1829, 2654, 6674, 23032, 3555, 2654, 7285, 25062, 32640, 3660, 29538, 39894, 3555, 4587, 7578, 12174, 32640, 3660, 8608, 10721, 4587, 3714, 29245, 49401, 13672, 1829, 6156, 30543, 8608, 6027, 49401, 37037, 24192, 3714, 29245, 49401, 44381, 25062, 32640, 3660, 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"start": 856.59, "end": 883.15, "text": "الـ FXX والله إذا كان FXX سالبة يبقى لدي local maximum FXX موجبة يبقى local minimum طب افترض إن المحدد لأن هذا أو المميز هذا كان أقل من ال zero وال FXX إيش ما كانت تكون موجبة سلمة ماتفرقش عني طلع القيمة إيش قيمة سلمة إن حدث ذلك", "tokens": [6027, 39184, 37849, 55, 16070, 43761, 11933, 15730, 25961, 37849, 55, 8608, 6027, 49401, 7251, 3555, 4587, 7578, 5296, 16254, 2654, 6674, 37849, 55, 3714, 29245, 49401, 7251, 3555, 4587, 7578, 2654, 7285, 23032, 3555, 1975, 5172, 2655, 43042, 36145, 9673, 24401, 3215, 5296, 33456, 23758, 34051, 9673, 2304, 1829, 11622, 23758, 25961, 5551, 4587, 1211, 9154, 2423, 4018, 16070, 37849, 55, 11933, 1829, 8592, 19446, 25961, 2655, 6055, 30544, 3714, 29245, 49401, 8608, 19528, 3660, 3714, 9307, 5172, 2288, 4587, 8592, 18871, 1829, 23032, 1211, 3615, 25062, 32640, 3660, 11933, 1829, 8592, 12174, 32640, 3660, 8608, 19528, 3660, 36145, 11331, 3215, 12984, 29910, 23275], "avg_logprob": -0.2725530654754279, 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"word": " domain", "probability": 0.99658203125}, {"start": 2687.71, "end": 2688.27, "word": " تبعها", "probability": 0.814697265625}, {"start": 2688.27, "end": 2688.55, "word": " بيات", "probability": 0.4507242838541667}, {"start": 2688.55, "end": 2688.67, "word": " ال", "probability": 0.79833984375}, {"start": 2688.67, "end": 2689.11, "word": " domain", "probability": 0.99755859375}, {"start": 2689.11, "end": 2690.49, "word": " كمنطقة", "probability": 0.8857421875}, {"start": 2690.49, "end": 2691.39, "word": " محدودة", "probability": 0.957275390625}, {"start": 2691.39, "end": 2691.53, "word": " و", "probability": 0.97705078125}, {"start": 2691.53, "end": 2692.01, "word": " كذلك", "probability": 0.91162109375}, {"start": 2692.01, "end": 2692.77, "word": " منطقة", "probability": 0.96142578125}, {"start": 2692.77, "end": 2693.61, "word": " محدودة", "probability": 0.632293701171875}], "temperature": 1.0}, {"id": 96, "seek": 271921, "start": 2694.21, "end": 2719.21, "text": "طبعا بعد قليل هقولك ليش منطقة مغلقة و ليش منطقة محدودة بقول to find the absolute maximum او absolute minimum make the following steps بدنا نعمل خطوات أتانية الخطوة الأولى بقول less than internal constantly قائمة بالنقاط الداخلية ل region R بحيث الدالة F", "tokens": [9566, 3555, 3615, 995, 39182, 12174, 20292, 1211, 8032, 39648, 4117, 32239, 8592, 9154, 9566, 28671, 3714, 17082, 1211, 28671, 4032, 32239, 8592, 9154, 9566, 28671, 3714, 24401, 23328, 3660, 4724, 39648, 281, 915, 264, 8236, 6674, 1975, 2407, 8236, 7285, 652, 264, 3480, 4439, 47525, 8315, 8717, 25957, 1211, 16490, 9566, 2407, 9307, 5551, 2655, 7649, 10632, 33962, 9566, 2407, 3660, 16247, 12610, 7578, 4724, 39648, 1570, 813, 6920, 6460, 12174, 16373, 46007, 20666, 1863, 4587, 41193, 32748, 47283, 1211, 10632, 5296, 4458, 497, 4724, 5016, 1829, 12984, 32748, 6027, 3660, 479], "avg_logprob": -0.3480718009015347, "compression_ratio": 1.5635593220338984, "no_speech_prob": 7.748603820800781e-07, "words": [{"start": 2694.21, "end": 2695.49, "word": "طبعا", "probability": 0.777099609375}, {"start": 2695.49, "end": 2695.75, "word": " بعد", "probability": 0.88330078125}, {"start": 2695.75, "end": 2696.25, "word": " قليل", "probability": 0.9658203125}, {"start": 2696.25, "end": 2696.73, "word": " هقولك", "probability": 0.4964192708333333}, {"start": 2696.73, "end": 2696.99, "word": " ليش", "probability": 0.880859375}, {"start": 2696.99, "end": 2697.71, "word": " منطقة", "probability": 0.9376627604166666}, {"start": 2697.71, "end": 2698.73, "word": " مغلقة", "probability": 0.9420166015625}, {"start": 2698.73, "end": 2698.95, "word": " و", "probability": 0.58251953125}, {"start": 2698.95, "end": 2699.23, "word": " ليش", "probability": 0.81689453125}, {"start": 2699.23, "end": 2699.97, "word": " منطقة", "probability": 0.8502604166666666}, {"start": 2699.97, "end": 2700.97, "word": " محدودة", "probability": 0.8951416015625}, {"start": 2700.97, "end": 2701.71, "word": " بقول", "probability": 0.6229248046875}, {"start": 2701.71, "end": 2701.91, "word": " to", "probability": 0.1192626953125}, {"start": 2701.91, "end": 2702.25, "word": " find", "probability": 0.92041015625}, {"start": 2702.25, "end": 2702.51, "word": " the", "probability": 0.650390625}, {"start": 2702.51, "end": 2702.99, "word": " absolute", "probability": 0.90087890625}, {"start": 2702.99, "end": 2703.51, "word": " maximum", "probability": 0.8115234375}, {"start": 2703.51, "end": 2703.83, "word": " او", "probability": 0.755126953125}, {"start": 2703.83, "end": 2704.35, "word": " absolute", "probability": 0.281005859375}, {"start": 2704.35, "end": 2705.33, "word": " minimum", "probability": 0.97021484375}, {"start": 2705.33, "end": 2706.19, "word": " make", "probability": 0.546875}, {"start": 2706.19, "end": 2706.41, "word": " the", "probability": 0.90478515625}, {"start": 2706.41, "end": 2706.75, "word": " following", "probability": 0.80126953125}, {"start": 2706.75, "end": 2707.33, "word": " steps", "probability": 0.85009765625}, {"start": 2707.33, "end": 2707.67, "word": " بدنا", "probability": 0.429718017578125}, {"start": 2707.67, "end": 2707.97, "word": " نعمل", "probability": 0.9923502604166666}, {"start": 2707.97, "end": 2708.79, "word": " خطوات", "probability": 0.8028564453125}, {"start": 2708.79, "end": 2710.01, "word": " أتانية", "probability": 0.6353759765625}, {"start": 2710.01, "end": 2710.97, "word": " الخطوة", "probability": 0.8570556640625}, {"start": 2710.97, "end": 2711.89, "word": " الأولى", "probability": 0.9671223958333334}, {"start": 2711.89, "end": 2712.25, "word": " بقول", "probability": 0.853271484375}, {"start": 2712.25, "end": 2712.49, "word": " less", "probability": 0.476806640625}, {"start": 2712.49, "end": 2712.71, "word": " than", "probability": 0.8828125}, {"start": 2712.71, "end": 2713.17, "word": " internal", "probability": 0.1812744140625}, {"start": 2713.17, "end": 2713.83, "word": " constantly", "probability": 0.3603515625}, {"start": 2713.83, "end": 2714.69, "word": " قائمة", "probability": 0.8570963541666666}, {"start": 2714.69, "end": 2715.41, "word": " بالنقاط", "probability": 0.79486083984375}, {"start": 2715.41, "end": 2716.55, "word": " الداخلية", "probability": 0.9842529296875}, {"start": 2716.55, "end": 2717.13, "word": " ل", "probability": 0.447998046875}, {"start": 2717.13, "end": 2717.55, "word": " region", "probability": 0.82080078125}, {"start": 2717.55, "end": 2717.99, "word": " R", "probability": 0.775390625}, {"start": 2717.99, "end": 2718.37, "word": " بحيث", "probability": 0.658294677734375}, {"start": 2718.37, "end": 2718.95, "word": " الدالة", "probability": 0.6580403645833334}, {"start": 2718.95, "end": 2719.21, "word": " F", "probability": 0.796875}], "temperature": 1.0}, {"id": 97, "seek": 273829, "start": 2719.59, "end": 2738.29, "text": "ممكن تاخد local maximum او local minimum على هذه المنطقة و احسبلي قيمتي الدالة عند main، عند هذه النقاط، يبقى انوش بيقولي اتلي كل نقاط الحريجة على المنطقة المعطالة، بدناياهم هدول", "tokens": [2304, 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"probability": 0.708984375}, {"start": 2722.29, "end": 2722.69, "word": " local", "probability": 0.93603515625}, {"start": 2722.69, "end": 2723.25, "word": " minimum", "probability": 0.98583984375}, {"start": 2723.25, "end": 2723.63, "word": " على", "probability": 0.79736328125}, {"start": 2723.63, "end": 2724.09, "word": " هذه", "probability": 0.97412109375}, {"start": 2724.09, "end": 2724.89, "word": " المنطقة", "probability": 0.990478515625}, {"start": 2724.89, "end": 2725.49, "word": " و", "probability": 0.61083984375}, {"start": 2725.49, "end": 2726.07, "word": " احسبلي", "probability": 0.74273681640625}, {"start": 2726.07, "end": 2726.73, "word": " قيمتي", "probability": 0.8096516927083334}, {"start": 2726.73, "end": 2727.51, "word": " الدالة", "probability": 0.91064453125}, {"start": 2727.51, "end": 2727.83, "word": " عند", "probability": 0.7109375}, {"start": 2727.83, "end": 2728.59, "word": " main،", "probability": 0.23052978515625}, {"start": 2728.59, "end": 2728.85, "word": " عند", "probability": 0.9033203125}, {"start": 2728.85, "end": 2729.21, "word": " هذه", "probability": 0.97900390625}, {"start": 2729.21, "end": 2729.67, "word": " النقاط،", "probability": 0.85009765625}, {"start": 2729.67, "end": 2729.95, "word": " يبقى", "probability": 0.7529296875}, {"start": 2729.95, "end": 2730.29, "word": " انوش", "probability": 0.6389973958333334}, {"start": 2730.29, "end": 2730.85, "word": " بيقولي", "probability": 0.69378662109375}, {"start": 2730.85, "end": 2731.55, "word": " اتلي", "probability": 0.8570963541666666}, {"start": 2731.55, "end": 2731.87, "word": " كل", "probability": 0.99072265625}, {"start": 2731.87, "end": 2732.43, "word": " نقاط", "probability": 0.9778645833333334}, {"start": 2732.43, "end": 2733.69, "word": " الحريجة", "probability": 0.9066162109375}, {"start": 2733.69, "end": 2735.01, "word": " على", "probability": 0.9013671875}, {"start": 2735.01, "end": 2735.85, "word": " المنطقة", "probability": 0.988037109375}, {"start": 2735.85, "end": 2737.13, "word": " المعطالة،", "probability": 0.774169921875}, {"start": 2737.13, "end": 2737.97, "word": " بدناياهم", "probability": 0.79364013671875}, {"start": 2737.97, "end": 2738.29, "word": " هدول", "probability": 0.445068359375}], "temperature": 1.0}, {"id": 98, "seek": 276485, "start": 2738.67, "end": 2764.85, "text": "وعندي النقاط اللي حاليا بدي أحسب مين القيم تبعت هذه الدالة و أقولهم اطيعوا شوية بس نكمل باقى الشغل و بعد هيك بنروح لمين؟ List the boundary points يبقى أول شغلة جيبنا ال internal points يبقى احنا داخل ال open region يبقى مضل عندنا ال boundary اللي على الحدود", "tokens": [2407, 3615, 1863, 16254, 28239, 4587, 41193, 13672, 1829, 11331, 6027, 25528, 4724, 16254, 5551, 5016, 35457, 3714, 9957, 25062, 32640, 6055, 3555, 34268, 29538, 32748, 6027, 3660, 4032, 5551, 39648, 16095, 1975, 9566, 40228, 14407, 13412, 2407, 10632, 4724, 3794, 8717, 24793, 1211, 4724, 995, 4587, 7578, 25124, 17082, 1211, 4032, 39182, 39896, 4117, 44945, 32887, 5016, 32767, 9957, 22807, 17668, 264, 12866, 2793, 7251, 3555, 4587, 7578, 5551, 12610, 13412, 17082, 37977, 10874, 1829, 3555, 8315, 2423, 6920, 2793, 7251, 3555, 4587, 7578, 1975, 5016, 8315, 11778, 47283, 1211, 2423, 1269, 4458, 7251, 3555, 4587, 7578, 3714, 11242, 1211, 43242, 8315, 2423, 12866, 13672, 1829, 15844, 21542, 3215, 23328], "avg_logprob": -0.27776228290583405, "compression_ratio": 1.6857142857142857, "no_speech_prob": 0.0, "words": [{"start": 2738.67, "end": 2739.39, "word": "وعندي", "probability": 0.50970458984375}, {"start": 2739.39, "end": 2739.87, "word": " النقاط", "probability": 0.81396484375}, {"start": 2739.87, "end": 2740.01, "word": " اللي", "probability": 0.7373046875}, {"start": 2740.01, "end": 2740.29, "word": " حاليا", "probability": 0.8802083333333334}, {"start": 2740.29, "end": 2740.53, "word": " بدي", "probability": 0.5606689453125}, {"start": 2740.53, "end": 2740.83, "word": " أحسب", "probability": 0.8738606770833334}, {"start": 2740.83, "end": 2741.23, "word": " مين", 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2747.35, "word": " الشغل", "probability": 0.98876953125}, {"start": 2747.35, "end": 2748.09, "word": " و", "probability": 0.52294921875}, {"start": 2748.09, "end": 2748.41, "word": " بعد", "probability": 0.91015625}, {"start": 2748.41, "end": 2748.89, "word": " هيك", "probability": 0.884765625}, {"start": 2748.89, "end": 2749.75, "word": " بنروح", "probability": 0.7484537760416666}, {"start": 2749.75, "end": 2750.73, "word": " لمين؟", "probability": 0.6492513020833334}, {"start": 2750.73, "end": 2751.07, "word": " List", "probability": 0.440185546875}, {"start": 2751.07, "end": 2751.39, "word": " the", "probability": 0.8017578125}, {"start": 2751.39, "end": 2751.81, "word": " boundary", "probability": 0.8388671875}, {"start": 2751.81, "end": 2752.47, "word": " points", "probability": 0.86865234375}, {"start": 2752.47, "end": 2752.71, "word": " يبقى", "probability": 0.775634765625}, {"start": 2752.71, "end": 2752.97, "word": " أول", "probability": 0.890869140625}, {"start": 2752.97, "end": 2753.37, "word": " شغلة", "probability": 0.6180826822916666}, {"start": 2753.37, "end": 2753.79, "word": " جيبنا", "probability": 0.9404296875}, {"start": 2753.79, "end": 2753.93, "word": " ال", "probability": 0.87353515625}, {"start": 2753.93, "end": 2754.39, "word": " internal", "probability": 0.202392578125}, {"start": 2754.39, "end": 2755.15, "word": " points", "probability": 0.9091796875}, {"start": 2755.15, "end": 2756.27, "word": " يبقى", "probability": 0.90771484375}, {"start": 2756.27, "end": 2756.65, "word": " احنا", "probability": 0.8502604166666666}, {"start": 2756.65, "end": 2758.63, "word": " داخل", "probability": 0.9803059895833334}, {"start": 2758.63, "end": 2758.85, "word": " ال", "probability": 0.9560546875}, {"start": 2758.85, "end": 2759.53, "word": " open", "probability": 0.92822265625}, {"start": 2759.53, "end": 2760.73, "word": " region", "probability": 0.95166015625}, {"start": 2760.73, "end": 2761.39, "word": " يبقى", "probability": 0.9464111328125}, {"start": 2761.39, "end": 2761.93, "word": " مضل", "probability": 0.4055582682291667}, {"start": 2761.93, "end": 2762.49, "word": " عندنا", "probability": 0.74072265625}, {"start": 2762.49, "end": 2762.93, "word": " ال", "probability": 0.88330078125}, {"start": 2762.93, "end": 2763.39, "word": " boundary", "probability": 0.93310546875}, {"start": 2763.39, "end": 2764.03, "word": " اللي", "probability": 0.881103515625}, {"start": 2764.03, "end": 2764.25, "word": " على", "probability": 0.85888671875}, {"start": 2764.25, "end": 2764.85, "word": " الحدود", "probability": 0.9658203125}], "temperature": 1.0}, {"id": 99, "seek": 278707, "start": 2765.15, "end": 2787.07, "text": "يبقى بدنا نجيب less كمان بال boundary region للدالة F اللى عندها ممكن تاخد local maximum و local minimum و نحصل قيم الدالة عندنا هذا إذا صرت عندى الحمد لله قيم كتيرة قيم تبع ال interior points و قيم تبع ال boundary points باجي في الآخر خطوة تالتة و الأخيرة", "tokens": [1829, 3555, 4587, 7578, 47525, 8315, 8717, 7435, 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"probability": 0.2098388671875}, {"start": 2766.65, "end": 2767.17, "word": " كمان", "probability": 0.723876953125}, {"start": 2767.17, "end": 2767.39, "word": " بال", "probability": 0.89453125}, {"start": 2767.39, "end": 2767.97, "word": " boundary", "probability": 0.80419921875}, {"start": 2767.97, "end": 2768.61, "word": " region", "probability": 0.8984375}, {"start": 2768.61, "end": 2769.77, "word": " للدالة", "probability": 0.9193115234375}, {"start": 2769.77, "end": 2770.01, "word": " F", "probability": 0.56884765625}, {"start": 2770.01, "end": 2770.31, "word": " اللى", "probability": 0.69873046875}, {"start": 2770.31, "end": 2770.89, "word": " عندها", "probability": 0.99169921875}, {"start": 2770.89, "end": 2771.33, "word": " ممكن", "probability": 0.98779296875}, {"start": 2771.33, "end": 2772.01, "word": " تاخد", "probability": 0.9640299479166666}, {"start": 2772.01, "end": 2772.77, "word": " local", "probability": 0.830078125}, {"start": 2772.77, "end": 2773.35, "word": " maximum", "probability": 0.927734375}, {"start": 2773.35, "end": 2773.63, "word": " و", "probability": 0.94970703125}, {"start": 2773.63, "end": 2773.89, "word": " local", "probability": 0.64453125}, {"start": 2773.89, "end": 2774.41, "word": " minimum", "probability": 0.9736328125}, {"start": 2774.41, "end": 2774.95, "word": " و", "probability": 0.95849609375}, {"start": 2774.95, "end": 2775.39, "word": " نحصل", "probability": 0.80078125}, {"start": 2775.39, "end": 2775.77, "word": " قيم", "probability": 0.965576171875}, {"start": 2775.77, "end": 2776.57, "word": " الدالة", "probability": 0.98828125}, {"start": 2776.57, "end": 2777.55, "word": " عندنا", "probability": 0.830810546875}, {"start": 2777.55, "end": 2777.87, "word": " هذا", "probability": 0.278564453125}, {"start": 2777.87, "end": 2778.53, "word": " إذا", "probability": 0.55035400390625}, {"start": 2778.53, "end": 2778.87, "word": " صرت", "probability": 0.830322265625}, {"start": 2778.87, "end": 2779.21, "word": " عندى", "probability": 0.5777587890625}, {"start": 2779.21, "end": 2779.51, "word": " الحمد", "probability": 0.828369140625}, {"start": 2779.51, "end": 2779.73, "word": " لله", "probability": 0.8916015625}, {"start": 2779.73, "end": 2780.07, "word": " قيم", "probability": 0.97802734375}, {"start": 2780.07, "end": 2780.67, "word": " كتيرة", "probability": 0.91162109375}, {"start": 2780.67, "end": 2781.39, "word": " قيم", "probability": 0.902587890625}, {"start": 2781.39, "end": 2781.67, "word": " تبع", "probability": 0.87548828125}, {"start": 2781.67, "end": 2781.83, "word": " ال", "probability": 0.73388671875}, {"start": 2781.83, "end": 2782.17, "word": " interior", "probability": 0.52490234375}, {"start": 2782.17, "end": 2782.61, "word": " points", "probability": 0.8935546875}, {"start": 2782.61, "end": 2782.75, "word": " و", "probability": 0.9765625}, {"start": 2782.75, "end": 2782.97, "word": " قيم", "probability": 0.81640625}, {"start": 2782.97, "end": 2783.25, "word": " تبع", "probability": 0.9666341145833334}, {"start": 2783.25, "end": 2783.45, "word": " ال", "probability": 0.96923828125}, {"start": 2783.45, "end": 2783.91, "word": " boundary", "probability": 0.927734375}, {"start": 2783.91, "end": 2784.47, "word": " points", "probability": 0.83251953125}, {"start": 2784.47, "end": 2784.97, "word": " باجي", "probability": 0.6411946614583334}, {"start": 2784.97, "end": 2785.07, "word": " في", "probability": 0.48974609375}, {"start": 2785.07, "end": 2785.51, "word": " الآخر", "probability": 0.90576171875}, {"start": 2785.51, "end": 2786.25, "word": " خطوة", "probability": 0.97802734375}, {"start": 2786.25, "end": 2786.61, "word": " تالتة", "probability": 0.841552734375}, {"start": 2786.61, "end": 2786.71, "word": " و", "probability": 0.75341796875}, {"start": 2786.71, "end": 2787.07, "word": " الأخيرة", "probability": 0.87451171875}], "temperature": 1.0}, {"id": 100, "seek": 280993, "start": 2787.41, "end": 2809.93, "text": "بطلع أكبر قيمة بقول هذه ال absolute maximum و أقل قيمة بقول main هذه ال absolute minimum مكافئة الله بالسرعليمة يبقى هذا باختصار اللي بدنا نعمله يبقى أول حاجة بده أحسب ال internal points اللي الدالة ممكن تاخد عندها local maximum أو local minimum بعد هيك", "tokens": [3555, 9566, 1211, 3615, 5551, 4117, 26890, 12174, 32640, 3660, 4724, 39648, 29538, 2423, 8236, 6674, 4032, 5551, 4587, 1211, 12174, 32640, 3660, 4724, 39648, 2135, 29538, 2423, 8236, 7285, 3714, 4117, 31845, 19986, 3660, 21984, 20666, 3794, 2288, 3615, 20292, 46007, 7251, 3555, 4587, 7578, 23758, 4724, 47283, 2655, 9381, 9640, 13672, 1829, 47525, 8315, 8717, 25957, 43761, 7251, 3555, 4587, 7578, 5551, 12610, 11331, 26108, 3660, 47525, 3224, 5551, 5016, 35457, 2423, 6920, 2793, 13672, 1829, 32748, 6027, 3660, 3714, 43020, 6055, 47283, 3215, 43242, 11296, 2654, 6674, 34051, 2654, 7285, 39182, 39896, 4117], "avg_logprob": -0.20006443298969073, "compression_ratio": 1.768181818181818, "no_speech_prob": 0.0, "words": [{"start": 2787.41, "end": 2788.21, 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0.7689615885416666}, {"start": 2804.43, "end": 2804.99, "word": " ممكن", "probability": 0.989501953125}, {"start": 2804.99, "end": 2805.47, "word": " تاخد", "probability": 0.97216796875}, {"start": 2805.47, "end": 2805.81, "word": " عندها", "probability": 0.991455078125}, {"start": 2805.81, "end": 2806.09, "word": " local", "probability": 0.88427734375}, {"start": 2806.09, "end": 2806.71, "word": " maximum", "probability": 0.95751953125}, {"start": 2806.71, "end": 2807.41, "word": " أو", "probability": 0.6494140625}, {"start": 2807.41, "end": 2807.93, "word": " local", "probability": 0.927734375}, {"start": 2807.93, "end": 2808.59, "word": " minimum", "probability": 0.98193359375}, {"start": 2808.59, "end": 2809.49, "word": " بعد", "probability": 0.86474609375}, {"start": 2809.49, "end": 2809.93, "word": " هيك", "probability": 0.9267578125}], "temperature": 1.0}, {"id": 101, "seek": 283672, "start": 2810.12, "end": 2836.72, "text": "بدي اجي الى ال boundary points اللي ممكن الذالة تكون عندها local maximum و local minimum عند هذه النقاط في حالة ال intro هو ال boundary بدي احسب قداش القيم المختلفة لهذه الذالة بعدين بدي اقارن بين هذه القيمة القيم اللي عندها اكبر قيمة بقول هي absolute maximum واقل قيمة بقول هي main absolute minimum لهذه الذالة اعظم موضوع احتلالي", "tokens": [3555, 16254, 1975, 7435, 1829, 2423, 7578, 2423, 12866, 2793, 13672, 1829, 3714, 43020, 32545, 6027, 3660, 6055, 30544, 43242, 11296, 2654, 6674, 4032, 2654, 7285, 43242, 29538, 28239, 4587, 41193, 8978, 11331, 6027, 3660, 2423, 12897, 31439, 2423, 12866, 4724, 16254, 1975, 5016, 35457, 12174, 3215, 33599, 25062, 32640, 9673, 46456, 46538, 3660, 46740, 24192, 32545, 6027, 3660, 39182, 9957, 4724, 16254, 1975, 4587, 9640, 1863, 49374, 29538, 25062, 32640, 3660, 25062, 32640, 13672, 1829, 43242, 11296, 1975, 4117, 26890, 12174, 32640, 3660, 4724, 39648, 39896, 8236, 6674, 4032, 995, 4587, 1211, 12174, 32640, 3660, 4724, 39648, 39896, 2135, 8236, 7285, 46740, 24192, 32545, 6027, 3660, 1975, 3615, 19913, 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"word": " يوم", "probability": 0.98974609375}, {"start": 5520.4, "end": 5521.82, "word": " تمانتاشر", "probability": 0.89482421875}, {"start": 5521.82, "end": 5523.1, "word": " تمانية", "probability": 0.9650065104166666}, {"start": 5523.1, "end": 5523.58, "word": " و", "probability": 0.494140625}, {"start": 5523.58, "end": 5524.04, "word": " الامتحان", "probability": 0.97685546875}, {"start": 5524.04, "end": 5524.24, "word": " اظن", "probability": 0.953125}, {"start": 5524.24, "end": 5524.4, "word": " انت", "probability": 0.625}, {"start": 5524.4, "end": 5524.7, "word": " خمسة", "probability": 0.8701171875}, {"start": 5524.7, "end": 5524.8, "word": " و", "probability": 0.9208984375}, {"start": 5524.8, "end": 5525.26, "word": " عشرين", "probability": 0.74609375}, {"start": 5525.26, "end": 5526.16, "word": " انا", "probability": 0.433837890625}, {"start": 5526.16, "end": 5527.04, "word": " ماشي", "probability": 0.9016927083333334}, {"start": 5527.04, "end": 5527.28, "word": " يبقى", 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" أول", "probability": 0.750732421875}, {"start": 5531.7, "end": 5532.4, "word": " بأول", "probability": 0.99267578125}, {"start": 5532.4, "end": 5533.5, "word": " حتى", "probability": 0.666259765625}, {"start": 5533.5, "end": 5534.78, "word": " تستفيدوا", "probability": 0.99208984375}, {"start": 5534.78, "end": 5535.04, "word": " ان", "probability": 0.72412109375}, {"start": 5535.04, "end": 5535.36, "word": " شاء", "probability": 0.9873046875}, {"start": 5535.36, "end": 5535.64, "word": " الله", "probability": 0.9619140625}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 5536.45, "duration_after_vad": 4835.278468750006}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/xMNKd8BQ9Wg_raw.srt b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/xMNKd8BQ9Wg_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..9e76bcce8b4acbf8405064c7c2ba7138e22f754e
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/xMNKd8BQ9Wg_raw.srt
@@ -0,0 +1,3076 @@
+1
+00:00:14,640 --> 00:00:19,860
+بسم الله الرحمن الرحيم لان بنرجع مرة ثانية لل
+
+2
+00:00:19,860 --> 00:00:23,910
+section اللي بدناها في نهاية المحاضرة الماضيةفكرنا
+
+3
+00:00:23,910 --> 00:00:30,690
+العنوان ال extreme values and saddle points طبعا
+
+4
+00:00:30,690 --> 00:00:34,390
+أعطينا تعريف لل local maximum و ال local minimum
+
+5
+00:00:34,390 --> 00:00:38,750
+أو ان شئ تمقوله ال local extrema لكن ال saddle
+
+6
+00:00:38,750 --> 00:00:43,030
+point لم نعطي لها تعريفوعرفنا في حالة ال local
+
+7
+00:00:43,030 --> 00:00:47,550
+maximum النقطة بقول عنها local maximum إذا كانت
+
+8
+00:00:47,550 --> 00:00:51,830
+قيمة الدالة عند هذه النقطة أكبر من أي قيمة في
+
+9
+00:00:51,830 --> 00:00:56,130
+المنطقة المجاورة لهذه النقطة في ال domain تبعها
+
+10
+00:00:56,130 --> 00:01:00,830
+يعني وكذلك بالنسبة لمين لل local منما بكون قيمتها
+
+11
+00:01:00,830 --> 00:01:06,170
+أقلمن جميع قيم الدالة خلال المنطقة المعرفة دي أو
+
+12
+00:01:06,170 --> 00:01:11,310
+على open disk من جزء من ال domain تبع هذه الدالة
+
+13
+00:01:11,310 --> 00:01:15,390
+طبعا التعريف لاحظه المرة الماضية انه في شبه كبير
+
+14
+00:01:15,390 --> 00:01:18,150
+جدا بينه بين تعريف ال local maximum و local
+
+15
+00:01:18,150 --> 00:01:24,070
+minimum for the function ofone variable طيب وصلنا
+
+16
+00:01:24,070 --> 00:01:27,830
+الأن لماين لتعريف ال settle point اللي هي النقطة
+
+17
+00:01:27,830 --> 00:01:34,990
+السارجية التي تقابل نقطة الانقلاب أو نقطة الانعطاف
+
+18
+00:01:34,990 --> 00:01:40,030
+وين في ال calculus ايه او ال functions of one
+
+19
+00:01:40,030 --> 00:01:43,950
+variable التعريف بيقول ايش بيقول ال differentiable
+
+20
+00:01:43,950 --> 00:01:50,360
+function f of x و y has a settle pointيبقى بيكون
+
+21
+00:01:50,360 --> 00:01:55,600
+عندى نقطة سارجية at a critical point a و b عند
+
+22
+00:01:55,600 --> 00:02:01,000
+النقطة الحاجة a و b if in every open disk centered
+
+23
+00:02:01,000 --> 00:02:07,040
+at a و b روحنا على جزء من ال domain النقطة ل a و b
+
+24
+00:02:07,040 --> 00:02:12,300
+أخدنا disk حوالها there are domain points x و y
+
+25
+00:02:12,300 --> 00:02:18,570
+where f of x و y أكبر من ال f of a و bيعني في نقاط
+
+26
+00:02:18,570 --> 00:02:24,730
+في ال domain قيمة الدالة عندها أكبر من قيم الدالة
+
+27
+00:02:24,730 --> 00:02:29,490
+f of a و b أو قيمة الدالة f of a و b و كذلك domain
+
+28
+00:02:29,490 --> 00:02:34,650
+point x و y حيث f of x و y أقل على عكس اللي فوق
+
+29
+00:02:34,650 --> 00:02:41,760
+أقل من f of a و b ال pointالـA والـB والـF of A وB
+
+30
+00:02:41,760 --> 00:02:48,140
+on the surface لأن هذا اسمه point of the surface
+
+31
+00:02:48,140 --> 00:02:53,800
+الان مش هنفهم هذا ال definition تعالوا الى احدى أو
+
+32
+00:02:53,800 --> 00:02:58,660
+بعض ال surfaces اللي مرت علينا دراستها قبل ذلك في
+
+33
+00:02:58,660 --> 00:03:05,480
+هذا المقرر فكان عندنا الشكل لأن هذا الرسم الرقم 6
+
+34
+00:03:05,480 --> 00:03:07,300
+من الرسومات ال 6
+
+35
+00:03:11,110 --> 00:03:17,210
+هذا الشكل اليوم رسمناه يشبه السرج تبع الحصان وزي
+
+36
+00:03:17,210 --> 00:03:21,830
+ما تشوفين فعلا يشبه السرج تبع الحصان الان لو جيت
+
+37
+00:03:21,830 --> 00:03:26,830
+للنقطة اللي عندنا هذه على سبيل المثال يبقى النقطة
+
+38
+00:03:26,830 --> 00:03:31,870
+اللي عندنا هذه زي ما انتوا شايفين لو جيت أخدت نقطة
+
+39
+00:03:31,870 --> 00:03:37,120
+تانية على السطح زي النقطة اللي عندنا هذهطبعا هذه
+
+40
+00:03:37,120 --> 00:03:41,920
+لو جيت أسقطها على القاعدة هنا بيكون F of A وB
+
+41
+00:03:41,920 --> 00:03:46,720
+اليمين النقطة اللي عندنا هذه تمام لو جيتنا النقطة
+
+42
+00:03:46,720 --> 00:03:53,480
+دي قيمة الدالة أكبر من قيمة الدالة عند هذه النقطة
+
+43
+00:03:53,480 --> 00:03:59,830
+تمام طب لو جيت أخد نقطة زي النقطة هذهعلى السطح
+
+44
+00:03:59,830 --> 00:04:03,330
+اللي جهتنا يا بنات أخدتها يبقى قيمة الدالة أنها
+
+45
+00:04:03,330 --> 00:04:09,910
+مالها أقل من هذه النقطة بل هنا كانت Z ب Zero هنا Z
+
+46
+00:04:09,910 --> 00:04:15,170
+بقيمة سالبة وبالتالي الإحداث رقم تلاتة بقيمة سالبة
+
+47
+00:04:15,170 --> 00:04:20,610
+إذا هي عندي نقاطقيمة الدالة عندها بتكون أكبر من
+
+48
+00:04:20,610 --> 00:04:25,810
+قيمة الدالة عند النقطة السرجية وكذلك نقاط أخرى
+
+49
+00:04:25,810 --> 00:04:30,690
+قيمة الدالة عندها أقل من قيمة النقطة السرجية إذا
+
+50
+00:04:30,690 --> 00:04:35,330
+حدث ذلك يبقى بقول النقطة هذه settle point نقطة
+
+51
+00:04:35,330 --> 00:04:41,170
+سرجية إذا يا بنات النقطة هذه اللي هنا بقول settle
+
+52
+00:04:41,170 --> 00:04:48,900
+pointيبقى هذه سدل point اللى هى النقطة سرجى لعامة
+
+53
+00:04:48,900 --> 00:04:55,000
+الانفون فهمنا هذا التعريف ان قيمة الدالة عند اى
+
+54
+00:04:55,000 --> 00:05:01,040
+نقطة في دومينها اكبر من قيمة الدالة اللى هو f of a
+
+55
+00:05:01,040 --> 00:05:05,240
+وb وفي المقابل برضه قيمة عند نقطة اخرى
+
+56
+00:05:13,640 --> 00:05:17,880
+هذه العملية صعبة شوية و نقعد أجيب نقاط و أحسب
+
+57
+00:05:17,880 --> 00:05:24,020
+عددها لذلك بعد قليل هنحط قاعدة من خلالها نحدد ماهي
+
+58
+00:05:24,020 --> 00:05:27,540
+ال local maximum و ماهي ال local minimum و ماهي
+
+59
+00:05:27,540 --> 00:05:34,270
+النقاط السرجيةبس هاذي بروح لمين لاختبار المشتقة
+
+60
+00:05:34,270 --> 00:05:38,410
+الثانية طبعا في الcalculus ايه بجينا نجيب ال local
+
+61
+00:05:38,410 --> 00:05:41,030
+maximum و ال local minimum و ال reflection point
+
+62
+00:05:41,030 --> 00:05:45,730
+برضه بالاختبارين و خاصة الاختبار الثاني وهنا كذلك
+
+63
+00:05:45,970 --> 00:05:49,870
+بالاختبار الثاني إذا مشان نحسب ال settle points
+
+64
+00:05:49,870 --> 00:05:53,450
+عمليا و كذلك ال local maximum و ال local minimum
+
+65
+00:05:53,450 --> 00:05:57,290
+اللي عرفناها المرة الماضية بدنا نيجي نحط القاعدة
+
+66
+00:05:57,290 --> 00:06:03,350
+المستقبل ثانية وبناء عليها نشتغل إذا بدنا نروح نحط
+
+67
+00:06:03,350 --> 00:06:08,330
+عنها هنقول second derivative test
+
+68
+00:06:16,200 --> 00:06:23,960
+test for local
+
+69
+00:06:23,960 --> 00:06:32,720
+extreme values
+
+70
+00:06:48,210 --> 00:07:00,910
+طريقه was that ان ال f of x و y and its first and
+
+71
+00:07:00,910 --> 00:07:15,790
+its first and second partially
+
+72
+00:07:15,790 --> 00:07:16,450
+derivatives
+
+73
+00:07:26,290 --> 00:07:36,610
+partial derivatives are continuous a
+
+74
+00:07:36,610 --> 00:07:44,690
+throw a
+
+75
+00:07:44,690 --> 00:07:45,630
+disc center
+
+76
+00:07:59,480 --> 00:08:08,420
+centred at اللي هو النقطة A وB and
+
+77
+00:08:08,420 --> 00:08:14,080
+that ال
+
+78
+00:08:14,080 --> 00:08:21,500
+Fx عند النقطة A وB يساوي
+
+79
+00:08:21,500 --> 00:08:34,710
+ال Fy عند النقطة A وB يساوي 0ثم امرا واحد ال F has
+
+80
+00:08:34,710 --> 00:08:47,970
+local maximum ال F has local maximum at نقطة A و B
+
+81
+00:08:47,970 --> 00:08:58,000
+F إذا كان ال F XX أكبر من أقل من ال zeroأقل من الـ
+
+82
+00:08:58,000 --> 00:09:11,360
+0 and الـ Fxx مضروب في الـ Fyy ناقص F²xy كله
+
+83
+00:09:11,360 --> 00:09:15,720
+greater than 0 حتى النقطة A وD
+
+84
+00:09:18,950 --> 00:09:25,590
+الـ f has local minimum عند النقطة a و b إذا كان
+
+85
+00:09:25,590 --> 00:09:38,090
+ال fxx greater than zero and ال fxx fyy ناقص f²xy
+
+86
+00:09:38,090 --> 00:09:48,490
+f²xy برضه كان greater than zero عند النقطة a و b
+
+87
+00:09:53,930 --> 00:10:07,250
+فـ has a saddle point نقطة سرجية at النقطة A وB
+
+88
+00:10:07,250 --> 00:10:11,930
+فإذا كان الـ F XX
+
+89
+00:10:18,300 --> 00:10:28,680
+أقل من الـ zero at النقطة A وB النقطة الرابعة
+
+90
+00:10:28,680 --> 00:10:36,080
+والأخيرة من هذا الاختبار تقول The test is
+
+91
+00:10:36,080 --> 00:10:42,420
+inconclusive at
+
+92
+00:10:42,420 --> 00:10:56,230
+A وBعند النقطة A وB إذا كان الـ Fxx Fyy ناقص Fxy²
+
+93
+00:10:56,230 --> 00:11:04,490
+بده يساوي Zero at اللي هو من النقطة A وB
+
+94
+00:11:38,880 --> 00:11:43,580
+بعدين نرجع لهذا الاختبار مرة ثانية نحاول نقرأه
+
+95
+00:11:43,580 --> 00:11:48,300
+كويس نفهم الشيء اللي موجود فيه اقول second
+
+96
+00:11:48,300 --> 00:11:52,920
+derivative test for local extreme value اختبار
+
+97
+00:11:52,920 --> 00:11:58,620
+المشتق ايه الثاني لمعرفة ال local minimum و ال
+
+98
+00:11:58,620 --> 00:12:03,060
+local maximum و الsettled point الان نفترض ان هذا
+
+99
+00:12:03,060 --> 00:12:07,020
+f of x و y and is first and second partial
+
+100
+00:12:07,020 --> 00:12:07,840
+derivative
+
+101
+00:12:18,730 --> 00:12:20,130
+YYYYYYYYYYYYYYYYYYYYY
+
+102
+00:12:37,480 --> 00:12:42,340
+قال لي و كذلك كان ال fx عند ال a و ال b بده يساوي
+
+103
+00:12:42,340 --> 00:12:47,300
+0 و ال fy عند ال a و ال b بده يساوي 0 طب ليش هذا
+
+104
+00:12:47,300 --> 00:12:52,360
+ال condition حطه؟ مش هنضمن ان في عندي critical
+
+105
+00:12:52,360 --> 00:12:56,970
+pointيبقى ال Fx لما نسويها بالزيرو و ال Fy لما
+
+106
+00:12:56,970 --> 00:13:01,870
+نسويها بالزيرو أو لو كانت إحداهما أو كلاهما is
+
+107
+00:13:01,870 --> 00:13:05,590
+undefined عندها نقطة بقول هنا هذه critical points
+
+108
+00:13:05,590 --> 00:13:10,570
+اللي ممكن يكون local maximum أو local minimum
+
+109
+00:13:16,570 --> 00:13:21,250
+النقطة الأولى الـ f has local maximum عند النقطة
+
+110
+00:13:21,250 --> 00:13:25,490
+الأولى إذا كان fxx أقل من الـ zero
+
+111
+00:13:28,870 --> 00:13:34,290
+مقدار المتباين يجب أن يكون أكبر من الـ 0 FXX
+
+112
+00:13:34,290 --> 00:13:42,970
+ضربتها في FYY و نقصتها أو طرحتها من الـ FXY لكل
+
+113
+00:13:42,970 --> 00:13:43,550
+تربيع
+
+114
+00:13:48,120 --> 00:13:54,880
+القيمة هذه قيمة موجبة والقيمة هذه قيمة سالبة يبقى
+
+115
+00:13:54,880 --> 00:13:59,500
+بقول اني local maximum طب local minimum القيمة هذه
+
+116
+00:13:59,500 --> 00:14:04,740
+بتبقى قيمة سأق موجبة اللي فوق سالبة وهذه موجبة لكن
+
+117
+00:14:04,740 --> 00:14:09,220
+القيمة هذه مالها موجبة المحدد او المميز اللي عندنا
+
+118
+00:14:09,220 --> 00:14:14,200
+هذا في كل الأمرين بقيمة موجبة طب مين بدي افرق مع
+
+119
+00:14:14,200 --> 00:14:18,590
+ال local maximum و ال local minimum؟الـ FXX والله
+
+120
+00:14:18,590 --> 00:14:23,630
+إذا كان FXX سالبة يبقى لدي local maximum FXX موجبة
+
+121
+00:14:23,630 --> 00:14:29,710
+يبقى local minimum طب افترض إن المحدد لأن هذا أو
+
+122
+00:14:29,710 --> 00:14:35,970
+المميز هذا كان أقل من ال zero وال FXX إيش ما كانت
+
+123
+00:14:35,970 --> 00:14:40,610
+تكون موجبة سلمة ماتفرقش عني طلع القيمة إيش قيمة
+
+124
+00:14:40,610 --> 00:14:46,730
+سلمة إن حدث ذلكيبقى بقول النقطة الان هنا settle
+
+125
+00:14:46,730 --> 00:14:51,830
+point طب لو كله يسوي zero باختبارنا فشل و بدنا
+
+126
+00:14:51,830 --> 00:14:55,390
+نرجع لمين؟ للاختبار الأول اللي اتكلمنا عليه المرة
+
+127
+00:14:55,390 --> 00:14:58,810
+الماضية اللي هو ال first derivative test for four
+
+128
+00:14:58,810 --> 00:15:03,070
+local extreme values ما علينا مرة ثانية بقول
+
+129
+00:15:03,070 --> 00:15:10,240
+باختصاريبقى يا بنات المشتقة الأولى لدى ال F
+
+130
+00:15:10,240 --> 00:15:15,920
+والمشتقة التانية Fxx بتلعب دور كبير فيه تحديد هل
+
+131
+00:15:15,920 --> 00:15:20,180
+هي ال local maximum أو ال local minimum هذه ال
+
+132
+00:15:20,180 --> 00:15:24,500
+inequality هنا أكبر من ال zero في الحالتين يبقى
+
+133
+00:15:24,500 --> 00:15:27,100
+بدأ فرق من ال local maximum و ال local minimum
+
+134
+00:15:27,100 --> 00:15:32,400
+بتطلع لل Fxx والله إذا كانت أكبر من ال zero يبقى
+
+135
+00:15:32,400 --> 00:15:38,230
+local minimum أقل من ال zero يبقى localأفترض أنها
+
+136
+00:15:38,230 --> 00:15:41,970
+كانت أقل من الـ zero اللي هو اللي انقلت التاني إلى
+
+137
+00:15:41,970 --> 00:15:45,770
+اليمين و ال fxx ايش ما تكون تكون موجة و الله سالبة
+
+138
+00:15:45,770 --> 00:15:49,890
+ما تفرقش عني بهمنها دي إذا و الله طلعت سالبة يبقى
+
+139
+00:15:49,890 --> 00:15:55,450
+يبقى هذي ال settle point يبقى من هنا فرقت ما بين
+
+140
+00:15:55,450 --> 00:15:58,370
+ال settle point و ال local maximum و ال local
+
+141
+00:15:58,370 --> 00:16:00,830
+minimum فرقت ما بين ال local maximum و ال local
+
+142
+00:16:00,830 --> 00:16:06,900
+minimum بقيمة ال fxxفرق بينهم وبين ال settle point
+
+143
+00:16:06,900 --> 00:16:11,540
+بواسطة ال main inequality اللي عندنا طب أطلع النتج
+
+144
+00:16:11,540 --> 00:16:16,560
+هذا يساوي zero يبقى لا أستطيع الحكم على المسألة
+
+145
+00:16:16,560 --> 00:16:21,580
+اللي عندنا عشان نثبت هذه المعلومات ناخد مثال نحسب
+
+146
+00:16:21,580 --> 00:16:25,000
+فيه ال local maximum و ال local minimum و ال
+
+147
+00:16:25,000 --> 00:16:27,700
+settle point طب نقول example
+
+148
+00:16:51,380 --> 00:17:01,720
+local extremum and settled points and settled
+
+149
+00:17:01,720 --> 00:17:11,600
+points of the function لدالة f of x y بده ساوي
+
+150
+00:17:11,600 --> 00:17:21,840
+اللي هو x تكيب زائد y تكيب زائد تلاتة x ترابيعناقص
+
+151
+00:17:21,840 --> 00:17:31,280
+تلاتة وايت ربيع ناقص تماني solution
+
+152
+00:18:05,060 --> 00:18:08,880
+خلّيني أخبركم أني حقا أقول هذه الـ local extreme
+
+153
+00:18:08,880 --> 00:18:12,740
+values اللي عندك وهذه ال settle points للدالة اللي
+
+154
+00:18:12,740 --> 00:18:19,920
+عندنا هذا يبقى بدي أرجع لازم أحسب له FXX, FYY, FXY
+
+155
+00:18:19,920 --> 00:18:23,540
+يبقى هي دول التلاتة اللي هم بيلعبوا الدور الكبير
+
+156
+00:18:23,540 --> 00:18:27,080
+في معرفة ال local extreme أو settle points لميار
+
+157
+00:18:27,080 --> 00:18:32,790
+ال function اللي عندناإذا بدي أبدأ بال Fx يساوي
+
+158
+00:18:32,790 --> 00:18:41,930
+تلاتة X تربيع زائد ستة X والباقي بطيئة بالمرة نحسب
+
+159
+00:18:41,930 --> 00:18:51,770
+Fxx فيساوي نشتغل كمان مرة يبقى ستة X زائد ستة
+
+160
+00:18:51,770 --> 00:18:53,810
+فاهمين كويس؟
+
+161
+00:18:56,480 --> 00:19:01,440
+أنا لم أحصل على نقطة محددة في المثل ، لذلك انا
+
+162
+00:19:01,440 --> 00:19:08,280
+سأخرج النقطة لوحدي النقطة لوحدي من اين؟ من ال Fx
+
+163
+00:19:08,280 --> 00:19:13,960
+يبقى شرطنا هنا انوش يا بنات بديها قدر تساوي؟ تساوي
+
+164
+00:19:13,960 --> 00:19:19,660
+Zero إذا بدي أخد ال Fx بده تساوي Zero وهذا بتعطينا
+
+165
+00:19:20,050 --> 00:19:25,910
+إنه تلاتة X تربيه زائد ستة X بدي ساوي Zero هذا بدي
+
+166
+00:19:25,910 --> 00:19:35,170
+يعطينا ميم انه ستة X و الله كدهش تلاتة تلاتة X بضل
+
+167
+00:19:35,170 --> 00:19:42,180
+عند هنا X زائد اتنين كله بدي ساوي كدهش Zeroإذا
+
+168
+00:19:42,180 --> 00:19:48,840
+بنقل عليه هذا بده يعطينا ان X بدها تساوي 0 و X بده
+
+169
+00:19:48,840 --> 00:20:00,120
+يساوي كده؟ سالي 2 طيب اروح نجيب FY يساوييبقى fy
+
+170
+00:20:00,120 --> 00:20:07,860
+انا بدأت مع السلامة هذه تلاتة وي تربع و هنا ناقص
+
+171
+00:20:07,860 --> 00:20:12,120
+ستة وي و نسويها بالزيرو مشان نجيب ال critical
+
+172
+00:20:12,120 --> 00:20:17,780
+points كلهم مرة واحدة يبقى بناء عليه هذا بدي يعطي
+
+173
+00:20:17,780 --> 00:20:24,910
+نمينا بناء تلاتة ويفي Y ناقص اتنين بده يساوي قداش
+
+174
+00:20:24,910 --> 00:20:30,110
+بده يساوي زيرو يهجر هذا بده يعطينا ميم ان ال Y بده
+
+175
+00:20:30,110 --> 00:20:35,770
+يساوي زيرو وY تساوي ميم اتنين يبقى كام critical
+
+176
+00:20:35,770 --> 00:20:41,290
+point عندي انتين ولا اربعة اربعة اربعة critical
+
+177
+00:20:41,290 --> 00:20:49,170
+points يبقى باجي بقول هنا ده critical points
+
+178
+00:20:52,470 --> 00:21:03,430
+أه Zero و Zero و كذلك Zero و اتنين و نقص اتنين و
+
+179
+00:21:03,430 --> 00:21:11,120
+Zero و نقص اتنين و اتنينإذا بدنا نبحث كل نقطة من
+
+180
+00:21:11,120 --> 00:21:15,840
+هذه النقاط مين منهم settle point مين منهم local
+
+181
+00:21:15,840 --> 00:21:21,540
+maximum مين منهم local minimum لذلك بدنا نروح نجيب
+
+182
+00:21:21,540 --> 00:21:33,060
+من F Y Y إذا بدنا نرجع نجيب هنا F Y Y 7 نشتق هذه
+
+183
+00:21:33,060 --> 00:21:36,220
+كمان مرة إذا 6Y-6
+
+184
+00:21:51,580 --> 00:21:59,680
+يبدأ يتزاوي partial على partial Y لمن؟ لل Fx يبقى
+
+185
+00:21:59,680 --> 00:22:03,840
+partial على partial Y ليه؟ نرجع ل Fx اللي هي تلاتة
+
+186
+00:22:03,840 --> 00:22:09,880
+X تربية زائد ستة X اللي هي تلاتة X تربية زائد ستة
+
+187
+00:22:09,880 --> 00:22:11,860
+X بالمستقبل كده؟
+
+188
+00:22:30,130 --> 00:22:45,700
+النقطة الأولى 0 و 0 فنحسب F X Xعند النقطة 00 بيبقى
+
+189
+00:22:45,700 --> 00:22:50,600
+0 زائد
+
+190
+00:22:50,600 --> 00:22:52,280
+6 و لو بيبقى 6 بيبقى 6
+
+191
+00:23:02,300 --> 00:23:13,180
+يبقى ال FXY يبقى 0 على طول الخط جاهزين نبدأ من هنا
+
+192
+00:23:13,180 --> 00:23:24,060
+نحسب من الانقلة اللي عندنا يبقى بداخله FXX في FYY
+
+193
+00:23:24,060 --> 00:23:32,990
+نقص FXY2Y7 احنا ال FXX عندنا كده يا بنات هناقيمة
+
+194
+00:23:32,990 --> 00:23:37,970
+موجبة مظبوط او لا طيب يبقى انيش نشوف هذا اللي بدي
+
+195
+00:23:37,970 --> 00:23:43,910
+يعطينا يبقى هذا بدي يعطينا ستة و ال FYY عندنا
+
+196
+00:23:43,910 --> 00:23:50,990
+بقدرش اللي هو سالب ستة وهنا ناقص Zero لكل تربيع و
+
+197
+00:23:50,990 --> 00:23:55,570
+يساوي سالب ستة و تلاتين يبقى لين كلتي مالها
+
+198
+00:24:05,820 --> 00:24:13,140
+فبتعود بالنقاط اللي قالنا في المعادلة الأصلية اذا
+
+199
+00:24:13,140 --> 00:24:19,740
+بروح بقول الف زيرو وزيرو هذا سواء ان سالف تمانية
+
+200
+00:24:19,740 --> 00:24:30,160
+خلاصنا يبقى هنا هذا بدي يعطينا ان الف لديه
+
+201
+00:24:31,670 --> 00:24:38,410
+Settle point at
+
+202
+00:24:38,410 --> 00:24:44,530
+two zero و zero ايش السبب يا بنات ان ال link والتي
+
+203
+00:24:44,530 --> 00:24:51,490
+هذه طلعت قيمة سالبة اللي هو نقطة رقم تلاتة عندنا
+
+204
+00:24:51,490 --> 00:24:57,210
+تمام؟ خلصنا النقطة هذه بناروح للنقطة التانية
+
+205
+00:24:57,210 --> 00:24:59,790
+بنااخدها النقطة
+
+206
+00:25:17,970 --> 00:25:25,590
+يبقى برضه ستة و الستة مالها يا بنات أكبر من مين؟
+
+207
+00:25:25,590 --> 00:25:32,330
+أكبر من الزرع يجب أن أحسبله fyy فإن الـ zero و
+
+208
+00:25:32,330 --> 00:25:38,510
+اتنين هي فوق يبقى في قدرات؟ في ستة ولا في سلف ستة؟
+
+209
+00:25:38,510 --> 00:25:43,350
+ستة موجة اه ممتاز جدا هذه ماحطت اتنين ماعنديش X
+
+210
+00:25:43,350 --> 00:25:46,370
+يبقى بصير هنا ستة
+
+211
+00:25:52,350 --> 00:26:01,370
+هو الـ Fxy في أي نقطة كلها بـ 0 على طول القطع فانا
+
+212
+00:26:01,370 --> 00:26:11,550
+باخد الـ Fxx في الـ Fyy نقص Fxy² و يساوي
+
+213
+00:26:25,400 --> 00:26:28,800
+يبقى Fx6 أكبر من الـ Zero Fx6 أكبر من الـ Zero Fx6
+
+214
+00:26:28,800 --> 00:26:30,020
+أكبر من الـ Zero Fx6 أكبر من الـ Zero Fx6 أكبر من
+
+215
+00:26:30,020 --> 00:26:32,780
+الـ Zero Fx6 أكبر من الـ Zero Fx6 أكبر من الـ Zero
+
+216
+00:26:32,780 --> 00:26:40,000
+Fx6 أكبر من الـ Zero Fx6 أكبر من الـ Zero Fx6 أكبر
+
+217
+00:26:40,000 --> 00:26:42,870
+من الـ Zeroالـ F of 0 و 2
+
+218
+00:27:06,710 --> 00:27:13,250
+بنقص تمانية مع السلامة واربع في تلاتة بسالف اتناش
+
+219
+00:27:13,250 --> 00:27:21,310
+يبقى سالف اتناش فاروح بقول الفيه has local minimum
+
+220
+00:27:21,310 --> 00:27:29,210
+اللي هي سالف اتناش at the point عند النقطة اللي هو
+
+221
+00:27:29,210 --> 00:27:33,630
+main اللي موجودة في domainها اللي هي main zero و
+
+222
+00:27:33,630 --> 00:27:38,910
+اتنانخلصنا النقطة التانية بنروح لمين للنقطة
+
+223
+00:27:38,910 --> 00:27:46,490
+التالتة يبقى بالداخل ناخد ال point النقطة
+
+224
+00:27:46,490 --> 00:27:54,070
+التالتة اللي هو سالب اتنين و زيب سالب اتنين و زيب
+
+225
+00:27:54,070 --> 00:28:04,050
+طيب يبقى بدنا نجي نعود في mean في المعادلة الأصلية
+
+226
+00:28:04,050 --> 00:28:04,670
+و نحسب
+
+227
+00:28:08,080 --> 00:28:12,720
+يبقى مثل ما بدأنا بالضبط تماما في الأول بدي أخد
+
+228
+00:28:12,720 --> 00:28:19,820
+fxx عند النقطة سالب اتنين و زيه إذا بدي أشيل كل x
+
+229
+00:28:19,820 --> 00:28:27,480
+و أحط مكانها سالب في اتنين يبقى ستة في سالب اتنين
+
+230
+00:28:27,480 --> 00:28:32,760
+زي ستة و يسوي سالب ستة و زي ما انتوا شايفين مالها
+
+231
+00:28:33,590 --> 00:28:41,970
+أقل من زيرو كمية سالك يبقى مضاجي اخد كمان ال F Y Y
+
+232
+00:28:41,970 --> 00:28:47,930
+اللي هو عند النقطة اللي هو سالب اتنين وزيرو يساوي
+
+233
+00:28:47,930 --> 00:28:54,850
+F Y Y فوق اللي هو عبارة عن زيرو سالب ستة ويساوي
+
+234
+00:28:54,850 --> 00:29:01,970
+سالب ستة و ال F X Y هذه ثابتة ما هيبت زيرو للكل
+
+235
+00:29:02,650 --> 00:29:04,870
+يبقى بتروح اخد F
+
+236
+00:29:31,790 --> 00:29:40,090
+XX أقل من الـ Zero أقل من ال Zero وهذه أكبر من 100
+
+237
+00:29:40,090 --> 00:29:44,170
+من ال Zero في ال Calculus Maximum إذا بدنا نروح
+
+238
+00:29:44,170 --> 00:29:52,810
+نحسب كده ال F أو نقص 2 و Zero في الجسم بدنا نشيل
+
+239
+00:29:52,810 --> 00:29:57,930
+كل Y و نحط مكانها Zero و نشيل كل X و نحط مكانها
+
+240
+00:29:57,930 --> 00:29:58,090
+Zero
+
+241
+00:30:07,580 --> 00:30:15,640
+الكل تان ربيع وهنا ناقص Zero ناقص تمانية وهي ستة
+
+242
+00:30:15,640 --> 00:30:22,860
+طبعا هنا ناقص تمانية وهنا ناقص تمانية تصير ناقص
+
+243
+00:30:22,860 --> 00:30:30,820
+ستة عشر وهنا اتناش بضل قداش ناقص اربع اذا بروح
+
+244
+00:30:30,820 --> 00:30:39,690
+بقول له if has local maximumاللي هو قداش؟ سالف
+
+245
+00:30:39,690 --> 00:30:45,050
+أربع at the
+
+246
+00:30:45,050 --> 00:30:53,350
+point عند النقطة اللي هو سالف اتنين وزي اذا طلعت
+
+247
+00:30:53,350 --> 00:30:56,770
+واحدة سادي ال point واحدة local maximum واحدة
+
+248
+00:30:56,770 --> 00:31:01,850
+local minimum بقيت ال نقطة الأخيرة
+
+249
+00:31:28,870 --> 00:31:35,130
+يبقى النقطة الأخيرة يا بناتي اللي هي point كده؟
+
+250
+00:31:35,130 --> 00:31:42,350
+سالب اتنين و اتنين بدنا نروح نحسب اللي هو الف اكس
+
+251
+00:31:42,350 --> 00:31:48,750
+اكس عند النقطة سالب اتنين و اتنين وقت السابق وين
+
+252
+00:31:48,750 --> 00:31:52,990
+الف اكس اكس؟ مسحناها يعني كان ستة اكس زي ستة،
+
+253
+00:31:52,990 --> 00:32:02,870
+مظبوط؟ يبقى ستةفى ناقص اتنين ذائد ستة ويسوي كده؟
+
+254
+00:32:02,870 --> 00:32:13,650
+ناقص ستة لما لها اقل من ال zero فبنحسب FYY FYY عند
+
+255
+00:32:13,650 --> 00:32:20,190
+النقطة ناقص اتنين و اتنين و ال FYY هيقول يبقى هنا
+
+256
+00:32:20,190 --> 00:32:29,850
+ستةفى اتنين ناقص ستة ويسوي كدهش ستة ومعروف ال Fxy
+
+257
+00:32:29,850 --> 00:32:34,350
+عند اى نقطة كلها تساوي Zero على طول الخط
+
+258
+00:32:53,910 --> 00:33:00,430
+اللي فوق بتهمنيش سالبة ولا موجبة يبقى النقطة هذه
+
+259
+00:33:00,430 --> 00:33:01,630
+تعتبر مين
+
+260
+00:33:31,710 --> 00:33:38,970
+نقص تمانية نقص تمانيةيبقى هذا الكلام لو جيت فاكتهم
+
+261
+00:33:38,970 --> 00:33:45,110
+بصير ناقص تمانية و هنا زائد تمانية و هنا زائد
+
+262
+00:33:45,110 --> 00:33:51,870
+اتناشر و هنا ناقص اتناشر و هنا ناقص تمانية هذه و
+
+263
+00:33:51,870 --> 00:33:56,130
+هذه مع بعض و هذه و هذه مع السلامة يبقى الجواب
+
+264
+00:33:56,130 --> 00:34:04,030
+قداشر سالب تمانية يبقى ال F has saddle point
+
+265
+00:34:24,820 --> 00:34:28,840
+الأشياء اللي ليس بالضرورة ممكن تكون كل القيم موجبة
+
+266
+00:34:29,360 --> 00:34:35,260
+النسبة للمسألة اللى عندك يعني احنا بدل سالب تمانية
+
+267
+00:34:35,260 --> 00:34:40,180
+في المسألة لو حطينا زائد تمانية هيجيكي أحيانا صفر
+
+268
+00:34:40,180 --> 00:34:45,300
+و أحيانا رقم مش هتلاقي ولا رقم سالب صحيح ولا لا؟
+
+269
+00:34:47,800 --> 00:34:54,140
+لكن هناك موقع آخر و ليس في نفس الموقع يعني نقطة
+
+270
+00:34:54,140 --> 00:34:57,560
+اتغيرت مش نفس النقطة وبالتالي انتقلنا مثلا عند
+
+271
+00:34:57,560 --> 00:35:00,560
+النقطة هذه في local maximum عند النقطة هذه في
+
+272
+00:35:00,560 --> 00:35:03,340
+settle point عند النقطة هذه في settle point عند
+
+273
+00:35:03,340 --> 00:35:07,330
+النقطة تالتة في local minimum و هكذايعني طالع و
+
+274
+00:35:07,330 --> 00:35:11,450
+نازل الرسمة طبعا لا يمكن نقل نقص من الرسمة لأنه
+
+275
+00:35:11,450 --> 00:35:15,470
+رسم كمبيوتر تمام كل الرسمة اللي بتشوفها في الكتاب
+
+276
+00:35:15,470 --> 00:35:22,690
+رسمت كمبيوتر وبالتالي بتلاقي مجسمات أينها حد بتسأل
+
+277
+00:35:22,690 --> 00:35:28,870
+أي سؤال هنا كمان خلاص طيب فالان بننتقل إلى النقطة
+
+278
+00:35:28,870 --> 00:35:31,930
+الثانية من هذا ال section وهي
+
+279
+00:35:37,450 --> 00:35:43,430
+وخاصة الامتحانات النهائية اللي هو بنجيبها بنات ال
+
+280
+00:35:43,430 --> 00:35:49,210
+absolute maximum و ال absolute minimum لل function
+
+281
+00:35:49,210 --> 00:35:53,470
+نفس تعريف ال absolute maximum و ال absolute
+
+282
+00:35:53,470 --> 00:35:58,770
+minimum في حالة ال function of one variable اللي
+
+283
+00:35:58,770 --> 00:36:03,430
+درسناه في Calculus A قبل ذلك
+
+284
+00:36:42,650 --> 00:36:46,490
+على منطقة مغلفة ومحدودة
+
+285
+00:36:59,820 --> 00:37:14,020
+maximum او absolute minimum او absolute minimum او
+
+286
+00:37:14,020 --> 00:37:16,080
+absolute minimum او absolute minimum او absolute
+
+287
+00:37:16,080 --> 00:37:16,400
+minimum او absolute minimum او absolute minimum او
+
+288
+00:37:16,400 --> 00:37:16,740
+absolute minimum او absolute minimum او absolute
+
+289
+00:37:16,740 --> 00:37:16,960
+minimum او absolute minimum او absolute minimum او
+
+290
+00:37:16,960 --> 00:37:17,020
+absolute minimum او absolute minimum او absolute
+
+291
+00:37:17,020 --> 00:37:17,020
+minimum او absolute minimum او absolute minimum او
+
+292
+00:37:17,020 --> 00:37:17,020
+absolute minimum او absolute minimum او absolute
+
+293
+00:37:17,020 --> 00:37:17,020
+minimum او absolute minimum او absolute minimum او
+
+294
+00:37:17,020 --> 00:37:17,020
+absolute minimum او absolute minimum او absolute
+
+295
+00:37:17,020 --> 00:37:17,020
+minimum او absolute minimum او absolute minimum او
+
+296
+00:37:17,020 --> 00:37:17,020
+absolute minimum او absolute minimum او absolute
+
+297
+00:37:17,020 --> 00:37:17,020
+minimum او absolute minimum او absolute minimum او
+
+298
+00:37:17,020 --> 00:37:17,020
+absolute minimum او absolute minimum او absolute
+
+299
+00:37:17,020 --> 00:37:17,020
+minimum او absolute minimum او absolute minimum او
+
+300
+00:37:17,020 --> 00:37:17,020
+absolute minimum او absolute minimum او absolute
+
+301
+00:37:17,020 --> 00:37:17,020
+minimum او absolute minimum او absolute minimum او
+
+302
+00:37:17,020 --> 00:37:17,020
+absolute minimum او absolute minimum او absolute
+
+303
+00:37:17,020 --> 00:37:17,020
+minimum او absolute minimum او absolute minimum او
+
+304
+00:37:17,020 --> 00:37:17,020
+absolute minimum او absolute minimum او absolute
+
+305
+00:37:17,020 --> 00:37:17,060
+minimum او absolute minimum او absolute minimum او
+
+306
+00:37:17,060 --> 00:37:23,160
+absolute minimum او absolute minimum
+
+307
+00:37:23,160 --> 00:37:28,140
+او absolute minimum
+
+308
+00:37:39,160 --> 00:37:48,600
+النقطة الداخلية للمنطقة R where
+
+309
+00:37:48,600 --> 00:37:54,560
+ال F may
+
+310
+00:37:54,560 --> 00:38:00,760
+have may have local maximum
+
+311
+00:38:03,860 --> 00:38:14,260
+local maximum or local minimum or local
+
+312
+00:38:14,260 --> 00:38:19,320
+minima and evaluate the function's value and
+
+313
+00:38:19,320 --> 00:38:31,930
+evaluate the function's value قيمة الدالةat this
+
+314
+00:38:31,930 --> 00:38:42,690
+point at this point عند هذه النقاط these
+
+315
+00:38:42,690 --> 00:38:46,210
+are
+
+316
+00:38:46,210 --> 00:38:51,990
+the points هذه
+
+317
+00:38:51,990 --> 00:39:02,970
+النقاط where ال fx يتساوي ال fy يتساوي ال zeroor
+
+318
+00:39:02,970 --> 00:39:09,270
+where
+
+319
+00:39:09,270 --> 00:39:22,330
+one or both of Fx
+
+320
+00:39:22,330 --> 00:39:27,850
+and Fy fail to exist
+
+321
+00:39:32,840 --> 00:39:43,220
+بعد ذلك هذه المقاومة الموجودة في
+
+322
+00:39:43,220 --> 00:39:47,440
+المقاومة هذه المقاومة
+
+323
+00:39:47,440 --> 00:39:53,100
+الموجودة في المقاومة الموجودة في المقاومة R اذا
+
+324
+00:39:53,100 --> 00:39:58,720
+F كان
+
+325
+00:39:58,720 --> 00:40:02,240
+لديه مقاومة
+
+326
+00:40:04,690 --> 00:40:20,110
+maximum هو local minimum and find the
+
+327
+00:40:20,110 --> 00:40:27,130
+function value
+
+328
+00:40:27,130 --> 00:40:38,870
+قيمة الدولةat these points
+
+329
+00:40:38,870 --> 00:40:50,450
+عند هذه اللحظة ثلاثة لـ maximum and
+
+330
+00:40:50,450 --> 00:40:55,390
+minimum ماليوز
+
+331
+00:41:02,670 --> 00:41:09,410
+او اذا انطقت
+
+332
+00:41:09,410 --> 00:41:17,990
+سيكون الـ Absolute سيكون الـ Absolute
+
+333
+00:41:17,990 --> 00:41:21,390
+maximum
+
+334
+00:41:21,390 --> 00:41:24,530
+و
+
+335
+00:41:24,530 --> 00:41:30,230
+Absolute minimum
+
+336
+00:41:31,830 --> 00:41:44,650
+respectively examples
+
+337
+00:41:44,650 --> 00:41:50,410
+اتحول
+
+338
+00:41:50,410 --> 00:41:59,770
+لثالث by the absolute maximum by the absolute
+
+339
+00:42:02,720 --> 00:42:11,240
+maximum and minimum of
+
+340
+00:42:11,240 --> 00:42:16,600
+the function لدى
+
+341
+00:42:16,600 --> 00:42:22,780
+f of x و y بساوية
+
+342
+00:42:25,610 --> 00:42:37,390
+معقس XY زائد Y تربيع زائد واحد on the closed
+
+343
+00:42:37,390 --> 00:42:49,310
+triangle closed triangle plate in
+
+344
+00:42:49,310 --> 00:42:50,130
+the first
+
+345
+00:42:54,840 --> 00:43:03,940
+الـ first quadrant او
+
+346
+00:43:03,940 --> 00:43:13,060
+البيان العين او
+
+347
+00:43:13,060 --> 00:43:22,220
+البيان العين X تساوي Zero وY تساوي أربعة and
+
+348
+00:43:24,440 --> 00:43:26,740
+Y مستوى S
+
+349
+00:44:28,050 --> 00:44:32,050
+نرجع الكلام اللي كتبناه على اللوح تاني نقرأ كل
+
+350
+00:44:32,050 --> 00:44:37,150
+نقطة ي و كل حيثية لك نفهم شو اللي مطلوب منه و بعد
+
+351
+00:44:37,150 --> 00:44:43,190
+ذلك بنروح نحل المثال تبعه بيقول لي ده نجل ال
+
+352
+00:44:43,190 --> 00:44:46,030
+absolute maximum و ال absolute minimum اللي يدال
+
+353
+00:44:46,030 --> 00:44:51,530
+على ال domain تبعها بيات ال domain كمنطقة محدودة و
+
+354
+00:44:51,530 --> 00:44:57,710
+كذلك منطقة محدودةطبعا بعد قليل هقولك ليش منطقة
+
+355
+00:44:57,710 --> 00:45:02,990
+مغلقة و ليش منطقة محدودة بقول to find the absolute
+
+356
+00:45:02,990 --> 00:45:06,750
+maximum او absolute minimum make the following
+
+357
+00:45:06,750 --> 00:45:12,250
+steps بدنا نعمل خطوات أتانية الخطوة الأولى بقول
+
+358
+00:45:12,250 --> 00:45:15,410
+less than internal constantly قائمة بالنقاط
+
+359
+00:45:15,410 --> 00:45:21,330
+الداخلية ل region R بحيث الدالة Fممكن تاخد local
+
+360
+00:45:21,330 --> 00:45:26,070
+maximum او local minimum على هذه المنطقة و احسبلي
+
+361
+00:45:26,070 --> 00:45:30,290
+قيمتي الدالة عند main، عند هذه النقاط، يبقى انوش
+
+362
+00:45:30,290 --> 00:45:37,130
+بيقولي اتلي كل نقاط الحريجة على المنطقة المعطالة،
+
+363
+00:45:37,130 --> 00:45:41,230
+بدناياهم هدولوعندي النقاط اللي حاليا بدي أحسب مين
+
+364
+00:45:41,230 --> 00:45:46,530
+القيم تبعت هذه الدالة و أقولهم اطيعوا شوية بس نكمل
+
+365
+00:45:46,530 --> 00:45:51,810
+باقى الشغل و بعد هيك بنروح لمين؟ List the boundary
+
+366
+00:45:51,810 --> 00:45:56,270
+points يبقى أول شغلة جيبنا ال internal points يبقى
+
+367
+00:45:56,270 --> 00:46:02,930
+احنا داخل ال open region يبقى مضل عندنا ال
+
+368
+00:46:02,930 --> 00:46:07,170
+boundary اللي على الحدوديبقى بدنا نجيب less كمان
+
+369
+00:46:07,170 --> 00:46:12,010
+بال boundary region للدالة F اللى عندها ممكن تاخد
+
+370
+00:46:12,010 --> 00:46:16,570
+local maximum و local minimum و نحصل قيم الدالة
+
+371
+00:46:16,570 --> 00:46:21,670
+عندنا هذا إذا صرت عندى الحمد لله قيم كتيرة قيم تبع
+
+372
+00:46:21,670 --> 00:46:24,470
+ال interior points و قيم تبع ال boundary points
+
+373
+00:46:24,470 --> 00:46:29,570
+باجي في الآخر خطوة تالتة و الأخيرةبطلع أكبر قيمة
+
+374
+00:46:29,570 --> 00:46:33,310
+بقول هذه ال absolute maximum و أقل قيمة بقول main
+
+375
+00:46:33,310 --> 00:46:36,710
+هذه ال absolute minimum مكافئة الله بالسرعليمة
+
+376
+00:46:36,710 --> 00:46:41,010
+يبقى هذا باختصار اللي بدنا نعمله يبقى أول حاجة بده
+
+377
+00:46:41,010 --> 00:46:45,470
+أحسب ال internal points اللي الدالة ممكن تاخد
+
+378
+00:46:45,470 --> 00:46:50,500
+عندها local maximum أو local minimum بعد هيكبدي
+
+379
+00:46:50,500 --> 00:46:53,300
+اجي الى ال boundary points اللي ممكن الذالة تكون
+
+380
+00:46:53,300 --> 00:46:56,840
+عندها local maximum و local minimum عند هذه النقاط
+
+381
+00:46:56,840 --> 00:46:59,900
+في حالة ال intro هو ال boundary بدي احسب قداش
+
+382
+00:46:59,900 --> 00:47:04,660
+القيم المختلفة لهذه الذالة بعدين بدي اقارن بين هذه
+
+383
+00:47:04,660 --> 00:47:08,940
+القيمة القيم اللي عندها اكبر قيمة بقول هي absolute
+
+384
+00:47:08,940 --> 00:47:13,700
+maximum واقل قيمة بقول هي main absolute minimum
+
+385
+00:47:13,700 --> 00:47:19,700
+لهذه الذالة اعظم موضوع احتلاليحد بتسأل اي سؤال قبل
+
+386
+00:47:19,700 --> 00:47:27,820
+ان نبدأ ان يكان؟ في اي تساؤل؟ طيب انا بنسأل،
+
+387
+00:47:27,820 --> 00:47:32,140
+مظبوط؟ ليش قاللي المنطقة بدأ تبقى closed، ماكان
+
+388
+00:47:32,140 --> 00:47:33,580
+قاللي open و رايحني؟
+
+389
+00:47:36,870 --> 00:47:42,270
+لا ممكن يكون، بس ايش؟ بصير اللي على الحدود هذه
+
+390
+00:47:42,270 --> 00:47:45,990
+البابرة بصير مغرب ليش علاقة فيها، يبقى كأنه لغيت
+
+391
+00:47:45,990 --> 00:47:51,050
+مين، لغيت الخطوة هذهتمام و احنا دلوقت راجعنا ل
+
+392
+00:47:51,050 --> 00:47:55,550
+Calculus ايه بجينا ممكن يكون في absolute في
+
+393
+00:47:55,550 --> 00:47:59,750
+maximum او minimum على مين على ال interval المعرف
+
+394
+00:47:59,750 --> 00:48:03,210
+عليها تالع عند اول interval او نهاية ال interval
+
+395
+00:48:03,210 --> 00:48:07,630
+هو بالتالع ممكن يكون عند ال boundary points عندنا
+
+396
+00:48:07,630 --> 00:48:12,170
+يكون في عند local maximum او local minimum ومن هنا
+
+397
+00:48:12,170 --> 00:48:16,820
+اشتغلنا المنطقة بدون get lost regionيعني ال
+
+398
+00:48:16,820 --> 00:48:20,800
+boundary بدهم يدخلوا في الأحساب عندك و هات الصورة
+
+399
+00:48:20,800 --> 00:48:26,960
+طيب نجي نسأل سؤالها وقول هات ال absolute maximum و
+
+400
+00:48:26,960 --> 00:48:31,420
+ال absolute من و لمين لدلة لإنها دي و أعطاني دلة و
+
+401
+00:48:31,420 --> 00:48:34,380
+أعطاني closed in triangle plate
+
+402
+00:48:40,880 --> 00:48:45,900
+يبقى لما أقول عند هنا على ال close triangle plate
+
+403
+00:48:45,900 --> 00:48:51,580
+يعني مثلث مصمد زي ما نقول قرص في حالة الدائرة يبقى
+
+404
+00:48:51,580 --> 00:48:56,960
+هنا بقول close triangle plate مثلث مصمد يعني كل
+
+405
+00:48:56,960 --> 00:49:04,720
+نقاط المثلثمالها هي نقاط ك domain للدل اللي عندنا
+
+406
+00:49:04,720 --> 00:49:09,440
+تمام مش بس على المحيط و بس على المحيط و داخل
+
+407
+00:49:09,440 --> 00:49:13,260
+المدلات هاي المقصود فيه هنا يبقى on a closed
+
+408
+00:49:13,260 --> 00:49:16,960
+triangular plane in the first quadrant في الرابع
+
+409
+00:49:16,960 --> 00:49:22,520
+الأول و المحدود بالثلاثة فطوط اللي قدامنا X تساوي
+
+410
+00:49:26,490 --> 00:49:32,670
+محور y هو y تساوي 4 موازي لمحور x هو y تساوي x
+
+411
+00:49:32,670 --> 00:49:37,990
+الخط المنصف للربع الأول والربع الثالث لكن احنا كنا
+
+412
+00:49:37,990 --> 00:49:41,830
+في الربع الأول يبقى مالنا علاقة بمين بالربع التالت
+
+413
+00:49:41,830 --> 00:49:47,610
+يريد كبل نبدأ خلينا نرسم المنطقة تبعتنا طب المنطقة
+
+414
+00:49:47,610 --> 00:49:54,760
+بنات هذه هي domain الدالة والدالة نفسهاdomain
+
+415
+00:49:54,760 --> 00:49:59,000
+الدالة يعني الدالة بتبقى كأنه surface فاض
+
+416
+00:49:59,000 --> 00:50:03,620
+وعالمستوى XY plane المثلثة اللي احنا رسمناها هذا
+
+417
+00:50:03,620 --> 00:50:07,620
+جزء من domain الدالة احنا بنحسب على هذا الجزء من
+
+418
+00:50:07,620 --> 00:50:10,820
+ال domain اللي هو local maximum و local absolute
+
+419
+00:50:10,820 --> 00:50:16,740
+maximum و absolute minimum بسيطة لذا لو روحنا
+
+420
+00:50:16,740 --> 00:50:22,560
+رسمنا روح ناخد المحاور اللي عندنا هذا محور X وهذا
+
+421
+00:50:22,560 --> 00:50:29,860
+اللي عندنا مالهاللي هو محور Y يبقى هذا اللي هو
+
+422
+00:50:29,860 --> 00:50:36,420
+محور Y لأنه هذه نقطة الاصل قال
+
+423
+00:50:36,420 --> 00:50:41,920
+لي الخط الأول هو X تساوي 0 اتفاجنا اللي هو محور Y
+
+424
+00:50:41,920 --> 00:50:48,960
+الخط التاني Y تساوي 4 وY تساوي 4 خط موازي لمحور X
+
+425
+00:50:48,960 --> 00:50:55,460
+بالشكل ان هذا يبقى هذا Y تساوي 4الخط التالت هو Y
+
+426
+00:50:55,460 --> 00:51:02,480
+تساوي X اللى بنصف الربع تماما بهذا الشكل يبقى هذا
+
+427
+00:51:02,480 --> 00:51:08,800
+الخط اللى هو Y تساوي X بدءا عليه أصبحت إحداثيات
+
+428
+00:51:08,800 --> 00:51:15,740
+النقطة هذه معلومة لـ 0 0 و النقطة هذه كده شبنات؟ 0
+
+429
+00:51:15,740 --> 00:51:23,530
+و 4 طب النقطة هذه كدهش؟أربعة وأربعة لإن Y تساوي X
+
+430
+00:51:23,530 --> 00:51:31,890
+فY هيها و X هيها يبقى هذا النقطة أربعة وكذلك أربعة
+
+431
+00:51:31,890 --> 00:51:39,750
+يبقى هذه المنطقة اللي تعتبر Domain الدالة طيب إذا
+
+432
+00:51:39,750 --> 00:51:43,710
+احنا بدنا نمشي حسب ما احنا كاتبين نروح واخد Domain
+
+433
+00:52:03,420 --> 00:52:11,560
+النقطة الأولى للـ interior points النقطة
+
+434
+00:52:11,560 --> 00:52:17,400
+الداخليةيقول ان انترال فورس بتجيبهم لما تجيب
+
+435
+00:52:17,400 --> 00:52:21,560
+المشتقة بالنسبة ل X مستويها بالزيرو و تجيب المشتقة
+
+436
+00:52:21,560 --> 00:52:25,920
+بالنسبة ل Y مستويها بالزيرو بمجرد ما بسيطة احنا
+
+437
+00:52:25,920 --> 00:52:32,540
+عندنا ان ال F of XY بده يساوي اللي هي امين X تربيع
+
+438
+00:52:32,540 --> 00:52:38,620
+ناقص XY زائد Y تربيع زائد واحد
+
+439
+00:52:44,450 --> 00:52:58,570
+2x-y ونسويها بالزيرو ونجيب له fy نشتقها كمان ناقص
+
+440
+00:52:58,570 --> 00:53:03,950
+x زائد 2y ونسوي بالزيرو
+
+441
+00:53:06,860 --> 00:53:12,580
+بدي أجيب النقاط الحرجة لهذه الدلالة في السؤال اللي
+
+442
+00:53:12,580 --> 00:53:17,120
+قبل شوية بنات طلعت المشتقة الأولى كلها بدلالة X
+
+443
+00:53:17,120 --> 00:53:21,500
+وطلعت المشتقة التانية كلها بدلالة Y مظبوط مثال
+
+444
+00:53:21,500 --> 00:53:24,580
+اللي قبل قليل لكن هذا لأ طلعت المشتقة الأولى
+
+445
+00:53:24,580 --> 00:53:27,860
+بدلالة X وY والمشتقة الأولى في الحالة التانية
+
+446
+00:53:27,860 --> 00:53:33,280
+بدلالة X وY بروح بحل المعادلتين مع بعض و بطلع قيمة
+
+447
+00:53:33,280 --> 00:53:36,400
+X وY بجي بقولك وايد
+
+448
+00:53:41,020 --> 00:53:45,380
+المعادلة الأولى في اتنين لو ضربنا اتنين ايش بيصير
+
+449
+00:53:45,380 --> 00:53:50,140
+عندى اربعة اكس ناقص اتنين Y بيكونوا سوى Zero
+
+450
+00:53:50,140 --> 00:53:56,630
+المعادلة التانية ناقص X زائد اتنين Y تسوى Zeroأيه
+
+451
+00:53:56,630 --> 00:54:01,030
+يا جماعة لو جميعنا بروح قعدل مع بعض بظل أهدي قداش
+
+452
+00:54:01,030 --> 00:54:06,610
+تلاتة X يساوي Zero هذا بدي يعطيلك ان X يساوي قداش
+
+453
+00:54:06,610 --> 00:54:12,790
+Zero لو X ساوي Zero يبقى Y قداش Zero يبقى هذا بدي
+
+454
+00:54:12,790 --> 00:54:19,690
+يعطيك ان Y يساوي Zero يبقى هذا بدي يعطيك ان Zero
+
+455
+00:54:19,690 --> 00:54:24,650
+Zero is a critical point
+
+456
+00:54:27,980 --> 00:54:33,160
+السؤال هو إيش رأيك في النقطة هذه interior ولا
+
+457
+00:54:33,160 --> 00:54:38,620
+boundary الحمد لله طالما ماعنديش ولا interior
+
+458
+00:54:38,620 --> 00:54:44,420
+point يبقى المدام حسبتها إذا خليني أجيب قيمة
+
+459
+00:54:44,420 --> 00:54:51,100
+الدالة عندها إذا يا بنات بتروح أجيب ال F on 00
+
+460
+00:54:51,100 --> 00:54:57,020
+يبقى هذا الكلام بده يسوي بده يفوت تسوي قداش واحد
+
+461
+00:54:57,540 --> 00:55:03,520
+يبقى بنوزيها وروح نخليها لإن لنا إليها عودة بعد
+
+462
+00:55:03,520 --> 00:55:08,340
+قليل ان شاء الله تعالى يبقى خلاصنا النقطة الأولى
+
+463
+00:55:08,340 --> 00:55:11,280
+اللى هو ال interior points و جينا نحسب ال interior
+
+464
+00:55:11,280 --> 00:55:15,300
+طولها فعنا main boundary يبقى ماعناش مشكلة يبقى
+
+465
+00:55:15,300 --> 00:55:18,380
+عندنا أحسبهم ال boundary بروحش أحسبها تانية مرة
+
+466
+00:55:18,380 --> 00:55:22,440
+تانية لو حسبناها خلاصهم يبقى بداني على main ال
+
+467
+00:55:22,440 --> 00:55:23,740
+boundary points
+
+468
+00:55:34,380 --> 00:55:40,360
+أنا بتمشي على الحدود الإقليمية يبقى بروح أسمي
+
+469
+00:55:40,360 --> 00:55:45,580
+المثلث بالروح السابعة بدي أقول هذه مثلا النقطة A
+
+470
+00:55:45,580 --> 00:55:54,420
+وهذه النقطة B وهذه النقطة C و بدي أبدأه هنا بدي
+
+471
+00:55:54,420 --> 00:56:01,600
+أقول on the line على الخط A B
+
+472
+00:56:05,720 --> 00:56:14,220
+على الخط AB كم مقدار X؟ Zero يبقى هنا ال X بدها
+
+473
+00:56:14,220 --> 00:56:23,060
+ساوي Zero هذا بده يعطيك ان ال F هو Zero Yيعني انا
+
+474
+00:56:23,060 --> 00:56:27,420
+هشيل كل X و احط مكانها Zero ثم بقول ماذا يجب ان
+
+475
+00:56:27,420 --> 00:56:32,100
+يسوي هاي الدالة فوق Zero بصير عن اليمين بيبقى طبعا
+
+476
+00:56:32,100 --> 00:56:38,260
+Zero لان عندي Y تربيع زائد واحد و ال Y هتتغير من
+
+477
+00:56:38,260 --> 00:56:44,750
+وين وين لبناء من صفر لغاية أربعة ممتاز جدايبقى من
+
+478
+00:56:44,750 --> 00:56:52,570
+0 لغاية 4 سؤال هو هل هذه صارت دالة في متغيرين ولا
+
+479
+00:56:52,570 --> 00:56:57,770
+متغير واحد؟ متغير واحد يبقى بروح بقوله بدي أجيب له
+
+480
+00:56:57,770 --> 00:57:05,910
+ال F primeيعني كأنه بده يجيب ال point على الخط على
+
+481
+00:57:05,910 --> 00:57:11,270
+ال interval من 0 ل 4 يبقى هذا الكلام دي ساوي كده؟
+
+482
+00:57:11,270 --> 00:57:19,070
+اتنين واحد و ساوي مين؟ يبقى هذا بدي اعطيك ان واحد
+
+483
+00:57:19,070 --> 00:57:20,290
+ساوي زيت
+
+484
+00:57:22,940 --> 00:57:31,380
+تمام طيب لما ال y تساوي zero إذا إذا لو عوضت هنا
+
+485
+00:57:31,380 --> 00:57:35,820
+بصير قيمة الدالة عندك كده واحد يعني تطلع النقطة
+
+486
+00:57:35,820 --> 00:57:41,120
+اللي عندها هذه الأصلية كما كانت تمام يبقى هذا بدي
+
+487
+00:57:41,120 --> 00:57:46,980
+يعطيك نفس النقطة الأصلية وبالتالي بنحسب f of zero
+
+488
+00:57:46,980 --> 00:57:54,390
+و zero يبقى هذا بدي يعطيكالـ F of 00 هي الواحد
+
+489
+00:57:54,390 --> 00:57:59,410
+اللي حصل عليها مالها قبل قليل يبقى لم نأتي بمين
+
+490
+00:57:59,410 --> 00:58:07,230
+بأي جديد عندنا تمام طيب لازلنا مع ال line AB اللي
+
+491
+00:58:07,230 --> 00:58:13,500
+عندنا هذا وبالتاليبدي احسب اخر ال line يعني
+
+492
+00:58:13,500 --> 00:58:18,520
+ملاقيتش نقطة داخل ال line ولا نقطة اجيت عند ال 00
+
+493
+00:58:18,520 --> 00:58:26,880
+مضلش عند ال main نقطة 04 يبقى بروح بحسبله F of 04
+
+494
+00:58:26,880 --> 00:58:32,140
+يبقى هذا الكلام مضي السبب ارجع للدلة اللى فوق و
+
+495
+00:58:32,140 --> 00:58:38,050
+الله هيها عندي جازة و مبسطة موجودة هييبقى ماجي
+
+496
+00:58:38,050 --> 00:58:43,870
+بيقوله هذه بدت سوى أربعة تربيه زائد واحد يسوى قداش
+
+497
+00:58:43,870 --> 00:58:51,170
+سبعتاش هاي بروزناها وسنرجع لها بعد قليل بعد هيك
+
+498
+00:58:51,170 --> 00:59:00,290
+بدت أجي أقوله on the line بي سي على ال بي سي وايف
+
+499
+00:59:00,290 --> 00:59:10,550
+قداش أربع تمام كويس يبقى هناالـ Y تساوي 4 معناته
+
+500
+00:59:10,550 --> 00:59:17,370
+هذه بدها تصير F of X و 4 Y ساوية يبقى بدنا نرجع
+
+501
+00:59:17,370 --> 00:59:24,990
+للدالة اللي عندنا هنا بتضالها X تربيع ناقص 4X زائد
+
+502
+00:59:24,990 --> 00:59:34,870
+16 زائد 1 يبقى صارت منها تدالة F of X و 4 اللي
+
+503
+00:59:34,870 --> 00:59:43,220
+تساوي مين؟x تربيع نقص اربعة x زائد سبعة عشر بدا
+
+504
+00:59:43,220 --> 00:59:48,820
+اشوف على هذا الخط في عندى نقاط داخلية ولا لا يمكنش
+
+505
+00:59:48,820 --> 01:00:00,220
+بعمل اشتق ف prime of x واربعة y سبعة اتنين x ناقص
+
+506
+01:00:00,220 --> 01:00:05,720
+اربعة و سوى بمين يا بنات بال zero لما سوى بال zero
+
+507
+01:00:05,980 --> 01:00:11,340
+بدي أطلع عندى 2X بدي أسوأ الاربعة يبقى ال X بدي
+
+508
+01:00:11,340 --> 01:00:16,900
+أسوأ كده؟ اتنين يبقى فاصيل النقطة مين؟ اتنين
+
+509
+01:00:16,900 --> 01:00:21,300
+واربعة و اين النقطة اتنين واربعة بتجيلي هنا في
+
+510
+01:00:21,300 --> 01:00:26,860
+النصتنين يعني مشيت اتنين وطلعت اربعة يبقى هذا
+
+511
+01:00:26,860 --> 01:00:32,120
+النقطة اتنين واربعة اللي عندها قد يكون local
+
+512
+01:00:32,120 --> 01:00:37,260
+maximum او local minimum اذا بروح بحسبله النقطة F
+
+513
+01:00:37,260 --> 01:00:43,420
+اتنين واربعة تسابر هيفضل جاهزة عندى يعني هنا معوض
+
+514
+01:00:43,420 --> 01:00:49,900
+باربعة ضل بس عوض بمن؟ باتنين يبقى هذه اتنين تربيع
+
+515
+01:00:50,110 --> 01:00:58,110
+نقص اربعة في اتنين زي سبعتاشر يسام هنا اربعة وهنا
+
+516
+01:00:58,110 --> 01:01:03,730
+سالب تمانية بيظل سالب اربعة من سبعتاشر بيظل
+
+517
+01:01:03,730 --> 01:01:12,090
+ثلاثاشر وهذه باروزناها كذا ضالت مين عندي اربعة
+
+518
+01:01:12,090 --> 01:01:12,730
+اربعة اربعة اربعة اربعة اربعة اربعة اربعة اربعة
+
+519
+01:01:12,730 --> 01:01:17,990
+اربعة اربعة اربعة اربعة اربعة اربعة اربعة
+
+520
+01:01:40,400 --> 01:01:48,280
+طبعا هنا احنا عندنا f of x و 4 يبقى هاي هجازة بده
+
+521
+01:01:48,280 --> 01:01:53,000
+اشيل كل x وحط مكانها 4 يبقى هادي بده يتسرب
+
+522
+01:01:58,370 --> 01:02:05,030
+العشرة عشر زائد سبعتاش هو يسوى السبعة عشرة عشرة
+
+523
+01:02:05,030 --> 01:02:20,230
+عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة
+
+524
+01:02:20,710 --> 01:02:28,250
+طيب على هذا ال line يا بناه Y تساوي X طبعا Y تساوي
+
+525
+01:02:28,250 --> 01:02:36,170
+X أنا بدي أقولك ان F of X و X يعني هشيل كل Y وحق
+
+526
+01:02:36,170 --> 01:02:41,270
+مكانها او العكس هشيل كل X وحق مكان Y واحدة متنتين
+
+527
+01:02:41,270 --> 01:02:45,490
+مش واحدتنتين يمجي هنا بقول له هذا الكلام يساوي
+
+528
+01:02:45,490 --> 01:02:46,790
+برجع لمثلة
+
+529
+01:03:10,760 --> 01:03:16,900
+يبقى هنا و ال X أكبر من أو تساوي Zero و أقل من أو
+
+530
+01:03:16,900 --> 01:03:21,600
+تساوي أربع يعني الخط هذا مش على طول و طالع فوقنا
+
+531
+01:03:21,600 --> 01:03:25,920
+لأ بس أنا بدي أغنى الفترة من Zero لأربع من Zero
+
+532
+01:03:25,920 --> 01:03:29,400
+لغاية هذه هنا أربعة
+
+533
+01:03:38,420 --> 01:03:46,160
+يبقى X هو X يبقى نقطة زي
+
+534
+01:03:46,160 --> 01:03:53,760
+نقطة زي نقطة نقطة نقطة نقطة نقطة نقطة نقطة نقطة
+
+535
+01:03:53,760 --> 01:04:00,580
+نقطة نقطة نقطة نقطة نقطة نقطة نقطة نقطة نقطة نقطة
+
+536
+01:04:00,580 --> 01:04:01,500
+نقطة نقطة نقطة نقطة نقطة نقطة نقطة نقطة نقطة نقطة
+
+537
+01:04:01,500 --> 01:04:01,500
+نقطة نقطة نقطة نقطة نقطة نقطة نقطة نقطة نقطة نقطة
+
+538
+01:04:01,500 --> 01:04:01,500
+نقطة نقطة نقطة نقطة نقطة نقطة نقطة نقطة نقطة نقطة
+
+539
+01:04:01,500 --> 01:04:01,500
+نقطة نقطة نقطة نقطة نقطة نقطة نقطة نقطة نقطة نقطة
+
+540
+01:04:01,500 --> 01:04:05,780
+نقطة نقطة نقطة نقطة نقطة نقطة نقطة نقطة نقطة
+
+541
+01:04:05,780 --> 01:04:05,880
+نقط
+
+542
+01:04:18,690 --> 01:04:23,870
+النقطة على الـ 00 هي فهي اختلطت ليش ولا نقطة في
+
+543
+01:04:23,870 --> 01:04:28,830
+الطريق ف4 و 4 حسبناها مع اللي قبلها بروحش بتغيرها
+
+544
+01:04:28,830 --> 01:04:34,960
+تاني انتهينا الان من الخطواتمن كل الـ boundary
+
+545
+01:04:34,960 --> 01:04:39,360
+points و من كل ال interior points تمام؟ شو بدي
+
+546
+01:04:39,360 --> 01:04:44,120
+أعمل الآن؟ بدي أعقد مقارنة أكبر قيمة بقول هذا
+
+547
+01:04:44,120 --> 01:04:48,020
+absolute maximum و الأقل قيمة absolute minimum
+
+548
+01:04:48,020 --> 01:04:53,280
+باجي بطلع في المربعات اللي عندى أنا بروزتهم هنا
+
+549
+01:04:53,280 --> 01:05:00,680
+يبقى أكبر قيمة جديدة و أقل قيمة ممتازة ده بروح
+
+550
+01:05:00,680 --> 01:05:12,690
+بقولها ال Fhas absolute maximum 17 at the points
+
+551
+01:05:12,690 --> 01:05:18,770
+في موقعين الموقع الأول يا بناتله كدهش؟ Zero و
+
+552
+01:05:18,770 --> 01:05:27,090
+أربعة Zero و أربعة و الموقع التاني and أربعة و
+
+553
+01:05:27,090 --> 01:05:27,550
+أربعة
+
+554
+01:05:53,020 --> 01:06:02,270
+طب افترض يا بنات كان مش مثلت مربع او مستطيليبقى
+
+555
+01:06:02,270 --> 01:06:06,890
+نفسنا نروح نديله الضلع الرابع و هكذا طبعا انا بس
+
+556
+01:06:06,890 --> 01:06:11,870
+السؤال انه كيف الكتاب مثال تبقى مستطيل يبقى حاجة
+
+557
+01:06:11,870 --> 01:06:16,150
+زي المحلين المثلث بالعلم المستطيل بالضبط تماما بس
+
+558
+01:06:16,150 --> 01:06:20,910
+بضلمين الضلع الرابع لكن انا لخاطر اعطيكم مثال غير
+
+559
+01:06:20,910 --> 01:06:26,750
+مستطيل مش موجود زيه في الكتاب و مرة جئنا به في
+
+560
+01:06:26,750 --> 01:06:34,480
+احدى الامتحاناتلذلك بدنا نروح نعطيكي مثال ما هو لا
+
+561
+01:06:34,480 --> 01:06:44,040
+مستقيم ولا مُثلّد ولا حتى مُربّع. إيش المثال هذا؟
+
+562
+01:06:44,040 --> 01:06:52,080
+بقولك ستراهنه حالا ان شاء الله تعالى بعد ان نكمل
+
+563
+01:06:52,080 --> 01:06:54,220
+مسح اللوحيين
+
+564
+01:07:10,870 --> 01:07:12,810
+مثال 2
+
+565
+01:07:30,490 --> 01:07:47,590
+and minimum values of the function للدالة f of x y
+
+566
+01:07:47,590 --> 01:07:56,850
+تساوي واحد زي x y ناقص تلاتة x on the closed
+
+567
+01:07:56,850 --> 01:08:08,850
+region on theA closed region bounded by
+
+568
+01:08:08,850 --> 01:08:22,070
+والمحدودة ب The parabola بالقطع المكافئ Y تساوي X
+
+569
+01:08:22,070 --> 01:08:29,870
+تربيع and the line Y تساوي R
+
+570
+01:08:46,910 --> 01:08:52,110
+أحد المدرسين كان بدرس صيفي زي الصيف هذا فقام جاب
+
+571
+01:08:52,110 --> 01:08:58,010
+السؤال لأطلال اللي بدرسهم احنا بنعطيكوا ياه كمثال
+
+572
+01:08:58,010 --> 01:09:01,490
+ان شاء الله و تعالى بيقول هات الأبسلوت maximum و
+
+573
+01:09:01,490 --> 01:09:05,530
+الأبسلوت minimum للدالة اللي قدام هذه على المنطقة
+
+574
+01:09:05,530 --> 01:09:10,170
+المغنطة المحدودة بالقطع المكافئ Y تساوي X تربية
+
+575
+01:09:10,170 --> 01:09:16,870
+وكلك الخط Y تساوي Aلو روحنا نتعرف على المنطقة اللي
+
+576
+01:09:16,870 --> 01:09:23,270
+عندنا هذه بقول هي المحاول وهذا محور X وهذا محور Y
+
+577
+01:09:23,270 --> 01:09:31,190
+وهذه نقطة الاصل القرابل اللي عندنا أبعد مشهور
+
+578
+01:09:31,190 --> 01:09:35,490
+عندنا من الكاركورا الصحيح كلنا بنعرف رسمته يبقى
+
+579
+01:09:35,490 --> 01:09:37,390
+هذا Y تسوى X
+
+580
+01:09:40,430 --> 01:09:47,170
+Y تساوي أربعة خط يوازي محور X ويبقى عنده مسافة
+
+581
+01:09:47,170 --> 01:09:53,470
+مقدارها أربعة يبقى هذه أربعة وهذا الخط يوازي محور
+
+582
+01:09:53,470 --> 01:09:54,130
+X ويبقى هذه أربعة وهذا الخط يوازي محور X ويبقى هذه
+
+583
+01:09:54,130 --> 01:09:56,790
+أربعة وهذا الخط يوازي محور X ويبقى هذه أربعة وهذا
+
+584
+01:09:56,790 --> 01:09:57,410
+الخط يوازي محور X ويبقى هذه أربعة وهذا الخط يوازي
+
+585
+01:09:57,410 --> 01:09:57,410
+محور X ويبقى هذه أربعة وهذا الخط يوازي محور X
+
+586
+01:09:57,410 --> 01:09:57,410
+ويبقى هذه أربعة وهذا الخط يوازي محور X ويبقى هذه
+
+587
+01:09:57,410 --> 01:10:00,510
+أربعة وهذا الخط يوازي محور X ويبقى هذه أربعة وهذا
+
+588
+01:10:00,510 --> 01:10:01,750
+الخط يوازي محور X و
+
+589
+01:10:09,360 --> 01:10:16,020
+الانترال قوائز النقاط الداخلية وبعد ذلك بروح لمين
+
+590
+01:10:16,020 --> 01:10:21,040
+للنقاط الخارجية إذا بدنا نروح ونجيب له مين يا بنات
+
+591
+01:10:21,040 --> 01:10:28,180
+F X نشتغل بالنسبة ل X هي اللي قدامنا هنا تظهر من Y
+
+592
+01:10:28,180 --> 01:10:35,700
+ناقص ثلاثة ونسوى بال Zero إذا ال Y تسوى كم؟ ثلاثة
+
+593
+01:10:35,700 --> 01:10:37,680
+بالمثل بدنا نجيب له F
+
+594
+01:10:43,690 --> 01:10:50,450
+فقط لغير تمام و نسوي بال zero إذا ال X بدي ساوي
+
+595
+01:10:50,450 --> 01:10:58,050
+قداش Zero يبقى ال interior point اللي يبقى Zero و
+
+596
+01:10:58,050 --> 01:11:08,010
+تلاتة is a
+
+597
+01:11:08,010 --> 01:11:10,430
+critical point
+
+598
+01:11:15,350 --> 01:11:22,270
+0.3 يعني وين بده تيجي 0.3 هنا هذا النقطة اللي هي 0
+
+599
+01:11:22,270 --> 01:11:27,670
+هو 3 بيبقى أجد داخل المنطقة مش ده السؤال اللي قبل
+
+600
+01:11:27,670 --> 01:11:31,570
+ما لاجيناش ولا نقطة داخل المنطقة لاجيناها على الحد
+
+601
+01:11:31,570 --> 01:11:36,990
+ده هذه لاجيناها نقطة داخل المنطقة اللي عندناها إذا
+
+602
+01:11:36,990 --> 01:11:39,250
+بدنا نروح نحسبله جديش
+
+603
+01:11:57,260 --> 01:12:01,700
+خليها وسنرجع لها ان شاء الله بعد هيك بدنا نروح
+
+604
+01:12:01,700 --> 01:12:10,600
+لمين لل boundary points النقاط
+
+605
+01:12:10,600 --> 01:12:18,600
+الحديد ايش رايك نبدأ في الفرابنة في الأول يبقى
+
+606
+01:12:18,930 --> 01:12:23,890
+باجي بقوله بقولش on the line يبقى on the curve Y
+
+607
+01:12:23,890 --> 01:12:33,910
+تساوي X تربيع او on the parabola اللي
+
+608
+01:12:33,910 --> 01:12:42,870
+هو Y تساوي X تربيع ويهاد بدي أصير F of X ومين
+
+609
+01:12:42,870 --> 01:12:47,570
+أبناده؟ و X تربيع مش ال Y بحط على X تربيع فبنجي
+
+610
+01:12:47,570 --> 01:12:56,550
+علي مثلتنابصير تساوي واحد زائد تساوي
+
+611
+01:12:56,550 --> 01:12:59,990
+واحد
+
+612
+01:12:59,990 --> 01:13:01,770
+زائد تساوي واحد زائد تساوي واحد زائد تساوي واحد
+
+613
+01:13:01,770 --> 01:13:02,010
+زائد تساوي واحد زائد تساوي واحد زائد تساوي واحد
+
+614
+01:13:02,010 --> 01:13:03,770
+زائد تساوي واحد زائد تساوي واحد زائد تساوي واحد
+
+615
+01:13:03,770 --> 01:13:06,410
+زائد تساوي واحد زائد تساوي واحد زائد تساوي واحد
+
+616
+01:13:06,410 --> 01:13:06,410
+زائد تساوي واحد زائد تساوي واحد زائد تساوي واحد
+
+617
+01:13:06,410 --> 01:13:08,150
+زائد تساوي واحد زائد تساوي واحد زائد تساوي واحد
+
+618
+01:13:08,150 --> 01:13:12,510
+زائد تساوي واحد زائد تساوي واحد زائد تساوي واحد
+
+619
+01:13:12,510 --> 01:13:17,770
+زائد تساوي واحد زائد تساوي وا
+
+620
+01:13:21,120 --> 01:13:27,100
+نقص تلاتة يعني تلاتة في X تربيع ناقص واحد يعني
+
+621
+01:13:27,100 --> 01:13:32,560
+تلاتة في X ناقص واحد في X زاد واحد ونسوي بالزيرو
+
+622
+01:13:32,560 --> 01:13:41,440
+يبقى باجي بيقولوا هذا بيعطي كذا critical points at
+
+623
+01:13:41,440 --> 01:13:52,400
+X تساوي واحد و X تساوي كده؟ سالب واحدطبعا إذا بدنا
+
+624
+01:13:52,400 --> 01:14:01,180
+نجيب F of واحد وواحد تربيع في الثانوية شيلنا ال
+
+625
+01:14:01,180 --> 01:14:07,320
+Exo وحطينا مكانها واحد يبقى واحد زائد واحد ناقص
+
+626
+01:14:07,320 --> 01:14:14,970
+تلاتة ويسوي جدا ناقص واحدبعدها بدنا نجيب F أو سالب
+
+627
+01:14:14,970 --> 01:14:21,610
+واحد و سالب واحد تربيه هو تساوي واحد سالب واحد
+
+628
+01:14:21,610 --> 01:14:28,190
+تكيب ناقص تلاتة في ناقص واحد. يبقى ايه تلاتة؟ واحد
+
+629
+01:14:28,190 --> 01:14:35,910
+اربع. شيل منهم واحد بالسالب يظل كده؟ يظل تلاتة هذه
+
+630
+01:14:35,910 --> 01:14:45,510
+الوزنة. تمام؟ طيبالان جيبنا اللى هو على ال
+
+631
+01:14:45,510 --> 01:14:49,250
+boundary points جيبنا الحمد لله بدلا من قيمة انت
+
+632
+01:14:49,250 --> 01:14:55,090
+انت شو ضايل عندى نقطتين اللى هو النقطة اللى عندنا
+
+633
+01:14:55,090 --> 01:15:02,590
+هذه و النقطة اللى عندنا هذه هذه ها بدي اعرف كده
+
+634
+01:15:02,590 --> 01:15:09,570
+قيمة x عندها وهذه بدي اعرف كده قيمة x عندها تمام
+
+635
+01:15:09,570 --> 01:15:13,600
+طيب بدي اعرفها من وينهذه النقطة بتجي على الخط
+
+636
+01:15:13,600 --> 01:15:20,040
+المستقيم وبتيجي كمان على المنحلة يعني لو حلت
+
+637
+01:15:20,040 --> 01:15:25,800
+التنتين مع بعض بكون جيب احداثيات النقطة تل اتنين
+
+638
+01:15:25,800 --> 01:15:32,380
+هدوش احنا انا y تساوي x تربع وعندي y تساوي اربعة
+
+639
+01:15:32,380 --> 01:15:40,720
+يبقى x قديم يساوي او ناقص اتنينهذه تكون اتنين وهذه
+
+640
+01:15:40,720 --> 01:15:46,600
+كم؟ سالب اتنين يبقى النقطة هذه ايضا كم؟ سالب اتنين
+
+641
+01:15:46,600 --> 01:15:55,200
+واربع وهذه النقطة اتنين واربع اذا بدي اشتغل F of
+
+642
+01:15:55,200 --> 01:16:01,140
+سالب اتنين واربع وF of اتنين واربع يبقى بدي اشتغل
+
+643
+01:16:01,140 --> 01:16:09,350
+F of سالب اتنين واربع وY سالبأتدالة هيصرت فوق عنا
+
+644
+01:16:09,350 --> 01:16:14,750
+بالشكل هذا، يبقى الأربع هذه كأنها لا قيمة لها،
+
+645
+01:16:14,750 --> 01:16:16,750
+يبقى شو بتصير؟ واحد
+
+646
+01:16:19,390 --> 01:16:27,030
+-2-3-2-8
+
+647
+01:16:27,030 --> 01:16:30,070
+-6
+
+648
+01:16:30,070 --> 01:16:34,810
+-14
+
+649
+01:16:34,810 --> 01:16:45,550
+-6-1-7-8-1
+
+650
+01:16:46,910 --> 01:16:52,870
+بالمعنى فإننا نجيب له F of اتنين واربع واي وسبع
+
+651
+01:16:52,870 --> 01:17:00,190
+يبقى يصير واحد زائد اتنين لكل تكيب نقص تلاتة في
+
+652
+01:17:00,190 --> 01:17:07,150
+اتنين واي وسبع تمانية واحد تسعة هتشيله نوم ستة هضل
+
+653
+01:17:07,150 --> 01:17:16,090
+قداش تلاتة طب إيش رأيك؟لما حولنا هذه هيك يبقى
+
+654
+01:17:16,090 --> 01:17:22,590
+حصرنا X بين مين ومين إذا لو حطيت فاصلة وقلت ناقص
+
+655
+01:17:22,590 --> 01:17:28,190
+اتنين اقل من او يساوي X اقل من او يساوي اتنين يكون
+
+656
+01:17:28,190 --> 01:17:33,970
+افضل كتير فالان مين ضايل عندين على ال line الهن
+
+657
+01:17:33,970 --> 01:17:41,490
+هذا Y تساوي اربع يعني بدي أشيل كل Yوحق مكانها
+
+658
+01:17:41,490 --> 01:17:48,870
+اربعة وشوف ايش بصير اذا بدى اجي اقول ان ال I Y
+
+659
+01:17:48,870 --> 01:17:57,410
+تساوي اربعة يبقى بدى اصير عندى F of X واربعة حسبنا
+
+660
+01:17:57,410 --> 01:18:03,350
+قبل هيك F X واربعة طبعا لا تمام يبقى بدى ارجع على
+
+661
+01:18:03,350 --> 01:18:07,770
+المثل انا بدى اشيل كل Y واحق مكانها اربعة يبقى
+
+662
+01:18:07,770 --> 01:18:18,200
+اصير عندى واحدزائد اربعة X وناخذ تلاتة X بظبط يعني
+
+663
+01:18:18,200 --> 01:18:25,980
+بيقول اني جداش واحد زائد X وال X بتتغير ما بين
+
+664
+01:18:25,980 --> 01:18:33,600
+ثاني باتنين وما بين اتنين كذلك يبقى F prime of X
+
+665
+01:18:33,600 --> 01:18:38,000
+الجداش يا بناتبنسوي بال zero اه بدنا نسوي بال zero
+
+666
+01:18:38,000 --> 01:18:44,720
+ايش رأيك؟ مفقود؟ impossible غير ممكن يبقى
+
+667
+01:18:44,720 --> 01:18:52,860
+impossible يعني لا يمكن انه يجد نقطة على هذا ال
+
+668
+01:18:52,860 --> 01:18:59,020
+line تبقى a critical point يبقى بضلش الا ميم طرفين
+
+669
+01:18:59,020 --> 01:19:04,700
+الخط المستقيم طب احنا حسبناهم الطرفينرح نكرر تاني؟
+
+670
+01:19:04,700 --> 01:19:12,660
+لأ انتهينا منه إذا بدا أجي أقول لهم f has absolute
+
+671
+01:19:12,660 --> 01:19:19,520
+maximum أبصر قداشر دعنا ندور هاي واحد و سالف واحد
+
+672
+01:19:19,520 --> 01:19:25,560
+و تلاتة و سالف واحد و تلاتة يبقى تلاتة at the
+
+673
+01:19:25,560 --> 01:19:34,420
+pointsعند النقطتين اللي هو سالب واحد وواحد اللي هو
+
+674
+01:19:34,420 --> 01:19:39,040
+السالب واحد وواحد لما نضعها بصير هذي كتير واحد
+
+675
+01:19:39,040 --> 01:19:48,340
+واتنين واربع and اتنين واربع وقالك if هذا absolute
+
+676
+01:19:48,340 --> 01:19:58,490
+minimum سالب واحد هنا واحد راحوهنا سالب واحد عند
+
+677
+01:19:58,490 --> 01:20:07,670
+النقطة at the point عند النقطة تانية الواحد واحد
+
+678
+01:20:07,670 --> 01:20:13,790
+والتانية and سالبي اتنين اقل
+
+679
+01:20:21,950 --> 01:20:28,730
+طيب افنجوا الآن لل exercises exercises لمين؟
+
+680
+01:20:28,730 --> 01:20:37,690
+لاربعتاشر سبعة المسائلة هنا من تلاتة لغاية تلاتين
+
+681
+01:20:37,690 --> 01:20:48,730
+من تلاتة من واحد لتلاتين الو multiple of
+
+682
+01:20:48,730 --> 01:21:01,760
+threeوبعد ذلك من واحد و تلاتين لغاية اربعين القادة
+
+683
+01:21:01,760 --> 01:21:10,800
+و
+
+684
+01:21:10,800 --> 01:21:14,100
+اول section منه اللي هو double integrals
+
+685
+01:21:31,790 --> 01:21:36,710
+Power Integrals over rectangles
+
+686
+01:22:14,480 --> 01:22:24,060
+Rectangular Rectangular Region R
+
+687
+01:22:24,060 --> 01:22:27,620
+X أقل من أو يساوي
+
+688
+01:22:32,680 --> 01:22:42,420
+وY أكبر من أو يساوي C أقل من أو يساوي D then the
+
+689
+01:22:42,420 --> 01:22:55,700
+double integral over
+
+690
+01:22:55,700 --> 01:23:01,000
+double integral over R
+
+691
+01:23:03,280 --> 01:23:17,140
+R defined by عرفت تالي تكامنين على R من F of X و Y
+
+692
+01:23:17,140 --> 01:23:28,220
+دي A تكامن من A إلى B تكامن من C إلى D من F of X و
+
+693
+01:23:28,220 --> 01:23:37,480
+Y دي Xدي واي دي
+
+694
+01:23:37,480 --> 01:23:49,160
+واي طبعاً دي اكس تساوي تكامل من C إلى D ومن هنا من
+
+695
+01:23:49,160 --> 01:23:56,100
+A إلى B لل F of X وY دي اكس دي واي
+
+696
+01:24:07,790 --> 01:24:14,790
+مثالات أو النساء الذين
+
+697
+01:24:14,790 --> 01:24:21,470
+تتبعون
+
+698
+01:24:34,130 --> 01:24:42,770
+متتكامن من باقي لغاية اتنين باقي ومتكامن من Zero
+
+699
+01:24:42,770 --> 01:24:53,170
+لغاية باقي لمين؟ لصين ال X ذاته وصين ال Y كله في
+
+700
+01:24:53,170 --> 01:24:55,710
+ال D X في ال D Y
+
+701
+01:25:27,320 --> 01:25:31,260
+الشبكة الماضية كانت بنات partial derivatives كله
+
+702
+01:25:31,260 --> 01:25:36,760
+بتلزم الاشتغالات من أوله إلى آخره هذا ان شاء الله
+
+703
+01:25:36,760 --> 01:25:41,000
+كله تكاملات بس مش تكامل واحد زي ما درسنا بال
+
+704
+01:25:41,000 --> 01:25:45,340
+calculus a و b ممكن يكون تكاملين ممكن يكون تلت
+
+705
+01:25:45,340 --> 01:25:50,820
+تكاملات ممكن يكون إحداثيات كورتيزية ممكن يكون
+
+706
+01:25:50,820 --> 01:25:56,480
+إحداثياتقطبية وكيف يمكن التحويل من تكابلات في
+
+707
+01:25:56,480 --> 01:26:01,760
+الاحداثيات الكارتزية للاحداثيات القطبية وبالعكس
+
+708
+01:26:01,760 --> 01:26:07,640
+وممكن يكون في احداثيات الاحداثيات أسطوانية وفي
+
+709
+01:26:07,640 --> 01:26:13,140
+احداثيات كوروية كما هنحسب التكابلات فيها يوم أن
+
+710
+01:26:13,140 --> 01:26:18,480
+نصلها ان شاء الله تعالى لكن هنبدأ بأوسط الأشياء هو
+
+711
+01:26:18,480 --> 01:26:22,550
+أول section section 15 راحطب ال integrant of a
+
+712
+01:26:22,550 --> 01:26:27,270
+rectangle يبقى احنا بدنا نحسب قداش التكاملات
+
+713
+01:26:27,270 --> 01:26:31,890
+الثلائية على مستطيلات كده لازم اقول قاعة الغرفة
+
+714
+01:26:31,890 --> 01:26:36,950
+هذه عبارة عن مستطيل له طول وله عرض إذا نكس هتتغير
+
+715
+01:26:36,950 --> 01:26:41,370
+من بين الرقمين و ال Y هتتغير من بين الرقمين يبقى
+
+716
+01:26:41,370 --> 01:26:47,590
+داش متكاملة على منطقة مستطيلة الشكل تعريف كتاني خد
+
+717
+01:26:47,590 --> 01:26:54,630
+دلف و بكس دلة متصلةخلال هذه المنطقة المستقلة X
+
+718
+01:26:54,630 --> 01:27:00,370
+محصورة بين A وB وY محصورة بين C وD يعني لو رحنا
+
+719
+01:27:00,370 --> 01:27:05,150
+وقلنا هذه المحاولة وقلنا هذه محور X وهذه محور Y
+
+720
+01:27:05,150 --> 01:27:10,270
+وهذه عندي خاتين وجينا خاتين بالشكل هذا وقلنا هذه
+
+721
+01:27:10,270 --> 01:27:16,250
+المنطقة A وهذه B وهذه Cوهذه دي يبقى المنطقة
+
+722
+01:27:16,250 --> 01:27:21,370
+المظللة اللى عندنا هذه هي المحصوة بين ال A والD
+
+723
+01:27:21,370 --> 01:27:27,730
+والC والD فده نحسب مقدار المساحة تبع Game تبعت هذه
+
+724
+01:27:27,730 --> 01:27:32,370
+المنطقة فبقول double integral على المنطقة هذه
+
+725
+01:27:32,370 --> 01:27:38,250
+بعرفه كتالي تكاملين على المنطقة اقررن F of X وY دي
+
+726
+01:27:38,250 --> 01:27:50,940
+ايه يعني دي ايه الامندي ايه؟ دي ايه؟ دي ايه؟ دي
+
+727
+01:27:50,940 --> 01:27:57,580
+ايه؟ دي ايه؟ دي ايه؟
+
+728
+01:27:57,580 --> 01:28:04,010
+دي ايه؟ دي ايه؟DY DX يبقى أول ما بدي أكمل بالنسبة
+
+729
+01:28:04,010 --> 01:28:08,970
+ل Y فبحط حدود ال Y من C إلى D ثم اللي ينتج بدي
+
+730
+01:28:08,970 --> 01:28:14,430
+أكمله بالنسبة إلى X فبحط حدود ال X ل A و B لو كنت
+
+731
+01:28:14,430 --> 01:28:18,950
+بدي أكمل بالنسبة ل X في الأول فبحط حدود ال X ل A و
+
+732
+01:28:18,950 --> 01:28:23,070
+B ثم بدي أكمل ل Y بحط حدود الحدود اللي أكمل ليمين
+
+733
+01:28:23,070 --> 01:28:29,430
+C وDالآن هذا كلام مضغوط، سنضعه على أرض الواقع ببعض
+
+734
+01:28:29,430 --> 01:28:33,850
+الأمثلة، سنأخذ بس المثال البسيط والمواجهة ان شاء
+
+735
+01:28:33,850 --> 01:28:38,430
+الله سنكمل عليه يبقى قال لي أحسبني كل من التكاملة
+
+736
+01:28:38,430 --> 01:28:43,570
+التالية وعطاني لسه أول تكاملة تكاملة من zero ل باي
+
+737
+01:28:43,570 --> 01:28:48,450
+ومن باي لثانه باي، فهذه منطقة مستطيلة لأنه عطاني
+
+738
+01:28:48,450 --> 01:28:55,560
+أرقام لمين لصين ال X Cos YDXDYمخلنيش يعني حيران
+
+739
+01:28:55,560 --> 01:28:59,460
+لكنك تكمل بالنسبة ل X من الأول و بعدين تكمل
+
+740
+01:28:59,460 --> 01:29:04,600
+بالنسبة ل Y زي بلات لما كنا بالفضل ل X بعتبر ال Y
+
+741
+01:29:04,600 --> 01:29:09,200
+constant و هنا لما كمل بالنسبة ل X بتعتبر ال Y
+
+742
+01:29:09,200 --> 01:29:13,840
+constant كامل بالنسبة ل Y بعتبر ال X constant و
+
+743
+01:29:13,840 --> 01:29:20,680
+هكذا يبقى هذا الكلام بترسالتكامل من الـπي للإتنين
+
+744
+01:29:20,680 --> 01:29:26,500
+الـπي تكامل من السلمين للإكس يبقى تكامل الـPsi
+
+745
+01:29:26,500 --> 01:29:33,280
+سالب كوساين يبقى سالب كوساين للإكس كوساين هو يعتبر
+
+746
+01:29:33,280 --> 01:29:36,900
+من الضرر ثالث زي اتنين او تلاتة
+
+747
+01:29:49,800 --> 01:29:56,100
+يبقى هذا الكلام يبدو يساوي integration من بايت
+
+748
+01:29:56,100 --> 01:30:01,520
+لغاية اتنين بايت ليه؟ بضعوط بالقيمة اللي فوق مصطلح
+
+749
+01:30:01,520 --> 01:30:09,620
+الـ180 جدرس سالف واحد يبقى معه سالف سالف سالف واحد
+
+750
+01:30:10,190 --> 01:30:13,370
+هذا يجب أن أضع X أكثر من Y
+
+751
+01:30:16,810 --> 01:30:22,890
+يبقى باي في cos y خلصنا القيم اللى فوق نعود بالقيم
+
+752
+01:30:22,890 --> 01:30:28,850
+اللى اتحاد ناقص مع ناقص بالصير زاد وcos صفر اللى
+
+753
+01:30:28,850 --> 01:30:35,950
+هو بواحد و هنا ناقص zero في cos y اللى هو بقدر F
+
+754
+01:30:35,950 --> 01:30:42,650
+zero كله بالنسبة الى dy يبقى صارت المسألة تكامل من
+
+755
+01:30:42,650 --> 01:30:49,660
+باي الى اتنين باي لمينلالي اتنين هذه ناقص واحد وهي
+
+756
+01:30:49,660 --> 01:30:55,240
+زائد، في زائد يا بنت هناايوة يبقى هنا واحد هو واحد
+
+757
+01:30:55,240 --> 01:31:03,300
+في اتنين زائد باي في كوصين ال Y في ال D Y ويساوي
+
+758
+01:31:03,300 --> 01:31:09,460
+انا بدأ اكمل و اصل ال Y يبقى اتنين Y زائد باي في
+
+759
+01:31:09,460 --> 01:31:16,260
+صين ال Y كله من باي لغاية قداشر اتنين باي يبقى هذا
+
+760
+01:31:16,260 --> 01:31:25,190
+الكلام بده يساوي اتنينفي اتنين باى زائد باى في صين
+
+761
+01:31:25,190 --> 01:31:32,730
+اتنين باى اللي هو بقداش بزيرو ناقص اتنين باى ناقص
+
+762
+01:31:32,730 --> 01:31:40,200
+باى في صين الزيرو اللي هو بزيرو شكل انايبقى الجواب
+
+763
+01:31:40,200 --> 01:31:47,160
+اربعة باى ناقص اتنين باى و يسوي قداش اتنين باى
+
+764
+01:31:47,160 --> 01:31:52,260
+نتيجة تمين نتيجة التكامل لا حد هنا stop المرة
+
+765
+01:31:52,260 --> 01:31:57,280
+الجاية ان شاء الله بنكمل اخر محاضرة مش الأربعاء
+
+766
+01:31:57,280 --> 01:32:01,820
+القادم الأربعاء اللي بعدها بيكون يوم تمانتاشر
+
+767
+01:32:01,820 --> 01:32:07,040
+تمانية و الامتحان اظن انت خمسة و عشرين انا ماشي
+
+768
+01:32:07,040 --> 01:32:12,400
+يبقى شد حيالكواركزوا معلوماتكوا، ذاكروا أول بأول
+
+769
+01:32:12,400 --> 01:32:15,640
+حتى تستفيدوا ان شاء الله
+
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/yfbRUZY5IbA.srt b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/yfbRUZY5IbA.srt
new file mode 100644
index 0000000000000000000000000000000000000000..ed05315e12ac2e72eb1e20e41cd36164fc2c541a
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/yfbRUZY5IbA.srt
@@ -0,0 +1,2759 @@
+1
+00:00:00,000 --> 00:00:02,680
+موسيقى
+
+2
+00:00:09,870 --> 00:00:15,410
+بسم الله الرحمن الرحيم. المرة الماضية ابتدأنا في
+
+3
+00:00:15,410 --> 00:00:20,530
+section 12-5، وأخذنا ثلاث نقاط. طبعاً، الـ section كله
+
+4
+00:00:20,530 --> 00:00:25,170
+يتكلم عن الـ lines والـ planes. أخذنا النقطة الأولى
+
+5
+00:00:25,170 --> 00:00:28,530
+هي الـ lines في الفراغ، وعرفنا الـ parametric
+
+6
+00:00:28,530 --> 00:00:33,650
+equations لهذه الـ lines.  ثانياً، المسافة ما بين نقطة
+
+7
+00:00:33,650 --> 00:00:39,830
+وخط مستقيم في الفراغ. ثالثاً، معادلة مستوى في الفراغ.
+
+8
+00:00:39,830 --> 00:00:44,350
+هذا ما درس في هذا الـ section حتى نهاية المحاضرة
+
+9
+00:00:44,350 --> 00:00:48,850
+الماضية. اليوم، نكمل على نفس الـ section، وبنجي
+
+10
+00:00:48,850 --> 00:00:52,190
+للنقطة التالية، اللي هي distance from a point to a
+
+11
+00:00:52,190 --> 00:00:56,810
+plane. المرة الماضية، distance من point to a line. المرة
+
+12
+00:00:56,810 --> 00:01:01,910
+هذه، distance from a point to a plane. كويس، يبقى لو
+
+13
+00:01:01,910 --> 00:01:09,920
+جئتَ  تخيل أن عندي plane. تمام، الـ plane هذا سميته M
+
+14
+00:01:09,920 --> 00:01:16,400
+على سبيل المثال. في نقطة عندنا هنا فوق، نقطة S
+
+15
+00:01:16,400 --> 00:01:25,500
+موجودة في الفراغ. البعد بينها وبين الـ plane سميته D.
+
+16
+00:01:25,500 --> 00:01:33,450
+بدي أعرف كم مقدار البعد هذا D اللي موجود عندنا. بقول
+
+17
+00:01:33,450 --> 00:01:39,070
+لك: عشان أعرف هذا البعد، بروح آخذ أي نقطة في
+
+18
+00:01:39,070 --> 00:01:46,310
+الـ plane. أي نقطة موجودة في هذا المستوى، ولتكن هذه
+
+19
+00:01:46,310 --> 00:01:54,360
+النقطة، على سبيل المثال، النقطة P. طبعاً، كل plane في
+
+20
+00:01:54,360 --> 00:01:58,700
+الفراغ، بقدر أكتبه بدلالة normal vector عليه، زي ما
+
+21
+00:01:58,700 --> 00:02:03,520
+شوفنا المرة الماضية. المعادلة تبعته: ax زائد by زائد
+
+22
+00:02:03,520 --> 00:02:08,740
+cz يساوي d، حيث الـ a والـ b والـ c هي معاملات الـ vector
+
+23
+00:02:08,740 --> 00:02:16,160
+العمودي على هذا الـ plane. طبعاً، إذا لو جئتَ تخيل أن
+
+24
+00:02:16,160 --> 00:02:17,880
+هذا هو normal
+
+25
+00:02:26,460 --> 00:02:32,660
+يبقى الآن نبحث عن مقدار distance D ما بين النقطة S
+
+26
+00:02:32,660 --> 00:02:37,200
+اللي في الفراغ، والـ plane M.  بنروح وبناخذ أي
+
+27
+00:02:37,200 --> 00:02:41,460
+نقطة P موجودة في الـ plane، وبنرسم الـ normal على الـ
+
+28
+00:02:41,460 --> 00:02:46,380
+plane، اللي هو الـ normal هذا، وسميته N.
+
+29
+00:03:01,060 --> 00:03:07,160
+لو جئت من النقطة S، ونزلت عمود على N بهذا الشكل،
+
+30
+00:03:07,160 --> 00:03:12,540
+البعاد اللي عندنا هذا، والبعد هذا، شو العلاقة بينهم؟
+
+31
+00:03:13,540 --> 00:03:17,980
+هما متساويتان. إن هما البعد العمودي بين النقطة S وبين
+
+32
+00:03:17,980 --> 00:03:26,560
+الـ plane D. طيب، هذا الطول من النقطة P إلى نقطة S هو
+
+33
+00:03:26,560 --> 00:03:33,420
+طول متجه PS. بس، إذا لو ضربت PS في cosine
+
+34
+00:03:33,420 --> 00:03:39,340
+الزاوية ثيتا، بيعطيني مين؟ البعد بين النقطة S وما بين
+
+35
+00:03:39,340 --> 00:03:45,560
+الـ plane. يبقى بناء عليه، الـ distance D بدي أساويه
+
+36
+00:03:45,560 --> 00:03:50,720
+بطول PS في cosine الزاوية ثيتا.
+
+37
+00:03:54,620 --> 00:04:00,100
+كويس. طيب، نجي لـ cosine الزاوية هذه ثيتا. بدي أستخدم
+
+38
+00:04:00,100 --> 00:04:04,820
+ما سبق دراسته من الـ dot product في كتابة cosine
+
+39
+00:04:04,820 --> 00:04:10,880
+الثيتا بشكل آخر. طبعاً، خلنا نحصل ضرب متجهين u في v كـ
+
+40
+00:04:10,880 --> 00:04:15,800
+dot product. طول الـ u في طول الـ v في cosine الزاوية
+
+41
+00:04:15,800 --> 00:04:21,100
+ثيتا. إذا cosine الزاوية ثيتا يساوي u dot v على
+
+42
+00:04:21,100 --> 00:04:26,550
+طول الـ u في طول الـ v. إذا بناء عليه، هذا بدي يعطينا
+
+43
+00:04:26,550 --> 00:04:37,790
+طول PS مضروب فيه cosine ثيتا.  اللي هو PS dot N
+
+44
+00:04:37,790 --> 00:04:51,470
+مقسوماً على طول N.  بس هيك لا، على طول PS في طول
+
+45
+00:04:51,470 --> 00:04:58,950
+N. مضبوط هيك؟ طيب تمام. الآن، في اختصارات. يبقى لو
+
+46
+00:04:58,950 --> 00:05:04,590
+اختصرت طول PS مع طول PS، يبقى هذا الكلام بده
+
+47
+00:05:04,590 --> 00:05:14,110
+يعطينا PS dot N، لو  N متجه N، مقسوماً على طول
+
+48
+00:05:14,110 --> 00:05:15,910
+المتجه N.
+
+49
+00:05:20,300 --> 00:05:25,980
+إذا من الآن فصاعداً، مشان نحسب قداش المسافة ما بين
+
+50
+00:05:25,980 --> 00:05:30,300
+نقطة و plane، بدنا ما يأتي: بدنا نوجد نقطة في الـ
+
+51
+00:05:30,300 --> 00:05:35,360
+plane، ونجيب قداش المسافة من النقطة هذه إلى النقطة
+
+52
+00:05:35,360 --> 00:05:41,230
+اللي في الفراغ. بصير عندي متجه، بدي اسميه PS، من
+
+53
+00:05:41,230 --> 00:05:44,230
+معادلة الـ plane، بقدر أجيب المتجه العمودي على
+
+54
+00:05:44,230 --> 00:05:47,810
+الـ plane. صار عندي two vectors. من خلال الـ two
+
+55
+00:05:47,810 --> 00:05:52,390
+vectors هذول، بقدر أعرف كده الـ distance هذه المبينة
+
+56
+00:05:52,390 --> 00:05:55,690
+في الرسم اللي عندنا. المسافة هذه، أو المسافة اللي
+
+57
+00:05:55,690 --> 00:06:01,430
+عندنا، هذه كده مقدار الـ D. بقول: PS dot N على
+
+58
+00:06:01,430 --> 00:06:06,440
+طول الـ N.  هل هناك أي أسئلة هنا قبل أن ندخل
+
+59
+00:06:06,440 --> 00:06:18,520
+إلى المثال؟  أيه؟ طيب، نجي ناخد مثال. example: find
+
+60
+00:06:18,520 --> 00:06:28,020
+the distance from the point. find the distance from
+
+61
+00:06:33,780 --> 00:06:41,920
+النقطة (2، -3، 4) to the plane
+
+62
+00:06:41,920 --> 00:06:46,880
+الـ
+
+63
+00:06:46,880 --> 00:06:56,580
+plane اللي هو x زائد 2y زائد 2z يساوي
+
+64
+00:06:56,580 --> 00:06:57,900
+13.
+
+65
+00:07:09,620 --> 00:07:14,100
+سؤال مرة ثانية. بيقول لي: هذا، ليه قداش المسافة من
+
+66
+00:07:14,100 --> 00:07:19,860
+النقطة اللي هي (2، -3، 4) للمستوى x
+
+67
+00:07:19,860 --> 00:07:24,600
+زائد 2y زائد 2z يساوي 13. عشان نحسب
+
+68
+00:07:24,600 --> 00:07:29,260
+هذه المسافة، بيدي نقطة في الـ plane، وبيدي المتجه
+
+69
+00:07:29,260 --> 00:07:33,040
+العمودي على هذا الـ plane. الحمد لله، المتجه بيجيبه
+
+70
+00:07:33,040 --> 00:07:37,540
+من شكل المعادلة تبع الـ plane.  يا جماعة، بقول ليه؟
+
+71
+00:07:49,460 --> 00:07:58,080
+إن متجه N يساوي: المعادلة i زائد 2j زائد
+
+72
+00:07:58,080 --> 00:07:59,060
+2k.
+
+73
+00:08:05,390 --> 00:08:10,170
+كيف بدي أجيب نقطة في هذا الـ plane؟ يعني بدي
+
+74
+00:08:10,170 --> 00:08:16,470
+إحداثيات نقطة هذا الـ plane يمر بها. كيف ممكن أخذ
+
+75
+00:08:16,470 --> 00:08:21,310
+بدل النقطة (3، 0، 0).  إذا بدك (20، 0، 0) ماشي الحال، مش
+
+76
+00:08:21,310 --> 00:08:25,170
+مشكلة. احنا بدنا بس نقطة واحدة. يبقى أبسط شغل شو
+
+77
+00:08:25,170 --> 00:08:30,890
+أعمله؟ مثلاً،
+
+78
+00:08:30,890 --> 00:08:32,130
+يبقى الاخت
+
+79
+00:08:35,900 --> 00:08:41,840
+الزميلة إيناس بتقول ما يأتي: أنه نضع two variables كل
+
+80
+00:08:41,840 --> 00:08:46,180
+واحد بصفر، وبطلع منها قيمة الـ variable الثالث.
+
+81
+00:08:46,180 --> 00:08:49,560
+وبالتالي، هذول بيكونوا إحداثيات نقطة موجودة في هذا
+
+82
+00:08:49,560 --> 00:08:53,980
+الـ plane. كلامها سليم مئة بالمئة. يبقى لو جينا
+
+83
+00:08:53,980 --> 00:08:55,080
+قلنا: put
+
+84
+00:09:12,450 --> 00:09:18,470
+يعني هذا ليس بالضرورة أن يكون هذول. ممكن آخذ هذول
+
+85
+00:09:18,470 --> 00:09:24,090
+برقم آخر كمان. ليس بالضرورة يكون صفر. المهم، بدي أنا
+
+86
+00:09:24,090 --> 00:09:28,570
+أدور على نقطة. لكن لما أحط y تساوي z تساوي صفر،
+
+87
+00:09:28,570 --> 00:09:34,630
+أسهل لي في الحسابات. لما تكون… اكتشف عمود في معدل
+
+88
+00:09:34,630 --> 00:09:40,910
+البلد… تصير x زائد صفر زائد صفر يساوي 13.
+
+89
+00:09:40,910 --> 00:09:41,770
+يبقى x
+
+90
+00:09:47,620 --> 00:09:56,600
+النقطة اللي هي (13، 0، 0) lie in the
+
+91
+00:09:56,600 --> 00:10:02,160
+given plane. إذاً،
+
+92
+00:10:02,160 --> 00:10:07,340
+هذه يا بنات صارت هي النقطة P، والنقطة المعلومة
+
+93
+00:10:07,340 --> 00:10:10,980
+اللي عندنا هذه، مين بدها تكون؟ حسب الرسم اللي عندنا،
+
+94
+00:10:10,980 --> 00:10:16,460
+اسمها S، اللي هي النقطة S. إذا، بيلزمني أجيب المتجه PS.
+
+95
+00:10:45,370 --> 00:10:56,330
+ناقص 11i ناقص 3j زائد 4k. عرفنا إيه هو
+
+96
+00:10:56,330 --> 00:11:03,530
+المتجه PS، والمتجه N موجود عندنا هيه. إذا، بقدر أجيب الـ
+
+97
+00:11:03,530 --> 00:11:06,770
+distance D. يبقى distance
+
+98
+00:11:29,280 --> 00:11:36,440
+هذه يا بنات، طول هذه، هي absolute value. صحيح، ليها
+
+99
+00:11:36,440 --> 00:11:37,080
+والله، عيب.
+
+100
+00:11:46,580 --> 00:11:52,280
+أو الطول يجب أن يكون قيمة موجبة. فبآخذ الـ
+
+101
+00:11:52,280 --> 00:11:56,280
+absolute value. إذا، هذا الكلام بده يساوي الـ
+
+102
+00:11:56,280 --> 00:12:01,420
+absolute value بده يعمل dot product ما بين PS
+
+103
+00:12:01,420 --> 00:12:04,040
+وN. يبقى
+
+104
+00:12:08,880 --> 00:12:15,480
+بعدين ناقص ثلاثة في اثنين، ناقص ستة. وبعدين أربعة
+
+105
+00:12:15,480 --> 00:12:21,820
+في اثنين، زائد ثمانية. كله على الجذر التربيعي
+
+106
+00:12:44,670 --> 00:12:50,170
+إذا، نقول المسافة من النقطة هذه للـ plane يساوي كده؟
+
+107
+00:12:50,170 --> 00:12:56,190
+يساوي ثلاثة من وحدات الطول. ودي هي الـ remark التالية.
+
+108
+00:12:56,190 --> 00:13:01,890
+remark:
+
+109
+00:13:01,890 --> 00:13:10,170
+Two planes are perpendicular
+
+110
+00:13:14,530 --> 00:13:23,090
+أو perpendicular أو parallel.
+
+111
+00:13:23,090 --> 00:13:31,110
+المتعامدتان أو المتوازيتان have their normals
+
+112
+00:13:42,820 --> 00:13:51,280
+يا جماعة، دي في الأرض؟ أو أهلاً؟
+
+113
+00:13:51,280 --> 00:14:03,820
+هاد
+
+114
+00:14:03,820 --> 00:14:09,030
+أعقبلكم معي هنا، والله أعلم. لو جئتَ تخيلت أن عندي
+
+115
+00:14:09,030 --> 00:14:15,630
+مستويين، ومستويين متوازيين. رسمت الـ vector العمودي على
+
+116
+00:14:15,630 --> 00:14:20,150
+المستوى الأول، والـ vector العمودي على المستوى
+
+117
+00:14:20,150 --> 00:14:23,810
+الثاني، شو العلاقة بين هذين الـ two vectors؟
+
+118
+00:14:40,350 --> 00:14:46,070
+أنا عندي الآن two planes، اثنان are parallel. بدي
+
+119
+00:14:46,070 --> 00:14:49,830
+أرسم العمود على الأول، والعمود على الثاني. شو العلاقة
+
+120
+00:14:49,830 --> 00:14:54,130
+بينهم؟  الاثنان parallel. إذاً، if two planes
+
+121
+00:14:54,130 --> 00:14:58,310
+are parallel، then their normals are parallel. والعكس، لو كانت
+
+122
+00:14:58,310 --> 00:15:02,130
+two normals are parallel، you get two
+
+123
+00:15:02,130 --> 00:15:05,970
+planes are parallel. نجي لحكاية التعامد. خلّيكي
+
+124
+00:15:05,970 --> 00:15:06,750
+هاتِ لي هذا.
+
+125
+00:15:11,270 --> 00:15:14,710
+إحنا لدينا الآن two planes بالشكل اللي لدينا هنا.
+
+126
+00:15:14,710 --> 00:15:18,830
+يبقى هذول الـ two planes are perpendicular. اثنان
+
+127
+00:15:18,830 --> 00:15:23,390
+متعامدان. الزاوية بين المستويين هي تسعين درجة.
+
+128
+00:15:23,390 --> 00:15:28,310
+بترسم العمود على المستوى الأول، والعمود على
+
+129
+00:15:28,310 --> 00:15:32,870
+المستوى الثاني. إيش العلاقة بين الـ two lines أو الـ two
+
+130
+00:15:32,870 --> 00:15:37,110
+lines  perpendicular؟ يبقى اثنان are orthogonal. يبقى بناء
+
+131
+00:15:37,110 --> 00:15:44,960
+عليه، لو عندي two planes، العموديان على هذين المستقيمين
+
+132
+00:15:44,960 --> 00:15:48,020
+يكونان متعامدان.
+
+133
+00:15:54,230 --> 00:15:59,710
+أنا عندي هذا plane وهذا الـ plane. اثنان
+
+134
+00:15:59,710 --> 00:16:03,550
+أعرف إنهم perpendicular في الـ corner اللي عندي. لو جئتَ
+
+135
+00:16:03,550 --> 00:16:08,730
+رسمت من هنا عمود على الـ plane الأول، ورسمت عمود
+
+136
+00:16:08,730 --> 00:16:12,510
+على الـ plane الثاني، هكذا، بينهم تسعين درجة. هي اللي
+
+137
+00:16:12,510 --> 00:16:16,470
+بتقوله الريمان. بتقولي: two planes are perpendicular،
+
+138
+00:16:16,470 --> 00:16:23,290
+اثنان بيكونوا متعامدان أو متوازيان if their normal vectors
+
+139
+00:16:23,290 --> 00:16:27,470
+إذا جبت normal على كل واحد من الـ
+
+140
+00:16:27,470 --> 00:16:30,290
+two vectors هذول، بلاقي اثنين إذا perpendicular
+
+141
+00:16:30,290 --> 00:16:34,110
+بيكونوا perpendicular.  إذا parallel، بيكون اثنان هذول
+
+142
+00:16:34,110 --> 00:16:40,910
+ما لهما parallel.  نعطي مثال على ذلك. يبقى example:
+
+143
+00:16:49,120 --> 00:16:58,520
+بقول: شوّه the two planes. show that the two planes A
+
+144
+00:16:58,520 --> 00:17:08,040
+و B، هي لإنه مستويان، اللي هو 3x زائد 6y
+
+145
+00:17:08,040 --> 00:17:10,720
+ناقص 9z
+
+146
+00:17:15,180 --> 00:17:26,220
+و الـ x زائد 2y ناقص 3z يساوي واحد. اثنان
+
+147
+00:17:26,220 --> 00:17:29,700
+اثنان
+
+148
+00:17:29,700 --> 00:17:37,700
+متوازيان، and find the distance
+
+149
+00:17:42,400 --> 00:17:46,020
+و أوجد المسافة between them.
+
+150
+00:18:25,560 --> 00:18:30,520
+سؤال مرة ثانية. ما طاني معادلتين لـ two planes. كل
+
+151
+00:18:30,520 --> 00:18:34,980
+واحد المعادلة، وقال لي: بيقول إن two planes هذول are
+
+152
+00:18:34,980 --> 00:18:38,420
+parallel. كيف بنثبت إن two planes هذول هذول هذول
+
+153
+00:18:38,420 --> 00:18:44,520
+هذول هذول هذول هذول
+
+154
+00:18:44,520 --> 00:18:44,560
+هذول هذول هذول هذول هذول هذول هذول هذول هذول هذول
+
+155
+00:18:44,560 --> 00:18:44,600
+هذول هذول هذول هذول هذول هذول هذول هذول هذول هذول
+
+156
+00:18:44,600 --> 00:18:46,240
+هذول هذول هذول هذول هذول هذول هذول هذول هذول هذول
+
+157
+00:18:46,240 --> 00:18:49,820
+هذول هذول هذول هذول هذول هذول هذول هذول هذول هذول
+
+158
+00:18:49,820 --> 00:18:49,840
+هذول هذول هذول هذول هذول هذول هذول هذول هذول هذول
+
+159
+00:18:49,840 --> 00:18:51,780
+هذول هذول هذول هذول هذول هذول هذول هذول هذول هذول
+
+160
+00:19:15,670 --> 00:19:24,450
+normal to the first plane
+
+161
+00:19:24,450 --> 00:19:28,430
+is
+
+162
+00:19:28,430 --> 00:19:29,090
+a vector
+
+163
+00:19:34,270 --> 00:19:46,990
+3i زائد 6j ناقص 9k.  normal to the second plane  بيعمل
+
+164
+00:19:46,990 --> 00:19:50,170
+عمودي عليه، عمودي على المستوى، أسهل.
+
+165
+00:19:56,220 --> 00:20:00,240
+طبعاً، واضح أنه في عامل مشترك هو مين؟ ثلاثة. يعني لو
+
+166
+00:20:00,240 --> 00:20:06,340
+أخذت ثلاثة، بصير عندي i زائد 2j ناقص 3k.
+
+167
+00:20:06,340 --> 00:20:12,200
+المتجه بين القوسين هو المتجه مين؟ الـ two. يبقى
+
+168
+00:20:12,200 --> 00:20:18,920
+هذا الكلام يساوي ثلاثة in one  هذا. بدي يعطينا in one
+
+169
+00:20:18,920 --> 00:20:25,460
+and in two.  اثنان معاً are parallel.
+
+170
+00:20:31,990 --> 00:20:36,730
+يبقى المستويين اثنان بتاعتهم… يبقى هذا اللي
+
+171
+00:20:36,730 --> 00:20:44,030
+يعطينا هي the two given
+
+172
+00:20:44,030 --> 00:20:48,190
+planes
+
+173
+00:20:48,190 --> 00:20:52,510
+are parallel.
+
+174
+00:20:55,080 --> 00:20:59,340
+يبقى المستويان هذول متوازيان. هذا المطلوب الأول من
+
+175
+00:20:59,340 --> 00:21:03,8
+
+223
+00:27:34,860 --> 00:27:40,620
+مرحباً بكم، أنتم من الصفر السابع لغاية الصفر
+
+224
+00:27:40,620 --> 00:27:45,940
+التاسع، مرحلة الإعدادية، هذه الزاوية بين المستقيمين
+
+225
+00:27:45,940 --> 00:27:50,040
+تساوي الزاوية بين العمودين على هذين المستقيمين
+
+226
+00:27:50,040 --> 00:27:55,400
+يعني الزاوية المحصورة بين المستقيمين المتقاطعين
+
+227
+00:27:55,400 --> 00:28:01,800
+تساوي الزاوية بين المستقيمين، اللي هما العمودين على
+
+228
+00:28:01,800 --> 00:28:06,840
+هذين المستقيمين، سمعتوا فيه؟ تمام، احنا هنا نفس
+
+229
+00:28:06,840 --> 00:28:11,580
+الفكرة، بنقول الزاوية بين two intersecting planes
+
+230
+00:28:11,580 --> 00:28:16,180
+هي الزاوية بين الـ normal vectors، يبقى احنا بدنا
+
+231
+00:28:16,180 --> 00:28:23,240
+نروح ندور على مين؟ على two intersecting planes، يبقى
+
+232
+00:28:23,240 --> 00:28:24,280
+لو روحت قلت
+
+233
+00:28:32,590 --> 00:28:38,090
+وفي عندي مستوى ثاني، المستوى الثاني كان بهذا الشكل
+
+234
+00:28:38,090 --> 00:28:45,530
+يبقى المستويان هذان تقاطعا في خط التقاطع
+
+235
+00:28:45,530 --> 00:28:49,270
+اللي عندنا، كويس
+
+236
+00:28:49,910 --> 00:28:56,030
+هذا خط يقطع المستويين، بدي أرسم عمودياً على
+
+237
+00:28:56,030 --> 00:29:01,670
+المستوى الأول، وكذلك عمودياً على المستوى الثاني، لو
+
+238
+00:29:01,670 --> 00:29:08,190
+جيت قلت هذا عمودي على المستوى الأول، اللي هو N1
+
+239
+00:29:08,190 --> 00:29:13,910
+يعني الأزرق عمودي على المستوى الأزرق هذا، والـ
+
+240
+00:29:13,910 --> 00:29:19,770
+vector، قصدنا الـ vector N1، وجيت هنا كمان رسمت عمود
+
+241
+00:29:25,630 --> 00:29:33,510
+طبعاً الزاوية هذه هي الزاوية ما بين two normal
+
+242
+00:29:33,510 --> 00:29:38,270
+vectors، عمودي على المستوى الأول، والخط الأزرق
+
+243
+00:29:38,270 --> 00:29:44,130
+عمودي على المستوى الأزرق، والخط الأسود عمودي على
+
+244
+00:29:44,130 --> 00:29:50,680
+المستوى الأسود، الآن بدي أجد الزاوية بين المستويين
+
+245
+00:29:50,680 --> 00:29:54,620
+طبعاً الزاوية يا بنات هي الزاوية الزوجية بين
+
+246
+00:29:54,620 --> 00:30:01,040
+المستويين، الزاوية هذه، يعني لما أجيب two planes، هات
+
+247
+00:30:01,040 --> 00:30:06,860
+شوية بلغة، لما أجيب الـ two planes المتقاطعين بهذا
+
+248
+00:30:06,860 --> 00:30:13,750
+الشكل، أجد الاثنين هذين بينهم إيش؟ بينهم زاوية على طول
+
+249
+00:30:13,750 --> 00:30:17,570
+خط التقاطع، هذه بالعامة بسميها الزاوية الزوجية
+
+250
+00:30:17,570 --> 00:30:22,290
+the angle between two intersecting planes
+
+251
+00:30:22,290 --> 00:30:29,190
+تتقاطع
+
+252
+00:30:36,740 --> 00:30:41,920
+الزاوية المحصورة بين two normal vectors تساوي
+
+253
+00:30:41,920 --> 00:30:46,660
+عملياً الزاوية الموجودة بين المستويين
+
+254
+00:30:52,930 --> 00:30:57,390
+يعني ارسم المتجه العمودي على المستوى الأول، وارسم
+
+255
+00:30:57,390 --> 00:31:02,130
+المتجه العمودي على المستوى الثاني، الزاوية بينهما هي
+
+256
+00:31:02,130 --> 00:31:11,110
+الزاوية الزوجية بين المستويين، تمام، نعطي مثالاً على
+
+257
+00:31:11,110 --> 00:31:11,710
+ذلك
+
+258
+00:31:26,930 --> 00:31:42,630
+the angle between the planes بين المستويين ال...
+
+259
+00:31:42,630 --> 00:31:50,930
+اللي هو X زائد أربعة Y ناقص ثلاثة Z يساوي واحد
+
+260
+00:31:50,930 --> 00:32:03,470
+and اللي هو ناقص ثلاثة X زائد ستة Y زائد سبعة Z
+
+261
+00:32:40,400 --> 00:32:43,720
+بنحسب من المستويين هذين أنني بدي أجيب
+
+262
+00:32:43,720 --> 00:32:49,140
+الـ normal vector على كل من المستويين، يبقى بدي أجيب
+
+263
+00:32:49,140 --> 00:32:59,020
+هأقول N1 اللي هو I زائد أربعة J ناقص ثلاثة K، normal to
+
+264
+00:32:59,020 --> 00:33:03,820
+the first
+
+265
+00:33:03,820 --> 00:33:04,360
+plane
+
+266
+00:33:12,070 --> 00:33:22,650
+N2 اللي هو عبارة عن ناقص ثلاثة I زائد ستة J زائد
+
+267
+00:33:22,650 --> 00:33:31,070
+سبعة K، normal to the second، أطلقه
+
+268
+00:33:31,070 --> 00:33:36,470
+المتجه، أطلقه الآن، بدي أستعمل  dot product ما
+
+269
+00:33:36,470 --> 00:33:44,220
+بينهما، فأنا أجيب الـ N1 dot
+
+270
+00:33:44,220 --> 00:33:51,720
+N2، المتجه الثاني، N2 يساوي طول الـ
+
+271
+00:33:56,420 --> 00:34:02,440
+الزاوية بينهما، الآن بدي أعمل ضرباً نقطياً بينهما، يبقى
+
+272
+00:34:02,440 --> 00:34:08,360
+هذا ناقص ثلاثة، واللي بعدها أربعة في ستة، بزائد
+
+273
+00:34:08,360 --> 00:34:15,660
+أربعة وعشرين، واللي بعدها ناقص ثلاثة في سبعة،  بناقص واحد وعشرين، بدي أساوي
+
+274
+00:34:19,140 --> 00:34:25,020
+|N1| اللي هو جذر واحد زائد ستة عشر زائد تسعة، واحد زائد
+
+275
+00:34:25,020 --> 00:34:31,120
+ستة عشر زائد تسعة، والجذر الثاني اللي هو المتجه
+
+276
+00:34:31,120 --> 00:34:39,020
+الثاني، اللي هو تسعة زائد ستة وثلاثين، تسعة زائد ستة
+
+277
+00:34:39,020 --> 00:34:47,520
+وثلاثين زائد تسعة وأربعين في كوساين الزاوية، بيساوي
+
+278
+00:34:47,520 --> 00:34:52,900
+هذا، أمانة الطرف الشمالي، صفر، إذا أقسم على مين؟
+
+279
+00:34:52,900 --> 00:34:57,860
+على حاصل ضرب الجذرين، بيسير عندي كوساين ثيتا بيساوي
+
+280
+00:34:57,860 --> 00:35:02,780
+كم؟ صفر، فنطرح السؤال التالي، مين الزاوية اللي
+
+281
+00:35:02,780 --> 00:35:06,800
+جيب تمامها يساوي صفر؟ تسعون درجة
+
+282
+00:35:17,100 --> 00:35:29,980
+يبقى this means that the two planes are
+
+283
+00:35:29,980 --> 00:35:31,380
+perpendicular
+
+284
+00:35:40,480 --> 00:35:45,740
+احنا حسبنا الزاوية وجدنا أن المستويين are perpendicular
+
+285
+00:35:45,740 --> 00:35:51,000
+عليكم أن ينتهي هذا الـ section، ونجي للـ exercises
+
+286
+00:35:51,000 --> 00:35:59,940
+اثنا عشر، خمسة مسائل من واحد لغاية ثمانية وأربعين، الـ
+
+287
+00:35:59,940 --> 00:36:02,700
+ومن ثلاثة وخمسين
+
+288
+00:36:41,170 --> 00:36:45,970
+بنجي للـ section التالي، وهو آخر section في هذا
+
+289
+00:36:45,970 --> 00:36:53,210
+الـ chapter، اللي هو section اثنا عشر ستة، يتحدث عن الـ
+
+290
+00:36:53,210 --> 00:36:59,130
+cylinder، cylinders
+
+291
+00:36:59,130 --> 00:37:09,710
+and quadric surfaces
+
+292
+00:37:15,480 --> 00:37:23,960
+نبدأ أول شيء بملاحظة الـ cylinders، إيش
+
+293
+00:37:23,960 --> 00:37:29,660
+معنى cylinders يا بنات؟ بالعربي أسطوانة، ممتاز، طيب
+
+294
+00:37:29,660 --> 00:37:35,820
+الأسطوانة، هل ضروري يكون مقطعها عبارة عن دائرة؟
+
+295
+00:37:37,770 --> 00:37:42,070
+الأسطوانة العادية، لو قطعتها هي عبارة عن دائرة، لكن
+
+296
+00:37:42,070 --> 00:37:46,730
+هل لما أقول cylinder في الفراغ بالضرورة أن يكون
+
+297
+00:37:46,730 --> 00:37:52,730
+المقطع دائرة؟ لا، شوفي من هنا، لو جيت قلت هذا
+
+298
+00:37:52,730 --> 00:37:57,490
+عبارة عن سطح، الشكل اللي عندنا، أنتي شوفي اللي أنتي
+
+299
+00:37:57,490 --> 00:38:03,690
+شايفينه أنا، كويس؟ هذا بسميه cylinder، سطح
+
+300
+00:38:03,690 --> 00:38:06,330
+أسطواني، حتى لو لم يكن مغلقاً
+
+301
+00:38:14,680 --> 00:38:20,060
+يبقى المقطع عبارة عن إيه؟ عبارة عن دائرة، يبقى
+
+302
+00:38:20,060 --> 00:38:24,720
+دائرية، الشكل اللي عندنا هذا، مش واضح، بلاش، نوضح
+
+303
+00:38:31,300 --> 00:38:37,320
+يبقى هذه cylinder، وكذلك لو خليتها بهذا الشكل، يبقى
+
+304
+00:38:37,320 --> 00:38:43,340
+هنا cylinder، لو كبرتها ووضحت أكثر مثل هذا السطح
+
+305
+00:38:43,340 --> 00:38:48,860
+هو عبارة عن إيش؟ عبارة عن cylinder، لو خليته مفتوحاً
+
+306
+00:38:48,860 --> 00:38:53,960
+بالشكل هذا cylinder، لو جبت شكل آخر مثله، وخليته من
+
+307
+00:38:53,960 --> 00:39:00,300
+ناحية أخرى، و الاثنين مع بعض، كذلك يعتبر cylinder، طيب
+
+308
+00:39:00,300 --> 00:39:06,820
+إيش الـ quadric surface أو الـ quadric surfaces، إيش
+
+309
+00:39:06,820 --> 00:39:12,400
+معنى quadric بالعربي؟ ثنائي، مش مربع، إذًا square
+
+310
+00:39:12,400 --> 00:39:16,860
+مربع، يبقى الـ quadric ثنائي، surface سطح، يبقى
+
+311
+00:39:16,860 --> 00:39:24,080
+الأسطح الثنائية، يعني المجسمات بالعربي اللي بتكون
+
+312
+00:39:24,080 --> 00:39:31,800
+في الفرضيات، وأنتم جاهزون تعتبرون مجسم موجود في
+
+313
+00:39:31,800 --> 00:39:38,260
+الفراغ، أو شكله الخارجي يعتبر quadric surface، تمام؟
+
+314
+00:39:38,260 --> 00:39:41,820
+يبقى هذا الـ quadric surface، اللي احنا بدنا نميز ما
+
+315
+00:39:41,820 --> 00:39:46,000
+بين الـ quadric surfaces والـ cylinder، هناخد ستة
+
+316
+00:39:46,000 --> 00:39:51,420
+quadric surfaces، ستة أسطح ثنائية، ونعرف معادلة كل
+
+317
+00:39:51,420 --> 00:39:56,500
+سطح من هذه الأسطح، طبعاً هذه الأسطح مشهورة، وقبلها
+
+318
+00:39:56,500 --> 00:40:03,340
+هناخد وضع الـ cylinder، ونشوف كيف بنرسم كل واحدة من
+
+319
+00:40:03,340 --> 00:40:10,320
+الـ quadric surfaces، وكذلك الـ cylinder المختلفة، طيب على
+
+320
+00:40:10,320 --> 00:40:15,200
+أي حال في الفراغ بالنسبة للـ cylinder، أجد معادلة
+
+321
+00:40:15,200 --> 00:40:18,980
+فيها رمزين فقط، طبعاً احنا بنشتغل في الـ
+
+322
+00:40:39,280 --> 00:40:43,780
+طيب الكلمتين اللي أنتم سمعتوهم، بدي أكتبهما، وبعدين نشوف
+
+323
+00:40:43,780 --> 00:40:49,160
+كيف بدنا نرسم بعدين اللي هو بعض الـ cylinder، فأنا أجيب
+
+324
+00:40:49,160 --> 00:40:49,620
+بأقول
+
+325
+00:41:05,940 --> 00:41:15,780
+Y أو Z، أي واحد منهم مفقود من
+
+326
+00:41:15,780 --> 00:41:21,000
+المعادلة
+
+327
+00:41:21,000 --> 00:41:27,300
+مش موجود في المعادلة، تبع، في الصفر of a surface
+
+328
+00:41:27,300 --> 00:41:34,920
+then the surface then the surface
+
+329
+00:41:45,110 --> 00:41:51,510
+هو عبارة عن سطح مع جنريتر
+
+330
+00:41:51,510 --> 00:41:57,590
+مولد
+
+331
+00:41:57,590 --> 00:41:58,710
+للسيلندر
+
+332
+00:42:22,150 --> 00:42:30,950
+to the axis corresponding ..
+
+333
+00:42:30,950 --> 00:42:40,450
+corresponding المناظر to the missing variable
+
+334
+00:42:40,450 --> 00:42:46,690
+example
+
+335
+00:42:58,900 --> 00:43:13,860
+half of the following cylinders المرأة
+
+336
+00:43:13,860 --> 00:43:24,860
+الـ X تربيع زائد أربعة Z تربيع يساوي ستة عشر،  نمرة B، X يساوي Y تربيع، نمرة C، Z تساوي تسعة ناقص Y
+
+337
+00:43:24,860 --> 00:43:36,650
+تربيع، نمرة D، Y تربيع على أربعة ناقص X تربيع على
+
+338
+00:43:36,650 --> 00:43:45,570
+تسعة يساوي واحد
+
+339
+00:43:45,570 --> 00:43:47,610
+يساوي واحد
+
+340
+00:44:10,030 --> 00:44:15,570
+بنشوف كيف بنحكم على رسمة أنّه عندي رسمة أسطوانة أو
+
+341
+00:44:15,570 --> 00:44:20,510
+غيرها، وإذا كانت أسطوانة، يبقى لها محور، بدنا نعرف
+
+342
+00:44:20,510 --> 00:44:28,270
+مين هو المحور اللي عندنا هذا، ولها مولد، تمام، طلعوا يا
+
+343
+00:44:28,270 --> 00:44:34,350
+بنات، هنا لو أنا ثبت اللي عندي، المستقيم الأزرق اللي
+
+344
+00:44:34,350 --> 00:44:39,670
+شايفينه، وروح جبت موازياً له، اللي هو مين؟ الأسود اللي
+
+345
+00:44:39,670 --> 00:44:44,150
+عندنا هنا، وقلت أنت يا أزرق ضلك ثابت، تصحى تتحرك
+
+346
+00:44:44,150 --> 00:44:51,050
+أنت يا أسود بدك تتحرك حوالي الأزرق، فعشان تضلك ماشي
+
+347
+00:44:51,050 --> 00:44:56,410
+على منحنى، وتضلك موازياً للأزرق، أنت جالس هيرسم لي من
+
+348
+00:44:56,410 --> 00:45:03,170
+الخارج سطح أسطواني، تمام؟ المنطقة اللي بمسحها الخط
+
+349
+00:45:03,170 --> 00:45:07,320
+اللي عندنا هنا كلها، بدي أسميها مين؟ سطح، هذا السطح
+
+350
+00:45:07,320 --> 00:45:13,420
+بسميه أسطوانة، أو بسميه cylinder، يبقى هذا اللي هو
+
+351
+00:45:13,420 --> 00:45:16,940
+الكلام أو السطرين اللي أنا كاتبهم هنا، لو كان
+
+352
+00:45:16,940 --> 00:45:21,420
+واحد من المتغيرات مفقود من المعادلة، يبقى الـ
+
+353
+00:45:21,420 --> 00:45:24,560
+surface اللي عندي، بدي أقول هو عبارة عن cylinder
+
+354
+00:45:24,560 --> 00:45:29,720
+ولها مولد، شو مولد؟ يعني اللي بدي أولد السطح
+
+355
+00:45:29,720 --> 00:45:37,690
+الخارجي تبع الـ cylinder، وهذا بدي يكون موازياً للـ axis
+
+356
+00:45:37,690 --> 00:45:43,210
+المناظر لمين؟ للمتغير المفقود، يعني إيش يا بنات قصد
+
+357
+00:45:43,210 --> 00:45:47,910
+يقول بالضبط من الكلامين اللي كتبتهما هذين؟ يقول لمن
+
+358
+00:45:47,910 --> 00:45:53,570
+يعطيك معادلة، وتقدر تعرفها معادلة سيلندر ولا لا، تطلع
+
+359
+00:45:53,570 --> 00:45:56,930
+على المعادلة هذه، المعادلة في الفراغ أصلاً فيها
+
+360
+00:45:56,930 --> 00:46:03,210
+ثلاثة متغيرات X و Y و Z، لو جيت واحد منهم مفقود، مش موجود
+
+361
+00:46:03,210 --> 00:46:07,690
+يعني يا إما X و Z اللي موجودين، يا إما X و Y، يا إما Y
+
+362
+00:46:07,690 --> 00:46:13,050
+و Z، رمزين فقط، ما أشوفش غير رمزين، إذا هذه معادلة
+
+363
+00:46:13,050 --> 00:46:19,770
+سيلندر، I imagine، مين الـ axis تبع السيلندر اللي هو
+
+364
+00:46:19,770 --> 00:46:25,530
+الرمز الغائب، أو ما يوازيه، ممكن يكون معمول له شفت
+
+365
+00:46:25,530 --> 00:46:29,650
+وبالتالي ما يكونش إيش؟ اللي هو المحور الغائب، أو
+
+366
+00:46:29,650 --> 00:46:30,630
+الرمز الغائب
+
+367
+00:46:51,540 --> 00:46:54,260
+الكلام اللي احنا قلناه بيروح للتطبيق على أرض
+
+368
+00:46:54,260 --> 00:47:01,010
+الواقع، قال لي مثال: ارسم لي كل من الأسطوانات الآتية
+
+369
+00:47:01,010 --> 00:47:05,090
+التالية، وقال لي: X تربيع زائد أربعة Z تربيع يساوي
+
+370
+00:47:05,090 --> 00:47:10,250
+ستة عشر، لو سألت وقلت لك هذه المعادلة فيديو ليه؟ ترجع
+
+371
+00:47:10,250 --> 00:47:14,890
+معادلة إيش؟ معادلة
+
+372
+00:47:14,890 --> 00:47:22,450
+إيش؟  إليبس، ممتاز، على ستة عشر، يبقى  X تربيع على
+
+373
+00:47:22,450 --> 00:47:26,800
+ستة عشر زائد Z تربيع على أربعة يساوي واحد، عنها دي دائرة
+
+374
+00:47:26,800 --> 00:47:34,260
+تُلفّ، تُلفّ، تمام، أيوة، يبقى هذه لو أخذت مقطعاً، اللي
+
+375
+00:47:34,260 --> 00:47:39,740
+بيكون  هذا  اللي  ساكن أنا في الفراغ، الرمزين اللي
+
+376
+00:47:39,740 --> 00:47:48,060
+موجودين، اللي هما، الرمز الغائب، إذا Y هو المحور، أو
+
+377
+00:47:48,060 --> 00:47:52,520
+الموازي للمحور، إذا وصلنا لمولدها، Chef، هل هذا مولد
+
+378
+00:47:52,520 --> 00:47:56,300
+الـ Chef؟  في الـ Chef، ممتاز،  إذن المحور تبع
+
+379
+00:47:56,300 --> 00:48:02,300
+الـ Cylinder هذه هو الـ Y Axis، طبعاً؟ أيوة، تعالوا
+
+380
+00:48:02,300 --> 00:48:09,100
+نرسمه، إذن هذا لما اتفقنا على أنها الـ Cylinder، بس
+
+381
+00:48:09,100 --> 00:48:14,120
+المقطع تبعها دائرة ولا ellipse اللي بيكون على شكل
+
+382
+00:48:14,120 --> 00:48:18,880
+ellipse، المحور تبع هذه الدائرة ده هو محور
+
+383
+00:48:42,970 --> 00:48:46,570
+تمام؟ طيب والمقطع اللي يقول على شكل إيش؟ اللي
+
+384
+00:48:46,570 --> 00:48:53,330
+يقول على شكل ellipse، إذا لو جيت قلت هذا الـ ellipse، ومن
+
+385
+00:48:53,330 --> 00:48:57,010
+الناحية الثانية بالشكل اللي عندنا هذا، وهذا هو
+
+386
+00:48:57,010 --> 00:49:03,010
+إيش؟ هو الشكل اللي عندنا، لأن هذه الأسطوانة، المقطع
+
+387
+00:49:03,010 --> 00:49:04,610
+تبعها عبارة عن
+
+388
+00:49:16,130 --> 00:49:26,310
+تمام؟ يبقى هذا يكون يعني لهنا شوية، يبقى
+
+389
+00:49:26,310 --> 00:49:30,670
+هذا المقطع، أو هذا المجسم اللي اتكون عندنا، أو هذه
+
+390
+00:49:30,670 --> 00:49:35,370
+هي الـ cylinder اللي تكون عندنا، هذه رسمة يا بنات
+
+391
+00:49:35,370 --> 00:49:42,810
+تعتبر رسمة سهلة، يعني ما فيش فيها أي صعوبة، مباشرة، أمانة
+
+392
+00:49:42,810 --> 00:49:47,570
+طيب نيجي للرسمة الثانية، ونشوف إيش قصتها، هذا X
+
+393
+00:49:47,570 --> 00:49:52,330
+يساوي Y تربيع، لو قصتك في الكلام، هذه معناها كده
+
+394
+00:49:52,330 --> 00:49:58,610
+Parabola، تظهر مكبرة، لكن أنا بدي إياها تقول في الفراغ
+
+395
+00:49:58,610 --> 0
+
+445
+00:55:35,380 --> 00:55:42,860
+إيه؟ وين Z و Y؟ هذا عندي Z و Y، كويس؟ مدّ هذا عندي
+
+446
+00:55:42,860 --> 00:55:49,900
+Z و Y يبقى المحور هو بيكون X أو موازٍ له، بس الـ Y
+
+447
+00:55:49,900 --> 00:55:58,350
+بمدى السينات، آه يعني يا بنات لو كان هذا يساوي Y
+
+448
+00:55:58,350 --> 00:56:04,430
+تربيعه بده ينقلب ويسير لوين؟ لأسفل، يبقى بده يسير
+
+449
+00:56:04,430 --> 00:56:09,190
+عن هناك مظبوط؟
+
+450
+00:56:09,190 --> 00:56:14,050
+وبعد هيك shift لوين؟ لأعلى بمقدار تسعة، يبدو أمشي
+
+451
+00:56:14,050 --> 00:56:19,950
+كرّسي هذا واعملي إزاحة لفوق بمقدار تسعة، يبقى
+
+452
+00:56:29,310 --> 00:56:34,210
+موازي لمحور X، بعد ما رسمنا هذا الموازي بدي أعمل
+
+453
+00:56:34,210 --> 00:56:39,350
+الـ main shift اللي عندنا هذا، يبقى هذه النقطة اللي
+
+454
+00:56:39,350 --> 00:56:47,510
+هي صفر، وصفر، وتسعة، وبتروح ترسمي هذه parabola
+
+455
+00:56:47,510 --> 00:56:52,170
+يبقى هذا لو جيت مدّه على استقامته يجب أن يقابلني
+
+456
+00:56:52,170 --> 00:56:55,530
+هنا، يبقى أنا عندي parabola
+
+457
+00:57:01,650 --> 00:57:09,910
+طيب يبقى هذه النقطة اللي فوق بدها تكون قمة الـ
+
+458
+00:57:09,910 --> 00:57:15,550
+parabola، بمعنى هي الرسمة زي هيك، أنا عملت نقطة، إذا
+
+459
+00:57:15,550 --> 00:57:21,410
+هذا الخط بيمر بالنقطة موازٍ لمين؟ للمحور اللي
+
+460
+00:57:21,410 --> 00:57:28,210
+عندنا، معناته في عندي خط بيظل موازٍ لمحور X
+
+461
+00:57:31,390 --> 00:57:35,930
+وهذا بيكون كل الـ parabolas مصفوفة جانب بعض بحيث
+
+462
+00:57:35,930 --> 00:57:40,030
+الـ parabolas تبقى عليها بالشكل اللي قدامك هنا، يبقى إيش
+
+463
+00:57:40,030 --> 00:57:45,170
+بديجيكي؟ بديجيكي هنا كمان، ههه، بالشكل اللي عندنا،
+
+464
+00:57:45,170 --> 00:57:52,790
+parabola ثانية، هيك، وهذه بتيجي هنا، هي هي parabola،
+
+465
+00:57:52,790 --> 00:57:57,530
+ومن هنا بتيجيكي كمان هنا، كمان parabola بالشكل اللي
+
+466
+00:57:57,530 --> 00:58:02,550
+عندك، وهذا بالشكل اللي عندك، يبقى إيش اللي حصل؟
+
+467
+00:58:02,550 --> 00:58:08,250
+كأنها parabola بالشكل هيك وقلبناها على الأرض بهذا
+
+468
+00:58:08,250 --> 00:58:13,670
+الشكل، واضحة؟ السبب اللي خلانا نقلبها هو الـ shift
+
+469
+00:58:13,670 --> 00:58:16,870
+تبعها واللي خلّاها بالشكل اللي عندنا
+
+470
+00:58:20,640 --> 00:58:26,320
+آه واضحة؟ دي بالك هذه مش نقطة تقاطع، هذا نبعدها
+
+471
+00:58:26,320 --> 00:58:30,080
+مع بعض شوية، ما لحك تقولي هذه المرة ما لها علاقة
+
+472
+00:58:30,080 --> 00:58:35,000
+بالموضوع. يبقى هذه الـ parabolas جاية بالشكل اللي عندها.
+
+473
+00:58:39,740 --> 00:58:48,860
+وهذا شُنّاب المرة ما له نزول. يبقى يا بنات ثاني مرة
+
+474
+00:58:48,860 --> 00:58:54,050
+بدي أحكي، إحنا عندنا Z تساوي تسعة ناقص Y تربيع
+
+475
+00:58:54,050 --> 00:58:58,830
+باعتبار لا عندي تسعة ولا عندي ساعة، يبقى Z تساوي 100
+
+476
+00:58:58,830 --> 00:59:05,370
+إذا نرسم حول محور Z، تمام؟ حول محور Z، هي محور
+
+477
+00:59:05,370 --> 00:59:10,380
+Z، يبقى هيك بدأت، تبقى الـ parameter لكن الـ Y تربيعها
+
+478
+00:59:10,380 --> 00:59:15,720
+السالبة بإشارة سالبة، الإعطاءات في الرسم بتجلب
+
+479
+00:59:15,720 --> 00:59:20,860
+لتحت فوق وفوق تحت، يبقى بدل ما الرسمة كلها
+
+480
+00:59:20,860 --> 00:59:27,000
+فوق قلبناها وصارت وين؟ تحت، والمنحنى كله أضفنا له
+
+481
+00:59:27,000 --> 00:59:32,300
+تسعة، بلغة الـ shift بدك تعملي إزاحة إلى أعلى بمقدار
+
+482
+00:59:32,300 --> 00:59:34,860
+تسعة، مسّكنا الـ parabola
+
+483
+00:59:38,660 --> 00:59:44,360
+بطل أزرق اللي عندنا، تمام؟ يبقى هذه الـ parabolas اللي
+
+484
+00:59:44,360 --> 00:59:49,880
+عندنا، طيب كويس، معناته في عندك parabolas كلهم موازية
+
+485
+00:59:49,880 --> 00:59:55,080
+لبعض، بيكونوا، بيكونوا، هذا المجسم، إذا مش واضح
+
+486
+00:59:55,080 --> 01:00:03,680
+كثير، بوضح لك هذا لقدام شوية، هذا هيك هو طول الرسمة
+
+487
+01:00:03,680 --> 01:00:04,220
+بتيجي
+
+488
+01:00:16,830 --> 01:00:23,870
+بنجي هنا بيكون هيك وهنا بتيجي هيك، أمامك؟ تبقى
+
+489
+01:00:23,870 --> 01:00:28,450
+صورة الرسمة بالشكل اللي عندنا هنا، تبقى هذا قوّال
+
+490
+01:00:28,450 --> 01:00:34,270
+لمين؟ قوّال اللي هو السطح الأوسط، وإنه اللي بيكون
+
+491
+01:00:34,270 --> 01:00:40,590
+بهذا الشكل تماماً كأنه على الأرض هيك وهذا قوّاله،
+
+492
+01:00:40,590 --> 01:00:48,920
+خلاص؟ طيب هذا من الأشكال اللي هو... يعني رسمته
+
+493
+01:00:48,920 --> 01:00:53,280
+برضه جدران عليها، زي ولا تشبيه زي السرير، سرير
+
+494
+01:00:53,280 --> 01:00:59,260
+الولد الصغير، بس مقلوب على وجهه، وهذا قاع السرير
+
+495
+01:00:59,260 --> 01:01:04,670
+بس على جانبه، واقف تماماً بالضبط، طيب ندى بالرسم اللي
+
+496
+01:01:04,670 --> 01:01:09,210
+بعدها اللي بعدها بيقول لي Y تربيع على أربعة ناقص X
+
+497
+01:01:09,210 --> 01:01:14,470
+تربيع على تسعة بده يساوي واحد، في الـ plane هذه، معادلة
+
+498
+01:01:14,470 --> 01:01:20,030
+إيه؟ هي parabola، تمام، يبقى رسمتنا هذه بدنا نرسمها
+
+499
+01:01:20,030 --> 01:01:27,670
+بحيث تكون هي parabola متوازية أو إن شئت فقولوا
+
+500
+01:01:27,670 --> 01:01:29,530
+parabola على اليمين
+
+501
+01:01:37,050 --> 01:01:42,930
+الثاني، يلا، آخر معادلة عندنا من المعادلات هي Y
+
+502
+01:01:42,930 --> 01:01:46,930
+تربيع على أربعة ناقص X تربيع على تسعة بده يساوي
+
+503
+01:01:46,930 --> 01:01:50,510
+الواحد، بتطلع على الرمز الغريب، الرمز الغريب اللي
+
+504
+01:01:50,510 --> 01:01:57,130
+هنا Z، يبقى الـ axis بده يكون محور Z أو محور موازٍ
+
+505
+01:01:57,130 --> 01:02:02,170
+له، هدف الـ plane عبارة، عبارة عن hyperbola، إذا
+
+506
+01:02:02,170 --> 01:02:07,090
+بدنا نروح نرسم الـ hyperbola كأنها في أحد الـ planes
+
+507
+01:02:07,090 --> 01:02:08,610
+يبقى لو جئت
+
+508
+01:02:11,690 --> 01:02:16,810
+اللي هي الـ hyperbola الأولى، يبقى بدأت تظهر واحدة
+
+509
+01:02:16,810 --> 01:02:24,210
+زيها من الناحية الثانية بالشكل اللي عندها، تمام؟ هي
+
+510
+01:02:24,210 --> 01:02:32,590
+اللي بدأت تيجي موازية لها كمان بهذا الشكل، ومن
+
+511
+01:02:32,590 --> 01:02:37,270
+الناحية الثانية زيها، لو مدّينا محور X على استقامته
+
+512
+01:02:51,480 --> 01:02:59,500
+بنقرب الشكل اللي عندها، وبنقرب الشكل اللي عندها
+
+513
+01:02:59,500 --> 01:03:01,340
+وبنقرب الشكل اللي عندها، وبنقرب الشكل اللي عندها
+
+514
+01:03:01,340 --> 01:03:01,960
+وبنقرب الشكل اللي عندها، وبنقرب الشكل اللي عندها
+
+515
+01:03:01,960 --> 01:03:02,000
+وبنقرب الشكل اللي عندها، وبنقرب الشكل اللي عندها
+
+516
+01:03:02,000 --> 01:03:02,020
+وبنقرب الشكل اللي عندها، وبنقرب الشكل اللي عندها
+
+517
+01:03:02,020 --> 01:03:02,060
+وبنقرب الشكل اللي عندها، وبنقرب الشكل اللي عندها
+
+518
+01:03:02,060 --> 01:03:02,080
+وبنقرب الشكل اللي عندها، وبنقرب الشكل اللي عندها
+
+519
+01:03:02,080 --> 01:03:03,280
+وبنقرب الشكل اللي عندها، وبنقرب الشكل اللي عندها
+
+520
+01:03:03,280 --> 01:03:07,180
+وبنقرب الشكل اللي
+
+521
+01:03:07,180 --> 01:03:13,460
+عندها، وبنقرب الشكل
+
+522
+01:03:13,460 --> 01:03:14,880
+اللي عندها، عندها، وبن
+
+523
+01:03:38,710 --> 01:03:48,170
+هذا مفتوح جهة اليمين، هذا مفتوح جهة اليسار
+
+524
+01:04:39,070 --> 01:04:46,750
+بتجي هذه الـ cylinder كأنها... كأنها اللي هو جيوب
+
+525
+01:04:46,750 --> 01:04:51,410
+بهذا الشكل، وجيوب ثاني زيّه بهذا الشكل، واتنين
+
+526
+01:04:51,410 --> 01:04:56,030
+متلاصقين مع بعض، كل واحد موجه على شجرة، تمام؟ يبقى
+
+527
+01:04:56,030 --> 01:05:00,610
+اتنين مع بعض كقطعة واحدة، بقول إيه؟ هذا هو الـ
+
+528
+01:05:00,610 --> 01:05:05,130
+cylinder اللي عندنا، يبقى الـ cylinder، السؤال الأول كان
+
+529
+01:05:05,130 --> 01:05:10,210
+على شكل أسطوانة، والمقطع تبعها ellipse، الثاني
+
+530
+01:05:10,210 --> 01:05:13,670
+أسطوانة، والمقطع تبعها parabola، الثالثة المقطع
+
+531
+01:05:13,670 --> 01:05:18,550
+تبعها parabola، الرابعة المقطع تبعها hyperbola، و
+
+532
+01:05:18,550 --> 01:05:25,640
+هكذا، إذا انتهى بنا الأمر بننظر لمن؟ للعنصر الغريب، نجي
+
+533
+01:05:25,640 --> 01:05:31,880
+للنقطة الثانية بالأسفل، الـ quadrics، الأسفل، السطوح
+
+534
+01:05:31,880 --> 01:05:39,800
+الثانية، نمسح هذا، خلاص؟ خلاص؟ طيب نجي للنقطة الثانية
+
+535
+01:05:39,800 --> 01:05:43,080
+في هذا الـ section اللي هو الـ quadrics
+
+536
+01:05:51,840 --> 01:05:58,180
+جات ستة من هذه السطوح الأوسطوانية، أول واحد منهم
+
+537
+01:05:58,180 --> 01:06:05,880
+بيسمّيه الـ ellipsoid، في جاء مرة، اتنين، اللي هي
+
+538
+01:06:05,880 --> 01:06:12,620
+quadric، ستة، أول
+
+539
+01:06:12,620 --> 01:06:17,920
+واحد منهم بيسمّيه الـ ellipsoid
+
+540
+01:06:26,030 --> 01:06:28,750
+المجسم الناقص بالعربية
+
+541
+01:06:54,260 --> 01:06:58,500
+بنحاول نرسم هذا المجسم.
+
+542
+01:07:06,260 --> 01:07:17,280
+هذا محور X، هذا محور Y، وهذا محور اللي هو Z.
+
+543
+01:07:31,880 --> 01:07:37,680
+لما أقول ellipsoid جاء من كلمة ellipse، ellipse قطع
+
+544
+01:07:37,680 --> 01:07:43,400
+ناقص، يبقى المقطع دائماً وأبداً هو عبارة عن قطع ناقص
+
+545
+01:07:43,400 --> 01:07:48,700
+كيف القطع الناقص كله ناقص ما فيه، كله خلاص، دي الشكل
+
+546
+01:07:48,700 --> 01:07:52,420
+اللي عندنا على الشكل هيك
+
+547
+01:07:55,700 --> 01:08:00,900
+هذا اللي هو كان الـ ellipse اللي عندنا، تبعه كان
+
+548
+01:08:00,900 --> 01:08:06,100
+الـ force بيه طبعاً النظر
+
+549
+01:08:09,440 --> 01:08:14,700
+مش هيقول لي هذا نفسه، بس مشان أميّزه بدي أروح
+
+550
+01:08:14,700 --> 01:08:22,260
+أرسم مقطعه مع المستوى XZ، هذا، هذا مقطعه مع المستوى
+
+551
+01:08:22,260 --> 01:08:28,960
+YZ، مقطعه مع المستوى XZ، بروح أرسمه بهذا الشكل، هذا
+
+552
+01:08:28,960 --> 01:08:35,240
+مظهره لي من جهتنا، بيقول أنا هذا مظهره، ليش هرسمه
+
+553
+01:08:35,240 --> 01:08:43,250
+منقطِع بهذا الشكل، يوصف الشكل أن هذا مجسم، واضح أن هذا
+
+554
+01:08:43,250 --> 01:08:46,810
+عبارة عن مجسم، مش عاجزاكوا بس
+
+555
+01:08:50,510 --> 01:08:57,770
+بهذا الشكل، فهذا بيجينا كمان هكذا، خلّيني أقول في
+
+556
+01:08:57,770 --> 01:09:05,470
+الأصل، يبقى واضح الآن أن هذا مجسم، طيب الآن ليش
+
+557
+01:09:05,470 --> 01:09:11,470
+سمّينا ellipsoid؟ هذا السؤال، ellipsoid جاء من كلمة
+
+558
+01:09:11,470 --> 01:09:17,430
+ellipse، الإجابة لأن مقطعه مع كل مستوى من مستويات
+
+559
+01:09:17,430 --> 01:09:21,760
+الإحداثيات هو عبارة عن إيش؟ هو عبارة عن ellipse.
+
+560
+01:09:22,120 --> 01:09:26,720
+أنا أقول إن إيه يا بنات؟ كيف يعني؟ نعم؟ الآن لو
+
+561
+01:09:26,720 --> 01:09:30,840
+بأخذ مقطعه مع المستوى، هو ellipse يا بنات
+
+562
+01:09:44,410 --> 01:09:53,830
+الخط الأسود الخارجي، يبقى هذا ما هو المقطع تبعه مع
+
+563
+01:09:53,830 --> 01:09:58,470
+المستوى اللي إحنا بنرسمه، يبقى الخط الأسود هذا اللي
+
+564
+01:09:58,470 --> 01:10:04,650
+هو Y تربيع على B تربيع زائد Z تربيع على C تربيع
+
+565
+01:10:04,650 --> 01:10:05,650
+يساوي واحد
+
+566
+01:10:08,490 --> 01:10:15,290
+يبقى هذا مقطعه مع المستوى YZ، يبقى مقطعه مع المستوى
+
+567
+01:10:15,290 --> 01:10:21,450
+XZ، XZ، يبقى Y بقدر أشيّلها بصفر، يبقى لما أشيل Y بصفر
+
+568
+01:10:21,450 --> 01:10:24,930
+مضالعش عندنا ellipse اللي هو مين؟ الـ ellipse اللي
+
+569
+01:10:24,930 --> 01:10:28,030
+عندنا، هي أكتبه لك اللي هو
+
+570
+01:10:36,690 --> 01:10:44,220
+على C تربيع يساوي، بده يساوي واحد، صح، يبقى الأزرق
+
+571
+01:10:44,220 --> 01:10:50,880
+يا بنات هذا في مستوى XZ، الأسود في مستوى YZ
+
+572
+01:10:50,880 --> 01:10:58,180
+طبعاً هنسأل السؤال التالي، وأين المستوى XY؟ نقول له
+
+573
+01:10:58,180 --> 01:11:04,480
+Z تساوي صفر، اللي هو الـ ellipse الأزرق هذا، تمام؟
+
+574
+01:11:04,480 --> 01:11:09,340
+يبقى الأزرق هذا الـ ellipse، هذا معادلته
+
+575
+01:11:14,570 --> 01:11:20,830
+Y تربيع على B تربيع زائد X تربيع على A تربيع يساوي واحد، إذا كل مقطع
+
+576
+01:11:20,830 --> 01:11:25,290
+من هذه، المقطع عبارة عن ellipse، ومن هنا سمينا
+
+577
+01:11:25,290 --> 01:11:31,510
+ellipsoid، بتيجي واحدة تقول طب لو جيت قطعته من فوق
+
+578
+01:11:31,510 --> 01:11:37,430
+وأنا من تحت، شوية، مظبوط؟ اللي بنجيبه بيصير Z تساوي
+
+579
+01:11:37,430 --> 01:11:43,200
+Z note، يعني رقم، المقطع في هذه الحالة كمان
+
+580
+01:11:43,200 --> 01:11:48,260
+ellipse؟ راح يكون ellipse، طيب كيف نجيب هذا اللي هو؟
+
+581
+01:11:48,260 --> 01:11:54,780
+أقول لك بسيطة، لو كان الـ Z يساوي C note فوق أو C note
+
+582
+01:11:54,780 --> 01:11:58,770
+تحت، سواء كان فوق أو تحت، سيما ما تفرقش عامةً لأن عند
+
+583
+01:11:58,770 --> 01:12:04,270
+تربيعه بيصير قيمة موجبة، يبقى Z تساوي absolute
+
+584
+01:12:04,270 --> 01:12:10,610
+value لـ C0 بيكون أعلى الـ XY plane أو أسفل الـ XY
+
+585
+01:12:10,610 --> 01:12:15,910
+plane، إذا لو جيت قطعته بالمقطع اللي عندنا هذا هيك
+
+586
+01:12:15,910 --> 01:12:21,590
+مش هيظهر، وهذا بيظهر الشكل اللي عندنا هذا، يبقى هذا
+
+587
+01:12:21,590 --> 01:12:25,690
+المستوى اللي هو Z يساوي Z0
+
+588
+01:12:33,920 --> 01:12:42,360
+Z يساوي Z note، the question is اللي هو مين؟ X تربيع
+
+589
+01:12:42,360 --> 01:12:49,640
+على A تربيع زائد Y تربيع على B تربيع بده يساوي واحد، نقول
+
+590
+01:12:49,640 --> 01:12:58,340
+Z note تربيع على C تربيع، طبعاً لو قسمت الطرفين عليه
+
+591
+01:12:58,340 --> 01:13:02,480
+مش هذا رقم، لو قسمت عليه مش حيصير معادلة، إيه
+
+592
+01:13:12,150 --> 01:13:18,910
+على C تربيع زائد Y تربيع على B تربيع، واحد ناقص Z
+
+593
+01:13:18,910 --> 01:13:24,850
+note تربيع على C تربيع، كله يساوي واحد، وهذا كمان الـ
+
+594
+01:13:24,850 --> 01:13:30,710
+main اللي هو الـ ellipse، يتجول مثلاً، طيب اتجه لمفتاح
+
+595
+01:13:30,710 --> 01:13:37,440
+إيش؟ ellipse، طيب هذه ملاحظة، ملاحظة ثانية، السؤال هو هل
+
+596
+01:13:37,440 --> 01:13:44,000
+المجسم يا بنات متماثل بالنسبة لمستويات الإحداثيات؟
+
+597
+01:13:44,000 --> 01:13:49,180
+يعني نشوف، يعني لو جئت لمستوى الـ XY اللي قطعه في
+
+598
+01:13:49,180 --> 01:13:53,520
+المقطع الأزرق، هل النص اللي فوق ونص اللي تحت آه
+
+599
+01:13:53,520 --> 01:13:55,860
+صحيح، لأن النقطة اللي فوق
+
+600
+01:14:06,420 --> 01:14:08,420
+هذه النقطة
+
+601
+01:14:16,210 --> 01:14:22,470
+و P و صفر، إذا المجسم هذا متماثل بالنسبة لإيش؟
+
+602
+01:14:22,470 --> 01:14:26,670
+المستويات الإحداثية، يعني يعني المستوى الإحداثي
+
+603
+01:14:26,670 --> 01:14:32,610
+لما أجيبه من فوق لتحت بقسمه نصين زي بعض تماماً، لو
+
+604
+01:14:32,610 --> 01:14:38,450
+أفقيّاً نصين زي بعض، لو المستوى الثالث بقسمه كمان إلى
+
+605
+01:14:38,450 --> 01:14:43,670
+نصين، والاتنين زي بعض تماماً، يبقى ما أقدر أقول
+
+606
+01:14:43,920 --> 01:14:49,320
+الغرافية متناظرة مع الـ coordinate planes، يبقى
+
+607
+01:14:49,320 --> 01:14:55,320
+بأجي بقول هنا الغرافية
+
+608
+01:14:55,320 --> 01:14:59,020
+متناظرة
+
+609
+01:14:59,020 --> 01:15:05,780
+حول
+
+610
+01:15:05,780 --> 01:15:06,300
+محاور
+
+611
+01:15:16,830 --> 01:15:20,690
+in place، طب
+
+612
+01:15:20,690 --> 01:15:27,810
+كويس، إذا جبنا كل مقطع وكل معادلة، إيه؟ آه، اجت واحدة
+
+613
+01:15:27,810 --> 01:15:32,730
+من البنات قالت، قبلتها، ليش عملت الاستطالة تطلع فوق
+
+614
+01:15:32,730 --> 
+
+667
+01:22:34,780 --> 01:22:37,480
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+668
+01:22:37,480 --> 01:22:37,520
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+669
+01:22:37,520 --> 01:22:37,540
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+670
+01:22:37,540 --> 01:22:37,580
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+671
+01:22:37,580 --> 01:22:37,680
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+672
+01:22:37,680 --> 01:22:43,030
+Zero Zero نرجع للّي احنا بنقوله وبنقول بدنا
+
+673
+01:22:43,030 --> 01:22:50,290
+نسأل سؤالين، السؤال الأول: لو بدّي لك رسم للمعادلة
+
+674
+01:22:50,290 --> 01:22:55,990
+X تربيع على A تربيع + Y تربيع على B تربيع = Z
+
+675
+01:22:55,990 --> 01:23:04,470
+-Z على C، بدنا نقله ونخليه أسفل، يعني بدنا نصير
+
+676
+01:23:04,470 --> 01:23:05,470
+بالشكل هذا
+
+677
+01:23:08,750 --> 01:23:17,350
+هذا X وهذا Y وهذا Z يصبح هذا R شكله
+
+678
+01:23:17,350 --> 01:23:24,110
+يعني تمام؟ هذا لو كانت إيش؟ لو كان X تربيع على A
+
+679
+01:23:24,110 --> 01:23:29,730
+تربيع + Y تربيع على B تربيع = -Z على C
+
+680
+01:23:29,730 --> 01:23:33,790
+يبقى بنجيب الرسمة في هذه الحالة، وتصبح
+
+681
+01:23:37,050 --> 01:23:44,330
+سؤال الثاني: هل المجسم متماثل بالنسبة لمستويات
+
+682
+01:23:44,330 --> 01:23:50,870
+الإحداثيات؟ لأ طبعاً، ليش؟ لأنه تحت الـ X Y Plane
+
+683
+01:23:50,870 --> 01:23:57,090
+ماعنديش كل الرسم أعلى الـ X Y Plane، تمام؟ لكن لو جت
+
+684
+01:23:57,090 --> 01:24:08,110
+كنت بالمستوى YZ، المجسم متماثل YZ و XZ متماثل لكن
+
+685
+01:24:08,110 --> 01:24:12,810
+المستوى XY يبعد، الله، يبقى هذا متماثل بالنسبة
+
+686
+01:24:12,810 --> 01:24:19,790
+لمستويين من مستويات الإحداثيات فقط، وليس بالنسبة للمستويات الثلاثة.
+
+687
+01:24:19,790 --> 01:24:29,370
+طيب، الآن لو جيت قلت لك: أين الـ X Y
+
+688
+01:24:29,370 --> 01:24:34,870
+Plane؟ بتبقى Z بقدر إيه؟ آه، الـ X Y Plane بتبقى Z
+
+689
+01:24:34,870 --> 01:24:39,290
+بقدر إيه؟ Zero. إذاً لو حطيت Z بـ Zero، إيش بصير؟ X
+
+690
+01:24:39,290 --> 01:24:41,690
+تربيع على A تربيع + Y تربيع على B تربيع
+
+691
+01:24:41,690 --> 01:24:48,830
+= C يساوي الصفر. هل معقول أن مجموع كميتين مربعتين
+
+692
+01:24:48,830 --> 01:24:50,210
+يساوي الصفر؟
+
+693
+01:24:53,180 --> 01:24:58,660
+معقول؟ ليش مش معقول؟ إلاّ مرة واحدة في الدنيا، لو كان
+
+694
+01:24:58,660 --> 01:25:04,660
+الـ X بـ Zero والـ Y بـ Zero، فماذا يكون؟ نقطة الأصل
+
+695
+01:25:04,660 --> 01:25:09,120
+فأنا عندي Z بـ Zero، صح؟ ووجدت كمان X تربيع = 0
+
+696
+01:25:09,120 --> 01:25:12,780
+و Y = 0. إذاً، هي نقطة الأصل، إذاً الـ
+
+697
+01:25:12,780 --> 01:25:19,100
+Plane في المجسم في هذه الحالة يمثل الـ X Y Plane في
+
+698
+01:25:19,100 --> 01:25:24,720
+النقطة (0، 0، 0)، نقطة الأصل، واضح؟ يبقى الـ elliptic
+
+699
+01:25:24,720 --> 01:25:39,340
+paraboloid واضح
+
+700
+01:25:39,340 --> 01:25:46,180
+الشغل، أظن طيب. هذا بالنسبة لمين؟ للمجسم الثاني
+
+701
+01:25:50,060 --> 01:25:53,120
+المجسم الثالث يا بنات، اللي هو الـ Elliptic cone
+
+702
+01:25:53,120 --> 01:26:06,520
+اللي هو
+
+703
+01:26:06,520 --> 01:26:12,500
+المخروط، اللي مقطعه عبارة عن ellipse. المعادلة
+
+704
+01:26:12,500 --> 01:26:18,840
+تبعته: X تربيع على A تربيع + Y تربيع على B تربيع
+
+705
+01:26:27,910 --> 01:26:30,950
+جاب المبدأ في الـ elliptic cone اللي خاطر أسأل
+
+706
+01:26:30,950 --> 01:26:36,650
+كمان سؤال على الـ elliptic paraboloid هذا، تمام؟
+
+707
+01:26:36,650 --> 01:26:40,250
+لو كانت المعادلة على الشكل التالي، فادرسوها كويس
+
+708
+01:26:40,690 --> 01:26:46,950
+أنتم ملاحظين أن الرسم، محوره تبعه مين؟ Z، XY زي
+
+709
+01:26:46,950 --> 01:26:52,150
+زي
+
+710
+01:26:52,150 --> 01:26:56,590
+زي زي زي زي زي زي زي زي زي زي زي زي زي زي زي
+
+711
+01:27:05,600 --> 01:27:10,940
+يبقى المحور تبع مين هو؟ يبقى الرمز اللي ما هو مش
+
+712
+01:27:10,940 --> 01:27:15,860
+مربع في الـ elliptic paraboloid بيكون هو مين؟ هو
+
+713
+01:27:15,860 --> 01:27:21,880
+المحور تبع مين؟ تبع المجسم. دي ملاحظة، لكن من قصة الـ
+
+714
+01:27:21,880 --> 01:27:25,600
+ellipsoid اللي في الأول، كله زي بعضه، ما قدرت أميّز
+
+715
+01:27:25,600 --> 01:27:31,780
+يبقى هذا بميزه من شكل المتغير غير المربع. طيب نيجي
+
+716
+01:27:31,780 --> 01:27:37,980
+لمين؟ للـ elliptical اللي هو المخروط، اللي مقطعه
+
+717
+01:27:37,980 --> 01:27:43,580
+عبارة عن ellipse. كيف هذا؟ أقول لك، آه، لو جيتي
+
+718
+01:27:43,580 --> 01:27:44,380
+قولتي ليه؟
+
+719
+01:28:00,150 --> 01:28:09,170
+بشكل عام، وبعد
+
+720
+01:28:09,170 --> 01:28:18,790
+هيك، جيت طبعاً هي محاور الإحداثيات هذا
+
+721
+01:28:18,790 --> 01:28:24,630
+محور X، هذا محور Y، وهذا محور Z
+
+722
+01:28:32,240 --> 01:28:37,700
+طيب هذه المعادلة اللي عندناها، اللي هو معادلة
+
+723
+01:28:37,700 --> 01:28:44,320
+elliptic اللي هو المخروط، مقطعه عبارة
+
+724
+01:28:44,320 --> 01:28:48,540
+عن ellipse. ليش كل مقطع المخروط عبارة عن ellipse
+
+725
+01:28:48,540 --> 01:28:53,460
+وما هي المقاطع الأخرى؟ أول شيء، خلّيني أطلع على
+
+726
+01:28:53,460 --> 01:28:56,990
+المعادلة، وبعدين بنجاوب على هذه التساؤلات. طالعي
+
+727
+01:28:56,990 --> 01:29:01,950
+للمعادلة اللي قمنا بكتابتها. معادلة صفرية، يبقى بصير
+
+728
+01:29:01,950 --> 01:29:07,630
+هي معادلة الـ ellipsoid، بس بتختلف عنها في أمرين: بدل
+
+729
+01:29:07,630 --> 01:29:12,550
+الواحد بيكون صفر، وهادي بدل الموجب بصير إيه؟ سالب
+
+730
+01:29:12,550 --> 01:29:18,230
+ممتاز. يبقى لو اطلعت تلات كميات مربعة، اثنتين في جهة وثلاثة
+
+731
+01:29:18,230 --> 01:29:24,130
+في جهة ثانية، إذا هذه معادلة المخروط، تمام؟ هذه مش
+
+732
+01:29:24,130 --> 01:29:28,070
+هنميّز بينها وبين المعادلة. تفضلي، تفضلي، تفضلي، تفضلي
+
+733
+01:29:28,070 --> 01:29:47,410
+تفضلي، تفضلي، تفضلي، تفضلي، تفضلي، تفضلي، تفضلي
+
+734
+01:29:47,510 --> 01:29:56,810
+الآن لو جيت للمجسم اللي عندنا هذا، وجيت أخدت الـ yz
+
+735
+01:29:56,810 --> 01:30:02,890
+Plane، يعني إكس بقد إيش؟ Zero. يعني لما إكس = Zero، تروح
+
+736
+01:30:02,890 --> 01:30:07,750
+بالشكل هذا، مع النتيجة دي. لو أخدت الجذر التربيعي
+
+737
+01:30:07,750 --> 01:30:14,960
+للطرفين، خط مستقيم، صح؟ ولا يعني، كيلو، وزير مين؟ Y تساوي
+
+738
+01:30:14,960 --> 01:30:20,600
+ب على C في Z أو Y تساوي -ب على C في Z، مظبوط؟
+
+739
+01:30:20,600 --> 01:30:24,780
+اللي هو الخط المستقيم الأول والثاني، هو الخط
+
+740
+01:30:24,780 --> 01:30:33,040
+المستقيم الثاني. يرجى، يا بنات، هذا الخط لحاله، اللي
+
+741
+01:30:33,040 --> 01:30:33,980
+هو مين؟
+
+742
+01:30:36,770 --> 01:30:43,230
+اللي هو Y تربيع على B تربيع = Z تربيع على C
+
+743
+01:30:43,230 --> 01:30:51,390
+تربيع، أو الشيء اللي تقوليه: Y تساوي B على C في Z، يبقى
+
+744
+01:30:51,390 --> 01:30:57,270
+هذا، من الناحية الثانية، يكون Y تساوي -B
+
+745
+01:30:57,270 --> 01:31:05,120
+على C في Z. هذا التقاطع مع الـ YZ Plane. بدي أجيب
+
+746
+01:31:05,120 --> 01:31:10,120
+التقاطع مع الـ XZ Plane، مع الـ R، لازم أرسم
+
+747
+01:31:10,120 --> 01:31:14,640
+مستقيمين، اثنين، بحيث يفجروا أين؟ المستقيمين الاثنين
+
+748
+01:31:14,640 --> 01:31:19,860
+بدي أجيب المستقيم الأول بهذا الشكل، من جهة هنا، هيكون
+
+749
+01:31:19,860 --> 01:31:24,960
+هذا مبين، ومن جهة الثانية يا بنات مش
+
+750
+01:31:24,960 --> 01:31:28,340
+هيميل، هيكون اللقطة بهذا الشكل
+
+751
+01:31:31,530 --> 01:31:37,890
+من الناحية هذه مش هيظهر، ومن الناحية الثانية هيظهر
+
+752
+01:31:37,890 --> 01:31:43,110
+بالشكل الآخر. يبقى الخطين السود الغامقات، هو تقاطع
+
+753
+01:31:43,110 --> 01:31:49,490
+الـ XZ Plane مع المجسم اللي عندنا. طيب، في الـ XZ
+
+754
+01:31:49,490 --> 01:31:55,350
+Plane، يبقى واقف كده؟ P0، معناه هذا، الفلاح، إن الخط
+
+755
+01:31:55,350 --> 01:31:57,550
+اللي عندي هذا، الأسود
+
+756
+01:32:14,660 --> 01:32:27,900
+C في Z، بشارة سالبة. وهنا هيكون، هذا يفتح، هذا، يبقى X
+
+757
+01:32:27,900 --> 01:32:36,180
+تساوي A على C في، من، في Z، طيب
+
+758
+01:32:36,180 --> 01:32:41,720
+لو حطيت Z تساوي Z نوت، يعني رقم
+
+759
+01:32:48,570 --> 01:32:53,970
+النقطة اللي عندها، يبقى بدي أجيب المقطع مين؟ اللي فوق
+
+760
+01:32:53,970 --> 01:33:00,310
+Z نوت، يبقى هذا كله بدي يصير رقم، لو قسمت عليه، يصير
+
+761
+01:33:00,310 --> 01:33:05,510
+عندي ellipse، وهذا اللي تحت كمان إيه؟ كمان ellipse
+
+762
+01:33:05,510 --> 01:33:08,330
+زيّه، و double تماماً، يبقى
+
+763
+01:33:16,170 --> 01:33:23,670
+يكون X تربيع على A تربيع + Y تربيع على B تربيع
+
+764
+01:33:23,670 --> 01:33:30,510
+= Z نوت تربيع على C تربيع، هذا رقم، لو قسمت عليه
+
+765
+01:33:30,510 --> 01:33:32,770
+الطرفين، بصير عندنا معادلة
+
+766
+01:34:00,970 --> 01:34:08,050
+لو جيت على المعادلة، لو حطيت مكانها اللي هو Z تساوي
+
+767
+01:34:10,730 --> 01:34:15,910
+مجموع كميتين مربعتين يساوي صفر، هذا لا يمكن إلا إذا
+
+768
+01:34:15,910 --> 01:34:20,690
+كان كل واحد منهم صفر، يبقى الـ X بـ Zero والـ Y بـ Zero، و
+
+769
+01:34:20,690 --> 01:34:27,250
+بتقول حصلنا على مين؟ على نقطة الأصل، واضح كلامنا؟
+
+770
+01:34:27,250 --> 01:34:36,220
+طيب، مين المحور غير هذا؟ Z، تمام، اللي لحالها، ممتاز
+
+771
+01:34:36,220 --> 01:34:39,660
+جداً. اللي، اللي بتبقى لحالها على اليمين بيكون
+
+772
+01:34:39,660 --> 01:34:45,380
+المتغير تبعها هو المحور تبع مين؟ تبع المجسم اللي عامل
+
+773
+01:35:09,720 --> 01:35:16,160
+في عندي كمان آخر تلات مجسمات هي بالشكل التالي، أول
+
+774
+01:35:16,160 --> 01:35:23,140
+واحد اللي هو، أو أدنى، برا، أربعة، بسالين، هاي paraboloid
+
+775
+01:35:23,140 --> 01:35:32,780
+hyperboloid hyperboloid of one
+
+776
+01:35:44,770 --> 01:35:48,090
+على V تربيع - Z تربيع
+
+777
+01:36:21,460 --> 01:36:30,640
+زي ولا تشبهت قبله، ومضبوط تماماً، وهي اسمها، والمقطع
+
+778
+01:36:30,640 --> 01:36:41,180
+الثاني هيكون بهذا الشكل، و
+
+779
+01:36:41,180 --> 01:36:47,380
+هذا المقطع الثالث
+
+780
+01:36:47,380 --> 01:36:50,480
+بهذا الشكل، والمقطع الثالث
+
+781
+01:36:58,250 --> 01:37:07,930
+يبقى هذا المجسم hyperboloid، المجسم المقابل ذو طية واحدة،
+
+782
+01:37:07,930 --> 01:37:12,050
+sheet، يعني طية، تطوي الشغل، أكمل
+
+783
+01:37:14,010 --> 01:37:18,710
+واضح أن المجسم هذا متماثل بالنسبة لمستويات
+
+784
+01:37:18,710 --> 01:37:24,770
+الإحداثيات. بدي تجيبي التقاطع، الأسود هذا، اللي هو
+
+785
+01:37:24,770 --> 01:37:29,390
+المستوى yz، بروح، وحط x بـ صفر، وبغسله. المقطع عبارة
+
+786
+01:37:29,390 --> 01:37:35,690
+عن إيش منه؟ hyperbola. يبقى الخط الأسود هذا مع
+
+787
+01:37:35,690 --> 01:37:41,900
+الخط الأسود الثاني، اللي هو الـ hyperbola، على P تربيع
+
+788
+01:37:41,900 --> 01:37:47,160
+ناقص Z تربيع على C تربيع = 1. وهكذا
+
+789
+01:37:47,160 --> 01:37:53,240
+بالنسبة لمين؟ للقطعة الأفقية. Z تساوي Zero، فبيطلع هذا
+
+790
+01:37:53,240 --> 01:37:58,680
+يظل عنده Ellipse. يبقى هذا hyperbola، لكن هذا
+
+791
+01:37:58,680 --> 01:38:04,700
+Ellipse. إيش معادلته؟ معادلته X تربيع على
+
+792
+01:38:09,020 --> 01:38:18,780
+في عندك المجسم ذو الطية الثانية، رقم خمسة، اللي هو الـ
+
+793
+01:38:18,780 --> 01:38:27,220
+hyperboloid of
+
+794
+01:38:27,220 --> 01:38:28,080
+two sheets
+
+795
+01:38:53,250 --> 01:39:00,370
+هذا محور X، هذا Y، هذا Z، ندى، هذه على استماعك بهذا
+
+796
+01:39:00,370 --> 01:39:08,050
+الشكل. شايفة هذا يا بنات؟ هو هذا بس، واحدة موجبة فوق
+
+797
+01:39:08,050 --> 01:39:16,230
+وواحدة تحت، وهكذا. طيبة، طيبة موجة، يبقى هذا هكذا
+
+798
+01:39:16,230 --> 01:39:17,570
+والتاني هكذا.
+
+799
+01:39:27,020 --> 01:39:33,120
+يبقى هذا الـ hyperboloid of two sheets، لو قطعته
+
+800
+01:39:33,120 --> 01:39:38,860
+أفقي، بتلاقي ellipse، هذا عبارة عن ellipse، وهذا
+
+801
+01:39:38,860 --> 01:39:43,480
+عبارة عن إيش؟ ellipse. لو قطعته رأسي بتلاقي
+
+802
+01:39:43,480 --> 01:39:46,800
+hyperbola، وهاي hyperbola، اثنتين مع بعض، هاي
+
+803
+01:39:46,800 --> 01:39:50,380
+hyperbola بالمستوى xz
+
+804
+01:39:56,430 --> 01:40:01,430
+فأضع اللي هيك ومن
+
+805
+01:40:01,430 --> 01:40:09,150
+هنا مش هيظهر، ومن هنا هيك يظهر، ومن اللي هيتاني
+
+806
+01:40:09,150 --> 01:40:16,400
+لبس هذا الشكل. طيب السؤال: هل هذا يمر بنقطة الأصل؟ لأ
+
+807
+01:40:16,400 --> 01:40:21,760
+لأن لو بدي أحط Z تساوي Zero في المعادلة، بيصير
+
+808
+01:40:21,760 --> 01:40:26,940
+مجموع كميتين سالبتين يساوي كمية موجبة، صحيح؟ يعني لو
+
+809
+01:40:26,940 --> 01:40:29,560
+ضرّبت فيه سالب بيصير X سلبي - Y تربيع
+
+810
+01:40:32,950 --> 01:40:36,830
+هذا كلام ممنوع، وفي وقت ما يتم إرسال كيماسة، وهذا
+
+811
+01:40:36,830 --> 01:40:43,210
+مفهوم. إذن، يمكن للمستوى XY نقطع هذا المجسم، لكن الـ
+
+812
+01:40:43,210 --> 01:40:48,590
+XY، المجسم هذا متماثل بالنسبة للنص اللي فوق، زي النص
+
+813
+01:40:48,590 --> 01:40:51,890
+اللي تحت، النص اللي على مين؟ زي النص اللي عشرة، النص
+
+814
+01:40:51,890 --> 01:40:56,690
+هذه، يعني متماثل بالنسبة لمستويات الإحداثيات
+
+815
+01:41:19,790 --> 01:41:26,170
+يبقى آخر حاجة هي النقطة رقم ستة هي:
+
+816
+01:41:26,170 --> 01:41:28,230
+hyperbolic paraboloid
+
+817
+01:41:39,790 --> 01:41:44,530
+المعادلة التي أتبعها هي Y
+
+818
+01:41:44,530 --> 01:41:52,510
+تربيع على B تربيع ناقص X تربيع على A تربيع =
+
+819
+01:41:52,510 --> 01:41:57,290
+Z على C، والـ C أكبر من
+
+820
+01:42:16,250 --> 01:42:22,490
+رسمه، أولاً بأول، بدنا نرسم parabola حوالي المحور
+
+821
+01:42:22,490 --> 01:42:28,770
+Z، من أول، بنبقى بالدرجة، أقول لك أدي parabola ومن
+
+822
+01:42:28,770 --> 01:42:35,510
+الناحية التالية، وذات جينها طبعاً
+
+823
+01:42:35,510 --> 01:42:39,190
+عالية، أكيد، بدنا نزلها بس لتحت شوية
+
+824
+01:42:49,920 --> 01:43:05,540
+بعد ذلك، بدي من النقطة هذه، أرسم parabola، بعد ذلك
+
+825
+01:43:05,540 --> 01:43:11,340
+بنزلها هنا، وهذه هي الشكل اللي عملناه
+
+826
+01:43:20,510 --> 01:43:29,050
+تمام؟ هذا يظهر عليك على شكل دوس، الشكل هنا، وهذا
+
+827
+01:43:29,050 --> 01:43:44,830
+هنا، يقول دوس، تمام، الشكل واضحة الرسمة، و
+
+828
+01:43:44,830 --> 01:43:46,090
+بعد هيك
+
+829
+01:43:55,780 --> 01:44:06,680
+يبقى هاي parabola وهي parabola كمان، زي الملتقى، شاكرة يا بنات
+
+830
+01:44:06,680 --> 01:44:07,220
+منها
+
+831
+01:44:14,430 --> 01:44:20,110
+هذه المعادلة اللي قدامها، من المحور تبعها زي ما
+
+832
+01:44:20,110 --> 01:44:28,350
+تشوفيه، اللي هو محور الـ Z، بالضبط تماماً، على
+
+833
+01:44:28,350 --> 01:44:35,790
+شكل قوس، وليس خطاً مستقيماً، زي، ولا تشبيه السرج تبع
+
+834
+01:44:35,790 --> 01:44:42,170
+الفرس، سرج الفرس، بالضبط، هذا هو عبارة عن سرج فرس
+
+835
+01:44:42,170 --> 01:44:49,110
+طيب، بدنا يا بنات، المسائل التالية منكم، exercises
+
+836
+01:44:49,110 --> 01:44:52,310
+اثنتا عشرة
+
+837
+01:44:52,310 --> 01:45:03,470
+ستة، مسائل من واحد لغاية ثلاثة وأربعين، four، على
+
+838
+01:45:03,470 --> 01:45:08,210
+هيك يكون انتهى الـ chapter. المرة القادمة إن شاء الله
+
+839
+0
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/yfbRUZY5IbA_postprocess.srt b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/yfbRUZY5IbA_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..0bfb125a17e86fd53c8fdcd826e0ea8975fed67a
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/yfbRUZY5IbA_postprocess.srt
@@ -0,0 +1,3356 @@
+1
+00:00:00,000 --> 00:00:02,680
+موسيقى
+
+2
+00:00:09,870 --> 00:00:15,410
+بسم الله الرحمن الرحيم المرة الماضية ابتدأنا في
+
+3
+00:00:15,410 --> 00:00:20,530
+section 12-5 و أخدنا ثلاث نقاط طبعا ال section كله
+
+4
+00:00:20,530 --> 00:00:25,170
+بتكلم عن ال lines و ال planes أخدنا النقطة الأولى
+
+5
+00:00:25,170 --> 00:00:28,530
+هي ال lines في الفراق و عرفنا ال parametric
+
+6
+00:00:28,530 --> 00:00:33,650
+equations لهذه ال lines اتنين المسافة ما بين نقطة
+
+7
+00:00:33,650 --> 00:00:39,830
+و خط مستقيم في الفراقتلاتة معادلة مستوى في الفرق
+
+8
+00:00:39,830 --> 00:00:44,350
+هذا ما دُرس في هذا section حتى نهاية المحاضرة
+
+9
+00:00:44,350 --> 00:00:48,850
+الماضية اليوم بنكمل على نفس ال section وبنجي
+
+10
+00:00:48,850 --> 00:00:52,190
+للنقطة الراجعة اللي هي distance from a point to a
+
+11
+00:00:52,190 --> 00:00:56,810
+plane المرة فيها distance من point to a line المرة
+
+12
+00:00:56,810 --> 00:01:01,910
+هي distance from a point to a plane كويس يبقى لو
+
+13
+00:01:01,910 --> 00:01:09,920
+جيت تفيّل انه عندى planeتمام الـ plane هذا سميته M
+
+14
+00:01:09,920 --> 00:01:16,400
+على سبيل المثال في نقطة عندنا هنا فوق نقطة S
+
+15
+00:01:16,400 --> 00:01:25,500
+موجودة في القرار البعد بينها وبين ال plane سميته D
+
+16
+00:01:25,500 --> 00:01:33,450
+بدي أعرف كم مقدار البعد هذا D اللي موجود عندنابقول
+
+17
+00:01:33,450 --> 00:01:39,070
+لك بيس عشان اعرف هذا البعد بروح اخد any point في
+
+18
+00:01:39,070 --> 00:01:46,310
+ال plane اي نقطة موجودة في هذا المستوى والتكن هذه
+
+19
+00:01:46,310 --> 00:01:54,360
+النقطة على سبيل المثال النقطة Pطبعا كل plane في
+
+20
+00:01:54,360 --> 00:01:58,700
+الفراغ بقدر اكتره بدلالة normal vector عليه زي ما
+
+21
+00:01:58,700 --> 00:02:03,520
+شوفنا المرة الماضية المعادلة تبعته ax زائد dy زائد
+
+22
+00:02:03,520 --> 00:02:08,740
+cz يساوي d حيث ال a والb والc هي معاملة ال vector
+
+23
+00:02:08,740 --> 00:02:16,160
+العمودي على هذا ال plane طبعا إذا لو جيت تخيل ان
+
+24
+00:02:16,160 --> 00:02:17,880
+هذا هو normal
+
+25
+00:02:26,460 --> 00:02:32,660
+يبقى الان نبحث عن مقدار distance D ما بين النقطة S
+
+26
+00:02:32,660 --> 00:02:37,200
+اللي بالفرار و ال plane M كلنا بنروح و بناخد اي
+
+27
+00:02:37,200 --> 00:02:41,460
+نقطة P موجودة في ال plane و بنرسم ال normal على ال
+
+28
+00:02:41,460 --> 00:02:46,380
+plane اللي عنها ال normal هذا روحت سميته N
+
+29
+00:03:01,060 --> 00:03:07,160
+لو جيت من النقطة S و نزلت عمود على N بهذا الشكل
+
+30
+00:03:07,160 --> 00:03:12,540
+البعد اللي عندنا هذا و البعد هذا شو العلاقة بينهم؟
+
+31
+00:03:13,540 --> 00:03:17,980
+هي متساوية ان هما البعد العمودي بين النقطة S و بين
+
+32
+00:03:17,980 --> 00:03:26,560
+ال plane D طيب هذا الطول من النقطة P لنقطة S هو
+
+33
+00:03:26,560 --> 00:03:33,420
+طول تبع المتجه Mبس إذا لو ضربت بي اس في cosine
+
+34
+00:03:33,420 --> 00:03:39,340
+الزاوية تيتا بيعطيني مين البعد بين النقطة S ومابين
+
+35
+00:03:39,340 --> 00:03:45,560
+ال plane F يبقى بناء عليه ال distance D بدي ساوي
+
+36
+00:03:45,560 --> 00:03:50,720
+طول ال P S في cosine الزاوية تيتا
+
+37
+00:03:54,620 --> 00:04:00,100
+كويس طيب ننجي لكوصين الزاوية هذا ثيتا بدي استخدم
+
+38
+00:04:00,100 --> 00:04:04,820
+ما سبق دراسته من ال dot product في كتابة كوصين
+
+39
+00:04:04,820 --> 00:04:10,880
+الثيتا بشكل آخر طبعا خلنا نحصل ضرب متجهين u في v ك
+
+40
+00:04:10,880 --> 00:04:15,800
+dot product طول ال u في طول ال v في كوصين الزاوية
+
+41
+00:04:15,800 --> 00:04:21,100
+ثيتا إذا كوصين الزاوية ثيتا بدل زاوية u dot v على
+
+42
+00:04:21,100 --> 00:04:26,550
+طول ال u في طول ال vإذا بناء عليه هذا بدي يعطينا
+
+43
+00:04:26,550 --> 00:04:37,790
+طول ال PS مضروب فيه أسين تيتا الومين ال PS ضد ال N
+
+44
+00:04:37,790 --> 00:04:51,470
+مفسومة على طول ال N بس هيك لا على طول ال PS في طول
+
+45
+00:04:51,470 --> 00:04:58,950
+ال Nمصبوط هيك؟ طيب تمام الان في اختصارات يبقى لو
+
+46
+00:04:58,950 --> 00:05:04,590
+اختصرت طول ال PS مع طول ال PS يبقى هذا الكلام بده
+
+47
+00:05:04,590 --> 00:05:14,110
+يعطينا PS ضد ال N لو L متجة N مقسوما على طول
+
+48
+00:05:14,110 --> 00:05:15,910
+المتجة N
+
+49
+00:05:20,300 --> 00:05:25,980
+إذا من الآن فصاعدا مشان نحسب قداش المسافة ما بين
+
+50
+00:05:25,980 --> 00:05:30,300
+نقطة و plane بدنا ما ياتي بدنا نوجد نقطة في ال
+
+51
+00:05:30,300 --> 00:05:35,360
+plane و نجيب قداش المسافة من النقطة هذه إلى النقطة
+
+52
+00:05:35,360 --> 00:05:41,230
+اللي في الفراروبصير عندي متجة بدي اسميه PS من
+
+53
+00:05:41,230 --> 00:05:44,230
+معادلة الـplane بقدر أجيب المتجة العمودي على
+
+54
+00:05:44,230 --> 00:05:47,810
+الـplane صار عندي two vectors من خلال الـtwo
+
+55
+00:05:47,810 --> 00:05:52,390
+vectors هدول بقدر أعرف كده ال distance دي المبينة
+
+56
+00:05:52,390 --> 00:05:55,690
+في الرسم اللي عندنا مسافة هذه أو المسافة اللي
+
+57
+00:05:55,690 --> 00:06:01,430
+عندنا هذه كده مقدار الـD بقول الـPS ضد ال N على
+
+58
+00:06:01,430 --> 00:06:06,440
+main على طول الـPMحد ألا يستفسر هنا قبل أن ندخل
+
+59
+00:06:06,440 --> 00:06:18,520
+إلى المثال إيه؟ طيب نجي ناخد مثال example find
+
+60
+00:06:18,520 --> 00:06:28,020
+the distance from the point find the distance from
+
+61
+00:06:33,780 --> 00:06:41,920
+من النقطة اتنين و سالم تلاتة واربع to the plane
+
+62
+00:06:41,920 --> 00:06:46,880
+للـ
+
+63
+00:06:46,880 --> 00:06:56,580
+plane اللي هو X زائد اتنين Y زائد اتنين Z يزاوي
+
+64
+00:06:56,580 --> 00:06:57,900
+تلات باشر
+
+65
+00:07:09,620 --> 00:07:14,100
+سؤال مرة تانية بيقول لي هذا ليه جداش المسافة من
+
+66
+00:07:14,100 --> 00:07:19,860
+النقطة اللي هي اتنين وسلب تلاتة واربعة للمستوى X
+
+67
+00:07:19,860 --> 00:07:24,600
+زي دي اتنين Y زي دي اتنين Z يساوي تلتاش عشان نحسب
+
+68
+00:07:24,600 --> 00:07:29,260
+هذه المسافة بيدي نقطة في ال plane وبيدي المتجه
+
+69
+00:07:29,260 --> 00:07:33,040
+العمودي على هذا ال plane الحمد لله المتجه بيجيبه
+
+70
+00:07:33,040 --> 00:07:37,540
+من شكل المعادلة تبعت ال plane يا جباجي بقول ليه؟
+
+71
+00:07:49,460 --> 00:07:58,080
+أز مرتجع M يساوي المعادلة I زائد اتنين J زائد
+
+72
+00:07:58,080 --> 00:07:59,060
+اتنين K
+
+73
+00:08:05,390 --> 00:08:10,170
+كيف بدي أجيب نقطة في هذا ال plane يعني بدي
+
+74
+00:08:10,170 --> 00:08:16,470
+إحداثيات نقطة هذا ال plane يمر بها كيف ممكن أخلك
+
+75
+00:08:16,470 --> 00:08:21,310
+بدل النقطة تلاتة و إذا بدك عشرين ماشي الحال مش
+
+76
+00:08:21,310 --> 00:08:25,170
+مشكلة احنا بدنا بس نقطة واحدة يبقى أبسط شغل شو
+
+77
+00:08:25,170 --> 00:08:30,890
+أعمله مثلا
+
+78
+00:08:30,890 --> 00:08:32,130
+يبقى الأخت
+
+79
+00:08:35,900 --> 00:08:41,840
+لغة enas بتقول ما ياتي انه نضع two variables كل
+
+80
+00:08:41,840 --> 00:08:46,180
+واحد ب zero وبتطلع منها قيمة ال variable التالت
+
+81
+00:08:46,180 --> 00:08:49,560
+وبالتالي هدول بيكونوا احداثيات نقطة موجودة في هذا
+
+82
+00:08:49,560 --> 00:08:53,980
+ال plane كلامها سليم مائة بالمائة يبقى لو جينا
+
+83
+00:08:53,980 --> 00:08:55,080
+قولنا put
+
+84
+00:09:12,450 --> 00:09:18,470
+يعني هذا ليس بالضرورة ان يكونوا هذول ممكن اخد هذول
+
+85
+00:09:18,470 --> 00:09:24,090
+برقم اخر كمان ليس بالضرورة يكون Zero المهم بدي انا
+
+86
+00:09:24,090 --> 00:09:28,570
+ادور على نقطة لكن لما احط واي تساوي زده يساوي Zero
+
+87
+00:09:28,570 --> 00:09:34,630
+اسهللي في الحسابات لما تكون اكتشف عموض في معدل
+
+88
+00:09:34,630 --> 00:09:40,910
+البلد تصير ال X زائد Zero زائد Zero يساوي تلتاشر
+
+89
+00:09:40,910 --> 00:09:41,770
+يبقى X
+
+90
+00:09:47,620 --> 00:09:56,600
+النقطة اللي هي تلتاشر و zero و zero lie in the
+
+91
+00:09:56,600 --> 00:10:02,160
+given plane إذا
+
+92
+00:10:02,160 --> 00:10:07,340
+هذه يا بنات صارت هي النقطة P و النقطة المعلومة
+
+93
+00:10:07,340 --> 00:10:10,980
+اللي عندنا هذه مين بدها تكون حسب الرسم اللي عندنا
+
+94
+00:10:10,980 --> 00:10:16,460
+اسمه S اللي هو النقطة S إذا بلزمني أجيب المتجة ES
+
+95
+00:10:45,370 --> 00:10:56,330
+نقص احد عشر I نقص تلاتة J زائد اربع K عرفنا ايه هو
+
+96
+00:10:56,330 --> 00:11:03,530
+المتجه PS والمتجه N موجود عند هيه اذا بقدر اجيب ال
+
+97
+00:11:03,530 --> 00:11:06,770
+distance D يبقى distance
+
+98
+00:11:29,280 --> 00:11:36,440
+هذه البنات لطول هذه هي absolute value صحيح ليها
+
+99
+00:11:36,440 --> 00:11:37,080
+والله عيب
+
+100
+00:11:46,580 --> 00:11:52,280
+أو الطول يجب أن يكون قيمة موجبة فباخده الـ
+
+101
+00:11:52,280 --> 00:11:56,280
+absolute value إذا هذا الكلام بده يساوي ال
+
+102
+00:11:56,280 --> 00:12:01,420
+absolute value بده يعمل dot product ما بين ال P S
+
+103
+00:12:01,420 --> 00:12:04,040
+و ال N يبقى
+
+104
+00:12:08,880 --> 00:12:15,480
+بعدين ناقص ثلاثة في اتنين ناقص ستة و بعدين اربعة
+
+105
+00:12:15,480 --> 00:12:21,820
+في اتنين زائد تمانية كله على الجذر التربيهي
+
+106
+00:12:44,670 --> 00:12:50,170
+إذا نقول المسافة من النقطة هذه للـplane يساوي كده؟
+
+107
+00:12:50,170 --> 00:12:56,190
+يساوي ثلاثة من وحدات الطول و دي هي remark التالية
+
+108
+00:12:56,190 --> 00:13:01,890
+remark
+
+109
+00:13:01,890 --> 00:13:10,170
+two planes two planes are perpendicular
+
+110
+00:13:14,530 --> 00:13:23,090
+أتر تنديكيونار أو Parallel
+
+111
+00:13:23,090 --> 00:13:31,110
+المتعمقين أو المتوازين have their normals
+
+112
+00:13:42,820 --> 00:13:51,280
+يا الفن دي في الأرض؟ أو أهلا؟
+
+113
+00:13:51,280 --> 00:14:03,820
+هاد
+
+114
+00:14:03,820 --> 00:14:09,030
+أقبلكوا معايا هنا والله يعالىلو جيت تخيلت ان عندي
+
+115
+00:14:09,030 --> 00:14:15,630
+مستوين ومستوين متوازين رسمت ال vector العمودي على
+
+116
+00:14:15,630 --> 00:14:20,150
+المستوى الأول و ال vector العمودي على المستوى
+
+117
+00:14:20,150 --> 00:14:23,810
+الثاني شو العلاقة بين هذين ال two vectors
+
+118
+00:14:40,350 --> 00:14:46,070
+انا عندى الان two planes اتنين are parallel بدي
+
+119
+00:14:46,070 --> 00:14:49,830
+ارسم العمود على الاول و العمود على التانى شو له
+
+120
+00:14:49,830 --> 00:14:54,130
+لقب اللي اتنين اتنين parallel اذا if two planes
+
+121
+00:14:54,130 --> 00:14:58,310
+are parallel then their normals are parallel و
+
+122
+00:14:58,310 --> 00:15:02,130
+العكس لو كانت two normals are parallel you get two
+
+123
+00:15:02,130 --> 00:15:05,970
+vectors are parallel نيجى لحكاية التعامل خلّيكي
+
+124
+00:15:05,970 --> 00:15:06,750
+هاتيلي هذا
+
+125
+00:15:11,270 --> 00:15:14,710
+أحنا لدينا الان two planes بالشكل اللي لدينا هنا
+
+126
+00:15:14,710 --> 00:15:18,830
+يبقى دول ال two planes are perpendicular اتنين
+
+127
+00:15:18,830 --> 00:15:23,390
+متعمدين الزاوية الزوجية بين المستوين له تسعين درجة
+
+128
+00:15:23,390 --> 00:15:28,310
+بترسم العمود على المستوى الأول و العمود على
+
+129
+00:15:28,310 --> 00:15:32,870
+المستوى الثاني ايش العلاقة بين ال two line او two
+
+130
+00:15:32,870 --> 00:15:37,110
+perpendicular يبقى اتنين are orthogonal يبقى بناء
+
+131
+00:15:37,110 --> 00:15:44,960
+عليه لو عندي two planesالعمودين على هذه المستقيمين
+
+132
+00:15:44,960 --> 00:15:48,020
+يكونان متعامدان
+
+133
+00:15:54,230 --> 00:15:59,710
+انا عندى هذا plane و هذا ال plane تبع السكين اتنين
+
+134
+00:15:59,710 --> 00:16:03,550
+اعرفى perpendicular فى ال corner اللى عندى لو جيت
+
+135
+00:16:03,550 --> 00:16:08,730
+رسمت من هنا عمود على ال plane الاول و رسمت عمود
+
+136
+00:16:08,730 --> 00:16:12,510
+على ال plane التانى كذا بينهم تسعين درجة هى اللى
+
+137
+00:16:12,510 --> 00:16:16,470
+بتقوله الريمانبتقولي two planes are perpendicular
+
+138
+00:16:16,470 --> 00:16:23,290
+اتنين بيكونوا متعامدين او متوازية if they are
+
+139
+00:16:23,290 --> 00:16:27,470
+normal vectors اذا جبت normal على كل واحد من ال
+
+140
+00:16:27,470 --> 00:16:30,290
+two vectors هدول بلاقي اتنين اذا perpendicular
+
+141
+00:16:30,290 --> 00:16:34,110
+بيكون perpendicular اذا parallel بيكون اتنين هدول
+
+142
+00:16:34,110 --> 00:16:40,910
+مالهم parallel نعطي مثال على ذلك يبقى example
+
+143
+00:16:49,120 --> 00:16:58,520
+بقول شو ده the two planes show that the two A
+
+144
+00:16:58,520 --> 00:17:08,040
+planes هي لإنه مستويين اللي هو تلاتة X زائد ستة Y
+
+145
+00:17:08,040 --> 00:17:10,720
+ناقص تسعة Z
+
+146
+00:17:15,180 --> 00:17:26,220
+والـ X زائد اتنين Y نقص ثانوتها Z بيكون واحد اتنين
+
+147
+00:17:26,220 --> 00:17:29,700
+اتنين
+
+148
+00:17:29,700 --> 00:17:37,700
+متوازين and find the distance
+
+149
+00:17:42,400 --> 00:17:46,020
+وأتولى المسافة between them
+
+150
+00:18:25,560 --> 00:18:30,520
+سؤال مرة تانية ماطيني معادلتين ل two players كل
+
+151
+00:18:30,520 --> 00:18:34,980
+واحد المعادلةوقال لي بيقول ان two planes هدول are
+
+152
+00:18:34,980 --> 00:18:38,420
+parallel كيف بنفسي ان two planes هدول هدول هدول
+
+153
+00:18:38,420 --> 00:18:44,520
+هدول هدول هدول هدول
+
+154
+00:18:44,520 --> 00:18:44,560
+هدول هدول هدول هدول هدول هدول هدول هدول هدول هدول
+
+155
+00:18:44,560 --> 00:18:44,600
+هدول هدول هدول هدول هدول هدول هدول هدول هدول هدول
+
+156
+00:18:44,600 --> 00:18:46,240
+هدول هدول هدول هدول هدول هدول هدول هدول هدول هدول
+
+157
+00:18:46,240 --> 00:18:49,820
+هدول هدول هدول هدول هدول هدول هدول هدول هدول هدول
+
+158
+00:18:49,820 --> 00:18:49,840
+هدول هدول هدول هدول هدول هدول هدول هدول هدول هدول
+
+159
+00:18:49,840 --> 00:18:51,780
+هدول هدول هدول هدول هدول هدول هدول هدول هدول هدول
+
+160
+00:19:15,670 --> 00:19:24,450
+normal first to play into
+
+161
+00:19:24,450 --> 00:19:28,430
+as
+
+162
+00:19:28,430 --> 00:19:29,090
+a vector
+
+163
+00:19:34,270 --> 00:19:46,990
+نقص ثلاثة كيلو مو اعمل to the second place بيهامد
+
+164
+00:19:46,990 --> 00:19:50,170
+عمودي عالمين على المستوى أسهل
+
+165
+00:19:56,220 --> 00:20:00,240
+طبعاً واضح انه في عامل مشترك هو مين تلاتة يعني لو
+
+166
+00:20:00,240 --> 00:20:06,340
+أخدت تلاتة بصير عندي I زائدي اتنين J ناقص تلاتة
+
+167
+00:20:06,340 --> 00:20:12,200
+كيلو المتجه بين القوصين هو المتجه مين ال two يبقى
+
+168
+00:20:12,200 --> 00:20:18,920
+هذا الكلام بيسوي تلاتة into هذا بدي يعطينا in one
+
+169
+00:20:18,920 --> 00:20:25,460
+and in two اتنين معاهم are parallel
+
+170
+00:20:31,990 --> 00:20:36,730
+يبقى المستويات الاتنين بتاعتهم يبقى هذا اللي
+
+171
+00:20:36,730 --> 00:20:44,030
+يعطيها هي the two given
+
+172
+00:20:44,030 --> 00:20:48,190
+planes
+
+173
+00:20:48,190 --> 00:20:52,510
+are parallel
+
+174
+00:20:55,080 --> 00:20:59,340
+يبقى المستوى هذول متوازين هذا المطلوب الأول من
+
+175
+00:20:59,340 --> 00:21:03,800
+المثلة المطلوب التاني جال يهدف المسافة ما بين ال
+
+176
+00:21:03,800 --> 00:21:08,440
+two planes هذول يعني يا بنات لو لينا قلنا هذا هو
+
+177
+00:21:08,440 --> 00:21:15,140
+المستوى الأول على سبيل المثال وهذا هو المستوى
+
+178
+00:21:15,140 --> 00:21:21,060
+الثانيبدي اعرف كده المسافة ما بين الاتنين المسافة
+
+179
+00:21:21,060 --> 00:21:26,060
+ما بين الاتنين هي المسافة العمودية طبعا هذا المتجه
+
+180
+00:21:26,060 --> 00:21:36,160
+اللي هو مين M1 العمودي على الأول شكل على هذا وهذا
+
+181
+00:21:36,160 --> 00:21:43,550
+المتجه التانياللي هو into العمودي على المستوى
+
+182
+00:21:43,550 --> 00:21:50,950
+الثاني قاللي هذا كده البعد فيما بينهما بقول والله
+
+183
+00:21:50,950 --> 00:21:56,990
+كويس إذا جدرنا نجيب نقطتين في هذين المستوى النقطة
+
+184
+00:21:56,990 --> 00:22:01,890
+في المستوى الأول ونقطة في المستوى الثاني ووصلت
+
+185
+00:22:01,890 --> 00:22:08,190
+فيما بينهم إذا بصير هذا PSبدي متجه عمودي على أحد
+
+186
+00:22:08,190 --> 00:22:11,930
+المستويين الحمد لله عند اثنين متجه عمودي على الأول
+
+187
+00:22:11,930 --> 00:22:16,850
+و متجه عمودي على التاني و اتنين are parallel مظبوط
+
+188
+00:22:16,850 --> 00:22:22,750
+يبقى بس تلنا نقطة أو نقطتين في المستويين اللي
+
+189
+00:22:22,750 --> 00:22:28,550
+عندنا بدي نقطة في كل من المستويين شو أعمل؟
+
+190
+00:22:35,620 --> 00:22:42,520
+بنفس الطريقة بقدر أجيب اللي هو نقطة في كل من
+
+191
+00:22:42,520 --> 00:22:50,720
+المستوى يعني إذا لو جيت قلت هنا هو مثلا y سوى z
+
+192
+00:22:50,720 --> 00:23:01,840
+سوى zero in the given airplanes we getبنحصل علامات
+
+193
+00:23:01,840 --> 00:23:06,500
+في الدرجة اللي اتنين الأول بصير عندي تلاتة X يساوي
+
+194
+00:23:06,500 --> 00:23:12,540
+درجة أربعة والتاني بصير عندي X يساوي واحدة
+
+195
+00:23:28,980 --> 00:23:34,100
+جت سميت النقطة هذه اللي هي النقطة S اللي هي مين؟
+
+196
+00:23:34,100 --> 00:23:41,360
+أربع على تلاتة وزير وزير تمام جت سميت النقطة هذه
+
+197
+00:23:41,360 --> 00:23:47,380
+اللي هي النقطة P اللي أحدثيها او أحدثيتها واحد
+
+198
+00:23:47,380 --> 00:23:54,340
+وزير وزير إذا بقدر أجيب المتجة بـS اللي عندها يبقى
+
+199
+00:23:54,340 --> 00:23:55,720
+هذا هو ال vector
+
+200
+00:24:05,170 --> 00:24:13,070
+كويس اذا انا بعد البعد العمودي ما بين الاتنين اللي
+
+201
+00:24:13,070 --> 00:24:18,030
+هو البعد مين البعد هذا اللي هو دي اعمل لي زاوية
+
+202
+00:24:18,030 --> 00:24:23,770
+تيتا ما بين المتجانين اذا هذا يعتبر موازي لمين
+
+203
+00:24:23,770 --> 00:24:27,550
+موازي لل vector n هذا
+
+204
+00:24:32,160 --> 00:24:39,300
+متجه N2 اذا على ان اتنين ادوات متوازية اذا بدي
+
+205
+00:24:39,300 --> 00:24:50,680
+اجيب ال distance D بقول هي ال PS ضاد من N2 على طول
+
+206
+00:24:50,680 --> 00:24:53,420
+ال N2
+
+207
+00:25:05,280 --> 00:25:11,580
+أربعة على تلاتة أربعة على تلاتة ناقص واحد في اتجاه
+
+208
+00:25:11,580 --> 00:25:16,800
+الـ I يبقى المُركّبات الأثناء كل واحدة بصفر الباقي
+
+209
+00:25:16,800 --> 00:25:25,500
+يبقى هذا بيساوي طول I يبقى ال distance دي بدها
+
+210
+00:25:25,500 --> 00:25:32,140
+تساوي اللي هو ال absolute value لمن؟ لل P S ضد ال
+
+211
+00:25:32,140 --> 00:25:39,990
+N2 اللي هو طولفاهمين في ال N2 وين ال N2 لنا اللي
+
+212
+00:25:39,990 --> 00:25:48,210
+هو ال I يبقى طول في واحد والباقي قداش Zero Zero
+
+213
+00:25:48,210 --> 00:25:54,170
+أخرى خلصنا يبقى هذه الأحداثيات ال PS اللي عندنا
+
+214
+00:25:54,170 --> 00:26:02,310
+عالميا على طول المتجه N2 اللي هو الجدري التربيعي
+
+215
+00:26:02,310 --> 00:26:04,690
+لل N2
+
+216
+00:26:15,440 --> 00:26:23,940
+يبقى هذه المسافة بين المستويين المتوازيين نجي الآن
+
+217
+00:26:23,940 --> 00:26:27,960
+للنقطة الأخيرة بيانة السمش اللبنان لنقطة أربع من
+
+218
+00:26:27,960 --> 00:26:31,260
+خمسة هحطها على صفرة ال definition
+
+219
+00:26:53,160 --> 00:26:58,260
+الزاوية بين المستوين المبدأ قاعة عين is the angle
+
+220
+00:26:58,260 --> 00:27:08,940
+between is the angle between is
+
+221
+00:27:08,940 --> 00:27:13,800
+the angle between their
+
+222
+00:27:13,800 --> 00:27:20,900
+normal vectors between their normal vectors
+
+223
+00:27:34,860 --> 00:27:40,620
+مرحباً بكموانتوا من الصفر السابع لغاية الصفر
+
+224
+00:27:40,620 --> 00:27:45,940
+التاسع مرحلة الاعدادية هذه الزاوية بين المستقيمين
+
+225
+00:27:45,940 --> 00:27:50,040
+تساوي الزاوية بين العمودين علي هدين المستقيمين
+
+226
+00:27:50,040 --> 00:27:55,400
+يعني الزاوية المحصورة بين المستقيمين متقاطعين
+
+227
+00:27:55,400 --> 00:28:01,800
+تساوي الزاوية بين المستقيمين اللي هو العمودين علي
+
+228
+00:28:01,800 --> 00:28:06,840
+هدين المستقيمين سمعتوا فيهاتمام احنا هنا نفس
+
+229
+00:28:06,840 --> 00:28:11,580
+الفكرة بنقول الزاوية بين two intersecting planes
+
+230
+00:28:11,580 --> 00:28:16,180
+هي الزاوية بين ال normal vectors يبقى احنا بدنا
+
+231
+00:28:16,180 --> 00:28:23,240
+نروح ندور على مين على two intersecting planes يبقى
+
+232
+00:28:23,240 --> 00:28:24,280
+لو روحت قلت
+
+233
+00:28:32,590 --> 00:28:38,090
+وفي عندى مستوى ثانى المستوى الثانى كان بهذا الشكل
+
+234
+00:28:38,090 --> 00:28:45,530
+يبقى المستوى الاتنين هدول اتقاطعوا في خط التقاطع
+
+235
+00:28:45,530 --> 00:28:49,270
+اللى عندنا كويس
+
+236
+00:28:49,910 --> 00:28:56,030
+هي بهذا خط قاطع المستوين بدي أرسم عمودي على
+
+237
+00:28:56,030 --> 00:29:01,670
+المستوى الأول و كذلك عمودي على المستوى الثاني لو
+
+238
+00:29:01,670 --> 00:29:08,190
+جيت قلت هذا عمودي على المستوى الأول اللي هو N1
+
+239
+00:29:08,190 --> 00:29:13,910
+يعني الأزرق عمودي على المستوى الأزرق هذا و ال
+
+240
+00:29:13,910 --> 00:29:19,770
+vector قصد ال vector N1 و جيت هنا كمان رسمت عمود
+
+241
+00:29:25,630 --> 00:29:33,510
+طبعا الزاوية هذه هي الزاوية ما بين two normal
+
+242
+00:29:33,510 --> 00:29:38,270
+vectors عمودي على المستوى الأول و الخط الأزرق
+
+243
+00:29:38,270 --> 00:29:44,130
+عمودي على المستوى الأزرق و الخط الأسود عمودي على
+
+244
+00:29:44,130 --> 00:29:50,680
+المستوى الأسودالان بدى جدش الزاوية بين المستوان
+
+245
+00:29:50,680 --> 00:29:54,620
+طبعا الزاوية البنات هي الزاوية الزوجية بين
+
+246
+00:29:54,620 --> 00:30:01,040
+المستوان الزاوية هادي يعني لما اجيب two planes هات
+
+247
+00:30:01,040 --> 00:30:06,860
+شوية بلغتها لما اجيب ال two planes المتقطعين بهذا
+
+248
+00:30:06,860 --> 00:30:13,750
+الشكل يجد اتنين هدول بينهم ايش؟ بينهم زاويةعلى طول
+
+249
+00:30:13,750 --> 00:30:17,570
+خط التقاطع هذه بالعامة بسميها الزاوية الزوجية
+
+250
+00:30:17,570 --> 00:30:22,290
+الانجل تتوين تتقاطع تتقاطع تتقاطع تتقاطع تتقاطع
+
+251
+00:30:22,290 --> 00:30:29,190
+تتقاطع تتقاطع
+
+252
+00:30:36,740 --> 00:30:41,920
+الزاوية المحصورة بين two normal vectors تساوي
+
+253
+00:30:41,920 --> 00:30:46,660
+عمليا الزاوية الموجودة بين المستويين
+
+254
+00:30:52,930 --> 00:30:57,390
+يعني ارسم المتجه العمودي على المستوى الأول و ارسم
+
+255
+00:30:57,390 --> 00:31:02,130
+المتجه العمودي على المستوى التالي الزاوية بينهم هي
+
+256
+00:31:02,130 --> 00:31:11,110
+الزاوية الزوجية بين المستويين تمام نعطي مثال على
+
+257
+00:31:11,110 --> 00:31:11,710
+ذلك
+
+258
+00:31:26,930 --> 00:31:42,630
+the angle between the planes بين المستويين ال ..
+
+259
+00:31:42,630 --> 00:31:50,930
+اللي هو X زائد أقع واحد ناقص تلاتة Z يساوي واحد
+
+260
+00:31:50,930 --> 00:32:03,470
+and اللي هو ناقص تلاتة Xستة Y زائد سبعة Z
+
+261
+00:32:40,400 --> 00:32:43,720
+بنزّه من المستوات اللي اتنين هدول ان انا بده اجيب
+
+262
+00:32:43,720 --> 00:32:49,140
+ال normal vector على كل من المستوات يبقى بداجي
+
+263
+00:32:49,140 --> 00:32:59,020
+هقول N1 اللي هو I زائد 4J نقص تلاتة K normal to
+
+264
+00:32:59,020 --> 00:33:03,820
+the first
+
+265
+00:33:03,820 --> 00:33:04,360
+plane
+
+266
+00:33:12,070 --> 00:33:22,650
+into الهو عبارة عن ناقص ثلاثة I زائد ستة G زائد
+
+267
+00:33:22,650 --> 00:33:31,070
+سبعة K normal to the second اتلقى
+
+268
+00:33:31,070 --> 00:33:36,470
+المضتج اتلقى الآن بدي اتزامر بعمل product ضد ما
+
+269
+00:33:36,470 --> 00:33:44,220
+بينهما فماجي بقولهالـ N1 ضد
+
+270
+00:33:44,220 --> 00:33:51,720
+N2 متجه الثاني N2 يساوي طول الـ
+
+271
+00:33:56,420 --> 00:34:02,440
+الزاوية بينهما.الان بدي اعمل ضطمة بين الفلين يبقى
+
+272
+00:34:02,440 --> 00:34:08,360
+هذه ناقص ثلاثة واللي بعدها اربعة في ستة بزائد
+
+273
+00:34:08,360 --> 00:34:15,660
+اربعة وعشرين واللي بعدها ناقص واحد وعشرين بدي ساوي
+
+274
+00:34:19,140 --> 00:34:25,020
+in one اللي هو واحد زائد ستاشر زائد تسعة واحد زائد
+
+275
+00:34:25,020 --> 00:34:31,120
+ستاشر زائد تسعة والجدار التاني اللي هو المتجه
+
+276
+00:34:31,120 --> 00:34:39,020
+التاني اللي هو تسعة زائد ستة وتلاتين تسعة زائد ستة
+
+277
+00:34:39,020 --> 00:34:47,520
+وتلاتين زائد تسعة واربعين في كساين الزاوية ديقدرش
+
+278
+00:34:47,520 --> 00:34:52,900
+دي أمانة الطرف الشمالي؟ Zero. إذا بقسم على مين؟
+
+279
+00:34:52,900 --> 00:34:57,860
+على حصر ضرب الجدرين، بسيري عندي وصين تيتا سواء
+
+280
+00:34:57,860 --> 00:35:02,780
+قدر؟ Zero. فبنسأل السؤال التالي، مين الزاوية اللي
+
+281
+00:35:02,780 --> 00:35:06,800
+جيب تمامها يسوى صفر؟ 90 درجة.
+
+282
+00:35:17,100 --> 00:35:29,980
+يبقى this means that the two planes are
+
+283
+00:35:29,980 --> 00:35:31,380
+perpendicular
+
+284
+00:35:40,480 --> 00:35:45,740
+أحنا حسبنا الزاوية وجينا اتنين are perpendicular
+
+285
+00:35:45,740 --> 00:35:51,000
+عليك يكون انتهى ال section ونجي لل exercises
+
+286
+00:35:51,000 --> 00:35:59,940
+اتناشر خمسة المسائل من واحد لتمانية واربعين ال pod
+
+287
+00:35:59,940 --> 00:36:02,700
+ومن تلاتة وخمسين
+
+288
+00:36:41,170 --> 00:36:45,970
+بنجي لل section اللي ياليه وهو اخر section في هذا
+
+289
+00:36:45,970 --> 00:36:53,210
+ال chapter اللي هو section اتناشر ستة يتحدث عن ال
+
+290
+00:36:53,210 --> 00:36:59,130
+cylinder cylinders
+
+291
+00:36:59,130 --> 00:37:09,710
+and quadric surfaces
+
+292
+00:37:15,480 --> 00:37:23,960
+نبدأ أول شيء بملاحظة الـ cylinders إيش
+
+293
+00:37:23,960 --> 00:37:29,660
+معناه cylinders يا بنات؟ بالعربى أسطوانة ممتاز طيب
+
+294
+00:37:29,660 --> 00:37:35,820
+الأسطوانة هل ضروري يكون مقطع تبعها عبارة عن دائرة؟
+
+295
+00:37:37,770 --> 00:37:42,070
+مصورة عادية لو قطعت المطبع هي عبارة عن دائرة لكن
+
+296
+00:37:42,070 --> 00:37:46,730
+هل لما أقول cylinder في الفرار بالضرورة أن يكون
+
+297
+00:37:46,730 --> 00:37:52,730
+المطبع دائرة؟ لأ، شوفي من هنا، لو جيت قلت هذا
+
+298
+00:37:52,730 --> 00:37:57,490
+عبارة عن سطح الشكل اللي عندنا، انت شوفي اللي انت
+
+299
+00:37:57,490 --> 00:38:03,690
+شايفينه أنا، كويس؟ يجي هذا بسميه cylinder، سطح
+
+300
+00:38:03,690 --> 00:38:06,330
+أسواني، حتى لو لم يكن مغلق
+
+301
+00:38:14,680 --> 00:38:20,060
+يبقى المقطع عبارة عن إيه؟ عبارة عن دائرة، يبقى
+
+302
+00:38:20,060 --> 00:38:24,720
+دائرها الشكل اللي عندنا هذا، مش واضح، بلاش، بنوضح
+
+303
+00:38:31,300 --> 00:38:37,320
+يبقى هذه cylinder و كذلك لو خليتها بهذا الشكل يبقى
+
+304
+00:38:37,320 --> 00:38:43,340
+هنا cylinder لو كبرتها و وضحت اكتر مثلك هذا السطح
+
+305
+00:38:43,340 --> 00:38:48,860
+هو عبارة عن ايش عبارة عن cylinder لو خليته مفتوح
+
+306
+00:38:48,860 --> 00:38:53,960
+بالشكل هذا cylinder لو جبت شكل تاني زيه و خليته من
+
+307
+00:38:53,960 --> 00:39:00,300
+ناحية تانية و اتنين مع بعض كذلك يعتبر cylinderطيب
+
+308
+00:39:00,300 --> 00:39:06,820
+ايش ال quadric surface او ال quadric surfaces ايش
+
+309
+00:39:06,820 --> 00:39:12,400
+معناه quadric بالعربي؟ ثنائي مش مربع، اذاك square
+
+310
+00:39:12,400 --> 00:39:16,860
+مربع، يبقى ال quadric ثنائي، surface سطح، يبقى
+
+311
+00:39:16,860 --> 00:39:24,080
+السطوح الثنائية، يعني المجسمات بالعربي اللي بتكون
+
+312
+00:39:24,080 --> 00:39:31,800
+ا في الفرارسياتك وانت جاهز تعتبري مجسم موجود في
+
+313
+00:39:31,800 --> 00:39:38,260
+الفراغ أو شكلك الخارجي يعتبر quadric surface تمام؟
+
+314
+00:39:38,260 --> 00:39:41,820
+يبقى هذا ال quadric surface اللي انا بدنا نميز ما
+
+315
+00:39:41,820 --> 00:39:46,000
+بين ال quadric surfaces و ال cylinderهناخد ستة
+
+316
+00:39:46,000 --> 00:39:51,420
+quadric surfaces ست سطوح ثنائية ونعرف معادلة كل
+
+317
+00:39:51,420 --> 00:39:56,500
+سطح من هذه السطوح طبعا هذه السطوح مشهورة وقبلهم
+
+318
+00:39:56,500 --> 00:40:03,340
+هناخد وضع A السيلندر ونشوف كيف بنرسم كل واحدة من
+
+319
+00:40:03,340 --> 00:40:10,320
+ال quadric surfaces وكذلك السيلندر المختلفةطيب على
+
+320
+00:40:10,320 --> 00:40:15,200
+اي حال في الفراغ بالنسبة للسيلندر بلاقي معادلة
+
+321
+00:40:15,200 --> 00:40:18,980
+فيها رمزين فقط طبعا احنا بنشتغل في ال
+
+322
+00:40:39,280 --> 00:40:43,780
+طيب الكلمتين اللي انت سمعتهم بده اكتبهم و بعد نشوف
+
+323
+00:40:43,780 --> 00:40:49,160
+كيف بده نرسم بعد اللي هو بعض ال cylinder فباجي
+
+324
+00:40:49,160 --> 00:40:49,620
+بقول
+
+325
+00:41:05,940 --> 00:41:15,780
+Y أو Z أي واحد منهم مفقود من
+
+326
+00:41:15,780 --> 00:41:21,000
+المعادلة
+
+327
+00:41:21,000 --> 00:41:27,300
+مش موجود في المعادلة تبع في الصفر of a surface
+
+328
+00:41:27,300 --> 00:41:34,920
+then the surface then the surface
+
+329
+00:41:45,110 --> 00:41:51,510
+هو عبارة عن صوالة مع جنريتر
+
+330
+00:41:51,510 --> 00:41:57,590
+مولد
+
+331
+00:41:57,590 --> 00:41:58,710
+للسيلندر
+
+332
+00:42:22,150 --> 00:42:30,950
+to the axis corresponding ..
+
+333
+00:42:30,950 --> 00:42:40,450
+corresponding المناظر to the missing variable
+
+334
+00:42:40,450 --> 00:42:46,690
+example
+
+335
+00:42:58,900 --> 00:43:13,860
+half of the following cylinders المرأة
+
+336
+00:43:13,860 --> 00:43:24,860
+ال X تربيع زائد اربع زت تربيع ددرساه يوم ستة عشر
+
+337
+00:43:24,860 --> 00:43:36,650
+مرة BX يساوي Y تربيع نمرة C Z تساوي تسعة نقص Y
+
+338
+00:43:36,650 --> 00:43:45,570
+تربيع نمرة D Y تربيع على أربعة نقص X تربيع على
+
+339
+00:43:45,570 --> 00:43:47,610
+تسعة يساوي واحدة
+
+340
+00:44:10,030 --> 00:44:15,570
+بنشوف كيف بنحكم على رسمة انها عندى رسمة أسطوانة أو
+
+341
+00:44:15,570 --> 00:44:20,510
+غيره وإذا كانت أسطوانة يبقى إلها محور بدنا نعرف
+
+342
+00:44:20,510 --> 00:44:28,270
+مين هو المحور اللى عندنا هذا ولها مولد تمام طلع يا
+
+343
+00:44:28,270 --> 00:44:34,350
+بنات هنا لو أنا ثبت اللى عندى المستقبل الأزرق اللى
+
+344
+00:44:34,350 --> 00:44:39,670
+شايفهو روح جيبت موازي له اللي همين الأسود اللي
+
+345
+00:44:39,670 --> 00:44:44,150
+عندنا هنا و قولت انت يا أزرق ضلك سابقا تصحى تتحرك
+
+346
+00:44:44,150 --> 00:44:51,050
+انت يا أسود بدك تتحرك حوالي الأزرق فعشان تضلك ماشي
+
+347
+00:44:51,050 --> 00:44:56,410
+على منحنى و تضلك موازي للأزرق انت جالس هيرسملي من
+
+348
+00:44:56,410 --> 00:45:03,170
+الخارج سطح أسطواني تمام؟ المنطقة اللي بمسحها الخطة
+
+349
+00:45:03,170 --> 00:45:07,320
+اللي عندنا هنا كلهابدي أرسلهم لمين؟ سطح، هذا السطح
+
+350
+00:45:07,320 --> 00:45:13,420
+بسميه أسوانة أو بسميه cylinder يبقى هذا اللي هو
+
+351
+00:45:13,420 --> 00:45:16,940
+الكلام أو السطرين اللي أنا كاتبينهم هنا لو كان
+
+352
+00:45:16,940 --> 00:45:21,420
+واحد من المتغيرات مفقود من المعادلة يبقى ال
+
+353
+00:45:21,420 --> 00:45:24,560
+surface اللي عندي بدي أقول هو عبارة عن cylinder
+
+354
+00:45:24,560 --> 00:45:29,720
+ولها مولد، شو مولد؟ يعني اللي بدي أولد السطح
+
+355
+00:45:29,720 --> 00:45:37,690
+الخارجي تبع ال cylinderوهذا بدي يكون موازن لل axis
+
+356
+00:45:37,690 --> 00:45:43,210
+المناظر لمين للمتغير المفقود يعني ايش يا بنات قصد
+
+357
+00:45:43,210 --> 00:45:47,910
+يقول بالظبط من الكلابين اللي كتبهم هدول؟يقول لمن
+
+358
+00:45:47,910 --> 00:45:53,570
+يعطيك معادلة وقدر تعرفها معادلة سيلندر ولا لا تطلع
+
+359
+00:45:53,570 --> 00:45:56,930
+على المعادلة هذه المعادلة في الفرح أصلا تلت
+
+360
+00:45:56,930 --> 00:46:03,210
+متغيرات X وY وZ لو لجيت واحد منهم مفهوم مش موجود
+
+361
+00:46:03,210 --> 00:46:07,690
+يعني يا إما X وZ اللي موجود، يا إما X وY، يا إما Y
+
+362
+00:46:07,690 --> 00:46:13,050
+وZرمزين من الحد ماشوفش غير رمزين إذا هذه معادنة
+
+363
+00:46:13,050 --> 00:46:19,770
+سيلندر I imagine مين ال axis تبع السيلندر اللي هو
+
+364
+00:46:19,770 --> 00:46:25,530
+الرمز الغائب أو ما يوازيه ممكن يكون معمول لكثير
+
+365
+00:46:25,530 --> 00:46:29,650
+وبالتالي مايكونش ايه اللي هو المحور الغائب او
+
+366
+00:46:29,650 --> 00:46:30,630
+الرمز الغائب
+
+367
+00:46:51,540 --> 00:46:54,260
+الكلام اللي احنا بيقوله بيروح التطبق على أرض
+
+368
+00:46:54,260 --> 00:47:01,010
+الواقعقال لي مثال ارسم لي كل من الاستوانات اية
+
+369
+00:47:01,010 --> 00:47:05,090
+تالية وقال لي X تربية زائد اربعة زيت تربية تساوي
+
+370
+00:47:05,090 --> 00:47:10,250
+ستة عشر لو سألت وقلتلك هذه المعادلة فيديو ليه ترجع
+
+371
+00:47:10,250 --> 00:47:14,890
+معادلة ايه معادلة
+
+372
+00:47:14,890 --> 00:47:22,450
+ايه الأولى ممتاز ع ستة عشر يبقى فيديو X تربية ع
+
+373
+00:47:22,450 --> 00:47:26,800
+ستة عشرذا زدت فيه علقة ما يسوي واحد عنها دي دارة
+
+374
+00:47:26,800 --> 00:47:34,260
+تلفت تلفت تمام ايوة يبقى هادى لو اخدت ليلي الليل
+
+375
+00:47:34,260 --> 00:47:39,740
+بيكون هذا اليف ساكن انا في الفرار الرمزين اللي
+
+376
+00:47:39,740 --> 00:47:48,060
+موجودين اللي هم الرمز غايم ، إذا Y هو المحور أو
+
+377
+00:47:48,060 --> 00:47:52,520
+الموازي للمحور إذا وصلنا لمعمولها Chef. هل هذا رصد
+
+378
+00:47:52,520 --> 00:47:56,300
+الـChef؟ في الـChef ممتاز يرجى المحور تبع
+
+379
+00:47:56,300 --> 00:48:02,300
+الـCylinder هذي هو الـY Axis. طبعا؟ أيوة تعالى
+
+380
+00:48:02,300 --> 00:48:09,100
+نرسمه. يرجى هذا لما اتفاقنا على إنها الـCylinderبس
+
+381
+00:48:09,100 --> 00:48:14,120
+المقطع تبعها دائرة ولا ellipse اللي بيكون على شكل
+
+382
+00:48:14,120 --> 00:48:18,880
+ellipse المحور تبع هذه الوسطه ده هو محور
+
+383
+00:48:42,970 --> 00:48:46,570
+تمام؟ طيب و المقطع اللي يقول على شكل إيه؟ اللي
+
+384
+00:48:46,570 --> 00:48:53,330
+يقول على شكل Alex إذا لو جيت قلت هذا ال Alex و من
+
+385
+00:48:53,330 --> 00:48:57,010
+الناحية التانية بالشكل اللي عندنا هذا و هذا هو
+
+386
+00:48:57,010 --> 00:49:03,010
+إيه؟ هو الشكل اللي عندنا لأن هذه الأسطورة المقطع
+
+387
+00:49:03,010 --> 00:49:04,610
+تباعها عبارة عن
+
+388
+00:49:16,130 --> 00:49:26,310
+تمام؟ يبقى هذا يكون يعني لهنا شوية يبقى
+
+389
+00:49:26,310 --> 00:49:30,670
+هذه المقطع او هذا المجسم اللي اتكون عندنا او هذه
+
+390
+00:49:30,670 --> 00:49:35,370
+هي ال cylinder اللي تكون عندنا هذه رسم يا بنات
+
+391
+00:49:35,370 --> 00:49:42,810
+تعتبر رسم سهلة يعني مافيش فيها اي صعوبة مباشرةأمان
+
+392
+00:49:42,810 --> 00:49:47,570
+طيب نيجي للرسمة التانية و نشوف إيش قصته هذا X
+
+393
+00:49:47,570 --> 00:49:52,330
+يساوي Y تربيع لو قصتك في الكليل هذه معناه كده
+
+394
+00:49:52,330 --> 00:49:58,610
+Parabola فتطهر مكبر لكن أنا بدي يها تقول في الفراغ
+
+395
+00:49:58,610 --> 00:50:04,650
+إذا يا بنات ال parabola هتصير في الفراغ بهذا الشكل
+
+396
+00:50:04,650 --> 00:50:11,050
+من هنا كده من هنا كده من هنا كده من هنا كده من هنا
+
+397
+00:50:11,050 --> 00:50:11,150
+كده من هنا كده من هنا كده من هنا كده من هنا كده من
+
+398
+00:50:11,150 --> 00:50:14,700
+كده من هنا كده من هنا كدطبعا إذا بدأ أصير كأنه بدأ
+
+399
+00:50:14,700 --> 00:50:20,880
+صخرة بولات جنبها يبقاش مصير عندي المجسم أو الشكل
+
+400
+00:50:20,880 --> 00:50:25,440
+اللي عندنا هذا اللي هو الشكل أوسطواني هذا على
+
+401
+00:50:25,440 --> 00:50:30,220
+الطبيعة لكن احنا بدنا نروح نرسم إيه؟ نرسم رسم إذا
+
+402
+00:50:30,220 --> 00:50:35,200
+لو جيت أرسم رسم باجي بطل عمينة و هم زرغاية
+
+403
+00:50:42,040 --> 00:50:49,620
+يجب ان يكون الـ Z هو المحور او فضل موازن له ،شفت
+
+404
+00:50:49,620 --> 00:51:00,600
+مافيش يبقى وضل هو المحور كيف كانت تانية؟ هده X و
+
+405
+00:51:00,600 --> 00:51:06,080
+هده Y و هده اللي عندنا اللي هو Z لو ماديته على
+
+406
+00:51:06,080 --> 00:51:11,890
+استقامته مافي مشكلة الشكل عندنا هذاطيب يا مانات
+
+407
+00:51:11,890 --> 00:51:17,090
+تعالى نذكركوا شوية لما كنت اقول Y تساوي X تربيه
+
+408
+00:51:17,090 --> 00:51:21,990
+معادة البرامجيبقى Y تساوي X تربيعه مانيش لما احاول
+
+409
+00:51:21,990 --> 00:51:27,490
+يبقى Y تساوي يعني الملحنة حوالين Y مش حوالين X
+
+410
+00:51:27,490 --> 00:51:33,870
+تربيع تمام اذا هذا لما اقول X يساوي Y تربيع يبقى
+
+411
+00:51:33,870 --> 00:51:40,870
+حوالين X مظبوط ولا لأ ايوة يبقى هذا يبقى ترابط
+
+412
+00:51:40,870 --> 00:51:46,690
+حوالين مين حوالين محور X يبقى يبقى بالشكل هذا
+
+413
+00:51:50,710 --> 00:51:56,330
+مظبوط؟ طيب و الباقي كيف شكله؟ بقولك اه بدك تروسي
+
+414
+00:51:56,330 --> 00:52:01,550
+.. تروسني برابو لازمو شبه الموازيه يعني لأن
+
+415
+00:52:01,550 --> 00:52:05,610
+الموازيه للخط المستقيم يقول يبقى بده يجيكي منحلة
+
+416
+00:52:05,610 --> 00:52:14,270
+هيك منحلة هيك و من هنا بده يجيكي بالشكل يعني و من
+
+417
+00:52:14,270 --> 00:52:16,390
+تحت بنفس الطريقة
+
+418
+00:52:40,900 --> 00:52:47,840
+يبقى كأنه هي برابلة وهي البرابلة التانية وهي
+
+419
+00:52:47,840 --> 00:52:57,840
+البرابلة التالية طبعا هذه يبقى
+
+420
+00:52:57,840 --> 00:53:01,180
+هذه البرابلز اللي عندنا وزي ما انت شايفها حوالي
+
+421
+00:53:01,180 --> 00:53:06,640
+المين حوالي المحوركز كأنه كيف كأنه جيت وقلت هذه
+
+422
+00:53:11,950 --> 00:53:16,810
+واضحة؟ تمام؟ يبقى هذه بسميها مين؟ بسميها ال
+
+423
+00:53:16,810 --> 00:53:23,970
+cylinder كمان هذه من الرسمات السهلة طيب نجي نتقل
+
+424
+00:53:23,970 --> 00:53:24,910
+القيلة شوية
+
+425
+00:53:35,370 --> 00:53:40,830
+أحنا بنشتغل في المستوى والله في الفراغ ممتاز جدا
+
+426
+00:53:40,830 --> 00:53:46,980
+حاطنا للقاعدة فوق الفراغ تلت محاور X Y و Zقلنا لك
+
+427
+00:53:46,980 --> 00:53:50,880
+إذا لجيت لعب صغير إذا ان هي cylinder يعني مش في ال
+
+428
+00:53:50,880 --> 00:53:56,080
+plane يعني إحنا مش في leaf lane وإنما وين في
+
+429
+00:53:56,080 --> 00:54:00,260
+الفرار اختماش
+
+430
+00:54:00,260 --> 00:54:05,820
+بقى انت في كل قلصي تشتغل في ال plane وانا في
+
+431
+00:54:05,820 --> 00:54:10,470
+الفرارمن يوم بمدينة في الفرق صحيح و لا لا كل شغل
+
+432
+00:54:10,470 --> 00:54:14,330
+في الفرق إذا بدك تفضي دائما و بدك عندك ثلاثة
+
+433
+00:54:14,330 --> 00:54:22,570
+متغيرات واحد بقى يبدو سلوك عشان؟ ايو ايو اللي ورا؟
+
+434
+00:54:22,570 --> 00:54:25,890
+اللي ورا اه اللي وزد تساوي تسعة ناقص واحد ثالث
+
+435
+00:54:25,890 --> 00:54:30,350
+ناقص، ازاي؟ حالك محور ال .. محور او الموازي له
+
+436
+00:54:30,350 --> 00:54:32,970
+تتنقطع ناقص
+
+437
+00:54:42,720 --> 00:54:49,400
+طبعا ناقص الرمزي المربعات هى ده رمز مربع هذا لأ
+
+438
+00:54:49,400 --> 00:54:55,960
+أنا لو شيلت التسعة والسالفشة زدت شوية واحدة زيها
+
+439
+00:54:56,660 --> 00:55:01,680
+يبقى parabola، بس إيش صار؟ حطيته إشارة سالم، يبقى
+
+440
+00:55:01,680 --> 00:55:05,340
+إن كان مرسوم الناحية، هاد بيصير الناحية العكسية،
+
+441
+00:55:05,340 --> 00:55:09,200
+مش هكذا إزاي التسعة بيتمليله shift، مظبوط؟ هذا مش
+
+442
+00:55:09,200 --> 00:55:13,760
+السؤال اللي جابله، بيعمله shift، إذا تعالى نشوف
+
+443
+00:55:13,760 --> 00:55:15,420
+الشكل كيف بيكون
+
+444
+00:55:27,980 --> 00:55:35,380
+تعالوا نفكر كيف بالرسالة أنا عندي مين؟ Z وY، صح؟
+
+445
+00:55:35,380 --> 00:55:42,860
+ايه؟ وين Z وY؟ هذا عندي Z وY، كويس؟ مداب هذا عندي
+
+446
+00:55:42,860 --> 00:55:49,900
+Z وY يبقى المحور هو بيكون X أو موازن له، بس ال Y
+
+447
+00:55:49,900 --> 00:55:58,350
+بمدى السوقات، اه يعني يا بنات لو كان هذاتساوي Y
+
+448
+00:55:58,350 --> 00:56:04,430
+تربية بده ينقلب و يسير لوين؟ لأسفل يبقى بده يسير
+
+449
+00:56:04,430 --> 00:56:09,190
+عن هناك مظبوط؟
+
+450
+00:56:09,190 --> 00:56:14,050
+و بعد هيك shift لوين؟ لأعلى بمقدار تسعة يبدو أمشي
+
+451
+00:56:14,050 --> 00:56:19,950
+كرسم هذه و أعملي لإزاحة لفوق بمقدار تسعة يبقى
+
+452
+00:56:29,310 --> 00:56:34,210
+موازي لمحور اكس بعد ما رسمنا هذا الموازي بدي اعمل
+
+453
+00:56:34,210 --> 00:56:39,350
+main ال shift اللي عندنا هذا يبقى هذه النقطة اللي
+
+454
+00:56:39,350 --> 00:56:47,510
+هي Zero و Zero و تسعة و بتروح ارسم هذه الفرابولة
+
+455
+00:56:47,510 --> 00:56:52,170
+يبقى هذا لو جيت ماده على استقباله يجب ان يقابلني
+
+456
+00:56:52,170 --> 00:56:55,530
+هنا يبقى انا عندي فرابولة
+
+457
+00:57:01,650 --> 00:57:09,910
+طيب يبقى هذه النقطة اللي فوق بدها تكون حفة ال
+
+458
+00:57:09,910 --> 00:57:15,550
+parabola بمعنى هاي الرسم زي هيك انا عملت نقطة اذا
+
+459
+00:57:15,550 --> 00:57:21,410
+هذا الخط بيمر بالنقطة موازي لمين؟ للمحور اللي
+
+460
+00:57:21,410 --> 00:57:28,210
+عندنا معناته في عندي خط بيظل موازي لمحور X
+
+461
+00:57:31,390 --> 00:57:35,930
+وهذا بيكون كل البرابلات مصفتات جانب بعض بحيث
+
+462
+00:57:35,930 --> 00:57:40,030
+البرتقال تبقى عليه بالشكل اللي قدامك هنا يبقى ايش
+
+463
+00:57:40,030 --> 00:57:45,170
+بديجيكي؟ بديجيكي هنا كمان هه بالشكل اللي عندنا،
+
+464
+00:57:45,170 --> 00:57:52,790
+برابلة تانية، هك، وهذه بيجي هنا، هم هاي برابلة،
+
+465
+00:57:52,790 --> 00:57:57,530
+ومن هنا بيجيكي كمان هنا، كمان برابلة بالشكل اللي
+
+466
+00:57:57,530 --> 00:58:02,550
+عندك، وهذا بالشكل اللي عندكيبقى إيش اللي حصل؟
+
+467
+00:58:02,550 --> 00:58:08,250
+كأنها فرابولة بالشكل هيك وقلبناها على الأرض بهذا
+
+468
+00:58:08,250 --> 00:58:13,670
+الشكل واضحة؟ السبب اللي خلانا أقلبناه هو ال shift
+
+469
+00:58:13,670 --> 00:58:16,870
+تبعها واللي خلاناها بالشكل اللي عندنا
+
+470
+00:58:20,640 --> 00:58:26,320
+أه واضحة؟ دي لبالك هذه مش نقطة تقاطة، هذا نبعدها
+
+471
+00:58:26,320 --> 00:58:30,080
+مع بعض شوية، مالاشي تقولي هذه المرة مالاشي علاقة
+
+472
+00:58:30,080 --> 00:58:35,000
+بالموضوع. يبقى هذا القرابل جاية بالشكل اللي عندها.
+
+473
+00:58:39,740 --> 00:58:48,860
+وهذا شناب المرة مالوش نزوله. يبقى يا بنات تاني مرة
+
+474
+00:58:48,860 --> 00:58:54,050
+بدي أحكي.أحنا عندنا z تسوى تسعة ناقص واي ترهيب
+
+475
+00:58:54,050 --> 00:58:58,830
+بعتبر لا عندي تسعة ولا عندي ساعة يبقى z تسوى مائة
+
+476
+00:58:58,830 --> 00:59:05,370
+إذا نرسم حوالين محور z تمام؟ حوالين محور z هي محور
+
+477
+00:59:05,370 --> 00:59:10,380
+z يبقى هيك بدأت تبقى ال parameterلكن الواي تربيها
+
+478
+00:59:10,380 --> 00:59:15,720
+السابقة بإشارة من ثاني الإعضارات في سلب الرسم بجلب
+
+479
+00:59:15,720 --> 00:59:20,860
+لتحت فوق و لفوق تحت يبقى بدل من الرسم أكلت كلها
+
+480
+00:59:20,860 --> 00:59:27,000
+فوق جلبناها و صارت وين تحت و بالمنحنة كله أضفتله
+
+481
+00:59:27,000 --> 00:59:32,300
+تسعة بلغة ال shift بدك تعمل إزاحة إلى أعلى بمقدار
+
+482
+00:59:32,300 --> 00:59:34,860
+تسعة مسكنها ال parabola
+
+483
+00:59:38,660 --> 00:59:44,360
+بطل أزرق اللي عندنا تمام؟ يبقى هذا القرابل اللي
+
+484
+00:59:44,360 --> 00:59:49,880
+عندنا طيب كويس معناته في عندك قرابل كلهم موازية
+
+485
+00:59:49,880 --> 00:59:55,080
+بعض بيكونوا بين بيكونوا هذا المجسم إذا مش واضح
+
+486
+00:59:55,080 --> 01:00:03,680
+كثير بزوجلك هذه لقدام شوية هذه هيك هو بطول الرسمة
+
+487
+01:00:03,680 --> 01:00:04,220
+بيجي
+
+488
+01:00:16,830 --> 01:00:23,870
+بنجي هنا بيكون هيك و هنا بتيجي هيك، أمامك؟ تبقى
+
+489
+01:00:23,870 --> 01:00:28,450
+سارة الرسمة بالشكل اللي عندنا هنا تبقى هذا كوال
+
+490
+01:00:28,450 --> 01:00:34,270
+لمين؟ كوال اللي هو السطح الأوسط واني اللي بيكون
+
+491
+01:00:34,270 --> 01:00:40,590
+بهذا الشكل تماما كأنه على الأرض هيك و هذا حظاني،
+
+492
+01:00:40,590 --> 01:00:48,920
+خلاص؟ طيبهذا من الأشكال اللي هو .. يعني راسمتها
+
+493
+01:00:48,920 --> 01:00:53,280
+برضه جادرين عليها زي ولا تشبيه زي السير السرير
+
+494
+01:00:53,280 --> 01:00:59,260
+الولد الصغير بس مقلبية على وجهه وهذا أبدا السرير
+
+495
+01:00:59,260 --> 01:01:04,670
+بس على جانبه واقف تماما بالضبططيب ندى بالرسم اللى
+
+496
+01:01:04,670 --> 01:01:09,210
+بعدها اللى بعدها بيقولى Y تربيه على أربعة ناقص X
+
+497
+01:01:09,210 --> 01:01:14,470
+تربيه على تسعة بده يساوى لو في ال plane هذه معادلة
+
+498
+01:01:14,470 --> 01:01:20,030
+ايه؟ هاي فرابولة تمام يبقى رسمتنا هذه بدنا نرسمها
+
+499
+01:01:20,030 --> 01:01:27,670
+بحيث تكون هاي فرابولة متوازية او ان شتوا فقولوا
+
+500
+01:01:27,670 --> 01:01:29,530
+فرابولة على اليمين
+
+501
+01:01:37,050 --> 01:01:42,930
+الثاني يالاأخر معادلة عندنا من المعادلات هي y
+
+502
+01:01:42,930 --> 01:01:46,930
+تربيه على أربعة نقص x تربيه على تسعة بده يساوي
+
+503
+01:01:46,930 --> 01:01:50,510
+الواحدة بتطلع على الرمز الغابي الرمز الغابي اللي
+
+504
+01:01:50,510 --> 01:01:57,130
+همين z يبقى ال axis بده يكون محور z أو محور موازن
+
+505
+01:01:57,130 --> 01:02:02,170
+لأ هدف ال plane عبارة علشان عبارة عن hyperbola إذا
+
+506
+01:02:02,170 --> 01:02:07,090
+بدنا نروح نرسم ال hyperbola كأنها في أحد ال planes
+
+507
+01:02:07,090 --> 01:02:08,610
+يبقى لو جيت
+
+508
+01:02:11,690 --> 01:02:16,810
+اللي هي الـ Hyperabula الأول يبقى بدأ تظهر واحدة
+
+509
+01:02:16,810 --> 01:02:24,210
+زيها من الناحية التانية بالشكل اللي عندها تمام؟ هي
+
+510
+01:02:24,210 --> 01:02:32,590
+اللي بدأ تيجي موازية لها كمان بهذا الشكل ومن
+
+511
+01:02:32,590 --> 01:02:37,270
+الناحية التانية زيها لو مدينا محور X على استقلال
+
+512
+01:02:51,480 --> 01:02:59,500
+بنقرب الشكل اللي عندها وبنقرب الشكل اللي عندها
+
+513
+01:02:59,500 --> 01:03:01,340
+وبنقرب الشكل اللي عندها وبنقرب الشكل اللي عندها
+
+514
+01:03:01,340 --> 01:03:01,960
+وبنقرب الشكل اللي عندها وبنقرب الشكل اللي عندها
+
+515
+01:03:01,960 --> 01:03:02,000
+وبنقرب الشكل اللي عندها وبنقرب الشكل اللي عندها
+
+516
+01:03:02,000 --> 01:03:02,020
+وبنقرب الشكل اللي عندها وبنقرب الشكل اللي عندها
+
+517
+01:03:02,020 --> 01:03:02,060
+وبنقرب الشكل اللي عندها وبنقرب الشكل اللي عندها
+
+518
+01:03:02,060 --> 01:03:02,080
+وبنقرب الشكل اللي عندها وبنقرب الشكل اللي عندها
+
+519
+01:03:02,080 --> 01:03:03,280
+وبنقرب الشكل اللي عندها وبنقرب الشكل اللي عندها
+
+520
+01:03:03,280 --> 01:03:07,180
+وبنقرب الشكل اللي
+
+521
+01:03:07,180 --> 01:03:13,460
+عندها وبنقرب الشكل
+
+522
+01:03:13,460 --> 01:03:14,880
+اللي عندها عندها وبن
+
+523
+01:03:38,710 --> 01:03:48,170
+هذا مفتوح جهة اليمن هذا مفتوح جهة الشمال
+
+524
+01:04:39,070 --> 01:04:46,750
+يفجي هذه الـ cylinder كأنها .. كأنها اللي هو تجيوب
+
+525
+01:04:46,750 --> 01:04:51,410
+بهذا الشكل و تجيوب تاني زيه بهذا الشكل و اتنين
+
+526
+01:04:51,410 --> 01:04:56,030
+زعلانين مع بعض، كل واحد موجه على شجرةتمام؟ يبقى
+
+527
+01:04:56,030 --> 01:05:00,610
+اتنين مع بعض كقطع واحدة بقوله ايه هذا هو ال
+
+528
+01:05:00,610 --> 01:05:05,130
+cylinder اللي عندنا يبقى cylinder السؤال الأول كان
+
+529
+01:05:05,130 --> 01:05:10,210
+على شكل أسطوانة و المقطع تبعها ellipse التاني
+
+530
+01:05:10,210 --> 01:05:13,670
+أسطوانة و المقطع تبعها Parabola التالتة المقطع
+
+531
+01:05:13,670 --> 01:05:18,550
+تبعها Parabola الرابعة المقطع تبعها Iparabola و
+
+532
+01:05:18,550 --> 01:05:25,640
+هكذاإذا انتمنوا أبدًا بننظر لمن؟ للعنصر الغاية نجي
+
+533
+01:05:25,640 --> 01:05:31,880
+للنقطة الثانية بالأسفل الـ Quadrics الاسفل السطوح
+
+534
+01:05:31,880 --> 01:05:39,800
+أثناء نمسح هذا خلاص؟ خلاص؟ طيب نجي للنقطة الثانية
+
+535
+01:05:39,800 --> 01:05:43,080
+في هذا ال section اللي هو ال Quadrics
+
+536
+01:05:51,840 --> 01:05:58,180
+جا ستة من هذه السطوح الأوسطوانية أول واحد منهم
+
+537
+01:05:58,180 --> 01:06:05,880
+بيسميه ال ellipsoid يفجأ لمرة اتنين اللي هي
+
+538
+01:06:05,880 --> 01:06:12,620
+quadric ستة أول
+
+539
+01:06:12,620 --> 01:06:17,920
+واحد منهم بيسميه ال ellipsoid
+
+540
+01:06:26,030 --> 01:06:28,750
+المجسم الناقص بالعرب
+
+541
+01:06:54,260 --> 01:06:58,500
+بنحاول نرسم هذا المجسم.
+
+542
+01:07:06,260 --> 01:07:17,280
+هذا محور X، هذا محور Y، وهذا محور اللي هو Z.
+
+543
+01:07:31,880 --> 01:07:37,680
+لما أقول ellipsoid جاء من كلمة ellipse ellipse قطع
+
+544
+01:07:37,680 --> 01:07:43,400
+ناقص يبقى المقطع دائما و أبدا هو عبارة عن قطع ناقص
+
+545
+01:07:43,400 --> 01:07:48,700
+كيف القطع الناقص كله نقص مافيه كله خلاص دي الشكل
+
+546
+01:07:48,700 --> 01:07:52,420
+اللي عندنا على الشكل هيك
+
+547
+01:07:55,700 --> 01:08:00,900
+هذا اللي هو كان الـ Ellipse اللي عندنا تبعه كان
+
+548
+01:08:00,900 --> 01:08:06,100
+الـForce بيه طبعا النظر
+
+549
+01:08:09,440 --> 01:08:14,700
+مش هيقوللي هذا نفسه بسقط لكن مشان اميزه بدي اروح
+
+550
+01:08:14,700 --> 01:08:22,260
+ارسم مقطعه مع المستوى XZ هذا هذا مقطعه مع المستوى
+
+551
+01:08:22,260 --> 01:08:28,960
+YZ مقطعه مع المستوى XZ هروح ارسمه بهذا الشكل هذا
+
+552
+01:08:28,960 --> 01:08:35,240
+مظهر لي من جهتنا بيقول انا هذا مظهر ليش هرسمه
+
+553
+01:08:35,240 --> 01:08:43,250
+منقطع بهذا الشكليوصف الشكل ان هذا مجسم واضح ان هذا
+
+554
+01:08:43,250 --> 01:08:46,810
+عبارة عن مجسم مش عاجزاكوا بس
+
+555
+01:08:50,510 --> 01:08:57,770
+بهذا الشكل فهذا يجينا كمان هكذا خلّيني أقول في
+
+556
+01:08:57,770 --> 01:09:05,470
+الأصل يبقى واضح الأن أن هذا مجسم طيب الآن ليش
+
+557
+01:09:05,470 --> 01:09:11,470
+سمينا ellipsoid هذا السؤال ellipsoid جاء من كلمة
+
+558
+01:09:11,470 --> 01:09:17,430
+syllables الإجابة لأن مقع مع كل مستوى من مستويات
+
+559
+01:09:17,430 --> 01:09:21,760
+الأفتراضياتهو عبارة عن ايش؟ هو عبارة عن التلفزيون.
+
+560
+01:09:22,120 --> 01:09:26,720
+أنا أقول ان إيه يا بنات؟ كيف يعني نعم؟ الأن لو
+
+561
+01:09:26,720 --> 01:09:30,840
+بفاجأي أخد مقطعه مع المستوى هو يزيد يا بنات
+
+562
+01:09:44,410 --> 01:09:53,830
+الخط الأسود الخارجي يبقى هذا ما هو المقطع تبعه مع
+
+563
+01:09:53,830 --> 01:09:58,470
+المستوى اللي احنا بناه يبقى الخط الأسود هذا اللي
+
+564
+01:09:58,470 --> 01:10:04,650
+هو Y تربيع على B تربيع زي Z تربيع على C تربيع
+
+565
+01:10:04,650 --> 01:10:05,650
+يساوي واحد
+
+566
+01:10:08,490 --> 01:10:15,290
+يبقى هذا تقطع مع المستوى YZ يبقى تقطع مع المستوى
+
+567
+01:10:15,290 --> 01:10:21,450
+XZ XZ يبقى Y فقدراش Zero يبقى لما أشيل Y ب Zero
+
+568
+01:10:21,450 --> 01:10:24,930
+مضالعش عندنا Ellipse اللي هو مين ال Ellipse اللي
+
+569
+01:10:24,930 --> 01:10:28,030
+عندنا هي هكتبه لك اللي هو
+
+570
+01:10:36,690 --> 01:10:44,220
+على C تربية يساوي يدها يساوي واحد صحيايبقى الأزرق
+
+571
+01:10:44,220 --> 01:10:50,880
+يا بنات هذا في مستوى XZ رأسي الأسود في مستوى YZ
+
+572
+01:10:50,880 --> 01:10:58,180
+طبعا هنسأل السؤال التالي و أين المستوى XY؟ نقول له
+
+573
+01:10:58,180 --> 01:11:04,480
+Z تساوي Zero اللي هو الـEllipse الأزرق هذا تمام؟
+
+574
+01:11:04,480 --> 01:11:09,340
+يبقى الأزرق هذا الـEllipse هذا معادلته
+
+575
+01:11:14,570 --> 01:11:20,830
+Y تربيع على V تربيعي تساوي جداش واحد اذا كل مقطع
+
+576
+01:11:20,830 --> 01:11:25,290
+من هذه المقطع عبارة عن ellipse ومن هنا سمنا
+
+577
+01:11:25,290 --> 01:11:31,510
+ellipsoid تيجي واحدة تقول طب لو جت قطعته من فوق
+
+578
+01:11:31,510 --> 01:11:37,430
+وانا من تحت، شوية، مظبوط؟ اللي جابت بيصير Z تساوي
+
+579
+01:11:37,430 --> 01:11:43,200
+Z نور، يعني رقمهل المطبع في هذه الحلقة كمان
+
+580
+01:11:43,200 --> 01:11:48,260
+ellipse؟ رابعا ellipse طب كيف نجيب هذا اللي هو؟
+
+581
+01:11:48,260 --> 01:11:54,780
+اقولك بسيطة لو كان الذد يساوي C note فوق او C note
+
+582
+01:11:54,780 --> 01:11:58,770
+تحت سواء كان فوق او تحت سيها ماتفرقش عامةلأن عند
+
+583
+01:11:58,770 --> 01:12:04,270
+مربعه بيصير قيمة يعيش موجبة يبقى Z تساوي absolute
+
+584
+01:12:04,270 --> 01:12:10,610
+value ل C0 بيكون أعلى ال XY plane أو أسفل ال XY
+
+585
+01:12:10,610 --> 01:12:15,910
+plane إذا لو جيت قطعته بالمقطع اللي عندنا هذا هيك
+
+586
+01:12:15,910 --> 01:12:21,590
+مش هيظهر وهذا بيظهر الشكل اللي عندنا هذا يبقى هذا
+
+587
+01:12:21,590 --> 01:12:25,690
+المستوى اللي هو Z يساوي Z0
+
+588
+01:12:33,920 --> 01:12:42,360
+ز يسوى z نوت the question is اللي هو مين x تربيع
+
+589
+01:12:42,360 --> 01:12:49,640
+على a تربيع y تربيع على b تربيع بدي يسوى واحد نقل
+
+590
+01:12:49,640 --> 01:12:58,340
+z نوت تربيع على z تربيع طبعا لو قسمت الطرفين عليهم
+
+591
+01:12:58,340 --> 01:13:02,480
+مش هذا رقم لو قسمت عليه مش مصير معادلة ايه
+
+592
+01:13:12,150 --> 01:13:18,910
+على C تربيع زائد Y تربيع على B تربيع واحد ناقص Z
+
+593
+01:13:18,910 --> 01:13:24,850
+نوت تربيع على C تربيع كله يسوى واحد وهذا كمان ال
+
+594
+01:13:24,850 --> 01:13:30,710
+mainly اللي هو ال Alex يتجول مثلا طيب اتجه لمفتاح
+
+595
+01:13:30,710 --> 01:13:37,440
+ايش Alex طيبهذه ملاحظة ملاحظة ثانية السؤال هو هل
+
+596
+01:13:37,440 --> 01:13:44,000
+المجسم يا بنات متمثل بالنسبة لمستويات الأحداثيات
+
+597
+01:13:44,000 --> 01:13:49,180
+يعني نشوف يعني لو جيت لمستوى ال XY اللي قطعه في
+
+598
+01:13:49,180 --> 01:13:53,520
+المقطع الأزرق هل النص اللي فوق و نص اللي تا اه
+
+599
+01:13:53,520 --> 01:13:55,860
+صحيح لإن النقطة اللي فوق
+
+600
+01:14:06,420 --> 01:14:08,420
+هذه النقطة
+
+601
+01:14:16,210 --> 01:14:22,470
+وP و Zero إذا المجسم هذا متماثل بالنسبة لإيه
+
+602
+01:14:22,470 --> 01:14:26,670
+المستويات الأحداثية يعني يعني المستوى الأحداثية
+
+603
+01:14:26,670 --> 01:14:32,610
+لما أجيبه من فوق لتحت بقصه نصين زي بعض تماما، لو
+
+604
+01:14:32,610 --> 01:14:38,450
+أفقي نصين زي بعض، لو المستوى التالت بقسمه كمان إلى
+
+605
+01:14:38,450 --> 01:14:43,670
+نصين ونصين الاتنين زي بعض تماما، يبقى ما أقدر أقول
+
+606
+01:14:43,920 --> 01:14:49,320
+الغرافية متساومة مع الـ coordinate planes يبقى
+
+607
+01:14:49,320 --> 01:14:55,320
+باجي بقول هنا الغرافية
+
+608
+01:14:55,320 --> 01:14:59,020
+لجانب
+
+609
+01:14:59,020 --> 01:15:05,780
+الكلب متساومة
+
+610
+01:15:05,780 --> 01:15:06,300
+حوالي
+
+611
+01:15:16,830 --> 01:15:20,690
+in place طب
+
+612
+01:15:20,690 --> 01:15:27,810
+كويس إذا جبنا كل مقطع وكل معادلة ايه؟ اه اجت واحدة
+
+613
+01:15:27,810 --> 01:15:32,730
+من البنات قالت قبلتها ليش عملت الاستقالة تلعطى فوق
+
+614
+01:15:32,730 --> 01:15:36,890
+و تحت؟ ليش فالبنات مش عارفة احوان واي والله عارفة
+
+615
+01:15:36,890 --> 01:15:43,590
+وعكس مش هذا تساؤلنقول لك مشان تحكمي هل استطالة في
+
+616
+01:15:43,590 --> 01:15:49,370
+اتجاه محور X وY بتطلع الى اكبر رقم في المقام بيكون
+
+617
+01:15:49,370 --> 01:15:55,230
+المتغير اللي فوقه هو اكبر محور اذا احنا رسمنا هذه
+
+618
+01:15:55,230 --> 01:16:00,410
+الرسمة على اساس انه فيه اكبر من مين؟ من ايه؟
+
+619
+01:16:10,260 --> 01:16:16,840
+لو كدت بيه هي اللي أكبر، بدى يصير هذا الاستطالة في
+
+620
+01:16:16,840 --> 01:16:23,190
+اتجاه نحو الواقعطب لو كان ال A هي الأكبر بده يصير
+
+621
+01:16:23,190 --> 01:16:29,250
+الاستثالة في اتجاه محور S إذا لما يعطيكي معادلة
+
+622
+01:16:29,250 --> 01:16:35,370
+عددية من خلال أسئلة التمرين و بدك ترسميها أو يقولك
+
+623
+01:16:35,370 --> 01:16:38,950
+شوفي اللي الرسم يعطيك شوية رسمات لما ضمن التمرين
+
+624
+01:16:38,950 --> 01:16:42,930
+بجي اتناشر رسمة و حطت اتناشر معادلة و قالك بس
+
+625
+01:16:42,930 --> 01:16:46,910
+واصليه من المعادلة الرسمة يعني قول المعادلة هذه من
+
+626
+01:16:46,910 --> 01:16:51,950
+الرسمة هذهإذا بقى مرة خلّيلك يا رأسي و مرة وفقي و
+
+627
+01:16:51,950 --> 01:16:56,750
+مرة كذا إلى آخرين يبقى بطل على مين يا بنات؟ لرقم
+
+628
+01:16:56,750 --> 01:17:02,410
+المقام صاحب المقام الرفيع يكون هو من؟ هو الاستطالة
+
+629
+01:17:02,410 --> 01:17:07,710
+في التجارة و ارهاد؟ تمام؟ طيب لحد هنا stop انتهينا
+
+630
+01:17:07,710 --> 01:17:12,710
+من نمرة واحد الكلب صيد بدنا نيجي لنمرة اتنين
+
+631
+01:17:31,200 --> 01:17:38,360
+المعادلة تبت على شكل X تربيع على A تربيع زائد Y
+
+632
+01:17:38,360 --> 01:17:46,480
+تربيع على Z تربيع زائد Y تربيع على B تربيع
+
+633
+01:18:12,510 --> 01:18:15,010
+كلمة elliptic جاء من أين؟
+
+634
+01:18:31,850 --> 01:18:36,690
+طيب لو جيت راسنتو هذا يبقى ده ياخد الشكل التالي
+
+635
+01:18:36,690 --> 01:18:38,310
+الشكل اللي عندها
+
+636
+01:18:58,410 --> 01:19:07,610
+شكل ديكي بس كمان مش هنوضحه أكتر يكون هيك
+
+637
+01:19:07,610 --> 01:19:18,710
+هذا الشكل كمان كم مقطع عندي في الرسم هنا تقريبا
+
+638
+01:19:18,710 --> 01:19:23,690
+انا اتنتينالزرجة والسودا، الزرجة والسودا، يبقى في
+
+639
+01:19:23,690 --> 01:19:27,790
+عندي two parabolas وفي كمان عندي ماين الاسم، بتعرف
+
+640
+01:19:27,790 --> 01:19:31,510
+مين كل واحدة من هدول، يبقى يا بنات ال elliptic
+
+641
+01:19:31,510 --> 01:19:35,890
+paraboloids زي الخوذة تبعت الجندر أو زي ما تقص نص
+
+642
+01:19:35,890 --> 01:19:40,170
+بطيخة وتجوريها، يبقى هذا الاسم اياش elliptic
+
+643
+01:19:40,170 --> 01:19:47,430
+paraboloidطيب بالضغط الأن أشوف المقطع تبع المجسم
+
+644
+01:19:47,430 --> 01:19:52,830
+اللي عندنا هذا مع ال YZ Plane مع ال YZ Plane يعني
+
+645
+01:19:52,830 --> 01:19:57,430
+X بجداش Zero يبقى ال X ب Zero بتطير ال term اللي
+
+646
+01:19:57,430 --> 01:20:01,930
+عندنا هذا يبقى هذا إيش بيصير؟ بيصير المعادلة اللي
+
+647
+01:20:01,930 --> 01:20:02,370
+عندنا
+
+648
+01:20:15,920 --> 01:20:22,120
+ممتاز جدا يبقى القرابل السوداء هذه أبدا خطة
+
+649
+01:20:25,730 --> 01:20:34,890
+هو Y تربيع على B تربيع بيكون Z على C وهذه ترابولة
+
+650
+01:20:34,890 --> 01:20:43,690
+تمام هاي لو جيت للزرق هذا لو حطيت ال Y ب Zero ال Y
+
+651
+01:20:43,690 --> 01:20:47,050
+ب Zero بصير X تربيع على A تربيع بيكون Z على A
+
+652
+01:20:59,560 --> 01:21:05,120
+يزد على C. يبقى هذه معادلة Parabola. لكن يا بنات
+
+653
+01:21:05,120 --> 01:21:11,760
+اللي فوق المقطع هذا لو كانت إحداث النقطة هذه هي
+
+654
+01:21:11,760 --> 01:21:21,160
+مثلا Z نوت و Zero و Zero. إذن تقصير المعادلة اللي
+
+655
+01:21:21,160 --> 01:21:23,340
+عندنا دقيقة اللي هي
+
+656
+01:21:29,720 --> 01:21:36,760
+زيت نودة على C لو جسمت عليها تمام ايش بيعطيني هذا
+
+657
+01:21:36,760 --> 01:21:48,030
+بيصير عندي X تربيع على A تربيعZ node على C زائد Y
+
+658
+01:21:48,030 --> 01:21:53,630
+تربية B تربية Z node على C كله يسوى واحد صحيح يبقى
+
+659
+01:21:53,630 --> 01:21:58,910
+مين هذا ال ellipse يبقى هذا يتفق مع الكلام اللي
+
+660
+01:21:58,910 --> 01:22:03,690
+قلناه قبل قليل من الاسم اللي هو ال ellipse
+
+661
+01:22:03,690 --> 01:22:08,950
+Parabola يبقى أحد المقاطع اللي وفقه عبارة عن ال
+
+662
+01:22:08,950 --> 01:22:14,320
+ellipse والبجيات الأثنينهم عبارة عن مين؟ عن قراه
+
+663
+01:22:14,320 --> 01:22:20,900
+لازم طيب فى عندى سؤالين بدى أسألهم هسألهم يجيبوا
+
+664
+01:22:20,900 --> 01:22:23,520
+على سؤالهم بدون ما تسألوا انا سأقرا عليهم السؤال
+
+665
+01:22:23,520 --> 01:22:31,200
+زت نود و Zero و Zero Zero Zero Zero Zero Zero Zero
+
+666
+01:22:31,200 --> 01:22:34,780
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+667
+01:22:34,780 --> 01:22:37,480
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+668
+01:22:37,480 --> 01:22:37,520
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+669
+01:22:37,520 --> 01:22:37,540
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+670
+01:22:37,540 --> 01:22:37,580
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+671
+01:22:37,580 --> 01:22:37,680
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+672
+01:22:37,680 --> 01:22:43,030
+Zero Zeroنرجع لكمال اللي احنا بنقوله وبنقول بدنا
+
+673
+01:22:43,030 --> 01:22:50,290
+نسأل سؤالين السؤال الأول لو بديش لك رسمي للمعادلة
+
+674
+01:22:50,290 --> 01:22:55,990
+X تربية علي A تربية زي Y تربية علي B تربية تساوي Z
+
+675
+01:22:55,990 --> 01:23:04,470
+سالب Z علي C بدنا نقله ونخليه أسفل يعني بدنا نصير
+
+676
+01:23:04,470 --> 01:23:05,470
+بالشكل هذا
+
+677
+01:23:08,750 --> 01:23:17,350
+هذا X وهذا Y وهذا Z يصبح هذا R شكل
+
+678
+01:23:17,350 --> 01:23:24,110
+يعني تمام؟ هذا لو كانت ايش؟ لو كان X تربيع علي A
+
+679
+01:23:24,110 --> 01:23:29,730
+تربيع زاد Y تربيع علي B تربيع يسوي سالب Z على C
+
+680
+01:23:29,730 --> 01:23:33,790
+يبقى بنجلب الرسمة في هذه الحالة وتصبح
+
+681
+01:23:37,050 --> 01:23:44,330
+سؤال الثاني هل المجسم متمثل بالنسبة لمستويات
+
+682
+01:23:44,330 --> 01:23:50,870
+الأحداثية؟ لأ طبعا ليش؟ لأنه تحت ال X Y Plane
+
+683
+01:23:50,870 --> 01:23:57,090
+ماعنديش كل الرسم أعلى ال X Y Plane تمام؟ لكن لو جت
+
+684
+01:23:57,090 --> 01:24:08,110
+كنت بالمستوى YZ المجسم متمثلYZ و XZ متماثل لكن
+
+685
+01:24:08,110 --> 01:24:12,810
+المستوي XY يبعد الله يبقى هذا متماثل بالنسبة
+
+686
+01:24:12,810 --> 01:24:19,790
+لمستويين من مستويات الإعداد فقط لغير وليس متساوية
+
+687
+01:24:19,790 --> 01:24:29,370
+من وسلمين للتالت طيبالان لو جيت قلت لك اين ال X Y
+
+688
+01:24:29,370 --> 01:24:34,870
+Plane بتبقى Z بقدر ايه؟ اه ال X Y Plane بتبقى Z
+
+689
+01:24:34,870 --> 01:24:39,290
+بقدر ايه؟ Zero إذا لو حطيت Z ب Zero ايش بصيها؟ X
+
+690
+01:24:39,290 --> 01:24:41,690
+تربيه على A تربيه على Z و لا تربيه على B تربيه على
+
+691
+01:24:41,690 --> 01:24:48,830
+C يساوي الصفر هل يؤقل ان مجموعة كميتين مربعتين
+
+692
+01:24:48,830 --> 01:24:50,210
+يساوي الصفر؟
+
+693
+01:24:53,180 --> 01:24:58,660
+معقول ليش مش معقول بس مرة واحدة في الدنيا لو كان
+
+694
+01:24:58,660 --> 01:25:04,660
+ال X بزيرو و ال Y بزيرو فما الهي مين؟ نقطة الأصل
+
+695
+01:25:04,660 --> 01:25:09,120
+فانا عندي زد بزيرو صح؟ و وجدت كمان X تربية ال X
+
+696
+01:25:09,120 --> 01:25:12,780
+بزيرو و ال Y بزيرو إذا مستيقظ النقطة الأصل إذا ال
+
+697
+01:25:12,780 --> 01:25:19,100
+plane في ال مجسم في هذه الحالة يمث ال X Y plane في
+
+698
+01:25:19,100 --> 01:25:24,720
+النقطة 00000 نقطة الأصلواضح؟ يبقى الـ elliptic
+
+699
+01:25:24,720 --> 01:25:39,340
+paraboloid الواضح
+
+700
+01:25:39,340 --> 01:25:46,180
+الشغل أظن طيب هذا بالنسبة لمين؟ لمجسم التاني
+
+701
+01:25:50,060 --> 01:25:53,120
+المجسم التالت يا بنات اللي هو الـ Elliptic cone
+
+702
+01:25:53,120 --> 01:26:06,520
+اللي هو
+
+703
+01:26:06,520 --> 01:26:12,500
+المخروض اللي المقطع تبعه عبارة عن ellipse المعادلة
+
+704
+01:26:12,500 --> 01:26:18,840
+تبعته X تربيع على A تربيع زائد Y تربيع على B تربيع
+
+705
+01:26:27,910 --> 01:26:30,950
+جاب المبدأ في الـ elliptic cone اللي خاطر أسأل
+
+706
+01:26:30,950 --> 01:26:36,650
+كمان سؤال على الـ elliptic paraboloid هذا، تمام؟
+
+707
+01:26:36,650 --> 01:26:40,250
+لو كانت المعادلة على الشكل التالي، فدبركوا كويس
+
+708
+01:26:40,690 --> 01:26:46,950
+انتوا ملاحظين ان الرسم المحور تبعها مين؟ Z XY زي
+
+709
+01:26:46,950 --> 01:26:52,150
+زي
+
+710
+01:26:52,150 --> 01:26:56,590
+زي زي زي زي زي زي زي زي زي زي زي زي زي زي زي زي
+
+711
+01:27:05,600 --> 01:27:10,940
+يبقى المحور تبع مين هو يبقى الرمز اللي ما هو مش
+
+712
+01:27:10,940 --> 01:27:15,860
+مربع في ال elliptic paraboloid بيكون هو مين هو
+
+713
+01:27:15,860 --> 01:27:21,880
+المحور تبع مين تبع المجسم دي ملاحظة لكن من قصة ال
+
+714
+01:27:21,880 --> 01:27:25,600
+ellipsoid اللي في أول كله زي بعضه ماقدرتش أميّن
+
+715
+01:27:25,600 --> 01:27:31,780
+يبقى هذا بميز من شكل المتغير غير المربعطيب نيجي
+
+716
+01:27:31,780 --> 01:27:37,980
+لمين؟ لل elliptical اللي هو المخروض اللي المقطع
+
+717
+01:27:37,980 --> 01:27:43,580
+تبعه عبارة عن ellipse كيف هذا؟ اقولك اه لو جيتي
+
+718
+01:27:43,580 --> 01:27:44,380
+قولتي ليه؟
+
+719
+01:28:00,150 --> 01:28:09,170
+بشكل عام و بعد
+
+720
+01:28:09,170 --> 01:28:18,790
+هيك جيت طبعا هي محاول الأحداثيات هذا
+
+721
+01:28:18,790 --> 01:28:24,630
+محور X هذا محور Y و هذا محور Z
+
+722
+01:28:32,240 --> 01:28:37,700
+طيب هذه المعادلة اللي عندناها اللي هو معادلة
+
+723
+01:28:37,700 --> 01:28:44,320
+elliptic اللي هو الكون المخروط للمقطع تبعه عبارة
+
+724
+01:28:44,320 --> 01:28:48,540
+عن ellipse ليش كل المخروط تبعه عبارة عن ellipse
+
+725
+01:28:48,540 --> 01:28:53,460
+وما هي المقاطع الأخرى أول شيء خلّيني أطلع على
+
+726
+01:28:53,460 --> 01:28:56,990
+المعادلة و بعدين بنجيب على هذه التساؤلاتطالعي
+
+727
+01:28:56,990 --> 01:29:01,950
+للمعادلة اللي قمنا بتكتبها معادلة صفرية يبقاش بصير
+
+728
+01:29:01,950 --> 01:29:07,630
+هي معادة ال ellipsoid بس بتختلف عنها فيه أمرين بدل
+
+729
+01:29:07,630 --> 01:29:12,550
+الواحد بده zero وهادي بدل الموجة بصير إيه أش سالب
+
+730
+01:29:12,550 --> 01:29:18,230
+ممتاز يبقى لو أطالي تلت كميات مربعة تنتين في شجة و
+
+731
+01:29:18,230 --> 01:29:24,130
+تلتة في شجة تانية إذا هذه معادة المخرج تمام؟هذه مش
+
+732
+01:29:24,130 --> 01:29:28,070
+هانميز بينها وبين المعادلة تفضلي تفضلي تفضلي تفضلي
+
+733
+01:29:28,070 --> 01:29:47,410
+تفضلي تفضلي تفضلي تفضلي تفضلي تفضلي تفضلي
+
+734
+01:29:47,510 --> 01:29:56,810
+الان لو جيت للمجسم اللي عندنا هذا و جيت اخد ال yz
+
+735
+01:29:56,810 --> 01:30:02,890
+plane يعني اكسب جداش؟ Zero يعني لما تكسب Zero تروح
+
+736
+01:30:02,890 --> 01:30:07,750
+بالشكل هذا مع النتيجة دي لو اخدت الجدر الترفيه
+
+737
+01:30:07,750 --> 01:30:14,960
+للطرفينخط مستقيم صح ولا يعني كيلو وزير مين؟ Y تسوى
+
+738
+01:30:14,960 --> 01:30:20,600
+بي على C في زب أو Y تسوى سالب بي على C في زب مظبوط
+
+739
+01:30:20,600 --> 01:30:24,780
+اللي هو الخط المستقيم الأول والثاني هو الخط
+
+740
+01:30:24,780 --> 01:30:33,040
+المستقيم الثاني يرجى يا بنات هذا الخط لحاله اللي
+
+741
+01:30:33,040 --> 01:30:33,980
+هو مين؟
+
+742
+01:30:36,770 --> 01:30:43,230
+اللي هو y تربيع على b تربيع تسوى z تربيع على c
+
+743
+01:30:43,230 --> 01:30:51,390
+تربيع او الشيء اللي تقوله y تسوى b على c في z يبقى
+
+744
+01:30:51,390 --> 01:30:57,270
+هذا الرقم من الناحية التانية يكون y تسوى سالم b
+
+745
+01:30:57,270 --> 01:31:05,120
+على c في zهذا التقاطع مع ال YZ Plane بدي اجيب
+
+746
+01:31:05,120 --> 01:31:10,120
+التقاطع مع ال XZ Plane مع ال R لازم اشيروا
+
+747
+01:31:10,120 --> 01:31:14,640
+مستقيمات اتنين بمان يفجروا اين المستقيمات الاتنين
+
+748
+01:31:14,640 --> 01:31:19,860
+بدي اجيك المستقيم الاول بهذا الشكل من جهتنا هيكون
+
+749
+01:31:19,860 --> 01:31:24,960
+هذا مبين و غالب من الناحية التانية يا بنات مش
+
+750
+01:31:24,960 --> 01:31:28,340
+هيغالب هيكون اللقط بهذا الشكل
+
+751
+01:31:31,530 --> 01:31:37,890
+من الناحية هذه مش هيظهر ومن الناحية التانية هيظهر
+
+752
+01:31:37,890 --> 01:31:43,110
+بالشكل الأخر يبقى الخطين السود الغامقات هو تقاطع
+
+753
+01:31:43,110 --> 01:31:49,490
+ال XZ Plane مع المجسم اللي عندنا طيب في ال XZ
+
+754
+01:31:49,490 --> 01:31:55,350
+Plane يبقى واقف كده؟ P0 معناه هذا الفلاح ان الخط
+
+755
+01:31:55,350 --> 01:31:57,550
+اللي عندى هذا الأسود
+
+756
+01:32:14,660 --> 01:32:27,900
+C في Z بشارة سالف وهنا هد يكون هذا يفتح هذا يبقى X
+
+757
+01:32:27,900 --> 01:32:36,180
+ساوية A على C في من في Z طيب
+
+758
+01:32:36,180 --> 01:32:41,720
+لو حطيت Z تساوي Z نوت يعني رقم
+
+759
+01:32:48,570 --> 01:32:53,970
+النقطة اللي عندها يبقى بدي جيه المقطع مين اللي فوق
+
+760
+01:32:53,970 --> 01:33:00,310
+زد نول يبقى هذا كله بدي يصير رقم لو قسمت عليه يصير
+
+761
+01:33:00,310 --> 01:33:05,510
+عندي ellipse و هذا اللي تحت كمان ايه كمان ellipse
+
+762
+01:33:05,510 --> 01:33:08,330
+زيه وال double تماما يبقى
+
+763
+01:33:16,170 --> 01:33:23,670
+يكون X تربيع على A تربيع زائد Y تربيع على B تربيع
+
+764
+01:33:23,670 --> 01:33:30,510
+بساوي Z نوت تربيع على C تربيع هذا رقم لو قسمت عليه
+
+765
+01:33:30,510 --> 01:33:32,770
+الطرفين بصير عندنا معادلة
+
+766
+01:34:00,970 --> 01:34:08,050
+لو جيت على المعانلة لو حطيت مكانها اللي هو z تساوي
+
+767
+01:34:10,730 --> 01:34:15,910
+مجموع كميتين مربعتين يساوي صفر هذا لا يمكن إلا إذا
+
+768
+01:34:15,910 --> 01:34:20,690
+كان كل واحد منهم صفر يبقى ال X بزير و ال Y بزير و
+
+769
+01:34:20,690 --> 01:34:27,250
+بتقول حصلنا على مين؟ على نقطة الأصل واضح كلامنا؟
+
+770
+01:34:27,250 --> 01:34:36,220
+طيب مين المحور غير هذا؟زد تمام اللي لحالها ممتاز
+
+771
+01:34:36,220 --> 01:34:39,660
+جدا اللي اللي بتبقى لحالها على اليمين بيكون
+
+772
+01:34:39,660 --> 01:34:45,380
+المتغير تبعها هو المحور تبع من تبع المجسم اللي عام
+
+773
+01:35:09,720 --> 01:35:16,160
+في عندي كمان اخر تلت مجسمات هي بالشكل التالي اول
+
+774
+01:35:16,160 --> 01:35:23,140
+واحد اللي هو او ادن بره اربع بسالين هاي ترابولويد
+
+775
+01:35:23,140 --> 01:35:32,780
+هاي ترابولويد هاي ترابولويد of one
+
+776
+01:35:44,770 --> 01:35:48,090
+على V تردية ضعف الزيت تردية
+
+777
+01:36:21,460 --> 01:36:30,640
+زي و لا تشبهت قبله و مضبط تماما و هي اسم و المقطع
+
+778
+01:36:30,640 --> 01:36:41,180
+الثاني هيكون بهذا الشكل و
+
+779
+01:36:41,180 --> 01:36:47,380
+هذا المقطع التالت
+
+780
+01:36:47,380 --> 01:36:50,480
+بهذا الشكل و المقطع التالت
+
+781
+01:36:58,250 --> 01:37:07,930
+يبقى هذا المجسم hyperboloid المجسم المقافق ذو طيّة
+
+782
+01:37:07,930 --> 01:37:12,050
+sheet يعني طيّة تطوي شغل أكمل
+
+783
+01:37:14,010 --> 01:37:18,710
+واضح ان المجسم هذا متماثل بالنسبة لمستويات
+
+784
+01:37:18,710 --> 01:37:24,770
+الاحداثية بدي تجيبي التقطع الأسود هذا اللي هو
+
+785
+01:37:24,770 --> 01:37:29,390
+المستوى yz بروح وحط x بمية بزي وغسيل المقطع عبارة
+
+786
+01:37:29,390 --> 01:37:35,690
+عن ايش منها؟ hyperbola يبقى الخط الأسود هذا مع
+
+787
+01:37:35,690 --> 01:37:41,900
+الخط الأسود التاني اللي هو ال hyperbolaعلى P تربية
+
+788
+01:37:41,900 --> 01:37:47,160
+ناقص Z تربية على C تربية بساوية واحدة. وهكذا
+
+789
+01:37:47,160 --> 01:37:53,240
+بالنسبة لمين تتلوجت للأفقي. Z تساوي Zero فطير هذا
+
+790
+01:37:53,240 --> 01:37:58,680
+يظل عنده Ellipse. يبقى هذا high parabola لكن هذا
+
+791
+01:37:58,680 --> 01:38:04,700
+Ellipse. إيش معادلته؟ معادلته X تربية على
+
+792
+01:38:09,020 --> 01:38:18,780
+في عندك المجسم ذوق طي تاني رقم خمسة اللي هو ال
+
+793
+01:38:18,780 --> 01:38:27,220
+high parabolite of
+
+794
+01:38:27,220 --> 01:38:28,080
+two sheets
+
+795
+01:38:53,250 --> 01:39:00,370
+هذا محور X، هذا Y، هذا Z، ندى هذه على استماعك بهذا
+
+796
+01:39:00,370 --> 01:39:08,050
+الشكل. شايف هذا يا بنات؟ هو هذا بس، واحدة موجة فوق
+
+797
+01:39:08,050 --> 01:39:16,230
+وواحدة تحت، وهكذا. طيبة طيبة موجة، يبقى هذا هكذا
+
+798
+01:39:16,230 --> 01:39:17,570
+والتاني هكذا.
+
+799
+01:39:27,020 --> 01:39:33,120
+يبقى هذا الـ hyperboloid of two sheets لو قطعته
+
+800
+01:39:33,120 --> 01:39:38,860
+أفقي بتلاقي ellipse هذا عبارة عن ellipse وهذا
+
+801
+01:39:38,860 --> 01:39:43,480
+عبارة عن إيش ellipse لو قطعته رأسي بتلاقي
+
+802
+01:39:43,480 --> 01:39:46,800
+hyperbola و هاي hyperbola جتين مع بعض هاي
+
+803
+01:39:46,800 --> 01:39:50,380
+hyperbola بالمستوى x زاد
+
+804
+01:39:56,430 --> 01:40:01,430
+فأضع اللي هيك ومن
+
+805
+01:40:01,430 --> 01:40:09,150
+هنا مش هيظهر و من هنا هيك يظهر و من اللي هيتاني
+
+806
+01:40:09,150 --> 01:40:16,400
+لبس هذا الشكلطب السؤال هل هذا يمر بنقطة أصيله؟ لأ
+
+807
+01:40:16,400 --> 01:40:21,760
+لإن لو بده احط زيت تساوي zero في المعادلة بيصير
+
+808
+01:40:21,760 --> 01:40:26,940
+مجموعة كميتين سلبتين يساوي كمية جوجل صحيح؟ يعني لو
+
+809
+01:40:26,940 --> 01:40:29,560
+ضرر فيه شبة ناقص بيصير X سلبي عليها تلقى
+
+810
+01:40:32,950 --> 01:40:36,830
+هذا كلام ممنوع وفي وقت ما يتم ارسال كيمياسانة وهذا
+
+811
+01:40:36,830 --> 01:40:43,210
+مفهوم إذن يمكن للمستوى XY نقطع هذا المجسم لكن ال
+
+812
+01:40:43,210 --> 01:40:48,590
+XY المجسم هذا متمثل بالنسبة للنص اللي فوق زي النص
+
+813
+01:40:48,590 --> 01:40:51,890
+اللي تا النص اللي علي مين زي النص اللي عشرة للنص
+
+814
+01:40:51,890 --> 01:40:56,690
+هذه يعني متمثل بالنسبة لمستويات الأحداثيات
+
+815
+01:41:19,790 --> 01:41:26,170
+يبقى اخر حاجة هي النقطة الرقم ستة هي عنامين
+
+816
+01:41:26,170 --> 01:41:28,230
+hyperbolic paraboloid
+
+817
+01:41:39,790 --> 01:41:44,530
+المعادلة التي اتبعتها هي Y
+
+818
+01:41:44,530 --> 01:41:52,510
+تربيع على B تربيع ناقص X تربيع على A تربيع بدها
+
+819
+01:41:52,510 --> 01:41:57,290
+تسوى Z على C والـC أكتر من
+
+820
+01:42:16,250 --> 01:42:22,490
+رسم I أولا بأولا بدا نرسم I فرابولا حوالي المحور
+
+821
+01:42:22,490 --> 01:42:28,770
+زد من أول نبقى بالدرجة أقول له ادي اي فرابولا و من
+
+822
+01:42:28,770 --> 01:42:35,510
+الناحية التالية و ذات جينها طبعا
+
+823
+01:42:35,510 --> 01:42:39,190
+عالية اكيد بدا نزلها بس لتحت شوية
+
+824
+01:42:49,920 --> 01:43:05,540
+بعد ذلك بدي من النقطة هذه ارسم برابطة بعد ذلك
+
+825
+01:43:05,540 --> 01:43:11,340
+بنزلها هنا وهذه هي الشكل اللي عملنا
+
+826
+01:43:20,510 --> 01:43:29,050
+تمام ؟ هذا يظهر عليك على شكل دوس الشكل هنا و هذا
+
+827
+01:43:29,050 --> 01:43:44,830
+هنا يقول دوس تمام الشكل واضحة الرسمة و
+
+828
+01:43:44,830 --> 01:43:46,090
+بعد هيك
+
+829
+01:43:55,780 --> 01:44:06,680
+يبقى هاي فراغلة وهي فراغلة كمان زي ملتشاكر يبنيس
+
+830
+01:44:06,680 --> 01:44:07,220
+منها
+
+831
+01:44:14,430 --> 01:44:20,110
+هذه المعادلة اللي قدامها من المحور تبعها زي ما
+
+832
+01:44:20,110 --> 01:44:28,350
+تشايفها اللي هو محور الـ Z بالضبط تماما على
+
+833
+01:44:28,350 --> 01:44:35,790
+شكل قص وليس خطا مستقيما زي ولا تشبيه السرج تبع
+
+834
+01:44:35,790 --> 01:44:42,170
+الفرصةسارج الفرص بالضبط هذا هو عبارة عن سارج الفرص
+
+835
+01:44:42,170 --> 01:44:49,110
+طيب بدنا يا بنات المسائل التالية منكم exercises
+
+836
+01:44:49,110 --> 01:44:52,310
+أتناشر
+
+837
+01:44:52,310 --> 01:45:03,470
+ستة المسائل من واحد لغاية تلاتة واربعين الفور على
+
+838
+01:45:03,470 --> 01:45:08,210
+هيك يكون انتهى ال chapterالمرة القادمة ان شاء الله
+
+839
+01:45:08,210 --> 01:45:14,710
+بناخد نين نخس في chapter 13 ان شاء الله و تعالى
+
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/yfbRUZY5IbA_raw.json b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/yfbRUZY5IbA_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..fe731fc11c5054dd30ff4dae51893e7683acd47e
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/yfbRUZY5IbA_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 268, "start": 0.0, "end": 2.68, "text": "موسيقى", "tokens": [2304, 41779, 1829, 4587, 7578], "avg_logprob": -0.3541666766007741, "compression_ratio": 0.5714285714285714, "no_speech_prob": 0.002925872802734375, "words": [{"start": 0.0, "end": 2.68, "word": "موسيقى", "probability": 0.7367919921875}], "temperature": 1.0}, {"id": 2, "seek": 3583, "start": 9.87, "end": 35.83, "text": "بسم الله الرحمن الرحيم المرة الماضية ابتدأنا في section 12-5 و أخدنا ثلاث نقاط طبعا ال section كله بتكلم عن ال lines و ال planes أخدنا النقطة الأولى هي ال lines في الفراق و عرفنا ال parametric equations لهذه ال lines اتنين المسافة ما بين نقطة و خط مستقيم في الفراق", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 9673, 25720, 9673, 46958, 10632, 48127, 2655, 3215, 10721, 8315, 8978, 3541, 2272, 12, 20, 4032, 5551, 9778, 3215, 8315, 38637, 1211, 5718, 104, 8717, 4587, 41193, 23032, 3555, 3615, 995, 2423, 3541, 28242, 3224, 39894, 4117, 19528, 18871, 2423, 3876, 4032, 2423, 14952, 5551, 9778, 3215, 8315, 28239, 47432, 3660, 16247, 12610, 7578, 39896, 2423, 3876, 8978, 27188, 23557, 4587, 4032, 6225, 28480, 8315, 2423, 6220, 17475, 11787, 46740, 24192, 2423, 3876, 1975, 2655, 1863, 9957, 9673, 3794, 31845, 3660, 19446, 49374, 8717, 47432, 3660, 4032, 16490, 9566, 3714, 14851, 4587, 32640, 8978, 27188, 23557, 4587], "avg_logprob": -0.11674941560932409, "compression_ratio": 1.7721518987341771, "no_speech_prob": 2.562999725341797e-06, "words": [{"start": 9.87, "end": 10.19, "word": "بسم", "probability": 0.93115234375}, {"start": 10.19, "end": 10.41, "word": " الله", "probability": 0.958984375}, {"start": 10.41, "end": 10.97, "word": " الرحمن", "probability": 0.97509765625}, {"start": 10.97, "end": 11.39, "word": " الرحيم", "probability": 0.9939778645833334}, {"start": 11.39, "end": 13.65, "word": " المرة", "probability": 0.6778564453125}, {"start": 13.65, "end": 14.29, "word": " الماضية", "probability": 0.9833984375}, {"start": 14.29, "end": 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0.962890625}, {"start": 20.53, "end": 21.03, "word": " بتكلم", "probability": 0.9093424479166666}, {"start": 21.03, "end": 21.25, "word": " عن", "probability": 0.98583984375}, {"start": 21.25, "end": 21.43, "word": " ال", "probability": 0.97021484375}, {"start": 21.43, "end": 21.85, "word": " lines", "probability": 0.8974609375}, {"start": 21.85, "end": 22.09, "word": " و", "probability": 0.93798828125}, {"start": 22.09, "end": 22.19, "word": " ال", "probability": 0.85791015625}, {"start": 22.19, "end": 22.69, "word": " planes", "probability": 0.818359375}, {"start": 22.69, "end": 23.95, "word": " أخدنا", "probability": 0.946044921875}, {"start": 23.95, "end": 24.71, "word": " النقطة", "probability": 0.9747721354166666}, {"start": 24.71, "end": 25.17, "word": " الأولى", "probability": 0.97607421875}, {"start": 25.17, "end": 25.37, "word": " هي", "probability": 0.8984375}, {"start": 25.37, "end": 25.61, "word": " ال", "probability": 0.90576171875}, {"start": 25.61, "end": 26.01, "word": " lines", "probability": 0.953125}, {"start": 26.01, "end": 26.27, "word": " في", "probability": 0.826171875}, {"start": 26.27, "end": 27.01, "word": " الفراق", "probability": 0.750244140625}, {"start": 27.01, "end": 27.53, "word": " و", "probability": 0.865234375}, {"start": 27.53, "end": 27.85, "word": " عرفنا", "probability": 0.92724609375}, {"start": 27.85, "end": 27.99, "word": " ال", "probability": 0.9658203125}, {"start": 27.99, "end": 28.53, "word": " parametric", "probability": 0.91650390625}, {"start": 28.53, "end": 29.11, "word": " equations", "probability": 0.8720703125}, {"start": 29.11, "end": 29.61, "word": " لهذه", "probability": 0.94091796875}, {"start": 29.61, "end": 29.79, "word": " ال", "probability": 0.96923828125}, {"start": 29.79, "end": 30.17, "word": " lines", "probability": 0.93798828125}, {"start": 30.17, "end": 31.31, "word": " اتنين", "probability": 0.8297119140625}, {"start": 31.31, "end": 32.73, "word": " المسافة", "probability": 0.9375}, {"start": 32.73, "end": 32.93, "word": " ما", "probability": 0.83056640625}, {"start": 32.93, "end": 33.21, "word": " بين", "probability": 0.98193359375}, {"start": 33.21, "end": 33.65, "word": " نقطة", "probability": 0.9853515625}, {"start": 33.65, "end": 33.81, "word": " و", "probability": 0.99755859375}, {"start": 33.81, "end": 34.17, "word": " خط", "probability": 0.947998046875}, {"start": 34.17, "end": 34.97, "word": " مستقيم", "probability": 0.9737548828125}, {"start": 34.97, "end": 35.17, "word": " في", "probability": 0.95849609375}, {"start": 35.17, "end": 35.83, "word": " الفراق", "probability": 0.9303385416666666}], "temperature": 1.0}, {"id": 3, "seek": 6391, "start": 36.31, "end": 63.91, "text": "تلاتة معادلة مستوى في الفرق هذا ما دُرس في هذا section حتى نهاية المحاضرة الماضية اليوم بنكمل على نفس ال section وبنجي للنقطة الراجعة اللي هي distance from a point to a plane المرة فيها distance من point to a line المرة هي distance from a point to a plane كويس يبقى لو جيت تفيّل انه عندى plane", 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{"start": 783.03, "end": 783.91, "word": " planes", "probability": 0.92138671875}, {"start": 783.91, "end": 785.69, "word": " two", "probability": 0.43896484375}, {"start": 785.69, "end": 788.35, "word": " planes", "probability": 0.9453125}, {"start": 788.35, "end": 789.41, "word": " are", "probability": 0.92626953125}, {"start": 789.41, "end": 790.17, "word": " perpendicular", "probability": 0.87841796875}], "temperature": 1.0}, {"id": 29, "seek": 81111, "start": 794.53, "end": 811.11, "text": "أتر تنديكيونار أو Parallel المتعمقين أو المتوازين have their normals", "tokens": [10721, 2655, 2288, 6055, 1863, 16254, 4117, 1829, 2407, 8315, 2288, 34051, 3457, 336, 338, 9673, 2655, 25957, 4587, 9957, 34051, 9673, 2655, 2407, 31377, 9957, 362, 641, 2026, 1124], "avg_logprob": -0.4523689419992508, "compression_ratio": 1.10752688172043, "no_speech_prob": 0.0, "words": [{"start": 794.5300000000001, "end": 795.9300000000001, "word": "أتر", "probability": 0.3824869791666667}, {"start": 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الأول", "probability": 0.886474609375}, {"start": 926.51, "end": 927.39, "word": " و", "probability": 0.396240234375}, {"start": 927.39, "end": 928.05, "word": " العمود", "probability": 0.9384765625}, {"start": 928.05, "end": 928.31, "word": " على", "probability": 0.943359375}, {"start": 928.31, "end": 929.07, "word": " المستوى", "probability": 0.96435546875}, {"start": 929.07, "end": 929.85, "word": " الثاني", "probability": 0.9349365234375}, {"start": 929.85, "end": 930.25, "word": " ايش", "probability": 0.7900390625}, {"start": 930.25, "end": 930.65, "word": " العلاقة", "probability": 0.8987630208333334}, {"start": 930.65, "end": 930.85, "word": " بين", "probability": 0.8662109375}, {"start": 930.85, "end": 931.03, "word": " ال", "probability": 0.62841796875}, {"start": 931.03, "end": 931.31, "word": " two", "probability": 0.91162109375}, {"start": 931.31, "end": 932.35, "word": " line", "probability": 0.367919921875}, {"start": 932.35, "end": 932.69, "word": " او", "probability": 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1.0}, {"id": 35, "seek": 97335, "start": 954.23, "end": 973.35, "text": "انا عندى هذا plane و هذا ال plane تبع السكين اتنين اعرفى perpendicular فى ال corner اللى عندى لو جيت رسمت من هنا عمود على ال plane الاول و رسمت عمود على ال plane التانى كذا بينهم تسعين درجة هى اللى بتقوله الريمان", "tokens": [7649, 995, 43242, 7578, 23758, 5720, 4032, 23758, 2423, 5720, 6055, 3555, 3615, 21136, 4117, 9957, 1975, 2655, 1863, 9957, 1975, 3615, 28480, 7578, 26734, 6156, 7578, 2423, 4538, 13672, 7578, 43242, 7578, 45164, 10874, 36081, 12602, 38251, 2655, 9154, 34105, 6225, 2304, 23328, 15844, 2423, 5720, 42963, 12610, 4032, 12602, 38251, 2655, 6225, 2304, 23328, 15844, 2423, 5720, 16712, 7649, 7578, 9122, 15730, 49374, 16095, 6055, 3794, 3615, 9957, 11778, 47341, 3660, 8032, 7578, 13672, 7578, 39894, 39648, 3224, 2423, 16572, 2304, 7649], "avg_logprob": -0.22702206162845387, "compression_ratio": 1.8440860215053763, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 954.23, "end": 954.61, 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"word": " تسعين", "probability": 0.8787841796875}, {"start": 971.77, "end": 972.23, "word": " درجة", "probability": 0.966796875}, {"start": 972.23, "end": 972.39, "word": " هى", "probability": 0.69384765625}, {"start": 972.39, "end": 972.51, "word": " اللى", "probability": 0.969482421875}, {"start": 972.51, "end": 972.89, "word": " بتقوله", "probability": 0.8728841145833334}, {"start": 972.89, "end": 973.35, "word": " الريمان", "probability": 0.8316650390625}], "temperature": 1.0}, {"id": 36, "seek": 100091, "start": 973.79, "end": 1000.91, "text": "بتقولي two planes are perpendicular اتنين بيكونوا متعامدين او متوازية if they are normal vectors اذا جبت normal على كل واحد من ال two vectors هدول بلاقي اتنين اذا perpendicular بيكون perpendicular اذا parallel بيكون اتنين هدول مالهم parallel نعطي مثال على ذلك يبقى example", "tokens": [3555, 2655, 39648, 1829, 732, 14952, 366, 26734, 1975, 2655, 1863, 9957, 4724, 1829, 30544, 14407, 44650, 3615, 10943, 3215, 9957, 1975, 2407, 44650, 2407, 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"probability": 0.66949462890625}, {"start": 1020.96, "end": 1022.2, "word": " مستويين", "probability": 0.73736572265625}, {"start": 1022.2, "end": 1023.14, "word": " اللي", "probability": 0.841552734375}, {"start": 1023.14, "end": 1023.34, "word": " هو", "probability": 0.96630859375}, {"start": 1023.34, "end": 1024.38, "word": " تلاتة", "probability": 0.8975830078125}, {"start": 1024.38, "end": 1024.9, "word": " X", "probability": 0.74560546875}, {"start": 1024.9, "end": 1026.4, "word": " زائد", "probability": 0.8759765625}, {"start": 1026.4, "end": 1027.56, "word": " ستة", "probability": 0.974609375}, {"start": 1027.56, "end": 1028.04, "word": " Y", "probability": 0.4853515625}, {"start": 1028.04, "end": 1029.44, "word": " ناقص", "probability": 0.9525146484375}, {"start": 1029.44, "end": 1030.14, "word": " تسعة", "probability": 0.9853515625}, {"start": 1030.14, "end": 1030.72, "word": " Z", "probability": 0.96826171875}], "temperature": 1.0}, {"id": 38, "seek": 105770, "start": 1035.18, "end": 1057.7, "text": "والـ X زائد اتنين Y نقص ثانوتها Z بيكون واحد اتنين اتنين متوازين and find the distance", "tokens": [2407, 6027, 39184, 1783, 30767, 16373, 3215, 1975, 2655, 1863, 9957, 398, 8717, 4587, 9381, 38637, 7649, 35473, 11296, 1176, 4724, 1829, 30544, 36764, 24401, 1975, 2655, 1863, 9957, 1975, 2655, 1863, 9957, 44650, 2407, 31377, 9957, 293, 915, 264, 4560], "avg_logprob": -0.651785732734771, "compression_ratio": 1.25, "no_speech_prob": 4.76837158203125e-07, "words": [{"start": 1035.1799999999998, "end": 1036.58, "word": "والـ", "probability": 0.175933837890625}, {"start": 1036.58, "end": 1036.98, "word": " X", "probability": 0.51416015625}, {"start": 1036.98, "end": 1037.98, "word": " زائد", "probability": 0.4826253255208333}, {"start": 1037.98, "end": 1038.52, "word": " اتنين", "probability": 0.78741455078125}, {"start": 1038.52, "end": 1039.18, "word": " Y", "probability": 0.572265625}, {"start": 1039.18, "end": 1040.4, "word": " نقص", "probability": 0.78466796875}, {"start": 1040.4, "end": 1041.24, "word": " ثانوتها", "probability": 0.6519775390625}, {"start": 1041.24, "end": 1041.58, "word": " Z", "probability": 0.77392578125}, {"start": 1041.58, "end": 1042.62, "word": " بيكون", "probability": 0.5334879557291666}, {"start": 1042.62, "end": 1043.62, "word": " واحد", "probability": 0.77734375}, {"start": 1043.62, "end": 1046.22, "word": " اتنين", "probability": 0.561614990234375}, {"start": 1046.22, "end": 1049.7, "word": " اتنين", "probability": 0.65948486328125}, {"start": 1049.7, "end": 1051.34, "word": " متوازين", "probability": 0.76446533203125}, {"start": 1051.34, "end": 1052.48, "word": " and", "probability": 0.08258056640625}, {"start": 1052.48, "end": 1054.12, "word": " find", "probability": 0.64404296875}, {"start": 1054.12, "end": 1055.76, "word": " the", "probability": 0.378662109375}, {"start": 1055.76, "end": 1057.7, "word": " distance", "probability": 0.9453125}], "temperature": 1.0}, {"id": 39, "seek": 106602, "start": 1062.4, "end": 1066.02, "text": "وأتولى المسافة between them", "tokens": [2407, 10721, 2655, 12610, 7578, 9673, 3794, 31845, 3660, 1296, 552], "avg_logprob": -0.4820963690678279, "compression_ratio": 0.851063829787234, "no_speech_prob": 0.0, "words": [{"start": 1062.4, "end": 1062.98, "word": "وأتولى", "probability": 0.486865234375}, {"start": 1062.98, "end": 1064.28, "word": " المسافة", "probability": 0.9832763671875}, {"start": 1064.28, "end": 1065.28, "word": " between", "probability": 0.1781005859375}, {"start": 1065.28, "end": 1066.02, "word": " them", "probability": 0.95263671875}], "temperature": 1.0}, {"id": 40, "seek": 111142, "start": 1105.56, "end": 1111.42, "text": "سؤال مرة تانية ماطيني معادلتين ل two players كل واحد المعادلة", "tokens": [3794, 33604, 6027, 3714, 25720, 6055, 7649, 10632, 3714, 41193, 9957, 1829, 20449, 18513, 1211, 2655, 9957, 5296, 732, 4150, 28242, 36764, 24401, 9673, 3615, 18513, 37977], "avg_logprob": -0.28989953973463606, 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بنات لو لينا قلنا هذا هو المستوى الأول على سبيل المثال وهذا هو المستوى الثاني", "tokens": [1829, 3555, 4587, 7578, 9673, 14851, 2407, 7578, 8032, 8848, 12610, 44650, 2407, 31377, 9957, 23758, 9673, 9566, 1211, 37746, 16247, 12610, 9154, 9673, 12984, 37977, 9673, 9566, 1211, 37746, 16712, 7649, 1829, 10874, 6027, 7251, 3224, 3215, 5172, 9673, 3794, 31845, 3660, 19446, 49374, 2423, 732, 14952, 8032, 8848, 12610, 37495, 22653, 35186, 4724, 8315, 2655, 45164, 32239, 8315, 12174, 1211, 8315, 23758, 31439, 9673, 14851, 2407, 7578, 16247, 12610, 15844, 8608, 21292, 1211, 9673, 12984, 6027, 37037, 15730, 31439, 9673, 14851, 2407, 7578, 6024, 104, 7649, 1829], "avg_logprob": -0.1648437456952201, "compression_ratio": 2.0409356725146197, "no_speech_prob": 2.9802322387695312e-06, "words": [{"start": 1255.08, "end": 1255.54, "word": "يبقى", "probability": 0.80255126953125}, {"start": 1255.54, "end": 1255.98, "word": " المستوى", "probability": 0.9083251953125}, {"start": 1255.98, "end": 1256.54, 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"text": "بدي اعرف كده المسافة ما بين الاتنين المسافة ما بين الاتنين هي المسافة العمودية طبعا هذا المتجه اللي هو مين M1 العمودي على الأول شكل على هذا وهذا المتجه التاني", "tokens": [3555, 16254, 1975, 3615, 28480, 9122, 3215, 3224, 9673, 3794, 31845, 3660, 19446, 49374, 2423, 9307, 1863, 9957, 9673, 3794, 31845, 3660, 19446, 49374, 2423, 9307, 1863, 9957, 39896, 9673, 3794, 31845, 3660, 18863, 2304, 2407, 16254, 3660, 23032, 3555, 3615, 995, 23758, 9673, 2655, 7435, 3224, 13672, 1829, 31439, 3714, 9957, 376, 16, 18863, 2304, 2407, 16254, 15844, 16247, 12610, 13412, 28820, 15844, 23758, 37037, 15730, 9673, 2655, 7435, 3224, 16712, 7649, 1829], "avg_logprob": -0.2516666563351949, "compression_ratio": 2.0802919708029197, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1277.08, "end": 1277.44, "word": "بدي", "probability": 0.55047607421875}, {"start": 1277.44, "end": 1277.76, "word": " اعرف", "probability": 0.859375}, {"start": 1277.76, "end": 1278.2, "word": " كده", 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"probability": 0.361328125}, {"start": 2244.58, "end": 2244.78, "word": " يا", "probability": 0.96826171875}, {"start": 2244.78, "end": 2245.58, "word": " بنات؟", "probability": 0.6898193359375}, {"start": 2245.58, "end": 2246.6, "word": " بالعربى", "probability": 0.71240234375}, {"start": 2246.6, "end": 2247.68, "word": " أسطوانة", "probability": 0.75543212890625}, {"start": 2247.68, "end": 2248.38, "word": " ممتاز", "probability": 0.844970703125}, {"start": 2248.38, "end": 2249.66, "word": " طيب", "probability": 0.7969563802083334}, {"start": 2249.66, "end": 2251.72, "word": " الأسطوانة", "probability": 0.9525553385416666}, {"start": 2251.72, "end": 2252.36, "word": " هل", "probability": 0.90673828125}, {"start": 2252.36, "end": 2253.04, "word": " ضروري", "probability": 0.95458984375}, {"start": 2253.04, "end": 2253.34, "word": " يكون", "probability": 0.7646484375}, {"start": 2253.34, "end": 2253.96, "word": " مقطع", "probability": 0.88330078125}, {"start": 2253.96, "end": 2254.46, 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{"start": 2328.86, "end": 2329.74, "word": " بالشكل", "probability": 0.773681640625}, {"start": 2329.74, "end": 2330.18, "word": " هذا", "probability": 0.9677734375}, {"start": 2330.18, "end": 2330.98, "word": " cylinder", "probability": 0.79248046875}, {"start": 2330.98, "end": 2331.66, "word": " لو", "probability": 0.9111328125}, {"start": 2331.66, "end": 2332.0, "word": " جبت", "probability": 0.94482421875}, {"start": 2332.0, "end": 2332.42, "word": " شكل", "probability": 0.9609375}, {"start": 2332.42, "end": 2332.84, "word": " تاني", "probability": 0.9435221354166666}, {"start": 2332.84, "end": 2333.28, "word": " زيه", "probability": 0.9915364583333334}, {"start": 2333.28, "end": 2333.4, "word": " و", "probability": 0.9931640625}, {"start": 2333.4, "end": 2333.84, "word": " خليته", "probability": 0.8389892578125}, {"start": 2333.84, "end": 2333.96, "word": " من", "probability": 0.986328125}, {"start": 2333.96, "end": 2334.42, "word": " ناحية", "probability": 0.951171875}, {"start": 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{"start": 4115.24, "end": 4116.08, "word": " منقطع", "probability": 0.7449544270833334}, {"start": 4116.08, "end": 4116.72, "word": " بهذا", "probability": 0.955810546875}, {"start": 4116.72, "end": 4117.22, "word": " الشكل", "probability": 0.982666015625}], "temperature": 1.0}, {"id": 147, "seek": 412681, "start": 4119.39, "end": 4126.81, "text": "يوصف الشكل ان هذا مجسم واضح ان هذا عبارة عن مجسم مش عاجزاكوا بس", "tokens": [1829, 2407, 9381, 5172, 25124, 28820, 16472, 23758, 3714, 7435, 38251, 4032, 46958, 5016, 16472, 23758, 6225, 3555, 9640, 3660, 18871, 3714, 7435, 38251, 37893, 6225, 26108, 11622, 995, 4117, 14407, 4724, 3794], "avg_logprob": -0.2750459611415863, "compression_ratio": 1.3614457831325302, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 4119.39, "end": 4120.07, "word": "يوصف", "probability": 0.624359130859375}, {"start": 4120.07, "end": 4120.57, "word": " الشكل", "probability": 0.92138671875}, {"start": 4120.57, "end": 4120.83, "word": " ان", 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415867, "start": 4130.51, "end": 4158.67, "text": "بهذا الشكل فهذا يجينا كمان هكذا خلّيني أقول في الأصل يبقى واضح الأن أن هذا مجسم طيب الآن ليش سمينا ellipsoid هذا السؤال ellipsoid جاء من كلمة syllables الإجابة لأن مقع مع كل مستوى من مستويات الأفتراضيات", "tokens": [3555, 3224, 15730, 25124, 28820, 6156, 3224, 15730, 7251, 7435, 1829, 8315, 9122, 2304, 7649, 8032, 4117, 15730, 16490, 1211, 11703, 9957, 1829, 5551, 39648, 8978, 16247, 36520, 7251, 3555, 4587, 7578, 4032, 46958, 5016, 16247, 1863, 14739, 23758, 3714, 7435, 38251, 23032, 1829, 3555, 6024, 48506, 32239, 8592, 8608, 2304, 1829, 8315, 8284, 647, 539, 327, 23758, 21136, 33604, 6027, 8284, 647, 539, 327, 10874, 16606, 9154, 9122, 19528, 3660, 45364, 33688, 7435, 16758, 3660, 5296, 33456, 3714, 4587, 3615, 20449, 28242, 3714, 14851, 2407, 7578, 9154, 3714, 14851, 45865, 9307, 16247, 5172, 2655, 2288, 46958, 1829, 9307], "avg_logprob": -0.37718750417232516, "compression_ratio": 1.7222222222222223, "no_speech_prob": 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على C تربية بساوية واحدة. وهكذا بالنسبة لمين تتلوجت للأفقي. Z تساوي Zero فطير هذا يظل عنده Ellipse. يبقى هذا high parabola لكن هذا Ellipse. إيش معادلته؟ معادلته X تربية على", "tokens": [3615, 23942, 430, 6055, 2288, 21292, 3660, 8717, 995, 4587, 9381, 1176, 6055, 2288, 21292, 3660, 15844, 383, 6055, 2288, 21292, 3660, 4724, 3794, 995, 2407, 10632, 36764, 24401, 3660, 13, 37037, 4117, 15730, 20666, 1863, 35457, 3660, 32767, 9957, 6055, 2655, 1211, 29245, 2655, 24976, 10721, 5172, 38436, 13, 1176, 6055, 3794, 995, 45865, 17182, 6156, 9566, 13546, 23758, 7251, 19913, 1211, 43242, 3224, 8353, 48041, 13, 7251, 3555, 4587, 7578, 23758, 1090, 45729, 4711, 44381, 23758, 8353, 48041, 13, 11933, 1829, 8592, 20449, 18513, 1211, 47395, 22807, 20449, 18513, 1211, 47395, 1783, 6055, 2288, 21292, 3660, 15844], "avg_logprob": -0.3637500071525574, "compression_ratio": 1.595, "no_speech_prob": 3.1054019927978516e-05, "words": [{"start": 5860.16, "end": 5861.06, "word": "على", "probability": 0.527801513671875}, {"start": 5861.06, "end": 5861.26, "word": " P", 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1.0}, {"id": 213, "seek": 590808, "start": 5889.02, "end": 5908.08, "text": "في عندك المجسم ذوق طي تاني رقم خمسة اللي هو ال high parabolite of two sheets", "tokens": [41185, 43242, 4117, 9673, 7435, 38251, 29910, 30543, 23032, 1829, 6055, 7649, 1829, 12602, 4587, 2304, 16490, 2304, 3794, 3660, 13672, 1829, 31439, 2423, 1090, 45729, 401, 642, 295, 732, 15421], "avg_logprob": -0.3359374972060323, "compression_ratio": 1.0666666666666667, "no_speech_prob": 4.76837158203125e-07, "words": [{"start": 5889.02, "end": 5890.42, "word": "في", "probability": 0.07415771484375}, {"start": 5890.42, "end": 5890.9, "word": " عندك", "probability": 0.760009765625}, {"start": 5890.9, "end": 5891.66, "word": " المجسم", "probability": 0.9451497395833334}, {"start": 5891.66, "end": 5892.2, "word": " ذوق", "probability": 0.613525390625}, {"start": 5892.2, "end": 5892.86, "word": " طي", "probability": 0.896240234375}, {"start": 5892.86, "end": 5893.88, "word": " تاني", "probability": 0.71826171875}, {"start": 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بس، واحدة موجة فوق وواحدة تحت، وهكذا. طيبة طيبة موجة، يبقى هذا هكذا والتاني هكذا.", "tokens": [3224, 15730, 3714, 5016, 13063, 1783, 12399, 23758, 398, 12399, 23758, 1176, 12399, 8717, 3215, 7578, 29538, 15844, 44713, 15042, 3615, 4117, 39627, 15730, 25124, 28820, 13, 13412, 995, 33911, 23758, 35186, 4724, 8315, 2655, 22807, 31439, 23758, 4724, 3794, 12399, 36764, 24401, 3660, 3714, 29245, 3660, 6156, 30543, 4032, 14407, 24401, 3660, 6055, 33753, 12399, 37037, 4117, 15730, 13, 23032, 1829, 49401, 23032, 1829, 49401, 3714, 29245, 3660, 12399, 7251, 3555, 4587, 7578, 23758, 8032, 4117, 15730, 16070, 2655, 7649, 1829, 8032, 4117, 15730, 13], "avg_logprob": -0.36135058498930656, "compression_ratio": 1.7730061349693251, "no_speech_prob": 0.0, "words": [{"start": 5933.25, "end": 5933.65, "word": "هذا", "probability": 0.64404296875}, {"start": 5933.65, "end": 5934.13, "word": " محور", "probability": 0.79248046875}, {"start": 5934.13, "end": 5935.21, "word": " X،", "probability": 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0.7030843098958334}, {"start": 6284.05, "end": 6284.99, "word": " بدنا", "probability": 0.7403564453125}, {"start": 6284.99, "end": 6285.13, "word": " يا", "probability": 0.95166015625}, {"start": 6285.13, "end": 6285.41, "word": " بنات", "probability": 0.859375}, {"start": 6285.41, "end": 6286.09, "word": " المسائل", "probability": 0.865966796875}, {"start": 6286.09, "end": 6286.77, "word": " التالية", "probability": 0.9532877604166666}, {"start": 6286.77, "end": 6287.41, "word": " منكم", "probability": 0.8232421875}, {"start": 6287.41, "end": 6289.11, "word": " exercises", "probability": 0.6552734375}, {"start": 6289.11, "end": 6292.31, "word": " أتناشر", "probability": 0.666357421875}, {"start": 6292.31, "end": 6293.17, "word": " ستة", "probability": 0.876953125}, {"start": 6293.17, "end": 6294.41, "word": " المسائل", "probability": 0.9376220703125}, {"start": 6294.41, "end": 6294.65, "word": " من", "probability": 0.96240234375}, {"start": 6294.65, "end": 6295.19, "word": " واحد", "probability": 0.9833984375}, {"start": 6295.19, "end": 6295.75, "word": " لغاية", "probability": 0.9835205078125}, {"start": 6295.75, "end": 6296.43, "word": " تلاتة", "probability": 0.69598388671875}, {"start": 6296.43, "end": 6297.21, "word": " واربعين", "probability": 0.87705078125}, {"start": 6297.21, "end": 6297.93, "word": " الفور", "probability": 0.4073486328125}, {"start": 6297.93, "end": 6303.47, "word": " على", "probability": 0.57861328125}, {"start": 6303.47, "end": 6303.75, "word": " هيك", "probability": 0.92333984375}, {"start": 6303.75, "end": 6304.09, "word": " يكون", "probability": 0.7197265625}, {"start": 6304.09, "end": 6304.49, "word": " انتهى", "probability": 0.94580078125}, {"start": 6304.49, "end": 6304.63, "word": " ال", "probability": 0.434326171875}, {"start": 6304.63, "end": 6304.95, "word": " chapter", "probability": 0.8818359375}], "temperature": 1.0}, {"id": 227, "seek": 631471, "start": 6305.71, "end": 6314.71, "text": "المرة القادمة ان شاء الله بناخد نين نخس في chapter 13 ان شاء الله و تعالى", "tokens": [45340, 25720, 25062, 18513, 46007, 16472, 13412, 16606, 21984, 44945, 47283, 3215, 8717, 9957, 8717, 9778, 3794, 8978, 7187, 3705, 16472, 13412, 16606, 21984, 4032, 37279, 6027, 7578], "avg_logprob": -0.30226294336647824, "compression_ratio": 1.2842105263157895, "no_speech_prob": 0.00567626953125, "words": [{"start": 6305.71, "end": 6306.31, "word": "المرة", "probability": 0.7178955078125}, {"start": 6306.31, "end": 6306.97, "word": " القادمة", "probability": 0.9933268229166666}, {"start": 6306.97, "end": 6307.29, "word": " ان", "probability": 0.52099609375}, {"start": 6307.29, "end": 6307.67, "word": " شاء", "probability": 0.984375}, {"start": 6307.67, "end": 6308.21, "word": " الله", "probability": 0.966796875}, {"start": 6308.21, "end": 6309.47, "word": " بناخد", "probability": 0.77685546875}, {"start": 6309.47, "end": 6309.93, "word": " نين", "probability": 0.52191162109375}, {"start": 6309.93, "end": 6311.47, "word": " نخس", "probability": 0.718017578125}, {"start": 6311.47, "end": 6311.65, "word": " في", "probability": 0.92236328125}, {"start": 6311.65, "end": 6312.13, "word": " chapter", "probability": 0.5771484375}, {"start": 6312.13, "end": 6313.49, "word": " 13", "probability": 0.80126953125}, {"start": 6313.49, "end": 6313.83, "word": " ان", "probability": 0.7724609375}, {"start": 6313.83, "end": 6314.09, "word": " شاء", "probability": 0.98583984375}, {"start": 6314.09, "end": 6314.27, "word": " الله", "probability": 0.9443359375}, {"start": 6314.27, "end": 6314.43, "word": " و", "probability": 0.57958984375}, {"start": 6314.43, "end": 6314.71, "word": " تعالى", "probability": 0.8395182291666666}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 6315.8045, "duration_after_vad": 5062.899718750031}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/yfbRUZY5IbA_raw.srt b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/yfbRUZY5IbA_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..bd9a637149d4ac883dfd09d213a25fd9cbd6aae0
--- /dev/null
+++ b/PL9fwy3NUQKwZ3Vc5NGzzNwnA5qKW4lNoy/yfbRUZY5IbA_raw.srt
@@ -0,0 +1,3404 @@
+1
+00:00:00,000 --> 00:00:02,680
+موسيقى
+
+2
+00:00:09,870 --> 00:00:15,410
+بسم الله الرحمن الرحيم المرة الماضية ابتدأنا في
+
+3
+00:00:15,410 --> 00:00:20,530
+section 12-5 و أخدنا ثلاث نقاط طبعا ال section كله
+
+4
+00:00:20,530 --> 00:00:25,170
+بتكلم عن ال lines و ال planes أخدنا النقطة الأولى
+
+5
+00:00:25,170 --> 00:00:28,530
+هي ال lines في الفراق و عرفنا ال parametric
+
+6
+00:00:28,530 --> 00:00:33,650
+equations لهذه ال lines اتنين المسافة ما بين نقطة
+
+7
+00:00:33,650 --> 00:00:39,830
+و خط مستقيم في الفراقتلاتة معادلة مستوى في الفرق
+
+8
+00:00:39,830 --> 00:00:44,350
+هذا ما دُرس في هذا section حتى نهاية المحاضرة
+
+9
+00:00:44,350 --> 00:00:48,850
+الماضية اليوم بنكمل على نفس ال section وبنجي
+
+10
+00:00:48,850 --> 00:00:52,190
+للنقطة الراجعة اللي هي distance from a point to a
+
+11
+00:00:52,190 --> 00:00:56,810
+plane المرة فيها distance من point to a line المرة
+
+12
+00:00:56,810 --> 00:01:01,910
+هي distance from a point to a plane كويس يبقى لو
+
+13
+00:01:01,910 --> 00:01:09,920
+جيت تفيّل انه عندى planeتمام الـ plane هذا سميته M
+
+14
+00:01:09,920 --> 00:01:16,400
+على سبيل المثال في نقطة عندنا هنا فوق نقطة S
+
+15
+00:01:16,400 --> 00:01:25,500
+موجودة في القرار البعد بينها وبين ال plane سميته D
+
+16
+00:01:25,500 --> 00:01:33,450
+بدي أعرف كم مقدار البعد هذا D اللي موجود عندنابقول
+
+17
+00:01:33,450 --> 00:01:39,070
+لك بيس عشان اعرف هذا البعد بروح اخد any point في
+
+18
+00:01:39,070 --> 00:01:46,310
+ال plane اي نقطة موجودة في هذا المستوى والتكن هذه
+
+19
+00:01:46,310 --> 00:01:54,360
+النقطة على سبيل المثال النقطة Pطبعا كل plane في
+
+20
+00:01:54,360 --> 00:01:58,700
+الفراغ بقدر اكتره بدلالة normal vector عليه زي ما
+
+21
+00:01:58,700 --> 00:02:03,520
+شوفنا المرة الماضية المعادلة تبعته ax زائد dy زائد
+
+22
+00:02:03,520 --> 00:02:08,740
+cz يساوي d حيث ال a والb والc هي معاملة ال vector
+
+23
+00:02:08,740 --> 00:02:16,160
+العمودي على هذا ال plane طبعا إذا لو جيت تخيل ان
+
+24
+00:02:16,160 --> 00:02:17,880
+هذا هو normal
+
+25
+00:02:26,460 --> 00:02:32,660
+يبقى الان نبحث عن مقدار distance D ما بين النقطة S
+
+26
+00:02:32,660 --> 00:02:37,200
+اللي بالفرار و ال plane M كلنا بنروح و بناخد اي
+
+27
+00:02:37,200 --> 00:02:41,460
+نقطة P موجودة في ال plane و بنرسم ال normal على ال
+
+28
+00:02:41,460 --> 00:02:46,380
+plane اللي عنها ال normal هذا روحت سميته N
+
+29
+00:03:01,060 --> 00:03:07,160
+لو جيت من النقطة S و نزلت عمود على N بهذا الشكل
+
+30
+00:03:07,160 --> 00:03:12,540
+البعد اللي عندنا هذا و البعد هذا شو العلاقة بينهم؟
+
+31
+00:03:13,540 --> 00:03:17,980
+هي متساوية ان هما البعد العمودي بين النقطة S و بين
+
+32
+00:03:17,980 --> 00:03:26,560
+ال plane D طيب هذا الطول من النقطة P لنقطة S هو
+
+33
+00:03:26,560 --> 00:03:33,420
+طول تبع المتجه Mبس إذا لو ضربت بي اس في cosine
+
+34
+00:03:33,420 --> 00:03:39,340
+الزاوية تيتا بيعطيني مين البعد بين النقطة S ومابين
+
+35
+00:03:39,340 --> 00:03:45,560
+ال plane F يبقى بناء عليه ال distance D بدي ساوي
+
+36
+00:03:45,560 --> 00:03:50,720
+طول ال P S في cosine الزاوية تيتا
+
+37
+00:03:54,620 --> 00:04:00,100
+كويس طيب ننجي لكوصين الزاوية هذا ثيتا بدي استخدم
+
+38
+00:04:00,100 --> 00:04:04,820
+ما سبق دراسته من ال dot product في كتابة كوصين
+
+39
+00:04:04,820 --> 00:04:10,880
+الثيتا بشكل آخر طبعا خلنا نحصل ضرب متجهين u في v ك
+
+40
+00:04:10,880 --> 00:04:15,800
+dot product طول ال u في طول ال v في كوصين الزاوية
+
+41
+00:04:15,800 --> 00:04:21,100
+ثيتا إذا كوصين الزاوية ثيتا بدل زاوية u dot v على
+
+42
+00:04:21,100 --> 00:04:26,550
+طول ال u في طول ال vإذا بناء عليه هذا بدي يعطينا
+
+43
+00:04:26,550 --> 00:04:37,790
+طول ال PS مضروب فيه أسين تيتا الومين ال PS ضد ال N
+
+44
+00:04:37,790 --> 00:04:51,470
+مفسومة على طول ال N بس هيك لا على طول ال PS في طول
+
+45
+00:04:51,470 --> 00:04:58,950
+ال Nمصبوط هيك؟ طيب تمام الان في اختصارات يبقى لو
+
+46
+00:04:58,950 --> 00:05:04,590
+اختصرت طول ال PS مع طول ال PS يبقى هذا الكلام بده
+
+47
+00:05:04,590 --> 00:05:14,110
+يعطينا PS ضد ال N لو L متجة N مقسوما على طول
+
+48
+00:05:14,110 --> 00:05:15,910
+المتجة N
+
+49
+00:05:20,300 --> 00:05:25,980
+إذا من الآن فصاعدا مشان نحسب قداش المسافة ما بين
+
+50
+00:05:25,980 --> 00:05:30,300
+نقطة و plane بدنا ما ياتي بدنا نوجد نقطة في ال
+
+51
+00:05:30,300 --> 00:05:35,360
+plane و نجيب قداش المسافة من النقطة هذه إلى النقطة
+
+52
+00:05:35,360 --> 00:05:41,230
+اللي في الفراروبصير عندي متجة بدي اسميه PS من
+
+53
+00:05:41,230 --> 00:05:44,230
+معادلة الـplane بقدر أجيب المتجة العمودي على
+
+54
+00:05:44,230 --> 00:05:47,810
+الـplane صار عندي two vectors من خلال الـtwo
+
+55
+00:05:47,810 --> 00:05:52,390
+vectors هدول بقدر أعرف كده ال distance دي المبينة
+
+56
+00:05:52,390 --> 00:05:55,690
+في الرسم اللي عندنا مسافة هذه أو المسافة اللي
+
+57
+00:05:55,690 --> 00:06:01,430
+عندنا هذه كده مقدار الـD بقول الـPS ضد ال N على
+
+58
+00:06:01,430 --> 00:06:06,440
+main على طول الـPMحد ألا يستفسر هنا قبل أن ندخل
+
+59
+00:06:06,440 --> 00:06:18,520
+إلى المثال إيه؟ طيب نجي ناخد مثال example find
+
+60
+00:06:18,520 --> 00:06:28,020
+the distance from the point find the distance from
+
+61
+00:06:33,780 --> 00:06:41,920
+من النقطة اتنين و سالم تلاتة واربع to the plane
+
+62
+00:06:41,920 --> 00:06:46,880
+للـ
+
+63
+00:06:46,880 --> 00:06:56,580
+plane اللي هو X زائد اتنين Y زائد اتنين Z يزاوي
+
+64
+00:06:56,580 --> 00:06:57,900
+تلات باشر
+
+65
+00:07:09,620 --> 00:07:14,100
+سؤال مرة تانية بيقول لي هذا ليه جداش المسافة من
+
+66
+00:07:14,100 --> 00:07:19,860
+النقطة اللي هي اتنين وسلب تلاتة واربعة للمستوى X
+
+67
+00:07:19,860 --> 00:07:24,600
+زي دي اتنين Y زي دي اتنين Z يساوي تلتاش عشان نحسب
+
+68
+00:07:24,600 --> 00:07:29,260
+هذه المسافة بيدي نقطة في ال plane وبيدي المتجه
+
+69
+00:07:29,260 --> 00:07:33,040
+العمودي على هذا ال plane الحمد لله المتجه بيجيبه
+
+70
+00:07:33,040 --> 00:07:37,540
+من شكل المعادلة تبعت ال plane يا جباجي بقول ليه؟
+
+71
+00:07:49,460 --> 00:07:58,080
+أز مرتجع M يساوي المعادلة I زائد اتنين J زائد
+
+72
+00:07:58,080 --> 00:07:59,060
+اتنين K
+
+73
+00:08:05,390 --> 00:08:10,170
+كيف بدي أجيب نقطة في هذا ال plane يعني بدي
+
+74
+00:08:10,170 --> 00:08:16,470
+إحداثيات نقطة هذا ال plane يمر بها كيف ممكن أخلك
+
+75
+00:08:16,470 --> 00:08:21,310
+بدل النقطة تلاتة و إذا بدك عشرين ماشي الحال مش
+
+76
+00:08:21,310 --> 00:08:25,170
+مشكلة احنا بدنا بس نقطة واحدة يبقى أبسط شغل شو
+
+77
+00:08:25,170 --> 00:08:30,890
+أعمله مثلا
+
+78
+00:08:30,890 --> 00:08:32,130
+يبقى الأخت
+
+79
+00:08:35,900 --> 00:08:41,840
+لغة enas بتقول ما ياتي انه نضع two variables كل
+
+80
+00:08:41,840 --> 00:08:46,180
+واحد ب zero وبتطلع منها قيمة ال variable التالت
+
+81
+00:08:46,180 --> 00:08:49,560
+وبالتالي هدول بيكونوا احداثيات نقطة موجودة في هذا
+
+82
+00:08:49,560 --> 00:08:53,980
+ال plane كلامها سليم مائة بالمائة يبقى لو جينا
+
+83
+00:08:53,980 --> 00:08:55,080
+قولنا put
+
+84
+00:09:12,450 --> 00:09:18,470
+يعني هذا ليس بالضرورة ان يكونوا هذول ممكن اخد هذول
+
+85
+00:09:18,470 --> 00:09:24,090
+برقم اخر كمان ليس بالضرورة يكون Zero المهم بدي انا
+
+86
+00:09:24,090 --> 00:09:28,570
+ادور على نقطة لكن لما احط واي تساوي زده يساوي Zero
+
+87
+00:09:28,570 --> 00:09:34,630
+اسهللي في الحسابات لما تكون اكتشف عموض في معدل
+
+88
+00:09:34,630 --> 00:09:40,910
+البلد تصير ال X زائد Zero زائد Zero يساوي تلتاشر
+
+89
+00:09:40,910 --> 00:09:41,770
+يبقى X
+
+90
+00:09:47,620 --> 00:09:56,600
+النقطة اللي هي تلتاشر و zero و zero lie in the
+
+91
+00:09:56,600 --> 00:10:02,160
+given plane إذا
+
+92
+00:10:02,160 --> 00:10:07,340
+هذه يا بنات صارت هي النقطة P و النقطة المعلومة
+
+93
+00:10:07,340 --> 00:10:10,980
+اللي عندنا هذه مين بدها تكون حسب الرسم اللي عندنا
+
+94
+00:10:10,980 --> 00:10:16,460
+اسمه S اللي هو النقطة S إذا بلزمني أجيب المتجة ES
+
+95
+00:10:45,370 --> 00:10:56,330
+نقص احد عشر I نقص تلاتة J زائد اربع K عرفنا ايه هو
+
+96
+00:10:56,330 --> 00:11:03,530
+المتجه PS والمتجه N موجود عند هيه اذا بقدر اجيب ال
+
+97
+00:11:03,530 --> 00:11:06,770
+distance D يبقى distance
+
+98
+00:11:29,280 --> 00:11:36,440
+هذه البنات لطول هذه هي absolute value صحيح ليها
+
+99
+00:11:36,440 --> 00:11:37,080
+والله عيب
+
+100
+00:11:46,580 --> 00:11:52,280
+أو الطول يجب أن يكون قيمة موجبة فباخده الـ
+
+101
+00:11:52,280 --> 00:11:56,280
+absolute value إذا هذا الكلام بده يساوي ال
+
+102
+00:11:56,280 --> 00:12:01,420
+absolute value بده يعمل dot product ما بين ال P S
+
+103
+00:12:01,420 --> 00:12:04,040
+و ال N يبقى
+
+104
+00:12:08,880 --> 00:12:15,480
+بعدين ناقص ثلاثة في اتنين ناقص ستة و بعدين اربعة
+
+105
+00:12:15,480 --> 00:12:21,820
+في اتنين زائد تمانية كله على الجذر التربيهي
+
+106
+00:12:44,670 --> 00:12:50,170
+إذا نقول المسافة من النقطة هذه للـplane يساوي كده؟
+
+107
+00:12:50,170 --> 00:12:56,190
+يساوي ثلاثة من وحدات الطول و دي هي remark التالية
+
+108
+00:12:56,190 --> 00:13:01,890
+remark
+
+109
+00:13:01,890 --> 00:13:10,170
+two planes two planes are perpendicular
+
+110
+00:13:14,530 --> 00:13:23,090
+أتر تنديكيونار أو Parallel
+
+111
+00:13:23,090 --> 00:13:31,110
+المتعمقين أو المتوازين have their normals
+
+112
+00:13:42,820 --> 00:13:51,280
+يا الفن دي في الأرض؟ أو أهلا؟
+
+113
+00:13:51,280 --> 00:14:03,820
+هاد
+
+114
+00:14:03,820 --> 00:14:09,030
+أقبلكوا معايا هنا والله يعالىلو جيت تخيلت ان عندي
+
+115
+00:14:09,030 --> 00:14:15,630
+مستوين ومستوين متوازين رسمت ال vector العمودي على
+
+116
+00:14:15,630 --> 00:14:20,150
+المستوى الأول و ال vector العمودي على المستوى
+
+117
+00:14:20,150 --> 00:14:23,810
+الثاني شو العلاقة بين هذين ال two vectors
+
+118
+00:14:40,350 --> 00:14:46,070
+انا عندى الان two planes اتنين are parallel بدي
+
+119
+00:14:46,070 --> 00:14:49,830
+ارسم العمود على الاول و العمود على التانى شو له
+
+120
+00:14:49,830 --> 00:14:54,130
+لقب اللي اتنين اتنين parallel اذا if two planes
+
+121
+00:14:54,130 --> 00:14:58,310
+are parallel then their normals are parallel و
+
+122
+00:14:58,310 --> 00:15:02,130
+العكس لو كانت two normals are parallel you get two
+
+123
+00:15:02,130 --> 00:15:05,970
+vectors are parallel نيجى لحكاية التعامل خلّيكي
+
+124
+00:15:05,970 --> 00:15:06,750
+هاتيلي هذا
+
+125
+00:15:11,270 --> 00:15:14,710
+أحنا لدينا الان two planes بالشكل اللي لدينا هنا
+
+126
+00:15:14,710 --> 00:15:18,830
+يبقى دول ال two planes are perpendicular اتنين
+
+127
+00:15:18,830 --> 00:15:23,390
+متعمدين الزاوية الزوجية بين المستوين له تسعين درجة
+
+128
+00:15:23,390 --> 00:15:28,310
+بترسم العمود على المستوى الأول و العمود على
+
+129
+00:15:28,310 --> 00:15:32,870
+المستوى الثاني ايش العلاقة بين ال two line او two
+
+130
+00:15:32,870 --> 00:15:37,110
+perpendicular يبقى اتنين are orthogonal يبقى بناء
+
+131
+00:15:37,110 --> 00:15:44,960
+عليه لو عندي two planesالعمودين على هذه المستقيمين
+
+132
+00:15:44,960 --> 00:15:48,020
+يكونان متعامدان
+
+133
+00:15:54,230 --> 00:15:59,710
+انا عندى هذا plane و هذا ال plane تبع السكين اتنين
+
+134
+00:15:59,710 --> 00:16:03,550
+اعرفى perpendicular فى ال corner اللى عندى لو جيت
+
+135
+00:16:03,550 --> 00:16:08,730
+رسمت من هنا عمود على ال plane الاول و رسمت عمود
+
+136
+00:16:08,730 --> 00:16:12,510
+على ال plane التانى كذا بينهم تسعين درجة هى اللى
+
+137
+00:16:12,510 --> 00:16:16,470
+بتقوله الريمانبتقولي two planes are perpendicular
+
+138
+00:16:16,470 --> 00:16:23,290
+اتنين بيكونوا متعامدين او متوازية if they are
+
+139
+00:16:23,290 --> 00:16:27,470
+normal vectors اذا جبت normal على كل واحد من ال
+
+140
+00:16:27,470 --> 00:16:30,290
+two vectors هدول بلاقي اتنين اذا perpendicular
+
+141
+00:16:30,290 --> 00:16:34,110
+بيكون perpendicular اذا parallel بيكون اتنين هدول
+
+142
+00:16:34,110 --> 00:16:40,910
+مالهم parallel نعطي مثال على ذلك يبقى example
+
+143
+00:16:49,120 --> 00:16:58,520
+بقول شو ده the two planes show that the two A
+
+144
+00:16:58,520 --> 00:17:08,040
+planes هي لإنه مستويين اللي هو تلاتة X زائد ستة Y
+
+145
+00:17:08,040 --> 00:17:10,720
+ناقص تسعة Z
+
+146
+00:17:15,180 --> 00:17:26,220
+والـ X زائد اتنين Y نقص ثانوتها Z بيكون واحد اتنين
+
+147
+00:17:26,220 --> 00:17:29,700
+اتنين
+
+148
+00:17:29,700 --> 00:17:37,700
+متوازين and find the distance
+
+149
+00:17:42,400 --> 00:17:46,020
+وأتولى المسافة between them
+
+150
+00:18:25,560 --> 00:18:30,520
+سؤال مرة تانية ماطيني معادلتين ل two players كل
+
+151
+00:18:30,520 --> 00:18:34,980
+واحد المعادلةوقال لي بيقول ان two planes هدول are
+
+152
+00:18:34,980 --> 00:18:38,420
+parallel كيف بنفسي ان two planes هدول هدول هدول
+
+153
+00:18:38,420 --> 00:18:44,520
+هدول هدول هدول هدول
+
+154
+00:18:44,520 --> 00:18:44,560
+هدول هدول هدول هدول هدول هدول هدول هدول هدول هدول
+
+155
+00:18:44,560 --> 00:18:44,600
+هدول هدول هدول هدول هدول هدول هدول هدول هدول هدول
+
+156
+00:18:44,600 --> 00:18:46,240
+هدول هدول هدول هدول هدول هدول هدول هدول هدول هدول
+
+157
+00:18:46,240 --> 00:18:49,820
+هدول هدول هدول هدول هدول هدول هدول هدول هدول هدول
+
+158
+00:18:49,820 --> 00:18:49,840
+هدول هدول هدول هدول هدول هدول هدول هدول هدول هدول
+
+159
+00:18:49,840 --> 00:18:51,780
+هدول هدول هدول هدول هدول هدول هدول هدول هدول هدول
+
+160
+00:19:15,670 --> 00:19:24,450
+normal first to play into
+
+161
+00:19:24,450 --> 00:19:28,430
+as
+
+162
+00:19:28,430 --> 00:19:29,090
+a vector
+
+163
+00:19:34,270 --> 00:19:46,990
+نقص ثلاثة كيلو مو اعمل to the second place بيهامد
+
+164
+00:19:46,990 --> 00:19:50,170
+عمودي عالمين على المستوى أسهل
+
+165
+00:19:56,220 --> 00:20:00,240
+طبعاً واضح انه في عامل مشترك هو مين تلاتة يعني لو
+
+166
+00:20:00,240 --> 00:20:06,340
+أخدت تلاتة بصير عندي I زائدي اتنين J ناقص تلاتة
+
+167
+00:20:06,340 --> 00:20:12,200
+كيلو المتجه بين القوصين هو المتجه مين ال two يبقى
+
+168
+00:20:12,200 --> 00:20:18,920
+هذا الكلام بيسوي تلاتة into هذا بدي يعطينا in one
+
+169
+00:20:18,920 --> 00:20:25,460
+and in two اتنين معاهم are parallel
+
+170
+00:20:31,990 --> 00:20:36,730
+يبقى المستويات الاتنين بتاعتهم يبقى هذا اللي
+
+171
+00:20:36,730 --> 00:20:44,030
+يعطيها هي the two given
+
+172
+00:20:44,030 --> 00:20:48,190
+planes
+
+173
+00:20:48,190 --> 00:20:52,510
+are parallel
+
+174
+00:20:55,080 --> 00:20:59,340
+يبقى المستوى هذول متوازين هذا المطلوب الأول من
+
+175
+00:20:59,340 --> 00:21:03,800
+المثلة المطلوب التاني جال يهدف المسافة ما بين ال
+
+176
+00:21:03,800 --> 00:21:08,440
+two planes هذول يعني يا بنات لو لينا قلنا هذا هو
+
+177
+00:21:08,440 --> 00:21:15,140
+المستوى الأول على سبيل المثال وهذا هو المستوى
+
+178
+00:21:15,140 --> 00:21:21,060
+الثانيبدي اعرف كده المسافة ما بين الاتنين المسافة
+
+179
+00:21:21,060 --> 00:21:26,060
+ما بين الاتنين هي المسافة العمودية طبعا هذا المتجه
+
+180
+00:21:26,060 --> 00:21:36,160
+اللي هو مين M1 العمودي على الأول شكل على هذا وهذا
+
+181
+00:21:36,160 --> 00:21:43,550
+المتجه التانياللي هو into العمودي على المستوى
+
+182
+00:21:43,550 --> 00:21:50,950
+الثاني قاللي هذا كده البعد فيما بينهما بقول والله
+
+183
+00:21:50,950 --> 00:21:56,990
+كويس إذا جدرنا نجيب نقطتين في هذين المستوى النقطة
+
+184
+00:21:56,990 --> 00:22:01,890
+في المستوى الأول ونقطة في المستوى الثاني ووصلت
+
+185
+00:22:01,890 --> 00:22:08,190
+فيما بينهم إذا بصير هذا PSبدي متجه عمودي على أحد
+
+186
+00:22:08,190 --> 00:22:11,930
+المستويين الحمد لله عند اثنين متجه عمودي على الأول
+
+187
+00:22:11,930 --> 00:22:16,850
+و متجه عمودي على التاني و اتنين are parallel مظبوط
+
+188
+00:22:16,850 --> 00:22:22,750
+يبقى بس تلنا نقطة أو نقطتين في المستويين اللي
+
+189
+00:22:22,750 --> 00:22:28,550
+عندنا بدي نقطة في كل من المستويين شو أعمل؟
+
+190
+00:22:35,620 --> 00:22:42,520
+بنفس الطريقة بقدر أجيب اللي هو نقطة في كل من
+
+191
+00:22:42,520 --> 00:22:50,720
+المستوى يعني إذا لو جيت قلت هنا هو مثلا y سوى z
+
+192
+00:22:50,720 --> 00:23:01,840
+سوى zero in the given airplanes we getبنحصل علامات
+
+193
+00:23:01,840 --> 00:23:06,500
+في الدرجة اللي اتنين الأول بصير عندي تلاتة X يساوي
+
+194
+00:23:06,500 --> 00:23:12,540
+درجة أربعة والتاني بصير عندي X يساوي واحدة
+
+195
+00:23:28,980 --> 00:23:34,100
+جت سميت النقطة هذه اللي هي النقطة S اللي هي مين؟
+
+196
+00:23:34,100 --> 00:23:41,360
+أربع على تلاتة وزير وزير تمام جت سميت النقطة هذه
+
+197
+00:23:41,360 --> 00:23:47,380
+اللي هي النقطة P اللي أحدثيها او أحدثيتها واحد
+
+198
+00:23:47,380 --> 00:23:54,340
+وزير وزير إذا بقدر أجيب المتجة بـS اللي عندها يبقى
+
+199
+00:23:54,340 --> 00:23:55,720
+هذا هو ال vector
+
+200
+00:24:05,170 --> 00:24:13,070
+كويس اذا انا بعد البعد العمودي ما بين الاتنين اللي
+
+201
+00:24:13,070 --> 00:24:18,030
+هو البعد مين البعد هذا اللي هو دي اعمل لي زاوية
+
+202
+00:24:18,030 --> 00:24:23,770
+تيتا ما بين المتجانين اذا هذا يعتبر موازي لمين
+
+203
+00:24:23,770 --> 00:24:27,550
+موازي لل vector n هذا
+
+204
+00:24:32,160 --> 00:24:39,300
+متجه N2 اذا على ان اتنين ادوات متوازية اذا بدي
+
+205
+00:24:39,300 --> 00:24:50,680
+اجيب ال distance D بقول هي ال PS ضاد من N2 على طول
+
+206
+00:24:50,680 --> 00:24:53,420
+ال N2
+
+207
+00:25:05,280 --> 00:25:11,580
+أربعة على تلاتة أربعة على تلاتة ناقص واحد في اتجاه
+
+208
+00:25:11,580 --> 00:25:16,800
+الـ I يبقى المُركّبات الأثناء كل واحدة بصفر الباقي
+
+209
+00:25:16,800 --> 00:25:25,500
+يبقى هذا بيساوي طول I يبقى ال distance دي بدها
+
+210
+00:25:25,500 --> 00:25:32,140
+تساوي اللي هو ال absolute value لمن؟ لل P S ضد ال
+
+211
+00:25:32,140 --> 00:25:39,990
+N2 اللي هو طولفاهمين في ال N2 وين ال N2 لنا اللي
+
+212
+00:25:39,990 --> 00:25:48,210
+هو ال I يبقى طول في واحد والباقي قداش Zero Zero
+
+213
+00:25:48,210 --> 00:25:54,170
+أخرى خلصنا يبقى هذه الأحداثيات ال PS اللي عندنا
+
+214
+00:25:54,170 --> 00:26:02,310
+عالميا على طول المتجه N2 اللي هو الجدري التربيعي
+
+215
+00:26:02,310 --> 00:26:04,690
+لل N2
+
+216
+00:26:15,440 --> 00:26:23,940
+يبقى هذه المسافة بين المستويين المتوازيين نجي الآن
+
+217
+00:26:23,940 --> 00:26:27,960
+للنقطة الأخيرة بيانة السمش اللبنان لنقطة أربع من
+
+218
+00:26:27,960 --> 00:26:31,260
+خمسة هحطها على صفرة ال definition
+
+219
+00:26:53,160 --> 00:26:58,260
+الزاوية بين المستوين المبدأ قاعة عين is the angle
+
+220
+00:26:58,260 --> 00:27:08,940
+between is the angle between is
+
+221
+00:27:08,940 --> 00:27:13,800
+the angle between their
+
+222
+00:27:13,800 --> 00:27:20,900
+normal vectors between their normal vectors
+
+223
+00:27:34,860 --> 00:27:40,620
+مرحباً بكموانتوا من الصفر السابع لغاية الصفر
+
+224
+00:27:40,620 --> 00:27:45,940
+التاسع مرحلة الاعدادية هذه الزاوية بين المستقيمين
+
+225
+00:27:45,940 --> 00:27:50,040
+تساوي الزاوية بين العمودين علي هدين المستقيمين
+
+226
+00:27:50,040 --> 00:27:55,400
+يعني الزاوية المحصورة بين المستقيمين متقاطعين
+
+227
+00:27:55,400 --> 00:28:01,800
+تساوي الزاوية بين المستقيمين اللي هو العمودين علي
+
+228
+00:28:01,800 --> 00:28:06,840
+هدين المستقيمين سمعتوا فيهاتمام احنا هنا نفس
+
+229
+00:28:06,840 --> 00:28:11,580
+الفكرة بنقول الزاوية بين two intersecting planes
+
+230
+00:28:11,580 --> 00:28:16,180
+هي الزاوية بين ال normal vectors يبقى احنا بدنا
+
+231
+00:28:16,180 --> 00:28:23,240
+نروح ندور على مين على two intersecting planes يبقى
+
+232
+00:28:23,240 --> 00:28:24,280
+لو روحت قلت
+
+233
+00:28:32,590 --> 00:28:38,090
+وفي عندى مستوى ثانى المستوى الثانى كان بهذا الشكل
+
+234
+00:28:38,090 --> 00:28:45,530
+يبقى المستوى الاتنين هدول اتقاطعوا في خط التقاطع
+
+235
+00:28:45,530 --> 00:28:49,270
+اللى عندنا كويس
+
+236
+00:28:49,910 --> 00:28:56,030
+هي بهذا خط قاطع المستوين بدي أرسم عمودي على
+
+237
+00:28:56,030 --> 00:29:01,670
+المستوى الأول و كذلك عمودي على المستوى الثاني لو
+
+238
+00:29:01,670 --> 00:29:08,190
+جيت قلت هذا عمودي على المستوى الأول اللي هو N1
+
+239
+00:29:08,190 --> 00:29:13,910
+يعني الأزرق عمودي على المستوى الأزرق هذا و ال
+
+240
+00:29:13,910 --> 00:29:19,770
+vector قصد ال vector N1 و جيت هنا كمان رسمت عمود
+
+241
+00:29:25,630 --> 00:29:33,510
+طبعا الزاوية هذه هي الزاوية ما بين two normal
+
+242
+00:29:33,510 --> 00:29:38,270
+vectors عمودي على المستوى الأول و الخط الأزرق
+
+243
+00:29:38,270 --> 00:29:44,130
+عمودي على المستوى الأزرق و الخط الأسود عمودي على
+
+244
+00:29:44,130 --> 00:29:50,680
+المستوى الأسودالان بدى جدش الزاوية بين المستوان
+
+245
+00:29:50,680 --> 00:29:54,620
+طبعا الزاوية البنات هي الزاوية الزوجية بين
+
+246
+00:29:54,620 --> 00:30:01,040
+المستوان الزاوية هادي يعني لما اجيب two planes هات
+
+247
+00:30:01,040 --> 00:30:06,860
+شوية بلغتها لما اجيب ال two planes المتقطعين بهذا
+
+248
+00:30:06,860 --> 00:30:13,750
+الشكل يجد اتنين هدول بينهم ايش؟ بينهم زاويةعلى طول
+
+249
+00:30:13,750 --> 00:30:17,570
+خط التقاطع هذه بالعامة بسميها الزاوية الزوجية
+
+250
+00:30:17,570 --> 00:30:22,290
+الانجل تتوين تتقاطع تتقاطع تتقاطع تتقاطع تتقاطع
+
+251
+00:30:22,290 --> 00:30:29,190
+تتقاطع تتقاطع
+
+252
+00:30:36,740 --> 00:30:41,920
+الزاوية المحصورة بين two normal vectors تساوي
+
+253
+00:30:41,920 --> 00:30:46,660
+عمليا الزاوية الموجودة بين المستويين
+
+254
+00:30:52,930 --> 00:30:57,390
+يعني ارسم المتجه العمودي على المستوى الأول و ارسم
+
+255
+00:30:57,390 --> 00:31:02,130
+المتجه العمودي على المستوى التالي الزاوية بينهم هي
+
+256
+00:31:02,130 --> 00:31:11,110
+الزاوية الزوجية بين المستويين تمام نعطي مثال على
+
+257
+00:31:11,110 --> 00:31:11,710
+ذلك
+
+258
+00:31:26,930 --> 00:31:42,630
+the angle between the planes بين المستويين ال ..
+
+259
+00:31:42,630 --> 00:31:50,930
+اللي هو X زائد أقع واحد ناقص تلاتة Z يساوي واحد
+
+260
+00:31:50,930 --> 00:32:03,470
+and اللي هو ناقص تلاتة Xستة Y زائد سبعة Z
+
+261
+00:32:40,400 --> 00:32:43,720
+بنزّه من المستوات اللي اتنين هدول ان انا بده اجيب
+
+262
+00:32:43,720 --> 00:32:49,140
+ال normal vector على كل من المستوات يبقى بداجي
+
+263
+00:32:49,140 --> 00:32:59,020
+هقول N1 اللي هو I زائد 4J نقص تلاتة K normal to
+
+264
+00:32:59,020 --> 00:33:03,820
+the first
+
+265
+00:33:03,820 --> 00:33:04,360
+plane
+
+266
+00:33:12,070 --> 00:33:22,650
+into الهو عبارة عن ناقص ثلاثة I زائد ستة G زائد
+
+267
+00:33:22,650 --> 00:33:31,070
+سبعة K normal to the second اتلقى
+
+268
+00:33:31,070 --> 00:33:36,470
+المضتج اتلقى الآن بدي اتزامر بعمل product ضد ما
+
+269
+00:33:36,470 --> 00:33:44,220
+بينهما فماجي بقولهالـ N1 ضد
+
+270
+00:33:44,220 --> 00:33:51,720
+N2 متجه الثاني N2 يساوي طول الـ
+
+271
+00:33:56,420 --> 00:34:02,440
+الزاوية بينهما.الان بدي اعمل ضطمة بين الفلين يبقى
+
+272
+00:34:02,440 --> 00:34:08,360
+هذه ناقص ثلاثة واللي بعدها اربعة في ستة بزائد
+
+273
+00:34:08,360 --> 00:34:15,660
+اربعة وعشرين واللي بعدها ناقص واحد وعشرين بدي ساوي
+
+274
+00:34:19,140 --> 00:34:25,020
+in one اللي هو واحد زائد ستاشر زائد تسعة واحد زائد
+
+275
+00:34:25,020 --> 00:34:31,120
+ستاشر زائد تسعة والجدار التاني اللي هو المتجه
+
+276
+00:34:31,120 --> 00:34:39,020
+التاني اللي هو تسعة زائد ستة وتلاتين تسعة زائد ستة
+
+277
+00:34:39,020 --> 00:34:47,520
+وتلاتين زائد تسعة واربعين في كساين الزاوية ديقدرش
+
+278
+00:34:47,520 --> 00:34:52,900
+دي أمانة الطرف الشمالي؟ Zero. إذا بقسم على مين؟
+
+279
+00:34:52,900 --> 00:34:57,860
+على حصر ضرب الجدرين، بسيري عندي وصين تيتا سواء
+
+280
+00:34:57,860 --> 00:35:02,780
+قدر؟ Zero. فبنسأل السؤال التالي، مين الزاوية اللي
+
+281
+00:35:02,780 --> 00:35:06,800
+جيب تمامها يسوى صفر؟ 90 درجة.
+
+282
+00:35:17,100 --> 00:35:29,980
+يبقى this means that the two planes are
+
+283
+00:35:29,980 --> 00:35:31,380
+perpendicular
+
+284
+00:35:40,480 --> 00:35:45,740
+أحنا حسبنا الزاوية وجينا اتنين are perpendicular
+
+285
+00:35:45,740 --> 00:35:51,000
+عليك يكون انتهى ال section ونجي لل exercises
+
+286
+00:35:51,000 --> 00:35:59,940
+اتناشر خمسة المسائل من واحد لتمانية واربعين ال pod
+
+287
+00:35:59,940 --> 00:36:02,700
+ومن تلاتة وخمسين
+
+288
+00:36:41,170 --> 00:36:45,970
+بنجي لل section اللي ياليه وهو اخر section في هذا
+
+289
+00:36:45,970 --> 00:36:53,210
+ال chapter اللي هو section اتناشر ستة يتحدث عن ال
+
+290
+00:36:53,210 --> 00:36:59,130
+cylinder cylinders
+
+291
+00:36:59,130 --> 00:37:09,710
+and quadric surfaces
+
+292
+00:37:15,480 --> 00:37:23,960
+نبدأ أول شيء بملاحظة الـ cylinders إيش
+
+293
+00:37:23,960 --> 00:37:29,660
+معناه cylinders يا بنات؟ بالعربى أسطوانة ممتاز طيب
+
+294
+00:37:29,660 --> 00:37:35,820
+الأسطوانة هل ضروري يكون مقطع تبعها عبارة عن دائرة؟
+
+295
+00:37:37,770 --> 00:37:42,070
+مصورة عادية لو قطعت المطبع هي عبارة عن دائرة لكن
+
+296
+00:37:42,070 --> 00:37:46,730
+هل لما أقول cylinder في الفرار بالضرورة أن يكون
+
+297
+00:37:46,730 --> 00:37:52,730
+المطبع دائرة؟ لأ، شوفي من هنا، لو جيت قلت هذا
+
+298
+00:37:52,730 --> 00:37:57,490
+عبارة عن سطح الشكل اللي عندنا، انت شوفي اللي انت
+
+299
+00:37:57,490 --> 00:38:03,690
+شايفينه أنا، كويس؟ يجي هذا بسميه cylinder، سطح
+
+300
+00:38:03,690 --> 00:38:06,330
+أسواني، حتى لو لم يكن مغلق
+
+301
+00:38:14,680 --> 00:38:20,060
+يبقى المقطع عبارة عن إيه؟ عبارة عن دائرة، يبقى
+
+302
+00:38:20,060 --> 00:38:24,720
+دائرها الشكل اللي عندنا هذا، مش واضح، بلاش، بنوضح
+
+303
+00:38:31,300 --> 00:38:37,320
+يبقى هذه cylinder و كذلك لو خليتها بهذا الشكل يبقى
+
+304
+00:38:37,320 --> 00:38:43,340
+هنا cylinder لو كبرتها و وضحت اكتر مثلك هذا السطح
+
+305
+00:38:43,340 --> 00:38:48,860
+هو عبارة عن ايش عبارة عن cylinder لو خليته مفتوح
+
+306
+00:38:48,860 --> 00:38:53,960
+بالشكل هذا cylinder لو جبت شكل تاني زيه و خليته من
+
+307
+00:38:53,960 --> 00:39:00,300
+ناحية تانية و اتنين مع بعض كذلك يعتبر cylinderطيب
+
+308
+00:39:00,300 --> 00:39:06,820
+ايش ال quadric surface او ال quadric surfaces ايش
+
+309
+00:39:06,820 --> 00:39:12,400
+معناه quadric بالعربي؟ ثنائي مش مربع، اذاك square
+
+310
+00:39:12,400 --> 00:39:16,860
+مربع، يبقى ال quadric ثنائي، surface سطح، يبقى
+
+311
+00:39:16,860 --> 00:39:24,080
+السطوح الثنائية، يعني المجسمات بالعربي اللي بتكون
+
+312
+00:39:24,080 --> 00:39:31,800
+ا في الفرارسياتك وانت جاهز تعتبري مجسم موجود في
+
+313
+00:39:31,800 --> 00:39:38,260
+الفراغ أو شكلك الخارجي يعتبر quadric surface تمام؟
+
+314
+00:39:38,260 --> 00:39:41,820
+يبقى هذا ال quadric surface اللي انا بدنا نميز ما
+
+315
+00:39:41,820 --> 00:39:46,000
+بين ال quadric surfaces و ال cylinderهناخد ستة
+
+316
+00:39:46,000 --> 00:39:51,420
+quadric surfaces ست سطوح ثنائية ونعرف معادلة كل
+
+317
+00:39:51,420 --> 00:39:56,500
+سطح من هذه السطوح طبعا هذه السطوح مشهورة وقبلهم
+
+318
+00:39:56,500 --> 00:40:03,340
+هناخد وضع A السيلندر ونشوف كيف بنرسم كل واحدة من
+
+319
+00:40:03,340 --> 00:40:10,320
+ال quadric surfaces وكذلك السيلندر المختلفةطيب على
+
+320
+00:40:10,320 --> 00:40:15,200
+اي حال في الفراغ بالنسبة للسيلندر بلاقي معادلة
+
+321
+00:40:15,200 --> 00:40:18,980
+فيها رمزين فقط طبعا احنا بنشتغل في ال
+
+322
+00:40:39,280 --> 00:40:43,780
+طيب الكلمتين اللي انت سمعتهم بده اكتبهم و بعد نشوف
+
+323
+00:40:43,780 --> 00:40:49,160
+كيف بده نرسم بعد اللي هو بعض ال cylinder فباجي
+
+324
+00:40:49,160 --> 00:40:49,620
+بقول
+
+325
+00:41:05,940 --> 00:41:15,780
+Y أو Z أي واحد منهم مفقود من
+
+326
+00:41:15,780 --> 00:41:21,000
+المعادلة
+
+327
+00:41:21,000 --> 00:41:27,300
+مش موجود في المعادلة تبع في الصفر of a surface
+
+328
+00:41:27,300 --> 00:41:34,920
+then the surface then the surface
+
+329
+00:41:45,110 --> 00:41:51,510
+هو عبارة عن صوالة مع جنريتر
+
+330
+00:41:51,510 --> 00:41:57,590
+مولد
+
+331
+00:41:57,590 --> 00:41:58,710
+للسيلندر
+
+332
+00:42:22,150 --> 00:42:30,950
+to the axis corresponding ..
+
+333
+00:42:30,950 --> 00:42:40,450
+corresponding المناظر to the missing variable
+
+334
+00:42:40,450 --> 00:42:46,690
+example
+
+335
+00:42:58,900 --> 00:43:13,860
+half of the following cylinders المرأة
+
+336
+00:43:13,860 --> 00:43:24,860
+ال X تربيع زائد اربع زت تربيع ددرساه يوم ستة عشر
+
+337
+00:43:24,860 --> 00:43:36,650
+مرة BX يساوي Y تربيع نمرة C Z تساوي تسعة نقص Y
+
+338
+00:43:36,650 --> 00:43:45,570
+تربيع نمرة D Y تربيع على أربعة نقص X تربيع على
+
+339
+00:43:45,570 --> 00:43:47,610
+تسعة يساوي واحدة
+
+340
+00:44:10,030 --> 00:44:15,570
+بنشوف كيف بنحكم على رسمة انها عندى رسمة أسطوانة أو
+
+341
+00:44:15,570 --> 00:44:20,510
+غيره وإذا كانت أسطوانة يبقى إلها محور بدنا نعرف
+
+342
+00:44:20,510 --> 00:44:28,270
+مين هو المحور اللى عندنا هذا ولها مولد تمام طلع يا
+
+343
+00:44:28,270 --> 00:44:34,350
+بنات هنا لو أنا ثبت اللى عندى المستقبل الأزرق اللى
+
+344
+00:44:34,350 --> 00:44:39,670
+شايفهو روح جيبت موازي له اللي همين الأسود اللي
+
+345
+00:44:39,670 --> 00:44:44,150
+عندنا هنا و قولت انت يا أزرق ضلك سابقا تصحى تتحرك
+
+346
+00:44:44,150 --> 00:44:51,050
+انت يا أسود بدك تتحرك حوالي الأزرق فعشان تضلك ماشي
+
+347
+00:44:51,050 --> 00:44:56,410
+على منحنى و تضلك موازي للأزرق انت جالس هيرسملي من
+
+348
+00:44:56,410 --> 00:45:03,170
+الخارج سطح أسطواني تمام؟ المنطقة اللي بمسحها الخطة
+
+349
+00:45:03,170 --> 00:45:07,320
+اللي عندنا هنا كلهابدي أرسلهم لمين؟ سطح، هذا السطح
+
+350
+00:45:07,320 --> 00:45:13,420
+بسميه أسوانة أو بسميه cylinder يبقى هذا اللي هو
+
+351
+00:45:13,420 --> 00:45:16,940
+الكلام أو السطرين اللي أنا كاتبينهم هنا لو كان
+
+352
+00:45:16,940 --> 00:45:21,420
+واحد من المتغيرات مفقود من المعادلة يبقى ال
+
+353
+00:45:21,420 --> 00:45:24,560
+surface اللي عندي بدي أقول هو عبارة عن cylinder
+
+354
+00:45:24,560 --> 00:45:29,720
+ولها مولد، شو مولد؟ يعني اللي بدي أولد السطح
+
+355
+00:45:29,720 --> 00:45:37,690
+الخارجي تبع ال cylinderوهذا بدي يكون موازن لل axis
+
+356
+00:45:37,690 --> 00:45:43,210
+المناظر لمين للمتغير المفقود يعني ايش يا بنات قصد
+
+357
+00:45:43,210 --> 00:45:47,910
+يقول بالظبط من الكلابين اللي كتبهم هدول؟يقول لمن
+
+358
+00:45:47,910 --> 00:45:53,570
+يعطيك معادلة وقدر تعرفها معادلة سيلندر ولا لا تطلع
+
+359
+00:45:53,570 --> 00:45:56,930
+على المعادلة هذه المعادلة في الفرح أصلا تلت
+
+360
+00:45:56,930 --> 00:46:03,210
+متغيرات X وY وZ لو لجيت واحد منهم مفهوم مش موجود
+
+361
+00:46:03,210 --> 00:46:07,690
+يعني يا إما X وZ اللي موجود، يا إما X وY، يا إما Y
+
+362
+00:46:07,690 --> 00:46:13,050
+وZرمزين من الحد ماشوفش غير رمزين إذا هذه معادنة
+
+363
+00:46:13,050 --> 00:46:19,770
+سيلندر I imagine مين ال axis تبع السيلندر اللي هو
+
+364
+00:46:19,770 --> 00:46:25,530
+الرمز الغائب أو ما يوازيه ممكن يكون معمول لكثير
+
+365
+00:46:25,530 --> 00:46:29,650
+وبالتالي مايكونش ايه اللي هو المحور الغائب او
+
+366
+00:46:29,650 --> 00:46:30,630
+الرمز الغائب
+
+367
+00:46:51,540 --> 00:46:54,260
+الكلام اللي احنا بيقوله بيروح التطبق على أرض
+
+368
+00:46:54,260 --> 00:47:01,010
+الواقعقال لي مثال ارسم لي كل من الاستوانات اية
+
+369
+00:47:01,010 --> 00:47:05,090
+تالية وقال لي X تربية زائد اربعة زيت تربية تساوي
+
+370
+00:47:05,090 --> 00:47:10,250
+ستة عشر لو سألت وقلتلك هذه المعادلة فيديو ليه ترجع
+
+371
+00:47:10,250 --> 00:47:14,890
+معادلة ايه معادلة
+
+372
+00:47:14,890 --> 00:47:22,450
+ايه الأولى ممتاز ع ستة عشر يبقى فيديو X تربية ع
+
+373
+00:47:22,450 --> 00:47:26,800
+ستة عشرذا زدت فيه علقة ما يسوي واحد عنها دي دارة
+
+374
+00:47:26,800 --> 00:47:34,260
+تلفت تلفت تمام ايوة يبقى هادى لو اخدت ليلي الليل
+
+375
+00:47:34,260 --> 00:47:39,740
+بيكون هذا اليف ساكن انا في الفرار الرمزين اللي
+
+376
+00:47:39,740 --> 00:47:48,060
+موجودين اللي هم الرمز غايم ، إذا Y هو المحور أو
+
+377
+00:47:48,060 --> 00:47:52,520
+الموازي للمحور إذا وصلنا لمعمولها Chef. هل هذا رصد
+
+378
+00:47:52,520 --> 00:47:56,300
+الـChef؟ في الـChef ممتاز يرجى المحور تبع
+
+379
+00:47:56,300 --> 00:48:02,300
+الـCylinder هذي هو الـY Axis. طبعا؟ أيوة تعالى
+
+380
+00:48:02,300 --> 00:48:09,100
+نرسمه. يرجى هذا لما اتفاقنا على إنها الـCylinderبس
+
+381
+00:48:09,100 --> 00:48:14,120
+المقطع تبعها دائرة ولا ellipse اللي بيكون على شكل
+
+382
+00:48:14,120 --> 00:48:18,880
+ellipse المحور تبع هذه الوسطه ده هو محور
+
+383
+00:48:42,970 --> 00:48:46,570
+تمام؟ طيب و المقطع اللي يقول على شكل إيه؟ اللي
+
+384
+00:48:46,570 --> 00:48:53,330
+يقول على شكل Alex إذا لو جيت قلت هذا ال Alex و من
+
+385
+00:48:53,330 --> 00:48:57,010
+الناحية التانية بالشكل اللي عندنا هذا و هذا هو
+
+386
+00:48:57,010 --> 00:49:03,010
+إيه؟ هو الشكل اللي عندنا لأن هذه الأسطورة المقطع
+
+387
+00:49:03,010 --> 00:49:04,610
+تباعها عبارة عن
+
+388
+00:49:16,130 --> 00:49:26,310
+تمام؟ يبقى هذا يكون يعني لهنا شوية يبقى
+
+389
+00:49:26,310 --> 00:49:30,670
+هذه المقطع او هذا المجسم اللي اتكون عندنا او هذه
+
+390
+00:49:30,670 --> 00:49:35,370
+هي ال cylinder اللي تكون عندنا هذه رسم يا بنات
+
+391
+00:49:35,370 --> 00:49:42,810
+تعتبر رسم سهلة يعني مافيش فيها اي صعوبة مباشرةأمان
+
+392
+00:49:42,810 --> 00:49:47,570
+طيب نيجي للرسمة التانية و نشوف إيش قصته هذا X
+
+393
+00:49:47,570 --> 00:49:52,330
+يساوي Y تربيع لو قصتك في الكليل هذه معناه كده
+
+394
+00:49:52,330 --> 00:49:58,610
+Parabola فتطهر مكبر لكن أنا بدي يها تقول في الفراغ
+
+395
+00:49:58,610 --> 00:50:04,650
+إذا يا بنات ال parabola هتصير في الفراغ بهذا الشكل
+
+396
+00:50:04,650 --> 00:50:11,050
+من هنا كده من هنا كده من هنا كده من هنا كده من هنا
+
+397
+00:50:11,050 --> 00:50:11,150
+كده من هنا كده من هنا كده من هنا كده من هنا كده من
+
+398
+00:50:11,150 --> 00:50:11,150
+هنا كده من هنا كده من هنا كده من هنا كده من هنا
+
+399
+00:50:11,150 --> 00:50:11,150
+كده من هنا كده من هنا كده من هنا كده من هنا كده من
+
+400
+00:50:11,150 --> 00:50:11,150
+هنا كده من هنا كده من هنا كده من هنا كده من هنا
+
+401
+00:50:11,150 --> 00:50:14,700
+كده من هنا كده من هنا كدطبعا إذا بدأ أصير كأنه بدأ
+
+402
+00:50:14,700 --> 00:50:20,880
+صخرة بولات جنبها يبقاش مصير عندي المجسم أو الشكل
+
+403
+00:50:20,880 --> 00:50:25,440
+اللي عندنا هذا اللي هو الشكل أوسطواني هذا على
+
+404
+00:50:25,440 --> 00:50:30,220
+الطبيعة لكن احنا بدنا نروح نرسم إيه؟ نرسم رسم إذا
+
+405
+00:50:30,220 --> 00:50:35,200
+لو جيت أرسم رسم باجي بطل عمينة و هم زرغاية
+
+406
+00:50:42,040 --> 00:50:49,620
+يجب ان يكون الـ Z هو المحور او فضل موازن له ،شفت
+
+407
+00:50:49,620 --> 00:51:00,600
+مافيش يبقى وضل هو المحور كيف كانت تانية؟ هده X و
+
+408
+00:51:00,600 --> 00:51:06,080
+هده Y و هده اللي عندنا اللي هو Z لو ماديته على
+
+409
+00:51:06,080 --> 00:51:11,890
+استقامته مافي مشكلة الشكل عندنا هذاطيب يا مانات
+
+410
+00:51:11,890 --> 00:51:17,090
+تعالى نذكركوا شوية لما كنت اقول Y تساوي X تربيه
+
+411
+00:51:17,090 --> 00:51:21,990
+معادة البرامجيبقى Y تساوي X تربيعه مانيش لما احاول
+
+412
+00:51:21,990 --> 00:51:27,490
+يبقى Y تساوي يعني الملحنة حوالين Y مش حوالين X
+
+413
+00:51:27,490 --> 00:51:33,870
+تربيع تمام اذا هذا لما اقول X يساوي Y تربيع يبقى
+
+414
+00:51:33,870 --> 00:51:40,870
+حوالين X مظبوط ولا لأ ايوة يبقى هذا يبقى ترابط
+
+415
+00:51:40,870 --> 00:51:46,690
+حوالين مين حوالين محور X يبقى يبقى بالشكل هذا
+
+416
+00:51:50,710 --> 00:51:56,330
+مظبوط؟ طيب و الباقي كيف شكله؟ بقولك اه بدك تروسي
+
+417
+00:51:56,330 --> 00:52:01,550
+.. تروسني برابو لازمو شبه الموازيه يعني لأن
+
+418
+00:52:01,550 --> 00:52:05,610
+الموازيه للخط المستقيم يقول يبقى بده يجيكي منحلة
+
+419
+00:52:05,610 --> 00:52:14,270
+هيك منحلة هيك و من هنا بده يجيكي بالشكل يعني و من
+
+420
+00:52:14,270 --> 00:52:16,390
+تحت بنفس الطريقة
+
+421
+00:52:40,900 --> 00:52:47,840
+يبقى كأنه هي برابلة وهي البرابلة التانية وهي
+
+422
+00:52:47,840 --> 00:52:57,840
+البرابلة التالية طبعا هذه يبقى
+
+423
+00:52:57,840 --> 00:53:01,180
+هذه البرابلز اللي عندنا وزي ما انت شايفها حوالي
+
+424
+00:53:01,180 --> 00:53:06,640
+المين حوالي المحوركز كأنه كيف كأنه جيت وقلت هذه
+
+425
+00:53:11,950 --> 00:53:16,810
+واضحة؟ تمام؟ يبقى هذه بسميها مين؟ بسميها ال
+
+426
+00:53:16,810 --> 00:53:23,970
+cylinder كمان هذه من الرسمات السهلة طيب نجي نتقل
+
+427
+00:53:23,970 --> 00:53:24,910
+القيلة شوية
+
+428
+00:53:35,370 --> 00:53:40,830
+أحنا بنشتغل في المستوى والله في الفراغ ممتاز جدا
+
+429
+00:53:40,830 --> 00:53:46,980
+حاطنا للقاعدة فوق الفراغ تلت محاور X Y و Zقلنا لك
+
+430
+00:53:46,980 --> 00:53:50,880
+إذا لجيت لعب صغير إذا ان هي cylinder يعني مش في ال
+
+431
+00:53:50,880 --> 00:53:56,080
+plane يعني إحنا مش في leaf lane وإنما وين في
+
+432
+00:53:56,080 --> 00:54:00,260
+الفرار اختماش
+
+433
+00:54:00,260 --> 00:54:05,820
+بقى انت في كل قلصي تشتغل في ال plane وانا في
+
+434
+00:54:05,820 --> 00:54:10,470
+الفرارمن يوم بمدينة في الفرق صحيح و لا لا كل شغل
+
+435
+00:54:10,470 --> 00:54:14,330
+في الفرق إذا بدك تفضي دائما و بدك عندك ثلاثة
+
+436
+00:54:14,330 --> 00:54:22,570
+متغيرات واحد بقى يبدو سلوك عشان؟ ايو ايو اللي ورا؟
+
+437
+00:54:22,570 --> 00:54:25,890
+اللي ورا اه اللي وزد تساوي تسعة ناقص واحد ثالث
+
+438
+00:54:25,890 --> 00:54:30,350
+ناقص، ازاي؟ حالك محور ال .. محور او الموازي له
+
+439
+00:54:30,350 --> 00:54:32,970
+تتنقطع ناقص
+
+440
+00:54:42,720 --> 00:54:49,400
+طبعا ناقص الرمزي المربعات هى ده رمز مربع هذا لأ
+
+441
+00:54:49,400 --> 00:54:55,960
+أنا لو شيلت التسعة والسالفشة زدت شوية واحدة زيها
+
+442
+00:54:56,660 --> 00:55:01,680
+يبقى parabola، بس إيش صار؟ حطيته إشارة سالم، يبقى
+
+443
+00:55:01,680 --> 00:55:05,340
+إن كان مرسوم الناحية، هاد بيصير الناحية العكسية،
+
+444
+00:55:05,340 --> 00:55:09,200
+مش هكذا إزاي التسعة بيتمليله shift، مظبوط؟ هذا مش
+
+445
+00:55:09,200 --> 00:55:13,760
+السؤال اللي جابله، بيعمله shift، إذا تعالى نشوف
+
+446
+00:55:13,760 --> 00:55:15,420
+الشكل كيف بيكون
+
+447
+00:55:27,980 --> 00:55:35,380
+تعالوا نفكر كيف بالرسالة أنا عندي مين؟ Z وY، صح؟
+
+448
+00:55:35,380 --> 00:55:42,860
+ايه؟ وين Z وY؟ هذا عندي Z وY، كويس؟ مداب هذا عندي
+
+449
+00:55:42,860 --> 00:55:49,900
+Z وY يبقى المحور هو بيكون X أو موازن له، بس ال Y
+
+450
+00:55:49,900 --> 00:55:58,350
+بمدى السوقات، اه يعني يا بنات لو كان هذاتساوي Y
+
+451
+00:55:58,350 --> 00:56:04,430
+تربية بده ينقلب و يسير لوين؟ لأسفل يبقى بده يسير
+
+452
+00:56:04,430 --> 00:56:09,190
+عن هناك مظبوط؟
+
+453
+00:56:09,190 --> 00:56:14,050
+و بعد هيك shift لوين؟ لأعلى بمقدار تسعة يبدو أمشي
+
+454
+00:56:14,050 --> 00:56:19,950
+كرسم هذه و أعملي لإزاحة لفوق بمقدار تسعة يبقى
+
+455
+00:56:29,310 --> 00:56:34,210
+موازي لمحور اكس بعد ما رسمنا هذا الموازي بدي اعمل
+
+456
+00:56:34,210 --> 00:56:39,350
+main ال shift اللي عندنا هذا يبقى هذه النقطة اللي
+
+457
+00:56:39,350 --> 00:56:47,510
+هي Zero و Zero و تسعة و بتروح ارسم هذه الفرابولة
+
+458
+00:56:47,510 --> 00:56:52,170
+يبقى هذا لو جيت ماده على استقباله يجب ان يقابلني
+
+459
+00:56:52,170 --> 00:56:55,530
+هنا يبقى انا عندي فرابولة
+
+460
+00:57:01,650 --> 00:57:09,910
+طيب يبقى هذه النقطة اللي فوق بدها تكون حفة ال
+
+461
+00:57:09,910 --> 00:57:15,550
+parabola بمعنى هاي الرسم زي هيك انا عملت نقطة اذا
+
+462
+00:57:15,550 --> 00:57:21,410
+هذا الخط بيمر بالنقطة موازي لمين؟ للمحور اللي
+
+463
+00:57:21,410 --> 00:57:28,210
+عندنا معناته في عندي خط بيظل موازي لمحور X
+
+464
+00:57:31,390 --> 00:57:35,930
+وهذا بيكون كل البرابلات مصفتات جانب بعض بحيث
+
+465
+00:57:35,930 --> 00:57:40,030
+البرتقال تبقى عليه بالشكل اللي قدامك هنا يبقى ايش
+
+466
+00:57:40,030 --> 00:57:45,170
+بديجيكي؟ بديجيكي هنا كمان هه بالشكل اللي عندنا،
+
+467
+00:57:45,170 --> 00:57:52,790
+برابلة تانية، هك، وهذه بيجي هنا، هم هاي برابلة،
+
+468
+00:57:52,790 --> 00:57:57,530
+ومن هنا بيجيكي كمان هنا، كمان برابلة بالشكل اللي
+
+469
+00:57:57,530 --> 00:58:02,550
+عندك، وهذا بالشكل اللي عندكيبقى إيش اللي حصل؟
+
+470
+00:58:02,550 --> 00:58:08,250
+كأنها فرابولة بالشكل هيك وقلبناها على الأرض بهذا
+
+471
+00:58:08,250 --> 00:58:13,670
+الشكل واضحة؟ السبب اللي خلانا أقلبناه هو ال shift
+
+472
+00:58:13,670 --> 00:58:16,870
+تبعها واللي خلاناها بالشكل اللي عندنا
+
+473
+00:58:20,640 --> 00:58:26,320
+أه واضحة؟ دي لبالك هذه مش نقطة تقاطة، هذا نبعدها
+
+474
+00:58:26,320 --> 00:58:30,080
+مع بعض شوية، مالاشي تقولي هذه المرة مالاشي علاقة
+
+475
+00:58:30,080 --> 00:58:35,000
+بالموضوع. يبقى هذا القرابل جاية بالشكل اللي عندها.
+
+476
+00:58:39,740 --> 00:58:48,860
+وهذا شناب المرة مالوش نزوله. يبقى يا بنات تاني مرة
+
+477
+00:58:48,860 --> 00:58:54,050
+بدي أحكي.أحنا عندنا z تسوى تسعة ناقص واي ترهيب
+
+478
+00:58:54,050 --> 00:58:58,830
+بعتبر لا عندي تسعة ولا عندي ساعة يبقى z تسوى مائة
+
+479
+00:58:58,830 --> 00:59:05,370
+إذا نرسم حوالين محور z تمام؟ حوالين محور z هي محور
+
+480
+00:59:05,370 --> 00:59:10,380
+z يبقى هيك بدأت تبقى ال parameterلكن الواي تربيها
+
+481
+00:59:10,380 --> 00:59:15,720
+السابقة بإشارة من ثاني الإعضارات في سلب الرسم بجلب
+
+482
+00:59:15,720 --> 00:59:20,860
+لتحت فوق و لفوق تحت يبقى بدل من الرسم أكلت كلها
+
+483
+00:59:20,860 --> 00:59:27,000
+فوق جلبناها و صارت وين تحت و بالمنحنة كله أضفتله
+
+484
+00:59:27,000 --> 00:59:32,300
+تسعة بلغة ال shift بدك تعمل إزاحة إلى أعلى بمقدار
+
+485
+00:59:32,300 --> 00:59:34,860
+تسعة مسكنها ال parabola
+
+486
+00:59:38,660 --> 00:59:44,360
+بطل أزرق اللي عندنا تمام؟ يبقى هذا القرابل اللي
+
+487
+00:59:44,360 --> 00:59:49,880
+عندنا طيب كويس معناته في عندك قرابل كلهم موازية
+
+488
+00:59:49,880 --> 00:59:55,080
+بعض بيكونوا بين بيكونوا هذا المجسم إذا مش واضح
+
+489
+00:59:55,080 --> 01:00:03,680
+كثير بزوجلك هذه لقدام شوية هذه هيك هو بطول الرسمة
+
+490
+01:00:03,680 --> 01:00:04,220
+بيجي
+
+491
+01:00:16,830 --> 01:00:23,870
+بنجي هنا بيكون هيك و هنا بتيجي هيك، أمامك؟ تبقى
+
+492
+01:00:23,870 --> 01:00:28,450
+سارة الرسمة بالشكل اللي عندنا هنا تبقى هذا كوال
+
+493
+01:00:28,450 --> 01:00:34,270
+لمين؟ كوال اللي هو السطح الأوسط واني اللي بيكون
+
+494
+01:00:34,270 --> 01:00:40,590
+بهذا الشكل تماما كأنه على الأرض هيك و هذا حظاني،
+
+495
+01:00:40,590 --> 01:00:48,920
+خلاص؟ طيبهذا من الأشكال اللي هو .. يعني راسمتها
+
+496
+01:00:48,920 --> 01:00:53,280
+برضه جادرين عليها زي ولا تشبيه زي السير السرير
+
+497
+01:00:53,280 --> 01:00:59,260
+الولد الصغير بس مقلبية على وجهه وهذا أبدا السرير
+
+498
+01:00:59,260 --> 01:01:04,670
+بس على جانبه واقف تماما بالضبططيب ندى بالرسم اللى
+
+499
+01:01:04,670 --> 01:01:09,210
+بعدها اللى بعدها بيقولى Y تربيه على أربعة ناقص X
+
+500
+01:01:09,210 --> 01:01:14,470
+تربيه على تسعة بده يساوى لو في ال plane هذه معادلة
+
+501
+01:01:14,470 --> 01:01:20,030
+ايه؟ هاي فرابولة تمام يبقى رسمتنا هذه بدنا نرسمها
+
+502
+01:01:20,030 --> 01:01:27,670
+بحيث تكون هاي فرابولة متوازية او ان شتوا فقولوا
+
+503
+01:01:27,670 --> 01:01:29,530
+فرابولة على اليمين
+
+504
+01:01:37,050 --> 01:01:42,930
+الثاني يالاأخر معادلة عندنا من المعادلات هي y
+
+505
+01:01:42,930 --> 01:01:46,930
+تربيه على أربعة نقص x تربيه على تسعة بده يساوي
+
+506
+01:01:46,930 --> 01:01:50,510
+الواحدة بتطلع على الرمز الغابي الرمز الغابي اللي
+
+507
+01:01:50,510 --> 01:01:57,130
+همين z يبقى ال axis بده يكون محور z أو محور موازن
+
+508
+01:01:57,130 --> 01:02:02,170
+لأ هدف ال plane عبارة علشان عبارة عن hyperbola إذا
+
+509
+01:02:02,170 --> 01:02:07,090
+بدنا نروح نرسم ال hyperbola كأنها في أحد ال planes
+
+510
+01:02:07,090 --> 01:02:08,610
+يبقى لو جيت
+
+511
+01:02:11,690 --> 01:02:16,810
+اللي هي الـ Hyperabula الأول يبقى بدأ تظهر واحدة
+
+512
+01:02:16,810 --> 01:02:24,210
+زيها من الناحية التانية بالشكل اللي عندها تمام؟ هي
+
+513
+01:02:24,210 --> 01:02:32,590
+اللي بدأ تيجي موازية لها كمان بهذا الشكل ومن
+
+514
+01:02:32,590 --> 01:02:37,270
+الناحية التانية زيها لو مدينا محور X على استقلال
+
+515
+01:02:51,480 --> 01:02:59,500
+بنقرب الشكل اللي عندها وبنقرب الشكل اللي عندها
+
+516
+01:02:59,500 --> 01:03:01,340
+وبنقرب الشكل اللي عندها وبنقرب الشكل اللي عندها
+
+517
+01:03:01,340 --> 01:03:01,960
+وبنقرب الشكل اللي عندها وبنقرب الشكل اللي عندها
+
+518
+01:03:01,960 --> 01:03:02,000
+وبنقرب الشكل اللي عندها وبنقرب الشكل اللي عندها
+
+519
+01:03:02,000 --> 01:03:02,020
+وبنقرب الشكل اللي عندها وبنقرب الشكل اللي عندها
+
+520
+01:03:02,020 --> 01:03:02,060
+وبنقرب الشكل اللي عندها وبنقرب الشكل اللي عندها
+
+521
+01:03:02,060 --> 01:03:02,060
+وبنقرب الشكل اللي عندها وبنقرب الشكل اللي عندها
+
+522
+01:03:02,060 --> 01:03:02,080
+وبنقرب الشكل اللي عندها وبنقرب الشكل اللي عندها
+
+523
+01:03:02,080 --> 01:03:03,280
+وبنقرب الشكل اللي عندها وبنقرب الشكل اللي عندها
+
+524
+01:03:03,280 --> 01:03:07,180
+وبنقرب الشكل اللي
+
+525
+01:03:07,180 --> 01:03:13,460
+عندها وبنقرب الشكل
+
+526
+01:03:13,460 --> 01:03:14,880
+اللي عندها عندها وبن
+
+527
+01:03:38,710 --> 01:03:48,170
+هذا مفتوح جهة اليمن هذا مفتوح جهة الشمال
+
+528
+01:04:39,070 --> 01:04:46,750
+يفجي هذه الـ cylinder كأنها .. كأنها اللي هو تجيوب
+
+529
+01:04:46,750 --> 01:04:51,410
+بهذا الشكل و تجيوب تاني زيه بهذا الشكل و اتنين
+
+530
+01:04:51,410 --> 01:04:56,030
+زعلانين مع بعض، كل واحد موجه على شجرةتمام؟ يبقى
+
+531
+01:04:56,030 --> 01:05:00,610
+اتنين مع بعض كقطع واحدة بقوله ايه هذا هو ال
+
+532
+01:05:00,610 --> 01:05:05,130
+cylinder اللي عندنا يبقى cylinder السؤال الأول كان
+
+533
+01:05:05,130 --> 01:05:10,210
+على شكل أسطوانة و المقطع تبعها ellipse التاني
+
+534
+01:05:10,210 --> 01:05:13,670
+أسطوانة و المقطع تبعها Parabola التالتة المقطع
+
+535
+01:05:13,670 --> 01:05:18,550
+تبعها Parabola الرابعة المقطع تبعها Iparabola و
+
+536
+01:05:18,550 --> 01:05:25,640
+هكذاإذا انتمنوا أبدًا بننظر لمن؟ للعنصر الغاية نجي
+
+537
+01:05:25,640 --> 01:05:31,880
+للنقطة الثانية بالأسفل الـ Quadrics الاسفل السطوح
+
+538
+01:05:31,880 --> 01:05:39,800
+أثناء نمسح هذا خلاص؟ خلاص؟ طيب نجي للنقطة الثانية
+
+539
+01:05:39,800 --> 01:05:43,080
+في هذا ال section اللي هو ال Quadrics
+
+540
+01:05:51,840 --> 01:05:58,180
+جا ستة من هذه السطوح الأوسطوانية أول واحد منهم
+
+541
+01:05:58,180 --> 01:06:05,880
+بيسميه ال ellipsoid يفجأ لمرة اتنين اللي هي
+
+542
+01:06:05,880 --> 01:06:12,620
+quadric ستة أول
+
+543
+01:06:12,620 --> 01:06:17,920
+واحد منهم بيسميه ال ellipsoid
+
+544
+01:06:26,030 --> 01:06:28,750
+المجسم الناقص بالعرب
+
+545
+01:06:54,260 --> 01:06:58,500
+بنحاول نرسم هذا المجسم.
+
+546
+01:07:06,260 --> 01:07:17,280
+هذا محور X، هذا محور Y، وهذا محور اللي هو Z.
+
+547
+01:07:31,880 --> 01:07:37,680
+لما أقول ellipsoid جاء من كلمة ellipse ellipse قطع
+
+548
+01:07:37,680 --> 01:07:43,400
+ناقص يبقى المقطع دائما و أبدا هو عبارة عن قطع ناقص
+
+549
+01:07:43,400 --> 01:07:48,700
+كيف القطع الناقص كله نقص مافيه كله خلاص دي الشكل
+
+550
+01:07:48,700 --> 01:07:52,420
+اللي عندنا على الشكل هيك
+
+551
+01:07:55,700 --> 01:08:00,900
+هذا اللي هو كان الـ Ellipse اللي عندنا تبعه كان
+
+552
+01:08:00,900 --> 01:08:06,100
+الـForce بيه طبعا النظر
+
+553
+01:08:09,440 --> 01:08:14,700
+مش هيقوللي هذا نفسه بسقط لكن مشان اميزه بدي اروح
+
+554
+01:08:14,700 --> 01:08:22,260
+ارسم مقطعه مع المستوى XZ هذا هذا مقطعه مع المستوى
+
+555
+01:08:22,260 --> 01:08:28,960
+YZ مقطعه مع المستوى XZ هروح ارسمه بهذا الشكل هذا
+
+556
+01:08:28,960 --> 01:08:35,240
+مظهر لي من جهتنا بيقول انا هذا مظهر ليش هرسمه
+
+557
+01:08:35,240 --> 01:08:43,250
+منقطع بهذا الشكليوصف الشكل ان هذا مجسم واضح ان هذا
+
+558
+01:08:43,250 --> 01:08:46,810
+عبارة عن مجسم مش عاجزاكوا بس
+
+559
+01:08:50,510 --> 01:08:57,770
+بهذا الشكل فهذا يجينا كمان هكذا خلّيني أقول في
+
+560
+01:08:57,770 --> 01:09:05,470
+الأصل يبقى واضح الأن أن هذا مجسم طيب الآن ليش
+
+561
+01:09:05,470 --> 01:09:11,470
+سمينا ellipsoid هذا السؤال ellipsoid جاء من كلمة
+
+562
+01:09:11,470 --> 01:09:17,430
+syllables الإجابة لأن مقع مع كل مستوى من مستويات
+
+563
+01:09:17,430 --> 01:09:21,760
+الأفتراضياتهو عبارة عن ايش؟ هو عبارة عن التلفزيون.
+
+564
+01:09:22,120 --> 01:09:26,720
+أنا أقول ان إيه يا بنات؟ كيف يعني نعم؟ الأن لو
+
+565
+01:09:26,720 --> 01:09:30,840
+بفاجأي أخد مقطعه مع المستوى هو يزيد يا بنات
+
+566
+01:09:44,410 --> 01:09:53,830
+الخط الأسود الخارجي يبقى هذا ما هو المقطع تبعه مع
+
+567
+01:09:53,830 --> 01:09:58,470
+المستوى اللي احنا بناه يبقى الخط الأسود هذا اللي
+
+568
+01:09:58,470 --> 01:10:04,650
+هو Y تربيع على B تربيع زي Z تربيع على C تربيع
+
+569
+01:10:04,650 --> 01:10:05,650
+يساوي واحد
+
+570
+01:10:08,490 --> 01:10:15,290
+يبقى هذا تقطع مع المستوى YZ يبقى تقطع مع المستوى
+
+571
+01:10:15,290 --> 01:10:21,450
+XZ XZ يبقى Y فقدراش Zero يبقى لما أشيل Y ب Zero
+
+572
+01:10:21,450 --> 01:10:24,930
+مضالعش عندنا Ellipse اللي هو مين ال Ellipse اللي
+
+573
+01:10:24,930 --> 01:10:28,030
+عندنا هي هكتبه لك اللي هو
+
+574
+01:10:36,690 --> 01:10:44,220
+على C تربية يساوي يدها يساوي واحد صحيايبقى الأزرق
+
+575
+01:10:44,220 --> 01:10:50,880
+يا بنات هذا في مستوى XZ رأسي الأسود في مستوى YZ
+
+576
+01:10:50,880 --> 01:10:58,180
+طبعا هنسأل السؤال التالي و أين المستوى XY؟ نقول له
+
+577
+01:10:58,180 --> 01:11:04,480
+Z تساوي Zero اللي هو الـEllipse الأزرق هذا تمام؟
+
+578
+01:11:04,480 --> 01:11:09,340
+يبقى الأزرق هذا الـEllipse هذا معادلته
+
+579
+01:11:14,570 --> 01:11:20,830
+Y تربيع على V تربيعي تساوي جداش واحد اذا كل مقطع
+
+580
+01:11:20,830 --> 01:11:25,290
+من هذه المقطع عبارة عن ellipse ومن هنا سمنا
+
+581
+01:11:25,290 --> 01:11:31,510
+ellipsoid تيجي واحدة تقول طب لو جت قطعته من فوق
+
+582
+01:11:31,510 --> 01:11:37,430
+وانا من تحت، شوية، مظبوط؟ اللي جابت بيصير Z تساوي
+
+583
+01:11:37,430 --> 01:11:43,200
+Z نور، يعني رقمهل المطبع في هذه الحلقة كمان
+
+584
+01:11:43,200 --> 01:11:48,260
+ellipse؟ رابعا ellipse طب كيف نجيب هذا اللي هو؟
+
+585
+01:11:48,260 --> 01:11:54,780
+اقولك بسيطة لو كان الذد يساوي C note فوق او C note
+
+586
+01:11:54,780 --> 01:11:58,770
+تحت سواء كان فوق او تحت سيها ماتفرقش عامةلأن عند
+
+587
+01:11:58,770 --> 01:12:04,270
+مربعه بيصير قيمة يعيش موجبة يبقى Z تساوي absolute
+
+588
+01:12:04,270 --> 01:12:10,610
+value ل C0 بيكون أعلى ال XY plane أو أسفل ال XY
+
+589
+01:12:10,610 --> 01:12:15,910
+plane إذا لو جيت قطعته بالمقطع اللي عندنا هذا هيك
+
+590
+01:12:15,910 --> 01:12:21,590
+مش هيظهر وهذا بيظهر الشكل اللي عندنا هذا يبقى هذا
+
+591
+01:12:21,590 --> 01:12:25,690
+المستوى اللي هو Z يساوي Z0
+
+592
+01:12:33,920 --> 01:12:42,360
+ز يسوى z نوت the question is اللي هو مين x تربيع
+
+593
+01:12:42,360 --> 01:12:49,640
+على a تربيع y تربيع على b تربيع بدي يسوى واحد نقل
+
+594
+01:12:49,640 --> 01:12:58,340
+z نوت تربيع على z تربيع طبعا لو قسمت الطرفين عليهم
+
+595
+01:12:58,340 --> 01:13:02,480
+مش هذا رقم لو قسمت عليه مش مصير معادلة ايه
+
+596
+01:13:12,150 --> 01:13:18,910
+على C تربيع زائد Y تربيع على B تربيع واحد ناقص Z
+
+597
+01:13:18,910 --> 01:13:24,850
+نوت تربيع على C تربيع كله يسوى واحد وهذا كمان ال
+
+598
+01:13:24,850 --> 01:13:30,710
+mainly اللي هو ال Alex يتجول مثلا طيب اتجه لمفتاح
+
+599
+01:13:30,710 --> 01:13:37,440
+ايش Alex طيبهذه ملاحظة ملاحظة ثانية السؤال هو هل
+
+600
+01:13:37,440 --> 01:13:44,000
+المجسم يا بنات متمثل بالنسبة لمستويات الأحداثيات
+
+601
+01:13:44,000 --> 01:13:49,180
+يعني نشوف يعني لو جيت لمستوى ال XY اللي قطعه في
+
+602
+01:13:49,180 --> 01:13:53,520
+المقطع الأزرق هل النص اللي فوق و نص اللي تا اه
+
+603
+01:13:53,520 --> 01:13:55,860
+صحيح لإن النقطة اللي فوق
+
+604
+01:14:06,420 --> 01:14:08,420
+هذه النقطة
+
+605
+01:14:16,210 --> 01:14:22,470
+وP و Zero إذا المجسم هذا متماثل بالنسبة لإيه
+
+606
+01:14:22,470 --> 01:14:26,670
+المستويات الأحداثية يعني يعني المستوى الأحداثية
+
+607
+01:14:26,670 --> 01:14:32,610
+لما أجيبه من فوق لتحت بقصه نصين زي بعض تماما، لو
+
+608
+01:14:32,610 --> 01:14:38,450
+أفقي نصين زي بعض، لو المستوى التالت بقسمه كمان إلى
+
+609
+01:14:38,450 --> 01:14:43,670
+نصين ونصين الاتنين زي بعض تماما، يبقى ما أقدر أقول
+
+610
+01:14:43,920 --> 01:14:49,320
+الغرافية متساومة مع الـ coordinate planes يبقى
+
+611
+01:14:49,320 --> 01:14:55,320
+باجي بقول هنا الغرافية
+
+612
+01:14:55,320 --> 01:14:59,020
+لجانب
+
+613
+01:14:59,020 --> 01:15:05,780
+الكلب متساومة
+
+614
+01:15:05,780 --> 01:15:06,300
+حوالي
+
+615
+01:15:16,830 --> 01:15:20,690
+in place طب
+
+616
+01:15:20,690 --> 01:15:27,810
+كويس إذا جبنا كل مقطع وكل معادلة ايه؟ اه اجت واحدة
+
+617
+01:15:27,810 --> 01:15:32,730
+من البنات قالت قبلتها ليش عملت الاستقالة تلعطى فوق
+
+618
+01:15:32,730 --> 01:15:36,890
+و تحت؟ ليش فالبنات مش عارفة احوان واي والله عارفة
+
+619
+01:15:36,890 --> 01:15:43,590
+وعكس مش هذا تساؤلنقول لك مشان تحكمي هل استطالة في
+
+620
+01:15:43,590 --> 01:15:49,370
+اتجاه محور X وY بتطلع الى اكبر رقم في المقام بيكون
+
+621
+01:15:49,370 --> 01:15:55,230
+المتغير اللي فوقه هو اكبر محور اذا احنا رسمنا هذه
+
+622
+01:15:55,230 --> 01:16:00,410
+الرسمة على اساس انه فيه اكبر من مين؟ من ايه؟
+
+623
+01:16:10,260 --> 01:16:16,840
+لو كدت بيه هي اللي أكبر، بدى يصير هذا الاستطالة في
+
+624
+01:16:16,840 --> 01:16:23,190
+اتجاه نحو الواقعطب لو كان ال A هي الأكبر بده يصير
+
+625
+01:16:23,190 --> 01:16:29,250
+الاستثالة في اتجاه محور S إذا لما يعطيكي معادلة
+
+626
+01:16:29,250 --> 01:16:35,370
+عددية من خلال أسئلة التمرين و بدك ترسميها أو يقولك
+
+627
+01:16:35,370 --> 01:16:38,950
+شوفي اللي الرسم يعطيك شوية رسمات لما ضمن التمرين
+
+628
+01:16:38,950 --> 01:16:42,930
+بجي اتناشر رسمة و حطت اتناشر معادلة و قالك بس
+
+629
+01:16:42,930 --> 01:16:46,910
+واصليه من المعادلة الرسمة يعني قول المعادلة هذه من
+
+630
+01:16:46,910 --> 01:16:51,950
+الرسمة هذهإذا بقى مرة خلّيلك يا رأسي و مرة وفقي و
+
+631
+01:16:51,950 --> 01:16:56,750
+مرة كذا إلى آخرين يبقى بطل على مين يا بنات؟ لرقم
+
+632
+01:16:56,750 --> 01:17:02,410
+المقام صاحب المقام الرفيع يكون هو من؟ هو الاستطالة
+
+633
+01:17:02,410 --> 01:17:07,710
+في التجارة و ارهاد؟ تمام؟ طيب لحد هنا stop انتهينا
+
+634
+01:17:07,710 --> 01:17:12,710
+من نمرة واحد الكلب صيد بدنا نيجي لنمرة اتنين
+
+635
+01:17:31,200 --> 01:17:38,360
+المعادلة تبت على شكل X تربيع على A تربيع زائد Y
+
+636
+01:17:38,360 --> 01:17:46,480
+تربيع على Z تربيع زائد Y تربيع على B تربيع
+
+637
+01:18:12,510 --> 01:18:15,010
+كلمة elliptic جاء من أين؟
+
+638
+01:18:31,850 --> 01:18:36,690
+طيب لو جيت راسنتو هذا يبقى ده ياخد الشكل التالي
+
+639
+01:18:36,690 --> 01:18:38,310
+الشكل اللي عندها
+
+640
+01:18:58,410 --> 01:19:07,610
+شكل ديكي بس كمان مش هنوضحه أكتر يكون هيك
+
+641
+01:19:07,610 --> 01:19:18,710
+هذا الشكل كمان كم مقطع عندي في الرسم هنا تقريبا
+
+642
+01:19:18,710 --> 01:19:23,690
+انا اتنتينالزرجة والسودا، الزرجة والسودا، يبقى في
+
+643
+01:19:23,690 --> 01:19:27,790
+عندي two parabolas وفي كمان عندي ماين الاسم، بتعرف
+
+644
+01:19:27,790 --> 01:19:31,510
+مين كل واحدة من هدول، يبقى يا بنات ال elliptic
+
+645
+01:19:31,510 --> 01:19:35,890
+paraboloids زي الخوذة تبعت الجندر أو زي ما تقص نص
+
+646
+01:19:35,890 --> 01:19:40,170
+بطيخة وتجوريها، يبقى هذا الاسم اياش elliptic
+
+647
+01:19:40,170 --> 01:19:47,430
+paraboloidطيب بالضغط الأن أشوف المقطع تبع المجسم
+
+648
+01:19:47,430 --> 01:19:52,830
+اللي عندنا هذا مع ال YZ Plane مع ال YZ Plane يعني
+
+649
+01:19:52,830 --> 01:19:57,430
+X بجداش Zero يبقى ال X ب Zero بتطير ال term اللي
+
+650
+01:19:57,430 --> 01:20:01,930
+عندنا هذا يبقى هذا إيش بيصير؟ بيصير المعادلة اللي
+
+651
+01:20:01,930 --> 01:20:02,370
+عندنا
+
+652
+01:20:15,920 --> 01:20:22,120
+ممتاز جدا يبقى القرابل السوداء هذه أبدا خطة
+
+653
+01:20:25,730 --> 01:20:34,890
+هو Y تربيع على B تربيع بيكون Z على C وهذه ترابولة
+
+654
+01:20:34,890 --> 01:20:43,690
+تمام هاي لو جيت للزرق هذا لو حطيت ال Y ب Zero ال Y
+
+655
+01:20:43,690 --> 01:20:47,050
+ب Zero بصير X تربيع على A تربيع بيكون Z على A
+
+656
+01:20:59,560 --> 01:21:05,120
+يزد على C. يبقى هذه معادلة Parabola. لكن يا بنات
+
+657
+01:21:05,120 --> 01:21:11,760
+اللي فوق المقطع هذا لو كانت إحداث النقطة هذه هي
+
+658
+01:21:11,760 --> 01:21:21,160
+مثلا Z نوت و Zero و Zero. إذن تقصير المعادلة اللي
+
+659
+01:21:21,160 --> 01:21:23,340
+عندنا دقيقة اللي هي
+
+660
+01:21:29,720 --> 01:21:36,760
+زيت نودة على C لو جسمت عليها تمام ايش بيعطيني هذا
+
+661
+01:21:36,760 --> 01:21:48,030
+بيصير عندي X تربيع على A تربيعZ node على C زائد Y
+
+662
+01:21:48,030 --> 01:21:53,630
+تربية B تربية Z node على C كله يسوى واحد صحيح يبقى
+
+663
+01:21:53,630 --> 01:21:58,910
+مين هذا ال ellipse يبقى هذا يتفق مع الكلام اللي
+
+664
+01:21:58,910 --> 01:22:03,690
+قلناه قبل قليل من الاسم اللي هو ال ellipse
+
+665
+01:22:03,690 --> 01:22:08,950
+Parabola يبقى أحد المقاطع اللي وفقه عبارة عن ال
+
+666
+01:22:08,950 --> 01:22:14,320
+ellipse والبجيات الأثنينهم عبارة عن مين؟ عن قراه
+
+667
+01:22:14,320 --> 01:22:20,900
+لازم طيب فى عندى سؤالين بدى أسألهم هسألهم يجيبوا
+
+668
+01:22:20,900 --> 01:22:23,520
+على سؤالهم بدون ما تسألوا انا سأقرا عليهم السؤال
+
+669
+01:22:23,520 --> 01:22:31,200
+زت نود و Zero و Zero Zero Zero Zero Zero Zero Zero
+
+670
+01:22:31,200 --> 01:22:34,780
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+671
+01:22:34,780 --> 01:22:37,480
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+672
+01:22:37,480 --> 01:22:37,520
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+673
+01:22:37,520 --> 01:22:37,520
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+674
+01:22:37,520 --> 01:22:37,540
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+675
+01:22:37,540 --> 01:22:37,580
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+676
+01:22:37,580 --> 01:22:37,580
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+677
+01:22:37,580 --> 01:22:37,580
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+678
+01:22:37,580 --> 01:22:37,580
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+679
+01:22:37,580 --> 01:22:37,580
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+680
+01:22:37,580 --> 01:22:37,580
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+681
+01:22:37,580 --> 01:22:37,580
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+682
+01:22:37,580 --> 01:22:37,580
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+683
+01:22:37,580 --> 01:22:37,680
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+684
+01:22:37,680 --> 01:22:43,030
+Zero Zeroنرجع لكمال اللي احنا بنقوله وبنقول بدنا
+
+685
+01:22:43,030 --> 01:22:50,290
+نسأل سؤالين السؤال الأول لو بديش لك رسمي للمعادلة
+
+686
+01:22:50,290 --> 01:22:55,990
+X تربية علي A تربية زي Y تربية علي B تربية تساوي Z
+
+687
+01:22:55,990 --> 01:23:04,470
+سالب Z علي C بدنا نقله ونخليه أسفل يعني بدنا نصير
+
+688
+01:23:04,470 --> 01:23:05,470
+بالشكل هذا
+
+689
+01:23:08,750 --> 01:23:17,350
+هذا X وهذا Y وهذا Z يصبح هذا R شكل
+
+690
+01:23:17,350 --> 01:23:24,110
+يعني تمام؟ هذا لو كانت ايش؟ لو كان X تربيع علي A
+
+691
+01:23:24,110 --> 01:23:29,730
+تربيع زاد Y تربيع علي B تربيع يسوي سالب Z على C
+
+692
+01:23:29,730 --> 01:23:33,790
+يبقى بنجلب الرسمة في هذه الحالة وتصبح
+
+693
+01:23:37,050 --> 01:23:44,330
+سؤال الثاني هل المجسم متمثل بالنسبة لمستويات
+
+694
+01:23:44,330 --> 01:23:50,870
+الأحداثية؟ لأ طبعا ليش؟ لأنه تحت ال X Y Plane
+
+695
+01:23:50,870 --> 01:23:57,090
+ماعنديش كل الرسم أعلى ال X Y Plane تمام؟ لكن لو جت
+
+696
+01:23:57,090 --> 01:24:08,110
+كنت بالمستوى YZ المجسم متمثلYZ و XZ متماثل لكن
+
+697
+01:24:08,110 --> 01:24:12,810
+المستوي XY يبعد الله يبقى هذا متماثل بالنسبة
+
+698
+01:24:12,810 --> 01:24:19,790
+لمستويين من مستويات الإعداد فقط لغير وليس متساوية
+
+699
+01:24:19,790 --> 01:24:29,370
+من وسلمين للتالت طيبالان لو جيت قلت لك اين ال X Y
+
+700
+01:24:29,370 --> 01:24:34,870
+Plane بتبقى Z بقدر ايه؟ اه ال X Y Plane بتبقى Z
+
+701
+01:24:34,870 --> 01:24:39,290
+بقدر ايه؟ Zero إذا لو حطيت Z ب Zero ايش بصيها؟ X
+
+702
+01:24:39,290 --> 01:24:41,690
+تربيه على A تربيه على Z و لا تربيه على B تربيه على
+
+703
+01:24:41,690 --> 01:24:48,830
+C يساوي الصفر هل يؤقل ان مجموعة كميتين مربعتين
+
+704
+01:24:48,830 --> 01:24:50,210
+يساوي الصفر؟
+
+705
+01:24:53,180 --> 01:24:58,660
+معقول ليش مش معقول بس مرة واحدة في الدنيا لو كان
+
+706
+01:24:58,660 --> 01:25:04,660
+ال X بزيرو و ال Y بزيرو فما الهي مين؟ نقطة الأصل
+
+707
+01:25:04,660 --> 01:25:09,120
+فانا عندي زد بزيرو صح؟ و وجدت كمان X تربية ال X
+
+708
+01:25:09,120 --> 01:25:12,780
+بزيرو و ال Y بزيرو إذا مستيقظ النقطة الأصل إذا ال
+
+709
+01:25:12,780 --> 01:25:19,100
+plane في ال مجسم في هذه الحالة يمث ال X Y plane في
+
+710
+01:25:19,100 --> 01:25:24,720
+النقطة 00000 نقطة الأصلواضح؟ يبقى الـ elliptic
+
+711
+01:25:24,720 --> 01:25:39,340
+paraboloid الواضح
+
+712
+01:25:39,340 --> 01:25:46,180
+الشغل أظن طيب هذا بالنسبة لمين؟ لمجسم التاني
+
+713
+01:25:50,060 --> 01:25:53,120
+المجسم التالت يا بنات اللي هو الـ Elliptic cone
+
+714
+01:25:53,120 --> 01:26:06,520
+اللي هو
+
+715
+01:26:06,520 --> 01:26:12,500
+المخروض اللي المقطع تبعه عبارة عن ellipse المعادلة
+
+716
+01:26:12,500 --> 01:26:18,840
+تبعته X تربيع على A تربيع زائد Y تربيع على B تربيع
+
+717
+01:26:27,910 --> 01:26:30,950
+جاب المبدأ في الـ elliptic cone اللي خاطر أسأل
+
+718
+01:26:30,950 --> 01:26:36,650
+كمان سؤال على الـ elliptic paraboloid هذا، تمام؟
+
+719
+01:26:36,650 --> 01:26:40,250
+لو كانت المعادلة على الشكل التالي، فدبركوا كويس
+
+720
+01:26:40,690 --> 01:26:46,950
+انتوا ملاحظين ان الرسم المحور تبعها مين؟ Z XY زي
+
+721
+01:26:46,950 --> 01:26:52,150
+زي
+
+722
+01:26:52,150 --> 01:26:56,590
+زي زي زي زي زي زي زي زي زي زي زي زي زي زي زي زي
+
+723
+01:27:05,600 --> 01:27:10,940
+يبقى المحور تبع مين هو يبقى الرمز اللي ما هو مش
+
+724
+01:27:10,940 --> 01:27:15,860
+مربع في ال elliptic paraboloid بيكون هو مين هو
+
+725
+01:27:15,860 --> 01:27:21,880
+المحور تبع مين تبع المجسم دي ملاحظة لكن من قصة ال
+
+726
+01:27:21,880 --> 01:27:25,600
+ellipsoid اللي في أول كله زي بعضه ماقدرتش أميّن
+
+727
+01:27:25,600 --> 01:27:31,780
+يبقى هذا بميز من شكل المتغير غير المربعطيب نيجي
+
+728
+01:27:31,780 --> 01:27:37,980
+لمين؟ لل elliptical اللي هو المخروض اللي المقطع
+
+729
+01:27:37,980 --> 01:27:43,580
+تبعه عبارة عن ellipse كيف هذا؟ اقولك اه لو جيتي
+
+730
+01:27:43,580 --> 01:27:44,380
+قولتي ليه؟
+
+731
+01:28:00,150 --> 01:28:09,170
+بشكل عام و بعد
+
+732
+01:28:09,170 --> 01:28:18,790
+هيك جيت طبعا هي محاول الأحداثيات هذا
+
+733
+01:28:18,790 --> 01:28:24,630
+محور X هذا محور Y و هذا محور Z
+
+734
+01:28:32,240 --> 01:28:37,700
+طيب هذه المعادلة اللي عندناها اللي هو معادلة
+
+735
+01:28:37,700 --> 01:28:44,320
+elliptic اللي هو الكون المخروط للمقطع تبعه عبارة
+
+736
+01:28:44,320 --> 01:28:48,540
+عن ellipse ليش كل المخروط تبعه عبارة عن ellipse
+
+737
+01:28:48,540 --> 01:28:53,460
+وما هي المقاطع الأخرى أول شيء خلّيني أطلع على
+
+738
+01:28:53,460 --> 01:28:56,990
+المعادلة و بعدين بنجيب على هذه التساؤلاتطالعي
+
+739
+01:28:56,990 --> 01:29:01,950
+للمعادلة اللي قمنا بتكتبها معادلة صفرية يبقاش بصير
+
+740
+01:29:01,950 --> 01:29:07,630
+هي معادة ال ellipsoid بس بتختلف عنها فيه أمرين بدل
+
+741
+01:29:07,630 --> 01:29:12,550
+الواحد بده zero وهادي بدل الموجة بصير إيه أش سالب
+
+742
+01:29:12,550 --> 01:29:18,230
+ممتاز يبقى لو أطالي تلت كميات مربعة تنتين في شجة و
+
+743
+01:29:18,230 --> 01:29:24,130
+تلتة في شجة تانية إذا هذه معادة المخرج تمام؟هذه مش
+
+744
+01:29:24,130 --> 01:29:28,070
+هانميز بينها وبين المعادلة تفضلي تفضلي تفضلي تفضلي
+
+745
+01:29:28,070 --> 01:29:47,410
+تفضلي تفضلي تفضلي تفضلي تفضلي تفضلي تفضلي
+
+746
+01:29:47,510 --> 01:29:56,810
+الان لو جيت للمجسم اللي عندنا هذا و جيت اخد ال yz
+
+747
+01:29:56,810 --> 01:30:02,890
+plane يعني اكسب جداش؟ Zero يعني لما تكسب Zero تروح
+
+748
+01:30:02,890 --> 01:30:07,750
+بالشكل هذا مع النتيجة دي لو اخدت الجدر الترفيه
+
+749
+01:30:07,750 --> 01:30:14,960
+للطرفينخط مستقيم صح ولا يعني كيلو وزير مين؟ Y تسوى
+
+750
+01:30:14,960 --> 01:30:20,600
+بي على C في زب أو Y تسوى سالب بي على C في زب مظبوط
+
+751
+01:30:20,600 --> 01:30:24,780
+اللي هو الخط المستقيم الأول والثاني هو الخط
+
+752
+01:30:24,780 --> 01:30:33,040
+المستقيم الثاني يرجى يا بنات هذا الخط لحاله اللي
+
+753
+01:30:33,040 --> 01:30:33,980
+هو مين؟
+
+754
+01:30:36,770 --> 01:30:43,230
+اللي هو y تربيع على b تربيع تسوى z تربيع على c
+
+755
+01:30:43,230 --> 01:30:51,390
+تربيع او الشيء اللي تقوله y تسوى b على c في z يبقى
+
+756
+01:30:51,390 --> 01:30:57,270
+هذا الرقم من الناحية التانية يكون y تسوى سالم b
+
+757
+01:30:57,270 --> 01:31:05,120
+على c في zهذا التقاطع مع ال YZ Plane بدي اجيب
+
+758
+01:31:05,120 --> 01:31:10,120
+التقاطع مع ال XZ Plane مع ال R لازم اشيروا
+
+759
+01:31:10,120 --> 01:31:14,640
+مستقيمات اتنين بمان يفجروا اين المستقيمات الاتنين
+
+760
+01:31:14,640 --> 01:31:19,860
+بدي اجيك المستقيم الاول بهذا الشكل من جهتنا هيكون
+
+761
+01:31:19,860 --> 01:31:24,960
+هذا مبين و غالب من الناحية التانية يا بنات مش
+
+762
+01:31:24,960 --> 01:31:28,340
+هيغالب هيكون اللقط بهذا الشكل
+
+763
+01:31:31,530 --> 01:31:37,890
+من الناحية هذه مش هيظهر ومن الناحية التانية هيظهر
+
+764
+01:31:37,890 --> 01:31:43,110
+بالشكل الأخر يبقى الخطين السود الغامقات هو تقاطع
+
+765
+01:31:43,110 --> 01:31:49,490
+ال XZ Plane مع المجسم اللي عندنا طيب في ال XZ
+
+766
+01:31:49,490 --> 01:31:55,350
+Plane يبقى واقف كده؟ P0 معناه هذا الفلاح ان الخط
+
+767
+01:31:55,350 --> 01:31:57,550
+اللي عندى هذا الأسود
+
+768
+01:32:14,660 --> 01:32:27,900
+C في Z بشارة سالف وهنا هد يكون هذا يفتح هذا يبقى X
+
+769
+01:32:27,900 --> 01:32:36,180
+ساوية A على C في من في Z طيب
+
+770
+01:32:36,180 --> 01:32:41,720
+لو حطيت Z تساوي Z نوت يعني رقم
+
+771
+01:32:48,570 --> 01:32:53,970
+النقطة اللي عندها يبقى بدي جيه المقطع مين اللي فوق
+
+772
+01:32:53,970 --> 01:33:00,310
+زد نول يبقى هذا كله بدي يصير رقم لو قسمت عليه يصير
+
+773
+01:33:00,310 --> 01:33:05,510
+عندي ellipse و هذا اللي تحت كمان ايه كمان ellipse
+
+774
+01:33:05,510 --> 01:33:08,330
+زيه وال double تماما يبقى
+
+775
+01:33:16,170 --> 01:33:23,670
+يكون X تربيع على A تربيع زائد Y تربيع على B تربيع
+
+776
+01:33:23,670 --> 01:33:30,510
+بساوي Z نوت تربيع على C تربيع هذا رقم لو قسمت عليه
+
+777
+01:33:30,510 --> 01:33:32,770
+الطرفين بصير عندنا معادلة
+
+778
+01:34:00,970 --> 01:34:08,050
+لو جيت على المعانلة لو حطيت مكانها اللي هو z تساوي
+
+779
+01:34:10,730 --> 01:34:15,910
+مجموع كميتين مربعتين يساوي صفر هذا لا يمكن إلا إذا
+
+780
+01:34:15,910 --> 01:34:20,690
+كان كل واحد منهم صفر يبقى ال X بزير و ال Y بزير و
+
+781
+01:34:20,690 --> 01:34:27,250
+بتقول حصلنا على مين؟ على نقطة الأصل واضح كلامنا؟
+
+782
+01:34:27,250 --> 01:34:36,220
+طيب مين المحور غير هذا؟زد تمام اللي لحالها ممتاز
+
+783
+01:34:36,220 --> 01:34:39,660
+جدا اللي اللي بتبقى لحالها على اليمين بيكون
+
+784
+01:34:39,660 --> 01:34:45,380
+المتغير تبعها هو المحور تبع من تبع المجسم اللي عام
+
+785
+01:35:09,720 --> 01:35:16,160
+في عندي كمان اخر تلت مجسمات هي بالشكل التالي اول
+
+786
+01:35:16,160 --> 01:35:23,140
+واحد اللي هو او ادن بره اربع بسالين هاي ترابولويد
+
+787
+01:35:23,140 --> 01:35:32,780
+هاي ترابولويد هاي ترابولويد of one
+
+788
+01:35:44,770 --> 01:35:48,090
+على V تردية ضعف الزيت تردية
+
+789
+01:36:21,460 --> 01:36:30,640
+زي و لا تشبهت قبله و مضبط تماما و هي اسم و المقطع
+
+790
+01:36:30,640 --> 01:36:41,180
+الثاني هيكون بهذا الشكل و
+
+791
+01:36:41,180 --> 01:36:47,380
+هذا المقطع التالت
+
+792
+01:36:47,380 --> 01:36:50,480
+بهذا الشكل و المقطع التالت
+
+793
+01:36:58,250 --> 01:37:07,930
+يبقى هذا المجسم hyperboloid المجسم المقافق ذو طيّة
+
+794
+01:37:07,930 --> 01:37:12,050
+sheet يعني طيّة تطوي شغل أكمل
+
+795
+01:37:14,010 --> 01:37:18,710
+واضح ان المجسم هذا متماثل بالنسبة لمستويات
+
+796
+01:37:18,710 --> 01:37:24,770
+الاحداثية بدي تجيبي التقطع الأسود هذا اللي هو
+
+797
+01:37:24,770 --> 01:37:29,390
+المستوى yz بروح وحط x بمية بزي وغسيل المقطع عبارة
+
+798
+01:37:29,390 --> 01:37:35,690
+عن ايش منها؟ hyperbola يبقى الخط الأسود هذا مع
+
+799
+01:37:35,690 --> 01:37:41,900
+الخط الأسود التاني اللي هو ال hyperbolaعلى P تربية
+
+800
+01:37:41,900 --> 01:37:47,160
+ناقص Z تربية على C تربية بساوية واحدة. وهكذا
+
+801
+01:37:47,160 --> 01:37:53,240
+بالنسبة لمين تتلوجت للأفقي. Z تساوي Zero فطير هذا
+
+802
+01:37:53,240 --> 01:37:58,680
+يظل عنده Ellipse. يبقى هذا high parabola لكن هذا
+
+803
+01:37:58,680 --> 01:38:04,700
+Ellipse. إيش معادلته؟ معادلته X تربية على
+
+804
+01:38:09,020 --> 01:38:18,780
+في عندك المجسم ذوق طي تاني رقم خمسة اللي هو ال
+
+805
+01:38:18,780 --> 01:38:27,220
+high parabolite of
+
+806
+01:38:27,220 --> 01:38:28,080
+two sheets
+
+807
+01:38:53,250 --> 01:39:00,370
+هذا محور X، هذا Y، هذا Z، ندى هذه على استماعك بهذا
+
+808
+01:39:00,370 --> 01:39:08,050
+الشكل. شايف هذا يا بنات؟ هو هذا بس، واحدة موجة فوق
+
+809
+01:39:08,050 --> 01:39:16,230
+وواحدة تحت، وهكذا. طيبة طيبة موجة، يبقى هذا هكذا
+
+810
+01:39:16,230 --> 01:39:17,570
+والتاني هكذا.
+
+811
+01:39:27,020 --> 01:39:33,120
+يبقى هذا الـ hyperboloid of two sheets لو قطعته
+
+812
+01:39:33,120 --> 01:39:38,860
+أفقي بتلاقي ellipse هذا عبارة عن ellipse وهذا
+
+813
+01:39:38,860 --> 01:39:43,480
+عبارة عن إيش ellipse لو قطعته رأسي بتلاقي
+
+814
+01:39:43,480 --> 01:39:46,800
+hyperbola و هاي hyperbola جتين مع بعض هاي
+
+815
+01:39:46,800 --> 01:39:50,380
+hyperbola بالمستوى x زاد
+
+816
+01:39:56,430 --> 01:40:01,430
+فأضع اللي هيك ومن
+
+817
+01:40:01,430 --> 01:40:09,150
+هنا مش هيظهر و من هنا هيك يظهر و من اللي هيتاني
+
+818
+01:40:09,150 --> 01:40:16,400
+لبس هذا الشكلطب السؤال هل هذا يمر بنقطة أصيله؟ لأ
+
+819
+01:40:16,400 --> 01:40:21,760
+لإن لو بده احط زيت تساوي zero في المعادلة بيصير
+
+820
+01:40:21,760 --> 01:40:26,940
+مجموعة كميتين سلبتين يساوي كمية جوجل صحيح؟ يعني لو
+
+821
+01:40:26,940 --> 01:40:29,560
+ضرر فيه شبة ناقص بيصير X سلبي عليها تلقى
+
+822
+01:40:32,950 --> 01:40:36,830
+هذا كلام ممنوع وفي وقت ما يتم ارسال كيمياسانة وهذا
+
+823
+01:40:36,830 --> 01:40:43,210
+مفهوم إذن يمكن للمستوى XY نقطع هذا المجسم لكن ال
+
+824
+01:40:43,210 --> 01:40:48,590
+XY المجسم هذا متمثل بالنسبة للنص اللي فوق زي النص
+
+825
+01:40:48,590 --> 01:40:51,890
+اللي تا النص اللي علي مين زي النص اللي عشرة للنص
+
+826
+01:40:51,890 --> 01:40:56,690
+هذه يعني متمثل بالنسبة لمستويات الأحداثيات
+
+827
+01:41:19,790 --> 01:41:26,170
+يبقى اخر حاجة هي النقطة الرقم ستة هي عنامين
+
+828
+01:41:26,170 --> 01:41:28,230
+hyperbolic paraboloid
+
+829
+01:41:39,790 --> 01:41:44,530
+المعادلة التي اتبعتها هي Y
+
+830
+01:41:44,530 --> 01:41:52,510
+تربيع على B تربيع ناقص X تربيع على A تربيع بدها
+
+831
+01:41:52,510 --> 01:41:57,290
+تسوى Z على C والـC أكتر من
+
+832
+01:42:16,250 --> 01:42:22,490
+رسم I أولا بأولا بدا نرسم I فرابولا حوالي المحور
+
+833
+01:42:22,490 --> 01:42:28,770
+زد من أول نبقى بالدرجة أقول له ادي اي فرابولا و من
+
+834
+01:42:28,770 --> 01:42:35,510
+الناحية التالية و ذات جينها طبعا
+
+835
+01:42:35,510 --> 01:42:39,190
+عالية اكيد بدا نزلها بس لتحت شوية
+
+836
+01:42:49,920 --> 01:43:05,540
+بعد ذلك بدي من النقطة هذه ارسم برابطة بعد ذلك
+
+837
+01:43:05,540 --> 01:43:11,340
+بنزلها هنا وهذه هي الشكل اللي عملنا
+
+838
+01:43:20,510 --> 01:43:29,050
+تمام ؟ هذا يظهر عليك على شكل دوس الشكل هنا و هذا
+
+839
+01:43:29,050 --> 01:43:44,830
+هنا يقول دوس تمام الشكل واضحة الرسمة و
+
+840
+01:43:44,830 --> 01:43:46,090
+بعد هيك
+
+841
+01:43:55,780 --> 01:44:06,680
+يبقى هاي فراغلة وهي فراغلة كمان زي ملتشاكر يبنيس
+
+842
+01:44:06,680 --> 01:44:07,220
+منها
+
+843
+01:44:14,430 --> 01:44:20,110
+هذه المعادلة اللي قدامها من المحور تبعها زي ما
+
+844
+01:44:20,110 --> 01:44:28,350
+تشايفها اللي هو محور الـ Z بالضبط تماما على
+
+845
+01:44:28,350 --> 01:44:35,790
+شكل قص وليس خطا مستقيما زي ولا تشبيه السرج تبع
+
+846
+01:44:35,790 --> 01:44:42,170
+الفرصةسارج الفرص بالضبط هذا هو عبارة عن سارج الفرص
+
+847
+01:44:42,170 --> 01:44:49,110
+طيب بدنا يا بنات المسائل التالية منكم exercises
+
+848
+01:44:49,110 --> 01:44:52,310
+أتناشر
+
+849
+01:44:52,310 --> 01:45:03,470
+ستة المسائل من واحد لغاية تلاتة واربعين الفور على
+
+850
+01:45:03,470 --> 01:45:08,210
+هيك يكون انتهى ال chapterالمرة القادمة ان شاء الله
+
+851
+01:45:08,210 --> 01:45:14,710
+بناخد نين نخس في chapter 13 ان شاء الله و تعالى
+
diff --git a/PL9fwy3NUQKwaBhVI6LPr803vc5wWl9Iy_/2G_muh64saE_raw.json b/PL9fwy3NUQKwaBhVI6LPr803vc5wWl9Iy_/2G_muh64saE_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..c2c7321cc6379d75f7643cec6e400a8101efca30
--- /dev/null
+++ b/PL9fwy3NUQKwaBhVI6LPr803vc5wWl9Iy_/2G_muh64saE_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 3718, "start": 21.6, "end": 37.18, "text": "طيب بسم الله الرحمن الرحيم السلام عليكم اليوم هنبدأ في موضوع ال measurement notation وحدة القياس هنحاول أنه نعيد وحدات القياس مع بعض مرة تانية", "tokens": [9566, 1829, 3555, 4724, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 21136, 37440, 25894, 24793, 45595, 20498, 8032, 1863, 44510, 10721, 8978, 3714, 2407, 11242, 45367, 2423, 13160, 24657, 4032, 24401, 3660, 25062, 25528, 3794, 8032, 1863, 5016, 995, 12610, 14739, 3224, 8717, 3615, 25708, 4032, 24401, 9307, 25062, 25528, 3794, 20449, 45030, 11242, 3714, 25720, 6055, 7649, 10632], "avg_logprob": -0.08824282982310311, "compression_ratio": 1.5253164556962024, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 21.6, "end": 21.88, "word": "طيب", "probability": 0.9763997395833334}, {"start": 21.88, "end": 22.08, "word": " بسم", "probability": 0.77392578125}, {"start": 22.08, "end": 22.26, "word": " الله", "probability": 0.97412109375}, 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31.6, "word": " القياس", "probability": 0.8865559895833334}, {"start": 31.6, "end": 33.44, "word": " هنحاول", "probability": 0.96591796875}, {"start": 33.44, "end": 33.74, "word": " أنه", "probability": 0.595947265625}, {"start": 33.74, "end": 34.16, "word": " نعيد", "probability": 0.9903971354166666}, {"start": 34.16, "end": 35.1, "word": " وحدات", "probability": 0.9456380208333334}, {"start": 35.1, "end": 35.82, "word": " القياس", "probability": 0.9635416666666666}, {"start": 35.82, "end": 36.12, "word": " مع", "probability": 0.98876953125}, {"start": 36.12, "end": 36.46, "word": " بعض", "probability": 0.989990234375}, {"start": 36.46, "end": 36.72, "word": " مرة", "probability": 0.986328125}, {"start": 36.72, "end": 37.18, "word": " تانية", "probability": 0.9840494791666666}], "temperature": 1.0}, {"id": 2, "seek": 6456, "start": 38.05, "end": 64.57, "text": "لأنه شعرت أنه في بعض ال confusion اللي هو التباك عند بعض الطالبات فهنحاول أنه نعيد بالنسبة للست متر وإذا كانت متغيرة المسافة 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"text": "بدي احولها ايوة اه اللي هي ال visual ال 6 على 30 يعني ال visual acuity هان اللي هي ال 6 على 30 okay ال x مية هي كاتب انا اللي هي ال 6 على 30 بساوة 20 على 100 okay طيب بالنسبة لل decimal", "tokens": [3555, 16254, 1975, 5016, 12610, 11296, 1975, 1829, 2407, 3660, 1975, 3224, 13672, 1829, 39896, 2423, 5056, 2423, 1386, 15844, 2217, 37495, 22653, 2423, 5056, 696, 21757, 8032, 7649, 13672, 1829, 39896, 2423, 1386, 15844, 2217, 1392, 2423, 2031, 3714, 10632, 39896, 9122, 9307, 3555, 1975, 8315, 13672, 1829, 39896, 2423, 1386, 15844, 2217, 4724, 3794, 995, 2407, 3660, 945, 15844, 2319, 1392, 23032, 1829, 3555, 20666, 1863, 35457, 3660, 24976, 26601], "avg_logprob": -0.24293665036763232, "compression_ratio": 1.7375, "no_speech_prob": 0.0, "words": [{"start": 126.88, "end": 127.16, "word": "بدي", "probability": 0.54541015625}, {"start": 127.16, "end": 127.98, "word": " احولها", "probability": 0.8648681640625}, {"start": 127.98, "end": 130.02, "word": " ايوة", "probability": 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{"start": 632.04, "end": 632.58, "word": " صراحة", "probability": 0.86865234375}, {"start": 632.58, "end": 633.42, "word": " يعني", "probability": 0.879638671875}, {"start": 633.42, "end": 633.66, "word": " أنا", "probability": 0.75439453125}, {"start": 633.66, "end": 634.26, "word": " عادي", "probability": 0.8367513020833334}, {"start": 634.26, "end": 634.94, "word": " بنظن", "probability": 0.84326171875}, {"start": 634.94, "end": 635.12, "word": " أنه", "probability": 0.410888671875}, {"start": 635.12, "end": 635.34, "word": " نعيد", "probability": 0.7582194010416666}, {"start": 635.34, "end": 635.5, "word": " من", "probability": 0.97998046875}, {"start": 635.5, "end": 635.7, "word": " هلأ", "probability": 0.5694173177083334}, {"start": 635.7, "end": 636.72, "word": " بكرا", "probability": 0.82177734375}, {"start": 636.72, "end": 637.32, "word": " اللي", "probability": 0.903564453125}, {"start": 637.32, "end": 637.48, "word": " مش", "probability": 0.98828125}, {"start": 637.48, "end": 637.84, "word": " فاهمة", "probability": 0.9337158203125}, {"start": 637.84, "end": 638.16, "word": " لازم", "probability": 0.9583333333333334}, {"start": 638.16, "end": 638.6, "word": " أنه", "probability": 0.80859375}, {"start": 638.6, "end": 639.36, "word": " تحكيلي", "probability": 0.93916015625}, {"start": 639.36, "end": 639.5, "word": " أنا", "probability": 0.67822265625}, {"start": 639.5, "end": 639.7, "word": " مش", "probability": 0.98388671875}, {"start": 639.7, "end": 640.32, "word": " فاهمة", "probability": 0.959716796875}, {"start": 640.32, "end": 641.24, "word": " أفضل", "probability": 0.6302490234375}], "temperature": 1.0}, {"id": 25, "seek": 66633, "start": 649.97, "end": 666.33, "text": "طب الحمد لله يعني فاهمها لما حليتي هيك طبعا اي واحدة مش فاهمة راجعا تحكيلي انه انا مش فاهمه عشان انه نعيد مرة و مرتين و تلاتة okay اه تفضلي", "tokens": [9566, 3555, 21542, 2304, 3215, 24976, 3224, 37495, 22653, 6156, 995, 16095, 11296, 5296, 15042, 11331, 20292, 31371, 39896, 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"end": 694.82, "text": "هل قلت okay ادينا في السؤال مثلا اذا كانت تمانتاش مش عشرين مثلا على تلاتين بنحقق بال feet؟ اه و هم بيقدروا نحويلها لعشرين بعدها لستة ولا كده؟ كيف؟ قالت اه okay ادينا بدل عشرين على اربعمية feet مثلا هم بيقدروا نحويلها تمانتاش او خمستاش على تلاتين او على اي رقم؟ خمستاش على تلاتين؟ كيف فعلت؟ اه يعني مثلا ات خمستاشر feet نحويلها اول اشهر بال", "tokens": [3224, 1211, 12174, 1211, 2655, 1392, 1975, 16254, 8315, 8978, 21136, 33604, 6027, 50113, 15040, 1975, 15730, 25961, 2655, 46811, 7649, 2655, 33599, 37893, 6225, 46309, 9957, 50113, 15040, 15844, 6055, 1211, 9307, 9957, 44945, 5016, 4587, 4587, 20666, 3521, 22807, 1975, 3224, 4032, 8032, 2304, 4724, 1829, 28543, 2288, 14407, 8717, 5016, 2407, 26895, 11296, 5296, 3615, 46309, 9957, 39182, 11296, 5296, 14851, 3660, 49429, 9122, 3215, 3224, 22807, 9122, 33911, 22807, 50239, 2655, 1975, 3224, 1392, 1975, 16254, 8315, 47525, 1211, 6225, 46309, 9957, 15844, 1975, 25513, 25957, 10632, 3521, 50113, 15040, 8032, 2304, 4724, 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44, "seek": 125900, "start": 1234.22, "end": 1259.0, "text": "this occurs at a distance of thirty to forty centimeters that called the reading distance or working distance اذا هذه بتحدث للمسافة من تلاتين لاربعين سانتي وبسميها ايش ال working distance مسافة العمل او ال reading distance او ال writing distance يعني كلها مسمة واحد", "tokens": [11176, 11843, 412, 257, 4560, 295, 11790, 281, 15815, 23300, 300, 1219, 264, 3760, 4560, 420, 1364, 4560, 1975, 15730, 29538, 39894, 24401, 12984, 5296, 19528, 3794, 31845, 3660, 9154, 6055, 1211, 9307, 9957, 5296, 9640, 3555, 3615, 9957, 8608, 7649, 31371, 46599, 38251, 1829, 11296, 1975, 1829, 8592, 2423, 1364, 4560, 47524, 31845, 3660, 18863, 42213, 1975, 2407, 2423, 3760, 4560, 1975, 2407, 2423, 3579, 4560, 37495, 22653, 28242, 11296, 3714, 38251, 3660, 36764, 24401], "avg_logprob": -0.21306817794775035, "compression_ratio": 1.7024390243902439, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1234.22, "end": 1234.58, "word": "this", 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{"start": 1602.07, "end": 1602.43, "word": " Geiger", "probability": 0.603271484375}, {"start": 1602.43, "end": 1603.09, "word": " خطوط", "probability": 0.8577880859375}, {"start": 1603.09, "end": 1604.05, "word": " مختلفة", "probability": 0.995849609375}, {"start": 1604.05, "end": 1604.43, "word": " يعني", "probability": 0.767333984375}, {"start": 1604.43, "end": 1605.29, "word": " J1,", "probability": 0.825439453125}, {"start": 1605.61, "end": 1606.11, "word": " J2,", "probability": 0.92626953125}, {"start": 1606.45, "end": 1606.93, "word": " J3,", "probability": 0.952880859375}, {"start": 1607.23, "end": 1607.81, "word": " J4,", "probability": 0.9755859375}, {"start": 1608.33, "end": 1608.87, "word": " J10", "probability": 0.978271484375}, {"start": 1608.87, "end": 1609.65, "word": " واضح", "probability": 0.8416341145833334}, {"start": 1609.65, "end": 1610.13, "word": " حسب", "probability": 0.926513671875}, {"start": 1610.13, "end": 1610.99, "word": " المسافة", "probability": 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1626.31, "end": 1626.63, "word": " هي", "probability": 0.72265625}, {"start": 1626.63, "end": 1627.07, "word": " عبارة", "probability": 0.9959716796875}, {"start": 1627.07, "end": 1627.33, "word": " عن", "probability": 0.9970703125}, {"start": 1627.33, "end": 1627.69, "word": " ال", "probability": 0.80029296875}, {"start": 1627.69, "end": 1628.29, "word": " smallest", "probability": 0.99267578125}, {"start": 1628.29, "end": 1628.73, "word": " ايش", "probability": 0.8103841145833334}, {"start": 1628.73, "end": 1629.69, "word": " optotype", "probability": 0.6702880859375}, {"start": 1629.69, "end": 1630.03, "word": " او", "probability": 0.86328125}, {"start": 1630.03, "end": 1630.15, "word": " ال", "probability": 0.89208984375}, {"start": 1630.15, "end": 1630.67, "word": " smallest", "probability": 0.9970703125}, {"start": 1630.67, "end": 1631.29, "word": " letter", "probability": 0.98193359375}, {"start": 1631.29, "end": 1632.35, "word": " okay", "probability": 0.3330078125}, {"start": 1632.35, "end": 1633.67, "word": " فأصغر", "probability": 0.9365234375}, {"start": 1633.67, "end": 1633.91, "word": " اللي", "probability": 0.97021484375}, {"start": 1633.91, "end": 1634.17, "word": " هو", "probability": 0.99609375}, {"start": 1634.17, "end": 1634.59, "word": " خط", "probability": 0.988525390625}, {"start": 1634.59, "end": 1635.07, "word": " بقرا", "probability": 0.8681640625}, {"start": 1635.07, "end": 1635.33, "word": " عليه", "probability": 0.9658203125}, {"start": 1635.33, "end": 1635.79, "word": " المريض", "probability": 0.9910481770833334}, {"start": 1635.79, "end": 1636.15, "word": " هذا", "probability": 0.140380859375}, {"start": 1636.15, "end": 1636.77, "word": " بنسميه", "probability": 0.9326171875}, {"start": 1636.77, "end": 1637.09, "word": " ايش", "probability": 0.8211263020833334}, {"start": 1637.09, "end": 1637.89, "word": " J1", "probability": 0.882080078125}, {"start": 1637.89, "end": 1638.95, "word": " بالنسبة", "probability": 0.9857177734375}, 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"text": "يعني لو سألتي السؤال انه هل ال near vision بعمل ال both eye together ولا each eye separated كل عين على حده زي ما بتعملي ال visual acuity بغطي اليمين بغطي الشمال بعمل كل عين على حده okay واضح؟ اه تفضل ممكن هو اللي قلت انه لو كان عنده near vision رح يكون في العين تاني عنده near vision ممكن يكون في عين واحدة عندها far vision واحدة under vision", "tokens": [40228, 22653, 45164, 8608, 10721, 1211, 31371, 21136, 33604, 6027, 16472, 3224, 8032, 1211, 2423, 2651, 5201, 4724, 25957, 1211, 2423, 1293, 3313, 1214, 49429, 1184, 3313, 12005, 28242, 6225, 9957, 15844, 11331, 3215, 3224, 30767, 1829, 19446, 39894, 25957, 20292, 2423, 5056, 696, 21757, 4724, 17082, 9566, 1829, 2423, 32640, 9957, 4724, 17082, 9566, 1829, 25124, 2304, 6027, 4724, 25957, 1211, 28242, 6225, 9957, 15844, 11331, 3215, 3224, 1392, 4032, 46958, 5016, 22807, 1975, 3224, 6055, 5172, 11242, 1211, 3714, 43020, 31439, 13672, 1829, 12174, 1211, 2655, 16472, 3224, 45164, 25961, 43242, 3224, 2651, 5201, 12602, 5016, 7251, 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213946, "start": 2114.62, "end": 2139.46, "text": "obtain the best vision with the response from the patient", "tokens": [996, 15209, 264, 1151, 5201, 365, 264, 4134, 490, 264, 4537], "avg_logprob": -0.15104167287548384, "compression_ratio": 1.0178571428571428, "no_speech_prob": 0.0, "words": [{"start": 2114.62, "end": 2115.3, "word": "obtain", "probability": 0.767333984375}, {"start": 2115.3, "end": 2118.22, "word": " the", "probability": 0.93017578125}, {"start": 2118.22, "end": 2120.92, "word": " best", "probability": 0.9462890625}, {"start": 2120.92, "end": 2123.44, "word": " vision", "probability": 0.80126953125}, {"start": 2123.44, "end": 2130.06, "word": " with", "probability": 0.92431640625}, {"start": 2130.06, "end": 2130.58, "word": " the", "probability": 0.6103515625}, {"start": 2130.58, "end": 2134.92, "word": " response", "probability": 0.95703125}, {"start": 2134.92, "end": 2138.98, "word": " from", "probability": 0.91943359375}, {"start": 2138.98, "end": 2139.18, "word": " the", "probability": 0.92236328125}, {"start": 2139.18, "end": 2139.46, "word": " patient", "probability": 0.947265625}], "temperature": 1.0}, {"id": 80, "seek": 216500, "start": 2149.96, "end": 2165.0, "text": "إذا ما عندنا ال objective method it is a preliminary estimation of the refractive error بمعنى تقدير أولي للخطأ الانكساري للعين without a response from the patient دون تدخل المريض", "tokens": [28814, 15730, 19446, 43242, 8315, 2423, 10024, 3170, 309, 307, 257, 28817, 35701, 295, 264, 45353, 488, 6713, 4724, 2304, 3615, 1863, 7578, 6055, 28543, 13546, 5551, 12610, 1829, 24976, 9778, 9566, 10721, 2423, 7649, 4117, 3794, 9640, 1829, 24976, 3615, 9957, 1553, 257, 4134, 490, 264, 4537, 11778, 11536, 6055, 3215, 9778, 1211, 9673, 16572, 11242], "avg_logprob": -0.14062500539524803, "compression_ratio": 1.3038674033149171, "no_speech_prob": 6.556510925292969e-07, "words": [{"start": 2149.96, "end": 2150.24, "word": "إذا", "probability": 0.686767578125}, {"start": 2150.24, "end": 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"end": 3043.1, "text": "ليست اقل من اربع ملي ميتر، نعم This plan peripherated mirror ان هذه المرأة المسطحة okay طبعا هل هي convex ولا plan ولا concave mirror؟ هي تعتبر plan mirror يعني بمعنى عدسة اي شمالها مسطحة This plan peripherated mirror ان هذه العدسة المسطحة reflects", "tokens": [20292, 14851, 1975, 4587, 1211, 9154, 1975, 25513, 3615, 3714, 20292, 3714, 36081, 2288, 12399, 8717, 25957, 639, 1393, 680, 21240, 770, 8013, 16472, 29538, 9673, 2288, 10721, 3660, 9673, 3794, 9566, 5016, 3660, 1392, 23032, 3555, 3615, 995, 8032, 1211, 39896, 42432, 49429, 1393, 49429, 416, 50126, 8013, 22807, 39896, 6055, 34268, 26890, 1393, 8013, 37495, 22653, 4724, 2304, 3615, 1863, 7578, 6225, 3215, 3794, 3660, 1975, 1829, 13412, 2304, 6027, 11296, 47524, 9566, 5016, 3660, 639, 1393, 680, 21240, 770, 8013, 16472, 29538, 18863, 3215, 3794, 3660, 9673, 3794, 9566, 5016, 3660, 18926], "avg_logprob": -0.186035157336543, "compression_ratio": 1.7450980392156863, "no_speech_prob": 0.0, "words": [{"start": 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الآن بنعكس في عين المريض فإيش بيبين معاه؟", "tokens": [259, 1353, 264, 4537, 311, 3313, 8978, 6225, 9957, 9673, 16572, 11242, 597, 17057, 264, 3256, 300, 393, 312, 1612, 538, 27878, 3313, 382, 2182, 23802, 807, 264, 5777, 5193, 4724, 2304, 3615, 1863, 7578, 6024, 48506, 9673, 16572, 11242, 4724, 1829, 30544, 2423, 11242, 2407, 38207, 34051, 2423, 1442, 4009, 44945, 3615, 4117, 3794, 4032, 9957, 8978, 6225, 9957, 9673, 16572, 11242, 30767, 1829, 6156, 4117, 25720, 2423, 1533, 17094, 13960, 13672, 1829, 14739, 2655, 14407, 13412, 17082, 6027, 9957, 25894, 11296, 6024, 48506, 44945, 3615, 4117, 3794, 8978, 6225, 9957, 9673, 16572, 11242, 6156, 28814, 1829, 8592, 4724, 1829, 3555, 9957, 20449, 40294, 22807], "avg_logprob": -0.17537967401130178, "compression_ratio": 1.6746987951807228, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 3053.26, "end": 3053.6, "word": "into", "probability": 0.454345703125}, {"start": 3053.6, "end": 3053.8, "word": " the", "probability": 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"فبتلاقي انه دايما ايش بيكون شكله بالشكل هذا انه بيكون oblique فانا بحالك الضوء او ال streak تاع ال retinascope بيكون موازي لمين ل ال red reflex okay يعني دايما ال streak تاع ال retinascope بيكون موازي لمين ل ال red reflex ل ال facial", "tokens": [5172, 3555, 2655, 15040, 38436, 16472, 3224, 11778, 47302, 15042, 1975, 1829, 8592, 4724, 1829, 30544, 13412, 28820, 3224, 20666, 8592, 28820, 23758, 16472, 3224, 4724, 1829, 30544, 23740, 1925, 6156, 7649, 995, 4724, 5016, 6027, 4117, 6024, 114, 2407, 38207, 1975, 2407, 2423, 35634, 6055, 45761, 2423, 1533, 17094, 13960, 4724, 1829, 30544, 3714, 2407, 31377, 1829, 32767, 9957, 5296, 2423, 2182, 23802, 1392, 37495, 22653, 11778, 47302, 15042, 2423, 35634, 6055, 45761, 2423, 1533, 17094, 13960, 4724, 1829, 30544, 3714, 2407, 31377, 1829, 32767, 9957, 5296, 2423, 2182, 23802, 5296, 2423, 15642], "avg_logprob": -0.22253288940379495, "compression_ratio": 1.9720670391061452, "no_speech_prob": 0.0, "words": [{"start": 3492.92, "end": 3493.38, 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بنكون هيك اكتفنا من محاضرة اليوم", "tokens": [1353, 445, 309, 307, 5178, 23032, 3555, 3615, 995, 493, 760, 420, 1252, 281, 1252, 37495, 22653, 16472, 3224, 4724, 1829, 30544, 493, 760, 13672, 1829, 31439, 1975, 2407, 1252, 281, 1252, 558, 281, 1411, 23032, 3555, 3615, 995, 45595, 20498, 44945, 30544, 39896, 4117, 1975, 4117, 2655, 5172, 8315, 9154, 3714, 5016, 46958, 25720, 45595, 20498], "avg_logprob": -0.14951508697764626, "compression_ratio": 1.4827586206896552, "no_speech_prob": 2.086162567138672e-06, "words": [{"start": 4122.09, "end": 4122.35, "word": "to", "probability": 0.265869140625}, {"start": 4122.35, "end": 4123.17, "word": " just", "probability": 0.89111328125}, {"start": 4123.17, "end": 4124.31, "word": " it", "probability": 0.37841796875}, {"start": 4124.31, "end": 4124.49, "word": " is", "probability": 0.92333984375}, {"start": 4124.49, "end": 4124.97, "word": " focused", "probability": 0.48388671875}, {"start": 4124.97, "end": 4125.53, "word": " طبعا", "probability": 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwaBhVI6LPr803vc5wWl9Iy_/38tMh_s_134_postprocess.srt b/PL9fwy3NUQKwaBhVI6LPr803vc5wWl9Iy_/38tMh_s_134_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..6f594ea0995c232343298e2dd6b894a2f6787249
--- /dev/null
+++ b/PL9fwy3NUQKwaBhVI6LPr803vc5wWl9Iy_/38tMh_s_134_postprocess.srt
@@ -0,0 +1,2688 @@
+1
+00:00:20,790 --> 00:00:25,770
+بسم الله الرحمن الرحيم في المحاضرة السابقة اتكلمنا
+
+2
+00:00:25,770 --> 00:00:31,250
+عن مفهوم ال visual acuity حدة الإبصار طبعا اليوم
+
+3
+00:00:31,250 --> 00:00:39,550
+هنبدأ بتعريف حدة الإبصار من مفهوم آخر لتبسيط
+
+4
+00:00:39,550 --> 00:00:46,140
+المادة العلمية أكثرvisual acuity كتعريف له it is a
+
+5
+00:00:46,140 --> 00:00:50,160
+measurement of spatial resolving capacity of the
+
+6
+00:00:50,160 --> 00:00:55,300
+eye and is applied to central vision يعني بيستخدم
+
+7
+00:00:55,300 --> 00:01:04,000
+في قياس قداش الصورة اللى بتتكون من العين وقداش
+
+8
+00:01:04,000 --> 00:01:08,960
+الرؤية المركزية للعين okay طيب ال special
+
+9
+00:01:08,960 --> 00:01:14,340
+resolvingحدنا سمع في تعريف ال special resolving شو
+
+10
+00:01:14,340 --> 00:01:22,800
+هو؟ نعم قوة التباين بس
+
+11
+00:01:22,800 --> 00:01:27,900
+هان عندنا في ال visual acuity كتعريف لها انه جديش
+
+12
+00:01:27,900 --> 00:01:32,840
+القدرة على تكوين الصورة سواء بواسطة كاميرا الجوال
+
+13
+00:01:32,840 --> 00:01:38,900
+بواسطة العين او بواسطة ال microscopeيعني القدرة
+
+14
+00:01:38,900 --> 00:01:45,680
+على تكوين الصورة بواسطة العين أو بواسطة ال
+
+15
+00:01:45,680 --> 00:02:02,480
+microscope أو بواسطة الكاميرا ال special resolving
+
+16
+00:02:11,200 --> 00:02:23,420
+it is an ability image
+
+17
+00:02:23,420 --> 00:02:27,600
+forming
+
+18
+00:02:27,600 --> 00:02:33,680
+device
+
+19
+00:02:33,680 --> 00:02:39,300
+such
+
+20
+00:02:39,300 --> 00:02:51,550
+asعلى سبيل المثال عندنا مثلا camera eye
+
+21
+00:02:51,550 --> 00:02:55,410
+microscope
+
+22
+00:03:02,000 --> 00:03:06,940
+إذا القدرة على تكوين الصورة اللى بشكلها ممكن
+
+23
+00:03:06,940 --> 00:03:12,620
+كاميرا ممكن العين ممكن ال microscope okay هذا
+
+24
+00:03:12,620 --> 00:03:18,440
+تعريف ال special resolving فال
+
+25
+00:03:18,440 --> 00:03:23,780
+visual acuity بقيس جداش ال special resolving للآي
+
+26
+00:03:23,780 --> 00:03:28,280
+جداش يعني كمية هذا ال special resolving بتاعة الآي
+
+27
+00:03:28,830 --> 00:03:32,270
+وزائد انه بقيس ايش ال central vision الرؤية
+
+28
+00:03:32,270 --> 00:03:40,310
+المركزية لمن؟ للعين okay importance of testing
+
+29
+00:03:40,310 --> 00:03:47,450
+visual acuity شو أهمية قياس حدة الأبصار testing
+
+30
+00:03:47,450 --> 00:03:51,550
+visual acuity is very important in all of the
+
+31
+00:03:51,550 --> 00:03:57,950
+cases becauseليش حدة الإبصار تعتبر يعني إلها أهمية
+
+32
+00:03:57,950 --> 00:04:03,350
+كبيرة؟ أول حاجة it gives us an accurate diagnosis
+
+33
+00:04:03,350 --> 00:04:08,170
+for the patient diagnosis بمعنى تشخيص يعني بتعطي
+
+34
+00:04:08,170 --> 00:04:14,490
+تشخيص دقيق للمريض لحالة المريض and indicate the
+
+35
+00:04:14,490 --> 00:04:18,970
+severity of the problem وبيشير إلى حدة اللي هو كده
+
+36
+00:04:18,970 --> 00:04:21,990
+عنده مشكلة طبعا كلمة severe
+
+37
+00:04:24,940 --> 00:04:34,540
+بمعنى حاد وعكسه mild بمعنى اللي هو يعني قليل يعني
+
+38
+00:04:34,540 --> 00:04:44,580
+زي مثلا واحد بيقول عنده severe headache و واحد اخر
+
+39
+00:04:44,580 --> 00:04:49,980
+ايش بيقول مثلا mild headache
+
+40
+00:04:54,860 --> 00:05:01,520
+عنا moderate، متوسط،
+
+41
+00:05:01,520 --> 00:05:06,400
+headache يعني لما انتوا أخدتوا ال history من
+
+42
+00:05:06,400 --> 00:05:10,520
+المريض ممكن أنه المريض يقول أنا عندي mild اللي هو
+
+43
+00:05:10,520 --> 00:05:14,900
+headache أنه صداع لكن إش ما له خفيف أو moderate
+
+44
+00:05:14,900 --> 00:05:19,200
+headache أنه صداع لكن إش متوسط أو severe headache
+
+45
+00:05:19,200 --> 00:05:22,100
+أنه بيكون صداع لكن إش ما له حاد
+
+46
+00:05:26,120 --> 00:05:29,800
+number two it may helps us to discover a new
+
+47
+00:05:29,800 --> 00:05:32,820
+problem at the patient which is not the main
+
+48
+00:05:32,820 --> 00:05:37,900
+problem that the patient complained for مثال عليها
+
+49
+00:05:37,900 --> 00:05:42,680
+مثلا إيجا مريض حكى في ال history بتاعه أنا مثلا
+
+50
+00:05:42,680 --> 00:05:47,220
+عندي headache، severe headache، الآن هذه تعتبر
+
+51
+00:05:47,220 --> 00:05:51,630
+إيش؟ ال history بتاعة المريضك examiner او ك
+
+52
+00:05:51,630 --> 00:05:56,310
+optometrist يما احنا جسنا ال visual acuity بتاعته
+
+53
+00:05:56,310 --> 00:06:00,770
+لجينا عنده blurred vision for distance يعني عنده
+
+54
+00:06:00,770 --> 00:06:06,230
+مشكلة في اللي بعيد okay فهذه المشكلة مين كشفها ال
+
+55
+00:06:06,230 --> 00:06:11,490
+visual acuity okay يعني الآن لو انا مثلا اجيب لك
+
+56
+00:06:11,490 --> 00:06:15,430
+case studyال case study هذه مثلا عندها headache،
+
+57
+00:06:15,430 --> 00:06:18,550
+severe headache أو mild headache أو moderate
+
+58
+00:06:18,550 --> 00:06:22,970
+headache، لكن عندها في ال visual acuity blurred
+
+59
+00:06:22,970 --> 00:06:27,110
+fore vision، إذا ال visual acuity بتاعة المريض
+
+60
+00:06:27,110 --> 00:06:33,750
+بتتوقع يكون impaired، ضعيف ولا good ولا جيد؟ ضعيف،
+
+61
+00:06:33,750 --> 00:06:40,270
+صح؟واضح الأمور؟ الآن ايجي انا عندى طفل او مثلا
+
+62
+00:06:40,270 --> 00:06:46,810
+female or male عمرها تسعتاشر سنة وشكى انه عنده
+
+63
+00:06:46,810 --> 00:06:51,070
+headache طبعا هذه سواء severe او mild او moderate
+
+64
+00:06:51,070 --> 00:06:56,360
+headache هذه تعتبر ايش؟ال history .. ال history of
+
+65
+00:06:56,360 --> 00:07:01,060
+the patient صح؟ الآن أنا عملت visual acuity جسد جد
+
+66
+00:07:01,060 --> 00:07:05,280
+.. جديش حدة الإبصار للمريض فطلع عنده blurred لل
+
+67
+00:07:05,280 --> 00:07:08,480
+vision يعني ال vision عنده مثلا ستة على ستين أو
+
+68
+00:07:08,480 --> 00:07:12,240
+ستة على أربع و عشرين فانا هذا بديني indicate ل ال
+
+69
+00:07:12,240 --> 00:07:18,020
+visual acuity impaired, bad or good؟ bad صح؟
+
+70
+00:07:18,020 --> 00:07:18,380
+impaired
+
+71
+00:07:21,280 --> 00:07:24,020
+it is also help us in the following up the
+
+72
+00:07:24,020 --> 00:07:27,660
+patients case to compare between pre and post the
+
+73
+00:07:27,660 --> 00:07:33,260
+treatment اليوم أربع عشرة جسنا لسين من الناس ال
+
+74
+00:07:33,260 --> 00:07:37,940
+visual acuity بتاعته كانت مثلا أربع على ستين okay
+
+75
+00:07:37,940 --> 00:07:43,820
+لكن هذا المريض كان عنده مشكلة ال eye disease يعني
+
+76
+00:07:43,820 --> 00:07:50,690
+مرض في العينأربعة واحد 2017 جسنا ال visual acuity
+
+77
+00:07:50,690 --> 00:07:55,790
+حدث الإبصار لجينا باختلف عن المرة الفاتة ليش؟ لأن
+
+78
+00:07:55,790 --> 00:08:00,550
+السبب راح اللي هو اللي .. انه ليش هو كان عنده
+
+79
+00:08:00,550 --> 00:08:04,670
+visual acuity impaired السبب اللي هو ال eye
+
+80
+00:08:04,670 --> 00:08:08,150
+disease فال eye disease علجناه يعني احنا علجنا
+
+81
+00:08:08,150 --> 00:08:11,650
+اللي هو ال causes فمدام انت علجت ال causes فال
+
+82
+00:08:11,650 --> 00:08:14,630
+visual acuity إيش ماله هيتحسن صح؟
+
+83
+00:08:17,570 --> 00:08:21,810
+for all of these reasons visual acuity must be
+
+84
+00:08:21,810 --> 00:08:25,490
+tested for all of the patients before visiting the
+
+85
+00:08:25,490 --> 00:08:31,610
+ophthalmologist طبعا أي كتاب في العيون تفتحي في 4
+
+86
+00:08:31,610 --> 00:08:37,720
+O دايما مكتوبة 4 O شو معناها ال 4 O؟الـ 4O معناها
+
+87
+00:08:37,720 --> 00:08:43,540
+أنه أفثالمولوجي طبيب الطب العيون أفثالمولوجيست
+
+88
+00:08:43,540 --> 00:08:48,760
+اللي هي طبيب العيون في الoptometrist علم البصريات
+
+89
+00:08:48,760 --> 00:08:54,660
+أخصاء البصريات في ال orthoptist اللي هو علم
+
+90
+00:08:54,660 --> 00:08:59,820
+الحوالي و في
+
+91
+00:08:59,820 --> 00:09:05,140
+التعون اللي .. اللي بيقص النضارات و فيه ال
+
+92
+00:09:05,140 --> 00:09:16,500
+optician اللي هو فن البصريات فعنا 4O هان دايما
+
+93
+00:09:16,500 --> 00:09:24,100
+أي كتاب في العيون بيكون كاتب 4O شو معناه ال 4O؟
+
+94
+00:09:24,100 --> 00:09:28,500
+زي هيك بيكون كاتب 4 O
+
+95
+00:09:30,340 --> 00:09:52,940
+عنا الـ ophthalmologist بمعنى
+
+96
+00:09:52,940 --> 00:09:55,880
+طب العيون طبيب العيون okay
+
+97
+00:10:08,960 --> 00:10:19,200
+optometrist وفي عندنا ال orthoptics المختص
+
+98
+00:10:19,200 --> 00:10:24,540
+في الحوالي orthoptist
+
+99
+00:10:24,540 --> 00:10:30,780
+وفي
+
+100
+00:10:30,780 --> 00:10:32,080
+عندنا ال optics
+
+101
+00:10:39,510 --> 00:10:46,170
+optician اللي بيكون مختص في علم النضارات، يعني
+
+102
+00:10:46,170 --> 00:10:50,550
+اللي بيقص النضارات، اللي هو فن بصريات، okay فالآن
+
+103
+00:10:50,550 --> 00:10:56,240
+أية مريضبروح لطبيب العيون لازم يقاس له حدة
+
+104
+00:10:56,240 --> 00:11:00,480
+الإبصار، قداش حدة الإبصار لهذا المريض، طبعا ال
+
+105
+00:11:00,480 --> 00:11:03,920
+function هذا أو ال task هذا الوظيفة مين اللي بيقوم
+
+106
+00:11:03,920 --> 00:11:07,640
+فيها؟ اللي هو ال optometrist، optometry علم
+
+107
+00:11:07,640 --> 00:11:10,760
+البصريات، ال optometrist اللي هو ال examiner،
+
+108
+00:11:10,760 --> 00:11:16,210
+أخصائه البصرياتand this is the mission of the
+
+109
+00:11:16,210 --> 00:11:20,290
+optometrist who is the specialist examiner in this
+
+110
+00:11:20,290 --> 00:11:23,690
+examination يعني هذه ال mission الوظيفة أو ال
+
+111
+00:11:23,690 --> 00:11:28,170
+occupation اللي بيقوم فيها مين طبيب أو أخصائي
+
+112
+00:11:28,170 --> 00:11:33,930
+البصرية okay طيب
+
+113
+00:11:33,930 --> 00:11:38,890
+testing visual acuity in preverbal children قياس
+
+114
+00:11:38,890 --> 00:11:45,800
+حدث الإبصار للأطفال الغير ناطقينأول حاجة عندنا is
+
+115
+00:11:45,800 --> 00:11:54,480
+occlusion of one eye انه اغطي عين واحدة it is
+
+116
+00:11:54,480 --> 00:11:57,960
+a simple method for testing the visual acuity in
+
+117
+00:11:57,960 --> 00:12:03,550
+preverbal children and infantsطبعا هو طريقة بسيطة
+
+118
+00:12:03,550 --> 00:12:07,670
+جدا لقياس حدة الإبصار للعين في الأطفال الغير
+
+119
+00:12:07,670 --> 00:12:12,030
+ناطقين والردع okay we cover one eye and if
+
+120
+00:12:12,030 --> 00:12:15,890
+strongly objected by the child indicates poorer
+
+121
+00:12:15,890 --> 00:12:20,430
+acuity in the other eye الآن بنغطي عين يعني مثلا
+
+122
+00:12:20,430 --> 00:12:25,270
+الآن بدي أفحص العين اليمين بغطي مين العين الشمال
+
+123
+00:12:26,180 --> 00:12:31,640
+بشوف قداش اللي هو إذا مثلا الطفل قاوم هذه التغطاية
+
+124
+00:12:31,640 --> 00:12:35,940
+إنه رفع الغطاء عن العين فبيكون poor لل visual
+
+125
+00:12:35,940 --> 00:12:41,740
+acuity in the right eye okay okay
+
+126
+00:12:41,740 --> 00:12:46,620
+الآن أنا مثلا بدي أجيس ال visual acuity للعين
+
+127
+00:12:46,620 --> 00:12:53,500
+اليمين بغطي مين؟ العين الشماللو الطفل قاوم اللي هو
+
+128
+00:12:53,500 --> 00:12:57,180
+التغطية بتاعته، يعني رفع الغطاء اللي أنا غطيت فيه
+
+129
+00:12:57,180 --> 00:13:01,520
+العين الشمال، حيكون شو معناه؟ انه الطفل مش شايف في
+
+130
+00:13:01,520 --> 00:13:05,400
+العين اليمين صح؟ فهو بعنيلي ان ال visual acuity in
+
+131
+00:13:05,400 --> 00:13:09,800
+the right eye is poor or impaired بس هذا الفحص مش
+
+132
+00:13:09,800 --> 00:13:13,700
+دقيق لإن الأطفال مابتحملوش أي شيء مثل هذا؟ بالظبط
+
+133
+00:13:19,220 --> 00:13:23,420
+هو هذا اللي قولنا الفحص هو عبارة عن ايه؟ انه قولنا
+
+134
+00:13:23,420 --> 00:13:29,640
+roughly .. roughly test انه مجرد يعني فحص يعني
+
+135
+00:13:29,640 --> 00:13:33,820
+أولى انه بس مجرد انه اعرف هل هذا الطفل اللي عنده
+
+136
+00:13:33,820 --> 00:13:38,160
+good visual acuity ولا bad visual acuity لكن
+
+137
+00:13:38,160 --> 00:13:42,400
+السؤال هي طرح السؤال بس انا بدي أصيغه بشكل اخر انه
+
+138
+00:13:42,400 --> 00:13:46,120
+هل هذا الفحص يعتبر quantitative ولا qualitative
+
+139
+00:13:46,120 --> 00:13:51,520
+test يعني اللي هو ..equalitative اللي هو إيش يعتبر
+
+140
+00:13:51,520 --> 00:13:55,860
+.. اللي هو وصفه، ليش؟ لأنه ماتدانيش اللي هو إيه
+
+141
+00:13:55,860 --> 00:13:59,700
+رقم، يعني هذا ممكن أنا مثلا أسأل السؤال، ليش أنا
+
+142
+00:13:59,700 --> 00:14:02,360
+مثلا ال inclusion of one eye is a qualitative
+
+143
+00:14:02,360 --> 00:14:09,000
+test؟ why؟ بالظبط، مش مادانيش، أنا يا إما بقولي ال
+
+144
+00:14:09,000 --> 00:14:13,510
+visual acuity good or bad، okay؟ما بيحكيليش مثلا
+
+145
+00:14:13,510 --> 00:14:18,210
+ال visual acuity ستة ع ستين أو واحد ع ستين لأ مجرد
+
+146
+00:14:18,210 --> 00:14:26,350
+انه بيقوللي ال visual acuity good او bad okay this
+
+147
+00:14:26,350 --> 00:14:29,530
+method just indicate if the visual acuity is good
+
+148
+00:14:29,530 --> 00:14:32,070
+or poor and doesn't give us an accurate
+
+149
+00:14:32,070 --> 00:14:35,730
+measurement هو ما بيعطيه اللي هو تشخيص دقيق طبعا
+
+150
+00:14:35,730 --> 00:14:37,450
+احنا هنطبق الفحص هذا
+
+151
+00:14:41,550 --> 00:14:48,190
+بدنا طالبة طبعا الان هي اول حاجة نفترض انه عندنا
+
+152
+00:14:48,190 --> 00:15:01,670
+طفل okay ألبسي هذه في العين الشمال شجة
+
+153
+00:15:01,670 --> 00:15:08,770
+هذه شايفين تعالي تتهمي الان
+
+154
+00:15:08,770 --> 00:15:15,760
+انا غطيت عين okayللي هو المريض الطفل الأمامي طبعا
+
+155
+00:15:15,760 --> 00:15:20,080
+دايما الطفل يما بعمله ال visual acuity لازم يكون
+
+156
+00:15:20,080 --> 00:15:24,020
+here or his parents معاه okay انه دايما اللي هو
+
+157
+00:15:24,020 --> 00:15:28,580
+والده بيكونوا معاه بغطي عين أول حاجة طبعا أنا بده
+
+158
+00:15:28,580 --> 00:15:32,140
+أفحص اللي هو ال right eye الآن لو ال visual acuity
+
+159
+00:15:32,140 --> 00:15:36,340
+بتاعة المريض بيكون ضعيف إيش هيعمل؟ حطول هيرفع ال
+
+160
+00:15:36,340 --> 00:15:40,400
+cover فهي المقصود في انه strongly objected of the
+
+161
+00:15:40,400 --> 00:15:44,500
+coverOkay؟ لكن لو كان ال visual acuity بتاعته
+
+162
+00:15:44,500 --> 00:15:48,540
+جيدة، إيش ماله؟ هيحافظ عليه، هيخليه، بس بعض
+
+163
+00:15:48,540 --> 00:15:51,440
+الأطفال مثلا بتلاقي حتى لو كان عنده ال visual
+
+164
+00:15:51,440 --> 00:15:56,020
+acuity كويس بتاعته و good visual acuity، بحاول أنه
+
+165
+00:15:56,020 --> 00:16:01,720
+يرفعله هذا، بس يعني هو مجرد أنه رفلي، رفلي بمعنى
+
+166
+00:16:01,720 --> 00:16:05,020
+إيش؟ يعني سطحي، أنه هل بتدين ال visual acuity good
+
+167
+00:16:05,020 --> 00:16:09,980
+or bad، okay؟طبعا هي مثلا ال test هان مطبقه ال
+
+168
+00:16:09,980 --> 00:16:14,180
+examiner اللي هو الطبيب أول حاجة هي املاحظة أنت
+
+169
+00:16:14,180 --> 00:16:21,860
+الطفل مع أمه okay الدكتور غطى العين اليمين و العين
+
+170
+00:16:21,860 --> 00:16:25,660
+الشمال بتلاحظي أنه الطفل إيش بيحاول أنه يرفع العين
+
+171
+00:16:25,660 --> 00:16:30,700
+صح؟ اليد عفوا من عينه هان بيكون إيش ماله bad
+
+172
+00:16:30,700 --> 00:16:34,440
+visual acuityممكن اجيبلكم صورة شو التشخيص بتاعك
+
+173
+00:16:34,440 --> 00:16:40,220
+هان اذا هان ايش bad visual acuity هان الطفل ايش
+
+174
+00:16:40,220 --> 00:16:43,900
+ماله smile صح فهان يعتبر اللي هو good visual
+
+175
+00:16:43,900 --> 00:16:50,220
+acuity طيب
+
+176
+00:16:50,220 --> 00:16:57,820
+ال test الآخر ال fixation test كلمة fixation شو
+
+177
+00:16:57,820 --> 00:17:04,690
+معناها انه تثبيتهذه طريقة جيدة جدا لتجربة الـ
+
+178
+00:17:04,690 --> 00:17:11,130
+visual acuity و تتصرف كتابة أول حاجة بنستخدم
+
+179
+00:17:14,270 --> 00:17:18,710
+طبعا في حالة الأطفال هذا عبارة عن ال prism bar شو
+
+180
+00:17:18,710 --> 00:17:25,490
+بيسموه ال prism bar هي مدرج من واحد اتنين اربعة
+
+181
+00:17:25,490 --> 00:17:30,670
+ستة تمانية عشرة اتناشر اربعتاشر ستاشر لحدية forty
+
+182
+00:17:30,670 --> 00:17:34,770
+هذه عبارة عن ال prism قولنا دايما ال prism فيه إلو
+
+183
+00:17:34,770 --> 00:17:41,590
+إيش apex وفيه base ال apex دايما بيكون الصورة هي
+
+184
+00:17:41,590 --> 00:17:42,370
+رسمة ال
+
+185
+00:17:47,650 --> 00:17:52,690
+هي عندنا ال apex و
+
+186
+00:17:52,690 --> 00:17:59,990
+عندنا ال base دايما الصورة باتجاه مين ال apex و
+
+187
+00:17:59,990 --> 00:18:03,770
+الشعاع دايما بكون باتجاه ال base لو رسمنا الرسم
+
+188
+00:18:03,770 --> 00:18:10,390
+بالشكل هذه okayالان الطفل ياما بدي اعمل لطفل واحد
+
+189
+00:18:10,390 --> 00:18:15,390
+لازم انه استخدم ايش one prism زي هيك زي ما هم
+
+190
+00:18:15,390 --> 00:18:19,810
+استخدموا لكن احنا بدنا نحاول انه نعمل ك actor انه
+
+191
+00:18:19,810 --> 00:18:27,090
+طفل عندنا وكيف نعمل ال test هذا okay دايما
+
+192
+00:18:27,090 --> 00:18:30,850
+الصورة باتجاه ال apex اه و الشعاع باتجاه ال base
+
+193
+00:18:30,850 --> 00:18:32,670
+يعني طبعا اول حاجة
+
+194
+00:18:40,860 --> 00:18:48,060
+16 بحط اللي هو ال 16 بريزم عمل fixation هان لأ لأ
+
+195
+00:18:48,060 --> 00:18:53,600
+على ايدي ايدي ايدي ايوة هان الان المريض عمل
+
+196
+00:18:53,600 --> 00:18:57,980
+fixation okay الان اذا كان بس بيلاحظ اللي هو ال
+
+197
+00:18:57,980 --> 00:19:01,700
+fixation ايه شماله في elevation up يعني شوية العين
+
+198
+00:19:01,700 --> 00:19:06,460
+انحرفت لفوق شايفين هيك ولا كده طب تعالي شوية هيك
+
+199
+00:19:09,610 --> 00:19:14,870
+طيب هى احنا حطينا اول حاجة الست عشر بريزم ديوبتر
+
+200
+00:19:14,870 --> 00:19:17,890
+okay طبعا
+
+201
+00:19:20,190 --> 00:19:24,830
+هو 16 ل 20 يا ما بتاخد 16 يا 20 ال prism عشان تعمل
+
+202
+00:19:24,830 --> 00:19:28,650
+العين elevation انه ترتفع شوية لفوق فالان انا بحط
+
+203
+00:19:28,650 --> 00:19:32,890
+ال 16 prism قدام العين صارت فيها شوية elevation
+
+204
+00:19:32,890 --> 00:19:38,310
+لفوق الان الطفل بيكون عامل ايش fixation okay الان
+
+205
+00:19:38,310 --> 00:19:44,840
+لو انا رفعت الغطاOkay إذا ال fixation راح على
+
+206
+00:19:44,840 --> 00:19:48,340
+العين التانية إيش هيصير؟ إنه ال visual acuity
+
+207
+00:19:48,340 --> 00:19:54,200
+هيكون poor Okay هلجيت
+
+208
+00:19:54,200 --> 00:19:59,520
+الطفل هو .. أغطي العين .. أه هلجيت العين ال .. ال
+
+209
+00:19:59,520 --> 00:20:04,020
+.. ال left مغطية Okay الآن الطفل عامل إيش؟
+
+210
+00:20:04,020 --> 00:20:08,480
+Fixation الآن هو محافظ على ال fixation في العين
+
+211
+00:20:08,480 --> 00:20:13,260
+مين؟الصحيحة الصحيحة الصحيحة الصحيحة الصحيحة
+
+212
+00:20:13,260 --> 00:20:18,020
+الصحيحة الصحيحة الصحيحة الصحيحة الصحيحة الصحيحة
+
+213
+00:20:18,020 --> 00:20:21,920
+الصحيحة الصحيحة الصحيحة الصحيحة الصحيحة الصحيحة
+
+214
+00:20:21,920 --> 00:20:25,760
+الصحيحة الصحيحة الصحيحة الصحيحة الصحيحة الصحيحة
+
+215
+00:20:25,760 --> 00:20:28,820
+الصحيحة
+
+216
+00:20:28,820 --> 00:20:38,100
+الصحيحة
+
+217
+00:20:38,100 --> 00:20:39,600
+الصحيحة الصحيحة الصحيحة الصحيحة الصحيحة الصحيحة
+
+218
+00:20:39,600 --> 00:20:40,980
+الصحيحة الصحيحة الصحيحة الصحيحةيعني ايه؟ فيه
+
+219
+00:20:40,980 --> 00:20:46,580
+fixation في العين ال right رفعت الغطاء خلال خمس
+
+220
+00:20:46,580 --> 00:20:51,300
+ثوانة اتغير ال fixation للعين التانية شو معناها؟
+
+221
+00:20:51,300 --> 00:20:56,880
+انه في اللي هو عنده fixation في ال right eye لكن
+
+222
+00:20:56,880 --> 00:21:00,500
+ايه اشمله ال visual acuity unsteady او un central
+
+223
+00:21:00,500 --> 00:21:09,100
+انه مش ثابت مفهومة تانية؟ خلال خمس ثوانة طيبالان
+
+224
+00:21:09,100 --> 00:21:13,600
+برضه غطى العين الان
+
+225
+00:21:13,600 --> 00:21:17,460
+حطيت اللى هو ستة عشر prism واطف العامل fixation
+
+226
+00:21:17,460 --> 00:21:23,300
+رفعت الغطه عن العين خلال عشر ثوانة عمل fixation
+
+227
+00:21:23,300 --> 00:21:26,880
+يعني عمل fixation بس خلال عشر ثوانة حول ال
+
+228
+00:21:26,880 --> 00:21:31,920
+fixation للعين التانية يعني هذه فضلت التانية على
+
+229
+00:21:31,920 --> 00:21:37,210
+الأولىيعني بتلاحظ أن العين ال .. بس خليني أسمع،
+
+230
+00:21:37,210 --> 00:21:40,990
+بتلاحظ العين اليمين انحرفت وعمل fixation في العين
+
+231
+00:21:40,990 --> 00:21:44,470
+إيش؟ الشماليعني العين الشمال هي اللي صار فيها
+
+232
+00:21:44,470 --> 00:21:47,910
+fixation، اه صارت اللي هو ثابتة، انه فيها
+
+233
+00:21:47,910 --> 00:21:52,070
+fixation، يعني central، okay؟ اه فإنما بيعمل
+
+234
+00:21:52,070 --> 00:21:55,330
+fixation في العين الشمال، اللي هو معناه انه خلال
+
+235
+00:21:55,330 --> 00:21:59,070
+عشر ثواني، انه هان ال visual acuity بتاعته، اللي
+
+236
+00:21:59,070 --> 00:22:02,450
+هو حوالي قداش؟ ستة على أربع وعشرين لستة على
+
+237
+00:22:02,450 --> 00:22:08,590
+تمانتاش، okay؟طيب لو الآن انا مثلا عمل المريض برضه
+
+238
+00:22:08,590 --> 00:22:13,290
+غطى عينه عمل fixation في العين ال right لكن اما
+
+239
+00:22:13,290 --> 00:22:16,770
+رفعت الغطى عن العين الشمال حافظ على ال fixation في
+
+240
+00:22:16,770 --> 00:22:21,290
+ال right لكن بعد عشرين ثانية غير ال fixation للعين
+
+241
+00:22:21,290 --> 00:22:25,150
+الشمال اذا هنا ايش معناه انه ال visual acuity
+
+242
+00:22:25,150 --> 00:22:33,450
+بتاعه 6 ع 12 ل 6 ع 9 اخر حاجةواضحة؟ اخر حاجة لو هو
+
+243
+00:22:33,450 --> 00:22:38,250
+مثلا حطيت ال prism لكن عمل fixation وين؟ مال رهان
+
+244
+00:22:38,250 --> 00:22:41,450
+و مال رهان بعد تلاتين ثانية معناه ان ال visual
+
+245
+00:22:41,450 --> 00:22:48,800
+acuity ستة ع ستة in both eyes واضحة ولا كيف؟ببساطة
+
+246
+00:22:48,800 --> 00:22:54,740
+ال fixation test هو أهم يعني أهم و أفضل test من
+
+247
+00:22:54,740 --> 00:23:00,200
+ناحية الأطفال سهل جدا أنا بستخدم .. بس ركزوا شوية
+
+248
+00:23:00,200 --> 00:23:05,100
+معايا بستخدم ال prism okay ال prism دايما ال apex
+
+249
+00:23:05,100 --> 00:23:09,500
+بتاعته بتكون up و ال base بتكون down إذا السورة
+
+250
+00:23:09,500 --> 00:23:13,700
+تاعته وين هتكون على ال apex okay الآن العين
+
+251
+00:23:13,700 --> 00:23:18,960
+التانية مغطيةبدام العين التانية مغطية ما بعرف أنا
+
+252
+00:23:18,960 --> 00:23:24,680
+عاملة fixation ولا لأ الان انا ايش عملت العين ال
+
+253
+00:23:24,680 --> 00:23:28,560
+right نفرض اللي حاطط عليها ال prism عاملة fixation
+
+254
+00:23:28,560 --> 00:23:34,000
+روحت رفعت الغطا عن العين الشمال ع طول ال fixation
+
+255
+00:23:34,000 --> 00:23:38,000
+راح للعين التانية لل left eye اذا شو معناه انه
+
+256
+00:23:38,000 --> 00:23:42,180
+poor اللي هو ال visual acuity embedded مابديش تحفظ
+
+257
+00:23:42,180 --> 00:23:46,910
+تحفظيافهمه كفهم انه معناه ان ال visual acuity
+
+258
+00:23:46,910 --> 00:23:50,890
+impaired لانه ممكن ألعب فيها الصورة okay معناها
+
+259
+00:23:50,890 --> 00:23:54,310
+انه في a fixation انه صار مافيش شيء اللي هو
+
+260
+00:23:54,310 --> 00:24:01,090
+fixation في العين okay الشغل
+
+261
+00:24:01,090 --> 00:24:06,350
+التاني لو مثلا انا امغط العين الشمال و العين
+
+262
+00:24:06,350 --> 00:24:09,890
+اليمين صار لها حطيت ال prism على العين اللي هو
+
+263
+00:24:09,890 --> 00:24:16,860
+الشمالالعين اليمين رفعت الغطاء عنها okay الآن
+
+264
+00:24:16,860 --> 00:24:22,440
+صارلها حافظت على ال fixation لكن بعد خمس ثوانة راح
+
+265
+00:24:22,440 --> 00:24:25,640
+ال fixation بتاعها شو معناه؟ ان ال visual acuity
+
+266
+00:24:25,640 --> 00:24:32,080
+بتاعه يعني أربع على ستين، ستة على ستين شوف انا
+
+267
+00:24:32,080 --> 00:24:35,900
+لحظة انه هان ال visual acuity يعتبر estimation
+
+268
+00:24:35,900 --> 00:24:41,260
+تقديري و ليس accurate يعني مش بالضبطيعني صح هو
+
+269
+00:24:41,260 --> 00:24:45,260
+يعتبر ال fixation test يعتبر quantitative صح ولا
+
+270
+00:24:45,260 --> 00:24:48,880
+لا؟ انه رقمي، الداني رقم، لكن يعتبر accurate ولا
+
+271
+00:24:48,880 --> 00:24:56,780
+estimation؟ estimation يعتبر، صح؟ النقطة التالتة،
+
+272
+00:24:56,780 --> 00:25:01,270
+الطفل عمل fixationلكن ال fixation هذا ايه صار فيه
+
+273
+00:25:01,270 --> 00:25:06,170
+انه بعد عشر ثوانة حول على العين التانية اذا بمعنى
+
+274
+00:25:06,170 --> 00:25:11,250
+انه صار عنده الطفل fixation لكن اتغير للعين الأخرى
+
+275
+00:25:11,250 --> 00:25:16,050
+فهذا معناه ان ال visual acuity للطفل ممكن يكون ستة
+
+276
+00:25:16,050 --> 00:25:21,750
+على ستين يعني لست على اللي هو ستة و تلاتين او ستة
+
+277
+00:25:21,750 --> 00:25:23,470
+على اربع و عشرين okay
+
+278
+00:25:26,610 --> 00:25:32,090
+النقطة الرابعة الطفل عمل fixation لكن بعد حوالي
+
+279
+00:25:32,090 --> 00:25:36,030
+عشرين ثانية فضل ال fixation على العين التانية okay
+
+280
+00:25:36,030 --> 00:25:39,730
+ال visual acuity ستة ع اتناش لستة ع تسعة ستة ع
+
+281
+00:25:39,730 --> 00:25:44,370
+سبعة و نص ممكن الأخيرة عمل fixation لكن إيش متبادل
+
+282
+00:25:44,370 --> 00:25:48,610
+مرة في ال right مرة في ال left يعني إذا ستة ع ستة
+
+283
+00:25:48,610 --> 00:25:53,310
+طيب ليش أنا استخدمت ال ال ست عشرين prism ديوبتر أو
+
+284
+00:25:53,310 --> 00:25:58,950
+عشرين prism ديوبترعشان انه ايش يعمل اللي هو ال
+
+285
+00:25:58,950 --> 00:26:02,970
+elevation up انه يعمل الطفل اللي هو elevation up
+
+286
+00:26:02,970 --> 00:26:06,930
+to take fixation up انه دايما انه يكون وين ال
+
+287
+00:26:06,930 --> 00:26:11,190
+fixation بتاعه للأعلى لكن لو حطيت مثلا اتنين بريسم
+
+288
+00:26:11,190 --> 00:26:15,370
+ديوبتر او تلاتة بريسم ديوبتر مابيقدرش انه يعمل
+
+289
+00:26:15,370 --> 00:26:18,070
+اللي هو fixation up okay؟
+
+290
+00:26:20,240 --> 00:26:30,120
+يعني نعمل fixation
+
+291
+00:26:30,120 --> 00:26:33,580
+مرة في العين و مرة في الـ left خلال تلاتين ثانية
+
+292
+00:26:33,580 --> 00:26:38,120
+تقريبا انه بيعمل اللي هو مرة هيك و مرة هيك انه
+
+293
+00:26:38,120 --> 00:26:46,320
+بيكون ستة على ستة alternate fixation ال fixation
+
+294
+00:26:46,320 --> 00:26:50,280
+معناها ثابتةيعني أنا حاطط أصبعي زي ما كنت حاطط
+
+295
+00:26:50,280 --> 00:26:54,680
+أصبعي مجرد ما رفعت الغطا عن العين اتحول هذه العين
+
+296
+00:26:54,680 --> 00:26:59,060
+أخدت اللي هو يا لليمين انحرفت يا لليمين يا للشمال
+
+297
+00:26:59,060 --> 00:27:04,920
+والعين التانية هي اللي عملت fixation واضح؟ يعني
+
+298
+00:27:04,920 --> 00:27:07,260
+هيك أنا حاولت أن أبسطه أكثر ما يمكن
+
+299
+00:27:10,920 --> 00:27:16,480
+طيب بالنسبة ل ال sweet test طبعا هذا الفحص يعتبر
+
+300
+00:27:16,480 --> 00:27:21,140
+شائع عندنا كتير طبعا ال sweet test هيو حيكون زي ما
+
+301
+00:27:21,140 --> 00:27:25,620
+أنا ماسك ب .. بإيدي بالظبط زي هيك لازم انا اوزع
+
+302
+00:27:25,620 --> 00:27:30,040
+اللي هو الحبات بتاعتي في مختلف إيدي مش مثلا أحطها
+
+303
+00:27:30,040 --> 00:27:35,870
+في ال center شايفين انتوا ولا كيف؟يعني دايما في ال
+
+304
+00:27:35,870 --> 00:27:39,910
+sweet test مابحطش اللي هو ال .. الإيدة في نص ال ..
+
+305
+00:27:39,910 --> 00:27:43,050
+ال .. يعني الحبات هدول ال sweet في ال .. في ال
+
+306
+00:27:43,050 --> 00:27:52,530
+center دايما لازم مثلا على الأطراف زي هيك و بالظبط
+
+307
+00:27:52,530 --> 00:27:56,950
+ال color لازم يكون مختلف بتاعة ال sweet ليش طيب؟
+
+308
+00:27:56,950 --> 00:27:58,910
+واحدة بس واحدة
+
+309
+00:28:03,790 --> 00:28:09,370
+ارفع يدك و جاوبي الان انا لما بستخدم ال sweet test
+
+310
+00:28:09,370 --> 00:28:12,790
+لازم يكون الألوان مختلفة فيه يعني الحبات بتاعتها
+
+311
+00:28:12,790 --> 00:28:23,910
+لازم تكون مختلفة ال color بتاعها ليش؟ نعم طيب
+
+312
+00:28:23,910 --> 00:28:27,670
+ليش مثلا ماحطيته أحمر كله أو كله أبيض أو كله أصفر؟
+
+313
+00:28:31,210 --> 00:28:36,310
+لأ الان لو انا مثلا .. لو انا مثلا حطيت الأحمر
+
+314
+00:28:36,310 --> 00:28:40,430
+اللون الأحمر الطفل ممكن ينتبه عليهم ان كل الموجود
+
+315
+00:28:40,430 --> 00:28:44,590
+ايش أحمر ف ال .. ال .. ال wavelength الطول الموجي
+
+316
+00:28:44,590 --> 00:28:48,450
+بتاعته هيركز عليه ان كل الموجود أحمر فهيقدر ايش
+
+317
+00:28:48,450 --> 00:28:52,710
+انه يلتقطه واضح؟ لو مثلا حطيته أبيض برضه نفس
+
+318
+00:28:52,710 --> 00:28:59,190
+الحاجة طيب ممكن اعمل هيك انا صح هيك؟ عامل؟لازم
+
+319
+00:28:59,190 --> 00:29:05,190
+اللي هو التوزيع طيب كيف انا يعني الان كيف
+
+320
+00:29:05,190 --> 00:29:11,750
+بده اقيم ال visual acuity في ال suite test بالظبط
+
+321
+00:29:11,750 --> 00:29:17,040
+خدي من هناالان بالظبط انه ايش عمل الطفل اللي هو
+
+322
+00:29:17,040 --> 00:29:21,780
+pick up انه بالظبط انه ايش لجت لكن لو حسيت انه
+
+323
+00:29:21,780 --> 00:29:26,280
+الطفل اجا مد ايده لكن عمل هيك شو معناها انه عنده
+
+324
+00:29:26,280 --> 00:29:30,720
+impaired visual acuity لو انا مثلا شعرت ان هو
+
+325
+00:29:30,720 --> 00:29:34,940
+الطفل مركز على ال center يعني الكف الإيد في ال
+
+326
+00:29:34,940 --> 00:29:39,560
+center بروح احط اللي هو ال sweet هيك في إيدي واضح؟
+
+327
+00:29:39,560 --> 00:29:46,410
+زي هيك واضح ولا كيف؟ شايفين؟بحطه بين أصابعي ليش
+
+328
+00:29:46,410 --> 00:29:49,850
+لأنه لو حطيته في المركز الطفل خلاص حفظ المكان
+
+329
+00:29:49,850 --> 00:29:54,410
+تاعتهم وين فهيروح اطول ايش يدور في المركز طيب ايش
+
+330
+00:29:54,410 --> 00:29:58,750
+ممكن اكتب ال visual acuity للطفل هذا عندنا ال
+
+331
+00:29:58,750 --> 00:29:59,570
+sweet taste
+
+332
+00:30:05,720 --> 00:30:10,600
+بكتب ال visual acuity زي هيك مثلا ال right eye هذا
+
+333
+00:30:10,600 --> 00:30:16,080
+لو الطفل اللي هو لقط more than or equal 6 على 24
+
+334
+00:30:16,080 --> 00:30:25,120
+more detail picked up by
+
+335
+00:30:25,120 --> 00:30:29,120
+child
+
+336
+00:30:31,930 --> 00:30:38,810
+left eye more than or equal 6 على 24 picked up by
+
+337
+00:30:38,810 --> 00:30:43,210
+child طيب لو كان هذا لو كان ايش ال visual acuity
+
+338
+00:30:43,210 --> 00:30:51,710
+عنده good لو كان ال visual acuity impaired or poor
+
+339
+00:30:51,710 --> 00:30:57,610
+هيكون
+
+340
+00:30:57,610 --> 00:30:58,210
+ال right
+
+341
+00:31:03,250 --> 00:31:23,150
+visual acuity less the
+
+342
+00:31:23,150 --> 00:31:30,530
+child not pick up
+
+343
+00:31:37,690 --> 00:31:42,790
+Sweet Test هذي ال evaluation لطفل لو كان عنده ال
+
+344
+00:31:42,790 --> 00:31:48,450
+visual acuity اقل او اكثر من 6 على 24 من ناحية
+
+345
+00:31:48,450 --> 00:31:52,690
+اللي هو ال sweet test طيب في عندنا ال rotation
+
+346
+00:31:52,690 --> 00:31:56,510
+test الان
+
+347
+00:31:56,510 --> 00:32:01,470
+اخدنا occlusion of one eye اذا غطينا عينخدنا ال
+
+348
+00:32:01,470 --> 00:32:06,190
+fixation test وخدنا كمان اللي هو ال sweet test ال
+
+349
+00:32:06,190 --> 00:32:12,350
+rotation test هو بيعتبر qualitative test انه
+
+350
+00:32:12,350 --> 00:32:16,170
+اختبار ايش ماله كم يعني مابتديني جديش ال visual
+
+351
+00:32:16,170 --> 00:32:21,470
+acuity للمريض for the infant to fixate with both
+
+352
+00:32:21,470 --> 00:32:26,510
+eyes open ان العنتين بتكون مفتحة يعني ملاحظين في
+
+353
+00:32:26,510 --> 00:32:31,110
+ال occlusion of one eye في ال fixation testفي ال
+
+354
+00:32:31,110 --> 00:32:34,810
+sweet test التلاتة كانوا انه عملنا occlusion of
+
+355
+00:32:34,810 --> 00:32:38,850
+one eye لكن في ال rotation test open both eye
+
+356
+00:32:38,850 --> 00:32:45,430
+واضح؟ اه تاخد ال right و ال left هاين الكتاب تيكي
+
+357
+00:32:45,430 --> 00:32:52,230
+the examiner holds the infant facing him and
+
+358
+00:32:52,230 --> 00:33:00,130
+rotates a bicycle 360 degreeالان احنا عندنا هان
+
+359
+00:33:00,130 --> 00:33:08,370
+عروسة لو فرضنا هي الطفل okay بمسك الطفل يا اما من
+
+360
+00:33:08,370 --> 00:33:14,110
+رأسه او بمسكه مثلا من اديه زي هيك بثبته بالشكل هذا
+
+361
+00:33:14,110 --> 00:33:20,610
+والان كيف بعمل؟ انا الان examiner okayو مثلا ال
+
+362
+00:33:20,610 --> 00:33:25,390
+parents والدي أمامي فبعمل rotation، شو بعمل؟ بدور
+
+363
+00:33:25,390 --> 00:33:30,490
+زي هيك فيه، بالشكل هذا، الآن الأهل بدهم ينتبهوا
+
+364
+00:33:30,490 --> 00:33:34,580
+على مين؟ على حركة العينإذا صار عنده eye movement
+
+365
+00:33:34,580 --> 00:33:39,360
+حركة للعين فبيكون عنده ال visual acuity good لكن
+
+366
+00:33:39,360 --> 00:33:42,260
+لو مافيش رقرة في العين، العين ثابتة، بيكون ال
+
+367
+00:33:42,260 --> 00:33:45,800
+visual acuity بتاعته إيش، impaired، okay؟ هي
+
+368
+00:33:45,800 --> 00:33:49,400
+ببساطة يعني بتعتمد على ال eye movement، ال
+
+369
+00:33:49,400 --> 00:33:53,900
+nystagmus، اللي هي رقرة العين مش بتعرفوا الرقرة
+
+370
+00:33:53,900 --> 00:33:57,680
+تاعت العين؟ okay؟ يعني هذا ال test ال rotation
+
+371
+00:33:57,680 --> 00:34:02,260
+test هو يعتبر qualitative testnumber one number
+
+372
+00:34:02,260 --> 00:34:08,240
+two انه بيعتمد على ال eye movement وبيعتمد على ال
+
+373
+00:34:08,240 --> 00:34:13,120
+neck movement number three انه بيعتمد على ال
+
+374
+00:34:13,120 --> 00:34:17,000
+parents الوالدين ان هم بيشوفوا حركة العين بتاعة
+
+375
+00:34:17,000 --> 00:34:21,500
+الطفلإذا عمل الطفل eye movement أو نستاج مصر،
+
+376
+00:34:21,500 --> 00:34:25,800
+بيكون ال visual acuity عنده good، إذا العين بجت
+
+377
+00:34:25,800 --> 00:34:29,580
+اللي هو fixed ثابتة، بمعنى indicate to the visual
+
+378
+00:34:29,580 --> 00:34:32,080
+acuity is bad or in pair
+
+379
+00:34:35,900 --> 00:34:40,740
+الطفل قام بإصلاح مواجهات تتحرك خلف الاختبار، إذا
+
+380
+00:34:40,740 --> 00:34:44,580
+كانت النظرية عامة، فالعين ستتحرك، تتحرك بمعنى شو؟
+
+381
+00:34:44,580 --> 00:34:50,000
+انه هيوضحلي انه optokinetic nystagmus الآن ال
+
+382
+00:34:50,000 --> 00:34:54,720
+optokinetic nystagmus هي هذه الآلة، هناخدها شوية
+
+383
+00:34:54,720 --> 00:34:55,660
+بعد ال test هذا
+
+384
+00:35:00,380 --> 00:35:04,040
+when rotation stops يما انا بوقف اللي هو دوران
+
+385
+00:35:04,040 --> 00:35:10,260
+الطفل okay نستاجموس stop three to five seconds due
+
+386
+00:35:10,260 --> 00:35:14,240
+to suppression of both rotatory nystagmus by
+
+387
+00:35:14,240 --> 00:35:19,480
+fixation الان انا وقفت الدوران بتاع الطفل ايش هي
+
+388
+00:35:19,480 --> 00:35:24,060
+بعد تلت لخمس ثواني ال fixation بتاعه ايش ماله
+
+389
+00:35:24,060 --> 00:35:28,230
+هيثبتو هيصير فيش نيستاجموس يعني فيش أي movement
+
+390
+00:35:28,230 --> 00:35:35,110
+لمين؟ لعين الطفل واضح؟ يعني الآن الفكرة بتاعته أنه
+
+391
+00:35:35,110 --> 00:35:40,030
+ال examiner أو ال optometrist بمسك مين؟ الطفل و
+
+392
+00:35:40,030 --> 00:35:45,530
+بعمل rotation له okay ال parents لازم يلاحظوا مين؟
+
+393
+00:35:45,530 --> 00:35:50,750
+حركة عين الطفلإنه لازم ال eye movement or نستجمس
+
+394
+00:35:50,750 --> 00:35:55,210
+نستجمس بمعنى رأرة العين فالآن هم بيعملوا
+
+395
+00:35:55,210 --> 00:35:59,910
+observation ملاحظة لمين لعين الطفل إذا الطفل إثناء
+
+396
+00:35:59,910 --> 00:36:04,290
+الدوران اتحركت العين يعني صار فيها اللي هو
+
+397
+00:36:04,290 --> 00:36:08,030
+movement إذا معنى إنه ال visual acuity تعته
+
+398
+00:36:08,030 --> 00:36:14,370
+إشمالها good لكن إذا مثلا الطفل عمل fixationبكون
+
+399
+00:36:14,370 --> 00:36:19,710
+ال visual acuity بتاعته إيش impaired if
+
+400
+00:36:19,710 --> 00:36:23,390
+vision is severely impaired non-stigmatized but
+
+401
+00:36:23,390 --> 00:36:26,970
+eye deviated to one side لو كانت اللي هو فيه
+
+402
+00:36:26,970 --> 00:36:31,030
+severe ال vision عندهإيش معناه؟ إنه ال visual
+
+403
+00:36:31,030 --> 00:36:35,830
+acuity impaired، إنه ضعيف، خلاص يعني هو مركز على
+
+404
+00:36:35,830 --> 00:36:41,550
+شغلة معينة أو عامل deviation في one side ومش مركز
+
+405
+00:36:41,550 --> 00:36:44,230
+أيش أصلا في ال test بتاعنا، فمعناه إنه ال visual
+
+406
+00:36:44,230 --> 00:36:45,690
+acuity impaired، تفضل ...
+
+407
+00:37:00,430 --> 00:37:05,030
+لأ بس انا بعمل قاعد rotation على تلاتمية و ستين
+
+408
+00:37:05,030 --> 00:37:09,190
+درجة بمعنى انه انا قاعد برجع نفس النقطة اللي انا
+
+409
+00:37:09,190 --> 00:37:15,510
+انطلقت منها okay الان هم اهله للطفل هم ثابتين صح
+
+410
+00:37:15,510 --> 00:37:19,490
+ولا لأ فهو انا بدي اشوف هل الطفل يما انا بعمل ال
+
+411
+00:37:19,490 --> 00:37:23,670
+rotation العين هل بيصير لها حركة انه هل مثلا تتحرك
+
+412
+00:37:23,670 --> 00:37:29,030
+بصير لنستاجمص ولا لأ اه نستاجمص اللي هي حركة رقرقة
+
+413
+00:37:29,030 --> 00:37:33,730
+للعينانت اللي بتحكي قاعدة لو انا مثلا قاعد بحرك
+
+414
+00:37:33,730 --> 00:37:39,010
+الطفل مثلا على 180 أو 90 درجة صح ممكن تاخد العين
+
+415
+00:37:39,010 --> 00:37:42,230
+على طول deviation انحراف يا لليمين يا للشمال
+
+416
+00:37:42,230 --> 00:37:45,610
+وماتتحركش اصلا معاه بس انا قاعد برجع نفس النقطة
+
+417
+00:37:45,610 --> 00:37:49,890
+اللي انطلقت منها يعني كأنه يعني مثلا انا عندي نقطة
+
+418
+00:37:49,890 --> 00:37:54,690
+صفر انطلقت منها ورجعت عندها بالظبط فهيكون اللي هو
+
+419
+00:37:54,690 --> 00:37:56,490
+ايش rotation دوران
+
+420
+00:38:01,770 --> 00:38:07,530
+ال optokinetic nystagmus drum هو نفس فكرة مين؟ نفس
+
+421
+00:38:07,530 --> 00:38:15,670
+فكرة ال rotation test لكن شو الخلاف بينهم؟ اه
+
+422
+00:38:15,670 --> 00:38:21,910
+بس شو الفرق الجوهري بينهم؟ امتازة واحدة
+
+423
+00:38:21,910 --> 00:38:26,590
+quantitative واحدة qualitative ال rotation test اي
+
+424
+00:38:26,590 --> 00:38:30,550
+نص درجالك ال rotation test يعتبر اللي هو ايش؟
+
+425
+00:38:31,220 --> 00:38:35,500
+equalitative لكن الـ nystagmus drum ايش يعتبر
+
+426
+00:38:35,500 --> 00:38:40,860
+quantitative عددي احنا طبيعي في الجامعة يعتبر اللي
+
+427
+00:38:40,860 --> 00:38:44,680
+هو توضيح هان يعني dimension عندنا ماعناهش اللي هو
+
+428
+00:38:44,680 --> 00:38:51,180
+كل ال testات فهي هذا مثلا تقريبا يعتبر 6 على 90 او
+
+429
+00:38:51,180 --> 00:38:57,860
+6 على 60 بنعتبرهبيعتمد النستاجمس ال drum لو انتوا
+
+430
+00:38:57,860 --> 00:39:02,960
+شايفين فيه اللي هو خطين عندنا الأبيض و الأسود okay
+
+431
+00:39:02,960 --> 00:39:08,380
+بيعتمد على اللي هو الحركة الان كل هيتكم تعالوا
+
+432
+00:39:08,380 --> 00:39:12,660
+ورايا خليك انت بس قاعدة الان ال test هذا بيكون على
+
+433
+00:39:12,660 --> 00:39:17,460
+مسافة جديش اللي هو تلاتين لخمسين صنتي الان تطلعوا
+
+434
+00:39:17,460 --> 00:39:21,240
+على عين زملتكم هتلاقوا فيها حصير نستاجمس يعني ان
+
+435
+00:39:21,240 --> 00:39:26,970
+انا بدي احرك اللي هذاشايف كيف؟ انه صار .. لأ طلعي
+
+436
+00:39:26,970 --> 00:39:31,010
+هان، اعملي fixation هون،
+
+437
+00:39:31,010 --> 00:39:35,170
+شايف العين؟ قاعدة بتمشي، تعملي اللي هي رقرا، واضح
+
+438
+00:39:35,170 --> 00:39:42,750
+ولا كيف؟ تعالي هان، تعالي تفضلي هان مين
+
+439
+00:39:42,750 --> 00:39:46,630
+شافها طيب اللي رقرا؟ شفتواها؟ طب خلي زميلتك تيجي
+
+440
+00:39:46,630 --> 00:39:47,870
+مكانك، مدام شفتيها
+
+441
+00:39:52,420 --> 00:39:58,200
+شوفت انتي ولا كيف؟ تعالى هاي
+
+442
+00:39:58,200 --> 00:40:02,500
+الان ال stigma syndrome بدي اعتمد على حركة اللي هو
+
+443
+00:40:02,500 --> 00:40:08,200
+ايه هي الواضحة تتحرك جاعدة يمين و شمال حسب اللي هو
+
+444
+00:40:08,200 --> 00:40:15,100
+حركة من ال strip الخطوط تعالى شوفي اكيد؟
+
+445
+00:40:15,100 --> 00:40:16,840
+هذا
+
+446
+00:40:26,300 --> 00:40:30,340
+شايفة كيف الحركة بتاعة العين بتعمل زي نستاجمس eye
+
+447
+00:40:30,340 --> 00:40:36,360
+movement هي مش شايفة العين البقب بتحلق طبعا
+
+448
+00:40:36,360 --> 00:40:42,740
+بالنسبة لنستاجمس ال drum هو
+
+449
+00:40:42,740 --> 00:40:49,760
+بيكون كيف جهاز automatic بتحط فيه عدة أرقام يعني
+
+450
+00:40:49,760 --> 00:40:54,060
+ستة ع ستينستة ع ستة و تلاتين، ستة على اربع عشرين،
+
+451
+00:40:54,060 --> 00:40:57,620
+ستة ع تسعة زي ما جالت زملتكم انه يعتبر هو ايه؟
+
+452
+00:40:57,620 --> 00:41:04,040
+quantitative test فبحط و الجهاز ايش ماله؟ بلوف و
+
+453
+00:41:04,040 --> 00:41:07,920
+بعتمد على اللي هو حركة مين؟ حركة اللي هو عين
+
+454
+00:41:07,920 --> 00:41:14,280
+المريض فإذا كان فيه eye movement مع ال .. مع ال ..
+
+455
+00:41:14,280 --> 00:41:17,660
+ال nostagmus هذا بشير ان ال visual acuity بتاعته
+
+456
+00:41:17,660 --> 00:41:19,200
+للمريض ايش مالها؟ good
+
+457
+00:41:23,020 --> 00:41:26,780
+ما هي هذا مثلا انا بقولك ستة على تسعين او ستة على
+
+458
+00:41:26,780 --> 00:41:32,040
+ستين في كيف مثلا اه سؤال محترم انه كيف ال .. ال ..
+
+459
+00:41:32,040 --> 00:41:35,480
+كل مقل اللي هو ال strip ما بين الخطين الأبيض و
+
+460
+00:41:35,480 --> 00:41:39,620
+الأسود هذي بمعنى ان ال visual acuity جل يعني
+
+461
+00:41:39,620 --> 00:41:45,920
+التمييز ما بين الخطين بجل okay واضح ولا كيف ال
+
+462
+00:41:45,920 --> 00:41:51,170
+judge شايفين هذهالمسافة كبيرة بالظبط، الآن لما بقل
+
+463
+00:41:51,170 --> 00:41:54,610
+ال visual acuity، يعني بصير مثلا ستة ع تسعة أو ستة
+
+464
+00:41:54,610 --> 00:41:58,990
+ع اتناش، المسافة بينهم بتقل، بتصير thinner، نحيفة،
+
+465
+00:41:58,990 --> 00:42:10,470
+واضح؟ واضح ولا كيف؟ يعني الآن بالنسبة ل .. انا
+
+466
+00:42:10,470 --> 00:42:14,870
+بكون دايما عندك اللي هو جهاز automatic، okay، بتحط
+
+467
+00:42:14,870 --> 00:42:19,440
+اللي .. اللي هو ال drum بتاعتكال standardized okay
+
+468
+00:42:19,440 --> 00:42:23,560
+drum بتحطي مثلا هذه الستة ع ستين زي ما عملنا
+
+469
+00:42:23,560 --> 00:42:27,300
+لزميلتك لجينا مثلا فين ال stagmas إذا معنات أنه ال
+
+470
+00:42:27,300 --> 00:42:31,120
+visual acuity ستة ع ستين بنحط اللي هي ستة ع ستة و
+
+471
+00:42:31,120 --> 00:42:36,160
+تلاتين بنرفع واحدة و بنحط التاني okay يعني مش كلهم
+
+472
+00:42:36,160 --> 00:42:40,520
+مع بعضيعني كأنه فيه أكتر من واحدة، بيكون أكتر من
+
+473
+00:42:40,520 --> 00:42:44,560
+شريحة، فيه ستة ع ستين، ستة ع ستة و تلاتين، أربع
+
+474
+00:42:44,560 --> 00:42:48,520
+عشرين، تمانتعش، تسعة، زي كأنك بتفحص ال visual
+
+475
+00:42:48,520 --> 00:42:58,140
+acuity عادي فعنا
+
+476
+00:42:58,140 --> 00:43:04,650
+ال nystagmus اللي هو ال drumStandardized drum هو
+
+477
+00:43:04,650 --> 00:43:09,830
+عبارة عن استوانة، انبوب استواني، drum بمعنى انبوب
+
+478
+00:43:09,830 --> 00:43:16,430
+استواني that contain scripts بيحتوي على خطوط which
+
+479
+00:43:16,430 --> 00:43:20,510
+subtend small fractions of the infant's visual
+
+480
+00:43:20,510 --> 00:43:25,890
+field are available كمان من فائدة ال nostagmus
+
+481
+00:43:25,890 --> 00:43:30,350
+drum مش فقط بجيس ال visual acuity، في حاجة بيسموها
+
+482
+00:43:30,350 --> 00:43:34,530
+ال visual fieldال visual field هي عبارة عن الساحة
+
+483
+00:43:34,530 --> 00:43:40,450
+البصرية للعين تعريف الساحة البصرية أو مجال الرؤية
+
+484
+00:43:40,450 --> 00:43:45,430
+ال visual field هو عبارة عن island يعني جزيرة من
+
+485
+00:43:45,430 --> 00:43:50,410
+الرؤية اللي انت بتشوفيها محاطة بإيش a sea of
+
+486
+00:43:50,410 --> 00:43:56,550
+darkness محاطة بعتامة واضح؟ إذا مجال الرؤية اللي
+
+487
+00:43:56,550 --> 00:44:00,880
+هي عبارة عنال island الجزيرة بتاعة الرؤية اللي انت
+
+488
+00:44:00,880 --> 00:44:07,660
+بتشوفيها حواليك محاطة بإيش بعتامة صح ولا لأ واضح؟
+
+489
+00:44:07,660 --> 00:44:12,200
+يعني محاطة بأشياء معتمة انه حواليك بتكون هلأ تعريف
+
+490
+00:44:12,200 --> 00:44:13,040
+ال visual field
+
+491
+00:44:26,210 --> 00:44:31,630
+طبعا هنطبق اللي هو ال test داعي ال visual field
+
+492
+00:44:31,630 --> 00:44:42,830
+this
+
+493
+00:44:42,830 --> 00:44:48,230
+island of
+
+494
+00:44:48,230 --> 00:44:48,610
+vision
+
+495
+00:44:57,920 --> 00:45:06,040
+surrounded by a
+
+496
+00:45:06,040 --> 00:45:11,320
+darkness of
+
+497
+00:45:11,320 --> 00:45:19,220
+sea عبارة عن جزيرة من الرؤية محاطة ببحر من الظلام
+
+498
+00:45:20,570 --> 00:45:23,570
+طيب بدنا نطبق ال .. فيه test لل visual field هو
+
+499
+00:45:23,570 --> 00:45:27,710
+عبارة عن ال confrontation test ال test يعتبر بسيط
+
+500
+00:45:27,710 --> 00:45:30,770
+هذا بعد ما نخلص المحاضرة ممكن الكل يعملوا لل ..
+
+501
+00:45:30,770 --> 00:45:36,290
+يعني لزميله تفضلي أول حاجة بتطلب من ال .. من ال ..
+
+502
+00:45:36,290 --> 00:45:40,030
+المريض أنه يعمل fixation يعمل fixation هنا على
+
+503
+00:45:40,030 --> 00:45:48,090
+وصفتي شايفة هيك؟ هيك؟ وصفتي شايفة؟ وصفتي تاني؟
+
+504
+00:45:48,090 --> 00:45:58,350
+هيك؟لأ لأ، بس طلعي هون، هيك شايفة، هيك، هيك،
+
+505
+00:45:58,350 --> 00:46:01,890
+لما ماقلش شوفيه، قوليلي، بس ما تعملي ال fixation
+
+506
+00:46:01,890 --> 00:46:07,530
+عليه، hand fixation، okay؟ هيك، هي مجال الرؤية،
+
+507
+00:46:07,530 --> 00:46:11,270
+يعني هذه تعتبر إيش؟ هذه ال blind spot، النقطة اللي
+
+508
+00:46:11,270 --> 00:46:16,460
+ما شفتهاش، هذه تعتبر أمر طبيعي، شكرايعني هذا يعتبر
+
+509
+00:46:16,460 --> 00:46:21,920
+اللي هو ايه في theology انه نقطة فدايما بتكون في
+
+510
+00:46:21,920 --> 00:46:26,520
+ال temporal انه temporary بتكون حوالي مية يعني شوف
+
+511
+00:46:26,520 --> 00:46:31,600
+صنع اللهان الإنسان دايما العين من ناحية اللي هو
+
+512
+00:46:31,600 --> 00:46:36,540
+الطرف بتكون يعني أخطر مكان لضرب العين، ليش؟ لأنه
+
+513
+00:46:36,540 --> 00:46:40,140
+هان مافيش حماية إلها، واضح؟ فدايما ال temporal
+
+514
+00:46:40,140 --> 00:46:43,640
+بيكون لو واحد أكل ضربة من ال temporal مافيش له
+
+515
+00:46:43,640 --> 00:46:48,220
+حماية هان، فهان الرؤية قداش مية في المية ال visual
+
+516
+00:46:48,220 --> 00:46:52,140
+field بتاعته، الساحة البصريةلكن في ال nasal في
+
+517
+00:46:52,140 --> 00:46:55,920
+حماية ال nose صح ولا لا فال .. قداش بتكون الرؤية
+
+518
+00:46:55,920 --> 00:47:02,080
+ال visual field ستين .. ستين degree في فرق بين ال
+
+519
+00:47:02,080 --> 00:47:08,320
+up و ال down أكيد هان فيه إيشفي زي اللي هو bone في
+
+520
+00:47:08,320 --> 00:47:12,520
+المحجر يعني في اللي هو عضمة موجودة في المحجر بتاعة
+
+521
+00:47:12,520 --> 00:47:17,060
+العين مش هذا المحجر يعتبر لكن هذا مافيش فدايما في
+
+522
+00:47:17,060 --> 00:47:23,120
+ال down يعتبر ال visual field أعلى من وين من ال up
+
+523
+00:47:23,120 --> 00:47:28,920
+يعني ممكن ال temporal يكون من سبعين ل تمانين ال up
+
+524
+00:47:28,920 --> 00:47:31,560
+يعتبر من خمسين ل ستين degree
+
+525
+00:47:36,600 --> 00:47:46,760
+أه ال inferior أو ال down لأ
+
+526
+00:47:46,760 --> 00:47:51,400
+دايما المنطقة ال temporal اللي هي هذه مافيش حماية
+
+527
+00:47:51,400 --> 00:47:55,380
+يعني انت لو شوف عينك هان مافيش لها حماية صح لكن في
+
+528
+00:47:55,380 --> 00:48:02,000
+ال nasal في اللي هو ال nose بصد ممكن
+
+529
+00:48:02,000 --> 00:48:05,560
+يكون planted trauma ممكن ضربة يعني حسب اللي هو قوة
+
+530
+00:48:05,560 --> 00:48:10,850
+الضربةيعني ما بتقدر تحدديها إلا تعرف إيش هي مثلا،
+
+531
+00:48:10,850 --> 00:48:15,130
+هل هي مثلا plant trauma مثلا، box أو هل مثلا كورة،
+
+532
+00:48:15,130 --> 00:48:21,910
+football أو .. يعني حسب الدربة اللي هو اتعرض إليها
+
+533
+00:48:21,910 --> 00:48:23,230
+Okay
+
+534
+00:48:25,570 --> 00:48:29,510
+فال .. ال .. المريض أو الطفل ايش بيعمل
+
+535
+00:48:29,510 --> 00:48:34,170
+alternating، بيعمل تبادل لل black and white strips
+
+536
+00:48:34,170 --> 00:48:40,500
+with sharp distant interfacesهلجيت زي ما لاحظنا في
+
+537
+00:48:40,500 --> 00:48:44,260
+نفس داجما سيد رام انه انا يما حركت ال .. ال ..
+
+538
+00:48:44,260 --> 00:48:48,440
+الأداء المريض ايش عمل؟ رقرة في العين، eye movement
+
+539
+00:48:48,440 --> 00:48:52,940
+فهذه الرقرة شو عملت؟ انه مرة بعمل .. يعني بعمل
+
+540
+00:48:52,940 --> 00:48:56,540
+تداخل للخطين، للأبيض والأسود، يعني مرة بحاول يشوف
+
+541
+00:48:56,540 --> 00:48:59,500
+الأبيض ومرة الأسود، مرة بحاول الأبيض والأسود،
+
+542
+00:48:59,500 --> 00:49:02,500
+فبتلاقي بيصير ايش؟ تداخل في العين، okay؟
+
+543
+00:49:05,950 --> 00:49:11,730
+They are spun بمعنى بيسرع at varying uncelebrated
+
+544
+00:49:11,730 --> 00:49:15,490
+rates and are bathed in variable illumination
+
+545
+00:49:16,390 --> 00:49:20,090
+الإضاءة ال illumination بتاعتي بتكون مختلفة و
+
+546
+00:49:20,090 --> 00:49:24,310
+دايما هو المريض باعتمد على سرعة اللي هو إيش الجهاز
+
+547
+00:49:24,310 --> 00:49:29,390
+جداش الجهاز فيه إله مثلا لو جونا automated بختلف
+
+548
+00:49:29,390 --> 00:49:33,330
+عن ال manual لو مثلا كانت ال .. ال .. ال .. ال
+
+549
+00:49:33,330 --> 00:49:37,970
+drum هادي ستة ع ستين بتختلف لو كانت مثلا ستة على
+
+550
+00:49:37,970 --> 00:49:41,450
+أربع عشرين ليش؟ لأن الخطوط بتكون متداخلة مع بعض
+
+551
+00:49:41,450 --> 00:49:46,550
+أكثرفكل هذه العوامل يعني بتحددلي قداش ال visual
+
+552
+00:49:46,550 --> 00:49:51,070
+acuity لالطفل يعني هلأ السرعة اللي لما انت تعمل
+
+553
+00:49:51,070 --> 00:49:55,910
+ميكروفيت بتاع ستين هتكون سرعة أكتر من ميكروفيت ستة
+
+554
+00:49:55,910 --> 00:49:59,390
+و ستة عامة؟ لو كان automated أه بتلاقي السرعة
+
+555
+00:49:59,390 --> 00:50:03,790
+أعلى، ليش؟ لأنه التمييز بيكون سهل
+
+556
+00:50:06,600 --> 00:50:10,140
+this method measures acuity by means of a motor
+
+557
+00:50:10,140 --> 00:50:14,120
+response في عندنا دائما two response هدول مهمات
+
+558
+00:50:14,120 --> 00:50:18,400
+كثير في عندنا ال motor response وفي عندنا ال
+
+559
+00:50:18,400 --> 00:50:22,860
+sensory response ال motor response إيش معناه؟ بدنا
+
+560
+00:50:22,860 --> 00:50:26,300
+نفهم فهم إنه بعتمد على ال eye movement إنه على
+
+561
+00:50:26,300 --> 00:50:32,170
+حركة العين okay؟ال sensory response دايما باعتمد
+
+562
+00:50:32,170 --> 00:50:37,490
+على مين؟ على ال nerves العصاب انه شيء إحساسي okay
+
+563
+00:50:37,490 --> 00:50:43,230
+طيب من ال testات اللي أخدناهم مين يعتبر motor؟ أول
+
+564
+00:50:43,230 --> 00:50:49,510
+حاجة ال rotation test عندنا ال nystagmus drum ال
+
+565
+00:50:49,510 --> 00:50:55,480
+fixation testOcclusion of one eye هذول الأربع
+
+566
+00:50:55,480 --> 00:51:02,500
+يعتبروا motor response يعني اعتمدوا على حركة العين
+
+567
+00:51:02,500 --> 00:51:09,660
+بس
+
+568
+00:51:09,660 --> 00:51:16,320
+فيه تعتبر sensor لأنه التقطها ماحركش عينه الطفل
+
+569
+00:51:16,320 --> 00:51:17,220
+أثناءها
+
+570
+00:51:20,920 --> 00:51:25,220
+في عندنا ال fourth choice preferational looking
+
+571
+00:51:25,220 --> 00:51:30,840
+بمعنى إجبار الطفل على الرؤية يعني كيف أنا بدي أجبر
+
+572
+00:51:30,840 --> 00:51:38,060
+الطفل على مين على أنه يشوف خلال الفحص بتاعي this
+
+573
+00:51:38,060 --> 00:51:40,920
+behavioral technique is based on the observation
+
+574
+00:51:40,920 --> 00:51:44,640
+that infants prefer to view a better stimulus than
+
+575
+00:51:44,640 --> 00:51:50,390
+homogeneous fieldدايما طبيعة الطفل مابحبش يشوف صور
+
+576
+00:51:50,390 --> 00:51:55,150
+متعددة، دايما بحب يشوف صورة واحدة، يعني دايما
+
+577
+00:51:55,150 --> 00:51:59,050
+الطفل لو انت مثلا مسكتي، دايما الطفل بحاول انه
+
+578
+00:51:59,050 --> 00:52:02,910
+يشوف صورة مميزة عنده، يعني وين الصورة المميزة،
+
+579
+00:52:02,910 --> 00:52:05,930
+دايما بحاول انه ينظر اليها، حتى لو كان في غرفة
+
+580
+00:52:05,930 --> 00:52:10,210
+معزول هيك، دايما بحاول انه .. اه ال discrimination
+
+581
+00:52:10,210 --> 00:52:14,480
+image، يعني اللي هي الصورة المميزة في المكانفانا
+
+582
+00:52:14,480 --> 00:52:18,940
+دايما إيش في ال test هذا بحث صورة واحدة مابحاولش
+
+583
+00:52:18,940 --> 00:52:23,360
+اللي هو أعمل homogeneous تجانس لأكتر من إيش من شكل
+
+584
+00:52:23,360 --> 00:52:29,400
+The child must be alert and able to generate neck
+
+585
+00:52:29,400 --> 00:52:32,800
+and eye movements like optokinetic nystagmus
+
+586
+00:52:32,800 --> 00:52:36,400
+technique. Vision is evaluated by means of a motor
+
+587
+00:52:36,400 --> 00:52:42,380
+responseالان هذا الفحص بيعتمد على حركة عين الطفل
+
+588
+00:52:42,380 --> 00:52:48,880
+زائد بيعتمد على حركة رقبة الطفل واضح؟ ليش؟ لأنه
+
+589
+00:52:48,880 --> 00:52:53,680
+انا بدي احاول انه اغير الموضع الصورة في ال test
+
+590
+00:52:53,680 --> 00:52:58,200
+هذا بمعنى ان مرة بدي احط الصورة في ال up مرة بدي
+
+591
+00:52:58,200 --> 00:53:02,260
+احطها في ال down مرة بدي احطها nasal مرة temporal
+
+592
+00:53:02,260 --> 00:53:05,140
+يعني الصورة بدها تكون ايه شمالها؟
+
+593
+00:53:07,640 --> 00:53:12,560
+متغيرة طبعا هو مش هذا ال task احنا اللي قصدله بس
+
+594
+00:53:12,560 --> 00:53:15,760
+انا بدي يعني تعرفوا اللي هو التنبيه بتاعه او
+
+595
+00:53:15,760 --> 00:53:21,040
+التقريب يعني بالنسبة للشكل الان هالي اللي هو تفاحة
+
+596
+00:53:21,040 --> 00:53:25,440
+okay الان المريض ع مسافة تلاتين سانت مرة بعمل زي
+
+597
+00:53:25,440 --> 00:53:30,600
+هيك مرة بحاول اغير زي هيك الان في شغل مهمة ال
+
+598
+00:53:30,600 --> 00:53:34,340
+examiner لازم مايعرفش وين اتجاه الصورة لان لو انا
+
+599
+00:53:34,340 --> 00:53:39,090
+جيت اعرض الصورة للطفل هذهو اطلعت في الصورة مثلا
+
+600
+00:53:39,090 --> 00:53:43,730
+الصورة كانت up اول ما اطلع الطفل وين هينظر؟ على
+
+601
+00:53:43,730 --> 00:53:47,770
+عينك، فهيعرف وين اتجاه العين بتاعته، يعني اطلعت
+
+602
+00:53:47,770 --> 00:53:51,730
+انا up، هو هيطلع up معاك، فدايما لازم ال test ايش
+
+603
+00:53:51,730 --> 00:53:56,940
+يكون كاتب، مثلا هذه الصورة upواضح خلف الصورة، يعني
+
+604
+00:53:56,940 --> 00:54:01,340
+الآن هي ال .. هي الشكل، okay، الآن لازم انا يكون
+
+605
+00:54:01,340 --> 00:54:05,500
+كtip لي hand up، انه لفوق، فانا بفهم الصورة وين
+
+606
+00:54:05,500 --> 00:54:11,700
+هتكون up، فالطفل وين هيتطلع؟ فوق، ياما بدي .. حتى
+
+607
+00:54:11,700 --> 00:54:13,860
+ياما بدي أحاول .. يعني الآن بدي أعرض
+
+608
+00:54:20,520 --> 00:54:24,120
+ممكن انا اجي اغير هيك بالشكل هذا لإنه غطي وجهي و
+
+609
+00:54:24,120 --> 00:54:30,360
+حاول اغير زي هيك okay هذا بالنسبة لل tiller card
+
+610
+00:54:30,360 --> 00:54:36,580
+فعندك tiller acuity cards black strips of varying
+
+611
+00:54:36,580 --> 00:54:42,840
+thickness لو هاي بتشوفيها في عندنا خطوط وفقية ممكن
+
+612
+00:54:42,840 --> 00:54:48,240
+تكون عبودية okay ومختلفة ايش السماكة okay يعني
+
+613
+00:54:48,240 --> 00:54:49,820
+سماكتها بتكون مختلفة
+
+614
+00:54:52,280 --> 00:54:57,180
+الcardiff acuity cards shapes of variable outline,
+
+615
+00:54:57,540 --> 00:55:02,500
+bold lines, thin lines, it used for early infancy
+
+616
+00:55:02,500 --> 00:55:07,900
+دايما بالنسبة لcardiff card، هذا مهم، test يعتبر
+
+617
+00:55:07,900 --> 00:55:13,520
+كتير مهم للأطفال اللي بيكونوا preverbal الآن
+
+618
+00:55:13,520 --> 00:55:17,940
+الصورة مثلا بحطها مرة في النص، مرة بحطها up, down,
+
+619
+00:55:19,160 --> 00:55:24,390
+temporal, nasalفي الو يعتبر ال card if card يعتبر
+
+620
+00:55:24,390 --> 00:55:29,330
+quantitative مش qualitative، رقمي، كل ما أنا بمشي
+
+621
+00:55:29,330 --> 00:55:34,910
+مثلا، الآن ستة ع ستين، الطفل شافها up، واضحة، الآن
+
+622
+00:55:34,910 --> 00:55:39,530
+ستة ع اربع عشرين هتكون أفتح من مين؟ من ستة ع ستين
+
+623
+00:55:39,530 --> 00:55:44,680
+واتجاهها وين هيكون مختلف عن الستة ع اربع عشرينمثلا
+
+624
+00:55:44,680 --> 00:55:48,420
+لو أنا عملت الان ستة ع ستين لجيتها اب، روحت نجلت
+
+625
+00:55:48,420 --> 00:55:51,540
+على ستة عارفه عشرين لجيتها اب، أنا بصير إيش؟ أغير
+
+626
+00:55:51,540 --> 00:55:55,720
+الاتجاه، واضح؟ أحاول أغير الاتجاه، لأن الطفل ممكن
+
+627
+00:55:55,720 --> 00:55:59,680
+هو يحفظ، وانا حتى حكيتلكم إياها في الناس الأكبر،
+
+628
+00:55:59,680 --> 00:56:02,760
+دايما ما تبدو ال visual acute من الكبيرة، لأن هو
+
+629
+00:56:02,760 --> 00:56:06,380
+لما بقعد عندك فترة بتاخد ال history هو already
+
+630
+00:56:06,380 --> 00:56:15,080
+إيش؟ حفظفهو حافظها وين حتى ال 36 بكون برضه حافظها
+
+631
+00:56:15,080 --> 00:56:25,840
+فدايما حاول ايش اعمل ايه تمويه ل ال مريض okay فيه
+
+632
+00:56:25,840 --> 00:56:29,140
+له ال drawbacks فيه له عيوب اللي هو ال card of
+
+633
+00:56:29,140 --> 00:56:36,090
+card او ما يسمى فيه ال teller card اول حاجةthe
+
+634
+00:56:36,090 --> 00:56:40,350
+strips in one orientation vertical يعني دايما
+
+635
+00:56:40,350 --> 00:56:44,730
+بيكون الاتجاه بتاعه في محور واحد يا اما vertical
+
+636
+00:56:44,730 --> 00:56:48,990
+يا horizontal فدايما بيكون في اتجاه واحد هذا معناه
+
+637
+00:56:48,990 --> 00:56:53,250
+اذا كان عند الطفل astigmatism ماهيقدرش يكتشفه ليش؟
+
+638
+00:56:53,250 --> 00:56:56,370
+لان قلنا احنا دايما ال astigmatism بيكون two
+
+639
+00:56:56,370 --> 00:57:00,650
+meridian و بيكون له two power لو كان السفير عادي
+
+640
+00:57:00,650 --> 00:57:06,380
+انه بيقدر انه يكتشفهبرضه لو كان children who have
+
+641
+00:57:06,380 --> 00:57:09,840
+nystagmus unable to fixate on the targets
+
+642
+00:57:09,840 --> 00:57:17,520
+accurately الان في ناس ال albino البيض الشجر دايما
+
+643
+00:57:17,520 --> 00:57:20,400
+بيكون عندهم nystagmus اللي حطوا عليهم رقرة في
+
+644
+00:57:20,400 --> 00:57:24,900
+العين اليوم لو في حد عندكم عنده اللي هو albino
+
+645
+00:57:24,900 --> 00:57:30,540
+البيض الشجر لازم يكون عنده albinismلحظة عليه بيكون
+
+646
+00:57:30,540 --> 00:57:35,280
+عنده هقرأة في العين، العين بتتحرك دايما، واضح؟
+
+647
+00:57:35,280 --> 00:57:39,080
+فهذا بيكون من الصعب انه يعمل fixation على مين؟ على
+
+648
+00:57:39,080 --> 00:57:42,220
+ال card if او على ال tiller انه من الصعب انه يعمل
+
+649
+00:57:42,220 --> 00:57:47,060
+fixation على الصورة، okay؟ هذا من عيوب مين؟ ال
+
+650
+00:57:47,060 --> 00:57:51,910
+tiller card او ال card if cardchildren who have
+
+651
+00:57:51,910 --> 00:57:55,970
+visual field defects may have difficulty finding
+
+652
+00:57:55,970 --> 00:57:59,910
+the targets لو الآن مثلا زملتكم عملناها ال visual
+
+653
+00:57:59,910 --> 00:58:04,810
+field كان normal لو عندنا طفل عنده ال visual field
+
+654
+00:58:04,810 --> 00:58:08,470
+مش normal يعني abnormal هيكون من الصعب انه يشوف
+
+655
+00:58:08,470 --> 00:58:12,550
+الصورة لما اعملها temporal او nasal او up or down
+
+656
+00:58:12,550 --> 00:58:18,750
+okay فدايما انا هذه تعتبر العيوب بالنسبة لcardiff
+
+657
+00:58:18,750 --> 00:58:27,530
+cardطب هيك بس ورقة صغيرة طلعوا يلا ساكر كل حاجة لو
+
+658
+00:58:27,530 --> 00:58:33,270
+سمحتوا ال quiz عبارة عن دقيقتين okay انا هلمه منكم
+
+659
+00:58:33,270 --> 00:58:38,050
+اللي مش هتسلمني همشي ومش ه .. مش هطلع فيها بعد هيك
+
+660
+00:58:38,050 --> 00:58:46,310
+okay تفاجنا هكتب
+
+661
+00:58:46,310 --> 00:58:49,950
+عشان اسمك تقرأ او هكتب حق بس هكتب انا بكتب
+
+662
+00:59:04,250 --> 00:59:18,390
+visual acuity testing in pre verbal children شو
+
+663
+00:59:18,390 --> 00:59:21,830
+هم ال visual acuity testing in pre verbal children
+
+664
+00:59:21,830 --> 00:59:27,990
+امنع
+
+665
+00:59:27,990 --> 00:59:34,680
+الكلام ارفع يدك علي القلمارفع يديك عن القلم امنع
+
+666
+00:59:34,680 --> 00:59:58,120
+الكلام خلاص حط القلم لو سمحت حط القلم دي
+
+667
+00:59:58,120 --> 01:00:01,780
+اليوم كلها هذه امانة ما تكتبيش ولا حاجة
+
+668
+01:00:31,990 --> 01:00:37,230
+هيك سلمته؟ هيك ان شاء الله بنكون في المحاضرة هذه
+
+669
+01:00:37,230 --> 01:00:43,310
+خلصنا ال visual acuity حدة الإبصار مع قياسات حدة
+
+670
+01:00:43,310 --> 01:00:47,170
+الإبصار للأطفال الغير ناطقيين في المحاضرة القادمة
+
+671
+01:00:47,170 --> 01:00:51,130
+ان شاء الله هنبدأ how to measure visual acuity in
+
+672
+01:00:51,130 --> 01:00:53,510
+verbal children يعطيكم العافية
+
diff --git a/PL9fwy3NUQKwaBhVI6LPr803vc5wWl9Iy_/3nXmI7_Zb7Q_postprocess.srt b/PL9fwy3NUQKwaBhVI6LPr803vc5wWl9Iy_/3nXmI7_Zb7Q_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..6d14f5a01abf74c8750cb564a2bc33ec03f736ba
--- /dev/null
+++ b/PL9fwy3NUQKwaBhVI6LPr803vc5wWl9Iy_/3nXmI7_Zb7Q_postprocess.srt
@@ -0,0 +1,2300 @@
+1
+00:00:20,770 --> 00:00:23,850
+طيب بسم الله الرحمن الرحيم السلام عليكم و رحمة
+
+2
+00:00:23,850 --> 00:00:29,910
+الله و بركاته في المحاضرة السابقة تناولنا موضوع
+
+3
+00:00:29,910 --> 00:00:37,690
+أنواع العدسات أنهينا من موضوع العدسات ال spherical
+
+4
+00:00:37,690 --> 00:00:40,850
+lenses العدسات الكراوية
+
+5
+00:00:45,140 --> 00:00:51,120
+in general بالنسبة للعدسات وبعدين هنتطلق لموضوع ال
+
+6
+00:00:51,120 --> 00:00:55,380
+cylindrical lenses العدسات الأسطوانية و ال sphero
+
+7
+00:00:55,380 --> 00:01:01,100
+cylindrical lenses اللي هي التوريك لينزز بداية ال
+
+8
+00:01:01,100 --> 00:01:06,580
+type of lenses أنواع العدسات lenses may be سفير زي
+
+9
+00:01:06,580 --> 00:01:11,160
+ما اتفقنا أن العدسة أو العدسات ممكن أن تكون كراوية
+
+10
+00:01:12,370 --> 00:01:17,730
+cylinders استوانية أو sphero cylinders sphero
+
+11
+00:01:17,730 --> 00:01:22,450
+cylinders شو معناها؟ انه turret lenses ال turret
+
+12
+00:01:22,450 --> 00:01:27,670
+lenses combination of the sphere and cylinder lens
+
+13
+00:01:27,670 --> 00:01:32,490
+بالظبط لو مثلا انا عند استوانة واخدت من الاستوانة
+
+14
+00:01:32,490 --> 00:01:36,910
+انه قطعة هذه القطعة هي بنسميها ال sphero cylinder
+
+15
+00:01:36,910 --> 00:01:38,250
+واضح؟
+
+16
+00:01:48,620 --> 00:01:54,160
+العدسة الكراوية بتكون القوة في جميع اتجاهاتها
+
+17
+00:01:54,160 --> 00:02:00,260
+متساوية يعني كل الاتجاهات مابكونش لها access يعني
+
+18
+00:02:00,260 --> 00:02:09,230
+بالشكل هذا ان لو فرضنا قوة العدسة plus twoهذه بفهم
+
+19
+00:02:09,230 --> 00:02:12,910
+أن العدسة كلها تمنجميع المحاور هي plus two أو
+
+20
+00:02:12,910 --> 00:02:17,750
+minus three واضح؟
+
+21
+00:02:17,750 --> 00:02:21,950
+convex spherical lenses converge light rays and
+
+22
+00:02:21,950 --> 00:02:27,050
+are called plus lenses العدسات الموجبة بتعمل على
+
+23
+00:02:27,050 --> 00:02:28,430
+تجميع الأشعة
+
+24
+00:02:35,300 --> 00:02:40,620
+العدسات السالبة بتعمل على تفريق الأشعة و بنديها
+
+25
+00:02:40,620 --> 00:02:42,080
+الإشارة A الـ minus
+
+26
+00:02:54,890 --> 00:03:01,130
+دايما النقطة البقارية للعدسة الموجبة بتكون أمام
+
+27
+00:03:01,130 --> 00:03:06,390
+العدسة طبعا الأشعة هتكون إيش؟ convergence اتطالعة
+
+28
+00:03:06,390 --> 00:03:13,310
+من العدسة و هتعمل على تشكيل الصورة يعني لو فرضنا
+
+29
+00:03:13,310 --> 00:03:18,550
+هي مثلا عدسة plus واضح الصورة اللي هتكون
+
+30
+00:03:23,040 --> 00:03:31,920
+أي شمالها اللى هى Convergent هتكون
+
+31
+00:03:31,920 --> 00:03:39,120
+ال rails متجمعة The focal point of a minus lens is
+
+32
+00:03:39,120 --> 00:03:41,200
+the point which parallel lies
+
+33
+00:03:45,280 --> 00:03:50,000
+إن الأشعة اللي بتكون خارجا من العدسة السالبة هتكون
+
+34
+00:03:50,000 --> 00:03:55,520
+متفرقة وبعطيها الإشارة السالبة In the case of
+
+35
+00:03:55,520 --> 00:04:01,700
+convex or concave plus or minus lenses using the
+
+36
+00:04:01,700 --> 00:04:06,780
+mathematical formula D equal one over F طبعا ال D
+
+37
+00:04:06,780 --> 00:04:10,100
+يكون الديوبتريك power أو ال virgins power ال F
+
+38
+00:04:10,100 --> 00:04:14,520
+الفوكر length in millimeterيعني انا لو مثلا جيب
+
+39
+00:04:14,520 --> 00:04:19,200
+السؤال in the case of convicts or concave lenses
+
+40
+00:04:19,200 --> 00:04:22,880
+using the mathematical formula D equal one over F
+
+41
+00:04:22,880 --> 00:04:26,100
+true or false؟ true لإن اللي هو ال lenses هي ال
+
+42
+00:04:26,100 --> 00:04:35,840
+concave انه in the case of plus or minus okay okay
+
+43
+00:04:35,840 --> 00:04:44,310
+cylindrical lenses العدسات الإسبانيةhave virgin's
+
+44
+00:04:44,310 --> 00:04:49,970
+power in only one meridian دايما بتحتوي قوة فقط في
+
+45
+00:04:49,970 --> 00:04:55,730
+محور واحد واضح؟ دايما العدسات الاستوانية القوة
+
+46
+00:04:55,730 --> 00:04:58,950
+بتاعتها بتكون على محور واحد that is perpendicular
+
+47
+00:04:58,950 --> 00:05:02,830
+to the axis of the cylinder وهذا بيكون عمودي على
+
+48
+00:05:02,830 --> 00:05:07,110
+مين؟ على ال axis يعني دايما قوة في العدسة
+
+49
+00:05:07,110 --> 00:05:10,090
+الاستوانية بتكون عمودي على مين؟
+
+50
+00:05:14,130 --> 00:05:19,250
+هي عدسة سلندر في عندنا ال plano و في عندنا ال
+
+51
+00:05:19,250 --> 00:05:23,390
+minus three دايما القوة بتكون عمودية عمين على ال
+
+52
+00:05:23,390 --> 00:05:31,670
+axis they
+
+53
+00:05:31,670 --> 00:05:35,210
+have no power in the meridian parallel to the axis
+
+54
+00:05:36,300 --> 00:05:40,980
+these lenses focus light rays to a line، دايما هذه
+
+55
+00:05:40,980 --> 00:05:47,320
+العدسات بتجمع الضوء إيه؟ في خط واحد، لكن في ال
+
+56
+00:05:47,320 --> 00:05:51,100
+spherical lens، الضوء بتجمع في إيش؟ في نقطة، في
+
+57
+00:05:51,100 --> 00:05:55,500
+point، لكن في ال cylindrical lenses، الأشعة بتتجمع
+
+58
+00:05:55,500 --> 00:06:01,830
+إيش؟ في خط واحد، في line، واضح؟Spherical and
+
+59
+00:06:01,830 --> 00:06:05,890
+cylindrical lenses can be combined in one lens to
+
+60
+00:06:05,890 --> 00:06:10,450
+form a spherocylindrical lens also known as
+
+61
+00:06:10,450 --> 00:06:15,070
+compound lens or toric lens دايما ال toric lens
+
+62
+00:06:15,070 --> 00:06:23,790
+بتتكون من combination لالسفير plus two مثلا زائد
+
+63
+00:06:23,790 --> 00:06:25,350
+السلندر
+
+64
+00:06:30,760 --> 00:06:35,800
+و minus مثلا ال three فبتكون ال spherical cylinder
+
+65
+00:06:35,800 --> 00:06:40,280
+minus one plus
+
+66
+00:06:40,280 --> 00:06:42,120
+two واضح؟
+
+67
+00:06:44,270 --> 00:06:50,150
+هذه اللصوص تركز على عدسة الوضع في خطة فكاية دائما
+
+68
+00:06:50,150 --> 00:06:54,190
+العدسة الاسفيرو سيلندر او التورك لينز بيكون لها
+
+69
+00:06:54,190 --> 00:06:59,830
+اتو فكاية خطة لكن العدسة الاسفيريكال بيكون لها
+
+70
+00:06:59,830 --> 00:07:09,250
+واحد نقطة فوكالة حسنا شكل العضلات التي تركز على
+
+71
+00:07:09,250 --> 00:07:10,590
+عدسة الوضع في خطة سفيرو سيلندر
+
+72
+00:07:17,120 --> 00:07:22,820
+اللي بتتركز بواسطة العدسة الـ Spherocylindrical أو
+
+73
+00:07:22,820 --> 00:07:26,200
+الـ Torque Lens بنسميها الـ Strum of Cunoid أو
+
+74
+00:07:26,200 --> 00:07:32,360
+Cunoid of Strum شو تعريف الـ Cunoid of Strum؟ بدنا
+
+75
+00:07:32,360 --> 00:07:41,100
+نفهم أول حاجة الـ Cunoid of Strum كيف بتشكل بداية
+
+76
+00:07:41,100 --> 00:07:42,120
+هذه عندى مثلا
+
+77
+00:07:47,640 --> 00:07:52,980
+Horizontal وعنا Vertical الأشعة دايما بتكون ايش؟
+
+78
+00:07:52,980 --> 00:07:59,480
+Divergent واضح؟
+
+79
+00:07:59,480 --> 00:08:02,860
+ال
+
+80
+00:08:02,860 --> 00:08:07,580
+strum of conoid ان الأشعة بتاعة ال horizontal rays
+
+81
+00:08:07,580 --> 00:08:12,300
+و ال vertical rays بتكون ايه؟ Divergent و بتكون
+
+82
+00:08:12,300 --> 00:08:19,100
+متساوية هذا كمفهوم ل strum of conoidلأ انه بتكون
+
+83
+00:08:19,100 --> 00:08:25,200
+ال divergence يعني قيمة التشتت بتاعها متساوية okay
+
+84
+00:08:25,200 --> 00:08:33,140
+ال strum of
+
+85
+00:08:33,140 --> 00:08:37,940
+conoid او conoid of strum
+
+86
+00:08:55,000 --> 00:09:01,000
+rays of the
+
+87
+00:09:01,000 --> 00:09:07,700
+horizontal and
+
+88
+00:09:07,700 --> 00:09:11,440
+vertical
+
+89
+00:09:11,440 --> 00:09:15,080
+as
+
+90
+00:09:15,080 --> 00:09:22,880
+wellإنه بتكون الأشعة السواق العمودية أو الأشعة
+
+91
+00:09:22,880 --> 00:09:28,560
+الأفقية متفارقة و بيكونوا متساويين في اللي هي
+
+92
+00:09:28,560 --> 00:09:33,720
+التشتتت بتاعهم واضح؟ هذا كمفهوم ال strum of conoid
+
+93
+00:09:33,720 --> 00:09:37,760
+طبعا هذا وين بتكون ال strum of conoid؟ في العدسة
+
+94
+00:09:37,760 --> 00:09:40,860
+اللي بتكون toric lens ال سفير و ال cylinder lens
+
+95
+00:09:40,860 --> 00:09:44,340
+اللي هي combination of the sphere and cylindrical
+
+96
+00:09:44,340 --> 00:09:49,130
+lensإن اتحاد ما بين العدسة الكراوية و العدسة
+
+97
+00:09:49,130 --> 00:09:55,690
+الاسطوانية okay
+
+98
+00:09:55,690 --> 00:10:00,730
+the shape of the light rays as they are focused by
+
+99
+00:10:00,730 --> 00:10:04,650
+the spherocylindrical lens is called the conoid of
+
+100
+00:10:04,650 --> 00:10:05,290
+strum or
+
+101
+00:10:16,140 --> 00:10:20,540
+الان الأشعة المتفرقة من ال vertical و ال
+
+102
+00:10:20,540 --> 00:10:26,120
+horizontal ray هذا بيكوّللي حاجة هان بنسميها ال
+
+103
+00:10:26,120 --> 00:10:32,860
+circle of least
+
+104
+00:10:32,860 --> 00:10:36,020
+confusion
+
+105
+00:10:41,280 --> 00:10:45,720
+طبعا أكيد سمعتوا في العدسة ال cross-cylinder ال
+
+106
+00:10:45,720 --> 00:10:50,620
+cross-cylinder ال basic بتاعها بتعتمد على ال
+
+107
+00:10:50,620 --> 00:10:56,120
+circle of least confusion طبعا العدسة ال cross
+
+108
+00:10:56,120 --> 00:11:00,880
+-cylinder هي combination ما بين ال sphere و ال
+
+109
+00:11:00,880 --> 00:11:05,470
+cylinder lensال principle تاعها المبدأ تاعها انه
+
+110
+00:11:05,470 --> 00:11:08,970
+بيعتمد على مين؟ على ال circle of least confusion
+
+111
+00:11:08,970 --> 00:11:13,730
+ال circle of least confusion انه بيكون ال
+
+112
+00:11:13,730 --> 00:11:19,990
+divergent ray ل ال horizontal مساوي ل ال
+
+113
+00:11:19,990 --> 00:11:24,670
+convergent ray ل ال verticalفحتى بتلاحظ أن أفضل
+
+114
+00:11:24,670 --> 00:11:29,730
+صورة يعني بيكون the best image أنه أفضل صورة من
+
+115
+00:11:29,730 --> 00:11:36,430
+خلال ال circle of least confusion واضح؟ يعني الآن
+
+116
+00:11:36,430 --> 00:11:41,870
+الأشعة كلها متفارقة هذه بنسميها إيش ال scrum of
+
+117
+00:11:41,870 --> 00:11:47,850
+conoid الآن بينتج عندي حاجة بنسميها ال circle of
+
+118
+00:11:47,850 --> 00:11:51,800
+least confusionالcircle of least confusion إيش
+
+119
+00:11:51,800 --> 00:11:56,820
+بصير إنه الأشعة هذه ال divergence trait بتاعة ال
+
+120
+00:11:56,820 --> 00:12:00,040
+vertical و ال convergent trait بتاعة ال horizontal
+
+121
+00:12:00,040 --> 00:12:03,080
+بكونوا exactly equal متساويين
+
+122
+00:12:06,210 --> 00:12:10,250
+ما هي عبارة عن combination انه اتحاد ما بين عدستين
+
+123
+00:12:10,250 --> 00:12:15,950
+واحدة سفير واحدة سلندر واضح؟ و ال cross cylinder
+
+124
+00:12:15,950 --> 00:12:20,250
+الآن في حاجة بتسميها ال spherical equivalent ال
+
+125
+00:12:20,250 --> 00:12:26,130
+سفير plus half السلندر اللي هو القانون بتاعها ال
+
+126
+00:12:26,130 --> 00:12:34,050
+spherical equivalent عندنا
+
+127
+00:12:34,050 --> 00:12:43,270
+السفيرplus half السليندر من خلالها بينتج عندي
+
+128
+00:12:43,270 --> 00:12:51,030
+مفهوم لcircle of least confusion واضح؟ يعني الآن
+
+129
+00:12:51,030 --> 00:12:58,590
+العدسة التوريك لينز فيه لها two foci line او two
+
+130
+00:12:58,590 --> 00:13:02,910
+foci point متفاجئين ع هيك؟ شو معناته؟ يعني الآن
+
+131
+00:13:02,910 --> 00:13:05,330
+العدسة اللي بتكون السفير
+
+132
+00:13:12,820 --> 00:13:17,960
+أو بتكون اللي هو نقطتين زي هيك واضح؟ الآن هذه
+
+133
+00:13:17,960 --> 00:13:21,520
+الأشعة كلها إيه شمالها؟ divergence يعني كلها
+
+134
+00:13:21,520 --> 00:13:26,220
+متفارقة سواء لل vertical أو ال horizontal ray فهذا
+
+135
+00:13:26,220 --> 00:13:31,060
+بنتج مفهوم إيش؟ ال strum of conoid ال strum of
+
+136
+00:13:31,060 --> 00:13:35,100
+conoid بينتج دي حاجة بنسميها ال circle of least
+
+137
+00:13:35,100 --> 00:13:37,860
+confusion شو هو تعريف ال circle of least
+
+138
+00:13:37,860 --> 00:13:44,780
+confusion؟ إنه الأشعةالمتشتتة من المحور الأفقي
+
+139
+00:13:44,780 --> 00:13:50,420
+والأشعة المتجمعة من المحور العمودي كلها هتكون
+
+140
+00:13:50,420 --> 00:13:56,780
+متساوية واضح ان كلها بتكون are exactly equal يعني
+
+141
+00:13:56,780 --> 00:14:06,620
+كلها بتكون هذه الأشعة متساوية واضح ولا كذا؟
+
+142
+00:14:16,950 --> 00:14:24,110
+الcircle of least
+
+143
+00:14:24,110 --> 00:14:33,750
+confusion
+
+144
+00:14:47,200 --> 00:14:53,320
+divergent of the
+
+145
+00:14:53,320 --> 00:14:59,780
+vertical and
+
+146
+00:14:59,780 --> 00:15:03,620
+horizontal
+
+147
+00:15:03,620 --> 00:15:10,080
+rays
+
+148
+00:15:10,080 --> 00:15:12,520
+are
+
+149
+00:15:17,900 --> 00:15:26,900
+exactly equal مفهوم بصير جدا الان ال focal point
+
+150
+00:15:26,900 --> 00:15:32,920
+في أي عدسة ال spherical بيكون عبارة عن نقطةلكن في
+
+151
+00:15:32,920 --> 00:15:38,360
+العدسة السيلندر بيكون عبارة عن two foci point او
+
+152
+00:15:38,360 --> 00:15:42,020
+في العدسة التوريك لينز برضه بيكون two foci point
+
+153
+00:15:42,020 --> 00:15:46,800
+انه نقطتين ببساطة ليش؟ لأن في نقطة واحدة للاسفير
+
+154
+00:15:46,800 --> 00:15:53,180
+والاخرى بتكون لمين للسيلندر واضح؟ الآن في مفهوم
+
+155
+00:15:53,180 --> 00:15:57,920
+عنده ال strum of conoid ان كل الأشعة ايش بتكون
+
+156
+00:15:57,920 --> 00:16:01,200
+divergence سواء من ال vertical او ال horizontal
+
+157
+00:16:01,200 --> 00:16:05,520
+rateطيب هذه فيه لها ايه؟ application يعني فيه لها
+
+158
+00:16:05,520 --> 00:16:10,380
+استعمالات الاستعمال بتاعها زي في اللي هو عدسة مين
+
+159
+00:16:10,380 --> 00:16:14,860
+ال cross cylinder ال cross cylinder هي عبارة عن
+
+160
+00:16:14,860 --> 00:16:20,860
+عدسة متحدة ما بين ال sphere وال cylinder يعني it
+
+161
+00:16:20,860 --> 00:16:23,780
+is a combination of the cylinder and the sphere
+
+162
+00:16:23,780 --> 00:16:30,180
+lens واضح؟الان ال principle بتاع العدسة ال cross
+
+163
+00:16:30,180 --> 00:16:33,940
+cylinder بعتمد على مين؟ على ال circle of least
+
+164
+00:16:33,940 --> 00:16:39,620
+confusion اللي هو حكينا تعريفه ان ال divergent
+
+165
+00:16:39,620 --> 00:16:44,360
+rays من ال vertical او ال convergent ray من ال
+
+166
+00:16:44,360 --> 00:16:48,320
+horizontal كله بيكون ايش؟ are exactly equal انه
+
+167
+00:16:48,320 --> 00:16:49,240
+بيكون متساوي
+
+168
+00:16:55,840 --> 00:16:59,980
+which represent the point of the best overall
+
+169
+00:16:59,980 --> 00:17:04,360
+focus for the lens وهذا بتديني ال best image يعني
+
+170
+00:17:04,360 --> 00:17:09,520
+أفضل صورة ممكن انه لو مريض يعاني من ال stigma هذا
+
+171
+00:17:09,520 --> 00:17:21,380
+بتديني أفضل صورة ممكن ان المريض يشوفها visual
+
+172
+00:17:21,380 --> 00:17:27,400
+acuity حدة الإبصارماذا تعني في ال visual acuity؟
+
+173
+00:17:27,400 --> 00:17:37,740
+حدة الإبصار كمفهوم له أنه بيقيس ال resolving
+
+174
+00:17:37,740 --> 00:17:43,260
+capacity of the eye و القدرة على استخدام ال
+
+175
+00:17:43,260 --> 00:17:47,300
+central vision it is a measurement of the spatial
+
+176
+00:17:47,300 --> 00:17:51,800
+resolving capacity of the eye and is applied to
+
+177
+00:17:51,800 --> 00:18:02,330
+theوالقدرة على استخدام من الرؤية المركزية واضح؟
+
+178
+00:18:02,330 --> 00:18:04,550
+كتابته هذا صح؟
+
+179
+00:18:20,050 --> 00:18:28,790
+طبعا ال visual acuity اختصاره VA it
+
+180
+00:18:28,790 --> 00:18:39,470
+is a measurement of
+
+181
+00:18:39,470 --> 00:18:42,590
+spatial
+
+182
+00:18:54,610 --> 00:19:01,350
+resolving كبسة of
+
+183
+00:19:01,350 --> 00:19:08,950
+the I and
+
+184
+00:19:08,950 --> 00:19:14,150
+is
+
+185
+00:19:14,150 --> 00:19:14,750
+applied
+
+186
+00:19:27,740 --> 00:19:32,980
+to central vision
+
+187
+00:19:32,980 --> 00:19:39,520
+انه بيقيص ال special resolving capacity انه
+
+188
+00:19:39,520 --> 00:19:45,780
+capacity بمعنى سعة التمييز ما بين يعني او احنا
+
+189
+00:19:45,780 --> 00:19:50,640
+بنعرف كنا ال optotype او الحرف واضح فهو بيشوف يعني
+
+190
+00:19:50,640 --> 00:19:50,940
+وين
+
+191
+00:19:57,950 --> 00:20:04,190
+فهو بجيس ليه التشقق هذا يعني الموجود في داخل الحرف
+
+192
+00:20:04,190 --> 00:20:09,150
+أو ال broken الإنكسار الموجود it is a measurement
+
+193
+00:20:09,150 --> 00:20:13,610
+of spatial resolving capacity of the eye and is
+
+194
+00:20:13,610 --> 00:20:17,370
+applied طبعا إحنا لما نجيس ال visual acuity ما
+
+195
+00:20:17,370 --> 00:20:21,330
+بجيس ال peripheral vision بجيس أنا مين ال central
+
+196
+00:20:21,330 --> 00:20:23,470
+vision واضح؟
+
+197
+00:20:27,210 --> 00:20:32,030
+visual acuity it is the function not only of the
+
+198
+00:20:32,030 --> 00:20:36,890
+diopteric apparatus of the eye but also of the
+
+199
+00:20:36,890 --> 00:20:40,810
+retina, visual pathway and central nervous
+
+200
+00:20:40,810 --> 00:20:48,450
+mechanisms الحدة الإبصار هي ليست وظيفة أنه بس أحدد
+
+201
+00:20:48,450 --> 00:20:53,370
+من خلالها القوة البصرية للعين يعني مش مثلا أقول
+
+202
+00:20:53,370 --> 00:20:59,840
+أنه ال visual acuityللعين اليمين 6 على 9، للعين
+
+203
+00:20:59,840 --> 00:21:05,420
+الشمال 6 على 12، لأ الهدف منها كمان ايش برضه؟ انه
+
+204
+00:21:05,420 --> 00:21:12,320
+اشوف قداش قوة الشبكية يعني او صلاح اللي هو الشبكية
+
+205
+00:21:12,320 --> 00:21:16,600
+فيها من خلال مثلا ال sensitivity اللي هي حساسية
+
+206
+00:21:16,600 --> 00:21:21,600
+الشبكية او ال visual pathway، بنعرف احنا فيه ال
+
+207
+00:21:21,600 --> 00:21:21,860
+visual path
+
+208
+00:21:33,430 --> 00:21:37,270
+بقول ال visual pathway بمعنى الممرب البصري للعين
+
+209
+00:21:37,270 --> 00:21:41,990
+يعني الآن الشبكية بتصل للعين إيه شمالها؟ مجلوبة
+
+210
+00:21:41,990 --> 00:21:47,170
+صح؟ وين .. وين الصورة بتنجلب؟ في ال optic tract
+
+211
+00:21:47,170 --> 00:21:52,110
+صح؟ فالآن بعد الشبكية بعد ما الصورة تصل للشبكية
+
+212
+00:21:52,110 --> 00:21:56,050
+بتروح وين؟ على ال optic nerve اللي هو العصب البصري
+
+213
+00:22:03,420 --> 00:22:07,560
+واخر واحدة اللي هي ال visual cortex واضح؟ هذه
+
+214
+00:22:07,560 --> 00:22:12,340
+عبارة عن ال visual pathway للعين and the central
+
+215
+00:22:12,340 --> 00:22:16,980
+nervous mechanism اللي هي مركز الأعصاب بتاعت العين
+
+216
+00:22:16,980 --> 00:22:21,860
+فعنا هنا ال
+
+217
+00:22:21,860 --> 00:22:30,340
+visual pathway
+
+218
+00:22:35,420 --> 00:22:42,040
+optic nerve اللي هو العصب الثاني number
+
+219
+00:22:42,040 --> 00:22:48,880
+two عندنا ال optic كيازما
+
+220
+00:22:48,880 --> 00:22:53,540
+number
+
+221
+00:22:53,540 --> 00:23:04,180
+three optic tract number
+
+222
+00:23:04,180 --> 00:23:04,680
+four
+
+223
+00:23:08,540 --> 00:23:16,300
+optic radiation number
+
+224
+00:23:16,300 --> 00:23:23,000
+five lateral geniculate
+
+225
+00:23:23,000 --> 00:23:23,360
+body
+
+226
+00:23:41,750 --> 00:23:49,150
+number six ال visual cortex
+
+227
+00:23:49,150 --> 00:23:52,550
+هذه
+
+228
+00:23:52,550 --> 00:23:55,870
+عبارة عن ال visual با ثوية للعين okay
+
+229
+00:24:25,730 --> 00:24:29,290
+طبعا optic nerve, optic chiasma, optic tract,
+
+230
+00:24:29,430 --> 00:24:31,790
+optic radiation, lateral geniculate body and
+
+231
+00:24:31,790 --> 00:24:40,090
+visual cortex خلصته؟
+
+232
+00:24:40,090 --> 00:24:45,110
+visual acuity is determined by the smallest
+
+233
+00:24:45,110 --> 00:24:52,190
+retinal image حدة الإبصار بتحدد بواسطة الصورة اللي
+
+234
+00:24:52,190 --> 00:24:56,250
+واقع على الشبكيةthe form of which can be
+
+235
+00:24:56,250 --> 00:25:00,710
+appreciated يعني قداش هذه الصورة اللي هتشكل على
+
+236
+00:25:00,710 --> 00:25:05,530
+الشبكية كم هي بتقدر زي ما حكينا في ال refractive
+
+237
+00:25:05,530 --> 00:25:09,750
+error الأخطاء الانكسارية أن الصورة في حالة ال
+
+238
+00:25:09,750 --> 00:25:13,910
+immature يما تكون ال normal patient بتقع على
+
+239
+00:25:13,910 --> 00:25:18,730
+الشبكية في حالة الmyope بتقع أمام الشبكية و
+
+240
+00:25:18,730 --> 00:25:20,850
+الhyper mature خلف الشبكية
+
+241
+00:25:23,710 --> 00:25:27,870
+it is determined by the smallest retinal image the
+
+242
+00:25:27,870 --> 00:25:31,570
+form of which can be appreciated and it is
+
+243
+00:25:31,570 --> 00:25:34,970
+measured the smallest object which can be clearly
+
+244
+00:25:34,970 --> 00:25:42,250
+seen at a certain distance كمان بتقيس جديش الجسم
+
+245
+00:25:42,250 --> 00:25:47,690
+يعني حجم الجسم اللي بيقع على الشبكية و ممكن جديش
+
+246
+00:25:47,690 --> 00:25:52,470
+الصورة أنه بتوضح هذا الجسم يعني الآن لو فرضنا أنا
+
+247
+00:25:52,470 --> 00:26:01,470
+كنت ميوبقداش انا الشبكية هتقدر اتوضحلي الصورة على
+
+248
+00:26:01,470 --> 00:26:06,270
+الشبكية فانا بعرف قداش ال visual acuity بتاعي او
+
+249
+00:26:06,270 --> 00:26:09,770
+مثلا لو كنت hyper metroid عندي طول نظر فالشبكية
+
+250
+00:26:09,770 --> 00:26:14,190
+بتديني قداش ال visual acuity المحتمل بتاعي من خلال
+
+251
+00:26:14,190 --> 00:26:20,800
+فحص من ال visual acuity واضح الصورة؟يعني الآن لو
+
+252
+00:26:20,800 --> 00:26:25,000
+أنا normal patient in a metro الصورة وين بتقع؟ على
+
+253
+00:26:25,000 --> 00:26:26,300
+الشبكية، على الشبكية، على الشبكية، على الشبكية،
+
+254
+00:26:26,300 --> 00:26:27,580
+على الشبكية، على الشبكية، على الشبكية، على
+
+255
+00:26:27,580 --> 00:26:30,780
+الشبكية، على الشبكية، على الشبكية، على الشبكية،
+
+256
+00:26:30,780 --> 00:26:34,640
+على الشبكية، على الشبكية، على الشبكية، على
+
+257
+00:26:34,640 --> 00:26:35,460
+الشبكية، على الشبكية، على الشبكية، على الشبكية،
+
+258
+00:26:35,460 --> 00:26:35,700
+على الشبكية، على الشبكية، على الشبكية، على
+
+259
+00:26:35,700 --> 00:26:37,060
+الشبكية، على الشبكية، على الشبكية، على الشبكية،
+
+260
+00:26:37,060 --> 00:26:40,560
+على الشبكية، على الشبكية،
+
+261
+00:26:41,280 --> 00:26:47,340
+طيب لو كنت انا مثلا مايوب، اذا الصورة هتقع وين؟
+
+262
+00:26:47,340 --> 00:26:51,340
+امام الشبكية، فهتوقع ان المريض عنده a blurred
+
+263
+00:26:51,340 --> 00:26:55,740
+vision far distance، اذا الصورة ماهتكونش واضحة، صح
+
+264
+00:26:55,740 --> 00:26:58,360
+ولا لأ؟ يجب ان انا اعمل اللي هو ال test بتاع ال
+
+265
+00:26:58,360 --> 00:27:01,720
+visual acuity و هكذا بالنسبة لل hyper micro
+
+266
+00:27:08,450 --> 00:27:13,550
+Importance of testing visual acuity شو أهمية قياس
+
+267
+00:27:13,550 --> 00:27:19,410
+حدة الإبصار Testing visual acuity is very
+
+268
+00:27:19,410 --> 00:27:24,670
+important in all of the cases because يعني قياس
+
+269
+00:27:24,670 --> 00:27:29,850
+حدة الإبصار مهم جدا لكل الحالات اللي احنا نذكرها
+
+270
+00:27:31,260 --> 00:27:36,580
+طبعا شو السبب أن حدة الإبصار مهمة أو قياس حدة
+
+271
+00:27:36,580 --> 00:27:41,660
+الإبصار أنه مهمة بالنسبة لل patient؟ number one it
+
+272
+00:27:41,660 --> 00:27:45,100
+gives us an accurate diagnosis for the patient
+
+273
+00:27:45,100 --> 00:27:45,640
+case
+
+274
+00:27:50,890 --> 00:27:57,830
+اللي هو تشخيص دقيق للمريض لحالة المريض وبشير إلى
+
+275
+00:27:57,830 --> 00:28:03,650
+ايه؟ إلى ال severity حدة المشكلة يعني number one
+
+276
+00:28:03,650 --> 00:28:08,910
+بتديني تشخيص دقيق accurate diagnosis عبارة عن
+
+277
+00:28:08,910 --> 00:28:15,390
+تشخيص دقيق للمريض أو حالة المريض وبشير إلى قداش ال
+
+278
+00:28:15,390 --> 00:28:20,100
+severity حدة المرضيعني من خلال يما انا اعرف ال
+
+279
+00:28:20,100 --> 00:28:23,600
+visual acuity اول حاجة بتديني accurate diagnosis
+
+280
+00:28:23,600 --> 00:28:28,860
+ان والله هذا ال patient إمتراب، هذا hypermetrop,
+
+281
+00:28:29,040 --> 00:28:32,520
+هذا ميوب، هذا astigmatism فبتحدد accurate
+
+282
+00:28:32,520 --> 00:28:39,890
+diagnosis تشخيص دقيق number twoit may help .. it
+
+283
+00:28:39,890 --> 00:28:43,050
+may helps us to discover a new problem at the
+
+284
+00:28:43,050 --> 00:28:46,490
+patient which is .. which is not the main problem
+
+285
+00:28:46,490 --> 00:28:50,370
+that the patient complained for ممكن الآن في ال
+
+286
+00:28:50,370 --> 00:28:53,970
+clinic بتاعي ييجي المريض يقول أنا عنده blurred
+
+287
+00:28:53,970 --> 00:28:59,130
+vision for distanceلكن أنا لما أجي أعمل ال visual
+
+288
+00:28:59,130 --> 00:29:04,090
+acuity هو يكون يعني المشكلة اللي جاي إلها المريض
+
+289
+00:29:04,090 --> 00:29:08,370
+والتشخيص داعي مختلف عن بعض، صح ولا لا؟ يعني ممكن
+
+290
+00:29:08,370 --> 00:29:12,470
+أنه يكون هو عنده مشكلة في البعيدلكن السبب في هذه
+
+291
+00:29:12,470 --> 00:29:16,510
+المشكلة مش هو والله النظر ممكن يكون سببه اللي هو
+
+292
+00:29:16,510 --> 00:29:20,910
+headache صداع سواء كان frontal أو occipital فمن
+
+293
+00:29:20,910 --> 00:29:25,170
+خلال ال visual acuity انا بقدر انه اكتشف ايش امور
+
+294
+00:29:25,170 --> 00:29:31,490
+يعني جديدة غير اللي شكاها المريض ممكن مثلا المريض
+
+295
+00:29:31,490 --> 00:29:36,030
+يحكي انا عنده blurred vision for nearيما افحص
+
+296
+00:29:36,030 --> 00:29:39,390
+المريض يطلع عنده إبلارة vision fournier اللي هي ال
+
+297
+00:29:39,390 --> 00:29:42,810
+hyper metroid طول النظر زائد انه يكون عنده
+
+298
+00:29:42,810 --> 00:29:48,450
+astigmatism لا بقرية فمن خلالها ايش؟ بقدر انه من
+
+299
+00:29:48,450 --> 00:29:52,410
+خلال قياس ال visual acuity يعني من خلال قياس حتة
+
+300
+00:29:52,410 --> 00:29:57,790
+الإبصار باكتشف أشياء جديدة المريض ماشكاش منها،
+
+301
+00:29:57,790 --> 00:30:03,030
+واضح؟Number three it is also help us in the
+
+302
+00:30:03,030 --> 00:30:07,010
+following up the patients case to compare between
+
+303
+00:30:07,010 --> 00:30:11,290
+pre and post the treatment من خلال قياس حدة
+
+304
+00:30:11,290 --> 00:30:17,150
+الإبصار بقدر أنه أعمل follow-up مراجعة للمريض زي
+
+305
+00:30:17,150 --> 00:30:21,570
+مثلا الآن إيجي مريض عنده زي ما انتوا كلهيتكم عندكم
+
+306
+00:30:21,570 --> 00:30:26,590
+الآن ال data file فحصته مثلا في شهر أربعة كان ال
+
+307
+00:30:26,590 --> 00:30:31,850
+visual acuity عنده ستة ع ستيناستخدمت له نضارة صار
+
+308
+00:30:31,850 --> 00:30:37,210
+النظر عنده ستة ع ستة، الآن شو بتوقع؟ يما ييجي مثلا
+
+309
+00:30:37,210 --> 00:30:42,990
+في شهر تمانية okay يكون ال visual acuity ستة ع ستة
+
+310
+00:30:43,810 --> 00:30:47,830
+لكن طلع مثلا ال visual acute ستة ع تسعة فهذا سهل
+
+311
+00:30:47,830 --> 00:30:51,730
+علي بإيش؟ بعملية المراجعة على المريض و أنا قرنت ما
+
+312
+00:30:51,730 --> 00:30:55,390
+بين النتائج ما بين شهر أربعة يما أنا لبسته النضارة
+
+313
+00:30:55,390 --> 00:30:59,650
+كان ستة ع ستة و ما بين شهر مثلا تسعة أو ثمانية كان
+
+314
+00:30:59,650 --> 00:31:04,850
+النظر ستة على أتناش أو ستة على تسعة فانا إيش عملت؟
+
+315
+00:31:04,850 --> 00:31:08,190
+اللي هو follow up للمريض و عملت compare between
+
+316
+00:31:08,190 --> 00:31:09,910
+the pre and post treatment
+
+317
+00:31:13,600 --> 00:31:17,640
+for all of these reasons visual acuity must be
+
+318
+00:31:17,640 --> 00:31:22,460
+tested for all of the patients before visiting the
+
+319
+00:31:22,460 --> 00:31:26,480
+ophthalmologist يعني أي تمريض قبل ما يزور طبيب
+
+320
+00:31:26,480 --> 00:31:31,660
+العيون لازم انه يقيس حدة الإبصار طيب مين بيقوم
+
+321
+00:31:31,660 --> 00:31:37,520
+بقياس حدة الإبصار اللي هو كoptometrist الأخصائي
+
+322
+00:31:37,520 --> 00:31:38,780
+البصريات؟
+
+323
+00:31:40,600 --> 00:31:44,140
+and this is the mission or the occupation of the
+
+324
+00:31:44,140 --> 00:31:49,180
+optometrist who is the specialist examiner in this
+
+325
+00:31:49,180 --> 00:31:53,700
+examination يعني هو بيكون مختص في قياس حدة الإبصار
+
+326
+00:31:53,700 --> 00:31:59,760
+للمريض واضح؟
+
+327
+00:31:59,760 --> 00:32:02,860
+في
+
+328
+00:32:02,860 --> 00:32:07,160
+عندنا ال testing visual acuity in preverbal
+
+329
+00:32:07,160 --> 00:32:14,180
+childrenقياس حدة الإبصار للأطفال الغير ناطقين يعني
+
+330
+00:32:14,180 --> 00:32:18,600
+الآن أنا عند طفل غير ناطق ما بتكلم كيف أنا ممكن
+
+331
+00:32:18,600 --> 00:32:25,200
+أقيسله حدة الإبصار okay أول
+
+332
+00:32:25,200 --> 00:32:30,540
+test occlusion of one eye أنه بنغطي عين واحدة أنه
+
+333
+00:32:30,540 --> 00:32:34,260
+تغطية العين بنشوف ال occlusion of one eye
+
+334
+00:32:38,330 --> 00:32:44,250
+occlusion of one eye it is a simple method for
+
+335
+00:32:44,250 --> 00:32:47,990
+testing the visual acuity in preverbal children
+
+336
+00:32:47,990 --> 00:32:57,110
+and infants هو يعني فحص بسيط جدا بقيس حدة الإبصار
+
+337
+00:32:57,110 --> 00:33:03,610
+للأطفال الغير ناطقين ولا الرضّع okay شو أنا بعمل
+
+338
+00:33:03,610 --> 00:33:10,250
+we cover one eye بنغطى عينand if strongly objected
+
+339
+00:33:10,250 --> 00:33:14,610
+by the child indicates poorer acuity in the other
+
+340
+00:33:14,610 --> 00:33:19,730
+eye الآن المريض .. الطفل .. أنا غطيتله عينه إذا
+
+341
+00:33:19,730 --> 00:33:23,530
+لاحظت أن الطفل بيسحب مثلا إيد أمه أو إيد ال
+
+342
+00:33:23,530 --> 00:33:30,090
+examiner بشكل اللي هو يعني عنيف هذا بتديني دلالة
+
+343
+00:33:30,090 --> 00:33:34,510
+أو إشارة أن ال visual acuity في العين التانية
+
+344
+00:33:34,510 --> 00:33:41,530
+ضعيفة واضح؟يعني الآن هي الطفل أمامي باجي بغطي عينه
+
+345
+00:33:41,530 --> 00:33:45,610
+اليمين، لاحظت أن الطفل إيه شماله؟ على طول أول ما
+
+346
+00:33:45,610 --> 00:33:49,950
+غطيت العين رفع إيدي، فانا إيش بدل هذا؟ إن ال
+
+347
+00:33:49,950 --> 00:33:54,530
+visual acute للمريض عنده إيه؟ فيه ضعف، ممكن طريقة
+
+348
+00:33:54,530 --> 00:33:58,250
+أخرى، ماستخدمش الإيد، لو أنا بدي أستخدم اللي هو ال
+
+349
+00:33:58,250 --> 00:33:59,590
+cover، cover للعين
+
+350
+00:34:02,460 --> 00:34:07,800
+و في ال cover تلاقي الطفل يرفع ال cover أو الغطاء
+
+351
+00:34:11,120 --> 00:34:15,900
+this method just indicate if the visual acuity is
+
+352
+00:34:15,900 --> 00:34:19,100
+good or poor and doesn't give us an accurate
+
+353
+00:34:19,100 --> 00:34:23,700
+measurements يعني هذا بس بيدينا إن هل حدة الإبصار
+
+354
+00:34:23,700 --> 00:34:28,940
+للمريض جيدة أو ضعيفة لكن ما بيعطينا accurate
+
+355
+00:34:28,940 --> 00:34:34,240
+measurement يعني قياس دقيق لمين لحدة الإبصار إذا
+
+356
+00:34:34,240 --> 00:34:37,880
+number one testing visual acuity in a preverbal
+
+357
+00:34:37,880 --> 00:34:42,850
+children occlusion of one eyeOcclusion of one eye
+
+358
+00:34:42,850 --> 00:34:47,910
+indicate only visual acuity is good or poor لو انا
+
+359
+00:34:47,910 --> 00:34:55,550
+مثلا اجيت سأل السؤال Occlusion of one eye measure
+
+360
+00:34:55,550 --> 00:35:02,930
+the visual acuity in accurate .. sorry Occlusion
+
+361
+00:35:02,930 --> 00:35:08,690
+of one eye is an accurate measurement correct اذا
+
+362
+00:35:08,690 --> 00:35:14,770
+فالسإذا سمبل method to measure visual acuity and
+
+363
+00:35:14,770 --> 00:35:18,130
+indicate to if the visual acuity is good or poor
+
+364
+00:35:18,130 --> 00:35:23,590
+okay number
+
+365
+00:35:23,590 --> 00:35:30,990
+two fixation test this is very important testThis
+
+366
+00:35:30,990 --> 00:35:36,770
+is a very good method يعني منهج جيد جدا in testing
+
+367
+00:35:36,770 --> 00:35:42,310
+visual acuity في فحص حدة الإبصار and it is
+
+368
+00:35:42,310 --> 00:35:46,450
+performed as following الخطوات المتبعة في هذا
+
+369
+00:35:46,450 --> 00:35:53,030
+الفحص طبعا ال fixation test هو يعتبر أفضل test من
+
+370
+00:35:53,030 --> 00:35:58,730
+ناحية فحص ل ال pre verbal children واضح؟
+
+371
+00:36:02,120 --> 00:36:05,600
+أما انتوا عارفين فكساشن معناها أنه ثبت العين اللي
+
+372
+00:36:05,600 --> 00:36:14,320
+هي ثابت a 16 prism based on طبعا الprism ديوبتر
+
+373
+00:36:14,320 --> 00:36:22,760
+هذه عبارة عن وحدة قياس زاوية
+
+374
+00:36:22,760 --> 00:36:23,400
+الحوالب
+
+375
+00:36:34,390 --> 00:36:42,430
+يما أشير مثلا D indicate to a diopter صح؟ اللي هي
+
+376
+00:36:42,430 --> 00:36:53,130
+ال power يما أشير ل المثلث زي هذا بمعنى a prism
+
+377
+00:36:53,130 --> 00:37:00,450
+diopter فهذه
+
+378
+00:37:00,450 --> 00:37:01,950
+بتجيس ال angle
+
+379
+00:37:05,490 --> 00:37:14,870
+of deviation انه
+
+380
+00:37:14,870 --> 00:37:25,390
+زاوية الحول واضح number
+
+381
+00:37:25,390 --> 00:37:29,790
+one a sixteen a prism diopter based down
+
+382
+00:37:36,690 --> 00:37:44,150
+الأبريزم بتكون من شغلتين في عندنا ال apex عفوا
+
+383
+00:37:44,150 --> 00:37:51,070
+ان هاد ال base وعندنا
+
+384
+00:37:51,070 --> 00:37:55,710
+ال apex الصورة
+
+385
+00:37:55,710 --> 00:38:01,150
+وين بتتجمع دايما؟ باتجاه ال apex okay يعني دايما
+
+386
+00:38:01,150 --> 00:38:03,190
+الصورة تكون الصورة هنا
+
+387
+00:38:08,300 --> 00:38:16,560
+خانة بالنسبة له ال image ف a 16 prism diopter base
+
+388
+00:38:16,560 --> 00:38:21,920
+down انه ال base down انا حطيته عشان الصورة وين
+
+389
+00:38:21,920 --> 00:38:26,440
+تتجمع في ال apex ممكن هذا السؤال انا اسأله ليش انا
+
+390
+00:38:26,440 --> 00:38:30,960
+حطيت مثلا a 16 prism diopter base down ليش مش base
+
+391
+00:38:30,960 --> 00:38:42,190
+up عشان الصورة وين تتجمعبالتجاه الابيكس 16 بريزم
+
+392
+00:38:42,190 --> 00:38:48,830
+ديوبتر بيس داون بيس على واحد العين والاخر مخفف
+
+393
+00:38:48,830 --> 00:38:50,190
+باستخدام مصادر ضوء
+
+394
+00:38:53,030 --> 00:38:59,390
+العين مثلا افترضنا اليمين حطينا ال prism 16 فوق
+
+395
+00:38:59,390 --> 00:39:03,450
+العين اليمين العين التانية يا بستخدم ال light
+
+396
+00:39:03,450 --> 00:39:07,870
+source يا انا ايش بعمل occlusion اللي هو غطى لكن
+
+397
+00:39:07,870 --> 00:39:12,190
+يكون الغطى هذا ايه شفاف للعين الشمال لكن المستخدم
+
+398
+00:39:12,190 --> 00:39:15,570
+عمليا اللي هو ال light torch اللي هو الضوء او
+
+399
+00:39:15,570 --> 00:39:20,630
+المصدر الضوءطيب، في سؤال تاني، ليش هنا أنا استخدمت
+
+400
+00:39:20,630 --> 00:39:25,470
+16 بريسم ديوبتر، based on؟ ليش أنا الرقم 16
+
+401
+00:39:25,470 --> 00:39:29,470
+استخدمت؟ مثلا، أنا ممكن أسأل ليش مثلا أنا استخدمت
+
+402
+00:39:29,470 --> 00:39:37,810
+اتنين أو أربع ديوبتر؟ ليش رقم 16؟
+
+403
+00:39:40,350 --> 00:39:45,310
+واضح السؤال؟ الان السؤال انا استخدمت ال 16 بريزم
+
+404
+00:39:45,310 --> 00:39:50,130
+ديوبتر based on طيب ممكن واحد من الجمهور يسأل ليش
+
+405
+00:39:50,130 --> 00:39:54,350
+انا مثلا مابستخدم اتنين بريزم ديوبتر؟ او ليش مثلا
+
+406
+00:39:54,350 --> 00:40:00,330
+مابستخدم اربع بريزم ديوبتر؟ ليش الرقم 16؟ okay
+
+407
+00:40:00,330 --> 00:40:06,230
+تفضلي ممكن تكون هذا هو هي اللي قادرة على ان تكوين
+
+408
+00:40:06,230 --> 00:40:12,270
+الصورة بشكل اوب او أكترطيب ليش؟ إيش السبب؟ لأن
+
+409
+00:40:12,270 --> 00:40:16,410
+العين هي خمستاشر تقريبا، لأ، خمستاشر تقريبا
+
+410
+00:40:16,410 --> 00:40:28,190
+another answer؟ طيب،
+
+411
+00:40:28,190 --> 00:40:33,090
+الآن العين، طبيعة العين، كما أنا بتطلع في ال
+
+412
+00:40:33,090 --> 00:40:39,680
+elevation عندك اتنين prison dioptersفانا لو روحت
+
+413
+00:40:39,680 --> 00:40:44,580
+حطيت برزم ديوبتر اتنين هتكون ايش متساوية equal
+
+414
+00:40:44,580 --> 00:40:51,780
+فانا بحط اللي هو برزم ديوبتر سكستين عشان تكون خمس
+
+415
+00:40:51,780 --> 00:40:56,580
+عشر مرة جد الاتنين عشان تقدر انه ايش ترفع العين
+
+416
+00:40:56,580 --> 00:40:58,740
+انه تعمل elevation لل up
+
+417
+00:41:02,550 --> 00:41:07,250
+طبعا هو ال sixteen based on the .. يعني بناء على
+
+418
+00:41:07,250 --> 00:41:11,050
+المكتشف في هذا الفحص بس هو مثلا ليش مستخدمش رقم
+
+419
+00:41:11,050 --> 00:41:15,010
+صغير؟ يعني اتنين أو اربع أو تلاتة أو خمسة؟ ليش
+
+420
+00:41:15,010 --> 00:41:19,730
+مثلا عشرين أو مثلا ستاشر؟ هو المهم أنه رقم أكبر من
+
+421
+00:41:19,730 --> 00:41:24,810
+يعني العشرةيعني الآن اما انا بستخدم بكرا بتاخدوه
+
+422
+00:41:24,810 --> 00:41:28,510
+في الحوال ال Prismات ياما تكون من عشرة فما فوق
+
+423
+00:41:28,510 --> 00:41:34,490
+بيكون رقم كبير يعني مش تظهر انه رقم 16 واضح؟ فهذه
+
+424
+00:41:34,490 --> 00:41:37,450
+المعلومة انه تظل انه انا ليش استخدمت ان ال 16
+
+425
+00:41:37,450 --> 00:41:45,550
+Prism ديوبتر مش اتنين ولا اربع حاضر هلجيت انا
+
+426
+00:41:45,550 --> 00:41:51,510
+استخدمت ال Prism 16ممكن يعني واحد يقول ليش مثلا
+
+427
+00:41:51,510 --> 00:41:57,010
+أنا استخدمت ال prism اتنين او تلاتر، الآن العين
+
+428
+00:41:57,010 --> 00:42:02,850
+فيها اتنين ديوبتر في ال vertical، واضح؟ هذا يعني
+
+429
+00:42:02,850 --> 00:42:07,170
+constant، ثابت، لو انا استخدمت ال prism اتنين
+
+430
+00:42:07,170 --> 00:42:11,230
+ديوبتر، هيكون متساوي مع مين؟ مع العين، مع العين،
+
+431
+00:42:11,230 --> 00:42:11,390
+مع العين، مع العين، مع العين، مع العين، مع العين،
+
+432
+00:42:11,390 --> 00:42:11,750
+مع العين، مع العين، مع العين، مع العين، مع العين،
+
+433
+00:42:11,750 --> 00:42:13,590
+مع العين، مع العين، مع العين، مع العين، مع العين،
+
+434
+00:42:13,590 --> 00:42:16,450
+مع العين، مع العين، مع العين، مع العين، مع العين،
+
+435
+00:42:16,450 --> 00:42:16,510
+مع العين، مع العين، مع العين، مع العين، مع العين،
+
+436
+00:42:16,510 --> 00:42:26,590
+مع العينإن ارتفاع للصورة واضح؟
+
+437
+00:42:26,590 --> 00:42:30,850
+okay the eye behind the prism is therefore forced
+
+438
+00:42:30,850 --> 00:42:36,430
+to alleviate to take up fixationيعني نفس الكلام
+
+439
+00:42:36,430 --> 00:42:42,170
+اللي انا حكيته انه العين اللي خلف ال prism بقوة
+
+440
+00:42:42,170 --> 00:42:46,670
+هتعمل إيش elevation لأنه ال 16 بريسم ده يبتدر
+
+441
+00:42:46,670 --> 00:42:52,850
+تعتبر قوة كبيرة okay
+
+442
+00:42:52,850 --> 00:42:56,850
+the eye behind the prism is then observed يعني
+
+443
+00:42:56,850 --> 00:43:01,510
+العين اللي بتكون خلف الصورة هيصير لعملية observed
+
+444
+00:43:01,510 --> 00:43:02,490
+اللي هو فحص
+
+445
+00:43:11,220 --> 00:43:16,460
+الهدف انا من قياس حدة الإبصار في حالة ال fixation
+
+446
+00:43:16,460 --> 00:43:21,000
+test انه اشوف هل العين فيها center يعني هل هي
+
+447
+00:43:26,560 --> 00:43:31,120
+أو مثلا العيل مش ثابتة، هي الهدف من أنا ليش بقيس
+
+448
+00:43:31,120 --> 00:43:36,620
+ال visual acuity في حالة ال fixation test واضح؟
+
+449
+00:43:36,620 --> 00:43:41,260
+انه بدي اشوف ال central or uncentral steady or
+
+450
+00:43:41,260 --> 00:43:43,180
+unsteady بالنسبة للعيل
+
+451
+00:43:53,520 --> 00:43:59,540
+العين التاني اشمالها مش مغطاة واضح عشان انا احافظ
+
+452
+00:43:59,540 --> 00:44:03,600
+على ال fixation الثبات يعني مش مثلا انا الآن بعمل
+
+453
+00:44:03,600 --> 00:44:10,020
+ال test العين الأخرى بلاقيها مثلا مخدة زي مبرح في
+
+454
+00:44:10,020 --> 00:44:13,740
+بنات فحص ال visual acute كان المريض مثلا عامل turn
+
+455
+00:44:13,740 --> 00:44:18,320
+ولا عامل مثلا tiltبرضه لازم تكون العين الأخرى عايش
+
+456
+00:44:18,320 --> 00:44:24,000
+في ال fixation انه ثابتة واضح؟
+
+457
+00:44:24,000 --> 00:44:27,860
+if fixation immediately returns to the uncovered
+
+458
+00:44:27,860 --> 00:44:30,460
+eye, the visual acuity is impaired
+
+459
+00:44:34,690 --> 00:44:38,510
+ووضع ال fixation impaired بمعنى poor يعني ال
+
+460
+00:44:38,510 --> 00:44:43,710
+visual acuity هيكون لطفل انه ضعيف اذا ما عمل
+
+461
+00:44:43,710 --> 00:44:47,810
+fixation فبتلاقي دايما حتى الناس الاكبار اذا هو
+
+462
+00:44:47,810 --> 00:44:51,170
+اتعود انه مايعملش fixation دايما تلاقي يعمل ال
+
+463
+00:44:51,170 --> 00:44:56,310
+visual acuity راسه ايا على اليمين او الشمسفانا
+
+464
+00:44:56,310 --> 00:44:59,730
+دايما بقولكم هذه النقطة المهمة ان الراس دايما في
+
+465
+00:44:59,730 --> 00:45:02,430
+ال primary position دايما اركز على موضوع ال
+
+466
+00:45:02,430 --> 00:45:05,690
+primary position ان ال head and the eye is
+
+467
+00:45:05,690 --> 00:45:09,590
+straight واضح؟
+
+468
+00:45:09,590 --> 00:45:13,950
+while if fixation is maintained through a blink
+
+469
+00:45:13,950 --> 00:45:18,910
+ten seconds then visual acuity is goodإذا الطفل
+
+470
+00:45:18,910 --> 00:45:24,070
+جدر يحافظ على ال fixation خلال عشر ثوانة، بيكون
+
+471
+00:45:24,070 --> 00:45:28,350
+عنده ال visual acuity ماله جيد، يعني خلال العشر
+
+472
+00:45:28,350 --> 00:45:32,070
+ثوانة جدر يحافظ على ال fixation للعين، فانا
+
+473
+00:45:32,070 --> 00:45:35,010
+بيعنيلي ان ال visual acuity بتاع المريض جيد
+
+474
+00:45:38,440 --> 00:45:42,920
+Okay if the patient alternate fixation لو مرة
+
+475
+00:45:42,920 --> 00:45:46,060
+بيعمل fixation في ال right و مرة في ال left، إيش
+
+476
+00:45:46,060 --> 00:45:49,560
+بيعني لهذا؟ إنه ال visual acuity متساوي في
+
+477
+00:45:49,560 --> 00:45:53,700
+العينتين، يعني مرة بيستخدم ال right و مرة بيستخدم
+
+478
+00:45:53,700 --> 00:45:57,660
+ال left، بيكون ال fixation مرة في اليمين و مرة في
+
+479
+00:45:57,660 --> 00:46:02,140
+الإشمال، then the two eyes have equal vision
+
+480
+00:46:03,640 --> 00:46:06,820
+التجارب مرتبطة مع البرزم على الجهة الأخرى
+
+481
+00:46:06,820 --> 00:46:14,860
+مونوكولار
+
+482
+00:46:14,860 --> 00:46:19,580
+يجب أن يكون مركزيا مستقل ومحافظ في كل عين
+
+483
+00:46:26,140 --> 00:46:30,960
+Okay لازم أنه تكون العين central زائد أنه تكون
+
+484
+00:46:30,960 --> 00:46:35,500
+steady أنا عارف قد يكون شوية الفهم في الموضوع يعني
+
+485
+00:46:35,500 --> 00:46:40,360
+أنه تخيلي أكثر ما هو .. لأنه نظره لكن أنا ان شاء
+
+486
+00:46:40,360 --> 00:46:44,200
+الله هطبقلكم إياه في المعمل من ناحية المعمل هنحاول
+
+487
+00:46:44,200 --> 00:46:47,740
+أنه نجيب أطفال و نطبق هذا ال test لأن هذا ال test
+
+488
+00:46:47,740 --> 00:46:52,850
+مهم جدا ال fixation testلو رحت يعني في العالم كله
+
+489
+00:46:52,850 --> 00:46:56,210
+بيستخدم هذا الفحص اللي هو ال fixation test
+
+490
+00:46:56,210 --> 00:47:01,490
+correlation
+
+491
+00:47:01,490 --> 00:47:05,370
+between visual acuity and fixation patterns
+
+492
+00:47:05,370 --> 00:47:11,170
+العلاقة ما بين حدة الإبصار و ما بين اللي هو العين
+
+493
+00:47:11,170 --> 00:47:17,020
+اللي ماتكون ثابتةA gross eccentric fixation or
+
+494
+00:47:17,020 --> 00:47:21,060
+affixation يمّا يكون الطفل ما عندهوش fixation يعني
+
+495
+00:47:21,060 --> 00:47:24,920
+العين بمعنى إنه زائغة يعني يا على اليمين أو الشمال
+
+496
+00:47:24,920 --> 00:47:28,680
+إنه مافيش لها fixation هذا بيدل إنه إيش ال visual
+
+497
+00:47:28,680 --> 00:47:36,100
+acuity impaired or poor واحد ع ستين واضح؟
+
+498
+00:47:36,100 --> 00:47:42,900
+number twounsteady central fixation less than five
+
+499
+00:47:42,900 --> 00:47:48,400
+seconds الطفل عمل fixation لكن يما عمل fixation
+
+500
+00:47:48,400 --> 00:47:53,520
+أقل من خمس ثواني هذا بيدل أن ال visual acuity تقع
+
+501
+00:47:53,520 --> 00:47:59,710
+أربع على ستين واضح؟إذا الحالة الأولى الطفل ماعملش
+
+502
+00:47:59,710 --> 00:48:04,430
+fixation ال visual acuity قداش واحدة ستين الحالة
+
+503
+00:48:04,430 --> 00:48:08,530
+التانية عمل fixation لكن أقل من خمس ثواني احنا
+
+504
+00:48:08,530 --> 00:48:12,870
+قلنا ال normal قداش عشر ثواني يما بيعمل fixation
+
+505
+00:48:12,870 --> 00:48:17,190
+أقل من خمس ثواني بيكون ال visual acuity اربعة ستين
+
+506
+00:48:17,190 --> 00:48:24,060
+الحالة التالتة central steady fixationbut will not
+
+507
+00:48:24,060 --> 00:48:28,160
+hold fixation when the cover removed from the
+
+508
+00:48:28,160 --> 00:48:32,920
+other eye الان هو عمل fixation وممكن عمل fixation
+
+509
+00:48:32,920 --> 00:48:37,100
+عشر ثواني لكن أول ما بترفع ال cover من عين التانية
+
+510
+00:48:37,100 --> 00:48:42,060
+بتلاقي ايش ال fixation بيمتقل للعين الأخرى فبيكون
+
+511
+00:48:42,060 --> 00:48:46,140
+ال visual acuity للمريض من ستة ع ستين لست على أربع
+
+512
+00:48:46,140 --> 00:48:50,180
+عشرين يعني دايما انا في ال test هذا بدي اركز على
+
+513
+00:48:50,180 --> 00:48:51,140
+ال both eyes
+
+514
+00:48:57,800 --> 00:49:00,520
+الـ Fixation تغير للعين الأخرى، إذا الـ Visual
+
+515
+00:49:00,520 --> 00:49:05,120
+Acuity قداش من ستة ع ستين لستة على أربع و عشرين
+
+516
+00:49:05,120 --> 00:49:08,780
+Central
+
+517
+00:49:08,780 --> 00:49:12,980
+is steady fixation but will hold fixation with
+
+518
+00:49:12,980 --> 00:49:16,140
+deviating eye when the cover is removed but
+
+519
+00:49:16,140 --> 00:49:21,040
+prefers fixation with other eye برضه الطفل عمل
+
+520
+00:49:21,040 --> 00:49:27,360
+fixationوانا يما أزلت ال cover عن العين التانية
+
+521
+00:49:27,360 --> 00:49:32,540
+استمر ان المريض عنده ايه؟ Fixation لكن هو فضل ال
+
+522
+00:49:32,540 --> 00:49:37,480
+fixation بالعين التانية بكون هذا بيدل ان ال visual
+
+523
+00:49:37,480 --> 00:49:44,040
+acuity من 6 ع 18 ل 6 ع 9 again،
+
+524
+00:49:44,040 --> 00:49:48,620
+الآن المريض عمل fixation حلو؟ وعمل fixation ممكن
+
+525
+00:49:48,620 --> 00:49:52,820
+اكتر من خمس ثواني او عشر ثوانيرفعنا الغطاء عن
+
+526
+00:49:52,820 --> 00:49:58,560
+العين وجد انه عمل fixation لكن هو الطفل بعد فترة
+
+527
+00:49:58,560 --> 00:50:02,920
+عمل اللي هو fixation بالعين التانية يعني بعد مثلا
+
+528
+00:50:02,920 --> 00:50:07,820
+خمس ثواني فضل ال fixation بالعين الثانية واضح؟
+
+529
+00:50:07,820 --> 00:50:12,300
+فهنا ال visual acuity بتاع المريض يكون من 6 على ..
+
+530
+00:50:12,300 --> 00:50:19,060
+هو من 6 ع 12 ل 6 ع 9 او 18 ل 12 طيب لو عمل
+
+531
+00:50:19,060 --> 00:50:25,200
+alternativeSpontaneous يعني متبادل مرة في العين
+
+532
+00:50:25,200 --> 00:50:29,080
+اليمين و مرة في الشمال هان بيكون ال visual acuity
+
+533
+00:50:29,080 --> 00:50:33,980
+متساوي و بيكون indicate to good visual acuity ال
+
+534
+00:50:33,980 --> 00:50:40,060
+both eye 6 على 6 طبعا
+
+535
+00:50:40,060 --> 00:50:45,340
+هان هنطبقوا ال test للمريض يعني .. في حاجة؟
+
+536
+00:50:50,510 --> 00:50:53,650
+الاخر واحدة، لو المريض مثلا عمل مرة fixation في
+
+537
+00:50:53,650 --> 00:50:58,430
+العين اليمين و مرة في العين الشمال، okay؟ يعني مرة
+
+538
+00:50:58,430 --> 00:51:02,590
+عملها في اليمين، بعد عشر ثوان عمل في الشمال، بعد
+
+539
+00:51:02,590 --> 00:51:06,670
+العشر ثوان عمل في اليمين، يعني متبادل، alternate،
+
+540
+00:51:06,670 --> 00:51:09,810
+بيكون ال visual acuity good أو و بيكون ستة ع ستة
+
+541
+00:51:15,770 --> 00:51:21,950
+100 and 1000 suite test طبعا هذا فحص بسيط جدا و
+
+542
+00:51:21,950 --> 00:51:26,130
+معظم العيادات عندنا هان بيستخدموه لكن ده انه بدك
+
+543
+00:51:26,130 --> 00:51:31,170
+تعرفيه ان هذا الفحص فقط بيشير ان ال visual acuity
+
+544
+00:51:31,170 --> 00:51:34,030
+للمريض 6 على 24 او اقل
+
+545
+00:51:39,510 --> 00:51:44,370
+وشيء لازم هدول الحبات الحلو زي ما هي موجودة في
+
+546
+00:51:44,370 --> 00:51:49,650
+الصورة أنه يكونوا مختلفة الألوان، يعني أبيض، أحمر،
+
+547
+00:51:49,650 --> 00:51:53,710
+أزرق، أنه مايكونوش متساوين في اللون، مختلفين
+
+548
+00:51:53,710 --> 00:52:01,530
+الألوان و أشوف أنه مثلا أغطي العين الشمال للمريضو
+
+549
+00:52:01,530 --> 00:52:07,410
+اخلى المريض ايش انه .. او الطفل انه يلقط هذه ال ..
+
+550
+00:52:07,410 --> 00:52:13,230
+هذه ال sweet test او ال sweet هذه الحلوية طيب لو
+
+551
+00:52:13,230 --> 00:52:18,290
+لجيت مثلا الطفل بدور على هذه الحلوة، هو عارف انه
+
+552
+00:52:18,290 --> 00:52:24,000
+في كفة، لكن لو لجيته مثلا اجى و بدور عليهاواضح؟
+
+553
+00:52:24,000 --> 00:52:28,120
+انا بعرف انه ال poor عنده ال visual acuity او مثلا
+
+554
+00:52:28,120 --> 00:52:33,120
+ماعرفش يلجطها برضه نفس الحاجة هي عملية اللي هو ايش
+
+555
+00:52:33,120 --> 00:52:39,440
+ده شوف ال attention بتاع الطفل كده واضح؟ طبعا is a
+
+556
+00:52:39,440 --> 00:52:44,400
+gross taste which is seldom or rarely performed
+
+557
+00:52:44,400 --> 00:52:48,640
+يعني هو نادرا مابيستخدم لكن سبحان الله عندنا ايش
+
+558
+00:52:48,640 --> 00:52:53,770
+more commonin a principle if the child is able to
+
+559
+00:52:53,770 --> 00:52:59,110
+see and pick up a small sweet at 33 cm, visual
+
+560
+00:52:59,110 --> 00:53:05,770
+acuity is at least 6 over 24 إذا الطفل استطاع أنه
+
+561
+00:53:05,770 --> 00:53:09,570
+يلقط هذه الحلويات، بيكون عنده ال visual acuity
+
+562
+00:53:09,570 --> 00:53:12,050
+more than or equal
+
+563
+00:53:25,080 --> 00:53:30,400
+هذا إذا المريض او الطفل استطاع انه إيش يلقط هذه ال
+
+564
+00:53:30,400 --> 00:53:36,220
+sweetبس أهم شيء في ال sweet test أول شغلة أنه تكون
+
+565
+00:53:36,220 --> 00:53:41,100
+ال sweet مختلفة الألوان من ناحية ال contrast من
+
+566
+00:53:41,100 --> 00:53:45,900
+ناحية كمان أن الطفل مثلا ممكن هو بيستطيع أنه يشوف
+
+567
+00:53:45,900 --> 00:53:50,460
+اللون الأبيض لكن ما بيقدر يميز اللون الأحمر أو
+
+568
+00:53:50,460 --> 00:53:55,000
+اللون الأزرق فلازم أنه يكونوا مختلفين أيضا أنه ال
+
+569
+00:53:55,000 --> 00:53:57,300
+sweet test مايكونش في منطقة واحدة
+
+570
+00:54:18,080 --> 00:54:25,380
+بالنسبة لـ hundred and thousand sweet testطبعا هيك
+
+571
+00:54:25,380 --> 00:54:30,800
+بنكون اليوم اكتفينا في ال visual acuity test in
+
+572
+00:54:30,800 --> 00:54:34,460
+pre verbal children في المحاضرة القادمة ان شاء
+
+573
+00:54:34,460 --> 00:54:39,820
+الله هنكمل ال test بتاعون ال visual acuity in pre
+
+574
+00:54:39,820 --> 00:54:45,440
+verbal children اي سؤال اي استفسار شكرا يعطيكم
+
+575
+00:54:45,440 --> 00:54:45,880
+العافية
+
diff --git a/PL9fwy3NUQKwaBhVI6LPr803vc5wWl9Iy_/RObt8Y8hYFc_raw.json b/PL9fwy3NUQKwaBhVI6LPr803vc5wWl9Iy_/RObt8Y8hYFc_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..5792e0cdbe2cbe9fa0340605a5f06086e978d13c
--- /dev/null
+++ b/PL9fwy3NUQKwaBhVI6LPr803vc5wWl9Iy_/RObt8Y8hYFc_raw.json
@@ -0,0 +1 @@
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0.9794921875}], "temperature": 1.0}, {"id": 7, "seek": 20368, "start": 176.68, "end": 203.68, "text": "للعدسة ال cylinder باعرض ال astigmatic fan للمريض إذا شاف المريض كل الخطوط بنفس الوضوح هذا بيدل على إن المريض ما عندهوش astigmatism يعني ال astigmatism is not present for the patient طيب لو قال للمريض إنه في خط أوضح من الخط من الخطوط الأخرى يعني في خط واضح يعني", "tokens": [1211, 1211, 3615, 3215, 3794, 3660, 2423, 17884, 4724, 45761, 43042, 2423, 5357, 20181, 2399, 3429, 5296, 19528, 16572, 11242, 11933, 15730, 13412, 31845, 9673, 16572, 11242, 28242, 33962, 9566, 2407, 9566, 44945, 36178, 2423, 2407, 11242, 2407, 5016, 23758, 4724, 25708, 1211, 15844, 36145, 9673, 16572, 11242, 19446, 43242, 3224, 2407, 8592, 5357, 46496, 1434, 37495, 22653, 2423, 5357, 46496, 1434, 307, 406, 1974, 337, 264, 4537, 23032, 1829, 3555, 45164, 50239, 5296, 19528, 16572, 11242, 36145, 3224, 8978, 16490, 9566, 34051, 11242, 5016, 9154, 33962, 9566, 9154, 33962, 9566, 2407, 9566, 16247, 34740, 7578, 37495, 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astigmatism", "probability": 0.89404296875}, {"start": 191.0, "end": 191.4, "word": " يعني", "probability": 0.854248046875}, {"start": 191.4, "end": 191.48, "word": " ال", "probability": 0.72509765625}, {"start": 191.48, "end": 192.3, "word": " astigmatism", "probability": 0.8909505208333334}, {"start": 192.3, "end": 192.54, "word": " is", "probability": 0.74072265625}, {"start": 192.54, "end": 192.84, "word": " not", "probability": 0.95263671875}, {"start": 192.84, "end": 193.66, "word": " present", "probability": 0.89404296875}, {"start": 193.66, "end": 194.12, "word": " for", "probability": 0.89404296875}, {"start": 194.12, "end": 194.32, "word": " the", "probability": 0.857421875}, {"start": 194.32, "end": 194.66, "word": " patient", "probability": 0.9453125}, {"start": 194.66, "end": 195.88, "word": " طيب", "probability": 0.9462890625}, {"start": 195.88, "end": 196.46, "word": " لو", "probability": 0.76025390625}, {"start": 196.46, "end": 196.68, "word": " قال", "probability": 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202.44, "word": " خط", "probability": 0.995849609375}, {"start": 202.44, "end": 203.18, "word": " واضح", "probability": 0.9622395833333334}, {"start": 203.18, "end": 203.68, "word": " يعني", "probability": 0.960205078125}], "temperature": 1.0}, {"id": 8, "seek": 22766, "start": 204.08, "end": 227.66, "text": "more clear compared to the other lines هذا بمعنى ان المريض have a stigmatism يعني must be have a stigmatism okay يعني معناه ان هذا المريض لازم يكون عنده ايه a stigmatism طيب الآن هذا الخط لو فرضنا هي خط واضح", "tokens": [3138, 1850, 5347, 281, 264, 661, 3876, 23758, 4724, 2304, 3615, 1863, 7578, 16472, 9673, 16572, 11242, 362, 257, 342, 46496, 1434, 37495, 22653, 1633, 312, 362, 257, 342, 46496, 1434, 1392, 37495, 22653, 20449, 8315, 3224, 16472, 23758, 9673, 16572, 11242, 5296, 31377, 2304, 7251, 30544, 43242, 3224, 1975, 1829, 3224, 257, 342, 46496, 1434, 23032, 1829, 3555, 6024, 48506, 23758, 33962, 9566, 45164, 6156, 43042, 8315, 39896, 16490, 9566, 4032, 46958, 5016], 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{"start": 217.3, "end": 217.48, "word": " ان", "probability": 0.822265625}, {"start": 217.48, "end": 217.82, "word": " هذا", "probability": 0.92578125}, {"start": 217.82, "end": 218.4, "word": " المريض", "probability": 0.994140625}, {"start": 218.4, "end": 219.7, "word": " لازم", "probability": 0.9947916666666666}, {"start": 219.7, "end": 219.94, "word": " يكون", "probability": 0.994384765625}, {"start": 219.94, "end": 220.34, "word": " عنده", "probability": 0.99169921875}, {"start": 220.34, "end": 220.66, "word": " ايه", "probability": 0.8128255208333334}, {"start": 220.66, "end": 220.92, "word": " a", "probability": 0.34375}, {"start": 220.92, "end": 221.68, "word": " stigmatism", "probability": 0.9000651041666666}, {"start": 221.68, "end": 223.02, "word": " طيب", "probability": 0.974609375}, {"start": 223.02, "end": 223.8, "word": " الآن", "probability": 0.6851806640625}, {"start": 223.8, "end": 224.1, "word": " هذا", "probability": 0.943359375}, {"start": 224.1, "end": 224.52, 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{"start": 253.45, "end": 253.61, "word": " ال", "probability": 0.896484375}, {"start": 253.61, "end": 253.91, "word": " axis", "probability": 0.96044921875}, {"start": 253.91, "end": 254.51, "word": " تسعين", "probability": 0.9700927734375}, {"start": 254.51, "end": 254.89, "word": " صح", "probability": 0.92529296875}, {"start": 254.89, "end": 255.43, "word": " اللي", "probability": 0.85498046875}, {"start": 255.43, "end": 255.61, "word": " هو", "probability": 0.98828125}, {"start": 255.61, "end": 255.75, "word": " ال", "probability": 0.95703125}, {"start": 255.75, "end": 256.15, "word": " vertical", "probability": 0.92138671875}, {"start": 256.15, "end": 256.61, "word": " line", "probability": 0.970703125}, {"start": 256.61, "end": 257.41, "word": " لو", "probability": 0.87255859375}, {"start": 257.41, "end": 257.65, "word": " جلي", "probability": 0.896484375}, {"start": 257.65, "end": 257.93, "word": " هذا", "probability": 0.6826171875}, {"start": 257.93, "end": 258.45, "word": " 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renders بمعنى reduces the outline اي بمعنى the shape شكل of the whole lines الخطوط كلها يعني كل الخطوط الموجودة في الastigmatic fan هتقللها equally clear it's the amount of astigmatism", "tokens": [13690, 8807, 6125, 433, 4724, 2304, 3615, 1863, 7578, 16472, 18863, 3215, 3794, 3660, 2423, 33546, 9566, 2407, 7649, 10632, 46740, 15730, 21136, 3555, 3555, 8032, 2655, 19913, 3224, 2288, 16472, 3224, 8032, 2655, 4587, 1211, 1211, 6125, 433, 4724, 2304, 3615, 1863, 7578, 18081, 264, 16387, 1975, 1829, 4724, 2304, 3615, 1863, 7578, 264, 3909, 13412, 28820, 295, 264, 1379, 3876, 33962, 9566, 2407, 9566, 28242, 11296, 37495, 22653, 28242, 33962, 9566, 2407, 9566, 9673, 29245, 23328, 3660, 8978, 2423, 525, 20181, 2399, 3429, 8032, 2655, 4587, 1211, 1211, 11296, 12309, 1850, 309, 311, 264, 2372, 295, 5357, 46496, 1434], "avg_logprob": -0.19454657520149268, "compression_ratio": 1.6199095022624435, "no_speech_prob": 0.0, "words": [{"start": 904.13, "end": 904.59, "word": "which", "probability": 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according", "probability": 0.9267578125}, {"start": 962.87, "end": 963.15, "word": " to", "probability": 0.9833984375}, {"start": 963.15, "end": 963.53, "word": " the", "probability": 0.93212890625}, {"start": 963.53, "end": 964.35, "word": " sign", "probability": 0.6845703125}, {"start": 964.35, "end": 964.61, "word": " of", "probability": 0.97998046875}, {"start": 964.61, "end": 964.77, "word": " the", "probability": 0.92431640625}, {"start": 964.77, "end": 965.11, "word": " cylinder", "probability": 0.74072265625}, {"start": 965.11, "end": 965.45, "word": " lens", "probability": 0.84375}, {"start": 965.45, "end": 966.03, "word": " يعني", "probability": 0.92578125}, {"start": 966.03, "end": 966.31, "word": " الآن", "probability": 0.6903076171875}, {"start": 966.31, "end": 966.45, "word": " لو", "probability": 0.98876953125}, {"start": 966.45, "end": 966.75, "word": " واحد", "probability": 0.987060546875}, {"start": 966.75, "end": 967.39, "word": " بيشتغل", "probability": 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1530.34, "end": 1530.98, "word": " حصلش", "probability": 0.6671549479166666}, {"start": 1530.98, "end": 1532.02, "word": " فيها؟", "probability": 0.8670247395833334}, {"start": 1532.02, "end": 1533.96, "word": " ولا", "probability": 0.382568359375}, {"start": 1533.96, "end": 1534.22, "word": " مع", "probability": 0.9716796875}, {"start": 1534.22, "end": 1534.52, "word": " كلهم", "probability": 0.6690673828125}, {"start": 1534.52, "end": 1534.74, "word": " حتى", "probability": 0.81005859375}, {"start": 1534.74, "end": 1534.84, "word": " لو", "probability": 0.89013671875}, {"start": 1534.84, "end": 1535.04, "word": " كان", "probability": 0.9814453125}, {"start": 1535.04, "end": 1535.24, "word": " هنا", "probability": 0.7763671875}, {"start": 1535.24, "end": 1535.42, "word": " open", "probability": 0.2059326171875}, {"start": 1535.42, "end": 1535.94, "word": " media", "probability": 0.464111328125}, {"start": 1535.94, "end": 1537.78, "word": " هذا", "probability": 0.471923828125}, {"start": 1537.78, "end": 1538.76, "word": " بيحدد", "probability": 0.85284423828125}, {"start": 1538.76, "end": 1539.08, "word": " بس", "probability": 0.992431640625}, {"start": 1539.08, "end": 1539.24, "word": " ال", "probability": 0.97607421875}, {"start": 1539.24, "end": 1539.7, "word": " access", "probability": 0.5888671875}, {"start": 1539.7, "end": 1540.1, "word": " هي", "probability": 0.67578125}, {"start": 1540.1, "end": 1540.62, "word": " use", "probability": 0.80126953125}, {"start": 1540.62, "end": 1540.84, "word": " to", "probability": 0.98095703125}, {"start": 1540.84, "end": 1541.28, "word": " detect", "probability": 0.98291015625}, {"start": 1541.28, "end": 1541.58, "word": " انا", "probability": 0.685302734375}, {"start": 1541.58, "end": 1542.04, "word": " لو", "probability": 0.990234375}, {"start": 1542.04, "end": 1542.52, "word": " تصور", "probability": 0.97314453125}, {"start": 1542.52, "end": 1542.96, "word": " شوية", "probability": 0.91455078125}, {"start": 1542.96, "end": 1543.64, "word": " بكمل", "probability": 0.9869791666666666}], "temperature": 1.0}, {"id": 60, "seek": 156689, "start": 1544.43, "end": 1566.89, "text": "Use to detect إذا بيستخدم لكشف the axis of astigmatism if present، إذا بيستخدم لكشف مين؟ ال axis داعي ال astigmatism، يعني أنا بدي أتأكد إن هل هذا ال axis اللي بدي أديه للمريض اللي طلعته من جهاز ال auto refractometer أو ال retinascope صح أو خطأ، هي الهدف منه", "tokens": [52, 405, 281, 5531, 11933, 15730, 4724, 1829, 14851, 9778, 40448, 5296, 4117, 8592, 5172, 264, 10298, 295, 5357, 46496, 1434, 498, 1974, 12399, 11933, 15730, 4724, 1829, 14851, 9778, 40448, 5296, 4117, 8592, 5172, 3714, 9957, 22807, 2423, 10298, 11778, 45761, 1829, 2423, 5357, 46496, 1434, 12399, 37495, 22653, 41850, 4724, 16254, 5551, 2655, 10721, 4117, 3215, 36145, 8032, 1211, 23758, 2423, 10298, 13672, 1829, 4724, 16254, 5551, 16254, 3224, 5296, 19528, 16572, 11242, 13672, 1829, 23032, 1211, 34268, 3224, 9154, 10874, 3224, 31377, 2423, 8399, 45353, 13606, 34051, 2423, 1533, 17094, 13960, 20328, 5016, 34051, 16490, 9566, 10721, 12399, 39896, 2423, 3224, 3215, 5172, 9154, 3224], "avg_logprob": -0.1823394479007896, "compression_ratio": 1.645021645021645, "no_speech_prob": 0.0, "words": [{"start": 1544.43, "end": 1544.93, "word": "Use", "probability": 0.6190185546875}, {"start": 1544.93, "end": 1545.07, "word": " to", "probability": 0.92822265625}, {"start": 1545.07, "end": 1545.55, "word": " detect", "probability": 0.97509765625}, {"start": 1545.55, "end": 1545.99, "word": " إذا", "probability": 0.4998779296875}, {"start": 1545.99, "end": 1546.93, "word": " بيستخدم", "probability": 0.983984375}, {"start": 1546.93, "end": 1547.69, "word": " لكشف", "probability": 0.9759521484375}, {"start": 1547.69, "end": 1548.13, "word": " the", "probability": 0.406494140625}, {"start": 1548.13, "end": 1548.73, "word": " axis", "probability": 0.744140625}, {"start": 1548.73, "end": 1549.19, "word": " of", "probability": 0.97998046875}, {"start": 1549.19, "end": 1550.17, "word": " astigmatism", "probability": 0.8997395833333334}, {"start": 1550.17, "end": 1550.55, "word": " if", "probability": 0.52734375}, {"start": 1550.55, "end": 1551.67, "word": " present،", "probability": 0.59130859375}, {"start": 1551.67, "end": 1551.93, "word": " إذا", "probability": 0.906494140625}, {"start": 1551.93, "end": 1552.67, "word": " بيستخدم", "probability": 0.99580078125}, {"start": 1552.67, "end": 1553.25, "word": " لكشف", "probability": 0.9857177734375}, {"start": 1553.25, "end": 1553.77, "word": " مين؟", "probability": 0.8279622395833334}, {"start": 1553.77, "end": 1554.19, "word": " ال", "probability": 0.92138671875}, {"start": 1554.19, "end": 1554.59, "word": " axis", "probability": 0.79150390625}, {"start": 1554.59, "end": 1554.97, "word": " داعي", "probability": 0.579833984375}, {"start": 1554.97, "end": 1555.05, "word": " ال", "probability": 0.85986328125}, {"start": 1555.05, "end": 1556.17, "word": " astigmatism،", "probability": 0.7650146484375}, {"start": 1556.17, "end": 1556.47, "word": " يعني", "probability": 0.949951171875}, {"start": 1556.47, "end": 1556.71, "word": " أنا", "probability": 0.85009765625}, {"start": 1556.71, "end": 1556.97, "word": " بدي", "probability": 0.889892578125}, {"start": 1556.97, "end": 1557.55, "word": " أتأكد", "probability": 0.9650390625}, {"start": 1557.55, "end": 1557.77, "word": " إن", "probability": 0.4521484375}, {"start": 1557.77, "end": 1558.11, "word": " هل", "probability": 0.7236328125}, {"start": 1558.11, "end": 1558.41, "word": " هذا", "probability": 0.87939453125}, {"start": 1558.41, "end": 1558.59, "word": " ال", "probability": 0.99560546875}, {"start": 1558.59, "end": 1559.01, "word": " axis", "probability": 0.93896484375}, {"start": 1559.01, "end": 1559.29, "word": " اللي", "probability": 0.95703125}, {"start": 1559.29, "end": 1559.53, "word": " بدي", "probability": 0.65576171875}, {"start": 1559.53, "end": 1559.81, "word": " أديه", "probability": 0.8821614583333334}, {"start": 1559.81, "end": 1560.33, "word": " للمريض", "probability": 0.939697265625}, {"start": 1560.33, "end": 1560.53, "word": " اللي", "probability": 0.931396484375}, {"start": 1560.53, "end": 1561.05, "word": " طلعته", "probability": 0.9876708984375}, {"start": 1561.05, "end": 1561.19, "word": " من", "probability": 0.99462890625}, {"start": 1561.19, "end": 1561.57, "word": " جهاز", "probability": 0.9807942708333334}, {"start": 1561.57, "end": 1561.71, "word": " ال", "probability": 0.95361328125}, {"start": 1561.71, "end": 1561.95, "word": " auto", "probability": 0.39404296875}, {"start": 1561.95, "end": 1562.77, "word": " refractometer", "probability": 0.909912109375}, {"start": 1562.77, "end": 1563.17, "word": " أو", "probability": 0.8330078125}, {"start": 1563.17, "end": 1563.51, "word": " ال", "probability": 0.916015625}, {"start": 1563.51, "end": 1564.15, "word": " retinascope", "probability": 0.7307942708333334}, {"start": 1564.15, "end": 1564.45, "word": " صح", "probability": 0.98828125}, {"start": 1564.45, "end": 1564.63, "word": " أو", "probability": 0.955078125}, {"start": 1564.63, "end": 1565.89, "word": " خطأ،", "probability": 0.9608154296875}, {"start": 1565.89, "end": 1566.09, "word": " هي", "probability": 0.27978515625}, {"start": 1566.09, "end": 1566.55, "word": " الهدف", "probability": 0.9697265625}, {"start": 1566.55, "end": 1566.89, "word": " منه", "probability": 0.99072265625}], "temperature": 1.0}, {"id": 61, "seek": 158955, "start": 1567.97, "end": 1589.55, "text": "إذا ليش بيستخدم الستينوبيكسليت to detect the axis of the astigmatism if present؟ okay إذا بيستخدم في تحديد ال axis بتاع العدسة الإستوانية إذا المريض كان عنده إيه astigmatism فكرته تختلف عن مين بينهم؟", "tokens": [28814, 15730, 32239, 8592, 4724, 1829, 14851, 9778, 40448, 2423, 14851, 9957, 2407, 21292, 4117, 3794, 20292, 2655, 281, 5531, 264, 10298, 295, 264, 5357, 46496, 1434, 498, 1974, 22807, 1392, 11933, 15730, 4724, 1829, 14851, 9778, 40448, 8978, 6055, 5016, 16254, 3215, 2423, 10298, 39894, 45761, 18863, 3215, 3794, 3660, 33688, 14851, 2407, 7649, 10632, 11933, 15730, 9673, 16572, 11242, 25961, 43242, 3224, 11933, 1829, 3224, 5357, 46496, 1434, 6156, 4117, 43500, 3224, 6055, 46456, 46538, 18871, 3714, 9957, 49374, 16095, 22807], "avg_logprob": -0.2669270730444363, "compression_ratio": 1.5532994923857868, "no_speech_prob": 0.0, "words": [{"start": 1567.97, "end": 1568.31, "word": "إذا", "probability": 0.70654296875}, {"start": 1568.31, "end": 1568.81, "word": " ليش", "probability": 0.965087890625}, {"start": 1568.81, "end": 1569.51, "word": " بيستخدم", "probability": 0.98203125}, {"start": 1569.51, "end": 1570.77, "word": " الستينوبيكسليت", "probability": 0.6192287868923612}, {"start": 1570.77, "end": 1571.23, "word": " to", "probability": 0.2042236328125}, {"start": 1571.23, "end": 1571.85, "word": " detect", "probability": 0.95947265625}, {"start": 1571.85, "end": 1572.29, "word": " the", "probability": 0.869140625}, {"start": 1572.29, "end": 1572.67, "word": " axis", "probability": 0.82080078125}, {"start": 1572.67, "end": 1573.21, "word": " of", "probability": 0.97509765625}, {"start": 1573.21, "end": 1573.49, "word": " the", "probability": 0.8330078125}, {"start": 1573.49, "end": 1574.39, "word": " astigmatism", "probability": 0.9583333333333334}, {"start": 1574.39, "end": 1574.75, "word": " if", "probability": 0.75830078125}, {"start": 1574.75, "end": 1576.01, "word": " present؟", "probability": 0.74951171875}, {"start": 1576.01, "end": 1576.21, "word": " okay", "probability": 0.41748046875}, {"start": 1576.21, "end": 1577.01, "word": " إذا", "probability": 0.70263671875}, {"start": 1577.01, "end": 1577.85, "word": " بيستخدم", "probability": 0.99384765625}, {"start": 1577.85, "end": 1578.41, "word": " في", "probability": 0.8779296875}, {"start": 1578.41, "end": 1579.19, "word": " تحديد", "probability": 0.9862060546875}, {"start": 1579.19, "end": 1579.61, "word": " ال", "probability": 0.9775390625}, {"start": 1579.61, "end": 1580.11, "word": " axis", "probability": 0.74169921875}, {"start": 1580.11, "end": 1580.69, "word": " بتاع", "probability": 0.59564208984375}, {"start": 1580.69, "end": 1581.33, "word": " العدسة", "probability": 0.9263916015625}, {"start": 1581.33, "end": 1582.37, "word": " الإستوانية", "probability": 0.767919921875}, {"start": 1582.37, "end": 1582.91, "word": " إذا", "probability": 0.941650390625}, {"start": 1582.91, "end": 1583.31, "word": " المريض", "probability": 0.96826171875}, {"start": 1583.31, "end": 1583.55, "word": " كان", "probability": 0.9931640625}, {"start": 1583.55, "end": 1583.93, "word": " عنده", "probability": 0.989013671875}, {"start": 1583.93, "end": 1584.19, "word": " إيه", "probability": 0.7391357421875}, {"start": 1584.19, "end": 1586.03, "word": " astigmatism", "probability": 0.7539876302083334}, {"start": 1586.03, "end": 1587.05, "word": " فكرته", "probability": 0.75677490234375}, {"start": 1587.05, "end": 1587.67, "word": " تختلف", "probability": 0.99365234375}, {"start": 1587.67, "end": 1587.89, "word": " عن", "probability": 0.96142578125}, {"start": 1587.89, "end": 1588.19, "word": " مين", "probability": 0.915283203125}, {"start": 1588.19, "end": 1589.55, "word": " بينهم؟", "probability": 0.5575358072916666}], "temperature": 1.0}, {"id": 62, "seek": 161857, "start": 1592.83, "end": 1618.57, "text": "when put before the eye يمّا أنا بضع ال stenopic slit أمام العين it allows only rays of light in a particular meridian to enter the eye إذا هيسمح فقط لحزمة من الضوء أنه تدخل بشكل إيه elongated اللي هو طولة يعني فقط من ال slit اللي موجود في منتصف من ال disk", "tokens": [18822, 829, 949, 264, 3313, 7251, 2304, 11703, 995, 41850, 4724, 11242, 3615, 2423, 28031, 40216, 43182, 5551, 2304, 10943, 18863, 9957, 309, 4045, 787, 24417, 295, 1442, 294, 257, 1729, 3551, 34681, 281, 3242, 264, 3313, 11933, 15730, 39896, 38251, 5016, 6156, 47432, 5296, 5016, 11622, 46007, 9154, 6024, 114, 2407, 38207, 14739, 3224, 6055, 3215, 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before the eye قبل العين the vertical meridian قلنا دايما ال meridian هو عكس مين ال axis", "tokens": [9566, 1829, 3555, 498, 264, 43182, 11933, 15730, 29538, 27188, 2655, 5016, 3660, 1392, 2423, 40786, 770, 4340, 2405, 307, 7074, 3714, 41361, 11296, 12750, 8032, 47302, 4724, 2304, 3615, 1863, 7578, 5551, 5172, 38436, 20666, 8592, 28820, 23758, 30767, 1829, 19446, 8978, 34892, 38251, 3660, 949, 264, 3313, 12174, 36150, 18863, 9957, 264, 9429, 3551, 34681, 12174, 1211, 8315, 11778, 47302, 15042, 2423, 3551, 34681, 31439, 6225, 4117, 3794, 3714, 9957, 2423, 10298], "avg_logprob": -0.19010417143503824, "compression_ratio": 1.4093023255813955, "no_speech_prob": 0.0, "words": [{"start": 1623.8, "end": 1624.54, "word": "طيب", "probability": 0.9560546875}, {"start": 1624.54, "end": 1624.8, "word": " if", "probability": 0.59375}, {"start": 1624.8, "end": 1625.0, "word": " the", "probability": 0.89453125}, {"start": 1625.0, "end": 1625.38, "word": " slit", "probability": 0.9873046875}, {"start": 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" الastigmatic", "probability": 0.826904296875}, {"start": 2309.06, "end": 2309.76, "word": " fan،", "probability": 0.693603515625}, {"start": 2309.76, "end": 2309.88, "word": " ال", "probability": 0.81005859375}, {"start": 2309.88, "end": 2310.14, "word": " more", "probability": 0.794921875}, {"start": 2310.14, "end": 2310.98, "word": " clear،", "probability": 0.711181640625}, {"start": 2310.98, "end": 2311.22, "word": " less", "probability": 0.91015625}, {"start": 2311.22, "end": 2311.98, "word": " immature،", "probability": 0.4130859375}, {"start": 2311.98, "end": 2312.6, "word": " ال", "probability": 0.87255859375}, {"start": 2312.6, "end": 2312.84, "word": " less", "probability": 0.900390625}, {"start": 2312.84, "end": 2313.54, "word": " clear،", "probability": 0.864501953125}, {"start": 2313.54, "end": 2313.96, "word": " more", "probability": 0.96435546875}, {"start": 2313.96, "end": 2314.88, "word": " immature،", "probability": 0.868408203125}, {"start": 2314.88, "end": 2315.12, 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"end": 2343.85, "word": " الفرق", "probability": 0.98681640625}, {"start": 2343.85, "end": 2344.03, "word": " ما", "probability": 0.89892578125}, {"start": 2344.03, "end": 2344.27, "word": " بين", "probability": 0.9833984375}, {"start": 2344.27, "end": 2344.53, "word": " ال", "probability": 0.84619140625}, {"start": 2344.53, "end": 2345.15, "word": " astigmatic", "probability": 0.84423828125}, {"start": 2345.15, "end": 2345.53, "word": " fan", "probability": 0.94482421875}, {"start": 2345.53, "end": 2346.01, "word": " و", "probability": 0.875}, {"start": 2346.01, "end": 2346.35, "word": " ال", "probability": 0.74755859375}, {"start": 2346.35, "end": 2346.79, "word": " stenopic", "probability": 0.95263671875}, {"start": 2346.79, "end": 2347.29, "word": " slit", "probability": 0.9794921875}, {"start": 2347.29, "end": 2349.69, "word": " طبعا", "probability": 0.9921875}, {"start": 2349.69, "end": 2350.17, "word": " انبيه", "probability": 0.4482828776041667}, {"start": 2350.17, "end": 2350.75, "word": " اختصار", "probability": 0.976318359375}, {"start": 2350.75, "end": 2351.01, "word": " ل", "probability": 0.771484375}, {"start": 2351.01, "end": 2351.35, "word": " note", "probability": 0.499267578125}, {"start": 2351.35, "end": 2351.63, "word": " book", "probability": 0.50830078125}, {"start": 2351.63, "end": 2352.19, "word": " okay", "probability": 0.73193359375}], "temperature": 1.0}, {"id": 92, "seek": 238003, "start": 2353.81, "end": 2380.03, "text": "دائما كلمة كما بكتب الدكتور او الأستاذ notebook ك abbreviation اختصار okay rotation of drill screw طبعا هذه طريقة بسيطة جدا انه بتعتمد على المريض بعد ما انا بعمل ال objective refraction سواء كان ال retinascope او ال auto refractometer", "tokens": [3215, 16373, 15042, 9122, 19528, 3660, 9122, 15042, 4724, 4117, 2655, 3555, 32748, 4117, 2655, 13063, 1975, 2407, 16247, 14851, 45636, 21060, 9122, 35839, 399, 1975, 46456, 9381, 9640, 1392, 12447, 295, 11392, 5630, 23032, 3555, 3615, 995, 29538, 23032, 16572, 28671, 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okay فبيحرك اللي هو البرغي هذا، لكن بطلب من المريض انه يحرك بشكل ايه؟ بطيء، مش يحرك بشكل سريع عشان .. طيب الحركة اما تكون بشكل بطيء، هذا المريض هيستطيع انه ايه؟ يلاحظ اللي هو التغير", "tokens": [3555, 9566, 46152, 9154, 9673, 16572, 11242, 39182, 19446, 11331, 9566, 18863, 3215, 3794, 3660, 12399, 21136, 26895, 41260, 2288, 12399, 16472, 3224, 7251, 25957, 1211, 6225, 42213, 10632, 1975, 1829, 3224, 22807, 6055, 5016, 16572, 4117, 12399, 16472, 3224, 6055, 5016, 16572, 4117, 32767, 9957, 22807, 9154, 16490, 1211, 6027, 2423, 5630, 12399, 5630, 4724, 2304, 3615, 1863, 7578, 4724, 2288, 17082, 1829, 12399, 1392, 6156, 21292, 5016, 31747, 13672, 1829, 31439, 2423, 26890, 17082, 1829, 23758, 12399, 44381, 4724, 9566, 46152, 9154, 9673, 16572, 11242, 16472, 3224, 7251, 5016, 31747, 4724, 8592, 28820, 1975, 1829, 3224, 22807, 4724, 9566, 1829, 38207, 12399, 37893, 7251, 5016, 31747, 4724, 8592, 28820, 8608, 16572, 3615, 6225, 8592, 7649, 4386, 23032, 1829, 3555, 21542, 31747, 3660, 1975, 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"probability": 0.609375}, {"start": 2468.28, "end": 2468.52, "word": " هو", "probability": 0.94140625}, {"start": 2468.52, "end": 2468.92, "word": " عبارة", "probability": 0.9940185546875}, {"start": 2468.92, "end": 2469.12, "word": " عن", "probability": 0.9912109375}, {"start": 2469.12, "end": 2469.4, "word": " ايه؟", "probability": 0.8707275390625}, {"start": 2469.4, "end": 2469.76, "word": " disk", "probability": 0.4833984375}, {"start": 2469.76, "end": 2470.0, "word": " و", "probability": 0.611328125}, {"start": 2470.0, "end": 2470.44, "word": " بتكون", "probability": 0.904541015625}, {"start": 2470.44, "end": 2470.68, "word": " من", "probability": 0.9951171875}, {"start": 2470.68, "end": 2471.04, "word": " تلت", "probability": 0.9345703125}, {"start": 2471.04, "end": 2471.84, "word": " three", "probability": 0.25390625}, {"start": 2471.84, "end": 2472.9, "word": " components", "probability": 0.92041015625}, {"start": 2472.9, "end": 2473.5, "word": " okay", "probability": 0.5126953125}, {"start": 2473.5, "end": 2474.3, "word": " تلت", "probability": 0.87841796875}, {"start": 2474.3, "end": 2474.5, "word": " اللي", "probability": 0.90478515625}, {"start": 2474.5, "end": 2474.86, "word": " هو", "probability": 0.9609375}, {"start": 2474.86, "end": 2475.84, "word": " فتحات", "probability": 0.8858642578125}, {"start": 2475.84, "end": 2476.24, "word": " ممكن", "probability": 0.984375}, {"start": 2476.24, "end": 2476.56, "word": " أحط", "probability": 0.8232421875}, {"start": 2476.56, "end": 2476.84, "word": " فيها", "probability": 0.994140625}, {"start": 2476.84, "end": 2477.38, "word": " الاسفير", "probability": 0.932373046875}, {"start": 2477.38, "end": 2477.66, "word": " ال", "probability": 0.51025390625}, {"start": 2477.66, "end": 2478.04, "word": " cylinder", "probability": 0.371826171875}, {"start": 2478.04, "end": 2478.74, "word": " زائد", "probability": 0.7705891927083334}, {"start": 2478.74, "end": 2478.94, "word": " ال", "probability": 0.97705078125}, {"start": 2478.94, "end": 2479.52, "word": " accessory", "probability": 0.896484375}, {"start": 2479.52, "end": 2480.36, "word": " lens", "probability": 0.9541015625}], "temperature": 1.0}, {"id": 97, "seek": 248702, "start": 2480.94, "end": 2487.02, "text": "Okay لكن حتى لو اتحاربكت العدسة الاسمية have the same power in all the ingredients", "tokens": [8297, 44381, 11331, 49975, 45164, 1975, 2655, 5016, 9640, 3555, 4117, 2655, 18863, 3215, 3794, 3660, 2423, 32277, 2304, 10632, 362, 264, 912, 1347, 294, 439, 264, 6952], "avg_logprob": -0.21012931445549274, "compression_ratio": 1.0373831775700935, "no_speech_prob": 0.0, "words": [{"start": 2480.94, "end": 2481.34, "word": "Okay", "probability": 0.55908203125}, {"start": 2481.34, "end": 2482.0, "word": " لكن", "probability": 0.447509765625}, {"start": 2482.0, "end": 2482.28, "word": " حتى", "probability": 0.9541015625}, {"start": 2482.28, "end": 2482.46, "word": " لو", "probability": 0.98828125}, {"start": 2482.46, "end": 2483.46, "word": " اتحاربكت", "probability": 0.8528529575892857}, {"start": 2483.46, "end": 2483.9, "word": " العدسة", "probability": 0.965576171875}, {"start": 2483.9, "end": 2484.3, "word": " الاسمية", "probability": 0.72784423828125}, {"start": 2484.3, "end": 2484.92, "word": " have", "probability": 0.493896484375}, {"start": 2484.92, "end": 2485.1, "word": " the", "probability": 0.93017578125}, {"start": 2485.1, "end": 2485.38, "word": " same", "probability": 0.90380859375}, {"start": 2485.38, "end": 2485.68, "word": " power", "probability": 0.90478515625}, {"start": 2485.68, "end": 2485.92, "word": " in", "probability": 0.97119140625}, {"start": 2485.92, "end": 2486.34, "word": " all", "probability": 0.96337890625}, {"start": 2486.34, "end": 2486.7, "word": " the", "probability": 0.90771484375}, {"start": 2486.7, "end": 2487.02, "word": " ingredients", "probability": 0.734375}], "temperature": 1.0}, {"id": 98, "seek": 251652, "start": 2488.64, "end": 2516.52, "text": "to rotate the cylindrical lens in the trial frame, the patient will rotate the screw until he or she sees the best clear image يعني انه لحد ما انا بصل لأفضل رؤية لمين للمريض يعني انا برشد المريض انه يحرك البرغي هذا لحد ما يصل إلى صورة ايش بتكون هي ال best clear image له", "tokens": [1353, 13121, 264, 28044, 15888, 6765, 294, 264, 7308, 3920, 11, 264, 4537, 486, 13121, 264, 5630, 1826, 415, 420, 750, 8194, 264, 1151, 1850, 3256, 37495, 22653, 16472, 3224, 5296, 24401, 19446, 1975, 8315, 4724, 36520, 5296, 10721, 5172, 11242, 1211, 12602, 33604, 10632, 32767, 9957, 5296, 19528, 16572, 11242, 37495, 22653, 1975, 8315, 4724, 2288, 8592, 3215, 9673, 16572, 11242, 16472, 3224, 7251, 5016, 31747, 2423, 26890, 17082, 1829, 23758, 5296, 24401, 19446, 7251, 36520, 30731, 20328, 13063, 3660, 1975, 1829, 8592, 39894, 30544, 39896, 2423, 1151, 1850, 3256, 46740], "avg_logprob": -0.16969086213778423, "compression_ratio": 1.6327433628318584, "no_speech_prob": 0.0, "words": [{"start": 2488.64, "end": 2488.86, "word": "to", "probability": 0.53759765625}, {"start": 2488.86, "end": 2489.22, "word": " rotate", "probability": 0.97021484375}, {"start": 2489.22, "end": 2489.5, "word": " the", "probability": 0.92041015625}, {"start": 2489.5, "end": 2490.22, "word": " cylindrical", "probability": 0.948974609375}, {"start": 2490.22, "end": 2490.82, "word": " lens", "probability": 0.94189453125}, {"start": 2490.82, "end": 2491.12, "word": " in", "probability": 0.9599609375}, {"start": 2491.12, "end": 2491.26, "word": " the", "probability": 0.9013671875}, {"start": 2491.26, "end": 2491.52, "word": " trial", "probability": 0.63037109375}, {"start": 2491.52, "end": 2491.98, "word": " frame,", "probability": 0.8896484375}, {"start": 2492.34, "end": 2492.44, "word": " the", "probability": 0.85791015625}, {"start": 2492.44, "end": 2492.84, "word": " patient", "probability": 0.9033203125}, {"start": 2492.84, "end": 2493.12, "word": " will", "probability": 0.9130859375}, {"start": 2493.12, "end": 2493.5, "word": " rotate", "probability": 0.96044921875}, {"start": 2493.5, "end": 2493.78, "word": " the", "probability": 0.9267578125}, {"start": 2493.78, "end": 2494.12, "word": " screw", "probability": 0.95166015625}, {"start": 2494.12, "end": 2494.58, "word": " until", "probability": 0.88427734375}, {"start": 2494.58, "end": 2494.84, "word": " he", "probability": 0.95166015625}, {"start": 2494.84, "end": 2496.3, "word": " or", "probability": 0.361083984375}, {"start": 2496.3, "end": 2496.68, "word": " she", "probability": 0.94091796875}, {"start": 2496.68, "end": 2497.16, "word": " sees", "probability": 0.5087890625}, {"start": 2497.16, "end": 2497.74, "word": " the", "probability": 0.93017578125}, {"start": 2497.74, "end": 2498.1, "word": " best", "probability": 0.91064453125}, {"start": 2498.1, "end": 2498.68, "word": " clear", "probability": 0.94189453125}, {"start": 2498.68, "end": 2499.16, "word": " image", "probability": 0.94580078125}, {"start": 2499.16, "end": 2500.02, "word": " يعني", "probability": 0.939453125}, {"start": 2500.02, "end": 2500.48, "word": " انه", "probability": 0.680908203125}, {"start": 2500.48, "end": 2500.84, "word": " لحد", "probability": 0.990478515625}, {"start": 2500.84, "end": 2501.48, "word": " ما", "probability": 0.955078125}, {"start": 2501.48, "end": 2501.72, "word": " انا", "probability": 0.79248046875}, {"start": 2501.72, "end": 2502.1, "word": " بصل", "probability": 0.9326171875}, {"start": 2502.1, "end": 2502.92, "word": " لأفضل", "probability": 0.93603515625}, {"start": 2502.92, "end": 2503.24, "word": " رؤية", "probability": 0.9816080729166666}, {"start": 2503.24, "end": 2503.68, "word": " لمين", "probability": 0.788818359375}, {"start": 2503.68, "end": 2504.74, "word": " للمريض", "probability": 0.8927001953125}, {"start": 2504.74, "end": 2506.06, "word": " يعني", "probability": 0.58843994140625}, {"start": 2506.06, "end": 2506.32, "word": " انا", "probability": 0.78564453125}, {"start": 2506.32, "end": 2508.32, "word": " برشد", "probability": 0.921875}, {"start": 2508.32, "end": 2508.96, "word": " المريض", "probability": 0.99560546875}, {"start": 2508.96, "end": 2509.38, "word": " انه", "probability": 0.889892578125}, {"start": 2509.38, "end": 2509.9, "word": " يحرك", "probability": 0.9513346354166666}, {"start": 2509.9, "end": 2510.9, "word": " البرغي", "probability": 0.71490478515625}, {"start": 2510.9, "end": 2511.26, "word": " هذا", "probability": 0.935546875}, {"start": 2511.26, "end": 2511.96, "word": " لحد", "probability": 0.97998046875}, {"start": 2511.96, "end": 2512.06, "word": " ما", "probability": 0.966796875}, {"start": 2512.06, "end": 2512.38, "word": " يصل", "probability": 0.96533203125}, {"start": 2512.38, "end": 2512.6, "word": " إلى", "probability": 0.401123046875}, {"start": 2512.6, "end": 2513.0, "word": " صورة", "probability": 0.9713541666666666}, {"start": 2513.0, "end": 2513.3, "word": " ايش", "probability": 0.7529296875}, {"start": 2513.3, "end": 2513.8, "word": " بتكون", "probability": 0.889892578125}, {"start": 2513.8, "end": 2514.1, "word": " هي", "probability": 0.90576171875}, {"start": 2514.1, "end": 2514.82, "word": " ال", "probability": 0.95703125}, {"start": 2514.82, "end": 2515.26, "word": " best", "probability": 0.409423828125}, {"start": 2515.26, "end": 2515.92, "word": " clear", "probability": 0.95166015625}, {"start": 2515.92, "end": 2516.28, "word": " image", "probability": 0.95361328125}, {"start": 2516.28, "end": 2516.52, "word": " له", "probability": 0.82275390625}], "temperature": 1.0}, {"id": 99, "seek": 254373, "start": 2516.85, "end": 2543.73, "text": "Okay عندها يكون هذا ال axis ايه correct صحيح هو ال axis المطلوب منه طيب لو بقى اللي blurred لل vision شو بيعنيلك؟ انه ممكن يكون ال power طبعا ممكن انه ال power بتاع العدسة انه مايكونش اللي هو correct فلذلك انه دايما انا بصلح في ال cylinder ال power قبل ال axis صح؟ يعني مثلا المريض عنده minus نص", "tokens": [8297, 43242, 11296, 7251, 30544, 23758, 2423, 10298, 1975, 1829, 3224, 3006, 20328, 5016, 1829, 5016, 31439, 2423, 10298, 9673, 9566, 1211, 37746, 9154, 3224, 23032, 1829, 3555, 45164, 4724, 4587, 7578, 13672, 1829, 43525, 24976, 5201, 13412, 2407, 4724, 40228, 22653, 23275, 22807, 16472, 3224, 3714, 43020, 7251, 30544, 2423, 1347, 23032, 3555, 3615, 995, 3714, 43020, 16472, 3224, 2423, 1347, 39894, 45761, 18863, 3215, 3794, 3660, 16472, 3224, 19446, 1829, 30544, 8592, 13672, 1829, 31439, 3006, 6156, 1211, 8848, 23275, 16472, 3224, 11778, 47302, 15042, 1975, 8315, 4724, 36520, 5016, 8978, 2423, 17884, 2423, 1347, 12174, 36150, 2423, 10298, 20328, 5016, 22807, 37495, 22653, 50113, 15040, 9673, 16572, 11242, 43242, 3224, 3175, 8717, 9381], "avg_logprob": -0.17374465506300968, "compression_ratio": 1.811023622047244, "no_speech_prob": 0.0, "words": [{"start": 2516.85, "end": 2517.25, "word": "Okay", "probability": 0.81591796875}, {"start": 2517.25, "end": 2517.97, "word": " عندها", "probability": 0.844482421875}, {"start": 2517.97, "end": 2518.25, "word": " يكون", "probability": 0.831298828125}, {"start": 2518.25, "end": 2518.47, "word": " هذا", "probability": 0.95849609375}, {"start": 2518.47, "end": 2518.59, "word": " ال", "probability": 0.9755859375}, {"start": 2518.59, "end": 2518.87, "word": " axis", "probability": 0.80224609375}, {"start": 2518.87, "end": 2519.53, "word": " ايه", "probability": 0.79541015625}, {"start": 2519.53, "end": 2519.85, "word": " correct", "probability": 0.6357421875}, {"start": 2519.85, "end": 2520.61, "word": " صحيح", "probability": 0.97607421875}, {"start": 2520.61, "end": 2520.81, "word": " هو", "probability": 0.97119140625}, {"start": 2520.81, "end": 2520.95, "word": " ال", "probability": 0.990234375}, {"start": 2520.95, "end": 2521.23, "word": " axis", "probability": 0.974609375}, {"start": 2521.23, "end": 2521.79, "word": " المطلوب", "probability": 0.8753662109375}, {"start": 2521.79, "end": 2522.45, "word": " منه", "probability": 0.799072265625}, {"start": 2522.45, "end": 2522.97, "word": " طيب", "probability": 0.953125}, {"start": 2522.97, "end": 2523.29, "word": " لو", "probability": 0.98583984375}, {"start": 2523.29, "end": 2524.03, "word": " بقى", "probability": 0.7819010416666666}, {"start": 2524.03, "end": 2524.29, "word": " اللي", "probability": 0.6712646484375}, {"start": 2524.29, "end": 2524.53, "word": " blurred", "probability": 0.91748046875}, {"start": 2524.53, "end": 2524.85, "word": " لل", "probability": 0.86865234375}, {"start": 2524.85, "end": 2525.23, "word": " vision", "probability": 0.9384765625}, {"start": 2525.23, "end": 2526.39, "word": " شو", "probability": 0.9072265625}, {"start": 2526.39, "end": 2528.15, "word": " بيعنيلك؟", "probability": 0.714501953125}, {"start": 2528.15, "end": 2528.45, "word": " انه", "probability": 0.62060546875}, {"start": 2528.45, "end": 2528.65, "word": " ممكن", "probability": 0.97265625}, {"start": 2528.65, "end": 2528.87, "word": " يكون", "probability": 0.6728515625}, {"start": 2528.87, "end": 2529.03, "word": " ال", "probability": 0.94091796875}, {"start": 2529.03, "end": 2529.27, "word": " power", "probability": 0.91455078125}, {"start": 2529.27, "end": 2529.67, "word": " طبعا", "probability": 0.78350830078125}, {"start": 2529.67, "end": 2530.91, "word": " ممكن", "probability": 0.61688232421875}, {"start": 2530.91, "end": 2531.27, "word": " انه", "probability": 0.655029296875}, {"start": 2531.27, "end": 2531.29, "word": " ال", "probability": 0.97509765625}, {"start": 2531.29, "end": 2531.53, "word": " power", "probability": 0.9189453125}, {"start": 2531.53, "end": 2532.09, "word": " بتاع", "probability": 0.833984375}, {"start": 2532.09, "end": 2533.53, "word": " العدسة", "probability": 0.95654296875}, {"start": 2533.53, "end": 2533.79, "word": " انه", "probability": 0.835205078125}, {"start": 2533.79, "end": 2534.27, "word": " مايكونش", "probability": 0.8546142578125}, {"start": 2534.27, "end": 2534.49, "word": " اللي", "probability": 0.980224609375}, {"start": 2534.49, "end": 2534.79, "word": " هو", "probability": 0.9921875}, {"start": 2534.79, "end": 2535.41, "word": " correct", "probability": 0.9609375}, {"start": 2535.41, "end": 2536.81, "word": " فلذلك", "probability": 0.9591064453125}, {"start": 2536.81, "end": 2537.07, "word": " انه", "probability": 0.87939453125}, {"start": 2537.07, "end": 2537.35, "word": " دايما", "probability": 0.9200846354166666}, {"start": 2537.35, "end": 2537.59, "word": " انا", "probability": 0.90673828125}, {"start": 2537.59, "end": 2538.21, "word": " بصلح", "probability": 0.93310546875}, {"start": 2538.21, "end": 2538.41, "word": " في", "probability": 0.92333984375}, {"start": 2538.41, "end": 2538.53, "word": " ال", "probability": 0.382568359375}, {"start": 2538.53, "end": 2539.01, "word": " cylinder", "probability": 0.8896484375}, {"start": 2539.01, "end": 2539.61, "word": " ال", "probability": 0.96240234375}, {"start": 2539.61, "end": 2539.93, "word": " power", "probability": 0.9208984375}, {"start": 2539.93, "end": 2540.41, "word": " قبل", "probability": 0.994384765625}, {"start": 2540.41, "end": 2540.57, "word": " ال", "probability": 0.994140625}, {"start": 2540.57, "end": 2541.01, "word": " axis", "probability": 0.95068359375}, {"start": 2541.01, "end": 2541.89, "word": " صح؟", "probability": 0.8409830729166666}, {"start": 2541.89, "end": 2542.13, "word": " يعني", "probability": 0.937744140625}, {"start": 2542.13, "end": 2542.39, "word": " مثلا", "probability": 0.982666015625}, {"start": 2542.39, "end": 2542.71, "word": " المريض", "probability": 0.8497721354166666}, {"start": 2542.71, "end": 2543.01, "word": " عنده", "probability": 0.993896484375}, {"start": 2543.01, "end": 2543.33, "word": " minus", "probability": 0.90283203125}, {"start": 2543.33, "end": 2543.73, "word": " نص", "probability": 0.980224609375}], "temperature": 1.0}, {"id": 100, "seek": 257327, "start": 2544.43, "end": 2573.27, "text": "Okay لو حطيتله minus ربع و كان ال axis مثلا تسعين الاصلي و انا حطيتله axis تمانين طب انا مقلل ايش ال power صح فانا بدي اصل ل maximum power و بعدين بصلح من ال axis okay اذا دايما في حالة ال cylinder بصلح ال power و بعدين بصلح من ال axis at this point", "tokens": [8297, 45164, 11331, 9566, 36081, 43761, 3175, 12602, 3555, 3615, 4032, 25961, 2423, 10298, 50113, 15040, 6055, 3794, 3615, 9957, 2423, 33546, 20292, 4032, 1975, 8315, 11331, 9566, 36081, 43761, 10298, 46811, 7649, 9957, 23032, 3555, 1975, 8315, 3714, 4587, 1211, 1211, 1975, 1829, 8592, 2423, 1347, 20328, 5016, 6156, 7649, 995, 4724, 16254, 1975, 36520, 5296, 6674, 1347, 4032, 39182, 9957, 4724, 36520, 5016, 9154, 2423, 10298, 1392, 1975, 15730, 11778, 47302, 15042, 8978, 11331, 6027, 3660, 2423, 17884, 4724, 36520, 5016, 2423, 1347, 4032, 39182, 9957, 4724, 36520, 5016, 9154, 2423, 10298, 412, 341, 935], "avg_logprob": -0.17649871749537333, "compression_ratio": 1.8423645320197044, "no_speech_prob": 0.0, "words": [{"start": 2544.43, "end": 2544.83, "word": "Okay", "probability": 0.55419921875}, {"start": 2544.83, "end": 2545.19, "word": " لو", 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"probability": 0.709228515625}, {"start": 2550.37, "end": 2550.87, "word": " حطيتله", "probability": 0.946044921875}, {"start": 2550.87, "end": 2551.23, "word": " axis", "probability": 0.818359375}, {"start": 2551.23, "end": 2551.75, "word": " تمانين", "probability": 0.8836263020833334}, {"start": 2551.75, "end": 2552.17, "word": " طب", "probability": 0.8583984375}, {"start": 2552.17, "end": 2552.31, "word": " انا", "probability": 0.7261962890625}, {"start": 2552.31, "end": 2552.75, "word": " مقلل", "probability": 0.9345703125}, {"start": 2552.75, "end": 2553.05, "word": " ايش", "probability": 0.9119466145833334}, {"start": 2553.05, "end": 2553.19, "word": " ال", "probability": 0.53173828125}, {"start": 2553.19, "end": 2553.45, "word": " power", "probability": 0.89990234375}, {"start": 2553.45, "end": 2554.01, "word": " صح", "probability": 0.951416015625}, {"start": 2554.01, "end": 2554.49, "word": " فانا", "probability": 0.8719075520833334}, {"start": 2554.49, "end": 2554.65, "word": " بدي", "probability": 0.770263671875}, {"start": 2554.65, "end": 2554.95, "word": " اصل", "probability": 0.865478515625}, {"start": 2554.95, "end": 2555.35, "word": " ل", "probability": 0.75048828125}, {"start": 2555.35, "end": 2556.39, "word": " maximum", "probability": 0.689453125}, {"start": 2556.39, "end": 2556.99, "word": " power", "probability": 0.90673828125}, {"start": 2556.99, "end": 2557.47, "word": " و", "probability": 0.8955078125}, {"start": 2557.47, "end": 2557.79, "word": " بعدين", "probability": 0.9619140625}, {"start": 2557.79, "end": 2558.31, "word": " بصلح", "probability": 0.880859375}, {"start": 2558.31, "end": 2558.53, "word": " من", "probability": 0.41748046875}, {"start": 2558.53, "end": 2558.89, "word": " ال", "probability": 0.95556640625}, {"start": 2558.89, "end": 2559.61, "word": " axis", "probability": 0.95361328125}, {"start": 2559.61, "end": 2560.23, "word": " okay", "probability": 0.52978515625}, {"start": 2560.23, "end": 2561.93, "word": " اذا", "probability": 0.71240234375}, {"start": 2561.93, "end": 2562.45, "word": " دايما", "probability": 0.9132486979166666}, {"start": 2562.45, "end": 2562.79, "word": " في", "probability": 0.865234375}, {"start": 2562.79, "end": 2563.27, "word": " حالة", "probability": 0.994140625}, {"start": 2563.27, "end": 2563.51, "word": " ال", "probability": 0.4091796875}, {"start": 2563.51, "end": 2563.93, "word": " cylinder", "probability": 0.84814453125}, {"start": 2563.93, "end": 2564.79, "word": " بصلح", "probability": 0.9345703125}, {"start": 2564.79, "end": 2564.95, "word": " ال", "probability": 0.958984375}, {"start": 2564.95, "end": 2565.23, "word": " power", "probability": 0.916015625}, {"start": 2565.23, "end": 2565.63, "word": " و", "probability": 0.72802734375}, {"start": 2565.63, "end": 2565.87, "word": " بعدين", "probability": 0.979736328125}, {"start": 2565.87, "end": 2566.37, "word": " بصلح", "probability": 0.9412434895833334}, {"start": 2566.37, "end": 2566.57, "word": " من", "probability": 0.97998046875}, {"start": 2566.57, "end": 2567.27, "word": " ال", "probability": 0.98828125}, {"start": 2567.27, "end": 2567.73, "word": " axis", "probability": 0.97607421875}, {"start": 2567.73, "end": 2572.63, "word": " at", "probability": 0.716796875}, {"start": 2572.63, "end": 2572.93, "word": " this", "probability": 0.96630859375}, {"start": 2572.93, "end": 2573.27, "word": " point", "probability": 0.9814453125}], "temperature": 1.0}, {"id": 101, "seek": 259453, "start": 2573.99, "end": 2594.53, "text": "The rotation is stopped and we can determine the accurate axis of the cylindrical lens يعني عند هذه النقطة بنجف عملية إيش الدوران و بيكون هذا يما أنا بصل ل ال base a clear image بتكون هان ال axis هو إيه صحيح بالنسبة للمريض", "tokens": [2278, 12447, 307, 5936, 293, 321, 393, 6997, 264, 8559, 10298, 295, 264, 28044, 15888, 6765, 37495, 22653, 43242, 29538, 28239, 47432, 3660, 44945, 7435, 5172, 6225, 42213, 10632, 11933, 1829, 8592, 32748, 13063, 7649, 4032, 4724, 1829, 30544, 23758, 7251, 15042, 41850, 4724, 36520, 5296, 2423, 3096, 257, 1850, 3256, 39894, 30544, 8032, 7649, 2423, 10298, 31439, 11933, 1829, 3224, 20328, 5016, 1829, 5016, 20666, 1863, 35457, 3660, 5296, 19528, 16572, 11242], "avg_logprob": -0.22508445341844815, "compression_ratio": 1.4090909090909092, "no_speech_prob": 0.0, "words": [{"start": 2573.99, "end": 2574.23, "word": "The", "probability": 0.0601806640625}, {"start": 2574.23, "end": 2574.73, "word": " rotation", "probability": 0.94873046875}, {"start": 2574.73, "end": 2575.19, "word": " is", "probability": 0.955078125}, {"start": 2575.19, "end": 2575.69, "word": " stopped", "probability": 0.65625}, {"start": 2575.69, "end": 2576.21, "word": " and", "probability": 0.8291015625}, {"start": 2576.21, "end": 2576.43, "word": " we", "probability": 0.9423828125}, {"start": 2576.43, "end": 2576.81, "word": " can", "probability": 0.93310546875}, {"start": 2576.81, "end": 2577.95, "word": " determine", "probability": 0.9365234375}, {"start": 2577.95, "end": 2578.23, "word": " the", "probability": 0.931640625}, {"start": 2578.23, "end": 2578.73, "word": " accurate", "probability": 0.7939453125}, {"start": 2578.73, "end": 2579.29, "word": " axis", "probability": 0.95361328125}, {"start": 2579.29, "end": 2579.73, "word": " of", "probability": 0.9716796875}, {"start": 2579.73, "end": 2579.93, "word": " the", "probability": 0.89013671875}, {"start": 2579.93, "end": 2580.49, "word": " cylindrical", "probability": 0.955078125}, {"start": 2580.49, "end": 2580.87, "word": " lens", "probability": 0.9248046875}, {"start": 2580.87, "end": 2581.49, "word": " يعني", "probability": 0.5933837890625}, {"start": 2581.49, "end": 2581.97, "word": " عند", "probability": 0.978515625}, {"start": 2581.97, "end": 2582.23, "word": " هذه", "probability": 0.82080078125}, {"start": 2582.23, "end": 2582.87, "word": " النقطة", "probability": 0.9757486979166666}, {"start": 2582.87, "end": 2583.47, "word": " بنجف", "probability": 0.7545572916666666}, {"start": 2583.47, "end": 2583.97, "word": " عملية", "probability": 0.98486328125}, {"start": 2583.97, "end": 2584.35, "word": " إيش", "probability": 0.81689453125}, {"start": 2584.35, "end": 2585.13, "word": " الدوران", "probability": 0.7967122395833334}, {"start": 2585.13, "end": 2585.77, "word": " و", "probability": 0.471435546875}, {"start": 2585.77, "end": 2586.15, "word": " بيكون", "probability": 0.759033203125}, {"start": 2586.15, "end": 2586.65, "word": " هذا", "probability": 0.80224609375}, {"start": 2586.65, "end": 2586.97, "word": " يما", "probability": 0.5640869140625}, {"start": 2586.97, "end": 2587.15, "word": " أنا", "probability": 0.73583984375}, {"start": 2587.15, "end": 2587.51, "word": " بصل", "probability": 0.911865234375}, {"start": 2587.51, "end": 2588.35, "word": " ل", "probability": 0.6484375}, {"start": 2588.35, "end": 2588.73, "word": " ال", "probability": 0.703125}, {"start": 2588.73, "end": 2589.11, "word": " base", "probability": 0.8515625}, {"start": 2589.11, "end": 2589.47, "word": " a", "probability": 0.54150390625}, {"start": 2589.47, "end": 2589.77, "word": " clear", "probability": 0.94775390625}, {"start": 2589.77, "end": 2590.19, "word": " image", "probability": 0.95703125}, {"start": 2590.19, "end": 2590.79, "word": " بتكون", "probability": 0.9189453125}, {"start": 2590.79, "end": 2591.05, "word": " هان", "probability": 0.6810302734375}, {"start": 2591.05, "end": 2591.19, "word": " ال", "probability": 0.8798828125}, {"start": 2591.19, "end": 2591.67, "word": " axis", "probability": 0.84619140625}, {"start": 2591.67, "end": 2591.99, "word": " هو", "probability": 0.95751953125}, {"start": 2591.99, "end": 2592.53, "word": " إيه", "probability": 0.7964680989583334}, {"start": 2592.53, "end": 2593.07, "word": " صحيح", "probability": 0.9757080078125}, {"start": 2593.07, "end": 2593.63, "word": " بالنسبة", "probability": 0.991455078125}, {"start": 2593.63, "end": 2594.53, "word": " للمريض", "probability": 0.922119140625}], "temperature": 1.0}, {"id": 102, "seek": 261604, "start": 2595.76, "end": 2616.04, "text": "و بيكون هذا ال axis تعمل العدسة الاستوانية يعني بطلب من المركز بقوله عمال ليه عدسة minus one على minus two axis تسايم هذه اللي هتركب وين؟ فى لدّارة المارين okay ال Jackson cross cylinder", "tokens": [2407, 4724, 1829, 30544, 23758, 2423, 10298, 6055, 25957, 1211, 18863, 3215, 3794, 3660, 42963, 14851, 2407, 7649, 10632, 37495, 22653, 4724, 9566, 46152, 9154, 9673, 31747, 11622, 4724, 39648, 3224, 6225, 2304, 6027, 32239, 3224, 6225, 3215, 3794, 3660, 3175, 472, 15844, 3175, 732, 10298, 6055, 3794, 995, 32640, 29538, 13672, 1829, 8032, 2655, 31747, 3555, 4032, 9957, 22807, 6156, 7578, 5296, 3215, 11703, 9640, 3660, 9673, 9640, 9957, 1392, 2423, 10647, 3278, 17884], "avg_logprob": -0.35402959114626836, "compression_ratio": 1.4948453608247423, "no_speech_prob": 0.0, "words": [{"start": 2595.76, "end": 2595.96, "word": "و", "probability": 0.76220703125}, {"start": 2595.96, "end": 2596.24, "word": " بيكون", "probability": 0.6444091796875}, {"start": 2596.24, "end": 2596.58, "word": " هذا", "probability": 0.83056640625}, {"start": 2596.58, "end": 2596.94, "word": " ال", "probability": 0.94140625}, {"start": 2596.94, "end": 2597.28, "word": " axis", "probability": 0.439453125}, {"start": 2597.28, "end": 2597.86, "word": " تعمل", "probability": 0.7191569010416666}, {"start": 2597.86, "end": 2598.76, "word": " العدسة", "probability": 0.9593505859375}, {"start": 2598.76, "end": 2599.64, "word": " الاستوانية", "probability": 0.787646484375}, {"start": 2599.64, "end": 2600.06, "word": " يعني", "probability": 0.873046875}, {"start": 2600.06, "end": 2600.48, "word": " بطلب", "probability": 0.8489583333333334}, {"start": 2600.48, "end": 2600.72, "word": " من", "probability": 0.9951171875}, {"start": 2600.72, "end": 2601.46, "word": " المركز", "probability": 0.9720052083333334}, {"start": 2601.46, "end": 2602.0, "word": " بقوله", "probability": 0.658447265625}, {"start": 2602.0, "end": 2602.26, "word": " عمال", "probability": 0.6181640625}, {"start": 2602.26, "end": 2602.46, "word": " ليه", "probability": 0.682373046875}, {"start": 2602.46, "end": 2602.88, "word": " عدسة", "probability": 0.982666015625}, {"start": 2602.88, "end": 2603.14, "word": " minus", "probability": 0.728515625}, {"start": 2603.14, "end": 2603.58, "word": " one", "probability": 0.8154296875}, {"start": 2603.58, "end": 2603.8, "word": " على", "probability": 0.5224609375}, {"start": 2603.8, "end": 2604.1, "word": " minus", "probability": 0.98828125}, {"start": 2604.1, "end": 2604.44, "word": " two", "probability": 0.94873046875}, {"start": 2604.44, "end": 2604.92, "word": " axis", "probability": 0.85009765625}, {"start": 2604.92, "end": 2605.6, "word": " تسايم", "probability": 0.8193359375}, {"start": 2605.6, "end": 2605.96, "word": " هذه", "probability": 0.09661865234375}, {"start": 2605.96, "end": 2606.08, "word": " اللي", "probability": 0.95068359375}, {"start": 2606.08, "end": 2606.6, "word": " هتركب", "probability": 0.95654296875}, {"start": 2606.6, "end": 2607.18, "word": " وين؟", "probability": 0.597412109375}, {"start": 2607.18, "end": 2607.28, "word": " فى", "probability": 0.6478271484375}, {"start": 2607.28, "end": 2607.88, "word": " لدّارة", "probability": 0.7419921875}, {"start": 2607.88, "end": 2608.42, "word": " المارين", "probability": 0.74072265625}, {"start": 2608.42, "end": 2609.62, "word": " okay", "probability": 0.181396484375}, {"start": 2609.62, "end": 2614.42, "word": " ال", "probability": 0.376708984375}, {"start": 2614.42, "end": 2614.86, "word": " Jackson", "probability": 0.3369140625}, {"start": 2614.86, "end": 2615.58, "word": " cross", "probability": 0.46337890625}, {"start": 2615.58, "end": 2616.04, "word": " cylinder", "probability": 0.56787109375}], "temperature": 1.0}, {"id": 103, "seek": 265098, "start": 2622.36, "end": 2650.98, "text": "طبعا جاكسون cross cylinder عبارة عن عدسة بتتكون من عدستين عدسة بتكون plus و عدسة minus التنتين ايه صار لهم عملية damage okay ففي الآخر أداني عدسة قوتها من طرف plus مثلا نص", "tokens": [9566, 3555, 3615, 995, 10874, 995, 4117, 3794, 11536, 3278, 17884, 6225, 3555, 9640, 3660, 18871, 6225, 3215, 3794, 3660, 39894, 2655, 30544, 9154, 6225, 3215, 3794, 2655, 9957, 6225, 3215, 3794, 3660, 39894, 30544, 1804, 4032, 6225, 3215, 3794, 3660, 3175, 16712, 29399, 9957, 1975, 1829, 3224, 20328, 9640, 5296, 16095, 6225, 42213, 10632, 4344, 1392, 6156, 41185, 6024, 95, 34740, 5551, 3215, 7649, 1829, 6225, 3215, 3794, 3660, 12174, 35473, 11296, 9154, 23032, 28480, 1804, 50113, 15040, 8717, 9381], "avg_logprob": -0.14900914216186942, "compression_ratio": 1.5568181818181819, "no_speech_prob": 0.0, "words": [{"start": 2622.36, "end": 2622.82, "word": "طبعا", "probability": 0.9705810546875}, {"start": 2622.82, "end": 2623.6, "word": " جاكسون", "probability": 0.789111328125}, {"start": 2623.6, "end": 2623.98, "word": " cross", "probability": 0.58984375}, {"start": 2623.98, "end": 2624.52, 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2877.64, "text": "All a cross-cylinder lenses have a spherical equivalent power of zero إبلانو أخدت قانون الـ spherical equivalent الاسفير زائد السيلندر إشماله نص السيلندر بساوي زيرو صح؟ Spherical equivalent ماخدتها؟ طيب", "tokens": [7868, 257, 3278, 12, 1344, 75, 5669, 18059, 362, 257, 37300, 10344, 1347, 295, 4018, 11933, 36150, 7649, 2407, 5551, 9778, 3215, 2655, 12174, 7649, 11536, 2423, 39184, 37300, 10344, 2423, 32277, 5172, 13546, 30767, 16373, 3215, 21136, 1829, 1211, 41260, 2288, 11933, 8592, 2304, 6027, 3224, 8717, 9381, 21136, 26895, 41260, 2288, 4724, 3794, 995, 45865, 30767, 13546, 2407, 20328, 5016, 22807, 1738, 34340, 10344, 3714, 47283, 3215, 2655, 11296, 22807, 23032, 1829, 3555], "avg_logprob": -0.3213404628791307, "compression_ratio": 1.5191256830601092, "no_speech_prob": 0.0, "words": [{"start": 2857.88, "end": 2858.32, "word": "All", "probability": 0.48388671875}, {"start": 2858.32, "end": 2858.62, "word": " a", "probability": 0.3203125}, {"start": 2858.62, "end": 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إلها استعمالات بمعنى الآن لو جاني مثلا مريض كان minus one ع minus sorry minus نص خلينا نقل شوية ع minus ثلاثة okay x is مية و تمانين بحكيلك عملينه spherical equivalent بتروح تعمل القانون هذا عمليات ال cataract اللي بتشوفوها الناس اللي عندهم بيعملوا عمليات مية بيضا", "tokens": [1211, 10721, 39896, 11933, 1211, 11296, 3861, 11933, 1211, 11296, 44713, 25957, 6027, 9307, 4724, 2304, 3615, 1863, 7578, 6024, 48506, 45164, 10874, 7649, 1829, 50113, 15040, 3714, 16572, 11242, 25961, 3175, 472, 6225, 3175, 2597, 3175, 8717, 9381, 16490, 20292, 8315, 8717, 4587, 1211, 13412, 2407, 10632, 6225, 3175, 38637, 1211, 5718, 104, 3660, 1392, 2031, 307, 3714, 10632, 4032, 46811, 7649, 9957, 4724, 5016, 4117, 1829, 23275, 6225, 42213, 9957, 3224, 37300, 10344, 39894, 32887, 5016, 6055, 25957, 1211, 25062, 7649, 11536, 23758, 6225, 2304, 20292, 9307, 2423, 3857, 289, 578, 13672, 1829, 39894, 8592, 38688, 2407, 11296, 2423, 8315, 3794, 13672, 1829, 43242, 16095, 4724, 1829, 25957, 1211, 14407, 6225, 2304, 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اللي بتم زراعتها وين في ال anterior shape okay", "tokens": [40228, 22653, 4724, 3555, 3794, 41193, 3660, 16472, 2423, 37300, 10344, 20449, 18513, 37977, 2423, 32277, 5172, 13546, 20666, 3794, 995, 45865, 2423, 32277, 5172, 13546, 30767, 16373, 3215, 8717, 9381, 21136, 1211, 9957, 3215, 2288, 1392, 13412, 2407, 2423, 3861, 39894, 995, 34268, 11296, 5551, 16095, 3714, 2407, 11242, 45367, 13672, 1829, 31439, 2423, 10647, 3278, 17884, 1975, 2407, 2423, 3278, 17884, 1975, 1829, 11242, 995, 4032, 9957, 39894, 14851, 9778, 40448, 2423, 3861, 9154, 48812, 27842, 8978, 6225, 2304, 20292, 9307, 2423, 3857, 289, 578, 7930, 24976, 6765, 13672, 1829, 39894, 2304, 30767, 23557, 34268, 11296, 4032, 9957, 8978, 2423, 364, 34345, 284, 3909, 1392], "avg_logprob": -0.2638888759193597, "compression_ratio": 1.7088122605363985, "no_speech_prob": 0.0, "words": [{"start": 3075.82, "end": 3076.16, "word": "يعني", "probability": 0.8916015625}, {"start": 3076.16, "end": 3076.78, "word": " ببساطة", "probability": 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{"start": 3187.12, "end": 3187.38, "word": " cross", "probability": 0.89111328125}, {"start": 3187.38, "end": 3187.92, "word": " cylinder", "probability": 0.724609375}, {"start": 3187.92, "end": 3188.9, "word": " for", "probability": 0.96337890625}, {"start": 3188.9, "end": 3191.58, "word": " x's", "probability": 0.48974609375}, {"start": 3191.58, "end": 3191.92, "word": " length", "probability": 0.666015625}, {"start": 3191.92, "end": 3192.3, "word": " and", "probability": 0.93701171875}, {"start": 3192.3, "end": 3192.72, "word": " for", "probability": 0.9150390625}, {"start": 3192.72, "end": 3193.86, "word": " x's", "probability": 0.982177734375}, {"start": 3193.86, "end": 3194.68, "word": " power", "probability": 0.8720703125}, {"start": 3194.68, "end": 3198.02, "word": " طيب", "probability": 0.8512369791666666}, {"start": 3198.02, "end": 3198.28, "word": " لها", "probability": 0.789306640625}, {"start": 3198.28, "end": 3198.42, "word": " ان", "probability": 0.70068359375}, {"start": 3198.42, "end": 3198.64, "word": " شاء", "probability": 0.967041015625}, {"start": 3198.64, "end": 3198.74, "word": " الله", "probability": 0.96533203125}, {"start": 3198.74, "end": 3199.4, "word": " بنتوقف", "probability": 0.8299560546875}, {"start": 3199.4, "end": 3199.66, "word": " في", "probability": 0.94287109375}, {"start": 3199.66, "end": 3201.08, "word": " المحاضرة،", "probability": 0.775732421875}, {"start": 3201.08, "end": 3201.26, "word": " في", "probability": 0.8798828125}, {"start": 3201.26, "end": 3201.44, "word": " أي", "probability": 0.62548828125}, {"start": 3201.44, "end": 3202.2, "word": " سؤال؟", "probability": 0.8759765625}, {"start": 3202.2, "end": 3202.28, "word": " أي", "probability": 0.783203125}, {"start": 3202.28, "end": 3207.72, "word": " استفسار؟", "probability": 0.9239501953125}, {"start": 3207.72, "end": 3207.96, "word": " طيب", "probability": 0.90380859375}, {"start": 3207.96, "end": 3208.4, "word": " شكرا", "probability": 0.9430338541666666}, {"start": 3208.4, "end": 3208.94, "word": " يعطيكم", "probability": 0.75152587890625}, {"start": 3208.94, "end": 3209.34, "word": " العافية", "probability": 0.9503580729166666}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3209.9961875, "duration_after_vad": 3053.8556249999856}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwaBhVI6LPr803vc5wWl9Iy_/Yn5Ckh9qadE.srt b/PL9fwy3NUQKwaBhVI6LPr803vc5wWl9Iy_/Yn5Ckh9qadE.srt
new file mode 100644
index 0000000000000000000000000000000000000000..02916134b1840afc8ec414fb1926081b8aa54e25
--- /dev/null
+++ b/PL9fwy3NUQKwaBhVI6LPr803vc5wWl9Iy_/Yn5Ckh9qadE.srt
@@ -0,0 +1,1485 @@
+1
+00:00:20,810 --> 00:00:23,910
+طيب بسم الله الرحمن الرحيم السلام عليكم ورحمة الله
+
+2
+00:00:23,910 --> 00:00:27,690
+وبركاته and a very good afternoon to all of you
+
+3
+00:00:27,690 --> 00:00:32,290
+بالنسبة لموضوع diachrome test موضوع ال
+
+4
+00:00:32,290 --> 00:00:39,140
+astigmatic fan موضوع يعني مهم جداً في معمل أو مادة ال
+
+5
+00:00:39,140 --> 00:00:42,980
+refraction لازم تكونوا مستوعبينها مئة في المئة
+
+6
+00:00:42,980 --> 00:00:48,280
+الديوكروم تست، أُعطيكم بعض الأمثلة عشان نُصبح أيش
+
+7
+00:00:48,280 --> 00:00:55,560
+نتدرب أكثر، okay. يعني الآن لو مثلاً حكينا في مثال ال
+
+8
+00:00:55,560 --> 00:01:00,260
+right eye minus
+
+9
+00:01:00,260 --> 00:01:05,560
+نصف ديوبتر سفير، okay.
+
+10
+00:01:09,780 --> 00:01:13,200
+إذا في ال right eye minus نصف ديوبتر سفير، لو
+
+11
+00:01:13,200 --> 00:01:19,520
+أنا حاطّه قدام العين minus one ديوبتر سفير، شو
+
+12
+00:01:19,520 --> 00:01:25,320
+يجب أن يصير؟ بالظبط،  نريد دائماً نتكلم كمصطلح over
+
+13
+00:01:25,320 --> 00:01:29,880
+correction، إذا minus one سيُحدث over correction،
+
+14
+00:01:29,880 --> 00:01:34,500
+أي بمعنى أن ال light rays أين ستتركز؟ هايبر متروبية
+
+15
+00:01:34,500 --> 00:01:39,440
+أي بمعنى سيُصبح artificial هايبر متروبية، okay؟ إذا هذا
+
+16
+00:01:39,440 --> 00:01:44,320
+artificial
+
+17
+00:01:44,320 --> 00:01:48,200
+hypermetropia
+
+18
+00:01:48,200 --> 00:01:51,660
+أي
+
+19
+00:01:51,660 --> 00:01:55,560
+بمعنى hypermetropia  قصر نظر كاذب، artificial كاذب أو
+
+20
+00:01:55,560 --> 00:02:02,340
+صناعي، okay؟ لماذا يا نديم؟ لماذا ال minus one أصبح
+
+21
+00:02:02,340 --> 00:02:05,160
+artificial hypermetropia؟ لأنه over
+
+22
+00:02:05,160 --> 00:02:13,560
+correction، صحيح؟ طيب لو أنا حطيت minus نصف بالضبط
+
+23
+00:02:13,560 --> 00:02:18,920
+لكن يُقال في بعض الكتب أنه دائماً ال red slightly
+
+24
+00:02:18,920 --> 00:02:24,020
+compared to green، okay. يعني دائماً ال red يكون
+
+25
+00:02:24,020 --> 00:02:30,200
+أوضح بدرجة بسيطة عن من؟ عن ال green، okay. إذا هنا
+
+26
+00:02:30,200 --> 00:02:40,140
+ال minus two، علينا أن نكتب red color is
+
+27
+00:02:40,140 --> 00:02:45,260
+slightly clearer
+
+28
+00:02:45,260 --> 00:02:48,500
+compared
+
+29
+00:02:48,500 --> 00:02:53,000
+to
+
+30
+00:02:53,000 --> 00:02:58,220
+green color
+
+31
+00:02:59,610 --> 00:03:05,130
+طيب، الآن أنا استخدمت أيش؟ minus نصف، صحيح، الآن لو
+
+32
+00:03:05,130 --> 00:03:12,330
+سألتُكم سؤال، why the red color is slightly clearer
+
+33
+00:03:12,330 --> 00:03:19,850
+compared to green color في ال minus نصف؟ بمعنى
+
+34
+00:03:19,850 --> 00:03:25,590
+لماذا المريض رأى درجة أوضح أو اللونين
+
+35
+00:03:25,590 --> 00:03:28,870
+متساويتي الوضوح في ال minus نصف؟
+
+36
+00:03:31,880 --> 00:03:35,860
+التفسير دائماً،  التفسير يجب أن يكون منطقي logic
+
+37
+00:03:35,860 --> 00:03:40,480
+أنه جعل الأشياء تتركز على الحقيقة بالضبط، هذه
+
+38
+00:03:40,480 --> 00:03:43,520
+الإجابة، أن incident light rays are brought to
+
+39
+00:03:43,520 --> 00:03:49,920
+focus on the retina، okay. إذا هنا ماذا أكتب؟ أن
+
+40
+00:03:49,920 --> 00:03:55,940
+incident light
+
+41
+00:03:55,940 --> 00:03:59,380
+rays
+
+42
+00:04:08,520 --> 00:04:14,620
+to focus on
+
+43
+00:04:14,620 --> 00:04:19,740
+the retina،  ممكن
+
+44
+00:04:19,740 --> 00:04:23,740
+واحدة أخرى تكتب sharply on the retina، okay. نفس
+
+45
+00:04:23,740 --> 00:04:29,140
+المعنى، أو on the retina. طيب الآن يا ولدي،
+
+46
+00:04:29,140 --> 00:04:34,880
+استخدمنا ال minus one، أصبح عنده بالضبط over
+
+47
+00:04:34,880 --> 00:04:36,480
+correction، ماذا تعني؟
+
+48
+00:04:39,260 --> 00:04:44,500
+بالضبط، أنّه تركزت أين؟ خلف ال retina، واضحة النقطة
+
+49
+00:04:44,500 --> 00:04:48,300
+هذه، طالبات
+
+50
+00:04:48,300 --> 00:04:51,260
+الجدد، الآن نحن نشرح في موضوع ال
+
+51
+00:04:51,260 --> 00:04:54,900
+diachrome test، أخذنا عن diachrome test quiz كان
+
+52
+00:04:54,900 --> 00:05:00,220
+صغيراً، كيف تتم عملية التصحيح أو ال verification
+
+53
+00:05:09,400 --> 00:05:13,940
+الآن، مريض patient كان عنده minus نصف ديوبتر سفير
+
+54
+00:05:13,940 --> 00:05:18,800
+okay، في ال right eye. طيب، أنا وضعت data minus
+
+55
+00:05:18,800 --> 00:05:24,020
+one ديوبتر سفير، ماذا يعني ال data؟ بالضبط، ماذا
+
+56
+00:05:24,020 --> 00:05:28,540
+يعني؟ مصطلح over correction. طيب، الآن ال minus one
+
+57
+00:05:28,540 --> 00:05:31,100
+ماذا يعني بالنسبة لهذا ال patient؟
+
+58
+00:05:35,680 --> 00:05:38,600
+يعني ال refractive state الحالة الانكسارية الخاصة به
+
+59
+00:05:38,600 --> 00:05:42,260
+أصبحت over correction، إذا ال light... ال incident
+
+60
+00:05:42,260 --> 00:05:46,640
+light rays are brought to focus where؟ behind the
+
+61
+00:05:46,640 --> 00:05:51,460
+retina، صحيح؟ في ال artificial hypermetropia. طيب الحالة
+
+62
+00:05:51,460 --> 00:05:55,820
+الثانية، data minus نصف، إذا ماذا سيحدث له؟ يعني
+
+63
+00:05:55,820 --> 00:05:58,940
+أنا مثلاً أعطي minus نصف،  إنه يصحح ال data، التصحيح الكامل
+
+64
+00:05:58,940 --> 00:06:01,660
+full correction، إذا ال light rays أين ستتركز؟
+
+65
+00:06:29,690 --> 00:06:33,250
+طب، لو افترضنا ال left eye كان عنده hypermetropia
+
+66
+00:06:33,250 --> 00:06:37,950
+ممكن تكون hypermetropia؟ ممكن عين ميوبية، وواحدة hyper
+
+67
+00:06:37,950 --> 00:06:47,110
+metropia، ال left كانت plus ثلاثة ديوبتر سفير، طيب
+
+68
+00:06:47,110 --> 00:06:54,290
+الآن، شخص من الناس استخدم plus اثنين ديوبتر سفير
+
+69
+00:06:54,290 --> 00:06:58,050
+ماذا يعني؟ من سيرى أوضح؟
+
+70
+00:07:06,900 --> 00:07:11,920
+أعطيته plus two، إذا ماذا يعني؟ under أم over
+
+71
+00:07:11,920 --> 00:07:16,000
+correction؟ أم correction؟ under correction، صحيح؟
+
+72
+00:07:16,000 --> 00:07:18,960
+يعني أقل من القيمة المطلوبة
+
+73
+00:07:48,350 --> 00:07:52,070
+behind the retina، لأنه ما زال يُعتبر أيش؟ hyper
+
+74
+00:07:52,070 --> 00:07:59,510
+metropia، واضح يا فاطمة؟ طيب، لو استخدمنا plus two point
+
+75
+00:07:59,510 --> 00:08:03,390
+fifty، فاطمة،
+
+76
+00:08:03,390 --> 00:08:08,070
+ماذا سيكون؟ under correction، إذا أين ال light rays
+
+77
+00:08:08,070 --> 00:08:11,050
+ستتركز؟ behind the retina
+
+78
+00:08:23,680 --> 00:08:26,940
+ميوبية، صحيح؟ يعني، when ال incident light rays are
+
+79
+00:08:26,940 --> 00:08:31,560
+brought to focus where؟ in front، ممتازة. طيب، لو
+
+80
+00:08:31,560 --> 00:08:35,860
+أعطيتم plus ثلاثة؟ بالضبط
+
+81
+00:08:55,340 --> 00:09:04,340
+ال hypermetropia، okay، واضحة في
+
+82
+00:09:04,340 --> 00:09:08,200
+ال place، ماذا فعلت؟  جعلتنا نفهم أنها عملت Artificial
+
+83
+00:09:08,200 --> 00:09:11,400
+myopia، يعني أين incident light rays are brought
+
+84
+00:09:11,400 --> 00:09:14,720
+to focus where؟ in front، إذا أصبح أيش؟ myopia
+
+85
+00:09:14,720 --> 00:09:19,260
+من سيرى الأوضح؟ هل هناك من لا يفهم هذه النقطة؟
+
+86
+00:09:19,260 --> 00:09:22,780
+هذه
+
+87
+00:09:22,780 --> 00:09:23,660
+مهمة جداً
+
+88
+00:09:29,610 --> 00:09:33,610
+ممكن تجدون خارجاً من لا يعرف كلام diachrome test
+
+89
+00:09:33,610 --> 00:09:40,050
+واضح، مهم جداً، وهذه أمانة أحملها إليكم، من لا
+
+90
+00:09:40,050 --> 00:09:44,630
+يفهم،  يُخبرني، okay. يعني هذه المواضيع مهمة جداً لأنّ
+
+91
+00:09:44,630 --> 00:09:49,650
+ال diachrome test تعتبر very accurate دقيقة جداً، وتحتاج
+
+92
+00:09:49,650 --> 00:09:55,450
+إلى أشخاص يكون عندهم knowledge علم جيد، بالإضافة إلى
+
+93
+00:09:55,450 --> 00:10:00,070
+خبرة، هذه فهمناها الآن أعتقد، يعني أي سؤال أو
+
+94
+00:10:00,070 --> 00:10:05,490
+أي مثال تستطيعون حله، طبعاً بالإضافة للتطبيق العملي
+
+95
+00:10:05,490 --> 00:10:12,190
+أنا
+
+96
+00:10:12,190 --> 00:10:18,070
+أعرف astigmatic fan هي المحبطة قليلاً، الصعبة،  لكن
+
+97
+00:10:18,070 --> 00:10:22,590
+الآن نحاول أن نجيب لكم مسائل، إن شاء الله تصبح سهلة
+
+98
+00:10:22,590 --> 00:10:22,950
+جداً
+
+99
+00:10:34,240 --> 00:10:45,020
+انتهيتي؟ حاضر. ال right eye، بلانه على minus ثلاثة
+
+100
+00:10:45,020 --> 00:10:55,540
+اكسز 40، هذا ما هو؟ يعني الوصفة هذه، cylinder هذه
+
+101
+00:10:55,540 --> 00:10:59,620
+عبارة عن final objective refraction، يعني أخذتها
+
+102
+00:10:59,620 --> 00:11:03,500
+من retinoscope أو auto refractometer، إذا هذه
+
+103
+00:11:03,500 --> 00:11:10,400
+أيش؟ final objective
+
+104
+00:11:22,690 --> 00:11:28,870
+طيب، الآن minus 3 cylinder، ال sphere كم؟ plano
+
+105
+00:11:28,870 --> 00:11:33,710
+يعني ما عندي أيش؟ ال sphere، يعني الآن،  أنا أضع
+
+106
+00:11:33,710 --> 00:11:37,510
+في ال right، أحضر عدسة minus 3 وأضعها أمام العين
+
+107
+00:11:37,510 --> 00:11:42,030
+okay. نأتي، نريد أن نفهم كيف أستخدم ال astigmatic
+
+108
+00:11:42,030 --> 00:11:46,510
+fan، astigmatic fan عبارة عن مجموعة من
+
+109
+00:11:46,510 --> 00:11:53,430
+الخطوط، الآن، أُعرض هذه الخطوط لمن؟ للمريض، أسأل المريض
+
+110
+00:11:53,430 --> 00:11:58,390
+which line is more clear، يعني أي واحد من الخطوط هو
+
+111
+00:11:58,390 --> 00:12:04,010
+أوضح مقارنة بالخطوط الأخرى، okay؟ الآن، كما
+
+112
+00:12:04,010 --> 00:12:08,470
+أنتم تعرفون، لدينا التسعين والمئة وثمانون
+
+113
+00:12:28,440 --> 00:12:33,040
+تقريباً هنا، إذا هذا الخط سيكون أيش هو؟ more clear
+
+114
+00:12:33,040 --> 00:12:39,040
+يعني أوضح خط سيرى أيش؟ المريض،  أنا آتي
+
+115
+00:12:39,040 --> 00:12:43,520
+أستخدم العدسات، ماذا أضع؟ ال access  الذي عنده ال 40
+
+116
+00:12:43,520 --> 00:12:50,660
+فال 40 عمودي على من؟ إذا هو يصحح من؟ ال 130، صحيح؟
+
+117
+00:12:50,660 --> 00:12:56,080
+واضح هكذا، إذا العملية... لأن ال access عمودي على من؟
+
+118
+00:12:56,080 --> 00:13:01,370
+ال power، فأنا الآن، إما وضعت على ال axis 130،  عملت
+
+119
+00:13:01,370 --> 00:13:07,350
+تصحيح لمن؟ لل... لل axis ال 40، يعني العمودي عليه
+
+120
+00:13:07,350 --> 00:13:12,870
+okay. فنحن قلنا ال more clear هو يُعتبر less
+
+121
+00:13:12,870 --> 00:13:17,210
+immature، وال less clear يُعتبر أيش؟ more immature
+
+122
+00:13:17,210 --> 00:13:20,330
+ال more clear
+
+123
+00:13:29,300 --> 00:13:35,920
+less immature، و
+
+124
+00:13:35,920 --> 00:13:39,480
+less clear
+
+125
+00:13:39,480 --> 00:13:47,220
+more clear، more immature، okay. إذا علاقة أيش أصبحت؟
+
+126
+00:13:47,220 --> 00:13:50,720
+inverse relation، علاقة عكسية
+
+127
+00:13:59,550 --> 00:14:05,550
+بالريتينوسكوب، أحضرت مريضاً، غطيت عينه اليسرى،  وجدت ال
+
+128
+00:14:05,550 --> 00:14:10,270
+line الواضح عنده كان 30، أعرف أين أضع
+
+129
+00:14:10,270 --> 00:14:15,930
+ال trial cell على ال 120، لو غطيت العين و
+
+130
+00:14:15,930 --> 00:14:22,330
+مثلاً جاءني الواضح 10، كم؟ من يُجيب؟ 100،
+
+131
+00:14:22,330 --> 00:14:26,210
+لماذا؟  أضفنا 90، طيب لو قلنا 130، الذي كان هو ال
+
+132
+00:14:26,210 --> 00:14:26,770
+more clear
+
+133
+00:14:30,160 --> 00:14:34,280
+نريد أن نجرب أيش؟ 90... 90... واضحة... واضحة...
+
+134
+00:14:34,280 --> 00:14:40,280
+واضحة... واضحة
+
+135
+00:14:40,280 --> 00:14:45,460
+... واضحة... واضح... واضح... واضح... واضح... واضح
+
+136
+00:14:45,460 --> 00:14:46,180
+واضح... واضح... واضح... واضح... واضح... واضح...
+
+137
+00:14:46,180 --> 00:14:49,960
+واضح... واضح... واضح... واضح... واضح... واضح...
+
+138
+00:14:49,960 --> 00:14:56,280
+واضح... واضح... واضح... واضح...
+
+139
+00:15:02,250 --> 00:15:10,510
+فهو سيصحح من؟ ال 130، طيب
+
+140
+00:15:10,510 --> 00:15:13,590
+لو
+
+141
+00:15:13,590 --> 00:15:17,210
+افترضنا patient has refractive error بال left eye
+
+142
+00:15:17,210 --> 00:15:27,910
+حلو، هذا plus one على minus four، ال
+
+143
+00:15:27,910 --> 00:15:31,310
+left eye plus one
+
+144
+00:15:41,000 --> 00:15:46,880
+أي line سيكون واضحاً؟ لو طلبت منك أن ترسم
+
+145
+00:15:46,880 --> 00:15:54,720
+أن ترسم ال... ال... نعم، بالضبط
+
+146
+00:15:54,720 --> 00:15:58,540
+في الرابع، الثاني، أستطيع أن أرسمه، أضع هو ال more
+
+147
+00:15:58,540 --> 00:16:02,360
+clear compared to the other lines، okay.
+
+148
+00:16:05,890 --> 00:16:10,770
+هل هناك من لا يفهم ال astigmatic fan؟ يعني الآن ال
+
+149
+00:16:10,770 --> 00:16:14,530
+astigmatic fan، لو واحد كان عنده astigmatism أستطيع
+
+150
+00:16:14,530 --> 00:16:18,970
+أن أعرف كم ال axis من خلال أيش؟ ال chart، بدون لا
+
+151
+00:16:18,970 --> 00:16:26,630
+auto ولا أيش؟ ولا retinoscope،  تفضل.
+
+152
+00:16:35,420 --> 00:16:41,520
+ال 105 more clear، هو الواضح، فهمت عليّ؟ يعني
+
+153
+00:16:41,520 --> 00:16:49,200
+هذا الخط يكون مميزاً عن الخطوط الأخرى، هو... هو
+
+154
+00:16:49,200 --> 00:16:52,880
+الذي فيه ال defect من ناحية أيش؟ أن المريض يراه
+
+155
+00:16:52,880 --> 00:16:55,920
+أوضح من الخطوط الأخرى، لكن ال access الخاص بي هو
+
+156
+00:16:55,920 --> 00:17:00,460
+ال 105، ال access الذي هو ال original الذي أخذته
+
+157
+00:17:00,460 --> 00:17:03,020
+أنا من أين؟ من ال retinoscope أو من ال auto
+
+158
+00:17:03,020 --> 00:17:10,360
+refractometer، أو من ال auto...
+
+159
+00:17:10,360 --> 00:17:13,440
+طبعاً
+
+160
+00:17:13,440 --> 00:17:17,660
+هذه ستطبقونها عملياً، يعني الآن أقول لكِ، اشتغلي على ال
+
+161
+00:17:17,660 --> 00:17:20,740
+auto أو على ال retinoscope، هكذا،  أحصل على ال axis
+
+162
+00:17:20,740 --> 00:17:24,740
+مثلاً 90، إذا من سيكون غير واضح؟ ال... الواضح كثيراً
+
+163
+00:17:24,740 --> 00:17:28,800
+من سيكون عند ال... ال 180، العمودي عليه، okay.
+
+164
+00:17:30,990 --> 00:17:33,570
+طبعاً، هذه أين نعملها؟ في ال minus cylinder
+
+165
+00:17:33,570 --> 00:17:37,190
+according to the minus cylinder lens، لكن لو قلت لك
+
+166
+00:17:37,190 --> 00:17:40,810
+according to the plus cylinder lens،  عكس الأشياء،  اه
+
+167
+00:17:40,810 --> 00:17:45,110
+بس، أيش يجب أن يكون العكس؟ عكس أن ال 105...
+
+168
+00:17:45,110 --> 00:17:49,650
+اه، بالضبط. اه. طيب، اليوم موضوعنا عن ال Jackson
+
+169
+00:17:49,650 --> 00:17:52,890
+cross cylinder،  Jackson cross cylinder هي
+
+170
+00:17:52,890 --> 00:17:57,850
+عبارة عن عدسة تتكون من عدستين
+
+171
+00:18:04,410 --> 00:18:10,290
+الاثنتان متساويتان في ال power، يعني plus ربع، minus
+
+172
+00:18:10,290 --> 00:18:13,790
+ربع، إذا الاثنتان أيش؟ متساويتان في ال power
+
+173
+00:18:13,790 --> 00:18:19,910
+مختلفان من ناحية أيش؟ الإشارة. طيب الآن هاتين
+
+174
+00:18:19,910 --> 00:18:24,470
+العدستان،  نراهما عدسة واحدة، صحيح؟ إذا هما متحدتان أيش؟
+
+175
+00:18:24,470 --> 00:18:30,090
+مع بعض، صحيح؟ okay. هذا ال Jackson، أعود إليكم
+
+176
+00:18:33,340 --> 00:18:41,140
+يكون ال power فيهما أيش؟ تفضل
+
+177
+00:18:41,140 --> 00:18:48,540
+أيش؟ إذا الاثنتان يكون فيهما... ترون الخطين؟ ركزوا
+
+178
+00:18:48,540 --> 00:18:54,280
+على الخط الأسود والأحمر، لدينا خطين، صحيح؟  هناك خط
+
+179
+00:18:54,280 --> 00:18:58,780
+أحمر، وهناك خط أسود، بسرعة قليلاً،  ليرى الجميل
+
+180
+00:19:14,480 --> 00:19:19,620
+من حيث الإشارة، مُتعاكدان ال power أيش؟ على بعضهما، كل
+
+181
+00:19:19,620 --> 00:19:24,420
+axis واحدة، مثلاً تكون 135، والأخرى
+
+182
+00:19:24,420 --> 00:19:30,060
+كذا؟ 45، إذا ال axis أيش؟ متعامدان، لاحظوا في
+
+183
+00:19:30,060 --> 00:19:36,540
+العدسة لدينا خط أحمر، ولدينا خط أسود، صحيح؟ الآن أنا
+
+184
+00:19:36,540
+
+223
+00:23:26,340 --> 00:23:31,480
+موازي على مين؟ على ال 30 هي موازي وين؟ على ال 30
+
+224
+00:23:31,480 --> 00:23:39,860
+okay؟ إذا بقول للمريض هيك واضح ولا هيك؟ ولا هيك؟
+
+225
+00:23:39,860 --> 00:23:46,240
+يعني عندك ثلاث خيارات، بدونهم أفضل، إذا ال access
+
+226
+00:23:46,240 --> 00:23:51,780
+ده يعني صح، صح، صح، واضحة
+
+227
+00:23:51,780 --> 00:23:56,800
+النقطة الأولى، إذا بس حطيت هذه، يعني كأنها موازية للـ
+
+228
+00:23:56,800 --> 00:24:00,740
+access طيب
+
+229
+00:24:00,740 --> 00:24:06,260
+الحالة الثانية الآن، حطيت هذه موازية، يعني أنا أعطيته
+
+230
+00:24:06,260 --> 00:24:11,120
+الصورة الأولى، جلب اتجاه جلب الصورة الأولى أوضح، إذا
+
+231
+00:24:11,120 --> 00:24:12,780
+هاي أنت شايفها في plus، صح
+
+232
+00:24:22,270 --> 00:24:29,310
+الآن هنحرك شوية باتجاه ال plus، يعني
+
+233
+00:24:29,310 --> 00:24:34,130
+مجانبة اللي هو rotation، تدوير، طيب الآن نرجع على
+
+234
+00:24:34,130 --> 00:24:39,510
+الثلاثين، الآن أنا حركت باتجاه ال plus
+
+235
+00:24:43,600 --> 00:24:47,800
+ياما راحت، حركت باتجاه ال minus، جالي واضحة، بروح
+
+236
+00:24:47,800 --> 00:24:51,400
+بحرك باتجاه مين؟ ال minus، إذا ال access بتاعي بيكون
+
+237
+00:24:51,400 --> 00:25:01,240
+باتجاه ال minus، تفضلي
+
+238
+00:25:01,240 --> 00:25:06,800
+ألغيت أه، هذا السؤال ممتاز، الآن حطيت مثلاً على الخمسة
+
+239
+00:25:06,800 --> 00:25:11,400
+عشر، كان ال access بتاعي الجديد بالظبط، مرة ثانية
+
+240
+00:25:11,960 --> 00:25:16,360
+بجيب الـ ال handle بتاعة العدسة موازي وين؟
+
+241
+00:25:16,360 --> 00:25:21,940
+للخمسة عشر، ومرة ثانية بعمل rotation للـ ايه؟
+
+242
+00:25:21,940 --> 00:25:33,640
+للعدسة، واضحة؟ مين مش فاهم؟ صراحة؟ في حاجة مش فاهم؟
+
+243
+00:25:33,640 --> 00:25:38,880
+نعم، في الـ
+
+244
+00:25:42,620 --> 00:25:48,980
+السماء، هاي الـ الأسود هو ال plus، يعني كيف
+
+245
+00:25:48,980 --> 00:25:55,700
+يعني؟ يعني زي ما أنا مثلاً حركت من هنا، okay، يعني
+
+246
+00:25:55,700 --> 00:25:59,440
+بدي أحرك، جالي هيك أوضح، إذا بدي أطلع فوق جالي مثلاً
+
+247
+00:25:59,440 --> 00:26:03,680
+هيك أوضح، يا ما أطلع هيك، إذا بدي أنزل لتحت، okay
+
+248
+00:26:03,680 --> 00:26:08,180
+يعني باتجاه، بدي أطلع على الأسهم، أنا وين جالي أوضح
+
+249
+00:26:08,180 --> 00:26:23,630
+okay، طيب بدي ننتقل للعيون، تفضلي، الآن
+
+250
+00:26:23,630 --> 00:26:33,530
+في عندنا لو
+
+251
+00:26:33,530 --> 00:26:38,370
+فرضنا ال right plus
+
+252
+00:26:38,370 --> 00:26:38,770
+3
+
+253
+00:26:41,810 --> 00:26:50,270
+مينوس اثنين، اكسز مئة وثلاثين، الآن بدنا نعمل
+
+254
+00:26:50,270 --> 00:26:53,850
+verification، سيبك من ال plus ثلاثة اللي هي الاسفير
+
+255
+00:26:53,850 --> 00:26:56,690
+لأن الاسفير بدنا نستخدم اليها ايه؟ ال diachrome
+
+256
+00:26:56,690 --> 00:27:01,010
+test، صح؟ الآن أنا بدي أعمل verification لمن؟ للـ
+
+257
+00:27:01,010 --> 00:27:07,430
+cylinder، احنا مش موجود عندنا واحد ونصف، يعني اعتبري
+
+258
+00:27:07,430 --> 00:27:11,030
+هذه مينوس اثنين، كده يبقى ال power، الآن وأنت كـتحط
+
+259
+00:27:12,870 --> 00:27:17,770
+هتبريها، هي ال patient، okay، هي ال occlusion وحط
+
+260
+00:27:17,770 --> 00:27:22,410
+العدسة، أعمال verification لل access، هتبريها الـ
+
+261
+00:27:22,410 --> 00:27:22,650
+patient
+
+262
+00:27:49,410 --> 00:28:01,350
+دعوها مجال، دعوها مجال، حاضر، Westpire،
+
+263
+00:28:01,350 --> 00:28:05,550
+خطة دلوقت يعني
+
+264
+00:28:05,550 --> 00:28:06,690
+ذات؟
+
+265
+00:28:25,160 --> 00:28:28,760
+أسألها ايه؟ هلجيت وين ال access؟ الـ ال handle
+
+266
+00:28:28,760 --> 00:28:34,460
+هيكون وين؟ على مئة وثلاثين بالظبط
+
+267
+00:28:34,460 --> 00:28:38,500
+لازم يكون مئة وثلاثين، هل هو؟ مافيش أرقام لـ لأ
+
+268
+00:28:38,500 --> 00:28:45,520
+هي هي جداش؟ مئة وعشرون، هي تقريباً مئة وثلاثين
+
+269
+00:28:45,520 --> 00:28:51,520
+هون صح؟ هلجيت وين ال handle اللي بدك تحطيه؟ على مئة
+
+270
+00:28:51,520 --> 00:29:01,030
+وثلاثين، هي هيك صح؟ صحي هيك
+
+271
+00:29:01,030 --> 00:29:11,070
+لازم برميل متوازي بالظبط، هيك بمسك، هيك هيك أوضح أنا
+
+272
+00:29:11,070 --> 00:29:18,430
+عارف، هيك أوضح ولا هيك؟ مرة ثانية، يعني بالظبط لازم
+
+273
+00:29:18,430 --> 00:29:19,510
+يكون متوازي له
+
+274
+00:29:23,690 --> 00:29:27,450
+هي ال handle، okay، هذه ال handle لازم يكون على الـ
+
+275
+00:29:27,450 --> 00:29:35,170
+axis، الأحمر، البيضا، مش الخط، أه أنا فاكر، هات فوضى ورد
+
+276
+00:29:35,170 --> 00:29:38,990
+هات
+
+277
+00:29:38,990 --> 00:29:50,650
+لأ مش شايفها، هلجيت هي المئة وثلاثين، صح؟ تمام، هلجيت
+
+278
+00:29:50,650 --> 00:29:56,340
+هذه ال handle، هي الخط الأبيض، وهي ال handle بتاعتها
+
+279
+00:29:56,340 --> 00:30:03,400
+بجيب، لازم أصلاً معملي touch مع ال frame، هيك أوضح و
+
+280
+00:30:03,400 --> 00:30:10,100
+لا هيك ولا هيك، okay، يعني ال handle يجي على المئة
+
+281
+00:30:10,100 --> 00:30:14,580
+وثلاثين، الخط الأبيض هذا، وين يجي؟ موازي على المئة
+
+282
+00:30:14,580 --> 00:30:22,040
+وثلاثين، okay، دي ولا واحد واضح، هي مشكلة ال power
+
+283
+00:30:22,040 --> 00:30:29,960
+طيب لو قلنا ال left eye plus واحد ونصف على minus
+
+284
+00:30:29,960 --> 00:30:34,980
+واحد ونصف، axis خمسة وعشرون، اعمل ايه؟ هذا ال left
+
+285
+00:30:34,980 --> 00:30:35,200
+eye
+
+286
+00:31:05,380 --> 00:31:10,940
+أه، مرة ثانية بالله، جيت لهالي خمسة عشر، عشرين، لأ مرة
+
+287
+00:31:10,940 --> 00:31:15,900
+خمس وعشرون، احنا قلنا، شايفة هاي التدريج، هاي خمسة عشر
+
+288
+00:31:15,900 --> 00:31:21,840
+بعدين عشرين، خمس وعشرون، ثلاثين، يعني بيكون بالظبط
+
+289
+00:31:21,840 --> 00:31:29,360
+هون، هي ال frame، في مشكلة إنها هالي هيت وأنا هيت و
+
+290
+00:31:29,360 --> 00:31:34,980
+أنا بدوني بالظبط، هاي المثل في another group
+
+291
+00:31:47,630 --> 00:32:00,470
+طيب، إنها right، إبلاه
+
+292
+00:32:00,470 --> 00:32:04,330
+نه، على minus نصف
+
+293
+00:32:07,460 --> 00:32:09,120
+access خمسة
+
+294
+00:32:39,830 --> 00:32:44,690
+هذه مئة وخمسة شوية
+
+295
+00:32:44,690 --> 00:32:54,590
+ده؟ على الخمسة والتسعين، شوفها
+
+296
+00:32:54,590 --> 00:33:00,350
+هاي مئة، هاي خمسة عشر، بعدين عشرة، بعدين هاي خمسة، يعني
+
+297
+00:33:00,350 --> 00:33:05,710
+جري بع المئة وثمانين، وانزليها تحت كمان
+
+298
+00:33:05,710 --> 00:33:11,580
+انزليها، مش هيك، مئة وثمانين، صح؟ إذا وين بتنزل كمان؟
+
+299
+00:33:11,580 --> 00:33:16,840
+ده تحت، هاي خمسة، عايش؟ access خمسة، شوف كيف هي خمسة
+
+300
+00:33:16,840 --> 00:33:26,440
+طيب وين الـ
+
+301
+00:33:26,440 --> 00:33:31,180
+لأ
+
+302
+00:33:31,180 --> 00:33:36,080
+هاي ال handle وين بيكون؟ على الخمسة، على الخمسة، اه
+
+303
+00:33:36,080 --> 00:33:39,060
+شكرا، okay
+
+304
+00:33:40,530 --> 00:33:46,230
+هذه one، تسأل المريض، طيب
+
+305
+00:33:46,230 --> 00:33:50,770
+هيك؟ أحسن؟
+
+306
+00:33:50,770 --> 00:33:54,070
+نفس
+
+307
+00:33:54,070 --> 00:34:00,130
+الحاجة هي، ليش بتغيري يدك؟ هي واحدة، اثنتين، أو
+
+308
+00:34:00,130 --> 00:34:05,010
+هيك، يعني بس بتعمل عملية rotation، flip، إنه بده و
+
+309
+00:34:05,010 --> 00:34:05,510
+مرة ثانية
+
+310
+00:34:18,510 --> 00:34:22,750
+Okay؟ هعملوا rotation، خليها هي تشتغل، يعني دائماً
+
+311
+00:34:22,750 --> 00:34:25,950
+الـ ال handle بتاعة ال cross cylinder بحطها
+
+312
+00:34:25,950 --> 00:34:29,610
+موازية على مين؟ ال axis اللي أنا حطيته، بشوف هل هذا
+
+313
+00:34:29,610 --> 00:34:33,990
+ال axis صح ولا لأ، okay؟ أه، تفضلي
+
+314
+00:34:48,310 --> 00:34:57,890
+على الـ كم بدك تحطيه؟ خمسة خمسة خمسة
+
+315
+00:34:57,890 --> 00:35:02,530
+خمسة
+
+316
+00:35:02,530 --> 00:35:03,230
+خمسة خمسة خمسة خمسة خمسة خمسة
+
+317
+00:35:03,230 --> 00:35:03,350
+خمسة خمسة خمسة خمسة خمسة خمسة
+
+318
+00:35:03,350 --> 00:35:03,790
+خمسة خمسة خمسة خمسة خمسة خمسة
+
+319
+00:35:03,790 --> 00:35:03,850
+خمسة خمسة خمسة خمسة خمسة خمسة
+
+320
+00:35:03,850 --> 00:35:03,930
+خمسة خمسة خمسة خمسة خمسة خمسة
+
+321
+00:35:03,930 --> 00:35:11,550
+خمسة خمسة خمسة خمسة خمسة خمسة
+
+322
+00:35:11,550 --> 00:35:17,310
+خمسة خمسة
+
+323
+00:35:17,310 --> 00:35:24,720
+هيك الخمسة، صح؟ اه، هلجيت بجيب العدسة ال handle
+
+324
+00:35:24,720 --> 00:35:30,280
+بتاعتها، بدها تكون موازية لمين؟ للخمسة؟ يعني هيك؟
+
+325
+00:35:30,280 --> 00:35:39,620
+بالظبط، ايه ليش بترجع؟ هيك؟ اه، أو هيك؟ صحيح، أو هيك؟
+
+326
+00:35:39,620 --> 00:35:44,920
+بالظبط، okay، طب
+
+327
+00:35:44,920 --> 00:35:46,280
+اعمل على ال axis ثلاثين
+
+328
+00:35:54,020 --> 00:36:08,740
+أعمل ال lift، أسألك عشان مقصور من ال ride في
+
+329
+00:36:08,740 --> 00:36:11,800
+حد مش فاهم ال jacks on a cross cylinder، هذا
+
+330
+00:36:11,800 --> 00:36:13,500
+verification لل access
+
+331
+00:36:24,670 --> 00:36:31,010
+احنا بنعمله لمين؟ لل access، okay، after that we
+
+332
+00:36:31,010 --> 00:36:38,230
+will start for cylinder، for power cylinder
+
+333
+00:36:38,230 --> 00:36:46,670
+عرفت زي ما هي دي؟ ثانية، قلنا الأكم؟ ثلاثين، ممتاز
+
+334
+00:36:46,670 --> 00:36:47,170
+ايه؟
+
+335
+00:36:54,540 --> 00:37:00,440
+بالظبط، أن يكون موازي لمين؟ الآن، طيب بالنسبة
+
+336
+00:37:00,440 --> 00:37:04,740
+للموضوع ال power، إنه كيف ال jason، ال cross
+
+337
+00:37:04,740 --> 00:37:10,920
+cylinder، بعمل verification لل power، الآن لما أنا
+
+338
+00:37:10,920 --> 00:37:16,400
+ببدأ في ال power already، أنا صلحت من ال axis، okay
+
+339
+00:37:16,400 --> 00:37:24,130
+الآن زي ما أنتم شايفين، في الخط اللي الأسود وفي
+
+340
+00:37:24,130 --> 00:37:29,190
+الخط الأحمر، صح؟ الآن هدول الخطوط هما اللي هيكونوا
+
+341
+00:37:29,190 --> 00:37:37,810
+ايش؟ متوازين مع ال access بتاعي، يعني بمعنى أنه
+
+342
+00:37:37,810 --> 00:37:42,050
+الآن، هانحرك، حطيت رهد ثلاثين، okay؟
+
+343
+00:37:46,910 --> 00:37:53,190
+يعني لو كان أنا مثلاً عندي الآن minus واحد ونصف
+
+344
+00:37:53,190 --> 00:37:57,090
+يعني بحط ال minus واحد وربع، بيصير كده sorry
+
+345
+00:37:57,090 --> 00:38:02,350
+minus ربع، minus واحد ونصف، بيصير كده؟ واحد وخمس و
+
+346
+00:38:02,350 --> 00:38:09,230
+سبعين، okay، إذا بجيب الأحمر، بحط موازية مين؟ للـ
+
+347
+00:38:09,230 --> 00:38:15,880
+ثلاثين، ممكن أقبل أسود، يعني مرة بعمل، بزود، هين زودت
+
+348
+00:38:15,880 --> 00:38:24,160
+ال minus، بقوله هيك أوضح ولا هيك، okay، أو هيك، يعني
+
+349
+00:38:24,160 --> 00:38:29,100
+بمعنى، يما حطيت ال minus ربع، شو أنا عملت؟ زودت الـ
+
+350
+00:38:29,100 --> 00:38:33,560
+minus، زودت ال minus، ويما حطيت plus ربع، قللت الـ
+
+351
+00:38:33,560 --> 00:38:38,860
+minus، صح؟ فمرة بجرب في ال plus ومرة فيه ال minus
+
+352
+00:38:40,060 --> 00:38:43,940
+طيب، إذا قال لي الاثنتين مش واضحات، بيكون ال power
+
+353
+00:38:43,940 --> 00:38:52,360
+اللي أنا موجود فيه ايه؟ صح، واضح، مرة ثانية، الآن أنا
+
+354
+00:38:52,360 --> 00:38:58,000
+حاطط على ال axes ثلاثين، okay، هي في عندي زي ما
+
+355
+00:38:58,000 --> 00:39:01,700
+أنتم شفتوا في ال black وفي ال red، ال black والـ
+
+356
+00:39:01,700 --> 00:39:06,480
+red، معنى ال black أنه بدي أضيف، أضيف plus ربع، الـ
+
+357
+00:39:06,480 --> 00:39:09,920
+minus، بمعنى بدي أقلل، يعني بدي أطرح، okay
+
+358
+00:39:12,510 --> 00:39:19,250
+وين بحطه؟ موازي موازي لمين؟ لل access بتاعك، هي
+
+359
+00:39:19,250 --> 00:39:27,110
+هيك أو هيك، يعني بمعنى هيك، نقصت، وهيك ايه؟
+
+360
+00:39:27,110 --> 00:39:33,570
+زودت، فهنا إذا مثلاً قال لي في الوضع الأول أوضح، يعني
+
+361
+00:39:33,570 --> 00:39:37,090
+لو فرضنا الأسود هو الوضع الأول، بقول minus واحد و
+
+362
+00:39:37,090 --> 00:39:43,450
+نصف ناقص الربع، قداش؟ plus ربع، minus واحد وربع، صح؟ لو
+
+363
+00:39:43,450 --> 00:39:49,210
+مثلاً ال minus ربع، طلعتها من ال minus واحد ونصف
+
+364
+00:39:49,210 --> 00:39:53,830
+صارت واحد وخمسة وسبعين، okay؟
+
+365
+00:39:58,040 --> 00:40:06,100
+ال red slash موازية لمين؟ لل access بتاعي، okay، هذه
+
+366
+00:40:06,100 --> 00:40:10,380
+طريقة مين؟ ال power، طيب مين ببدأ في الأول؟ ال access
+
+367
+00:40:10,380 --> 00:40:22,100
+ولا ال power، في ال cylinder، why؟ السؤال
+
+368
+00:40:22,100 --> 00:40:25,820
+مين ببدأ في الأول؟ ال power ولا ال access، why؟
+
+369
+00:40:34,580 --> 00:40:38,480
+نبدأ بال access، why؟ لأن لو احنا حطينا له العدسة و
+
+370
+00:40:38,480 --> 00:40:42,000
+نسينا نعمل Jackson، بس إذا ما شفناش ولا واحد، أقول أنا
+
+371
+00:40:42,000 --> 00:40:48,000
+عندي ال power ولا ال access، بور
+
+372
+00:40:48,000 --> 00:40:51,320
+ولا ال access؟ ال access، يعني أنه احنا هال program
+
+373
+00:40:51,320 --> 00:40:54,380
+أول شغلة نعملها في ال access، لو ما شفناش ال access
+
+374
+00:40:54,380 --> 00:40:57,200
+ولا يعني ما شفناش ال access ولا عدسة ال Jackson
+
+375
+00:40:57,200 --> 00:41:00,320
+أقول أنا عندي ال power ولا ال access، okay، another
+
+376
+00:41:00,320 --> 00:41:04,670
+answer، لأن لو حددنا ال power الصح، فلما يعني الـ
+
+377
+00:41:04,670 --> 00:41:07,310
+access غلط، وال power الصح هو مش عارف شوفيه، فبنعمل
+
+378
+00:41:07,310 --> 00:41:10,410
+ال access عشان نثبت أن ال power الصح هو بالظبط
+
+379
+00:41:10,410 --> 00:41:13,210
+أنه هتكون ايش؟ blurred لل vision، يعني ال access أنا
+
+380
+00:41:13,210 --> 00:41:16,670
+بعرف الصح، يعني لو أنا روحت على ال astigmatic fan
+
+381
+00:41:16,670 --> 00:41:20,690
+هيديني واحد من ال line هيكون more clear compared
+
+382
+00:41:20,690 --> 00:41:23,770
+to the other، فدائماً أنا ببدأ في ال access، بعدين
+
+383
+00:41:23,770 --> 00:41:26,530
+بأخذ مين؟ ال power، طب حتى لو ال power خلاني الـ
+
+384
+00:41:26,530 --> 00:41:30,170
+power هتكون blurred؟ okay، بس الـ ال power دائماً
+
+385
+00:41:30,170 --> 00:41:33,750
+في ال astigmatism ما بيكونش تأثيره أعلى من ال access
+
+386
+00:41:40,380 --> 00:41:44,700
+يكون discomfort، مش مرتاح، طيب ممكن نعمل الـ
+
+387
+00:41:44,700 --> 00:41:49,660
+procedure بتاعة الـ ال power، فيه بدنا two groups
+
+388
+00:41:49,660 --> 00:41:53,140
+بتاعي
+
+389
+00:41:53,140 --> 00:42:04,580
+ايمان، بتاع حنان ونور، مين كمان؟ ورانيا، يلا أسرع
+
+390
+00:42:24,920 --> 00:42:33,720
+في minus واحد ونصف، مين بتكلم؟ حاضر
+
+391
+00:42:33,720 --> 00:42:45,740
+طب، فهمت ال method؟ okay، تعالى، يصيبون، Axis ثلاثين و
+
+392
+00:42:45,740 --> 00:43:17,160
+left eye، لأنه في minus واحد ونصف، access عشرين، اختصار
+
+393
+00:43:17,160 --> 00:43:23,300
+لجهاز cross-cylinder، بتكتب بشكل هذا، إيمان وحنان، أنت
+
+394
+00:43:23,300 --> 00:43:26,480
+اشتغلي الها ال right، وأنت ال left، يعني اعملوا
+
+395
+00:43:26,480 --> 00:43:29,900
+rotation، okay؟ أه، تفضلي
+
+396
+00:43:45,040 --> 00:43:50,160
+المريض، أه، ال right، لأن تتعامل مع المريض بيكون
+
+397
+00:43:50,160 --> 00:43:56,240
+الدقة في الأول، يعني ال accuracy مهمة كتير، بس
+
+398
+00:43:56,240 --> 00:43:59,
+
+445
+00:49:33,440 --> 00:49:38,320
+شيوع ال excess كده إيش؟
+
+446
+00:49:43,620 --> 00:49:51,380
+بالظبط بستخدم اللي هو مين ال screw، okay، هاي الصح؟
+
+447
+00:49:51,380 --> 00:49:56,540
+اه هاي
+
+448
+00:49:56,540 --> 00:50:02,820
+الأحمر؟ لأ، عليها، ارفعي يدك شوية، سابرين، هاتي شوية الـ
+
+449
+00:50:02,820 --> 00:50:08,200
+.. الـ gen two امتازة، حطيتي على التلاتين، صح؟ اه، هاي
+
+450
+00:50:08,200 --> 00:50:13,600
+العدسة هي موازية للتلاتين، هيك أفضل ولا هيك ولا هيك؟
+
+451
+00:50:13,600 --> 00:50:32,080
+okay، one، two، three، اه
+
+452
+00:50:32,080 --> 00:50:36,960
+والتالتة without، هي مرة تانية
+
+453
+00:50:43,620 --> 00:50:57,300
+هي one، two، three، okay، again، ممتاز
+
+454
+00:50:57,300 --> 00:51:01,840
+طيب، إن شاء الله بنكون هيك أنهينا الـ Jackson cross
+
+455
+00:51:01,840 --> 00:51:06,520
+cylinder، في المحاضرة القادمة إن شاء الله هنترجم
+
+456
+00:51:06,520 --> 00:51:09,080
+بعض الأمور عن الـ Jackson cross cylinder
diff --git a/PL9fwy3NUQKwaBhVI6LPr803vc5wWl9Iy_/Yn5Ckh9qadE_raw.json b/PL9fwy3NUQKwaBhVI6LPr803vc5wWl9Iy_/Yn5Ckh9qadE_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..5c4f19848fbc952145932410a2c381df44078a66
--- /dev/null
+++ b/PL9fwy3NUQKwaBhVI6LPr803vc5wWl9Iy_/Yn5Ckh9qadE_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 3485, "start": 20.81, "end": 34.85, "text": "طيب بسم الله الرحمن الرحيم السلام عليكم ورحمة الله وبركاته and a very good afternoon to all of you بالنسبة لموضوع ال diachrome test موضوع ال astigmatic fan موضوع يعني مهم", "tokens": [9566, 1829, 3555, 4724, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 21136, 37440, 25894, 24793, 4032, 2288, 35571, 3660, 21984, 4032, 26890, 4117, 9307, 3224, 293, 257, 588, 665, 6499, 281, 439, 295, 291, 20666, 1863, 35457, 3660, 32767, 2407, 11242, 45367, 2423, 1026, 608, 11505, 1500, 3714, 2407, 11242, 45367, 2423, 5357, 20181, 2399, 3429, 3714, 2407, 11242, 45367, 37495, 22653, 3714, 16095], "avg_logprob": -0.17234848191340765, "compression_ratio": 1.5149700598802396, "no_speech_prob": 8.14199447631836e-05, "words": [{"start": 20.81, "end": 21.07, "word": "طيب", "probability": 0.8678385416666666}, {"start": 21.07, "end": 21.27, "word": " بسم", "probability": 0.810302734375}, {"start": 21.27, "end": 21.39, "word": " 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17822, "start": 149.54, "end": 178.22, "text": "إذا هان ال minus two إنه بدنا نكتب ال red color is slightly clear compared to green color", "tokens": [28814, 15730, 8032, 7649, 2423, 3175, 732, 36145, 3224, 47525, 8315, 8717, 4117, 2655, 3555, 2423, 2182, 2017, 307, 4748, 1850, 5347, 281, 3092, 2017], "avg_logprob": -0.22490985978108186, "compression_ratio": 1.1111111111111112, "no_speech_prob": 0.0, "words": [{"start": 149.54, "end": 149.84, "word": "إذا", "probability": 0.677734375}, {"start": 149.84, "end": 150.2, "word": " هان", "probability": 0.5281982421875}, {"start": 150.2, "end": 150.44, "word": " ال", "probability": 0.96484375}, {"start": 150.44, "end": 150.84, "word": " minus", "probability": 0.630859375}, {"start": 150.84, "end": 151.3, "word": " two", "probability": 0.56005859375}, {"start": 151.3, "end": 152.96, "word": " إنه", "probability": 0.6571044921875}, {"start": 152.96, "end": 153.14, "word": " بدنا", "probability": 0.9736328125}, {"start": 153.14, "end": 153.68, 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color is slightly clear compared to green color في ال minus نص؟ بمعنى ليش أنه المريض شاف درجة شوية أوضح أو التنتين متساويات الوضوح في ال minus نص؟", "tokens": [9566, 1829, 3555, 12399, 6024, 48506, 41850, 44713, 9778, 40448, 2655, 11933, 1829, 8592, 22807, 3175, 8717, 9381, 12399, 20328, 5016, 12399, 6024, 48506, 45164, 8608, 6027, 31371, 8608, 33604, 6027, 983, 264, 2182, 2017, 307, 4748, 1850, 5347, 281, 3092, 2017, 8978, 2423, 3175, 8717, 9381, 22807, 4724, 2304, 3615, 1863, 7578, 32239, 8592, 14739, 3224, 9673, 16572, 11242, 13412, 31845, 11778, 47341, 3660, 13412, 2407, 10632, 34051, 11242, 5016, 34051, 16712, 29399, 9957, 44650, 3794, 995, 45865, 9307, 2423, 2407, 11242, 2407, 5016, 8978, 2423, 3175, 8717, 9381, 22807], "avg_logprob": -0.13637907624892567, "compression_ratio": 1.5714285714285714, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 179.60999999999999, "end": 180.73, "word": "طيب،", "probability": 0.7413330078125}, {"start": 180.73, "end": 181.01, "word": 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"words": [{"start": 2500.38, "end": 2500.56, "word": "يكون", "probability": 0.55792236328125}, {"start": 2500.56, "end": 2501.54, "word": " discomfort", "probability": 0.9111328125}, {"start": 2501.54, "end": 2501.8, "word": " مش", "probability": 0.87158203125}, {"start": 2501.8, "end": 2502.26, "word": " مرتاح", "probability": 0.9762369791666666}, {"start": 2502.26, "end": 2503.4, "word": " طيب", "probability": 0.9295247395833334}, {"start": 2503.4, "end": 2504.2, "word": " ممكن", "probability": 0.973388671875}, {"start": 2504.2, "end": 2504.56, "word": " نعمل", "probability": 0.9978841145833334}, {"start": 2504.56, "end": 2504.7, "word": " ال", "probability": 0.97412109375}, {"start": 2504.7, "end": 2505.2, "word": " procedure", "probability": 0.95166015625}, {"start": 2505.2, "end": 2505.72, "word": " بتاعة", "probability": 0.9537760416666666}, {"start": 2505.72, "end": 2505.96, "word": " ال", "probability": 0.9736328125}, {"start": 2505.96, "end": 2506.32, "word": " ..", 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{"start": 2555.98, "end": 2556.3, "word": " فهمت", "probability": 0.9860026041666666}, {"start": 2556.3, "end": 2556.5, "word": " ال", "probability": 0.953125}, {"start": 2556.5, "end": 2557.94, "word": " method؟", "probability": 0.818115234375}, {"start": 2557.94, "end": 2558.2, "word": " okay", "probability": 0.4619140625}, {"start": 2558.2, "end": 2559.6, "word": " تعالى", "probability": 0.677734375}, {"start": 2559.6, "end": 2559.92, "word": " يصيبون", "probability": 0.5215576171875}, {"start": 2559.92, "end": 2561.68, "word": " Axis", "probability": 0.47509765625}, {"start": 2561.68, "end": 2563.58, "word": " تلاتين", "probability": 0.8880615234375}, {"start": 2563.58, "end": 2565.74, "word": " و", "probability": 0.65576171875}, {"start": 2565.74, "end": 2566.0, "word": " left", "probability": 0.47216796875}, {"start": 2566.0, "end": 2566.44, "word": " eye", "probability": 0.861328125}, {"start": 2566.44, "end": 2568.7, "word": " بلانه", "probability": 0.6547698974609375}, 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اشرين", "probability": 0.595947265625}, {"start": 2574.9, "end": 2597.16, "word": " اختصار", "probability": 0.6143341064453125}, {"start": 2597.16, "end": 2597.6, "word": " لجهاز", "probability": 0.458984375}, {"start": 2597.6, "end": 2597.86, "word": " cross", "probability": 0.1622314453125}, {"start": 2597.86, "end": 2598.48, "word": "-cylinder", "probability": 0.69146728515625}, {"start": 2598.48, "end": 2598.98, "word": " بتكتب", "probability": 0.7833251953125}, {"start": 2598.98, "end": 2599.4, "word": " بشكل", "probability": 0.8250325520833334}, {"start": 2599.4, "end": 2599.68, "word": " هذا", "probability": 0.9052734375}], "temperature": 1.0}, {"id": 85, "seek": 260990, "start": 2601.26, "end": 2609.9, "text": "إمان و حنان انت اشتغلي الها ال right و انت ال left يعني اعملوا rotation okay؟ اه تفضلي", "tokens": [28814, 2304, 7649, 4032, 11331, 1863, 7649, 16472, 2655, 1975, 8592, 2655, 17082, 20292, 2423, 11296, 2423, 558, 4032, 16472, 2655, 2423, 1411, 37495, 22653, 1975, 25957, 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"probability": 0.954345703125}, {"start": 3058.58, "end": 3058.68, "word": " الله", "probability": 0.9609375}, {"start": 3058.68, "end": 3059.2, "word": " بنكون", "probability": 0.92626953125}, {"start": 3059.2, "end": 3059.82, "word": " هيك", "probability": 0.937255859375}, {"start": 3059.82, "end": 3060.86, "word": " أنهينا", "probability": 0.8956298828125}, {"start": 3060.86, "end": 3061.2, "word": " ال", "probability": 0.89794921875}, {"start": 3061.2, "end": 3061.5, "word": " Jackson", "probability": 0.5927734375}, {"start": 3061.5, "end": 3061.84, "word": " cross", "probability": 0.7177734375}, {"start": 3061.84, "end": 3062.32, "word": " cylinder", "probability": 0.69287109375}, {"start": 3062.32, "end": 3062.98, "word": " في", "probability": 0.7607421875}, {"start": 3062.98, "end": 3063.58, "word": " المحاضرة", "probability": 0.98974609375}, {"start": 3063.58, "end": 3064.22, "word": " القادمة", "probability": 0.9895833333333334}, {"start": 3064.22, "end": 3064.4, "word": " ان", "probability": 0.89794921875}, {"start": 3064.4, "end": 3064.56, "word": " شاء", "probability": 0.99560546875}, {"start": 3064.56, "end": 3064.8, "word": " الله", "probability": 0.96142578125}, {"start": 3064.8, "end": 3066.52, "word": " هنترجم", "probability": 0.966552734375}, {"start": 3066.52, "end": 3066.84, "word": " بعض", "probability": 0.989990234375}, {"start": 3066.84, "end": 3067.38, "word": " الأمور", "probability": 0.9855143229166666}, {"start": 3067.38, "end": 3067.68, "word": " عن", "probability": 0.99755859375}, {"start": 3067.68, "end": 3067.84, "word": " ال", "probability": 0.5244140625}, {"start": 3067.84, "end": 3068.2, "word": " Jackson", "probability": 0.8564453125}, {"start": 3068.2, "end": 3068.82, "word": " cross", "probability": 0.9130859375}, {"start": 3068.82, "end": 3069.08, "word": " cylinder", "probability": 0.81005859375}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3069.213625, "duration_after_vad": 2471.381874999991}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwaBhVI6LPr803vc5wWl9Iy_/Yn5Ckh9qadE_raw.srt b/PL9fwy3NUQKwaBhVI6LPr803vc5wWl9Iy_/Yn5Ckh9qadE_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..4d489bfb243aa02a19f2ae8782c4fa60fe205639
--- /dev/null
+++ b/PL9fwy3NUQKwaBhVI6LPr803vc5wWl9Iy_/Yn5Ckh9qadE_raw.srt
@@ -0,0 +1,1840 @@
+1
+00:00:20,810 --> 00:00:23,910
+طيب بسم الله الرحمن الرحيم السلام عليكم ورحمة الله
+
+2
+00:00:23,910 --> 00:00:27,690
+وبركاته and a very good afternoon to all of you
+
+3
+00:00:27,690 --> 00:00:32,290
+بالنسبة لموضوع ال diachrome test موضوع ال
+
+4
+00:00:32,290 --> 00:00:39,140
+astigmatic fan موضوع يعني مهملو في معمل أو مادة ال
+
+5
+00:00:39,140 --> 00:00:42,980
+refraction لازم تكونوا مستوعبينها مية في المية
+
+6
+00:00:42,980 --> 00:00:48,280
+الديوكروم تست حديكم بعض الأمثلة عشان انه نصير ايش
+
+7
+00:00:48,280 --> 00:00:55,560
+نتدرب اكثر okay يعني الان لو مثلا حكينا في مثال ال
+
+8
+00:00:55,560 --> 00:01:00,260
+right eye minus
+
+9
+00:01:00,260 --> 00:01:05,560
+نص ديوبتر سفير okay
+
+10
+00:01:09,780 --> 00:01:13,200
+إذا في ال right eye minus نص ده يبتر السفير، لو
+
+11
+00:01:13,200 --> 00:01:19,520
+أنا حاطيه قدام العين minus one ده يبتر السفير، شو
+
+12
+00:01:19,520 --> 00:01:25,320
+بدي يصير؟ بالظبط، بدنا دايما اتكلمي كمصطلح over
+
+13
+00:01:25,320 --> 00:01:29,880
+correction، إذا minus one هيعمل over correction،
+
+14
+00:01:29,880 --> 00:01:34,500
+أي بمعنى إن ال light rays وين هتتركز؟بهايبر اتنق
+
+15
+00:01:34,500 --> 00:01:39,440
+اي بمعنى هيصير artificial هايبرمتروب okay؟ اذا هذا
+
+16
+00:01:39,440 --> 00:01:44,320
+artificial
+
+17
+00:01:44,320 --> 00:01:48,200
+hypermetrop
+
+18
+00:01:48,200 --> 00:01:51,660
+اي
+
+19
+00:01:51,660 --> 00:01:55,560
+بمعنى hypermetrop اشماله كاذب، artificial كاذب او
+
+20
+00:01:55,560 --> 00:02:02,340
+صناعي okay؟ ليش يا نديم؟ليش ال minus one صار
+
+21
+00:02:02,340 --> 00:02:05,160
+artificial hypermetroid؟ لأنه ال data over
+
+22
+00:02:05,160 --> 00:02:13,560
+connection صح؟ طيب لو أنا حطيت minus نص بالظبط
+
+23
+00:02:13,560 --> 00:02:18,920
+لكن بيقول في بعض الكتب أنه دايما ال red slightly
+
+24
+00:02:18,920 --> 00:02:24,020
+compared to green okay يعني دايما ال red بيكون
+
+25
+00:02:24,020 --> 00:02:30,200
+أوضح بدرجة بسيطة عن مين؟ عن اللي green okayإذا هان
+
+26
+00:02:30,200 --> 00:02:40,140
+ال minus two إنه بدنا نكتب ال red color is
+
+27
+00:02:40,140 --> 00:02:45,260
+slightly clear
+
+28
+00:02:45,260 --> 00:02:48,500
+compared
+
+29
+00:02:48,500 --> 00:02:53,000
+to
+
+30
+00:02:53,000 --> 00:02:58,220
+green color
+
+31
+00:02:59,610 --> 00:03:05,130
+طيب، الآن أنا استخدمت إيش؟ minus نص، صح، الآن لو
+
+32
+00:03:05,130 --> 00:03:12,330
+سالتي سؤال why the red color is slightly clear
+
+33
+00:03:12,330 --> 00:03:19,850
+compared to green color في ال minus نص؟ بمعنى
+
+34
+00:03:19,850 --> 00:03:25,590
+ليش أنه المريض شاف درجة شوية أوضح أو التنتين
+
+35
+00:03:25,590 --> 00:03:28,870
+متساويات الوضوح في ال minus نص؟
+
+36
+00:03:31,880 --> 00:03:35,860
+تفسير دايما ال interruption لازم يكون logic منطق
+
+37
+00:03:35,860 --> 00:03:40,480
+انه خلانا الأشياء هتتركز على ال truth بالظبط هاي
+
+38
+00:03:40,480 --> 00:03:43,520
+الجواب ان ال incident light rays are brought to
+
+39
+00:03:43,520 --> 00:03:49,920
+focus on the truth okay اذا هان ايش بكتب ان ال
+
+40
+00:03:49,920 --> 00:03:55,940
+incident light
+
+41
+00:03:55,940 --> 00:03:59,380
+rays
+
+42
+00:04:08,520 --> 00:04:14,620
+to focus on
+
+43
+00:04:14,620 --> 00:04:19,740
+the retina ممكن
+
+44
+00:04:19,740 --> 00:04:23,740
+واحدة تانية تكتب sharply the retina okay نفس
+
+45
+00:04:23,740 --> 00:04:29,140
+المعنى أو on the retina طيب الآن يا ولا يما
+
+46
+00:04:29,140 --> 00:04:34,880
+استخدمنا ال minus one صار إيش في عنده بالظبط over
+
+47
+00:04:34,880 --> 00:04:36,480
+correction شو معناها؟
+
+48
+00:04:39,260 --> 00:04:44,500
+بالظبط انه تركزت وين behind ال retina واضحة النقطة
+
+49
+00:04:44,500 --> 00:04:48,300
+هذه طالبات
+
+50
+00:04:48,300 --> 00:04:51,260
+اللي اجوا جداد الان احنا بنشرح في موضوع ال
+
+51
+00:04:51,260 --> 00:04:54,900
+diachrome test أخدنا عن ال diachrome test quiz كان
+
+52
+00:04:54,900 --> 00:05:00,220
+صغير انه كيف بتم تصحيح او ال verification
+
+53
+00:05:09,400 --> 00:05:13,940
+الان اجانب patient كان عنده minus نص ديوبتر السفير
+
+54
+00:05:13,940 --> 00:05:18,800
+okay في ال right eye طيب انا روحت ال data minus
+
+55
+00:05:18,800 --> 00:05:24,020
+one ديوبتر السفير ايش معناه ال data؟ بالظبط شو
+
+56
+00:05:24,020 --> 00:05:28,540
+معناه مصطلح over correction طيب الان ال minus one
+
+57
+00:05:28,540 --> 00:05:31,100
+شو معناته صار هذا ال patient؟
+
+58
+00:05:35,680 --> 00:05:38,600
+يعني الـ refractive state الحالة الإنكسرية بتاعته
+
+59
+00:05:38,600 --> 00:05:42,260
+صارت over correction إذا ال light .. ال incident
+
+60
+00:05:42,260 --> 00:05:46,640
+light rays are brought to focus where؟ behind the
+
+61
+00:05:46,640 --> 00:05:51,460
+retina صح؟ في ال artificial hyper metro طيب الحالة
+
+62
+00:05:51,460 --> 00:05:55,820
+التانية ال data minus نص إذا إيش هيصير عنده؟ يعني
+
+63
+00:05:55,820 --> 00:05:58,940
+أنا مثلا أدي minus نص إنه صلحته ال data ال full
+
+64
+00:05:58,940 --> 00:06:01,660
+correction إذا ال light rays وين هتتركّر؟
+
+65
+00:06:29,690 --> 00:06:33,250
+طب لو افترضنا ال left eye كانت عنده hyper metroid
+
+66
+00:06:33,250 --> 00:06:37,950
+ممكن تكون hyper metroid؟ ممكن عين ميوب واحدة hyper
+
+67
+00:06:37,950 --> 00:06:47,110
+metroid ال left كانت plus three ديوب تر سفير طيب
+
+68
+00:06:47,110 --> 00:06:54,290
+الآن سين من الناس استخدمت plus اتنين ديوب تر سفير
+
+69
+00:06:54,290 --> 00:06:58,050
+شو معناه؟ مين هيشوف اوضح؟
+
+70
+00:07:06,900 --> 00:07:11,920
+أديته plus two، إذا شو معناها؟ under ولا over
+
+71
+00:07:11,920 --> 00:07:16,000
+correction؟ ولا correction؟ under correction صح؟
+
+72
+00:07:16,000 --> 00:07:18,960
+يعني أقل من القيمة المطلوبة
+
+73
+00:07:48,350 --> 00:07:52,070
+behind the retina لأنه ما زال هو يعتبر ايه hyper
+
+74
+00:07:52,070 --> 00:07:59,510
+metro واضح يا فاطمة طيب لو استخدمنا plus two point
+
+75
+00:07:59,510 --> 00:08:03,390
+fifty فاطمة
+
+76
+00:08:03,390 --> 00:08:08,070
+ايش هيكون under correction اذا وين ال light rays
+
+77
+00:08:08,070 --> 00:08:11,050
+هتتركز behind the retina
+
+78
+00:08:23,680 --> 00:08:26,940
+ميوب صح؟ يعني when ال incident light rays are
+
+79
+00:08:26,940 --> 00:08:31,560
+brought to focus where؟ in the front امتازة طيب لو
+
+80
+00:08:31,560 --> 00:08:35,860
+اديتوا plus ثلاثة؟ بالظبط
+
+81
+00:08:55,340 --> 00:09:04,340
+الـ Hyper Metro Okay واضحة في
+
+82
+00:09:04,340 --> 00:09:08,200
+ال place 4 ايش عملت؟ مابدى احفظنا عملت Artificial
+
+83
+00:09:08,200 --> 00:09:11,400
+Myopic يعني وين ال incident light rays are brought
+
+84
+00:09:11,400 --> 00:09:14,720
+to focus where؟ in front إذا صار هو ايش؟ Myopic
+
+85
+00:09:14,720 --> 00:09:19,260
+مين هيشوف الأوضح؟ الرب في حدا مش فاهم النقطة هذه
+
+86
+00:09:19,260 --> 00:09:22,780
+هذه
+
+87
+00:09:22,780 --> 00:09:23,660
+مهمة جدا
+
+88
+00:09:29,610 --> 00:09:33,610
+ممكن تلاقوا خارجين مابيعرفوش كلام الديوكروم تست
+
+89
+00:09:33,610 --> 00:09:40,050
+واضح مهم كثير وهذه أمانة أنا بحملكم إياها اللي مش
+
+90
+00:09:40,050 --> 00:09:44,630
+فاهمة تحكي okay يعني هذه المواضيع المهمة جدا لأن
+
+91
+00:09:44,630 --> 00:09:49,650
+الديوكروم تست تعتبر very accurate دقيقة كثير وبدها
+
+92
+00:09:49,650 --> 00:09:55,450
+ناس ان يكون عندهم knowledge كعلم كويس وزائد اللي
+
+93
+00:09:55,450 --> 00:10:00,070
+هو خبرة هاي احنا فهمناها الآن اعتقديعني اي سؤال او
+
+94
+00:10:00,070 --> 00:10:05,490
+اي تمثلة بتقدر تحليها طبعا بالاضافة للتطبيق العملي
+
+95
+00:10:05,490 --> 00:10:12,190
+انا
+
+96
+00:10:12,190 --> 00:10:18,070
+عارف ال astigmatic fan هي المحبط شوية اللي صعبة بس
+
+97
+00:10:18,070 --> 00:10:22,590
+الآن بنحاول نجيب اكم مسألة ان شاء الله بصير سهلة
+
+98
+00:10:22,590 --> 00:10:22,950
+كثير
+
+99
+00:10:34,240 --> 00:10:45,020
+خلصتي؟ حاضر ال right eye بلانه على minus تلاتة
+
+100
+00:10:45,020 --> 00:10:55,540
+اكسز قلبي هد ايش هد؟يعني الوصفة هذه cylinder هذه
+
+101
+00:10:55,540 --> 00:10:59,620
+عبارة عن ال final objective refraction يعني أخدتها
+
+102
+00:10:59,620 --> 00:11:03,500
+من ال retroscope أو ال auto refractometer إذا هذه
+
+103
+00:11:03,500 --> 00:11:10,400
+ايه؟ final objective
+
+104
+00:11:22,690 --> 00:11:28,870
+طيب الان minus 3 cylinder ال sphere قداش ال plano
+
+105
+00:11:28,870 --> 00:11:33,710
+يعني ماعنديش ايه ال sphere يعني الان يما باجيت بحط
+
+106
+00:11:33,710 --> 00:11:37,510
+في ال right بجيب عدسة minus 3 و بحطها قدام العين
+
+107
+00:11:37,510 --> 00:11:42,030
+okay نيجي بدنا نفهم كيف بدي استخدم ال astigmatic
+
+108
+00:11:42,030 --> 00:11:46,510
+fan ال astigmatic fan عبارة عن مجموعة ايه من
+
+109
+00:11:46,510 --> 00:11:53,430
+الخطوط الان بعرض الخطوط هذه لمين للمريضبسأل المريض
+
+110
+00:11:53,430 --> 00:11:58,390
+which line is more clear يعني أي واحد من الخطوط هو
+
+111
+00:11:58,390 --> 00:12:04,010
+أوضح مقارنة في الخطوط التانية okay؟ الآن زي ما
+
+112
+00:12:04,010 --> 00:12:08,470
+انتوا عارفين في عندنا التسعين والمية و تمانين
+
+113
+00:12:28,440 --> 00:12:33,040
+تقريبا هنا اذا هذا الخط هيكون ايش هو ال more clear
+
+114
+00:12:33,040 --> 00:12:39,040
+يعني اوضح خط هيشوفه ايه المريض ياما باجي انا
+
+115
+00:12:39,040 --> 00:12:43,520
+بستخدم العدسات ايش بحط ال access اللي عنده ال 40
+
+116
+00:12:43,520 --> 00:12:50,660
+فال 40 هي عمودي على مين اذا هو صلح مين ال 130 صح
+
+117
+00:12:50,660 --> 00:12:56,080
+واضح هيك اذا عملية .. لان ال access عمودي على مين
+
+118
+00:12:56,080 --> 00:13:01,370
+ال powerفانا الآن إما حطيت على ال axis 130 عملت
+
+119
+00:13:01,370 --> 00:13:07,350
+تصحيح لمين؟ لل .. لل axis ال 40 يعني العمودي عليه
+
+120
+00:13:07,350 --> 00:13:12,870
+okay فاحنا حكينا ال more clear هو يعتبر less
+
+121
+00:13:12,870 --> 00:13:17,210
+immature و ال less clear يعتبر ايه؟ more immature
+
+122
+00:13:17,210 --> 00:13:20,330
+ال more clear
+
+123
+00:13:29,300 --> 00:13:35,920
+less immature و
+
+124
+00:13:35,920 --> 00:13:39,480
+less clear
+
+125
+00:13:39,480 --> 00:13:47,220
+more clear more immature okay إذا علاقة إيه صارت
+
+126
+00:13:47,220 --> 00:13:50,720
+inverse relation علاقة عكسية
+
+127
+00:13:59,550 --> 00:14:05,550
+ولا ريتنسكوب جبت مريض غطيت عينه الشمال لقيت ال
+
+128
+00:14:05,550 --> 00:14:10,270
+line الواضح عنده كانت تلاتين بعرف ان وين بده أحط
+
+129
+00:14:10,270 --> 00:14:15,930
+ال trial cell على ال مية و عشرين لو غطيت العين و
+
+130
+00:14:15,930 --> 00:14:22,330
+مثلا جالي الواضح عشرة قداش طيب؟ محدد يجاوب؟ مية
+
+131
+00:14:22,330 --> 00:14:26,210
+ليش؟ ضفنا طيب لو قلنا مية و تلاتين اللي كان هو ال
+
+132
+00:14:26,210 --> 00:14:26,770
+more clear
+
+133
+00:14:30,160 --> 00:14:34,280
+بدنا نجس ايه؟ تسعين .. تسعين .. واضحة .. واضحة ..
+
+134
+00:14:34,280 --> 00:14:40,280
+واضحة .. واضحة
+
+135
+00:14:40,280 --> 00:14:45,460
+.. واضحة .. واضح .. واضح .. واضح .. واضح .. واضح
+
+136
+00:14:45,460 --> 00:14:45,460
+.. واضح .. واضح .. واضح .. واضح .. واضح .. واضح ..
+
+137
+00:14:45,460 --> 00:14:46,180
+واضح .. واضح .. واضح .. واضح .. واضح .. واضح ..
+
+138
+00:14:46,180 --> 00:14:46,180
+واضح .. واضح .. واضح .. واضح .. واضح .. واضح ..
+
+139
+00:14:46,180 --> 00:14:46,180
+واضح .. واضح .. واضح .. واضح .. واضح .. واضح ..
+
+140
+00:14:46,180 --> 00:14:46,180
+واضح .. واضح .. واضح .. واضح .. واضح .. واضح ..
+
+141
+00:14:46,180 --> 00:14:49,960
+واضح .. واضح .. واضح .. واضح .. واضح .. واضح ..
+
+142
+00:14:49,960 --> 00:14:56,280
+واضح .. واضح .. واضح .. واضح ..
+
+143
+00:15:02,250 --> 00:15:10,510
+فهو هيصلح مين ال 130 طيب
+
+144
+00:15:10,510 --> 00:15:13,590
+لو
+
+145
+00:15:13,590 --> 00:15:17,210
+فرضنا patient has refractive error بال left eye
+
+146
+00:15:17,210 --> 00:15:27,910
+حلو هذا plus one على minus four ال
+
+147
+00:15:27,910 --> 00:15:31,310
+left eye plus one
+
+148
+00:15:41,000 --> 00:15:46,880
+مين ال line اللي هيكون واضح؟ لو طلبت منك انه draw
+
+149
+00:15:46,880 --> 00:15:54,720
+انه ترسم ال .. ال هذا نعم بالظبط
+
+150
+00:15:54,720 --> 00:15:58,540
+في الرابع التاني بقدر انه ارسمه بحط هو ال more
+
+151
+00:15:58,540 --> 00:16:02,360
+clear compared to the other lines okay
+
+152
+00:16:05,890 --> 00:16:10,770
+في حد اللي مش فاهم ال astigmatic fan يعني الآن ال
+
+153
+00:16:10,770 --> 00:16:14,530
+astigmatic fan لو واحد كان عنده astigmatism بقدر
+
+154
+00:16:14,530 --> 00:16:18,970
+انه اعرف جديش ال axis من خلال ايه ال chart بدون لا
+
+155
+00:16:18,970 --> 00:16:26,630
+auto ولا ايه ولا retinascope اه تفضل اه
+
+156
+00:16:35,420 --> 00:16:41,520
+المية و خمساش more clear هو الواضح فاهم عيكي؟ يعني
+
+157
+00:16:41,520 --> 00:16:49,200
+هذا الخط بيكون مميز عن الخطوط التانية هو .. هو
+
+158
+00:16:49,200 --> 00:16:52,880
+اللي فيه ال defect من ناحية إيش؟ إن المريض شايفه
+
+159
+00:16:52,880 --> 00:16:55,920
+أوضح من الخطوط التانية لكن ال access بتاعي هو
+
+160
+00:16:55,920 --> 00:17:00,460
+الخمساش ال access اللي هو ال originalاللي أخدته
+
+161
+00:17:00,460 --> 00:17:03,020
+أنا من وين؟ من ال written scope أو من ال auto
+
+162
+00:17:03,020 --> 00:17:10,360
+refractometer أو من ال auto ..
+
+163
+00:17:10,360 --> 00:17:13,440
+طبعا
+
+164
+00:17:13,440 --> 00:17:17,660
+هذه هتطبقوها عملي يعني الآن هقولك اشتغلي على ال
+
+165
+00:17:17,660 --> 00:17:20,740
+auto أو على ال written scope كده اشطلع من ال axis
+
+166
+00:17:20,740 --> 00:17:24,740
+مثلا تسعين إذا مين هيكون مش واضح ال .. الواضح كتير
+
+167
+00:17:24,740 --> 00:17:28,800
+مين هيكون عند ال .. ال 108 العمودي عليه okay
+
+168
+00:17:30,990 --> 00:17:33,570
+طبعا هذه وين بنشتغل؟ في ال minus cylinder
+
+169
+00:17:33,570 --> 00:17:37,190
+according to the minus cylinder lens لكن لو قلتلك
+
+170
+00:17:37,190 --> 00:17:40,810
+according to the plus cylinder lens عكس الاشياء اه
+
+171
+00:17:40,810 --> 00:17:45,110
+بس ايه ايش بده يكون العكس؟ عكس انه الخمس عاشر ..
+
+172
+00:17:45,110 --> 00:17:49,650
+اه بالظبط اه طيب اليوم موضوعنا عن ال jackson
+
+173
+00:17:49,650 --> 00:17:52,890
+across cylinder ال jackson across cylinder هي
+
+174
+00:17:52,890 --> 00:17:57,850
+عبارة عن عدسة بتتكون من عدستين
+
+175
+00:18:04,410 --> 00:18:10,290
+التنتين متساويات في ال power يعني plus ربوع minus
+
+176
+00:18:10,290 --> 00:18:13,790
+ربوع إذا التنتين إيش مالهم؟ متساويات في ال power
+
+177
+00:18:13,790 --> 00:18:19,910
+مختلفين من ناحية إيش؟ الإشارة طيب الآن هدول
+
+178
+00:18:19,910 --> 00:18:24,470
+العدستين شايفهم عدسة واحدة صح؟ إذا هم متحدين إيه؟
+
+179
+00:18:24,470 --> 00:18:30,090
+مع بعض صح؟ okay هذا ال Jackson برجع عندك
+
+180
+00:18:33,340 --> 00:18:41,140
+بكون ال power فيهم ايه؟ فضل
+
+181
+00:18:41,140 --> 00:18:48,540
+ايه؟ اذا التنتين بكون فيهم .. شايفين الخطين؟ ركزوا
+
+182
+00:18:48,540 --> 00:18:54,280
+على الخط الأسود و الأحمر، في عندك خطين صح؟ في خط
+
+183
+00:18:54,280 --> 00:18:58,780
+أحمر و في خط أسود، بس شوية بسرعة عشان يشوف الجميل
+
+184
+00:19:14,480 --> 00:19:19,620
+من حيث الإشارة متعمدين ال power ايه؟ على بعض كل
+
+185
+00:19:19,620 --> 00:19:24,420
+axis واحدة مثلا بتكون مية و خمسة و تلاتين والتانية
+
+186
+00:19:24,420 --> 00:19:30,060
+كده؟ خمسة و أربعين اذا ال axis ايه؟ متعمد لاحظة في
+
+187
+00:19:30,060 --> 00:19:36,540
+العدسة في عندنا خط أحمر و في خط أسود صح؟ الآن انا
+
+188
+00:19:36,540 --> 00:19:39,060
+مثلا طبعا ال Jackson cross اللي
+
+189
+00:19:44,350 --> 00:19:50,410
+لمن؟ للسلندر ولا لل .. للسلندر .. للسلندر الان
+
+190
+00:19:50,410 --> 00:19:55,850
+مثلا انا فرضت عنده hand تلاتين يعني طلعت .. هانجدش
+
+191
+00:19:55,850 --> 00:20:00,550
+ال power واحد و نص شكرا
+
+192
+00:20:00,550 --> 00:20:08,910
+لو انا فرضت عنده plano على
+
+193
+00:20:08,910 --> 00:20:16,750
+minus واحد و نصaccess تلاتين هذا ايش ال final
+
+194
+00:20:16,750 --> 00:20:22,430
+objective reflection بروح الآن هي minus واحد و نص
+
+195
+00:20:22,430 --> 00:20:27,830
+على ال access جديش تلاتين طبعا هان بده يكون ايه
+
+196
+00:20:27,830 --> 00:20:31,930
+occluder للعين التانية لانه دايما بشتغل ايه
+
+197
+00:20:31,930 --> 00:20:34,810
+monocular monocular fashion
+
+198
+00:20:38,180 --> 00:20:42,020
+إذا هين حطيت العدسة للسلندر على ال axis كام؟
+
+199
+00:20:42,020 --> 00:20:47,620
+تلاتين الآن بدي انا اعمل verification لل axis زي
+
+200
+00:20:47,620 --> 00:20:54,660
+ما انتوا شايفين في عندنا واحدة ال black وفي عندنا
+
+201
+00:20:54,660 --> 00:20:59,780
+ال red okay الآن التنتين إيش معلهم؟ متعمدين على
+
+202
+00:20:59,780 --> 00:21:04,700
+بعضهم صح؟ إذا واحدة مثلا على خمسة و أربعين والتاني
+
+203
+00:21:04,700 --> 00:21:09,770
+على كم؟ مية و خمسة و تلاتينلهان واضح؟ لهان واضح
+
+204
+00:21:09,770 --> 00:21:18,730
+بجيب الآن ال handle ال E بتاعتها okay بحطها
+
+205
+00:21:18,730 --> 00:21:23,230
+وين؟ متعامدة مع ال access بتاعي على التلاتين hand
+
+206
+00:21:23,230 --> 00:21:30,370
+بالظبط بقول للمريض هيك أوضح ولا هيك أوضح ولا هيك
+
+207
+00:21:39,120 --> 00:21:42,880
+يعني حطيتها يعني متعامد على وين؟ على التلاتين okay
+
+208
+00:21:42,880 --> 00:21:49,940
+فبقول للمريض هيك أحسن ولا هيك ولا هيك إذا جلت
+
+209
+00:21:49,940 --> 00:21:54,360
+تلاتة زي بعض بعرف أنه عندي مشكلة إيه في ال power
+
+210
+00:21:54,360 --> 00:21:58,180
+يعني لسه أنا مش مصلح ال power كويس خليني أجابل
+
+211
+00:21:58,180 --> 00:22:01,080
+النقطة هذه الآن لو جل مثلا
+
+212
+00:22:03,960 --> 00:22:09,800
+بدونهم أفضل، بالظبط، إذا ال access بتاعي إيش؟ صح،
+
+213
+00:22:09,800 --> 00:22:15,220
+okay إذا هي ال handle وان حطيتها parallel to the
+
+214
+00:22:15,220 --> 00:22:20,260
+access بتاعيإذا يعني متوازي مع مين؟ مع ال access
+
+215
+00:22:20,260 --> 00:22:25,500
+فانا الآن في زي ما اتفقنا من جهة بتكون خمسة
+
+216
+00:22:25,500 --> 00:22:29,260
+واربعين ومن جهة التانية قداشر؟ مية وخمسة و تلاتين
+
+217
+00:22:29,260 --> 00:22:34,500
+حطيتهم إيش مالهم متوازية بشكل متوازي يعني ال
+
+218
+00:22:34,500 --> 00:22:39,740
+handle هيك متوازي okay بحرك هيك و هيك طيب لو قاللي
+
+219
+00:22:39,740 --> 00:22:47,910
+مثلا من اتجاه الصورة الأولى هي الأوضحبالظبط قال لي
+
+220
+00:22:47,910 --> 00:22:51,410
+واحدة واحدة واحدة واحدة اذا الصورة الاولى قاللي هي
+
+221
+00:22:51,410 --> 00:22:55,890
+الاوضح اذا ايش انا شايف الاسوأ الصح اذا وين بروح
+
+222
+00:22:55,890 --> 00:23:03,030
+بحرك بحرك باتجاه ال plus ال
+
+223
+00:23:03,030 --> 00:23:07,130
+اولى
+
+224
+00:23:07,130 --> 00:23:17,340
+فهمتوها حاضر الان هي العدسة كده ع minusعلى axis 30
+
+225
+00:23:17,340 --> 00:23:21,440
+صح؟ متفقين على الفور؟ يعني انا روح اتحطيت العدسة
+
+226
+00:23:21,440 --> 00:23:26,340
+على ال axis 30 هي ال handle تع مين؟ العدسة بحط
+
+227
+00:23:26,340 --> 00:23:31,480
+موازي على مين؟ على ال 30 هي موازي وين؟ على ال 30
+
+228
+00:23:31,480 --> 00:23:39,860
+okay؟ اذا بقول للمريض هيك واضح ولا هيك؟ ولا هيك؟
+
+229
+00:23:39,860 --> 00:23:46,240
+يعني عندك تلت خياراتلأ بدونهم افضل اذا ال access
+
+230
+00:23:46,240 --> 00:23:51,780
+ده يعني صح صح صح واضحة
+
+231
+00:23:51,780 --> 00:23:56,800
+النقطة الاولى اذا بس حطيت هذه يعني كأنها موازية لل
+
+232
+00:23:56,800 --> 00:24:00,740
+access طيب
+
+233
+00:24:00,740 --> 00:24:06,260
+الحالة التانية الان حطيت هذه موازية يعني انا اديته
+
+234
+00:24:06,260 --> 00:24:11,120
+الصورة الاولى جلب اتجاه جلب الصورة الاولى اوضح اذا
+
+235
+00:24:11,120 --> 00:24:12,780
+هاي انتش شايفه في plus صح
+
+236
+00:24:22,270 --> 00:24:29,310
+الان هنركيش شوية باتجاه ال plus يعني
+
+237
+00:24:29,310 --> 00:24:34,130
+مجانبة اللي هو rotation تدوير طيب الان نرجع على
+
+238
+00:24:34,130 --> 00:24:39,510
+التلاتين الان انا حركت باتجاه ال plus
+
+239
+00:24:43,600 --> 00:24:47,800
+ياما راحت حركت باتجاه ال minus جالي واضحة بروح
+
+240
+00:24:47,800 --> 00:24:51,400
+بحرك باتجاه مين ال minus إذا ال access بتاعي بيكون
+
+241
+00:24:51,400 --> 00:25:01,240
+باتجاه ال minus تفضلي مانا
+
+242
+00:25:01,240 --> 00:25:06,800
+ألجيت أه هذا السؤال ممتاز الآن حطيت مثلا على الخمس
+
+243
+00:25:06,800 --> 00:25:11,400
+عاشر كان ال access بتاعي الجديد بالظبط مرة تانية
+
+244
+00:25:11,960 --> 00:25:16,360
+بجيب ال .. ال handle بتاعة العدسة موازي وين؟
+
+245
+00:25:16,360 --> 00:25:21,940
+للخمساش و مرة تانية بعمل rotation لل .. ايه؟
+
+246
+00:25:21,940 --> 00:25:33,640
+للعدسة واضحة؟ مين مش فاهم؟ صراحة؟ في حاجة مش فاهم؟
+
+247
+00:25:33,640 --> 00:25:38,880
+نعم في ال ..
+
+248
+00:25:42,620 --> 00:25:48,980
+السماء هاي ال .. ال أسود هو ال plus يعني .. كيف
+
+249
+00:25:48,980 --> 00:25:55,700
+يعني؟ يعني زي ما أنا مثلا حركت من هان okay يعني
+
+250
+00:25:55,700 --> 00:25:59,440
+بدي أحرك جالي هيك أوضح إذا بدي أطلع فوق جالي مثلا
+
+251
+00:25:59,440 --> 00:26:03,680
+هيك أوضح يا ما أطلع هيك إذا بدي أنزل لتحت okay
+
+252
+00:26:03,680 --> 00:26:08,180
+يعني باتجاه بدي أطلع على الأسهم أنا وين جالي أوضح
+
+253
+00:26:08,180 --> 00:26:23,630
+okay طيب بدي تنتينيلا بالعجب فضلي الان
+
+254
+00:26:23,630 --> 00:26:33,530
+في عندنا لو
+
+255
+00:26:33,530 --> 00:26:38,370
+فرضنا ال right plus
+
+256
+00:26:38,370 --> 00:26:38,770
+3
+
+257
+00:26:41,810 --> 00:26:50,270
+مينوس اتنين اكسز مية و تلاتين الان بدنا نعمل
+
+258
+00:26:50,270 --> 00:26:53,850
+verification سيبك من ال plus ثلاثة اللي هي الاسفير
+
+259
+00:26:53,850 --> 00:26:56,690
+لان الاسفير بدنا نستخدم اليها ايه ال diachrome
+
+260
+00:26:56,690 --> 00:27:01,010
+test صح؟ الان انا بدي اعمل verification لمن؟ لل
+
+261
+00:27:01,010 --> 00:27:07,430
+cylinder احنا مش موجود عندنا واحد و نص يعني اعتبري
+
+262
+00:27:07,430 --> 00:27:11,030
+هذه مينوس اتنين كده يبترك ال power الان وانت كتحط
+
+263
+00:27:12,870 --> 00:27:17,770
+هتبريها هي ال patient okay هي ال occlusion وحط
+
+264
+00:27:17,770 --> 00:27:22,410
+العدسة اعمال verification لل access هتبريها ال
+
+265
+00:27:22,410 --> 00:27:22,650
+patient
+
+266
+00:27:49,410 --> 00:28:01,350
+دعوها مجال، دعوها مجال، حاضر Westpire،
+
+267
+00:28:01,350 --> 00:28:05,550
+خطة دلوقتي يعني
+
+268
+00:28:05,550 --> 00:28:06,690
+ذات؟
+
+269
+00:28:25,160 --> 00:28:28,760
+أسألها ايه؟ هلجيت وين ال access؟ ال .. ال handle
+
+270
+00:28:28,760 --> 00:28:34,460
+هيكون وين؟ ع مية و تلاتين بالظبط
+
+271
+00:28:34,460 --> 00:28:38,500
+لازم يكون مية و تلاتين هل هو مافيش أرقام ل .. لأ
+
+272
+00:28:38,500 --> 00:28:45,520
+هي .. هي جداش؟ مية و عشرين هي تقريبا مية و تلاتين
+
+273
+00:28:45,520 --> 00:28:51,520
+هون صح؟ هلجيت وين ال handle اللي بدك تحطيه؟ ع مية
+
+274
+00:28:51,520 --> 00:29:01,030
+و تلاتينهي هيك صح؟ صحي هيك
+
+275
+00:29:01,030 --> 00:29:11,070
+لازم برميل متوازي بالظبط هيك بمسك هيك هيك أوضح انا
+
+276
+00:29:11,070 --> 00:29:18,430
+عارف هيك أوضح ولا هيك مرة تانية يعني بالظبط لازم
+
+277
+00:29:18,430 --> 00:29:19,510
+يكون متوازي له
+
+278
+00:29:23,690 --> 00:29:27,450
+هي ال handle okay هذه ال handle لازم يكون على ال
+
+279
+00:29:27,450 --> 00:29:35,170
+axis أحمر ال بيضا مش الخط أه أنا فاكر هات فوضى ورد
+
+280
+00:29:35,170 --> 00:29:38,990
+هات
+
+281
+00:29:38,990 --> 00:29:50,650
+لأ مش شايفها هلجيت هى المية و تلاتين صح تمام هلجيت
+
+282
+00:29:50,650 --> 00:29:56,340
+هذه ال handle هى الخطالأبيض وهي ال handle بتاعتها
+
+283
+00:29:56,340 --> 00:30:03,400
+بجيب لازم أصلا معملي touch مع ال frame هيك أوضح و
+
+284
+00:30:03,400 --> 00:30:10,100
+لا هيك و لا هيك okay يعني ال handle ايجي على المية
+
+285
+00:30:10,100 --> 00:30:14,580
+و تلاتين الخط الأبيض هذا وين ايجي موازي على المية
+
+286
+00:30:14,580 --> 00:30:22,040
+و تلاتين okay دي ولا واحد واضحهي مشيلها ال power
+
+287
+00:30:22,040 --> 00:30:29,960
+طيب لو قلنا ال left eye plus واحد و نص على minus
+
+288
+00:30:29,960 --> 00:30:34,980
+واحد و نص axis خمسة و عشرين اعمل ايه هذا ال left
+
+289
+00:30:34,980 --> 00:30:35,200
+eye
+
+290
+00:31:05,380 --> 00:31:10,940
+أه مرة تانية بالله جيت هالي خمس عشر عشرين لأ مرة
+
+291
+00:31:10,940 --> 00:31:15,900
+خمس عشرين احنا قولنا شايفة هاي التدريج هاي خمس عشر
+
+292
+00:31:15,900 --> 00:31:21,840
+بعدين انه عشرين خمس عشرين تلاتين يعني بيكون بالظبط
+
+293
+00:31:21,840 --> 00:31:29,360
+هون هي ال frame في مشكلة انها هالي هيت و انا هيت و
+
+294
+00:31:29,360 --> 00:31:34,980
+انا بدوني بالظبط هاي المثل في another group
+
+295
+00:31:47,630 --> 00:32:00,470
+طيب إنها right إبلاه
+
+296
+00:32:00,470 --> 00:32:04,330
+نه ع minus نص
+
+297
+00:32:07,460 --> 00:32:09,120
+access خمسة
+
+298
+00:32:39,830 --> 00:32:44,690
+هذه مية و خمسة شويه
+
+299
+00:32:44,690 --> 00:32:54,590
+ده؟ على الخمسة وتسعين شوفها
+
+300
+00:32:54,590 --> 00:33:00,350
+هاي مية هاي خمس عشر بعدين عشرة بعدين هاي خمسة يعني
+
+301
+00:33:00,350 --> 00:33:05,710
+جري بع المية و تمانين و انزليها تحت كمان
+
+302
+00:33:05,710 --> 00:33:11,580
+انزليها مش هيك مية و تمانين صح؟إذا وين بتنزل كمان؟
+
+303
+00:33:11,580 --> 00:33:16,840
+ده تحت، هاي خمسة عايش؟ اكسس خمسة شوف كيف هي خمسة
+
+304
+00:33:16,840 --> 00:33:26,440
+طيب وين ال ..
+
+305
+00:33:26,440 --> 00:33:31,180
+لأ
+
+306
+00:33:31,180 --> 00:33:36,080
+هاي ال handle وين بيكون؟ على الخمسة على الخمسة اه
+
+307
+00:33:36,080 --> 00:33:39,060
+شكرا okay
+
+308
+00:33:40,530 --> 00:33:46,230
+هذه one تسأل المريض طيب
+
+309
+00:33:46,230 --> 00:33:50,770
+هيك؟ أحسن؟
+
+310
+00:33:50,770 --> 00:33:54,070
+نفس
+
+311
+00:33:54,070 --> 00:34:00,130
+الحاجة هي .. ليش بتغيري إيدك؟ هي واحدة، اتنتين أو
+
+312
+00:34:00,130 --> 00:34:05,010
+هيك يعني بس بتعمل عملية rotation flip إنه بده و
+
+313
+00:34:05,010 --> 00:34:05,510
+مرة تانية
+
+314
+00:34:18,510 --> 00:34:22,750
+Okay؟ هعملوا rotation، خليها هي تشتغل، يعني دايما
+
+315
+00:34:22,750 --> 00:34:25,950
+ال .. ال handle بتاعة ال cross cylinder بحطها
+
+316
+00:34:25,950 --> 00:34:29,610
+موازي على مين ال axis اللي أنا حطيته، بشوف هل هذا
+
+317
+00:34:29,610 --> 00:34:33,990
+ال axis صح ولا لأ، okay؟ أه تفضلي
+
+318
+00:34:48,310 --> 00:34:57,890
+ع ال .. كم بدك تحطيه؟ خمسة .. خمسة .. خمسة ..
+
+319
+00:34:57,890 --> 00:35:02,530
+خمسة
+
+320
+00:35:02,530 --> 00:35:03,230
+.. خمسة .. خمسة .. خمسة .. خمسة .. خمسة .. خمسة ..
+
+321
+00:35:03,230 --> 00:35:03,350
+خمسة .. خمسة .. خمسة .. خمسة .. خمسة .. خمسة ..
+
+322
+00:35:03,350 --> 00:35:03,790
+خمسة .. خمسة .. خمسة .. خمسة .. خمسة .. خمسة ..
+
+323
+00:35:03,790 --> 00:35:03,850
+خمسة .. خمسة .. خمسة .. خمسة .. خمسة .. خمسة ..
+
+324
+00:35:03,850 --> 00:35:03,930
+خمسة .. خمسة .. خمسة .. خمسة .. خمسة .. خمسة ..
+
+325
+00:35:03,930 --> 00:35:11,550
+خمسة .. خمسة .. خمسة .. خمسة .. خمسة .. خمسة ..
+
+326
+00:35:11,550 --> 00:35:17,310
+خمسة .. خمسة
+
+327
+00:35:17,310 --> 00:35:24,720
+.. خهيك الخمسة صح؟ اه هلجيت بجيب العدسة ال handle
+
+328
+00:35:24,720 --> 00:35:30,280
+بتاعتها بدها تكون موازية لمين للخمسة؟ يعني هيك؟
+
+329
+00:35:30,280 --> 00:35:39,620
+بالظبط ايه ليش بترجع؟ هيك؟ اه او هيك؟ صحيح او هيك؟
+
+330
+00:35:39,620 --> 00:35:44,920
+بالظبط okay طب
+
+331
+00:35:44,920 --> 00:35:46,280
+اعمل على ال axis تلاتين
+
+332
+00:35:54,020 --> 00:36:08,740
+أعمل ال lift أسألك عشان مقصور من ال ride في
+
+333
+00:36:08,740 --> 00:36:11,800
+حد مش فاهم ال jacks on a cross cylinder هذا
+
+334
+00:36:11,800 --> 00:36:13,500
+verification لل access
+
+335
+00:36:24,670 --> 00:36:31,010
+أحنا بنعمله لمين؟ لل access okay after that we
+
+336
+00:36:31,010 --> 00:36:38,230
+will start for cylinder for power cylinder
+
+337
+00:36:38,230 --> 00:36:46,670
+عرفت زي ما هي دي؟ تانية قولنا الأكم؟ تلاتين ممتاز
+
+338
+00:36:46,670 --> 00:36:47,170
+ايه؟
+
+339
+00:36:54,540 --> 00:37:00,440
+بالظبط ان يكون موازي لمين بالان طيب بالنسبة
+
+340
+00:37:00,440 --> 00:37:04,740
+لالموضوع ال power انه كيف ال jason ال cross
+
+341
+00:37:04,740 --> 00:37:10,920
+cylinder بعمل verification ل ال power الان لما انا
+
+342
+00:37:10,920 --> 00:37:16,400
+ببدأ في ال power already انا صلحت من ال axis okay
+
+343
+00:37:16,400 --> 00:37:24,130
+الان زي ما انتوا شايفين في الخط الليالأسود و في
+
+344
+00:37:24,130 --> 00:37:29,190
+الخط الأحمر صح؟ الآن هدول الخطوط هما اللي هيكونوا
+
+345
+00:37:29,190 --> 00:37:37,810
+ايش؟ متوازين مع ال access بتاعي يعني بمعنى انه
+
+346
+00:37:37,810 --> 00:37:42,050
+الآن هانجدنيش حطات رهد تلاتين okay؟
+
+347
+00:37:46,910 --> 00:37:53,190
+يعني لو كان أنا مثلا عندي الآن minus واحد و نص
+
+348
+00:37:53,190 --> 00:37:57,090
+يعني بحط ال minus واحد و ربع بيصير كده .. sorry
+
+349
+00:37:57,090 --> 00:38:02,350
+minus ربع minus واحد و نص بيصير كده؟ واحد و خمس و
+
+350
+00:38:02,350 --> 00:38:09,230
+سبعين okay إذا بجيب الأحمر بحط موازلة مين؟ لل
+
+351
+00:38:09,230 --> 00:38:15,880
+تلاتينممكن أقبل أسود يعني مرة بعمل بزود هين زوّدت
+
+352
+00:38:15,880 --> 00:38:24,160
+ال minus بقوله هيك أوضح ولا هيك okay او هيك يعني
+
+353
+00:38:24,160 --> 00:38:29,100
+بمعنى يما حطت ال minus ربع شو أنا عملت؟ زوّدت ال
+
+354
+00:38:29,100 --> 00:38:33,560
+minus زوّدت ال minus و يما حطت plus ربع جلّلت ال
+
+355
+00:38:33,560 --> 00:38:38,860
+minus صح؟ فمرة بجرب في ال plus و مرة فيه ال minus
+
+356
+00:38:40,060 --> 00:38:43,940
+طيب إذا قال لي التنتين مش واضحات بيكون ال power
+
+357
+00:38:43,940 --> 00:38:52,360
+اللي انا موجود فيه ايه صح واضح مرة تانية الآن انا
+
+358
+00:38:52,360 --> 00:38:58,000
+حاطط على ال axes تلاتين okay هى في عندى زى ما
+
+359
+00:38:58,000 --> 00:39:01,700
+انتوا شوفته في ال black وفي ال red ال black و ال
+
+360
+00:39:01,700 --> 00:39:06,480
+red معنى ال black انه بدي اضيف اضيف plus ربع ال
+
+361
+00:39:06,480 --> 00:39:09,920
+minus بمعنى بدي اجلل يعني بدي اطرح okay
+
+362
+00:39:12,510 --> 00:39:19,250
+وين بحطه؟ موازي .. موازي لمين؟ لل access بتاعك هي
+
+363
+00:39:19,250 --> 00:39:27,110
+.. هيك أو هيك، يعني بمعنى هيك، نقصت و هيك إيه؟
+
+364
+00:39:27,110 --> 00:39:33,570
+زولتفهنا إذا مثلا قال لي في الوضع الأول أوضح يعني
+
+365
+00:39:33,570 --> 00:39:37,090
+لو فرضنا الأسود هو الوضع الأول بقول minus واحد و
+
+366
+00:39:37,090 --> 00:39:43,450
+نص من الربع قداش plus ربع minus واحد و ربع صح؟ لو
+
+367
+00:39:43,450 --> 00:39:49,210
+مثلا ال minus ربع طلعتها من ال minus واحد و نص
+
+368
+00:39:49,210 --> 00:39:53,830
+صارت واحد و خمسة سبع okay؟
+
+369
+00:39:58,040 --> 00:40:06,100
+ال red slash موازلة مين لل access بتاعي okay هذه
+
+370
+00:40:06,100 --> 00:40:10,380
+طريقة مين ال power طيب مين ببدأ في الأول ال access
+
+371
+00:40:10,380 --> 00:40:22,100
+ولا ال power في ال cylinder why السؤال
+
+372
+00:40:22,100 --> 00:40:25,820
+مين ببدأ في الأول ال power ولا ال access why
+
+373
+00:40:34,580 --> 00:40:38,480
+نبدأ بال access why؟ لإن لو احنا نحطوله العدسة و
+
+374
+00:40:38,480 --> 00:40:42,000
+نسينا ندفل Jackson بس اذا ماشيفش ولا واحد اقول انا
+
+375
+00:40:42,000 --> 00:40:48,000
+عندي ال power ولا ال access بور
+
+376
+00:40:48,000 --> 00:40:51,320
+ولا ال access؟ ال access يعني انه احنا هال program
+
+377
+00:40:51,320 --> 00:40:54,380
+أول اشينا نعمل في ال access لو ماشيفش ال access
+
+378
+00:40:54,380 --> 00:40:57,200
+ولا ال يعني ماشيفش ال access ولا عدسة ال Jackson
+
+379
+00:40:57,200 --> 00:41:00,320
+اقول انا عندي ال power ولا ال access okay another
+
+380
+00:41:00,320 --> 00:41:04,670
+answer لإن لو حدنا ال power الصح فلما ..يعني ال
+
+381
+00:41:04,670 --> 00:41:07,310
+access غلط و ال power الصح هو مش عارف شوفيه فبنعمل
+
+382
+00:41:07,310 --> 00:41:10,410
+ال access عشان نفكر ان ال power الصح هو .. بالظبط
+
+383
+00:41:10,410 --> 00:41:13,210
+انه هتكون إيش blurred لل vision يعني ال access أنا
+
+384
+00:41:13,210 --> 00:41:16,670
+تعرف الصح يعني لو أنا روحت على ال astigmatic fan
+
+385
+00:41:16,670 --> 00:41:20,690
+هيديني واحد من ال line هيكون more clear compared
+
+386
+00:41:20,690 --> 00:41:23,770
+to the other فدايما أنا ببدأ في ال access بعدين
+
+387
+00:41:23,770 --> 00:41:26,530
+باخد مين ال power طب حتى لو ال power خلاني ال
+
+388
+00:41:26,530 --> 00:41:30,170
+power هتكون blurred؟ okay بس ال .. ال power دايما
+
+389
+00:41:30,170 --> 00:41:33,750
+في ال astigmatism مابكونش تأثيره أعلى من ال access
+
+390
+00:41:40,380 --> 00:41:44,700
+يكون discomfort مش مرتاح طيب ممكن نعمل ال
+
+391
+00:41:44,700 --> 00:41:49,660
+procedure بتاعة ال .. ال power فيه بدنا two group
+
+392
+00:41:49,660 --> 00:41:53,140
+بتاعي
+
+393
+00:41:53,140 --> 00:42:04,580
+ايمان بتاع حنان و نور مين كمان و رانيا يلا اسرع
+
+394
+00:42:24,920 --> 00:42:33,720
+فى minus واحد و نص مين بتكلم؟ حاضر
+
+395
+00:42:33,720 --> 00:42:45,740
+طب فهمت ال method؟ okay تعالى يصيبون Axis تلاتين و
+
+396
+00:42:45,740 --> 00:43:17,160
+left eye بلانه فى minus واحد و نصاكسس اشرين اختصار
+
+397
+00:43:17,160 --> 00:43:23,300
+لجهاز cross-cylinder بتكتب بشكل هذاإمان و حنان انت
+
+398
+00:43:23,300 --> 00:43:26,480
+اشتغلي الها ال right و انت ال left يعني اعملوا
+
+399
+00:43:26,480 --> 00:43:29,900
+rotation okay؟ اه تفضلي
+
+400
+00:43:45,040 --> 00:43:50,160
+المريد اه ال right لان تتعامل مع المريض بيكون
+
+401
+00:43:50,160 --> 00:43:56,240
+الدقة في الأول يعني ال accuracy مهمة كتير بس
+
+402
+00:43:56,240 --> 00:43:59,540
+المريض مابشعر بيقولك مافيش فرق ممكن مرة مرتين
+
+403
+00:43:59,540 --> 00:44:03,660
+تلاتة اعملها المريض بيحكي انه مافيش ايه فرق فانا
+
+404
+00:44:03,660 --> 00:44:07,320
+بدي اكون ايه يعني دقيق في هذه الناحية كتير okay
+
+405
+00:44:07,320 --> 00:44:11,400
+يعني ممكن اعيد ال test مرة و مرتين و تلاتة okay
+
+406
+00:44:20,750 --> 00:44:35,150
+على كدهش؟ تلاتين؟ بس إيدك شوية مالش
+
+407
+00:44:35,150 --> 00:44:41,910
+لإن هم بيشتغلوا في معمل عشان هيك دخلي من هنا لأ
+
+408
+00:44:41,910 --> 00:44:42,250
+هيك
+
+409
+00:44:51,160 --> 00:44:54,860
+الآن حطيتها على التلاتين؟ اه بحط هذا .. ممتازة ..
+
+410
+00:44:54,860 --> 00:45:02,620
+اسمها شوية .. اه .. الآن up to you .. بناها ال
+
+411
+00:45:02,620 --> 00:45:05,900
+power ..
+
+412
+00:45:05,900 --> 00:45:11,380
+ممتازة .. الأحمر موازي لمين؟ لل .. ال axis بتاعك
+
+413
+00:45:11,380 --> 00:45:15,540
+اللي هو تاع ال train .. بالظبط .. اه .. و انا
+
+414
+00:45:15,540 --> 00:45:19,180
+مسكها .. اه .. و انا مسكها .. اه .. هيك .. بالظبط
+
+415
+00:45:20,250 --> 00:45:27,470
+لأ مرة تانية هى واحدة هيك افضل ولا هيك ولا هيك
+
+416
+00:45:27,470 --> 00:45:37,970
+موازة
+
+417
+00:45:37,970 --> 00:45:42,030
+اه
+
+418
+00:45:42,030 --> 00:45:50,760
+الأحمر ممتازة او التالتة and without okayانت عمل
+
+419
+00:45:50,760 --> 00:46:13,300
+left I plano minus 1.50 X 26 طب
+
+420
+00:46:13,300 --> 00:46:17,040
+ع المريض لازم يمسك ال .. ال frame ايه ايدك شوية
+
+421
+00:46:17,040 --> 00:46:18,220
+اللي بيصيح اللي بيصيح
+
+422
+00:46:22,700 --> 00:46:30,860
+جبان احط هنا و اتهبط شوية ايوة جميل okay
+
+423
+00:46:53,060 --> 00:46:57,880
+الان ال image clear, you are optometrist, okay
+
+424
+00:46:57,880 --> 00:47:00,980
+clear ال image من ناحية ال diachrome test,
+
+425
+00:47:01,280 --> 00:47:04,660
+astigmatic fan و ال jackson cross cylinder ل ال
+
+426
+00:47:04,660 --> 00:47:08,900
+axis و لل power هذول تقريبا هم أهم تلات تستات من
+
+427
+00:47:08,900 --> 00:47:13,500
+ناحية ال verification ل ال sphere and cylinder for
+
+428
+00:47:13,500 --> 00:47:14,600
+power and axis
+
+429
+00:47:21,260 --> 00:47:26,760
+الان ال axis كدهش؟ ال عشرين لأ وين العشرين؟ هال
+
+430
+00:47:26,760 --> 00:47:33,340
+مية و خمس و ستين هى اهو طيب لأ هى هى العشرين هى
+
+431
+00:47:33,340 --> 00:47:40,180
+الصفر هى خمس و عشر هى العشرين صح؟ هى خمس و عشر
+
+432
+00:47:40,180 --> 00:47:45,880
+بعدين عشرين خمس و عشرين تلاتين صح؟ يعني هو هى كده
+
+433
+00:47:45,880 --> 00:47:54,510
+اه هى تدريجي هو بعدين هيكون موازن؟up to you يا
+
+434
+00:47:54,510 --> 00:48:01,650
+بتبدأ في ال plus or minus ارفع
+
+435
+00:48:01,650 --> 00:48:13,370
+يدك يا حنان ايوة
+
+436
+00:48:13,370 --> 00:48:19,370
+بس
+
+437
+00:48:19,370 --> 00:48:30,620
+هيك في rotationهى إيدي هى one two or three okay
+
+438
+00:48:30,620 --> 00:48:37,020
+again طبعا
+
+439
+00:48:37,020 --> 00:48:41,160
+هى بدها trick يعني بسرعة لازم أنك تستخدميها لإنه
+
+440
+00:48:41,160 --> 00:48:46,760
+المريض يعني نعم اه
+
+441
+00:48:46,760 --> 00:48:50,920
+طيب تعالى هان كمان تعالى
+
+442
+00:48:58,140 --> 00:49:02,140
+طيب ال right eye خليه على نفس ال .. ال .. ال
+
+443
+00:49:02,140 --> 00:49:10,760
+meridian او ال axis لأ
+
+444
+00:49:10,760 --> 00:49:14,680
+في هى انا جايبلكم هان ماانتبهتيش على القوة هان
+
+445
+00:49:14,680 --> 00:49:19,340
+minuszero point two five فيه ممكن تكون minus zero
+
+446
+00:49:19,340 --> 00:49:23,500
+point fifty ممكن minus zero point seventy five or
+
+447
+00:49:23,500 --> 00:49:26,980
+one دي أكتر بس ال more common اللي احنا بنشتغل
+
+448
+00:49:26,980 --> 00:49:33,440
+فيها minus zero point two five okay يعني الأكثر
+
+449
+00:49:33,440 --> 00:49:38,320
+شيوع ال excess كده إيش؟
+
+450
+00:49:43,620 --> 00:49:51,380
+بالظبط بستخدم اللي هو مين ال screw okay هاي الصح؟
+
+451
+00:49:51,380 --> 00:49:56,540
+اه هاي
+
+452
+00:49:56,540 --> 00:50:02,820
+الأحمر؟ لأ عليها ارفع يدي شوية سابرين هاتي شوية ال
+
+453
+00:50:02,820 --> 00:50:08,200
+.. ال gen two امتازة حطيتي على التلاتين صح؟ اه هاي
+
+454
+00:50:08,200 --> 00:50:13,600
+العدسةهي موازية للتلاتين هيك أفضل ولا هيك ولا هيك
+
+455
+00:50:13,600 --> 00:50:32,080
+okay one two three اه
+
+456
+00:50:32,080 --> 00:50:36,960
+و التالتة without هي مرة تانية
+
+457
+00:50:43,620 --> 00:50:57,300
+هي one two three okay again ممتاز
+
+458
+00:50:57,300 --> 00:51:01,840
+طيب ان شاء الله بنكون هيك أنهينا ال Jackson cross
+
+459
+00:51:01,840 --> 00:51:06,520
+cylinder في المحاضرة القادمة ان شاء الله هنترجم
+
+460
+00:51:06,520 --> 00:51:09,080
+بعض الأمور عن ال Jackson cross cylinder
+
diff --git a/PL9fwy3NUQKwaBhVI6LPr803vc5wWl9Iy_/cYWI8vSbdjQ_raw.srt b/PL9fwy3NUQKwaBhVI6LPr803vc5wWl9Iy_/cYWI8vSbdjQ_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..2f3d73f90c37f8c3236e57c08492b4ed9a58935d
--- /dev/null
+++ b/PL9fwy3NUQKwaBhVI6LPr803vc5wWl9Iy_/cYWI8vSbdjQ_raw.srt
@@ -0,0 +1,1492 @@
+1
+00:00:20,920 --> 00:00:24,100
+طيب بسم الله الرحمن الرحيم السلام عليكم ورحمة الله
+
+2
+00:00:24,100 --> 00:00:28,000
+وبركاته and a very good afternoon to all of you
+
+3
+00:00:28,000 --> 00:00:34,520
+بداية محاضرة اليوم هنتكلم how to give answer for a
+
+4
+00:00:34,520 --> 00:00:39,860
+question طبعا هذه محاضرة in general يعني بشكل عام
+
+5
+00:00:39,860 --> 00:00:47,840
+لأي امتحان بتمر فيه في قسم البصريات الطبية طبعا
+
+6
+00:00:47,840 --> 00:00:53,960
+بداية طبيعة الامتحانأول ما ببدأ الدكتور أو المحاضر
+
+7
+00:00:53,960 --> 00:00:59,000
+أو الأستاذ في الامتحان بكتب please answer all the
+
+8
+00:00:59,000 --> 00:01:03,560
+following questions يعني من فضلك إجابة كل الأسئلة
+
+9
+00:01:03,560 --> 00:01:09,540
+التالية في صيغة أخرى ممكن بستخدمها الدكتور please
+
+10
+00:01:09,540 --> 00:01:14,260
+answer only five from the following questions أي
+
+11
+00:01:14,260 --> 00:01:19,100
+بمعنى إنه اختاري خمس أسئلة من .. بيكون مثلا ستة أو
+
+12
+00:01:19,100 --> 00:01:25,370
+سبعة و اكترOkay طبعا هان الدكتور يما بيجي بصليح أو
+
+13
+00:01:25,370 --> 00:01:30,410
+المحاضر بصليح على خلاص مثلا حكى أنه خمس أسئلة one,
+
+14
+00:01:30,530 --> 00:01:34,870
+two, three, four, five بس لو أنت حل ست أسئلة هو
+
+15
+00:01:34,870 --> 00:01:39,230
+بصليح بس الخمسة الأولى نجيه يعني ما بيصليح مثلا
+
+16
+00:01:39,230 --> 00:01:43,270
+أنت بدك تكترك السادس أو .. لأ هو بعرف أنه أول خمس
+
+17
+00:01:43,270 --> 00:01:46,090
+أسئلة okay هذا نقطة كتير مهمة
+
+18
+00:01:49,300 --> 00:01:53,840
+طيب أنواع الأسئلة type of equations كيف الأسئلة
+
+19
+00:01:53,840 --> 00:01:58,760
+بشكل عام أنه بتكون يعني ك shape of the equation
+
+20
+00:01:58,760 --> 00:02:03,980
+يعني أو ال style أنه شكل بتاع الأسئلة بشكل عام أول
+
+21
+00:02:03,980 --> 00:02:10,060
+حاجة ممكن true or false أي بمعنى state whether the
+
+22
+00:02:10,060 --> 00:02:14,020
+following sentences are true or false طبعا في
+
+23
+00:02:14,020 --> 00:02:15,240
+موضوع ال true or false
+
+24
+00:02:51,140 --> 00:02:55,580
+ولو انت كنت قصارها الصح أو خطأ، مش عارف يعني، او
+
+25
+00:02:55,580 --> 00:02:55,920
+في مثل ..
+
+26
+00:03:34,290 --> 00:03:39,130
+يعني خلاص إنه لازم الإنسان يلتزم بالسؤال في صيغة
+
+27
+00:03:39,130 --> 00:03:43,410
+أخرى ممكن state whether the following sentences
+
+28
+00:03:43,410 --> 00:03:47,990
+are true or false and correct the false sentences
+
+29
+00:03:47,990 --> 00:03:54,470
+أي بمعنى صلح الأخطاء الجمال okay؟
+
+30
+00:04:32,610 --> 00:04:37,970
+مثلا الأولى true والتانية false وهكذا هذا طب يعني
+
+31
+00:04:37,970 --> 00:04:46,210
+style آخر من الأسئلة واضح النقطة هذه؟ choose
+
+32
+00:04:46,210 --> 00:04:50,070
+the correct answer or select the correct answer
+
+33
+00:04:50,070 --> 00:04:55,090
+يعني اختاري الإجابة الصحيحة okay طبعا إذا كان شوية
+
+34
+00:04:55,090 --> 00:04:58,730
+صعب الدكتور بيجيب الأسئلة هذا
+
+35
+00:05:02,550 --> 00:05:10,690
+أكتر من إجابة صحيحة لكن هو بده إيه؟ الأصحى طيب
+
+36
+00:05:10,690 --> 00:05:16,210
+في سؤال ممكن define the following بنصح في ال
+
+37
+00:05:16,210 --> 00:05:20,970
+define دايما أكتب خاصة في الامتحان النهائي في ال
+
+38
+00:05:20,970 --> 00:05:25,880
+more detail يعني أية معلومة بتعرفيها اكتبيهاإذا ك
+
+39
+00:05:25,880 --> 00:05:30,780
+details أنه لازم تكون كاملة okay لأنه الامتحان
+
+40
+00:05:30,780 --> 00:05:34,720
+النهائي تقريبا عليه ما بين ستين و سبعين علامة
+
+41
+00:05:34,720 --> 00:05:39,260
+بمعنى أن الدكتور عنده range كبير من الدرجات okay
+
+42
+00:05:39,260 --> 00:05:45,580
+فلازم أنه يكون إيش أنه أكتب ك full answer أنه
+
+43
+00:05:45,580 --> 00:05:52,020
+إجابة إيش ما كاملة okay ممكن
+
+44
+00:05:52,020 --> 00:05:53,980
+سؤال match the following
+
+45
+00:06:02,960 --> 00:06:08,160
+ممكن اقولك العضلة و ال action بتاعها فبعمل عملية
+
+46
+00:06:08,160 --> 00:06:09,960
+توصيل لإيه؟ لكل عضلة
+
+47
+00:06:46,110 --> 00:06:52,150
+انه مديكي نقاط معينة مازليش عنها okay and mention
+
+48
+00:06:52,150 --> 00:06:56,510
+its types with drawings يعني بدي اعمل وصف لهذه
+
+49
+00:06:56,510 --> 00:07:01,210
+الأنواع زائد انه ايش انه بدي ارسم اذا with a
+
+50
+00:07:01,210 --> 00:07:06,250
+drawing اذا هان السؤال شمل define و mention و
+
+51
+00:07:06,250 --> 00:07:13,650
+drawing تلت شغلات مع بعض okay في
+
+52
+00:07:13,650 --> 00:07:15,250
+صيغة أخرى mention
+
+53
+00:07:27,030 --> 00:07:32,950
+مثلا لديو كروم تست او مثلا لجاكسون كروس سيلندر او
+
+54
+00:07:32,950 --> 00:07:37,890
+ل ال muscle ال extraocular muscle فال main factors
+
+55
+00:07:37,890 --> 00:07:41,750
+العوامل الأساسية فقط اللي بدوها ممكن يكون هم عشرين
+
+56
+00:07:41,750 --> 00:07:45,450
+عامل لكن انا بدي احط ايه ال main three factors
+
+57
+00:07:45,450 --> 00:07:50,750
+okay mention
+
+58
+00:07:50,750 --> 00:07:52,090
+يعني بمعنى
+
+59
+00:07:56,600 --> 00:08:00,380
+بدي اعمل وصف for example هنا مثلا ل ال prince role
+
+60
+00:08:00,380 --> 00:08:04,960
+إذا وضحت زائد أنه إيه بدي أفصل في ال prince role
+
+61
+00:08:04,960 --> 00:08:11,060
+دايما كلمة illustrate بتيجي ل ال mention هدول
+
+62
+00:08:11,060 --> 00:08:15,520
+التنتين مع بعض بمعنى أنه توضيح ووصف okay
+
+63
+00:08:38,350 --> 00:08:43,990
+ممكن يكون هم three or four or five لكن هو حدد only
+
+64
+00:08:43,990 --> 00:08:47,850
+two types objective and subjective methods okay
+
+65
+00:08:47,850 --> 00:08:52,050
+mention
+
+66
+00:08:52,050 --> 00:08:58,600
+the main types okay of causesايضا بكون اكتر من نوع
+
+67
+00:08:58,600 --> 00:09:03,740
+ل ال doses لكن انا بدي احدد ايه ال main الأساسي
+
+68
+00:09:03,740 --> 00:09:08,380
+طبعا هذه الأسئلة هي شوية معظمها هي ال .. هي هذه
+
+69
+00:09:08,380 --> 00:09:11,560
+الصعبة لأن هذا اللي بيقدر .. يعني الدكتور يعمل
+
+70
+00:09:11,560 --> 00:09:18,020
+subtract من الطالب okay انه بده إجابة لكن تكون
+
+71
+00:09:18,020 --> 00:09:23,340
+more detail في شغل معين لو هو سائل okay وامتحان
+
+72
+00:09:23,340 --> 00:09:28,020
+النهائي في الغالب بيكون هيكطيب mention the
+
+73
+00:09:28,020 --> 00:09:30,760
+different types of a primary and secondary
+
+74
+00:09:30,760 --> 00:09:34,880
+glaucoma اذا different types أنواع مختلفة هانفتح
+
+75
+00:09:34,880 --> 00:09:38,800
+المجال يعني فيه اتناشر type بدي اذكر الاتناشر type
+
+76
+00:09:38,800 --> 00:09:43,800
+okay illustrate
+
+77
+00:09:43,800 --> 00:09:48,780
+the finished lens dimension هانتوضيح دايما كلمة
+
+78
+00:09:48,780 --> 00:09:53,160
+illustrate إذا فيه drawing رسم حط معها الرسمOkay
+
+79
+00:09:53,160 --> 00:09:57,140
+يعني دايما بيجيوا التنتين مع بعض انه حتى لو هو مش
+
+80
+00:09:57,140 --> 00:10:02,000
+طالب منك طيب
+
+81
+00:10:02,000 --> 00:10:07,400
+mention in brief only for aging changes of the
+
+82
+00:10:07,400 --> 00:10:12,900
+lead هان فقط بدي وصف لكن ايش briefly باختصار يعني
+
+83
+00:10:12,900 --> 00:10:18,910
+تصفي شغل معينة لكن باختصار معينOkay و هان بيكون
+
+84
+00:10:18,910 --> 00:10:24,490
+السؤال يعني سهل .. سهل لطالب من حيث انه يحصل على
+
+85
+00:10:24,490 --> 00:10:29,250
+علامة كاملة ليش؟ لأنه اي نقطة انت هتكتبيها هو هيحط
+
+86
+00:10:29,250 --> 00:10:33,810
+عليها صح لأن هو هنحط السؤال ك general a question
+
+87
+00:10:33,810 --> 00:10:37,670
+زائد انه طلب انه in brief باختصار
+
+88
+00:10:40,930 --> 00:10:47,010
+طيب في عندنا ال describe هذا سؤال شويه صعب، دايما
+
+89
+00:10:47,010 --> 00:10:53,270
+describe يعني أي تمعلومة بدك تذكريها يعني الآن ال
+
+90
+00:10:53,270 --> 00:10:57,750
+myopic vandas يحكيلي عن ال myopic vandas ال
+
+91
+00:10:57,750 --> 00:11:01,910
+define، التعريف، ال types، الأنواع، ال
+
+92
+00:11:01,910 --> 00:11:06,210
+classification، التصنيف، ال treatment، العلاج، ال
+
+93
+00:11:06,210 --> 00:11:12,180
+methodأى حاجة فيها describe بدك تكون الإجابة full
+
+94
+00:11:12,180 --> 00:11:17,160
+answer okay discuss
+
+95
+00:11:17,160 --> 00:11:22,300
+briefly the process of glazing دايما كلمة discuss
+
+96
+00:11:22,300 --> 00:11:26,700
+و مع كلمة briefly فيه process زى مثلا عندنا مثلا
+
+97
+00:11:26,700 --> 00:11:28,440
+ال retinoscopic okay
+
+98
+00:11:30,880 --> 00:11:34,300
+إذا عملية ال ريتناسكوبي okay the reforming of
+
+99
+00:11:34,300 --> 00:11:39,060
+retinascope هان بدك تكتب باختصار العملية هذه okay
+
+100
+00:11:39,060 --> 00:11:42,300
+طيب
+
+101
+00:11:42,300 --> 00:11:46,560
+الصيغة الأخرى ممكن تقولك what is gonioscope هان
+
+102
+00:11:46,560 --> 00:11:50,740
+بمعنى define كتعريف وتقولنا دايما التعريف بدك تكتب
+
+103
+00:11:50,740 --> 00:11:56,270
+full answer okaydescribe the angle of the anterior
+
+104
+00:11:56,270 --> 00:12:00,910
+chamber يعني هان بده تعريف و هان سهلها على الطالب
+
+105
+00:12:00,910 --> 00:12:04,650
+أكتر انه قالك what is جونيوسكوبيه كان بيسأل شو
+
+106
+00:12:04,650 --> 00:12:10,730
+التعريف و بعدين قالك describe انه أوصف ال angle of
+
+107
+00:12:10,730 --> 00:12:13,170
+anterior chamber
+
+108
+00:12:15,730 --> 00:12:19,830
+why we do his secret هل اعتقد جبته انا في المصفة
+
+109
+00:12:19,830 --> 00:12:23,590
+سؤال يعني اتفهمته كيف الصيغة بتاعته انه دايما ال
+
+110
+00:12:23,590 --> 00:12:27,610
+reason السبب السبب دايما بيكون واضح اللي هو ال
+
+111
+00:12:27,610 --> 00:12:31,750
+main يعني اما واحد بيسألك why يعني ال main reason
+
+112
+00:12:31,750 --> 00:12:38,650
+السبب الرئيسي okayWhy a flare exists in soft
+
+113
+00:12:38,650 --> 00:12:41,810
+lenses than in rigid lenses؟ خلاص، بدي أركز ع
+
+114
+00:12:41,810 --> 00:12:45,930
+شغلتين، إذا ال flare أي بمعنى ال cloud الضباب في
+
+115
+00:12:45,930 --> 00:12:51,250
+ال rigid و في ال hard، يعني فقط بنوعين معينين، في
+
+116
+00:12:51,250 --> 00:12:54,730
+عدة أنواع من ال contact lens، لكن أنا بدي أركز في
+
+117
+00:12:54,730 --> 00:12:55,950
+إيه؟ في two types
+
+118
+00:12:59,830 --> 00:13:03,850
+what happened after plant injury هان برضه زي كأنه
+
+119
+00:13:03,850 --> 00:13:09,370
+سؤال discuss أو سؤال describe زي مثلك discuss what
+
+120
+00:13:09,370 --> 00:13:13,620
+happens during the retinoscopicهنا بدى يكون full
+
+121
+00:13:13,620 --> 00:13:19,360
+answer برضه، يعني السؤال كبير بنصح نصيحة دايما
+
+122
+00:13:19,360 --> 00:13:23,460
+اطلع في بعض الدكاترة بكتبوا علامة العلامة بتاعة
+
+123
+00:13:23,460 --> 00:13:27,700
+السؤال كل ما كانت العلامة كبيرة للسؤال معناه
+
+124
+00:13:27,700 --> 00:13:30,780
+الكلام ان ال answer بده تكون كبيرة في بعض الأحيان
+
+125
+00:13:30,780 --> 00:13:35,220
+مش دايما okay يعني مش مثلا السؤال عليه خمس عشر
+
+126
+00:13:35,220 --> 00:13:40,940
+علامة اكتبله سطرين او تلاتةOkay؟ يعني مثلا ال
+
+127
+00:13:40,940 --> 00:13:45,880
+characteristics ل .. نقول الكورنيا هو حاطط ال
+
+128
+00:13:45,880 --> 00:13:50,440
+characteristics مثلا عليه سبع علامات و عندي مثلا
+
+129
+00:13:50,440 --> 00:13:54,700
+هم عشرة خلاص، بدك تكتب لازم أقل شيء تسعة لأن هو في
+
+130
+00:13:54,700 --> 00:14:00,140
+الآخر هيدي كل واحدة علامة Okay؟ إذا عديت الخمسة
+
+131
+00:14:00,140 --> 00:14:04,380
+صح، هو هيديك ال full mark Okay؟
+
+132
+00:14:06,210 --> 00:14:09,930
+طيب what is the principle of the lensometer؟ أهم
+
+133
+00:14:09,930 --> 00:14:12,950
+شيء في ال principle يعني إذا واحد يجي سؤال ال
+
+134
+00:14:12,950 --> 00:14:17,250
+principle اكتب it depends on أنه بيعتمد على يعني
+
+135
+00:14:17,250 --> 00:14:20,970
+مثلا ال Jackson cross cylinder اللي معناه تعتمد
+
+136
+00:14:20,970 --> 00:14:24,410
+على إيش ال circle of least confusion هذه لازم
+
+137
+00:14:24,410 --> 00:14:29,830
+تحطيها يعني كبداية الصفحة بتاعتك يعني الآن المبدأ
+
+138
+00:14:29,830 --> 00:14:34,370
+بتاعه على إيش بيعتمد okay بعدها بتكمل ال answer
+
+139
+00:14:34,370 --> 00:14:41,730
+بتاعتكبشكل سهل إذا أي سؤال فيه بيكون principle
+
+140
+00:14:41,730 --> 00:14:50,490
+مبدأ لازم أحط انه it depends on انه بيعتمد على طيب
+
+141
+00:14:50,490 --> 00:14:55,410
+how can you test the field of vision يعني كيف أنا
+
+142
+00:14:55,410 --> 00:15:02,310
+بدي أفحص ال test of vision okay هذي howإذا السؤال
+
+143
+00:15:02,310 --> 00:15:06,810
+بعدها حكى what is the extent of normal field هان ك
+
+144
+00:15:06,810 --> 00:15:12,150
+definition لل normal field okay how to calculate
+
+145
+00:15:12,150 --> 00:15:16,490
+IOL طبعا كلمة how دايما الإجابة بدها تكون قصيرة
+
+146
+00:15:16,490 --> 00:15:20,030
+بمعنى one, two, three يعني مثلا السؤال هذا لو بدي
+
+147
+00:15:20,030 --> 00:15:24,530
+أجابه إن كيف بدنا نقسم ال IOL هذه ال intraocular
+
+148
+00:15:24,530 --> 00:15:28,310
+lens العدسة الداخلية اللي داخل العين أول حاجة باخد
+
+149
+00:15:28,310 --> 00:15:33,430
+الكراتوميترK1 و K2 سواء من الجفال أي بمعنى ال K
+
+150
+00:15:33,430 --> 00:15:36,830
+Reading يعني قداش تحدي بالقرانية أعتقد في بعض
+
+151
+00:15:36,830 --> 00:15:40,610
+الطلبات عملتلهم التحدي بتاع القرانية بعدين بدي
+
+152
+00:15:40,610 --> 00:15:45,330
+أستخدم جهاز الاسكت هاي خطوفين هاي تسابق إذا دايما
+
+153
+00:15:45,330 --> 00:15:50,510
+كلمة how بدو يكون short answer إجابة قصيرة و عبارة
+
+154
+00:15:50,510 --> 00:15:58,170
+عن steps خطوات okay طيب comment زي كلمة describe
+
+155
+00:16:04,330 --> 00:16:10,570
+Uses of sign up to 4 كلمة uses هذه in general برضه
+
+156
+00:16:10,570 --> 00:16:14,250
+استخدامات in general لكن لو قال لي ال main uses
+
+157
+00:16:14,250 --> 00:16:18,370
+الاستخدامات الرئيسية بعرف انه ايش انه في one two
+
+158
+00:16:18,370 --> 00:16:20,770
+three هدول main uses
+
+159
+00:16:24,740 --> 00:16:27,560
+طيب امتحاني هيكون ان شاء الله
+
+160
+00:16:30,360 --> 00:16:35,860
+في جانوري صح؟ هيكون الامتحان شكل الامتحان هو اللي
+
+161
+00:16:35,860 --> 00:16:40,220
+أمامكم طبعا هذه وفقا ال .. ال .. ال .. ال
+
+162
+00:16:40,220 --> 00:16:44,260
+commentات بتاعتكم و ال recommendation طبعا هيكون
+
+163
+00:16:44,260 --> 00:16:48,580
+السؤال الأول هو عبارة عن choose the correct answer
+
+164
+00:16:48,580 --> 00:16:54,040
+okay خمس عشر سؤال define the following خمس أسئلة
+
+165
+00:16:54,040 --> 00:16:58,600
+describe وصف لشغل معينة okay
+
+166
+00:17:01,560 --> 00:17:06,000
+أو only قولنا short answer السؤال الخامس what are
+
+167
+00:17:06,000 --> 00:17:09,340
+the differences مقارنة between two groups okay
+
+168
+00:17:09,340 --> 00:17:15,920
+أيضا what are the define and describe وصف السؤال
+
+169
+00:17:15,920 --> 00:17:20,920
+السابع mention in briefly only steps خطوات فقط
+
+170
+00:17:20,920 --> 00:17:26,320
+والسؤال الأخير هم عبارة عن تلت فقرات اربع فقرات
+
+171
+00:17:26,320 --> 00:17:29,380
+بتختاري منهم ايه تلتة okay
+
+172
+00:17:32,560 --> 00:17:37,840
+اه ستين .. طبعا هيكون امتحان ستين على أربعةأه
+
+173
+00:17:37,840 --> 00:17:43,160
+أربعة أسئلة تختار منهم تلاتة هيكون الامتحان ستين
+
+174
+00:17:43,160 --> 00:17:48,280
+علامة ان شاء الله بتمنى لكم التوفيق طبعا الامتحان
+
+175
+00:17:48,280 --> 00:17:53,940
+ما هيكونش خارج من المادة العلمية و من خلال
+
+176
+00:17:53,940 --> 00:17:57,940
+المناقشة اللي كنا نتناقش مع بعض زي أنه هيكون
+
+177
+00:17:57,940 --> 00:18:02,320
+الامتحان يعني ممكن سؤال أو سؤالين بيكون فيهم idea
+
+178
+00:18:02,320 --> 00:18:08,630
+فكرة للتمييز ما بين الطالبينفالناس في ال .. ممكن
+
+179
+00:18:08,630 --> 00:18:13,350
+تشيري من الناس في ال .. في العقد؟ In general
+
+180
+00:18:13,350 --> 00:18:19,270
+الامتحان بس هو التقسيم انه بيكون عشرين لقبل
+
+181
+00:18:19,270 --> 00:18:24,730
+الامتحان يعني according ل الجامعة انه عشرين قبل
+
+182
+00:18:24,730 --> 00:18:28,610
+يعني الامتحان النصف عشرين في المية و بعد المادة
+
+183
+00:18:28,610 --> 00:18:32,890
+تقريبا سبعين او تمانين في المية يعني بعد امتحان
+
+184
+00:18:32,890 --> 00:18:33,250
+النصف
+
+185
+00:18:36,140 --> 00:18:39,760
+طبعا هذه طبيعة امتحان .. يعني الامتحانات بشكل عام
+
+186
+00:18:39,760 --> 00:18:43,340
+في الجامعة مابيخرجش الامتحان عن هدول الأسئلة أنا
+
+187
+00:18:43,340 --> 00:18:47,900
+ان شاء الله هحمل ال .. الصيدات هدول على الصفحة ان
+
+188
+00:18:47,900 --> 00:18:52,180
+شاء الله يعني أي تمتحان ماهيخرجش عن مجموعة الأسئلة
+
+189
+00:18:52,180 --> 00:18:58,760
+هدول، okay؟ طيب، الآن بنبقى مع مجموعة من الطالبات
+
+190
+00:18:58,760 --> 00:19:03,800
+حوال موضوع ال visual acuityال pre verbal children
+
+191
+00:19:03,800 --> 00:19:12,120
+عمل كل من الطالبة إيمان ياغي و سجة عودة و حفص زين
+
+192
+00:19:12,120 --> 00:19:18,360
+الدين و ندى أبو ذية و وعد الحلبة بسم الله الرحمن
+
+193
+00:19:18,360 --> 00:19:21,720
+الرحيم أنا الطالبة ندى أبو ذيةاليوم بدي أقدم عاية
+
+194
+00:19:21,720 --> 00:19:25,600
+انه بموضوع testing visual acuity in very very bald
+
+195
+00:19:25,600 --> 00:19:29,300
+children اللي هو الأطفال الصغير، الغير ناطقين ممكن
+
+196
+00:19:29,300 --> 00:19:35,860
+يكون عمرهم من الموليد لحد سنتين و نص و بنبدأ أول
+
+197
+00:19:35,860 --> 00:19:39,360
+إشي عندنا different type من ال visual acuity in
+
+198
+00:19:39,360 --> 00:19:42,980
+infants عند الموليد نفحص طرق مختلفة أول إشي عندنا
+
+199
+00:19:42,980 --> 00:19:45,800
+inclusion of one eye ثاني إشي عندنا fixation test
+
+200
+00:19:45,800 --> 00:19:48,640
+و بعدين عندنا الopticaي نترك الدرام نستجمس الدرام
+
+201
+00:19:48,640 --> 00:19:52,670
+andfirst choice for differential blocking and
+
+202
+00:19:52,670 --> 00:19:55,150
+hundred or thousand sweep test and rotation test
+
+203
+00:19:55,150 --> 00:20:00,350
+أول إشي عندنا فيه اختلاف بين الأساليب الفحص
+
+204
+00:20:00,350 --> 00:20:04,390
+للإكبار و للصغار عند الموليد و عند البالغين لإنهم
+
+205
+00:20:04,390 --> 00:20:11,240
+تلت أسبابأول إشي أن المواليد عندنا ما .. ما بقدرش
+
+206
+00:20:11,240 --> 00:20:14,240
+نفحصلهم بنفس الطريقة و بنفس المواد و الأساليب اللي
+
+207
+00:20:14,240 --> 00:20:17,840
+بنستخدمها مع ال Dubai تاني إشي أنه .. أنه أساليب
+
+208
+00:20:17,840 --> 00:20:23,540
+الفحص عندنا متطوعة و لازم أنه يكون يعني الصغير
+
+209
+00:20:23,540 --> 00:20:26,300
+قادر إنهم يفهموا هذه الأساليب و عنده أساليب خاصة
+
+210
+00:20:26,300 --> 00:20:30,540
+ممكن .. احنا ممكن نستعملها اللي هي مع ال infants و
+
+211
+00:20:30,540 --> 00:20:34,180
+ما بقدرش أنه يطبقها ال ..نطبقها مع الإكبار،
+
+212
+00:20:34,180 --> 00:20:37,680
+مابقدرش نطبقها مع ال infants زي مثلا إن ال HI
+
+213
+00:20:37,680 --> 00:20:39,920
+مابقدرش مثلا إن حد بدي كفه اتجاه الفحص اللي ممكن
+
+214
+00:20:39,920 --> 00:20:44,380
+يكون و زي هي كتفانة و احنا بنسهل، بنجيبلنا أشياء
+
+215
+00:20:44,380 --> 00:20:48,160
+ان تكون سهلة، حاجة العين أو بنقل صورة أو حاجات
+
+216
+00:20:48,160 --> 00:20:52,880
+مقلوفة لهم و
+
+217
+00:20:52,880 --> 00:20:56,400
+بنتكلم عن أول موضوع اللي هو inclusion of one eye
+
+218
+00:20:56,400 --> 00:21:01,830
+مع إيمان ياغيEclosion of one eye، عينها بيهيب هو
+
+219
+00:21:01,830 --> 00:21:06,450
+عبارة عن طاقة فحص، monocular طبعا، بيكون مغطي في
+
+220
+00:21:06,450 --> 00:21:10,810
+عين واحدة، مغطي فيها العين السليمة، ال normal eye،
+
+221
+00:21:10,810 --> 00:21:17,580
+و بعدين بيعمل fixation لل ..بنشوف رد اتفاعل الطفل
+
+222
+00:21:17,580 --> 00:21:20,980
+evolution of one eye بنغطي أي حد اللي بحث نستخدم
+
+223
+00:21:20,980 --> 00:21:27,580
+غطغة عين سليمة للطفل و بعدين بنشوف رد اتفاعل الطفل
+
+224
+00:21:27,580 --> 00:21:31,980
+من حسب إذا ما كانت .. لو استخدمنا غطية عين ال
+
+225
+00:21:31,980 --> 00:21:35,620
+right هتكون الرد اتفاعل إذا كان فيها رد عفر لعين
+
+226
+00:21:35,620 --> 00:21:40,320
+ال left هتكون إذا مش سليمة راح يحاول إنه يبعد في
+
+227
+00:21:40,320 --> 00:21:43,800
+إيد الفاحث عنه و إذا لأ راح يبعدها هنعرف إنه في
+
+228
+00:21:43,800 --> 00:21:50,000
+عين ضاقعنده ضعف في العين هادي و إذا غطينا العين ال
+
+229
+00:21:50,000 --> 00:21:54,300
+left أو خلينا ال right اللي هي المكشوفة هنكون حاسس
+
+230
+00:21:54,300 --> 00:21:58,400
+بارتياح أنه مافيش اي غرق .. مشكلة في العين ال
+
+231
+00:21:58,400 --> 00:22:03,880
+right و بنستخدم طبعا الدم ياقن عشان نبضل نركز على
+
+232
+00:22:03,880 --> 00:22:10,940
+ال .. ال هذا مع ال .. مع الفحص هاي هنا طبعا غطينا
+
+233
+00:22:10,940 --> 00:22:16,990
+العينال right كانت ال left هي المكشوفة كانت اللي
+
+234
+00:22:16,990 --> 00:22:21,170
+هنا الطفل سليم و مافيش اي مشكلة لما غبطيها العين
+
+235
+00:22:21,170 --> 00:22:24,110
+ال left خلال المرحلة هي المكشوفة كان عندي مشكلة
+
+236
+00:22:24,110 --> 00:22:27,930
+بحاول انه يبعد ال .. ال .. ال occlusive ال
+
+237
+00:22:27,930 --> 00:22:33,590
+occluder لنجيب بصل ماء هنغطيه الآن عين واحدة
+
+238
+00:22:47,720 --> 00:22:50,980
+الثانية هي test اللى هو ال hundred and thousand
+
+239
+00:22:50,980 --> 00:22:55,610
+sweet testهو عبارة عن أنه بنجيب ال .. ال sweet
+
+240
+00:22:55,610 --> 00:23:00,090
+بتكون different color and small، بنحطها طبعا في
+
+241
+00:23:00,090 --> 00:23:03,570
+الإيد بشكل متباعد و مش كتير متباعد ولا قريب من
+
+242
+00:23:03,570 --> 00:23:06,810
+بعض، بتكون مسافة الإيد من ال patient .. ال patient
+
+243
+00:23:06,810 --> 00:23:10,690
+يعني و الإيدنا تلات و تلاتين سانتر تقريباو بيكون
+
+244
+00:23:10,690 --> 00:23:16,910
+.. اذا كان الطفل مش قادر انه يمسك .. ياخد من هذا
+
+245
+00:23:16,910 --> 00:23:21,670
+الحلو ال sweet بيكون عنده visual equity ضعيف اما
+
+246
+00:23:21,670 --> 00:23:26,630
+اذا قادر انه يمسك .. يعني يلقط شوية من تسطها دي
+
+247
+00:23:26,630 --> 00:23:31,950
+حسب ما كانش يحرك ايده نيح بيها فهيكون عنده طقل
+
+248
+00:23:31,950 --> 00:23:36,330
+visual equity سليم تقريبا 24 ع 6، 6 ع 24
+
+249
+00:23:40,890 --> 00:23:44,030
+I want to .. now I want to talk about a third
+
+250
+00:23:44,030 --> 00:23:47,430
+method اللي هي فاصد شاير بريفينالوكينج This
+
+251
+00:23:47,430 --> 00:23:50,230
+behavioral tonic pattern is based on the
+
+252
+00:23:50,230 --> 00:23:54,170
+observation that infants prefer a pew but in
+
+253
+00:23:54,170 --> 00:23:58,350
+stimulation that they are really well split بمعنى
+
+254
+00:23:58,350 --> 00:24:03,970
+أن هذه الطريقة تقنية سلوكية بتعتمد على ملاحظة
+
+255
+00:24:03,970 --> 00:24:08,360
+الأطفال و ملاحظهم كيف هم حركتهمطبعا أبضع من أنه ..
+
+256
+00:24:08,360 --> 00:24:11,620
+بتكون هي نمط محفظ لإنهم أكتر من أنه يكون مثلا
+
+257
+00:24:11,620 --> 00:24:16,360
+أشكال و .. خليط من أشكال و أي شغلات The shape must
+
+258
+00:24:16,360 --> 00:24:19,720
+be altered and able to generate neck and eye
+
+259
+00:24:19,720 --> 00:24:20,480
+movement
+
+260
+00:24:22,910 --> 00:24:27,010
+Evaluated by means of motor response اللي هم لازم
+
+261
+00:24:27,010 --> 00:24:31,550
+يكونوا منتبهين و لازم يكونوا قادرين على حركة
+
+262
+00:24:31,550 --> 00:24:38,370
+يركبتهم يعني و حركة العين حركة عينهم طبعا هذا
+
+263
+00:24:38,370 --> 00:24:42,030
+الاشي اللي بسميه احنا رؤية اللي هي استجابة حركية
+
+264
+00:24:42,030 --> 00:24:45,330
+ال motor responseفيه هنا نوعين منه اللي هو
+
+265
+00:24:45,330 --> 00:24:48,890
+teleacuity gardens black هو عبارة عن black strips
+
+266
+00:24:48,890 --> 00:24:53,470
+of varying thickness اللي هو عبارة عن خطوط سودة
+
+267
+00:24:53,470 --> 00:24:59,690
+مختلفة السماكة guarded acuity guards shape of
+
+268
+00:24:59,690 --> 00:25:03,330
+variable outline bloodline و cell lines اللي هو
+
+269
+00:25:03,330 --> 00:25:08,870
+عبارة عن أشكال مختلفة it used from every infants
+
+270
+00:25:08,870 --> 00:25:11,610
+اللي هو بيستخدمها .. بيستخدمها الطريقة بس الأطفال
+
+271
+00:25:16,440 --> 00:25:22,060
+it's useful at age 3 to 12 months but can be used
+
+272
+00:25:22,060 --> 00:25:26,440
+up to 3 years المريض يستخدم من 3 شهور إلى 12 شهر
+
+273
+00:25:26,440 --> 00:25:30,300
+أو ممكن كمان لتالت سنين this test is very well
+
+274
+00:25:30,300 --> 00:25:34,120
+accurate using strips, black and white strips in a
+
+275
+00:25:34,120 --> 00:25:39,480
+bath it varying a size of width of the strips from
+
+276
+00:25:39,480 --> 00:25:43,970
+very close, very less and very fineالأول زى ما هو
+
+277
+00:25:43,970 --> 00:25:48,450
+جايبى بالصورة الموضحانة أن الشكل بيكون فيه خطوط
+
+278
+00:25:48,450 --> 00:25:53,570
+سودة و فيه خطوط بيضا مختلفة بالثمن و احنا باختصار
+
+279
+00:25:53,570 --> 00:25:58,430
+شديد ان احنا نجيب الطفل و نقعده و نجيب هذه الأدوات
+
+280
+00:25:58,430 --> 00:26:03,130
+اللى هى ال .. ال .. ال tiller أو ال garden و نسير
+
+281
+00:26:03,130 --> 00:26:07,270
+نواجهينها الأطفال و ال .. و ال examiner بيسير
+
+282
+00:26:07,270 --> 00:26:11,930
+يلاحظ كده حركة العين للطفل و كيف حاجة طيبتهإذا كان
+
+283
+00:26:11,930 --> 00:26:16,070
+هم بيستجيب ل .. لإله كيف بتطلع نيح فإنه بيكون
+
+284
+00:26:16,070 --> 00:26:20,590
+الرؤية عنده نيحة، إذا ما كان واضح كتير و يعني ما
+
+285
+00:26:20,590 --> 00:26:24,850
+بتحرك ريبته نيح حسب ال .. كيف هو بيجيب الأشكال،
+
+286
+00:26:24,850 --> 00:26:30,030
+بيكون عنده مشكلة في الرؤية طبعا خلّنا بنكمل مع سجة
+
+287
+00:26:30,030 --> 00:26:32,910
+My name is Sajada and I will talk about
+
+288
+00:26:32,910 --> 00:26:34,770
+autokinetic and stigmas test
+
+289
+00:26:37,880 --> 00:26:40,500
+أول شي بقولنا evaluation of the presence or
+
+290
+00:26:40,500 --> 00:26:44,000
+absence of optokinetic nystagmus was the first
+
+291
+00:26:44,000 --> 00:26:47,140
+technological approach to acute measurements in
+
+292
+00:26:47,140 --> 00:26:51,800
+preverbal children بقولنا تقييم وجود أو غياب هو
+
+293
+00:26:51,800 --> 00:26:56,840
+كان أول تقنية لتحديد ال acuity اللي هو حدد الأبصار
+
+294
+00:26:56,840 --> 00:26:59,740
+عند الأطفال بقولنا ال nystagmus is elected by
+
+295
+00:26:59,740 --> 00:27:03,200
+passinga succession of black and white strips
+
+296
+00:27:03,200 --> 00:27:05,980
+through the patient's field of view بيقولنا
+
+297
+00:27:05,980 --> 00:27:10,980
+الرقرقة بتصير عند مرور الخطوط البيضا و السودا هي
+
+298
+00:27:10,980 --> 00:27:14,160
+عبارة عن .. ال drama أولا شهية عبارة عن جهاز فيه
+
+299
+00:27:14,160 --> 00:27:17,340
+خطوط بيضا و سودا فهذه الخطوط راح تفوت لل visual
+
+300
+00:27:17,340 --> 00:27:21,940
+field لل patientبحكينا the visual angle substended
+
+301
+00:27:21,940 --> 00:27:26,220
+by the smallest strip اللي هو هذا ال drum عبارة عن
+
+302
+00:27:26,220 --> 00:27:31,580
+strips black and white راح نحركها قدام عين ال
+
+303
+00:27:31,580 --> 00:27:36,520
+patient عشان نشوف كيف حركة عين الطفل هتكون بيقولنا
+
+304
+00:27:36,520 --> 00:27:40,460
+ال visual angle substended by the smallest strip
+
+305
+00:27:40,460 --> 00:27:45,660
+الخط الصغيرراح يفوت لعين المريض و هو راح يسبب
+
+306
+00:27:45,660 --> 00:27:49,060
+الحركة و من خلاله بنقدر نقيص ال visual acuity أول
+
+307
+00:27:49,060 --> 00:27:53,080
+شي هذا ال test بيصير لما يكون العين تان عند الطفل
+
+308
+00:27:53,080 --> 00:27:57,300
+مفتوحين مابينغطيش أي عين فبعد هيك راح نحرك ال ..
+
+309
+00:27:57,300 --> 00:28:02,080
+ال drum هتصير في حركة في عين الطفل لما يشوف ال ..
+
+310
+00:28:02,080 --> 00:28:07,090
+ال drum بتحركفالطفل رح يكون مركز عينه على ال drum
+
+311
+00:28:07,090 --> 00:28:10,490
+فلما تتحرك عينه ما حركت ال drum رح تكون عين الطفل
+
+312
+00:28:10,490 --> 00:28:14,310
+سليمة لما يكون عامل تركيزه فبحكينا انه احنا ليش
+
+313
+00:28:14,310 --> 00:28:17,790
+اختارنا ال black و ال white strips لإن هدول عبارة
+
+314
+00:28:17,790 --> 00:28:22,490
+عن خطوط متباينة فالطفل رح يكون مركز عينه على
+
+315
+00:28:22,490 --> 00:28:26,140
+الخطوط السودة فبالتالي بنقدر نقلس ال ..ال visual
+
+316
+00:28:26,140 --> 00:28:31,580
+acuity لعين الطفل بيحكينا ال acuity عندنا 6 على
+
+317
+00:28:31,580 --> 00:28:36,780
+120 ل ال newborns، للموليد الجداد أو 6 على 20 ل ..
+
+318
+00:28:36,780 --> 00:28:41,780
+لعمرهم شهرين أو ممكن 6 على 6 من .. من عشرين
+
+319
+00:28:41,780 --> 00:28:46,860
+لتلاتين شهر هلأ راح نطبق ال .. الكلام اللي حكيته
+
+320
+00:28:46,860 --> 00:28:48,080
+شجرة على الطفل الساعة
+
+321
+00:29:15,940 --> 00:29:20,300
+لأ بما أنه احنا عملنا هذا ال test للطفلة هي صارت
+
+322
+00:29:20,300 --> 00:29:23,940
+عندها الأراضي العامة We will continue with
+
+323
+00:29:23,940 --> 00:29:27,920
+fixation test Fixation
+
+324
+00:29:27,920 --> 00:29:34,280
+test is a quantitative test and هو يعني ال more
+
+325
+00:29:34,280 --> 00:29:39,400
+accurate test بكل الاختبارات تبع ال preferable
+
+326
+00:29:39,400 --> 00:29:45,800
+childrenعن طريقية الفحص فيه أول شغلة لو .. لما ن
+
+327
+00:29:45,800 --> 00:29:48,780
+.. لما نيجي نفحص طبعا من غطي العين السليمة، من
+
+328
+00:29:48,780 --> 00:29:54,780
+الفحص العين اللي شاكين فيها مشكلة، هنحط برزم قيمته
+
+329
+00:29:54,780 --> 00:29:58,620
+16 based on .. ليش based on؟ عشان الصورة هتتكوّل
+
+330
+00:29:58,620 --> 00:30:04,460
+عند ال apex فنظر ال ..ال baby او الطفل هيكون مركز
+
+331
+00:30:04,460 --> 00:30:08,800
+على الصورة المكونة ان هي up طبعا هو هيكون
+
+332
+00:30:08,800 --> 00:30:11,640
+molecular زى ما قولنا هنغطي العين السليمة و نفحص
+
+333
+00:30:11,640 --> 00:30:17,880
+العين المستليمة و هنشوف مقدار ال fixation للطفل
+
+334
+00:30:17,880 --> 00:30:21,580
+اذا كان central او non central و اذا كان steady او
+
+335
+00:30:21,580 --> 00:30:25,000
+non steadyلمّا نجي نفحص العين اللي احنا مش
+
+336
+00:30:25,000 --> 00:30:28,200
+مغطيينها العين اللي هي اللي قدامها ال prism إذا
+
+337
+00:30:28,200 --> 00:30:33,520
+يعني لما نشيل ال occluder إذا الطفل راح غير نظره
+
+338
+00:30:33,520 --> 00:30:37,840
+أو ال fixation غيره مباشرة بعد فترة من الزمن أقل
+
+339
+00:30:37,840 --> 00:30:41,320
+من عشر ثواني بيكون عنده ال visual acuity impaired
+
+340
+00:30:41,320 --> 00:30:46,020
+أما إذا غير ال fixation بعد عشر ثواني بيكون عنده
+
+341
+00:30:46,020 --> 00:30:50,450
+ال visual acuity goodزي ما كنا نحكي .. بنحكي هلأ
+
+342
+00:30:50,450 --> 00:30:55,430
+كيف .. قدش قيمة ال visual acuity لكل حالة إذا
+
+343
+00:30:55,430 --> 00:31:00,030
+مباشرة يعني احنا رفعنا ال occluder عن العنص تريمة
+
+344
+00:31:00,030 --> 00:31:04,470
+و مباشرة غير ال fixation فبيكون نظره واحد على ستين
+
+345
+00:31:04,670 --> 00:31:10,570
+أما إذا كان يعني ال fixation عنده unsteady يعني مش
+
+346
+00:31:10,570 --> 00:31:15,610
+ثابت مش مركز على ال prison و يعني لمدة أقل من خمس
+
+347
+00:31:15,610 --> 00:31:19,070
+ثواني بيكون نظره أربع على ستين أما إذا كان عنده ال
+
+348
+00:31:19,070 --> 00:31:23,090
+central with steady fixation لكن لما احنا رفعنا ال
+
+349
+00:31:23,090 --> 00:31:29,350
+occluder غيرها يعني غير ال fixation بعد مدة أكتر
+
+350
+00:31:29,350 --> 00:31:32,630
+من خمس ثواني و أقل من عشر ثوانيبكون endotoxin with
+
+351
+00:31:32,630 --> 00:31:37,990
+acuity 6 على 60 أو 6 على 24إذا كان برضه Central
+
+352
+00:31:37,990 --> 00:31:41,930
+وستر ال fixation لكن برضه تفضل أنه يعمل ال
+
+353
+00:31:41,930 --> 00:31:44,890
+fixation على العين التانية ويكون عنده another 6
+
+354
+00:31:44,890 --> 00:31:49,670
+على 18 أو 6 على 9 أما إذا كان صار ال fixation
+
+355
+00:31:49,670 --> 00:31:53,070
+عاملها وضلوا .. لما رفعنا ال .. ال occluder ضلوا
+
+356
+00:31:53,070 --> 00:31:57,230
+ال fixation ثابت لعين .. لحد عشر ثواني و بعدين
+
+357
+00:31:57,230 --> 00:32:00,690
+غيروا من عين لعين يعني عشر ثواني بالعين ال right
+
+358
+00:32:00,690 --> 00:32:05,180
+بعدين ال left ويكون عنده visual acuityستة ع ستة
+
+359
+00:32:05,180 --> 00:32:09,760
+يعني good visual ability okay thank you so much
+
+360
+00:32:09,760 --> 00:32:14,500
+for your representation any comment? do you have
+
+361
+00:32:14,500 --> 00:32:20,760
+any comment? any answer? any question? rotation
+
+362
+00:32:20,760 --> 00:32:22,540
+test
+
+363
+00:32:28,230 --> 00:32:31,330
+الطفل أخذ محاولة حلوة الوضع الوضع الوضع الوضع
+
+364
+00:32:31,330 --> 00:32:37,710
+الوضع الوضع
+
+365
+00:32:37,710 --> 00:32:44,210
+الوضع الوضع
+
+366
+00:32:44,210 --> 00:32:44,730
+الوضع الوضع الوضع الوضع الوضع الوضع الوضع الوضع
+
+367
+00:32:44,730 --> 00:32:45,050
+الوضع الوضع الوضع الوضع الوضع الوضع الوضع الوضع
+
+368
+00:32:45,050 --> 00:32:45,170
+الوضع الوضع الوضع الوضع الوضع الوضع الوضع الوضع
+
+369
+00:32:45,170 --> 00:32:45,190
+الوضع الوضع الوضع الوضع الوضع الوضع الوضع الوضع
+
+370
+00:32:45,190 --> 00:32:46,130
+الوضع الوضع الوضع الوضع الوضع الوضع الوضع الوضع
+
+371
+00:32:46,130 --> 00:32:52,470
+الوضع الوضع الوضع الوضع
+
+372
+00:32:58,930 --> 00:33:03,430
+Decimal six over twenty four zero point two five
+
+373
+00:33:03,430 --> 00:33:05,550
+okay thank you
+
diff --git a/PL9fwy3NUQKwaBhVI6LPr803vc5wWl9Iy_/jKoWhOTxEsY_raw.srt b/PL9fwy3NUQKwaBhVI6LPr803vc5wWl9Iy_/jKoWhOTxEsY_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..ed3afc7625f357ee61d4ff957a417dfad27cc44b
--- /dev/null
+++ b/PL9fwy3NUQKwaBhVI6LPr803vc5wWl9Iy_/jKoWhOTxEsY_raw.srt
@@ -0,0 +1,1720 @@
+1
+00:00:21,020 --> 00:00:24,580
+بسم الله الرحمن الرحيم السلام عليكم و رحمة الله و
+
+2
+00:00:24,580 --> 00:00:33,080
+بركاته و أهلاً جميعاً لكم اليوم هنبدأ في موضوع الـ
+
+3
+00:00:33,080 --> 00:00:38,560
+Subjective Verification for Refractionطبعا اتكلمنا
+
+4
+00:00:38,560 --> 00:00:45,620
+من ناحية عملية، اليوم هنبدأ لو من ناحية الترجمة ك
+
+5
+00:00:45,620 --> 00:00:49,540
+Diachrome test Verification for spherical power
+
+6
+00:00:49,540 --> 00:00:57,290
+تأكيد للقوة الكروية الاسفير okayVerification or
+
+7
+00:00:57,290 --> 00:01:01,710
+refinement for spherical power أي بمعنى تأكيد
+
+8
+00:01:01,710 --> 00:01:08,310
+للقوة الإنكسارية الكروية في عندنا ال biochrome
+
+9
+00:01:08,310 --> 00:01:17,030
+test or red green testالـ two side، green side و
+
+10
+00:01:17,030 --> 00:01:21,990
+red side okay typical wavelength of colors typical
+
+11
+00:01:21,990 --> 00:01:26,650
+بمعنى ال characteristics أي بمعنى خواص الطول
+
+12
+00:01:26,650 --> 00:01:32,790
+الموجة للألوان يعني شو هي ال typical او ال
+
+13
+00:01:32,790 --> 00:01:38,940
+characteristics الخواص للأطوال الموجية للألوانفي
+
+14
+00:01:38,940 --> 00:01:43,800
+عندنا لو بدأنا من ال short wavelength ل ال long
+
+15
+00:01:43,800 --> 00:01:50,540
+wavelength بنبدأ ال violet اللون الأزرق عندنا
+
+16
+00:01:50,540 --> 00:01:56,620
+indigo ليني blue أزرق green أخضر yellow أصفر
+
+17
+00:01:56,620 --> 00:02:03,040
+orange برتقالي red أصفر okay أحمر هذه بالنسبة
+
+18
+00:02:03,040 --> 00:02:07,060
+لأطوال الموجية المختلفة ايش ال wavelength الطول
+
+19
+00:02:07,060 --> 00:02:11,850
+الموجيطبعا وحدة القياس بتكون ايه؟ بالنانو ميتر
+
+20
+00:02:11,850 --> 00:02:19,110
+النانو ميتر بيمثل عشرة اقصى minus تسعة okay ديو
+
+21
+00:02:19,110 --> 00:02:24,550
+كروم تست the index of refraction معامل الانكسار
+
+22
+00:02:24,550 --> 00:02:30,530
+okay varies for different wavelengths of light اذا
+
+23
+00:02:30,530 --> 00:02:35,410
+المعامل الانكسار بيتغير مع تغير الاطلاق
+
+24
+00:02:38,130 --> 00:02:42,930
+بحيث إذا كان معامل الانكسار عالي بيكون ال
+
+25
+00:02:42,930 --> 00:02:47,930
+wavelength أشماله قليل يعني ال red color بيمتلك
+
+26
+00:02:47,930 --> 00:02:52,270
+طول موجي عالي صح إذا ال refractive index لها هيكون
+
+27
+00:02:52,270 --> 00:02:56,870
+جليل okay the
+
+28
+00:02:56,870 --> 00:03:00,390
+index of refraction is a creator for short
+
+29
+00:03:00,390 --> 00:03:04,670
+wavelength light rays than for longer ones إذا
+
+30
+00:03:04,670 --> 00:03:11,850
+المعامل الانكسار لو قررناطول الموجة كل ما زاد
+
+31
+00:03:11,850 --> 00:03:18,570
+معامل الانكسار بقل ايه الطول الموجة نعم العلاقة
+
+32
+00:03:18,570 --> 00:03:24,230
+هتكون علاقة عكسية ال
+
+33
+00:03:24,230 --> 00:03:29,850
+green light الضوء الأخضر أو ال blue light الضوء
+
+34
+00:03:29,850 --> 00:03:36,940
+الأزرقالاتنين يعني الطول الموجي متقارب من بعض okay
+
+35
+00:03:36,940 --> 00:03:41,860
+فبعض المراجع هشوفه كاتبين green light وبعض المراجع
+
+36
+00:03:41,860 --> 00:03:47,200
+بيكتبوا blue light okay إذا ال green light الضوء
+
+37
+00:03:47,200 --> 00:03:52,080
+الأخضر is refracted to greater degree than yellow
+
+38
+00:03:52,080 --> 00:03:57,140
+light إذا بينكسر أكتر من الضوء الأصفر عشان هيك في
+
+39
+00:03:57,140 --> 00:04:00,900
+ال normal patient أو في ال emetrope وين هيتركز
+
+40
+00:04:05,260 --> 00:04:08,260
+Yellow color او ال yellow light وين هيتركز؟ On the
+
+41
+00:04:08,260 --> 00:04:12,400
+retina which is refracted to a greater degree than
+
+42
+00:04:12,400 --> 00:04:16,420
+red light and so on و ال red light وين هيتركز؟
+
+43
+00:04:16,420 --> 00:04:22,640
+Behind the retina Incoming
+
+44
+00:04:22,640 --> 00:04:28,940
+rays أي بمعنى external rays الأشعة الخارجية of
+
+45
+00:04:28,940 --> 00:04:33,940
+white light للضوء الأبيض are dispersed أي بمعنى
+
+46
+00:04:33,940 --> 00:04:34,900
+بتشتت
+
+47
+00:04:39,210 --> 00:04:45,990
+Why طيب؟ لأن معامل الإنكسار في الضوء الأزرق هيكون
+
+48
+00:04:45,990 --> 00:04:50,850
+أكتر من مين من معامل الإنكسار في الضوء الأحمر لأن
+
+49
+00:04:50,850 --> 00:04:57,510
+ال wavelength العلاقة بينهم إيه عكسية طبعا
+
+50
+00:04:57,510 --> 00:05:01,330
+وهي بتعتمد على مبدأ ال chromatic aberration الذيوغ
+
+51
+00:05:01,330 --> 00:05:08,430
+اللونيin an emetropic eye في أي تعين طبيعية normal
+
+52
+00:05:08,430 --> 00:05:13,850
+eye therefore or so لذلك yellow light is focused
+
+53
+00:05:13,850 --> 00:05:18,590
+الضوء الأصفر هيتركز on the retina، اذا وين هيكون
+
+54
+00:05:18,590 --> 00:05:24,590
+تركيز الضوء الأصفر؟ على الشبكية لأنه هيكون الضوء
+
+55
+00:05:24,590 --> 00:05:29,270
+الأصفر الطول الموجي middle يعني في منتصف ما بين
+
+56
+00:05:29,270 --> 00:05:34,710
+الأحمر و ما بين ال green صح؟إذا ال red هيكون ايش؟
+
+57
+00:05:34,710 --> 00:05:38,430
+أطول طول موجة و ال blue أو ال green هيكون أقل من
+
+58
+00:05:38,430 --> 00:05:43,150
+مين؟ ال yellow كطول موجة صح؟ فمعامل الانكسار هيكون
+
+59
+00:05:43,150 --> 00:05:49,230
+ايه بينهم؟ بين ال red و بين ال blue in an
+
+60
+00:05:49,230 --> 00:05:52,970
+emetropic eye في أي تعين طبيعي therefore or so
+
+61
+00:05:52,970 --> 00:05:57,010
+لذلك yellow light الضوء الأصفر is focused on the
+
+62
+00:05:57,010 --> 00:06:02,170
+retina هيتركز على الشبكية okay a green light
+
+63
+00:06:06,490 --> 00:06:13,050
+أو خلف الشبكية إذا نضوه الأحمر وين هيتركز خلف
+
+64
+00:06:13,050 --> 00:06:19,150
+الشبكية هتفضل هذا
+
+65
+00:06:19,150 --> 00:06:24,450
+من ناحية انه اتركز خلف الشبكية او خلف الشبكية
+
+66
+00:06:33,150 --> 00:06:37,850
+قاعد في ال right side وفي مثلا Z قاعد في ال left
+
+67
+00:06:37,850 --> 00:06:42,210
+side وانا مثلا قاعد هنا في المنتصف كله نحن نشوف
+
+68
+00:06:42,210 --> 00:06:46,510
+الأشعة إيش مالها متفارقة صح؟ الآن ال chromatic
+
+69
+00:06:46,510 --> 00:06:50,570
+aberration عبارة عن white light أنا جبت الرسمة
+
+70
+00:06:50,570 --> 00:06:55,050
+بتاعتها ال white light هتبدأ اللي هو الضوء هيمر في
+
+71
+00:06:55,050 --> 00:06:59,370
+optical system أي بمعنى نظام بصري سواء كانت lens
+
+72
+00:06:59,370 --> 00:07:02,810
+أو mirror بعدها هيديني من ال blue light أو ال
+
+73
+00:07:02,810 --> 00:07:06,340
+greenالـ yellow light و الـ red light حسب طول
+
+74
+00:07:06,340 --> 00:07:10,880
+الموجة تاعه وين هيتركز هل behind و لا in front و
+
+75
+00:07:10,880 --> 00:07:14,220
+لا on the retina يعني according to the wavelength
+
+76
+00:07:14,220 --> 00:07:21,600
+حسب طول الموجة لكله okay الـ
+
+77
+00:07:21,600 --> 00:07:25,140
+myopic eye طبعا ال light rays وين هيتركز في
+
+78
+00:07:25,140 --> 00:07:29,880
+الميوب؟In front the retina فى ال red light فى ال
+
+79
+00:07:29,880 --> 00:07:33,500
+myopic eye هيتركز ال light rays in front the
+
+80
+00:07:33,500 --> 00:07:38,880
+retina Red is closer to the retina okay while in
+
+81
+00:07:38,880 --> 00:07:43,460
+hypermetropic eye green is closer إذن فى حالة
+
+82
+00:07:43,460 --> 00:07:48,040
+الميوب ال red light الضوء الأحمر هيتركز على
+
+83
+00:07:48,040 --> 00:07:50,700
+الشبكية فى حالة ال hypermetrop
+
+84
+00:07:56,730 --> 00:08:01,690
+عشان هيك في حالة الميوب بتلاحظ ان المريض بيشوف
+
+85
+00:08:01,690 --> 00:08:07,490
+الأحمر ال red side أفضل من مين من الأخضر أو ال
+
+86
+00:08:07,490 --> 00:08:14,090
+green و العكس في حالة ال hypermetropia
+
+87
+00:08:14,090 --> 00:08:19,650
+if the red green test اذا اختبار اللون الأحمر
+
+88
+00:08:23,550 --> 00:08:29,130
+وكان هذا المريض عنده قصر نظر and insufficiently
+
+89
+00:08:29,130 --> 00:08:33,290
+corrected اي بمعنى ال correction اللي انا مديله يا
+
+90
+00:08:33,290 --> 00:08:37,990
+غير كافي insufficiently بمعنى غير كافي okay then
+
+91
+00:08:37,990 --> 00:08:41,990
+the letters on the right side will stand out
+
+92
+00:09:00,980 --> 00:09:05,800
+أنا أعتقد أن شاربر بيكون حاد يعني هيكون واضح بشكل
+
+93
+00:09:05,800 --> 00:09:10,060
+ايش كبير ان ال red color compared to the green
+
+94
+00:09:10,060 --> 00:09:13,940
+color هذا في حالة من؟ الميوب
+
+95
+00:09:17,130 --> 00:09:20,430
+They will require more minus power for the green
+
+96
+00:09:20,430 --> 00:09:26,270
+to be as distinct as the red عشان هيك بنطلب إضافة
+
+97
+00:09:26,270 --> 00:09:30,830
+minus power عشان نصل لحدية A ان التساوي ما بين ال
+
+98
+00:09:30,830 --> 00:09:36,330
+red و ما بين ال green color يعني
+
+99
+00:09:36,330 --> 00:09:40,670
+الآن لو اجانا مريض ميوب هيشوف ال red ولا ال green
+
+100
+00:09:40,670 --> 00:09:46,930
+أوضح؟ببدأ انه ازود بال minus لحد ما يصير ال red و
+
+101
+00:09:46,930 --> 00:09:51,130
+ال green ايش معله equally متساويين هاي السؤال
+
+102
+00:09:51,130 --> 00:09:58,730
+هتفضلي اه
+
+103
+00:09:58,730 --> 00:10:03,250
+اللونان بتركزوا على الشبكية يعني زي لأ هيصيروا زي
+
+104
+00:10:03,250 --> 00:10:06,370
+ال emetrap كيف هيصير
+
+105
+00:10:11,360 --> 00:10:14,500
+الريتينال سيتركز خلف الريتينال، وإذا كان هناك يلو
+
+106
+00:10:14,500 --> 00:10:18,360
+سيتركز على الريتينال. حسنا؟ هنا لدينا الـ long
+
+107
+00:10:18,360 --> 00:10:22,540
+trigonal أي بمعنى طولي اكزيال اكروماتيك ابراشن.
+
+108
+00:10:22,900 --> 00:10:27,260
+هناك نوع من أنواع الزيوغ اللوني بيسمى long
+
+109
+00:10:27,260 --> 00:10:31,940
+trigonal او اكزيال اكروماتيك ابراشن بمعنى طولي.
+
+110
+00:10:53,210 --> 00:10:57,170
+إذا ال blue one هيتركز in front of the retina و ال
+
+111
+00:10:57,170 --> 00:11:00,550
+red one هيتركز behind the retina in the emetropic
+
+112
+00:11:00,550 --> 00:11:07,550
+eye on the
+
+113
+00:11:07,550 --> 00:11:13,610
+other hand من ناحية أخرى if the same mayor is over
+
+114
+00:11:13,610 --> 00:11:18,950
+corrected and made over corrected or artificially
+
+115
+00:11:18,950 --> 00:11:24,560
+hyper metropic يعني بمعنى طول نظر كاذبOkay then
+
+116
+00:11:24,560 --> 00:11:28,520
+the letter against the green background appear
+
+117
+00:11:28,520 --> 00:11:34,160
+blacker, clearer and sharper من ناحية أخرى لو الآن
+
+118
+00:11:34,160 --> 00:11:39,480
+أنا مثلا صلحت patient ميوب و اديته under
+
+119
+00:11:39,480 --> 00:11:43,420
+correction يعني بمعنى هو كان عنده minus two point
+
+120
+00:11:43,420 --> 00:11:47,040
+five اديته minus two، هيشوف ال red أوضح ولا ال
+
+121
+00:11:47,040 --> 00:11:51,560
+green؟الرد ليش؟ لأنه under correction طيب لو فرضنا
+
+122
+00:11:51,560 --> 00:11:55,720
+ال data minus تلاتة هيصير over correction فمين
+
+123
+00:11:55,720 --> 00:12:02,340
+هيشوف أفضل؟ اللي green okay ال sphere is adjusted
+
+124
+00:12:02,340 --> 00:12:02,800
+until
+
+125
+00:12:08,660 --> 00:12:13,400
+بإضافة العدسة الاسفير سواء الـ plus أو ال minus
+
+126
+00:12:13,400 --> 00:12:18,260
+لحد ما نصل إلى إيه؟ إلى التساوي ما بين ال red و ال
+
+127
+00:12:18,260 --> 00:12:23,840
+green side okay؟ adjust بمعنى ضبط أو بمعنى
+
+128
+00:12:23,840 --> 00:12:30,040
+calibration معايرة الـ
+
+129
+00:12:30,040 --> 00:12:35,720
+diachrome test الفحص هذا is useful بيستخدم only ال
+
+130
+00:12:35,720 --> 00:12:37,640
+refining فقط في تأكيد
+
+131
+00:12:49,310 --> 00:12:53,730
+مالهوش مساهمة في مين في السيلندر سواء كان ال
+
+132
+00:12:53,730 --> 00:12:58,790
+access او ال power اعتقد معظمكم طبق في المعمل ال
+
+133
+00:12:58,790 --> 00:13:00,570
+diachrome test و بدأ
+
+134
+00:13:08,780 --> 00:13:16,630
+بحيث انه ممكن اقيت 0.12في عندنا هنا Refractive
+
+135
+00:13:16,630 --> 00:13:22,230
+state أي بمعنى الحالة الانكسارية ال color scene
+
+136
+00:13:22,230 --> 00:13:27,410
+طبعا هذه لخصت الفمياه كملخص لديو كروم تست بحيث ان
+
+137
+00:13:27,410 --> 00:13:31,930
+المريض لو كان امتراب هيشوف ال red و ال green بنفس
+
+138
+00:13:31,930 --> 00:13:35,870
+الوضوح لو كان corrected ميوب يعني صلحنا الميوب
+
+139
+00:13:35,870 --> 00:13:40,230
+ممكن ان يكون ال red اشمله slightly يعني بشيء بسيط
+
+140
+00:13:40,230 --> 00:13:44,540
+أوضح من مين من ال greenلو كان under correction
+
+141
+00:13:44,540 --> 00:13:48,520
+ميوب حيشوف ال red over corrected ميوب ال green أي
+
+142
+00:13:48,520 --> 00:13:52,380
+بمعنى under corrected زي المثال اللي استعرضناه
+
+143
+00:13:52,380 --> 00:13:56,920
+الآن انه لو كان عنده مريض minus 2.5 و اديته minus
+
+144
+00:13:56,920 --> 00:14:01,640
+2 مين حيشوف افضل؟ ال red ال over corrected اديته
+
+145
+00:14:01,640 --> 00:14:03,320
+minus 3 حيشوف ال green
+
+146
+00:14:27,320 --> 00:14:33,380
+لو اجاني مريض صلحتله لل addition بمعنى ال near
+
+147
+00:14:33,380 --> 00:14:42,500
+vision ممكن استخدم ال test for nearوالا لأ؟ و why؟
+
+148
+00:14:42,500 --> 00:14:47,760
+فهمت السؤال؟ الان اعملت واحد اجالك breast biop
+
+149
+00:14:47,760 --> 00:14:53,100
+وعملنا كان مثلا عنده plus two breast biop وصلحنا
+
+150
+00:14:53,100 --> 00:14:57,540
+له اياه بدنا نعمل verification لل breast biop ممكن
+
+151
+00:14:57,540 --> 00:15:01,520
+استخدم ال diachrome test و لا لأ؟ اتفضلي اه بسبب
+
+152
+00:15:01,520 --> 00:15:04,760
+ان مثلا فضعته ال cytokine بتاعة بالشميلة
+
+153
+00:15:07,180 --> 00:15:11,040
+لأ قصدي هل ممكن أن نستخدم ال Decrom test ك card
+
+154
+00:15:11,040 --> 00:15:18,580
+ولا لأ؟ مش في عليها أقام 3 أو 4 أو 4 أو 3 او 2 ..
+
+155
+00:15:18,580 --> 00:15:25,000
+why؟ ممكن لو سائل ثاني نستخدمه يعني فدلت يكون أقل
+
+156
+00:15:26,230 --> 00:15:31,230
+هو موجود الـ Dichrome Car Test موجود الفحص هذا بتم
+
+157
+00:15:31,230 --> 00:15:34,810
+استخدامه و نفس ال principle بتاع ال Dichrome Test
+
+158
+00:15:34,810 --> 00:15:42,000
+for distance يعني بتم استخدامه للقريب أيضالأنه هو
+
+159
+00:15:42,000 --> 00:15:45,100
+بيعتمد على مين ال chromatic aberration الزيوغ
+
+160
+00:15:45,100 --> 00:15:49,740
+اللوني فهو الان واحد hyper metropic إذا كان عنده
+
+161
+00:15:49,740 --> 00:15:53,520
+breast myopic وديته ال correction كامل هيشوف
+
+162
+00:15:53,520 --> 00:15:57,340
+التنين equal صح ولا لا أنا بهمنيش المسافة هان
+
+163
+00:15:57,340 --> 00:16:02,080
+بهمني انه هل هو ال refractive state الحالة
+
+164
+00:16:02,080 --> 00:16:05,460
+الانكسارية للعين هل هو myopic ولا hyper metropic
+
+165
+00:16:05,460 --> 00:16:09,880
+ولا astigmatism okay فإذا مثلا كان ال green أوضح
+
+166
+00:16:09,990 --> 00:16:13,050
+هيقول لي لأ و لما شاف ال green اوضح باعرف انه بده
+
+167
+00:16:13,050 --> 00:16:16,970
+كمان correction اذا شاف ال red اوضح باعرف انه بدى
+
+168
+00:16:16,970 --> 00:16:20,730
+اعمل under correction انازل شوية فى البواب اذا هل
+
+169
+00:16:20,730 --> 00:16:25,550
+بيستخدم للنير ممكن استخدامه للنير طيب لو واحد عنده
+
+170
+00:16:25,550 --> 00:16:31,270
+color vision defect ممكن استخدمه ولا لأ؟ ليه؟ ليش
+
+171
+00:16:31,270 --> 00:16:35,330
+ا .. ا لا؟ لأنه بعتمد على ال chromatic aberration
+
+172
+00:16:35,330 --> 00:16:37,530
+لكن ال color vision ايش بعتمد؟
+
+173
+00:16:39,880 --> 00:16:43,040
+على ال color discrimination ممتاز على التمييز
+
+174
+00:16:43,040 --> 00:16:43,660
+اللوني
+
+175
+00:16:47,940 --> 00:16:54,300
+and error بمعنى يعني كيثما واحد بعمل مثلا اكيد هذا
+
+176
+00:16:54,300 --> 00:16:59,260
+ال test كلكم عملته اللي هي جثة الملك و العشرة انه
+
+177
+00:16:59,260 --> 00:17:03,740
+في العملة في ال cones okay هذه اللي بتستخدم ك
+
+178
+00:17:03,740 --> 00:17:07,780
+common في ال subjective verification بمعنى اني
+
+179
+00:17:07,780 --> 00:17:12,480
+بزود ربع او بجلر ربع okay او بدونها
+
+180
+00:17:14,910 --> 00:17:19,290
+Trial and error this method is simply adding a
+
+181
+00:17:19,290 --> 00:17:25,490
+plus 0.25 diopter sphere and minus 0.25 diopter
+
+182
+00:17:25,490 --> 00:17:29,090
+sphere in a monocular fashion يعني هو عبارة عن
+
+183
+00:17:29,090 --> 00:17:34,970
+منهج بسيط بتم استخدام عدسة قوتها plus ربع او minus
+
+184
+00:17:34,970 --> 00:17:40,210
+ربع امام مين العين طبعا انا بستخدمه monocular يعني
+
+185
+00:17:40,210 --> 00:17:45,310
+دايمابأكد عليكم ان ال verification دايما لازم يكون
+
+186
+00:17:45,310 --> 00:17:50,550
+monocular ممنوع تعمليه عملية verification و
+
+187
+00:17:50,550 --> 00:17:54,770
+تعمليها binocular بعد ما انا بعمل كل عين على حدة
+
+188
+00:17:54,770 --> 00:17:59,290
+برفع ال occluder و بستخدمه ك binocular
+
+189
+00:18:01,480 --> 00:18:06,860
+and asking fashion بمعنى هان اللي هو طراز style أو
+
+190
+00:18:06,860 --> 00:18:11,760
+بمعنى مثلا اللي هو كادسة واحدة انه بيستخدم ك
+
+191
+00:18:11,760 --> 00:18:15,300
+fashion monocular fashion يعني فقط اللي هو كطراز
+
+192
+00:18:15,300 --> 00:18:21,960
+واحد يعني only one eye فقط العين واحدةand asking
+
+193
+00:18:21,960 --> 00:18:26,400
+the patient انه بسأل المريض if the vision is
+
+194
+00:18:26,400 --> 00:18:32,780
+better or worse يعني هل انه النظر بتحسن او بسيء
+
+195
+00:18:32,780 --> 00:18:39,660
+اذا بمعنى انه بضيف عدسة plus او minus و بشوف ردة
+
+196
+00:18:39,660 --> 00:18:45,280
+فعل من المريض هل النظر بتحسن ولا ايه بصير impaired
+
+197
+00:18:45,280 --> 00:18:45,840
+لل vision
+
+198
+00:18:49,950 --> 00:18:55,590
+إذا المريض بيان إنه
+
+199
+00:18:55,590 --> 00:19:00,370
+بدون عدسة أفضل، إذا المريض بيان إنه بدون عدسة
+
+200
+00:19:00,370 --> 00:19:07,230
+أفضل، إذا المريض بيان إنه بدون عدسة أفضل، إذا
+
+201
+00:19:07,230 --> 00:19:09,030
+المريض بيان إنه بدون عدسة أفضل، إذا المريض بيان
+
+202
+00:19:09,030 --> 00:19:12,950
+إنه بدون عدسة أفضل، إذا المريض بيان إنه بدون عدسة
+
+203
+00:19:12,950 --> 00:19:14,250
+أفضل، إذا المريض بيان إنه بدون عدسة أفضل، إذا
+
+204
+00:19:14,250 --> 00:19:15,310
+المريض بيان إنه بدون عدسة أفضل، إذا المريض بيان
+
+205
+00:19:15,310 --> 00:19:16,630
+إنه بدون عدسة أفضل، إذا المريض بيان إنه بدون عدسة
+
+206
+00:19:16,630 --> 00:19:25,000
+أفضل، إذا المريض بيان إنه بدون عدبالظبط طيب
+
+207
+00:19:25,000 --> 00:19:32,720
+اذا بيشان رابط انه أفضل ان اضافة الـ plus 0.25
+
+208
+00:19:32,720 --> 00:19:37,920
+تابع اضافة الـ plus حتى لا يتم افتحة أفضلإذا
+
+209
+00:19:37,920 --> 00:19:41,980
+المريض بيان لما أنا ضفت plus ربع صار improvement
+
+210
+00:19:41,980 --> 00:19:48,000
+تحسن للنظر بستمر بإضافة ال plus لحد ما أصل إلى
+
+211
+00:19:48,000 --> 00:19:55,730
+حالة no improvement مافيش تحسنفبضيف plus ربع شاف
+
+212
+00:19:55,730 --> 00:20:00,710
+ان المريض اتحسن شعرت انه مثلا شاف سطر 6 على 12
+
+213
+00:20:00,710 --> 00:20:05,450
+بعدها شاف 6 على 9 بعمل ايش؟ زيادة لل line يعني
+
+214
+00:20:05,450 --> 00:20:09,770
+بزود القوة لحد ما يصل انه no improvement مافيش
+
+215
+00:20:09,770 --> 00:20:10,690
+تحسن
+
+216
+00:20:15,660 --> 00:20:19,100
+then add the new addition power for his previous
+
+217
+00:20:19,100 --> 00:20:25,040
+prescription يعني بعمل عملية إضافة للعدسة الجديدة
+
+218
+00:20:25,040 --> 00:20:29,580
+previous prescription للوصفة القديمة يعني بعمل
+
+219
+00:20:29,580 --> 00:20:33,820
+الإضافة هذه على مين ال previous prescription يعني
+
+220
+00:20:33,820 --> 00:20:36,980
+الوصفة القديمة سواء اللي عملتيها في ال objective
+
+221
+00:20:36,980 --> 00:20:39,600
+refraction في ال ريتنسكوب أو في ال auto
+
+222
+00:20:39,600 --> 00:20:41,000
+refractometer
+
+223
+00:20:43,940 --> 00:20:49,280
+بمعنى الان انا طلع عنده قوة plus two ليبتر السفير
+
+224
+00:20:49,280 --> 00:20:55,220
+روحت جبت plus two point five و المريض صار عنده
+
+225
+00:20:55,220 --> 00:21:00,100
+تحسن معناه انه في ايه improvement okay شو بدي اعمل
+
+226
+00:21:00,100 --> 00:21:05,410
+بهذه الحالة؟بزود كمان ال power بجيب مثلا two point
+
+227
+00:21:05,410 --> 00:21:09,790
+five اتحسن النظر بجيب two point seven five بجيب
+
+228
+00:21:09,790 --> 00:21:13,250
+تلاتة لحد ما المريض يقول ليه انه مافيش improvement
+
+229
+00:21:13,250 --> 00:21:17,990
+مافيش تحسن okay فهذه النقطة يعني زي بالظبط ال
+
+230
+00:21:17,990 --> 00:21:21,670
+neutral point يعني نقطة التعادل او ال end point
+
+231
+00:21:21,670 --> 00:21:28,250
+يعني عندها مش ممكن انه يتحسن من النظرما أنا بصل
+
+232
+00:21:28,250 --> 00:21:32,330
+للمرحلة هادى، إيش بتكون؟ إنه هادى وصفة المريض، الـ
+
+233
+00:21:32,330 --> 00:21:38,450
+final prescription If the
+
+234
+00:21:38,450 --> 00:21:43,130
+patient responds that vision is worse, remove plus
+
+235
+00:21:43,130 --> 00:21:49,270
+0.25 dioptersphere or prepare to add minus 0.25,
+
+236
+00:21:49,770 --> 00:21:52,930
+ask the patient if the letters are sharper and
+
+237
+00:21:52,930 --> 00:21:59,100
+clearer or notإذا المريض يما أضفنا ال plus ربع شعر
+
+238
+00:21:59,100 --> 00:22:02,740
+أنه إيه ال vision صار فيه impaired أو جل ال
+
+239
+00:22:02,740 --> 00:22:06,960
+vision، في هذه الحالة إيش بعمل؟ remove، إزالة لل
+
+240
+00:22:06,960 --> 00:22:11,960
+plus ربع و بضيف إيه؟ ال minus و بستمر في مين؟ في
+
+241
+00:22:11,960 --> 00:22:12,660
+ال minus
+
+242
+00:22:17,710 --> 00:22:20,450
+إذا كان الأمر أفضل، إستمر في إضافة إضافة إضافة
+
+243
+00:22:20,450 --> 00:22:21,750
+إضافة إضافة إضافة إضافة إضافة إضافة إضافة إضافة
+
+244
+00:22:21,750 --> 00:22:23,310
+إضافة إضافة إضافة إضافة إضافة إضافة إضافة إضافة
+
+245
+00:22:23,310 --> 00:22:26,410
+إضافة إضافة إضافة إضافة إضافة إضافة إضافة إضافة
+
+246
+00:22:26,410 --> 00:22:33,750
+إضافة إضافة إضافة إضافة إضافة إضافة إضافة إضافة
+
+247
+00:22:33,750 --> 00:22:35,670
+إضافة إضافة إضافة إضافة إضافة إضافة إضافة إضافة
+
+248
+00:22:35,670 --> 00:22:41,750
+إضافة إضافة إضافة إضافة إضافة إضافة إضافة إضافة
+
+249
+00:22:41,750 --> 00:22:45,370
+إضافة
+
+250
+00:22:45,370 --> 00:22:45,370
+إض
+
+251
+00:22:49,400 --> 00:22:53,600
+this method of verification completely يعني بيعمل
+
+252
+00:22:53,600 --> 00:22:58,500
+عملية completely بمعنى totally يعني بشكل كامل أنه
+
+253
+00:22:58,500 --> 00:23:04,300
+بيعمل تأكيد بشكل كاملDepends on patients answer
+
+254
+00:23:04,300 --> 00:23:10,860
+بيعتمد على إجابة المريض So the accuracy لذلك أن
+
+255
+00:23:10,860 --> 00:23:18,100
+الدقة ستكون محددة according to the patient
+
+256
+00:23:18,100 --> 00:23:22,360
+observation يعني بناء على ملاحظة من المريض
+
+257
+00:23:29,600 --> 00:23:35,980
+number three ال pinhole بمعنى small aperture يعني
+
+258
+00:23:35,980 --> 00:23:42,680
+فتحة صغيرة طيب قبل ما نبدأ في ال pinhole شو هي ال
+
+259
+00:23:42,680 --> 00:23:47,400
+cases no improvement with pinhole؟
+
+260
+00:24:09,700 --> 00:24:14,460
+الحالات اللي مابتحسنش مع البن هول number one high
+
+261
+00:24:27,890 --> 00:24:33,150
+number three obesity media سواء كان عندنا corneal
+
+262
+00:24:33,150 --> 00:24:39,610
+scar or immature cataract انه cataract غير ناضجة
+
+263
+00:24:39,610 --> 00:24:45,110
+okay هدول التلات حالات اللى مابتحسنش فيهم النظر مع
+
+264
+00:24:45,110 --> 00:24:50,510
+البن هون طبعا شو السبب؟ لأن فيه بيكون problem غير
+
+265
+00:24:50,510 --> 00:24:52,250
+ال vision صح؟
+
+266
+00:24:59,570 --> 00:25:06,510
+عدسة الثقب الصغير is a lens عدسة that has a hole
+
+267
+00:25:06,510 --> 00:25:12,310
+ثقب in the center of lens عبارة عن عدسة بتمتلك ثقب
+
+268
+00:25:12,310 --> 00:25:20,130
+في المنتصف كما في الشكل في الفيجارة this hole has
+
+269
+00:25:20,130 --> 00:25:21,730
+the effect of reducing
+
+270
+00:25:34,940 --> 00:25:42,360
+هو يعمل عملية تجميع للأشعة الداخلة وبعمل تقليل
+
+271
+00:25:42,360 --> 00:25:48,020
+لعرض هذه الأشعة بحيث أنه تدخل عبارة عن بنسل of
+
+272
+00:25:48,020 --> 00:25:53,880
+light يعني عبارة عن حزم ضوئيطبعا من وين بتكون هذه
+
+273
+00:25:53,880 --> 00:26:00,940
+جاية coming آتيه from each point من أي نقطة on the
+
+274
+00:26:00,940 --> 00:26:05,540
+viewed object يعني من أي جسم إيش ماله حقيقي لإنه
+
+275
+00:26:05,540 --> 00:26:09,300
+زي ما اتكلمنا إنه أي جسم حقيقي بتكون الأشعة
+
+276
+00:26:09,300 --> 00:26:13,580
+الخارجة منه divergence وإلا لو الأشعة كانت
+
+277
+00:26:13,580 --> 00:26:18,080
+parallel أو conversion بالظبط إنه بيكون يعني فقط
+
+278
+00:26:18,080 --> 00:26:20,740
+في ال position اللي هو فيه بيكون إيه شايفة
+
+279
+00:26:23,970 --> 00:26:29,670
+Normally طبيعيًا the full opening أي بمعنى الفتحة
+
+280
+00:26:29,670 --> 00:26:34,370
+بتاعة ال pupil of the pupil admits light أنه بتسمح
+
+281
+00:26:34,370 --> 00:26:40,010
+بدخول الضوء يعني بالوضع الطبيعي okay بالوضع
+
+282
+00:26:40,010 --> 00:26:47,750
+الطبيعي ال pinhole بيسمح بتمرير الضوء okay لوين؟
+
+283
+00:26:47,750 --> 00:26:53,050
+لال pupil لأن الضوء بدخل عن طريق مين؟ البقبق okay
+
+284
+00:26:57,750 --> 00:27:03,830
+It is the improper أي بمعنى من الخطأ bending أي
+
+285
+00:27:03,830 --> 00:27:10,670
+انه ميلان او انحناء of the outermost rays انه
+
+286
+00:27:10,670 --> 00:27:15,670
+الأشعة الخارجة in that pencil of light which
+
+287
+00:27:15,670 --> 00:27:21,370
+causes refractive errors بمعنى الآن لو كان المريض
+
+288
+00:27:21,370 --> 00:27:27,150
+ميوبودخل الضوء divergent لل bin hole، إذا الضوء
+
+289
+00:27:27,150 --> 00:27:31,950
+هذا وين هيتجمع؟ خلف .. sorry in front of the
+
+290
+00:27:31,950 --> 00:27:36,310
+retina، صح؟ في حالة ال hypermetroid، هيتركز behind
+
+291
+00:27:36,310 --> 00:27:41,230
+the retina، الastigmatism okay، هيتركز كأنه إيه؟
+
+292
+00:27:41,230 --> 00:27:46,970
+عبارة عن lineبمعنى ان ال pinhole بعمل عملية تحسين
+
+293
+00:27:46,970 --> 00:27:51,910
+للرؤية في كل الحالات هدول، في حالة ال myop, ال
+
+294
+00:27:51,910 --> 00:27:56,550
+hypermetrop, ال astigmatism و ال presbyopia إذا
+
+295
+00:27:56,550 --> 00:28:00,850
+التلت حالات إيش بيعمللهم؟ improvement إذا الآن لو
+
+296
+00:28:00,850 --> 00:28:06,230
+اجال ال case حالة و كان مثلا عنده astigmatism هل
+
+297
+00:28:06,230 --> 00:28:09,830
+بستخدم معه ال pinhole ولا لأ؟ ممكن أستخدم معه
+
+298
+00:28:11,450 --> 00:28:15,570
+إيجاليك بيشان كان عنده مثلا ابلانه ع ماينوس تلاتة
+
+299
+00:28:15,570 --> 00:28:19,650
+اكسس تسعين، هل هذا المريض ممكن يستخدم معه ال
+
+300
+00:28:19,650 --> 00:28:24,290
+pinhole؟ نعم ممكن، ليش؟ لأن ال pinhole بعمل عملية
+
+301
+00:28:24,290 --> 00:28:28,110
+ال pinhole can bring، يعني ممكن أنه يجلب
+
+302
+00:28:28,110 --> 00:28:32,610
+improvement of the vision، يعني تحسين للرؤية، في
+
+303
+00:28:32,610 --> 00:28:36,930
+حالة مين؟ بيوب، hypermetrop, breast biop and
+
+304
+00:28:36,930 --> 00:28:41,430
+astigmatism، أي بمعنى كل الحالات الانكسارية للعين
+
+305
+00:28:41,530 --> 00:28:46,390
+Okay to
+
+306
+00:28:46,390 --> 00:28:50,530
+be noticeable أي بمعنى تكون ملاحظة يعني الحالات
+
+307
+00:28:50,530 --> 00:28:54,010
+هذه الإنكسارية ال myopia و ال hypermetropia و ال
+
+308
+00:28:54,010 --> 00:28:57,350
+breast myopia و ال astigmatism بتكون أيه؟ ملاحظة
+
+309
+00:28:57,350 --> 00:29:02,610
+من خلال ال pinhole pinhole can bring about a
+
+310
+00:29:02,610 --> 00:29:06,430
+clearer vision in all these conditions إذا بيعمل
+
+311
+00:29:06,430 --> 00:29:09,950
+عملية تحسين للرؤية في كل الحالات
+
+312
+00:29:14,950 --> 00:29:28,670
+by blocking these peripheral rays الديوكروم
+
+313
+00:29:28,670 --> 00:29:34,070
+تست يعتبر للسفير ال trial and error للسفير و
+
+314
+00:29:34,070 --> 00:29:39,170
+للسلندر ممكن minus ربع ازود للسلندر ايضا اجلل ال
+
+315
+00:29:39,170 --> 00:29:45,320
+minus ربع او ازود في السلندرلكن ال penhole also
+
+316
+00:29:45,320 --> 00:29:49,060
+for all the refractive errors لكل الأخطاء
+
+317
+00:29:49,060 --> 00:29:53,420
+الإنكسارية لأنه بيعمل المبدأ بتاعه بالظبط بتاع ال
+
+318
+00:29:53,420 --> 00:29:57,580
+penhole أنه عبارة عن aberration center aberration
+
+319
+00:29:57,580 --> 00:30:03,000
+of the lens فاتحة في منتصف العدسة بتسمح بتمرير
+
+320
+00:30:03,000 --> 00:30:08,780
+الضوء للعين إذا كان المريض ميوب الأشعة هتتركز
+
+321
+00:30:10,540 --> 00:30:15,180
+هيبرمتروب behind the retina ميوب on the retina ال
+
+322
+00:30:15,180 --> 00:30:20,920
+stigma هتتركز عبارة عن ايه؟ line okay الآن في حالة
+
+323
+00:30:20,920 --> 00:30:27,880
+يكون مثلا عندي مريض بدى استخدمله مدرامايد قطرة
+
+324
+00:30:27,880 --> 00:30:33,260
+قطرة ايش بتعمل المدرامايد؟ ديليت للبيوبل طيب هل
+
+325
+00:30:33,260 --> 00:30:36,100
+بنفع بعدها استخدم البنهول؟
+
+326
+00:30:42,850 --> 00:30:45,750
+لازم يكون البيوت برضه صغيرة، يعني أول حاجة معاهدة
+
+327
+00:30:45,750 --> 00:30:49,130
+عشان تقدر ترفن الأشياء، اما لو كانك بيت عارف تدخل
+
+328
+00:30:49,130 --> 00:30:56,190
+من منطقة أو منطقة، لأ مش عارف كده يعني بنفع
+
+329
+00:30:56,190 --> 00:30:59,370
+ولا بنفعاش أول؟ بس ال 6 دقيقة بس اللي هتتلقى
+
+330
+00:30:59,370 --> 00:31:03,610
+خلالها، يعني محتاج تنتصف، ماعندي بنفع يعني، ماشتغل
+
+331
+00:31:03,610 --> 00:31:04,070
+يعني، بقى و بقى
+
+332
+00:31:07,820 --> 00:31:14,660
+الان السؤال لو طفل قطرناله Cycloblegia او مثلا
+
+333
+00:31:14,660 --> 00:31:21,580
+بيشان اربعين سنة قطرناله Cyclobentilate okay يعني
+
+334
+00:31:21,580 --> 00:31:26,280
+عملنا عملية Medramide توصيع للبؤبه هل بعديها بعد
+
+335
+00:31:26,280 --> 00:31:29,820
+ال Medramide ممكن استخدم معه ال Benhol لتحسين
+
+336
+00:31:29,820 --> 00:31:30,780
+الرؤية او لا؟
+
+337
+00:31:36,340 --> 00:31:41,160
+فالبنهار بتقلل عده الأشعار ده فالسنة تتنفعش okay
+
+338
+00:31:41,160 --> 00:31:45,500
+another answer تفضلي لا مش هيفه لإن الأشعار بس
+
+339
+00:31:45,500 --> 00:31:49,520
+هتفوت في سنة تلت او تتنفع لا فلما هاللي بيستخدم ال
+
+340
+00:31:49,520 --> 00:31:53,880
+paint hall هو مصر هتفرق لو رجع البقبق تاني يعني
+
+341
+00:31:53,880 --> 00:32:00,080
+فهي محقق الموضوع okay answer
+
+342
+00:32:00,080 --> 00:32:05,280
+لأ طيب هو صح كلامكم أنه بعد ما نعمل ال ..
+
+343
+00:32:20,350 --> 00:32:23,190
+انه Cycloventilate يعني المريض بده ايه؟ قطر
+
+344
+00:32:23,190 --> 00:32:27,870
+التوسيع بعدها بعض الأحيان بقولك الدكتور اعمليله
+
+345
+00:32:27,870 --> 00:32:32,310
+Penhole وهذا خطأ لأنه الآن بعد ال .. ال Medramide
+
+346
+00:32:32,310 --> 00:32:36,590
+ايش بيصير؟ Dialate ل ال pupil فكمية الضوء اللي
+
+347
+00:32:36,590 --> 00:32:42,290
+بتكون داخلة للبقبق اشمالها كبيرة okay؟ الان صح ال
+
+348
+00:32:42,290 --> 00:32:42,950
+Penhole
+
+349
+00:32:51,970 --> 00:32:58,070
+يعني حزم ضوئية بيعمل إذا استخدمنا ال pinhole في
+
+350
+00:32:58,070 --> 00:33:02,130
+حالة المدرمايشو بيعمله striking لل vision يعني
+
+351
+00:33:02,130 --> 00:33:03,830
+بمعنى خلل بالرؤية
+
+352
+00:33:12,720 --> 00:33:16,880
+يعني مابتدخلش الأشعة من وين؟ من الأسرار، فعشان هيك
+
+353
+00:33:16,880 --> 00:33:22,260
+لا يمكن استخدام ال pen hole بعد ما بستخدم ال cycle
+
+354
+00:33:22,260 --> 00:33:24,920
+pentulate أو ال cycle Ebligia
+
+355
+00:33:39,310 --> 00:33:43,430
+and only lettering into the eye those rays which
+
+356
+00:33:43,430 --> 00:33:47,990
+pass through the central portion of the pupil, any
+
+357
+00:33:47,990 --> 00:33:51,530
+refractive error in the lens or cornea is not
+
+358
+00:33:51,530 --> 00:33:56,730
+noticed as much نفس فكرة ال mid ramite فكرة يما
+
+359
+00:33:56,730 --> 00:34:00,890
+يكون المريض عنده corneal scar او يكون عنده مثلا
+
+360
+00:34:00,890 --> 00:34:04,770
+immature cataract الآن ال immature cataract وين
+
+361
+00:34:04,770 --> 00:34:10,810
+هتكون؟ في منتصف العدسةالمياه البيضاء هتتركز في
+
+362
+00:34:10,810 --> 00:34:15,230
+منتصف العدسة فالان ال pin hole كل الضوء من وين
+
+363
+00:34:15,230 --> 00:34:20,350
+بدخل من المنتصف لما بستخدم ال pin hole هيمنع
+
+364
+00:34:20,350 --> 00:34:24,190
+التمرير وين الضوء فهتلاحظ ان ال patient
+
+365
+00:34:40,160 --> 00:34:47,800
+و نفس الفكرة استخدام ال mid ramide قطرة التوسيع
+
+366
+00:34:47,800 --> 00:34:52,060
+انه بيعمل ايه يعني زي كأنه border حاجز لتدخيل
+
+367
+00:34:52,060 --> 00:34:55,920
+الضوء فقط انه بدخل الضوء من المنتصف و ال
+
+368
+00:34:55,920 --> 00:34:59,880
+peripheral ايش بيعمله ignore يعني تجاهل لانه كأنه
+
+369
+00:34:59,880 --> 00:35:01,120
+border حاجز له
+
+370
+00:35:07,600 --> 00:35:11,500
+في بعض الناس حتى بيكون عندهم بقبق واسع ويمكن اللي
+
+371
+00:35:11,500 --> 00:35:14,760
+حطوه في ال written scope during the written scope
+
+372
+00:35:14,760 --> 00:35:18,920
+method but only the central portion فقط اللي هي
+
+373
+00:35:18,920 --> 00:35:24,380
+منطقة المنتصف is receiving light هو اللي هي stop
+
+374
+00:35:24,380 --> 00:35:30,370
+بالمين الضوءThe improvement in visual acuity can
+
+375
+00:35:30,370 --> 00:35:34,930
+be striking اذا التحسن في الرؤية البصرية ايش ممكن
+
+376
+00:35:34,930 --> 00:35:39,370
+انه striking اي تنضرب او انه يصير لها impaired
+
+377
+00:35:39,370 --> 00:35:44,810
+يعني اتقل في حال يما يكون ال pupil dilate يعني
+
+378
+00:35:44,810 --> 00:35:49,270
+ممكن هذه الحالة نضيفها انه من ال cases no improve
+
+379
+00:35:49,270 --> 00:35:49,950
+with بينهم
+
+380
+00:36:03,960 --> 00:36:08,560
+سينتر هيدخل الضوء بشكل كثيف okay فهيعمل ايه؟ no
+
+381
+00:36:08,560 --> 00:36:12,960
+improvement لل vision او هيعمل impaired لل vision
+
+382
+00:36:12,960 --> 00:36:16,880
+او striking انه لل visual acuity
+
+383
+00:36:20,940 --> 00:36:25,920
+So لذلك if the vision is improved لذلك إذا النظر
+
+384
+00:36:25,920 --> 00:36:30,580
+اتحسن when looking through the pinhole lens خلال
+
+385
+00:36:30,580 --> 00:36:35,620
+ما بننظر إلى عدسة ال pinhole that's mean the
+
+386
+00:36:35,620 --> 00:36:40,020
+prescription is not accurate بمعنى الآن احنا حطينا
+
+387
+00:36:44,310 --> 00:36:49,290
+بعد حطينا ال pinhole شعرنا ان النظر ايش ماله اتحسن
+
+388
+00:36:49,290 --> 00:36:53,970
+معناه الوصفة بتاعتك ايه مش صحيحة انه بدنا نضيف
+
+389
+00:36:53,970 --> 00:37:00,570
+كمان كpower اذا so لذلك if the vision اذا الرؤية
+
+390
+00:37:00,570 --> 00:37:07,010
+is improved اتحسنت when looking خلال ما ينظر خلال
+
+391
+00:37:07,010 --> 00:37:11,150
+عدسة ال pinhole that's mean معناه ان ال
+
+392
+00:37:11,150 --> 00:37:12,550
+prescription ان الوصفة
+
+393
+00:37:20,630 --> 00:37:26,090
+إذا العملية تأكيد ال power بكون هان إيش ماله ضروري
+
+394
+00:37:26,090 --> 00:37:31,670
+للمريض، okay؟ إذا بمعنى، الآن أنا كان عند المريض
+
+395
+00:37:31,670 --> 00:37:37,630
+في minus two، ديوبتر، حطينا العدسة لل right eye،
+
+396
+00:37:37,630 --> 00:37:40,870
+شعرنا لما حطينا ال pinhole في تحسن في الرؤية، شو
+
+397
+00:37:40,870 --> 00:37:45,360
+معناها؟إنه ب .. اه معناه إنه في improvement في ال
+
+398
+00:37:45,360 --> 00:37:49,360
+visual acuity يعني ال minus two is not enough for
+
+399
+00:37:49,360 --> 00:37:52,660
+the patient غير كافية أو ماعملتش ال correction
+
+400
+00:37:52,660 --> 00:37:59,040
+الكافة لمين للمريض okay النقطة الأخيرة إنه الآن
+
+401
+00:37:59,040 --> 00:38:05,200
+أنا مريض عنده minus two عنده minus two
+
+402
+00:38:05,200 --> 00:38:08,300
+dioptersphere okay
+
+403
+00:38:12,910 --> 00:38:18,770
+ضفنا ال minus 2 أمام العين بعدها لاحظنا في ال
+
+404
+00:38:18,770 --> 00:38:25,910
+minus 2 ال visual acuity كان 6 على 12 يما حطيت ال
+
+405
+00:38:25,910 --> 00:38:31,470
+pin hole صار فيه تحسن للمريض شو معناها؟ ان ال
+
+406
+00:38:31,470 --> 00:38:35,190
+minus 2 هذه أشمالها is not enough for the patient
+
+407
+00:38:35,190 --> 00:38:37,310
+يعني هذه in
+
+408
+00:38:46,180 --> 00:38:52,780
+لمن؟ for the patient نحنا
+
+409
+00:38:52,780 --> 00:38:56,540
+استخدمنا ال pinhole ال pinhole فوق ال minus two
+
+410
+00:38:56,540 --> 00:39:01,580
+لكن no improvement أو الحالة التانية أنه ماصارش
+
+411
+00:39:01,580 --> 00:39:06,640
+تحسن الحالة الأولى هان صار فيه تحسن okay إذا مدام
+
+412
+00:39:06,640 --> 00:39:10,500
+فيه تحسن إذا بدي أعمل إيش إضافة لل power بدي أجيب
+
+413
+00:39:10,500 --> 00:39:17,220
+مثلاأو minus two point five و هكذا طيب لو ماصارش
+
+414
+00:39:17,220 --> 00:39:20,680
+تحسن حطينا ال minus two و ماصارش تحسن في ال pin
+
+415
+00:39:20,680 --> 00:39:33,460
+hole شو معناها؟ ان الوصفة صحيحة مرة
+
+416
+00:39:33,460 --> 00:39:36,700
+تانية يعني حطينا ال .. عجبنا نعمل ال subject
+
+417
+00:39:50,730 --> 00:39:55,030
+لأن المريض بحب ال minus، يعني الآن مريض عنده minus
+
+418
+00:39:55,030 --> 00:39:59,930
+واحد و نص، لما هطلله minus اتنين، بكون الرؤية عنده
+
+419
+00:39:59,930 --> 00:40:03,530
+ايه؟ ممتازة، بقولك هذه هي العدسة اللي بدي إياها،
+
+420
+00:40:03,530 --> 00:40:08,110
+لكن مع الوقت إيش بتحدث له؟ تديه ال ice train، تديه
+
+421
+00:40:08,110 --> 00:40:08,730
+ال eye fatigue
+
+422
+00:40:12,380 --> 00:40:16,320
+يعني بيحب اللي عنده ميوب انه يزود في الميوب ال
+
+423
+00:40:16,320 --> 00:40:19,560
+hyper metrop دايما بيحب اقل يعني اذا مالبس plus
+
+424
+00:40:19,560 --> 00:40:23,700
+واحد بيحب يلبس plus zero point seven five او zero
+
+425
+00:40:23,700 --> 00:40:27,940
+point five فحسب المريض عشان هيك بدخل موضوع من ال
+
+426
+00:40:27,940 --> 00:40:32,220
+verification وافضل test من هذه بعد ما يصل ال
+
+427
+00:40:32,220 --> 00:40:35,280
+visual acuity ستة ع ستة ال diachrome test
+
+428
+00:40:40,820 --> 00:40:45,240
+لو ال green equal يعرف انه ايه انه الوصفة بتاعته
+
+429
+00:40:45,240 --> 00:40:54,960
+correct okay another answer another question طيب
+
+430
+00:40:54,960 --> 00:40:56,900
+خليني جف ل ال verification for
+