[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.00,0:00:05.25,Default,,0000,0000,0000,,
Dialogue: 0,0:00:05.25,0:00:07.85,Default,,0000,0000,0000,,PROFESSOR: I know you have\Nencountered difficulties
Dialogue: 0,0:00:07.85,0:00:12.67,Default,,0000,0000,0000,,on the last few problems,\Nmaybe four, maybe five, maybe
Dialogue: 0,0:00:12.67,0:00:14.60,Default,,0000,0000,0000,,the last 10, I don't know.
Dialogue: 0,0:00:14.60,0:00:19.10,Default,,0000,0000,0000,,But today, I want to--\Nwe have plenty of time.
Dialogue: 0,0:00:19.10,0:00:22.58,Default,,0000,0000,0000,,We still have time\Nfor chapter 13,
Dialogue: 0,0:00:22.58,0:00:25.05,Default,,0000,0000,0000,,and plenty of time\Nfor the final review.
Dialogue: 0,0:00:25.05,0:00:29.08,Default,,0000,0000,0000,,I can afford to spend two or\Nthree hours just reviewing
Dialogue: 0,0:00:29.08,0:00:31.87,Default,,0000,0000,0000,,chapter 12, if I wanted to.
Dialogue: 0,0:00:31.87,0:00:37.81,Default,,0000,0000,0000,,All right, so I have this\Nquestion from one of you saying
Dialogue: 0,0:00:37.81,0:00:43.74,Default,,0000,0000,0000,,what part of the problem is\Nthat in terms of a two point
Dialogue: 0,0:00:43.74,0:00:44.24,Default,,0000,0000,0000,,integral.
Dialogue: 0,0:00:44.24,0:00:50.66,Default,,0000,0000,0000,,We have a solid\Nbounded by z equals 3x,
Dialogue: 0,0:00:50.66,0:00:56.59,Default,,0000,0000,0000,,and z equals x squared,\Nand is a plane.
Dialogue: 0,0:00:56.59,0:00:59.73,Default,,0000,0000,0000,,And can anybody tell\Nme what this is?
Dialogue: 0,0:00:59.73,0:01:04.03,Default,,0000,0000,0000,,Just out of curiosity,\Nyou don't have to know.
Dialogue: 0,0:01:04.03,0:01:05.07,Default,,0000,0000,0000,,STUDENT: It's a parabola.
Dialogue: 0,0:01:05.07,0:01:06.48,Default,,0000,0000,0000,,PROFESSOR: It would\Nbe a parabola,
Dialogue: 0,0:01:06.48,0:01:08.21,Default,,0000,0000,0000,,if we were in\N[INTERPOSING VOICES]
Dialogue: 0,0:01:08.21,0:01:12.17,Default,,0000,0000,0000,,if we were in 2D.
Dialogue: 0,0:01:12.17,0:01:17.45,Default,,0000,0000,0000,,So the parabola is missing\Nthe y, and y could be anybody.
Dialogue: 0,0:01:17.45,0:01:21.13,Default,,0000,0000,0000,,So it's a parabola\Nthat's shifted along y.
Dialogue: 0,0:01:21.13,0:01:24.22,Default,,0000,0000,0000,,It's going to give you\Na cylindrical surface.
Dialogue: 0,0:01:24.22,0:01:29.42,Default,,0000,0000,0000,,It's like something used\Nfor drainage, I don't know.
Dialogue: 0,0:01:29.42,0:01:31.29,Default,,0000,0000,0000,,Water, like a valve.
Dialogue: 0,0:01:31.29,0:01:34.09,Default,,0000,0000,0000,,
Dialogue: 0,0:01:34.09,0:01:38.21,Default,,0000,0000,0000,,So this is what it is,\Na cylindrical surface.
Dialogue: 0,0:01:38.21,0:01:42.44,Default,,0000,0000,0000,,
Dialogue: 0,0:01:42.44,0:01:52.69,Default,,0000,0000,0000,,And you know that z must be\Nbetween x squared and 3x.
Dialogue: 0,0:01:52.69,0:01:58.62,Default,,0000,0000,0000,,How do you know which one is\Nbigger, which one is smaller?
Dialogue: 0,0:01:58.62,0:02:01.23,Default,,0000,0000,0000,,You should think about it.
Dialogue: 0,0:02:01.23,0:02:04.04,Default,,0000,0000,0000,,
Dialogue: 0,0:02:04.04,0:02:08.86,Default,,0000,0000,0000,,When you draw, you\Ndraw like that.
Dialogue: 0,0:02:08.86,0:02:18.20,Default,,0000,0000,0000,,
Dialogue: 0,0:02:18.20,0:02:19.57,Default,,0000,0000,0000,,Do these guys intersect?
Dialogue: 0,0:02:19.57,0:02:22.75,Default,,0000,0000,0000,,
Dialogue: 0,0:02:22.75,0:02:24.59,Default,,0000,0000,0000,,We are in the xz plane.
Dialogue: 0,0:02:24.59,0:02:26.16,Default,,0000,0000,0000,,Do these guys intersect?
Dialogue: 0,0:02:26.16,0:02:32.12,Default,,0000,0000,0000,,x squared equals\N3x intersect where?
Dialogue: 0,0:02:32.12,0:02:37.34,Default,,0000,0000,0000,,They intersect at 0, and at 3.
Dialogue: 0,0:02:37.34,0:02:40.19,Default,,0000,0000,0000,,x1 is 0, and x2 is 3.
Dialogue: 0,0:02:40.19,0:02:45.54,Default,,0000,0000,0000,,So when I want to draw this,\NI would say that indeed, it's
Dialogue: 0,0:02:45.54,0:02:48.36,Default,,0000,0000,0000,,a bounded domain.
Dialogue: 0,0:02:48.36,0:02:51.50,Default,,0000,0000,0000,,If it where unbounded, it\Nwouldn't ask for the volume,
Dialogue: 0,0:02:51.50,0:02:54.17,Default,,0000,0000,0000,,because the volume\Nwould be nothing.
Dialogue: 0,0:02:54.17,0:02:59.33,Default,,0000,0000,0000,,So this thing must\Nbe a bounded domain.
Dialogue: 0,0:02:59.33,0:03:03.48,Default,,0000,0000,0000,,x cannot go on, this\Nis the infinite part.
Dialogue: 0,0:03:03.48,0:03:09.81,Default,,0000,0000,0000,,So we are thinking of just this\Nstriped piece of a domain x
Dialogue: 0,0:03:09.81,0:03:16.10,Default,,0000,0000,0000,,here, where this piece is\Nbetween z equals x squared,
Dialogue: 0,0:03:16.10,0:03:19.01,Default,,0000,0000,0000,,then z equals 3x.
Dialogue: 0,0:03:19.01,0:03:23.07,Default,,0000,0000,0000,,This is 0 origin, and this is 3.
Dialogue: 0,0:03:23.07,0:03:26.67,Default,,0000,0000,0000,,
Dialogue: 0,0:03:26.67,0:03:30.74,Default,,0000,0000,0000,,So at 3, they meet again.
Dialogue: 0,0:03:30.74,0:03:31.97,Default,,0000,0000,0000,,Are you guys with me?
Dialogue: 0,0:03:31.97,0:03:34.71,Default,,0000,0000,0000,,At 3 o'clock they meet again.
Dialogue: 0,0:03:34.71,0:03:37.19,Default,,0000,0000,0000,,I'm just kidding, x\Ndoesn't have to be time.
Dialogue: 0,0:03:37.19,0:03:39.22,Default,,0000,0000,0000,,It's a special coordinate.
Dialogue: 0,0:03:39.22,0:03:42.68,Default,,0000,0000,0000,,
Dialogue: 0,0:03:42.68,0:03:48.89,Default,,0000,0000,0000,,And y is looking at you,\Nand is going towards you.
Dialogue: 0,0:03:48.89,0:03:52.88,Default,,0000,0000,0000,,Well, if it's toward like\Nthat, it's probably not
Dialogue: 0,0:03:52.88,0:03:53.78,Default,,0000,0000,0000,,positively oriented.
Dialogue: 0,0:03:53.78,0:03:57.83,Default,,0000,0000,0000,,So y should come from you,\Nand go into the board,
Dialogue: 0,0:03:57.83,0:04:00.78,Default,,0000,0000,0000,,and then keep going in that\Ndirection for the frame
Dialogue: 0,0:04:00.78,0:04:03.38,Default,,0000,0000,0000,,to be positive oriented.
Dialogue: 0,0:04:03.38,0:04:07.29,Default,,0000,0000,0000,,Positively oriented means x like\Nthat, y like this, z like that.
Dialogue: 0,0:04:07.29,0:04:11.20,Default,,0000,0000,0000,,So k must be the\Ncrossproduct between i and j.
Dialogue: 0,0:04:11.20,0:04:12.96,Default,,0000,0000,0000,,i cross j must be k.
Dialogue: 0,0:04:12.96,0:04:16.33,Default,,0000,0000,0000,,If I use the right hand\Nrule, and I go y like that,
Dialogue: 0,0:04:16.33,0:04:18.29,Default,,0000,0000,0000,,that means I changed\Nthe orientation.
Dialogue: 0,0:04:18.29,0:04:23.39,Default,,0000,0000,0000,,So the y, you have to imagine\Nthe y coming from you, going
Dialogue: 0,0:04:23.39,0:04:26.70,Default,,0000,0000,0000,,perpendicular to\Nthe board, then keep
Dialogue: 0,0:04:26.70,0:04:30.17,Default,,0000,0000,0000,,going inside the\Nboard infinitely much.
Dialogue: 0,0:04:30.17,0:04:34.84,Default,,0000,0000,0000,,Now, if we were to\Nplay with Play-Doh,
Dialogue: 0,0:04:34.84,0:04:42.03,Default,,0000,0000,0000,,and we were on the other side of\Nthat, like Alice in the mirror,
Dialogue: 0,0:04:42.03,0:04:47.31,Default,,0000,0000,0000,,we would have the y in the\Nmirror world, going between 0
Dialogue: 0,0:04:47.31,0:04:50.53,Default,,0000,0000,0000,,and 2, inside the board.
Dialogue: 0,0:04:50.53,0:04:53.41,Default,,0000,0000,0000,,If I were to draw\Nthis piece of cake,
Dialogue: 0,0:04:53.41,0:04:55.67,Default,,0000,0000,0000,,I start dreaming\Nagain, I apologize.
Dialogue: 0,0:04:55.67,0:05:05.53,Default,,0000,0000,0000,,But I'm dreaming of very\Nnice bounded pieces of solids
Dialogue: 0,0:05:05.53,0:05:07.13,Default,,0000,0000,0000,,that would be made of cheese.
Dialogue: 0,0:05:07.13,0:05:12.88,Default,,0000,0000,0000,,This is a perfect example where\Nyou have something like curve
Dialogue: 0,0:05:12.88,0:05:16.15,Default,,0000,0000,0000,,or linear shape, and you\Nkind of slice the cheese,
Dialogue: 0,0:05:16.15,0:05:17.71,Default,,0000,0000,0000,,and that's a piece\Nof the Parmesan.
Dialogue: 0,0:05:17.71,0:05:20.69,Default,,0000,0000,0000,,
Dialogue: 0,0:05:20.69,0:05:21.65,Default,,0000,0000,0000,,OK.
Dialogue: 0,0:05:21.65,0:05:27.49,Default,,0000,0000,0000,,So the y here is\Ngoing from 0 to 2.
Dialogue: 0,0:05:27.49,0:05:29.37,Default,,0000,0000,0000,,It's sort of the altitude.
Dialogue: 0,0:05:29.37,0:05:32.34,Default,,0000,0000,0000,,And this is the piece\Nof cake that you
Dialogue: 0,0:05:32.34,0:05:37.21,Default,,0000,0000,0000,,were looking-- or the cheese,\Nor whatever you're looking at.
Dialogue: 0,0:05:37.21,0:05:39.16,Default,,0000,0000,0000,,So what do you put here?
Dialogue: 0,0:05:39.16,0:05:44.66,Default,,0000,0000,0000,,You put z between\Nx squared and 3x.
Dialogue: 0,0:05:44.66,0:05:56.56,Default,,0000,0000,0000,,You put y between--\Ny is between 0 and 2.
Dialogue: 0,0:05:56.56,0:06:00.84,Default,,0000,0000,0000,,And you Mr. x as the last\Nof them, he can go from-- he
Dialogue: 0,0:06:00.84,0:06:04.52,Default,,0000,0000,0000,,goes from 0 to 3.
Dialogue: 0,0:06:04.52,0:06:08.92,Default,,0000,0000,0000,,So x has the freedom\Nto go from 0 to 3.
Dialogue: 0,0:06:08.92,0:06:13.51,Default,,0000,0000,0000,,y has the freedom to go\Nfrom flat line to flat line,
Dialogue: 0,0:06:13.51,0:06:17.64,Default,,0000,0000,0000,,from between to flat planes--\Nfrom two horizontal planes.
Dialogue: 0,0:06:17.64,0:06:24.73,Default,,0000,0000,0000,,But Mr. z is married to\Nx, he cannot escape this
Dialogue: 0,0:06:24.73,0:06:25.52,Default,,0000,0000,0000,,relationship.
Dialogue: 0,0:06:25.52,0:06:30.69,Default,,0000,0000,0000,,So we can only take this z\Nwith respect between these two
Dialogue: 0,0:06:30.69,0:06:34.15,Default,,0000,0000,0000,,values that depend on x.
Dialogue: 0,0:06:34.15,0:06:35.05,Default,,0000,0000,0000,,That's all.
Dialogue: 0,0:06:35.05,0:06:38.76,Default,,0000,0000,0000,,Now why would we have 1?
Dialogue: 0,0:06:38.76,0:06:41.36,Default,,0000,0000,0000,,Because by definition,\Nif you remember
Dialogue: 0,0:06:41.36,0:06:43.79,Default,,0000,0000,0000,,the volume was the\Ntriple integral
Dialogue: 0,0:06:43.79,0:06:48.69,Default,,0000,0000,0000,,of 1 dv over any\Nsolid value domain.
Dialogue: 0,0:06:48.69,0:06:50.91,Default,,0000,0000,0000,,Right?
Dialogue: 0,0:06:50.91,0:06:53.35,Default,,0000,0000,0000,,So whenever you see\Na problem like that,
Dialogue: 0,0:06:53.35,0:06:55.27,Default,,0000,0000,0000,,you know how to start it.
Dialogue: 0,0:06:55.27,0:06:58.29,Default,,0000,0000,0000,,One triple integrate,\Nand that's going to work.
Dialogue: 0,0:06:58.29,0:07:02.16,Default,,0000,0000,0000,,Something else that\Ngave you a big headache
Dialogue: 0,0:07:02.16,0:07:04.56,Default,,0000,0000,0000,,was the ice cream cone.
Dialogue: 0,0:07:04.56,0:07:09.27,Default,,0000,0000,0000,,The ice cream cone problem\Ngave a big headache
Dialogue: 0,0:07:09.27,0:07:13.23,Default,,0000,0000,0000,,to most of my students\Nover the past 14 years
Dialogue: 0,0:07:13.23,0:07:15.77,Default,,0000,0000,0000,,that I've been teaching Cal 3.
Dialogue: 0,0:07:15.77,0:07:17.25,Default,,0000,0000,0000,,It's a beautiful problem.
Dialogue: 0,0:07:17.25,0:07:18.88,Default,,0000,0000,0000,,It's one of my\Nfavorites problems,
Dialogue: 0,0:07:18.88,0:07:21.55,Default,,0000,0000,0000,,because it makes me\Nthink of food again.
Dialogue: 0,0:07:21.55,0:07:27.86,Default,,0000,0000,0000,,And not just any food, but\Nsome nice ice cream cone
Dialogue: 0,0:07:27.86,0:07:34.82,Default,,0000,0000,0000,,that's original ice cream, not\Nthe one you find in a box like
Dialogue: 0,0:07:34.82,0:07:36.94,Default,,0000,0000,0000,,Blue Bell or Ben and Jerry's.
Dialogue: 0,0:07:36.94,0:07:39.70,Default,,0000,0000,0000,,
Dialogue: 0,0:07:39.70,0:07:43.44,Default,,0000,0000,0000,,All right, so how is the\Nice cream cone problem
Dialogue: 0,0:07:43.44,0:07:49.64,Default,,0000,0000,0000,,that-- he showed it to me, but\NI forgot the problem number.
Dialogue: 0,0:07:49.64,0:07:50.51,Default,,0000,0000,0000,,It was--
Dialogue: 0,0:07:50.51,0:07:51.91,Default,,0000,0000,0000,,STUDENT: It's number 20.
Dialogue: 0,0:07:51.91,0:07:52.66,Default,,0000,0000,0000,,PROFESSOR: Number?
Dialogue: 0,0:07:52.66,0:07:53.39,Default,,0000,0000,0000,,STUDENT: 20.
Dialogue: 0,0:07:53.39,0:07:55.16,Default,,0000,0000,0000,,PROFESSOR: Number 20, thanks.
Dialogue: 0,0:07:55.16,0:07:57.94,Default,,0000,0000,0000,,And I want the data [INAUDIBLE].
Dialogue: 0,0:07:57.94,0:08:01.12,Default,,0000,0000,0000,,I want to test my memory,\Nsee how many neurons
Dialogue: 0,0:08:01.12,0:08:03.13,Default,,0000,0000,0000,,died since last time.
Dialogue: 0,0:08:03.13,0:08:04.93,Default,,0000,0000,0000,,Don't tell me.
Dialogue: 0,0:08:04.93,0:08:11.03,Default,,0000,0000,0000,,So I think the sphere was\Na radius 2, and the cone
Dialogue: 0,0:08:11.03,0:08:13.99,Default,,0000,0000,0000,,that we picked for you,\Nwe picked it on purpose.
Dialogue: 0,0:08:13.99,0:08:18.24,Default,,0000,0000,0000,,So that the results that\Ncome up for the ice cream
Dialogue: 0,0:08:18.24,0:08:21.99,Default,,0000,0000,0000,,cone boundaries will\Nbe nice and workable.
Dialogue: 0,0:08:21.99,0:08:25.85,Default,,0000,0000,0000,,So we can propose some data\Nwhere the ice cream cone will
Dialogue: 0,0:08:25.85,0:08:28.21,Default,,0000,0000,0000,,give you really nasty radii.
Dialogue: 0,0:08:28.21,0:08:29.35,Default,,0000,0000,0000,,Can I draw it?
Dialogue: 0,0:08:29.35,0:08:30.66,Default,,0000,0000,0000,,Hopefully.
Dialogue: 0,0:08:30.66,0:08:35.14,Default,,0000,0000,0000,,This ice cream cone is\Nbased off the waffle cone.
Dialogue: 0,0:08:35.14,0:08:40.16,Default,,0000,0000,0000,,I don't like the waffle\Ncone, because I'm dreaming.
Dialogue: 0,0:08:40.16,0:08:45.96,Default,,0000,0000,0000,,But the problem is, the waffle\Ncone is not a finite surface.
Dialogue: 0,0:08:45.96,0:08:49.35,Default,,0000,0000,0000,,It's infinite,\Nit's a double cone.
Dialogue: 0,0:08:49.35,0:08:51.41,Default,,0000,0000,0000,,It's the dream of every binger.
Dialogue: 0,0:08:51.41,0:08:55.93,Default,,0000,0000,0000,,So it goes to infinity,\Nand to negative infinity,
Dialogue: 0,0:08:55.93,0:08:57.91,Default,,0000,0000,0000,,and that's not my problem.
Dialogue: 0,0:08:57.91,0:09:02.82,Default,,0000,0000,0000,,My problem is to intersect\Nthis cone with the sphere,
Dialogue: 0,0:09:02.82,0:09:04.80,Default,,0000,0000,0000,,and make it finite.
Dialogue: 0,0:09:04.80,0:09:07.68,Default,,0000,0000,0000,,So to make it the\Ntrue waffle cone,
Dialogue: 0,0:09:07.68,0:09:14.24,Default,,0000,0000,0000,,I would have to draw a\Nsphere of what radius?
Dialogue: 0,0:09:14.24,0:09:17.08,Default,,0000,0000,0000,,Root 2.
Dialogue: 0,0:09:17.08,0:09:20.02,Default,,0000,0000,0000,,I'll try to draw a\Nsphere of root 2,
Dialogue: 0,0:09:20.02,0:09:21.39,Default,,0000,0000,0000,,but I cannot\Npredict the results.
Dialogue: 0,0:09:21.39,0:09:26.72,Default,,0000,0000,0000,,Now I'm going to only\Nlook at this v1 cone.
Dialogue: 0,0:09:26.72,0:09:31.29,Default,,0000,0000,0000,,I don't know what the problem\Nwanted, but I'm looking at,
Dialogue: 0,0:09:31.29,0:09:35.70,Default,,0000,0000,0000,,do they say in what domain?
Dialogue: 0,0:09:35.70,0:09:37.82,Default,,0000,0000,0000,,Above the plane?
Dialogue: 0,0:09:37.82,0:09:40.64,Default,,0000,0000,0000,,STUDENT: It just says\Nlies above the cone.
Dialogue: 0,0:09:40.64,0:09:43.39,Default,,0000,0000,0000,,PROFESSOR: That\Nlies above the cone.
Dialogue: 0,0:09:43.39,0:09:48.30,Default,,0000,0000,0000,,But look, if I turn my head like\Nthis, depending on my reference
Dialogue: 0,0:09:48.30,0:09:51.18,Default,,0000,0000,0000,,frame, I have\Ncervical spondylosis,
Dialogue: 0,0:09:51.18,0:09:53.64,Default,,0000,0000,0000,,this is also lying\Nabove the cone.
Dialogue: 0,0:09:53.64,0:09:56.40,Default,,0000,0000,0000,,So the problem is\Na little bit silly,
Dialogue: 0,0:09:56.40,0:09:58.45,Default,,0000,0000,0000,,that whoever wrote\Nit should have
Dialogue: 0,0:09:58.45,0:10:07.24,Default,,0000,0000,0000,,said the sphere lies above a\Ncone, for z greater than 0.
Dialogue: 0,0:10:07.24,0:10:10.36,Default,,0000,0000,0000,,In the basement,\Nit can continue--
Dialogue: 0,0:10:10.36,0:10:13.92,Default,,0000,0000,0000,,that's for z-- for z\Nless than 0 can continue
Dialogue: 0,0:10:13.92,0:10:18.68,Default,,0000,0000,0000,,upside down, and then between\Nthe sphere and the cone,
Dialogue: 0,0:10:18.68,0:10:22.36,Default,,0000,0000,0000,,you'll have another ice\Ncream cone outside that.
Dialogue: 0,0:10:22.36,0:10:24.51,Default,,0000,0000,0000,,But practically what\Nthey mean is just do v1
Dialogue: 0,0:10:24.51,0:10:26.99,Default,,0000,0000,0000,,and forget about this one.
Dialogue: 0,0:10:26.99,0:10:28.64,Default,,0000,0000,0000,,It's not very nicely phrased.
Dialogue: 0,0:10:28.64,0:10:29.54,Default,,0000,0000,0000,,Above, beyond.
Dialogue: 0,0:10:29.54,0:10:34.13,Default,,0000,0000,0000,,Are we above Australia?
Dialogue: 0,0:10:34.13,0:10:35.99,Default,,0000,0000,0000,,That's stupid, right?
Dialogue: 0,0:10:35.99,0:10:39.68,Default,,0000,0000,0000,,Because they may say, oh no,\Ndepends on where you are.
Dialogue: 0,0:10:39.68,0:10:41.54,Default,,0000,0000,0000,,We are above you guys.
Dialogue: 0,0:10:41.54,0:10:43.92,Default,,0000,0000,0000,,You think you're better\Nthan us because you
Dialogue: 0,0:10:43.92,0:10:46.04,Default,,0000,0000,0000,,are closer to the North Pole.
Dialogue: 0,0:10:46.04,0:10:50.47,Default,,0000,0000,0000,,But who made that rule that\Nt the North Pole is superior?
Dialogue: 0,0:10:50.47,0:10:55.28,Default,,0000,0000,0000,,If you look at the universe,\Nwho is above, who is beyond?
Dialogue: 0,0:10:55.28,0:10:56.96,Default,,0000,0000,0000,,There is no direction.
Dialogue: 0,0:10:56.96,0:10:58.84,Default,,0000,0000,0000,,So they would be very offended.
Dialogue: 0,0:10:58.84,0:11:00.79,Default,,0000,0000,0000,,I have a friend who\Nworks in Sydney.
Dialogue: 0,0:11:00.79,0:11:04.25,Default,,0000,0000,0000,,She is a brilliant geometer.
Dialogue: 0,0:11:04.25,0:11:07.33,Default,,0000,0000,0000,,And I bet if I asked\Nher, she would say
Dialogue: 0,0:11:07.33,0:11:10.05,Default,,0000,0000,0000,,who says you guys are above?
Dialogue: 0,0:11:10.05,0:11:14.36,Default,,0000,0000,0000,,Because it depends on where your\Nhead is and how you look at it.
Dialogue: 0,0:11:14.36,0:11:16.68,Default,,0000,0000,0000,,The planet is the\Nsame, so would you
Dialogue: 0,0:11:16.68,0:11:19.07,Default,,0000,0000,0000,,say that the people\Nwho are walking closer
Dialogue: 0,0:11:19.07,0:11:22.38,Default,,0000,0000,0000,,to the North Pole have\Ntheir body upside down?
Dialogue: 0,0:11:22.38,0:11:26.32,Default,,0000,0000,0000,,
Dialogue: 0,0:11:26.32,0:11:31.25,Default,,0000,0000,0000,,So it really matters how\Nyou look, what's above.
Dialogue: 0,0:11:31.25,0:11:36.41,Default,,0000,0000,0000,,So assume that above means--\Nthe word above means positive.
Dialogue: 0,0:11:36.41,0:11:40.90,Default,,0000,0000,0000,,And this is the ice cream cone.
Dialogue: 0,0:11:40.90,0:11:43.75,Default,,0000,0000,0000,,Now how do I find out\Nwhere to cut the waffle?
Dialogue: 0,0:11:43.75,0:11:46.03,Default,,0000,0000,0000,,Because this is the question.
Dialogue: 0,0:11:46.03,0:11:50.71,Default,,0000,0000,0000,,I need to know where the\Nboundary of the waffle is.
Dialogue: 0,0:11:50.71,0:11:53.68,Default,,0000,0000,0000,,I'm not allowed to eat\Nanything above that.
Dialogue: 0,0:11:53.68,0:11:56.86,Default,,0000,0000,0000,,So that's going\Nto be the waffle.
Dialogue: 0,0:11:56.86,0:12:01.73,Default,,0000,0000,0000,,And for that, any ideas-- how do\NI get to see what the circle--
Dialogue: 0,0:12:01.73,0:12:03.93,Default,,0000,0000,0000,,where the circle will be?
Dialogue: 0,0:12:03.93,0:12:05.48,Default,,0000,0000,0000,,STUDENT: Do they\Nmeet each other?
Dialogue: 0,0:12:05.48,0:12:06.56,Default,,0000,0000,0000,,PROFESSOR: They intersect.
Dialogue: 0,0:12:06.56,0:12:07.36,Default,,0000,0000,0000,,Excellent, Matthew.
Dialogue: 0,0:12:07.36,0:12:08.00,Default,,0000,0000,0000,,Thank you.
Dialogue: 0,0:12:08.00,0:12:14.01,Default,,0000,0000,0000,,So intersect the two surfaces\Nby setting up a system to solve.
Dialogue: 0,0:12:14.01,0:12:17.35,Default,,0000,0000,0000,,Solve the system.
Dialogue: 0,0:12:17.35,0:12:26.31,Default,,0000,0000,0000,,And the intersection of the two\Nis Mr. z, which is Mr. circle.
Dialogue: 0,0:12:26.31,0:12:26.81,Default,,0000,0000,0000,,All right.
Dialogue: 0,0:12:26.81,0:12:29.29,Default,,0000,0000,0000,,So what do I do?
Dialogue: 0,0:12:29.29,0:12:32.33,Default,,0000,0000,0000,,I'm going to say I have to\Nbe smart about that one.
Dialogue: 0,0:12:32.33,0:12:36.78,Default,,0000,0000,0000,,So if z squared from\Nhere plugging in,
Dialogue: 0,0:12:36.78,0:12:41.30,Default,,0000,0000,0000,,substitute, is the same as\Nx squared plus y squared.
Dialogue: 0,0:12:41.30,0:12:49.98,Default,,0000,0000,0000,,So that means this is if\Nand only if 2x squared
Dialogue: 0,0:12:49.98,0:12:51.63,Default,,0000,0000,0000,,plus y squared.
Dialogue: 0,0:12:51.63,0:12:54.45,Default,,0000,0000,0000,,2 times x squared\Nplus y squared.
Dialogue: 0,0:12:54.45,0:12:56.33,Default,,0000,0000,0000,,We have an x squared\Nplus y squared,
Dialogue: 0,0:12:56.33,0:12:59.43,Default,,0000,0000,0000,,and another x squared\Nplus y squared equals 2.
Dialogue: 0,0:12:59.43,0:13:02.46,Default,,0000,0000,0000,,You see how nicely the\Nproblem was picked?
Dialogue: 0,0:13:02.46,0:13:05.80,Default,,0000,0000,0000,,It was picked it's going\Nto give you some nice data.
Dialogue: 0,0:13:05.80,0:13:10.06,Default,,0000,0000,0000,,z equals-- z\Nsquared equals that.
Dialogue: 0,0:13:10.06,0:13:12.24,Default,,0000,0000,0000,,Keep going with if and only if.
Dialogue: 0,0:13:12.24,0:13:14.49,Default,,0000,0000,0000,,If you're a math major,\Nyou will understand
Dialogue: 0,0:13:14.49,0:13:18.00,Default,,0000,0000,0000,,why x squared plus\Ny squared equals 1.
Dialogue: 0,0:13:18.00,0:13:21.10,Default,,0000,0000,0000,,
Dialogue: 0,0:13:21.10,0:13:23.10,Default,,0000,0000,0000,,And z squared must be 1.
Dialogue: 0,0:13:23.10,0:13:26.09,Default,,0000,0000,0000,,
Dialogue: 0,0:13:26.09,0:13:28.94,Default,,0000,0000,0000,,Well so, we really\Nget two solutions,
Dialogue: 0,0:13:28.94,0:13:32.42,Default,,0000,0000,0000,,the one close to the South\NPole, and the one close
Dialogue: 0,0:13:32.42,0:13:35.70,Default,,0000,0000,0000,,to the North Pole,\Nbecause I'm going
Dialogue: 0,0:13:35.70,0:13:39.25,Default,,0000,0000,0000,,to have z equals plus minus 1.
Dialogue: 0,0:13:39.25,0:13:40.71,Default,,0000,0000,0000,,Where's the North Pole?
Dialogue: 0,0:13:40.71,0:13:44.12,Default,,0000,0000,0000,,The North Pole would be\N0, 0, square root of 2.
Dialogue: 0,0:13:44.12,0:13:48.37,Default,,0000,0000,0000,,The South Pole would be 0,\N0, minus square root of 2.
Dialogue: 0,0:13:48.37,0:13:52.99,Default,,0000,0000,0000,,And my plain here is\Ncut at which altitude?
Dialogue: 0,0:13:52.99,0:13:54.55,Default,,0000,0000,0000,,z equals 1.
Dialogue: 0,0:13:54.55,0:13:59.33,Default,,0000,0000,0000,,And I have another plane here,\Nand an imaginary intersection
Dialogue: 0,0:13:59.33,0:14:02.61,Default,,0000,0000,0000,,that I'm not going to talk\Nabout today. z equals minus y.
Dialogue: 0,0:14:02.61,0:14:08.06,Default,,0000,0000,0000,,I don't care about the mirror\Nimage of the-- with respect
Dialogue: 0,0:14:08.06,0:14:11.30,Default,,0000,0000,0000,,to the equator of the cone.
Dialogue: 0,0:14:11.30,0:14:12.80,Default,,0000,0000,0000,,All right, good.
Dialogue: 0,0:14:12.80,0:14:15.86,Default,,0000,0000,0000,,So we know who this\Nguy is, we know
Dialogue: 0,0:14:15.86,0:14:22.42,Default,,0000,0000,0000,,that he is-- I have a\Nred marker, and a green,
Dialogue: 0,0:14:22.42,0:14:25.36,Default,,0000,0000,0000,,and a blue.
Dialogue: 0,0:14:25.36,0:14:27.92,Default,,0000,0000,0000,,I cannot live without colors.
Dialogue: 0,0:14:27.92,0:14:29.80,Default,,0000,0000,0000,,Life is ugly enough.
Dialogue: 0,0:14:29.80,0:14:31.93,Default,,0000,0000,0000,,Let's try to make it colorful.
Dialogue: 0,0:14:31.93,0:14:35.82,Default,,0000,0000,0000,,x squared plus y\Nsquared, equals 1.
Dialogue: 0,0:14:35.82,0:14:39.86,Default,,0000,0000,0000,,
Dialogue: 0,0:14:39.86,0:14:44.91,Default,,0000,0000,0000,,We are happy, because\Nthat's a nice, simple circle
Dialogue: 0,0:14:44.91,0:14:47.38,Default,,0000,0000,0000,,of radius 1.
Dialogue: 0,0:14:47.38,0:14:49.56,Default,,0000,0000,0000,,Now you have to think\Nin which coordinate
Dialogue: 0,0:14:49.56,0:14:51.65,Default,,0000,0000,0000,,you can write this problem.
Dialogue: 0,0:14:51.65,0:14:54.57,Default,,0000,0000,0000,,And I'm going to\Nbeg of you to help
Dialogue: 0,0:14:54.57,0:14:59.04,Default,,0000,0000,0000,,me review the material for\Nthe final and for the midterm.
Dialogue: 0,0:14:59.04,0:15:01.62,Default,,0000,0000,0000,,Then again, on the midterm, I'm\Nnot going to put this problem.
Dialogue: 0,0:15:01.62,0:15:04.82,Default,,0000,0000,0000,,
Dialogue: 0,0:15:04.82,0:15:11.08,Default,,0000,0000,0000,,So for the final, do\Nexpect something like that.
Dialogue: 0,0:15:11.08,0:15:14.41,Default,,0000,0000,0000,,We may have, instead of\Nthe cone in the book,
Dialogue: 0,0:15:14.41,0:15:17.77,Default,,0000,0000,0000,,you'll have a paraboloid\Nand a sphere intersecting.
Dialogue: 0,0:15:17.77,0:15:21.81,Default,,0000,0000,0000,,It's sort of the same thing, but\Ninstead of the ice cream cone,
Dialogue: 0,0:15:21.81,0:15:25.16,Default,,0000,0000,0000,,you have the valley\Nfull of cream.
Dialogue: 0,0:15:25.16,0:15:27.97,Default,,0000,0000,0000,,
Dialogue: 0,0:15:27.97,0:15:30.14,Default,,0000,0000,0000,,I cannot stop, right?
Dialogue: 0,0:15:30.14,0:15:34.04,Default,,0000,0000,0000,,So if you do the volume\Nlike I told you before,
Dialogue: 0,0:15:34.04,0:15:38.41,Default,,0000,0000,0000,,you simply have\N[INTERPOSING VOICES]
Dialogue: 0,0:15:38.41,0:15:40.18,Default,,0000,0000,0000,,No, I'll do the volume first.
Dialogue: 0,0:15:40.18,0:15:41.71,Default,,0000,0000,0000,,I know you have\Nthe surface there,
Dialogue: 0,0:15:41.71,0:15:46.30,Default,,0000,0000,0000,,but what-- I'm doing the\Nvolume because I have plans,
Dialogue: 0,0:15:46.30,0:15:49.13,Default,,0000,0000,0000,,and I didn't want\Nto say what plans.
Dialogue: 0,0:15:49.13,0:15:50.76,Default,,0000,0000,0000,,You forgot what I said, right?
Dialogue: 0,0:15:50.76,0:15:53.77,Default,,0000,0000,0000,,
Dialogue: 0,0:15:53.77,0:15:58.25,Default,,0000,0000,0000,,So suppose somebody's\Nasking you for the volume.
Dialogue: 0,0:15:58.25,0:16:01.36,Default,,0000,0000,0000,,The volume-- how much\Nice cream you have inside
Dialogue: 0,0:16:01.36,0:16:03.74,Default,,0000,0000,0000,,depends on that very much.
Dialogue: 0,0:16:03.74,0:16:07.09,Default,,0000,0000,0000,,And I'd like you to\Nremember that the v is
Dialogue: 0,0:16:07.09,0:16:11.67,Default,,0000,0000,0000,,piratically against\Nthe ybc, right?
Dialogue: 0,0:16:11.67,0:16:17.00,Default,,0000,0000,0000,,Right until the Cartesian\Ncoordinates would be a killer,
Dialogue: 0,0:16:17.00,0:16:19.55,Default,,0000,0000,0000,,we try to write it\Nin either cylindrical
Dialogue: 0,0:16:19.55,0:16:23.25,Default,,0000,0000,0000,,or spherical to make\Nour life easier.
Dialogue: 0,0:16:23.25,0:16:27.10,Default,,0000,0000,0000,,If I want to make my life\Neasier, first in cylindrical
Dialogue: 0,0:16:27.10,0:16:31.40,Default,,0000,0000,0000,,coordinates, and then in\Nspherical coordinates.
Dialogue: 0,0:16:31.40,0:16:34.22,Default,,0000,0000,0000,,
Dialogue: 0,0:16:34.22,0:16:37.80,Default,,0000,0000,0000,,Could you help me\Nfind the limit points?
Dialogue: 0,0:16:37.80,0:16:41.30,Default,,0000,0000,0000,,
Dialogue: 0,0:16:41.30,0:16:44.84,Default,,0000,0000,0000,,And then we'll do the surface.
Dialogue: 0,0:16:44.84,0:16:47.55,Default,,0000,0000,0000,,Just remind me, OK?
Dialogue: 0,0:16:47.55,0:16:55.36,Default,,0000,0000,0000,,[INTERPOSING VOICES]\NThe volume of the-- OK.
Dialogue: 0,0:16:55.36,0:16:58.29,Default,,0000,0000,0000,,The volume occupied\Nby the ice cream.
Dialogue: 0,0:16:58.29,0:17:01.53,Default,,0000,0000,0000,,The ice cream is between\Nthis plastic cap,
Dialogue: 0,0:17:01.53,0:17:03.28,Default,,0000,0000,0000,,that is the sphere.
Dialogue: 0,0:17:03.28,0:17:05.16,Default,,0000,0000,0000,,We cover it for\Nhygiene purposes.
Dialogue: 0,0:17:05.16,0:17:10.86,Default,,0000,0000,0000,,
Dialogue: 0,0:17:10.86,0:17:18.52,Default,,0000,0000,0000,,So for cylindrical coordinates,\Nrho and theta are really nice.
Dialogue: 0,0:17:18.52,0:17:20.97,Default,,0000,0000,0000,,We don't worry about them yet.
Dialogue: 0,0:17:20.97,0:17:24.14,Default,,0000,0000,0000,,But z should be between?
Dialogue: 0,0:17:24.14,0:17:26.88,Default,,0000,0000,0000,,OK.
Dialogue: 0,0:17:26.88,0:17:27.80,Default,,0000,0000,0000,,Really, 0?
Dialogue: 0,0:17:27.80,0:17:30.59,Default,,0000,0000,0000,,
Dialogue: 0,0:17:30.59,0:17:34.94,Default,,0000,0000,0000,,So because it's\Nbetween the ice cream
Dialogue: 0,0:17:34.94,0:17:37.70,Default,,0000,0000,0000,,the cone-- do you\Nthink the waffle
Dialogue: 0,0:17:37.70,0:17:40.83,Default,,0000,0000,0000,,cone-- what's the equation\Nof the waffle cone?
Dialogue: 0,0:17:40.83,0:17:43.94,Default,,0000,0000,0000,,And how do you get to the\Nequation of the waffle cone?
Dialogue: 0,0:17:43.94,0:17:47.93,Default,,0000,0000,0000,,The waffle cone meant--\Noh guys, help me.
Dialogue: 0,0:17:47.93,0:17:50.78,Default,,0000,0000,0000,,z equals-- now you\Ntake the square root
Dialogue: 0,0:17:50.78,0:17:55.50,Default,,0000,0000,0000,,of x squared plus y squared,\Nbecause the other one would
Dialogue: 0,0:17:55.50,0:17:56.01,Default,,0000,0000,0000,,be here.
Dialogue: 0,0:17:56.01,0:17:58.05,Default,,0000,0000,0000,,The imaginary one, z equals\Nminus the square root
Dialogue: 0,0:17:58.05,0:17:59.85,Default,,0000,0000,0000,,of x squared plus y squared.
Dialogue: 0,0:17:59.85,0:18:04.68,Default,,0000,0000,0000,,Forget about the\Nworld in the basement.
Dialogue: 0,0:18:04.68,0:18:06.96,Default,,0000,0000,0000,,So you take z to\Nthe square root of,
Dialogue: 0,0:18:06.96,0:18:09.52,Default,,0000,0000,0000,,with a plus, plus y squared.
Dialogue: 0,0:18:09.52,0:18:14.56,Default,,0000,0000,0000,,In cylindrical coordinates,\Nwhat does this mean?
Dialogue: 0,0:18:14.56,0:18:16.01,Default,,0000,0000,0000,,In cylindrical coordinates?
Dialogue: 0,0:18:16.01,0:18:18.19,Default,,0000,0000,0000,,STUDENT: It equals r.
Dialogue: 0,0:18:18.19,0:18:19.69,Default,,0000,0000,0000,,PROFESSOR: This\Nequals r, very good.
Dialogue: 0,0:18:19.69,0:18:21.18,Default,,0000,0000,0000,,He's thinking faster.
Dialogue: 0,0:18:21.18,0:18:23.39,Default,,0000,0000,0000,,Do you guys\Nunderstand why he said
Dialogue: 0,0:18:23.39,0:18:25.24,Default,,0000,0000,0000,,x squared plus y\Nsquared, if we work
Dialogue: 0,0:18:25.24,0:18:27.12,Default,,0000,0000,0000,,with polar coordinates--\Nwhich is cylindrical
Dialogue: 0,0:18:27.12,0:18:29.25,Default,,0000,0000,0000,,coordinates it's the same\Nthing-- polar coordinates
Dialogue: 0,0:18:29.25,0:18:30.42,Default,,0000,0000,0000,,and cylindrical coordinates.
Dialogue: 0,0:18:30.42,0:18:33.57,Default,,0000,0000,0000,,x squared plus y squared\Nwould be little r squared.
Dialogue: 0,0:18:33.57,0:18:36.03,Default,,0000,0000,0000,,Under the square\Nroot would be r.
Dialogue: 0,0:18:36.03,0:18:39.10,Default,,0000,0000,0000,,So you'll see, we're between r.
Dialogue: 0,0:18:39.10,0:18:42.31,Default,,0000,0000,0000,,And now, another hard part.
Dialogue: 0,0:18:42.31,0:18:53.35,Default,,0000,0000,0000,,What is the z equals plus square\Nroot of-- What was it, guys?
Dialogue: 0,0:18:53.35,0:18:55.97,Default,,0000,0000,0000,,STUDENT: So are we taking\Nthe volume of all of the ice
Dialogue: 0,0:18:55.97,0:18:57.82,Default,,0000,0000,0000,,cream inside the cone?
Dialogue: 0,0:18:57.82,0:19:02.53,Default,,0000,0000,0000,,PROFESSOR: So between the\Ncone, ice cream lies here.
Dialogue: 0,0:19:02.53,0:19:05.02,Default,,0000,0000,0000,,Ice cream chips,\Nchocolate chips,
Dialogue: 0,0:19:05.02,0:19:06.51,Default,,0000,0000,0000,,between the cone and the sphere.
Dialogue: 0,0:19:06.51,0:19:09.15,Default,,0000,0000,0000,,
Dialogue: 0,0:19:09.15,0:19:13.34,Default,,0000,0000,0000,,The sphere is the bottom\Nfunction, the lower function.
Dialogue: 0,0:19:13.34,0:19:14.44,Default,,0000,0000,0000,,Is that good?
Dialogue: 0,0:19:14.44,0:19:15.56,Default,,0000,0000,0000,,STUDENT: 2 minus r squared.
Dialogue: 0,0:19:15.56,0:19:20.59,Default,,0000,0000,0000,,PROFESSOR: So I have the square\Nroot of 2 minus r squared.
Dialogue: 0,0:19:20.59,0:19:23.63,Default,,0000,0000,0000,,I don't like the\Nsquare root, I hate it.
Dialogue: 0,0:19:23.63,0:19:25.38,Default,,0000,0000,0000,,Can I do it with it?
Dialogue: 0,0:19:25.38,0:19:26.56,Default,,0000,0000,0000,,Yes, I can.
Dialogue: 0,0:19:26.56,0:19:29.13,Default,,0000,0000,0000,,Maybe I can apply the\Nuse of solution later.
Dialogue: 0,0:19:29.13,0:19:31.21,Default,,0000,0000,0000,,Don't worry about\Nme, I'll make it.
Dialogue: 0,0:19:31.21,0:19:34.99,Default,,0000,0000,0000,,I will live better if I didn't\Nhave any ugly things like that.
Dialogue: 0,0:19:34.99,0:19:36.22,Default,,0000,0000,0000,,So let's see what we have.
Dialogue: 0,0:19:36.22,0:19:37.51,Default,,0000,0000,0000,,Theta.
Dialogue: 0,0:19:37.51,0:19:41.23,Default,,0000,0000,0000,,Your cone is not just sliced\Ncone, it's all the cone.
Dialogue: 0,0:19:41.23,0:19:43.77,Default,,0000,0000,0000,,So you have 0 to 2 pi.
Dialogue: 0,0:19:43.77,0:19:46.14,Default,,0000,0000,0000,,One revolution,\Ncomplete revolution.
Dialogue: 0,0:19:46.14,0:19:49.54,Default,,0000,0000,0000,,How about rho?
Dialogue: 0,0:19:49.54,0:19:50.55,Default,,0000,0000,0000,,Rho is limited.
Dialogue: 0,0:19:50.55,0:19:53.32,Default,,0000,0000,0000,,Rho is what lies in the\Nplane in terms of radius.
Dialogue: 0,0:19:53.32,0:19:56.78,Default,,0000,0000,0000,,
Dialogue: 0,0:19:56.78,0:19:58.08,Default,,0000,0000,0000,,0, 2?
Dialogue: 0,0:19:58.08,0:20:01.43,Default,,0000,0000,0000,,How much is from here to here?
Dialogue: 0,0:20:01.43,0:20:04.79,Default,,0000,0000,0000,,How much is from here to here?
Dialogue: 0,0:20:04.79,0:20:07.73,Default,,0000,0000,0000,,Didn't we do it x squared\Nplus y squared equals 1?
Dialogue: 0,0:20:07.73,0:20:10.29,Default,,0000,0000,0000,,So what is this radius\Nfrom here to here?
Dialogue: 0,0:20:10.29,0:20:10.79,Default,,0000,0000,0000,,1.
Dialogue: 0,0:20:10.79,0:20:12.92,Default,,0000,0000,0000,,And what is this radius\Nfrom here to here?
Dialogue: 0,0:20:12.92,0:20:13.42,Default,,0000,0000,0000,,1.
Dialogue: 0,0:20:13.42,0:20:15.26,Default,,0000,0000,0000,,So the projection\Nof this ice cream
Dialogue: 0,0:20:15.26,0:20:19.22,Default,,0000,0000,0000,,cone-- if you had the\Neye of god is here,
Dialogue: 0,0:20:19.22,0:20:22.35,Default,,0000,0000,0000,,sun, you have a\Nshadow on the ground,
Dialogue: 0,0:20:22.35,0:20:25.85,Default,,0000,0000,0000,,coming from your ice cream\Ncone, and this is the shadow.
Dialogue: 0,0:20:25.85,0:20:29.48,Default,,0000,0000,0000,,Your shadow is simply\Na disk of radius 1.
Dialogue: 0,0:20:29.48,0:20:31.43,Default,,0000,0000,0000,,Good, that's the\Nprojection you have.
Dialogue: 0,0:20:31.43,0:20:34.06,Default,,0000,0000,0000,,So Mr. rho is between 0 and 1.
Dialogue: 0,0:20:34.06,0:20:38.78,Default,,0000,0000,0000,,For polar coordinates,\Nit's not so ugly actually.
Dialogue: 0,0:20:38.78,0:20:40.49,Default,,0000,0000,0000,,0 to 2 pi.
Dialogue: 0,0:20:40.49,0:20:42.82,Default,,0000,0000,0000,,0 to 1.
Dialogue: 0,0:20:42.82,0:20:46.76,Default,,0000,0000,0000,,r to square root of\N2 minus r squared.
Dialogue: 0,0:20:46.76,0:20:53.14,Default,,0000,0000,0000,,Instead of r, it's\NOK to react with rho.
Dialogue: 0,0:20:53.14,0:20:55.06,Default,,0000,0000,0000,,And here's the\Nbig j coordinates.
Dialogue: 0,0:20:55.06,0:20:57.67,Default,,0000,0000,0000,,I'm going to erase\Nj, don't write j.
Dialogue: 0,0:20:57.67,0:20:59.79,Default,,0000,0000,0000,,Jacobian in general is Jacobian.
Dialogue: 0,0:20:59.79,0:21:02.56,Default,,0000,0000,0000,,The one that does the\Ntransformation between
Dialogue: 0,0:21:02.56,0:21:04.47,Default,,0000,0000,0000,,coordinates to\Nother coordinates.
Dialogue: 0,0:21:04.47,0:21:06.25,Default,,0000,0000,0000,,Let me finish on that.
Dialogue: 0,0:21:06.25,0:21:08.72,Default,,0000,0000,0000,,How about this one?
Dialogue: 0,0:21:08.72,0:21:11.64,Default,,0000,0000,0000,,This is simply r, very good.
Dialogue: 0,0:21:11.64,0:21:12.59,Default,,0000,0000,0000,,Your old friend.
Dialogue: 0,0:21:12.59,0:21:17.11,Default,,0000,0000,0000,,So you [INAUDIBLE]\Nthe dz d, theta,
Dialogue: 0,0:21:17.11,0:21:24.64,Default,,0000,0000,0000,,dr, d is your [INAUDIBLE]\NIt's not easy there.
Dialogue: 0,0:21:24.64,0:21:28.10,Default,,0000,0000,0000,,If I were to continue--\Nmaybe on the final-- OK
Dialogue: 0,0:21:28.10,0:21:30.33,Default,,0000,0000,0000,,I'm talking too much, as usual.
Dialogue: 0,0:21:30.33,0:21:34.39,Default,,0000,0000,0000,,Maybe on whatever test\Nyou're going to have,
Dialogue: 0,0:21:34.39,0:21:39.85,Default,,0000,0000,0000,,this kind of stuff, with\Na formulation saying you
Dialogue: 0,0:21:39.85,0:21:42.60,Default,,0000,0000,0000,,do not have to compute it.
Dialogue: 0,0:21:42.60,0:21:46.29,Default,,0000,0000,0000,,But if you wanted to compute it,\Nwould it be hard from 0 to 1,
Dialogue: 0,0:21:46.29,0:21:52.16,Default,,0000,0000,0000,,from 0 to 2 pi, and say\Nforgot the stinky pi?
Dialogue: 0,0:21:52.16,0:21:56.00,Default,,0000,0000,0000,,Take the 2 pi out to\Nmake your life easier.
Dialogue: 0,0:21:56.00,0:21:59.37,Default,,0000,0000,0000,,Because the theta isn't\Ndepending from-- there
Dialogue: 0,0:21:59.37,0:22:01.48,Default,,0000,0000,0000,,is no theta inside.
Dialogue: 0,0:22:01.48,0:22:03.77,Default,,0000,0000,0000,,So take the 2 pi\Nout, and then you
Dialogue: 0,0:22:03.77,0:22:09.55,Default,,0000,0000,0000,,have an integral from 0 to\N1, and integral from-- now.
Dialogue: 0,0:22:09.55,0:22:11.45,Default,,0000,0000,0000,,R got out for a walk.
Dialogue: 0,0:22:11.45,0:22:13.56,Default,,0000,0000,0000,,This is r going out for a walk.
Dialogue: 0,0:22:13.56,0:22:17.06,Default,,0000,0000,0000,,Integral of 1 with\Nrespect to dz.
Dialogue: 0,0:22:17.06,0:22:21.62,Default,,0000,0000,0000,,So z is taken between r and\Nroot of 2 minus r squared.
Dialogue: 0,0:22:21.62,0:22:22.51,Default,,0000,0000,0000,,Right?
Dialogue: 0,0:22:22.51,0:22:27.48,Default,,0000,0000,0000,,So I would have to write\Nhere the 1 on top minus the 1
Dialogue: 0,0:22:27.48,0:22:30.42,Default,,0000,0000,0000,,on the bottom, which is a\Nlittle bit of a headache for me.
Dialogue: 0,0:22:30.42,0:22:35.19,Default,,0000,0000,0000,,I'm looking at it,\NI'm getting angry.
Dialogue: 0,0:22:35.19,0:22:39.01,Default,,0000,0000,0000,,Now, times the r that\Nwent out for a walk.
Dialogue: 0,0:22:39.01,0:22:42.47,Default,,0000,0000,0000,,
Dialogue: 0,0:22:42.47,0:22:45.30,Default,,0000,0000,0000,,So practically, the\N0 is solved, and I
Dialogue: 0,0:22:45.30,0:22:49.92,Default,,0000,0000,0000,,have the dr. And from 0 to 1.
Dialogue: 0,0:22:49.92,0:22:53.31,Default,,0000,0000,0000,,
Dialogue: 0,0:22:53.31,0:22:54.87,Default,,0000,0000,0000,,So I took care or who?
Dialogue: 0,0:22:54.87,0:22:57.77,Default,,0000,0000,0000,,I took care of the\Nintegral with respect to z.
Dialogue: 0,0:22:57.77,0:23:00.03,Default,,0000,0000,0000,,This is r here.
Dialogue: 0,0:23:00.03,0:23:03.04,Default,,0000,0000,0000,,This was done first.
Dialogue: 0,0:23:03.04,0:23:06.32,Default,,0000,0000,0000,,And you gave me that\Nbetween those two.
Dialogue: 0,0:23:06.32,0:23:07.43,Default,,0000,0000,0000,,So I got that.
Dialogue: 0,0:23:07.43,0:23:12.43,Default,,0000,0000,0000,,Times the r, between 0 and 1,\Nwith respect to r, and then
Dialogue: 0,0:23:12.43,0:23:14.27,Default,,0000,0000,0000,,the 2 pi gets outside.
Dialogue: 0,0:23:14.27,0:23:16.88,Default,,0000,0000,0000,,Now, if I split this\Ninto two integrals,
Dialogue: 0,0:23:16.88,0:23:18.38,Default,,0000,0000,0000,,it's going to be easy, right?
Dialogue: 0,0:23:18.38,0:23:20.81,Default,,0000,0000,0000,,Because I go--\Nthe first integral
Dialogue: 0,0:23:20.81,0:23:23.69,Default,,0000,0000,0000,,will be r times square\Nroot of 2 minus r squared.
Dialogue: 0,0:23:23.69,0:23:26.32,Default,,0000,0000,0000,,How can you do such an integral?
Dialogue: 0,0:23:26.32,0:23:27.40,Default,,0000,0000,0000,,We do substitution.
Dialogue: 0,0:23:27.40,0:23:32.80,Default,,0000,0000,0000,,For example, your u would\Nb 2 minus r squared.
Dialogue: 0,0:23:32.80,0:23:34.46,Default,,0000,0000,0000,,Can you keep going?
Dialogue: 0,0:23:34.46,0:23:37.44,Default,,0000,0000,0000,,The second integral\Nis a piece of cake.
Dialogue: 0,0:23:37.44,0:23:38.73,Default,,0000,0000,0000,,A piece of ice cream.
Dialogue: 0,0:23:38.73,0:23:40.58,Default,,0000,0000,0000,,The integral of r squared.
Dialogue: 0,0:23:40.58,0:23:44.26,Default,,0000,0000,0000,,r cubed over 3,\Nbetween 0 and 1, 1/3.
Dialogue: 0,0:23:44.26,0:23:49.92,Default,,0000,0000,0000,,So we can still solve the ice\Ncream cone volume like that.
Dialogue: 0,0:23:49.92,0:23:50.93,Default,,0000,0000,0000,,Do I like it?
Dialogue: 0,0:23:50.93,0:23:51.43,Default,,0000,0000,0000,,No.
Dialogue: 0,0:23:51.43,0:23:55.83,Default,,0000,0000,0000,,Can you suspect why\NI don't like it?
Dialogue: 0,0:23:55.83,0:23:56.93,Default,,0000,0000,0000,,Oh, by the way.
Dialogue: 0,0:23:56.93,0:23:59.96,Default,,0000,0000,0000,,Suppose you got to\Nthis on the final,
Dialogue: 0,0:23:59.96,0:24:05.29,Default,,0000,0000,0000,,how much do you get\Nfor-- you mess up
Dialogue: 0,0:24:05.29,0:24:07.51,Default,,0000,0000,0000,,the algebra, how\Nmuch do you get?
Dialogue: 0,0:24:07.51,0:24:17.94,Default,,0000,0000,0000,,
Dialogue: 0,0:24:17.94,0:24:21.25,Default,,0000,0000,0000,,You say, I can do\Nthat in my sleep,
Dialogue: 0,0:24:21.25,0:24:27.95,Default,,0000,0000,0000,,u equals 2 minus r squared, u\Nequals minus 2r, I can go on.
Dialogue: 0,0:24:27.95,0:24:32.14,Default,,0000,0000,0000,,Even if you mess up the\Nalgebra, you get most of it.
Dialogue: 0,0:24:32.14,0:24:33.53,Default,,0000,0000,0000,,Why don't I like it?
Dialogue: 0,0:24:33.53,0:24:36.19,Default,,0000,0000,0000,,Because it involves\Nwork, and I'm lazy.
Dialogue: 0,0:24:36.19,0:24:42.80,Default,,0000,0000,0000,,So can I find a\Nbetter way to do it?
Dialogue: 0,0:24:42.80,0:24:45.78,Default,,0000,0000,0000,,Can I get use\Nspherical coordinates?
Dialogue: 0,0:24:45.78,0:24:47.95,Default,,0000,0000,0000,,And how do I use\Nspherical coordinates?
Dialogue: 0,0:24:47.95,0:24:50.75,Default,,0000,0000,0000,,So let me see how I do that.
Dialogue: 0,0:24:50.75,0:24:53.72,Default,,0000,0000,0000,,In spherical coordinates,\Nit should be easier.
Dialogue: 0,0:24:53.72,0:25:00.16,Default,,0000,0000,0000,,
Dialogue: 0,0:25:00.16,0:25:03.93,Default,,0000,0000,0000,,Remember that for\Nmathematicians, they
Dialogue: 0,0:25:03.93,0:25:07.40,Default,,0000,0000,0000,,include this course Cal\N3 multivariable calculus.
Dialogue: 0,0:25:07.40,0:25:10.00,Default,,0000,0000,0000,,We are not studying geography.
Dialogue: 0,0:25:10.00,0:25:14.69,Default,,0000,0000,0000,,So for us, a lot can happen\Nbetween minus 90 and plus 90
Dialogue: 0,0:25:14.69,0:25:19.86,Default,,0000,0000,0000,,degrees, but it measures\Nfrom the North Pole,
Dialogue: 0,0:25:19.86,0:25:22.43,Default,,0000,0000,0000,,because we believe\Nin Santa Clause.
Dialogue: 0,0:25:22.43,0:25:23.88,Default,,0000,0000,0000,,Always remember that.
Dialogue: 0,0:25:23.88,0:25:29.31,Default,,0000,0000,0000,,So we go all the way from\N0 degrees to 180 degrees.
Dialogue: 0,0:25:29.31,0:25:34.29,Default,,0000,0000,0000,,So your-- in principle--\Nyour latitude
Dialogue: 0,0:25:34.29,0:25:39.60,Default,,0000,0000,0000,,will go from 0 to\Nall the way to pi.
Dialogue: 0,0:25:39.60,0:25:43.20,Default,,0000,0000,0000,,But it doesn't, because\Nit gets stuck here.
Dialogue: 0,0:25:43.20,0:25:46.39,Default,,0000,0000,0000,,What is the latitude\Nof the ice cream cone?
Dialogue: 0,0:25:46.39,0:25:50.86,Default,,0000,0000,0000,,So what is the pi angle\Nfor this ice cream cone?
Dialogue: 0,0:25:50.86,0:25:53.80,Default,,0000,0000,0000,,
Dialogue: 0,0:25:53.80,0:25:56.07,Default,,0000,0000,0000,,It's a 45 degree angle.
Dialogue: 0,0:25:56.07,0:25:58.62,Default,,0000,0000,0000,,That is true.
Dialogue: 0,0:25:58.62,0:26:05.15,Default,,0000,0000,0000,,For anything like that-- I'm\Nlooking again at this cone.
Dialogue: 0,0:26:05.15,0:26:07.05,Default,,0000,0000,0000,,z squared equals x\Nsquared plus y squared.
Dialogue: 0,0:26:07.05,0:26:10.89,Default,,0000,0000,0000,,
Dialogue: 0,0:26:10.89,0:26:13.51,Default,,0000,0000,0000,,I just want to talk a\Nlittle bit about that.
Dialogue: 0,0:26:13.51,0:26:23.27,Default,,0000,0000,0000,,So if you have x and\Ny, this is the x.
Dialogue: 0,0:26:23.27,0:26:26.47,Default,,0000,0000,0000,,This is x, you have to use\Nyour imagination on me.
Dialogue: 0,0:26:26.47,0:26:33.29,Default,,0000,0000,0000,,And the hypotenuse would be\Nx squared plus y squared.
Dialogue: 0,0:26:33.29,0:26:36.17,Default,,0000,0000,0000,,And this is the z.
Dialogue: 0,0:26:36.17,0:26:44.52,Default,,0000,0000,0000,,And then, I draw\Nwhat is in between.
Dialogue: 0,0:26:44.52,0:26:47.80,Default,,0000,0000,0000,,This has to be 45 degrees.
Dialogue: 0,0:26:47.80,0:26:50.27,Default,,0000,0000,0000,,Can you see what's going on?
Dialogue: 0,0:26:50.27,0:26:57.99,Default,,0000,0000,0000,,So theta has to be\Nbetween 0 and what?
Dialogue: 0,0:26:57.99,0:26:59.80,Default,,0000,0000,0000,,STUDENT: 2 pi.
Dialogue: 0,0:26:59.80,0:27:01.47,Default,,0000,0000,0000,,PROFESSOR: Yes, you\Nare smarter than me.
Dialogue: 0,0:27:01.47,0:27:02.63,Default,,0000,0000,0000,,That was the longitude.
Dialogue: 0,0:27:02.63,0:27:03.29,Default,,0000,0000,0000,,Thank you.
Dialogue: 0,0:27:03.29,0:27:05.93,Default,,0000,0000,0000,,I'm sorry, I meant to\Nwrite the latitude.
Dialogue: 0,0:27:05.93,0:27:10.60,Default,,0000,0000,0000,,Phi is between 0 and pi/4.
Dialogue: 0,0:27:10.60,0:27:14.12,Default,,0000,0000,0000,,How about the radius?
Dialogue: 0,0:27:14.12,0:27:17.15,Default,,0000,0000,0000,,Are you afraid of the radius?
Dialogue: 0,0:27:17.15,0:27:18.26,Default,,0000,0000,0000,,No.
Dialogue: 0,0:27:18.26,0:27:19.42,Default,,0000,0000,0000,,Why?
Dialogue: 0,0:27:19.42,0:27:21.01,Default,,0000,0000,0000,,The radius is your friend.
Dialogue: 0,0:27:21.01,0:27:23.81,Default,,0000,0000,0000,,It was not your friend before.
Dialogue: 0,0:27:23.81,0:27:25.29,Default,,0000,0000,0000,,Look how wobbly it is.
Dialogue: 0,0:27:25.29,0:27:30.07,Default,,0000,0000,0000,,But in this case, the radius\Ngoes all the way from 0
Dialogue: 0,0:27:30.07,0:27:33.80,Default,,0000,0000,0000,,to a finite value,\Nwhich is exactly
Dialogue: 0,0:27:33.80,0:27:37.50,Default,,0000,0000,0000,,the radius of the sphere.
Dialogue: 0,0:27:37.50,0:27:43.33,Default,,0000,0000,0000,,Because you have rays of light\Ncoming from the source origin,
Dialogue: 0,0:27:43.33,0:27:48.87,Default,,0000,0000,0000,,and they bounce\Nagainst this profile,
Dialogue: 0,0:27:48.87,0:27:51.92,Default,,0000,0000,0000,,which is the profile\Nof the sphere, which
Dialogue: 0,0:27:51.92,0:27:53.93,Default,,0000,0000,0000,,has radius square root of 2.
Dialogue: 0,0:27:53.93,0:27:58.44,Default,,0000,0000,0000,,So life is good for\Nyou in this case.
Dialogue: 0,0:27:58.44,0:28:00.62,Default,,0000,0000,0000,,Are you guys with me?
Dialogue: 0,0:28:00.62,0:28:01.71,Default,,0000,0000,0000,,Should it be easy?
Dialogue: 0,0:28:01.71,0:28:05.96,Default,,0000,0000,0000,,Yes, it should be easy to\Nwrite that in the integral,
Dialogue: 0,0:28:05.96,0:28:08.30,Default,,0000,0000,0000,,if you know how to write it.
Dialogue: 0,0:28:08.30,0:28:09.46,Default,,0000,0000,0000,,So you have.
Dialogue: 0,0:28:09.46,0:28:10.05,Default,,0000,0000,0000,,OK.
Dialogue: 0,0:28:10.05,0:28:11.34,Default,,0000,0000,0000,,What do you want to do first?
Dialogue: 0,0:28:11.34,0:28:14.18,Default,,0000,0000,0000,,It doesn't matter that you\Napply Fubini's theorem.
Dialogue: 0,0:28:14.18,0:28:19.22,Default,,0000,0000,0000,,You have fixed limits.
Dialogue: 0,0:28:19.22,0:28:27.97,Default,,0000,0000,0000,,You have 0 to 2 pi, 0 to\Npi/4, 0 to square root 2.
Dialogue: 0,0:28:27.97,0:28:32.03,Default,,0000,0000,0000,,Inside, there must be a\NJacobian that you know by heart,
Dialogue: 0,0:28:32.03,0:28:35.81,Default,,0000,0000,0000,,and I'm asking you to learn\Nit by heart before the final,
Dialogue: 0,0:28:35.81,0:28:38.22,Default,,0000,0000,0000,,if not for now, but\Nmaybe before the final.
Dialogue: 0,0:28:38.22,0:28:42.74,Default,,0000,0000,0000,,But by now, you should\Nknow it by heart.
Dialogue: 0,0:28:42.74,0:28:44.20,Default,,0000,0000,0000,,Thank you so much, Matthew.
Dialogue: 0,0:28:44.20,0:28:45.44,Default,,0000,0000,0000,,Yes.
Dialogue: 0,0:28:45.44,0:28:48.66,Default,,0000,0000,0000,,You don't have much to memorize,\Nbut this is one of the things
Dialogue: 0,0:28:48.66,0:28:51.91,Default,,0000,0000,0000,,that I told you I did not\Nmemorize it, I was a freshman,
Dialogue: 0,0:28:51.91,0:28:55.33,Default,,0000,0000,0000,,I was stubborn and silly.
Dialogue: 0,0:28:55.33,0:28:57.90,Default,,0000,0000,0000,,So I have to compute what?
Dialogue: 0,0:28:57.90,0:28:59.59,Default,,0000,0000,0000,,I have to compute the Jacobian.
Dialogue: 0,0:28:59.59,0:29:05.06,Default,,0000,0000,0000,,Imagine what work you have\Nwhen you're limited in time.
Dialogue: 0,0:29:05.06,0:29:09.09,Default,,0000,0000,0000,,dx, dr. dx, d theta.
Dialogue: 0,0:29:09.09,0:29:10.98,Default,,0000,0000,0000,,dx, d phi.
Dialogue: 0,0:29:10.98,0:29:13.34,Default,,0000,0000,0000,,I thought I was\Nabout to kill myself.
Dialogue: 0,0:29:13.34,0:29:23.36,Default,,0000,0000,0000,,dy, dr. dy, d theta. dy, d\Nphi, and finally, dz, dr. dz,
Dialogue: 0,0:29:23.36,0:29:24.83,Default,,0000,0000,0000,,d theta.
Dialogue: 0,0:29:24.83,0:29:27.28,Default,,0000,0000,0000,,dz d phi.
Dialogue: 0,0:29:27.28,0:29:28.76,Default,,0000,0000,0000,,And I did this.
Dialogue: 0,0:29:28.76,0:29:32.21,Default,,0000,0000,0000,,And I thought I was about to\Njust collapse and not finish
Dialogue: 0,0:29:32.21,0:29:32.71,Default,,0000,0000,0000,,my exam.
Dialogue: 0,0:29:32.71,0:29:37.37,Default,,0000,0000,0000,,I finished my exam, but since\Nthen, I didn't remember that.
Dialogue: 0,0:29:37.37,0:29:38.90,Default,,0000,0000,0000,,I had to compute it.
Dialogue: 0,0:29:38.90,0:29:42.26,Default,,0000,0000,0000,,It took me 10 minutes\Nto compute the Jacobian.
Dialogue: 0,0:29:42.26,0:29:45.53,Default,,0000,0000,0000,,So this is r squared, psi, phi.
Dialogue: 0,0:29:45.53,0:29:49.87,Default,,0000,0000,0000,,If you have nothing better\Nto do, you can do that.
Dialogue: 0,0:29:49.87,0:29:52.46,Default,,0000,0000,0000,,
Dialogue: 0,0:29:52.46,0:29:56.68,Default,,0000,0000,0000,,Do you remember what the\Nspherical coordinates were, out
Dialogue: 0,0:29:56.68,0:29:57.84,Default,,0000,0000,0000,,of curiosity?
Dialogue: 0,0:29:57.84,0:29:59.72,Default,,0000,0000,0000,,Who remembers that?
Dialogue: 0,0:29:59.72,0:30:02.56,Default,,0000,0000,0000,,There are some\Npre-med majors here,
Dialogue: 0,0:30:02.56,0:30:04.95,Default,,0000,0000,0000,,who probably remember that.
Dialogue: 0,0:30:04.95,0:30:10.43,Default,,0000,0000,0000,,So when you have a phi here,\Nyou have r-- sine or cosine?
Dialogue: 0,0:30:10.43,0:30:11.33,Default,,0000,0000,0000,,Cosine.
Dialogue: 0,0:30:11.33,0:30:12.73,Default,,0000,0000,0000,,r cosine phi.
Dialogue: 0,0:30:12.73,0:30:18.05,Default,,0000,0000,0000,,And then r sine phi\Nfor both times what?
Dialogue: 0,0:30:18.05,0:30:20.62,Default,,0000,0000,0000,,The first one comes\Nfrom theta, like that.
Dialogue: 0,0:30:20.62,0:30:23.56,Default,,0000,0000,0000,,It's going to be cosine\Ntheta, and sine theta.
Dialogue: 0,0:30:23.56,0:30:29.56,Default,,0000,0000,0000,,Well imagine me taking these\Nfunctions and differentiating,
Dialogue: 0,0:30:29.56,0:30:31.46,Default,,0000,0000,0000,,partial derivatives.
Dialogue: 0,0:30:31.46,0:30:37.83,Default,,0000,0000,0000,,And after I differentiated down,\Ncompute the 3 by 3 determining.
Dialogue: 0,0:30:37.83,0:30:42.34,Default,,0000,0000,0000,,It's an error, no matter how\Ngood you are at computing.
Dialogue: 0,0:30:42.34,0:30:45.69,Default,,0000,0000,0000,,So don't do that,\Njust memorize it.
Dialogue: 0,0:30:45.69,0:30:47.57,Default,,0000,0000,0000,,Don't do like I did.
Dialogue: 0,0:30:47.57,0:30:49.89,Default,,0000,0000,0000,,And then you have d what?
Dialogue: 0,0:30:49.89,0:30:54.11,Default,,0000,0000,0000,,dr, d phi, d theta.
Dialogue: 0,0:30:54.11,0:30:57.47,Default,,0000,0000,0000,,
Dialogue: 0,0:30:57.47,0:31:03.04,Default,,0000,0000,0000,,Now what is the volume\Nof the ice cream cone?
Dialogue: 0,0:31:03.04,0:31:05.62,Default,,0000,0000,0000,,Let me erase.
Dialogue: 0,0:31:05.62,0:31:07.27,Default,,0000,0000,0000,,This shouldn't be hard.
Dialogue: 0,0:31:07.27,0:31:10.46,Default,,0000,0000,0000,,This is the type\Nof problem where
Dialogue: 0,0:31:10.46,0:31:14.66,Default,,0000,0000,0000,,you have a product of\Nfunctions of several variables.
Dialogue: 0,0:31:14.66,0:31:21.98,Default,,0000,0000,0000,,You can separate as a product\Nof three independent integrals
Dialogue: 0,0:31:21.98,0:31:25.45,Default,,0000,0000,0000,,as a consequence of\NFubini's theorem.
Dialogue: 0,0:31:25.45,0:31:28.92,Default,,0000,0000,0000,,So you have integral from,\Nintegral from, integral from.
Dialogue: 0,0:31:28.92,0:31:29.71,Default,,0000,0000,0000,,Who's your friend?
Dialogue: 0,0:31:29.71,0:31:30.75,Default,,0000,0000,0000,,Who do you like the most?
Dialogue: 0,0:31:30.75,0:31:31.42,Default,,0000,0000,0000,,STUDENT: Theta.
Dialogue: 0,0:31:31.42,0:31:33.79,Default,,0000,0000,0000,,PROFESSOR: You like\Ntheta the most?
Dialogue: 0,0:31:33.79,0:31:37.30,Default,,0000,0000,0000,,Because it comes\Nfrom Santa Clause?
Dialogue: 0,0:31:37.30,0:31:38.47,Default,,0000,0000,0000,,No, the theta doesn't.
Dialogue: 0,0:31:38.47,0:31:42.72,Default,,0000,0000,0000,,This is the easiest step.
Dialogue: 0,0:31:42.72,0:31:44.91,Default,,0000,0000,0000,,So that's why you\Nlike it, because it's
Dialogue: 0,0:31:44.91,0:31:46.49,Default,,0000,0000,0000,,the easiest to deal with.
Dialogue: 0,0:31:46.49,0:31:48.01,Default,,0000,0000,0000,,How about phi?
Dialogue: 0,0:31:48.01,0:31:51.27,Default,,0000,0000,0000,,Sine phi, d phi.
Dialogue: 0,0:31:51.27,0:31:55.52,Default,,0000,0000,0000,,I agree with you,\Nit's not so easy,
Dialogue: 0,0:31:55.52,0:31:58.31,Default,,0000,0000,0000,,but it's going to be a\Npiece of cake anyway.
Dialogue: 0,0:31:58.31,0:32:03.66,Default,,0000,0000,0000,,How about this one, 0\Nto root 2 r squared dr.
Dialogue: 0,0:32:03.66,0:32:06.60,Default,,0000,0000,0000,,Is this guy hard to do?
Dialogue: 0,0:32:06.60,0:32:13.80,Default,,0000,0000,0000,,r cubed over 3 will give\Nme root 2 cubed over 3.
Dialogue: 0,0:32:13.80,0:32:16.08,Default,,0000,0000,0000,,How much is that, by the way?
Dialogue: 0,0:32:16.08,0:32:18.74,Default,,0000,0000,0000,,2 root 2 over 3.
Dialogue: 0,0:32:18.74,0:32:22.24,Default,,0000,0000,0000,,Oh bless your heart,\Nthat's not so hard.
Dialogue: 0,0:32:22.24,0:32:24.23,Default,,0000,0000,0000,,This is not a problem.
Dialogue: 0,0:32:24.23,0:32:25.73,Default,,0000,0000,0000,,How about that?
Dialogue: 0,0:32:25.73,0:32:28.60,Default,,0000,0000,0000,,
Dialogue: 0,0:32:28.60,0:32:29.43,Default,,0000,0000,0000,,What do you have?
Dialogue: 0,0:32:29.43,0:32:32.59,Default,,0000,0000,0000,,What is the integral of sine?
Dialogue: 0,0:32:32.59,0:32:33.86,Default,,0000,0000,0000,,Negative cosine.
Dialogue: 0,0:32:33.86,0:32:42.37,Default,,0000,0000,0000,,So you have minus cosine phi\Nbetween pi/4 up and 0 down.
Dialogue: 0,0:32:42.37,0:32:43.70,Default,,0000,0000,0000,,Good luck to you.
Dialogue: 0,0:32:43.70,0:32:48.17,Default,,0000,0000,0000,,Well, the first guy.
Dialogue: 0,0:32:48.17,0:32:49.99,Default,,0000,0000,0000,,Good, minus root 2 over 2.
Dialogue: 0,0:32:49.99,0:32:53.26,Default,,0000,0000,0000,,Minus, second guy?
Dialogue: 0,0:32:53.26,0:32:55.89,Default,,0000,0000,0000,,Minus, minus 1.
Dialogue: 0,0:32:55.89,0:32:57.36,Default,,0000,0000,0000,,Don't fall into the trap.
Dialogue: 0,0:32:57.36,0:32:59.00,Default,,0000,0000,0000,,Pay attention to the signs.
Dialogue: 0,0:32:59.00,0:33:00.82,Default,,0000,0000,0000,,Don't mess up,\Nbecause that's where
Dialogue: 0,0:33:00.82,0:33:06.85,Default,,0000,0000,0000,,you can hurt your grade by\Nmessing up with minus signs.
Dialogue: 0,0:33:06.85,0:33:15.97,Default,,0000,0000,0000,,So this is 1 plus 1,\N1 minus root 2 over 2.
Dialogue: 0,0:33:15.97,0:33:22.73,Default,,0000,0000,0000,,
Dialogue: 0,0:33:22.73,0:33:25.56,Default,,0000,0000,0000,,And finally, let's see what\Nthat is, the whole thing being.
Dialogue: 0,0:33:25.56,0:33:28.92,Default,,0000,0000,0000,,
Dialogue: 0,0:33:28.92,0:33:31.34,Default,,0000,0000,0000,,Can we write it nicely?
Dialogue: 0,0:33:31.34,0:33:34.30,Default,,0000,0000,0000,,What's 2 times-- 4.
Dialogue: 0,0:33:34.30,0:33:40.62,Default,,0000,0000,0000,,4, root 2 over 3 pi.
Dialogue: 0,0:33:40.62,0:33:41.96,Default,,0000,0000,0000,,The first and the last.
Dialogue: 0,0:33:41.96,0:33:47.14,Default,,0000,0000,0000,,4 times 2, pi/3 times this\Nnasty guy 1 minus root 2.
Dialogue: 0,0:33:47.14,0:33:51.64,Default,,0000,0000,0000,,I don't like it, let's\Nmake it look better.
Dialogue: 0,0:33:51.64,0:33:53.31,Default,,0000,0000,0000,,Well OK, you can\Ngive me this answer,
Dialogue: 0,0:33:53.31,0:33:56.06,Default,,0000,0000,0000,,of course you'll get 100%.
Dialogue: 0,0:33:56.06,0:33:57.61,Default,,0000,0000,0000,,But am I happy with it?
Dialogue: 0,0:33:57.61,0:34:00.18,Default,,0000,0000,0000,,If you were to publish\Nthis in a journal,
Dialogue: 0,0:34:00.18,0:34:02.43,Default,,0000,0000,0000,,how would you simplify?
Dialogue: 0,0:34:02.43,0:34:04.31,Default,,0000,0000,0000,,This is dry.
Dialogue: 0,0:34:04.31,0:34:07.83,Default,,0000,0000,0000,,OK so what do you have?
Dialogue: 0,0:34:07.83,0:34:11.31,Default,,0000,0000,0000,,1 is 2/2.
Dialogue: 0,0:34:11.31,0:34:21.56,Default,,0000,0000,0000,,2 minus root 2 pi,\N4 and 2 simplify.
Dialogue: 0,0:34:21.56,0:34:23.00,Default,,0000,0000,0000,,Are you guys with me?
Dialogue: 0,0:34:23.00,0:34:26.85,Default,,0000,0000,0000,,There is a 2 down, and a 4\Nup, so I'm going to have a 2
Dialogue: 0,0:34:26.85,0:34:29.52,Default,,0000,0000,0000,,and another 2, all over 3.
Dialogue: 0,0:34:29.52,0:34:33.19,Default,,0000,0000,0000,,
Dialogue: 0,0:34:33.19,0:34:35.50,Default,,0000,0000,0000,,So I have 2 and 2 pi,\Ntimes 2 minus root 2.
Dialogue: 0,0:34:35.50,0:34:37.67,Default,,0000,0000,0000,,Do you like it like that?
Dialogue: 0,0:34:37.67,0:34:38.35,Default,,0000,0000,0000,,I don't.
Dialogue: 0,0:34:38.35,0:34:39.49,Default,,0000,0000,0000,,So what do you do next?
Dialogue: 0,0:34:39.49,0:34:43.71,Default,,0000,0000,0000,,
Dialogue: 0,0:34:43.71,0:34:46.33,Default,,0000,0000,0000,,I can even pull\Nthe root 2 inside.
Dialogue: 0,0:34:46.33,0:34:51.67,Default,,0000,0000,0000,,So I go 4 root 2, minus what?
Dialogue: 0,0:34:51.67,0:34:56.91,Default,,0000,0000,0000,,Minus 4, because this is\N2 times 3 is 4, pi over--
Dialogue: 0,0:34:56.91,0:34:57.98,Default,,0000,0000,0000,,Do you like it?
Dialogue: 0,0:34:57.98,0:35:01.68,Default,,0000,0000,0000,,Still I don't,\Nbecause I'm stubborn.
Dialogue: 0,0:35:01.68,0:35:06.53,Default,,0000,0000,0000,,4 root 2 minus 1 over 3 is\Nthe most beautiful form.
Dialogue: 0,0:35:06.53,0:35:09.94,Default,,0000,0000,0000,,So I'll try to brush\Nit up, and put it
Dialogue: 0,0:35:09.94,0:35:12.64,Default,,0000,0000,0000,,in the most elegant form.
Dialogue: 0,0:35:12.64,0:35:15.84,Default,,0000,0000,0000,,
Dialogue: 0,0:35:15.84,0:35:17.71,Default,,0000,0000,0000,,It doesn't matter.
Dialogue: 0,0:35:17.71,0:35:21.92,Default,,0000,0000,0000,,If you want to give\Nme a correct answer,
Dialogue: 0,0:35:21.92,0:35:23.22,Default,,0000,0000,0000,,any form it would be OK.
Dialogue: 0,0:35:23.22,0:35:23.72,Default,,0000,0000,0000,,Yes?
Dialogue: 0,0:35:23.72,0:35:25.30,Default,,0000,0000,0000,,STUDENT: If it was\Nslightly different,
Dialogue: 0,0:35:25.30,0:35:30.94,Default,,0000,0000,0000,,how would we find phi for the\Nlimits in the second part?
Dialogue: 0,0:35:30.94,0:35:32.35,Default,,0000,0000,0000,,PROFESSOR: If you have a what?
Dialogue: 0,0:35:32.35,0:35:35.84,Default,,0000,0000,0000,,STUDENT: How would we find\Nphi if it wasn't obvious,
Dialogue: 0,0:35:35.84,0:35:37.92,Default,,0000,0000,0000,,if it wasn't x\Nsquared, or c squared?
Dialogue: 0,0:35:37.92,0:35:40.74,Default,,0000,0000,0000,,PROFESSOR: If it wasn't\Na 45 degree angle?
Dialogue: 0,0:35:40.74,0:35:41.24,Default,,0000,0000,0000,,[INAUDIBLE]
Dialogue: 0,0:35:41.24,0:35:44.63,Default,,0000,0000,0000,,
Dialogue: 0,0:35:44.63,0:35:47.71,Default,,0000,0000,0000,,It's not so bad, you\Nneed a calculator.
Dialogue: 0,0:35:47.71,0:35:55.55,Default,,0000,0000,0000,,Assume that I would have given\Nyou the sphere of radius 7,
Dialogue: 0,0:35:55.55,0:36:00.12,Default,,0000,0000,0000,,or square root of 7,\Nintersecting with this cone.
Dialogue: 0,0:36:00.12,0:36:03.15,Default,,0000,0000,0000,,Then to compute\Nthat phi, you would
Dialogue: 0,0:36:03.15,0:36:06.29,Default,,0000,0000,0000,,have needed to intersect\Nthe two surfaces
Dialogue: 0,0:36:06.29,0:36:10.17,Default,,0000,0000,0000,,and then compute it, maybe\Nlook at tangent inverse.
Dialogue: 0,0:36:10.17,0:36:13.53,Default,,0000,0000,0000,,Compute phi with\Ntangent inverse.
Dialogue: 0,0:36:13.53,0:36:15.45,Default,,0000,0000,0000,,And you will have tangent\Ninverse of a number.
Dialogue: 0,0:36:15.45,0:36:19.10,Default,,0000,0000,0000,,Well, you cannot put tangent\Ninverse of a number everywhere,
Dialogue: 0,0:36:19.10,0:36:20.87,Default,,0000,0000,0000,,it's not nice.
Dialogue: 0,0:36:20.87,0:36:23.90,Default,,0000,0000,0000,,So what you would\Ndo is in the end,
Dialogue: 0,0:36:23.90,0:36:26.26,Default,,0000,0000,0000,,you would do it with\Na calculator, come up
Dialogue: 0,0:36:26.26,0:36:30.16,Default,,0000,0000,0000,,with a nice truncated\Nresult with 5 decimals,
Dialogue: 0,0:36:30.16,0:36:34.43,Default,,0000,0000,0000,,or 10 decimals, whatever the\Ncalculator will give you.
Dialogue: 0,0:36:34.43,0:36:34.93,Default,,0000,0000,0000,,OK?
Dialogue: 0,0:36:34.93,0:36:37.53,Default,,0000,0000,0000,,
Dialogue: 0,0:36:37.53,0:36:39.00,Default,,0000,0000,0000,,Or, you can do it with MathLab.
Dialogue: 0,0:36:39.00,0:36:42.17,Default,,0000,0000,0000,,
Dialogue: 0,0:36:42.17,0:36:46.87,Default,,0000,0000,0000,,You can do it with scientific\Nsoftware, for sure.
Dialogue: 0,0:36:46.87,0:36:52.33,Default,,0000,0000,0000,,Let's do what I-- Ryan\Nyou said this was a what?
Dialogue: 0,0:36:52.33,0:36:53.95,Default,,0000,0000,0000,,STUDENT: Number 20\Nis for surface area.
Dialogue: 0,0:36:53.95,0:36:54.54,Default,,0000,0000,0000,,PROFESSOR: OK.
Dialogue: 0,0:36:54.54,0:36:58.32,Default,,0000,0000,0000,,So, it's-- read it to me again.
Dialogue: 0,0:36:58.32,0:37:02.05,Default,,0000,0000,0000,,What does it say?
Dialogue: 0,0:37:02.05,0:37:03.26,Default,,0000,0000,0000,,I'm coming to you.
Dialogue: 0,0:37:03.26,0:37:05.86,Default,,0000,0000,0000,,
Dialogue: 0,0:37:05.86,0:37:10.16,Default,,0000,0000,0000,,It says, find the surface area\Nof the part of the sphere that
Dialogue: 0,0:37:10.16,0:37:14.14,Default,,0000,0000,0000,,lies where you have 64.
Dialogue: 0,0:37:14.14,0:37:18.76,Default,,0000,0000,0000,,This is all because\Nof [INAUDIBLE]
Dialogue: 0,0:37:18.76,0:37:21.26,Default,,0000,0000,0000,,But yours is not\Nvery even, right?
Dialogue: 0,0:37:21.26,0:37:26.75,Default,,0000,0000,0000,,
Dialogue: 0,0:37:26.75,0:37:29.25,Default,,0000,0000,0000,,You shouldn't have bad results.
Dialogue: 0,0:37:29.25,0:37:30.41,Default,,0000,0000,0000,,And guess what?
Dialogue: 0,0:37:30.41,0:37:33.75,Default,,0000,0000,0000,,If you do, you use\Nyour calculator
Dialogue: 0,0:37:33.75,0:37:37.99,Default,,0000,0000,0000,,to find out the upper limit\Nof the angle for the volume.
Dialogue: 0,0:37:37.99,0:37:39.91,Default,,0000,0000,0000,,OK.
Dialogue: 0,0:37:39.91,0:37:47.28,Default,,0000,0000,0000,,So now, you say oh\Nmy god, this is ugly.
Dialogue: 0,0:37:47.28,0:37:48.87,Default,,0000,0000,0000,,I agree with you, it's not nice.
Dialogue: 0,0:37:48.87,0:37:56.12,Default,,0000,0000,0000,,
Dialogue: 0,0:37:56.12,0:38:03.21,Default,,0000,0000,0000,,You have square root of 2 minus\Nx squared minus y squared.
Dialogue: 0,0:38:03.21,0:38:10.14,Default,,0000,0000,0000,,And when you compute the\Nsurface area of the cap-- cup,
Dialogue: 0,0:38:10.14,0:38:13.05,Default,,0000,0000,0000,,cap means spherical cap.
Dialogue: 0,0:38:13.05,0:38:15.76,Default,,0000,0000,0000,,A little hat that\Nlooks like this?
Dialogue: 0,0:38:15.76,0:38:18.20,Default,,0000,0000,0000,,That's why it's called cap.
Dialogue: 0,0:38:18.20,0:38:20.62,Default,,0000,0000,0000,,That will integrate\Nover the disk d.
Dialogue: 0,0:38:20.62,0:38:35.33,Default,,0000,0000,0000,,
Dialogue: 0,0:38:35.33,0:38:40.20,Default,,0000,0000,0000,,Square root of 1\Nplus f of x squared
Dialogue: 0,0:38:40.20,0:38:49.39,Default,,0000,0000,0000,,plus f of y squared, dx da.
Dialogue: 0,0:38:49.39,0:38:52.37,Default,,0000,0000,0000,,Is that the only\Nway you can do this?
Dialogue: 0,0:38:52.37,0:38:53.14,Default,,0000,0000,0000,,No.
Dialogue: 0,0:38:53.14,0:38:57.31,Default,,0000,0000,0000,,You can actually do it with\Nparametrization of a sphere,
Dialogue: 0,0:38:57.31,0:39:01.07,Default,,0000,0000,0000,,and you have the\Nelement limit over here.
Dialogue: 0,0:39:01.07,0:39:05.45,Default,,0000,0000,0000,,So that might be easier.
Dialogue: 0,0:39:05.45,0:39:08.02,Default,,0000,0000,0000,,
Dialogue: 0,0:39:08.02,0:39:08.53,Default,,0000,0000,0000,,Yeah.
Dialogue: 0,0:39:08.53,0:39:10.36,Default,,0000,0000,0000,,You can also do it in homework.
Dialogue: 0,0:39:10.36,0:39:14.97,Default,,0000,0000,0000,,But what if you went up there--\Nlet's see, how hard is life?
Dialogue: 0,0:39:14.97,0:39:18.42,Default,,0000,0000,0000,,How hard would it be\Nto do it like this?
Dialogue: 0,0:39:18.42,0:39:21.22,Default,,0000,0000,0000,,
Dialogue: 0,0:39:21.22,0:39:22.64,Default,,0000,0000,0000,,That's good.
Dialogue: 0,0:39:22.64,0:39:24.51,Default,,0000,0000,0000,,First of all, let's\Nthink everything
Dialogue: 0,0:39:24.51,0:39:27.09,Default,,0000,0000,0000,,that's under the square root.
Dialogue: 0,0:39:27.09,0:39:28.26,Default,,0000,0000,0000,,And write it down.
Dialogue: 0,0:39:28.26,0:39:29.97,Default,,0000,0000,0000,,1 plus.
Dialogue: 0,0:39:29.97,0:39:33.30,Default,,0000,0000,0000,,Now, computing this problem\Nwith respect to x and you say,
Dialogue: 0,0:39:33.30,0:39:35.01,Default,,0000,0000,0000,,oh my god, that's hard.
Dialogue: 0,0:39:35.01,0:39:36.45,Default,,0000,0000,0000,,No, it's not.
Dialogue: 0,0:39:36.45,0:39:38.90,Default,,0000,0000,0000,,If you want to do the\Nhard one, and most of you
Dialogue: 0,0:39:38.90,0:39:41.25,Default,,0000,0000,0000,,were, and you have\Nthat professors who
Dialogue: 0,0:39:41.25,0:39:44.66,Default,,0000,0000,0000,,gave you enough practice,\Nwhat did you have done?
Dialogue: 0,0:39:44.66,0:39:47.11,Default,,0000,0000,0000,,Chain rule.
Dialogue: 0,0:39:47.11,0:39:51.79,Default,,0000,0000,0000,,On the bottom, you have\Nthis nasty guy twice.
Dialogue: 0,0:39:51.79,0:39:56.31,Default,,0000,0000,0000,,But on the top, your minus 2x.
Dialogue: 0,0:39:56.31,0:39:59.86,Default,,0000,0000,0000,,So when you simplify\Nyour life becomes easier.
Dialogue: 0,0:39:59.86,0:40:02.76,Default,,0000,0000,0000,,
Dialogue: 0,0:40:02.76,0:40:06.23,Default,,0000,0000,0000,,And you will square it.
Dialogue: 0,0:40:06.23,0:40:09.91,Default,,0000,0000,0000,,Are you guys with me,\Nhave I lost you yet?
Dialogue: 0,0:40:09.91,0:40:12.72,Default,,0000,0000,0000,,And then the same thing in y.
Dialogue: 0,0:40:12.72,0:40:19.23,Default,,0000,0000,0000,,Minus 2y, over 2 square root 2\Nminus x square minus y squared,
Dialogue: 0,0:40:19.23,0:40:19.82,Default,,0000,0000,0000,,square it.
Dialogue: 0,0:40:19.82,0:40:24.91,Default,,0000,0000,0000,,
Dialogue: 0,0:40:24.91,0:40:28.00,Default,,0000,0000,0000,,Some things cancel out.
Dialogue: 0,0:40:28.00,0:40:30.67,Default,,0000,0000,0000,,So let's be patient\Nand see what we have.
Dialogue: 0,0:40:30.67,0:40:34.07,Default,,0000,0000,0000,,
Dialogue: 0,0:40:34.07,0:40:37.94,Default,,0000,0000,0000,,First of all, 1 is not going to\Ngive you trouble, because let
Dialogue: 0,0:40:37.94,0:40:42.44,Default,,0000,0000,0000,,write 1 as this over itself.
Dialogue: 0,0:40:42.44,0:40:45.64,Default,,0000,0000,0000,,Plus, minus squared\Nis plus, thank god.
Dialogue: 0,0:40:45.64,0:40:51.03,Default,,0000,0000,0000,,x squared over 2 minus x squared\Nminus y squared plus y squared
Dialogue: 0,0:40:51.03,0:40:57.50,Default,,0000,0000,0000,,over 2 minus x squared\Nminus y squared.
Dialogue: 0,0:40:57.50,0:41:01.31,Default,,0000,0000,0000,,And these guys go for a walk.
Dialogue: 0,0:41:01.31,0:41:08.65,Default,,0000,0000,0000,,Minus x squared, minus y\Nsquared, plus y squared.
Dialogue: 0,0:41:08.65,0:41:12.40,Default,,0000,0000,0000,,
Dialogue: 0,0:41:12.40,0:41:14.65,Default,,0000,0000,0000,,They disappear\Ntogether in the dark.
Dialogue: 0,0:41:14.65,0:41:19.74,Default,,0000,0000,0000,,So you have 2 over 2 minus\Nx squared minus y squared.
Dialogue: 0,0:41:19.74,0:41:29.01,Default,,0000,0000,0000,,
Dialogue: 0,0:41:29.01,0:41:31.00,Default,,0000,0000,0000,,OK let's try to do that.
Dialogue: 0,0:41:31.00,0:41:33.57,Default,,0000,0000,0000,,
Dialogue: 0,0:41:33.57,0:41:35.58,Default,,0000,0000,0000,,Guys, I have to erase.
Dialogue: 0,0:41:35.58,0:41:36.98,Default,,0000,0000,0000,,I will erase.
Dialogue: 0,0:41:36.98,0:41:43.33,Default,,0000,0000,0000,,
Dialogue: 0,0:41:43.33,0:41:46.97,Default,,0000,0000,0000,,So what you see\Nhere, some people
Dialogue: 0,0:41:46.97,0:41:51.18,Default,,0000,0000,0000,,call it ds, and use the\Nelement of area on the surface.
Dialogue: 0,0:41:51.18,0:41:57.83,Default,,0000,0000,0000,,
Dialogue: 0,0:41:57.83,0:42:03.88,Default,,0000,0000,0000,,It's like the area of\Na small surface patch.
Dialogue: 0,0:42:03.88,0:42:07.73,Default,,0000,0000,0000,,
Dialogue: 0,0:42:07.73,0:42:09.05,Default,,0000,0000,0000,,So the curve linear squared.
Dialogue: 0,0:42:09.05,0:42:14.22,Default,,0000,0000,0000,,
Dialogue: 0,0:42:14.22,0:42:15.41,Default,,0000,0000,0000,,Alright.
Dialogue: 0,0:42:15.41,0:42:22.22,Default,,0000,0000,0000,,So area of the cup will be--\Nnow you say, well over the d,
Dialogue: 0,0:42:22.22,0:42:23.61,Default,,0000,0000,0000,,let me think.
Dialogue: 0,0:42:23.61,0:42:27.89,Default,,0000,0000,0000,,d represents those\Nxy's with a property
Dialogue: 0,0:42:27.89,0:42:36.42,Default,,0000,0000,0000,,that x squared plus y squared\Nwas between what and what?
Dialogue: 0,0:42:36.42,0:42:41.61,Default,,0000,0000,0000,,0 and 1, because\Nthat was our, the
Dialogue: 0,0:42:41.61,0:42:46.81,Default,,0000,0000,0000,,predicted domain on the\Nshadow on the ground.
Dialogue: 0,0:42:46.81,0:42:48.34,Default,,0000,0000,0000,,OK, that was this.
Dialogue: 0,0:42:48.34,0:42:51.65,Default,,0000,0000,0000,,
Dialogue: 0,0:42:51.65,0:42:56.40,Default,,0000,0000,0000,,And as you look at it, I have\Nto put it on the square root.
Dialogue: 0,0:42:56.40,0:42:58.71,Default,,0000,0000,0000,,Don't be afraid of\Nit, because it's not
Dialogue: 0,0:42:58.71,0:43:02.73,Default,,0000,0000,0000,,much up here than you thought.
Dialogue: 0,0:43:02.73,0:43:05.09,Default,,0000,0000,0000,,And let's solve this together.
Dialogue: 0,0:43:05.09,0:43:10.63,Default,,0000,0000,0000,,What is your luck that this is\Na symmetric polynomial index,
Dialogue: 0,0:43:10.63,0:43:14.50,Default,,0000,0000,0000,,and why x squared plus y squared\Nthat you can rewrite as r
Dialogue: 0,0:43:14.50,0:43:17.12,Default,,0000,0000,0000,,squared, polar coordinates?
Dialogue: 0,0:43:17.12,0:43:19.84,Default,,0000,0000,0000,,And Ryan asked, can I\Ndo polar coordinates?
Dialogue: 0,0:43:19.84,0:43:22.25,Default,,0000,0000,0000,,That's exactly what\Nyou're going to do.
Dialogue: 0,0:43:22.25,0:43:25.06,Default,,0000,0000,0000,,You didn't know, unless\Nyour intuition is strong.
Dialogue: 0,0:43:25.06,0:43:26.75,Default,,0000,0000,0000,,Yes?
Dialogue: 0,0:43:26.75,0:43:27.42,Default,,0000,0000,0000,,Alex tell me.
Dialogue: 0,0:43:27.42,0:43:29.75,Default,,0000,0000,0000,,STUDENT: I was going to ask,\Nif you could have done that
Dialogue: 0,0:43:29.75,0:43:35.11,Default,,0000,0000,0000,,by taking the r plane and\Nmultiplying that by 2 pi r?
Dialogue: 0,0:43:35.11,0:43:36.55,Default,,0000,0000,0000,,PROFESSOR: Yeah,\Nyou can do that.
Dialogue: 0,0:43:36.55,0:43:39.27,Default,,0000,0000,0000,,
Dialogue: 0,0:43:39.27,0:43:40.78,Default,,0000,0000,0000,,Well, that is a way to do that.
Dialogue: 0,0:43:40.78,0:43:43.48,Default,,0000,0000,0000,,So practically, he's\Nasking-- I don't
Dialogue: 0,0:43:43.48,0:43:47.99,Default,,0000,0000,0000,,know if you guys\Nremember, in Cal 2,
Dialogue: 0,0:43:47.99,0:43:50.86,Default,,0000,0000,0000,,you have the surface\Nof revolution, right?
Dialogue: 0,0:43:50.86,0:43:53.61,Default,,0000,0000,0000,,And if you knew the\Nlength of an arc,
Dialogue: 0,0:43:53.61,0:43:56.78,Default,,0000,0000,0000,,you would be able\Nto revolve that arc.
Dialogue: 0,0:43:56.78,0:43:58.11,Default,,0000,0000,0000,,This is the cap.
Dialogue: 0,0:43:58.11,0:44:01.36,Default,,0000,0000,0000,,And you take one of the\Nmeridians of the hat,
Dialogue: 0,0:44:01.36,0:44:03.97,Default,,0000,0000,0000,,and revolve it, can\Nredo with a form,
Dialogue: 0,0:44:03.97,0:44:08.97,Default,,0000,0000,0000,,like you did the washer\Nand dryer method.
Dialogue: 0,0:44:08.97,0:44:10.37,Default,,0000,0000,0000,,It always amuses me.
Dialogue: 0,0:44:10.37,0:44:14.76,Default,,0000,0000,0000,,Yes, you could have\Ndone that from Cal 2.
Dialogue: 0,0:44:14.76,0:44:17.49,Default,,0000,0000,0000,,Computing the area of\Nthe cap as a surface
Dialogue: 0,0:44:17.49,0:44:23.38,Default,,0000,0000,0000,,of revolution, chapter-- c'mon,\NI'm a co-author of this book.
Dialogue: 0,0:44:23.38,0:44:27.60,Default,,0000,0000,0000,,Chapter 7?
Dialogue: 0,0:44:27.60,0:44:28.82,Default,,0000,0000,0000,,What chapter?
Dialogue: 0,0:44:28.82,0:44:30.03,Default,,0000,0000,0000,,Chapter 6?
Dialogue: 0,0:44:30.03,0:44:31.85,Default,,0000,0000,0000,,No.
Dialogue: 0,0:44:31.85,0:44:33.51,Default,,0000,0000,0000,,The washer and dryer?
Dialogue: 0,0:44:33.51,0:44:35.63,Default,,0000,0000,0000,,Chapter 6, right?
Dialogue: 0,0:44:35.63,0:44:36.39,Default,,0000,0000,0000,,OK.
Dialogue: 0,0:44:36.39,0:44:38.51,Default,,0000,0000,0000,,But now we already\Nhave three, and we
Dialogue: 0,0:44:38.51,0:44:41.53,Default,,0000,0000,0000,,don't want to remember Cal 2\Nbecause it was a nightmare.
Dialogue: 0,0:44:41.53,0:44:44.25,Default,,0000,0000,0000,,Several of you told\Nme that this is
Dialogue: 0,0:44:44.25,0:44:48.19,Default,,0000,0000,0000,,easier, these things are\Ngenerally easier than Cal 2,
Dialogue: 0,0:44:48.19,0:44:50.62,Default,,0000,0000,0000,,because Cal 2 was headache.
Dialogue: 0,0:44:50.62,0:44:55.53,Default,,0000,0000,0000,,And what seemed to be giving\Nyou most of the headache
Dialogue: 0,0:44:55.53,0:44:59.02,Default,,0000,0000,0000,,was a salad of\Ndifferent ingredients
Dialogue: 0,0:44:59.02,0:45:01.38,Default,,0000,0000,0000,,that seemed to be unrelated.
Dialogue: 0,0:45:01.38,0:45:03.06,Default,,0000,0000,0000,,Which I agree.
Dialogue: 0,0:45:03.06,0:45:11.54,Default,,0000,0000,0000,,You have arcing, washer,\Nslices, then Greek substitution,
Dialogue: 0,0:45:11.54,0:45:13.16,Default,,0000,0000,0000,,the partial fractions.
Dialogue: 0,0:45:13.16,0:45:15.03,Default,,0000,0000,0000,,All sorts of things and\Nseries and sequences.
Dialogue: 0,0:45:15.03,0:45:19.15,Default,,0000,0000,0000,,And they are little\Nthings that don't quite
Dialogue: 0,0:45:19.15,0:45:22.15,Default,,0000,0000,0000,,follow one from another.
Dialogue: 0,0:45:22.15,0:45:24.65,Default,,0000,0000,0000,,They are a little bit unrelated.
Dialogue: 0,0:45:24.65,0:45:26.65,Default,,0000,0000,0000,,OK, how do you do that?
Dialogue: 0,0:45:26.65,0:45:30.83,Default,,0000,0000,0000,,You have to help me because\Nthat was the idea, that now you
Dialogue: 0,0:45:30.83,0:45:32.48,Default,,0000,0000,0000,,can help me, right?
Dialogue: 0,0:45:32.48,0:45:34.45,Default,,0000,0000,0000,,Square root of
Dialogue: 0,0:45:34.45,0:45:38.88,Default,,0000,0000,0000,,STUDENT: 2 over 2 minus r\Nsquared, times r, dr d theta.
Dialogue: 0,0:45:38.88,0:45:44.31,Default,,0000,0000,0000,,
Dialogue: 0,0:45:44.31,0:45:47.29,Default,,0000,0000,0000,,PROFESSOR: And do we like it?
Dialogue: 0,0:45:47.29,0:45:50.59,Default,,0000,0000,0000,,No, but we have to continue.
Dialogue: 0,0:45:50.59,0:45:55.08,Default,,0000,0000,0000,,0 to 1, this is 0 to 2 pi.
Dialogue: 0,0:45:55.08,0:46:03.45,Default,,0000,0000,0000,,I can get rid of the 2 pi,\Nand put it here and say, OK.
Dialogue: 0,0:46:03.45,0:46:12.41,Default,,0000,0000,0000,,I should be as good as taking\Nout square root of 2 from here.
Dialogue: 0,0:46:12.41,0:46:15.31,Default,,0000,0000,0000,,
Dialogue: 0,0:46:15.31,0:46:17.76,Default,,0000,0000,0000,,He goes out for a walk.
Dialogue: 0,0:46:17.76,0:46:24.70,Default,,0000,0000,0000,,And then I have integral 1 over\Nthis long line of fraction.
Dialogue: 0,0:46:24.70,0:46:30.56,Default,,0000,0000,0000,,
Dialogue: 0,0:46:30.56,0:46:35.51,Default,,0000,0000,0000,,STUDENT: And that would be 2r\Nso that the r will cancel out.
Dialogue: 0,0:46:35.51,0:46:41.92,Default,,0000,0000,0000,,PROFESSOR: So r dr, if\Nu is 2 minus r squared,
Dialogue: 0,0:46:41.92,0:46:43.13,Default,,0000,0000,0000,,the u is minus.
Dialogue: 0,0:46:43.13,0:46:48.03,Default,,0000,0000,0000,,I have to pay attention, so\NI don't mess up the signs.
Dialogue: 0,0:46:48.03,0:46:50.84,Default,,0000,0000,0000,,So rdr is a block.
Dialogue: 0,0:46:50.84,0:46:55.35,Default,,0000,0000,0000,,And this block is\Nsimply minus du/2.
Dialogue: 0,0:46:55.35,0:47:02.67,Default,,0000,0000,0000,,So I write it here,\Nminus 1/2, du/2.
Dialogue: 0,0:47:02.67,0:47:07.76,Default,,0000,0000,0000,,
Dialogue: 0,0:47:07.76,0:47:10.81,Default,,0000,0000,0000,,Don't be nervous\Nabout this minus,
Dialogue: 0,0:47:10.81,0:47:13.23,Default,,0000,0000,0000,,because it's not going to\Ngive me a minus result,
Dialogue: 0,0:47:13.23,0:47:15.48,Default,,0000,0000,0000,,a negative result.\NIf it did, that means
Dialogue: 0,0:47:15.48,0:47:18.04,Default,,0000,0000,0000,,that I was drunk when I\Ndid it, because I will
Dialogue: 0,0:47:18.04,0:47:21.07,Default,,0000,0000,0000,,get the area of the cap as\Na negative number, which
Dialogue: 0,0:47:21.07,0:47:22.88,Default,,0000,0000,0000,,is impossible.
Dialogue: 0,0:47:22.88,0:47:25.55,Default,,0000,0000,0000,,But it's going to happen\Nwhen I change the limits.
Dialogue: 0,0:47:25.55,0:47:26.38,Default,,0000,0000,0000,,Yes?
Dialogue: 0,0:47:26.38,0:47:28.27,Default,,0000,0000,0000,,STUDENT: Where did that\Nlast one come from?
Dialogue: 0,0:47:28.27,0:47:29.95,Default,,0000,0000,0000,,PROFESSOR: From this one.
Dialogue: 0,0:47:29.95,0:47:33.80,Default,,0000,0000,0000,,[INTERPOSING VOICES]\NOh, I put too many.
Dialogue: 0,0:47:33.80,0:47:38.09,Default,,0000,0000,0000,,So this guy is\Nthis guy, which is
Dialogue: 0,0:47:38.09,0:47:39.84,Default,,0000,0000,0000,,this guy minus the [INAUDIBLE].
Dialogue: 0,0:47:39.84,0:47:42.91,Default,,0000,0000,0000,,
Dialogue: 0,0:47:42.91,0:47:48.73,Default,,0000,0000,0000,,Now, do you want me to go\Nahead and cancel this out?
Dialogue: 0,0:47:48.73,0:47:50.12,Default,,0000,0000,0000,,Right?
Dialogue: 0,0:47:50.12,0:47:51.03,Default,,0000,0000,0000,,OK.
Dialogue: 0,0:47:51.03,0:47:54.58,Default,,0000,0000,0000,,I have squared 2 pi.
Dialogue: 0,0:47:54.58,0:47:56.68,Default,,0000,0000,0000,,I did not get the\Nendpoints, you have
Dialogue: 0,0:47:56.68,0:47:58.30,Default,,0000,0000,0000,,to help me put the endpoints.
Dialogue: 0,0:47:58.30,0:48:01.64,Default,,0000,0000,0000,,
Dialogue: 0,0:48:01.64,0:48:05.14,Default,,0000,0000,0000,,From 2 down.
Dialogue: 0,0:48:05.14,0:48:06.28,Default,,0000,0000,0000,,To 1.
Dialogue: 0,0:48:06.28,0:48:07.39,Default,,0000,0000,0000,,Which is crazy, right?
Dialogue: 0,0:48:07.39,0:48:08.83,Default,,0000,0000,0000,,Because 2 is bigger than 1.
Dialogue: 0,0:48:08.83,0:48:13.09,Default,,0000,0000,0000,,That's exactly where the next\Nminus is going to come from.
Dialogue: 0,0:48:13.09,0:48:18.38,Default,,0000,0000,0000,,So integral from 2 to 1 is\Nminus integral from 1 to 2.
Dialogue: 0,0:48:18.38,0:48:20.36,Default,,0000,0000,0000,,So I shouldn't be\Nworried, because I already
Dialogue: 0,0:48:20.36,0:48:23.82,Default,,0000,0000,0000,,have the minus out, with the\Nminus that's going to come out,
Dialogue: 0,0:48:23.82,0:48:25.45,Default,,0000,0000,0000,,I'm going to have a\Npositive variable.
Dialogue: 0,0:48:25.45,0:48:28.28,Default,,0000,0000,0000,,
Dialogue: 0,0:48:28.28,0:48:29.32,Default,,0000,0000,0000,,Square root 2 pi.
Dialogue: 0,0:48:29.32,0:48:32.74,Default,,0000,0000,0000,,
Dialogue: 0,0:48:32.74,0:48:37.15,Default,,0000,0000,0000,,Somebody was smarter than\Nme and said Magdalene,
Dialogue: 0,0:48:37.15,0:48:39.11,Default,,0000,0000,0000,,I think Alex-- was it you?
Dialogue: 0,0:48:39.11,0:48:43.52,Default,,0000,0000,0000,,You said, why don't you\Ntake advantage of the fact
Dialogue: 0,0:48:43.52,0:48:48.24,Default,,0000,0000,0000,,that you already have 1 over\N2 square root u and integrate?
Dialogue: 0,0:48:48.24,0:48:51.37,Default,,0000,0000,0000,,And that is going\Nto be squared u.
Dialogue: 0,0:48:51.37,0:48:52.79,Default,,0000,0000,0000,,Can you understand?
Dialogue: 0,0:48:52.79,0:48:53.89,Default,,0000,0000,0000,,Who said that?
Dialogue: 0,0:48:53.89,0:48:56.55,Default,,0000,0000,0000,,I heard a voice, it\Nwas not in my head.
Dialogue: 0,0:48:56.55,0:48:57.78,Default,,0000,0000,0000,,I'm Innocent.
Dialogue: 0,0:48:57.78,0:49:02.23,Default,,0000,0000,0000,,I heard a voice that told\Nme, if you are smart,
Dialogue: 0,0:49:02.23,0:49:04.74,Default,,0000,0000,0000,,you would understand\Nto pull out the minus.
Dialogue: 0,0:49:04.74,0:49:09.58,Default,,0000,0000,0000,,You would understand\Nthat this exactly
Dialogue: 0,0:49:09.58,0:49:12.75,Default,,0000,0000,0000,,is the derivative\Nof square root of u.
Dialogue: 0,0:49:12.75,0:49:16.40,Default,,0000,0000,0000,,And I will be faster than\Nyou, because you have just
Dialogue: 0,0:49:16.40,0:49:20.60,Default,,0000,0000,0000,,computed made between 1 and 2.
Dialogue: 0,0:49:20.60,0:49:22.04,Default,,0000,0000,0000,,Some people aren't too smart.
Dialogue: 0,0:49:22.04,0:49:23.25,Default,,0000,0000,0000,,I didn't think of that.
Dialogue: 0,0:49:23.25,0:49:27.07,Default,,0000,0000,0000,,Now I've been thing about that.
Dialogue: 0,0:49:27.07,0:49:30.95,Default,,0000,0000,0000,,Why cancel out the 2\Nwhen you can [INAUDIBLE].
Dialogue: 0,0:49:30.95,0:49:35.42,Default,,0000,0000,0000,,So you have a minus out.
Dialogue: 0,0:49:35.42,0:49:38.85,Default,,0000,0000,0000,,STUDENT: There still needs to\Nbe a 2 on the outside, right?
Dialogue: 0,0:49:38.85,0:49:40.81,Default,,0000,0000,0000,,PROFESSOR: Yes, I have\Nto put 2 together.
Dialogue: 0,0:49:40.81,0:49:42.78,Default,,0000,0000,0000,,Minus 2 and 2.
Dialogue: 0,0:49:42.78,0:49:45.73,Default,,0000,0000,0000,,2 pi, that's a collective thing.
Dialogue: 0,0:49:45.73,0:49:50.25,Default,,0000,0000,0000,,Squared and cubed\Nbetween 1 and 2.
Dialogue: 0,0:49:50.25,0:49:51.10,Default,,0000,0000,0000,,Do I like this?
Dialogue: 0,0:49:51.10,0:49:55.48,Default,,0000,0000,0000,,No, but you tell me\Nwhat is in the bracket.
Dialogue: 0,0:49:55.48,0:49:59.40,Default,,0000,0000,0000,,How much u minus 12, 13.
Dialogue: 0,0:49:59.40,0:50:02.53,Default,,0000,0000,0000,,1 minus square root of\N2 is a negative number.
Dialogue: 0,0:50:02.53,0:50:05.99,Default,,0000,0000,0000,,But with the minus outside,\NI"m going to fix it.
Dialogue: 0,0:50:05.99,0:50:08.48,Default,,0000,0000,0000,,And I'm going to get\Nsomething really ugly.
Dialogue: 0,0:50:08.48,0:50:15.95,Default,,0000,0000,0000,,
Dialogue: 0,0:50:15.95,0:50:17.66,Default,,0000,0000,0000,,Yeah.
Dialogue: 0,0:50:17.66,0:50:21.48,Default,,0000,0000,0000,,So when I'm multiplying sides,\Nthis by that, I get 4, right?
Dialogue: 0,0:50:21.48,0:50:22.77,Default,,0000,0000,0000,,Guys?
Dialogue: 0,0:50:22.77,0:50:23.60,Default,,0000,0000,0000,,I get a 4.
Dialogue: 0,0:50:23.60,0:50:29.03,Default,,0000,0000,0000,,This guy and this guy, minus,\Nminus, plus 2, 2 times 2 is 4.
Dialogue: 0,0:50:29.03,0:50:35.27,Default,,0000,0000,0000,,And then minus, to make\Nit look better, 2 root 2.
Dialogue: 0,0:50:35.27,0:50:37.90,Default,,0000,0000,0000,,And multiply out.
Dialogue: 0,0:50:37.90,0:50:40.14,Default,,0000,0000,0000,,Minus root 2 and the pi.
Dialogue: 0,0:50:40.14,0:50:43.54,Default,,0000,0000,0000,,Now, I don't care\Nwhere you stop.
Dialogue: 0,0:50:43.54,0:50:47.26,Default,,0000,0000,0000,,I swear that if you stop\Nhere, you'll still get 100%.
Dialogue: 0,0:50:47.26,0:50:50.58,Default,,0000,0000,0000,,Because what I care about is\Nnot to see a nice simplified
Dialogue: 0,0:50:50.58,0:50:51.98,Default,,0000,0000,0000,,result, so much.
Dialogue: 0,0:50:51.98,0:50:54.11,Default,,0000,0000,0000,,I won't go over your work.
Dialogue: 0,0:50:54.11,0:50:56.85,Default,,0000,0000,0000,,But to see that\Nyou understood how
Dialogue: 0,0:50:56.85,0:50:59.89,Default,,0000,0000,0000,,you solve this kind of problem.
Dialogue: 0,0:50:59.89,0:51:02.35,Default,,0000,0000,0000,,It's not the sign\Nof intelligence
Dialogue: 0,0:51:02.35,0:51:07.12,Default,,0000,0000,0000,,being able to simplify\Nanswers very much.
Dialogue: 0,0:51:07.12,0:51:12.49,Default,,0000,0000,0000,,But the method in itself, why\Nand how, what the steps are,
Dialogue: 0,0:51:12.49,0:51:15.13,Default,,0000,0000,0000,,that shows knowledge\Nand intelligence.
Dialogue: 0,0:51:15.13,0:51:18.83,Default,,0000,0000,0000,,
Dialogue: 0,0:51:18.83,0:51:19.83,Default,,0000,0000,0000,,Have I mess up?
Dialogue: 0,0:51:19.83,0:51:21.09,Default,,0000,0000,0000,,I don't think so.
Dialogue: 0,0:51:21.09,0:51:24.98,Default,,0000,0000,0000,,STUDENT: Does the order matter,\Nof the dr d theta, or dx/dy,
Dialogue: 0,0:51:24.98,0:51:28.62,Default,,0000,0000,0000,,does that matter which\Norder you put them in?
Dialogue: 0,0:51:28.62,0:51:30.02,Default,,0000,0000,0000,,PROFESSOR: In this case, no.
Dialogue: 0,0:51:30.02,0:51:31.32,Default,,0000,0000,0000,,STUDENT: Or over here?
Dialogue: 0,0:51:31.32,0:51:33.27,Default,,0000,0000,0000,,PROFESSOR: In this\Ncase, no again.
Dialogue: 0,0:51:33.27,0:51:36.36,Default,,0000,0000,0000,,But if you were\Nto swap them, you
Dialogue: 0,0:51:36.36,0:51:39.51,Default,,0000,0000,0000,,would have to swap\Nthe values as well.
Dialogue: 0,0:51:39.51,0:51:41.17,Default,,0000,0000,0000,,Why is that?
Dialogue: 0,0:51:41.17,0:51:42.71,Default,,0000,0000,0000,,That's a very good question.
Dialogue: 0,0:51:42.71,0:51:45.51,Default,,0000,0000,0000,,He's right, but why is that?
Dialogue: 0,0:51:45.51,0:51:49.00,Default,,0000,0000,0000,,It doesn't matter, why?
Dialogue: 0,0:51:49.00,0:51:50.46,Default,,0000,0000,0000,,In general, it matters.
Dialogue: 0,0:51:50.46,0:51:53.88,Default,,0000,0000,0000,,
Dialogue: 0,0:51:53.88,0:52:01.70,Default,,0000,0000,0000,,They have to be from a given\Nnumber to a given number.
Dialogue: 0,0:52:01.70,0:52:05.34,Default,,0000,0000,0000,,It's not like reversing--\Nwhen you reverse
Dialogue: 0,0:52:05.34,0:52:08.36,Default,,0000,0000,0000,,the order of integrals,\Nit's usually harder,
Dialogue: 0,0:52:08.36,0:52:11.18,Default,,0000,0000,0000,,because you have to draw\Nthe vertical strips.
Dialogue: 0,0:52:11.18,0:52:12.86,Default,,0000,0000,0000,,And you have it\Nbetween two functions.
Dialogue: 0,0:52:12.86,0:52:16.12,Default,,0000,0000,0000,,And then from vertical strips,\Nyou go to horizontal strips,
Dialogue: 0,0:52:16.12,0:52:17.50,Default,,0000,0000,0000,,and you have other\Ntwo functions.
Dialogue: 0,0:52:17.50,0:52:20.98,Default,,0000,0000,0000,,So you always have to think\Nhow to change the function.
Dialogue: 0,0:52:20.98,0:52:23.82,Default,,0000,0000,0000,,Here, you don't have\Nto think at all.
Dialogue: 0,0:52:23.82,0:52:27.51,Default,,0000,0000,0000,,You have a function\Nthat depends on r only.
Dialogue: 0,0:52:27.51,0:52:29.26,Default,,0000,0000,0000,,There is no theta\Nin the picture.
Dialogue: 0,0:52:29.26,0:52:31.88,Default,,0000,0000,0000,,Plus these two\Nare fixed numbers.
Dialogue: 0,0:52:31.88,0:52:35.04,Default,,0000,0000,0000,,You can reverse the\Nintegration in your sleep.
Dialogue: 0,0:52:35.04,0:52:37.12,Default,,0000,0000,0000,,OK, you get the same thing.
Dialogue: 0,0:52:37.12,0:52:40.08,Default,,0000,0000,0000,,All you have to do is\Nswap these two guys,
Dialogue: 0,0:52:40.08,0:52:42.05,Default,,0000,0000,0000,,and swap-- the 0 is the same.
Dialogue: 0,0:52:42.05,0:52:44.52,Default,,0000,0000,0000,,So I swap these two guys.
Dialogue: 0,0:52:44.52,0:52:48.96,Default,,0000,0000,0000,,STUDENT: How did you\Ntake the 2 pi out?
Dialogue: 0,0:52:48.96,0:52:50.97,Default,,0000,0000,0000,,PROFESSOR: What did I do?
Dialogue: 0,0:52:50.97,0:52:52.81,Default,,0000,0000,0000,,How did I take this out?
Dialogue: 0,0:52:52.81,0:52:55.68,Default,,0000,0000,0000,,STUDENT: No, the 2 pi.
Dialogue: 0,0:52:55.68,0:52:57.04,Default,,0000,0000,0000,,PROFESSOR: Oh, the 2 pi?
Dialogue: 0,0:52:57.04,0:52:57.86,Default,,0000,0000,0000,,OK.
Dialogue: 0,0:52:57.86,0:52:59.95,Default,,0000,0000,0000,,Let me show you it better\Nhere, because we've
Dialogue: 0,0:52:59.95,0:53:03.39,Default,,0000,0000,0000,,discussed about this before.
Dialogue: 0,0:53:03.39,0:53:06.100,Default,,0000,0000,0000,,When you have\Nintegral from a to b,
Dialogue: 0,0:53:06.100,0:53:11.40,Default,,0000,0000,0000,,or integral from c to\Nd of a function or r
Dialogue: 0,0:53:11.40,0:53:18.74,Default,,0000,0000,0000,,and a function of\Ntheta, what do you go?
Dialogue: 0,0:53:18.74,0:53:20.25,Default,,0000,0000,0000,,There is a theorem\Nthat says that--
Dialogue: 0,0:53:20.25,0:53:22.29,Default,,0000,0000,0000,,and thanks for this\Ntheorem and the fact
Dialogue: 0,0:53:22.29,0:53:23.43,Default,,0000,0000,0000,,that they're separable.
Dialogue: 0,0:53:23.43,0:53:26.26,Default,,0000,0000,0000,,The variables are\Nseparated in this product.
Dialogue: 0,0:53:26.26,0:53:31.40,Default,,0000,0000,0000,,This is the product between\Nintegral from a to b,
Dialogue: 0,0:53:31.40,0:53:34.19,Default,,0000,0000,0000,,here of theta to\Ntheta, and integral
Dialogue: 0,0:53:34.19,0:53:38.15,Default,,0000,0000,0000,,from c to d, f of r/dr.\NThey are nothing to one
Dialogue: 0,0:53:38.15,0:53:39.89,Default,,0000,0000,0000,,another but a product.
Dialogue: 0,0:53:39.89,0:53:41.19,Default,,0000,0000,0000,,So what do you do?
Dialogue: 0,0:53:41.19,0:53:46.98,Default,,0000,0000,0000,,You say this is integral\Nof 1, from 0 to pi d theta,
Dialogue: 0,0:53:46.98,0:53:49.08,Default,,0000,0000,0000,,times the other guy.
Dialogue: 0,0:53:49.08,0:53:53.22,Default,,0000,0000,0000,,So this is 2 pi.
Dialogue: 0,0:53:53.22,0:53:57.15,Default,,0000,0000,0000,,When theta doesn't appear\Ninside, it's a blessing.
Dialogue: 0,0:53:57.15,0:53:59.65,Default,,0000,0000,0000,,But if and if there\Nis, I have a question.
Dialogue: 0,0:53:59.65,0:54:00.91,Default,,0000,0000,0000,,What if theta appeared inside?
Dialogue: 0,0:54:00.91,0:54:03.82,Default,,0000,0000,0000,,
Dialogue: 0,0:54:03.82,0:54:06.35,Default,,0000,0000,0000,,Theta doesn't appear\Ninside by himself.
Dialogue: 0,0:54:06.35,0:54:09.31,Default,,0000,0000,0000,,He appears inside\Nof a trig function.
Dialogue: 0,0:54:09.31,0:54:13.84,Default,,0000,0000,0000,,So assume you have cosine\Ntheta here times r.
Dialogue: 0,0:54:13.84,0:54:17.86,Default,,0000,0000,0000,,You would have pulled\Ncosine theta out,
Dialogue: 0,0:54:17.86,0:54:21.00,Default,,0000,0000,0000,,and integrated cosine\Ntheta, that would be easy.
Dialogue: 0,0:54:21.00,0:54:25.95,Default,,0000,0000,0000,,And if you have a problem like\Nthat, you would have gotten 0.
Dialogue: 0,0:54:25.95,0:54:28.58,Default,,0000,0000,0000,,Because integral of\Ncourse of cosine theta
Dialogue: 0,0:54:28.58,0:54:32.96,Default,,0000,0000,0000,,would be sine of theta, and\Nthen theta between 0 and 2
Dialogue: 0,0:54:32.96,0:54:36.94,Default,,0000,0000,0000,,pi is sine of theta between,\Nwhich would give you 0.
Dialogue: 0,0:54:36.94,0:54:40.17,Default,,0000,0000,0000,,It happened to me,\Nmany times in the exam.
Dialogue: 0,0:54:40.17,0:54:40.92,Default,,0000,0000,0000,,It was a blessing.
Dialogue: 0,0:54:40.92,0:54:44.58,Default,,0000,0000,0000,,I was 19, and I was so happy.
Dialogue: 0,0:54:44.58,0:54:48.03,Default,,0000,0000,0000,,Professors wanted to\Nsee only the answer.
Dialogue: 0,0:54:48.03,0:54:52.45,Default,,0000,0000,0000,,Because in Romania,\Nit's different.
Dialogue: 0,0:54:52.45,0:54:55.42,Default,,0000,0000,0000,,You come take a written\Nexam, and the professor
Dialogue: 0,0:54:55.42,0:54:58.31,Default,,0000,0000,0000,,has five hours to grade it.
Dialogue: 0,0:54:58.31,0:55:02.35,Default,,0000,0000,0000,,The same day, two hours later,\Nyou have the oral examination.
Dialogue: 0,0:55:02.35,0:55:04.51,Default,,0000,0000,0000,,You pick up a ticket,\Non the ticket,
Dialogue: 0,0:55:04.51,0:55:07.55,Default,,0000,0000,0000,,you see three things to\Nsolve, four things to solve.
Dialogue: 0,0:55:07.55,0:55:09.12,Default,,0000,0000,0000,,You go take a seat.
Dialogue: 0,0:55:09.12,0:55:12.90,Default,,0000,0000,0000,,And while the professor and\Nthe assistant grade the exam,
Dialogue: 0,0:55:12.90,0:55:16.54,Default,,0000,0000,0000,,you actually think\Nof your oral exam.
Dialogue: 0,0:55:16.54,0:55:20.67,Default,,0000,0000,0000,,When you come and present\Nyour results on the board,
Dialogue: 0,0:55:20.67,0:55:23.25,Default,,0000,0000,0000,,they tell you,\Nyou messed up, you
Dialogue: 0,0:55:23.25,0:55:27.12,Default,,0000,0000,0000,,got a 60% on this sticking exam.
Dialogue: 0,0:55:27.12,0:55:28.30,Default,,0000,0000,0000,,This is how it goes.
Dialogue: 0,0:55:28.30,0:55:32.31,Default,,0000,0000,0000,,Or, on the contrary, hey,\Nlisten, you got a 95%
Dialogue: 0,0:55:32.31,0:55:33.97,Default,,0000,0000,0000,,on the written part, OK?
Dialogue: 0,0:55:33.97,0:55:36.57,Default,,0000,0000,0000,,I don't want to see\Nwhat you have there,
Dialogue: 0,0:55:36.57,0:55:37.97,Default,,0000,0000,0000,,it really looks good.
Dialogue: 0,0:55:37.97,0:55:39.66,Default,,0000,0000,0000,,I don't want to see\Nit, it's clear to me
Dialogue: 0,0:55:39.66,0:55:41.49,Default,,0000,0000,0000,,that you know what you're doing.
Dialogue: 0,0:55:41.49,0:55:44.69,Default,,0000,0000,0000,,So it's a different\Nkind of examination.
Dialogue: 0,0:55:44.69,0:55:47.64,Default,,0000,0000,0000,,I hear that Princeton\Ndoes that, I wonder
Dialogue: 0,0:55:47.64,0:55:49.12,Default,,0000,0000,0000,,how are all the exams here.
Dialogue: 0,0:55:49.12,0:55:51.87,Default,,0000,0000,0000,,I don't think people\Nare ready for them yet.
Dialogue: 0,0:55:51.87,0:55:54.42,Default,,0000,0000,0000,,But at Princeton they\Ndo a lot, all the same.
Dialogue: 0,0:55:54.42,0:55:59.19,Default,,0000,0000,0000,,They make a hat, and take a\N[INAUDIBLE], put tickets in it.
Dialogue: 0,0:55:59.19,0:56:02.10,Default,,0000,0000,0000,,And the teacher comes,\Nand closes his eyes
Dialogue: 0,0:56:02.10,0:56:06.40,Default,,0000,0000,0000,,and picks a ticket,\Nand says oh my god, I
Dialogue: 0,0:56:06.40,0:56:08.01,Default,,0000,0000,0000,,got proof of Fubini's theorem.
Dialogue: 0,0:56:08.01,0:56:11.16,Default,,0000,0000,0000,,And do these three\Ntriple integrals.
Dialogue: 0,0:56:11.16,0:56:15.13,Default,,0000,0000,0000,,This is a type of oral\Nexam that you would have.
Dialogue: 0,0:56:15.13,0:56:18.88,Default,,0000,0000,0000,,But if you know that,\Nbecause you studied,
Dialogue: 0,0:56:18.88,0:56:22.98,Default,,0000,0000,0000,,you're not afraid\Nto present them.
Dialogue: 0,0:56:22.98,0:56:26.24,Default,,0000,0000,0000,,But you have to present them,\Nand you have a limited time.
Dialogue: 0,0:56:26.24,0:56:30.29,Default,,0000,0000,0000,,Because there are other 30\Nstudents in the classroom.
Dialogue: 0,0:56:30.29,0:56:32.04,Default,,0000,0000,0000,,You only have five minutes.
Dialogue: 0,0:56:32.04,0:56:36.58,Default,,0000,0000,0000,,And I only pick-- I want to\Nsee your work on all of them.
Dialogue: 0,0:56:36.58,0:56:37.95,Default,,0000,0000,0000,,And I'll teach\Nyou how to present
Dialogue: 0,0:56:37.95,0:56:39.52,Default,,0000,0000,0000,,on this problem on the board.
Dialogue: 0,0:56:39.52,0:56:42.29,Default,,0000,0000,0000,,And then you have five\Nminutes to present.
Dialogue: 0,0:56:42.29,0:56:46.88,Default,,0000,0000,0000,,If you are really\Nembarrassed and you
Dialogue: 0,0:56:46.88,0:56:50.15,Default,,0000,0000,0000,,don't want to speak in public,\Nthen you have a problem.
Dialogue: 0,0:56:50.15,0:56:53.36,Default,,0000,0000,0000,,I've had many fears--\Nand in other countries--
Dialogue: 0,0:56:53.36,0:56:55.69,Default,,0000,0000,0000,,I heard that in England,\Nthey have the same system.
Dialogue: 0,0:56:55.69,0:56:59.46,Default,,0000,0000,0000,,There are people who are too\Nshy to show their results,
Dialogue: 0,0:56:59.46,0:57:01.56,Default,,0000,0000,0000,,or too shy to talk.
Dialogue: 0,0:57:01.56,0:57:05.37,Default,,0000,0000,0000,,And then they start stuttering.
Dialogue: 0,0:57:05.37,0:57:07.08,Default,,0000,0000,0000,,But they have to do it.
Dialogue: 0,0:57:07.08,0:57:10.14,Default,,0000,0000,0000,,There is no excuse,\Nthey don't care if you
Dialogue: 0,0:57:10.14,0:57:13.45,Default,,0000,0000,0000,,have problems with your speech.
Dialogue: 0,0:57:13.45,0:57:18.59,Default,,0000,0000,0000,,So I asked the people I\Nknew and I went to London,
Dialogue: 0,0:57:18.59,0:57:22.24,Default,,0000,0000,0000,,and they said most people\Nwill stutter in there.
Dialogue: 0,0:57:22.24,0:57:24.13,Default,,0000,0000,0000,,I was so scared.
Dialogue: 0,0:57:24.13,0:57:26.49,Default,,0000,0000,0000,,Most people who stutter\Nin our oral exams
Dialogue: 0,0:57:26.49,0:57:28.90,Default,,0000,0000,0000,,are people who\Nspend too much time
Dialogue: 0,0:57:28.90,0:57:31.84,Default,,0000,0000,0000,,in the pub the previous day.
Dialogue: 0,0:57:31.84,0:57:36.41,Default,,0000,0000,0000,,Pubs were everywhere and I saw\Nlots of students in the pubs.
Dialogue: 0,0:57:36.41,0:57:40.30,Default,,0000,0000,0000,,I went to University of Durham--\Nthis is where Harry Potter was
Dialogue: 0,0:57:40.30,0:57:42.32,Default,,0000,0000,0000,,filmed, by the way.
Dialogue: 0,0:57:42.32,0:57:45.48,Default,,0000,0000,0000,,I saw the castle, which\Nis a student dorm.
Dialogue: 0,0:57:45.48,0:57:47.97,Default,,0000,0000,0000,,You pay something\Nlike 500 pounds.
Dialogue: 0,0:57:47.97,0:57:51.59,Default,,0000,0000,0000,,Which would be like $100?
Dialogue: 0,0:57:51.59,0:57:53.83,Default,,0000,0000,0000,,$1,000?
Dialogue: 0,0:57:53.83,0:58:00.93,Default,,0000,0000,0000,,Less, because I think it's\N7.50, something like $800.
Dialogue: 0,0:58:00.93,0:58:04.28,Default,,0000,0000,0000,,It used to be that the\Npound was double the dollar.
Dialogue: 0,0:58:04.28,0:58:05.11,Default,,0000,0000,0000,,[INTERPOSING VOICES]
Dialogue: 0,0:58:05.11,0:58:10.50,Default,,0000,0000,0000,,
Dialogue: 0,0:58:10.50,0:58:16.38,Default,,0000,0000,0000,,So you could stay in that\Ndorm for $800 per month.
Dialogue: 0,0:58:16.38,0:58:21.06,Default,,0000,0000,0000,,And you've got the same table\Nwhere they ate in the movie.
Dialogue: 0,0:58:21.06,0:58:22.51,Default,,0000,0000,0000,,It was really nice.
Dialogue: 0,0:58:22.51,0:58:26.91,Default,,0000,0000,0000,,But the University of\NDurham is a isolated castle,
Dialogue: 0,0:58:26.91,0:58:29.60,Default,,0000,0000,0000,,the cathedral,\Neverything is very old,
Dialogue: 0,0:58:29.60,0:58:32.17,Default,,0000,0000,0000,,from the 11th\Ncentury, 12th century.
Dialogue: 0,0:58:32.17,0:58:37.23,Default,,0000,0000,0000,,But if you go into the\Ncity, it's full of pubs.
Dialogue: 0,0:58:37.23,0:58:38.92,Default,,0000,0000,0000,,Who is in the pubs?
Dialogue: 0,0:58:38.92,0:58:40.85,Default,,0000,0000,0000,,The calculus students.
Dialogue: 0,0:58:40.85,0:58:43.27,Default,,0000,0000,0000,,This is where they\Ndo their homework.
Dialogue: 0,0:58:43.27,0:58:47.63,Default,,0000,0000,0000,,And it amazes me how\Nthey don't get drunk.
Dialogue: 0,0:58:47.63,0:58:50.28,Default,,0000,0000,0000,,I'm not used to alcohol,\Nbecause I don't drink.
Dialogue: 0,0:58:50.28,0:58:52.03,Default,,0000,0000,0000,,Well they are used to it.
Dialogue: 0,0:58:52.03,0:58:56.53,Default,,0000,0000,0000,,So they may nicely can do\Ntheir homework, beautifully,
Dialogue: 0,0:58:56.53,0:59:01.06,Default,,0000,0000,0000,,next to a big draft\Nof Guinness like that.
Dialogue: 0,0:59:01.06,0:59:04.97,Default,,0000,0000,0000,,And still makes sense when\Nthey write the solution.
Dialogue: 0,0:59:04.97,0:59:07.16,Default,,0000,0000,0000,,They don't miss a minus\Nsign, they're amazing.
Dialogue: 0,0:59:07.16,0:59:10.10,Default,,0000,0000,0000,,
Dialogue: 0,0:59:10.10,0:59:12.99,Default,,0000,0000,0000,,Alright, is this hard?
Dialogue: 0,0:59:12.99,0:59:17.63,Default,,0000,0000,0000,,If you are interested, you\Ncan ask about study abroad.
Dialogue: 0,0:59:17.63,0:59:20.43,Default,,0000,0000,0000,,We don't have big\Nbusiness with England,
Dialogue: 0,0:59:20.43,0:59:22.48,Default,,0000,0000,0000,,but you could go to Seville.
Dialogue: 0,0:59:22.48,0:59:25.96,Default,,0000,0000,0000,,There are some programs\Nin the summer where
Dialogue: 0,0:59:25.96,0:59:29.11,Default,,0000,0000,0000,,one of our professors teaches\Ndifferential equations like I
Dialogue: 0,0:59:29.11,0:59:30.86,Default,,0000,0000,0000,,told you about.
Dialogue: 0,0:59:30.86,0:59:33.59,Default,,0000,0000,0000,,He teaches differential\Nequations this summer
Dialogue: 0,0:59:33.59,0:59:34.34,Default,,0000,0000,0000,,in Seville.
Dialogue: 0,0:59:34.34,0:59:39.52,Default,,0000,0000,0000,,
Dialogue: 0,0:59:39.52,0:59:44.28,Default,,0000,0000,0000,,I think you can still\Nadd in the next two days.
Dialogue: 0,0:59:44.28,0:59:47.39,Default,,0000,0000,0000,,Some of you did,\Nsome of you didn't.
Dialogue: 0,0:59:47.39,0:59:48.87,Default,,0000,0000,0000,,All right.
Dialogue: 0,0:59:48.87,0:59:53.21,Default,,0000,0000,0000,,Any questions about\Nother problems?
Dialogue: 0,0:59:53.21,0:59:57.88,Default,,0000,0000,0000,,I have to apologize,\NI played the game
Dialogue: 0,0:59:57.88,1:00:01.47,Default,,0000,0000,0000,,without telling you the truth.
Dialogue: 0,1:00:01.47,1:00:05.23,Default,,0000,0000,0000,,[INAUDIBLE] he came to\Nme last time and said,
Dialogue: 0,1:00:05.23,1:00:09.08,Default,,0000,0000,0000,,you never showed\Nus this notation.
Dialogue: 0,1:00:09.08,1:00:16.97,Default,,0000,0000,0000,,So what if one gives you x\Nof u, v equals 2x minus y.
Dialogue: 0,1:00:16.97,1:00:22.16,Default,,0000,0000,0000,,y of u, v equals 3x plus y.
Dialogue: 0,1:00:22.16,1:00:24.56,Default,,0000,0000,0000,,What the heck is that?
Dialogue: 0,1:00:24.56,1:00:27.03,Default,,0000,0000,0000,,He didn't say heck, because\Nhe's a gentlemen, right?
Dialogue: 0,1:00:27.03,1:00:35.93,Default,,0000,0000,0000,,But he said this is the\Nnotation used in web work,
Dialogue: 0,1:00:35.93,1:00:40.34,Default,,0000,0000,0000,,and the book is actually not\Nemphasizing it, which is true.
Dialogue: 0,1:00:40.34,1:00:45.65,Default,,0000,0000,0000,,The book is emphasizing the\NJacobian in section 12.8
Dialogue: 0,1:00:45.65,1:00:50.34,Default,,0000,0000,0000,,only, which is not covered,\Nit's not part of the menu.
Dialogue: 0,1:00:50.34,1:00:53.80,Default,,0000,0000,0000,,But the definition, you\Nshould at least know it.
Dialogue: 0,1:00:53.80,1:00:56.57,Default,,0000,0000,0000,,So what would be the\Ndefinition of this animal?
Dialogue: 0,1:00:56.57,1:01:00.64,Default,,0000,0000,0000,,You see that we have to take\Nthe partial derivative of x
Dialogue: 0,1:01:00.64,1:01:04.27,Default,,0000,0000,0000,,with respect to u, the partial\Nderivative of x with respect
Dialogue: 0,1:01:04.27,1:01:08.40,Default,,0000,0000,0000,,to v, the partial derivative\Nof y with respect to u,
Dialogue: 0,1:01:08.40,1:01:10.53,Default,,0000,0000,0000,,and the partial derivative\Nof y with respect to v.
Dialogue: 0,1:01:10.53,1:01:13.66,Default,,0000,0000,0000,,And that's exactly what\Nit is, indeterminate.
Dialogue: 0,1:01:13.66,1:01:15.00,Default,,0000,0000,0000,,Not matrix, but indeterminate.
Dialogue: 0,1:01:15.00,1:01:17.73,Default,,0000,0000,0000,,
Dialogue: 0,1:01:17.73,1:01:20.51,Default,,0000,0000,0000,,So do I bother to write it down?
Dialogue: 0,1:01:20.51,1:01:22.80,Default,,0000,0000,0000,,If I wanted to write\Ndown what it is,
Dialogue: 0,1:01:22.80,1:01:27.45,Default,,0000,0000,0000,,of course I would write\Nit down like that.
Dialogue: 0,1:01:27.45,1:01:31.35,Default,,0000,0000,0000,,I don't want to spend\Nall my time doing that,
Dialogue: 0,1:01:31.35,1:01:34.49,Default,,0000,0000,0000,,because it's such\Nan easy problem.
Dialogue: 0,1:01:34.49,1:01:35.58,Default,,0000,0000,0000,,What do you have to do?
Dialogue: 0,1:01:35.58,1:01:39.68,Default,,0000,0000,0000,,Just compute for such a simple\Ntransformation in plane.
Dialogue: 0,1:01:39.68,1:01:42.37,Default,,0000,0000,0000,,
Dialogue: 0,1:01:42.37,1:01:45.47,Default,,0000,0000,0000,,Actually, if you\Ntook linear-- again,
Dialogue: 0,1:01:45.47,1:01:49.53,Default,,0000,0000,0000,,who is enrolled\Nin linear algebra?
Dialogue: 0,1:01:49.53,1:01:50.54,Default,,0000,0000,0000,,Only 1, 2, 3?
Dialogue: 0,1:01:50.54,1:01:52.49,Default,,0000,0000,0000,,Thought there were only 2.
Dialogue: 0,1:01:52.49,1:01:53.46,Default,,0000,0000,0000,,OK.
Dialogue: 0,1:01:53.46,1:01:58.69,Default,,0000,0000,0000,,In linear algebra, you\Nwrote this differently.
Dialogue: 0,1:01:58.69,1:02:06.14,Default,,0000,0000,0000,,You wrote it like this. x and\Ny equals matrix multiplication.
Dialogue: 0,1:02:06.14,1:02:10.54,Default,,0000,0000,0000,,You have 2, minus\N1, 3, 1, by the way
Dialogue: 0,1:02:10.54,1:02:12.38,Default,,0000,0000,0000,,it's obvious the\Ndeterminate of this matrix
Dialogue: 0,1:02:12.38,1:02:13.64,Default,,0000,0000,0000,,is different from 0.
Dialogue: 0,1:02:13.64,1:02:18.68,Default,,0000,0000,0000,,This is the linear map that you\Nare applying to the vector xy.
Dialogue: 0,1:02:18.68,1:02:25.58,Default,,0000,0000,0000,,And in your algebra book,\Nyou're using Larson, am I right?
Dialogue: 0,1:02:25.58,1:02:28.58,Default,,0000,0000,0000,,
Dialogue: 0,1:02:28.58,1:02:29.64,Default,,0000,0000,0000,,Larson's book?
Dialogue: 0,1:02:29.64,1:02:30.88,Default,,0000,0000,0000,,It's a good book.
Dialogue: 0,1:02:30.88,1:02:35.92,Default,,0000,0000,0000,,So you have a of the vector x.
Dialogue: 0,1:02:35.92,1:02:42.85,Default,,0000,0000,0000,,a of the vector x\Nis the vector v.
Dialogue: 0,1:02:42.85,1:02:46.33,Default,,0000,0000,0000,,When you all get to\Nsee linear algebra,
Dialogue: 0,1:02:46.33,1:02:52.71,Default,,0000,0000,0000,,you'll like it more than Cal\N3, because it's more fun.
Dialogue: 0,1:02:52.71,1:02:55.60,Default,,0000,0000,0000,,So how do you do this\Nmatrix multiplication?
Dialogue: 0,1:02:55.60,1:02:56.22,Default,,0000,0000,0000,,It's very easy.
Dialogue: 0,1:02:56.22,1:02:58.58,Default,,0000,0000,0000,,This time that, minus\Nthis times this.
Dialogue: 0,1:02:58.58,1:03:04.37,Default,,0000,0000,0000,,
Dialogue: 0,1:03:04.37,1:03:07.29,Default,,0000,0000,0000,,So can computers do that?
Dialogue: 0,1:03:07.29,1:03:11.14,Default,,0000,0000,0000,,Yes, computers can, if you\Nhave the right program.
Dialogue: 0,1:03:11.14,1:03:14.17,Default,,0000,0000,0000,,And this is the first\Nprogram I learned in C++.
Dialogue: 0,1:03:14.17,1:03:16.20,Default,,0000,0000,0000,,No, it was the second program.
Dialogue: 0,1:03:16.20,1:03:21.04,Default,,0000,0000,0000,,How to write a little program\Nfor multiplication of two
Dialogue: 0,1:03:21.04,1:03:23.26,Default,,0000,0000,0000,,matrices.
Dialogue: 0,1:03:23.26,1:03:28.15,Default,,0000,0000,0000,,The first program I\Nhad, I learned in C++.
Dialogue: 0,1:03:28.15,1:03:30.96,Default,,0000,0000,0000,,It was to build an ATM machine.
Dialogue: 0,1:03:30.96,1:03:36.92,Default,,0000,0000,0000,,I hated that, because every time\NI went under 0 with my balance,
Dialogue: 0,1:03:36.92,1:03:40.04,Default,,0000,0000,0000,,I would have new word under 0.
Dialogue: 0,1:03:40.04,1:03:43.18,Default,,0000,0000,0000,,So I would have to prepare\Nfor all the possible cases
Dialogue: 0,1:03:43.18,1:03:44.64,Default,,0000,0000,0000,,and save.
Dialogue: 0,1:03:44.64,1:03:47.69,Default,,0000,0000,0000,,If you don't have\Nenough money, whatever.
Dialogue: 0,1:03:47.69,1:03:51.62,Default,,0000,0000,0000,,So that was the first\Nprogram we wrote.
Dialogue: 0,1:03:51.62,1:03:54.98,Default,,0000,0000,0000,,OK so, what do we have?
Dialogue: 0,1:03:54.98,1:04:01.70,Default,,0000,0000,0000,,2 minus 1, 3 and 1.
Dialogue: 0,1:04:01.70,1:04:03.67,Default,,0000,0000,0000,,What is the Jacobian\Nin this case?
Dialogue: 0,1:04:03.67,1:04:05.98,Default,,0000,0000,0000,,It's 2 plus 3, 5.
Dialogue: 0,1:04:05.98,1:04:07.42,Default,,0000,0000,0000,,Different from 0.
Dialogue: 0,1:04:07.42,1:04:10.78,Default,,0000,0000,0000,,
Dialogue: 0,1:04:10.78,1:04:14.17,Default,,0000,0000,0000,,You have one or two\Nproblems like that.
Dialogue: 0,1:04:14.17,1:04:14.79,Default,,0000,0000,0000,,Three problems.
Dialogue: 0,1:04:14.79,1:04:16.69,Default,,0000,0000,0000,,I was really mean.
Dialogue: 0,1:04:16.69,1:04:17.62,Default,,0000,0000,0000,,I apologize.
Dialogue: 0,1:04:17.62,1:04:19.70,Default,,0000,0000,0000,,But you still have time\Nto do those problems
Dialogue: 0,1:04:19.70,1:04:21.31,Default,,0000,0000,0000,,in case of the review.
Dialogue: 0,1:04:21.31,1:04:24.29,Default,,0000,0000,0000,,STUDENT: So we just take\Nthe determinate of it?
Dialogue: 0,1:04:24.29,1:04:28.41,Default,,0000,0000,0000,,PROFESSOR: And you take the\Ndeterminate of the matrix.
Dialogue: 0,1:04:28.41,1:04:30.25,Default,,0000,0000,0000,,And that's you Jacobian.
Dialogue: 0,1:04:30.25,1:04:31.58,Default,,0000,0000,0000,,STUDENT: What number is that?
Dialogue: 0,1:04:31.58,1:04:34.64,Default,,0000,0000,0000,,PROFESSOR: I don't remember.
Dialogue: 0,1:04:34.64,1:04:37.00,Default,,0000,0000,0000,,STUDENT: What if\Nit's the u and the v
Dialogue: 0,1:04:37.00,1:04:41.50,Default,,0000,0000,0000,,is at the top and x and\Nthe y at the bottom?
Dialogue: 0,1:04:41.50,1:04:43.46,Default,,0000,0000,0000,,PROFESSOR: So the\Ndeterminate will be the same.
Dialogue: 0,1:04:43.46,1:04:45.68,Default,,0000,0000,0000,,This is a very good question.
Dialogue: 0,1:04:45.68,1:04:46.99,Default,,0000,0000,0000,,Are you guys with me?
Dialogue: 0,1:04:46.99,1:04:51.53,Default,,0000,0000,0000,,So he said, what if you have\Nyour first equation's name
Dialogue: 0,1:04:51.53,1:04:53.02,Default,,0000,0000,0000,,would be this one.
Dialogue: 0,1:04:53.02,1:04:59.24,Default,,0000,0000,0000,,And you have your equations\Nwritten like that.
Dialogue: 0,1:04:59.24,1:05:01.16,Default,,0000,0000,0000,,Right?
Dialogue: 0,1:05:01.16,1:05:06.10,Default,,0000,0000,0000,,And so, when you\Nlook at this, you
Dialogue: 0,1:05:06.10,1:05:11.81,Default,,0000,0000,0000,,will go-- it depends how you--\Nin which order you do that.
Dialogue: 0,1:05:11.81,1:05:19.20,Default,,0000,0000,0000,,I wrote u, v. Sorry.
Dialogue: 0,1:05:19.20,1:05:24.04,Default,,0000,0000,0000,,u and v, but you\Nunderstood what I meant.
Dialogue: 0,1:05:24.04,1:05:24.76,Default,,0000,0000,0000,,Right?
Dialogue: 0,1:05:24.76,1:05:26.42,Default,,0000,0000,0000,,u and v.
Dialogue: 0,1:05:26.42,1:05:28.68,Default,,0000,0000,0000,,STUDENT: Can you\Ndo number three?
Dialogue: 0,1:05:28.68,1:05:30.03,Default,,0000,0000,0000,,It was a hard one.
Dialogue: 0,1:05:30.03,1:05:31.40,Default,,0000,0000,0000,,PROFESSOR: I will,\Njust a second.
Dialogue: 0,1:05:31.40,1:05:38.27,Default,,0000,0000,0000,,So d y, x with respect to u,\Nv. What would happen, I just I
Dialogue: 0,1:05:38.27,1:05:40.74,Default,,0000,0000,0000,,would flip the x and y.
Dialogue: 0,1:05:40.74,1:05:41.75,Default,,0000,0000,0000,,What will happen?
Dialogue: 0,1:05:41.75,1:05:46.77,Default,,0000,0000,0000,,I get 3, 1, it's still\Nthe same function.
Dialogue: 0,1:05:46.77,1:05:49.11,Default,,0000,0000,0000,,2, and minus 1.
Dialogue: 0,1:05:49.11,1:05:51.80,Default,,0000,0000,0000,,Why do I get minus 5?
Dialogue: 0,1:05:51.80,1:05:58.94,Default,,0000,0000,0000,,
Dialogue: 0,1:05:58.94,1:06:03.07,Default,,0000,0000,0000,,So imagine guys, what happens\Nwhen you have x and y?
Dialogue: 0,1:06:03.07,1:06:06.91,Default,,0000,0000,0000,,If you rotate, you don't\Nchange the sign of your matrix,
Dialogue: 0,1:06:06.91,1:06:07.52,Default,,0000,0000,0000,,or notation.
Dialogue: 0,1:06:07.52,1:06:11.74,Default,,0000,0000,0000,,Matrix notation will\Nalways have [INAUDIBLE].
Dialogue: 0,1:06:11.74,1:06:16.76,Default,,0000,0000,0000,,But if you flip it,\Nif you swap x and y,
Dialogue: 0,1:06:16.76,1:06:22.12,Default,,0000,0000,0000,,you are actually changing\Nthe sign of the Jacobian,
Dialogue: 0,1:06:22.12,1:06:24.45,Default,,0000,0000,0000,,the sign of the matrix.
Dialogue: 0,1:06:24.45,1:06:28.16,Default,,0000,0000,0000,,You are changing\Nyour orientation.
Dialogue: 0,1:06:28.16,1:06:31.17,Default,,0000,0000,0000,,That would be a\Nhypothetical situation.
Dialogue: 0,1:06:31.17,1:06:33.45,Default,,0000,0000,0000,,You are changing\Nyour orientation.
Dialogue: 0,1:06:33.45,1:06:37.03,Default,,0000,0000,0000,,Do you have a number, Ryan?
Dialogue: 0,1:06:37.03,1:06:38.00,Default,,0000,0000,0000,,Is it hard?
Dialogue: 0,1:06:38.00,1:06:39.26,Default,,0000,0000,0000,,Why is it hard?
Dialogue: 0,1:06:39.26,1:06:43.16,Default,,0000,0000,0000,,
Dialogue: 0,1:06:43.16,1:06:45.60,Default,,0000,0000,0000,,Yeah, let me do that.
Dialogue: 0,1:06:45.60,1:06:55.36,Default,,0000,0000,0000,,
Dialogue: 0,1:06:55.36,1:06:56.47,Default,,0000,0000,0000,,It's hard enough.
Dialogue: 0,1:06:56.47,1:06:59.94,Default,,0000,0000,0000,,
Dialogue: 0,1:06:59.94,1:07:00.93,Default,,0000,0000,0000,,It's computation.
Dialogue: 0,1:07:00.93,1:07:26.23,Default,,0000,0000,0000,,
Dialogue: 0,1:07:26.23,1:07:27.43,Default,,0000,0000,0000,,Were you able to do it?
Dialogue: 0,1:07:27.43,1:07:32.24,Default,,0000,0000,0000,,
Dialogue: 0,1:07:32.24,1:07:33.76,Default,,0000,0000,0000,,Not yet, right?
Dialogue: 0,1:07:33.76,1:07:40.35,Default,,0000,0000,0000,,So this is x, not-- OK.
Dialogue: 0,1:07:40.35,1:07:46.79,Default,,0000,0000,0000,,So you can write this also,\Ndifferently, except the y sub
Dialogue: 0,1:07:46.79,1:07:52.11,Default,,0000,0000,0000,,u, y sub v. Who\Ncan tell me-- there
Dialogue: 0,1:07:52.11,1:07:55.96,Default,,0000,0000,0000,,are ways to do it\Nin a simpler way.
Dialogue: 0,1:07:55.96,1:07:58.80,Default,,0000,0000,0000,,But I don't want to tell\Nyou yet what that way is.
Dialogue: 0,1:07:58.80,1:08:01.25,Default,,0000,0000,0000,,And I'll show you next time.
Dialogue: 0,1:08:01.25,1:08:02.67,Default,,0000,0000,0000,,What is x sub u?
Dialogue: 0,1:08:02.67,1:08:06.40,Default,,0000,0000,0000,,
Dialogue: 0,1:08:06.40,1:08:10.81,Default,,0000,0000,0000,,It shouldn't be so hard\Nbecause it's the quotient rule.
Dialogue: 0,1:08:10.81,1:08:15.74,Default,,0000,0000,0000,,You have 4 times u squared\Nplus v squared minus
Dialogue: 0,1:08:15.74,1:08:24.68,Default,,0000,0000,0000,,[INAUDIBLE] minus 2u the\Nderivative of this times 4u
Dialogue: 0,1:08:24.68,1:08:29.53,Default,,0000,0000,0000,,divided by the square of that.
Dialogue: 0,1:08:29.53,1:08:34.03,Default,,0000,0000,0000,,Did I go too fast?
Dialogue: 0,1:08:34.03,1:08:38.76,Default,,0000,0000,0000,,So what you have is 4u\Nsquared minus 8u squared
Dialogue: 0,1:08:38.76,1:08:45.73,Default,,0000,0000,0000,,equals minus 4u squared plus\N4v squared divided by that.
Dialogue: 0,1:08:45.73,1:08:54.10,Default,,0000,0000,0000,,
Dialogue: 0,1:08:54.10,1:08:54.82,Default,,0000,0000,0000,,v squared.
Dialogue: 0,1:08:54.82,1:08:55.54,Default,,0000,0000,0000,,Squared, sorry.
Dialogue: 0,1:08:55.54,1:08:58.15,Default,,0000,0000,0000,,
Dialogue: 0,1:08:58.15,1:09:01.56,Default,,0000,0000,0000,,x of v, that should be easier.
Dialogue: 0,1:09:01.56,1:09:02.78,Default,,0000,0000,0000,,Why is it easy?
Dialogue: 0,1:09:02.78,1:09:13.61,Default,,0000,0000,0000,,The first guy prime\Nminus the second guy
Dialogue: 0,1:09:13.61,1:09:15.95,Default,,0000,0000,0000,,So the first primes,\Nsecond not prime.
Dialogue: 0,1:09:15.95,1:09:20.89,Default,,0000,0000,0000,,Minus second prime, straight to\Nv, times the first not prime.
Dialogue: 0,1:09:20.89,1:09:25.39,Default,,0000,0000,0000,,
Dialogue: 0,1:09:25.39,1:09:29.39,Default,,0000,0000,0000,,Divided by u squared.
Dialogue: 0,1:09:29.39,1:09:34.89,Default,,0000,0000,0000,,Which is minus 8uv over that.
Dialogue: 0,1:09:34.89,1:09:41.19,Default,,0000,0000,0000,,Is this one of those that you\Nsaid you couldn't do it yet?
Dialogue: 0,1:09:41.19,1:09:41.69,Default,,0000,0000,0000,,You?
Dialogue: 0,1:09:41.69,1:09:43.28,Default,,0000,0000,0000,,Both?
Dialogue: 0,1:09:43.28,1:09:44.18,Default,,0000,0000,0000,,You did this one?
Dialogue: 0,1:09:44.18,1:09:47.77,Default,,0000,0000,0000,,You got the right answer, good.
Dialogue: 0,1:09:47.77,1:10:01.90,Default,,0000,0000,0000,,y sub v. Y sub u, it's OK\Nto have a minus 0 times
Dialogue: 0,1:10:01.90,1:10:04.70,Default,,0000,0000,0000,,the second one.
Dialogue: 0,1:10:04.70,1:10:13.63,Default,,0000,0000,0000,,Minus this prime with\Nrespect to u, times
Dialogue: 0,1:10:13.63,1:10:21.87,Default,,0000,0000,0000,,6v over the square of that.
Dialogue: 0,1:10:21.87,1:10:30.11,Default,,0000,0000,0000,,And finally, y sub v\Nequals minus the derivative
Dialogue: 0,1:10:30.11,1:10:34.66,Default,,0000,0000,0000,,of the top, with respect to\N6v times u squared plus v
Dialogue: 0,1:10:34.66,1:10:38.59,Default,,0000,0000,0000,,squared minus the derivative\Nof the bottom with respect
Dialogue: 0,1:10:38.59,1:10:51.75,Default,,0000,0000,0000,,to v. v times 6v divided\Nby the whole shebang.
Dialogue: 0,1:10:51.75,1:10:53.26,Default,,0000,0000,0000,,Now is it simplified?
Dialogue: 0,1:10:53.26,1:10:55.65,Default,,0000,0000,0000,,No, I will simplify in a second.
Dialogue: 0,1:10:55.65,1:10:59.48,Default,,0000,0000,0000,,You get minus 12uv.
Dialogue: 0,1:10:59.48,1:11:03.28,Default,,0000,0000,0000,,I'm not going to finish\Nit, but we are almost done.
Dialogue: 0,1:11:03.28,1:11:04.43,Default,,0000,0000,0000,,Why are we almost done?
Dialogue: 0,1:11:04.43,1:11:06.47,Default,,0000,0000,0000,,This is very easy.
Dialogue: 0,1:11:06.47,1:11:09.22,Default,,0000,0000,0000,,I mean, not very\Neasy, but doable.
Dialogue: 0,1:11:09.22,1:11:10.83,Default,,0000,0000,0000,,How about this guy?
Dialogue: 0,1:11:10.83,1:11:13.04,Default,,0000,0000,0000,,What do you get?
Dialogue: 0,1:11:13.04,1:11:17.73,Default,,0000,0000,0000,,A 6u squared, a 6v squared,\Na minus 12v squared.
Dialogue: 0,1:11:17.73,1:11:19.47,Default,,0000,0000,0000,,It's not that bad.
Dialogue: 0,1:11:19.47,1:11:24.56,Default,,0000,0000,0000,,So you have 6u squared\Nminus 6v squared,
Dialogue: 0,1:11:24.56,1:11:27.48,Default,,0000,0000,0000,,over u squared plus v squared.
Dialogue: 0,1:11:27.48,1:11:32.34,Default,,0000,0000,0000,,
Dialogue: 0,1:11:32.34,1:11:33.79,Default,,0000,0000,0000,,What did I do?
Dialogue: 0,1:11:33.79,1:11:37.69,Default,,0000,0000,0000,,
Dialogue: 0,1:11:37.69,1:11:39.26,Default,,0000,0000,0000,,Add a minus in front.
Dialogue: 0,1:11:39.26,1:11:40.94,Default,,0000,0000,0000,,I didn't copy.
Dialogue: 0,1:11:40.94,1:11:43.49,Default,,0000,0000,0000,,Let me make room\Nfor that, thank you.
Dialogue: 0,1:11:43.49,1:11:45.93,Default,,0000,0000,0000,,STUDENT: It's also the 12.
Dialogue: 0,1:11:45.93,1:11:49.84,Default,,0000,0000,0000,,It's 12uv, because there's\Na negative in front of it.
Dialogue: 0,1:11:49.84,1:11:52.30,Default,,0000,0000,0000,,It's minus times minus.
Dialogue: 0,1:11:52.30,1:11:53.10,Default,,0000,0000,0000,,PROFESSOR: Here?
Dialogue: 0,1:11:53.10,1:11:54.24,Default,,0000,0000,0000,,STUDENT: No, y sub u.
Dialogue: 0,1:11:54.24,1:11:55.31,Default,,0000,0000,0000,,The third one.
Dialogue: 0,1:11:55.31,1:11:57.99,Default,,0000,0000,0000,,PROFESSOR: Minus, minus,\Nplus, that's good.
Dialogue: 0,1:11:57.99,1:12:00.11,Default,,0000,0000,0000,,Thanks for observing things.
Dialogue: 0,1:12:00.11,1:12:03.15,Default,,0000,0000,0000,,Anything else that's fishy?
Dialogue: 0,1:12:03.15,1:12:04.12,Default,,0000,0000,0000,,Minus, minus, plus.
Dialogue: 0,1:12:04.12,1:12:06.63,Default,,0000,0000,0000,,
Dialogue: 0,1:12:06.63,1:12:07.60,Default,,0000,0000,0000,,OK that's better.
Dialogue: 0,1:12:07.60,1:12:09.11,Default,,0000,0000,0000,,Change the signs.
Dialogue: 0,1:12:09.11,1:12:13.85,Default,,0000,0000,0000,,When I move onto this one,\Nremind me to change the signs.
Dialogue: 0,1:12:13.85,1:12:15.01,Default,,0000,0000,0000,,So what is the Jacobian?
Dialogue: 0,1:12:15.01,1:12:18.12,Default,,0000,0000,0000,,I'm too lazy to\Nwrite this thing.
Dialogue: 0,1:12:18.12,1:12:21.62,Default,,0000,0000,0000,,I'm going to have-- so, x sub u.
Dialogue: 0,1:12:21.62,1:12:25.52,Default,,0000,0000,0000,,
Dialogue: 0,1:12:25.52,1:12:32.12,Default,,0000,0000,0000,,4 times v squared\Nminus u squared.
Dialogue: 0,1:12:32.12,1:12:37.14,Default,,0000,0000,0000,,Let's me count the OK.
Dialogue: 0,1:12:37.14,1:12:39.01,Default,,0000,0000,0000,,Let's do it over a.
Dialogue: 0,1:12:39.01,1:12:42.09,Default,,0000,0000,0000,,
Dialogue: 0,1:12:42.09,1:12:43.78,Default,,0000,0000,0000,,I'll show you what happens.
Dialogue: 0,1:12:43.78,1:12:45.67,Default,,0000,0000,0000,,Maybe you don't know\Nyet what happens,
Dialogue: 0,1:12:45.67,1:12:49.13,Default,,0000,0000,0000,,but I'll show you what happens.
Dialogue: 0,1:12:49.13,1:12:58.19,Default,,0000,0000,0000,,Then the next one is going to\Nbe x sub v minus 8, uv over a.
Dialogue: 0,1:12:58.19,1:13:04.83,Default,,0000,0000,0000,,y sub u, 12.
Dialogue: 0,1:13:04.83,1:13:12.72,Default,,0000,0000,0000,,uv over a, and last,\Nwith your help.
Dialogue: 0,1:13:12.72,1:13:18.38,Default,,0000,0000,0000,,It's plus this was\Nmy-- so 6 times v
Dialogue: 0,1:13:18.38,1:13:21.26,Default,,0000,0000,0000,,squared minus u squared over a.
Dialogue: 0,1:13:21.26,1:13:24.15,Default,,0000,0000,0000,,
Dialogue: 0,1:13:24.15,1:13:26.41,Default,,0000,0000,0000,,OK OK, let me erase.
Dialogue: 0,1:13:26.41,1:13:30.14,Default,,0000,0000,0000,,
Dialogue: 0,1:13:30.14,1:13:32.67,Default,,0000,0000,0000,,So you guys know\Nwhat happens when
Dialogue: 0,1:13:32.67,1:13:35.77,Default,,0000,0000,0000,,you have something like that?
Dialogue: 0,1:13:35.77,1:13:40.94,Default,,0000,0000,0000,,A determinate has one\Nline multiplied or column
Dialogue: 0,1:13:40.94,1:13:43.22,Default,,0000,0000,0000,,multiplied by a number.
Dialogue: 0,1:13:43.22,1:13:50.22,Default,,0000,0000,0000,,If you have alpha a,\Nalpha b, alpha c and d.
Dialogue: 0,1:13:50.22,1:13:55.23,Default,,0000,0000,0000,,The determinate of that\Nis alpha aut, a, b, c, d.
Dialogue: 0,1:13:55.23,1:13:56.90,Default,,0000,0000,0000,,I assume you know\Nthis from high school,
Dialogue: 0,1:13:56.90,1:14:00.37,Default,,0000,0000,0000,,but I know very well\Nthat many of you don't.
Dialogue: 0,1:14:00.37,1:14:02.12,Default,,0000,0000,0000,,How do you prove this?
Dialogue: 0,1:14:02.12,1:14:02.90,Default,,0000,0000,0000,,Very easily.
Dialogue: 0,1:14:02.90,1:14:05.91,Default,,0000,0000,0000,,This times that would be\Nan alpha out, minus this,
Dialogue: 0,1:14:05.91,1:14:07.75,Default,,0000,0000,0000,,and alpha out.
Dialogue: 0,1:14:07.75,1:14:10.55,Default,,0000,0000,0000,,It's very easy to prove.
Dialogue: 0,1:14:10.55,1:14:16.58,Default,,0000,0000,0000,,So when you have one line or one\Ncolumn multiplied by an alpha,
Dialogue: 0,1:14:16.58,1:14:19.17,Default,,0000,0000,0000,,that alpha gets out.
Dialogue: 0,1:14:19.17,1:14:23.46,Default,,0000,0000,0000,,So if you have two lines\Nmultiplied by an alpha,
Dialogue: 0,1:14:23.46,1:14:27.93,Default,,0000,0000,0000,,or two rows, alpha\Nsquared, excellent.
Dialogue: 0,1:14:27.93,1:14:29.26,Default,,0000,0000,0000,,So who gets out?
Dialogue: 0,1:14:29.26,1:14:37.33,Default,,0000,0000,0000,,1 over a squared, which\Nmeans this guy to the fourth.
Dialogue: 0,1:14:37.33,1:14:39.58,Default,,0000,0000,0000,,Sorry that this is so long.
Dialogue: 0,1:14:39.58,1:14:43.44,Default,,0000,0000,0000,,I don't like this problem,\Nbecause of this computation
Dialogue: 0,1:14:43.44,1:14:45.26,Default,,0000,0000,0000,,you have to go through here.
Dialogue: 0,1:14:45.26,1:14:51.68,Default,,0000,0000,0000,,
Dialogue: 0,1:14:51.68,1:14:56.71,Default,,0000,0000,0000,,So I would simplify\Nit as much as I could.
Dialogue: 0,1:14:56.71,1:15:02.31,Default,,0000,0000,0000,,Let's see, before I\Nmissed my a group.
Dialogue: 0,1:15:02.31,1:15:12.16,Default,,0000,0000,0000,,So you have 24 times v squared\Nminus u squared, plus 96,
Dialogue: 0,1:15:12.16,1:15:14.04,Default,,0000,0000,0000,,am I right?
Dialogue: 0,1:15:14.04,1:15:18.91,Default,,0000,0000,0000,,v squared divided by all\Nthis ugly guy which I hate,
Dialogue: 0,1:15:18.91,1:15:19.58,Default,,0000,0000,0000,,to the fourth.
Dialogue: 0,1:15:19.58,1:15:22.67,Default,,0000,0000,0000,,
Dialogue: 0,1:15:22.67,1:15:27.16,Default,,0000,0000,0000,,Fortunately, everybody's\Na multiple of 24.
Dialogue: 0,1:15:27.16,1:15:30.57,Default,,0000,0000,0000,,So we can pull a 24 out.
Dialogue: 0,1:15:30.57,1:15:35.10,Default,,0000,0000,0000,,and get it out of our life,\Nbecause it drives us crazy.
Dialogue: 0,1:15:35.10,1:15:39.69,Default,,0000,0000,0000,,And then you have v to the\Nfourth plus u to the 4,
Dialogue: 0,1:15:39.69,1:15:40.19,Default,,0000,0000,0000,,minus twice.
Dialogue: 0,1:15:40.19,1:15:42.18,Default,,0000,0000,0000,,Was that the binomial format?
Dialogue: 0,1:15:42.18,1:15:45.33,Default,,0000,0000,0000,,Minus 2 us squared, v squared.
Dialogue: 0,1:15:45.33,1:15:48.03,Default,,0000,0000,0000,,What was left when\NI pull this out?
Dialogue: 0,1:15:48.03,1:15:51.87,Default,,0000,0000,0000,,
Dialogue: 0,1:15:51.87,1:15:55.97,Default,,0000,0000,0000,,I pulled 24 out, 96 is what?
Dialogue: 0,1:15:55.97,1:15:56.47,Default,,0000,0000,0000,,4.
Dialogue: 0,1:15:56.47,1:16:01.95,Default,,0000,0000,0000,,So I have a 4 left.
Dialogue: 0,1:16:01.95,1:16:04.38,Default,,0000,0000,0000,,So I would put that down.
Dialogue: 0,1:16:04.38,1:16:09.07,Default,,0000,0000,0000,,4u squared, v squared over\Nthe-- it looks symmetric
Dialogue: 0,1:16:09.07,1:16:11.42,Default,,0000,0000,0000,,but-- that's OK.
Dialogue: 0,1:16:11.42,1:16:13.84,Default,,0000,0000,0000,,It's not so bad.
Dialogue: 0,1:16:13.84,1:16:15.30,Default,,0000,0000,0000,,So can you write this better?
Dialogue: 0,1:16:15.30,1:16:17.72,Default,,0000,0000,0000,,Look at it.
Dialogue: 0,1:16:17.72,1:16:19.66,Default,,0000,0000,0000,,Do you like it?
Dialogue: 0,1:16:19.66,1:16:22.09,Default,,0000,0000,0000,,There is a 3.
Dialogue: 0,1:16:22.09,1:16:26.82,Default,,0000,0000,0000,,The 4 the 2, 4\Nminus 2 is a plus 2.
Dialogue: 0,1:16:26.82,1:16:30.24,Default,,0000,0000,0000,,Just like when we did those\Ntricky things in high school.
Dialogue: 0,1:16:30.24,1:16:33.37,Default,,0000,0000,0000,,That would be, again,\Nthe binomial formula.
Dialogue: 0,1:16:33.37,1:16:35.15,Default,,0000,0000,0000,,u squared plus v squared.
Dialogue: 0,1:16:35.15,1:16:38.83,Default,,0000,0000,0000,,
Dialogue: 0,1:16:38.83,1:16:40.63,Default,,0000,0000,0000,,Are you guys with me?
Dialogue: 0,1:16:40.63,1:16:44.19,Default,,0000,0000,0000,,Because minus 2\Nplus 4 is plus 2.
Dialogue: 0,1:16:44.19,1:16:47.21,Default,,0000,0000,0000,,This is exactly the\Nsame thing as that.
Dialogue: 0,1:16:47.21,1:16:51.45,Default,,0000,0000,0000,,Over u squared plus v\Nsquared to the fourth.
Dialogue: 0,1:16:51.45,1:16:53.17,Default,,0000,0000,0000,,If you have problems\Ncomputing that,
Dialogue: 0,1:16:53.17,1:16:56.40,Default,,0000,0000,0000,,send me some emails from\NWebWork, because I'm
Dialogue: 0,1:16:56.40,1:16:59.40,Default,,0000,0000,0000,,going to help you do that, OK.
Dialogue: 0,1:16:59.40,1:17:03.14,Default,,0000,0000,0000,,24 divided by what?
Dialogue: 0,1:17:03.14,1:17:04.80,Default,,0000,0000,0000,,Yes?
Dialogue: 0,1:17:04.80,1:17:09.98,Default,,0000,0000,0000,,u squared plus v\Nsquared squared.
Dialogue: 0,1:17:09.98,1:17:12.67,Default,,0000,0000,0000,,Oh my god.
Dialogue: 0,1:17:12.67,1:17:13.30,Default,,0000,0000,0000,,All right.
Dialogue: 0,1:17:13.30,1:17:17.30,Default,,0000,0000,0000,,So, I'm not going to\Nthink lesser of you
Dialogue: 0,1:17:17.30,1:17:20.92,Default,,0000,0000,0000,,if you don't put\Nall of this here.
Dialogue: 0,1:17:20.92,1:17:25.77,Default,,0000,0000,0000,,Therefore, if you\Nget in trouble,
Dialogue: 0,1:17:25.77,1:17:30.76,Default,,0000,0000,0000,,click from the expression from\Nthe whatever you got, and say,
Dialogue: 0,1:17:30.76,1:17:33.89,Default,,0000,0000,0000,,this horrible problem gives\Nme a headache, help me.
Dialogue: 0,1:17:33.89,1:17:37.72,Default,,0000,0000,0000,,And I'm going to help you with\Nthat simple computation that
Dialogue: 0,1:17:37.72,1:17:39.68,Default,,0000,0000,0000,,is just algebra.
Dialogue: 0,1:17:39.68,1:17:42.84,Default,,0000,0000,0000,,That's not going to teach you\Nanything more about Cal 3.
Dialogue: 0,1:17:42.84,1:17:44.25,Default,,0000,0000,0000,,That's why I'm\Ngoing to help you.
Dialogue: 0,1:17:44.25,1:17:47.04,Default,,0000,0000,0000,,I'll help you with\Nthe answers on those.
Dialogue: 0,1:17:47.04,1:17:50.16,Default,,0000,0000,0000,,Just send me an email.
Dialogue: 0,1:17:50.16,1:17:57.21,Default,,0000,0000,0000,,I'm planning on still\Nreviewing even on Tuesday.
Dialogue: 0,1:17:57.21,1:18:00.08,Default,,0000,0000,0000,,I don't want to teach anything\Nnew, because I'm tired
Dialogue: 0,1:18:00.08,1:18:01.60,Default,,0000,0000,0000,,and-- I'm just kidding.
Dialogue: 0,1:18:01.60,1:18:05.02,Default,,0000,0000,0000,,I don't want to teach\Nanything new on Tuesday,
Dialogue: 0,1:18:05.02,1:18:09.55,Default,,0000,0000,0000,,because I want you to be very\Nwell prepared for the midterms.
Dialogue: 0,1:18:09.55,1:18:12.58,Default,,0000,0000,0000,,So I'll do a general\Nreview again,
Dialogue: 0,1:18:12.58,1:18:15.53,Default,,0000,0000,0000,,and I'll go over some\Nhomework like problems,
Dialogue: 0,1:18:15.53,1:18:20.64,Default,,0000,0000,0000,,but mostly over\Nexam like problems.
Dialogue: 0,1:18:20.64,1:18:26.39,Default,,0000,0000,0000,,So I want everybody to succeed,\Nto get very high scores.
Dialogue: 0,1:18:26.39,1:18:28.68,Default,,0000,0000,0000,,But we need to practice,\Npractice, practice.
Dialogue: 0,1:18:28.68,1:18:30.91,Default,,0000,0000,0000,,It's like you did\Nbefore your SATs.
Dialogue: 0,1:18:30.91,1:18:34.38,Default,,0000,0000,0000,,
Dialogue: 0,1:18:34.38,1:18:39.78,Default,,0000,0000,0000,,It's not that much, I mean what\Nhappens if you don't do great
Dialogue: 0,1:18:39.78,1:18:40.41,Default,,0000,0000,0000,,on the midterm?
Dialogue: 0,1:18:40.41,1:18:47.06,Default,,0000,0000,0000,,Well the midterms is\Na portion the final.
Dialogue: 0,1:18:47.06,1:18:50.07,Default,,0000,0000,0000,,But what I am trying\Nto do by reviewing
Dialogue: 0,1:18:50.07,1:18:52.77,Default,,0000,0000,0000,,so much for the\Nmidterm is also trying
Dialogue: 0,1:18:52.77,1:18:54.53,Default,,0000,0000,0000,,to help you for the final.
Dialogue: 0,1:18:54.53,1:18:57.28,Default,,0000,0000,0000,,Because on the final,\Nhalf of the problems
Dialogue: 0,1:18:57.28,1:19:00.19,Default,,0000,0000,0000,,will be just like the ones\Non the midterm Emphasizing
Dialogue: 0,1:19:00.19,1:19:02.92,Default,,0000,0000,0000,,the same type of concepts.
Dialogue: 0,1:19:02.92,1:19:05.62,Default,,0000,0000,0000,,It's good practice\Nfor the final as well.
Dialogue: 0,1:19:05.62,1:19:06.52,Default,,0000,0000,0000,,All right, good luck.
Dialogue: 0,1:19:06.52,1:19:08.62,Default,,0000,0000,0000,,I'll see you Tuesday.
Dialogue: 0,1:19:08.62,1:19:12.87,Default,,0000,0000,0000,,Let me know by email how\Nit goes with the problems.
Dialogue: 0,1:19:12.87,1:19:18.79,Default,,0000,0000,0000,,