1 00:00:00,000 --> 00:00:08,460 2 00:00:08,460 --> 00:00:11,690 PROFESSOR: Hi, I'm Gilbert Strang, and I'm a math 3 00:00:11,690 --> 00:00:13,710 professor at MIT. 4 00:00:13,710 --> 00:00:18,745 And I hope these highlights of calculus will be helpful. 5 00:00:18,745 --> 00:00:21,300 6 00:00:21,300 --> 00:00:26,290 I started the project this year, because the linear 7 00:00:26,290 --> 00:00:32,490 algebra lectures which were in class have been watched by a 8 00:00:32,490 --> 00:00:35,130 lot of people on OpenCourseWare. 9 00:00:35,130 --> 00:00:42,330 And so I looked at what there was for calculus. 10 00:00:42,330 --> 00:00:47,230 And I saw two or three types of things. 11 00:00:47,230 --> 00:00:53,885 One was lectures, sort of very serious, too mathy. 12 00:00:53,885 --> 00:00:56,630 13 00:00:56,630 --> 00:01:05,720 And another was supported by foundations, an effort to make 14 00:01:05,720 --> 00:01:10,410 math look so terrifically exciting and wonderful and 15 00:01:10,410 --> 00:01:12,690 connect with everything. 16 00:01:12,690 --> 00:01:17,150 And yet, I feel a lot of people are taking math 17 00:01:17,150 --> 00:01:23,730 courses, calculus, in high school, in college, and simply 18 00:01:23,730 --> 00:01:27,470 want a little help to see what's the main point. 19 00:01:27,470 --> 00:01:30,850 And maybe that's the idea of these lectures, is to try to 20 00:01:30,850 --> 00:01:36,170 tell you the main point without all the heavy things 21 00:01:36,170 --> 00:01:40,320 that a giant textbook would do, and without all the 22 00:01:40,320 --> 00:01:42,600 practice that you'll get in class, and doing 23 00:01:42,600 --> 00:01:44,200 exercises and so on. 24 00:01:44,200 --> 00:01:48,115 So these are kind of short, but I hope alive. 25 00:01:48,115 --> 00:01:51,900 26 00:01:51,900 --> 00:01:57,010 And if they help, I'm very happy. 27 00:01:57,010 --> 00:02:03,450 So I guess I'm hoping everybody might watch this 28 00:02:03,450 --> 00:02:07,740 who'd like a little help or a second look at calculus, both 29 00:02:07,740 --> 00:02:11,500 high school and college students. 30 00:02:11,500 --> 00:02:18,040 I wanted to capture key ideas that you could use for review 31 00:02:18,040 --> 00:02:21,310 and see new examples and see just coming 32 00:02:21,310 --> 00:02:23,630 from a second person. 33 00:02:23,630 --> 00:02:27,550 That seems to be what succeeds with linear algebra. 34 00:02:27,550 --> 00:02:33,860 The videos are sort of just to add, to supplement what you're 35 00:02:33,860 --> 00:02:38,060 actually seeing in class and in the textbook. 36 00:02:38,060 --> 00:02:41,500 I think of the textbooks as often so large and so many 37 00:02:41,500 --> 00:02:48,960 exercises that it's totally easy to lose the key point, 38 00:02:48,960 --> 00:02:52,400 what's essential about calculus and what is just kind 39 00:02:52,400 --> 00:02:58,330 of routine and practice. 40 00:02:58,330 --> 00:03:02,400 So in short videos, it has to be the essential points, the 41 00:03:02,400 --> 00:03:08,290 three groups of functions, like powers of x, sine and 42 00:03:08,290 --> 00:03:12,650 cosine of x, and e to the x. 43 00:03:12,650 --> 00:03:17,080 If you understand those, you've got the main ideas. 44 00:03:17,080 --> 00:03:21,940 We're starting out with a first group of five videos. 45 00:03:21,940 --> 00:03:28,300 Maybe big picture is the words that we think of for those. 46 00:03:28,300 --> 00:03:32,190 And then that'll be the first group that'll be on 47 00:03:32,190 --> 00:03:33,660 OpenCourseWare. 48 00:03:33,660 --> 00:03:41,580 And then I've done 12 after that, that do sort of the rest 49 00:03:41,580 --> 00:03:47,370 of differential calculus, big words just meaning how to find 50 00:03:47,370 --> 00:03:51,300 the derivative, the slope, the speed. 51 00:03:51,300 --> 00:03:53,380 You'll see in the videos. 52 00:03:53,380 --> 00:03:57,970 And then after that could come integral calculus, if you 53 00:03:57,970 --> 00:04:00,100 think I should. 54 00:04:00,100 --> 00:04:01,240 I don't think of a lot of 55 00:04:01,240 --> 00:04:03,770 prerequisites for these videos. 56 00:04:03,770 --> 00:04:09,160 I guess I'm always hopeful that you could watch them even 57 00:04:09,160 --> 00:04:15,100 if you haven't started calculus, to see what's 58 00:04:15,100 --> 00:04:16,350 coming, what it's about. 59 00:04:16,350 --> 00:04:20,260 60 00:04:20,260 --> 00:04:24,400 I've taught math for a long time, and it's so easy to get 61 00:04:24,400 --> 00:04:32,050 into the course and jump over the opening, the introduction 62 00:04:32,050 --> 00:04:34,890 that tells what's important here. 63 00:04:34,890 --> 00:04:39,270 And that's maybe what these videos are aimed at. 64 00:04:39,270 --> 00:04:41,060 FEMALE SPEAKER: This has been a production of MIT 65 00:04:41,060 --> 00:04:43,440 OpenCourseWare and Gilbert Strang. 66 00:04:43,440 --> 00:04:45,730 Funding for this video was provided by the Lord 67 00:04:45,730 --> 00:04:46,950 Foundation. 68 00:04:46,950 --> 00:04:50,070 To help OCW continue to provide free and open access 69 00:04:50,070 --> 00:04:53,160 to MIT courses, please make a donation at 70 00:04:53,160 --> 00:04:54,720 ocw.mit.edu/donate. 71 00:04:54,720 --> 00:04:56,750