MATH 21, Section M (Code 94550)

Fall Semester 2009

Meeting time and place: 12:50–1:40 MWF, 1:00–2:15 Tuesday, 102 Perkins

Instructor: Roger Cooke

Web page: http://www.cems.uvm.edu/~cooke

Office hours in Room 107 Lord: MWF 12:00–12:45, Tuesday 12:00–12:45 and 2:15–3:30. Other hours by appointment. Call me at 864-4129 and leave a message if I’m not there. (Please do not call after 9:00 PM or before 8:00 AM.)

Textbook (required): Calculus: Early Transcendentals, 6^th edition, by James Stewart

Administrative aspects of the course: You naturally want to know what is expected of you and how your work will be evaluated in this course. The main thing you need to do is come to class, hand in the homework (on time), and be prepared for the quizzes, the two midterm examinations, and the final examination. I’ll use the following algorithm for grading:

1. Each of the 100 homework problems that I collect and grade—they will be due at the next class meeting after the date to which they correspond in the table below—will be either 1 or 0. So there will be a total of 100 points for homework. Since homework will be ten percent of the evaluation, I’ll just divide the number of problems you got right by 10 for this portion of your grade.

2. There will be ten quizzes, given on Tuesdays, but not every Tuesday. These will be brief, with one or two questions on each. On quiz days, we’ll have a brief last-minute review for your questions, then a 15-minute quiz, then a normal class. Partial credit will be given on quizzes, and each quiz will be worth ten points. That will yield another 100 points, to count as 20 percent of your grade. In other words, I’ll divide your total quiz score by 5 (or multiply by 0.2) for this portion of the grade.

3. There will be three midterm examinations, again given on Tuesdays, so that you’ll have an extra 25 minutes to complete them, beyond the usual 50-minute class period. (They will be designed as 50-minute tests.) Partial credit will be given on the midterm examinations. Each of them will be graded on a basis of 100 points and count as 15 percent of your grade. Thus I’ll take the sum of your three midterm scores and multiply by 0.15 to get this portion of your grade.

4. The final examination will be a three-hour examination, but designed so that most people will be able to finish it in two hours. It will be graded on the basis of 100, and partial credit will be given. This will be 25 percent of your grade, so I’ll take your score and divide by 4 (or multiply by 0.25) to get this portion of the grade.

5. Once all the scores are in, I’ll add them up and round them to the nearest whole percent. Letter values will then be assigned on a very simple basis, 90–100 being an A, 80–89 a B, 70–79 a C, 60–69 a D, and below 60 an F. Pluses and minuses will be adjoined at the top and bottom of each range, as I think appropriate, in order to keep from having to make fine distinctions. (I think it would be unreasonable to award a C to a student who got 79 while giving a B to a student who got 80; however, it’s not unreasonable to award a C+ to the first and a B– to the second. The line has to be drawn somewhere.)

General rules and regulations:

1. You can hand in your homework by e-mail if you like. Collaboration on homework is allowed. Obviously, it is to your benefit to understand the homework problems, as you will be meeting them again on quizzes, midterms, and the final examination. If a friend can make them clearer to you, that’s fine; but you should write them up yourself to be sure you do understand them.

2. Collaboration on quizzes and midterms is of course not allowed. You may use a hand calculator to do arithmetic during examinations, but not a graphing calculator for the graphs or a computer algebra system to do the formula manipulation for you. (This point is explained in more detail below under “Academic aspects of the course.”)

3. If you have to miss a quiz or midterm examination, please see me to make it up as soon as possible during my office hours or some other time when we can meet. This must be done within one week.

4. If you have special needs in the classroom or on examinations and have the appropriate medical certification, please contact me confidentially, and I’ll arrange to accommodate you.

Schedule of class meetings, homework, and tests: (Section 3.7 may be omitted if we are falling behind this schedule.) Disclaimer: I am not guaranteeing that merely working the problems listed will enable you to master the material. I expect you to work many more problems than this. We have limited class time, however, so I list problems I hope everyone will try before coming to class; that way, we have a basis for classroom discussion.

Date	Section(s)	Homework (problems in boldface are to be handed in)
Aug. 31	1.3 & 1.5 (functions)	§1.3: 2, 3, 33, 57, 64; §1.5: 7, 8, 15, 21
Sept. 1	1.6 (inverse functions)	1, 4, 7, 8, 20, 22, 29, 43, 52, 58
Sept. 2	Appendix D (trigonometry)	2, 8, 24, 30, 38, 60
Sept. 4	Appendix D (trigonometry)	66, 78, 82, 84, 89
Sept. 8	Review and quiz
Sept. 9	2.1 (tangents and velocity)	2, 4, 5, 7, 8
Sept. 11	2.2 (limits: the concept)	2, 3, 6, 8, 12, 19, 29, 38, 40
Sept. 14	2.3 (limits: computation)	10, 22, 36, 40, 47, 50, 56, 62
Sept. 15	Quiz and 2.4 (limits: theory)	4, 14, 37, 38, 41
Sept. 16	2.5 (continuity)	4, 7, 32, 34, 42, 52, 60
Sept. 18	2.6 (horizontal asymptotes)	2, 4, 6, 48, 56, 62, 66
Sept. 21	2.7 (derivatives)	4, 8, 12, 16, 22, 44, 50
Sept. 22	Review and midterm 1
Sept. 23	2.8 (more on derivatives)	6, 10, 22, 36, 44, 48
Sept. 25	2.8, continued	52, 55, 57
Sept. 28	3.1 (polynomials and exponential functions)	2, 8, 20, 26, 30, 34, 52, 54
Sept. 29	Quiz and 3.2 (product rule)	4, 10, 28, 56
Sept. 30	3.2 (quotient rule)	2, 6, 30, 41, 48, 52
Oct. 2	3.3 (trigonometric functions)	4, 8, 22, 34, 36, 50
Oct. 5	3.4 (chain rule)	2, 6, 8, 14, 20, 24
Oct. 6	Quiz and 3.4, continued	48, 52, 60, 76, 79, 94
Oct. 7	3.5 (implicit differentiation)	2, 6, 14, 26, 28, 32, 46
Oct. 12	3.6 (logarithmic functions)	2, 6, 24, 34, 38
Oct. 13	Review and midterm 2
Oct. 14	3.7 (applications)*	6, 10, 14, 16, 18
Oct. 16	3.7, continued*	22, 27, 28, 33
Oct. 19	3.8 (exponential functions)	4, 5, 7, 10, 11, 16, 18
Oct. 20	Quiz and 3.9 (related rates)	2, 6, 10, 14, 26, 32
Oct. 21	3.9, continued	33, 36, 38, 42, 44
Oct. 23	3.10 (differentials)	4, 6, 12, 24, 34, 38
Oct. 26	3.11 (hyperbolic functions)	4, 20, 30, 40, 54, 55
Oct. 27	Quiz and 4.1 (extreme values)	4, 22, 32, 48, 69
Oct. 28	4.2 (the mean-value theorem)	7, 14, 18, 34, 35
Oct. 30	4.3 (graphing)	2, 6, 8, 20, 22, 32, 56
Nov. 2	4.3, continued	68, 69, 78, 82
Nov. 3	Quiz and 4.4 (indeterminate forms)	6, 10, 20, 42, 54
Nov. 4	4.4, continued	73, 74, 76, 78, 79
Nov. 6	4.5 (curve sketching)	2, 4, 6, 8, 20, 26, 40
Nov. 9	4.5, continued	54, 56, 58, 64, 72
Nov. 10	Quiz and 4.7 (optimization)	2, 4, 10, 14, 37
Nov. 11	4.7, continued	41,47, 49, 63, 64
Nov. 13	4.8 (Newton’s method)	9, 16, 24, 28, 40, 42
Nov. 16	4.9 (anti-derivatives)	4, 10, 22, 26, 48, 67
Nov. 17	Review and midterm 3
Nov. 18	5.1 and Appendix E (sigma notation)	§5.1: 2, 4, 6; Appendix E: 2, 16, 24
Nov. 20	5.1 (area and distance)	16, 19, 22, 25
Nov. 23	5.2 (definite integrals)	2, 4, 10, 15, 18
Nov. 24	5.2, continued	22, 26, 30, 45, 56
Nov. 30	5.3 (fundamental theorem of calculus)	3, 7, 18, 24, 43, 60
Dec. 1	Quiz and 5.3, continued	65, 66, 68, 73
Dec. 2	5.4 (indefinite integrals)	4, 6, 22, 28, 44, 48
Dec. 4	5.5 (integration by substitution)	2, 9, 30, 38, 44
Dec. 7	5.5, continued	48, 52, 58, 60, 74
Dec. 8	Quiz and review of the semester
Dec. 9	Review of the semester
Dec. 17	Final Examination (3:30–6:30)

Academic Aspects of the Course

This is a course about concepts more than computation. Even though you will be expected to learn a number of formula-manipulation skills that embody these concepts, I will be emphasizing the concepts for a number of reasons:

1. Many students who are taking this course will have had a previous course in calculus. If my past experience is any guide, what students retain from these courses is a set of computational skills, not the central ideas of the subject. They know how to take the derivatives of certain standard functions, but not when to do so.

2. Modern computers with symbolic capability are able to compute derivatives and integrals much faster and more accurately than any human being, student or professor, can do. In terms of professional qualification, having the ability to do only the computational parts of calculus is like being able to dig trenches with a pick and shovel. You’d never be able to compete with someone who knows how to

operate a backhoe. One symbolic algebra program, Mathematica, is available to you, and I will spend a small amount of time showing you how to use it. You can get even more help from Helen Read’s webpage. However, Mathematica also “knows” how to compute derivatives and integrals, but not when to do it. It is useless to you unless you know the conceptual basis of calculus.

3. Again, in terms of professional qualification, concepts are the main thing. An employer who may someday call on your ability in calculus will not say, “I need you to take the derivative of this function.” Rather, you’ll be presented with a practical problem to solve, and you will probably be the one who determines what function is involved and at what point you need the derivative. (As an example, such a problem may well involve statistics and the distribution function of a random variable.)

4. Understanding concepts enables you to formulate a problem “colloquially,” in a qualitative manner. Human beings don’t think in precise formulas most of the time, and having to do so would stifle your creativity. You need to have a qualitative picture of the problem you are solving and a good idea of the approximate solution. Exact formulas and the machines that compute with them may give a very

precise answer that is ludicrously wrong, especially if there is an unnoticed typographical error in the input data. Brilliant though they seem when you watch them instantly solve an equation that would have taken you days to do by hand, computers and computer programs are completely lacking in the most basic common sense. They will not recognize when an answer is not just wrong but insanely wrong. You need to be able to recognize when a computer is giving you an absurd answer and correct your data input or programming logic when that happens. (If the computer tells you the probability of an event is 3.5, something must be wrong!)

This first semester of calculus is a fairly complete exposition of differential calculus and the basic part of integral calculus. You can get an overview of what calculus amounts to by reading this essay.

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