SYLLABUS: CALCULUS I, Section 5 (Spring 2009, Tuesday/Thursday@6:10pm in 310 Fayerweather; Elliott Stein)

Prerequisites: The course assumes that you are familiar with basic pre-calculus mathematics, e.g., the idea of a function, elementary algebra, analytic geometry (x-y coordinates) and the basic trigonometric functions. The introduction to the textbook contains short diagnostic tests that allow you to evaluate how well you remember these topics. If it has been more than a year or two since your last math course, or if you have any doubt about your preparedness for Calculus I, you should take these diagnostic tests. Let me know if you have any questions.

The final grade is based on the two midterms (25% each), the final (40%) and the weekly homework (10%). The homework is composed of a written homework and homework done on the web.

Office hours: Tuesday and Thursday, 5pm-6pm, Math 516

Homework Assignments (All references are to Stewart, Calculus (Early Transcendentals), sixth edition) (subject to change):

DATE	TOPICS	SECTION OF BOOK	HOMEWORK PROBLEMS
January 20, 22	Introduction; functions	1.1 to 1.3, 1.5	1.1: 1, 2, 5, 6, 7, 21, 22, 56 1.2: 3, 4, 8 1.3: 31, 35, 36, 45, 46, 54 1.5: 13, 16, 17, 18, 19 Due January 27
January 27, 29	Inverse functions; limits and continuity	1.6, 2.1 to 2.5	1.6: 5, 6, 21, 24, 35, 36, 47, 48 2.2: 5, 6 2.3: 3, 8, 13, 18, 21, 22, 26, 48 2.5: 3, 4, 17, 35, 42 Due February 3
February 3, 5	Asymptotes; Derivatives: definition and formulas; higher derivatives	2.6 - 2.8, 3.1 - 3.2	2.6: 3, 4, 7, 10, 17, 30, 34, 42 2.7: 6, 7, 28, 31, 36 2.8: 21, 28 3.1: 7, 12, 13, 26, 52 3.2: 3, 12, 15, 24, 50 Due February 10
February 10, 12	Derivatives of trig functions; chain rule, implicit differentiation	3.3 to 3.5	3.3: 2, 3, 8, 11, 16, 22, 35, 41, 46 3.4: 5, 6, 13, 20, 23, 24, 31, 34, 75, 76 3.5: 1, 2, 9, 12, 45, 52 Due February 17 (no extension)
February 17	Derivatives of logarithmic functions, linear approximation	3.6, 3.10	3.6: 9, 12, 21, 34, 37, 46 3.10: 3, 4, 11, 18, 33, 36 Due February 24
February 19	MIDTERM 1
February 24, 26	Mean Value Theorem, Graphing I	4.1 to 4.3	4.1: 3, 6, 9, 10, 33, 34, 41, 44, 47, 54, 59, 60, 75 4.2: 13, 14, 16, 17, 36 Due March 3
March 3, 5	Graphing II, L’Hospital’s Rule	4.4, 4.5	4.3: 5, 6, 12, 13, 16, 41, 52, 64 4.4: 9. 10, 11, 12, 15, 17, 18, 37, 42, 49, 50, 59, 60 Due March 10
March 10, 12	Optimization	4.7	4.5: 22, 39, 59, 62 4.7: 11, 12, 17, 18, 23, 30, 52, 66 Due March 24
March 24, 26	Antiderivatives, Integration I	4.9, 5.1	4.9: 3, 10, 13, 14, 19, 28, 31, 32, 42, 49, 75, 76 5.1: 3, 16, 17, 18, 22 Due March 31
March 31	Integration I	5.2	5.2: 29, 30, 33, 34, 36, 39, 47, 48, 70 Due April 7
April 2	MIDTERM 2
April 7, 9	Integration II	5.3, 5.4	5.3: 3, 4, 9, 10, 11, 12, 15, 18, 21, 22, 25, 30, 42, 66 5.4: 4, 5, 10, 11, 12, 14, 27, 34, 43 Due April 14
April 14, 16	Integration III	5.5	5.5: 3, 4, 6, 7, 8, 13, 14, 21, 22, 25, 26, 41, 42, 51, 52, 57, 58, 60, 65, 66 Due April 21
April 21, 23	Applications of integration	6.1, 6.2	6.1: 4, 5, 6, 11, 12, 18, 19, 25, 26, 48 6.2: 1, 2, 9, 10, 29, 30, 49, 50, 60 Due April 28
April 28, 30	Applications of integration	6.3, 6.5	6.3: 4, 5, 6, 11, 12, 38, 39 6.5: 4, 5, 6, 7, 9, 10, 16, 17 Not to be handed in; solutions will be distributed May 5
Thursday, May 7, 6:10pm	REVIEW SESSION
Tues., May 12, 7:10pm	FINAL EXAM

• This syllabus will be updated weekly, usually on Sunday night, to post the assigned problems that relate to the material that will be covered in class in the upcoming week. Those problems are due on Tuesday of the following week, i.e. about nine days after they are posted. Homework can be handed in to me directly in class or can be left in my mailbox. Faculty mailboxes are located on a landing just downstairs from the main entrance to the Mathematics Building.
• Before attempting the homework problems, you should read the corresponding section(s) of the text, as indicated on the syllabus.
• Your homework papers do not have to follow any prescribed format, but you should (1) write legibly, (2) show how you get your answer and (3) staple the pages if you’re handing in more than one page. I keep a stapler in my office that you can use for this purpose.
• I will circulate solutions to the assigned problems by e-mail. Usually, this will happen a couple of days after the problems are due. If you hand in your paper late, but before I circulate the solutions, you will not be penalized for lateness. Homework that is turned in after the solutions are circulated will not be graded and will not receive credit.
• Each student has one “free pass” on the homework during the semester, meaning that you can not turn it in and there will be no penalty. If you turn in all the homework, I will discard your lowest grade before computing your overall written homework grade.
• You will get the most out of the homework if you do it on your own, but there is nothing wrong with discussing a problem with another student or getting an idea from another student, so long as you do not literally copy someone else’s work.
• Webwork is recommended but optional. You will receive an e-mail from the Webwork administrator when the problems for our section are online.
• You do not need a calculator in this course, and they are not permitted on the exams.
• The latest version of this syllabus can always be found at math.columbia.edu/~stein/Syllabus8.html. You might want to bookmark the site on your browser. It’s a good idea to hit the “refresh” button on your browser after logging onto this site to make sure that you’re not looking at an earlier version of the page that your computer has cached.
• You can reach me by e-mail at stein@math.columbia.edu. The phone in my office is 854-5545, but I’m rarely there except during office hours. E-mail is better.