SYLLABUS: CALCULUS I, Section 4 (Spring 2010, Tuesday/Thursday@6:10pm in Math 203; 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 since your last math course, or if you have any doubt about your preparedness for Calculus I, you should take these diagnostic tests, and take the results seriously. 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%).

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

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

DATE	TOPICS	SECTION OF BOOK	HOMEWORK PROBLEMS
January 19, 21	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 26
January 26, 27	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 2
February 2, 4	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 9
February 9, 11	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 16
February 16	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 23
February 18	MIDTERM 1
February 23, 25	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 2
March 2, 4	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 9
March 9, 11	Optimization	4.7	4.5: 22, 39, 59, 62 4.7: 11, 12, 17, 18, 23, 30, 52, 66 Due March 23
March 23, 25	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 30
March 30	Integration I	5.2	5.2: 29, 30, 33, 34, 36, 39, 47, 48, 70 Due April 6
April 1	MIDTERM 2
April 6, 8	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 13
April 13, 15	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 20
April 20, 22	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 27
April 27, 29	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 Due May 4 in 4^th floor mailbox
Thursday, May 6, 6:10pm, Math 203	REVIEW SESSION
Tuesday, May 11, 7:10pm, Math 203	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 the course mailbox outside Math 410.
• Before attempting the homework problems, you should read the corresponding section(s) of the text, as indicated on the syllabus. Better yet, read the material before it’s covered in class.
• 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. Please don’t hand in homework without your name on it.
• 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.
• 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/Syllabus10.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.