Math 275, Fall 2008, Andrei Caldararu

Lecture Section 1, 11:00-11:50am MWF, B231 VAN VLECK



Text:  Michael Spivak: Calculus Third Edition (1994), ISBN: 0-914098-89-6.

I don't have access to the new 2008 edition, but I don't expect there to be major differences from the 1994 edition, at least judging from the table of contents, which is identical (even page numbers match) between them. If you prefer to get the new one you're welcome to, but make sure the homework problems match.
 

Discussion Section: Attendance in a weekly discussion section is required. The section numbers are 301 -- 302. The TA for both sections is Nick Addington.
 

Office Hours: I will be in my office, 605 Van Vleck, from 1:30pm to 2:25pm MWF. These times may change, in which case the new times will be announced on my home page. Other good times to talk are right before or right after the class. It is also possible to ask questions by email, which will be generally answered within 24 hours. The more detailed your email question is, the more detailed the reply message will be. You can e-mail me by clicking here.
 

Examinations and homework: In addition to the final exam, there will be two 90 minute midterm exams. They will be given in class, on Wednesday, October 22 and on Wednesday, November 19, between 5:30 and 7:00pm, in 5231 Social Sciences Building.

Homework problems will be assigned in lecture, and collected during recitation. We expect all assignments to be written neatly, and handed in on time.
 

Missed exam policy: There are no makeups for missed midterm exams, regardless of the reason for absence. However, if you can not attend the midterm due to a valid reason, for example a medical emergency, the rest of your scores will be scaled to compensate for the missed test.
 

Final Examination: There will be a two-hour final examination given on Monday, December 15 at 12:25pm. The room for the exam is Social Sciences 6102. You must take the final examination at the time scheduled by the university; no final exams will be given earlier. In particular, examinations will not be rescheduled because of travel arrangements. It is your responsibility to schedule travel appropriately. If you can not take the final exam due to an emergency, you should let me know as soon as possible.
 

Grading: Your final grade will be based on your effort on the three exams given during the semester, the final exam, and the homework. The course will focus on ideas rather than computational techniques. If you work hard at the course material and the assigned problems, you should do well in the course.
 

Asking questions: The pace of the course will depend in part on how well the material is understood. Thus if there is something that you do not understand, it is important to ask questions. In particular, I encourage questions during lecture. I know that this takes courage, but if you do, it will help me and all the other students in the class. If you do not understand something, it is most probably the case that several other students are having the same difficulty. There is no such thing as a foolish question, with the exception of

"Will this material be on the exam?"

If you have a question, please try to be brave and do yourself, the rest of the class, and me a great favor by asking it. If you do not understand something, it is almost certain that there are others who do not understand it either. If you cannot bring yourself to ask a question during lecture, then be sure to ask during the recitation section or in office hours.
 

Schedule of Lectures: Given the above comments, it is difficult to predict the exact schedule of lectures. A very tentative schedule will be posted on this web page soon. However, it is subject to change. Please try to read the relevant textbook sections before the lecture. Be warned that my lectures may differ significantly from the book in emphasis and structure.

Additional comments: The purpose of Math 275 is to teach the fundamental ideas of the Differential and Integral Calculus. The course will cover material from Parts I-III of the text. While we will do some of the same kind of routine exercises that are given as homework in Math 221, the real focus of the course is on understanding mathematical ideas, and on using them with precision. Thus in addition to learning techniques of calculation, you will also be expected to learn and to reproduce mathematical definitions and mathematical proofs. This is often very difficult at first, but it does become easier with practice, and does not require that you be a mathematical genius. Learning mathematics is hard work, but also lots of fun. If you work hard at the material, you will receive a good grade.

Many of the students in the class have been exposed to calculus before, but this is not a prerequisite. My objective is to teach the material so that it is accessible to students with no prior experience in the subject, but also to make the course interesting for those who have seen some of the material before. If you find the course too easy, please let me know so that I can suggest further reading and additional interesting problems.

Suggested List of Lectures

Week Topics Homework
Sep. 3- Sep. 5 Chapter 1, complex numbers (Ch. 25) §1: 4, 7, 10, 14, 18, 25
Sep. 8-Sep. 12 Chapters 3, 5 §25: 3, 4, 9 §3: 1, 4, 8, 9, 10, 13, 21
Sep. 15-Sep. 19 Chapters 6, 7 §5: 1, 2, 3, 7, 9, 11, 12, 13
Sep. 22-Sep. 26 Chapter 9 §6: 1, 4, 7, 10, 13
Sep. 29-Oct. 3 Chapters 10, 11 §7: 2, 5, 7, 10, 11 §8: 1, 2, try to do 6 §9 1, 3, 7
Oct. 6-Oct. 10 Chapter 11 cont'd, Chapter 12, other topics on derivatives § 9: 11, 12, 16; § 10: 1, 2, 4, 7, 9, 12
Oct. 13-Oct. 17 Chapter 2 (induction), chapter 13 §10: 20, 22, 26 §11: 1, 3, 9, 11, 14, 19, 25, 36
Oct. 20-Oct. 24 Chapter 13 cont'd + Appendix; 1st Midterm §12: 1, 3, 5, 6, 14, 15 §2: 1, 2, 3, 4, 5, 13, 18, 19 Due 11/6.
Oct. 27-Oct. 31 Chapter 13 continued, explicit computations §13: 1, 5, 7, 8, 13, 14, 15
Nov. 3-Nov. 7 Chapter 14
Nov. 10-Nov. 14 Techniques of integration
Nov. 17-Nov. 21 Chapter 15; 2nd miterm §14: 2, 3, 4, 11, 12, 29 §15 2, 3, 4, 7, 8, 9, 14, 16 Due 12/4.
Nov. 24-Nov. 26 Chapter 18, Thanksgiving break
Dec. 1-Dec. 5 Chapter 18 continued, Chapter 19
Dec. 8-Dec. 12 Integrals of inverse functions §18: 2, 3, 7, 10, 12, 17, 24, 37 §19: 1, 2, 3, 7, 13, 24
12:25 pm, Monday December 15   Final Examination