COURSE SYLLABUS

Instructor- Paul Brock

E-mail- pwbrock@sciences.sdsu.edu

Office- GMCS 510

Office phone- 594-6835

Office Hours- 1530 to 1700 MW

Text- Advanced Calculus 2nd Edition , Patrick M. Fitzpatrick

Website: http://www-rohan.sdsu.edu/~pwbrock/math534B.htm

Prerequisites: Math 534A or equivalent.

Topics- Math 534B is Part 2 of a one-year long introductory course in advanced calculus. It is required for many math majors and is a prerequisite for graduate study in mathematics. We will cover the material in Chapters 8 through 15 in our textbook (with some omissions and additional material). Math 534B is a demanding course which even good students find challenging. The pace of the course is quite rapid. Please attend class regularly and keep up with the homework.

The main topics include:

§ Taylor polynomials

§ Sequences and series of functions

§ Euclidean n-space

§ Continuity and compactness

§ Differentiating real-valued functions of several variables

§ Local approximation of real-valued functions of several variables

§ The Implicit Function Theorem

Grading:

Homework-------50pts

Exam I------------100pts (Wednesday, March 3^rd)

Exam II-----------100pts (Wednesday, April 21^st)

Final--------------150pts (Monday, May 17^th, 1300 – 1500)

The class is given weekly problem sets which are posted on the course website. Except for Problem set 1, problem sets are posted on Mondays and collected IN CLASS on the Wednesday of the following week. Students are encouraged to discuss their solutions with others, but each student must write up his/her own solutions. Each problem set will be neatly prepared and STAPLED. Clips, tape or the corner-folding technique are not acceptable. Problem sets are worth five points each. A problem set that does not reach me in class on the due date will be considered late. A problem set that is late but reaches me by 5:00 PM on the due date is penalized one point. Problem sets that reach me after 5:00 PM on the due date are penalized two points. Solution keys for the problem sets are posted after the problem sets are returned. YOU SHOULD LOOK AT THESE KEYS. Problem sets will not be discussed during lecture; there is not sufficient time. Please bring all questions regarding problem sets (as well as all personal issues) to my office hours. As an alternative to making an actual visit to my office, YOU CAN USE EMAIL OR THE TELEPHONE (See above). The instructor reserves the right to suggest office hour consultation to any student at any time.

The exams will cover the content of the lecture and the problem sets. Students will be asked to give definitions and write proofs on exams. On the Friday before an exam, I will post a review sheet as a study aid. The review sheet will identify some important ideas which should not be ignored. The review sheet is not meant to be exhaustive; students must study the review sheet, their lecture notes, and the homework keys to be fully prepared for an exam. The class period on the Monday before an exam will be dedicated largely to review.