640:412 Spring 2009 Home

640:412

MATHEMATICAL ANALYSIS II

SPRING 2009

Basic information for Spring 2009

Instructor: Professor E. Speer, Hill Center 520, 732–445–2390 X1313, speer at math dot rutgers dot edu
Office hours:
- Monday and Wednesday 3:20–4:40 PM, Hill 520
- Wednesday 10:20–11:40 AM, Hill 520
- Or by appointment or chance in Hill 520
Detailed course information and policies: As web page and as a PDF file.
Hints on writing proofs:
- From your instructor: As web page and as a PDF file.
- From the author of the text used in Math 441, Introductory Topology, Professor James Munkres
Homework assignments.

The week of May 4–8

We will have an extra (make-up) class on Wednesday, May 6, 1:40-3:00 in ARC 205.
I will hold office hours on Wednesday, May 6, according to my usual Wednesday schedule (see above).
The final exam will be held Friday, May 8, from 4:00 PM to 7:00 PM, in ARC 108 (our usual classroom).
The exam is cumulative. Material we cover in the week of May 4 will not be included; the matrial covered on differential forms is that included (but in a very sketchy form) in the notes below.
Here is a proposed formula sheet for differential forms to be distributed with exam. I think that it includes all the formulas that are difficult to remember (and some that aren't); if you disagree, you can request that it be enlarged.

Announcements and additional resources

Notes on differential forms:
- Section 1
- Section 2 (second corrected version)
- Section 3 (corrected version)
- References
- Note: In the previously posted version of Section 2, formula (5) was incorrect: the coefficients should have been called b and c, not a and b . You can correct by hand or download the corrected version above.
Notes on the proof of Stirling's formula
Notes on the application of the Ascoli-Arzela Theorem to prove the existence of a solution of an ordinary differential equation

Exam 2

The second exam will be held Monday, April 13, at 5:00 PM in ARC 206. It will cover all our work since the first exam plus a little more (specifically, , starting with Fourier series, but including the uniform approximation of continuous periodic functions by trigonometric polynomials, which was also on Exam 1) through the discussion, on April 8, of differentiating under the integral sign. In terms of the text, this means roughly from Section 8.9 through the end of Chapter 9.

You should be able to state the implicit and inverse function theorems; you should know Bessel's inequality and Parseval's theorem by name.

In honor of the exam I am moving my morning office hour that week from Wednesday to Monday. Thus my office hours for the week of April 13 are:

Monday and Wednesday 3:20–4:40 PM, Hill 520
Monday 10:20–11:40 AM, Hill 520
Or by appointment or chance in Hill 520

There will be no homework collected the week of April 13

Exam 1

The first exam will be held Monday, March 2. It will cover all our work through the discussion, on February 18, of the uniform approximation of continuous periodic functions by trigonometric polynomials. In terms of the text, this means that of the material on Fourier series the exam will cover only 8.9 and 8.15.

In honor of the exam I am moving my morning office hour that week from Wednesday to Monday. Thus my office hours for the week of March 2 are:

Monday and Wednesday 3:20–4:40 PM, Hill 520
Monday 10:20–11:40 AM, Hill 520
Or by appointment or chance in Hill 520

There will be no homework collected the week of March 2.