# Math 511, Introduction to Analysis II

Spring 2018

## General Information

Instructor: Matthew Blair

Email Address: blair ["at"] math.unm.edu

Course Web Page: http://www.math.unm.edu/~blair/math511s18.html

Office: SMLC 330

Office Hours: 2:15-4:15pm on Mondays and 1:30-2:30pm on Tuesdays. Also by appointment.
**Texts:**

1. *Principles of Mathematical Analysis, 3rd Edition,* by Walter Rudin (Required)

2. *An Introduction to Analysis, 4th Edition,* by William R. Wade (Optional)

3. *A Geometric Introduction to Differential Forms, 2nd Edition,* by David Bachman (Optional)

**Meeting times/location:** Monday, Wednesday, and Friday 9-9:50am in SMLC 352.

**Course Description: **Continuation of 510. Exponential, logarithmic, and trigonometric functions (Ch. 8 Rudin). Fourier Series (Ch. 8 Rudin). Differentiation in R^n (Ch. 9 Rudin). Inverse/implicit function and rank theorems (Course notes and Ch. 9 Rudin). Integration in R^n (Ch. 12 Wade). Differential forms and Stokes' Theorem (Course notes and Bachman).

**Prerequisites**: Math 510.
Course Syllabus

Notes

Notes on the Inverse Function Theorem

Notes on Taylor's Theorem

Notes on differential forms and reparametrization of surfaces

Homework

Assignment #1--Due Wednesday, January 24

See handout

Assignment #2--Due Wednesday, January 31

See handout

Assignment #3--Due Wednesday, February 7

See handout

Assignment #4--Due Wednesday, February 14

See handout

Take Home Exam--Due Wednesday, February 21 (Not public)

Assignment #5--Due Wednesday, February 28

See handout

Assignment #6--Due Wednesday, March 7

See handout

Assignment #7--Due Wednesday, March 21

See handout

Assignment #8--Due Wednesday, March 28

See handout

In Class Exam--Wednesday, April 4 (Not public)

Assignment #9--Due Wednesday, April 11

See handout

Assignment #10--Due Wednesday, April 18

See handout

Assignment #11--Due Wednesday, April 25

See handout

Assignment #12--Due Wednesday, May 2

See handout