Math 511, Introduction to Analysis II
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.
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.
Notes on the Inverse Function Theorem
Notes on Taylor's Theorem
Notes on differential forms and reparametrization of surfaces
Assignment #1--Due Wednesday, January 24
Assignment #2--Due Wednesday, January 31
Assignment #3--Due Wednesday, February 7
Assignment #4--Due Wednesday, February 14
Take Home Exam--Due Wednesday, February 21 (Not public)
Assignment #5--Due Wednesday, February 28
Assignment #6--Due Wednesday, March 7
Assignment #7--Due Wednesday, March 21
Assignment #8--Due Wednesday, March 28
In Class Exam--Wednesday, April 4 (Not public)
Assignment #9--Due Wednesday, April 11
Assignment #10--Due Wednesday, April 18
Assignment #11--Due Wednesday, April 25
Assignment #12--Due Wednesday, May 2