Methods of Applied Mathematics I.

MATH 383C, Unique # 60460 and CAM 385C, Unique # 67535
Fall 2007

Instructor

Todd Arbogast
Office: RLM 11.162, Phone: 471-0166
Office: ACE 5.334, Phone: 475-8628
E-Mail: arbogast@ices.utexas.edu
Office Hours: MW 10:00-11:00 and Th 9-10:00 in RLM 11.162 (Also, unless the instructor has pressing business, he will be available to help students who come by.)

Teaching Assistant

Anthony Ditanna
Office: RLM 10.110, Phone: 475-9143
E-Mail: aditanna@math.utexas.edu
Office Hours: TTh 11:00-12:30 in RLM 10.110

General Information

Syllabus
Lecturer-prepared notes (2007 version): Available for purchase from the UT Copy Center in Welch 2.228.
Write-up on finite dimensional NLS's.
Problem discussion session: Wednesdays 5:00-6:00 pm in RLM 11.176

Homework and Exams

Final Exam. Friday, December 14, 9:00-12:00 noon in RLM 5.116.
Office hours: M 12/10, 4-5:00; Tu 12/11, 1-2:00; F 12/14, 9-10:00.

Problem Set 11. Due F 12/7
Ch. 4 # 4, 7, 8, 12, 14, 15

Problem Set 10. Due F 11/30
Ch. 3 # 17, 18, 19, 20, 21
Ch. 4 # 1, 2, 3, 6

Exam 2. Friday, November 16, 4:30-6:00 p.m. in RLM 11.176
Chapter 3, Hilbert spaces (except Ascoli-Arzela and Sturm-Liouville)

Problem Set 9. Due F 11/9
Kreyszig p. 411 # 6
Kreyszig p. 419 # 10
Kreyszig p. 464 # 6, 9, 10
Kreyszig p. 468 # 5, 6
Kreyszig p. 474 # 4, 9, 10, 15
Kreyszig p. 485 # 1
Kreyszig p. 490 # 2
Ch. 3 # 11, 12

Problem Set 8. Due F 11/2
Kreyszig p. 378 # 1, 2, 4, 5, 7, 9
Kreyszig p. 385 # 4 [See web exercise #1 below.]
Ch. 3 # 10, 13
Web exercises:
1. Prove that if X is Banach and T is in B(X,X), then the spectrum of T² is the square of the spectrum of T. [Hint, this is an example of the Spectral Mapping Theorem, Kreyszig p. 381.]
2. Prove that the eigenvectors corresponding to a distinct set of eigenvalues are linearly independent.

Problem Set 7. Due F 10/26
Kreyszig p. 150 # 7, 8, 9
Kreyszig p. 175 # 4
Kreyszig p. 200 # 3, 5, 8
Ch. 3 # 5, 9, 14

Problem Set 6. Due F 10/19
Kreyszig p. 135 # 2, 3, 7, 11
Kreyszig p. 140 # 4, 8, 10
Ch. 3 # 1, 2, 3, 4, 7

Exam 1. Friday, October 12, 4:30-6:00 p.m. in RLM 11.176
Chapter 2

Problem Set 5. Due F 10/5
Ch. 2 # 27, 29, 32, 33, 34, 42, 46

Problem Set 4. Due F 9/28.
Ch. 2 # 15, 20, 22, 25, 30, 35, 36, 43

Problem Set 3. Due F 9/21.
Ch. 2 # 16, 17, 18, 19, 23, 24, 26

Problem Set 2. Due F 9/14.
Ch. 2 # 8, 11 (the t_i must sum to 1), 14
Kreyszig p. 218 # 5
Kreyszig p. 224 # 8, 11, 14
Web exercise:
1. Verify that B(X,Y) is a vector space.

Problem Set 1. Due F 9/7.
Ch. 1 # 2, 4
Ch. 2 # 2, 3, 5
Kreyszig p. 8 # 2, 3, 13
Kreyszig p. 16 # 6
Web exercises:
1. Sketch the unit ball in R² using the l_p norm, for 1 <= p <= infinity.
2. Prove that the l_p norm is in fact a norm on l_p, for 1 <= p <= infinity.