MAT 207B, Winter Quarter, 2012

**Lectures:**
MWF 10:00–10:50 a.m., Wellman 209

**Office hours:**

MWF 2:30–3:30 p.m.

**Text:**
*Applied Mathematics*, David Logan, 3rd Ed.

John Hunter

Department of Mathematics

University of California

Davis, CA 95616, USA

e-mail: `jkhunter@ucdavis.edu`

Phone:

- (530) 554-1397 (Office)
- (530) 752-6653 (Fax)

Office: 3230 Mathematical Sciences Building

Solutions for the final exam are here. I've posted course grades to SmartSite.

S. Antman, The equations for large vibrations of strings (1980)

M. Kac, Can one hear the shape of a drum? (1966)

Here is a tentative outline of the topic we'll cover:

- Sturm-Liouville problems, Green's functions and integral equations for ODEs
- Calculus of variations and Euler-Lagrange equations for ODEs
- Laplace equation, potential theory, and Green's functions for PDEs
- The heat equation and diffusion
- The wave equation
- Some nonlinear PDEs

This material is covered in the following Chapters of Logan:

- Chapter 3. Calculus of Variations
- Chapter 4. Eigenvalue Problems, Integral Equations, and Green's Functions
- Chapter 6. Partial Differential Equations
- Chapter 7. Wave Phenomena

This book is a good resource for further information about Green's functions, BVPs, and related topics. It's available online from Wiley, free to UC addresses at:

Lecture notes which include further discussion of some of the topics covered in this class are here:

- 1. Sturm-Liouville problems
- 2. Eigenfunction expansions
- 3. Green's functions
- 4. Variational principles
- 5. Integral equations
- 6. Laplace's equation

Here are some sample final questions. Some brief solutions to the sample final questions are here. Don't consult them until you've tried all the problems yourself!

**Problem set 1** (Due Friday, Jan. 20)

LaTex file: Set 1

Solutions: Set 1

**Problem set 2** (Due Friday, Jan. 27)

LaTex file: Set 2

Solutions: Set 2

**Problem set 3** (Due Friday, Feb. 3)

LaTex file: Set 3

Solutions: Set 3

**Problem set 4** (Due Friday, Feb. 10)

LaTex file: Set 4

Solutions: Set 4

**Problem set 5** (Due Friday, Feb 17)

LaTex file: Set 5

Solutions: Set 5

**Problem set 6** (Due Friday, Feb 24)

LaTex file: Set 6

Solutions: Set 6

**Problem set 7** (Due Monday, Mar 5)

LaTex file: Set 7

Solutions: Set 7

**Problem set 8** (Due Monday, Mar 12)

LaTex file: Set 8

Solutions: Set 8