MAT 207B, Winter Quarter, 2016

**Lectures:**
MWF 10:00–10:50 a.m., Bainer 1128

**Text:**
*Boundary and Eigenvalue Problems in Mathematical Physics*, Hans Sagan (recommended but not required)

**Smart Site:**
The Smartsite for the class is
here

John Hunter

Department of Mathematics

University of California

Davis, CA 95616, USA

**Office:** 3230 Mathematical Sciences Building

**Office hours:**
MW 2:30–3:45 p.m.

**e-mail:** `jkhunter@ucdavis.edu`

**Phone:** (530) 601-4444 x4016 (Office); (530) 752-6653 (Fax)

**Office:** MSB 3229

**Office hours:**
R 1:30–2:30 p.m.

Solutions to the final exam are here.

This class will cover some of the classical methods of applied mathematics including:

- Calculus of variations and Euler-Lagrange equations
- Laplace equation, potential theory
- The heat and wave equations
- Separation of variables for linear PDEs
- Sturm-Liouville problems
- Eigenfunction expansions
- Green's functions
- Integral equations

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:

Naoki Saito has an extensive set of lecture notes on the topics covered in this class:

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

There will be one in-class Midterm and an in-class Final

- Midterm 1: Friday, Feb 19
- Final: Friday, Mar 18 10:30 a.m.–12:30 p.m. (Exam Code Q)

Solutions to the Midterm are here.

The Midterm will be in class on Friday, Feb 19. It will be closed book and cover the class material up to this point. A brief outline of topics together with the relevant sections of the text are as follows:

- Calculus of variations (Ch. I)
- Heat, wave, and Schrodinger equations (Ch. II)
- Vector analysis (Appendix I)
- Fourier series and Eigenfunction expansions. Solution of IBVPs for PDEs by separation of variables (Ch. IV)
- Differential operators and their adjoints. Sturm-Liouville eigenvalue problems(Ch. V)

**Problem set 1** (Due Friday, Jan 22)

**Latex file**

**Solutions: Set 1**

**Problem set 2** (Due Friday, Jan 29)

**Latex file**

**Solutions: Set 2**

**Problem set 3** (Due Friday, Feb 5)

**Latex file**

**Solutions: Set 3**

**Problem set 4** (Due Friday, Feb 12)

**Latex file**

**Solutions: Set 4**

**Problem set 5** (Due Friday, Feb 19)

**Latex file**

**Solutions: Set 5**

**Problem set 6** (Due Friday, Mar 4)

**Latex file**

**Solutions: Set 6**

**Problem set 7** ~~(Due Monday, Mar 14)~~ (Due Friday, Mar 18)

**Latex file**