## Course information

Department of Mathematics

University of California

Davis, CA 95616, USA

e-mail: `jkhunter@ucdavis.edu`

Office Phone: (530) 554-1397

Office: MSB 3230

Office hours: MF 3:10–4:00 p.m., W 3:10–4:30 p.m.

Classroom: Physics 140

## Announcements

Solutions to the Final are here.

## Exams

There will be two Midterms and a Final (in class).

- Midterm 1: Wed, Feb 5 (in class)
- Midterm 2: Wed, Mar 5 (in class)
- Final: Thr, Mar 20, 1:00 – 3:00 p.m. (Exam Code M)

## Grade

Grade will based on exams and homework, weighted as follows:

- 10% Homework
- 25% Each Midterm
- 40% Final

## Text

Text:
*Partial Differential Equations*, Walter Strauss, 2nd Ed., 2008.

## Syllabus

I plan to cover roughly Chapters 7, 9, 11, 12, 14 from the text:

- Ch. 7: Laplace equation
- Ch. 8: Wave and heat equation
- Ch. 11: Eigenvalue problems
- Ch. 12: Distributions and transforms
- Ch. 14: Nonlinear PDEs

The department syllabus for the class is here.

## Midterm 1

Midterm 1 will be in class on Wednesday, Feb 5. It will cover Chapter 7 of the text plus other material covered in class:

- Vector calculus. Gradient, curl, and divergence.
- Line, surface, and volume integrals. Divergence and Stokes theorem.
- Potential theory. Derivation of Laplace's equation for heat flow (Sec. 1.3).
- Green's functions for ODEs.
- Mean value property and maximum principle for Laplace's equation (Sec. 7.1).
- Green's first and second identities (Sec. 7.1-7.2).
- Free-space Green's function for the Laplacian (Sec. 6.1).
- Green's function representation of free-space solutions of Laplace's and Poisson's equation.
- Green's function representation of solutions of boundary value problems for Laplace's and Poisson's equation (Sec. 7.2-7.3).
- Method of images (Sec 7.4).

Some sample midterm questions are here.

Solutions to the sample midterm questions are here.

Solutions to Midterm 1 are here.

## Midterm 2

Solutions to Midterm 2 are here.

## Homework

Homework will be assigned weekly and a hard copy will be due in class on Fridays.
Please write clearly or type and *staple* your solutions.
If you want to type good-looking mathematics, the standard tool is LaTeX, or one of its many variants.
See here to get started.

Problem numbers refer to the exercises in the text.

**Set 1** (Fri, Jan 17)

Problem set is here.

Solutions are here.

**Set 2** (Fri, Jan 24)

Problem set is here.

Solutions are here.

**Set 3** (Fri, Jan 31)

Prove the mean value property of harmonic functions in two and three space dimensions (see p. 180-181 in the text)

Sec 7.1, p. 183: 1, 2

Sec 7.2, p. 187: 1, 2, 3

**Set 4** (Fri, Feb 7)

Sec 7.4, p. 196: 2, 6, 18

**Set 5** (Fri, Feb 14)

Sec. 12.3, p. 348: 2, 4, 9

Sec. 12.4, p. 352: 1, 2

**Set 6** (Fri, Feb 21)

Sec 12.1, p. 337: 2, 3, 5, 8, 9, 12

Sec 12.2, p. 342: 2, 13

**Set 7** (Fri, Feb 28)

Sec 14.1, p. 389: 3, 5, 6, 8, 10, 11, 12

**Set 8** (Mon, Mar 17)

Sec 14.2, p. 395: 1, 10

Sec 14.4, p. 406: 4