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