### Math 425: Partial Differential Equations

### MWF 12-1

### Course Description

Prerequisite(s): MATH 241 or permission of instructor. Knowledge of
physics 150-151 will be helpful, but not required.
We will study the wave, heat, and Laplace equations. These are the
classic examples of hyperbolic, parabolic, and elliptic equations,
respectively.

In addition, one or more of the following topics will be covered:
qualitative properties of solutions of various equations
(characteristics, maximum principles, uniqueness theorems), Laplace
and Fourier transform methods, nonlinear equations, and
rudimentary asymptotics.

There will be some discussion of numerical methods, as well as
computer demonstrations, however this will not be the focus of the
course.

Class Policy (homework, midterms, etc)

Homework due Wednesday January 21

Homework due Wednesday January 28

Homework due Wednesday February 4

Homework due Friday February 13

Homework due Wednesday February 18

Homework due Wednesday February 25

A maple worksheet on the periodic heat equation.

This includes homework due Wednesday March 4.

A maple worksheet on the wave equation with Dirichlet boundary condition.

This includes homework due Wednesday March 4.

A maple worksheet on the periodic wave equation.

Solutions to the Homework due Wednesday March 4

Homework due Wednesday March 18

Homework due Friday March 27

Homework due Wednesday April 1

Homework due Wednesday April 8

Homework due Wednesday April 15

Homework due Friday April 24

### FINAL EXAM: Monday May 4, 11 am - 1 pm in DRL 4C2