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