Math4202/8202 Theory of Partial Differential Equations

Lectures

Motivating problems
Cauchy–Kovalevskaya Theorem
Separation of variables
Laplace's equation
The heat equation
Schauder estimates
The maximum principle
Perron's method
Distributions and their properties
The Fourier transform, tempered distributions, and fundamental solutions
Weakly differentiable functions and their properties
Weak solutions and their regularity

(A non-trivial portion of these notes have been adapted from notes by Christopher Hopper.)

Assignments

Assignment 1
Assignment 2
Assignment 3
Assignment 4
Assignment 5