Math 232 - Introduction to Partial Differential Equations

Lecture notes (access restricted to Duke users)

• Introduction
• First order equations, method of characteristics
• Weak solutions, shocks, conservation laws
• Introduction to second order equations
• The wave equation in one dimension
• The wave equation in 2 and 3 dimensions
• The wave equation in bounded domains, separation of variables
• Laplace's equation, Poisson's equation, Green's functions
• The heat equation
• The Fourier transform and applications to PDE
• Introduction to weak derivatives
• Variational methods, eigenvalues and eigenfunctions