PDE Primer

A PDE Primer

The following four files contain material that is frequently covered in an Introduction to Partial Differential Equations course. This material follows a portion of the reading notes taken in 1964 by a student who was newly infatuated with the subject.

Introduction.pdf and Introduction.ps
1. Ordinary Differential Equations
2. First Order PDE
3. Second Order PDE
4. Characteristics and Canonical Forms
5. Characteristics and Discontinuities
6. PDE in N-dimensions
The Potential Equation.pdf and The Potential Equation.ps
1. Introduction
2. A Fundamental Representation
3. Harmonic Functions
4. Green's Function
5. Consequences of Poisson's Formula
6. The Dirichlet Problem
The Diffusion Equation.pdf and The Diffusion Equation.ps
1. Introduction
2. The Initial-Value Problem
3. Green's Function
The Wave Equation.pdf and The Wave Equation.ps
1. Introduction
2. The Cauchy Problem
3. Successive Approximations
4. The Effect of Data
5. Riemann's Representation
6. The Wave Equation in 3D
7. The Wave Equation in 2D
8. Energy Integrals
Appendix: The Divergence Theorem (4 pages)