MATH 442 Intro to Partial Differential Equations, Fall 2019

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Section numbers in Walter A. Strauss, Partial Differential Equations: An Introduction, Second Edition, John Wiley & Sons, 2008.
errata See the Department Syllabus for more details.

1. Where PDEs Come From

1. What is a Partial Differential Equation?
2. First-Order Linear Equations
3. Flows, Vibrations, and Diffusions
4. Initial and Boundary Conditions
5. Well-Posed Problems

2. Waves and Diffusions

1. The Wave Equation
2. Causality and Energy
3. The Maximum Principle
4. Diffusion on the Whole Line
5. Waves vs. Diffusion

3. Reflections and Sources

3. Diffusion with a Source
4. Waves with a Source

4. Boundary Problems

1. The Dirichlet Condition
2. The Neumann Condition

5. Fourier Series

1. The Coefficients
2. Even, Odd, Periodic, and Complex Functions
3. Orthogonality and General Fourier Series
4. Completeness
5. Uniform Convergence and the Gibbs Phenomenon

6. Harmonic Functions

1. Laplace's Equation
2. Rectangles and Cubes
3. Poisson's Formula