## 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