### Math 40750, PDE, Syllabus

Textbook:"Partial Differential Equations: An Introduction" by Walter A Strauss.

Syllabus:

```Chapter 1: Where PDEs Come From
1.1  Waht is a Partial Differential Equation?
1.2  First-order Linear Equations
1.3  Flows, Vibrations, and Diffusions
1.4  Initial and Boundary Conditions
1.5  Well-Posed Problems
1.6  Types of Second-order Equations

Chapter 2:  Waves and Diffusions
2.1  The Wave Equation
2.2  Causality and Energy
2.3  The Diffusion Equation
2.4  Diffusion on the Whole Line
2.5  Comparison of Waves and Diffusions'

Chapter 3: Reflections and Sources
3.1  Diffusion on the half-line
3.3  Diffusion with a Source

Chapter 4:  Boundary Problems
4.1  Seperation of Variables, the Dirichlet Condition
4.2  The Neumann Condition
4.3  The Robin Condition

Chapter 5:  Fourier Series
5.1  The Coefficients
5.2  Even, Odd, Periodic, and Complex Functions
5.3  Orthonality and General Fourier Series
5.4  Completeness

Chapter 6:  Harmonic Functions
6.1  Laplace's Equation
6.2  Rectangle and Cubes
6.3  Poisson's Formula
6.4  Circles, Wedges, and Annuli

Chapter 10: Boundaries in the Plane and in Space
10.1  Fourier's Method, Revisited