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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
10.2 Vibrations of a Drumhead
It the time allows -
Chapter 13: PDE Problems from Physics
13.3 Scattering