Teaching / Course archive
Math 580: Fall 2014
PDE 1
Course Record
Overview
PDE I course beginning with ODE methods and first order equations, then moving through Cauchy-Kovalevskaya theory, wave and heat equations, harmonic functions, and the Dirichlet problem.
Schedule and Topics
| Date | Topic |
|---|---|
| W 9/3 | Ordinary differential equations, local existence and uniqueness. |
| W 9/17 | Homogeneous linear first order equations and characteristic curves. |
| W 10/1 | Cauchy-Kovalevskaya theorem for first order linear systems. |
| W 10/15 | Basic classifications and the one-dimensional wave equation. |
| M 10/20 | Kirchhoff's formula for the wave equation. |
| W 10/29 | Geometric optics and the Euclidean heat kernel. |
| M 11/10 | Harnack inequality, Liouville's theorem, and maximum principles. |
| M 11/24 | Perron's method and boundary regularity. |
| W 12/3 | Hamilton-Jacobi equations. |
Topic List
- Linear first and second order equations
- Cauchy-Kovalevskaya theorem, characteristic surfaces, and well-posedness
- Wave equation, finite speed of propagation, Kirchhoff formula, and geometric optics
- Heat equation, parabolic maximum principles, and uniqueness
- Harmonic functions, Poisson formula, Harnack inequalities, and Perron's method
- Sobolev spaces, if time permits
Books and Related Pages
Books
- Lawrence C. Evans, Partial differential equations. AMS, 1998.
- Fritz John, Partial differential equations. Springer, 1982.
- Jurgen Jost, Partial differential equations. Springer, 2007.
- Qing Han, A basic course in partial differential equations. AMS, 2011.
Assignments and Projects
Assignments and Exams
- Assignments 1-5.
- Two take-home midterm exams and a final exam.
Local Materials
Notes
- Analytic pdf
- Firstorder pdf
- Perron pdf