Partial Differential Equations
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Table of Contents
Course content
This is a typical first-year course on partial differential equations offered in a Ph.D. program in mathematics.
Topics
- Transport equation
- Laplace’s equation & Poisson’s equation
- Heat equation
- Wave equation
- Method of characteristics in generality
- Scalar conservation laws, weak solutions, and shock theory
- Linear wave theory and solitons — Korteweg-de Vries equation
Lecture notes
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