Home page for Math 644, Partial Differential Equations, Fall 2020

Instructor: Charles L. Epstein

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This course is being given online this year, and run through its canvas page.

The Course

Tentative Syllabus

The first 4 topics are pretty well set, but 5-7 are subject to change.
  1. Quick Review of Ordinary Differential Equations
  2. The Physical Origins of Partial Differential Equations
  3. Basic Fourier Analysis
  4. The Equations of Mathematical Physics on Euclidean Space
    1. Laplace's equation: The Maximum Principle,  Dirichlet and Neumann problems, well and ill-posed problems, regularity in Sobolev spaces, connections to analytic functions in dimension 2
    2. The Heat Equation: The Maximum Principle, Cauchy's problem
    3. The Wave Equation: Energy estimates, finite propagation speed, the Cauchy problem, the Radon transform
  5. Sobolev spaces in bounded domains
  6. Boundary value problems for Laplace's equation
  7. Fundamental solutions and boundary integral methods for Laplace's equation


Problem Sets

  1. Problem set 1 is due September 15, 2020.

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