Math 647: Theory of Partial Differential Equations 1

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Catalog Information

Title

Theory of Partial Differential Equations 1.

Credit Hours

3

Prerequisite

Math 541, 547. It is proposed that Math 547 be dropped as a prerequisite, as these courses have always operated independently of each other.

Description

Desired Learning Outcomes

Prerequisites

Minimal learning outcomes

  1. Foundational theory for canonical linear PDEs
    • Transport equation
    • Laplace's equation
      • Fundamental solution
      • Mean-value and maximum principles
      • Energy methods
    • Heat equation
      • Fundamental solution
      • Mean-value and maximum principles
      • Energy methods
    • Wave equation
      • Spherical means
      • Energy methods
  2. Method of characteristics
  3. Sobolev spaces
    • Traces
    • Sobolev inequalities
    • Compactness

Textbooks

Possible textbooks for this course include (but are not limited to):

  • Lawrence C. Evans, Partial Differential Equations (Second Edition), American Mathematical Society, 2010.

Additional topics

If time permits, Hamilton-Jacobi equations and/or conservation laws could be introduced.

Courses for which this course is prerequisite