Difference between revisions of "Math 647: Theory of Partial Differential Equations 1"
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Revision as of 12:56, 31 May 2011
Contents
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
- 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
- Method of characteristics
- 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.
