Difference between revisions of "Math 647: Theory of Partial Differential Equations 1"

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(Minimal learning outcomes)
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#** Spherical means
 
#** Spherical means
 
#** Energy methods
 
#** Energy methods
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# Method of characteristics
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# Sobolev spaces
 +
#* Traces
 +
#* Sobolev inequalities
 +
#* Compactness
 
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Revision as of 11:54, 31 May 2011

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

Courses for which this course is prerequisite