Difference between revisions of "Math 547: Partial Differential Equations 1"
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Revision as of 10:39, 31 May 2011
Contents
Catalog Information
Title
Partial Differential Equations 1. [Recommended change: Applied Partial Differential Equations]
Credit Hours
3
Prerequisite
Math 334, 342; or equivalents.
Recommended(?)
Math 314, 341; or equivalents.
Description
Methods of analysis for hyperbolic, elliptic, and parabolic equations, including characteristic manifolds, distributions, Green's functions, maximum principles and Fourier analysis.
Desired Learning Outcomes
Prerequisites
Minimal learning outcomes
- General Cauchy problem
- Cauchy-Kowalevski Theorem
- Lewy Example
- Method of characteristics for first-order equations
- Semilinear case
- Quasilinear case
- General case
- Quasilinear systems of conservation laws on a line
- Riemann problem
- Rankine-Hugoniot jump condition
- Entropy condition
- Shocks
- Rarefaction waves
- Classification of general second-order equations
- Canonical forms for semilinear second-order equations
- Hyperbolic equations
- The wave equation
- Cauchy problem
- Problems with boundary data
- Huygens' principle
- Applications
- Elliptic equations
- Laplace's equation
- Poisson's equation
- Green's functions
- Maximum principles
- Applications
- Parabolic equations
- The heat equation
- Green's functions
- The heat kernel
- Maximum principles
- Applications
Textbooks
Possible textbooks for this course include (but are not limited to):
- John Ockendon, Sam Howison, Andrew Lacey, and Alexander Movchan, Applied Partial Differential Equations (Revised Edition), Oxford University Press, 1999.
