Difference between revisions of "Math 547: Partial Differential Equations 1"
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+ | === Title === | ||
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+ | === Offered === | ||
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+ | === Prerequisite === | ||
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+ | === Description === | ||
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== Chris Grant's Proposed Core Topics for Math 547/548 == | == Chris Grant's Proposed Core Topics for Math 547/548 == | ||
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Revision as of 09:36, 9 May 2008
Contents
Catalog Information
Title
(Credit Hours:Lecture Hours:Lab Hours)
Offered
Prerequisite
Description
Note
Chris Grant's Proposed Core Topics for Math 547/548
- General Cauchy problem
- Cauchy-Kovalevskaya 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
- Classical theory for the canonical second-order linear equations on Rn
- Laplace's equation
- Green's first and second identities
- Mean Value Principle and its converse
- Weak and strong maximum principles
- Uniqueness for the Dirichlet problem
- Poisson integral formula
- Existence for the Dirichlet Problem on a ball
- Fundamental solutions
- Green's functions
- Harnack inequality
- Liouville's Theorem
- Harnack's Convergence Theorem
- Existence for the Dirichlet Problem on domains with regular boundaries and for continuous boundary data
- Interior and exterior sphere conditions
- Wave equation
- Method of spherical means
- Hadamard’s method of descent
- Huygen’s Principle
- Conservation of Energy
- Domain of Dependence
- Heat equation
- Fourier transforms
- The heat kernel
- Existence for the IVP
- Weak and strong maximum principles
- Uniqueness for the IBVP
- Laplace's equation