Difference between revisions of "Math 447: Intro to Partial Differential Equations"
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Revision as of 13:57, 4 June 2009
Catalog Information
Title
Introduction to Partial Differential Equations.
(Credit Hours:Lecture Hours:Lab Hours)
(3:3:0)
Offered
W, Su
Prerequisite
Description
Boundary value problems; transform methods; Fourier series; Bessel functions; Legendre polynomials.
Chris Grant's Proposed Core Topics
- Basic classification of PDEs
- As nonlinear, linear homogeneous, linear inhomogeneous
- By order
- Of second-order linear PDEs in 2 variables as elliptic, parabolic, or hyperbolic
- Basic Modeling
- Derivation of the heat equation
- Derivation of the wave equation
- Derivation of Dirichlet, Neumann, and mixed boundary conditions for the heat equation
- Basic principles, techniques, and theory
- Principle of superposition
- Method of separation of variables
- Definition of eigenvalues and eigenfunctions corresponding to two-point BVPs
- Basic Sturm-Liouville theory
- Special eigensystems
- Fourier series
- Computation of the Fourier series of a p-periodic function on an interval of length p
- Computation of Fourier sine and cosine series of a symmetric p-periodic function on an interval of length p
- Fourier series of modifications and combinations of functions
- Theorems on pointwise, uniform, and L2 convergence
- Bessel's Inequality and Parseval's Equation
- Fourier integral representations of functions on lines and half-lines
- Bessel's equation and Bessel functions
- Legendre's differential equation and Legendre polynomials
- Fourier series
- Representation of solutions to the canonical equations on simple domains
- Laplace's equation
- Eigenfunction expansion of solutions on rectangles
- Integral representation of solutions on rectangular strips, quarter-planes, and half-planes
- Bessel function expansion of solutions on disks
- Legendre polynomial expansion on balls
- Wave equation
- Fourier expansion of solutions on bounded intervals
- D'Alembert's formula for solutions on lines and half-lines
- Bessel function expansion of solutions on disks
- Legendre polynomial expansion on balls
- Heat equation
- Steady-state solutions for IBVPs on bounded intervals
- Fourier expansion of solutions on bounded intervals
- Integral representation of solutions on lines and half-lines
- Eigenfunction expansion of solutions on rectangles
- Bessel function expansion of solutions on disks
- Legendre polynomial expansion of solutions on balls
- Laplace's equation
