AMATH 453 - Partial Differential Equations 2

Sivabal Sivaloganathan

Fall 2013

Course Notes by David Siegel

Cauchy Problem, Characteristic Curves, Integral Surfaces
Semi-Linear and Quasi-Linear Differential Equations, Cauchy Data, Cauchy-Kowalevski Theorem
Classification of Second Order Partial Differential Equations
First Order Systems, Well-Posedness
Elliptic Equations, Green's Identities
Maximum Principles, Mean Value Property
Green's Functions
Dirichlet Problem, Helmholtz Equation, Neumann Problem, Modified Green's Function
Riemann Mapping Theorem, Conformal Maps, Möbius Transformations
Fourier Series, Eigenvalues of the Laplacian
Hyperbolic Equations, Duhamel's Principle
Wave Equation in More Than 1-D, Huygen's Principle, Conservation of Energy
Parabolic Equations, Transfer Methods, Fourier Transform, Laplace Transform