Applied Partial Differential Equations

Catalog description

Inhomogeneous boundary value problems and solution by separation of variables. First order equations and their solution by characteristics. Higher order equations and systems, classification by characteristics. Hyperbolic equations and systems. The Riemann function, propagation of discontinuities and shocks. Boundary value problem for elliptic equations, maximum principle, Green's function. Potential theory, reduction of boundary value problem to an integral equation. Introduction to regular and singular perturbation solutions of non-linear equations.