MATH 8361 Partial Differential Equations
This course considers waves and diffusion, initial value problems for hyperbolic and parabolic equations, boundary value problems for elliptic equations. Topics include: first-order equations: characteristic ODEs, existence of smooth solutions, conservation law equations, shocks, rarefaction, integral solutions; second-order partial differential equations and classification; Wave equation: fundamental solutions in one, two and three dimensions, Duhamel's principle, energy methods, finite propagation speed; Laplace equation: mean-value property, smoothness, maximum principle, uniqueness of solutions, Hamack inequality, Liouville theorem; Poisson Equation: fundamental solution, Greens functions, energy methods. Heat Equation: fundamental solution, maximum principle, uniqueness of solutions on a bounded domain, energy methods etc.
Prerequisite
Departmental approval
Offered
As scheduled