Temple University 3 credits MATH
This course introduces fundamental concepts and results in the theory of elliptic, parabolic, and hyperbolic differential equations, preparing students for problem-solving in PDEs and their applications. Topics covered: Laplace's equation (maximum principles, Dirichlet problem, Green's function and Poisson kernel), Heat equation (initial boundary value problems, fundamental solution, mean value formula, maximum principle, uniqueness theorems, examples of non-uniqueness, backward heat equation, and energy methods), Wave equation (D'Alembert's formula, plane waves, solution by spherical means, Huygens' Principle, Energy methods: uniqueness, domain of dependence). Solution of the Cauchy problem for nonlinear first order PDEs. This course presupposes knowledge of undergraduate Real Analysis.
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