electiveHQ

This course provides a thorough introduction to the mathematical theory of partial differential equations both the classical theory of Laplace, Cauchy, Fourier, Gauss etc and more modern analytic developments. Topics include first order equations, Cauchy problems, characteristics, linear second-order equations, classification, boundary value problems for elliptic equations, perimeter and initial value problems for hyperbolic and parabolic equations, fundamental solutions, Green's functions, eigenfunction expansions, Fourier transforms, and maximum principles.