University at Buffalo 3 credits Mathematics
Transform theory for linear operators (Fourier transforms, Laplace transforms, Hankel transforms). Partial differential equations (theory of distributions, fundamental solutions to Laplace, wave and heat equations, construction of Green¿s functions using method of images, partial transforms, complete transforms, eigenfunction expansions). Asymptotic evaluation of integrals (integration by parts, Laplace¿s method, Watson¿s lemma, method of steepest descents, method of stationary phase). Regular perturbation theory (applications, method of strained coordinates, eigenvalues of nonlinear boundary-value problems, stationary and Hopf bifurcations). Singular perturbation theory (multiple scales analysis, singular perturbation theory for algebraic equations and boundary layer problems, WKB approximation, homogenization theory). Prerequisite: MTH306, MTH309, MTH 418 or consent of instructor
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