MATH-6640

Complex Variables and Integral Transforms with Applications

Review of basic complex variables theory; power series, analytic functions, singularities, and integration in the complex plane. Integral transforms (Laplace, Fourier, etc.) in the complex plane, with application to solution of PDEs and integral equations. Asymptotic expansions of integrals (Laplace method, methods of steepest descent and stationary phase), with emphasis on extraction of useful information from inversion integrals of transforms. Problems to be drawn from linear models in science and engineering. Prerequisites: MATH-4600 and familiarity with elementary ordinary and partial differential equations. Spring term odd-numbered years.

4 credit hours