Mathematical Methods 3

Description

Theory of complex functions (Cauchy-Riemann equations, analyticity, Cauchy's theorem, sums and series, singularities, contour integrals, residue theorem, Laurent series, analytic continuation, uniform convergence) Applications to two-dimensional electrodynamics problems, Moebius transformations The Gamma function and the Riemann zeta function and their maximal analytic extension Objectives: Become proficient in the manipulation of complex functions. Understand analytic functions and analytic continuation. Construct proofs for statements regarding analytic functions. Use of the residue theorem to calculate integrals, understand the underlying assumptions, and to be able to apply all of these to particular physics problem. Learn standard techniques to solve differential equations including Fourier and Laplace transforms, and to be able to apply them to a variety of physical problems.