Analytic Functions, Advanced Course
Official Course Description
The course is designed to be a deepening and continuation of the courses Function Theory/Complex analysis (FMAF01/FMA 037). It aims to exhibit a theory which is useful both within and outside Mathematics. For example is this the case in two-dimensional potential theory, Laplace- and other integral transforms and stability theory in control theory.
Contents Analytic continuation. Complex integration. The argument principle. Conformal mappings. Polynomials and their zeroes. Partial fractions, meromorphic functions. Infinite products. Ordinary differential equations. Integral transforms. Asymptotic methods. Potential theory.