Complexe Functietheorie

The basics of Complex Analysis: mapping behaviour of analytic functions, harmonic functions as related to analytic functions, many-valued functions and branches thereof, complex integration, the theorems of Cauchy and their applications such as series representations of analytic functions, and evaluation of (real) integrals using residue calculus. There are also some applications to Fourier and (inverse) Laplace transforms and their relations to PDEs.