250019 VO Complex analysis (2021W)

complex numbers, holomorphic functions, the Cauchy-Riemann equations, power series, contour integrals, winding numbers, Cauchy's theorem and the Cauchy integral formula, expansion of holomorphic functions in power series, the Identity Theorem, zeros and singularities, the Mean Value Theorem and the Maximum Principle, Cauchy estimates and Liouville's Theorem, and, as far as the circumstances allow, also: Laurent series, the Residue Theorem and applications