This course will provide a rigorous and thorough-treatment of the theory of functions of one complex variable. The topics to be covered include complex numbers, complex differentiation, the Cauchy-Riemann equations, analytic functions, Cauchy’s theorem, complex integration, the Cauchy integral formula, Liouville’s theorem, the Gauss mean value theorem, the maximum modulus theorem, Rouche’s theorem, the Poisson integral formula, Taylor-Laurent expansions, singularity theory, conformal mapping with applications, analytic continuation, Schwarz’s reflection principle and elliptic functions.
Prerequisites
knowledge of undergraduate analysis