Complex Analysis

MAT 3014

This course provides an introduction to analytic functions of one complex variable and their basic properties and applications. The material includes complex numbers, connectedness in the complex plane, conformal mappings, holomorphic functions, and Cauchy’s integral formulas, Liouville’s theorem, mean value property, and maximum modulus principle, Taylor and Laurent expansions, analytic functions, and analytic continuation principle, as well as residue theorem and evaluation of integrals by the method of residues.