Course Number:

Credit Hours:

4

Course Title:

Topics in Complex Analysis

Course Description:

Introduces complex analysis in one complex variable. Topics include holomorphic functions of one complex variable and their basic properties; geometrical and hydrodnamical interpretations of holomorphic functions; hyperbolic plane and its group of automorphisms; Cauchy-Riemann equations and Cauchy integral formula; Taylor series of holomorphic functions; Weierstrass and Runge theorems; Laurent series and classification of singular points of holomorphic functions; meromorphic functions; residues and their applications to the calculation of integrals; analytic continuation and Riemann surfaces; the maximum principle and Schwarz lemma; the Riemann mapping theorem; elements of the theory of elliptic functions; entire functions, their growth, and distribution of zeros; asymptotic expansions; and Laplace method and saddle point method for finding asymptotics of integrals.