This topic includes: Elementary mappings and transcendental functions in the complex domain; branch of argument; branch of logarithm. Complex power series, domain of convergence. Analytic functions; Cauchy-Riemann equations. Mobius transformation; conformal mapping; Schwarz-Christoffel transformations and applications. Taylor and Laurent series. Applications of the calculus of residues. Rouche's theorem. Infinite products.
This topic aims to ensure that the students have a basic understanding of the following: