Complex Analysis - A Short Course

The book entitled Complex Analysis – A Short Course contains five chapters. This book contains Power series representation of analytic function zeros of an analytic function the index of a closed curve Cauchy’s theorem and integral formula counting zeros the open mapping Theorem. Classification of singularities residues the argument principle the maximum principle Schwarz Lemma convex functions and Hadamard’s three circles theorem Phragmen lindelof theorem. Spaces of analytical functions Riemann’s mapping theorem Weierstrass factorization theorem factorization of sine function Gamma functions Riemann zeta functions. Runge’s theorem Mittag-Leffler’s theorem Schwarz reflection principle analytic continuation along a path Monodromy theorem Basic properties of harmonic functions harmonic functions on a disk Green’s functions. Entire functions Jensen’s formula Genus and order of an Entire functions Hadamard Factorization theorem Range of an analytic function Bloch’s theorem the little Picard theorem Schottky’s theorem the great Picard theorem.