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.