Fundamentals of Complex Analysis

Complex Analysis covers some basic results pertaining to the functions of complex variable, analytic function, entire function, laurent expansion, calculus of residues, uniform convergence and conformal mapping.

This book provides an introduction to complex analysis for students with some familiarity with complex numbers from high school. Students should be familiar with the Cartesian representation of complex numbers and with the algebra of complex numbers. A familiarity with multivariable calculus is also required, but here the fundamental ideas are reviewed. In fact, complex analysis provides a good training ground for multivariable calculus.

The book is designed to serve as a text for a first course on the classical theory complex functions or as a supplement to other standard texts. As a prerequisite the reader is expected to have adequate knowledge of the elements real analysis.

This book is organised into five parts and is based on the following structures and concepts: Complex numbers and its geometrical interpretation; Analytic functions and entire functions; Laurent series and calculus of residues; Uniform convergence of a sequence and series; Conformal mappings and its construction.