ABSTRACT

This book includes information on elementary general topology, the Cauchy Integral Theorem and concepts of homology and homotopy in their application to the Cauchy theory. It is intended for an introductory course in complex analysis at the first-year graduate and advanced undergraduate level.

chapter 1|27 pages

The Real and Complex Number Fields

chapter 2|19 pages

Sequences and Series

chapter 4|13 pages

Introduction to Power Series

chapter 5|24 pages

Some Elementary Topological Concepts

chapter 6|19 pages

Complex Differential Calculus

chapter 7|19 pages

The Exponential and Related Functions

chapter 8|21 pages

Complex Line Integrals

chapter 9|43 pages

Introduction to the Cauchy Theory

chapter 11|21 pages

Residues and Rational Functions

chapter 13|78 pages

Conformal Mapping