This is free a textbook for an introductory course in complex analysis. Complex Analysis by George Cain can be downloaded in pdf format free of charge. It has been used for undergraduate complex analysis course at Georgia Tech and at a few other places.

## Book Description

Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is useful in many branches of mathematics, including number theory and applied mathematics; as well as in physics, including hydrodynamics, thermodynamics, and electrical engineering.

Complex analysis is particularly concerned with the analytic functions of complex variables (or, more generally, meromorphic functions). Because the separate real and imaginary parts of any analytic function must satisfy Laplace’s equation, complex analysis is widely applicable to two-dimensional problems in physics.

## Table of Contents

- Complex Numbers
- Complex Functions
- Elementary Functions
- Integration
- Cauchy’s Theorem
- More Integration
- Harmonic Functions
- Series
- Taylor and Laurent Series
- Poles, Residues, and All That