Complex Analysis

by Theodore W. Gamelin

The book provides an introduction to complex analysis for students with some familiarity with complex numbers from high school. It conists of sixteen chapters. The first eleven chapters are aimed at an Upper Division undergraduate audience. The remaining five chapters are designed to complete the coverage of all background necessary for passing PhD qualifying exams in complex analysis. Topics studied in the book include Julia sets and the Mandelbrot set, Dirichlet series and the prime number theorem, and the uniformization theorem for Riemann surfaces. The three geometries, spherical, euclidean, and hyperbolic, are stressed. Exercises range from the very simple to the quite challenging, in all chapters. The book is based on lectures given over the years by the author at several places, including UCLA, Brown University, the universities at La Plata and Buenos Aires, Argentina; and the Universidad Autonomo de Valencia, Spain.

Genres: Mathematics, Textbooks, Nonfiction

Kindle Edition

First published May 18, 2001

Reviews

[Daniel Wright]

Solid run-through of the basics of complex analysis. Very useful as a reference and as a text for a first serious introduction to the subject.

[Lucas]

Good pacing and useful examples, but occasionally uses new concepts without introducing them at all, can be painfully dry, and could really use more figures

[Leon]

A great balance between readability and depth. Topics are motivated well and organized sensibly. Good examples. Nice cover.

This is the kind of book you can start a few days before your exam after a semester of not going to class and still grasp enough to do well. Fantastic for an irresponsible undergraduate.

[Ethan Jensen]

Best book I’ve seen introducing complex analysis. My favorite chapters were the ones on the approximation theorems, i.e Weierstrass factorization and Mittag-Lefler pole expansion.

[Phillip Zhou]

This is one of my least favorite math textbooks I have used in any class. It is not explicit enough, its notation is confusing and or inconsistent in some places, and it does not treat the subject with enough rigor. All of this combined to making this textbook very frustrating to use. Consider using Shakarchi and Stein's textbook instead.

[Olof]

I feel like this book is more geared towards applications than theory and to its merit is therefore very compact.

Much of the matters concerning convergence and metric space theory is brushed over and not fully explained so a background in metric space theory enables a greater understanding.