**Pure and Applied Undergraduate Texts**

Volume: 12;
2010;
163 pp;
Hardcover

MSC: Primary 30; 51; 26; 40;

Print ISBN: 978-0-8218-5274-3

Product Code: AMSTEXT/12

List Price: $60.00

Individual Member Price: $48.00

**Electronic ISBN: 978-1-4704-1125-1
Product Code: AMSTEXT/12.E**

List Price: $60.00

Individual Member Price: $48.00

#### You may also like

#### Supplemental Materials

# An Introduction to Complex Analysis and Geometry

Share this page
*John P. D’Angelo*

An Introduction to Complex Analysis and Geometry provides the
reader with a deep appreciation of complex analysis and how this subject
fits into mathematics. The book developed from courses given in the
Campus Honors Program at the University of Illinois Urbana-Champaign.
These courses aimed to share with students the way many mathematics and
physics problems magically simplify when viewed from the perspective of
complex analysis. The book begins at an elementary level but also
contains advanced material.

The first four chapters provide an introduction to complex analysis with
many elementary and unusual applications. Chapters 5 through 7 develop
the Cauchy theory and include some striking applications to calculus.
Chapter 8 glimpses several appealing topics, simultaneously unifying the
book and opening the door to further study.

The 280 exercises range from simple computations to difficult problems.
Their variety makes the book especially attractive.

A reader of the first four chapters will be able to apply complex
numbers in many elementary contexts. A reader of the full book will
know basic one complex variable theory and will have seen it integrated
into mathematics as a whole. Research mathematicians will discover
several novel perspectives.

#### Table of Contents

# Table of Contents

## An Introduction to Complex Analysis and Geometry

- Cover Cover11 free
- Title page iii4 free
- Contents v6 free
- Preface vii8 free
- From the real numbers to the complex numbers 114 free
- Complex numbers 2538
- Complex numbers and geometry 4962
- Power series expansions 6780
- Complex differentiation 8396
- Complex integration 99112
- Applications of complex integration 119132
- Additional topics 137150
- Bibliography 159172
- Index 161174 free
- Back Cover Back Cover1177

#### Readership

Undergraduate students interested in complex analysis.

#### Reviews

The book provides the reader with a deep appreciation of complex analysis and how this subject fits into mathematics.