**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

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#### Supplemental Materials

# An Introduction to Complex Analysis and Geometry

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*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.

-- Mathematical Reviews

The book under review provides a refreshing presentation of both classical and modern topics in and relating to complex analysis, which will be appreciated by mature undergraduates, budding graduate students, and even research mathematicians . . . The book's strengths lie in the characteristics which distinguish it from other undergraduate complex analysis texts. Throughout the book, numerous uncommon topics and rich examples tie complex analysis to farther areas of math, giving the reader a glimpse of the power of this intriguing subject . . . Overall, the text provides a mature view of basic concepts from complex analysis and also succeeds in giving a succinct introduction to the more sophisticated topics covered. It furthermore makes its collection of advanced and fascinating special topics accessible to the undergraduate.

-- Kealy Dias, Zentralblatt MATH