An Introduction to Complex Analysis and Geometry (Pure and Applied Undergraduate Texts); 2010; John P. D’Angelo (Author); ISBN-10: 0-8218-5274-4; ISBN-13: 978-0-8218-5274-3; [Hardcover]
Author: John P. D’Angelo, University of Illinois, Urbana, IL
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
Undergraduate students interested in complex analysis.
“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.”