
Preface  Preview Material  Table of Contents  Supplementary Material 
Pure and Applied Undergraduate Texts 2010; 163 pp; hardcover Volume: 12 ISBN10: 0821852744 ISBN13: 9780821852743 List Price: US$60 Member Price: US$48 Order Code: AMSTEXT/12 See also: Complex Variables  Joseph L Taylor Function Theory of One Complex Variable: Third Edition  Robert E Greene and Steven G Krantz Complex Made Simple  David C Ullrich Complex Function Theory: Second Edition  Donald Sarason  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 UrbanaChampaign. 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. Request an examination or desk copy. 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 


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