| Hardcover ISBN: | 978-0-8218-5274-3 |
| Product Code: | AMSTEXT/12 |
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| eBook ISBN: | 978-1-4704-1125-1 |
| Product Code: | AMSTEXT/12.E |
| List Price: | $75.00 |
| MAA Member Price: | $67.50 |
| AMS Member Price: | $60.00 |
| Hardcover ISBN: | 978-0-8218-5274-3 |
| eBook: ISBN: | 978-1-4704-1125-1 |
| Product Code: | AMSTEXT/12.B |
| List Price: | $154.00 $116.50 |
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| AMS Member Price: | $123.20 $93.20 |
| Hardcover ISBN: | 978-0-8218-5274-3 |
| Product Code: | AMSTEXT/12 |
| List Price: | $79.00 |
| MAA Member Price: | $71.10 |
| AMS Member Price: | $63.20 |
| eBook ISBN: | 978-1-4704-1125-1 |
| Product Code: | AMSTEXT/12.E |
| List Price: | $75.00 |
| MAA Member Price: | $67.50 |
| AMS Member Price: | $60.00 |
| Hardcover ISBN: | 978-0-8218-5274-3 |
| eBook ISBN: | 978-1-4704-1125-1 |
| Product Code: | AMSTEXT/12.B |
| List Price: | $154.00 $116.50 |
| MAA Member Price: | $138.60 $104.85 |
| AMS Member Price: | $123.20 $93.20 |
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Book DetailsPure and Applied Undergraduate TextsVolume: 12; 2010; 163 ppMSC: Primary 30; 51; 26; 40
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.
ReadershipUndergraduate students interested in complex analysis.
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Table of Contents
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Cover
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Title page
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Contents
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Preface
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From the real numbers to the complex numbers
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Complex numbers
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Complex numbers and geometry
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Power series expansions
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Complex differentiation
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Complex integration
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Applications of complex integration
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Additional topics
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Bibliography
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Index
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Back Cover
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Additional Material
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Reviews
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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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RequestsReview Copy – for publishers of book reviewsDesk Copy – for instructors who have adopted an AMS textbook for a courseExamination Copy – for faculty considering an AMS textbook for a coursePermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Reviews
- Requests
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.
Undergraduate students interested in complex analysis.
-
Cover
-
Title page
-
Contents
-
Preface
-
From the real numbers to the complex numbers
-
Complex numbers
-
Complex numbers and geometry
-
Power series expansions
-
Complex differentiation
-
Complex integration
-
Applications of complex integration
-
Additional topics
-
Bibliography
-
Index
-
Back Cover
-
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
