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An Introduction to Complex Analysis and Geometry
 
John P. D’Angelo University of Illinois, Urbana, IL
An Introduction to Complex Analysis and Geometry
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
An Introduction to Complex Analysis and Geometry
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An Introduction to Complex Analysis and Geometry
John P. D’Angelo University of Illinois, Urbana, IL
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
  • Book Details
     
     
    Pure and Applied Undergraduate Texts
    Volume: 122010; 163 pp
    MSC: 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.

    Readership

    Undergraduate students interested in complex analysis.

  • Table of Contents
     
     
    • 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
  • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Desk Copy – for instructors who have adopted an AMS textbook for a course
    Examination Copy – for faculty considering an AMS textbook for a course
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 122010; 163 pp
MSC: 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.

Readership

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
Review Copy – for publishers of book reviews
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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