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© 2010

Complex Analysis

Textbook

Part of the Undergraduate Texts in Mathematics book series (UTM)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Joseph Bak, Donald J. Newman
    Pages 1-20
  3. Joseph Bak, Donald J. Newman
    Pages 21-34
  4. Joseph Bak, Donald J. Newman
    Pages 35-43
  5. Joseph Bak, Donald J. Newman
    Pages 45-57
  6. Joseph Bak, Donald J. Newman
    Pages 59-75
  7. Joseph Bak, Donald J. Newman
    Pages 77-91
  8. Joseph Bak, Donald J. Newman
    Pages 93-105
  9. Joseph Bak, Donald J. Newman
    Pages 107-116
  10. Joseph Bak, Donald J. Newman
    Pages 117-128
  11. Joseph Bak, Donald J. Newman
    Pages 129-142
  12. Joseph Bak, Donald J. Newman
    Pages 161-168
  13. Joseph Bak, Donald J. Newman
    Pages 169-194
  14. Joseph Bak, Donald J. Newman
    Pages 195-214
  15. Joseph Bak, Donald J. Newman
    Pages 215-223
  16. Joseph Bak, Donald J. Newman
    Pages 225-239
  17. Joseph Bak, Donald J. Newman
    Pages 241-256
  18. Joseph Bak, Donald J. Newman
    Pages 257-272
  19. Joseph Bak, Donald J. Newman
    Pages 273-290

About this book

Introduction

This unusual and lively textbook offers a clear and intuitive approach to the classical and beautiful theory of complex variables. With very little dependence on advanced concepts from several-variable calculus and topology, the text focuses on the authentic complex-variable ideas and techniques. Notable additions to "Complex Analysis, Third Edition," include: • The solution of the cubic equation and Newton’s method for approximating the zeroes of any polynomial; • Expanded treatments of the Schwarz reflection principle and of the mapping properties of analytic functions on closed domains; • An introduction to Schwarz-Christoffel transformations and to Dirichlet series; • A streamlined proof of the prime number theorem, and more. Accessible to students at their early stages of mathematical study, this full first year course in complex analysis offers new and interesting motivations for classical results and introduces related topics stressing motivation and technique. Numerous illustrations, examples, and now 300 exercises, enrich the text. Students who master this textbook will emerge with an excellent grounding in complex analysis, and a solid understanding of its wide applicability.

Keywords

Analysis Complex analysis Funktionentheorie Residue theorem analytic function calculus maximum

Authors and affiliations

  1. 1.Department of MathematicsCity College of New YorkNew YorkUSA

About the authors

Dr. Joseph Bak is the Assistant Chair of the Mathematics department at The City College of New York. Joseph Bak's primary area of research is approximation theory. Dr. Donald J. Newman (July 27, 1930 - March 28, 2007) was a champion problem solver. His mathematical specialties included complex analysis, approximation theory and number theory. His career included posts as a Professor of Mathematics at MIT, Brown University, Yeshiva University, Temple University and a distinguished chair at Bar Ilan University in Israel. His publications include 150 papers and five books.

Bibliographic information

  • Book Title Complex Analysis
  • Authors Joseph Bak
    Donald J. Newman
  • Series Title Undergraduate Texts in Mathematics
  • DOI https://doi.org/10.1007/978-1-4419-7288-0
  • Copyright Information Springer Science+Business Media, LLC 2010
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-1-4419-7287-3
  • Softcover ISBN 978-1-4614-2636-3
  • eBook ISBN 978-1-4419-7288-0
  • Series ISSN 0172-6056
  • Series E-ISSN 2197-5604
  • Edition Number 3
  • Number of Pages XII, 328
  • Number of Illustrations 77 b/w illustrations, 0 illustrations in colour
  • Topics Analysis
  • Buy this book on publisher's site
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Reviews

From the reviews of the third edition:

“The book of the known mathematicians J. Bak and D. Newman is an excellent introduction into the theory of analytic functions of one complex variable. The book is written on an elementary level and so it supports students in the early stages of their mathematical studies. … The book also contains many illustrations, examples and exercises, which give additional information and explanations.” (Konstantin Malyutin, Zentralblatt MATH, Vol. 1205, 2011)