Overview
- Authors:
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Joseph Bak
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Department of Mathematics, City College of New York, New York, USA
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Donald J. Newman
- 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
- Includes supplementary material: sn.pub/extras
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Table of contents (19 chapters)
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- Joseph Bak, Donald J. Newman
Pages 1-20
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- Joseph Bak, Donald J. Newman
Pages 21-34
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- Joseph Bak, Donald J. Newman
Pages 35-43
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- Joseph Bak, Donald J. Newman
Pages 45-57
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- Joseph Bak, Donald J. Newman
Pages 59-75
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- Joseph Bak, Donald J. Newman
Pages 77-91
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- Joseph Bak, Donald J. Newman
Pages 93-105
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- Joseph Bak, Donald J. Newman
Pages 107-116
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- Joseph Bak, Donald J. Newman
Pages 117-128
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- Joseph Bak, Donald J. Newman
Pages 129-142
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- Joseph Bak, Donald J. Newman
Pages 143-160
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- Joseph Bak, Donald J. Newman
Pages 161-168
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- Joseph Bak, Donald J. Newman
Pages 169-194
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- Joseph Bak, Donald J. Newman
Pages 195-214
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- Joseph Bak, Donald J. Newman
Pages 215-223
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- Joseph Bak, Donald J. Newman
Pages 225-239
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- Joseph Bak, Donald J. Newman
Pages 241-256
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- Joseph Bak, Donald J. Newman
Pages 257-272
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- Joseph Bak, Donald J. Newman
Pages 273-290
About this book
Beginning with the ?rst edition of Complex Analysis, we have attempted to present the classical and beautiful theory of complex variables in the clearest and most intuitive form possible. The changes inthisedition, which include additions to ten of the nineteen chapters, are intended to provide the additional insights that can be obtainedby seeing a little more of the “bigpicture”.This includesadditional related results and occasional generalizations that place the results inaslightly broader context. The Fundamental Theorem of Algebra is enhanced by three related results. Section 1.3 offers a detailed look at the solution of the cubic equation and its role in the acceptance of complex numbers. While there is no formula for determining the rootsof a generalpolynomial,we added a section on Newton’sMethod,a numerical technique for approximating the zeroes of any polynomial. And the Gauss-Lucas Theorem provides an insight into the location of the zeroes of a polynomial and those of its derivative. Aseries of new results relate to the mapping properties of analytic functions. Arevised proof of Theorem 6.15 leads naturally to a discussion of the connection between critical points and saddle points in the complex plane. The proof of the SchwarzRe?ectionPrinciplehasbeenexpandedtoincludere?ectionacrossanalytic arcs, which plays a key role in a new section (14.3) on the mapping properties of analytic functions on closed domains. And our treatment of special mappings has been enhanced by the inclusion of Schwarz-Christoffel transformations.
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)
Authors and Affiliations
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Department of Mathematics, City College of New York, New York, USA
Joseph Bak
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.
