This unusually lively textbook on complex variables introduces the theory of analytic functions, explores its diverse applications and shows the reader how to harness its powerful techniques. "Complex Analysis" offers new and interesting motivations for classical results and introduces related topics that do not appear in this form in other texts. Stressing motivation and technique, and complete with exercise sets, this volume may be used both as a basic text and as a reference. For this second edition, the authors have revised some of the existing material and have provided new exercises and solutions.
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Book Description
Editorial Reviews
Review
From the reviews of the second edition:
"This is a clever, concise, concrete, and classical complex analysis book, aimed at undergraduates with no background beyond single-variable calculus. The book has an eclectic flavor … . There are many exercises … . Answers to all exercises are given in the back of the book … ." (Allen Stenger, The Mathematical Association of America, October, 2009)
From the Back Cover
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.
--This text refers to an alternate
Hardcover
edition.
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Most Helpful Customer Reviews
11 of 11 people found the following review helpful:
5.0 out of 5 stars
perhaps the best introduction to complex analysis,
By A Customer
This review is from: Complex Analysis (Hardcover)
This is the book that really made me understand basic complex analysis. It doesn't try to give the most sophisticated or slickest presentation for experts. Instead, it gives a beautiful, concrete, down to earth explanations. The best feature is the applications. D. J. Newman is one of the world's great problem solvers, and this book includes numerous examples of how to use complex analysis to solve problems in surprising ways. Even in the more standard applications, such as summing series, the book gives many unusual examples. It concludes with Newman's proof of the prime number theorem, which is substantially shorter and clearer than many other proofs.
14 of 15 people found the following review helpful:
5.0 out of 5 stars
Excellent!,
By
This review is from: Complex Analysis (Hardcover)
This is a brief text on complex analysis aimed at the traditional junior-senior course. As a text it may be a little too succinct for the average undergraduate. For example, I have no intention of teaching out of it. However, its clarity and presentation is absolutely refreshing. I think it is one of the best books written on complex analysis in the last twenty years. I recommend this book to any student of complex analysis.
15 of 17 people found the following review helpful:
5.0 out of 5 stars
a very good textbook,
By
This review is from: Complex Analysis (Hardcover)
In my viewpoint this book is one of the best complex analysis textbooks to date. It is succint and neat, without too many pages and too much content, while every facet of elementary complex analysis theory gets a chapter or two in it. It deals with power series first, then analytic fuctions, then singular pts and residue theorem, then conformal mapping. After these basic topic, it gives some futher theme like harmonic function and Riemann mapping theorem. And the last with some chapters, including a topic on proving prime number theorem, in application of the previous theorem. The pace of this book is very natural, the exercises adequate and well-selected. And in my experience, via this book students usually can handle the most some important topics and get a good structure feeling of this course. Highly recommended.
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Inside This Book
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First Sentence:
Numbers of the form a + b - 1, where a and b are real numbers-what we call complex numbers-appeared as early as the 16th century. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
closed curve theorem, regular closed curve, analytic polynomials, deleted neighborhood, analytic branch, modulus theorem, unit disc, conformal equivalence, many zeroes, power series representation, polygonal path, removable singularity, entire function, isolated singularity, conformal mapping, essential singularity Key Phrases - Capitalized Phrases (CAPs): (learn more)
Theorem Suppose, Uniqueness Theorem, Maximum-Modulus Theorem, Proof Let, Applications of the Residue Theorem, Cauchy Integral Formula, Properties of Analytic Functions, Liouville's Theorem, Dirichlet Problem, Schwarz Reflection Principle, Proof Suppose, Definition Suppose, Mean-Value Theorem, Cauchy's Theorem, Different Forms of Analytic Functions, Functions of the Complex Variable, Special Mappings, Definition Let, Rectangle Theorem, Application of Contour Integral Methods, Argument Principle, Evaluation of Definite Integrals, Integral Theorem, Proof Consider, Proof Note New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Numbers of the form a + b - 1, where a and b are real numbers-what we call complex numbers-appeared as early as the 16th century. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
closed curve theorem, regular closed curve, analytic polynomials, deleted neighborhood, analytic branch, modulus theorem, unit disc, conformal equivalence, many zeroes, power series representation, polygonal path, removable singularity, entire function, isolated singularity, conformal mapping, essential singularity Key Phrases - Capitalized Phrases (CAPs): (learn more)
Theorem Suppose, Uniqueness Theorem, Maximum-Modulus Theorem, Proof Let, Applications of the Residue Theorem, Cauchy Integral Formula, Properties of Analytic Functions, Liouville's Theorem, Dirichlet Problem, Schwarz Reflection Principle, Proof Suppose, Definition Suppose, Mean-Value Theorem, Cauchy's Theorem, Different Forms of Analytic Functions, Functions of the Complex Variable, Special Mappings, Definition Let, Rectangle Theorem, Application of Contour Integral Methods, Argument Principle, Evaluation of Definite Integrals, Integral Theorem, Proof Consider, Proof Note New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 96
books:
See all 96 books this book cites
100
books
cite this book:
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- Complex Analysis (Graduate Texts in Mathematics) by Serge Lang in Front Matter (1), Front Matter (2), and Back Matter
- Mathematical Reflections by Association of Teachers of Mathematics in Front Matter
- The Principles of Mathematical Analysis (International Series in Pure & Applied Mathematics) by Walter Rudin in Back Matter
- Linear Algebra (Oxford Science Publications) by Richard Kaye in Back Matter
- The Heritage of Thales (Undergraduate Texts in Mathematics / Readings in Mathematics) by W.S. Anglin in Front Matter
See all 96 books this book cites
- Math Talks for Undergraduates by Serge Lang on 4 pages
- Undergraduate Algebra (Undergraduate Texts in Mathematics) by Serge Lang in Front Matter, Back Matter (1), and Back Matter (2)
- Function Theory of One Complex Variable (Graduate Studies in Mathematics, 40) by Steven G. Krantz Robert E. Greene on page 471, page 474, and Back Matter
- Collected Papers Vol V: 1993-1999 (Collected Papers of Serge Lang) by Serge Lang on page 164, page 337, and page 388
- Ginzburg-Landau Phase Transition Theory and Superconductivity (International Series of Numerical Mathematics) by K.-H. Hoffmann in Back Matter (1), and Back Matter (2)
See all 100 books citing this book
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