Elementary Theory of Analytic Functions of One or Several Complex Variables

Elementary Theory of Analytic Functions of One or Several Complex Variables
Title Elementary Theory of Analytic Functions of One or Several Complex Variables PDF eBook
Author Henri Cartan
Publisher Courier Corporation
Pages 242
Release 2013-04-22
Genre Mathematics
ISBN 0486318672

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Basic treatment includes existence theorem for solutions of differential systems where data is analytic, holomorphic functions, Cauchy's integral, Taylor and Laurent expansions, more. Exercises. 1973 edition.

Complex Analysis: an Introduction to Theory of Analytic Functions of One Complex Variable

Complex Analysis: an Introduction to Theory of Analytic Functions of One Complex Variable
Title Complex Analysis: an Introduction to Theory of Analytic Functions of One Complex Variable PDF eBook
Author Ahlfors Lars V
Publisher
Pages 331
Release 1981
Genre
ISBN

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Complex Analysis

Complex Analysis
Title Complex Analysis PDF eBook
Author Lars Ahlfors
Publisher
Pages 352
Release 1979
Genre Education
ISBN

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A standard source of information of functions of one complex variable, this text has retained its wide popularity in this field by being consistently rigorous without becoming needlessly concerned with advanced or overspecialized material. Difficult points have been clarified, the book has been reviewed for accuracy, and notations and terminology have been modernized. Chapter 2, Complex Functions, features a brief section on the change of length and area under conformal mapping, and much of Chapter 8, Global-Analytic Functions, has been rewritten in order to introduce readers to the terminology of germs and sheaves while still emphasizing that classical concepts are the backbone of the theory. Chapter 4, Complex Integration, now includes a new and simpler proof of the general form of Cauchy's theorem. There is a short section on the Riemann zeta function, showing the use of residues in a more exciting situation than in the computation of definite integrals.

Function Theory of One Complex Variable

Function Theory of One Complex Variable
Title Function Theory of One Complex Variable PDF eBook
Author Robert Everist Greene
Publisher American Mathematical Soc.
Pages 536
Release 2006
Genre Mathematics
ISBN 9780821839621

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Complex analysis is one of the most central subjects in mathematics. It is compelling and rich in its own right, but it is also remarkably useful in a wide variety of other mathematical subjects, both pure and applied. This book is different from others in that it treats complex variables as a direct development from multivariable real calculus. As each new idea is introduced, it is related to the corresponding idea from real analysis and calculus. The text is rich with examples andexercises that illustrate this point. The authors have systematically separated the analysis from the topology, as can be seen in their proof of the Cauchy theorem. The book concludes with several chapters on special topics, including full treatments of special functions, the prime number theorem,and the Bergman kernel. The authors also treat $Hp$ spaces and Painleve's theorem on smoothness to the boundary for conformal maps. This book is a text for a first-year graduate course in complex analysis. It is an engaging and modern introduction to the subject, reflecting the authors' expertise both as mathematicians and as expositors.

Functions of One Complex Variable

Functions of One Complex Variable
Title Functions of One Complex Variable PDF eBook
Author J.B. Conway
Publisher Springer Science & Business Media
Pages 323
Release 2012-12-06
Genre Mathematics
ISBN 1461599725

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This book is intended as a textbook for a first course in the theory of functions of one complex variable for students who are mathematically mature enough to understand and execute E - I) arguments. The actual pre requisites for reading this book are quite minimal; not much more than a stiff course in basic calculus and a few facts about partial derivatives. The topics from advanced calculus that are used (e.g., Leibniz's rule for differ entiating under the integral sign) are proved in detail. Complex Variables is a subject which has something for all mathematicians. In addition to having applications to other parts of analysis, it can rightly claim to be an ancestor of many areas of mathematics (e.g., homotopy theory, manifolds). This view of Complex Analysis as "An Introduction to Mathe matics" has influenced the writing and selection of subject matter for this book. The other guiding principle followed is that all definitions, theorems, etc.

An Introduction to Complex Function Theory

An Introduction to Complex Function Theory
Title An Introduction to Complex Function Theory PDF eBook
Author Bruce P. Palka
Publisher Springer Science & Business Media
Pages 585
Release 1991
Genre Mathematics
ISBN 038797427X

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This book provides a rigorous yet elementary introduction to the theory of analytic functions of a single complex variable. While presupposing in its readership a degree of mathematical maturity, it insists on no formal prerequisites beyond a sound knowledge of calculus. Starting from basic definitions, the text slowly and carefully develops the ideas of complex analysis to the point where such landmarks of the subject as Cauchy's theorem, the Riemann mapping theorem, and the theorem of Mittag-Leffler can be treated without sidestepping any issues of rigor. The emphasis throughout is a geometric one, most pronounced in the extensive chapter dealing with conformal mapping, which amounts essentially to a "short course" in that important area of complex function theory. Each chapter concludes with a wide selection of exercises, ranging from straightforward computations to problems of a more conceptual and thought-provoking nature.

Analytic Functions of Several Complex Variables

Analytic Functions of Several Complex Variables
Title Analytic Functions of Several Complex Variables PDF eBook
Author Robert Clifford Gunning
Publisher American Mathematical Soc.
Pages 338
Release 2009
Genre Mathematics
ISBN 0821821652

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The theory of analytic functions of several complex variables enjoyed a period of remarkable development in the middle part of the twentieth century. This title intends to provide an extensive introduction to the Oka-Cartan theory and some of its applications, and to the general theory of analytic spaces.