Function Theory Of One Complex Variable

Author : Robert Everist Greene,Steven George Krantz
Publisher : American Mathematical Soc.
Page : 536 pages
File Size : 40,6 Mb
Release : 2006
Category : Mathematics
ISBN : 0821839624

Get Book

Function Theory of One Complex Variable by Robert Everist Greene,Steven George Krantz Pdf

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.

Author : J.B. Conway
Publisher : Springer Science & Business Media
Page : 323 pages
File Size : 52,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461599722

Get Book

Functions of One Complex Variable by J.B. Conway Pdf

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.

Author : Henri Cartan
Publisher : Courier Corporation
Page : 242 pages
File Size : 46,5 Mb
Release : 2013-04-22
Category : Mathematics
ISBN : 9780486318677

Get Book

Elementary Theory of Analytic Functions of One or Several Complex Variables by Henri Cartan Pdf

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.

Author : A. I. Markushevich
Publisher : American Mathematical Soc.
Page : 1178 pages
File Size : 54,9 Mb
Release : 2005
Category : Mathematics
ISBN : 9780821837801

Get Book

Theory of Functions of a Complex Variable by A. I. Markushevich Pdf

Includes over 150 illustrations and 700 exercises."

Author : J. B. Conway
Publisher : Unknown
Page : 328 pages
File Size : 55,6 Mb
Release : 1973-10-16
Category : Electronic
ISBN : 1461599733

Get Book

Functions of One Complex Variable by J. B. Conway Pdf

Author : Steven George Krantz
Publisher : American Mathematical Soc.
Page : 586 pages
File Size : 52,7 Mb
Release : 2001
Category : Functions of several complex variables
ISBN : 9780821827246

Get Book

Function Theory of Several Complex Variables by Steven George Krantz Pdf

Emphasizing integral formulas, the geometric theory of pseudoconvexity, estimates, partial differential equations, approximation theory, inner functions, invariant metrics, and mapping theory, this title is intended for the student with a background in real and complex variable theory, harmonic analysis, and differential equations.

Author : Gennadiĭ Mikhaĭlovich Goluzin
Publisher : American Mathematical Soc.
Page : 690 pages
File Size : 53,8 Mb
Release : 1969
Category : Functions of complex variables
ISBN : 082188655X

Get Book

Geometric Theory of Functions of a Complex Variable by Gennadiĭ Mikhaĭlovich Goluzin Pdf

Author : Donald Sarason
Publisher : American Mathematical Society
Page : 177 pages
File Size : 46,7 Mb
Release : 2021-02-16
Category : Mathematics
ISBN : 9781470463236

Get Book

Complex Function Theory by Donald Sarason Pdf

Complex Function Theory is a concise and rigorous introduction to the theory of functions of a complex variable. Written in a classical style, it is in the spirit of the books by Ahlfors and by Saks and Zygmund. Being designed for a one-semester course, it is much shorter than many of the standard texts. Sarason covers the basic material through Cauchy's theorem and applications, plus the Riemann mapping theorem. It is suitable for either an introductory graduate course or an undergraduate course for students with adequate preparation. The first edition was published with the title Notes on Complex Function Theory.

Author : Jerry R. Muir, Jr.
Publisher : John Wiley & Sons
Page : 280 pages
File Size : 45,6 Mb
Release : 2015-05-26
Category : Mathematics
ISBN : 9781118705278

Get Book

Complex Analysis by Jerry R. Muir, Jr. Pdf

A thorough introduction to the theory of complex functions emphasizing the beauty, power, and counterintuitive nature of the subject Written with a reader-friendly approach, Complex Analysis: A Modern First Course in Function Theory features a self-contained, concise development of the fundamental principles of complex analysis. After laying groundwork on complex numbers and the calculus and geometric mapping properties of functions of a complex variable, the author uses power series as a unifying theme to define and study the many rich and occasionally surprising properties of analytic functions, including the Cauchy theory and residue theorem. The book concludes with a treatment of harmonic functions and an epilogue on the Riemann mapping theorem. Thoroughly classroom tested at multiple universities, Complex Analysis: A Modern First Course in Function Theory features: Plentiful exercises, both computational and theoretical, of varying levels of difficulty, including several that could be used for student projects Numerous figures to illustrate geometric concepts and constructions used in proofs Remarks at the conclusion of each section that place the main concepts in context, compare and contrast results with the calculus of real functions, and provide historical notes Appendices on the basics of sets and functions and a handful of useful results from advanced calculus Appropriate for students majoring in pure or applied mathematics as well as physics or engineering, Complex Analysis: A Modern First Course in Function Theory is an ideal textbook for a one-semester course in complex analysis for those with a strong foundation in multivariable calculus. The logically complete book also serves as a key reference for mathematicians, physicists, and engineers and is an excellent source for anyone interested in independently learning or reviewing the beautiful subject of complex analysis.

Author : Reinhold Remmert
Publisher : Springer Science & Business Media
Page : 464 pages
File Size : 50,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461209393

Get Book

Theory of Complex Functions by Reinhold Remmert Pdf

A lively and vivid look at the material from function theory, including the residue calculus, supported by examples and practice exercises throughout. There is also ample discussion of the historical evolution of the theory, biographical sketches of important contributors, and citations - in the original language with their English translation - from their classical works. Yet the book is far from being a mere history of function theory, and even experts will find a few new or long forgotten gems here. Destined to accompany students making their way into this classical area of mathematics, the book offers quick access to the essential results for exam preparation. Teachers and interested mathematicians in finance, industry and science will profit from reading this again and again, and will refer back to it with pleasure.

Author : Robert C. Gunning,Hugo Rossi
Publisher : American Mathematical Society
Page : 334 pages
File Size : 53,7 Mb
Release : 2022-08-25
Category : Mathematics
ISBN : 9781470470661

Get Book

Analytic Functions of Several Complex Variables by Robert C. Gunning,Hugo Rossi Pdf

The theory of analytic functions of several complex variables enjoyed a period of remarkable development in the middle part of the twentieth century. After initial successes by Poincaré and others in the late 19th and early 20th centuries, the theory encountered obstacles that prevented it from growing quickly into an analogue of the theory for functions of one complex variable. Beginning in the 1930s, initially through the work of Oka, then H. Cartan, and continuing with the work of Grauert, Remmert, and others, new tools were introduced into the theory of several complex variables that resolved many of the open problems and fundamentally changed the landscape of the subject. These tools included a central role for sheaf theory and increased uses of topology and algebra. The book by Gunning and Rossi was the first of the modern era of the theory of several complex variables, which is distinguished by the use of these methods. The intention of Gunning and Rossi's book is to provide an extensive introduction to the Oka-Cartan theory and some of its applications, and to the general theory of analytic spaces. Fundamental concepts and techniques are discussed as early as possible. The first chapter covers material suitable for a one-semester graduate course, presenting many of the central problems and techniques, often in special cases. The later chapters give more detailed expositions of sheaf theory for analytic functions and the theory of complex analytic spaces. Since its original publication, this book has become a classic resource for the modern approach to functions of several complex variables and the theory of analytic spaces. Further information about this book, including updates, can be found at the following URL: www.ams.org/publications/authors/books/postpub/chel-368.

Author : Yūsaku Komatsu,Kiyoshi Niino,Chung-Chun Yang
Publisher : Longman
Page : 412 pages
File Size : 41,8 Mb
Release : 1989
Category : Analytic functions
ISBN : UCAL:B5008537

Get Book

Analytic Function Theory of One Complex Variable by Yūsaku Komatsu,Kiyoshi Niino,Chung-Chun Yang Pdf

Author : B. A. Fuchs,B. V. Shabat
Publisher : Elsevier
Page : 458 pages
File Size : 42,6 Mb
Release : 2014-08-01
Category : Mathematics
ISBN : 9781483155050

Get Book

Functions of a Complex Variable and Some of Their Applications by B. A. Fuchs,B. V. Shabat Pdf

Functions of a Complex Variable and Some of Their Applications, Volume 1, discusses the fundamental ideas of the theory of functions of a complex variable. The book is the result of a complete rewriting and revision of a translation of the second (1957) Russian edition. Numerous changes and additions have been made, both in the text and in the solutions of the Exercises. The book begins with a review of arithmetical operations with complex numbers. Separate chapters discuss the fundamentals of complex analysis; the concept of conformal transformations; the most important of the elementary functions; and the complex potential for a plane vector field and the application of the simplest methods of function theory to the analysis of such a field. Subsequent chapters cover the fundamental apparatus of the theory of regular functions, i.e. basic integral theorems and expansions in series; the general concept of an analytic function; applications of the theory of residues; and polygonal domain mapping. This book is intended for undergraduate and postgraduate students of higher technical institutes and for engineers wishing to increase their knowledge of theory.

Author : Wolfgang Ebeling
Publisher : American Mathematical Soc.
Page : 334 pages
File Size : 55,5 Mb
Release : 2007
Category : Functions of several complex variables
ISBN : 9780821833193

Get Book

Functions of Several Complex Variables and Their Singularities by Wolfgang Ebeling Pdf

The book provides an introduction to the theory of functions of several complex variables and their singularities, with special emphasis on topological aspects. The topics include Riemann surfaces, holomorphic functions of several variables, classification and deformation of singularities, fundamentals of differential topology, and the topology of singularities. The aim of the book is to guide the reader from the fundamentals to more advanced topics of recent research. All the necessary prerequisites are specified and carefully explained. The general theory is illustrated by various examples and applications.

Author : Hemant Kumar Pathak,Ravi Agarwal,Yeol Je Cho
Publisher : CRC Press
Page : 718 pages
File Size : 40,8 Mb
Release : 2015-10-14
Category : Mathematics
ISBN : 9781498720168

Get Book

Functions of a Complex Variable by Hemant Kumar Pathak,Ravi Agarwal,Yeol Je Cho Pdf

Functions of a Complex Variable provides all the material for a course on the theory of functions of a complex variable at the senior undergraduate and beginning graduate level. Also suitable for self-study, the book covers every topic essential to training students in complex analysis. It also incorporates special topics to enhance students’ understanding of the subject, laying the foundation for future studies in analysis, linear algebra, numerical analysis, geometry, number theory, physics, thermodynamics, or electrical engineering. After introducing the basic concepts of complex numbers and their geometrical representation, the text describes analytic functions, power series and elementary functions, the conformal representation of an analytic function, special transformations, and complex integration. It next discusses zeros of an analytic function, classification of singularities, and singularity at the point of infinity; residue theory, principle of argument, Rouché’s theorem, and the location of zeros of complex polynomial equations; and calculus of residues, emphasizing the techniques of definite integrals by contour integration. The authors then explain uniform convergence of sequences and series involving Parseval, Schwarz, and Poisson formulas. They also present harmonic functions and mappings, inverse mappings, and univalent functions as well as analytic continuation.