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Author: SHAHNAZ BATHUL
Publisher: PHI Learning Pvt. Ltd.
ISBN: 8120341937
Category : Mathematics
Languages : en
Pages : 534
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Book Description
This well-received book, which is a new edition of Textbook of Engineering Mathematics: Special Functions and Complex Variables by the same author, continues to discuss two important topics—special functions and complex variables. It analyzes special functions such as gamma and beta functions, Legendre’s equation and function, and Bessel’s function. Besides, the text explains the notions of limit, continuity and differentiability by giving a thorough grounding on analytic functions and their relations with harmonic functions. In addition, the book introduces the exponential function of a complex variable and, with the help of this function, defines the trigonometric and hyperbolic functions and explains their properties. While discussing different mathematical concepts, the book analyzes a number of theorems such as Cauchy’s integral theorem for the integration of a complex variable, Taylor’s theorem for the analysis of complex power series, the residue theorem for evaluation of residues, besides the argument principle and Rouche’s theorem for the determination of the number of zeros of complex polynomials. Finally, the book gives a thorough exposition of conformal mappings and develops the theory of bilinear transformation. Intended as a text for engineering students, this book will also be useful for undergraduate and postgraduate students of Mathematics and students appearing in competitive examinations. What is New to This Edition : Chapters have been reorganized keeping in mind changes in the syllabi. A new chapter is exclusively devoted to Graph Theory.
Author: SHAHNAZ BATHUL
Publisher: PHI Learning Pvt. Ltd.
ISBN: 8120341937
Category : Mathematics
Languages : en
Pages : 534
Get Book Here
Book Description
This well-received book, which is a new edition of Textbook of Engineering Mathematics: Special Functions and Complex Variables by the same author, continues to discuss two important topics—special functions and complex variables. It analyzes special functions such as gamma and beta functions, Legendre’s equation and function, and Bessel’s function. Besides, the text explains the notions of limit, continuity and differentiability by giving a thorough grounding on analytic functions and their relations with harmonic functions. In addition, the book introduces the exponential function of a complex variable and, with the help of this function, defines the trigonometric and hyperbolic functions and explains their properties. While discussing different mathematical concepts, the book analyzes a number of theorems such as Cauchy’s integral theorem for the integration of a complex variable, Taylor’s theorem for the analysis of complex power series, the residue theorem for evaluation of residues, besides the argument principle and Rouche’s theorem for the determination of the number of zeros of complex polynomials. Finally, the book gives a thorough exposition of conformal mappings and develops the theory of bilinear transformation. Intended as a text for engineering students, this book will also be useful for undergraduate and postgraduate students of Mathematics and students appearing in competitive examinations. What is New to This Edition : Chapters have been reorganized keeping in mind changes in the syllabi. A new chapter is exclusively devoted to Graph Theory.
Author: Robert C. Gunning
Publisher: American Mathematical Society
ISBN: 1470470667
Category : Mathematics
Languages : en
Pages : 334
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Book Description
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: Robert Everist Greene
Publisher: American Mathematical Soc.
ISBN: 9780821839621
Category : Mathematics
Languages : en
Pages : 536
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Book Description
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: Wolfgang Ebeling
Publisher: American Mathematical Soc.
ISBN: 0821833197
Category : Mathematics
Languages : en
Pages : 334
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Book Description
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: Henri Cartan
Publisher: Courier Corporation
ISBN: 0486318672
Category : Mathematics
Languages : en
Pages : 242
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Book Description
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: V. I. Smirnov
Publisher: Elsevier
ISBN: 1483185087
Category : Mathematics
Languages : en
Pages : 645
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Book Description
A Course of Higher Mathematics, Volume II: Advanced Calculus covers the theory of functions of real variable in advanced calculus. This volume is divided into seven chapters and begins with a full discussion of the solution of ordinary differential equations with many applications to the treatment of physical problems. This topic is followed by an account of the properties of multiple integrals and of line integrals, with a valuable section on the theory of measurable sets and of multiple integrals. The subsequent chapters deal with the mathematics necessary to the examination of problems in classical field theories in vector algebra and vector analysis and the elements of differential geometry in three-dimensional space. The final chapters explore the Fourier series and the solution of the partial differential equations of classical mathematical physics. This book will prove useful to advanced mathematics students, engineers, and physicists.
Author: Carlo Viola
Publisher: Springer
ISBN: 3319413457
Category : Mathematics
Languages : en
Pages : 172
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Book Description
The subjects treated in this book have been especially chosen to represent a bridge connecting the content of a first course on the elementary theory of analytic functions with a rigorous treatment of some of the most important special functions: the Euler gamma function, the Gauss hypergeometric function, and the Kummer confluent hypergeometric function. Such special functions are indispensable tools in "higher calculus" and are frequently encountered in almost all branches of pure and applied mathematics. The only knowledge assumed on the part of the reader is an understanding of basic concepts to the level of an elementary course covering the residue theorem, Cauchy's integral formula, the Taylor and Laurent series expansions, poles and essential singularities, branch points, etc. The book addresses the needs of advanced undergraduate and graduate students in mathematics or physics.
Author: Carlos A. Berenstein
Publisher: Springer Science & Business Media
ISBN: 1461384451
Category : Mathematics
Languages : en
Pages : 491
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Book Description
A companion volume to the text "Complex Variables: An Introduction" by the same authors, this book further develops the theory, continuing to emphasize the role that the Cauchy-Riemann equation plays in modern complex analysis. Topics considered include: Boundary values of holomorphic functions in the sense of distributions; interpolation problems and ideal theory in algebras of entire functions with growth conditions; exponential polynomials; the G transform and the unifying role it plays in complex analysis and transcendental number theory; summation methods; and the theorem of L. Schwarz concerning the solutions of a homogeneous convolution equation on the real line and its applications in harmonic function theory.
Author: Vasiliy Sergeyevich Vladimirov
Publisher: Courier Corporation
ISBN: 0486458121
Category : Mathematics
Languages : en
Pages : 370
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Book Description
This systematic exposition outlines the fundamentals of the theory of single sheeted domains of holomorphy. It further illustrates applications to quantum field theory, the theory of functions, and differential equations with constant coefficients. Students of quantum field theory will find this text of particular value. The text begins with an introduction that defines the basic concepts and elementary propositions, along with the more salient facts from the theory of functions of real variables and the theory of generalized functions. Subsequent chapters address the theory of plurisubharmonic functions and pseudoconvex domains, along with characteristics of domains of holomorphy. These explorations are further examined in terms of four types of domains: multiple-circular, tubular, semitubular, and Hartogs' domains. Surveys of integral representations focus on the Martinelli-Bochner, Bergman-Weil, and Bochner representations. The final chapter is devoted to applications, particularly those involved in field theory. It employs the theory of generalized functions, along with the theory of functions of several complex variables.
Author: R. Michael Range
Publisher: Springer Science & Business Media
ISBN: 1475719183
Category : Mathematics
Languages : en
Pages : 405
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Book Description
The subject of this book is Complex Analysis in Several Variables. This text begins at an elementary level with standard local results, followed by a thorough discussion of the various fundamental concepts of "complex convexity" related to the remarkable extension properties of holomorphic functions in more than one variable. It then continues with a comprehensive introduction to integral representations, and concludes with complete proofs of substantial global results on domains of holomorphy and on strictly pseudoconvex domains inC", including, for example, C. Fefferman's famous Mapping Theorem. The most important new feature of this book is the systematic inclusion of many of the developments of the last 20 years which centered around integral representations and estimates for the Cauchy-Riemann equations. In particu lar, integral representations are the principal tool used to develop the global theory, in contrast to many earlier books on the subject which involved methods from commutative algebra and sheaf theory, and/or partial differ ential equations. I believe that this approach offers several advantages: (1) it uses the several variable version of tools familiar to the analyst in one complex variable, and therefore helps to bridge the often perceived gap between com plex analysis in one and in several variables; (2) it leads quite directly to deep global results without introducing a lot of new machinery; and (3) concrete integral representations lend themselves to estimations, therefore opening the door to applications not accessible by the earlier methods.
