Special Functions And Complex Variables

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Special Functions And Complex Variables

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Author : SHAHNAZ BATHUL
language : en
Publisher: PHI Learning Pvt. Ltd.
Release Date : 2010-09-07

Special Functions And Complex Variables written by SHAHNAZ BATHUL and has been published by PHI Learning Pvt. Ltd. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-07 with Mathematics categories.

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.

Special Functions And Complex Variables Engineering Mathematics Iii

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Author : BATHUL, SHAHNAZ
language : en
Publisher: PHI Learning Pvt. Ltd.
Release Date : 2017-07-07

Special Functions And Complex Variables Engineering Mathematics Iii written by BATHUL, SHAHNAZ and has been published by PHI Learning Pvt. Ltd. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-07 with Mathematics categories.

This thoroughly revised book, now in its third edition, continues to discuss two important topics—special functions and complex variables. Chapters have been rearranged keeping in view the current syllabi of the universities. The book analyzes special functions, Legendre’s equation and function, and Bessel’s function. It explains how to solve Cauchy equations, differential equation with variable coefficients and Frobenius of solving differential equation at a regular singular point. Besides, the text also 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 trigonometric and hyperbolic functions and explains their properties. While discussing different mathematical concepts, the book discusses 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, the argument principle and Rouche’s theorem for the determination of the number of zeroes of complex polynomials. Finally, the book gives a thorough exposition of conformal mappings and develops the theory of bilinear transformation. Intended as a textbook for engineering students, this book will also be useful for undergraduate and postgraduate students of mathematics. NEW TO THE THIRD EDITION • Includes a new chapter on ‘Linear Ordinary Differential Equations with Variable Coefficients and Series Solutions’ • Incorporates ‘Short Questions and Answers’ to help students to prepare for examinations • Provides several worked-out problems and previous years’ questions and also includes more MCQs and exercises in each chapter

Complex Variables And Special Functions

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Author : BAIDYANATH PATRA
language : en
Publisher: PHI Learning Pvt. Ltd.
Release Date : 2014-01-01

Complex Variables And Special Functions written by BAIDYANATH PATRA and has been published by PHI Learning Pvt. Ltd. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-01 with Mathematics categories.

Author's aim is to make the readers easily understand the theory of complex variables. He explains this subject matter from a rudimentary to advanced level in a very simple manner. Organized in two parts, this book explains exact definitions of different terms used by supplying worked-out examples wherever found necessary. A large number of examples have been solved in the book to acquaint the readers with different techniques. Furthermore, a large number of problems have been supplied with answers at the end of each chapter. The first part of the book (Chapters 1 through 11) containing analysis of complex variables will be useful for the undergraduate students of engineering and science. The second part of the book (Chapters 12 through 20) is written in complex domain and is targeted towards advanced level readers who are either pursuing postgraduate studies in Mathematics or research in Applied Mathematics. The first part is prerequisite for this section of the book.

Functions Of A Complex Variable

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Author : Hemant Kumar Pathak
language : en
Publisher: Chapman & Hall/CRC
Release Date : 2016

Functions Of A Complex Variable written by Hemant Kumar Pathak and has been published by Chapman & Hall/CRC this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Mathematics categories.

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.

Entire Functions Of Several Complex Variables

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Author : Pierre Lelong
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Entire Functions Of Several Complex Variables written by Pierre Lelong and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

I - Entire functions of several complex variables constitute an important and original chapter in complex analysis. The study is often motivated by certain applications to specific problems in other areas of mathematics: partial differential equations via the Fourier-Laplace transformation and convolution operators, analytic number theory and problems of transcen dence, or approximation theory, just to name a few. What is important for these applications is to find solutions which satisfy certain growth conditions. The specific problem defines inherently a growth scale, and one seeks a solution of the problem which satisfies certain growth conditions on this scale, and sometimes solutions of minimal asymp totic growth or optimal solutions in some sense. For one complex variable the study of solutions with growth conditions forms the core of the classical theory of entire functions and, historically, the relationship between the number of zeros of an entire function f(z) of one complex variable and the growth of If I (or equivalently log If I) was the first example of a systematic study of growth conditions in a general setting. Problems with growth conditions on the solutions demand much more precise information than existence theorems. The correspondence between two scales of growth can be interpreted often as a correspondence between families of bounded sets in certain Frechet spaces. However, for applications it is of utmost importance to develop precise and explicit representations of the solutions.

Applied Complex Variables

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Author : John W. Dettman
language : en
Publisher: Courier Corporation
Release Date : 2012-05-07

Applied Complex Variables written by John W. Dettman and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-07 with Mathematics categories.

Fundamentals of analytic function theory — plus lucid exposition of 5 important applications: potential theory, ordinary differential equations, Fourier transforms, Laplace transforms, and asymptotic expansions. Includes 66 figures.

Analytic Functions Of Several Complex Variables

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Author : Robert Clifford Gunning
language : en
Publisher: American Mathematical Soc.
Release Date : 2009

Analytic Functions Of Several Complex Variables written by Robert Clifford Gunning and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.

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.

Function Theory Of One Complex Variable

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Author : Robert Everist Greene
language : en
Publisher: American Mathematical Soc.
Release Date : 2006

Function Theory Of One Complex Variable written by Robert Everist Greene and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.

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 covers complex variables as a direct development from multivariable real calculus.

Complex Analysis

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Author : Joseph Bak
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-08-02

Complex Analysis written by Joseph Bak and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-02 with Mathematics categories.

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. 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.

Functions Of Several Complex Variables And Their Singularities

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Author : Wolfgang Ebeling
language : en
Publisher: American Mathematical Soc.
Release Date : 2007

Functions Of Several Complex Variables And Their Singularities written by Wolfgang Ebeling and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.

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.