Author: Shahnaz Bathul
Publisher: PHI Learning Pvt. Ltd.
ISBN: 8120351002
Category :
Languages : en
Pages : 586
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Book Description
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.
Author: George F. Carrier
Publisher: SIAM
ISBN: 9780898719116
Category : Mathematics
Languages : en
Pages : 451
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Book Description
Functions of a complex variable are used to solve applications in various branches of mathematics, science, and engineering. Functions of a Complex Variable: Theory and Technique is a book in a special category of influential classics because it is based on the authors' extensive experience in modeling complicated situations and providing analytic solutions. The book makes available to readers a comprehensive range of these analytical techniques based upon complex variable theory. Advanced topics covered include asymptotics, transforms, the Wiener-Hopf method, and dual and singular integral equations. The authors provide many exercises, incorporating them into the body of the text. Audience: intended for applied mathematicians, scientists, engineers, and senior or graduate-level students who have advanced knowledge in calculus and are interested in such subjects as complex variable theory, function theory, mathematical methods, advanced engineering mathematics, and mathematical physics.
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: BAIDYANATH PATRA
Publisher: PHI Learning Pvt. Ltd.
ISBN: 8120348575
Category : Mathematics
Languages : en
Pages : 494
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Book Description
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.
Author: M. Ya Antimirov
Publisher: San Diego ; Toronto : Academic Press
ISBN:
Category : Mathematics
Languages : en
Pages : 516
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Book Description
Complex Variables is an extended course in complex analysis and its applications for engineering students and for those who use complex analysis in their work. In addition to classical results, it includes results recently obtained by the authors. Antimirov, Kolyshkin, and Vaillancourt have combined a rigorous presentation with clarity and many solved examples. The text introduces the theory of functions of one complex variable, and presents an evaluation of many new integration formulae and the summation of new infinite series by the calculus of residue. The book also includes the Fatou-Julia theory for meromorphic functions for finding selective roots of some transcendental equations as found in the applications. The exercises provided in the text are elementary and aim at the understanding of the theory of analytic functions. Answers to odd-numbered exercises are in the back of the book; answers to even-numbered exercises are provided in an accompanying instructor's manual. Key Features: * Uses direct mathematical language, avoiding unnecessary abstract style * Contains planes of domain and image of mappings which are always clearly specified and well-illustrated with figures * Provides several new integration and summation formulas, which may eventually find their way into symbolic softwares * Includes a large collection of exercises * Expands entire functions in infinite products into simpler forms than those found in many textbooks * Presents fresh information on the dynamics of meromorphic functions to solve transcendental equation found in the applications
Author: Wilbur R. LePage
Publisher: Courier Corporation
ISBN: 0486136442
Category : Technology & Engineering
Languages : en
Pages : 516
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Book Description
Acclaimed text on engineering math for graduate students covers theory of complex variables, Cauchy-Riemann equations, Fourier and Laplace transform theory, Z-transform, and much more. Many excellent problems.
Author: A. Kyrala
Publisher: John Wiley & Sons
ISBN:
Category : Mathematics
Languages : en
Pages : 406
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Book Description
Complex numbers and direct applications -- Functions of a complex variable -- Infinite series -- Cauchy's theorem -- Cauchy integral theorem -- Laurent series and residue theorem -- Singularities and analytical continuation -- Conformal mapping -- Laplace and Fourier transforms -- Infinite product and rational fraction expansions -- Dispersion relations -- Elliptic functions and integrals -- Differential equations and special functions -- Table 1. Laplace transforms -- Table 2. Fourier transforms -- Table 3. Conformal mapping -- Appendix A. Riemann mapping -- Appendix B. Green's theorem in the plane -- Appendix C. Phragmén-Lindelöf theorems.
Author: Steven G. Krantz
Publisher: CRC Press
ISBN: 1000007189
Category : Mathematics
Languages : en
Pages : 243
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Book Description
The idea of complex numbers dates back at least 300 years—to Gauss and Euler, among others. Today complex analysis is a central part of modern analytical thinking. It is used in engineering, physics, mathematics, astrophysics, and many other fields. It provides powerful tools for doing mathematical analysis, and often yields pleasing and unanticipated answers. This book makes the subject of complex analysis accessible to a broad audience. The complex numbers are a somewhat mysterious number system that seems to come out of the blue. It is important for students to see that this is really a very concrete set of objects that has very concrete and meaningful applications. Features: This new edition is a substantial rewrite, focusing on the accessibility, applied, and visual aspect of complex analysis This book has an exceptionally large number of examples and a large number of figures. The topic is presented as a natural outgrowth of the calculus. It is not a new language, or a new way of thinking. Incisive applications appear throughout the book. Partial differential equations are used as a unifying theme.
Author: Robert B. Ash
Publisher: Courier Corporation
ISBN: 0486462501
Category : Mathematics
Languages : en
Pages : 226
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Book Description
This text on complex variables is geared toward graduate students and undergraduates who have taken an introductory course in real analysis. It is a substantially revised and updated edition of the popular text by Robert B. Ash, offering a concise treatment that provides careful and complete explanations as well as numerous problems and solutions. An introduction presents basic definitions, covering topology of the plane, analytic functions, real-differentiability and the Cauchy-Riemann equations, and exponential and harmonic functions. Succeeding chapters examine the elementary theory and the general Cauchy theorem and its applications, including singularities, residue theory, the open mapping theorem for analytic functions, linear fractional transformations, conformal mapping, and analytic mappings of one disk to another. The Riemann mapping theorem receives a thorough treatment, along with factorization of analytic functions. As an application of many of the ideas and results appearing in earlier chapters, the text ends with a proof of the prime number theorem.
Author: Bathul
Publisher: PHI Learning Pvt. Ltd.
ISBN: 9788120333802
Category :
Languages : en
Pages : 0
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Book Description
