Fourier Analysis And Boundary Value Problems
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Fourier Analysis And Boundary Value Problems
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Author : Enrique A. Gonzalez-Velasco
language : en
Publisher: Elsevier
Release Date : 1996-11-28
Fourier Analysis And Boundary Value Problems written by Enrique A. Gonzalez-Velasco and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-11-28 with Mathematics categories.
Fourier Analysis and Boundary Value Problems provides a thorough examination of both the theory and applications of partial differential equations and the Fourier and Laplace methods for their solutions. Boundary value problems, including the heat and wave equations, are integrated throughout the book. Written from a historical perspective with extensive biographical coverage of pioneers in the field, the book emphasizes the important role played by partial differential equations in engineering and physics. In addition, the author demonstrates how efforts to deal with these problems have lead to wonderfully significant developments in mathematics. A clear and complete text with more than 500 exercises, Fourier Analysis and Boundary Value Problems is a good introduction and a valuable resource for those in the field. - Topics are covered from a historical perspective with biographical information on key contributors to the field - The text contains more than 500 exercises - Includes practical applications of the equations to problems in both engineering and physics
Fourier Series Transforms And Boundary Value Problems
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Author : J. Ray Hanna
language : en
Publisher: Courier Corporation
Release Date : 2008-06-11
Fourier Series Transforms And Boundary Value Problems written by J. Ray Hanna and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-06-11 with Mathematics categories.
This volume introduces Fourier and transform methods for solutions to boundary value problems associated with natural phenomena. Unlike most treatments, it emphasizes basic concepts and techniques rather than theory. Many of the exercises include solutions, with detailed outlines that make it easy to follow the appropriate sequence of steps. 1990 edition.
Boundary Value Problems And Fourier Expansions
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Author : Charles R. MacCluer
language : en
Publisher: Courier Corporation
Release Date : 2004-11-29
Boundary Value Problems And Fourier Expansions written by Charles R. MacCluer and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-11-29 with Mathematics categories.
Based on modern Sobolev methods, this text not only includes an informal introduction that develops students' physical and mathematical intuition, but also introduces Hilbert space in its natural environment, and then poses and solve standard problems. The final part covers Sturm-Liouville problems, Fourier integrals, Galerkin's method, and Sobolev methods. 64 figures. 2004 edition. Exercises.
Ordinary And Partial Differential Equations
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Author : Ravi P. Agarwal
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-11-13
Ordinary And Partial Differential Equations written by Ravi P. Agarwal 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 2008-11-13 with Mathematics categories.
In this undergraduate/graduate textbook, the authors introduce ODEs and PDEs through 50 class-tested lectures. Mathematical concepts are explained with clarity and rigor, using fully worked-out examples and helpful illustrations. Exercises are provided at the end of each chapter for practice. The treatment of ODEs is developed in conjunction with PDEs and is aimed mainly towards applications. The book covers important applications-oriented topics such as solutions of ODEs in form of power series, special functions, Bessel functions, hypergeometric functions, orthogonal functions and polynomials, Legendre, Chebyshev, Hermite, and Laguerre polynomials, theory of Fourier series. Undergraduate and graduate students in mathematics, physics and engineering will benefit from this book. The book assumes familiarity with calculus.
Harmonic Analysis And Boundary Value Problems In The Complex Domain
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Author : Mkhitar M. Djrbashian
language : en
Publisher: Springer Science & Business Media
Release Date : 1993
Harmonic Analysis And Boundary Value Problems In The Complex Domain written by Mkhitar M. Djrbashian 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 1993 with Mathematics categories.
As is well known, the first decades of this century were a period of elaboration of new methods in complex analysis. This elaboration had, in particular, one char acteristic feature, consisting in the interfusion of some concepts and methods of harmonic and complex analyses. That interfusion turned out to have great advan tages and gave rise to a vast number of significant results, of which we want to mention especially the classical results on the theory of Fourier series in L2 ( -7r, 7r) and their continual analog - Plancherel's theorem on the Fourier transform in L2 ( -00, +00). We want to note also two important Wiener and Paley theorems on parametric integral representations of a subclass of entire functions of expo nential type in the Hardy space H2 over a half-plane. Being under the strong influence of these results, the author began in the fifties a series of investigations in the theory of integral representations of analytic and entire functions as well as in the theory of harmonic analysis in the com plex domain. These investigations were based on the remarkable properties of the asymptotics of the entire function (p, J1 > 0), which was introduced into mathematical analysis by Mittag-Leffler for the case J1 = 1. In the process of investigation, the scope of some classical results was essentially enlarged, and the results themselves were evaluated.
Partial Differential Equations With Fourier Series And Boundary Value Problems
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Author : Nakhle H. Asmar
language : en
Publisher: Courier Dover Publications
Release Date : 2017-03-23
Partial Differential Equations With Fourier Series And Boundary Value Problems written by Nakhle H. Asmar and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-23 with Mathematics categories.
Rich in proofs, examples, and exercises, this widely adopted text emphasizes physics and engineering applications. The Student Solutions Manual can be downloaded free from Dover's site; instructions for obtaining the Instructor Solutions Manual is included in the book. 2004 edition, with minor revisions.
Unified Transform For Boundary Value Problems
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Author : Athanasios S. Fokas
language : en
Publisher: SIAM
Release Date : 2014-12-30
Unified Transform For Boundary Value Problems written by Athanasios S. Fokas and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-30 with Mathematics categories.
This book describes state-of-the-art advances and applications of the unified transform and its relation to the boundary element method. The authors present the solution of boundary value problems from several different perspectives, in particular the type of problems modeled by partial differential equations (PDEs). They discuss recent applications of the unified transform to the analysis and numerical modeling of boundary value problems for linear and integrable nonlinear PDEs and the closely related boundary element method, a well-established numerical approach for solving linear elliptic PDEs.? The text is divided into three parts. Part I contains new theoretical results on linear and nonlinear evolutionary and elliptic problems. New explicit solution representations for several classes of boundary value problems are constructed and rigorously analyzed. Part II is a detailed overview of variational formulations for elliptic problems. It places the unified transform approach in a classic context alongside the boundary element method and stresses its novelty. Part III presents recent numerical applications based on the boundary element method and on the unified transform.
Fourier Series And Boundary Value Problems
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Author : James Brown
language : en
Publisher: McGraw-Hill Science/Engineering/Math
Release Date : 2006-08-28
Fourier Series And Boundary Value Problems written by James Brown and has been published by McGraw-Hill Science/Engineering/Math this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-28 with Mathematics categories.
Published by McGraw-Hill since its first edition in 1941, this classic text is an introduction to Fourier series and their applications to boundary value problems in partial differential equations of engineering and physics. It will primarily be used by students with a background in ordinary differential equations and advanced calculus. There are two main objectives of this text. The first is to introduce the concept of orthogonal sets of functions and representations of arbitrary functions in series of functions from such sets. The second is a clear presentation of the classical method of separation of variables used in solving boundary value problems with the aid of those representations.
Fourier Analysis
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Author : Eric Stade
language : en
Publisher: John Wiley & Sons
Release Date : 2011-10-07
Fourier Analysis written by Eric Stade and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-07 with Mathematics categories.
A reader-friendly, systematic introduction to Fourier analysis Rich in both theory and application, Fourier Analysis presents a unique and thorough approach to a key topic in advanced calculus. This pioneering resource tells the full story of Fourier analysis, including its history and its impact on the development of modern mathematical analysis, and also discusses essential concepts and today's applications. Written at a rigorous level, yet in an engaging style that does not dilute the material, Fourier Analysis brings two profound aspects of the discipline to the forefront: the wealth of applications of Fourier analysis in the natural sciences and the enormous impact Fourier analysis has had on the development of mathematics as a whole. Systematic and comprehensive, the book: Presents material using a cause-and-effect approach, illustrating where ideas originated and what necessitated them Includes material on wavelets, Lebesgue integration, L2 spaces, and related concepts Conveys information in a lucid, readable style, inspiring further reading and research on the subject Provides exercises at the end of each section, as well as illustrations and worked examples throughout the text Based upon the principle that theory and practice are fundamentally linked, Fourier Analysis is the ideal text and reference for students in mathematics, engineering, and physics, as well as scientists and technicians in a broad range of disciplines who use Fourier analysis in real-world situations.