Author : J. Ray Hanna
Publisher : Courier Corporation
Page : 370 pages
File Size : 31,37 MB
Release : 2008-06-11
Category : Mathematics
ISBN : 0486466736
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.
Author : Enrique A. Gonzalez-Velasco
Publisher : Elsevier
Page : 565 pages
File Size : 47,48 MB
Release : 1996-11-28
Category : Mathematics
ISBN : 0080531938
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
Author : Athanasios S. Fokas
Publisher : SIAM
Page : 290 pages
File Size : 15,21 MB
Release : 2014-12-30
Category : Mathematics
ISBN : 1611973813
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.
Author : Robert S. Strichartz
Publisher : World Scientific
Page : 238 pages
File Size : 16,38 MB
Release : 2003
Category : Mathematics
ISBN : 9789812384300
This important book provides a concise exposition of the basic ideas of the theory of distribution and Fourier transforms and its application to partial differential equations. The author clearly presents the ideas, precise statements of theorems, and explanations of ideas behind the proofs. Methods in which techniques are used in applications are illustrated, and many problems are included. The book also introduces several significant recent topics, including pseudodifferential operators, wave front sets, wavelets, and quasicrystals. Background mathematical prerequisites have been kept to a minimum, with only a knowledge of multidimensional calculus and basic complex variables needed to fully understand the concepts in the book.A Guide to Distribution Theory and Fourier Transforms can serve as a textbook for parts of a course on Applied Analysis or Methods of Mathematical Physics, and in fact it is used that way at Cornell.
Author : Mark A. Pinsky
Publisher : American Mathematical Soc.
Page : 545 pages
File Size : 47,48 MB
Release : 2011
Category : Mathematics
ISBN : 0821868896
Building on the basic techniques of separation of variables and Fourier series, the book presents the solution of boundary-value problems for basic partial differential equations: the heat equation, wave equation, and Laplace equation, considered in various standard coordinate systems--rectangular, cylindrical, and spherical. Each of the equations is derived in the three-dimensional context; the solutions are organized according to the geometry of the coordinate system, which makes the mathematics especially transparent. Bessel and Legendre functions are studied and used whenever appropriate throughout the text. The notions of steady-state solution of closely related stationary solutions are developed for the heat equation; applications to the study of heat flow in the earth are presented. The problem of the vibrating string is studied in detail both in the Fourier transform setting and from the viewpoint of the explicit representation (d'Alembert formula). Additional chapters include the numerical analysis of solutions and the method of Green's functions for solutions of partial differential equations. The exposition also includes asymptotic methods (Laplace transform and stationary phase). With more than 200 working examples and 700 exercises (more than 450 with answers), the book is suitable for an undergraduate course in partial differential equations.
Author : Ian Naismith Sneddon
Publisher : Courier Corporation
Page : 564 pages
File Size : 27,31 MB
Release : 1995-01-01
Category : Mathematics
ISBN : 9780486685229
Focusing on applications of Fourier transforms and related topics rather than theory, this accessible treatment is suitable for students and researchers interested in boundary value problems of physics and engineering. 1951 edition.
Author : Nakhle H. Asmar
Publisher : Courier Dover Publications
Page : 818 pages
File Size : 14,72 MB
Release : 2017-03-23
Category : Mathematics
ISBN : 0486820831
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.
Author : Robert T. Seeley
Publisher : Courier Corporation
Page : 116 pages
File Size : 40,29 MB
Release : 2014-02-20
Category : Mathematics
ISBN : 0486151794
A compact, sophomore-to-senior-level guide, Dr. Seeley's text introduces Fourier series in the way that Joseph Fourier himself used them: as solutions of the heat equation in a disk. Emphasizing the relationship between physics and mathematics, Dr. Seeley focuses on results of greatest significance to modern readers. Starting with a physical problem, Dr. Seeley sets up and analyzes the mathematical modes, establishes the principal properties, and then proceeds to apply these results and methods to new situations. The chapter on Fourier transforms derives analogs of the results obtained for Fourier series, which the author applies to the analysis of a problem of heat conduction. Numerous computational and theoretical problems appear throughout the text.
Author : Athanassios S. Fokas
Publisher : SIAM
Page : 328 pages
File Size : 23,74 MB
Release : 2008-01-01
Category : Mathematics
ISBN : 089871706X
This text presents a new approach to analysing initial-boundary value problems for integrable partial differential equations.
Author : Ronald Newbold Bracewell
Publisher :
Page : pages
File Size : 15,42 MB
Release : 1978
Category : Fourier transformations
ISBN :
