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ISBN-13:9780078035975
Book Title:Fourier Series and Boundary Value Problems
Number of Pages:416 Pages
Language:English
Publication Name:Fourier Series and Boundary Value Problems
Publisher:Mcgraw-Hill Education-Europe
Publication Year:2011
Subject:Mathematics
Item Height:241 mm
Item Weight:687 g
Type:Textbook
Author:James Brown, Ruel Churchill
Item Width:185 mm
Format:Hardcover
Fourier Series and Boundary Value Problems by James Brown, Ruel Churchill Offers an introduction to Fourier series and their applications to boundary value problems in partial differential equations of engineering and physics. This title also introduces the concept of orthogonal sets of functions and representations of arbitrary functions in series of functions from such sets. FORMAT Hardcover LANGUAGE English CONDITION Brand New Publisher Description 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. The book is a thorough revision of the seventh edition and much care is taken to give the student fewer distractions when determining solutions of eigenvalue problems, and other topics have been presented in their own sections like Gibbs Phenomenon and the Poisson integral formula. Author Biography RUEL V. CHURCHILL (University of Michigan) Table of Contents Preface1 Fourier SeriesPiecewise Continuous FunctionsFourier Cosine SeriesExamplesFourier Sine SeriesExamplesFourier SeriesExamplesAdaptations to Other Intervals2 Convergence of Fourier SeriesOne-Sided DerivativesA Property of Fourier CoefficientsTwo LemmasA Fourier TheoremA Related Fourier TheoremExamplesConvergence on Other IntervalsA LemmaAbsolute and Uniform Convergence of Fourier SeriesThe Gibbs PhenomenonDifferentiation of Fourier SeriesIntegration of Fourier Series3 Partial Differential Equations of PhysicsLinear Boundary Value ProblemsOne-Dimensional Heat EquationRelated EquationsLaplacian in Cylindrical and Spherical CoordinatesDerivationsBoundary ConditionsDuhamels PrincipleA Vibrating StringVibrations of Bars and MembranesGeneral Solution of the Wave EquationTypes of Equations and Boundary Conditions4 The Fourier MethodLinear OperatorsPrinciple of SuperpositionExamplesEigenvalues and EigenfunctionsA Temperature ProblemA Vibrating String ProblemHistorical Development5 Boundary Value ProblemsA Slab with Faces at Prescribed TemperaturesRelated Temperature Problems Temperatures in a SphereA Slab with Internally Generated HeatSteady Temperatures in Rectangular CoordinatesSteady Temperatures in Cylindrical CoordinatesA String with Prescribed Initial ConditionsResonanceAn Elastic BarDouble Fourier SeriesPeriodic Boundary Conditions6 Fourier Integrals and ApplicationsThe Fourier Integral FormulaDirichlets IntegralTwo LemmasA Fourier Integral TheoremThe Cosine and Sine IntegralsSome Eigenvalue Problems on Undounded IntervalsMore on Superposition of SolutionsSteady Temperatures in a Semi-Infinite StripTemperatures in a Semi-Infinite SolidTemperatures in an Unlimited Medium7 Orthonormal SetsInner Products and Orthonormal SetsExamplesGeneralized Fourier SeriesExamplesBest Approximation in the MeanBessels Inequality and Parsevals EquationApplications to Fourier Series8 Sturm-Liouville Problems and ApplicationsRegular Sturm-Liouville ProblemsModificationsOrthogonality of Eigenfunctions adn Real EigenvaluesReal-Valued EigenfunctionsNonnegative EigenvaluesMethods of SolutionExamples of Eigenfunction ExpansionsA Temperature Problem in Rectangular CoordinatesSteady TemperaturesOther CoordinatesA Modification of the MethodAnother ModificationA Vertically Hung Elastic Bar9 Bessel Functions and ApplicationsThe Gamma FunctionBessel Functions Jn(x)Solutions When v = 0,1,2,…Recurrence RelationsBessels Integral FormSome Consequences of the Integral FormsThe Zeros of Jn(x)Zeros of Related FunctionsOrthogonal Sets of Bessel FunctionsProof of the TheoremsTwo LemmasFourier-Bessel SeriesExamplesTemperatures in a Long CylinderA Temperature Problem in Shrunken FittingsInternally Generated HeatTemperatures in a Long Cylindrical WedgeVibration of a Circular Membrane10 Legendre Polynomials and ApplicationsSolutions of Legendres EquationLegendre PolynomialsRodrigues FormulaLaplaces Integral FormSome Consequences of the Integral FormOrthogonality of Legendre PolynomialsNormalized Legendre PolynomialsLegendre SeriesThe Eigenfunctions Pn(cos θ)Dirichlet Problems in Spherical RegionsSteady Temperatures in a Hemisphere11 Verification of Solutions and UniquenessAbels Test for Uniform ConvergenceVerification of Solution of Temperature ProblemUniqueness of Solutions of the Heat EquationVerification of Solution of Vibrating String ProblemUniqueness of Solutions of the Wave EquationAppendixesBibliographySome Fourier Series ExpansionsSolutions of Some Regular Sturm-Liouville Problems Some Fourier-Bessel Series ExpansionsIndex Details ISBN007803597X Language English Edition 8th ISBN-10 007803597X ISBN-13 9780078035975 Media Book Format Hardcover Year 2011 Place of Publication London Country of Publication United States Short Title FOURIER SERIES & BOUNDARY V-8E Series Brown and Churchill UK Release Date 2011-03-16 Publication Date 2011-03-16 AU Release Date 2011-03-16 NZ Release Date 2011-03-16 US Release Date 2011-03-16 Imprint McGraw Hill Higher Education Author Ruel Churchill Pages 416 Publisher McGraw-Hill Education – Europe Edition Description 8th edition DEWEY 515.35 Audience Undergraduate Illustrations 82 Illustrations We’ve got this At The Nile, if you’re looking for it, we’ve got it. 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