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.
Auflage
Sprache
Verlagsort
Verlagsgruppe
McGraw-Hill Education - Europe
Zielgruppe
Für höhere Schule und Studium
Maße
Höhe: 259 mm
Breite: 137 mm
Dicke: 20 mm
Gewicht
ISBN-13
978-0-07-232570-6 (9780072325706)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
RUEL V. CHURCHILL (University of Michigan)
Preface1 Partial Differential Equations of PhysicsLinear Boundary Value ProblemsConduction of HeatHigher DimensionsCylindrical CoordinatesSpherical CoordinatesBoundary ConditionsA Vibrating StringVibrations of Bars and MembranesTypes of Equations and Boundary ConditionsMethods of Solution2 The Fourier MethodLinear OperatorsPrinciple of SuperpositionA GeneralizationA Temperature ProblemThe Nonhomogeneous ConditionA Vibrating String ProblemThe Nonhomogeneous ConditionHistorical Development3 Orthonormal Sets and Fourier SeriesPiecewise Continuous FunctionsInner Products and Orthonormal SetsExamplesGeneralized Fourier SeriesFourier Cosine SeriesFourier Sine SeriesFourier SeriesExamplesBest Approximation in the MeanBessel's Inequality and a Property of Fourier Constants4 Convergence of Fourier SeriesOne-Sided DerivativesTwo LemmasA Fourier TheoremDiscussion of the Theorem and Its CorollaryFourier Series on Other IntervalsA LemmaUniform Convergence of Fourier SeriesDifferentiation of Fourier SeriesIntegration of Fourier SeriesConvergence in the Mean5 Boundary Value ProblemsA Slab with Faces at Prescribed TemperaturesRelated ProblemsA Slab with Internally Generated HeatA Dirichlet ProblemCylindrical CoordinatesA String with Prescribed Initial VelocityResonanceAn Elastic BarDouble Fourier SeriesPeriodic Boundary Conditions6 Sturm-Liouville Problems and ApplicationsRegular Sturm-Liouville ProblemsModificationsOrthogonality of EigenfunctionsReal-Valued Eigenfunctions and Nonnegative EigenvaluesMethods of SolutionExamples of Eigenfunction ExpansionsSurface Heat TransferA Dirichlet ProblemModifications of the MethodA Vertically Hung Elastic Bar7 Fourier Integrals and ApplicationsThe Fourier Integral FormulaDirichlet's IntegralTwo LemmasA Fourier Integral TheoremThe Cosine and Sine IntegralsMore on Superposition of SolutionsTemperatures in a Semi-Infinite SolidTemperatures in an Unlimited Medium8 Bessel Functions and ApplicationsBessel Functions JnGeneral Solutions of Bessel's EquationRecurrence RelationsBessel's Integral FormThe Zeros of J0(x)Zeros of Related FunctionsOrthogonal Sets of Bessel FunctionsProof of TheoremThe Orthonormal FunctionsFourier-Bessel SeriesTemperatures in a Long CylinderInternally Generated HeatVibration of a Circular Membrane9 Legendre Polynomials and ApplicationsSolutions of Legendre's EquationLegendre PolynomialsOrthogonality of Legendre PolynomialsRodrigues' Formula and NormsLegendre SeriesThe Eigenfunctions Pn(cos theta)Dirichlet Problems in Spherical RegionsSteady Temperatures in a Hemisphere10 Verification of Solutions and UniquenessAbel's 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 EquationOn Laplace's and Poisson's EquationsAn ExampleAppendixes1 Bibliography2 Some Fourier Series Expansions3 Solutions of Some Regular Sturm-Liouville Problems
