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Fourier-Serie und Grenzwertprobleme 8. Auflage von Brown & Churchill Hardcover-
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Artikelmerkmale
- Artikelzustand
- Series
- Fourier Series
- Book Title
- Fourier Series and Boundary Value Problems (Brown and Churchill,
- Narrative Type
- Differential Equations
- Educational Level
- Adult & Further Education
- Level
- Intermediate, Advanced, Technical
- Features
- Illustrated
- ISBN
- 9780078035975
- Subject Area
- Mathematics
- Publication Name
- Fourier Series and Boundary Value Problems
- Publisher
- Mcgraw-Hill Education
- Item Length
- 9.5 in
- Subject
- Differential Equations / General, Differential Equations / Partial, Mathematical Analysis
- Publication Year
- 2011
- Type
- Textbook
- Format
- Hardcover
- Language
- English
- Item Height
- 0.8 in
- Item Weight
- 24.2 Oz
- Item Width
- 7.3 in
- Number of Pages
- 416 Pages
Über dieses Produkt
Product Identifiers
Publisher
Mcgraw-Hill Education
ISBN-10
007803597X
ISBN-13
9780078035975
eBay Product ID (ePID)
9038262507
Product Key Features
Number of Pages
416 Pages
Language
English
Publication Name
Fourier Series and Boundary Value Problems
Publication Year
2011
Subject
Differential Equations / General, Differential Equations / Partial, Mathematical Analysis
Type
Textbook
Subject Area
Mathematics
Format
Hardcover
Dimensions
Item Height
0.8 in
Item Weight
24.2 Oz
Item Length
9.5 in
Item Width
7.3 in
Additional Product Features
Edition Number
8
Intended Audience
College Audience
LCCN
2010-032734
Dewey Edition
22
Illustrated
Yes
Dewey Decimal
515/.2433
Table Of Content
Preface 1 Fourier Series Piecewise Continuous Functions Fourier Cosine Series Examples Fourier Sine Series Examples Fourier Series Examples Adaptations to Other Intervals 2 Convergence of Fourier Series One-Sided Derivatives A Property of Fourier Coefficients Two Lemmas A Fourier Theorem A Related Fourier Theorem Examples Convergence on Other Intervals A Lemma Absolute and Uniform Convergence of Fourier Series The Gibbs Phenomenon Differentiation of Fourier Series Integration of Fourier Series 3 Partial Differential Equations of Physics Linear Boundary Value Problems One-Dimensional Heat Equation Related Equations Laplacian in Cylindrical and Spherical Coordinates Derivations Boundary Conditions Duhamel''s Principle A Vibrating String Vibrations of Bars and Membranes General Solution of the Wave Equation Types of Equations and Boundary Conditions 4 The Fourier Method Linear Operators Principle of Superposition Examples Eigenvalues and Eigenfunctions A Temperature Problem A Vibrating String Problem Historical Development 5 Boundary Value Problems A Slab with Faces at Prescribed Temperatures Related Temperature Problems Temperatures in a Sphere A Slab with Internally Generated Heat Steady Temperatures in Rectangular Coordinates Steady Temperatures in Cylindrical Coordinates A String with Prescribed Initial Conditions Resonance An Elastic Bar Double Fourier Series Periodic Boundary Conditions 6 Fourier Integrals and Applications The Fourier Integral Formula Dirichlet''s Integral Two Lemmas A Fourier Integral Theorem The Cosine and Sine Integrals Some Eigenvalue Problems on Undounded Intervals More on Superposition of Solutions Steady Temperatures in a Semi-Infinite Strip Temperatures in a Semi-Infinite Solid Temperatures in an Unlimited Medium 7 Orthonormal Sets Inner Products and Orthonormal Sets Examples Generalized Fourier Series Examples Best Approximation in the Mean Bessel''s Inequality and Parseval''s Equation Applications to Fourier Series 8 Sturm-Liouville Problems and Applications Regular Sturm-Liouville Problems Modifications Orthogonality of Eigenfunctions adn Real Eigenvalues Real-Valued Eigenfunctions Nonnegative Eigenvalues Methods of Solution Examples of Eigenfunction Expansions A Temperature Problem in Rectangular Coordinates Steady Temperatures Other Coordinates A Modification of the Method Another Modification A Vertically Hung Elastic Bar 9 Bessel Functions and Applications The Gamma Function Bessel Functions Jn ( x ) Solutions When v = 0,1,2,... Recurrence Relations Bessel''s Integral Form Some Consequences of the Integral Forms The Zeros of Jn ( x ) Zeros of Related Functions Orthogonal Sets of Bessel Functions Proof of the Theorems Two Lemmas Fourier-Bessel Series Examples Temperatures in a Long Cylinder A Temperature Problem in Shrunken Fittings Internally Generated Heat Temperatures in a Long Cylindrical Wedge Vibration of a Circular Membrane 10 Legendre Polynomials and Applications Solutions of Legendre''s Equation Legendre Polynomials Rodrigues'' Formula Laplace''s Integral Form Some Consequences of the Integral Form Orthogonality of Legendre Polynomials Normalized Legendre Polynomials Legendre Series The Eigenfunctions Pn (cos θ ) Dirichlet Problems in Spherical Regions Steady Temperatures in a Hemisphere 11 Verification of Solutions and Uniqueness Abel''s Test for Uniform Convergence Verification of Solution of Temperature Problem Uniqueness of Solutions of the Heat Equation Verification of Solution of Vibrating String Problem Uniqueness of Solutions of the Wave Equation Appendixes Bibliography Some Fourier Series Expansions Solutions of Some Regular Sturm-Liouville Problems Some Fourier-Bessel Series Expansions Index
Synopsis
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.
LC Classification Number
QA404.B76 2011
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