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Fourier Series and Orthogonal Functions

ISBN-10: 0486659739
ISBN-13: 9780486659732
Edition: 1989
Authors: Harry F. Davis
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Book details

List price: $19.95
Copyright year: 1989
Publisher: Dover Publications, Incorporated
Publication date: 5/1/1989
Binding: Paperback
Pages: 432
Size: 5.50" wide x 8.50" long x 0.75" tall
Weight: 1.188
Language: English

Linear Spaces
Functions
Vectors
Linear Spaces
Finite-dimensional Linear Spaces
Infinite-dimensional Linear Spaces
Orthogonal Functions
Inner Products
Orthogonal Functions and Vectors
Orthogonal Sequences
Differential Operators
Integral Operators
Convolution and the Dirichlet Kernel
Fourier Series
Motivation
Definitions
Examples of Trigonometric Series
Sine and Cosine Series
The Gibbs Phenomenon
Local Convergence of Fourier Series
Uniform Convergence
Convergence of Fourier Series
Divergent Series
Generalized Functions
Practical Remarks
Legendre Polynomials and Bessel Functions
Partial Differential Equations
The Intuitive Meaning of the Laplacian Operator
Legendre Polynomials
Laplace's Equation in Spherical Coordinates
Spherical Harmonics
Bessel Functions
Heat and Temperature
Theory of Heat Conduction
Temperature of Plates
Temperature of Solids
Harmonic Functions
Existence Theorems
Heat Flow
Waves and Vibrations, Harmonic Analysis
The Vibrating String
The One-dimensional Wave Equation
The Weighted String
String with Variable Tension and Density
Vibrating Membranes
Waves in Two and Three Dimensions
The Fourier Integral
Algebraic Concepts in Analysis Supplementary
Exercises
Appendix
Functions on Groups
Answers and Notes
Index

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