傅立葉級數(shù)和邊值問題（第8版）

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
ALemma
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 a Wave Equation
Types of Equations and Boundary Conditions
……
4 The Fourier Method
5 Boundary Value Problems
6 Fourier Integrals and Applications
7 OrthonormaI Sets
8 Sturm-Liouville Problems and Applications
9 Bessel Functions and Applications
10 Legendre Polynomials and Applications
11 Verification of Solutions and Uniqueness
Appendixes
Index
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