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 編輯手記
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