Preface 0 A History of Fourier Series 1 Heat Conduction and Fourier Series 1.1 The Laplace equation in two dimensions 1.2 Solutions of the Laplace equation 1.3 The complete solution of the Laplace equation 2 Convergence of Fourier Series 2.1 Abel summability and Cesàro summability 2.2 The Dirichlet and the Fejér kernels 2.3 Pointwise convergence of Fourier series 2.4 Term by term integration and differentiation 2.5 Divergence of Fourier series 3 Odds and Ends 3.1 Sine and cosine series 3.2 Functions with arbitrary periods 3.3 Some simple examples 3.4 Infinite products 3.5 π and infinite series 3.6 Bernoulli numbers 3.7 sin x/x 3.8 The Gibbs phenomenon 3.9 Exercises 3.10 A historical digression 4 Convergence in L2 and L1 4.1 L2 convergence of Fourier series 4.2 Fourier coefficients of LI functions 5 Some Applications 5.1 An ergodic theorem and number theory 5.2 The isoperimetric problem 5.3 The vibrating string 5.4 Band matrices A A Note on Normalisation B A Brief Bibliography Index
