The Theory of Fourier Series and IntegralsA concise treatment of Fourier series and integrals, with particular emphasis on their relation and importance to science and engineering. Illustrates interesting applications which those with limited mathematical knowledge can execute. Key concepts are supported by examples and exercises at the end of each chapter. Includes background on elementary analysis, a comprehensive bibliography, and a guide to further reading for readers who want to pursue the subject in greater depth. |
Contents
Convergence Theory | 22 |
Exercises | 63 |
The Fourier Integral | 101 |
Copyright | |
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Common terms and phrases
A₁ absolutely convergent analytic apply boundary chapter complex numbers complex-valued consider constant continuity of f continuous function Corollary deduce defined Definition A.9 denote differentiable Dirichlet problem discontinuities einx equation Example exercise exists f₁ FC-function finite number follows formula Fourier coefficients Fourier series Fourier theory Fourier transform function f ƒ and g ƒ is continuous given half-plane harmonic conjugate harmonic function Hence Let f Let f(x Let ƒ limit Lipschitz continuous mapping nx dx obtain orthogonal P-summable partial sums piecewise monotone point of continuity Poisson integral Poisson kernel properties R₁ real number real values result Riemann-Lebesgue lemma say that f sequence shows that ƒ Sn(f solution subinterval suppose tends to zero Theorem 2.3 theory trigonometric polynomial uniform uniformly convergent unit circle write π π ди ду дх