Abstract: This chapter provides an overview of infinite series, Fourier series, Fourier integral, and Laplace transforms. Infinite series is another representation of the partial sum sequence. The chapter reviews convergent and divergent infinite series. It also discusses power series and methods for the expansion of functions in power series. It presents general statements on Fourier series, Fourier integrals, and Laplace transforms. Every unique periodic function f(x) = f(x + kT0) that is partially monotonous and continuous can be uniquely represented as a Fourier series with a decomposition into the spectrum of f(x) according to discrete frequencies kf0. Every unique function F(t), even if it is not periodic, that is partially monotone and continuous can be uniquely represented as a Fourier integral with a decomposition into a continuous spectrum of frequencies y in the infinite interval T0 ⇒ ∞; t Є (−∞, +∞). The chapter also discusses employment of Laplace transforms.
Publication Year: 1974
Publication Date: 1974-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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