Fourier series

Fourier series
an infinite series that involves linear combinations of sines and cosines and approximates a given function on a specified domain.
[1875-80; see FOURIER ANALYSIS]

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In mathematics, an infinite series used to solve special types of differential equations.

It consists of an infinite sum of sines and cosines, and because it is periodic (i.e., its values repeat over fixed intervals), it is a useful tool in analyzing periodic functions. Though investigated by Leonhard Euler, among others, the idea was named for Joseph Fourier, who fully explored its consequences, including important applications in engineering, particularly in heat conduction.

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Universalium. 2010.

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  • Fourier series — Fourier transforms Continuous Fourier transform Fourier series Discrete Fourier transform Discrete time Fourier transform Related transforms …   Wikipedia

  • Fourier series — Fourier eilutė statusas T sritis automatika atitikmenys: angl. Fourier series vok. Fourier Reihe, f rus. ряд Фурье, m pranc. série de Fourier, f ryšiai: sinonimas – Furjė eilutė …   Automatikos terminų žodynas

  • Fourier series — [foor′ē ər] n. [formulated by FOURIER Baron Jean Baptiste Joseph] Math. the expansion of a periodic function into a series of sines and cosines …   English World dictionary

  • Fourier series — Furjė eilutė statusas T sritis fizika atitikmenys: angl. Fourier series vok. Fourier Reihe, f rus. ряд Фурье, m pranc. série de Fourier, f …   Fizikos terminų žodynas

  • Fourier series — noun Etymology: Baron J.B.J. Fourier Date: 1877 an infinite series in which the terms are constants multiplied by sine or cosine functions of integer multiples of the variable and which is used in the analysis of periodic functions …   New Collegiate Dictionary

  • Fourier series — noun Mathematics an infinite series of trigonometric functions used to represent a given periodic function. Origin named after the 19th cent. French mathematician Jean B. J. Fourier …   English new terms dictionary

  • Fourier series — Fou′rier se ries n. math. an infinite series that approximates a given function on a specified domain by using linear combinations of sines and cosines • Etymology: 1875–80; see Fourier analysis …   From formal English to slang

  • Fourier series — noun A series of cosine and sine functions or complex exponentials resulting from the decomposition of a periodic function …   Wiktionary

  • Fourier series — n. Math. an expansion of a periodic function as a series of trigonometric functions …   Useful english dictionary

  • Fourier series — Смотри закон (или число) Фурье …   Энциклопедический словарь по металлургии

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