Definitions for fourier series
This page provides all possible meanings and translations of the word fourier series
Random House Webster's College Dictionary
an infinite series that approximates a given function on a specified domain by using linear combinations of sines and cosines.
Origin of Fourier series:
1875–80; see Fourier analysis
the sum of a series of trigonometric expressions; used in the analysis of periodic functions
a series of cosine and sine functions or complex exponentials resulting from the decomposition of a periodic function
Origin: Named after , a French mathematician
In mathematics, a Fourier series decomposes periodic functions or periodic signals into the sum of a set of simple oscillating functions, namely sines and cosines. The study of Fourier series is a branch of Fourier analysis. The Fourier series is named in honour of Jean-Baptiste Joseph Fourier, who made important contributions to the study of trigonometric series, after preliminary investigations by Leonhard Euler, Jean le Rond d'Alembert, and Daniel Bernoulli. Fourier introduced the series for the purpose of solving the heat equation in a metal plate, publishing his initial results in his 1807 Mémoire sur la propagation de la chaleur dans les corps solides, and publishing his Théorie analytique de la chaleur in 1822. Early ideas of decomposing a periodic function into the sum of simple oscillating functions date back to the 3rd century BC, when ancient astronomers proposed an empiric model of planetary motions, based on deferents and epicycles. The heat equation is a partial differential equation. Prior to Fourier's work, no solution to the heat equation was known in the general case, although particular solutions were known if the heat source behaved in a simple way, in particular, if the heat source was a sine or cosine wave. These simple solutions are now sometimes called eigensolutions. Fourier's idea was to model a complicated heat source as a superposition of simple sine and cosine waves, and to write the solution as a superposition of the corresponding eigensolutions. This superposition or linear combination is called the Fourier series.
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