The Fourier series which can reduce any periodic function to a sum of sine and cosine terms.
The Fourier transform, an integral transform that re-expresses a function in terms of sinusoidal basis functions.
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Fourier went with Napoleon on his Eastern expedition in 1798, and was made governor of Lower Egypt.
Fourier left an unfinished work on determinate equations which was edited by Claude Navier, and published in 1831; this contains much original matter, in particular there is a demonstration of Fourier's theorem on the position of the roots of an algebraic equation.
Fourier's proof is the same as that usually given in textbooks on the theory of equations.
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