= Joseph Fourier
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<Joseph Fourier> (1768–1830) developed the mathematical study of <heat conduction> by combining a <partial differential equation> for <diffusion> with expansions in <trigonometric functions>. His 1822 publication on the analytical theory of heat made the use of <Fourier series> central to this physical problem.https://mathshistory.st-andrews.ac.uk/Biographies/Fourier/[University of St Andrews, MacTutor biography, heat-conduction research and1822 publication]{ref}
For the <heat equation> $u_t=\kappa u_{xx}$ on a periodic domain, a spatial mode $e^{ikx}$ acquires the amplitude $e^{-\kappa k^2t}$. Shorter wavelengths therefore decay faster, making the physical smoothing visible one mode at a time. Reconstructing general initial data from those modes leads to questions of <orthogonality>, <convergence> of <Fourier series> and function-space approximation. The same decomposition later became useful far beyond heat, in <wave equations> and <signal processing>.
\Image[https://commons.wikimedia.org/wiki/Special:Redirect/file/Portrait%20of%20Joseph%20Fourier%2C%20Museum%20d'Auxerre.jpg?width=250]
{title=Portrait of <Joseph Fourier>}
{description=Attributed to Pierre-Claude Gautherot (died 1825), circa 1802–1803; Musée d'Auxerre; reproduction source listed on Commons. Public domain (life-plus-100, pre-1931 U.S. publication), faithful reproduction / PD-Art. Source and usage information on the linked Wikimedia file page.}
{source=https://commons.wikimedia.org/wiki/File:Portrait_of_Joseph_Fourier%2C_Museum_d'Auxerre.jpg}
{width=250}
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