Joseph Fourier

Joseph Fourier (1768–1830) was a French mathematician and physicist whose work on heat conduction developed Fourier series and transformed mathematical physics.

Fourier series: A representation of a periodic function as a sum of sines and cosines. Fourier used these expansions to describe temperature distributions in his theory of heat.
French Revolution: A period of political upheaval in France beginning in 1789 that ended the monarchy and reshaped the state. The Revolution disrupted Fourier’s early career and drew him into public service.
Jean-Baptiste Joseph Delambre: French astronomer and mathematician known for measuring the meridian arc and writing histories of astronomy. Delambre supported Fourier’s election to the French Academy of Sciences.
Fourier analysis: The study of representing functions and signals through sinusoidal frequency components. Fourier’s work on heat series helped establish this broad mathematical framework.
Théorie analytique de la chaleur: Fourier’s 1822 treatise presenting a mathematical theory of heat conduction. This book set out his heat equation methods and extensive use of trigonometric series.
Fourier transform: An integral transform that expresses a function in terms of its frequency components. It generalizes the decomposition into sines and cosines that grew from Fourier’s work.
École Normale: A Paris institution founded during the French Revolution to train teachers and advance education. Fourier studied there in 1795, where he encountered leading mathematicians.
Siméon Denis Poisson: French mathematician whose work included probability, mechanics, and mathematical physics. Poisson challenged aspects of Fourier’s heat theory and offered a competing analysis.
Harmonic analysis: The study of functions through oscillations, symmetries, and related decompositions. Fourier’s decompositions of temperature helped launch this wider field.
Fourier's law of heat conduction: A law stating that heat flux through a material is proportional to the negative temperature gradient. Fourier formulated the constitutive relation that connects temperature gradients with heat flow.

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