"The formula and even the method was... used by Euler in... 1777, published... 1798. (Fourier... having failed to refer to earlier works...) ...[A]s with Bernoulli, Fourier had acquired an intimate understanding of the physical meaning of the problem. Over... two years... Fourier repeated all important experiments... carried out in England, France, and Germany and added experiments of his own. ...[S]triking ...confirmations of his new theory ...together with his overcoming ...difficulties advanced by the old masters. Fourier mentioned the motion of fluids... propagation of sounds and...vibrations of elastic bodies, as other applications ...fully aware of having opened up a new era for the solution or partial differential equations... It was the era of linearization that would dominate mathematics for the first half of the nineteenth century and... has remained important... The diffusion equation is a : Linear combinations of solutions are still solutions. It was not the first such equation... in history... but the method opened up enormous... possibilities."
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Ref: 1) Leonhard Euler, "Remarques sur les mémoires précédens de M. Bernoulli," Mémoires de l’Académie Royale de Berlin, 9 (1753: publ. 1755), pp. 196-222. 2) Daniel Bernoulli, "Réflexions et éclaircissemens sur les nouvelles vibrations des cordes exposées dans les mémoires de l'Académie de 1747 et 1748," Mémoires de l'Académie Royale de Berlin, 9 (1753: publ. 1755), pp. 147-172.
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Joseph Fourier
Jean Baptiste Joseph Fourier (March 21, 1768 – May 16, 1830) was a French mathematician and physicist who is best known for initiating the investigation of Fourier series and their application to problems of heat flow. The Fourier transform is also named in his honor.
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