Jean Baptiste Joseph Fourier

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The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Fourier, Jean Baptiste Joseph

 

Born Mar. 21, 1768, in Auxerre; died May 16, 1830, in Paris. French mathematician. Member of the Académie des Sciences (1817).

After graduating from the military school in Auxerre, Fourier became a teacher at the school. From 1796 to 1798 he taught at the Ecole Polytechnique.

Fourier’s first works were on algebra. In 1796 he taught his students at the Ecole Polytechnique a theorem, now known as Fourier’s theorem, on the number of real roots of an algebraic equation that lie between given boundaries; the theorem was published in 1820. A complete solution of the problem of the number of real roots of an algebraic equation was obtained by J. C. F. Sturm in 1829. In 1818, Fourier investigated the problem of the conditions of applicability of I. Newton’s method for the numerical solution of equations. Results similar to Fourier’s had been obtained in 1768 by the French mathematician J. R. Mourraille; Fourier, however, did not know of his predecessor’s findings. Fourier’s work on numerical methods of the solution of equations was presented in The Analysis of Determinate Equations, which was published posthumously in 1831.

Fourier’s most important contributions were made in mathematical physics. In 1807 and 1811 he presented his first discoveries in the theory of heat propagation in a solid to the Académie des Sciences. In 1822 he published his famous work The Analytical Theory of Heat, which played an important role in the subsequent history of mathematics. In this work Fourier derived the differential equation of heat conduction and developed ideas that had been outlined by D. Bernoulli. In addition, he worked out the method of separation of variables for solving the equations of heat conduction under various boundary conditions and applied the method to a number of particular cases, such as the cube and cylinder. The method is based on the representation of functions by the trigonometric series now called Fourier series. Although such series had been considered previously, they did not become an effective and important tool of mathematical physics until Fourier used them.

The method of separation of variables was developed further by S. Poisson, M. V. Ostrogradskii, and other 19th-century mathematicians. The Analytical Theory of Heat was the starting point for the creation of the theory of trigonometric series and for the elaboration of some general problems of mathematical analysis. Fourier gave the first examples of the expansion in Fourier series of functions that are defined in different regions by different analytic expressions. He thereby made an important contribution to the resolution of the dispute over the concept of function that had involved the most prominent mathematicians of the 18th century. His attempt to prove the possibility of expanding any function in a Fourier series was unsuccessful but gave rise to an important group of studies devoted to the problem of the representability of functions by trigonometric series. P. Dirichlet, N. I. Lobachevskii, and B. Riemann were among the mathematicians who investigated the problem. The development of set theory and the theory of functions of a real variable was largely based on these studies.

WORKS

Oeuvres, vols. 1–2. Published by G. Darboux. Paris, 1888–90.
Analyse des équations déterminées, part 1. Paris, 1831.
The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
References in periodicals archive ?
Also, next year, Universite Joseph Fourier will merge with other Grenoble-based universities and research centres to create a super university called the Universite Grenoble Alpes.
It and collaborators the Los Alamos National Laboratory in New Mexico, USA, and the Joseph Fourier University, Grenoble, France, has provided new information about hydrogen bonds that connect the building blocks of cellulose, the main molecule in cotton fibres and most other plant cell walls.
The 18th Century mathematician Joseph Fourier created techniques which produce greater accuracy in the prediction of pattern.
A: The idea dates back more than 180 years to when the French scientist Joseph Fourier worked out the atmosphere helps keep the Earth warmer than it would be if there was no air - a bit like a greenhouse.
[6] Faculte de Medecine Universite Joseph Fourier Grenoble, France
In 1824--the same year that Carnot published his work on steam engines--the French physicist Jean-Baptiste Joseph Fourier (1786-1830) compared the warming of Earth's atmosphere by the Sun's rays with that occurring in the air within a greenhouse.
From there he went directly to the University of Rochester as an Assistant Professor of Chemistry where he was given a year leave to take up a NATO Science Fellowship at the Universite de Joseph Fourier with Peter Trommsorff.
Developed in the early 1800s by Joseph Fourier, Fourier transforms are approximations using the super: position of sines and cosines to represent other functions.
Current Board members are Marc Brown (Ariba Technologies), John Carroll (Virginia Tech), Joelle Coutaz (University Joseph Fourier), Wayne Gray (George Mason University), James Hollan (University of California, San Diego), Scott Hudson (CMU), Hiroshi Ishii (MIT), Robert Jacob (Tufts University), Bonnie John (CMU), Jock Mackinlay (Xerox PARC), Allan MacLean (Xerox Research Center Europe), Brad Myers (CMU), and Randy Pausch (CMU).
1820s -- French mathematician Jean-Baptiste Joseph Fourier suggests something in the atmosphere is keeping the world warmer than it would otherwise be, a hint at the greenhouse effect.