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Fourier, (Jean Baptiste) Joseph, Baron

heat series École egypt

[fooryay] (1768–1830) French mathematician: discovered Fourier series and the Fourier Integral Theorem.

Fourier, the son of a tailor, was orphaned at age 8. He had a mixed education, at military school, an abbey and later (after a narrow escape from the guillotine during the French Revolution in 1794) at the École Normale. He joined the staff of the École Normale, newly-formed to train senior teachers, and the École Polytechnique in Paris. When Napoleon invaded Egypt in 1798 Fourier accompanied him, but it is unlikely that he became governor of Lower Egypt as is often stated. He became the prefect of the département of Grenoble for 14 years but resigned during Napoleon’s Hundred Days campaign. Fourier died in 1830 of a disease contracted while in Egypt.

Fourier established linear partial differential equations as a powerful tool in mathematical physics, particularly in boundary value problems. For example, to find the conduction of heat through a body of a given shape when its boundaries are at particular temperatures, the heat diffusion equation can be solved as a sum of simpler trigonometric components (Fourier series). This way of solving the linear differential equations that often occur in physics has led to much use of the method on many new problems to the present day. Importantly, any arbitrary repeating function may be represented by a Fourier series; for instance, a complex musical waveform can always be represented as the sum of many individual frequencies. At a different level, the understanding of Fourier series and integrals has contributed greatly to the development of pure analysis, particularly of functional analysis. On the problem of heat conduction through a uniform solid, Fourier’s Law states that the heat flux is given by the product of the thermal conductivity and the temperature gradient.

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