Joseph Fourier, 1768-1830 ― A Survey of His Life and Work

Beyond being the first substantial publication on Fourier, this work contains thetext of Fourier's seminal paper of 1807 on the propagation of heat, marking the first time it hasever appeared in print. This paper incorporates many of the mathematical creations on whichFourier's fame rests, including derivation of the diffusion equation, the separation of thetreatment of surface phenomena from internal phenomena, the use of boundary values and initialconditions, and the development of "Fourier series" and the so-called "Bessel functions."Whensubmitted to the examiners of the Institut de France, the originality of the paper and thesurprising nature of some of its mathematical revelations caused great controversy, and it wasdenied publication both in 1807 and in later years. Fourier had the support, among the examiners, ofLaplace and Monge, but Lagrange was adamantly in opposition, so that Fourier's work did not appearin print until 1822, reworked into book form.Fourier's mathematical discoveries are intimatelyrelated to his interest in the solution of physical problems and their experimental verification.The mathematical methods he developed in connection with heat diffusion apply to physical situationsfar beyond the boundaries of this area. Generally, Fourier may be credited with one of the firstmajor extensions of mathematical physics beyond the applications of Newton's laws of motion anduniversal gravitation.The opening biographical chapter of this book follows Fourier's career up tothe submission of the 1807 paper, and the two closing chapters take up his life and work from thatpoint on. Fourier had strong political motivations and spent much of his life in the public service.These chapters trace his political difficulties, both before and after 1807, when he was the prefectof a department of France and was subjected to the dislocations of Napoleon's ups and downs. Thesechapters also describe aspects of the turbulent but productive development of French science fromthe Revolution to 1830.The core of the book presents the paper of 1807 in its original French andwith the original notation. Grattan-Guinness has divided the paper into sections by the sequence ofthe problems taken up, and he introduces and, where necessary, closes each section with commentaryrelevant to Fourier's later work in these areas. The paper itself (cllows the chronology ofFourier's discoveries, and among the topics treated are, in this order: heat diffusion betweendisjoint bodies and in continuous bodies; the appearance of partial differential equations; thespecial solution for the lamina; sine and cosine series for an arbitrary function; reflections onthe vibrating string problem; solution for the annulus; the full Fourier series for an arbitraryfunction; reflections on n-body analysis; solution for the sphere; solution for the cylinder;steady-state diffusion in the rectangular prism; time-dependent diffusion in the cube; and Fourier'sexperimental work.