Abstract
First edition. "This work marks an epoch in the history of both pure and applied mathematics. It is the source of all modern methods in mathematical physics involving the integration of partial differentia equations in problems where the boundary values are fixed... The gem of Fourier's great book is 'Fourier's series'." --Cajori, A History of Mathematics, p.270. "The first outstanding publication on the conduction of heat… Fourier demonstrated that problems in mathematical physics can be solved for any complex condition when one knows how to solve the simple periodic initial condition." --Milestones of Science, p.31. Fourier's methods find their widest application to problems of vibration such as in heat, sound, and fluid motion.