Théorie Analytique de la Chaleur

French mathematician Joseph Fourier's Théorie Analytique de la Chaleur was originally published in 1822. In this groundbreaking study, arguing that previous theories of mechanics advanced by such outstanding scientists as Archimedes, Galileo, Newton and their successors did not explain the laws of heat, Fourier set out to study the mathematical laws governing heat diffusion and proposed that an infinite mathematical series may be used to analyse the conduction of heat in solids: this is now known as the 'Fourier Series'. His work paved the way for modern mathematical physics. This book will be especially useful for mathematicians who are interested in trigonometric series and their applications, and it is reissued simultaneously with Alexander Freeman's English translation, The Analytical Theory of Heat, of 1878.

Discours Préliminaire; 1. Introduction; 2. Équations du mouvement de la chaleur; 3. Propagation de la chaleur dans un solide rectangulaire infini; 4. Du mouvement linéaire et varié de la chaleur dans une armille; 5. De la propagation de la chaleur dans une sphère solide; 6. Du mouvement de la chaleur dans un cylinder solide; 7. Propagation de la chaleur dans un prisme rectangulaire; 8. Du movement de la chaleur dans un cube solide; 9. De la diffusion de la chaleur.

This book, first published in 1822, presents Fourier's groundbreaking theories of the mathematical laws governing the diffusion of heat in solids. His work changed the way scientists perceived mathematical functions and paved the way for modern mathematical physics.