Analytical Theory of HeatJoseph Fourier

Fourier published the Analytical Theory of Heat (Théorie analytique de la chaleur) in 1822. Heat spreads through solid bodies. That is the problem. He sets out the heat equation, a partial differential equation relating temperature to position and time, and solves it by expanding arbitrary functions as infinite trigonometric series.

The book treats rings, cubes, spheres, and infinite solids. It distinguishes thermal capacity, internal conductivity, and surface conductivity. Fourier series, introduced as a tool for heat, became a general method of mathematical physics. Later work on wave equations, analysis, and signal processing descends from this treatise. The heat equation itself remains a standard model of diffusion.