The Analytical Theory of Heat

…analytique de la chaleur (1822; The Analytical Theory of Heat). He showed how the conduction of heat in solid bodies may be analyzed in terms of infinite mathematical series now called by his name, the Fourier series. Far transcending the particular subject of heat conduction, his work stimulated research in…

His major contribution, presented in The Analytical Theory of Heat (1822), was to the theory of heat diffusion in solid bodies. He proposed that any function could be written as an infinite sum of the trigonometric functions cosine and sine; for example,

…of the great mathematical classics, The Analytical Theory of Heat. Fourier began with a problem closely analogous to the vibrating violin string: the conduction of heat in a rigid rod of length l. If T(x, t) denotes the temperature at position x and time t, then it satisfies a partial…