Laplaces

Laplaces is a plural usage that may refer to topics named after the French mathematician Pierre-Simon Laplace, or more broadly to various persons bearing the Laplace surname.

In mathematics and physics, several constructs bear Laplace's name, including the Laplace transform, the Laplacian, Laplace's equation, Laplace's method, and the Laplace distribution. The Laplace transform is an integral transform that converts a function of time into a function of complex frequency and is widely used to solve linear differential equations. The Laplacian is a second-order differential operator denoted ∇^2 and appears in problems of heat flow, electrostatics, and quantum mechanics. Laplace's equation, ∇^2 φ = 0, is a fundamental equation in potential theory. Laplace's method is an asymptotic technique for evaluating integrals with large parameters, providing approximate contributions near maxima. The Laplace distribution, or double-exponential distribution, is a continuous probability distribution with a sharp peak and heavier tails than the normal distribution.

Historically, Pierre-Simon Laplace (1749–1827) was a French mathematician and astronomer whose work shaped celestial mechanics, probability theory, and statistics; many results and tools in these fields bear his name.

In modern usage, Laplace's name appears in possessive form for individual theorems or operators (Laplace's transform, Laplace's equation), while Laplaces as a plural is uncommon outside lists of items named after Laplace.