Laplacian

Part of speech: adjective, noun

Definitions

1. A mathematical operator that computes the sum of second partial derivatives of a function with respect to its variables
2. An operator used in calculus and physics representing the sum of second derivatives that measures the rate at which a quantity spreads out from a point
3. A differential operator finding how much a function deviates locally from its average value by summing its second partial derivatives with respect to spatial coordinates

Etymology: Pierre-Simon Laplace, the French mathematician and astronomer, never wrote the operator that bears his name in the form we use today, yet his work on gravitation and potential theory in the late eighteenth and early nineteenth centuries laid the groundwork for it. The term itself is simply the surname "Laplace" with the English adjectival suffix "-ian" attached, so the word functions as a tribute: a mathematical object named for the man whose methods made it central to the study of potentials. The operator sums the second partial derivatives of a function with respect to each spatial coordinate. Because of this, it describes how a quantity such as heat or electric potential tends to smooth out or diffuse away from a point, which is why it turns up throughout physics wherever spreading or equilibrium is at issue. The word can serve as a noun for the operator itself or as an adjective, as in "Laplacian operator" or "Laplacian field."