differential operator

mathematics

Also known as: del

Written and fact-checked by The Editors of Encyclopaedia Britannica

differential operator, In mathematics, any combination of derivatives applied to a function. It takes the form of a polynomial of derivatives, such as D²_xx − D²_xy · D²_yx, where D² is a second derivative and the subscripts indicate partial derivatives. Special differential operators include the gradient, divergence, curl, and Laplace operator (see Laplace’s equation). Differential operators provide a generalized way to look at differentiation as a whole, as well as a framework for discussion of the theory of differential equations.

This article was most recently revised and updated by William L. Hosch.