differential operator

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.

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differential operator [‚dif·ə′ren·chəl ′äp·ə‚rād·ər]

(mathematics)

An operator on a space of functions which maps a function ƒ into a linear combination of higher-order derivatives of ƒ.