# differential operator

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differential operator
a function, usually expressed as a polynomial, that indicates linear combinations of the derivatives of the expression on which it operates.

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In mathematics, any combination of derivatives applied to a function.

It takes the form of a polynomial of derivatives, such as D2xx -D2xy · D2yx, 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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Universalium. 2010.

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