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differential operator
(redirected from Order of a differential operator)

   Also found in: Wikipedia 0.02 sec.

differential operator

In mathematics, any combination of derivatives applied to a function. It takes the form of a polynomial of derivatives, such as D2xxD2xyD2yx, 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.


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.


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