differential operator


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

* * *

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.

* * *


Universalium. 2010.

Look at other dictionaries:

  • Differential operator — In mathematics, a differential operator is an operator defined as a function of the differentiation operator. It is helpful, as a matter of notation first, to consider differentiation as an abstract operation, accepting a function and returning… …   Wikipedia

  • differential operator — diferencialinis operatorius statusas T sritis fizika atitikmenys: angl. differential operator vok. Differentialoperator, m rus. дифференциальный оператор, m pranc. opérateur différentiel, m …   Fizikos terminų žodynas

  • differential operator — noun mathematics : a prescribed combination or sequence of operations involving differentiation …   Useful english dictionary

  • Pseudo-differential operator — In mathematical analysis a pseudo differential operator is an extension of the concept of differential operator. Pseudo differential operators are used extensively in the theory of partial differential equations and quantum field theory.… …   Wikipedia

  • Symbol of a differential operator — In mathematics, differential operators have symbols, which are roughly speaking the algebraic part of the terms involving the most derivatives.Formal definitionLet E 1, E 2 be vector bundles over a closed manifold X , and suppose: P: C^infty(E 1) …   Wikipedia

  • Differential geometry of surfaces — Carl Friedrich Gauss in 1828 In mathematics, the differential geometry of surfaces deals with smooth surfaces with various additional structures, most often, a Riemannian metric. Surfaces have been extensively studied from various perspectives:… …   Wikipedia

  • Operator (mathematics) — This article is about operators in mathematics. For other uses, see Operator (disambiguation). In basic mathematics, an operator is a symbol or function representing a mathematical operation. In terms of vector spaces, an operator is a mapping… …   Wikipedia

  • Differential ideal — In the theory of differential forms, a differential ideal I is an algebraic ideal in the ring of smooth differential forms on a smooth manifold, in other words a graded ideal in the sense of ring theory, that is further closed under exterior… …   Wikipedia

  • differential — differentially, adv. /dif euh ren sheuhl/, adj. 1. of or pertaining to difference or diversity. 2. constituting a difference; distinguishing; distinctive: a differential feature. 3. exhibiting or depending upon a difference or distinction. 4.… …   Universalium

  • Operator theory — In mathematics, operator theory is the branch of functional analysis that focuses on bounded linear operators, but which includes closed operators and nonlinear operators. Operator theory also includes the study of algebras of operators. Contents …   Wikipedia