DIFFERENTIAL OPERATOR Definition & Meaning

differential operator

noun

Mathematics.

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

differential operator

noun

any operator involving differentiation, such as the mathematical operator del ∇, used in vector analysis, where ∇ = i ∂/∂ x + j ∂/∂ y + k ∂/∂ z , i , j , and k being unit vectors and ∂/∂ x , ∂/∂ y , and ∂/∂ z the partial derivatives of a function in x , y , and z

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Example Sentences

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If X, Y are two linear differential operators, XY − YX is also a linear differential operator.

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The differential operator e1X1 + e2X2 + ... + erXr may then be regarded as defining the most general infinitesimal operation of the group.

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By a very convenient, though perhaps hardly justifiable, phraseology this differential operator is itself spoken of as the general infinitesimal operation of the group.

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The method of differential operators, of wide application to problems of combinatorial analysis, has for its leading idea the designing of a function and of a differential operator, Method of differential operators. so that when the operator is performed upon the function a number is reached which enumerates the solutions of the given problem.

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