differential operator

American  

noun

Mathematics.

1. 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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differential operator British  

noun

1. 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

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

From Project Gutenberg

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

From Project Gutenberg

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

From Project Gutenberg

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.

From Project Gutenberg