Sentence examples for operation of differentiation from inspiring English sources

The use of such filters invalidates the standard derivation of the basic equations for the filtered fields since the filtering operation in general does not commute with the operation of differentiation.

We find that if the influencing displacement field is the gradient of a harmonic function, then the calculation of the induced elastic field reduces to the operation of differentiation only.

Since the operation of differentiation is ill conditioned, to find a highly accurate approximation for the derivatives of the solution of a differential equation becomes problematic, especially when the smoothness is restricted.

The operations of differentiation and integration emerged in his work as analytic processes that could be applied generally to investigate curves.

The fractional calculus has authorized the operations of differentiation and integration to all fractional order [1 3].

Observe, in fact, that the operations of differentiation and transposition commute; that is, ( A ˙ ( t ) ) ⊤ = d d t ( A ( t ) ⊤ ).

By considering the moving line, or ordinate, as the moment of the area Newton established the generality of and reciprocal relationship between the operations of differentiation and integration, a fact that Barrow had grasped but had not put to systematic use.

cluster-of-differentiation 14 subtypes.

The fractional calculus has allowed the operations of integration and differentiation to be applied for any fractional order [17 21].

The fractional calculus has allowed the operations of integration and differentiation to be applied upon any fractional-order.

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