Sentence examples for use of the calculus from inspiring English sources

One criterion for finding that point, which makes use of the calculus of variations, is called the principle of virtual work.

Newton's use of the calculus in the Principia is illustrated by proposition 11 of Book I: if the orbit of a particle moving under a centripetal force is an ellipse with the centre of force at one focus, then the force is inversely proportional to the square of the distance from the centre.

This work is intended to motivate the use of the calculus of variations and optimal control problems on time scales in the study of economic models.

Moreover, some researchers have shown the advantageous use of the fractional calculus in the modeling and control of many dynamical systems.

First, by use of the fractional calculus techniques, we give the phase trajectories of the time-delayed FO Lorenz and time-delayed FO Chen chaotic systems.

The ∂-operator on an almost complex abstract Wiener space (B, H, μ, J) is defined by making use of the Malliavin calculus.

On the other hand, in the control area there was an increasing interest in the development of new strategies, which resulted in new algorithms where the use of the fractional calculus revealed an helpfull tool.

We recapture and make use of the convenient calculus on Fréchet spaces, as developed by Kriegl and Michor (The Convenient Setting for Global Analysis, Surveys and Monographs, Vol. 53, Amer. Math. Soc., Providence, RI, 1997).

The systematic use of the differential calculus for norms, as done here for the first time, could lead to major advances also in other branches of mathematics and of other sciences, notably in engineering, for example in the simulation of dynamic problems with excitation.

The use of fractional calculus in the mathematical modeling of engineering and physical problems has become increasingly popular in recent years.

This generalizes the winding number of functions on the circle and the average winding number of almost periodic functions on the real line and makes fundamental use of the quantized differential calculus of Alain Connes.