Sentence examples for calculus are shown from inspiring English sources

The summary of error calculus are shown in Table 7.

In this paper, some animations of the fundamental concepts of Calculus are shown, emphasizing the analysis of their geometric interpretations.

The DMFT scores, their components, their indices and the percentage of children with gingival bleeding and calculus are shown in Table  1.> Among 12- to 15-year-olds, only 5.3% had accurate knowledge concerning dental plaque; 41.5% agreed that dental caries is mainly caused by bacteria.

The situation has changed recently, fractional calculus was shown to be an excellent tool for the description of memory and hereditary properties of various materials and processes.

In the calculus it is shown that sin x and cos x are sums of power series.

In current years, a substantial attention to the fractional calculus has been shown, which allows us to consider integration and differentiation of any order.

These days, a substantial attention to the fractional calculus has been shown, which allows us to consider integration and differentiation of any order.

A recent interest in discrete fractional calculus has been shown by many scholars, such as Atici and Eloe, who in[15] discuss properties of the generalized falling function, a corresponding power rule for fractional delta-operators and the commutivity of fractional sums.

The derivation is a bit more involved, but after some calculus it can be shown that this polynomial has a single root located in (0,1): delta_{2} = left{ begin{aligned} &frac{beta_{2} - 4beta_{3} + sqrt{beta_{2}(beta_{2} + 8beta_{3})}}{4 beta_{2} - beta_{3})},quadtext{if}} beta_{2} neq beta_{3} &{textstylefrac{2}{3}}, qquadqquadqquadqquadqquadqquadtext{otherwise} end{aligned}right.

Utilizing the FO calculus, it is showed that the state trajectories of the closed-loop system reach the FO switching manifold in finite time.

By the calculus of variations, it can be shown that the functions h 1 x) and h 2 x) that minimize E ϕ, h 1, h 2) satisfy the following Euler-Lagrange equations: ∫ Ω K σ x − y 1 − I y h i x M i ϵ ϕ y dy = 0, i = 1, 2 (14).