Sentence examples for applying integration from inspiring English sources

Next, applying integration by parts to the third integral on the right-hand side of (3.23), we easily get int u^{n}cdotnablaoverline{p}^{n+1} overline{h}^{n+1} leq C intbiglvert nabla u^{n}bigrvert biglvert overline{rho}^{n+1}bigrvert biglvert overline{h}^{n+1} bigrvert +C intbiglvert u^{n}bigrvert biglvert overline{ rho}^{n+1}bigrvert biglvert nablaoverline {h}^{n+1} bigrvert.

The necessary condition represented by (3.12) is obtained by applying integration by parts in (3.7) and then substituting (3.11) in the resulting integrals.

Applying integration by parts in Lemma 2.2, by (iii) in Lemma 2.1, we get (4.4).

Integrating this and applying integration by parts, we obtain the term.

Similar to the proof of Theorem 2.1 applying integration by parts to identity (1.3) and then using identity (2.4).

Applying integration by parts and using conditions (1.2) and (1.3), we get alpha_{n}"(y -lambda_{n}^{2} alpha_{n}(y -lambda_{n

We apply integration by parts and the Cauchy inequality.

In order to prove the convergence of the last series, we apply integration by parts in (3.6).

In this study, we applied integration of neuro-fuzzy and GIS techniques for assessment of groundwater quality.

Let us suppose that the statement holds for m − 1 and let us apply integration by parts on the right-hand side of the formula.

An equation analyzer expanded the defined equation and the material properties, performed spatial differentiation, and applied integration by parts thereby reducing second order terms to create symbolic Galerkin equations for use in the weighted residual method.