Sentence examples for derivatives of equation from inspiring English sources

Taking the partial derivatives of Equation A1 with respect to, α k, gives (A8) (A8).

We take the homogeneous balance between nonlinear terms and highest order derivatives of equation (6) to determine the positive integer n.

A more formal analysis of partial derivatives of equation (7) with respect to different growth parameters is given in Appendix A.1.

It is straightforward to show that the signs of the partial derivatives of equation (11) are the same as those of equation (9).

After making the tedious partial derivatives of equation (34), the solution of the unknown parameters (a 1,a 2,…,a k ) and (b 1,b 2,…,b k ) can be derived.

By taking the derivatives of Equation 4 with respect to a and b, λ1 = λ2 is derived, and the directions a and b maximizing the correlation ρ can be calculated.

Discretizing the spatial derivatives of equations (3 - 5) by using PDQM at the point x i, we have d u i d t = ∑ j = 1 N b i j u j + α u i ( 1 − u i ), i = 1, 2, …, N, (39).

The conditions for the objective function to be convex if β ≠ 1 (case B), can be derived as follows: First, take the derivative of equation (14) with respect to n d : This expression will always be positive for β ≥ 2, and hence the objective function (equation (13)) convex.

We compute the derivative of equation (2.6) with respect to x to derive the following higher order partial differential equation: frac{partial^{k}}{partial x^{k}} bigl{ G t,x a,b,q) bigr} = ( tlog a ) ^{k}G t,x a,b,q), where k is a nonnegative integer.

The partial derivative of Equation 3 with respect to t was set to zero to derive Equations 4 and 5.

The first derivative of equation (1) expresses smoothness, and the subtracted part expresses observation error.