In sections on vector analysis, complex analysis, and Fourier analysis, they consider such topics as gradient vector fields, the

divergence theorem, complex integration, Fourier series, and applications to ordinary and partial differential equations.

As a result, the approach chosen for this study was based on a fundamental theorem in calculus, called the Divergence Theorem (see Taylor (2)), an analogue of Green's Theorem in two dimensional space.

Section 2 describes how a volume can be computed using the Divergence Theorem.

In this section we state the Divergence Theorem and indicate how it can be used to estimate the volume of a polyhedron.

21) That result is just what one needs for the

divergence theorem in a form suitable for generalized coordinates and hence slightly generalized from that in vector calculus, in order to get results independent of the merely conventional choice of coordinates.

The second edition adds a section on the

divergence theorem.

NULL LAGRANGIANS AND THE TOTAL

DIVERGENCE Theorem 8.

Their basic idea is to eliminate the divergence-terms by applying the Gaussian divergence theorem.

Using the Gaussian divergence theorem yields the evolutionary equation

The

divergence theorem may be applied at time t to the volume bounded by [S.

Applying the

divergence theorem and with the assumption that the turbulent diffusion flux is given by [Mathematical Expression Omitted], a balance equation for the probability density function is obtained

Topics include the Gauss map and the second fundamental form, the

divergence theorem, global extrinsic geometry, rigid motions and isometrics, and the Gauss-Bonnet theorem.