We need to consider

divergence theorem; to be more explicit we need the Green's identity of the first kind, in order to resolve the right-hand side of this equation.

If [omega] [member of] [H.sup.1]([R.sup.3]) [intersection] ([R.sup.3]), then the

divergence theorem andtrace theorem induce the following estimates:

The boundary of B, denoted by [partial derivative]B, is a sufficiently smooth surface to admit the application of

divergence theorem. The closure of B will be denoted by [bar.B].

Integrating (16) over the volume V (assumed to contain the electron core (-[e.sub.*], m)), and using the

divergence theorem, leads to [1, p.

Mimetic finite difference (MFD) approximations to differential vector operators along with compatible inner products satisfy a discrete analog of the Gauss

divergence theorem. On nodal grids, an important MFD family comprises the summation-by-part (SBP) difference operators, whose development and initial applications were focused on the conservative discretization of wave propagation problems [22, 23, 24, 30].

By application of the Gauss

divergence theorem to the tetrahedron, one can write:

Then using the Gauss'

divergence theorem, the above becomes

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.

Numerical integration using the

Divergence Theorem in the coordinates ([theta], [phi]).

integrate over [OMEGA], and use the

divergence theorem.

THE

DIVERGENCE THEOREM AND SETS OF FINITE PERIMETER.

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.