Gauss' theorem

Gauss' theorem

[′gau̇s ‚thir·əm]
(mathematics)
The assertion, under certain light restrictions, that the volume integral through a volume V of the divergence of a vector function is equal to the surface integral of the exterior normal component of the vector function over the boundary surface of V. Also known as divergence theorem; Green's theorem in space; Ostrogradski's theorem.
At a point on a surface the product of the principal curvatures is an invariant of the surface, called the Gaussian curvature.
References in periodicals archive ?
Applying Gauss' theorem and integrating over the surface of a sphere of radius r, one obtains for the energy-momentum distribution the following expression:
Therefore, as shown in Figure 2(b), the value of 3-cochain [rho] on i-th tet [V.sub.i] can be derived by 3-D Gauss' theorem:
And notice that, Gauss' theorem and Stokes' theorem can also be applied for complex structures, such as polygons or polyhedrons.
Then, by Gauss' theorem, the discrete divergence of this vector field [[nabla].sub.s] x D can be represented as a dual 2-cochain [sigma].
Using Gauss' theorem, we can rewrite this as a surface integral:
Again, we employ Gauss' theorem to express the total energy as a surface integral:
One more time, we employ Gauss' theorem to express the total energy as a surface integral:
Like our above illustration of the Poisson equation, a misunderstanding of Gauss' Theorem,
From this, we can conclude that although we may possess measurements [nabla] u and [[nabla].sup.2]u, we cannot determine the nature of the scalar field u simply from the Poisson equation or Gauss' Theorem.
So one can consider the hypothesis of continuity as a first approximation, and one can re-examine the Gauss' theorem