The divergence theorem is an equality relationship between surface integrals and volume integrals, with the divergence of a vector field involved.

Intuitively, it states that "the sum of all sources of the field in a region (with sinks regarded as negative sources) gives the net flux out of the region".

3 дек. 2015 г. · The short answer is yes. The divergence theorem holds for Cartesian tensors of any rank, ∫V∂Ti1,i2,…iq…ik∂xiqdV=∫∂VTi1,i2,…iq…ikniqdS,. Divergence theorem with rank 2 tensor. - Mathematics Stack Exchange Divergence theorem for tensor fields on manifolds Divergence of tensor fields - Math Stack Exchange Другие результаты с сайта math.stackexchange.com

Notation convention: it is often convenient to denote vectors and tensors in index notation, e.g., vi. (vi = v · ei) and Tpi (Tpi = êpTei), where the bases ...

1.14.5 The Divergence Theorem. The divergence theorem 1.7.12 can be extended to the case of higher-order tensors. Consider an arbitrary differentiable tensor ...

The divergence theorem, a pivotal concept in continuum mechanics, plays a significant role in connecting volume integrals, which provide a global view of a ...

So done. Integrals and the tensor divergence theorem. It is also ... Theorem (Divergence theorem for tensors). Z. S. T. ij···k`. n. ` dS = Z. V. ∂. ∂x.

Gauss's Divergence Theorem states that the flux of a vector field through a closed surface is equal to the divergence of that field over the volume enclosed ...

Продолжительность: 20:13
Опубликовано: 18 июн. 2014 г.

Coordinate and tensor divergence theorems ... ∫V∂λ(√guλ)dnx=∫∂V√gdx1(u)dn−1x=∫∂Vu1√gdn−1x, ∫ V ∂ λ ( g u λ ) d n x = ∫ ∂ V g d x 1 ( u ) d n − 1 x = ∫ ∂ V u 1 g d ...