All Questions
4
questions
0
votes
0
answers
126
views
Tensor and Gauss divergence theorem
I am trying to see whether, in spherical coordinates,
$$\int \left( \boldsymbol{r} \times \boldsymbol{\nabla} \cdot \boldsymbol{T} \right) \cdot \boldsymbol{e}_z dV$$ where $T$ is a 2D symmetric ...
- 21
1
vote
0
answers
58
views
Prove that if $V=\text{constant}$ then the second part in the paratheses after the integral sign is equal to $0$
$$\frac{\mathrm d}{\mathrm dt^i} \underset{\large V(t)}{\iiint} \Psi \,\mathrm dV= \underset{\large V(t)}{\iiint} \left({\frac{\partial \Psi}{\partial t}+\nabla\cdot\Psi\mathbf v_i}\right)\, \mathrm ...
- 8,382
7
votes
1
answer
3k
views
Divergence theorem for a second order tensor
I want to integrate by part the following integral in cylindrical coordinates
$$\int \vec{r} \times (\nabla \cdot \overline{T}) ~d^3\vec{r} $$
where $\overline{T}$ is a second order symmetric tensor ...
- 123
2
votes
1
answer
328
views
Integral/Vector calculus $\oint_{\partial S} u \vec \nabla v \cdot d \vec \lambda=\int_S (\vec \nabla u)\times (\vec \nabla v)\cdot d\vec S.$
I am trying to show that
$$
\oint_{\partial S} u \vec \nabla v \cdot d \vec \lambda=\int_S (\vec \nabla u)\times (\vec \nabla v)\cdot d\vec S
$$
using Levi Cevita notation methods only. The Levi ...
- 515