- #1
daudaudaudau
- 302
- 0
Hello.
How can I prove something like
[tex]
\nabla\cdot(\mathbf fv)=(\nabla v)\cdot\mathbf f+v(\nabla\cdot \mathbf f)
[/tex]
using only the definition of divergence
[tex]
\text{div}\mathbf V=\lim_{\Delta v\rightarrow0}\frac{\oint_S\mathbf V\cdot d\mathbf s}{\Delta v},
[/tex]
i.e. without referring to any particular coordinate system? I have yet to see a book that does not assume cartesian coordinates.
How can I prove something like
[tex]
\nabla\cdot(\mathbf fv)=(\nabla v)\cdot\mathbf f+v(\nabla\cdot \mathbf f)
[/tex]
using only the definition of divergence
[tex]
\text{div}\mathbf V=\lim_{\Delta v\rightarrow0}\frac{\oint_S\mathbf V\cdot d\mathbf s}{\Delta v},
[/tex]
i.e. without referring to any particular coordinate system? I have yet to see a book that does not assume cartesian coordinates.