0
$\begingroup$

Let the closed surface $S$ be delimit volume $E$ and let the scalar function $f$. I need to demonstrate that :

$$\unicode{x222F}_S{f(x,y,z)d\vec{S}}=\iiint_E{}\nabla f(x,y,z)dV$$

I do have some indication. First, I got to consider the vector field $\vec{F}=f(x,y,z)\vec{u}$ where $\vec{u}$ has components $u_1, u_2, u_3$ independent of $x,y,z$ and I need to use divergence theorem on $S$. Next, I got to use the theorem that if $\vec{a}\cdot\vec{c}=\vec{b}\cdot\vec{c}$ then $\vec{a}=\vec{b}$.

Unfortunately, these hints doesn't really help and I can't figure out how to demonstrate this result. The demonstration is supposed to take 1 or 2 lines only !

Thanks !

$\endgroup$
0
$\begingroup$

This is the proof Divergence Theorem.

bests!

$\endgroup$
  • $\begingroup$ That is for a vector field, my question pertains for a scalar field ..! $\endgroup$ – Bob Leponge Aug 4 '15 at 8:55
  • $\begingroup$ :) It has also been done here $\endgroup$ – uli.xu Aug 4 '15 at 9:06

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.