Thread: Variation of Gauss' Theorem

How do I show the following,
If U is a smooth scalar field and N is a unit normal then
SSS grad(U) dV = SS (U)N dS (Note the S's at the beginning are integral signs.) ?

I have to apply the Divergence Theorem (Gauss' Theorem) to F=Uc where c is an arbitrary constant vector to get the above identity.

How do I go about solving this?

Originally Posted by Five Star

How do I show the following,
If U is a smooth scalar field and N is a unit normal then
SSS grad(U) dV = SS (U)N dS (Note the S's at the beginning are integral signs.) ?

Look below. (This type of math seriously makes you look cool. Eventhough it is not as hard as it seems).

I have to apply the Divergence Theorem (Gauss' Theorem) to F=Uc where c is an arbitrary constant vector to get the above identity.

How do I go about solving this?

Is this a seperate question?

Originally Posted by ThePerfectHacker

This type of math seriously makes you look cool.

You're right about that!

Originally Posted by Jhevon

You're right about that!

Actually I made look a little bit cooler.

The Integral with a circle through them should not be there because I am considering a special case. Without them what I wrote will be even more general.