# Variation of Gauss' Theorem

• Mar 21st 2007, 08:33 AM
Five Star
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?
• Mar 21st 2007, 10:26 AM
ThePerfectHacker
Quote:

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).

Quote:

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?
• Mar 21st 2007, 11:24 AM
Jhevon
Quote:

Originally Posted by ThePerfectHacker
This type of math seriously makes you look cool.