My Math Forum Help with Multivariable calculus.. Flux in Space?

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 July 29th, 2009, 08:56 PM #1 Newbie   Joined: Jul 2009 Posts: 3 Thanks: 0 Help with Multivariable calculus.. Flux in Space? note that i'll use ? as "del" or basically the thing infront of a gradient. See http://en.wikipedia.org/wiki/Del for more info "Show that, if S is a closed surface bounding a region D, and if "ƒ" has continuous seocnd derivatives inside D, then S ? ? ƒ?ƒ•n dS = D ? ? ? (ƒ[?^2ƒ] + |?ƒ|^2) dV if I say that ?ƒ = F, or that ƒ is a potential for the gradient field F, and div(F) is the divergence of F, then prove: S ? ? ƒF•n dS = D ? ? ? (ƒ[div(F)] + |F|^2) dV If you coud help me with this proof I would appreciate it! Thanks.
 July 30th, 2009, 07:24 AM #2 Global Moderator   Joined: Dec 2006 Posts: 20,921 Thanks: 2203 Why not use ??
July 30th, 2009, 10:21 AM   #3
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Quote:
 Originally Posted by skipjack Why not use ??
Yeah, I posted this on another site and it didn't have the real del. I'll edit.

 July 30th, 2009, 12:21 PM #4 Global Moderator   Joined: Dec 2006 Posts: 20,921 Thanks: 2203 If a problem's been posted elsewhere, just post a link. In this case, a simple Google search finds two other websites with this problem. The first of the two is this pdf file (part B, problem 3(b)).
July 30th, 2009, 07:44 PM   #5
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Quote:
 Originally Posted by skipjack If a problem's been posted elsewhere, just post a link. In this case, a simple Google search finds two other websites with this problem. The first of the two is this pdf file (part B, problem 3(b)).
Thanks. I wasn't really sure of procedure, but that would make things much easier for me.

Can you help me with the actual proof?

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