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July 29th, 2009, 08:56 PM   #1
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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 "" has continuous seocnd derivatives inside D, then

S ? ? ?n dS = D ? ? ? ([?^2] + |?|^2) dV

if I say that ? = F, or that is a potential for the gradient field F, and div(F) is the divergence of F, then prove:

S ? ? Fn dS = D ? ? ? ([div(F)] + |F|^2) dV

If you coud help me with this proof I would appreciate it!

Thanks.
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July 30th, 2009, 07:24 AM   #2
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Why not use ??
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July 30th, 2009, 10:21 AM   #3
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Re:

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.
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July 30th, 2009, 12:21 PM   #4
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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)).
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July 30th, 2009, 07:44 PM   #5
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Re:

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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