divergence theorem

dopey9

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Jul 14, 2006
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in the divergence theorm you have div F, but i wanted to know how to show this is exactly the same as the divergence theorem but not with div f but with curl F instead???
 
I have no idea what all that means.
Can you please explain?
 
dopey9 said:
JakeD said:
dopey9 said:
in the divergence theorm you have div F, but i wanted to know how to show this is exactly the same as the divergence theorem but not with div f but with curl F instead???
Are you looking for the general Stokes' Theorem?

no i want to know how to show the curl theorem using the divergence theorem
Please correct me if I am wrong, but my understanding is that the curl theorem (Kelvin-Stokes theorem)

1fdf437d8e18a23191b63df96ae36916.png


and the divergence theorem

fb6cbe67ee035c366e49384a1a0fc4d8.png


are special cases of the general Stokes' Theorem

98da50d6b2b3b0abc3de5994d98c5562.png


So they can be proved by specializing the same general technique. But the curl theorem does not follow from divergence theorem.
 
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