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dopey9
05-09-2007, 03:14 PM
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???

pka
05-09-2007, 03:25 PM
I have no idea what all that means.
Can you please explain?

JakeD
05-10-2007, 12:18 AM
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 (http://en.wikipedia.org/wiki/Stokes%27_theorem)?

dopey9
05-10-2007, 10:23 PM
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 (http://en.wikipedia.org/wiki/Stokes%27_theorem)?

no i want to know how to show the curl theorem using the divergence theorem

JakeD
05-11-2007, 03:25 AM
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 (http://en.wikipedia.org/wiki/Stokes%27_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)

http://upload.wikimedia.org/math/1/f/d/1fdf437d8e18a23191b63df96ae36916.png

and the divergence theorem

http://upload.wikimedia.org/math/f/b/6/fb6cbe67ee035c366e49384a1a0fc4d8.png

are special cases of the general Stokes' Theorem (http://en.wikipedia.org/wiki/Stokes%27_theorem)

http://upload.wikimedia.org/math/9/8/d/98da50d6b2b3b0abc3de5994d98c5562.png

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