Stoke's and Gauss's Theorum in proving div(curlA)=0

  • #1

Homework Statement


The problem puts forth and identity for me to prove:
gif.gif
or
gif.gif
. It says that I can use "straight-forward" calculation to solve this using the definition of nabla or I can use Gauss's and Stoke's Theorum on an example in which I have a solid 3D shape nearly cut in two by a curve C.

Homework Equations


gif.gif
Divergence Theorum
gif.gif
Stoke's Theorum

The Attempt at a Solution


I just can't seem to figure out how to start this. The two equations above are clearly suited to proving this identity, but I just can't see how.
 

Answers and Replies

  • #2
ehild
Homework Helper
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I think it is easier to use the definition of Nabla, and the definitions of cross product and dot product.
 
  • #3
I think it is easier to use the definition of Nabla, and the definitions of cross product and dot product.
Oh and I misstated the equality above, it specifies that the div(curlA)=0 then it has continous second-order derivatives.
 

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