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

  1. Sep 15, 2015 #1
    1. The problem statement, all variables and given/known data
    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.

    2. Relevant equations
    gif.gif Divergence Theorum
    gif.gif Stoke's Theorum

    3. 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.
  2. jcsd
  3. Sep 16, 2015 #2


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    I think it is easier to use the definition of Nabla, and the definitions of cross product and dot product.
  4. Sep 16, 2015 #3
    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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