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

AI Thread Summary
The discussion focuses on proving the identity div(curl A) = 0 using either straightforward calculations or applying Gauss's and Stokes' Theorems. Participants express difficulty in determining how to start the proof, noting that while the equations are suitable for the identity, clarity is lacking. There is a preference for using the definition of Nabla along with the cross product and dot product for a more straightforward approach. The problem emphasizes the requirement of continuous second-order derivatives for the identity to hold. Overall, the conversation highlights the challenges in applying theoretical concepts to practical problems in vector calculus.
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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.
 
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I think it is easier to use the definition of Nabla, and the definitions of cross product and dot product.
 
ehild said:
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 continuous second-order derivatives.
 

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