Show, using Stokes' Theorm, that
Firstly Stokes gives us:
Expanding gives:
The second part of this is zero for any vector, so this leaves the integral as:
Anyone any ideas?
Cheers in advance!
Remember that is a scalar function!
Expand out what is inside the parenthesis and you will get zero (As long as is twice continuously differentiable)
Remember 2nd continuous partial derivatives commute Clairaut's theorem
Symmetry of second derivatives - Wikipedia, the free encyclopedia