Vector Calculus IdentitiesThe divergence of the curl is equal to zero: The curl of the gradient is equal to zero:

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Divergence TheoremThe volume integral of the divergence of a vector function is equal to the integral over the surface of the component normal to the surface.

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Stokes' Theorem The area integral of the curl of a vector function is equal to the line integral of the field around the boundary of the area.

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Vector IdentitiesIn the following identities, u and v are scalar functions while A and B are vector functions. The overbar shows the extent of the operation of the del operator. 
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