Here are two cute checks of the fundamental theorems:
(a) Combine Corollary 2 to the gradient theorem with Stokes’ theorem (v = ∇T , in this case). Show that the result is consistent with what you already knew about second derivatives.
(b) Combine Corollary 2 to Stokes’ theorem with the divergence theorem. Show that the result is consistent with what you already knew
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