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Home Vector Calculus Theorems of Stokes and Gauss Theorem 1  
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Theorem 1
THEOREM 1 Assume the function f(x, y, z) and vector field F(x, y, z) have continuous second partials. Then curl(grad f) = 0, div(curlF) = 0. PROOF We use the equality of mixed partials. The other proof is similar and is left as a problem.


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