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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.

13_vector_calculus-311.gif

13_vector_calculus-312.gif

The other proof is similar and is left as a problem.
Home Vector Calculus Theorems of Stokes and Gauss Theorem 1

Last Update: 2006-11-22