Question: What is Stokes Theorem? Explain how it generalizes Greens Theorem to three dimensions. THEOREM 6-Stokes' Theorem Let S be a piecewise smooth oriented surface having

What is Stokes’ Theorem? Explain how it generalizes Green’s Theorem to three dimensions. THEOREM 6-Stokes' Theorem Let S be a piecewise smooth oriented surface having

a piecewise smooth boundary curve C. Let F = Mi + Nj

THEOREM 6-Stokes' Theorem Let S be a piecewise smooth oriented surface having a piecewise smooth boundary curve C. Let F = Mi + Nj + Pk be a vector field whose components have continuous first partial derivatives on an open region containing S. Then the circulation of F around C in the direction counterclockwise with respect to the surface's unit normal vector n equals the integral of the curl vector field VX F over S: fr. dr = [[ x F.dr S Counterclockwise circulation VXF n do Curl integral (4)

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