in one side of Stoke's theorem we compute curl(F ) . ndA .(adsbygoogle = window.adsbygoogle || []).push({});

When we have computed curl(F ) in x-y-z coordinate, but have parametrized the surface in cylindrical / spherical coordinates, then in computing ndA, we do the cross product of the partials then times that by du dt (or somethin else) . Can we then transform curl(F ) using the transformation of the surface and dot the 2 quantities together ?

also, there are cases where curl(F ) and n are easy to compute in the x-y-z coordinates, but the surface can be described easily in spherical coordinate. In that case how do we correctly proceed ? do we have to make sure the vector n is normalized (in x-y-z) then compute dA as |dG/du x dG/dv|dudv ?

thanks

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# Computing ndA (dS) in Stoke's theorem

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