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13.2 The Curl in General Orthogonal Coordinate System

We may use Stokes' Theorem to deduce this by applying it to a tiny rectangle normal to the w1 direction with sides obeying one of dw= 0 and dw= 0, and then cyclically permuting the indices.
The surface integral in Stokes' theorem then becomes


while the path integrals become

which gives us: