A special case of Stokes' theorem in which F is a vector field and M is an oriented, compact embedded 2-manifold with boundary in R^3, and a generalization of Green's theorem from the plane into three-dimensional space. The curl theorem states integral_S( del xF)·d a = integral_(dS) F·d s, where the left side is a surface integral and the right side is a line integral. There are also alternate forms of the theorem. If F congruent c F, then integral_S d ax del F = integral_C F d s.
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