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Home Vector Calculus Theorems of Stokes and Gauss Curl of a Vector Field  
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Curl of a Vector Field
Both Stokes' Theorem and Gauss' Theorem are threedimensional generalizations of Green's Theorem. To state these theorems we need the notions of curl and divergence in three dimensions. The curl of a vector field in the plane is a scalar field, while the curl of a vector field in space is another vector field. However, the divergence in both cases is scalar. DEFINITION Given a vector field F(x, y, z) = Pi + Qj + Rk in space. The curl of F is the new vector field This can be remembered by writing the curl as a "determinant" The divergence of F is the real valued function


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