Changes

'''Stokes' Theorem''' expresses the surface integral of the [[curl]] of [[vector field]] in terms of its easier-to-compute [[circulation]]:

'''Stokes' Theorem''' expresses the surface integral of the [[curl]] of [[vector field]] in terms of its easier-to-compute [[circulation]]:

:<math>\iint_S (\nabla \times \vec F) \cdot \vec{\mathrm{d}F} = \oint_E \vec F \cdot \vec{\mathrm{d}r}\,</math>

:<math>\iint_S (\nabla \times \vec F) \cdot \vec{\mathrm{d}S} = \oint_C \vec F \cdot \vec{\mathrm{d}r}\,</math>

Stated another way, Stokes' Theorem equates the line integral of a vector fields to a surface integral of the same vector field.  For this identity to be true, the ''direction'' of the vector normal ''n'' must obey the right-hand rule for the direction of the contour, ''i.e.'', when walking along the contour the surface must be on your left.

Stated another way, Stokes' Theorem equates the line integral of a vector fields to a surface integral of the same vector field.  For this identity to be true, the ''direction'' of the vector normal ''n'' must obey the right-hand rule for the direction of the contour, ''i.e.'', when walking along the contour the surface must be on your left.