Curl Theorem
A special case of Stokes' theorem in which 
is a vector field and 
is an oriented, compact embedded 2-manifold
with boundary in 
, and a generalization of Green's
theorem from the plane into three-dimensional space. The curl theorem states
 |
(1)
|
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
 |
(2)
|
then
 |
(3)
|
and if
 |
(4)
|
then
 |
(5)
|
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vector algebra