Green’s theorem provides a connection between path integrals over a well-connected region in the plane and the area of the region bounded in the plane. Given a closed path bounding a region with area , and a vector-valued function over the plane,
where is the derivative of with respect to the th variable.
The corollary states that
We can easily prove this using Green’s theorem.
But since this is a gradient…
Since for any function with continuous partials, the corollary is proven.
|Date of creation||2013-03-22 12:15:55|
|Last modified on||2013-03-22 12:15:55|
|Last modified by||mathcam (2727)|