Green's Theorem      

The work integral over a conservative field is independent of path, is equal to the change in potential between the endpoints of the path, and is zero if the path is a closed curve.  But what if the field is not conservative?  What properties does the work integral have in that case?  Plenty and nearly every one is a consequence of Green's Theorem .  In this section, we will introduce and explore Green's theorem in the plane.  First, let's load some packages.  

>	restart:with(plots):with(plottools):with(VectorCalculus):

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NOTE: In this worksheet the symbol   will be used for the partial derivative symbol.

Area with a Line Integral

Green's Theorem

Area and Centroid Formulas

Exercises