Conceptual question on greens theorem/line integrals

[Mdhiggenz]

Homework Statement

Hey guys,

I just wanted to know, if it would be an incorrect assumption to say that greens theorem is directly correlated to a line integral.

The reason I am assuming that is because the formula for a line integral in my calc text is

∫f(x,y)dx+g(x,y)=∫f(x,y)dx+∫g(x,y)dy
c c c

Which is simply the left side of greens theorem.

I also am having a hard time putting the similarities between all three theorems. Greens, divergence, and stokes together in terms of what they all have in common.

Thanks

Higgenz

Homework Equations

The Attempt at a Solution

 

[happysauce]

Greens theorem is strict, the relation is true with a simple CLOSED contour but not in general. Take the line integral of a contour that isn't closed or simple and greens theorem will fail.

 

[Mdhiggenz]

How would we know if it fails?

 

[happysauce]

How would we know if it fails?

Small things like discontinuous functions would cause it to fail, if the contour isn't closed then it will most likely fail, if the contour is too complicated (it overlaps) then it will probably fail.