Please , can any one recommend me to a reference containing Full proof of Green theorem.
The theorem that you actually want is the generalized Stokes theorem. Greens theorem is a simple corollary from that.
There are several books out there that prove the generalized Stokes theorem. My favorite is "differential forms" by Weintraub.
Other books are
- "calculus on manifolds" by Spivak
- "Principles of Mathematical Analysis" by Rudin
- "Analysis on manifolds" by Munkres
There are probably lots more of books out there that deal with Stokes theorem, but I don't know them...
Micromass: I don't mean to diss you, but I think Rudin's proof is way too
ungeometric, in case Nanas wants a somewhat-geometric argument, i.e.
Rudin axiomatizes diff. forms, and does not give much of what I would
consider enough background. But that comes down to a matter of taste.
Most books in advanced calculus should have a proof
I completely agree!! Rudin's proof is horrible. I just included it because it has a proof of it, and because some people do tend to like Rudin. Don't know why though...
Green's theorem generalizes the fundamental theorem of calculus and if you give it a shot you will be able to prove it yourself. try it.
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