Where can I find a full proof of green theorem?

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    Green Proof Theorem
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Discussion Overview

The discussion centers around finding a reference that contains a full proof of Green's theorem, exploring related concepts such as the generalized Stokes theorem and the preferences for geometric versus non-geometric proofs. The scope includes theoretical aspects and references to various mathematical texts.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant requests recommendations for references containing a full proof of Green's theorem.
  • Another participant suggests that the generalized Stokes theorem is what the requester is actually looking for, noting that Green's theorem is a corollary of it.
  • Multiple books are recommended, including "Differential Forms" by Weintraub, "Calculus on Manifolds" by Spivak, "Principles of Mathematical Analysis" by Rudin, and "Analysis on Manifolds" by Munkres.
  • Concerns are raised about the geometric nature of Rudin's proof, with one participant expressing that it may not provide enough geometric background for those interested in a more geometric argument.
  • Another participant agrees with the critique of Rudin's proof, stating it is not well-received by some, although it is included for its completeness.
  • A later post suggests that understanding Green's theorem could be achieved through personal effort, implying that self-proving may be beneficial.

Areas of Agreement / Disagreement

Participants express differing opinions on the suitability of Rudin's proof, indicating a lack of consensus on the best approach to understanding Green's theorem. Some favor geometric arguments while others accept non-geometric proofs.

Contextual Notes

There are varying preferences for the style of proof (geometric versus non-geometric), and the discussion reflects differing opinions on the adequacy of background provided in certain texts. The conversation does not resolve which proof is superior or more appropriate.

Nanas
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Please , can anyone recommend me to a reference containing Full proof of Green theorem.

Thank you.
 
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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...
 
Thank you.
 
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
 
Bacle said:
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...
 
Nanas said:
Please , can anyone recommend me to a reference containing Full proof of Green theorem.

Thank you.

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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