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The Missing Link

  • Felipe Acker

Abstract

The goal of this article is to change the views of mathematicians throughout the world on three fundamental theorems of elementary analysis: Cauchy-Goursat’s Theorem, Stokes’ Theorem and the Mean Value Theorem. My claims are the following:
  1. 1.

    Cauchy-Goursat’s Theorem is really a mere corollary of Green’s.

     
  2. 2.

    The usual treatment of Stokes’ Theorem is misguided and I will do it properly.

     
  3. 3.

    The Mean Value Theorem does generalize to higher dimensions as an equality.

     

Keywords

Open Subset Differential Form Fundamental Theorem Exterior Derivative Exterior Differential Form 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    R Acker, The Mean Value Theorem for Differential Forms, 1997.Google Scholar
  2. 2.
    F. Acker, Advanced Calculus (in Portuguese), 1997.Google Scholar
  3. 3.
    V. Arnold, Mathematical Methods of Classical Mechanics, New York: Springer-Verlag, 1978.MATHGoogle Scholar
  4. 4.
    J. Dieudonné, Foundations of Modern Analysis, New York: Academic Press, 1960.MATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Felipe Acker

There are no affiliations available

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