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:
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1.
Cauchy-Goursat’s Theorem is really a mere corollary of Green’s.
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2.
The usual treatment of Stokes’ Theorem is misguided and I will do it properly.
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3.
The Mean Value Theorem does generalize to higher dimensions as an equality.
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References
R Acker, The Mean Value Theorem for Differential Forms, 1997.
F. Acker, Advanced Calculus (in Portuguese), 1997.
V. Arnold, Mathematical Methods of Classical Mechanics, New York: Springer-Verlag, 1978.
J. Dieudonné, Foundations of Modern Analysis, New York: Academic Press, 1960.
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Acker, F. (2001). The Missing Link. In: Mathematical Conversations. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-0195-0_19
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DOI: https://doi.org/10.1007/978-1-4613-0195-0_19
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6556-6
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