American Journal of Applied Mathematics

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A Variational Definition for Limit and Derivative

Received: 18 May 2016    Accepted:     Published: 22 May 2016
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Abstract

Using the topological notion of compacity, we present a variational definition for the concepts of limit and derivative of a function. The main result of these new definition is that they produce implementable tests to check whether a value is the limit or the derivative of a differenciable function.

DOI 10.11648/j.ajam.20160403.14
Published in American Journal of Applied Mathematics (Volume 4, Issue 3, June 2016)
Page(s) 137-141
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Variational, Limit, Derivative, Differenciation

References
[1] Dieudonne, J., Foundations of Modern Analysis, Pure and Applied Mathematics \textbf{10}, Academic Press, New York, 1960.
[2] J. V. Grabiner, J. V., Who Gave You the Epsilon? Cauchy and the Origins of Rigorous Calculus, The American Mathematica Monthly (90) (3), 185-194, 1983.
[3] W.H.Press, W. H., et al, Numerical Recipes: The Art of Scientific Computing, Cambridge University Press, New York, 2007.
[4] F. Riesz, F., Oeuvres complètes, 2 vol, Paris, Gauthier-Villars, 1960.
[5] J. V. Grabiner, J. V., The Changing Concept of Change: the derivative from Fermat to Weistrass, Mathematics magazine, vol 56, no. 14, pp 195-206, 1983.
[6] Rudin, Walter., Functional Analysis, Mc Graw-Hill, NY, 1991.
[7] Boyer, C. B., The History of Calculus and Its Conceptual Development, Dover, N Y, 1949.
[8] Henry, D. B., Differential Calculus in Banach Spaces, Dan Henry’s Manuscript, http//www.ime.usp.br/map/dhenry/danhenry/math.htm, 2006
[9] Kato, T., Pertubation Theory for Linear Operators, Springer-Verlag, N Y, 1986.
[10] Bordr, K. C. and Aliprantes C. D., Infinite Dimension Real Analysis, Springer-Verlag, N Y, 2006.
Author Information
  • Center of Mathematics, Computation and Cognition, Federal University of ABC, Santo André, Brasil

  • School of Arts, Sciences and Humanity, University of S?o Paulo, S?o Paulo, Brasil

  • Center of Mathematics, Computation and Cognition, Federal University of ABC, Santo André, Brasil; School of Arts, Sciences and Humanity, University of S?o Paulo, S?o Paulo, Brasil

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  • APA Style

    Munhoz Antonio Sergio, Souza Filho, Antonio Calixto. (2016). A Variational Definition for Limit and Derivative. American Journal of Applied Mathematics, 4(3), 137-141. https://doi.org/10.11648/j.ajam.20160403.14

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    ACS Style

    Munhoz Antonio Sergio; Souza Filho; Antonio Calixto. A Variational Definition for Limit and Derivative. Am. J. Appl. Math. 2016, 4(3), 137-141. doi: 10.11648/j.ajam.20160403.14

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    AMA Style

    Munhoz Antonio Sergio, Souza Filho, Antonio Calixto. A Variational Definition for Limit and Derivative. Am J Appl Math. 2016;4(3):137-141. doi: 10.11648/j.ajam.20160403.14

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  • @article{10.11648/j.ajam.20160403.14,
      author = {Munhoz Antonio Sergio and Souza Filho and Antonio Calixto},
      title = {A Variational Definition for Limit and Derivative},
      journal = {American Journal of Applied Mathematics},
      volume = {4},
      number = {3},
      pages = {137-141},
      doi = {10.11648/j.ajam.20160403.14},
      url = {https://doi.org/10.11648/j.ajam.20160403.14},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ajam.20160403.14},
      abstract = {Using the topological notion of compacity, we present a variational definition for the concepts of limit and derivative of a function. The main result of these new definition is that they produce implementable tests to check whether a value is the limit or the derivative of a differenciable function.},
     year = {2016}
    }
    

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