How to draw the graphs of the Exponential, Logistic, and Gaussian functions with pencil and ruler in an accurate way

• Torres Naranjo, Ricardo Felipe ^[1] ; Castillo, Samuel ^[2] ; Pinto, Manuel ^[3]
  1. [1] Universidad Austral de Chile

     Universidad Austral de Chile

     Valdivia, Chile

     
  2. [2] Universidad del Bío-Bío

     Universidad del Bío-Bío

     Comuna de Concepción, Chile

     
  3. [3] Universidad de Chile

     Universidad de Chile

     Santiago, Chile

     

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• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 42, Nº. 6, 2023, págs. 1653-1682
• Idioma: inglés
• DOI: 10.22199/issn.0717-6279-5936
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• Resumen

  • In this work, we will give a novel method to construct a continuous approximation of the Exponential, Logistic, and Gaussian functions that allow us to do a handmade drawing of their graphs for which there is no accuracy of drawing at elementary levels (even at advanced ones!). This method arises from solving the elementary ordinary differential equation x0 (t) = ax(t) combined with a suitable piecewise constant argument. The proposed approximation will allow us to generate several numerical schemes in an elementary way, generalizing the classical ones as, Euler’s schemes. No sophisticated mathematical tools are needed.

• Referencias bibliográficas
  • R. Bellman and K. L. Cooke, Modern Elementary Differential Equations, 2nd ed., Dover, 1995.
  • E. A. Coddington, An Introduction to Ordinary Differential Equations. 2nd ed., Dover, 1989.
  • A. Myshkis, “On certain problems in the theory of differential equations with deviating argument”, Russian Mathematical Surveys, vol. 32,...
  • K. Cooke and S. Busenberg, Models of vertical transmitted diseases with sequential-continuous dynamics, in Nonlinear Phenomena in Mathematical...
  • L. Dai, Nonlinear Dynamics of Piecewise Constant Systems and Implementation of Piecewise Constant Arguments. New York: World Scientific Press,...
  • F. Bozkurt, “Modeling a tumor growth with piecewise constant arguments”, Discrete Dynamics in Nature and Society, no. 418, 2013.
  • S. Elaydi, An Introduction to Difference Equations, 3rd ed., Springer, 2005.
  • M. Akhmet, Nonlinear Hybrid Continuous-Discrete-Time Models. Amsterdam: Atlantis, 2011.
  • M. Pinto, “Cauchy and green matrices type and stability in alternately advanced and delayed differential systems”, Journal of Diffence Equations...
  • E. A. Coddington and N. Levinson, Theory of Ordinary Differential Equations. New York: Mc Graw-Hill, 1955.
  • R. Torres, M. Pinto, S. Castillo and M. Kostic, “An uniform approximation of an impulsive cnn-hopfield type system by an impulsive differential...