Signals and Linear Systems: A Teaching Approach Based on Infinitesimal Calculus (Part I)

Authors

  • José Leonardos Simancas-García Universidad de la Costa
  • Kemel George-Gonzalez Fundaci´on Innovaci´on y Conocimiento (https://innovacionyconocimiento.com)

Keywords:

e-learning, signals and systems, Educational technology

Abstract

In this article, part I of II, the development of a course on linear signals and systems is presented, based on an infinitesimal calculus model, called MicroCalculus. Such a calculus model allows a didactic development of the fundamental concepts of a signal course. The signals are defined from the
fundamental elements of variable and function. MicroCalculus offers a new vision to signal classification, as well as a treatment of non-standard functions as generalized functions, which in the new calculus model can be treated as standard functions. Then, the development of the discrete and continuous convolution operation is presented, from a unified approach.
In part II of the article, the solution of the differential equations of linear systems using infinitesimal calculus is presented. Then, a unified development of the Fourier Analysis is performed, where the Fourier Series, the Transform and the Discrete Transform are presented as 3 versions of the same entity. Finally, a didactic development of the Discrete Fourier Transform is presented.

Author Biography

Kemel George-Gonzalez, Fundaci´on Innovaci´on y Conocimiento (https://innovacionyconocimiento.com)

Recibi´o grado de Licenciado en Matem´atica Educativa de la Universidad Aut´onoma de Guerrero, en M´exico,
grado de Mag´ıster en Matem´aticas del Centro de Investigaci´on y de Estudios Avanzados del IPN, en M´exico, en 1966, y grado de Doctor en Matem´aticas del Centro de Investigaci´on y de Estudios Avanzados del IPN, en M´exico, en 1999.
El Dr. George ha sido profesor de la Universidad Distrital “Francisco Jos´e de Caldas”, en Bogot´a, Colombia, durante los a˜nos 1974 - 1978, 1986 - 1996. Profesor de la Universidad del Magdalena, Santa Marta, Colombia,
2001 - 2004. Profesor de Universidad Tecnol´ogica de Bol´ıvar, en Cartagena, Colombia, 2004 - 2006. Y profesor de la Universidad Aut´onoma del Caribe, Barranquilla, Colombia, 2013 - 2018. En la actualidad dirige la Fundaci´on Innovaci´on y Conocimiento, en Barranquilla, Colombia.

Published

2020-10-06
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