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Appears in:
Pages: 4496-4504
Publication year: 2014
ISBN: 978-84-617-0557-3
ISSN: 2340-1117

Conference name: 6th International Conference on Education and New Learning Technologies
Dates: 7-9 July, 2014
Location: Barcelona, Spain

THE ENGINEERING GENERALIZED FUNCTIONS: AN EDUCATIONAL STUDY

P. Camarena Gallardo

Instituto Politécnico Nacional (MEXICO)
The research presented in this paper concerns itself with a very particular mathematical subject area, namely the Engineering Generalized Functions in the educational environment of the electronic engineering and related branches. It is necessary to mention that when we talk about Generalized Functions they are considered as a generic name, but in reality the Generalized Functions that are interesting for the electronic engineering and related branches are the Dirac delta and all those related with it through the mathematical analysis as described by Camarena (1993).

On the other hand, from our teaching experience it can be said that the problem begins with the particular definition made about these functions, since presenting a Generalized Function such as Dirac delta whose value is zero everywhere except at the point where it is not defined and whose integral is one, is inconsistent with the mathematics taught at high school, where for the student the integral of a function whose value is zero everywhere except at one point must be equal to zero, while the definition says that the integral must be one. This creates a conflict for the students, and furthermore, the mathematics known by the engineering students is not enough to deal with algebraic processes with expressions which include the Dirac’s delta function.

Besides, it is a fact that mathematics has strong basis to present and handle these functions through the Distributions theory (The theoretical basis of the Generalized Functions), but this requires complex stages of mathematical analysis which are not available for the engineering career students. Therefore, the Generalized Functions themselves are not the problem; the point is how to take them to the classroom in the engineering school without the Distributions theory.

To tackle this problem, these functions are analyzed from an educational point of view, so the student, the teacher and the content are considered, but also included were mathematics users and engineers as established in the Mathematics in the Context of Sciences theory. The objective of the research is to investigate an option to teach these functions without the distribution theory to the students of electronic engineering and related branches. The theoretical framework is the Mathematics in the Context of Sciences. The investigation has many steps, which are the five phases of Mathematics in the Context of Sciences theory. This paper only includes the epistemological phase, where this phase discovered three different ways to go to Dirac delta function.

References:
[1] Camarena, G. P. (1993). Curso de análisis de Fourier en el contexto del análisis de señales eléctricas. Editorial ESIME-IPN, México.
@InProceedings{CAMARENAGALLARDO2014ENG,
author = {Camarena Gallardo, P.},
title = {THE ENGINEERING GENERALIZED FUNCTIONS: AN EDUCATIONAL STUDY},
series = {6th International Conference on Education and New Learning Technologies},
booktitle = {EDULEARN14 Proceedings},
isbn = {978-84-617-0557-3},
issn = {2340-1117},
publisher = {IATED},
location = {Barcelona, Spain},
month = {7-9 July, 2014},
year = {2014},
pages = {4496-4504}}
TY - CONF
AU - P. Camarena Gallardo
TI - THE ENGINEERING GENERALIZED FUNCTIONS: AN EDUCATIONAL STUDY
SN - 978-84-617-0557-3/2340-1117
PY - 2014
Y1 - 7-9 July, 2014
CI - Barcelona, Spain
JO - 6th International Conference on Education and New Learning Technologies
JA - EDULEARN14 Proceedings
SP - 4496
EP - 4504
ER -
P. Camarena Gallardo (2014) THE ENGINEERING GENERALIZED FUNCTIONS: AN EDUCATIONAL STUDY, EDULEARN14 Proceedings, pp. 4496-4504.
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