Un error sistemático en los textos de cálculo para ingeniería
a common mistake in calculus textbooks for engineering
DOI:
https://doi.org/10.15446/rev.fac.cienc.v4n2.53585Keywords:
Abierto relativo, función real, funciones reales de varias variables, máximo relativo, mínimo relativo. (es)Open relative subset, real functions, real functions of several variables, relative maximum, relative minimum (en)
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En el presente artículo se pretende señalar un error que se comete cuando se denen dos conceptos fundamentales que se enseñan en los cursos de cálculo para ingeniería, en una y varias variables. El caso tratado en este artículo se centra en un par de conceptos comúnmente mal denidos: Las nociones de máximos y de mínimos relativos o locales de funciones en una y varias variables. Como punto de partida se toman dos textos clásicos, Leithold (1998) y Stewart (1999) libros guías durante muchos años, no únicamente en la Universidad Nacional de Colombia, sino también en otras universidades de prestigio, nacionales e internacionales.
This article intends to point out a common mistake in the teaching of two fundamental concepts that appear in the traditional courses of Calculus for engineering, in one and several variables. In the case discussed in this article, we focus on two concepts usually poorly dened: The notion of local or relative maximum and local or relative minimum of a function, in one and several variables. As a starting point, we take as reference two traditional texts, Leithold (1998) and Stewart (1999) books that have served for many years as a guide, not only at the Universidad Nacional de Colombia, but also in other prestigious universities, both national and international.
References
Apostol, Tom M (1973), Calculus, Volumen I, Editorial Reverté S.A., 813 p.
Kitchen, Joseph W. (1986), Cálculo, Mc Graw Hill, 863 p.
Leithold, Louis (1998), El Cálculo, Oxford University Press, 1360 p.
Spivak, Michael (1975), Calculus: Cálculo Innitesimal, Editorial Reverté, 413 p.
Stewart, James (1999), Cálculo, Conceptos y Contextos, International Thomson Editores, 991 p.
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