Una mirada somera a la ecuación logística
A cursory look at the logistic equation
Abstract (en)
The work presented is a shallow reflection of the differential equation logistics. The aim is to recognize or remember the usefulness, of the logistic equation in the study of population as well as in the study of particular sales of a particular product, and other besides some other examples where this equation can be used product. Logistics differential equation has several presentation possibilities that differ in structure, location and definition of the constants that form parameters that constructed it, but despite these differences, all serve to model populations of people, species of animals and market studies species. Precisely in view of this logistic equation, three authors who speak on this issue were addressed, the options of equation were taken, the solutions of two of those three authors were deducted (Zill and Larson), as since the third (Stewart) was very similar to the second. In addition the there is given solution to application problems by using both, their differential equations and their solutions. It was found that the graphs of the solutions in all three cases had the same behavior and solved problems could be resolved similar concerns.
Abstract (es)
El trabajo presentado consiste en una reflexión poco profunda acerca de la ecuación diferencial logística. El objetivo es reconocer o recordar la utilidad de la ecuación logística en casos como en el estudio de poblaciones, así como en el de ventas de un producto determinado, además de otros ejemplos en los que se puede utilizar dicha ecuación. La ecuación diferencial logística tiene varias posibilidades de presentación, difieren en estructura, ubicación y definición de las constantes que la conforman, pero, a pesar de esas diferencias, todas sirven para modelar poblaciones de personas, de especies animales y estudios de mercados. Precisamente en la mirada a esta ecuación logística se abordaron tres autores que hablan sobre este tema, y se tomaron las posibilidades de cada ecuación, se dedujeron las soluciones de dos de las tres (Zill y Larson), ya que la tercera (Stewart) era muy similar a la segunda. Además, se dio solución a problemas de aplicación en los que se utilizaron tanto las ecuaciones diferenciales como sus respectivas soluciones. Se encontró que las gráficas de las soluciones, en los tres casos, tuvieron el mismo comportamiento y en los problemas resueltos se pudieron aclarar inquietudes similares.
References
Larson, R. (2006). Cálculo. México DF: Mc Graw Hill.
Stewart, J. (2008). Cálculo de una variable. México DF: Cengage Learning.
Zill, D. (2011). Cálculo, Trascendentes tempranas.
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