Resolviendo ecuaciones diferenciales ordinarias con Maple y Mathematica
G.M. Ortigoza Capetillo
Facultad de Matemáticas, Universidad Veracruzana, e–mail: gortigoza@uv.mx
Recibido el 13 de septiembre de 2006
Aceptado el 23 de agosto de 2007
Resumen
En este trabajo se presentan soluciones de ecuaciones diferenciales ordinarias (EDOS) mediante el uso de dos paquetes simbólicos: Maple y Mathematica. Los comandos básicos de solución de ambos paquetes son explicados mediante una serie de ejemplos representativos de un curso tradicional. Entre los ejemplos seleccionados se incluyen ecuaciones diferenciales que se resuelven con métodos como: variables separables, ecuaciones lineales, coeficientes indeterminados, variación de parámetros, etc; así como aquellas que se resuelven usando series de potencias y transformada de Laplace. Estos paquetes permiten también la solución de sistemas lineales, así como la visualización del campo de direcciones. El objetivo de este trabajo es brindar al lector una guía práctica que le permita iniciar el estudios de las ecuaciones diferenciales mediante el uso de Maple y Mathematica y de esta manera beneficiarse del uso de estas herramientas computacionales; así cómo mostrar como el uso del cómputo simbólico, al ahorrar el esfuerzo del cómputo algebraico complejo, permite enfocar la atención en ideas y conceptos importantes como: analisis cualitativo de las soluciones, comportamiento asintótico y relaciones del modelo físico con la contraparte matemática de la ecuación que lo describe.
Descriptores: Enseñanza; herramientas computacionales; ecuaciones diferenciales ordinarias.
Abstract
In this work we present solutions of ordinary differential equations by using Maple and Mathematica. The basic commands in both packages are presented throught a series of examples that show some of the advantages of using computer algebra and graphical representation in the process of teaching and learning odes.
Keywords: Physics Education; ordinary differential equations; Maple; Mathematica.
PACS: 01.40Fk; 02.30Hq; 01.50.Ht
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