Introducción a los sistemas de ecuaciones diferenciales y sus aplicaciones

Abstract

The aim of the current Curricular Integration Work was to generate a study guide document regarding the systems of differential equations, supported by the existing and most relevant bibliography. The development of this documentary-type research work was carried out through the search, compilation, analysis and writing of information on the topic mentioned above; so, it was necessary to detail some resolution methods of these systems such as: the method with differential operators, elimination method, matrix methods, Laplace transform and variation parameters. In the same way, two applications which can be represented with a linear system of differential equations were studied; the first one had to do with interconnected tanks and the second one with electrical circuits. After completing this research, it was concluded that the study guide document called: Ïntroduction to the systems of differential equations", will help new and current students of Mathematics to understand and interpret situations modeling systems of differential equations, as well as their resolution and graphical representation. Finally, it is recommended to carry out a study on the circumstances or application problems, as an extension of this research; so that, it can be represented as a nonlinear system of differential equations, as well as the existing quantitative or qualitative methods for their resolution.