Abstract:

This paper describes a course on modeling dynamic systems using ordinary differential equations. The course was developed on the Canvas platform. The course contains five modules: first-order dynamical systems, system modeling with second-order differential equations, qualitative analysis, numerical methods, and the Laplace Transform. Each module contains support material, readings and videos, a semi-adaptive evaluation system and a set of computational practices in Matlab. For the evaluation, a scheme of five questions and three levels of response for each topic is followed. At the end, the reading of parts of the support material is suggested.

In the first module, population growth is analyzed using logistic and Alle models, classical ecological systems such as predator-prey, and temperature models such as Newton's Law of Cooling with quadratic corrections and with time-dependent ambient temperature. In the second module, mechanical vibration models are showed and several mechanical systems are modeled with differential equations. In the third module, different differential equations are graphically analyzed. In the numerical methods module, the classical Euler and RK4 methods for systems of differential equations are analyzed using simple and ingenious codes developed in Matlab. Finally, several of the previous models are analyzed with the use of the Laplace Transform.

In the course several problem situations are solved using simulation tools built in Matlab. Among the problem situations analyzed by the students are the SIR epidemiological model and the analysis of a vibration model with three degrees of freedom associated with the movement of a car. The problem situations are intended for the student to generate a solution proposal where the concepts seen in the course are used and develop skills such as analysis and synthesis of information, mathematical modeling and use of technology.

For the study of learning gain, work was done with 184 students divided into control and experimental groups. A diagnostic test was applied at the beginning of a final test. In the work, the results of the study are presented, as well as the analysis of the skills developed and some of the material used.

Keywords:

Differential Equations, Dynamical systems, Matlab, Semiadaptive learning.