Abstract:

Knowledge of Differential Equations is applied to various scientific fields such as physics, chemistry, biology and engineering and therefore often an important part in the basic subjects of mathematics in the first college courses related to those areas. The logic and common sense seems to indicate teachers use these basic skills acquired by students and employ them to curricula development in the following intensification courses, but unfortunately it is not usually the case. According to the authors, that is because instead of using a generic software to set up and solve the problems of Differential Equations that arise at different areas, what we have is a proliferation of software applied to solve special case problems. Some of these programs offer sophisticated graphical user interfaces to create complex system models, usually by putting together some library components, as if it were a puzzle, but without the need to set up the differential equations. According to the authors, this method, although valuable to solve some specific problems very quickly, is aberrant from the educational point of view, because it allows students to solve problems without knowing what they are doing or how they are doing. Worse, if a complication arises in the problem statement, for which there are no pieces in the puzzle, or execution errors occurs due to an incorrect construction, then they are not able solve the problem.

Because of this, software that does not hide the equations and with the user can know at any moment what he/she is doing, from the mathematical point of view, is missing. According to the authors, any simulation program including the System Dynamics paradigm meets this condition because its GUI is very close to differential equations and the Initial Value Problem. The modelling of a system using this paradigm is simply to raise because an initial value problem associated with the system is quickly represented by the graphical user interface of the simulation program.

This article presents some learning experiences focused on "problem based learning" using AnyLogic, which provides the System Dynamics paradigm to perform simulations of physical systems. The program provides a graphical environment that allows to perform animations very easily.

The first on is to simulate the filling of a tank of water where the model is a first order non-linear differential equation. This case is instructive as it is very easy to raise the initial value problem and may be valid to review some concepts already forgotten by the students such as for example the derivative, integral, differential equation and initial value problem.

Other simulation exercises posed to students are the control of a cart by a force, a parabolic shooting, and other mechanical, electrical and thermal examples.

Keywords:

Problem Based Learning, Differential Equations, System Dynamics, Technology-Enhanced Learning, Computer Software on Education, ECTS Experiences.