Ensino e aprendizagem de equações diferencias numa perspectiva motivacional: alguns modelos populacionais e aplicações.

Abstract

Considering that the studies indicate that the predominant methodology in the context of the teaching of Differential Equations (DE) is strongly focused on the analytical resolution of these equations, and may or may not be a sufficient factor for an adequate learning of the content, we bring in this work a motivation for the studies of this emerging discipline in higher education. This research, in general, marks all the steps of a theoretical study, characterizing itself as a review of the literature. Nevertheless, our intention to permeate other researches of this field of investigation and to synthesize them is that from this we can present teaching possibilities for the learning of ED. Two models describing the dynamics of tumor growth, described by the Gompertz equation and the Verhulst equation, were studied. Also, a mathematical model that represents the action of a certain treatment that aims to stabilize the growth or decrease the drug substance in the human body. For this, we used real parameters of this biological phenomenon reported in the literature and through an analytical-graphical and numerical approach with problem situations we explore their solutions with the aid of digital media, in order to investigate their reflexes on the motivation to learn. It was possible to perceive a better understanding of the concepts of ED through a non-algebraic approach, emphasizing the importance of the role of the technologies in this process, because from this we could also develop some activities of the mathematical modeling process, such as solving, analyzing and validating such models, especially, understand them through their application.