Modelling by differential equations

This paper aims to show the close relation between physics and mathematics taking into account especially the theory of differential equations. By analysing the problems posed by scientists in the seventeenth century, we note that physics is very important for the emergence of this theory. Taking into account this analysis, we show the characteristics of this relation both in current teaching and in the practices of first-year university students. We present the relation between the two disciplines in section 1. Section 2 deals with models and modelling. Having studied the emergence of differential equations in section 3, we focus on the status of modelling in current education in section 4. Lastly, we investigate the place of modelling in students’ practice and we finish by giving our conclusions in section 5.