La diferencial no es un incremento inifinitesimal. Evolución del concepto de diferencial y su clarificación en la enseñanza de la física

Abstract

Despite its frequent use, there is little understanding of the concept of differential among upper high school and undergraduate students of Physics. As a first step to identify the origin of this situation and to design proposals to revert it, we have done a historic and epistemologic study aimed at clarifying the role and the meaning of the differential in Physics. We describe the contributions of Leibniz and Cauchy, and stress their shortcomings, which are overcome by the alternative definition proposed by the French mathematician Fréchet, dating from early xx century. As a result of this study, we conclude by outlining a set of indicators of what would be a proper understanding of the concept of differential in Physics education.