On how to best introduce the concept of differential in physics

Abstract

Despite its frequent use, there is little understanding of the concept of differential among upper high school and undergraduate students of physics. We have tried to identify some causes for this situation, and have designed proposals to revert it, based on 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 the early XX century. We conclude by outlining a set of indicators of what would be a proper understanding of the concept of differential in Physics education.