Änderungsraten und Bestände von heute mit dem Infinitesimalkalkül von gestern?

Ein historisch inspirierter Beitrag zur Vermeidung vorschneller Fehlinterpretationen

Abstract

Lazare Carnot, Sadi’s father and one of Napoleon’s Ministers of War, wrote his Reflexions on the Metaphysical Principles of the Infinitesimal Analysis at the end of the 18th century. In it, he accepts an imperfect type of equality in order to handle “infinity and thenothing in between” without conflicts. This article discusses the question of whether Carnot’ sapproach might help school calculus “based on a propaedeutic understanding of limits” particularly in the context of “functional quantities like rates of change and (re-)constructed stocks” (KMK Bildungsstandards Mathematik Sek II, 2012, 22 f.). As is shown, it is indeed much easier to bring up the latter than to interpret them correctly. An approach inspired by Carnot, orientated towards engineering and exhausting the differential notation, can supportan understanding of these meaningful contexts.