A graphic approach to Euler's method - Archive ouverte HAL Accéder directement au contenu
Chapitre D'ouvrage Année : 2018

A graphic approach to Euler's method

Résumé

To solve differential equations and study transcendental curves appearing in problems of geometry, celestial mechanics, ballistics and physics, mathematicians have imagined numerous approaches since the 17 th century. Alongside integration by quadratures and the series method, we can notably quote the polygonal method formalised by Euler in 1768. He directly used Leibniz's vision of curves as polygons made up of segments of infinitely tiny tangents. After an historical introduction and the study of an appropriate extract from the work by Euler on integral calculus, this chapter recounts a teaching experiment with 18 year olds, the aim of which was to introduce the notion of differential equations with support from the graphic version of the polygonal method. Through the purely geometric construction of integral curves formed from tiny segments of tangents, the students were able to make useful transfers between algebra and geometry and actively discover the first concepts of infinitesimal calculation.
Fichier principal
Vignette du fichier
tournes_2015e_euler_method.pdf (12.76 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01484262 , version 1 (07-03-2017)

Licence

Paternité - Pas d'utilisation commerciale - Pas de modification

Identifiants

  • HAL Id : hal-01484262 , version 1

Citer

Dominique Tournès. A graphic approach to Euler's method. Évelyne Barbin (ed.). Let History into the Mathematics Classroom, Springer, pp.87-100, 2018. ⟨hal-01484262⟩
379 Consultations
1096 Téléchargements

Partager

Gmail Facebook X LinkedIn More