The graphical integration of ordinary differential equations
type: Item
instance of: scholarly article
title: The graphical integration of ordinary differential equations
zbMATH Open document ID: 1038.01011
DOI: 10.1016/S0315-0860(03)00033-8
author: Dominique Tournès
published in: Historia Mathematica
publication date: 2004-02-03T00:00:00Z
review text: The development of the graphic integration of ordinary differential equations is considered here as a ``little known phenomenon''. The article presents techniques and instruments used for the graphic integration and looks for their historic origins by going back to the beginning of calculus. In Sect. 1 the polygonal methods are described from Descartes (1639), Newton (1679). Leibniz (1694) a.o. to perfections in 20th century. In Sect. 2 the methods of radius of curvature are described from Poncelet (1827--1830) to Meissner (1913). Sect. 3 is devoted to the use of tractional motion for the conception of integraphs: Leibniz (1693), Bernoulli (1694), Perks (1706), Poleni (1728), the integraphs B. Abdank-Abakanowicz (1886), L.-F. Jacob (1707), E. Pascal (1910). In Sect. 4 the reduction to graphic quadratures is described: Montucla (1802), the planimeters by Hermann (1814), Amsler (1854), successive approximations by Thomson (1876), Runge (1907), Kholodovsky (1929). The text is illustrated by 28 figures, the extensive references are added.
Mathematics Subject Classification ID: 01A45
Mathematics Subject Classification ID: 01A50
Mathematics Subject Classification ID: 01A55
Mathematics Subject Classification ID: 01A60
Mathematics Subject Classification ID: 34-03
Mathematics Subject Classification ID: 65-03
Mathematics Subject Classification ID: 65S05
zbMATH DE Number: 2037203
zbMATH Keywords: Differential equations
zbMATH Keywords: Graphical integration
zbMATH Keywords: Integraphs
reviewed by: Ülo Lumiste
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2037203