Synthese

, Volume 186, Issue 1, pp 257–288

Diagrams in the theory of differential equations (eighteenth to nineteenth centuries)

Article

DOI: 10.1007/s11229-012-0069-z

Cite this article as:
Tournès, D. Synthese (2012) 186: 257. doi:10.1007/s11229-012-0069-z

Abstract

Diagrams have played an important role throughout the entire history of differential equations. Geometrical intuition, visual thinking, experimentation on diagrams, conceptions of algorithms and instruments to construct these diagrams, heuristic proofs based on diagrams, have interacted with the development of analytical abstract theories. We aim to analyze these interactions during the two centuries the classical theory of differential equations was developed. They are intimately connected to the difficulties faced in defining what the solution of a differential equation is and in describing the global behavior of such a solution.

Keywords

Differential equationDiagramGeometric intuitionVisual thinkingIntegral curveTractional motionQualitative integrationGraphical integration

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.LIM, EA 2525, University of La RéunionSaint-DenisFrance
  2. 2.SPHERE, UMR 7219, CNRS, University Paris DiderotParisFrance