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

Synthese 186 (1):257-288 (2012)
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 equation  Diagram  Geometric intuition  Visual thinking  Integral curve  Tractional motion  Qualitative integration  Graphical integration
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References found in this work BETA
Marcus Giaquinto (1994). Epistemology of Visual Thinking in Elementary Real Analysis. British Journal for the Philosophy of Science 45 (3):789-813.
Sun-Joo Shin & Giovanna Corsi (1997). The Logical Status of Diagrams. British Journal for the Philosophy of Science 48 (2).
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