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Lies, damn lies ... and differential equations

By David Tall


The title of this article is a misquotation of Disraeli's comment on statistics, but there is every reason to apply it to the way we currently teach differential equations at A-level. The problem is that we try to make the theory ‘easier’ for the students by concentrating on\ud simple special cases, not delving too deeply into the technicalities. This tactic has two fundamental flaws. First, the oversimplification of the theory can lead to misrepresentation and falsification of the mathematical facts. Second, the presentation of the theory as a\ud number of special cases may lead to the mistaken belief that differential equations are solved by a number of isolated techniques (separation of variables, exact solutions, integrating factors, and so on), without any perceivable overall rationale binding the theory\ud together.\ud \ud The arrival of the computer gives us the opportunity for a fresh look at the theory to give a clearer insight into the fundamental ideas. Using simple numerical methods it is possible to sketch the solutions of differential equations, showing visually how the theory works and under what circumstances there are likely to be difficulties

Topics: QA
Publisher: Association of Teachers of Mathematics
OAI identifier: oai:wrap.warwick.ac.uk:499

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