An Approach to the Teaching of Ordinary Differential Equations

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Abstract
A critical appraisal is made of the usual ways of teaching ordinary differential equations. In an attempt to improve students’ understanding of the structure and solution of a differential equation, the authors suggest an approach embodying the three methods of solution— analytical, numerical and analogue. They describe how this could be put into practice and, in particular, what would be done in the introductory lectures. The examples selected for illustration are the simple first‐order differential equation which expresses Newton's law of cooling, and the linear second‐order equations with constant coefficients which arise in problems involving damped and forced oscillations. An outline is given of the demonstrations, either filmed or on closed‐circuit television, using both digital and analogue computers, which are an essential feature of this approach.

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