moreover the objects modeled make it clear that

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Unformatted text preview: al inquiry, whether at the high school or university level.) Moreover, the objects modeled make it clear that there should be a constant tension between the discrete and continuous. For example, a vibrating string can be regarded profitably as a continuous object, yet if one looks at a fine enough scale, the string is made up of molecules, suggesting a discrete model with a large number of variables. Moreover, we will see that although a partial differential equation provides an elegant continuous model for a vibrating membrane, the numerical method used to do actual calculations may approximate this continuous model with a discrete mechanical system with a large number of degrees of freedom. The eigenvalue problem for a differential equation thereby becomes approximated by an eigenvalue problem for an n × n matrix where n is large, thereby providing a link between the techniques studied in linear algebra and those of partial differential equations. The reader should be aware that there are many cases in which a discrete model may actually provi...
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