Most mathematicians who teach have given serious thought and a fair amount of class time to applications of mathematics in the various sciences. Most of us are quick to say that we emphasize the applications in our elementary courses nearly as much as the mathematics itself. We don t realize that what looks to us like an application might look like pure theory to someone in the field of the application itself. For example, calculus texts usually contain common models of population growth, such as exponential and logistic growth models. These are applications of material as basic to calculus as integration.
Biologists look at the situation differently.
They see the techniques and rules of integration and differentiation as nearly useless to their students. As one ecologist told me, My students will never see a differential equation that they can solve explicitly. All we really need our students to know are what a phase portrait is and what an eigenvalue is. The answers to these questions are completely context-dependent, varying tremendously from field to field. It would be a terrible mistake to conclude that, by talking to the physicists, for example, we can get the single right answers to these questions.