I'm teaching an elementary DE's module to some engineering students. Now, every book out there, and every set of online notes, trots out two things:
- DE's are super-important, vital, can't live without 'em, applications in every possible branch of applied mathematics & the sciences etc etc
- Applications: population growth (exponential & logistic), cooling, mixing problems, occasionally a circuit problem or a springs problem. Oh - and orthogonal trajectories, so that you can justify teaching non-linear exact equations.
I can't believe that these same applications are still all that educators use for examples. Surely there must some interesting, new applications, which can be explained at (or simplified to) an elementary level? Interestingly, most of these "applications" are separable. Where are the linear non-separable equations; the linear systems?
I've been searching online for some time now, and remarkably enough there's very little out there. So either educators are completely stuck for good examples, or all the modern uses are simply too difficult and abstruse to be simplified down to beginners level.
However - if there are any interesting new & modern uses of DE's, explainable at an elementary level, I'd love to know about them.