Give Your ODEs a Singular Perturbation!

Singular perturbations occur when, contrary to natural expectations, small changes produce substantial effects. Consequently, special methods to approximate solutions, both computational and otherwise, are needed. The topic can provide one way to increase interest, motivation, and applicability of an ODE course or follow-up studies. This presentation is aimed at those well-grounded in the traditional coverage of scalar first-order ordinary differential equations and series solutions, rather than an applied audience needing to learn singular perturbations per se to asymptotically solve some physical problem they face. After figuring out the impact of singular perturbations on these special equations, we encourage the consideration of analogous perturbations for more general ODEs or even PDEs.