The radioactive decay sequence discussion can lead to interesting class discussions. Some of the students will go on to study this topic in more detail. Here is a good place to plant correct ideas about understanding the mathematical model. The local behavior of the nonlinear problems can then be studied productively. This section merely hints at the flavor of the subject.
Some mention is made of similar problems in higher dimensions.
These ideas can be applied in the analysis of the predator-prey problem of the next section. One of these problems is of interest to physicists and one and the other to biologists. The topic of this section is not widely known, but it is a special case of differential equations with algebraic side conditions, which has a large literature most of which has been written since 1970. I first studied the topic in 1964, when I showed that certain differential systems with interface conditions could be represented in this form. Differential systems with interface conditions have applicability in nuclear reactor design.