Catastrophe Theory
Catastrophe theory was in fancy 40-50 years ago but fell a bit into disgrace. This is a disgrace, because some aspects of the theory can be explained in a first calculus course. We have a function and look at the minima. Now, we deform the function. What can happen is that the minimum loses stability and the system settles to a completely different situation. This is often associated to a catastrophe, stock market crashes, revolutions, prison riots, material failures. It illustrates that as ingeneers or economists we want to be in a range where changing parameters does not risk that the system settles in a completely different (usually much worse) state.