Math 1a Spring 2021: Catastrophes

If a function f depends on a parameter c we can look at the number of stable equilibria (minima) and see how they change when we deform c. A point where the number of stable equilibria changes is called a catastrophe. For eample, for f(x)=x^4-c x^2, the parameter value c=0 is a catastrophe. This elementary catastrophe theory (together with more fancy singularity theory developed in the 1970ies) can explain surprisingly many phenomena. We just look at it as a wrap-up to the chapter on differentiation and before starting integration theory.