In elementary #mechanics we are taught about the #SimplePendulum, which is modelled as a point #mass hanging via a rigid #rod or #string of a given length, under uniform #gravity. This simple model is also useful in introducing #OrdinaryDifferentialEquations and helps us to understand #SimpleHarmonicMotion.
#OrdinaryDifferentialEquations
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It’s Friday afternoon at the end of Week 2 here at Maynooth so I’ve now completed the 4th lecture of my 4th-year module Differential Equations and Complex Analysis. We’ve now in the section of Sturm-Liouville Theory. I’ve never taught this module before and, as always, teaching a new thing reminds me of all the things I had forgotten since I was a student. In this particular case, I still have the notes I took when I was studying this topic as an undergraduate. It’s scary to think the notes shown above were written by me 40 years ago!
Anyway, as I like to know something about the people behind the names, Sturm-Liouville Theory is named after Jacques Charles François Sturm (1803–1855)* and Joseph Liouville (1809–1882). Contrary to what I’d always assumed, Sturm was not German but was born in Geneva, which is now in Switzerland but which had been annexed by revolutionary France in 1798 so technically speaking he was born in France. Liouville was born in Saint-Omer, near Calais, which to my knowledge has never been part of Switzerland but has been part of the Spanish Netherlands.
*Given the dates, Sturm must have collaborated with Liouville after his earlier work with Drang…