My favorite topic in an introductory differential equations course is mechanical and electrical vibrations. I enjoyed learning about it as a student and I enjoyed teaching it later. (Or more accurately, I enjoyed being exposed to it as a student and really learning it later when I had to teach it.)
John D. Cook on Mechanical vibrations
I’ve always thought that education is about learning, as much as parenting is about maturing and growing up. On the parenting side, you can’t really teach your kids how to live – you can’t even imagine the kind of world they will have to live from the time they’re born – but you can expose them to the best things you know. In doing so, they can at least have the chance to form an opinion on the many matters of life, they’ll surely make mistakes, but I bet they won’t regret much.
Education is a difficult topic. Everyone has something to say about it, yet no one seems to have true answers. I do think that education is much more about being exposed to something, rather than being taught that something. There’s an incredible difference between the two things.