Calculus and First Principles
I am getting to the age where my son is studying calculus under the tutilege of a private tutor. He is a few years ahead in school, but I have to admit the very thought of him doing derivatives makes me feel old. There's also nostalgia however, as I rekindled my interested in calculus by writing this piece -- and yes, I needed a memory jog from the Internet. Most people meet calculus as a set of rules. Differentiate this. Integrate that. Memorize formulas. Apply them until the answers come out correctly. It feels almost mechanical, like a toolkit you learn to use without ever opening it to see how it was built. But calculus is not really about formulas. At its core, it is about something much more fundamental: how change actually works when you zoom in close enough. The idea of first principles is simple. Instead of accepting shortcuts or memorized rules, you rebuild the concept from the most basic definition possible. In calculus, that...