[akalin]

I'm partial to Caratheodory's definition of the derivative, which avoid limits like the infinitesimal approach, but doesn't pull in all the extra baggage that come with infinitesimals (if you do it rigorously).

djb (yes, that one) has a pretty good primer on it: https://cr.yp.to/papers/calculus-19970403-retypeset20220326....

[Ericson2314]

Oh yes that's a good write-up!

At the very end

> I follow the Kurzweil-Henstock approach to integration. ... I learned about this from advertisements by Robert G. Bartle in the Bulletin and the Monthly.

I had just read https://math.vanderbilt.edu/schectex/ccc/gauge/letter/ so I got that reference :)