Learning (or Re-Learning) Calculus

I’ve watched the first lecture and a little past half of the second. They are not either particularly good nor particularly bad. The good is the part about avoiding zero divided by zero. There, he’s entirely correct. The bad is that he doesn’t understand, or doesn’t understand how to communicate, the truth about limits and calculus: there is no infinity, there is only “as much contextual precision as you need.”

As I understand it, calculus is a method of getting however much precision you need. (And you never need “infinite precision”–a Platonic idea.)

Then what’s really bad is the idea of sets. 

I also browsed through “Calculus Made Easy” by Silvanus Thompson.  Early in the book, he says you can think of dx as “a little bit of x”.  My first calculus teacher almost frothed at the mouth telling us that dx was NOT a little bit of x.  Perhaps one of our mathematicians could explain if “a little bit of x” is a valid, or even helpful, approach.