alt Hacker NewsEh. I think that the standard calculus approach is mostly fine, but just needs tweaking.
The only major change that I'd like to make is the removal of sequences and all the associated theorems from the introductory calculus. Instead, start with limits of functions and the notion of continuity.
It immediately leads to the notion of the derivative. And after that, it's just a lot of building blocks.
> the removal of sequences and all the associated theorems from the introductory calculus. Instead, start with limits of functions and the notion of continuity.
Strongly disagree.
Sequences(discrete) and Convergence are vital to understanding Calculus. Only then the idea of converging to a limit from left or right makes intuitive sense. Pair it with a graphical view of secants converging to a tangent(continuous) and you get the idea of instantaneous change however infinitesimal it might be.
You need both discrete and continuous ideas to build intuition before you introduce limits of functions and continuity.
Some books that i have found useful - https://news.ycombinator.com/item?id=49308281