The funny thing is, though, I did a lot better on the AP exam than the kids who did take a calculus class, the same class I would have taken if I'd finished the prerequisite class in time. And, after a semester of taking it in a class, I'd pretty much lost interest.
("more or less": This was in high school. I failed to put in much time on it during the summer, since I was busy traveling to Japan and falling in love, so I signed up for "study hall" as an elective, and spent that time studying calculus with a textbook. The structured time without much distraction was very helpful in making it through enough of the book to do well on the exam.)
What are some other topics that you very rarely see people learn other than by schooling? Machine learning, physics, surgery?
Through Thomson, Maxwell, and others, the general mathematical theory of potential developed by an obscure, self-taught miller's son would lead to the mathematical theories of electricity underlying twentieth-century industry.
http://www-history.mcs.st-andrews.ac.uk/Biographies/Green.ht... http://en.wikipedia.org/wiki/George_Green
I think I have learned myself a decent amount of calculus.I suggest anyone interested in self learning calculus to to try Infinitesimal Analysis first as its more intuitive. Epsilon delta becomes easier after. And for differential calculus, consider implementing a Higher Order Multivariate Automatic Differentiator able to deal with Jacobians and Hessians efficiently. That hands on learning helps a lot.
It's a shame, because understanding differentiation and integration has had a tremendous impact on the way I think. It literally was a gamechanger for me, and it's worth it even though I only use it in thought exercises now.
I've also seen people look up formulas in a book, and misapply them with no understanding. The formulas are understandable if you know calculus, but these people would get answers that didn't work and would just be befuddled.