Good calculus exercises/problems?

Question

I can't enroll in a university this year, so I'm studying calculus at home, but the only exercises about calculus that I find are the easy ones. Do you know a great page where I can find not only calculus exercises, but problems as well?

I want to find about:

hard limits,
derivatives and integrals,
and some problems

How do you differentiate between exercises and problems? If you've studied calculus, what text did you/are you using? It seems you're focused on "computational" calculus, and not so much on theory/proofs, which arguably present greater challenge than simply practicing the evaluation of limits, derivatives, and integrals. Of course, the theory and practice complement each other. — amWhy, May 26 '13 at 02:02
Spivak is the best! Take his Calculus book and in the end you'll know a lot of single variable calculus. In truth you'll be very well preapered to study analysis. — Gold, May 26 '13 at 02:11
I've been told that one doesn't know calculus until you get through Spivak. I am still struggling! I am certain there are even grad students in my university who doesn't know how to do a few of the problems in his book — Lemon, May 26 '13 at 02:12
Spivak is very good because he finds a way to bring together the modern rigorous approach, the motivations and the intuition behind everything and still teach how to compute efficiently, so he's very complete indeed. — Gold, May 26 '13 at 02:14
I also suggest getting Spivak's "Calculus". You may find some of my old class handouts of interest. Most (all?) that I've posted have been cook-bookish stuff, however: nontrivial rational function integrations, exponential indeterminates, basic limits, 13 miscellaneous items, Cauchy condensation test — Dave L. Renfro, May 26 '13 at 14:24

amWhy · Accepted Answer · 2013-05-26T02:13:50.547

11

Barring any more information, I'd suggest you acquire Michael Spivak's Calculus, and begin working your way through the material. There are plenty of exercises and examples, but you'll also deepen your conceptual understanding at the same time, which will help ensure the material "sticks with you" over the long-run, which I presume is a goal of yours, as you seem committed to enrolling at a university, perhaps even to pursuing math, and/or math-related fields.

Spivak will prepare you well.

edited May 26 '13 at 02:13

answered May 26 '13 at 02:07

amWhy

209,954

Is this the book you're talking about? http://www.cs.unicam.it/piergallini/home/materiale/geom4/testi/Spivak:Calculus%20on%20manifolds.pdf – jamesonhotg May 26 '13 at 02:29
That would be Spivak's "sequel" text: Calculus, then Calculus on Manifolds - both are excellent. – amWhy May 26 '13 at 02:31