Reddit reviews Differential and Integral Calculus, Vol. I

I did my schooling in India and we have a super hard on for old school Russian texts. One of the books I referred to for Calculus was by N. Piskunov.
I kept on returning to the book well until my undergrad math courses. It has 2 volumes, with a fairly good number of problems, most of them pretty good; and some solution manuals floating around somewhere.

EDIT:
Another undergraduate book you may want to check out would be Hall & Knight's Higher Algebra.
The book was first published in 1887 and has stood the test of time. It just contains pure, brutal, sadistic shit tonnes of algebra problems.

You can try Piskunov's Calulus series Vol 1 and 2. Amazon links below:

Vol 1:
http://www.amazon.com/Differential-Integral-Calculus-Vol-I/dp/8123904924/ref=pd_sim_sbs_b_1?ie=UTF8&refRID=0SXQVY4M0QXKTR7JTVH6

Vol2:
http://www.amazon.com/Differential-Integral-Calculus-Vol-II/dp/8123904932/ref=pd_sim_b_1?ie=UTF8&refRID=0C13CBBF0587M907R2P1

It has the rigor that you are looking for. I was looking for the same thing and this book has helped me a lot to understand calculus, the insights, the geometrical view point. Hope it helps.