# Rigorous Calculus Textbook

As a reader of I. M. Gelfand's algebra/trigonometry and A. P. Kiselev's geometry textbooks, I am struggling to find an equally rigorous calculus textbook. I've tried Stewart's "Calculus: Early Transcendentals", but it's way too (for lack of other words) fluffy. I enjoyed Gelfand/Kiselev books because of their succinctness and rigor, where the few exercises were never the same (i.e. solving 2 quadratic equations where $a$, $b$, and $c$ are just different numbers).

I'm looking into Tom Apostol's book, but there the only editions I've seen have terrible formatting and many typos. I attempted Thompson's book (the one Richard P. Feynman studied by), but there are typos even in the answer key, which confused me severely as a self-learning student new to calculus.

Also, as a bonus, but not a requirement, if the book includes some linear algebra (like Apostol's), that would be a plus.

• If you are a student new to calculus and you are a self learner, then why would you want to have such a rigorous textbook? – imranfat Nov 24 '16 at 4:44
• Why not? I managed Gelfand and Kiselev just fine. Regarding Thompson, I just didn't like the fact that when I thought I got an answer correct (which I did indeed), the answer key would tell me otherwise, finishing my confidence in my knowledge. – Fine Man Nov 24 '16 at 4:45
• Yes, correct, a textbook that has errors in the answer key is not good for learning experience, but if you are new to the topic (that's my assumption) and you have to learn all by yourself (not in a school setting?), then what would be wrong to learn from Stewart or any other staple calculus book first, and then move on to a real analysis textbook? It will certainly strengthen your foundation, a not unimportant matter... – imranfat Nov 24 '16 at 4:47
• You could try Infinitesimal Calculus - Spivak and/or Problems in Mathematical Analysis - Demidovich. Alternatively, you could learn basic calculus from any less rigorous book and then begin to study Real Analysis to really understand the theory behind calculus. – Vitor Borges Nov 24 '16 at 4:51
• Spivak's Calculus is the way to go. – yoyostein Nov 24 '16 at 5:50