I am having a difficult time choosing a calculis textbook. I have just finished the best trigonometry and college algebra book ever (Aufmann-Barker College Algebra) and I’m looking for something similiar (worked out solutions and proofs, lots of rigorous exercises and deep application problems).
The book I really want to work with is Spivak Calculus but I’ve decided to finish this this textbook on math proofing techniques before I can tackle Spivak.
I have begun readig and doing the exercises of Kline to give myself a background, but the lack of rigour is somewhat bothersome. Due to the wonderful book by Aufmann, I pride myself with strong algebraic agility and proved some theorems on my own but I really hope that I won’t lose the skills. I’d need more if I want to solve all of the problems in Spivak.
I was wondering if I would have a shot at AP calculus from exclusively going through Kline’s Calulus. Has anyone else tried Kline and passed the Calculus AB exam using Kline alone? If not, then what introductory calculus book do you recommend for self-teaching? Or any possible supplements to Kline?