Could anyone give any insight on Tom Apostol's Calculus Vol. 1 and Spivak's Calculus related to a proof-oriented calculus course covering the following topics: Axioms for the real numbers, Riemann integral, limits and continuous functions, derivatives of functions of one variable, fundamental theorem of calculus, Taylor's theorem, and infinite series, power series, and elementary functions? Pros/Cons of both? The course requires Apostol's but I would consider working through Spivak too if his treatment of this topics is better than Apostol's. Any link to a relevant thread is appreciated. Another two questions: Is Apostol's Vol. 2 at the same level of Spivak's Calculus on Manifolds? Is Apostol's coverage of Linear Algebra a sound basis for Lang's Linear Algebra?