I think Spivak is way less common as an initial calc text than Stewart. Spivak's approach is much more rigorous than most calc textbooks, and is in many ways al

I think Spivak is way less common as an initial calc text than Stewart. Spivak's approach is much more rigorous than most calc textbooks, and is in many ways almost an introduction to real analysis. Note, for example, that Spivak prefers to view the definite integral as the proper form of an integral rather than the typical approach taken by many introductory texts where the integral is viewed as the anti-derivative and then for ∫_a^b f(x)d(x) they just take F(b)-F(a) and call it a day. I would imagine that most introductory calculus students do close to zero proofs with most of the time spent on memorizing the various rubrics for finding derivatives and anti-derivatives. Spivak covers those, but the exercises are at least 50% proofs rather than being 90–100% calculation.