Rigorous calculus textbook for first and second year students

Question

I am going to be teaching calculus to first and second year students(in two separate courses) and I wanted a textbook for myself to go over the content so I can teach it better. I am a 4th year student and know advanced topics like scheme theory and connections on bundles, so really I just want to find a textbook that covers the content as rigorously as possible with as little handwaving as possible, that doesn't generalise to manifolds etc immediately. (I only mention advanced topics to emphasise that difficulty isn't a problem, but I do want it to focus on standard early concepts)

Which calculus textbooks teach first and second year content rigorously - I have heard bad things about Stewart, but I would like it to cover the same sort of level of content.

Answer 1

Calculus by Spivak serves this purpose for single variable Calculus.

Answer 2

In my opinion Apostol's Calculus (Volume 2 for Multivariable) when coupled with his Real Analysis Book is great. The former are computationally intense, and the latter offers a good foundation in the theory, I thought.

Answer 3

"Calculus Deconstructed: A Second Course in First year Calculus" by Zbigniew Niteki makes a very good read. However, I personally recommend "Undergraduate Analysis" by Serge Lang. Hope it helps.