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.
Best Answer
Calculus by Spivak serves this purpose for single variable Calculus.