> Spivak's Calculus is used as a first-year calculus textbook at lots of schools
Umm... where? Not at Stanford, where we used a mainstream, much easier book. So does Princeton. Harvard is famous for having developed a "touchy-feely" calculus book.
Perhaps abroad? It is typical of calculus courses in the US that the students come with fairly weak backgrounds, and a major purpose is to expose and patch holes in the students' backgrounds in algebra and trigonometry.
If you took me to mean the "default" first-year calculus textbook then yes, that's not common. But it's definitely aimed at first-year college students, or at least people who haven't had prior exposure to rigorous mathematical thinking. Compare the style to, say, Spivak's Calculus on Manifolds to see what I mean.
(Edit: I just read your HN bio and know you know the stylistic differences, etc. Sorry!)
Spivak is the first-year Honors Calculus textbook at my alma mater, the University of Chicago. Harvard is also famous for having the most difficult first-year math classes that use even more advanced textbooks like Rudin's Principles of Mathematical Analysis.
My HS background in mathematics was definitely "weak," too. My senior year was the first year my school district ever offered calculus of any stripe in its entire history and I still managed to handle Spivak my first year of college. I took the AP Calculus test on my own and got a 4/5. It's not that crazy.
Umm... where? Not at Stanford, where we used a mainstream, much easier book. So does Princeton. Harvard is famous for having developed a "touchy-feely" calculus book.
Perhaps abroad? It is typical of calculus courses in the US that the students come with fairly weak backgrounds, and a major purpose is to expose and patch holes in the students' backgrounds in algebra and trigonometry.