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This is from the MAA review of Baby Rudin (emphasis mine):

Calculus courses in the USA have been transformed from strong mathematical crucibles, in which approximation and geometrical proofs were part and parcel of the subject, into much less rigorous courses taken by all or most incoming freshman science majors. When Rudin wrote this book, calculus courses included epsilon-delta limit arguments and inequalities on the real line alongside related rates, solving differential equations and calculating volumes and areas using standard integral formulas. Looking at the books of the past — such as Lipman Bers’ Calculus and Edwin E. Moise’s Calculus — it’s easy to see why Rudin was the book of choice for analysis courses. It was reasonable to expect that students who did well in such calculus courses would have more then sufficient background to be able to tackle Rudin, despite the effort it would require of even good students.

Today’s students don’t stand a chance — most are simply overwhelmed due to lack of preparation. It’s as simple as that. Unless they’ve had the good fortune and talent to be guided through high school to a good honors calculus course as freshmen — such as those based on Spivak’s Calculus — reading this book is going to be a real struggle, to say nothing of the exercises.

Bers and Moise appear to have been published back in 1966-1967.

What are some other calculus books (let's say before calculus reform in 1987) besides Spivak and Apostol which were considered standard textbooks en route to Rudin?

Clarinetist
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  • Perhaps Courant & John, although I don’t know it nearly as well as Spivak and Apostol. – Ted Shifrin Jul 23 '23 at 01:52
  • Related question from Mathematics Educators Stack Exchange: When did US mathematics programs start failing to prepare incoming students for books like "Baby" Rudin? My two comments to this question mention two other real analysis texts that appeared the same year as Rudin's book (1953). Also, much more common in the 1950s-1970s were advanced calculus courses that one would spend two semesters with before taking an upper level real analysis course (examples here), (continued) – Dave L. Renfro Jul 23 '23 at 12:08
  • and epsilon-delta proofs were a major part of such courses. As these advanced calculus courses were being phased out (generally speaking) in the 1970s and 1980s, probably due to curriculum overload caused by math students increasingly taking computer science and discrete math and statistics courses, one-semester "transition to advanced mathematics" courses and one-semester beginning real analysis courses (example) began appearing to allow more room in students' schedules to take these other courses. (continued) – Dave L. Renfro Jul 23 '23 at 12:09
  • Also, the reviewer appears to be looking through a prism -- even in the 1950s and 1960s very few U.S. calculus courses covered epsilon-delta proofs in any nontrivial way (i.e. beyond exam problems where the maximum delta had a linear dependence on epsilon) and probably most essentially skipped mentioning it in class at all except maybe as a 15 minute digression during one class period. (continued) – Dave L. Renfro Jul 23 '23 at 12:09
  • On the other hand, honors calculus courses were much more common then (certainly during the 1960s and 1970s; this being before high school AP calculus enrollments surged, with the result that immediately after high school, U.S. students who otherwise would have taken single-variable honors calculus were going directly into 2nd year multivariable calculus), and students in such courses did cover epsilon-delta proofs in a nontrivial way. – Dave L. Renfro Jul 23 '23 at 12:09
  • Ok, Italian university programs are different, but I am of the class of '86 and I studied on the Rudin for the freshman calculus course. Probably nowadays it would be considered impracticable, but then it was standard stuff. – mau Jul 23 '23 at 14:05

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