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Since I've worked my way through Spivak's Calculus book, I thought I'd give Courant's allegedly fantastic exposition of the subject a go as well. However, I've run into a problem. People in stackexchange threads always praise and suggest Courant's Calculus without specifying whether that's supposed to be his "Differential and Integral Calculus" or his "Introduction to Calculus and Analysis" book.

So my question is: which one of these two is the "famous" and "legendary" Calculus book that everybody always talks about when the "great three" - Spivak, Apostol and Courant - are mentioned or recommended to people asking for a first course in calculus?

Note: I'm a math major. I'm mostly interested in what the oft-mentioned calculus book by Courant is, and not which of his two books would suit my prior exposure to calculus (Spivak) best in terms of the follow-up level. That is not to say I wouldn't appreciate an informed opinion on that matter, I certainly would (and I hope some experienced readers will be able to enlighten me), but I'm primarily asking this question to find out which is the more canonical one.

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  • $\begingroup$ It may be noted that the "contents" section of both texts are almost identical. $\endgroup$
    – MathematicsStudent1122
    Feb 8, 2016 at 4:24
  • $\begingroup$ I'm not familiar with these texts myself, but a question similar to yours was asked in another forum, and answered with an excerpt from the preface of the later book: physicsforums.com/threads/… It seems the later Introduction is a rewritten version of the earlier Calculus. If you've worked through Spivak, my own advice to you would be not to spend time studying single-variable calculus over again in a different introductory book. I would recommend studying either multivariable calculus or... $\endgroup$
    – David
    Feb 8, 2016 at 5:13
  • $\begingroup$ ...mathematical analysis at this point (or both). For multivariable calculus, you could use one of Courant's books or Vol. 2 of Apostol. $\endgroup$
    – David
    Feb 8, 2016 at 5:17
  • $\begingroup$ @David While I appreciate your reply, you haven't actually answered my question. "Introduction to Calculus and Analysis" originally came out in 1965. The fact that its based on his earlier work "Differential and Integral Calculus" is entirely irrelevant: it says nothing about which the most canonical work is. $\endgroup$
    – Ius Klesar
    Feb 8, 2016 at 5:22
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    $\begingroup$ I know that that doesn't answer your question exactly, but it says in the authors' words why the new book was necessary. Searching on the internet, I've found references to both books being very good, alongside Spivak and Apostol. It seems they're almost never mentioned together. It may be that neither one is more "canonical" than the other. This list ( ocf.berkeley.edu/~abhishek/chicmath.htm ) mentions the first, and this one (dasgupab.faculty.udmercy.edu/calc-books.html ) the second. See here as well: physicsforums.com/threads/calculus-courant-confusion.309600 $\endgroup$
    – David
    Feb 8, 2016 at 5:39

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Differential and Integral Calculus is the classic. The first edition in English came out in 1934. Introduction to Calculus and Analysis is a somewhat modified version co-authored by Fritz John. Careful attention to either version will give you (just about the same) very good grounding in calculus, so you may want to read which ever one is easier to get a copy of. But if you want to read the classic, it's Differential and Integral Calculus.

Another very lovely, old calculus text is A Course of Pure Mathematics by G. H. Hardy. It's impossible to learn the subject from the book by Landau (also called "Differential and Integral Calculus"), but it's worth a look once you already know the subject.

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  • $\begingroup$ Thank you Paul - I had already given up hope of ever having this question answered. I will look into reading "Differential and Integral Calculus", if only for the sake of having it in my collection. $\endgroup$
    – Ius Klesar
    Feb 26, 2016 at 0:26

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