Alright everybody, this is a fairly simple one. Obviously, Spivak's been mentioned very often on this forum, but I was wondering. A good friend of mine has decided to major in maths too. Now, the textbooks I had for calculus weren't all that great, so I wanted to buy him one that would really do the job at giving him a thorough, mathematical approach to calculus while at the same time lending itself for self-study. Multi-var calculus isn't really a concern yet. I have the opportunity to get Adam's "Calculus: A Complete Course 8ed", Lang's "A First Course in Calculus" and Spivak's classic "Calculus".

It'd be nice to see some people who have experience with Adams and/or Lang as well, not just Spivak. I myself have used Lang's "Linear Algebra" for an undergrad course in linear algebra, and I loved every page of that book. It was incredible. As such I'm wondering if his Calculus book(s) are comparably good, or if Spivak beats him to it. Also, Adams seems to be the book of choice for a number of reliable Calculus courses nowadays, so that sure made me curious as to what people's opinions are on his book. Especially in comparison to Spivak.


  • $\begingroup$ Are we talking calculus or analysis here? $\endgroup$ – Daniel W. Farlow Feb 7 '15 at 5:18
  • $\begingroup$ @induktio Calculus, actually. Albeit "thorough" calculus. Why? $\endgroup$ – Ius Klesar Feb 7 '15 at 16:00
  • $\begingroup$ @induktio Do you have any advice? I would really appreciate it - I haven't gotten any answers as of yet. $\endgroup$ – Ius Klesar Feb 8 '15 at 21:26

I don't know anything about the book by Adams.

Lang's calculus book isn't "rigorous" in the sense that Spivak and Apostol's books are. It doesn't emphasize the completeness property of the real numbers, and the proofs on limits are relegated to an appendix. It has more theory and is better written than typical calculus texts, however.

I would recommend Lang's book for someone who either needs a relatively quick introduction to calculus or doesn't have the mathematical ability or preparation required to learn from Apostol and Spivak's books.

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