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I'm a freshman in Maths major, but the recommanded textbook(Calculus:A Complete Course by Robert A. Adams) by Prof. of Calculus course is too much expensive, well, I found there're Serge Lang's two Calculus books in second-hand bookstore. is it okay to use these two books as textbook either ?

"A First course in Calculus", Serge Lang, UTM, Springer "Calculus of Several Variables", Serge Lang, UTM, Springer

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Which book did the prof. recommend? Try also to find a used copy of Spivak's Calculus. –  lhf Apr 8 '11 at 13:30
    
Is your teacher going to assign problems out of the book? –  Graphth Apr 8 '11 at 13:43
    
@Numth: Prof. has recommanded some calculation exercises in pointed textbook, and he gave us a list of required theoretical questions in order to be the requirement of final exam. And one of my friends told me that the Serge Lang's two calculus books are good, not only because more reasonable price to afford, but there're more proofs and, so to speak, more maths-major books. So I want to know whether it's fine for me to use these two as my calculus textbooks before the analysis course next year ? –  Xingdong Apr 8 '11 at 13:51
    
Most calc books are 90% the same. It doesn't matter which book you use. If you want to see more proofs, I'm sure Serge will help you out. You'll learn more if you put in more work and less if you put in less work, regardless of the book you use. The only reason you need a specific book is if you need to get problems out of it. If you have a friend who has the book and will let you look at the problems, then you can use whatever book you want. –  Graphth Apr 8 '11 at 14:56
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Why don't you ask your professor? None of us knows what your course covers. If you're asking whether Lang's book is good (instead of 'is it good to use in this particular course?'), then: yes, see Vladimir Sotirov's answer! –  wildildildlife Apr 8 '11 at 16:24
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Lang's book is great and I heartily recommend it. Unlike the rest of Lang's books, which he has written in order for he himself to learn the subject in question (and which books concern themselves with mathematics of significantly higher level), his Calculus books were written explicitly with the student in mind.

What this means is that it (at least his single-variable book; I haven't read the multi one) is the most well-arranged and pedagogically sane book on Calculus I've come across. Its intended audience consists of serious students who want to learn, but don't necessarily have a lot fo experience with mathematics: the book is more or less self-contained with respect to giving you all the necessary tools you need to solve the problems; it also has the virtue of being sufficiently rigorous and honest in its explanation of the key ideas. Many other textbooks either sacrifice ideas and intuition for logical formalism (Spivak's book is in fact an analysis book in disguise, I believe, so it's not even playing the same game), or they eschew a rigorous and careful treatment of ideas because the authors make no distinction between math being simple and math being easy.

But so, to answer your question, if you want to acquire a good understanding of Calculus, Lang will give you it, and may even give you a better one than other textbooks, if you read him closely enough (the real mathematician's answer of course, is that you go to the library and check out and read several books on Calculus to get an idea of the various perspectives since no one textbook is perfect, though in my eyes Lang's as close to perfect as we have).

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To Vladimir Sotirov, I agree with you very much, especially concerning Spivak's Calculus. In fact, too often I see Spivak's name mentioned and suggested to students who, from my point o view, would much more benefit from different types of treatments of the Calculus such as the one Lang's offers. Not to deny that some students would understand and assimilate Spivak's at first reading almost, but I believe that those students are so far and few in between that it is a waste of time and energy --for both the one who suggests it and the one who possibly tackles Spivak-- to even bother to mention –  user37084 Aug 2 '12 at 15:28
    
I posted some fairly positive comments about Lang's Calculus of Several Variables text in this 21 January 2011 Math Forum archived post. –  Dave L. Renfro Aug 2 '12 at 20:46
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