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I learned calculus I and II using stewart's. I also taught myself

  1. Aug 24, 2009 #1
    I learned calculus I and II using stewart's.

    I also taught myself vector calculus using Paul C. Matthew's book.

    However, I'm not very satisfied and would like to relearn it proper. Is it a good idea to start on Apostol Volume 2?

  2. jcsd
  3. Aug 24, 2009 #2


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    Re: Apostol?

    Sure, why not?
  4. Aug 24, 2009 #3
    Re: Apostol?

    I like Apostol's books myself, so I must say, go for it! It is quite rigorous though, which could make it a shock to the system if you have never had such an approach from an earlier math text. For example, he uses set notation without apology or explanation (though he does explain it in Volume I). I don't think it's impossible to do if you have not had any similar rigor in an earlier course, but I would imagine it to be difficult--moreso without Volume I.

    However, I think his books are easier to use if you've already learned the concepts of what he teaches--which you've done for the most part. It's not as hard learning the "whys" alone as learning the "whys" along with lots of new, difficult stuff at the same time! Note that the second edition of Volume II does cover some Linear Algebra, so there will be some new stuff to learn, though you can skip a fair chunk of it and do the multivariable calculus parts if you wish (then come back to the rest of the Linear Algebra afterwards, of course!).

    I don't know if such a level of rigor is necessary for anyone outside of someone who has an interest in math, since I'm not out of high school myself, but it certainly can't hurt, and I at least find it fun to learn math that way. It also is certainly a good idea to start getting used to rigor if you plan on taking other courses which are loaded with it later!
  5. Aug 24, 2009 #4
    Re: Apostol?

    Ok, so you know how to do calculus, now you need to learn the theory and understand its inner workings.

    Do you know how to do proofs? If not, then check out Velleman's book:

    If you know how to do proofs, then I recommend Spivak's "Calculus". It only covers single-variable stuff, but you need to thoroughly understand single-variable before you do multi-variable, so I think jumping straight in to Apostol vol.2 is a bad idea.
    Why Spivak and not Apostol vol.1? Well, I think since you know how to do calculus, you need more theory rather than theory+learning to do calculus, and I think Spivak is more to the point on the theory.

    After Spivak (or Apostol vol.1 if you like, they're both very good), you can move on to real analysis proper, from a book like baby Rudin "Principles of Mathematical Analysis", or even better I think, on to Pugh's "Real Mathematical Analysis". I don't think you should waste your time with Apostol vol.2, you need to learn other mathematics, you can't just be doing calculus all your life. Pugh would be a great next step after Spivak or Apostol vol.1, and it covers multi-variable calculus too. You'll need to learn linear algebra first for the multi-variable stuff though.

    EDIT: I just checked amazon.com and Spivak is cheaper too :D
    Last edited by a moderator: May 4, 2017
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