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A comprehensive course in calculus (What a tongue twister!)

  1. May 28, 2009 #1
    First off, sorry to have two threads right up at the top of the forum. (If one/both of my threads have sunk down the list, disregard this.) Anyway, I looked through the first five pages of this forum, but I couldn't find a thread relating to this, they were all about a specific class in calculus, or about a recommendation between two textbooks.

    So, to get to the point, I'm just about ready to start studying calculus, and I need to get some recommendations for some great calc textbooks. (I'm fortunate enough to have lots of money to spend on textbooks, and I'll buy used/paperback books, which is how I can afford to get several books.) Here's my tentative studying plan:

    Spivak, Calculus
    I've heard it's very well written, so I'll start with this instead of Apostol. The problems are supposed to be very hard.

    Apostol, Calculus, Vol 2
    Spivak's book is supposed to have pretty much the same material as Volume 1, only it's better written. I've heard Apostol's tone is rather dull, which is why I've substituted Spivak for Volume 1. Will this work, or should I just get volume 1?

    Buck Advanced Calculus
    I don't know much about this one. Is it even necessary? I've seen it recommended a lot.

    Widder Advanced Calculus
    Edwards Advanced Calculus of Several Variables
    They're Dover's, unless these are horrible, I may as well get them since they are so cheap.

    Spivak Calculus on Manifolds
    This is a book I plan not to get. I've heard that it is too terse.

    Sternberg Advanced Calculus
    This is supposed to be better than Spivak's Calculus on Manifolds, and it's avaliable for free. If this isn't good, I could just substitute Munkre's book instead.

    Please tell me, is this a good list? Are there any books I should drop, any books I should try I haven't listed? Will I truly understand calculus after this?
    Last edited: May 29, 2009
  2. jcsd
  3. May 28, 2009 #2


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    Are any of those you listed necessary if you never studied Calculus before?

    Are any of those listed suitable for someone who never yet studied any Calculus?

    If you recently studied and did well in Intermediate Algebra and Trigonometry, you could study the first three semesters-worth of Calculus using any of several older books not necessarily of any of those you listed. The only difficulty which would seem extreme would likely be epsilon-delta proofs of limits, something that is troublesome for MOST Calculus students, MOST of whom generally pass their courses successfully.

    I will not suggest which authors of these "several older books not ... listed", because brainy kevin seems mostly interested in specific other authors of Calculus books; I only suggest that for first time Calculus study, those he/you listed might not yet be necessary. This judgement of mine could be faulty, since I really have never examined or found any of them yet.
  4. May 29, 2009 #3
    I actually already know some calculus already. When I said I'm ready to study calculus, I meant study it rigorously. I've studied it before, but not much in depth.
  5. May 29, 2009 #4


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    My advise is not to get too much textbooks, since they cover pretty much the same material. Just choose one of Spivak, Apostol I and Courant, and you'll be more than fine (my choice would be Spivak). I can guarantee that if you buy them all three, two will be sitting on your shelf unused most of the time. Even if you have the money, better spend it on books you'll actually use.

    Did you study multivariable calculus at a computational (e.g. Stewert) level already? Then, after Spivak, I'd skip the advanced calculus books and either go to Analysis on Manifolds (Munkres or Spivak) or real analysis (Rudin, Pugh, Apostol's Mathematical Analysis).
  6. May 29, 2009 #5
    No, I haven't studied multivariable at a computational level yet. But I've removed Courant, since you're right, I won't really need it. Or would Courant be better than Apostol?
  7. May 29, 2009 #6


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    Marsden's Vector Calculus is a standard on multivariable/vector calculus. I think Apostol and Courant are pretty similar, but Courant has a few physics applications [Spivak is the best in my opinion, with masterful explanations and excellent exercises].
  8. May 30, 2009 #7
    Actually, I'm fairly sure you didn't search hard enough, or overlooked suggestions in one of your initial threads, but whatever.

    Forget pretty much the latter half of your list of books. Choose between Spivak and Apostol, it doesn't really matter if you actually want to learn calculus well. Protip: you can actually read through a few pages of many of these books on Google books. In other words, learn to find out whether a particular book suits you.
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