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Book Recommendation Advanced Calculus?

  1. Dec 3, 2009 #1
    Could someone recommend a good book to review Calculus leading up to Advanced Calculus. I have Advanced Calculus next semester and want to get a jump on it. It has been a couple of years since I had Calc II. and I am reviewing the Stewart Book. I am looking for something a little more concise. Thanks!
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  3. Dec 3, 2009 #2


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    More concise than James Stewart? I found the Stewart book quite concise, I'm not sure there is one more concise.

    I always recommend Stewart.

  4. Dec 3, 2009 #3
    Analysis is fairly different from standard computational courses in calculus. I would think the best way to prepare for your analysis class would be to get a head start reading the textbook that the course will be using.

    Several introductions to analysis will have an opening section on prerequisites. Your class may go over this section quickly or not at all, but if your book has such a section it may benefit you to read all of it before the class begins.

    Alternatively, you may want to pick up the calculus books by Apostol. As calculus books, these are high-powered; as analysis books, they are low-powered. So they should be a great warm-up for your advanced calculus class.
  5. Dec 4, 2009 #4


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    Do you have any experience doing proofs? If not, then I suggest that you get some! I recommend "analysis, with an introduction to proof" by Lay. I worked through a used copy of the second edition and thought that I learned a lot. The first two chapters will get you somewhat up to speed, teaching you logic, quantifiers, methods of proof, set theory, etc. I expect that there are better books out there for this, but Lay is what I am familiar with.

    Good luck,

  6. Dec 6, 2009 #5
    Together with jasonRF's suggestion, I would recommend David Brannan, An Introduction to Mathematical Analysis
  7. Dec 6, 2009 #6
    I second the nomination of Analysis by Steven Lay. It's a great introduction to proof techniques and analysis, and it isn't that long of a book, which makes it great for a preparation book. If you could give a little more detail on the topics of your course, that would help. Different courses can mean different things by advanced calculus.

    The calculus books by Richard Courant or Tom Apostol are excellent and rigorous presentations of calculus and basic analysis, but probably aren't texts you can go through over the Christmas break. Probably the best rigorous calculus book is by Michael Spivak, but again is something you wouldn't want to rush through. I've also heard good things about Understanding Analysis by Stephen Abbott, which would be aimed closer to what your course will probably be like, like the Lay book.
    This is a joke right? I'm sorry, but Stewart has to be the worst recommendation as preparation for an analysis course ever.
  8. Dec 7, 2009 #7
    What exactly does this "Advanced Calculus" course contain?

    out university offers a course of same title and it is a continuation of Calculus III (multivariable). AC course contains stuff like Div, Grid, Curl and more throughout detail of topics taught in multivariable Calculus. Here, this course does *NOT* require Analysis background (or any proof background whatsoever)..although it helps if we do.

    If that is the type of course you are taking then use Springer Vector Calculus book


    If this is Analysis type couse then get a good hold of Analysis first

    here's an Analysis book from Spirnger


    both listed Springer books are easy to follow and were written to be a guide for student as well as a formal text.

    if you need an introductory book for proofs, this is a good one


    pretty neat for self-study
    Last edited by a moderator: Apr 24, 2017
  9. Dec 7, 2009 #8


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    Who said anything about analysis and proofs?? The OP asked about advanced calculus books and stated that it had been a while since they had Calc II. If anything they are implying that they are taking Calc III next, which is typically multivariable calc. Hence, my recommendation.

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