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Good Multivariable Calc text?

  1. Dec 21, 2011 #1
    I'm taking multi-var calculus next semester and I found out that we are using this terrible excuse for a book:
    https://www.amazon.com/Calculus-Mul...1586/ref=sr_1_1?ie=UTF8&qid=1324521500&sr=8-1

    Anyway, I have been studying ahead using my huge copy of Stuart, which my university uses for Calc I and II. I asked my professor why we use this new book for Calc III, and he said it had something to do with money basically, but also, James Stuart's book is a little weak for calculus III.

    If Stuart is poor, and this book is horrible, what is a good book I can use to study Calculus III? I'm just going to ask a fellow student if I can copy the problems out of his book and forgo purchasing the required book.

    Is Stuart a reasonable Calc III book? I partially hope so, it would save me a ton of money.

    My Differential Equations class also uses a silly poor-ranking book that was picked by my school for some unknown ($) reason. What's a good alternative to that?
     
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  3. Dec 21, 2011 #2

    micromass

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    Apostol is a good book. It's very rigorous though. Maybe that isn't what you're looking for...

    What are you going to cover in your Differential Equations class??
     
  4. Dec 21, 2011 #3

    mathwonk

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    here's the book we used at harvard in 1969.

    http://www.abebooks.com/servlet/Sea...ng&kn=functions+of+several+variables&x=58&y=9


    i still have it on my shelf and regard it highly.

    another classic is the one by lets see... oh yes, williamson, crowell, trotter:

    https://www.amazon.com/Calculus-Vec...=sr_1_1?s=books&ie=UTF8&qid=1324527055&sr=1-1


    since this is one of the best books ever and available for as little as $1. this is a cannot miss buy.

    a short theoretical book i learned a lot from is the little calculus on manifolds by michael spivak.

    https://www.amazon.com/s/ref=nb_sb_...words=spivak,+calculus+on+manifolds&x=16&y=25
     
    Last edited: Dec 21, 2011
  5. Dec 21, 2011 #4
    The multivariable section of Stewart's Calculus is not terrible, especially if you enjoyed the sections on single variable calculus.

    If you're good with proofs, I recommend Vector Calculus by Marsden and Tromba. It's a good medium between more computational/applied texts like Stewart and theoretical texts like Apostol.
     
  6. Dec 22, 2011 #5
    My DEQ course:
    I'm absolutely picking up that $1 book, can't go wrong with that.

    I'm not fantastic with proofs, but I am not horrible either. I'll check out that "middle-ground" book.

    I don't really like the way that Stuart presents new concepts. It's basically "Here's the theorem, and here are some solved examples, and then it's just problem sets". That being said, I couldn't imagine trying to learn a new concept from Spivaks book. It's great once I already know what he's talking about though.
     
  7. Dec 22, 2011 #6

    micromass

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    Maybe try Boyce & Diprima for ODE's?? I've heard good things about the book.
     
  8. Dec 22, 2011 #7
    Spivak's book is the book we would use in the course taught at my school. Another book similar to it ( with many more details ) is the book Analysis on Manifolds by James Munkres.
     
  9. Dec 22, 2011 #8
    I second Boyce and DiPrima.

    Many people recommend Ordinary Differential Equations by Tenenbaum and Pollard as a supplemental textbook. It's from Dover, so it's inexpensive.
     
  10. Dec 22, 2011 #9
    you can also try "Vector Calculus, Linear Algebra, and Differential Forms" by John Hubbard. it provides a unified approach by introducing derivatives first, then teaching the necessary linear algebra to proceed with the study of manifolds (surfaces), integration involving multiple integrals, and line integrals, surface integrals, as well as generalizations of them. One thing not many books on Calculus III does is introduce the concepts of differential forms and how expressing the many integration theorems (Green's, Gauss's, Divergence) in this new language greatly simplifies things.

    this may not be what you are looking for, but if you wish to understand on a deeper level the concepts presented in Calculus III then this is a book I highly recommend.
     
  11. Dec 22, 2011 #10

    mathwonk

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    i myself preferred tenenbaum and pollard, and also martin braun ode books greatly over boyce and diprima. Indeed i never understood what anyone liked about boyce etc, as i never understood anything out of that book.
     
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