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What to read after Spivak? And Physics books

  1. Jun 21, 2012 #1
    Hello I am about to finished working though Spivak's Calculus. I am wondering if you guys could give me some recommendations on what to read after I'm done with the book. I am looking for something as rigorous as Spivak.

    Also a bit unrelated but I have also worked through an old edition of Calculus by Thomas (before spivak). So I recently bought kleppner and Kolenkow's Mechanics book but I also own a second edition of Halliday and Resnicks Physics for scientists and engineers. I have never formally taken a physics class before and I am wondering which book I should start with. Thank you for taking your time reading my post.
  2. jcsd
  3. Jun 21, 2012 #2
    For math: do you know linear algebra yet?
    For physics: I would just start out with Kleppner/Kolenkow. If it's too hard, you can always switch books and come back to it later.
  4. Jun 21, 2012 #3
    For mathematics, you could now read linear algebra or multivariable calculus. I recommend linear algebra first, since multivariable calculus will go easier with some knowledge of linear algebra.

    If you want rigorous books, then I can highly recommend "Linear algebra" by Serge Lang.
    For a multivariable calculus book, here are some suggestions, ranked from non-rigorous to extremely rigorous:

    "Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach" by Hubbard
    "Analysis on manifolds" by Munkres
    "Calculus on manifolds" by Spivak
    "Multidimensional Real Analysis" by Duistermaat and Kolk
  5. Jun 21, 2012 #4
    Ok I think thats what I'm going to do with Kleppner.

    I don't know Linear Algebra, yet. Do you think it will be a good choice to learn Linear Algebra before I begin my study of Multivariable and Vector Calculus at a rigorous level? If so what books would you recommend me to look at? Thanks.
  6. Jun 22, 2012 #5
    I'm working on Linear Algebra and have thoroughly researched all the books available.
    You should do Lin Alg before Multi Calc.

    My Primary Text is: Linear Algebra; A modern introduction. 2nd ed - David Poole (Great section on Markov Chains; pretty rigorous; good depth overall)
    Supplementing with: Matrix Analysis and Applied Linear Algebra - Carl D. Meyer (Great problems and depth) and Linear Algebra - Jim Hefferon. (Great optional chapters)

    I plan on gauging more depth later using Axler's and Ray, Kunze's texts on the same topic.

    Good Luck!


    PS: I'm working through Spivak right now. Any suggestions?! :)
  7. Jun 23, 2012 #6
    I also recommend you do linear algebra next. Lang's book is good, as is Hoffman/Kunze. Or you could take a non-traditional route and just learn linear and abstract algebra together out of Artin's Algebra.
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