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Apostol vs Spivak for physicists

  1. Jun 9, 2014 #1
    Hello PF!

    I was wondering which would be more helpful for a physicist.

    Also a little bit of a tangent, if I learn calculus from one of the "popular" books, how would I go back to rigorous math? And where would it be useful for a physicist?

    Thanks :)
  2. jcsd
  3. Jun 10, 2014 #2
    "Physicist" is a big word, it can mean a lot of things. It might be somebody into experimental condensed matter theory, or somebody into mathematical physics and string theory.

    Clearly, the level of math books one should read depends on what kind of physicist they want to be and how interesting they find the mathematics.

    For a general physicist, both Spivak and Apostol would probably be overkill. One of the "popular" calc books will work just fine. If you are interested in mathematics however, then you can try Apostol.

    If you're going into mathematical physics such as string theory (which I understood from your previous posts), then Spivak is a must to read. But it shouldn't be your very first book to read. Try some easier book like Lang or Apostol first. Spivak isn't really calculus anyway, but an intro to analysis.
  4. Jun 10, 2014 #3


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    As is Apostol, with some linear algebra thrown in. What makes you think Apostol is easier than Spivak? I have experience only with Apostol, but I've never seen that opinion before.
  5. Jun 10, 2014 #4
    Hmm, I am not sure which part of physics I will end up in, but I guess Spivak can't hurt. I didn't realize that Spivak > Apostol, thanks. Also does a computational calc class work as a prereq for spivaak?
  6. Jun 10, 2014 #5


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    I think you have Spivak now and probably you can answer half of the questions, that should be enough success to work through it. But if you're someone like me who hates to leave a question unconquered, it may prove difficult.
  7. Jun 10, 2014 #6
    In that way, I am just like you, verty. How long do you think it might take to do?
  8. Jun 10, 2014 #7


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    In my opinion, Spivak is easier to read because Apostol's proofs are less detailed. However, Spivak's exercises are harder.

    I would say they are both significantly harder than Lang, which is a very good introductory book.
  9. Jun 11, 2014 #8


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    Well I think you'll have to set some time limits, I mean you can't take a week to finish a chapter's questions. Probably you'll want to say, I'm going to try to answer all the questions but after 2 days, I'm moving on. But actually I would only do the questions that have answers (the easier questions I mean), go through book doing just those and come back later to try the harder ones.
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