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Multivariable calculus

  1. Jun 10, 2014 #1
    I am currently reading baby Rudin, but I only know single-variable calculus at the moment, so I think it would be a good idea to learn the multi-variable stuff non-rigorously before I do the analysis in Rudin (chapters 9-11).

    So I was thinking of either getting one of the many 'Mathematical methods for...' books or 'Calculus vol.2' by Apostol. Which would be better?
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  3. Jun 10, 2014 #2


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    Last edited by a moderator: May 6, 2017
  4. Jun 10, 2014 #3
    Yes, I was planning on doing that, I thought it might be quite difficult to learn it straight from Rudin though. I'll see how it goes.
  5. Jun 10, 2014 #4


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    Apostol is pretty rigorous and it will take you quite a while to hack your way through. If you want a less rigorous but really excellent introduction, get Lang's Calculus of Several Variables.

    Neither Apostol nor Lang does differential forms, though, and Rudin would be a horrible place to learn this (or any of the material in chapters 9-11, for that matter). An alternative would be Hubbard's Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach, which I have not read but which has a very good reputation. Personally I don't see the point of trying to learn differential forms without having learned the "classical" treatment as in Lang, but that's just my preference.

    If I recall correctly, Rudin does measure theory and Lebesgue integration in chapter 10 and/or 11. None of the above books will help you with this, and I would NOT advise learning it from Rudin. Almost any other book covering this material will be a better choice. A nice efficient (but expensive) choice would be Bartle's The Elements of Integration and Lebesgue Measure.
  6. Jun 11, 2014 #5
    I'd skip chapters 9-11 of Rudin. The materials are better treated elsewhere.

    You'll need vol 1 and vol 2 of Apostol for complete treatment of multivariable calculus.
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