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Second Calculus Book?

  1. Jan 15, 2013 #1
    Hi everyone. I've just gotten through the first 15 chapters of Spivak's Calculus. Though the rest of the book looks fascinating, I'm currently more interested in studying statistical thermodynamics in light of my new-found math knowledge. I am reading through Dill's Molecular Driving Forces, 2nd ed. The book uses partial derivatives and Lagrange multipliers to derive the Boltzmann distribution, which is the fundamental theorem of statistical thermo. Unfortunately, Spivak hasn't covered this in Calculus.

    I loved Spivak's style, and the treatment that these two math topics have gotten in the Dill book is criminal. (It's one of those chapters that is just there to give the teacher something off of which to teach. But I don't have a teacher, and I need a better treatment.) Can anyone recommend me a second calculus book written by a mathemetician, for mathemeticians, that includes partial derivatives and Lagrange multipliers?

    Best regards,

  2. jcsd
  3. Jan 15, 2013 #2


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    I can't remember if these included Lagrange Multipliers, but two books that met the criteria would be Courant Calculus volume II and or Apostol Volume II.
  4. Jan 15, 2013 #3
  5. Jan 15, 2013 #4
    Thanks all for the suggestions. I'm pleased to see three recommendations for "classics". Since the Courant book is $150, and the Edwards book is $15, I started there. But one day I'd like to add Courant (and Apostol) to my shelf.
  6. Jan 15, 2013 #5


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  7. Jan 15, 2013 #6
    Thanks, Wonk. I'd heard that it's a difficult read, but I'll certainly keep it in mind for further studies. I feel like it's hard to go wrong with some of these guys.

    MarneMath: Question about Courant: which book exactly?

    Methods of Mathematical Physics, Vol. 2 by Richard Courant and D. Hilbert (Jan 4, 1989)
    Differential and Integral Calculus, Vol. 2 by Richard Courant, Edward James McShane and Sam Sloan (Jun 13, 2010)

    Neither of these books are named Calculus, but the second one is closer.
  8. Jan 15, 2013 #7


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  9. Jan 16, 2013 #8


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  10. Jan 17, 2013 #9
    There is also a book by Munkres Calculus on Manifolds. Use Apostol vol. 2 & Courant vol. 2 together. Apostol is good but courant is little Rude.
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