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Calculus of variations?

  1. Dec 19, 2009 #1
    Can someone please tell me what the best book for learning calculus of variations is?
  2. jcsd
  3. Dec 20, 2009 #2


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    At what level, for what purposes? The physical, computational way, or the mathematically rigorous way?
  4. Dec 20, 2009 #3
    I'd prefer the mathematically rigorous way. I first encountered calculus of variations in my graduate mechanics class, and we did a few problems with it, but I never really understood it completely. (I understand that it's one way to derive the Euler-Lagrange equations.)

    Is there a text, adequate for self-study, that lays out the rigorous mathematical framework and then goes on to apply the theory to physical problems, like deriving the Euler-Lagrange equations or showing that the shortest path between two points in the plane is a straight line?
  5. Dec 20, 2009 #4


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    For the computational approach I would say Goldstein has a pretty clear explanation.
    https://www.amazon.com/Calculus-Variations-I-M-Gelfand/dp/0486414485 is a great classic text (Dover, cheap), see Google books to browse through it. It is theoretical, but with a lot of physics applications (and a clear lay out of Noethers theorem, which I couldn't really follow in one of my physics classes).

    A more modern book is https://www.amazon.com/Calculus-Var...r_1_12?ie=UTF8&s=books&qid=1261346582&sr=1-12 by Jürgen Jost and another Li-Jost. This one goes deeper, using functional analysis and measure theory in the second part.

    Then there's another https://www.amazon.com/Calculus-Variations-Universitext-Bruce-Brunt/dp/0387402470 (not very original names) which seems ok, but I haven't read this one.
    Last edited by a moderator: Apr 24, 2017
  6. Dec 21, 2009 #5
    Tray B. Dacorogna:Introduction to the Calculus of Variations (Paperback)

    Paperback: 300 pages
    Publisher: Imperial College Press; 2 edition (December 10, 2008)
    Language: English
    ISBN-10: 1848163347
    ISBN-13: 978-1848163348

  7. Dec 29, 2009 #6
    I learned to love the subject from Gelfand and Fomin.
  8. Dec 31, 2009 #7
    Yes, Gelfand & Fomin , a fine classic. Very nice. K.
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