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Calculus of variations

  1. Sep 28, 2006 #1
    I'm doing my final year in maths and am just away to start my 4th year project. It involves learning a subject on my own then submitting a report and doing a presentation. The topic I have to do is "Calculus of variations".

    I've been reading about the topic briefly on a few webpages and it does seem a bit daunting!

    Does anybody know any decent books worth reading that provide a good explanation of the subject? Also, would it be helpful if I revised certain areas of calculus before trying to learn the topic?

  2. jcsd
  3. Sep 29, 2006 #2
    Any good mechanics book would be an excellent place to start.
  4. Sep 29, 2006 #3


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    Actually, mechanics book most often treat the point from a physicla point of view. Not explaining what a variation is, using [itex]\delta[/itex] and using all kinds of theorems and properties of functions without much scrutiny.

    My advice is to go to your library and get a mathematical book which introduces the subject. Then take it with you and study it.
  5. Sep 29, 2006 #4
    Elementry level book: The Calculus of Variation by van Brunt (Mainly 1D 2D problems), Introduction to the calculus of Variations and its applications by Wan.
    Intermediate level: Calculus of Variation I and II by Giaquinta, and some sections of Tensors, Differential Forms, and Variational Principles.
    Masterpiece: Morse, The Calculus of Variations in the Large, and work by C. Caratheodory.

    Mechanic books often omit the discussion of sufficient condition of being max/min.
    Last edited: Sep 29, 2006
  6. Sep 29, 2006 #5
    I would suggest doing a presentation on some of the classic problems like the brachistochrone. Any book on the calculus of variations will tackle that one early on. You could throw in some historical intrigue here about the Bernoulli brothers.
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