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Common Prerequisites for the Calculus of Variations?

  1. Apr 28, 2012 #1
    I'm really interested in this subject. Would one be capable of learning this subject with a great working knowledge of Multi-var/Vector Calculus, ODE, Linear Algebra, and complex variables? What are some good books?
  2. jcsd
  3. Apr 28, 2012 #2
    I have Zeidler's applied functional analysis, which I liked at the time. For me, aside from calculus and other computational courses, some analysis courses were also prerequisite.

    If you are just interested in the physics, i.e. Euler Lagrange equations, Hamiltonian dnamics etc. I can recommend the current wikipedia pages in this order: 1,[/PLAIN] [Broken] 2, 3, 4, they're really quite good. Then your prerequisite knowledge should be some mechanics as well. A good book I never had for analytical mechanics/hamiltonian dynamics, although it is in fact one of my favorite subjects.
    Last edited by a moderator: May 5, 2017
  4. Apr 28, 2012 #3
    Indeed it was physics that got me interested in the subject. I will check that out, and read those wiki pages. I was also told that the Boa's book has a section on it, and indeed it does! Thanks for the information.
  5. Apr 29, 2012 #4
    Your background seems enough. A book that looks quite good to me, and which is also relatively cheap, is "Calculus of Variations" by Gelfand and Fomin. I am yet to work through it, but it looks good at first glance.
  6. Apr 29, 2012 #5
    Note that this is a pure mathematics text. If you're more interested in the applications, then there are better texts out there.
    The book "Calculus of variations with applications to physics and engineering" from Weinstock looks great!!
  7. Apr 29, 2012 #6


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  8. May 1, 2012 #7
    I'll see plenty of applications in my physics courses, I am more interested in the concepts. So, It would probably benefit me to first learn an intro to analysis you think? I should finish a my course on complex variables and a more rigorous vector calc in about a month or so, and then I will look into that book. You can't go wrong with a 6 dollar dover book! I understand all of the topics in the link astronuc posted (thanks).
  9. May 28, 2012 #8
    I am in similar position as OP. Very much interested in the subject and currently reading the book by Gelfand and Fomin. I would say that Real Analysis is probably mandatory for this book. I attempted this book 4 months ago (before taking Real Analysis) and could not make it far before getting stuck. Also, I have noticed that I am benefiting from my Numerical Analysis background while reading this book. Certain techniques such as finite difference methods, linear spaces and others have been ingrained after Numerical class.
    In conclusion, I would say that a certain maturity in analysis is needed.
  10. May 28, 2012 #9


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    a full sequence on Differentiable, and Integral calculus (multivariable is required) along with ODE course (and some linear algebra) is what you need. Are you studying Optimal Control, too? if so then a little knowledge of Nonlinear Programming might help.
  11. May 28, 2012 #10
    Quite frankly I found this subject impenetrable for a long time & because this seemed so difficult to me I'd ignored Lagrangian & Hamiltonian mechanics thinking I wasn't ready. When I felt I'd become ready the same sources still made no sense to me. After a lot of pain I stumbled upon this foolproof method of learning enough of the basics of the subject to know what's going on & see how relatively easy it is:

    The first four videos of this will set the stage & make sense of it.
    The first six videos of this will give a fantastic explanation of why it's useful in mechanics, you'll probably never see anything else like these...
    This video will get more mathematical & codify some of the things in the above videos.
    http://nptel.iitm.ac.in/video.php?subjectId=108105056 [Broken] videos provide models of how the stuff is used & goes into things like constraints which the others really don't.
    After this the subject should be trivial, & there are more NPTEL videos on the subject that you can look for yourself.
    Last edited by a moderator: May 6, 2017
  12. May 28, 2012 #11
    I'd say Mary Boas' Mathematical Methods book would be a good start although it never really goes beyond the euler lagrange equation iirc, most books have this same problem too..
    I'd say you are perfectly equipped to jump into it though if you can find a decent book.
  13. May 28, 2012 #12
    Yes. If you have that math background, functional analysis won't be hard.

    A lot depends on whether you want to look at it from a physics point of view or a math point of view. If you want to look at things from a physics point of view, the easiest thing is to go through an upper level book on classical mechanics. This will be done from a "physics viewpoint" in which they just hand wave most of the math arguments and then give you some cookbook formulas (actually, the one magic formula).
  14. Aug 3, 2012 #13
    Gelfand and Fomin contains a treatment of the Hamilton-Jacobi Equation, which is a partial diffrential equation. So would it not be better for the OP to develop familiarity with PDE's as well?

    Or am I just plain wrong?
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