I am currently working on problems that require familiarity with calculus of variations. I am fairly new to this field. Please suggest a good introductory book for the same that could help me pick up the concepts quickly.
edit: I would prefer books which are available in PDF format online.
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I know this post is old, but if anyone else is looking for a good, concise and intuitive introduction to the calculus of variations, the chapter 'calculus of variations' in Peter Olver's as yet unpublished 'Applied Mathematics' (well, the first 10 chapters are published as 'Applied Linear Algebra') is very readable.
As of September 2011, this chapter is available on Peter's website at http://www.math.umn.edu/~olver/appl.html
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Michael Struwe Variational Methods: Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems, Fourth Edition, Springer, 2008.
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I just purchased a copy of Gelfand and Fomin's Calculus of Variations. It's a Dover book, so it's really inexpensive (I paid $9, including shipping).
The book gets very good reviews, both on Amazon and MathOverflow. Just from reading the first few pages, it looks quite promising.
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Charles MacCluer wrote a book on the subject in 2008 for students with a minimal background (basically calculus and some differential equations), Calculus of Variations: Mechanics, Control and Other Applications. I haven't seen the whole book,but what I have seen is excellent and very readable. MacCluer says in the introduction his goal was to write a book on the subject that doesn't replace the old classics, but updates and supplements them with a lot of real-world applications and without heavy prerequisites. From what I've seen, he's succeeded and best of all, the book's available from Dover in a cheap paperback. This might be just what you're looking for.
If you're looking for something more mathematicially sophisticated and up-to-date, you can try the book by Bruce Van Brunt.
If you check out Wikipedia's entry on "Calculus of Variations: here, and scroll down to the bottom where "References" are listed:
You'll find a link to a pdf reference (Jon Fischer, Introduction to the Calculus of Variation, a quick and readable guide) that might be exactly what you're looking for, as well as some additional references (sample problems, guides, etc.).
In addition, you'll find a link to this site listed among the references.
There's also a chapter of a text that's available online: Chapter 8: Calculus of Variation from Optimization for Engineering Systems, by Ralph W. Pike.
There are also some additional texts and resources listed in the linked Wikipedia's entry, as well.