Can someone please tell me what the best book for learning calculus of variations is?
At what level, for what purposes? The physical, computational way, or the mathematically rigorous way?
For the computational approach I would say Goldstein has a pretty clear explanation.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.)
https://www.amazon.com/dp/0486414485/?tag=pfamazon01-20 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).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?