Reference request: calculus of variations I am searching for a good book to self-study calculus of variations. 
It should be fairly complete; build up gradually from the very basics; offer detailed explanations; have some emphasis on applications of variational methods.
 A: Well there are a huge amount of book suggestions regarding the calculus of variations gather-able from these links: https://mathoverflow.net/questions/46319/beginners-text-on-calculus-of-variations ; Introductory text for calculus of variations .
I will list links to sources considered to be the best:


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*Gelfand and Fomin's "Calculus of variations" http://www.amazon.com/Calculus-Variations-Dover-Books-Mathematics/dp/0486414485 . It has many advantages: It is cheap (so if you buy it and don't like it, it's not a big deal); It is written by good mathematicians, that are broad enough to see connections with many different areas; It has useful exercises, and they're reasonable and with an eye on applications; It has an appendix on Optimal Control.

*http://www2.math.uu.se/~gunnar/varcalc.pdf 

*https://www.cs.iastate.edu/~cs577/handouts/variations.pdf

*http://www.amazon.com/Lectures-Calculus-Variations-Optimal-Publishing/dp/0821826905

*Robert Weinstock's Calculus of Variations: with Applications to Physics and Engineering http://www.amazon.com/Calculus-Variations-Applications-Physics-Engineering/dp/0486630692/ref=pd_cp_b_2
I believe suggestions 1 and 5 will do the trick; I'm sure they'll be helpful.
A: http://www.amazon.com/The-Calculus-Variations-N-I-Akhiezer/dp/3718648059
This book may be worth checking out. I began learning from it and found it pretty thorough. You might want to have exposure to basic real analysis (convergence,  etc...).
