# Formal Variational Calculus Reference Request

I want to ask for a reference to study Variational Calculus from a formal point of view. What I mean is that many of the references that I've found are inside Physics books, and the authors do not care too much about mathematical rigour. For example, I think it's very important to make a distinction between a function $f: \mathbb{R} \to \mathbb{R}$ and it's value on some point $y = f(x)$, however, those references usually speak loosely like "the function $y(x)$" and I really think that this isn't good.

Can someone point out then what's a good reference to learn variational calculus from a mathematically rigorous point of view?

Sorry if this question is silly, and thanks in advance!

• Arnold's book "Mathematical Methods of Classical Mechanics" has something to say about that. You might be also interested in Bleecker's "Gauge theory and variational principles" – c.p. Apr 1 '13 at 23:42