In the calculus of variations, the integral itself is a "functional." It depends on the form of the function of the Lagrangian: q and q-dot(adsbygoogle = window.adsbygoogle || []).push({});

But I have seen this word "functional" used elsewhere in different contexts.

I have seen: "A functional is a real valued function on a vector space."

I have seen: "A function is a function of functions."

I understand how these are all used, but I am still bereft of a "precise" and "consistent" definition of this word.

Can someone provide it? (Perhaps the key is that there is no "consistent" definition?)

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# I What is a functional?

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