My background is in physics, not pure mathematics, so please try to explain in ways that we lay-people could understand ;)(adsbygoogle = window.adsbygoogle || []).push({});

I'm brushing up on my calculus of variations--specifically Hamilton's principle--in which it is stated that the integrand is a 'functional,' not a 'function.' I've read that a 'functional' is a mapping from a vector space to a scalar, e.g. from a vector space to its underlying field--but I don't quite understand the significance of this. If someone could elaborate on the explanation, or provide a physically-motivated example, that would be very helpful!

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# Function vs. Functional?

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