The Living Thing / Notebooks :

Functional derivatives

I guess the calculus of variations is useful sometimes after all.

So I will make some notes. See also optimisation, and the main use-case, Lagrangian mechanics, and also other functional equations

Fréchet derivative
generalises the idea of the derivative from real-valued functions of one real variable to functions on Banach spaces
Gâteaux derivative
generalises the idea of the directional derivative from real-valued functions of one real variable to functions on Banach spaces

TBD

“What is the quickest path through these mountains?”

Optimal control, Pontryagin’s maximum principle. Variational calculus, minimising functionals.