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.