It would be nice to some women. Can’t you figure out an excuse to, at least, get Emmy Noether in there.

]]>Thanks!

]]>https://franknielsen.github.io/GSI/ ]]>

Oh wait, I see it is … The text

Giaquinta, Mariano; Hildebrandt, Stefan (1996), Calculus of Variations 1. The Lagrangian Formalism.

Very interesting.

Courant and Hilbert? How classical can you get :-) Looks like the DWM haven’t been made obsolete quite yet.

I’m kind of amazed this isn’t covered by a more modern, mainstream textbook from some place like Springer. Maybe it is. Hopefully someone can make a suggestion.

]]>There must be a bunch, but I forget where I learned this stuff—probably here and there. It can’t hurt too much to start here:

• Wikipedia, Functional derivative.

They recommend a bunch of textbooks, starting with Courant and Hilbert and working on up to Gelfan’d and Fomin, which is a Dover book—so fairly cheap, I imagine. All four of these folks are famous.

]]>When I was a math major taking physics classes, the way physicists did variational derivatives seemed like black magic to me. Then I spent months reading how mathematicians rigorously justified these techniques.

Is there a half-way decent textbook that explains that?

Thanks.

]]>Okay, thanks—that’s interesting. Horn and Jackson introduced it in chemistry in 1972 and called it the “pseudo-Helmholtz function”:

• F. Horn and R. Jackson, General mass action kinetics,

*Arch. Ration. Mech. An.* **47** (1972), 81–116.

It plays an important role as a Lyapunov function in chemical reaction networks that are ‘complex balanced’.

]]>It occurs to me that this form of the KL-divergence is also what arises when you calculate the Bergman divergence of the usual entropy formula, but I can’t say I really understand Bregman divergences either :).

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