Just how important is Calculus of Variations for a physicist?

Very important!

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>>9117562
Very.
https://en.wikipedia.org/wiki/Principle_of_least_action
>he doesn't enjoy the comfy variational lemma and everything it brings him
Very sad desu. Maybe engineering is more your speed.

not exceptionally important, certainly not in its rigorous formulation, in most cases I get the feeling that physicists don't exactly know what they are talking about when they 'vary the action', so I wouldn't worry about it too much. pde's are far and away more important, and that should be any undergraduate's/beginning graduate's central focus.

>>9117690
But I hate engineering.

>>9117562
>for a physicist
lol

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>>9117701
Sorry anon but that's a problem you have to solve yourself.

Well, more or less it's a principle that's understood to be important when doing physics, but exact application of it is pretty rare. Usually we just use results from the calculus of variations (CV), like the Euler Lagrange equations. You'll find it's more important to understand the results of CV than the little details.

Most of the time it's applied to the principle of least action, which defines the equations of motion in a classical system and the on-shell solutions to a quantum field theory. In QFT there's an important use of the action principle but with non-zero action. These are known as instantons and are the essence of the non-classical behavior of quantum mechanics.

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>>9117562
>Calculus of Variations
Easy
*phenotype smug face*

>>9117562
It's pretty much all they do

>>9117690
>engineering
Optimal control theory relies on calculus of variations as well.

>>9117699
Is that so? Recommend me a decent book on PDE's. I find Farlow's book vapid and boring.

>>9117690
>the comfy variational lemma
I fucking hate braindead anime autists who replace every good adjective with "comfy"

>>9119767
http://4chan-science.wikia.com/wiki/Mathematics#Partial_Differential_Equations

>>9117562
>Calculus of Variations
>Doesnt enjoy it
>ostensibly wants to be a physicist
buckle up bud

>>9117718
Very true. Like in variational principles in neuroscience. Tje variational bit doesnt matter too much or atleast it has little direct application to the brain as of yet. Its the outcome in variational bayes though is - minimizing helmholtz free energy bounds

>>9117562
drop out now

you can thank me later

>>9117562
Thats basically physics