Classical Looking for simple materials for calculus of variations

[Haorong Wu]

Hi, there. I have not systematically learned the calculus of variations. I would like to learn it now. Are there simple materials for the purpose of learning how to do the calculation in physics? No need for deeper consideration in mathematics.

Is Mathematical methods for physicists by Arfken sufficient?

Thanks in advance.

 

[Frabjous]

Arfken is fine. The real question is does it go into enough detail for YOU?

I always liked the Dover book by Elsgolc
https://www.amazon.com/dp/0486457990/?tag=pfamazon01-20

 

[Haorong Wu]

Arfken is fine. The real question is does it go into enough detail for YOU?

I always liked the Dover book by Elsgolc
https://www.amazon.com/dp/0486457990/?tag=pfamazon01-20

Thanks! I will try Arfken's book first. If that is not enough, I will consult Dover's book.

 

[paralleltransport]

I've always learned calculus of variations directly from one of the physics books and found it to be adequate at a physicist's level (ability to push symbols and calculate). I learned it from Landau Lifshitz vol. 1 from the principle of least action calculation there. Goldstein Classical mechanics has a more verbose version of the same derivation. But beware that all those derivations are iffy.

For more subtle explanations of what is really going on (which is important but maybe not needed on the first run), you can consult the "structure and interpretation of classical mechanics" by Gerald Sussmann. What I found out was that a lot of the important subtleties are swept under the rug due to time in the typical physics course, but gerald sussman really emphasizes those.