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Lately I've been doing a lot of work related to solving variational problems (in the context of surface theory), and I'm getting really tired of going to local coordinates for everything.

So, I was wondering: does anyone know a good coordinate-free treatment for the calculus of variations? I've heard such literature exists, but I can't say I'm familiar with it.

Any suggested reading you all may have would be much appreciated.

Thanks in advance,

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  • $\begingroup$ Which books uses local coordinates for everything? Jost? $\endgroup$
    – user99914
    Commented Jan 3, 2018 at 0:41
  • $\begingroup$ Willmore and Gelfand/Fomin are also pretty heavy on coordinates IMO. I also had a tough time reading Lovelock and Rund for the same reason. $\endgroup$
    – MathIsArt
    Commented Jan 3, 2018 at 1:42
  • $\begingroup$ Did you try Struwe's Variational method? It seems that they do not have a lot of coordinate calculations. $\endgroup$
    – user99914
    Commented Jan 3, 2018 at 4:28
  • $\begingroup$ I'll take a look at it -- thanks for the recommendation. $\endgroup$
    – MathIsArt
    Commented Jan 3, 2018 at 4:33

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In case anyone else is curious, I've been getting some mileage out of Differential Geometry and the Calculus of Variations by Robert Hermann.

It's not exactly what I was looking for, but it's quite good, and I'm excited to apply some of the techniques in "Part 2" of the book.

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