Shortest path to the Calculus of Variations

[GoutamTmv]

Hello all,

A friend of mine has recently developed an interest (rather, an obsession) with the Calculus of Variations. He's familiar with linear algebra and also with the contents of Spivak's "Calculus on Manifolds", and is now looking for the shortest path to Gelfand and Fomin's "Calculus of Variations" book.

Is there such a "shortest path"?. Personally, I'm a little uncomfortable with the idea, so I'm posting here for clarification.

 

[chiro]

Hey GoutamTmv and welcome to the forums.

At my university, the pre-requisites for Calculus of Variations include Calc III and Linear Algebra.

If you friend really has a decent understanding of Spivak and LA, he should be OK but the thing will be on the focus of how its taught (informal? formal? proof? application? physics? engineering?)

 

[GoutamTmv]

He wants teach himself using Gelfand and Fomin's book.
G & F's book is rather theoretical (lot of proofs) with a few applications to physics ( it covers the Hamilton-Jacobi equation, and the principle of least action, for example).
Its tone is formal, if that's what you mean.

 

[chiro]

I guess the thing will be then his experience with proofs and how much of these proofs have be done (like if he has done say the stuff in Spivak).

The other thing will be that as a general rule, when you learn a new subject, you will have to do whatever it takes to fill in the gaps, so if he has the attitude where he will just fill the gaps as he goes, then he will probably get through the book.

Ultimately this is all just speculation and the best way to find out is to just get him to open the book up and take a look. There really is no better way IMO than doing that: he should know within a short time if he is ready or not.

Does he have a copy of the book or can he get a copy of the book for free for a short time?

 

[GoutamTmv]

Hmm, I see. Well both of us have the e-book actually. He's gone through the book (not worked through it). He feels the need to master ODE's before this, and for that he wants a quick and dirty tutorial, just enough to get him through.

 

[chiro]

I'm afraid I was taught DE's with internal lecture notes and not by a textbook so I can't give you any advice on that front: you might want to do a search on these forums for recommended books for DE's if someone doesn't respond for a while.

Alternatively, go to the DE forum and start a thread there asking for book or other resource recommendations.