Looking for Calculus of Variations resources

[jackiefrost]

Hi,

Does anyone have any recommendations on an exceptional Calc of Variations text or other resource? The few I've been able to preview at amazon.com didn't impress me. Any recommendations would be appreciated.

jf

 

[robphy]

What specific features are you looking for?
I like reading Lanczos "The Variational Principles of Mechanics" http://books.google.com/books?id=ZWoYYr8wk2IC (which will help me motivate various concepts to my students).

 

[jackiefrost]

Thanks robphy.

I was just looking to go a little deeper than I've been exposed to through introductory Classical Mechanics. I've never just studied Calc of Var itself - just through other textbooks on physics and PDEs.

jf

 

[jackiefrost]

Hey - the book "The Variational Principles of Mechanics" looks exceptional! Read through the preview and reader reviews. Looks like just what I need - a change in perspective. I ordered it. Thanks again for the tip robphy.

jf

 

[Brian_C]

I believe that Dover has another book on the variational calculus. I can't remember the name of it offhand.

 

[Andy Resnick]

Maybe it's "Tensors, Differential Forms, and Variational Principles" By David Lovelock and Hanno Rund.

http://books.google.com/books?id=ikPQFqxcyfMC

 

[jackiefrost]

I believe that Dover has another book on the variational calculus. I can't remember the name of it offhand.

It's "Calculus of Variations" by I.M. Gelfand and S.V. Fomin. It's translated from Russian by Richard Silverman. I've only briefly read through the first few pages but it seems pretty good. I can't get my head out of that Cornelius Lanczos book, "The Variational Principles of Mechanics". That book is amazing!

[I wonder if there's an english translation of Lagrange's "Mécanique Analytique"?]

jf

 

[robphy]

It's "Calculus of Variations" by I.M. Gelfand and S.V. Fomin. It's translated from Russian by Richard Silverman. I've only briefly read through the first few pages but it seems pretty good. I can't get my head out of that Cornelius Lanczos book, "The Variational Principles of Mechanics". That book is amazing!

[I wonder if there's an english translation of Lagrange's "Mécanique Analytique"?]

jf

Glad you are enjoying Lanczos' book.

Concerning Lagrange
(http://books.google.com/books?id=HTEVAAAAQAAJ
http://books.google.com/books?id=MTEVAAAAQAAJ http://books.google.com/books?id=QDEVAAAAQAAJ )...
here is a translation...
https://www.amazon.com/gp/product/0792343492/?tag=pfamazon01-20
http://www.worldcat.org/oclc/35919397

 

[jackiefrost]

Thanks Robphy. I wish I knew French. The $300 price tag is prohibitive - especially coupled with the poor reviews concerning the errors it supposedly contains.

The Lanczos book is opening new vistas for me. I'm also gaining a much deeper appreciation for Lagrange's amazing insights. Looking forward to digging into Jacobi and Hamilton. I have some questions but I'll save them for a while. It seems some of my questions have been getting answered as I progress in that book or switch back and forth with Dare Wells' "Theory and Problems in Lagrangian Dynamics" (Schaums outline). Even Goldstein's text makes more sense now. I owe you a big one for that recommendation!

jf

 

[AEM]

The current Dover catalog lists 5 book on the Calculus of Variations. You can find them listed on their website: http://www.doverpublications.com

Variational Principles by B. L. Moiseiwitsch (available from Dover) is good as are the other books mentioned by previous posters.