Calculus of Variations
April 14, 2011 by Actaphysica
Filed under Mathematical Physics Book Reviews
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Another great Silverman translation from the russian,
I used this book for a first year grad course in the calculus of variations some years ago. I found the book to be clear and pretty readable. I found the problem sets to be quite workable and covered the material well. I liked the fact that there were answers to many of them. The book is more rigourous than the treatments of this subjects found in math methods books like arfken but it is not highly abstract. (a style found in many math books at this level, and more difficult for me, not a professional mathematician, but a scientist) In fact I have found this quality to be a characteristic of most of the russian applied mathematics books translated by Richard Silverman, many of which are now published by Dover. This practical, clear, and rigourous approach of these books is excellent and I think almost all of these books on Dover have found their way onto my shelves.
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A great book by a great mathematician,
Gelfand was one of the leaders of the great school of mathematics which, somehow, thrived in Soviet Union. I used uncountable times the copy of our library, as the original English edition, in the excellent translation of R. Silvermann, became very hard to find. I put it in the top of the list of books I wanted to buy. Now Dover put it into their catalogue. Great choice. I already ordered my copy!
This is the best book on the Calculus of Variations. It contains, for instance, a wonderful treatment of Noether’s theorem, hardly to be surpassed. The Hamilton-Jacobi equation is also treated with brilliance and clarity. Gelfand (and Fomin!) developed a style in which the precision of the mathematics does not interfere with the general panorama. The applications are very well selected and perfectly illustrate the theory. A great book, a great mathematician who can write, a great translator, by less than 10 bucks!
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Clear but technical,
This book, of which I studied the first four chapters for an independent study course (I’m a senior undergrad) are very clear, very full, but beware it is mathematics and it is technical.
To appriciate the material you really should have a year of “advanced calculus” also called “intro. real analysis” at some places. This means the formalities of limits, continuity, derivatives, integration and series. This will prepare you to understand and work through the proofs in the text.
The problems are nice since they are varied (computational, physics, and proofs) and they do come with many answers and some hints, but you might find that having a mechanics book at your side motivates some of the problems.
Work hard, be thorough and there’s a lot of important ideas in this text, with chapter 4 being especially relevant to physicists (lots of mechanics and conservation theorems!).
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