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Title: Calculus of Variations by S. V. Fomin, I. M. Gelfand ISBN: 0-486-41448-5 Publisher: Dover Pubns Pub. Date: 16 October, 2000 Format: Paperback Volumes: 1 List Price(USD): $9.95 |
Average Customer Rating: 5 (5 reviews)
Rating: 5
Summary: Clear but technical
Comment: 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!).
Rating: 5
Summary: The best "introductory" book in Variational Calculus.
Comment: Readable books on Calculus of Variations are hard to come by, if not non-existent. This is one of the clearest and most readable and self-contained books in the topic. I used it in a fourth year course at Simon Fraser University, BC, Canada. This is an introductory book meant for undergraduates and it is very well suited for this level. I strongly recommend that all serious students in Physics, Chemistry, engineering, and computing science to take a serious look at the book as a starting point in studying this most underated and relevant topic as a necessary mathematical foundation. Virtually all fundamental laws of Physics, Chemistry, and Engineering have their origins from some form of variational prinicples. If anyone is interested in pursuing this topic, this should definitely be the first book one should read. The student should be equipped with at least one introductory course in Real Ananlysis in order to start studying Variational Calculus. Otherwise, the readable may not find this book readable. Just a practical (cook-book) style applied mathematics course in Calculus and Differential Equations is inadequate as preparation to study this topic. I most sincerely congratulate the author in having done such a superbly well organized job in writing such a highly readable book in this challenging and important topic.
Rating: 5
Summary: A great book by a great mathematician
Comment: 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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Title: Calculus of Variations by Robert Weinstock ISBN: 0486630692 Publisher: Dover Pubns Pub. Date: 01 June, 1974 List Price(USD): $14.95 |
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Title: Elements of the Theory of Functions and Functional Analysis by A. N. Kolmogorov, S. V. Fomin ISBN: 0486406830 Publisher: Dover Pubns Pub. Date: 17 February, 1999 List Price(USD): $12.95 |
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Title: Tensors, Differential Forms, and Variational Principles by David Lovelock, Hanno Rund ISBN: 0486658406 Publisher: Dover Pubns Pub. Date: 01 April, 1989 List Price(USD): $15.95 |
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Title: Introductory Real Analysis by A. N. Kolmogorov, S. V. Fomin ISBN: 0486612260 Publisher: Dover Pubns Pub. Date: 01 June, 1975 List Price(USD): $15.95 |
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Title: Calculus of Variations with Applications by George M. Ewing ISBN: 0486648567 Publisher: Dover Pubns Pub. Date: 01 April, 1985 List Price(USD): $15.95 |
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