Customer Reviews

Calculus of Variations (Dover Books on Mathematics)

5 star:		(12)
4 star:		(1)
3 star:		(1)
2 star:		(2)
1 star:		(0)

 

 

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.

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!

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!).

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.

Ok, not everyone needs to (or wants to) know calculus of variations. But if you are among the ones who, this is a great book to get started with (assuming you are in grad school and have a decent handle on calculus and some basis in dealing with differential equations). The text is clear and concise, and the financial investment is minimal. A good buy!

This book is intended primarily for graduate students with math background who wish to expand their applied math skills. Originally a Russian textbook, it offers an excellent overview of the theoretical background for the field without real heavy mathematics. All that is required is knowledge of calculus and a little ODE/PDE. Many classical examples, has an introduction to applications such as analytical mechanics, optimal control theory and approximate solution methods. The last edition I am aware of is pretty old, so this book should be tough to come by. A new edition would be welcome, with more examples and other applications.

As a physicist I want to find a book to refresh my memory on theoretical mechanics. I came across this one, and after reading its first 4 chapters in continuation, I kow I don't need any other book. What a treat! Written by a past master, the book costs you next to nothing; yet as it's written by sure hand, it hasn't slightest pretention, just plain and insightful, natural and smoth flow, leads you almost effortlessly fowward. Even though I learned the subject before, I don't know of or even imagine a better exposition. Wow, I started to love Russian mathematicians.

This book is really easy to get into. The first chapter on its own is worth the purchase price. After thumbing through that, I was in a position to start solving interesting problems. I was up and running with the basics within a day or so. Other books on the Calculus of Variations are a lot harder to get into and much more difficult to readily apply to problem solving.

Other books that present variational principles generally do it formally in terms of Frechet and Gateux derivatives on Banach spaces, whereas here, the approach is a little bit more ad hoc. The former approach can be heavy going for people who aren't comfortable with functional analysis and even then, actually solving specific problems can be headache. Fomin and Gelfand on the other hand demand very few prerequisites from their readers.

My acquintance with the book starts with a course in
calculus of variations in Israel Institute of Technology - Technion.
I recommend this book as a prepration for the advanced
methods in chapter 8 of Tensors Differential Forms and Variational Principles - David Lovelock and Hanno Rund. Anyone who is about to study a course in General Relativity should take a year or leisure two years and read both books. I also recommend this book to anyone who deals with
shape matching, signal processing and image processing.

First off, the content of this book is top-notch. Calculus of Variations comes across as slightly magical when you first encounter it, but this book lucidly explains in thorough detail how and why you can extend calculus to functions of functions.

That said, the binding of this book is really terrible. The cover--which is glued on--fell off after I opened the book 4 times! That is unacceptable, even for a book as inexpensive as this. The printing quality also isn't great, and some glyphs are difficult to discern, but it's not a huge deal compared to the cover falling off. Usually Dover books are better than that.