Calculus of Variations (Dover Books on Mathematics)

Concise and clearly written. Perfect for an introduction to the subject. Amazing value as well.

To eventually enhance my, presently, depth of knowledge/ skill of this subject.

Very good book on Calculus of Variations CofVComplements, Robert Wienstock's book on CofV.

It’s worth the price. Some prior knowledge on calculus and algebra is needed prior to studying this book.

Gelfand and Fomin wrote a wonderfully clear, rigorous, and concise introduction to the calculus of variations, and it requires little more than a calculus and analysis background (say, 1st or 2nd year math undergraduate) to understand much of the reasoning. Furthermore, the end-of-chapter problems are generally pretty straightforward to set up, and they often follow in-chapter examples, although the resulting algebra can be beastly.A word of advice for someone new to the calculus of variations: keep in mind that since this book is an older text, it lacks some modern context. For example, the variational derivative of a functional is just the Frechet derivative applied to the infinite-dimensional vector space of admissible variations. They use a norm on a Sobolev space without defining it as such. They make no mention of the Hamiltonian as the convex conjugate functional of the Lagrangian. If you're just looking to solve variational problems, you might be fine with this. On the other hand, if you're looking for more general insight, I think it would benefit you to first learn some basic functional analysis (e.g. Kreyszig, Luenberger) and then make it an exercise to match the concepts from this book to a more modern jargon.

I found this to be one of the more readable dover books translated from Russian. Author and translator have done a great job.

This book is in relation to the more interesting applications of the variations calculus at the integration theory.The arguments are traditionals and are directed around the more important contexts of this theory, let be the Euler equations or the extremal questions. It is a very useful text for the understanding the problems of superior difficulty or of more specific actuality.

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!

Las explicaciones que ofrece el libro son bastante claras, los ejemplos bien elegidos. El libro es muy formal pero no se centra en abstracciones innecesarias, eso sí, no es un tema básico, así que no es prudente esperar que los autores nos den el contenido como si de un tema elemental se tratase.

Book in good condition. It is worth to buy second hand books...(good for the environtment and for the ecanomy)

Excellent book, mathematically rigorous and asks to the reader a good background in mathematics (for instance, real analysis for a clear understand of proofs).

Il testo tratta i fondamenti del Calcolo delle Variazioni (CV) ed è scritto da due pezzi grossi della matematica russa, che, come noto, è rigorosa senza perdersi in un formalismo superfluo senza per questo essere ingenua e guardando sempre alle applicazioni (soprattutto fisiche). Infatti, nel caso di questo libro, vi è addirittura un capitolo in cui il CV si fonde con la Meccanica Analitica (principio di minima azione, trasformazioni canoniche, trasformata di Legendre, equazione di Hamilton-Jacobi, eccetera), inoltre, molto importante è la presenza di due capitoli sulle condizioni sufficienti di estremo (argomento molto delicato e spesso ignorato nelle trattazioni di base del CV, qui trattato in maniera estremamente rigorosa), tuttavia, in tale testo il CV è trattato in maniera piuttosto avanzata, pertanto lo sconsiglio a chi si accinge allo studio del CV per la prima volta, a costoro suggerisco prima di consultare i capitoli introduttivi sul CV presenti in alcuni testi di Meccanica Analitica o nelle appendici di testi di Complementi di Analisi Matematica o di Metodi Matematici della Fisica, oppure di cominciare col testo di Elsgolts https://www.amazon.it/Equazioni-differenziali-calcolo-delle-variazioni/dp/886473225X/ref=sr_1_2?ie=UTF8&qid=1516815159&sr=8-2&keywords=elsgoltsun po' più agevole di questo. In ogni caso questo libro rimane un riferimento fondamentale per chiunque si occupi di CV in maniera avanzata. Indicato soprattutto per fisici.

One of the best books that I have used on this subject. In fact, I use this book in my course as the main reference. I advice this book along with Elsgol's book on the subject for those who want to learn this subject (even as a self reading course). This book has very good Mathematical rigour and very simple to follow.