Calculus of Variations (Dover Books on Mathematics) Dover Books on Mathematics Edition

This book takes a more rigorous approach to variational calculus than the books by Elsgolc or Weinstock. If you have some background in real analysis, this book will be much more readable. It is well written and to the point, so expect to study the pages slowly and intentionally. In such a small book there is plenty to be learned and at the price it is hard to turn down.

I'm reading this book as a refresher along with Weinstock's book on Calc of Variations, which I applied in an Advanced Classical Mech course using Goldstein's textbook many years ago. It's nice to once again review the beauty of the mathematics and it's applications.

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.

it's alright

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

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

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

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.