--- product_id: 14033858 title: "Calculus of Variations (Dover Books on Mathematics)" price: "$29.62" currency: USD in_stock: true reviews_count: 13 url: https://www.desertcart.us/products/14033858-calculus-of-variations-dover-books-on-mathematics store_origin: US region: United States of America --- # Calculus of Variations (Dover Books on Mathematics) **Price:** $29.62 **Availability:** ✅ In Stock ## Quick Answers - **What is this?** Calculus of Variations (Dover Books on Mathematics) - **How much does it cost?** $29.62 with free shipping - **Is it available?** Yes, in stock and ready to ship - **Where can I buy it?** [www.desertcart.us](https://www.desertcart.us/products/14033858-calculus-of-variations-dover-books-on-mathematics) ## Best For - Customers looking for quality international products ## Why This Product - Free international shipping included - Worldwide delivery with tracking - 15-day hassle-free returns ## Description Based on a series of lectures given by I. M. Gelfand at Moscow State University, this book actually goes considerably beyond the material presented in the lectures. The aim is to give a treatment of the elements of the calculus of variations in a form both easily understandable and sufficiently modern. Considerable attention is devoted to physical applications of variational methods, e.g., canonical equations, variational principles of mechanics, and conservation laws. The reader who merely wishes to become familiar with the most basic concepts and methods of the calculus of variations need only study the first chapter. Students wishing a more extensive treatment, however, will find the first six chapters comprise a complete university-level course in the subject, including the theory of fields and sufficient conditions for weak and strong extrema. Chapter 7 considers the application of variational methods to the study of systems with infinite degrees of freedom, and Chapter 8 deals with direct methods in the calculus of variations. The problems following each chapter were made specially for this English-language edition, and many of them comment further on corresponding parts of the text. Two appendices and suggestions for supplementary reading round out the text. Substantially revised and corrected by the translator, this inexpensive new edition will be welcomed by advanced undergraduate and graduate students of mathematics and physics. Review: Wonderful book, but could use some modern context. - 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. Review: A Rigorous Introduction - 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. ## Technical Specifications | Specification | Value | |---------------|-------| | Best Sellers Rank | #223,193 in Books ( See Top 100 in Books ) #68 in Mathematical Physics (Books) #125 in Calculus (Books) #426 in Applied Mathematics (Books) | | Customer Reviews | 4.5 out of 5 stars 219 Reviews | ## Images ![Calculus of Variations (Dover Books on Mathematics) - Image 1](https://m.media-amazon.com/images/I/7159E-oLxML.jpg) ## Customer Reviews ### ⭐⭐⭐⭐⭐ Wonderful book, but could use some modern context. *by B***J on July 27, 2014* 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. ### ⭐⭐⭐⭐⭐ A Rigorous Introduction *by C***N on October 18, 2024* 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. ### ⭐⭐⭐⭐⭐ Another Excellent Book! *by J***O on June 3, 2024* 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. --- ## Why Shop on Desertcart? - 🛒 **Trusted by 1.3+ Million Shoppers** — Serving international shoppers since 2016 - 🌍 **Shop Globally** — Access 737+ million products across 21 categories - 💰 **No Hidden Fees** — All customs, duties, and taxes included in the price - 🔄 **15-Day Free Returns** — Hassle-free returns (30 days for PRO members) - 🔒 **Secure Payments** — Trusted payment options with buyer protection - ⭐ **TrustPilot Rated 4.5/5** — Based on 8,000+ happy customer reviews **Shop now:** [https://www.desertcart.us/products/14033858-calculus-of-variations-dover-books-on-mathematics](https://www.desertcart.us/products/14033858-calculus-of-variations-dover-books-on-mathematics) --- *Product available on Desertcart United States of America* *Store origin: US* *Last updated: 2026-05-17*