Calculus of Variations (Dover Books on Mathematics) by I. M. Gelfand (PDF)

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐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 is a good comprehensive introduction to the calculus of variations, specially considering its price. However, explanation lacks clearness at some points. Maybe the reader is supposed to have a stronger background in mathematics.

⭐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.

⭐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.

⭐One can never learn enough Calculus. This is a fantastic book if you like studying math. I strongly recommend it.

⭐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!

⭐* IntroductionI have chosen this book to further explore the topics around `Calculus of Variations’. Previously, I read and reviewed another book on this mathematical topic named `The Introduction to the Calculus of Variation’s’ that is also published by Dover. Just to make it clear this following book is not written by the author of the first book. This second volume is very well bound for a paperback, and its texts and graphics are both in black and white. Also of note is that the font sizes are adequate for those of us who may require glasses to read. The contents of this book are based on a Moscow state university series of courses, but with the original author’s permissions, these have been built upon and explored more deeply by the author who is also its translator into English. Dover, the publisher, has a tendency to reprint older, perfectly usable Math books at budget prices. This book has been read from May to July 2014.* A-level, H.N.D, Undergraduate, Graduate?The book is designed for advanced undergraduate (3rd year level Hons) and graduate level studies.* What is Calculus of Variations used for?The basic reasons for the study of this topic is to calculate finite -difference approximations to functions using linear methods with in areas arising in topics such as Analysis, Mechanics, Geometry that must apply technique’s using continuously differential functions that are within [a, b]. These can be accommodated several variables members in these approximations. Such calculations, such as to derive the length of a function. Or a where a derivative is zero, so finding a local maximum or minimum for example. These equations are different in that they can possess several variables. Unlike usual Mechanics having physical equivalents of up to the forth derivative, these can possess equations with many finite n – derivations.* Concisely, what topics are covered?The general equation that drives these calculations, and the whole book, is a generally applicable `Euler’s equation’. These can apply `Taylor series’ to generate the whole membership of a custom function series to be solved. This short and rather wonderful equation is reused and built upon several times to explore a whole raft of technique’s; some using symbolic notation upon matrices, many others applying symbolic techniques using partial differential equations in the usual level of mathematical short – hand to keep the book shorter than it would otherwise be. It’s the method that is being explored and is more important and not the specific equation. To explore the partial differential equations -that can be non-linear- the Euler equation is expanded to Hamilton – Jacobi equation representing canonical equation equivalents representing the characteristic system. This is further explored symbolically to apply to say for an example, 3-D (x, y, z, t) fields by using first derivative equivalents to map a finite number of particles to find where its reaches zero. As before, the classical mechanics equations exploring conservative systems in equilibrium with n – finite number of particles and kinetic and potential energies with observation of Lagrangian rules. Often present with multiple partial integrals. This level of mechanics I felt it became very helpfully explained, but not delving too deeply into another topic when exploring this component of variation topics.* SummaryI hope my humble summing up is not just a tissue of my butchered misunderstandings! But I have really enjoyed this book and have a better comprehension of these deeper calculus techniques that are written so much within concise mathematical symbolic notation. Its not at a super deep level, but its helpful along the ways to gain new comprehensions.

⭐I didn’t find this text very useful and it certainly is quite dated now. It’s very rigid and it’s description of terms and results are quite poor. You have to understand that there are honestly no great books out there on the topic of calculus of variations. The best I’ve seen is by Fox, that reads quite well and the analysis is decent and detailed. If you’re studying this topic, attend your lectures and don’t rely on a text solely.

⭐This book provides good coverage of the material but its commentary is awful. The second sentence is an example of this.People buy books such as this because they do not know the material. Obfuscating that material by adhering to opaque verbiage is unhelpful.It’s about time publishers rejected pretentious presentations in favour of lucid, transparent text.It would not be a mistake to buy this book but be prepared to work much harder that you ought to to understand it!

⭐Hardly something to love, but I do rate this as a must for anyone wanting to get into this subject. This is a fine example of the rigorous yet clear exposition developed by Soviet mathematicians of the 50s, 60s and beyond. There’s only one problem: I am somewhat familiar with this material yet still find it tough going despite a wonderful text and clever writers

⭐This is arguably the finest peice of work on the subject but a word of caution is required. This is a concise and difficult work on the subject and really should only be considered by postgraduates. I don’t think it’s fair to consider it as an introduction to this very powerful and underused subject.

Keywords

Free Download Calculus of Variations (Dover Books on Mathematics) in PDF format
Calculus of Variations (Dover Books on Mathematics) PDF Free Download
Download Calculus of Variations (Dover Books on Mathematics) PDF Free
Calculus of Variations (Dover Books on Mathematics) PDF Free Download
Download Calculus of Variations (Dover Books on Mathematics) PDF
Free Download Ebook Calculus of Variations (Dover Books on Mathematics)