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Science
Author: Hans Sagan
ISBN: 0486673669
Subcategory: Mathematics
Pages 480 pages
Publisher Dover Publications; Revised ed. edition (December 21, 1992)
Language English
Category: Science
Rating: 4.7
Votes: 681
ePUB size: 1985 kb
FB2 size: 1906 kb
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eBook Introduction to the Calculus of Variations (Dover Books on Mathematics) download

by Hans Sagan


Series: Dover Books on Mathematics. Paperback: 480 pages I've got a couple of texts on Calculus of Variations. The topic is not easy. Sagen's book is the clearest text on the matter that I've encountered.

Series: Dover Books on Mathematics. Paperback: 480 pages. I've got a couple of texts on Calculus of Variations.

The book is less formal than Sagan's book Introduction to the Calculus of Variations . If you are a scientist or an engineer, you may want to consider Elsgolc's Calculus of Variations (Dover Books on Mathematics) and Weinstock's books first and then Fox's book.

The book is less formal than Sagan's book Introduction to the Calculus of Variations (Dover Books on Mathematics) and Gelfand and Fomin's Calculus of Variations (Dover Books on Mathematics) but more rigorous than Weinstock's Calculus of Variations: with Applications to Physics and Engineering.

Introduction to the Calculus of Variations (Dover Books on Mathematics). However, this is not the right book to learn calculus of variations; I would have preferred a different title such as & to Optimization Problems' to make its content more obvious. Since the books selects several topics to present, one can hardly get a global picture for the traditional material of calculus of variations. Although the author says that the classics on the topic show their age, with all my apologies to him, I do actually prefer them.

This book, which includes many strategically placed problems and over 400 exercises, is directed to advanced undergraduate and graduate students with a. .The calculus of variations is a mathematical discipline that may best. Invariance of the eulerlagrange.

This book, which includes many strategically placed problems and over 400 exercises, is directed to advanced undergraduate and graduate students with a background in advanced calculus and intermediate differential equations, and is adaptable to either a one- or two-semester course on the subject.

American Mathematical Monthly The purpose of this text is to lay a broad foundation for an understanding of the problems of the calculus of variations and its many methods and techniques, and to prepare readers for the study of modern optimal control theory. The treatment is limited to a thorough discussion of single-integral problems in one or more unknown functions, where the integral is employed in the riemannian sense. The first three chapters deal with variational problems without constraints.

Start by marking Introduction to the Calculus of Variations (Dover Books on Mathematics) as Want to Read . Published November 1st 2012 by Dover Publications (first published December 21st 1992).

Start by marking Introduction to the Calculus of Variations (Dover Books on Mathematics) as Want to Read: Want to Read savin. ant to Read. Introduction to the Calculus of Variations.

Электронная книга "Introduction to the Calculus of Variations", Hans Sagan

Электронная книга "Introduction to the Calculus of Variations", Hans Sagan. Эту книгу можно прочитать в Google Play Книгах на компьютере, а также на устройствах Android и iOS. Выделяйте текст, добавляйте закладки и делайте заметки, скачав книгу "Introduction to the Calculus of Variations" для чтения в офлайн-режиме.

Автор: Sagan, Hans Название: Introduction to the Calculus of Variations ISBN: 0486673669 ISBN-13 . Описание: This book by Robert Weinstock was written to fill the need for a basic introduction to the calculus of variations

Описание: This book by Robert Weinstock was written to fill the need for a basic introduction to the calculus of variations. Simply and easily written, with an emphasis on the applications of this calculus, it has long been a standard reference of physicists, engineers, and applied mathematicians. The author begins slowly, introducing the reader to the calculus of variations, and supplying lists of essential formulae and derivations.

This clear, rigorous introduction to the calculus of variations covers applications to geometry, dynamics, and physics

This clear, rigorous introduction to the calculus of variations covers applications to geometry, dynamics, and physics. Focusing upon problems with one independent variable, the text connects the abstract theory to its use in concrete problems. This clear, rigorous introduction to the calculus of variations covers applications to geometry, dynamics, and physics. It offers a working knowledge of relevant techniques, plus an impetus for further study.

Hans Sagan: Introduction to the Calculus of Variations. 3. The Simplest Problem in the Calculus of Variations. 4. Necessary Conditions for Local Minima. Calculus of Variations. 5. Sufficient Conditions for the Simplest Problem. 6. Summary for the Simplest Problem. 7. Extensions and Generalizations.

". . . eminently suitable as a text for an introductory course: the style is pleasant; the prerequisites are kept to a minimum . . . and the paceof the development is appropriate for most students at the senior or first year graduate level." — American Mathematical MonthlyThe purpose of this text is to lay a broad foundation for an understanding of the problems of the calculus of variations andits many methods and techniques, and to prepare readers for the study of modern optimal control theory.The treatment is limited to a thorough discussion of single-integral problems in one or more unknown functions, where the integral is employed in the riemannian sense.The first three chapters deal with variational problems without constraints. Chapter 4 is a self-contained treatment of the homogeneous problem in the two-dimensional plane. In Chapter 5, the minimum principle of Pontryagin as it applies to optimal control problems of nonpredetermined duration, where the state variables satisfy an autonomous system of first-orderequations, is developed to the extent possible by classical means within the general framework of the Hamilton-Jacobi theory. Chapter 6 is devoted to a derivation of the multiplier rule for the problem of Mayer with fixed and variable endpoints and its application to the problem of Lagrange and the isoperimetric problem. In the last chapter, Legendre's necessary condition for a weak relative minimum and a sufficient condition for a weak relative minimum are derived withinthe framework of the theory of the second variation.This book, which includes many strategically placed problems and over 400 exercises, is directed to advanced undergraduate and graduate students with a background in advanced calculus and intermediate differential equations, and is adaptable to either a one- or two-semester course on the subject.
AnnyMars
There are several (if not many) well known texts in Calculus of Variations that have become classics. This text is one of them. And at the price of $7.95 (at the time of writing this review) the deal is so magnificent that you will regret it if you decide not to buy this book.

The book is less formal than Sagan's book Introduction to the Calculus of Variations (Dover Books on Mathematics) and Gelfand and Fomin's Calculus of Variations (Dover Books on Mathematics) but more rigorous than Weinstock's Calculus of Variations: with Applications to Physics and Engineering. Which one will become your favorite text (among all the popular texts on the topic) eventually it will be an issue of taste and your prior expectations. You may have to wrestle slightly with your ideas too (as I did). So I gave Sagan 4 stars only because I decided to rank some of the other texts first. (See next paragraph.)

If you are a scientist or an engineer, you may want to consider Elsgolc's Calculus of Variations (Dover Books on Mathematics) and Weinstock's books first and then Fox's book. Elsgolc's is a thin book that you can master fast. Then Weinstock's will show you lots of applications in science and engineering. These two books have you covered. You can certainly add Fox's for a different exposition if you like different perspectives. If you are a mathematician, you may want to consider Elsgolc's, Gelfand and Fomin's, Sagan's and, again if you wish, add Fox's book. So, in every case I would recommend Elsgolc's book as a first reading since it is thin and to the point. Then, according to your background and taste, you can select another text. Each has its own point of view, its own advantages and perhaps a few disadvantages.

Another reviewer reports `Some proofs skip a lot of steps. There are not a lot of examples. The typesetting is from 509 years ago, with equations and so on in the text not on a separate line. There are few diagrams.' Since this might create some false impressions, I would like to make some comments. The book skips as many steps in proofs as any other comparable book. It contains as many diagrams as any other comparable book. If these are to be considered problems, then all books on the topic have the same deficiencies. However, I do not really agree that they are problems. There is no need to pack a book with extra stuff which consequently creates a thick volume without providing many additional benefits. Regarding examples, it has enough to make the concepts clear. Adding too may of them, it becomes a collection-of-problems book, not a text. However, this is not the purpose of this book. And if one wants to see lots of applications, then Weinstock's book is the right choice since it was written with that goal in mind. Finally, regarding the typesetting. I think it is good. The fonts are not the Times Roman or the Computer Modern Roman (or some other comparable) fonts we might be used these days from computers, but they are good fonts. There is some math typed in-line but it is standard material that, according to the established rules of writing, we do not (and should not) place on a separate line. This is not a book written in the old-ex-Soviet style according to which (in order to save paper) everything was a long line.

Overall this is a really good book. And even if you decide to use another book as your primary reading for the topic you should still buy it and look at it. You will certainly benefit from it; I have no doubt.
Jode
This is a very good introductory text to the calculus of variations. I have also read similar texts by J. Gregory, C. Lin and by M. Denn, and I prefer this book. I am not a mathematician and I find this treatment more accessible than Denn, but more rigorous than Gregory & Lin. Previous reviews have noted that the author is not as explicit as he could be in all of the proofs and I concur, but as a result I find the level of rigor to be ideal for an introductory text. To disagree with a previous review I find the typesetting to be good and there are plenty of figures.
porosh
A nice book
Windworker
Good intro.
Brakora
I've got a couple of texts on Calculus of Variations. The topic is not easy. Sagen's book is the clearest text on the matter that I've encountered
JoJosho
Tried several times to get past the introductory pages but the author apparently enjoys wasting my time instead of getting to the point. Sorry I have better things to do.
Xanzay
I really couldn't get into this book. And I tried others and they weren't much better. This just must be a tough subject to write about. It comes across as an applied analysis text at the 1st year graduate level. the problems are sometimes hard to decode; once you know what he's asking they don't take much time. but it's tough to figure out what he's asking.

i'll keep looking.
I used this book as a compliment to a Theoretical Mechanics course. The section on Hamilton's equations is especially well written. Although probably more mathematically rigorous than anything I needed, the style is so silky smooth that anyone interested in mathematical physics will surely enjoy it. And it will be a surprise for many to find that the "proof" of equivalence between the Lagrangian and Hamiltonian formulations presented in most texts is half incomplete.
The book is complemented by good examples, clear notation and quite a number of graphics. Of course, proofs and arguments are absolutely rigorous, but well explained. This is a mathematics text, after all. I strongly recommend it, as well as any other of Sagan's books.