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An Introduction to the Calculus of Variations (Dover Books on Mathematics) Paperback – 17 Mar 2003

4.7 out of 5 stars 3 customer reviews

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Product details

  • Paperback: 304 pages
  • Publisher: Dover Publications Inc.; New edition edition (17 Mar. 2003)
  • Language: English
  • ISBN-10: 0486654990
  • ISBN-13: 978-0486654997
  • Product Dimensions: 13.8 x 1.4 x 21.5 cm
  • Average Customer Review: 4.7 out of 5 stars  See all reviews (3 customer reviews)
  • Amazon Bestsellers Rank: 535,907 in Books (See Top 100 in Books)

Product Description

About the Author

Fox (deceased) was a broadcaster and reviewer. He was the host of "Jazz Today", a weekly British radio program.

Susan Fox, a licensed pediatric neurodevelopmental therapist, is director of the Pediatric Therapy Clinic in Seattle. Her guide for fathers of babies in their first year, Rookie Dad, is available from Pocket Books. Fox teaches workshops on child development at Microsoft, and trains early childhood educators, therapists, nurses, and physicians.


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Top Customer Reviews

Format: Paperback
Thorough, concise, enjoyable and CHEAP book on the Calculus of variations. One of the few mathematics books that is simultaneously rigorous and entertaining. Illustrated with many examples and applications, drawn from physics and engineering. The proofs are brisk, though there is enough there to guide you on your way to complete understanding. A DEFINITE read for any mathematician or scientist!
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By A Customer on 9 Sept. 2005
Format: Paperback
I agree with the other reviews on this book, it is well written and designed to give clarity and understanding to the subject. I bought "calculus of variations" by I.M Gelfand and S.V Fomin, another Dover publication, and i found it a little confusing in the way it introduces its concepts early in the text. However, the book by I.M Gelfand and S.V Fomin takes the "normed linear space" approach to the subject of variational calculus, which, can make definitions seem abstract. But if you buy this book and read it along side I.M Gelfand and S.V Fomin's book, it gives clarity and then all is well in the world of variational calculus!
I would suggest that you buy "calculus or variations" by I.M Gelfand and S.V Fomin(or another text which you think is suitable) and this text together, since, as stated in previous reviews of this book, there is not a good amount of exercises and problems to get good practice.(but there are enough to totally understand the subject, its just if you need to practice of problem solving).
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By ab..c VINE VOICE on 10 July 2005
Format: Paperback Verified Purchase
* Physically

The book is printed on standard quality, paperback paper with a sturdy binding. The text and graphics are in B&W and have a nice typeface and font-size. This is for those of use that require specs to read. I have read this book April - May 2014.

* Target audience

The book is described as a third - year, hons student topic, so be aware it could be requiring a body of study time to absorb these areas. The author admits that with the body of other topics at this level, this important topic can be pushed aside and not all students undertake this areas.

* Areas studied

Do you recall the mathematical techniques of using the first derivative to find the stationary point of a curve, f'(a)=0. And using the 2nd derivative to classify the curve? This is a body of work that uses many derivatives above the first and second to discover the properties of this curve in areas such as in dynamics. This can be imagined as a Taylor series of these functions. If you take these types of curve that use analytical techniques to work with small and large changes, called variability responses, then use a standard equation that is independent of the equation submitted to it. This is called the 'Eulerian Characteristic Equation' . This equation is the backbone of many pages within this book.

The book has the usual concise mathematical format at this level of an equation used to explain not being explicit but of the form @F(x, y, y'). This being for example, any equation with an x component, a y component, and a single derivative in prime format. The book tells you early , 'We limit ourselves to a summing without proof...(page 74, item 3.9), and such formula such as on page 63 item (1).
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Most Helpful Customer Reviews on Amazon.com (beta)

Amazon.com: HASH(0x8d036978) out of 5 stars 5 reviews
24 of 25 people found the following review helpful
HASH(0x8d275dc8) out of 5 stars Geared for classical mechanics 20 Nov. 2000
By Ken Braithwaite - Published on Amazon.com
Format: Paperback
Good books on the calculus of variations are not thick on the ground, and this one is pretty good. It is organised around explicating Hamiltonian mechanics, but with mathematical rigor and clarity. Why not 5 stars then? 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.
If your interest is in physics this is a FAR better book to choose than Sagan.
19 of 19 people found the following review helpful
HASH(0x8d275318) out of 5 stars Excellent Book on the Calculus of Variations 14 Jun. 1999
By A Customer - Published on Amazon.com
Format: Paperback
Thorough, concise, enjoyable and CHEAP book on the Calculus of variations. One of the few mathematics books that is simultaneously rigorous and entertaining. Illustrated with many examples and applications, drawn from physics and engineering. The proofs are brisk, though there is enough there to guide you on your way to complete understanding. A DEFINITE read for any mathematician or scientist!
8 of 8 people found the following review helpful
HASH(0x8d8f9780) out of 5 stars One of the classics for Calculus of Variations 10 May 2013
By ScienceThinker - Published on Amazon.com
Format: Paperback Verified Purchase
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.
9 of 9 people found the following review helpful
HASH(0x8d2743b4) out of 5 stars Good exposition, thorough, and cheap 17 Jun. 2011
By J. Pacheco - Published on Amazon.com
Format: Paperback Verified Purchase
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.
3 of 4 people found the following review helpful
HASH(0x8cfc3fe4) out of 5 stars A must-read for anybody interested in practical math! 18 Mar. 2012
By Path Integral Master - Published on Amazon.com
Format: Paperback
Have you ever wondered about the shape of a hanging string? Or the surface of water in a spinning bucket? Or why E=mc^2? With this wonderful gem of a book, practical questions like these are answered in enjoyable prose and with a deluge of interesting examples. This book explains the calculus of variations, a theory coming from certain problems in integral calculus( involving minimizing certain expressions involving integrals) that turns out to have many practical applications. Charles Fox starts with simple considerations(deriving-with calculus- the result that a line gives the shortest distance between two points) and builds up to complicated considerations, like relativity and the least-action principle, using a vast variety of interesting practical examples to both illustrate the theory and show why it is useful. With a fantastic writing style, interesting topics and a vast class of practical problems, this book is a must-read for any person who wants to solve practical engineering and scientific problems!
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