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Customer Reviews (12)

Quite clear, straight-forward explanations
I like this book, certainly what I have read of it. I'm now digging around near page 75, and it struck me that for the first time I really "get it" - In particular, this was about the use of the Legendre transform. The authors start with a very gentle introduction of it, and then, while things become more abstract, the text never jumps too far and never leaves the reader too much in puzzling. It's ought to be studied though, and it's not "easy".

Calculus of Variations
This book is a "must have" for those wanting to study topics in functional analysis.

Great math book doesn't have to be expensive and pretentious.
As a physicist I want to find a book to refresh my memory on theoretical mechanics. I came across this one, and after reading its first 4 chapters in continuation, I kow I don't need any other book. What a treat! Written by a past master, the book costs you next to nothing; yet as it's written by sure hand, it hasn't slightest pretention, just plain and insightful, natural and smoth flow, leads you almost effortlessly fowward. Even though I learned the subject before, I don't know of or even imagine a better exposition. Wow, I started to love Russian mathematicians.

Review of Calculus of Variations
This is a classic text and I would recommend it to graduate students and mathematicians who need a review of the subject.Great for us physicists as well.

Great value...
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! ... Read more

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Customer Reviews (2)

Geared for classical mechanics
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.

Excellent Book on the Calculus of Variations
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 fromphysics and engineering. The proofs are brisk, though there is enough thereto guide you on your way to complete understanding. A DEFINITE read for anymathematician or scientist! ... Read more

Product Description
In this second English edition of Carathéodory's famous work (originally published in German), the two volumes of the first edition have been combined into one (with a combination of the two indexes into a single index). There is a deep and fundamental relationship between the differential equations that occur in the calculus of variations and partial differential equations of the first order: in particular, to each such partial differential equation there correspond variational problems. This basic fact forms the rationale for Carathéodory's masterpiece. Includes a Guide to the Literature and an Index.From the Preface: "The book consists of two parts. In the first part, I have made an attempt to simplify the presentation of the theory of partial differential equations to the first order so that its study will require little time and also be accessible to the average student of mathematics ... The second part, which contains the Calculus of Variations, can also be read independently if one refers back to earlier sections in Part I ... I have never lost sight of the fact that the Calculus of Variations, as it is presented in Part II, should above all be a servant of Mechanics. Therefore, I have in particular prepared everything from the very outset for treatment in multidimensional spaces." ... Read more

Customer Reviews (1)

supreme
I have followed the Analytical Mechanics class in my gradute school from this book.
It is supreme and Goldsteins book only is a cheap make up in compared to this book.
Thank you for folowing this book Dr.Yurdahan Guler, at that time
I used to think that you were making our life miserable,but now
I think it was the right thing to do to follow a book written by a true genius. ... Read more

Book Description

This book is a new edition of the authors previous book entitled Direct Methods in the Calculus of Variations, 1989. It is devoted to the study of vectorial problems in the calculus of variations. The book has been updated significantly and a number of additional examples have been included. The book will appeal researchers and graduate students in mathematics and engineering.

Book Description

Customer Reviews (4)

Good but could be better
I really like ("plain") books that are written in the definition, lemma, proposition, theorem, and examples style. Sagan does enunciate propositions, theorems, etc. but he does that after giving proofs for the things he will state latter. I simple don't like this style. Another point that I really dislike in Sagan book is the notation. He doen't change the notation, for instance, when he talks about a function y and the y coordinate. This is a little bit boring. Moreover, the exercises aren't stated clearly (I always have to look at the text, many pages before the exercise, to know what the exercise demands to be done). Besides this the book is very complete. A good but that could be better.

Wonderful
This book is neither too naive nor too brief, still I was able to read more than 80 pages in one day, simply because it is written very clearly. An excellent introduction in Calculus of variations, very concise and very clear. Some context is devoted to control theory, which can be considered as a generalization of calculus of variations.
The part on field embedding and Hilbert invariant integral is perfectly wriiten, actually the best that I have ever encountered.

Clear and well written
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.

Very nice book on variational calculus
This book is a more thorough treatment of the calculus of variations than some of the other books on the subject that you could buy.It's bit more expensive...I especially reccomend this book if you like Sagan's other book "Boundary and Eigenvalue Problems in Mathematical Physics". If you like his style of writing, and I do, he again shows nice touch ofexplaining the material in writing and then with examples.A good bookwith a nicely written and more thorough treatment of the subject (unlessyou want a full price text that is).. ... Read more

Customer Reviews (1)

'Must read' for Theoretical Physicists
The Preface to a book can sometimes say a lot about the book itself...and this one took me by storm. I am one of the many who struggle to find Physical connections to mathematical equations..partly due to my lack of insight, and partly because I have been trained as a Physicist and I fail to understand the subtle aspects of Pure Mathematics vis a vis nature..until I found this book which instilled the idea that Mathematics is the mother of all sciences..I think I am in a better position to enjoy Physics now ! ... Read more

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Customer Reviews (1)

Calculus of Variations by Lev D. Elsgolc
The reader is gently introduced to the problems solved by the Calculus of Variations and each solution is given in sufficient detail. ... Read more

Book Description

Customer Reviews (5)

Calculus of Variations
The book is very good

Will never collect dust
The importance of variational calculus cannot be overstated, as it now is being applied to myriads of different areas, these going way beyond the routine applications in physics and engineering. Indeed, it has been found to be useful in economics, network engineering, financial modeling, computational radiology, and in the new field of constraint programming. This book is now a classic, and has been the standard reference and textbook for variational calculus since its first date of publication. There have been many excellent books on variational calculus that have appeared since this one first did, but they do not provide the needed intuition in learning the subject. The clarity of the author's presentation in this book is outstanding, and, most importantly, he assigns challenging exercises to test the readers understanding of the subject. When the book was first published, computers were not being used as they are today, and the current strategy in solving variational problems is usually to use some sort of numerical software packages. In addition, the use of symbolic programming languages, such as Mathematica and Maple, have made the derivations in variational calculus almost trivial, and this is a promising trend since it allows the user to concentrate more on the concepts involved in applying it. Also, very efficient numerical routines exist in Fortran, C, and C++ that are designed and optimized for variational problems.

All of the beginning material on the calculus of variations is covered in the book, and its application to Lagrangian and Hamiltonian mechanics, elasticity, quantum mechanics, and electrostatics. Isoperimetric problems are treated, the vibrating string and membrane, and the Sturm-Liouville system and its origin as an eigenvalue problem in variational calculus. In the latter, the reader can see the origing of some of special function solutions, such as the Bessel functions and Laguerre polynomials. The reading of this book will amply prepare the reader for applying it to problems in quantum field theory, economics, radiology, financial engineering, logistics, optimization theory, computational geometry, control theory, and the theory of evolutionary strategies. In addition, the book will allow the reader to move on to more advanced areas of mathematics, such as the theory of minimal surfaces, Morse theory, and geometric measure theory.

A standard work on variational calculus
This is the ultimate applications of variations book. The book develops the variational calculus in a pretty succinct manner and then surveys areas of application such as vibrating membranes, optics, hamiltonian mechanics, elasticity theory, quantum mechanics and electrostatics. The book has a pretty reasonable amount of problems which tend to be fairly soluble and
have the feel of an engineer's book rather than a mathematicians text. Weinstock was a Stanford math professor,so the book is

fairly rigorous but the emphasis is not on proofs. Many books on this subject require an advanced knowledge of analysis including such things as the Lebesgue integral etcetera. This is not required here this is a book that a physicist or engineer will be entirely comfortable with. There are other books that introduce the fundamentals in a shorter space Gelfand and Fomin
being my favorite, but this book covers the basics from a pretty practical perspective and includes more applications than any other calculus of variations book I know of.

The book is good DESPITE its claims for mathematical rigour
Contary to the previous reviewer I generally do not care much ifpresentation is rigorous or not.It is much more important that the book can be understood easily, contains a lot of thoroughly selected exampleswhich illustrate general principles. In fact, the book is written in a wayallowing one to understand what isthe most essential in the subject evenif all proofs were omitted. Such a feature is a fingerprint of a classic.

I strongly recommend it for a standard course on variational calculus.

A brief , but wondeful textbook in Calculus of Variations
When I firstly see this book, I don't take it seriously for its length. But after I read it, I find it's an appropriate textbook for its brevity,rigor in mathematics,and a lot of examples helping you toillustrate its application. I think the most valuable point of this book isthe author's rigor in mathematics,which are often neglected by mostphysicists.Secondly is its master use of deduction. I recommend itheartedly. ... Read more

Book Description
The calculus of variations has a long history of interaction with other branches of mathematics, such as geometry and differential equations, and with physics, particularly mechanics. More recently, the calculus of variations has found applications in other fields such as economics and electrical engineering. Much of the mathematics underlying control theory, for instance, can be regarded as part of the calculus of variations.This book is an introductory account of the calculus of variations suitable for advanced undergraduate and graduate students of mathematics, physics, or engineering. The mathematical background assumed of the reader is a course in multivariable calculus, and some familiarity with the elements of real analysis and ordinary differential equations. The book focuses on variational problems that involve one independent variable. The fixed endpoint problem and problems with constraints are discussed in detail. In addition, more advanced topics such as the inverse problem, eigenvalue problems, separability conditions for the Hamilton-Jacobi equation, and Noether's theorem are discussed. The text contains numerous examples to illustrate key concepts along with problems to help the student consolidate the material. The book can be used as a textbook for a one semester course on the calculus of variations, or as a book to supplement a course on applied mathematics or classical mechanics. Bruce van Brunt is Senior Lecturer at Massey University, New Zealand. He is the author of The Lebesgue-Stieltjes Integral, with Michael Carter, and has been teaching the calculus of variations to undergraduate and graduate students for several years. ... Read more

Customer Reviews (1)

A delightful read.
Unlike so many math texts which seem to be compiled by computers, this book is very personable, interesting, and easily digested.If you are a senior math undergraduate, or a graduate student in science, this is great bedtime reading; a younger (strong) student who knows calculus would also profit from this book.Books of this quality remind math students how math can be so enjoyable.

Having said that, it is not intended to be an advanced reference.But if you are a researcher, you know that. ... Read more

Book Description

Malliavin calculus provides an infinite-dimensional differential calculus in the context of continuous paths stochastic processes. The calculus includes formulae of integration by parts and Sobolev spaces of differentiable functions defined on a probability space. This new book, demonstrating the relevance of Malliavin calculus for Mathematical Finance, starts with an exposition from scratch of this theory. Greeks (price sensitivities) are reinterpreted in terms of Malliavin calculus. Integration by parts formulae provide stable Monte Carlo schemes for numerical valuation of digital options. Finite-dimensional projections of infinite-dimensional Sobolev spaces lead to Monte Carlo computations of conditional expectations useful for computing American options. The discretization error of the Euler scheme for a stochastic differential equation is expressed as a generalized Watanabe distribution on the Wiener space. Insider information is expressed as an infinite-dimensional drift. The last chapter gives an introduction to the same objects in the context of jump processes where incomplete markets appear.

Book Description
This textbook on the calculus of variations leads the reader from the basics to modern aspects of the theory. One-dimensional problems and the classical issues such as Euler-Lagrange equations are treated, as are Noether's theorem, Hamilton-Jacobi theory, and in particular geodesic lines, thereby developing some important geometric and topological aspects. The basic ideas of optimal control theory are also given. The second part of the book deals with multiple integrals. After a review of Lebesgue integration, Banach and Hilbert space theory and Sobolev spaces (with complete and detailed proofs), there is a treatment of the direct methods and the fundamental lower semicontinuity theorems. Subsequent chapters introduce the basic concepts of the modern calculus of variations, namely relaxation, Gamma convergence, bifurcation theory and minimax methods based on the Palais-Smale condition. The prerequisites are knowledge of the basic results from calculus of one and several variables. After having studied this book, the reader will be well equipped to read research papers in the calculus of variations. ... Read more

Book Description

Customer Reviews (2)

Admirable, but hard to learn from
This book has one previous Amazon customer review, with 5 stars and a glowing review. I do not dispute that reviewer's assessment; rather I'll observe that his familiarity with calculus of variations is much deeper than mine. I find this book almost impossible to learn from, although there is much in it that I would like to learn. But I confess that I have difficulty with calculus of variations, and always have had.

For me, calculus of variations breaks neatly into two eras, before Weierstrass and after Weierstrass. Before Weierstrass there was no rigor in the subject, and practitioners from Bernoulli to Lagrange used whatever methods they could devise to solve particular problems, or classes of problems, that attracted their attention and that seemed to be tractable. Weierstrass turned the subject into a rigorous one, and was followed by a number of creative theoreticians, some of whom could also solve practical problems: Bolza, Hilbert, Bliss, McShane (whom I knew) and various others. They created mathematical theory that would have been incomprehensible to Euler, but which eliminates the slop in the subject.

When I look for literature on calculus of variations I seem to find the literature also divided into "before Weierstrass" and "after Weierstrass". I have no trouble with the "before Weierstrass" sort, but I would like to go further. And the trouble I have with this book is that despite the promise of a jacket blurb, it doesn't show how the subject developed from an intuitive art into rigorous mathematics; it determinedly sticks to the "modern" viewpoint. I note with amusement, for example, that Lagrange is mentioned only in one slightly pejorative paragraph on page 109, with no indication of how Lagrange actually solved variational problems.

So this book will sit in my personal collection of math books until I get tired of seeing it around and get rid of it (which is what happened to my copy of Bliss many years ago). Is there some text on calculus of variations that will permit a reader like me, with reasonable knowledge of measure theory, modern algebra and topology, and classical analysis, to learn how the calculus of variations has progressed in the last hundred years? This isn't it.

Very deep and detailed
I have had this gem of a book for ten years, and I'm still enjoying it. Actually, it turns out that the text itself was written some time ago, but don't let you be put off by that - this book is very scholarly and you really will be enlightened by it.

Now, where do you begin? Usually at University, I guess, this subject is treated in a way that makes most folks think that just about all "Calculus of Variations" problems can be solved with the Euler Lagrange equation, and from there on, you just have to solve the resulting differential equation. And I guess that's sometimes possible. But in the real world, sometimes you end up with that equation simply not working, and your problem is more messy and not expressible using "nice" functions. Now, this is where this book begins. We start by looking at "sufficient" and "necessary" conditions for solutions - and these are not the same things! This at least allows you to work out whether a solution is there, for goodness sake, before you waste time trying to find it.

Ewing does better in later chapters. He showcases a whole slew of problems which deserve special consideration, and this gets at times really exciting, covering all sorts of ideas about what we mean by optimum values for integrals, and how to specify systems of equations when one method doesn't really work too well.

One question which he digs into, which is very entertaining, is the problem of what an integral of a function really means. For example, we all know about the Riemann integral - the limit of a sum - but had you ever heard about the Weierstrass integral - or the Lebesgue integral?

Mr Ewing serves up these exotic and flavorsome new varieties in a most satisfactory fashion, with lots of examples to help.

The text never gets too far away from real problems. How easy that would have been! This book is so amazingly practical and also deeply committed to a really thorough treatment. He also gives excellent commentary on the history of this subject.

Overall I would say that this book is not one which belongs on the shelf with the numerical methods books, or the operational research section (thats what numerical optimisation is called over here in Britain), but I would get this now anyway before it goes out of print (if Dover are so crazy as to do that). ... Read more

Customer Reviews (8)

WRONG EDITION, NO RESPONSE FROM SELLER
They sent me the wrong edition of a solutions manuel I needed for a collge course, then when I attempted to contact the seller, they never returned my calls/e-mails. Would not do business with them again.

BEFORE YOU BUY...!!!
If you're buying this manual then chances are that you aren't stopping at Calculus III.This book DOES NOT include chapters beyond 12, so if you're seeking help in Calculus III, you won't find it here.

It's an okay solutin book.
Well you get solutions to all the odd numbers problems in the Book which is okay, but if you looking for even problems' sloutions This is not the book to spend money. Like most solution manuals, it do skip steps from time to time. Not the best book you can buy, but it does help you practice while you are alone and no one to help you with.

Beware!
It is a great addition to simply looking at the back of the book for the answers, and eases the learning process as you look through the problems. I would suggest that you get a math teacher to clarify any confusions you might have rather than rely entirely on this solutions manual because although it is helpful, I found it to be only a complement to the assistance of a human being.

There is one major flaw with this book. It does not contain solutions beyond chapter 12, so if you are planning to stop studying calculus midway, it is great. But who stops midway?!!! I am not sure where you can find the solutions manual for the rest of the book(perhaps it doesn't exist), but I caution you to buy this book thinking that it will give you all the answers(no pun intended).

It's worth it
The bottom line is, this book you will cut your study time down to just a few hours a week. Calculus is tough no matter how smart you are, and nothing that deals with calculus walks in baby steps. The reality is that the solutions in this book will make life a little easier for calc students.

This book covers both Calculus I and Calculus II from its respective text book. Some explanations are great, others are lacking. I found this book to be particularly useful for problems which require some "trick" that you would otherwise never know about. I used this book for both Calc I and II, and it helped me with every problem I faced. By my estimation, if you buy this book and it saves you a few headaches, it was probably worth it. ... Read more

Book Description
This is the most extensively visual book in the market—highlighted by hundreds of Mathematica and MATLAB generated figures throughout. It now contains a full chapter of material on matrices and eigenvalues up front. All of Multivariable Calculus has been rewritten with matrix notation.Chapter topics include infinite series, vectors and matrices, curves and surfaces in space, partial differentiation, multiple integrals, and vector calculus. ... Read more

Customer Reviews (3)

This is a Differential Equations solutions manual!
Despite other product information and reviews on this page about a calculus text this ISBN 0-13-047579-3 is for the student solutions manual for the Differential equations and boundary value problems computing and modeling 3rd edition by Edwards and Penney. As with many solutions manuals I have used before there are often steps that are skipped, but overall it is a useful book. It won't do your homework for you, but it will sure help you find some silly mistakes or clarify how to do a particular type of problemfaster than waiting to go to office hours.

Multivariable Calculus with (mention of) Matrices
I'm giving this book three stars not because it's not a good book, but rather because the introduction to the book is misleading (as well as the title). They mention calculus with matrices in a couple chapters is all, and it's stuff you can find in your Ordinary Differential Equations books-the Jacobian, there is no mention of the Wronskian though.
This is a good book to get if you took calculus BC (2.1) in high school and UNDERSTOOD it, and are looking for something to pick up on your own to learn more. As an undergrad student it could be a useful reference if you feel your calculus book was inadequate. If you're looking for matrix calculus (i.e. tensor analysis) get a book on tensor calculus or tensor analysis, otherwise this book would be a waste of your time and money.
Like I said, well written book, good examples and good hand waving proofs of many concepts are in this book. There are also historical facts which make for an interesting read.

Only has the answers to the odd numbered questions
This is the student solutions manual to the textbook: "Calculus, Early Transcendentals (6th Edition)"by C. Henry Edwards and David Penney.

Pearson Higher Education (Prentice Hall is one of their divisions) has an Instructor's Solutions Manualwhich has the answers to ALL of the problems in this book.

However, as of this writing, this Instructor's Manual is not available to the general public, nor are there any used copies floating around out there in the online used book markets.Pearson only sends this Manual out to college math departments.

The two separate Amazon listings for "Student Solutions Manual" and "Single Variable Calculus: Early Transcendentals, Sixth Edition, Student Soulutions Manual"are the same thing
... Read more

Book Description
This 2-volume treatise by two of the leading researchers and writers in the field, quickly established itself as a standard reference. It pays special attention to the historical aspects and the origins partly in applied problems - such as those of geometric optics - of parts of the theory. A variety of aids to the reader is provided, beginning with the detailed table of contents, and including an introduction to each chapter and each section and subsection, an overview of the relevant literature (in Volume II) besides the references in the Scholia to each chapter in the (historical) footnotes, and in the bibliography, and finally an index of the examples used through out the book. ... Read more

Book Description
This long-awaited book by two of the foremost researchers and writers in the field is the first part of a treatise that covers the subject in breadth and depth, paying special attention to the historical origins, partly in applications, e.g. from geometrical optics, of parts of the theory. A variety of aids to the reader is provided: besides the very detailed table of contents, an introduction to each chapter, section and subsection, an overview of the relevant literature (in Vol. 2) plus the references in the Scholia to each chapter, in the (historical) footnotes, and in the bibliography, and finally an index of the examples used throughout the book. Both individually and collectively these volumes have already become standard references. ... Read more

Book Description
Success in your calculus course starts here! James Stewart's CALCULUS texts are world-wide best-sellers for a reason: they are clear, accurate, and filled with relevant, real-world examples. With CALCULUS: EARLY TRANCENDENTALS, Sixth Edition, Stewart conveys not only the utility of calculus to help you develop technical competence, but also gives you an appreciation for the intrinsic beauty of the subject. His patient examples and built-in learning aids will help you build your mathematical confidence and achieve your goals in the course! ... Read more

Customer Reviews (1)

Excellent Textbook
This book was very helpful and insightful towards me learning calculus. The book was very understandable and a better investment then buying the Single Variable book. ... Read more

Book Description
This is the first truly up-to-date treatment of calculus of variations - and the first to incorporate a simple introduction to key concepts such as optimization, optimal control, bang-bang, Pontryagin's maximum principle, or LQ control design.Introduces all material using simple, easily understood applications that are worked and reprised several times throughout. Features a large number of exercises, ranging widely in difficulty. Gives readers a broader, "big picture" perspective that makes the material less overwhelming. Offers a useful, stand-alone discussion of MATLAB ("MATLAB Cookbook") in the appendices. Includes a clear introduction to weak/strong sufficiency.A useful reference for engineers, chemists, and forest/environmental managers. ... Read more