Product Description
The text provides an introduction to the variational methods used to formulate and solve mathematical and physical problems and gives the reader an insight into the systematic use of elementary (partial) convexity of differentiable functions in Euclidian space. By helping students directly characterize then the solutions for many minimization problems, the text serves as a prelude to the field theory for sufficiency. It lays the groundwork for further explorations in mathematics, physics, mechanical and electrical engineering, and computer science. ... Read more

Customer Reviews (1)

Introductory and readable, yet rigorous
I had read/studied most of this book when I was a graduate student in chemical engineering at Syracuse University (in 1987-88). I also took two courses on the subject from Professor Troutman. I strongly recommend thisbook to any "newcomer" to the subject. The author is amathematician, and a large fraction of the book consists of theorems,lemmas, propositions, corollaries (and their rigorous proofs). The bookalso contains, however, a good number of illustrative examples andexercises which make it useful to engineers and scientists as well as tostudents of mathematics who want to learn more about applications ofmathematics to physical sciences. ... Read more

Product 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, 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 (16)

Math Calculus 3
The book is pretty good. The cover is kind of tearing off, but overall it's still in good condition.

Perfect condition
This product was delivered quickly and efficiently. I received it faster than I was expecting it and in perfect condition just as stated. Thanks!

Book came as described
Economical alternative to the full Calculus book by James Stewart.This copy came in the condition it was described as and the bit of writing is not a problem.The book arrived before the estimated shipping date.

Great Calculus III book, NOT Early Transcendentals
This is a great book for College Calculus 3. If your class requires the "Early Transcendentals" edition, this is essentially the same book. It contains the EXACT same material as the Early Transcendentals edition but everything is pushed ahead one chapter. It has the exact same amount of chapters and the exact same questions so don't fret, this book will work for your class. Also the new price on Amazon is usually cheaper than the used price in your university's bookstore! (Note that you most likely won't be able to sell it back to your university because of it not being E.T.). Overall a great way to learn Calculus 3!

very pleased
The book I ordered arrived at my house within a week and it is in great condition, exactly as the shipper's description said. ... Read more

Product Description

Product 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 (6)

Plus and Minus
The content of the book was in great shape - pages clean and intact. However, the cover has a huge crease in the front. The product was marked as "good" but there was no indication that this was the defect. Purely cosmetic, but still dissatisfying.

best best seller!!!
this seller is the best!!! fast shipping!!! great condition!!! it took only two days!!! thaaaaaank you!

Excellent Service
Thank you very much. Item arrived on time and in great condition. Would definitely purchase again.

lots of theory with little applications
Order from Amazon was flawless as always.It seems like there are more pages of homework problems than pages explaining the math.Hope you have a good teacher because you wont understand it just from the book.

awesome book
math rocks, and this book does it justice. Too bad most students will only use a quarter of the book ... Read more

Product Description
Vector calculus is the foundation stone on which a vast amount of applied mathematics is based. Topics such as fluid dynamics, solid mechanics and electromagnetism depend heavily on the calculus of vector quantities in three dimensions. This book covers the material in a comprehensive but concise manner, combining mathematical rigour with physical insight. There are many diagrams to illustrate the physical meaning of the mathematical concepts, which is essential for a full understanding of the subject. Each chapter concludes with a summary of the most important points, and there are worked examples that cover all of the material. The final chapter introduces some of the most important applications of vector calculus, including mechanics and electromagnetism. ... Read more

Customer Reviews (13)

Just the Facts Book
I bought this book based on the other good reviews here and I was solely dissapointed.I have a Degree in Physics and Engineering and a Masters in Engineering as well and I bought this book to brush up my rusty fundamentals in prepping for a new job that involves a heavy amount of Electromagnetics which naturally means going back and redoing my Vector Calculus.Mr.Mathew does not believe in delving deep into any subject.Note that this is a very thin book, the theme here is more a stating of the facts than a rigorous treatment that would delve into each building block of Vector Calculus.So, if you are looking for an in-depth approach, lots of solved problems then dont buy this book.

Great Supplimentary text
{excuse me if my review does not flow. I'm not very good at connecting paragraphs. But I'll try to pinpoints things about these books. Hopefully you'll benefit from those.}

Like most other Springer books published under SUMS (Springer Undergraduate Mathematics Series) category, it shows following traits:

1) it follows a down to earth approach.
2) it is brief (if you cut out table of content, preface, index etc, you have 179 pages of reading material).
3) there are worked out examples in pretty much all sections.
4) exercises are at the end of each chapter. Worked out and fairly detailed solutions are at the end of the book.


Like other reviewers have mentioned, this book does not contain much of proof. Instead, explanations are given to justify a formula or how a formula can be thought of.

Another thing worth mentioning is the usage of Physics in this book. Author does make use of Physical examples sometimes, for example in section 1.2.1, Matthews uses F.d (force dot displacement) to illustrate application of dot product. These stuff are elementary Physics though. The more deeper usage of Physics is seen is at the end of the book. Last section of Chapter 7 provides two physical examples of tensor, namely Ohm's law and inertia tensor. Finally, the last chapter is all about Application of Vector Calculus which again involves Physics.


This book does NOT require you to know about vectors before hand. Infact, chapter one is all about vectors and it's properties (addition, dot product, cross etc). Even if you already know about vectors, it won't hurt to take a brief glimpse at this chapter.

This book should NOT be used as your only source for Vector Calculus course. I've heard some people say they've used this book as a text for Multivariable Calculus course, if you're in similar course, please get an additional text for yourself. I used Jon Rogawski's Calculus...quite of a decent book imo. A lot of other people recommend Stewart (i haven't used this one personally but i hear it's good). The issue is this book just does not have enough exercises for you. Plus, there is a whole lot more stuff coveredin typical Multivariable text but is absent on this one (arc length, curvature, center of mass, tangent planes, directional derivatives, optimization and Lagrange multipliers to name a few). On contrary, the book covers Suffix Notation, Curvilinear coordinates, Cartesian Tensor, and Physical Applications which typically are absent in Multivariable text.


chapter on Suffix Notation is quite a good one actually. I was taking "Mathematical Methods for Physicist" course where our professor quickly went over Kronecker delta and alternating tensor and kept using it for quite some time. I had to look into this book to understand what they meant and how they can facilitate calculation involving gradient.

Excellent Resource
I think this is a terrific review of vector calculus for those in the sciences. It is clear, concise, and very readable. In fact I read it in just a couple days trying to brush up on my vector calculus for the start of a new job.

I don't think it would be a sufficient introductory resource, especially for someone without the relevant science background as most the examples would be meaningless. I also don't think this would be great for a mathematician as I feel it's depth might not be sufficient. But it was perfect for me and I feel like I now understand the governing fluid and heat transfer equations with more clarity than ever before.

Only thing I think was left out is the convective operator...

Also, I haven't read the Schey book, which seems to be popular, so I can't compare but I can't imagine it being better.

Handicapped by a Big Slosh of English Snootiness and Geometrical Pomposity, but
its selection of problems and its focus on vector calculus are both quite good. Perhaps both are excellent, but my current experience and intuition in this subject area prevent me from being more certain.

Either way, a much more physically intuitive approach with more problem-solution examples and less geometrical rigor is possible, that much is certain.

Most importantly, in-text solutions are provided.There is no problem with merely an answer, all have something more. There are wayfewer problems as compared to a schaum's outline (on the order of 30 times fewer).Though it also costs two or three times more than a Schaum's, it's certainly much more physically intuitive than the Schaum's on vector/tensor analysis by Murray R. Spiegel.

I think this book would make its publisher and author a lot more money (by selling a hell of a lot more of them) if it were reduced in price. It would be a win-win for everybody who, I'm pretty certain, matters here.

Great intro for beginning undergraduate students
Very good introduction to Vector Calculus.Perfect appropriated for home study when you have a relative good knowledge of basic Calculus.
Theorems and formulas are physicaly supported in there explanation.Some proofs in the chapter of Tensors are less rigor to make them understandable.
Also contains some beautiful examples and exercises (could be more) of Mathematical Physics.Good balanced structure of the subject matter who brings you to the equation of Navier-Stokes and more in the last short chapter of applications.
Very readable book that I could understand entirly without help,even after leaving school with a limited mathematical education 25 years ago. ... Read more

Product Description
Clearly written text for advanced student covers: Necessary Conditions for an Extremum; Sufficient Conditions for an Extremum; Variations and Hamilton’s Principle; the Nonparametric Problem of Bolza; Parametric Problems; Direction Methods; Measure, Integrals and Derivatives; Variation Theory in Terms of Lebesque, more. 1969 ed.
... Read more

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

Product Description
From the reviews: "These books (Introduction to Calculus and Analysis Vol. I/II) are very well written. The mathematics are rigorous but the many examples that are given and the applications that are treated make the books extremely readable and the arguments easy to understand. These books are ideally suited for an undergraduate calculus course. Each chapter is followed by a number of interesting exercises. More difficult parts are marked with an asterisk. There are many illuminating figures...Of interest to students, mathematicians, scientists and engineers. Even more than that." Newsletter on Computational and Applied Mathematics, 1991 "...one of the best textbooks introducing several generations of mathematicians to higher mathematics. ... This excellent book is highly recommended both to instructors and students." Acta Scientiarum Mathematicarum, 1991 ... Read more

Customer Reviews (1)

Absolutely beautiful!
I give 5 stars to this book because it gives the reader the perfect combination between rigor and intuition. Volume 2 has solutions to almost all the exercises, which is great because some of the problems are very difficult. I really think this is a "must have" text for anyone who wants to learn calculus at a deep level. ... Read more

Product Description
The sequel to How to Ace Calculus, How to Ace the Rest of Calculus provides humorous and highly readable explanations of the key topics of second and third semester calculus—such as sequences and series, polor coordinates, and multivariable calculus—without the technical details and fine print that would be found in a formal text.
... Read more

Customer Reviews (30)

Great for brushing up on more difficult topics
I picked up this little book to help me brush up on Calc 2 and 3 topics so I could pick and choose topics to teach my AP class after the AP exam.The book reads very easily and is full of puns and math humor, including some great examples that will help concepts stick.My one gripe is that the actual problem examples are circumstantial and are not very extensive, so you would definitely have to pick up a textbook and try some problems of the same type before you can say you've "got it"... But I suspect most books of this type are similar.If it were a Barron's book, it would be twice the size, like the Barron's book is!But the topic selection is great and difficult to find in this format.Pick this one up.

Unless your Whole Genome Just Goes "A-D-H-D" this Book Will Help
The bad:
To do the hardest problems in the world, you're gonna need another book and your own gags to soften'm up--maybe a pencil with an eraser that looks like Gallagher's sledgehammer, or Maxwell's silver one. Theory queries need another book.

The good:
If you don't want to feel like killing while reading your math book, this'll feel like learning math from a Mahatma--and girls I've lent it to love it (an'if ya lak my styyyle, comment at me).

Bring Calculus To Its Knees
Two of my IT professors of the University of Minnesota recommended this book.
The three of us recommend it to anyone that is looking for down-to-earth perspectives, real world examples and the best darn calculus help money can buy.
This book will make asking your TA for help obsolete.

Best Calculus book I've read
This is by far the best Calculus book I've read.In the first 10 pages it helped me understand some fundametal ideas that were always obscure to me.I highly recommend this book.

Great Review - Textbook Companion
Should not replace your textbook, but is great for supplement.I decided to take multivariate calculus after not taking a math class for more than 3 years.I read the corresponding chapter in prior to each lecture and got an A in the class.Each chapter takes less than 20 min to read andprovided a great introduction with examples for all topics. Helped me understand the class lectures much more thoroughly.I would highly recommend this book. ... Read more

Product Description
Provides completely worked-out solutions to all odd-numbered exercises within the text, giving you a way to check your answers and ensure that you took the correct steps to arrive at an answer. ... Read more

Customer Reviews (17)

Excellent study tool
When you're unsure how to go about a problem, this book goes through attaining the answer in a step by step format. It's a great study tool and I recommend it to all Calculus students.

Not a good solutions manual!!
As with most "official" solutions manuals, this one is pretty much junk. It contains "full" solutions to only odd problems, and those "full" solutions generally skip steps, assume that you've already mastered the concepts (which you obviously haven't at this level), and on occasion, don't even solve problems the way the book recommends. Instead of purchasing a solutions manual for this Calculus book, I'd just recommend using Cramster. For free they've got AWESOME solutions to all odds which clearly explain what's going on, and for ten bucks a month they got you covered on all the evens as well. For some reason this site is not as well-known as it should be, but save yourself some money and headaches and check it out before buying crappy solutions manuals. Just use your favorite search engine for Cramster, it's one decision you won't regret!

Use wisely
When I was reading reviews for this several people complained that the problems and sections do not match up correctly. This is true. The math book this is based on has several versions and things keep getting moved around. The farther you get along in the book, the more that becomes apparent.

But. By checking the index, you can always find the section you need. And by scanning up and down the list of problems they solve, I was usually able to find a problem close enough to what stumped me to help me figure it out. If you want someone to do your thinking for you, don't bother. If you want an extra boost in understanding without the help of extra tutoring, this is perfect.

Does not match the Textbook
This solution book does not match the textbook they sell in the online and it does not include the problems but only have textbook's page and problem's number that it is totally useless. Only if you have matching textbook then you can buy it otherwise do not buy it. I returned it right after I received it three weeks ago but I still did not get credit. Again, Do not buy it unless you are absolutely sure you have matching textbook.

Great
Helps me on my Home Work. Prevents me from spending an hour on a hard problem. ... Read more

Product Description
Optimal control is a modern development of the calculus of variations and classical optimization theory. For that reason, this introduction to the theory of optimal control starts by considering the problem of minimizing a function of many variables. It moves through an exposition of the calculus of variations, to the optimal control of systems governed by ordinary differential equations. This approach should enable students to see the essential unity of important areas of mathematics, and also allow optimal control and the Pontryagin maximum principle to be placed in a proper context. Although this book is written for the advanced undergraduate mathematician, engineers and scientists who regularly rely on mathematics will also find it a useful text. ... Read more

Customer Reviews (3)

Superb
I have read a large number of books on this field. This is by far the most comprehensive book on the subject. It is suitable for self study, and gives a true jist for optimal control

Not enough words
If you have a good professor to guide your through, this book may be ok. If you're on your own - forget about it.

A genuinely readable introdution for the applied scientist
This is an excellent introduction to the calculus of variations and Pontryagin's Maximum Principle. It is written exceptionally clearly and gives the reader access to the calculus without becoming bogged down in lengthy diffcult proofs (which are left to the end).

I recommend this book to any student or scientist who is not a pure mathematician but wishes to understand and apply analytic tools of optimization. ... Read more

Product Description
Study smarter and work toward the grade you want with this helpful guide. You'll find a short list of key concepts; a short list of skills to master; a brief introduction to the ideas of each section; an elaboration of the concepts and skills, including extra worked-out examples; and links in the margin to earlier and later material in the text and Study Guide. ... Read more

Customer Reviews (5)

Looks great!
The book was perfect, in really good condition and no marks or highlighting at all! thank you!

Calculus made easy
This book has helped me a lot. Not only does it provide a specific summary, it also lists the important equations and rules learned in the chapter. It even has problems you can work and has the full solutions. This book is a must for those who have boring teachers, fall asleep in class, or who just need a review.

DO NOT BUY, poor study material
This book is not a SOLUTIONS GUIDE but a STUDY GUIDE.If give you a few isolated example problems and then has a synopsis of each section.At the end of each section there is a quiz which does not resemble homework problems, or any test problems I have had.I would not recommend this.On the other hand the SOLUTIONS GUIDE is an excellent resource.

Excellent study guide if you need step by step instruction
This book help me through the semester without carrying the heavy text book everyday.
This book is an excellent guide especially for a slow learner like myself. It explains the complicated calculus concepts in easy words. Since my professor did not used the text book much, except for a few homework assignments, I use this study guide book and my lecture note only to prepare for my exams.

Helpful Suppliment
This book really helps out when you have to learn on your own.It gives a detailed work out of each problem.Helps by showing the steps and process of working the problems.Definitely worth having. ... Read more

Product Description
From the reviews: "These books (Introduction to Calculusand Analysis Vol. I/II) are very well written. The mathematics arerigorous but the many examples that are given and the applicationsthat are treated make the books extremely readable and the argumentseasy to understand. These books are ideally suited for anundergraduate calculus course. Each chapter is followed by a number ofinteresting exercises. More difficult parts are marked with anasterisk. There are many illuminating figures...Of interest tostudents, mathematicians, scientists and engineers. Even more thanthat." Newsletter on Computational and Applied Mathematics, 1991"...one of the best textbooks introducing several generations ofmathematicians to higher mathematics. ... This excellent book ishighly recommended both to instructors and students. Acta ScientiarumMathematicarum, 1991 ... Read more

Customer Reviews (2)

Solutions to problems and exercises
Springer have reprinted the original 1960s Wiley editions of "Introduction to Calculus and Analysis" volumes I and II by Courant and John in three new volumes under their "Classics in Mathematics" title: "Introduction to Calculus and Analysis I (pages 1-661)" (ISBN: 3-540-65058-X), "Introduction to Calculus and Analysis II/1, Chapters 1-4 (pages 1-542)" (ISBN: 3-540-66569-2), and "Introduction to Calculus and Analysis II/2, Chapters 5-8 (pages 543-954)" (ISBN: 3-540-66570-6). The back section of Volume II/2 (pages 821-939) has solutions to the exercises in both the books comprising volume II, that is "Introduction to Calculus and Analysis II/1" and "Introduction to Calculus and Analysis II/2".

Note that when Volume I of the original Courant and John "Introduction to Calculus and Analysis" was published in the 1960s by Wiley, an accompanying solutions manual for Volume I was prepared by Prof. Albert A. Blank. When Volume II was published by Wiley, Prof. Blank's solutions were incorporated into the back of Volume II (in other words, Volume II comes with the answers to the questions at the back of the book... or in the back of Volume II/2 in the case of this Springer "Classics in Mathematics" reprint.) However, the Springer reprint of Wiley's Volume I lacks solutions to the exercises in the textbook.

If you buy Volume I, do a check on the Internet for an old 1960s copy of Prof. Albert Blank's "Problems in Calculus and Analysis", which is the original solutions manual to Courant's Volume I.

You must have this.
My review of the first volume pretty much applies here as well.How many *calculus* texts have an introduction to complex variables, and the theory of analytic functions?This is the only one I've ever seen, and I don't think anyone else could make it more enriching than Courant.Useful material on vector calculus, the theory of matrices, and even introductory material on the *calculus of variations* (something we usually don't see at *all* in the undergrad curriculum) is included.It is refreshing to have an instructor like Courant, who doesn't assume we can't follow higher mathematical roads, but also doesn't sit at the other end of the spectrum, just waving a wand and "poof, here is the result".

Courant also published a standard reference work (also two volumes, I believe) on Mathematical Physics.While the level of mathematics required is post-grad, I was still able to read sizeable sections of it without getting lost.

We can only hope Dover decides to publish Courant's works one day, to make them a little more affordable.But still, you can buy both volumes of Courant's intro to calculus for about the same price as a modern calculus text that waters down the material, and on top of that, provides inadequate explanation for the material it does cover. ... Read more

Product Description

From the reviews: "…the book contains a wealth of material essential to the researcher concerned with multiple integral variational problems and with elliptic partial differential equations. The book not only reports the researches of the author but also the contributions of his contemporaries in the same and related fields. The book undoubtedly will become a standard reference for researchers in these areas. …The book is addressed mainly to mature mathematical analysts. However, any student of analysis will be greatly rewarded by a careful study of this book."

M. R. Hestenes in Journal of Optimization Theory and Applications

"The work intertwines in masterly fashion results of classical analysis, topology, and the theory of manifolds and thus presents a comprehensive treatise of the theory of multiple integral variational problems."

L. Schmetterer in Monatshefte für Mathematik

 "The book is very clearly exposed and contains the last modern theory in this domain. A comprehensive bibliography ends the book."

M. Coroi-Nedeleu in Revue Roumaine de Mathématiques Pures et Appliquées

Product Description
This scarce antiquarian book is a selection from Kessinger Publishing's Legacy Reprint Series. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment to protecting, preserving, and promoting the world's literature. Kessinger Publishing is the place to find hundreds of thousands of rare and hard-to-find books with something of interest for everyone! ... Read more

Product Description

This is the first of two books on methods and techniques in the calculus of variations. Contemporary arguments are used throughout the text to streamline and present in a unified way classical results, and to provide novel contributions at the forefront of the theory.

This book addresses fundamental questions related to lower semicontinuity and relaxation of functionals within the unconstrained setting, mainly in L^p spaces. It prepares the ground for the second volume where the variational treatment of functionals involving fields and their derivatives will be undertaken within the framework of Sobolev spaces.

This book is self-contained. All the statements are fully justified and proved, with the exception of basic results in measure theory, which may be found in any good textbook on the subject. It also contains several exercises. Therefore,it may be used both as a graduate textbook as well as a reference text for researchers in the field.

Irene Fonseca is the Mellon College of Science Professor of Mathematics and is currently the Director of the Center for Nonlinear Analysis in the Department of Mathematical Sciences at Carnegie Mellon University.

Her research interests lie in the areas of continuum mechanics, calculus of variations, geometric measure theory and partial differential equations.

Giovanni Leoni is also a professor in the Department of Mathematical Sciences at Carnegie Mellon University. He focuses his research on calculus of variations, partial differential equations and geometric measure theory with special emphasis on applications to problems in continuum mechanics and in materials science.

Product Description
This scarce antiquarian book is a selection from Kessinger Publishing's Legacy Reprint Series. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment to protecting, preserving, and promoting the world's literature. Kessinger Publishing is the place to find hundreds of thousands of rare and hard-to-find books with something of interest for everyone! ... Read more

Product Description
This book contains exercises for courses in differential equations and calculus of variations at universities and technical institutes. It is designed for non-mathematics students and also for scientists and practising engineers who feel a need to refresh their knowledge. The book contains more than 260 examples and about 1400 problems to be solved by the students - much of which have been composed by the authors themselves. Numerous references are given at the end of the book to furnish sources for detailed theoretical approaches, together with expanded treatment of applications. ... Read more