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62 of 65 people found the following review helpful
on March 3, 2007
If you are just getting started in learning PDEs and want to see all the classical problems/solutions (Poisson, Laplace, Heat, and Wave Equations), then this book might be a little advanced for you, but it is solid in this content if you have a solid background in analysis (probably best to have at least one high-level analysis class that covers all the multivariable calculus material as you will find that your ability to identify and use Green's Theorems will make life much easier as you get started). This is considered "Part I" of the book.

Once you have covered all the nice problems that don't exist in practice, you are ready to move onto general linear PDE theory in Part II of the book. I would recommend you complete a course in measure theory before you start in on chapter 5, which covers Sobolev spaces. I would then recommend that you complete a course in functional analysis before starting chapter 6 or 7 (chapters 5-7 are Part II of this book). This is not necessary as you will have access to a fairly complete appendix of functional analysis results in this book, but once you understand functional analysis and measure theory, then you will be able to grasp the idea of an elliptic (or in chapter 7, parabolic or hyperbolic) operator acting on a function space (the function space being a Sobolev space) more easily and these ideas won't seem so abstract. Overall, the second part of this book is great if you have a lot of the prerequisites I just suggested because many of the proofs can easily be made to be three to five times longer as many steps that link ideas in functional analysis are skipped. The proofs on higher regularity will be hard to understand your first time through, so I wouldn't worry about it too much. Read through the chapters and then read through the regularity stuff again. If you just want to get the basic ideas you can skip either the parabolic or hyperbolic section in chapter 7 because the techniques in solving either type of problem are fairly similar.

Once you are done with the linear PDE theory and are ready to start chapter 8, I recommend putting the book down and getting a different one. Evans gets fairly abstract in the nonlinear part of the book (Part III). I would recommend getting "Navier-Stokes Equations: Theory and Numerical Analysis" by Temam as it is a great source for nonlinear PDE theory and has more results and better proofs than Evans on this subject. I just feel like the Evans book is a great book to learn from for your first two semesters of PDEs at a graduate level, but after that it is time to change texts.
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26 of 27 people found the following review helpful
on February 10, 2004
This is a textbook for a first-year graduate course in PDE (for mathematics students). You should take courses in analysis (on the level of Rudin) and measure theory before you expect to understand everything in this book.
This is by far the best book on PDE. The text is extremely clear, and most of the rather technical proofs are prefaced with "heuristic" calculations to help the reader understand what is going on. The chapter on the calculus of variations is the best exposition I have found of the subject, and Evans completely dispenses with the awful "delta" notation which never made any sense.
The text doesn't make much use of the Fourier transform and doesn't even mention distributions, and this gives his book a definite nonlinear flavor (which is a good thing). This should become the standard introduction to PDE on the graduate level.
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34 of 39 people found the following review helpful
on July 25, 2000
This book is a mathematician's book and not an engineer's--it hasn't a bit of material on approximating solutions of PDEs (which subject could fill several volumes by itself), and devotes a great deal of space to proving existence, regularity, and other properties of solutions to non-linear PDEs. The exposition is extremely compressed (many moderately difficult proofs are reduced to a paragraph or two).
It is also very much a graduate course (as the title indicates). Undergraduate students are advised to stay away unless they have excellent teachers, or are very good, or both.
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19 of 21 people found the following review helpful
on September 29, 1998
I have taught a one-year course in PDE based on Evans' book and found it extremely cogent and stimulating both for myself and for the students. The treatment is up-to-date, with a definite nonlinear flavor. Beyond that, the exercises are very good, and the treatment is sufficiently detailed to make class preparation fairly fast. It does demand mathematical dexterity and maturity of the students right from the start, though.
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13 of 16 people found the following review helpful
on February 24, 2006
After several bad lectures I had already almost given up on PDE. But when I got this book into my hands, I was immediately drawn into the subject and couldn't put it down until I finished it completely. After less than a month I felt how a new world had opened up to me, and I can since feel its effect when I go to lectures.

An important feature of this book is also its perfect layout which is very easy on the eye: I have seen so many mathbooks before that try to put as much information as possible on every square inch of paper, which is hard and slow to read - not this one: Evans' book is a pleasure to just look at.

Some experience in functional analysis is very helpful.
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13 of 16 people found the following review helpful
on November 18, 1999
This is a very well written textbook for graduate-level students as well as an excellent reference for researchers. The outlook of the author, a leader in his field, is non-linear and very broad and includes maechanics and geometry. Any department library needs this book.
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5 of 6 people found the following review helpful
on May 2, 2007
This is a superb exposition of a difficult, yet enriching subject. This book is intended only as a beginning text (in a relative sense) and is by no means an attempt to give an exhaustive view of many topics discussed therein.

The first few chapters discuss classical solution techniques to frequently encountered PDEs such as the heat and Laplace equation. Methods of solution are discussed including Fourier transform methods and other classical methods to obtain strong solutions and/or representation formulas. The author, from this point, focuses on weak solution techniques for second order PDEs and systems in addition to conservation laws and other nonlinear PDEs. There is also a self-contained chapter on Sobolev spaces that proves to be fairly useful.

There is a necessary mathematical maturity needed to fully benefit from this text. The reader should be relatively comfortable with standard topics from classical analysis. It would help if the reader has seen Lebesgue spaces and is familiar with basic functional analysis and operator theory although many of these topics are reviewed in the apendices.

While this book is dense and difficult at times, it has a prominent place on my bookshelf.
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4 of 5 people found the following review helpful
on June 6, 2006
If you're looking for a book to learn PDE's at a basic level, please don't buy this book. In the other hand, if you have already worked on this subject it's not surprising why the book doesn't include some topics or techniques. The appendix is for remembering basic facts while you are reading, so if you don't acknowledge this subjects, you have to study them before (you can't ask a book to have an appendix that covers all the related theories you need).There are several books which cover very well the classical theory and the linear cases in the weak sense. As one of the reviews says, this is an excellent book for a GRADUATED COURSE so it is assumed you have a basic background on the subject and you know what you should know about other subjects such as analysis. The book has the basic tools for THE NON-LINEAR CASES which can't be seen in a basic course. If you don't believe me, try to find a book which cover the same content in such an easy way.
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on May 22, 2015
Love it!!
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0 of 5 people found the following review helpful
on February 13, 2009
Used this for a two year sequence PDE class, our teacher is fantastic and she was a student from Evans'. Love it.
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