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Partial Differential Equations (Graduate Studies in Mathematics, Vol. 19) Hardcover – June 1, 1998

ISBN-13: 978-0821807729 ISBN-10: 0821807722 Edition: 1st

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Product Details

  • Hardcover: 662 pages
  • Publisher: Amer Mathematical Society; 1st edition (June 1, 1998)
  • Language: English
  • ISBN-10: 0821807722
  • ISBN-13: 978-0821807729
  • Product Dimensions: 7.4 x 10.4 inches
  • Shipping Weight: 2.8 pounds
  • Average Customer Review: 4.6 out of 5 stars  See all reviews (12 customer reviews)
  • Amazon Best Sellers Rank: #513,760 in Books (See Top 100 in Books)

Editorial Reviews

Review

"...Highly recommend the book for students as well as for lectures in PDE." -- Monatshefte fur Mathematik

"...entirely possible that the ...text could eventually become the benchmark. ...extremely well written..." -- SIAM Review

"For a student wishing to specialise in the theory of PDEs it provides a very solid foundation." -- The Mathematical Gazette

"Highly recommend the book for students as well as for lectures in PDE." -- Monatshefte fr Mathematik

"It is a standard treatment with good notation. It is extremely well written, with a very attractive format." -- SIAM Review

"This excellent textbook [is recommended] as the first textbook for anyone who wants to learn the theory of [PDE]" -- European Mathematical Society Newsletter

"Well written; proofs are given in full detail and pictures are inserted when needed; moreover, the exposition is perfectly self-contained, the development within each part and section being rigorous and complete." -- Mathematical Reviews

For a student wishing to specialise in the theory of PDEs it provides a very solid foundation. -- The Mathematical Gazette

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Most Helpful Customer Reviews

62 of 65 people found the following review helpful By T. Butler on March 3, 2007
Format: Hardcover
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.
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26 of 27 people found the following review helpful By A Customer on February 10, 2004
Format: Hardcover
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 By Quinn Noble on July 25, 2000
Format: Hardcover
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 By A Customer on September 29, 1998
Format: Hardcover
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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5 of 5 people found the following review helpful By ikantspel on May 2, 2007
Format: Hardcover
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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13 of 16 people found the following review helpful By Matthias Heymann on February 24, 2006
Format: Hardcover
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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