- Hardcover: 464 pages
- Publisher: Wiley; 2 edition (December 21, 2007)
- Language: English
- ISBN-10: 0470054565
- ISBN-13: 978-0470054567
- Product Dimensions: 6.4 x 0.8 x 9.1 inches
- Shipping Weight: 1.4 pounds (View shipping rates and policies)
- Average Customer Review: 3.4 out of 5 stars See all reviews (39 customer reviews)
- Amazon Best Sellers Rank: #416,134 in Books (See Top 100 in Books)
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Partial Differential Equations: An Introduction 2nd Edition
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In some ares of mathematics, a single, classic text whose exposition is top-notch, or that inspires despite its exposition, manages to cover the field well. For example, I'm thinking of books like Halmos (Measure Theory) or Segal and Kunze in real variables and integration theory; Lax or Reed and Simon 1 (Functional Analysis) in functional analysis; Lang in algebra; and Kelley or Milnor (Topology from the Differentiable Viewpoint) in topology. (Full citations are in Listmania; see my Amazon profile. All of these books are great texts for very different reasons, as my Listmania remarks suggest.)
I've yet to find a single reference for PDEs that addresses all of my questions, but a number of books taken together manage nicely. I jumped around in these books when I was learning the subject, and I'm convinced that such cherry-picking is the best approach for PDEs, since the field is so broad in theory and applications. The downsides, of course, are expense and potential confusion from conflicting notation and approach.Read more ›
The uniqueness - and as much as I hate to admit, what makes the text "good" - is in its treatment of methods for solving PDEs other than separation of variables. Using alternative methods to solve well known equations (i.e. wave, heat etc.) has the advantage of illustrating the differences between the solutions(For example does information "travel" towards infinity or dissipate?). These differences are impossible to teach through separation alone which treats all such equations as if they were the same. There is also the obvious problem of students ending up in a bind when they eventually come across a non-separable problem.
All in all, the book illustrates a very nice outline of what a good first course in PDEs should be - but it does just that and nothing else. Its unfriendly presentation of the material makes this work pedagogically unsound.
The book really isn't bad, and I learned a lot from it, but I had two major gripes:
Firstly, the author tried to pack so many supplemental (Graduate level!) chapters into the book, that the actual core material was neglected. The core chapters are very scant, and typically average only a few pages. Many important proofs are left as exercises, as well, which makes it difficult to understand the objectives of each sub-chapter. The book would be a lot better if the author had cut out four or five of the late chapters, and made the first five more detailed.
Secondly, there is a somewhat heavy emphasis on physics in this book. I'm well aware that physics and PDE are closely linked topics, but a math textbook should favor mathematical treatment of the subject matter, rather than assume that I know all about the physical meaning of equations from physics.
Most Recent Customer Reviews
Should be on the shelf of every applied mathematician. Work through the exercises, they are integral to understanding the PDEsPublished 16 days ago by Charles Bagley
Extremely well written by which I mean the author does not leave out essential information or expect you to know what he is referring to. Read morePublished 6 months ago by Michael
Definitely a graduate level text. I learned a lot. The problems were challenging and really reinforced the material.Published 10 months ago by Amazon Customer
Written in a rather terse style. He glosses over many steps in derivations of equations, theorems, etc. Read morePublished 14 months ago by Joshua Wilbur
This text is definitely far beyond the reach of normal undergraduates, especially when Fourier Analysis is not at disposal. Read morePublished 19 months ago by YOU ZHOU
This is a really excellent book, but please notice that this is an introduction for mathematician. I first touched it when I was in my second year in university (I was a math... Read morePublished 21 months ago by LI-JEN LIN
The book is an excellent reference, but not much more. It attempts to present topics in very few words, while also requiring the reader to fill in most of the details. Read morePublished 22 months ago by Doyle
Was required for a course, and is the ONLY reason I would even suggest getting it. Definitely not good enough for self study as each section is about a paragraph long. Read morePublished on January 24, 2014 by Nicole