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An Introduction to Partial Differential Equations, by Yehuda Pinchover, Jacob Rubinstein
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A complete introduction to partial differential equations, this textbook provides a rigorous yet accessible guide to students in mathematics, physics and engineering. The presentation is lively and up to date, paying particular emphasis to developing an appreciation of underlying mathematical theory. Beginning with basic definitions, properties and derivations of some basic equations of mathematical physics from basic principles, the book studies first order equations, classification of second order equations, and the one-dimensional wave equation. Two chapters are devoted to the separation of variables, whilst others concentrate on a wide range of topics including elliptic theory, Green's functions, variational and numerical methods. A rich collection of worked examples and exercises accompany the text, along with a large number of illustrations and graphs to provide insight into the numerical examples. Solutions to selected exercises are included for students and extended solution sets are available to lecturers from solutions@cambridge.org.
- Sales Rank: #966018 in Books
- Brand: Brand: Cambridge University Press
- Published on: 2005-06-13
- Released on: 2005-05-12
- Original language: English
- Number of items: 1
- Dimensions: 9.72" h x .79" w x 6.85" l, 1.65 pounds
- Binding: Paperback
- 384 pages
- Used Book in Good Condition
Review
"This is an introductory book on the subject of partial differential equations which is suitable for a large variety of basic courses on this topic. In particular, it can be used as a textbook or self-study book for large classes of readers with interests in mathematics, engineering, and related fields. Its usefulness stems from its clarity, balance and conciseness, achieved without compromising the mathematical rigor. One particularly attractive feature is the way in which the authors managed to emphasize the relevance of the theoretical tools in connection with practical applications."
Mathematical Reviews
Most helpful customer reviews
12 of 12 people found the following review helpful.
Good for starters
By Me
This book was the primary textbook for my first year graduate PDE's class (I am an Applied Math student). The supplementary textbook was the one written by Strauss, which is the traditional undergraduate leveled text. My background is in Physics so I have seen PDE's before, just not in any detail as this.
As a textbook, I liked it. It was easy to read through and the hints in the back of the book were helpful when I was having a tough time solving the problems (some of which are quite difficult, others less so). I can say that I learned enough PDE's to be able to solve them properly if I were to see a PDE lying around in a, say, physics book! You will learn solving techniques reading through this book.
This text, unfortunately, is far from thorough, as the other reviewer has pointed out. This is an Applied Math textbook, NOT a Pure Math textbook! I had Evans' book with me the whole time and they were worlds apart! I tried to go through Evans' book along-side after reviewing a subject (like The Method of Characteristics) from P&R and it was a challenge. You won't become an expert in PDE theory using this book. It is most certainly an introduction. You don't see one bit of Sobolev spaces in the entire text; the treatment of shocks and conservation laws are left to a minimum, you don't even see a statement about the Reimann Problem (which comes up in research today)! Yes, there are many application but one thing I find tragic (coming from physics) is that the *interpretation* is kept to a minimum as well! Many "applied" mathematicians feel free to do this, I find, and it irks me to no end. The chapters on Separation of Variables and Sturm-Liouville theory is not complete either - this is to be expected since the topic can span multiple books by themselves. They do a good job of *introducing* you to the material, however.
I found myself always looking up other texts for another point of view and, perhaps, an interpretation or a better understanding of some results. For Separation of Variable and a view of Sturm-Liouville problems from a different angle, I whole-heartedly recommend taking a look at Churchill and Brown's "Fourier Series and Boundary Value Problems" and "Fourier Analysis" by Korner. I find the treatment of Characteristcs to be done better and more intuitively by Zauderer. Uniqueness proofs are a strength of P&R and the only other book I found to be as easy to read regarding them is the one by Strauss.
All in all, this is a good book, don't get me wrong, it's just that you won't become an expert in the field. If you want a working knowledge of PDE's, I would recommend this book, Erich Zauderer's book, and Churchill and Brown's (excellent) book on Fourier Series; all of them to be read together.
9 of 11 people found the following review helpful.
Nice and efficient work for physicists and engineers
By TOE
This book will give physicists and engineers a working knowledge of partial differential equations, which permeate their fields but whose underlying mathematics too many students just still ignore. That text is written very fluently and theorems and proofs appear only when the concepts and methods at stakes have been carefully presented through many examples. I generally prefer the top-to-bottom approach but it appeared that the one used in this book works quite well if you want to become more familiar with PDEs but don't necessarily want to be an expert on this field.
2 of 2 people found the following review helpful.
Using this book was absolute HELL - 6 years later and I'm still thinking about it!
By A. Goncharov
I used this book in an undergraduate course at the University of Toronto. As a result of the course I took with this book, I specialized in subjects that were completely orthogonal to differential equations in my Master's studies in mathematics. So what was so bad about this book? Well, one funny factoid about this book was the amount of errors that we found as a class. This was a small specialized class consisting of future mathematics researchers in undergrad (At UofT there is a "Specialist Mathematics" major, for which this course is an option), and we actually started a PDF compilation of all the errors in the book and kept updating it almost every week and keeping it on the course website.
Usually when you have questions after a lecture, you go back and read the chapter of the book corresponding to this material. But this book doesn't allow you to do that, no matter how hard you try. The explanations skip steps, don't motivate the material, use words they haven't defined, and back up their arguments with diagrams that are not explained. I could go on and on, but why bother? The point is, the flaws I outlined are repeated over and over again, so the authors weren't interested in exposing the student to an exciting field while writing this book. The problem with people who understand very advanced material, is that it takes a completely different skill to teach it to someone. These authors wrote this book as if explaining something in their own words to themselves, but not assuming the elementary knowledge of someone who may first encounter these ideas. (By the way, isn't that known in logic as "begging the question", or "preaching to the choir"?)
So take this review with a grain of salt (like you should all reviews) but don't say I haven't warned you!
Good luck and I hope you get a GREAT professor.
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