Partial Differential Equations: An Introduction

By Walter A. Strauss

Book Overview

Covers the fundamental properties of partial differential equations (PDEs) and proven techniques useful in analyzing them. Uses a broad approach to illustrate the rich diversity of phenomena such as vibrations of solids, fluid flow, molecular structure, photon and electron interactions, radiation of electromagnetic waves encompassed by this subject as well as the role PDEs play in modern mathematics, especially geometry and analysis.

• Format: Hardcover
• Language: English
• ISBN: 0471548685
• ISBN13: 9780471548683
• Release Date: March 1992
• Publisher: Wiley
• Length: 440 Pages
• Weight: 1.72 lbs.
• Dimensions: 9.5" x 1.0" x 6.3"

Customer Reviews

What are you guys talking about? This book is AMAZING!

I have never commented on a book, up until now... and I do so only because I don't think that this book gets enough credit. People have complained Strauss may not have explained some proofs in as much detail as he could have, people complained that he didnt give enough examples, I think this is more of a problem with the readers than the writers. If you need someone to hold your hand through every step and detail, I think you should reconsider why you are studying what you study.- I am an undergraduate at NYU, one of the best research institutes for PDE's. I thoroughly enjoyed reading this book, it gives an amazing description of what PDE's are, how to solve them, and how they are used in science. One thing I REALLY enjoyed about this book was it did not do what many other books do: first dive into seperation of variables and focused only on that. Instead Strauss shows how to solve first and second order equations without boundary conditions, giving a very elegant prose doing so! However, I think much of the problem that people are having with this book is that it's not a "one-size fits all." (Which I don't think any book can be!) If you are a Scienctist or Engineer and just want to learn PDE's to solve problems in science.. find another book, because this book is not the book for you. That being said, if you are Mathematics student or interested in a more deep study of PDEs this is really a good book for you. You definitely should have taken Calc. 1-3, Linear Alegbra, ODE, and I recommend one semester of Analysis (for function spaces) before tackling this book, that is what I had, and I loved this course. PDE is a difficult subject/course and Strauss does an amazing job at explaining it, if someone like me can get PDEs so well from this course, than I seriously believe that complaints about this book is due to fault in the readers and not the writer.

Advanced undergraduate PDE text.

This 1992 title by Strauss (professor at MIT) has become a standard for teaching PDE theory to junior and senior applied math and engineering students in many American universities. Having been the actual class grader for two terms in 2004-2005, (and another year an informal teaching assistant), I found many of the students struggling with the concepts and exercises in the book. Admittedly the style of writing here is dense and if the reader does not have a strong background in the requisite topics (including physics), chances are high he or she will face a grand level of frustration with the exposition and the subject as a whole. One would need perseverance and dedication working numerous hours with this text before things start to settle in. After about the second or third chapter onward, those who were still taking the class had an easier time understanding the material and doing the excercises. Contentwise, after a brief and important introductory chapter (which should not be skipped by any reader!) the book first focuses on the properties and methods of solutions of the one-dimensional linear PDEs of hyperbolic and parabolic types. Then after two separate chapters, one on the trio of Dirichlet, Neumann, and Robin conditions and the other on the Fourier series, the author embarks upon the discussion of elliptic PDEs via the methods of harmonic analysis and Green's functions. Subsequently there is a brief introduction to the numerical techniques for finding approximate solutions to the three types of PDEs, mostly centered on the finite differences methods. The beginning of roughly the second half of the text is devoted to the higher-dimensional wave equations and boundary conditions in plane and space, utilizing the machinery of Bessel and Legendre functions, and ending up with a section on angular momentum in quantum mechanics. In the following, Dr. Strauss brings up the discussion of the general eigenvalue problems, and then proceeds with a treatment of the advanced subject of weak solutions and distribution theory. (This topic is normally skipped in an undergraduate course.) The last two chapters are a pure delight to read, dealing with the PDEs from physics as well as a survey of the nonlinear phenomena (shocks, solitons, bifurcation theory). A few appendixes at the end, summarize the analysis background needed for the course and must be consulted before and during the first reading. All in all this is a very splendid source for all the applied math and engineering students, that can be used in conjuction with other references to help break through the conceptual barriers. In fact, I recommended the book by Stanley Farlow to our students and many found the presentation there very modular and accessible. For example, some of the Strauss' homework problems, such as solving the Poisson equation on an annulus, were subjects of a single chapter in Farlow. In any event, please make sure to check out this book's accompanying student solution

A darn good book

I honestly don't understand several of the reviews here. At the one extreme, we have people who complain that there are not enough examples, and there are too many gaps in the proofs. Well, that is partly the point. At some point in math, you have to move beyond the spoon fed approach of a typical lower division calculus textbook and fill in the gaps and figure out the examples for yourself. At the other extreme, one person complained that the exercises were uninspired and did not lead away from the text. The only response I have to that is "are you reading the same text that I am?"The title is not misleading. The book is a concise introduction to PDEs. One should have had some upper divison analysis, and some lower divison ODEs but that's about it. I have had a graduate course in PDEs, which I basically failed to understand. I was able to get through the course, but without ever getting any "big picture". This is probably because I had never taken an undergraduate PDE course. I now have got to the point where I need to know undergraduate level PDEs and this textbook has been perfect. It is hard, but readable. The questions cover a lot of material and have a wide range of difficulty. As I've worked my way through the book, I feel that I am finally getting to grips with the subject, and beginning to see a big picture. One of the better textbooks in my collection

Well organized book

This book is very concise and to the point. It is exactly what its title suggests. Good reference book too, and good examples. I've checked out many books on this subject and this is probably the best. The appendices were also very helpful.