Ebook Free Partial Differential Equations: An Introduction, by Walter A. Strauss
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Partial Differential Equations: An Introduction, by Walter A. Strauss
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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.
- Sales Rank: #229416 in Books
- Published on: 1992-03-17
- Original language: English
- Number of items: 1
- Dimensions: 9.47" h x .99" w x 6.26" l, .0 pounds
- Binding: Hardcover
- 440 pages
From the Publisher
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.
Most helpful customer reviews
25 of 26 people found the following review helpful.
Advanced undergraduate PDE text.
By Mark Arjomandi
This 1992 title by Walter A. Strauss (professor at Brown) 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.
The second edition (2007) adds new exercises, subject material, comments, and corrections throughout. 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, water waves). 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 official accompanying student solutions manaual for extra help on doing the homework problems, and hopefully learning your course's target material in a more effective manner.
21 of 24 people found the following review helpful.
What are you guys talking about? This book is AMAZING!
By Michael Harmon
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.
24 of 29 people found the following review helpful.
A Truism: This is a terrible book on a fascinating subject
By G. Basilio
May I begin by stating that my critique is based on having read and used the first 7 chapters, with some familiarity with chapters 9, 11, and 13. With that said, just about every NEGATIVE comment and review posted prior to this review, I believe, is for the most part quite accurate and nightmarishly true. In particular, Strauss states the obvious, while omitting key and crucial steps (this isn't limited just to his proofs). One might notice that the last comment is similar to the Rudin style. Let me assure you that unlike Rudin, Strauss' presentation is not elegant, it does not inspire, and simply cannot be compared to Rudin. Some other major flaws include: hasty organization, lack of depth and breath in theory, and the problem sets consist mostly of trivial proofs and unimaginative applications. I would not recommend this book under any circumstances. If you want to learn PDEs, take the graduate course.
(Continue reading only if you have to use this book for a class)
If you are unfortunate enough to be forced to read this book, here is some advice:
::Prerequisites::
It is explicitly stated in the preface that this book is intended
for undergraduates at the junior/senior level. I believe that in order to learn anything meaningful from Strauss, it requires that you have already had the following courses: calculus, multivariate calc (vector calc), linear algebra, analysis, and ordinary differential eqns. (Complex analysis, is not necessary, but does illuminate specific areas. Fourier analysis, is not necessary. Since half the books tries to establish main theorems of Fourier analysis--may I add, not at a rigorous level.)
Part of the reason why this book is abhorred so much, is that it assumes the reader is somewhat 'mathematically mature'. To many this process begins after multivariable calc (unless you took the rigorous honors) with an *upper* division linear algebra or analysis course (lower division lin. alg. doesn't count). This is where the student is first asked to write his/her own proofs. After such courses, expressions such as "it is easy to show..." and "the reader can verify for him/herself..." imply that the student is encouraged, if not expected, to actually do it for themselves.
The student who has taken the aforementioned courses, should be adequately prepared to read Strauss. However, students with this much (actually its not much at all) preparation will probably find Stauss' book a joke and lacking in rigor. Ch 5 on Fourier Series attempted to develop L_2 theory and tried to set Fourier series on a rigorous base, but I feel it failed miserably.
::Conclusion::
Only mathematics majors will probably get something meaningful out of this book, but only if they are sufficiently prepared. Other like engineers or physicists, could learn PDEs from this book, but it is highly unlikely.
::Recommendations::
If you really want to learn PDEs, you should skip taking an undergraduate PDE course that uses this book and take a Graduate PDE course. You will heavily on analysis, thus try to take an Analysis Honors course at your school.
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