Containing both realistic exercises and advanced topics, this undergraduate introduction to the field provides an analysis of the Robin boundary condition and the need for Fourier expansions Schrodinger equations are also discussed, to illustrate the connection with chemistry and physics....
|Title||:||Partial Differential Equations: An Introduction|
|Publisher||:||John Wiley and Sons WIE Auflage International Ed 9 Juni 1992|
|Number of Pages||:||464 Seiten|
|File Size||:||684 KB|
|Status||:||Available For Download|
|Last checked||:||21 Minutes ago!|
Partial Differential Equations: An Introduction Reviews
This 1992 title by Strauss (professor at MIT) has become a standard for teaching PDE theory to junior and senior applied maths and engineering students in many American universities. During the academic year 2005-2006, I was the reader for a class taught based on this text, and I found many of the students struggling with the concepts and exercises therein. Admittedly the style of writing here is very dense and if the reader does not have a strong background in the topic, 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.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 (a region bounded in-between two concentric circles), were subjects of a single chapter in Farlow. In summary, Strauss provides a splendid source for all of the applied maths and engineering students, which can be used in conjuction with other references to help break through the conceptual barriers. Make sure to check out the accompanying student solutions manual for verifying your own proposed homework solutions.
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.
I used this book for an undergraduate level course on Partial Differential Equations. The book clearly states that it is meant for undergraduates, but my class had a healthy number of graduate students, and my professor noted that much of the book's material lands squarely in graduate territory. Depending on the sections that you study, I would suggest developing a strong background in analysis before delving into this book.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.
Like another reviewer said, if you persevere and log the long hours in the earlier chapters of this book, it pays off in dividends in later chapters and exercises. My senior PDEs class covered Chapters 1-7, 9 and 12. This is a tough book but many of the ideas and exercises are interlaced in such a way that a really diligent student will be able to follow. The key here is perseverance against all frustration; for you will be frustrated with this book in the first several chapters and with the exposition. Keep a pencil in hand and work through every step of every proof and example (including all of the intermediate steps that Strauss leaves out) and you will eventually get there.
In the introduction of this book the author says the text was meant for an undergraduate level course... we are currently using the text for my graduate level class. The text is vague and there are virtually no examples. Many of the proofs normally spelled out in a text book are actually exercises. There is a solutions manual, but the manual does not contain all the solutions--just the work for the ones which already have the answers in the back of the book. If you are looking for a challenge or perhaps a review of PDEs this is the book you want. However, if this is the first time you've ever seen PDEs or you are unsure of your math capabilities you might want to have another back up text for clarification like "Applied Partial Differential Equations" by Haberman or "Partial Differential Equations for Scientists and Engineers" by Farlow.
This text is probably quite useful if you already understand partial differential equations and just need to review topics that you have already covered and grasped in the past. It outlines all aspects of introductory PDE's well, and in the appropriate order. There are well-thought out problems at the end of each chapter with answers to selected exercises that will reinforce your recall of the material. However, if you have never studied partial differential equations before, you will never learn the subject merely by reading this book. Yes, the style is comprehensible and conversational, but the derivations leave out many important steps, and you will never be able to work the excellent problems at the end of each section merely by reading and understanding each section of this book. Instead, if you are a newby to this subject and you are forced to use this book as the result of taking a course in which it is the assigned textbook, I recommend that you use "Partial Differential Equations : An Introduction" by David Colton (ISBN 0486438341) in conjunction with this text. Colton's book does a pretty good job of mopping up after Strauss, in that Colton's text takes the time to show adequate proofs and examples of sufficient complexity that you can understand the material. In addition, it pretty much covers the same subjects as Strauss in the same order only with much more detail. In addition, Colton also has good exercises for each chapter and also has answers to selected exercises. In summary, read Strauss as an outline for review and problem sets, read Colton's book for a good explanation.
Easy and clear to understand. Proofs are a bit light on the rigor, but it doesn't get in the way of understanding and the exercise selection is excellent. Book arrived a little more beat up than anticipated.