Partial Differential Equations: An Introduction, 2nd Edition 2nd Edition by Walter A. Strauss (PDF)

Description

Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book just doesn’t do it for me. It’s really confusing, the text doesn’t prepare the student for answering the problems. The examples are difficult to follow. Strauss forward references way too much.

⭐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.

⭐This text is full of very nice and very practical topics relating to solving PDEs. This information unfortunately is largely inaccessible to most readers as the writing style is just downright BAD. OK – so nobody expects a course in PDEs to be anything but a formidable challenge. As such my complaint against this book is not that it is a difficult read – rather, my complaint is that it is unnecessarily so. There are many parts where arguments take large needless “logical jumps,” concepts are explained poorly and examples are often not helpfull at all. For every section of every chapter, I did not see much difference between the writings of this text and what an instructor’s lecture notes may look like. 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.

⭐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.

⭐I took a course on partial differential equations last semester using this book. At first, I was put off by how small the book was – I did not think it would be enough for me to learn from – but after working with it for a couple of weeks, I realized that it was just the right length. The chapters are very concise, but they have everything they need and a few examples per idea.I found that most of the practice problems in the book are just slightly beyond the examples given, so you do have to work to get the right answers. It wasn’t easy, but it definitely added more to my understanding than plug-and-chug questions would have. All in all, I am definitely keeping this book as a reference and would recommend it to others.

⭐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.

⭐Written in a rather terse style. He glosses over many steps in derivations of equations, theorems, etc. This can make learning purely from the text difficult, but with a decent professor to fill in the gaps it’s an ideal text. The skipped detail makes coming back to the text later in your career much more productive.

⭐Some sections are great and others are pretty terrible. By this I mean some explain the material well and have great examples that really help you learn a concept. However it seems like the author really didn’t spend too much time on other sections. Overall it was very easy to learn from and I would definitely recommend it.

⭐Great book, worth every penny! The solutions is a must too!

⭐This book is lacking in explanation and organization. Not a very good introductory PDEs book because it does not explain the concepts necessary to do more complicated examples than the ones that the book goes through. Formatting of examples is not consistent which drove me absolutely bananas.

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