Customer Reviews

Differential Equations (2nd Edition)

5 star:		(7)
4 star:		(2)
3 star:		(3)
2 star:		(0)
1 star:		(7)

 

 

I recently used this textbook in a sophomore-level Differential Equations course at UCLA, where I am majoring in Mathematics.

If you are looking for a relatively breezy introduction to Differential Equations, or are taking a course in the subject merely to fulfill a requirement or prerequisite at your school, this text is probably about as good as it gets. Contrary to many of the reviewers on this site, I found the book to be user-friendly almost to a fault; more so even than Stewart's Calculus. Topics in this book are treated cursorily, and emphasis is primarily on algorithmic problem solving.

On the other hand, were I studying this topic on my own, I would not choose this book. For one, exercises are relegated nearly entirely to the application of a procedure outlined in a given chapter, and it was only very rarely that I came across one which was challenging even after taking a glance back through the preceding section (and I did a lot of exercises). Though I feel that the chapters themselves are a bit elementary, I can't fault the authors too much for that; the book is after all an introduction.

After thoroughly studying this book, I do feel that I have a mechanical competency in the basic forms of differential equations treated in the text. That is, I am comfortable with the techniques covered, and I am familiar with a few new ideas. I suppose I can't ask for much more in an introduction, but I somehow feel that my time would have been better spent struggling with a text that was slightly beyond my grasp than mastering one that is well within it.

Pace the many negative reviews, as an autodidact who studies for pleasure (i.e. am under no pressure to pass tests or learn the material for a career), I found the first edition of Polking, Boggess & Arnold (2001, ISBN Differential Equations) well-organized, clear and amply illustrated with examples and diagrams. Polking might have serious limitations for students, as many of the reviews have detailed, but in my view, if you're studying for fun, this is a wonderful book to learn the basics of ordinary differential equations. It has definitely helped me understand the physics books I'm studying, which was my goal. When I'm studying physics and have gotten stuck with some differential equation, I've often found it easy to get the help I need from Polking so I can get back on track.

In contrast to Tannenbaum, which is a typical Dover small font, no frills publication, Polking is nicely produced and has nice graphics, making it a pleasure to read. Of course, if you have a need or inclination to achieve a deeper understanding of the differential equations, then Polking will not suffice. That's when I'd turn to Tannenbaum, which provides a lot more theory.

Overall, Polking is fine for self-study. The 2nd ed might be even better (or worse) but since I don't have it, I wouldn't know.

This book isn't really a five-star book, but it definitely isn't a two-star book. As another reviewer said, it'll give you a mechanical understanding of differential equations. It's not a hard book, which can be good or bad depending on what you're looking for. The chapters have more of the technical side of things, but the exercises are mostly on the easier side of things. If you have the algebra and calculus down pat, then using this textbook shouldn't give you any troubles.

The most important thing to keep in mind would be the intended audience of this book. Specifically, the concepts outlined in this text should complement the content provided by a legitimate math instructors. If I were to use this book to self-teach or something of the sorts, I'm sure I would hate this book as well. Although the examples are sometimes unclear, the summaries of techniques are the most helpful parts in the book. At the end of a section, a blue box outlining the fundamental steps in a process reveals the simplest way to approach any problem. For example, this text's summary of Variation of Parameters pretty much sums up everything about that process in a clear and concise way.

Anyways, it's not as if you have any other choice when the instructor assigns this text as a required material. If looking for a self-teach sort of book, this text is not that great. But if you're looking for a review of ODEs and whatnot, I would recommend this book.

First of I am a junior studying electrical engineering and vehicle engineering at Western Washington University. This book was the required text for WWU's math 321 course, it is called math for engineering majors or something similar but it is basically just a class were engineering majors learn diff EQ without going through all the other math classes required to take the normal diff EQ class.

Right from the get go this book was nice simply due to price; $20 compared to $150 is kind of a no brainer. Once using the book though it does not disappoint in quality. The chapters are well laid out and fairly thorough and seemed to compliment my professors lectures very well. I was able to take minimal notes in lecture and use those note combined with the explanations in the book to make it through chapters. Obviously a 300 level math class is not going to be easy and neither the book alone or the lecture alone is going to be enough to get you through diff EQ. Hopefully by the time you reach the 300 level you realize that classes aren't really optional and the subjects are so complex you can't expect a book to do all of the explaining for you.

The only major complaint(s) I have with this book are about the example problems in the chapters. Most importantly there aren't very many of them. In most sections, each section consisting of 7 or 8 pages, there are only 3 or 4 example problems. I feel that even just 2 more problems per section would go a long way in helping explain this subject. Also the explanations that go with the sample problems aren't the best in the world. Don't get more wrong you can definitely follow the example it just might take 5 or 6 time of reading though the text portion, whereas in most textbooks it only takes me 2 or 3 times to understand what is happening in the example problem.

Overall this is a decent book packaged with an excellent price, and those two factors combined make for a good book/value. If you are fortunate enough to take a diff EQ class good luck, it is interesting and applicable while being moderately challenging and if you're like me nothing is fun unless it presents challenges!

this book sucks-- plain and simple. Go and get some outlines and another textbook if you want to learn DiffE from this book. Examples are horrible, none of the problems correlate and this book just doesn't explain the in between steps. When i want to learn something, i need to see the complete though process, not spend hours trying to figure out how they got form point a to point b in the example.

and I don't "do" hyperbole.

As a math instructor (and math student), I have seen texts on everything from fundamentals of math to real analysis. This book is more practical, clear, and concise than any of them.

Students will not only learn techniques to solve differential equations, they will learn the scope and limitations of each technique. A student who truly reads and absorbs this book will walk away with not only an understanding of but also a healthy skepticism toward mathematical models. The harsh realities of mathematical modeling, such as sensitive dependence on initial conditions, are emphasized rather than downplayed. In the section on motion problems, students are treated to a discussion of how solar system models have evolved. Models must adapt to explain new data. Sometimes a model can be "tweaked" at the expense of simplicity, while some models must be scrapped altogether. Scientific ideas are not gospel, but merely a description of the world as we see it today.

Unfortunately, this text is the ONLY book I have seen which truly addresses the issues described above (and that's very sad because my undergrad degree is in chemistry). Aspiring scientists and engineers need to learn intellectual flexibility as much as they need to learn facts and formulas. This book teaches both.

If the applications in this book were not so overwhelmingly excellent, I would have started this review by exalting the proofs and derivations. They too are unusually well done. The authors do an excellent job of choosing which proofs to include, and they make them as readable as humanly possible. (I hear the bitter chuckles of innumerable math students as I type the previous sentence...)

Yes, learning to read proofs IS hard. But, trust me, this book is where you want to start. First graders think adding and subtracting whole numbers is hard. They're right; for them, it is. But imagine how much harder it would be if first graders had to work with fractions!

To paraphrase Aristotle, "learning is painful". No one can make differential equations easy (why do you think scientists and engineers get paid so well?). However, the authors of this text make it as easy and pleasant as possible.

I suspect that students who disliked this book but were able to "learn" diff. eq. merely learned enough to pass the test. Students who do not take advantage of the learning opportunity provided by this book are doing themselves a serious disservice.

Take home message- buy it and make it the central element in your studies of differential equations. You will be glad you did.

Because the guy who initiated the project of writing the book is here at Rice, the rest of us are unlucky enough to have to use this book. If your class uses this book, prepare to go to class. All the time. That's because if you fall behind, the book does not do a good job of explaining things to you. Examples are generally vague and only apply to a few types of problems provided at the back of each section. A lot of the time, I'd find myself stumped on a problem, looking back, and realizing there was no example problem for me to get ideas from.

Yes there are lots of problems and that's good, in a way. But what's the point of having all those problems if the book never teaches you how to do them?

Furthermore, it is a poorly written book. Generally, reading through the book is like searching for a needle in a haystack. Literally speaking. You spend all that time figuring out what the authors talk about and once you figure it out, it was not even worth all that time.

So go to class. All the time. If the prof isnt that great, get yourself another workbook. I havent seen Schaum's but I'm pretty sure they'll do a better job on covering the topics than this text does.

I loved this book. The examples are clear, the proofs are easy to follow, and the book has a major applications aspect regarding applying what you learn on the computer and Matlab. My only complaint is that ch 5 (Laplace Transformations) is a little too terse, but besides that it is perfect. This and Lay's Linear Algebra book are my favorite mathematics books I've used so far.

This is truly a great math textbook, in fact it's the first that I've ever noticed _good_ things about while working through it, instead of bad things. Also interesting is seeing Dr Polking teach, while reading through the book (I go to Rice) - I've never before seen an author of a math text. This book has a good but not over-bearing connection to technology; the accompanying MATLAB manual delves deeper into that aspect. The problem sets are interesting, instead of just being "grunt-work" they require some real thinking, and go into applications such as physics, etc. Overall a good buy.