Customer Reviews

Differential Equations, Student Solutions Manual: An Introduction to Modern Methods and Applications

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

 

 

This review is of the first edition (with the dam on the cover).

Short version: This book is terrible, stay away.

Less short version: I have taught a first course on differential equations out of several different books and this one is easily the worst. Differential equations is a beautiful topic, for many practical and theoretical reasons. This book does not in any way portray this spirit, and is probably scaring away talented young minds from pursuing mathematics and engineering. I can't wait to burn my (free) instructor's copy. My major issues with this book are:

1. My biggest complaint is that this book is obscenely overpriced for what you get. None of this material is new or specialized, it can all be found on the web for free. MIT has open courseware on differential equations with a far better presentation for example.

2. The book is poorly written #1: The notation used throughout the book ranges from atrocious to flat out ambiguous. For example, on p. 340 the author defines the indicator of the interval [c,d) by u_{cd}(t), where u_{a}(t) is the Heaviside function, which turns on from 0 to 1 at t=a. With this notation there is no difference in how the indicator of [2,3) and the Heaviside at t=23 are written, they both are u_{23}(t). This is a bad practice, and beginning students in mathematics and engineering should not be exposed to this practice.

3. The book is poorly written #2: Most of the sections of the book read like someone doing various problems taken from various topics for no rhyme nor reason. There is little to no discussion about building intuition of DEs or about how the topic in question fits in with the bigger picture. The sections on the "theory" are particularly bad. The Wronskian determinant is overused (even in the 2D case!) and not properly introduced, with no reason given as to why we need a fundamental set of solutions or what that even means. A good textbook first motivates new material, then highlights the important points through the use of instructive examples. Each example should have a specific purpose which shed light on the strengths and limitations of a particular theorem or technique. Furthermore this specific purpose in choosing the example should be clearly explained to the student before and after the example. The book by Blanchard, Devany, and Hall does a much better job of this overall, even though it's long-winded and "fluffy" at times (and extremely overpriced as well).

4. The book is poorly written #3: The exercises at the end of the section are dull and unimaginative, most just involve excessive calculations with no real educational value. Doing homework problems is where much of the learning process should take place, with this book it's a lesson in pain tolerance and boredom.

5. The answers to both odd and even problems are in the back. I prefer books that don't have ALL the answers, the temptation for most students is too great and this becomes a crutch.

6. Much of this book is "borrowed" from Boyce and DiPrima's "Elementary Differential Equations and Boundary Value Problems", which is a better book (but still overpriced, see the pattern?). In fact it is pretty easily to tell which sections come from that book because those are the sections that are somewhat readable.

7. There are errors that I hope are just misprints. For example, in Example 1 of section 6.3 on p. 414 the authors compute the vectors in the eigenspace for a repeated eigenvalue. In particular the eigenspace is written as an arbitrary linear combination of two basis vectors. They then go on to form two new vectors by choosing two particular linear combinations of the basis vectors (no reason given as to why those particular linear combinations were chosen) and say they are doing it to get a pair of linearly independent eigenvectors. The basis vectors they had WERE already linearly independent. My guess is that they wanted two orthogonal vectors. Why they would want to do this in the first place, I have no idea. There is no reason given. And again it is just a guess because there is no motivation given for anything done in this book.

The only good thing I can say about the book is that it includes some of the topics that engineering students will see in future courses that other introductory books do not. However this offers no advantage because the topics are poorly covered. A better alternative is Kreyszig's "Advanced Engineering Mathematics", but be sure to buy a used less expensive copy.

In conclusion, do not choose this book (if you have a choice). If you are a student shackled by the chains of bloodthirsty publishers, like Wiley in this case, my heart goes out to you. Speak up and do not tolerate this nonsense! There are good alternatives including (but of course not restricted to) some of the yellow Springer books, MIT opencourseware, even one of the other overpriced Intro to DE books (I like Blanchard, Devany, and Hall better than most for having clearer mathematics, and great examples and problems, Boyce and DiPrima is also better). As you can tell from this review I won't be nominating this book for any "Textbook of the Year" awards, and although this review is very harsh I hope you find it substantive. I also hope this review is helpful to you and saves you some frustration and $$$.

Never before have I encountered a [Math] book with as many words as the one that I am currently writing a review for. Rather than show the reader visually of why things are, the authors have taken it upon themselves to take the approach of explaining via verbose text why things are. While some may find this a better approach, the fact that there exists very little examples proves this method futile and frustrating. The ONLY thing salvageable from this book is the inclusion of the answers in the back of the book. Even then, if one wants to truly learn differential equations, another book should be sought.

This book is poorly written, overly verbose, and poorly structured. After having consulted some other references, having figured out how to do the problems, and having completed the assigned problems, I am still unable to make ANY sense at all out of the book's explanations. Another specific criticism: In just about every section, the author introduces some new method or theorem in the problems, leaving the exercise to the reader. These introductions are very incomplete, and leave students groping in the dark. Then there are additional problems, "Using the method of problem x, solve..." Quite frustrating. Seriously, textbook publishers give free books to instructors... Do they look at them before making a selection? And for the price of this book, I expect to be able to learn differential equations just by putting the book under my pillow at night.

Just looked back at this book a year after taking the class.

Don't miss class, because this book can't explain anything.

This is by far the worst math book i have ever worked with. it mostly consists of computer programmed solutions in the back which somtimes makes it impossible to get to that answer. my teacher even said it was horrible and not to follow it but just to do the problems out of it. how it explains to do the work is written like an essay and not shown very well in any form. if this is required for a class make sure you either have a good teacher or are in a good study group because just reading this book isnt going to help you at all. the only good thing about it is you have all the answers in the back of the book not just odds or evens

The book skips around too much and has way too many paragraphs for a math textbook. Steps are often skipped which means it can take an hour to figure out something that really takes 10min. My college seems to have a contract with Wiley Publishers as almost all our books are from them. Book is boring and confusing. Many of the chapters are not included in general topics for diff eq students. They are extra. The manual has been alot of help. That and other books. But not this book. Also, The "modern applications" part is very annoying.

Has solutions for only odd problems. No table of contents, and no distinct indicator for each individual section or chapter so finding the section you want to look for is a bit of a hassle.

Other than that, it explains the answers well (so far).

Working through the problems it does not show every step except sometimes in the beginning of a particular section, but if you get stuck it shows enough that you can work backwards and figure out how to unstick yourself and move on. I didn't read the book at all but used the solutions manual to work through the problems and it still makes sense.

Not a bad book at all. I wish all the solutions were in depth, but it gets the job done. I would recommend it.

WEll I couldn't do my homework without this, because if I go stuck and didn't have it then I was just stuck for a really reeeeally long time. The book sucks a lot but the solution manual is good. Although I didn't give it the full stars because sometimes it skips steps because it assumes you know how they got there, which sometimes you don't. I think there were maybe one or two problems on the 4th chapter where the corresponding answer was not associated with the number of the problem but the one next to it. I think it was the word problem section on chapter four. So be aware of that. But if your answer is not the one in the book you can just check the back of the textbook because the answers are on there too.

The skipping steps thing was the major issue with me, if it wasn't for that I would give it a 5 out of 5.