Customer Reviews

Differential Equations: A Modeling Perspective

5 star:		(6)
4 star:		(1)
3 star:		(0)
2 star:		(2)
1 star:		(8)

 

 

A terrible book to learn DEs from. Just finished a course using it, they expect you to know how to solve problems with poor examples or any examples at all. This book expects you to figure everything out on your own. Also, it is useless to study from, as there are only 1 or 2 questions that actually have answers in the back of the book. It is simply cryptic, and one has to waste more time than is really neccesary to be able to figure it out. Buy another book.

This text teaches Differential Equations using the models and tools that both mathematicians and engineers use. It uses the modeling process to show how the DEs are developed. It uses numerous examples showing how to understand a DEs behavior using numerical solvers as well as standard analytical techniques and (when they exist) solution formulas.

Because it doesn't use a cookbook approach to solving DEs, it isn't restricted to just those DEs for which there is a standard solution method. Since it can deal with this wider variety of DEs, it can introduce more interesting models (e.g., the autocatylator) which it would otherwise ignore. The graphs used to illustrate these models are easy to understand, incredibly detailed, and very pretty.

This book gives a very complete introduction to Differential Equations and to the models that they describe.

--A student at Harvey Mudd College

The book doesn't provide students with a good picture of basic techniques in DE. In fact, it doesn't teach them any technique on a regular basis. I teach Numerical Methods for Differential Equations in a math class which had this book as a textbook for their DE course. Unfortunately, the lecturer followed the book too closely. Kids have a very vague understanding how to work with DE's. Any reference to this book doesn't help - a simple concept may be spread across a few chapters and eventually shall be extracted from examples.

I wrote a first review, and the author hunted down my email address and emailed my differential equations teacher. In the email, he said, I should wait until I finished the course until I reviewed his book. I realized how wrong I was to shoot my mouth off. I should have been more sagacious and patient in order to tell the truth.

First the good: I only spent 40 bucks on this book and should be able to get my money back. And the author spent tons of time designing little computer cartoons because there's nothing I like better than being distracted by a funny cartoon.

The bad: If you don't have ADD before you pick up this book, you will after. Printed on wonderfully shiny paper, with multicolored graphs, headers, footers, pictures, and once in awhile even something haveing to do with differential equations, this book is next to impossible focus on. That's part of the reason some students like this book. They don't have to read. They can just look at the pictures then ask someone else for help.
Do you want to learn about differential equations? Well, if you buy this book, you might. If you pair this book up with another book that explains why this stuff makes sense. And then read only that book. Good understanding of the more difficult problems come from a good foundation. This book spends 2 chapters on the basics. But boy, you want to graph stuff, here's your chance. (You can even have an assignment to graph a kitten out of differential equations, i mean man, that's worth a star right there.) The author succumbs to greedius maximus, wherein he crams as much crap into a book to sell as many copies as possible, instead of focusing on one thing and doing it well. Because no one really needs more than 20 pages to describe all of second order differential equations. The computer can do all that for you.
Oh, and if you want to learn how to solve differential equations for something like physics class, good luck. You have two choices in this book, you can either guess and make up your own way of doing things, or you can use the cookbook approach. You won't really know why you want to take the exponential, but that doesn't matter because you just need a grade. So you follow the clever boxed text that says do this, this, than this. And voila, you have an answer. And to anyone who says, well, we have to graph most differential equations because we can't solve them, i say, wonderful? So, I can just move onto stuff no one understands and expect to make sense of it by not understanding the equations we do know how to solve.

And since I need to plug Dover to make my 20 dollar commission, buy Morris Tenenbaum's Ordinary Differential Equations book. It's not fancy, but it's well written and 800 pages long. Which is funny, because Borrelli's book is 790 pages long and tries to cover ODE's, PDE's and Linear Algebra. Telling detail? I think so. ( I bet you could even buy a couple of awesome Dover books on PDE's and Linear Algebra and still undercut the 115 dollar selling price by about 3/4. )

First, I would like to warn students wishing to introduce themselves to Differential Equations (DEs) to avoid this book if they do not have a strong mathematical background. The book does not use a linear approach common in other books, and tends to integrate DEs with other subjects such as engineering, physics, biology, and other fields of mathematics while spreading out the topics. At times, the book tends to skip algebraic steps, making it confusing for those who are not as strong in algebra. First-timers will find this book hard to follow on their own, but with the guidance of a good professor, it should not be too hard to tackle.

Unlike other textbooks that teaches one topic and proceeds to give thousands of examples, this book does not do that. Instead, it uses the "modeling approach" to show how DEs relates to other fields of science. A person interested in mathematics and science will find this book very intriguing because of how well it relates math to everything else in life. Problems in this book are generally harder than problems of average DEs books, but once the students become used to them, it will be much more helpful. Not only does this book help the students understand the new concept of DEs, it aids them in reviewing the calculus and algebra (along with complex numbers, linear algebra, and trigonometry).

Overall, this is a perfect book for someone who likes math but finds most "advanced" high school textbooks too simple. This book does not merely repeat examples until the student understands the material. The student is expected to work out practice problems on his own and check his answers with the back of the book. This book uses proofs to discover theorems instead of just stating it while leaving the motivated student perplexed on how mathematicians came up with the theorem. Finally, this book includes the ODE (Ordinary Differential Equations) CD, which assists the student in the learning process with visual aids and graphic demonstrations. While this program may not be as powerful as Mathematica or Maple, it runs much faster and is more convenient in learning DEs.

I used a preliminary version of this book when I was a student, and was later involved for 2 months with doing edits for the first edition. I am now teaching a differential equations course out of a different textbook. I keep going back to this book for examples to use, or for better ways to present material. It's a very good book, and the models that I was exposed to while studying from this book have significantly affected the course of my research since then.

A few words of warning: this book assumes that the students are comfortable with mathematical concepts and general science. If your students struggle with the fact that (a+b)^2 is not a^2 + b^2 or if they don't understand why e^{a+b} is not e^a + e^b, they are going to have a very hard time with this book. On the other hand, if you want your students to come out of the class knowing how to look at a physical problem and then figure out what the equations are that underlie it, and then to solve them, then this is a good book to use.

Having read the reviews out there, some responses to the negative reviews are in order. The most common criticisms I've seen are either that there aren't enough theorems and proofs, or that there is too much guessing going on. This book, in its title, states that it is a modeling perspective - if you want a theorem-proof book you can definitely find them. However, if you want to teach physicists and engineers and applied mathematicians the skills they need, then spending all your time on theorems and proofs isn't the right approach -- a colleague of mine once told me he didn't learn how to use an integrating factor until graduate school, but he knew all sorts of things about whether a solution existed or was unique. If you are concerned that there is too much emphasis on "guessing", then you haven't read many ODE textbooks. Most textbooks I've seen suggest that you guess a solution, and then after the fact turn to the Wronskian or some similar argument to show that the guess will work. My experience with Borrelli and Coleman was that I constructed the general solution form, and then I understood why the solution takes a form and so I have no problem making that guess.

To summarize: this is not an easy book intended for students who need to be constantly reminded of concepts from high school algebra. It assumes that the students have a moderate level of mathematical sophistication, and that they are comfortable with the idea that differential equations underlie most physical processes. If your intention is that the students understand how to find those equations and how to work with them in a wide variety of contexts, then this is the right book.

This is a very terrible book to learn differential equations from. Every professor I've talked to loves it. Ironically, every student I know (including myself) absloutely loaths it. I really need examples to learn something. This "modeling" thing just doesn't cut it.

This book is undeniably the worst math book I have ever used. While the authors and student editors are undoubtedly more comfortable with the subject matter and are intelligent people, I found the text to be uncomprehensible by people that didn't already understand the material.

If you are a student in an ODE course, I would recommend using another text. You may sleep better.

I too have found that this book is full of 'issues' that make learning ODEs not only a chore, but next to impossible. The problems presented in the book make little sense to anyone except for the profs. If you are planning on teaching an ODE course with this book, I beg you to reconsider your choice of books for the sake of your students.

I do not feel I learned much math from reading this book. There is no logical presentation or foundation. The problems are mostly complicated arithmetic, and one is lucky to get the right answer, let alone learn from it. I would prefer a more thorough, axiomatic approach. This is like a storm of equations thrown at you without being TAUGHT to you.