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Differential Equations (with CD-ROM), by Paul Blanchard, Robert L. Devaney, Glen R. Hall

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This text pioneers a new way of teaching the standard sophomore-level differential equations course. The authors stress a more balanced approach, one that includes analytic, numeric, and graphical techniques. The text emphasizes modeling and qualitative theory throughout the course. It employs technology significantly and consistently, presents linear and nonlinear systems in parallel, and includes an introduction to discrete dynamical systems. This text grew out of the Boston University Differential Equations Project, funded in part by the National Science Foundation.
- Sales Rank: #1049588 in Books
- Brand: Brand: Brooks Cole
- Published on: 2002-01-18
- Original language: English
- Number of items: 1
- Dimensions: 9.25" h x 8.00" w x 1.25" l,
- Binding: Hardcover
- 786 pages
Features
- Used Book in Good Condition
Review
"I liked the emphasis on qualitative and numerical solution methods in addition to the more traditional analytic techniques. Students come away from a course using this text with a better understanding of what an ordinary differential equation (ODE) is and what it means to "solve" such an equation."
"It is clearly the best undergraduate ODE text that I have ever looked at, and I am pushing to have the text adopted for all our undergraduate differential courses. . . The authors have jettisoned the classic "cookbook" approach in favor of one which fosters critical thinking. The students need to formulate, solve and interpret the solutions to the problems. In order to do this effectively, the students are taught some fundamentals of modeling and are presented with an arsenal of tools, including qualitative, numeric, and analytic approaches for solving differential equations."
"I really liked the way that systems are introduced at the beginning of the text and stressed throughout the remainder of the text. I thoroughly enjoyed the systems approach to solving DE's and my students did, too. In fact, when we hit the "lucky guess" methods in later sections, my students found these traditional methods of solving DE's to be a snap compared to the algebra they used when solving systems. . . I liked the continuous emphasis on qualitative analysis. It was made evident in the first section of the text that graphical analysis would be used as a significant problem solving tool and the value of qualitative analysis was repeatedly stressed throughout the remainder of the text. . . I liked the balance between graphical analysis and the traditional symbolic analysis required in your typical DE course. I do not feel in the least that my students were shortchanged on symbolic manipulations required to be successful in later courses. On the other hand, the authors were careful not to go overboard and introduce one symbolic technique after another. I really feel they struck a fair balance."
"There are many texts that claim to be written in the spirit of the so-called calculus reform movement. In my opinion, the text under review achieves this goal better than any book that I have seen. This book presents at a very elementary level the kinds of material that opens the door for the understanding of many of the great achievements in dynamical systems that have been accomplished over the last 30 years."
About the Author
Paul Blanchard is Associate Professor of Mathematics at Boston University. Paul grew up in Sutton, Massachusetts, spent his undergraduate years at Brown University, and received his Ph.D. from Yale University. He has taught college mathematics for twenty-five years, mostly at Boston University. In 2001, he won the Northeast Section of the Mathematical Association of America's Award for Distinguished Teaching in Mathematics. He has coauthored or contributed chapters to four different textbooks. His main area of mathematical research is complex analytic dynamical systems and the related point sets, Julia sets and the Mandelbrot set. Most recently his efforts have focused on reforming the traditional differential equations course, and he is currently heading the Boston University Differential Equations Project and leading workshops in this innovative approach to teaching differential equations. When he becomes exhausted fixing the errors made by his two coauthors, he usually closes up his CD store and heads to the golf course with his caddy, Glen Hall.
Robert L. Devaney is Professor of Mathematics at Boston University. Robert was raised in Methuen, Massachusetts. He received his undergraduate degree from Holy Cross College and his Ph.D. from the University of California, Berkeley. He has taught at Boston University since 1980. His main area of research is complex dynamical systems, and he has lectured extensively throughout the world on this topic. In 1996 he received the National Excellence in Teaching Award from the Mathematical Association of America. When he gets sick of arguing with his coauthors over which topics to include in the differential equations course, he either turns up the volume of his opera CDs, or heads for waters off New England for a long distance sail.
Glen R. Hall is Associate Professor of Mathematics at Boston University. Glen spent most of his youth in Denver, Colorado. His undergraduate degree comes from Carleton College and his Ph.D. comes from the University of Minnesota. His research interests are mainly in low-dimensional dynamics and celestial mechanics. He has published numerous articles on the dynamics of circle and annulus maps. For his research he has been awarded both NSF Postdoctoral and Sloan Foundation Fellowships. He has no plans to open a CD store since he is busy raising his two young sons. He is an untalented, but earnest, trumpet player and golfer. He once bicycled 148 miles in a single day.
Most helpful customer reviews
12 of 14 people found the following review helpful.
The Perfect Soph/Junior level DE book
By Nicholas Hoell
I used this book in a 2003 summer course in DE, and found it to be a wonderful introduction to the subject. I am not sure what some of the other people meant by saying it wasn't for math majors- I am one and found it wonderful. Not everything needs to be concise, (I gave Rudin's book five stars too BTW, so I AM a fan of some concise books).
It gave diverse examples of applications from all over--physics, EECS, ecology, biology, etc. The CD-Rom is a great learning tool. Ultimately analytic techniques are NOT what DE is about, and this book tries to show the student how to use qualitative and numerical methods early on. Anyone who wants to know DE must become familiar with numerics and the qualitative way of analyzing the equations.
This book will show you how to THINK about DE, and not how to mindlessly attack an equation based on its form.
This is the intro ODE book to which all others ought be compared.
If one wants an analytic reference just buy a cheap used copy of any of the countless DE cookbooks out there (I own a Shaums).
44 of 55 people found the following review helpful.
The Long and Fluffy Intro to Differential Equations
By Marc Corluy
I am an instructor teaching an introductory differential equations class using this book. Regrettably, the book is more of an extra weight to carry than a heplful tool.
Yet it is not so obvious to see why. A lot of the explonations are rather well done,
the examples are quite well chosen and constantly, th authors are trying to generate
a certain intuition in the reader.
I suppose the problem is that it is a full blooded ripoff textbook. It costs a whopping
$125 and therefore, it must have almost 800 pages, a shiny expensive looking
hardcover and a CD-ROM. The CD-ROM contains "Maple applet" like tools, that
come with huge drawbacks: often you can only choose the parameters in an equation in a very small interval and there is no normal way to print out any of the
graphics. You have to do a screen dump and then crop out the output screen of
these tools. Most freeware has more functionality.
To conclude, I suppose that my dislike for this book is mainly generated by the
fact that it has all the flaws of a textbook in todays perverted textbook market:
- overpriced
- comes with a semi-useless CD-rom
- explanations grotesquely drawn out, e.g. the basic theory of linear systems of
differential takes about 80 pages
- core concepts and ideas are freely mixed with tangential remarks and colorful
"faits divers" making no distinction between them whatsoever; when seeing diff. eq. for the first time you'll be as confused as humanly possible
Finally, I would like to end with a quote from the "Note to the Student" in the book:
"This book is probably different from most of your previous mathematics texts.
If you thumb through it, you will see that there are very few boxed formulas, no margin, notes and very few n-step procedures. We wrote the book this way because
we think that you are now at a point in your education were you should be learning
to identify and work effectively with the mathematics inherent in everyday life."
Can you believe this arrogance? This attitude is fine if you write a book for scientists and engineers to read by the fireplace on a cold winter evening while sipping from a glass of earthy and robust wine from the Bordeaux or Sud-Est regions, but not if you actually write it with students in mind, students that are going through their first diff. eq. class.
In short, as a reference it is useless, as a study guide it is mediocre at best, as "science leisure" book it is quite acceptable. But then, that would never fetch $125 on the free market.
33 of 35 people found the following review helpful.
A Student�s Perspective
By A Customer
As a recent differential equations student, I have mixed feelings about this book. I did thoroughly read those portions of the book covered by my instructor, and I did learn enough from it to get an A in the class. So I'll concede that it does a fairly good job as a textbook. In fact, I found it relatively easy to understand, which surprised me given the subject. However, the book has two serious shortcomings.
First, it's too verbose. The authors probably could have cut the size of this book in half without sacrificing any of its clarity or utility; in fact, they would likely have improved upon both had they done so. Mind you, I'm not suggesting that it's boring, it's just too long for a student in a hurry.
The second shortcoming is its questionable value as a reference book. Most math books with which I'm familiar have extensive indexes, and do a good job of highlighting important concepts and formulas. This book does neither. The index for this 786 page book is just over nine pages long. That might not sound bad, but many of the entries refer back to specific examples and homework problems with arcane names like "Magic Fingers", "Glass Harmonica", and "Robo-lobster", even while many key words were omitted. To make matter worse, the authors (according to their preface for students) made it a point not to mark important material in a way that would make it stand out. They also wrote many of their more advanced examples in a way that forces students to derive the intermediate steps on their own. This is arguably educational, as it forces students to practice earlier material while they're reading, but I can only imagine the hell it's going to put me through when I have to refer back to the book years from now.
In short, if you have a lot of time on your hands, this is a great book from which to learn differential equations. However, it's a terrible reference book, and nearly impossible to skim. In fact, it's even hard to study from.
See all 21 customer reviews...
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