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Differential Equations: A Modeling Perspective, by Robert L. Borrelli, Courtney S. Coleman
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This effective and practical new edition continues to focus on differential equations as a powerful tool in constructing mathematical models for the physical world. It emphasizes modeling and visualization of solutions throughout. Each chapter introduces a model and then goes on to look at solutions of the differential equations involved using an integrated analytical, numerical, and qualitative approach. The authors present the material in a way that's clear and understandable to students at all levels. Throughout the text the authors convey their enthusiasm and excitement for the study of ODEs.
- Sales Rank: #891353 in Books
- Published on: 2004-01-02
- Original language: English
- Number of items: 1
- Dimensions: 10.10" h x 1.20" w x 7.80" l, 3.38 pounds
- Binding: Hardcover
- 736 pages
From the Back Cover
Experience the power of mathematical modeling.
Borrelli and Coleman’s DIFFERENTIAL EQUATIONS: A MODELING PERSPECTIVE focuses on differential equations as a powerful tool in constructing mathematical models for the physical world.
Right from the start, the book provides a gentle introduction to modeling in Chapter 1. This chapter gathers the elementary principles of modeling in one place and uses simple examples. From there, you’ll explore specific models and examine solutions of the differential equations involved using an integrated analytical, numerical, and qualitative approach.
Build and solve your own ODEs with the ultimate ODE power tool!
This edition includes a CD containing ODE Architect–a prize-winning, state-of-the-art NSF-sponsored learning software package, which is Windows-compatible. A solver tool allows you to build your own models with ODEs and study them in a truly interactive point-and-click environment. The Architect includes an interactive library of over one hundred model differential systems with graphs of solutions. The Architect also has 14 interactive multimedia modules, which provide a range of models and phenomena, from a golf game to chaos.
Most helpful customer reviews
22 of 27 people found the following review helpful.
On second thought
By Lukas D.
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. )
9 of 11 people found the following review helpful.
Confusing, Disorganized, Too Little Examples
By College Student
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.
9 of 13 people found the following review helpful.
A good up-to-date introduction to Differential Equations
By A Customer
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
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