Differential Equations: A Modeling Perspective [Hardcover]

Robert L. Borrelli (Author), Courtney S. Coleman (Author)

Book Description

ISBN-10: 0471433322 | ISBN-13: 978-0471433323 | Publication Date: January 2, 2004 | Edition: 2

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.

Editorial Reviews

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.

Product Details

• Hardcover: 736 pages
• Publisher: Wiley; 2 edition (January 2, 2004)
• Language: English
• ISBN-10: 0471433322
• ISBN-13: 978-0471433323
• Product Dimensions: 10.2 x 8.2 x 1.2 inches
• Shipping Weight: 3.4 pounds (View shipping rates and policies)
• Average Customer Review: 2.7 out of 5 stars  See all reviews (17 customer reviews)
• Amazon Best Sellers Rank: #212,049 in Books (See Top 100 in Books)

More About the Author

Discover books, learn about writers, read author blogs, and more.

Customer Reviews

Most Helpful Customer Reviews

6 of 6 people found the following review helpful:

2.0 out of 5 stars Confusing, Disorganized, Too Little Examples, May 8, 2006

By 

College Student (Claremont, CA) - See all my reviews

This review is from: Differential Equations: A Modeling Perspective (Hardcover)

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.

8 of 11 people found the following review helpful:

5.0 out of 5 stars A good up-to-date introduction to Differential Equations, June 9, 1998

By A Customer

This review is from: Differential Equations: A Modeling Perspective (Hardcover)

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

7 of 10 people found the following review helpful:

1.0 out of 5 stars I would not recommend this book for a science or math class, October 28, 2004

By 

Lecturer (Australia) - See all my reviews

This review is from: Differential Equations: A Modeling Perspective (Hardcover)

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.