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Differential Equations with MATLAB

Brian R. Hunt, Ronald L. Lipsman, John E. Osborn and Jonathan M. Rosenberg
John Wiley
Publication Date: 
Number of Pages: 
[Reviewed by
Henry Ricardo
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In recent years, an increasing number of differential equations courses and texts have required the use of technology to treat the graphical, numerical, analytic, and qualitative aspects of a modern differential equations curriculum. This book, which had its origins in the SCHOLaR Project at the University of Maryland, College Park, is meant as a supplement to standard texts. In particular, the book is meant to complement the eighth edition of Elementary Differential Equations by Boyce and DiPrima.

Because the book assumes no prior experience with MATLAB®, there are four chapters of basic instructions for using MATLAB before a differential equation makes its appearance; and interspersed between ODE topics are discussions of additional MATLAB features, including Simulink®, an auxiliary simulation tool. The second edition corresponds to MATLAB 7 and Simulink 6. The list of ODE topics is comprehensive: direction fields, autonomous equations, numerical methods, second-order linear equations, series solutions, Laplace transforms, and higher-order equations/systems of linear equations. The qualitative analysis of systems is discussed, as are nonlinear systems.

The mathematical discussions are generally concise, most of the text being dedicated to useful commands and the creation of M-files. There are six Problem Sets, with some component exercises taken from Boyce and DiPrima. The book ends with a Glossary of MATLAB/Simulink information and a section of complete solutions to selected problems from the Problem Sets.

If an instructor were to embrace the spirit of the times and use technology in an ODE course, with MATLAB as the chosen software, then this volume would serve as an admirable reference. However, its thoroughness is also a drawback, possibly leading its user to a place from which he or she cannot see the forest for the trees.

Henry Ricardo ( is Professor of Mathematics at Medgar Evers College of The City University of New York and Secretary of the Metropolitan NY Section of the MAA. His book, A Modern Introduction to Differential Equations, was published by Houghton Mifflin in January, 2002; and he is currently writing a linear algebra text.

1 Introduction

2 Getting Started with MATLAB

3 Doing Mathematics with MATLAB

4 Using M-files and M-books

5 Solutions of Differential Equations

6 A Qualitative Approach to Differential Equations

7 Numerical Methods

8 Features of MATLAB

9 Using Simulink

10 Solving and Analyzing Second Order Linear Equations

11 Series Solutions

12 Laplace Transforms

13 Higher Order Equations and Systems of First Order Equations

14 Qualitative Theory for Systems of Differential Equations


Sample Solutions