Textbook

# Differential Equations with Matlab, 2nd Edition

• Overview
“Differential Equations with MATLAB” (2nd ed.) by B. Hunt, R. Lipsman, J.Osborn and J.Rosenberg is a supplemental text that can enrich and enhance any first course in ordinary differential equations. Designed to accompany Wiley’s ODE texts written by Boyce/DiPrima, Borrelli/Coleman and Lomen/Lovelock, this supplement helps instructors move towards an earlier use of numerical and geometric methods, place a greater emphasis on systems (including nonlinear ones), and increase discussions of both the benefits and possible pitfalls in numerical solution of ODEs. By providing an introduction to the software that is integrated with the relevant mathematics, “Differential Equations with MATLAB” can perfectly complement and enhance these texts.
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

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

Glossary

Sample Solutions

Index
Hallmark Features
The following four techniques, all quite important for today’s scientists and engineers, are included:

1. Symbolic Computation

Students use “dsolve” to find exact symbolic solutions to a wide variety of differential equations. These solutions are often in terms of elementary functions, but sometimes they involve special functions.

1. Geometric/Qualitative Analysis

Discusses direction fields, solution curves, stability, and the qualitative analysis of differential equations (especially autonomous equations). Students become proficient in using MATLAB to draw direction fields, to understand the implications of the direction field for the solutions, and to plot solution curves and phase portraits.

1. Numerical Computation

Students become proficient in using MATLAB’s ode45, a state-of-the-art numerical solver, and they develop a general understanding of numerical methods based on practical experience. This skill and understanding is developed in close connection with the usual elementary numerical methods (Euler, Improved Euler, and Runge-Kutta).

1. Use of Simulink

Simulink is a software package that enables one to model, simulate, and analyze systems whose outputs change over time. It is a convenient way to study the behavior of important dynamic systems: systems involving electric circuits, mechanical systems, etc. We present a concise, but accessible, introductory treatment.

## Available Versions

Differential Equations with Matlab, 2nd Edition
by Brian R. Hunt, Ronald L. Lipsman, John E. Osborn, Jonathan Rosenberg
ISBN 978-0-471-71812-3