Synopses & Reviews
This book and disk package is a supplement to any currently existing introductory text on Ordinary Differential Equations and uses Maple V as a computational tool to further understanding and importance. Maple is a powerful symbolic computer software package with which the student can learn to perform many tasks. This platform allows one to do many mundane tasks quickly and efficiently enabling new ways of illustrating and thinking about difficult concepts which will allow for new depths of understanding. Numerical and graphical information and methods are emphasized along with symbolic results throughout this manual in order to take advantage of the versatility of Maple and to increase the breadth of understanding of the student.
Synopsis
The Maple ODE Lab Book is intended to provide a thorough introduc- tion to using symbolic computation software to model, solve, explore, and visualize ordinary differential equations. It is best used as a supplement to existing texts (see the bibliography for some of our recommended texts). Maple was chosen as our software package because of its ease-of-use, affordability, and popularity at many universities and colleges around the world. The version being used is Maple V Release 4. If you have a previous release of Maple, some of the commands shown in this lab book will work differently (or not at all), but the basic groundwork for solving ODEs hasn't changed. Speak to your system administrator about upgrading to Release 4, or contact: Waterloo Maple Inc. 450 Phillip Street Waterloo, Ontario CANADA N2L 5J2 Phone: (519) 747-2373 FAX: (519) 747-5284 E-mail: info@maplesoft.com WWW: http: //www.maplesoft.com 1 2 - Chapter 1. Introduction How This Lab Book Is Organized Each subsequent chapter of this lab book contains information and ex- amples of how to apply Maple to various elements of ordinary differential equations. It is suggested that you read the chapters with your computer on and Maple V Release 4 running. You can then execute many of the com- mands yourself and experiment by changing various parameters and/or initial conditions, observing the corresponding changes in the results.
Table of Contents
Contents: Introduction.- Getting Started with Maple.- First-order ODEs.- Applications of First-order ODEs.- Graphical Methods.- Homogeneous Linear Differential Equations.- Non-homogeneous Linear Differential Equations.- Applications of Linear Differential Equations.- More Applications and Systems of Differential Equations.- Phase Planes.- Matrix Operations.- Matrix Methods of Solution.- Isoclines.- Series Solutions.- Numerical Methods.- The Laplace Transform.