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: 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.

1. Introduction.- How This Lab Book Is Organized.- Using the Diskette.- Where to Go for More Information.- Acknowledgments.- 2. Getting Started with Maple.- Starting Maple.- Basic Maple Syntax.- Basic Maple Objects.- Mixing and Matching Different Number Types.- Strings.- Maple Expressions.- Sets and Lists.- Calling Maple Commands.- Assignments and Equations.- The Use of Quotes in Maple.- Activities for
2.- 3. First-Order ODEs.- Defining and Solving First-Order ODEs.- Explicit vs. Implicit Solutions.- Activities for
3.- 4. Applications of First-Order ODEs.- Falling, Floating, or Accelerating Objects.- Mixture Problems.- Activities for
4.- 5. Graphical Methods.- Direction Fields.- Some Examples.- Activities for
5.- 6. Homogeneous Linear Differential Equations.- Activities for
6.- 7. Non-homogeneous Linear Differential Equations.- Activities for
7.- 8. Applications of Linear Differential Equations.- Free, Undamped Motion.- Free, Damped Motion.- Activities for
8.- 9. More Applications and Systems of Differential Equations.- Forced Motion.- Systems of Linear Differential Equations.- Activities for
9.- 10. Phase Planes.- Activities for
10.- 11. Matrix Operations.- Basic Concepts.- Characteristic Values and Characteristic Vectors.- Activities for
11.- 12. Matrix Methods of Solution.- Activities for
12.- 13. Isoclines.- Activities for
13.- 14. Series Solutions.- Activities for
14.- 15. Numerical Methods.- Problems with Numerical Methods.- Activities for
15.- 16. The Laplace Transform.- Activities for
16.