The Maple® O.D.E. Lab Book

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.