Differential and Difference Equations through Computer Experiments

This is a somewhat unusual book with a dual purpose. First, it is a manual to help readers learn how to use PRASER, the program on the accompanying diskette for mM personal computers. Second, it is an illustrated guide to the wonderful world of experimental and theoretical dynamics, one which presents dozens of concrete examples ranging from the most rudimentary, appropriate for the beginning student, to the highly complex, suitable for the research mathematician. Before indicating what PRASER does and how it works, let me describe how it came a.bout. During the past decade the field of differential and difference equations has witnessed a remarkable explo sion of knowledge, not only in theory but also in applications to discip lines as diverse as biology and fluid mechanics. Computers have played a crucial role in this process by making possible detailed analyses of specific systems. In this regard, one need only mention the work of Lorenz on strange attractors and the discoveries of Feigenbaum on the bifurcations of interval maps.

Zusammenfassung
Second, it is an illustrated guide to the wonderful world of experimental and theoretical dynamics, one which presents dozens of concrete examples ranging from the most rudimentary, appropriate for the beginning student, to the highly complex, suitable for the research mathematician.

Inhalt
I: Mathematical Synopsis.- 1. What is a Differential Equation?.- 2. Numerical Methods.- 3. What is a Difference Equation?.- II: Handbook of PHASER.- 4. Learning to Use PHASER.- 5. Lessons with PHASER.- 6. Reference Guide to Menus.- III: Library of Equations.- 7. Differential Equations.- 8. Difference Equations.- What remains to be done?.- Appendix A: PHASER Quick Reference.- Appendix B: Library of Equations.- References.