Computer Algebra Recipes

2 INTRODUCTION
B. Computer Algebra Recipes
The mathematics is not there till we put it there.
Sir Arthur Eddington, The Philosophy of Physical Science, 1939
The ODE and PDE recipes in our computer algebra \menu" have been organized
into three sections of increasing mathematical sophistication. The Appetizers
illustrate phase-plane portraits and analysis, the Entrees deal with
linear and nonlinear ODEs and linear PDEs, and the Desserts feature the
hunt for solitons and some nonlinear diagnostic tools. The recipes are intended
to ful¯ll not only a useful and serious pedagogical purpose but also to titillate
and stimulate the reader's intellect and imagination. Associated with each
recipe is an important scienti¯c model or method and usually some historical
background or an interesting story featuring an engineering or science student
who will guide you through the steps of the recipe. These storybook characters
are ¯ctitious composites of some of the more likeable, industrious, and brighter
students that the authors have had the privilege of teaching over the years.
Every topic or story in the text contains the Maple code or recipe to explore
that particular topic. To make life easier for you, all recipes have been placed
on the CD-ROM enclosed within the back cover of this text. The recipes are
ordered according to the chapter, section, and subsection (story) number. For
example, the recipe 01-2-3, entitled RÄossler's Strange Attractor, is associated
with Chapter 1, Section 2, Subsection 3. Although the recipes can be directly
accessed on the CD by clicking on the appropriate worksheet number, it is
recommended that you access them through the menu index ¯le, 00menu.
All recipes may be conveniently accessed from this menu using the hyperlinks.
Complete instructions on how to do this may be found in the menu ¯le.
The computer code on the CD is unannotated, so you will have to read the
text in order to understand what the code is trying to accomplish. The code has
been imported into the text and here is accompanied by detailed explanations
of the underlying modeling concepts and computational methods.
The recommended procedure for using this text is ¯rst to read a given
topic/story for overall comprehension and enjoyment. If you are having any
di±culty in understanding a piece of the text code, then you should execute
the corresponding Maple worksheet and try variations on the code. Keep in
mind that the same objective may often be achieved by a di®erent combination
of Maple commands from those used by the authors. After reading the topic,
you should execute the worksheet (if you have not already done so) to make
sure the code works as expected. At this point feel free to explore the topic.
Try rotating any three-dimensional graphs or running any animations in the
¯le. See what happens when changes in the model or Maple code are made and
then try to interpret any new results. This book is intended to be open-ended
and merely serve as a guide to what is possible in mathematical modeling using
a CAS, the possibilities being limited only by your own background and desires.
Each topic or story is self-contained and generally done completely, from