"Anyone with... an interest
in differential or difference equations should buy Huseyin Kocak's
Differential and Difference Equations Through Computer
Experiments. Both the book and its accompanying software are of
the highest quality in terms of mathematical taste, pedagogical
usefulness, and professional programming technique.
The package provides the software and explanation necessary
to study equations approachable only by experts just a few
years ago."
--- BYTE Magazine
"I also like the program because it motivates the study of dynamical systems.
When I first tried Phaser it displayed "phase portraits" for differential
equations that I found puzzling. As a result I began reading the referenced literature
on differential equations and dynamical systems. As I studied the references,
I began to understand dynamical systems better than I ever had in the past.
Without the program I doubt I would have been so motivated.
As one would expect given the role that computers play in the new science, Phaser helps illustrate
many ideas in chaos theory. James Gleick's best-selling book about chaos
provides historical details about several equation systems in Phaser's library. Conversely,
Phaser provides concrete examples of some dynamic models discussed in Gleick's book.
Conclusions: I concur that Phaser is "... an effective tool for performing mathematical experiments
and for illustrating the theory of dynamical systems with concrete examples..."
as the review of the second edition in Academic Computing stated. It can help students and
probably researchers also to access a sophisticated and elegant part of mathematics."
--- Notices of the American Mathematical Society
"There may be good reasons not to start up a computer lab for your ODEs course.
Thanks to Phaser, however, the
time and trouble of teaching students how to use the software isn't one of them.
No review of Phaser would be complete without mentioning the "manual".
In addition to 15 well-designed tutorial
lessons and a reference guide to the menus which contains just the right amount of detail,
the book contains a short
review of differential and difference equations and a short section on
numerical methods in general. These are
meant to supplement, not replace, a standard text on ODEs. Additionally,
all of the stored equations that come with
Phaser appear in a bestiary of equations and illustrations in the back of the book.
This section includes not just the
equation and the standard parameter settings, but also a short discussion of
the equation's significance, and
references to the literature. The value of this manual/reference book cannot be overemphasized.
If you want good software that can help your students learn about
the geometry of solutions of ODEs and
difference equations, software to introduce them to numerical methods,
then Phaser may just be your ticket."
--- C*ODE*E
(Consortium for Ordinary Differential Equations Experiments)
"Phaser is a menu-driven program which is easy to use.
The book doubles as a manual for Phaser and an introduction to nonlinear dynamics.
It seems to be extremely well suited for use by students following a course
in the subject...
The program worked so well that not only students, but also researchers, are
interested in using it."
--- Mathematical Reviews
(Journal published by the American Mathematical Society)