Mathwright Visualization Studio free Interactive Web Book:
Dynamical Systems Primer
This
23-page work, written in 1995 as a Mathwright WorkBook, was the substrate
for a college-level course in discrete dynamics taught by the author. It exemplifies
the goals of structured discovery learning so well that we have translated
it essentially without change to our Microworld format so that you may view
it either in your browser or offline. It is one of our new free Visualization
Studio Interactive Web Books in the Math Cafe,
and readers are invited to check it out before joining the Library to get
a glimpse of what is possible with Mathwright.
This
book also contains a "movie" that the user can generate, either online or
off, that illustrates the "flip" and "tangent" bifurcations of the logistic
map. At other places in the book, the reader may create cobweb diagrams using
a bifurcation diagram (that she may also create for any dynamic she chooses)
to select parameter values from the screen. The diagram below is an example.
The
Microworld features a new capability of Mathwright (available since version
2.10, May 12, 2003) that makes use of Windows Compiled HTML Help to tell the
mathematical story on each information page. These help pages use publisher
quality formatted mathematical text and illustrations to tell their story.
The activity pages offer the reader to experiment and to explore the properties
of discrete systems at her own pace, and with her own questions.
Download free MathwrightWeb to view
Microworlds in your browser, then press
or
Library
members, download the free Mathwright32
Reader, then press
For proper viewing, be sure to use Version 2.12 or later, dated Aug 14, 2003
Complimentary Microworld:
Dynamical
System Primer
Click the Hyperlink above
to visit the Microworld in your Browser.
Author:
Samad
Mortabit
This
Mathwright Microworld is an introduction to the basic ideas involved in the
study of chaotic scalar discrete dynamical systems. This is done in an environment
where exploring, reading, and writing all work together nicely. There is a
brief mathematical discussion of the concepts involved (statement of definitions
and some properties). It is not the intent of the author to develop those
concepts here but rather design a workbook that allows for visualization and
hands-on experiments. If the user is interested, we offer the following references:
[1] Robert L. Devaney, "An Introduction to Chaotic Dynamical Systems:, Addison-Wesley, 1989
[2] Denny Gullick, "Encounters With Chaos", McGraw Hill, 1992
[3] D. Assaf and S. Gadbois, "Definition of Chaos", American Mathematical Monthly 99 (1992) 865.
[4] J. Banks, J. Brooks, G. Cairns, G. Davis, and P. Stacey, "On Devaney's Definition of Chaos", American Mathematical Monthly 99 (1992) 332
[5] Carsten Knudsen, "Chaos Without Nonperiodicity", American Mathematical Monthly, (1994) 563
There
are three kinds of pages in this 23 page Interactive Web Book.
Once
you download our free Mathwright32 Reader above, then simply click
Get This Microworld, and it will be downloaded to your machine and
installed in a directory there. You may find it whenever you want to view
it, by going to the Start, Programs, Mathwright32 Reader menu.
To
visit our Microworlds in your browser, it must be able to read ActiveX
controls. Microsoft Internet Explorer 4.0 Browser (or later)
is so equipped. You should check that the Security Settings under Tools,
Internet Options, Security for the Internet, Custom Level has:
Return to the listing of MathwrightWeb Microworlds
| - James E. White, Ph.D. , Library Director, | ||
| author of this website, Mathwright 2000, MindScapes, | ||
| MathwrightWeb, and Mathwright32 |