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# Peer Review

## A System of Discrete Dynamical Systems

by Garrett Durand Heath

## Ratings

### Overall Rating:

Content Quality:
Effectiveness:
Ease of Use:
 Reviewed: Apr 18, 2005 by Mathematics Overview: This site consists of applets that present the graphical and numerical solutions for first-order, linear, homogeneous and non-homogeneous systems of discrete dynamical systems. This site is connected to a parent site, Math Tech, that has been reviewed separately in MERLOT. Learning Goals: To help students understand the nature of discrete dynamical systems and their behavior and stability with regard to different values for the parameters and initial conditions by allowing easy visual experimentation. Target Student Population: Students taking a course in dynamical systems. Prerequisite Knowledge or Skills: Some basic knowledge of discrete dynamical systems. Type of Material: Lecture/presentation with interactive Java applet or targeted supplementary material for student exploration and practice. Recommended Uses: Classroom demonstration or self-guided student exercise Technical Requirements: Java-enabled browser

### Content Quality

Rating:
 Strengths: The applets are simple and effective and graph the sequences of values resulting from the userÂ’s choice of parameters and initial conditions. The graph is color-coded for each sequence in the system and a table of numerical solutions is also provided for values of n<=50 in the homogeneous system and n<=10,000 in the non-homogeneous system. A brief analysis of the system is provided and includes the eigenvalues and eigenvectors, spectral radius, stability and long-term behavior. The analysis changes to match the parameters selected. Concerns: In the Points of Interest, reference is made to coupled systems, eigenvectors, and singular matrices but no mention of these is made in the content of the site.

### Potential Effectiveness as a Teaching Tool

Rating:
 Strengths: The applets are very nicely presented The user can choose to graph either or both of the color-coded sequences in the system. The system analysis is simple and effective. There are a limited number of exercises designed to lead students to a greater understanding of the behavior of a system of discrete dynamical systems. Concerns: There was not any instructional material provided on the how to find eigenvalues, eigenvectors, spectral radius or how to analyze the long term behavior. No examples, solutions or explanations were provided with the exercises.

### Ease of Use for Both Students and Faculty

Rating:
 Strengths: This site is very simple and easy to use and provides visual examples in an area not normally included in simpler graphing calculator type applications. Concerns: Instructor should be prepared to provide additional explanations of the material.(Applet failed to run on old Netscape for MAC)

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