TEACHER NOTES

ISSUES RELATED TO THE PROBLEM

The problems are designed to be worked with a computer algebra system and are not appropriate for "by-hands" work.

Prerequisites

An understanding of the derivative.

Time allotment - time management

Each part is a complete lesson requiring appropriately 1 to 1 and a half 50 minute periods each.

Expectations

My students had high success working through these problem sets. Expect success as long as the students are familiar with the computer algebra system that they are using.

Future payoffs

By the time students complete some or all of these exercises, they have a much better understanding of what a bifurcation diagram is and how to interpret it.

Extensions

Encourage students to develop more efficient code for producing Feigenbaum and Divergence Diagrams. Have the students study various other famous families of maps such as the tent and doubling families. Better yet, encourage the students to make up their own families of maps.

References and Sources