Read Section 3.3, pages 70 - 79 in your text. Do some parts of exercises 1 and 2, pages 79 - 80, to develop some intuition for numerical solutions of dynamical systems. You will find it helpful to plot some of your results and compare these to the examples discussed in the section. Important ideas here are stability, sensitivity to initial conditions, equilibrium values, periodic behavior, and chaotic behavior.
Meet with your group to discuss #3 and #4, page 80. Turn in one response from your group for these problems. Write a short paragraph discussing some practical real-life implications of the ideas illustrated by these examples. That is, what is the significance of stable or unstable equilibrium values in this kind of "real life" problem scenario?
Complete Project 3. Although you are encouraged to talk to each other about this problem, individual reports for this project are due on September 24. (This is a change from the original due date.) Some of the ideas in Section 3.3 will be useful in completing the project.
Read over Section 4.1: Proportionality. This is not a long section. We wil begin class with a short lecture, and then use class time for group work. Your group will be able to make petter use of class time if you have each looked over the material before class. We will use class time on Tuesday to discuss exercises #1, 2, 4, 5, and 6. You are encouraged to use a graphing calculator or spreadsheet for these problems.
Project 4: On Being the Right Size, will be available by Thursday, September 19. This project will use strategies which are based on proportionality and geometric similarity, the material covered in Chapter 4 of our text. Reports for this project are due on Thursday, October 3. If you do the work of this project together with your group, you may turn in a group report. You may find it helpful to use spreadsheet software as you work on this project.