Lab #2

• Do experiment 5.6, Page 48. Use the program Function Iterator at the DS & T website or a spreadsheet. Use the default distance of .001, not .00001 as stated in the book. If you need more than 10,000 iterations to get "convergence" then stop.

• Perform only the "Procedure" and "Results" part of the experiment, not the portion called "Notes and questions". Please do not hand in lists of orbits; turn in only the answers requested in the "Procedure" and the one page essay described in "Results."

• Also answer the following question in your essay: What is the relationship between the speed of convergence to neutral fixed points whose first derivative is equal to 1 (not -1) and the higher order derivatives (second and thrid) at the fixed point?

• You can change functions using the pull down menu over the orbit list. In each case you must input the appropriate parameter in the "parameter" window.

• Hint: The Function Iterator allows you to list the first 2000 points on an orbit. To list iterates number 2001 through 4000, you must copy iterate number 2000 into the x(0) = window.

  For an overview about what is expected in your lab reports, click here