CC MATHEMATICS   MATHEMATICAL EXPLORATIONSSYLLABUS

Homework 3: Due Wednesday 9/14 at 4PM

Turn in individual solutions. You may work together in solving the problems, or get help from others, but the final write-up should be your own. Show full work for full credit. Do not turn in anything you cannot explain completely.

Part I: From Schaum's Calculus  Problem Further instructions
Chapter 10 37, 40, 42, 47, 67  Note that for #67, you do not need a graphing calculator.
Chapter 14 23 h, 25, 26c, 27, 31, 33, 37 or 38 * Note that #25 is significant in statistics. 
Chapter 15 13b, 13h  
Chapter 17 25, 26, 29b, 30  
Chapter 26 8c 8h   

 Part II: Chaos Problems
Number Problem
1 For the logistic map with values of s between 1 and 3, almost all of the initial values converge to the fixed point 1-1/s under iteration. Describe the initial values for which the iterates DO NOT converge to 1-1/s.
2 For s between 3 and 3.449 the logistic map has an attracting 2-cycle. Show that there are infinitely many points that do not converge to this 2-cycle.
3

Consider the logistic map defined by s=3.1.
a) Determine all fixed points for this dynamical system.  Tell whether each is stable.  
b) According to the  handout  (pp.169 & 170),  there is an attractive 2-cycle for this dynamical system. Set up the equation f(f(x))=x, and find the solutions to this equation, using a calculator or computer (describe how you do this). Do you get the values reported in the text? How can you tell that the 2-cycle is stable?