CC MATHEMATICS   MATHEMATICAL EXPLORATIONSSYLLABUS

Homework 4: Due Monday 9/18 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 11 4b, 12  
Chapter 18 15, 19, 29a, b  
Chapter 21 22, 23 In 23 draw a diagram to show how Newton's method fails
Chapter 23 25, 26, 29b, 30  
Complex Numbers  1a, 1b, 1e, 1f, 2c, 5b, 5d  

 Part II: Chaos Problem
Use the website
http://www.emporia.edu/math-cs/yanikjoe/Chaos/Bifurcation.htm

Compute the Feigenbaum quotients for the logistic map using the website above.
Denote by s1 the s-value where the stable fixed point curve in the bifurcation diagram
intersects the line x=1/2, by s2 the s-value where a branch of the stable 2-cycle curves intersects the line x=1/2, and so on for s3 (4-cycle), s4 (8-cycle), and s5 (16-cycle).  Obtain these s values numerically from the website, and then compute the quotients (s2 -s1 )/(s3 -s2 ), (s3 -s2 )/(s4 -s3 ), and (s4 -s3 )/(s5 -s4 ).  In a sentence or two, discuss the convergence of this series of quotients.