CC MATHEMATICS   MATHEMATICAL EXPLORATIONSSYLLABUS

Homework 1: Due Wednesday 9/7 at 3PM

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. For homework, 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 3 9b  (show point slope AND slope intercept equation), 
Chapter 6 15 Also explain what this tells you about the function's graph
  18 b, k Show work and your plot clearly
Chapter 16 18 Show all work
  21 Explain which identity is used where in your proof
Chapter 26 17 Show all work and which rule of logs is being used
  18 Show all work
Chapter 28 17 Show all work 

 Part II: Chaos Problems
Number Problem
1 For the tent map with s=1.6, graph the second return map, labeling the coordinates of the turning points.  Use this graph and its equation to find all period 2 points for the tent map with s=1.6.  Tell which of these are actually fixed points and which are part of a 2-cycle.  (Note: period 2 just means that the point is part of the 2-cycle).
2 Use graphical iteration to locate four points which the tent map takes to the fixed point w of the picture.   
3 Solve the problem above numerically (i.e. find the points that map to the fixed point), but this time with the tent map for s = 2.  Explain how you could find as many points as you like, both geometrically and algebraically.