# Mathematica Tools for the Text

A series of 12 Mathematica notebooks with links to the Experiments in our text.

Mathematica Tools for A First Course in Chaotic Dynamical Systems

# Lecture Notes

### Topics: November

 Date Topics Notebooks 29, 31 Oct. Chap. 10: Chaos Chaos Slides 2 Nov Chaos Examples Examples Chaos 5 Nov Histograms: Sensitivity Histogram 7 Nov Chap 11: Period Three Period Three Notes Example: No Period Three No Period Three Homework: Extra Credit - Due, 9 Nov. Chapter 10 p. 131: 1, 4, 8, 21-23 Example: Period Three Window: Subshift Finite Type Subshift 9 Nov Chapter 11: Orbits Orbit Diagram 12 Nov Chapter 11: Period Order Homework: Extra Credit - Due, 14 Nov. Chapter 11 p. 151: 1,4,7, 10-14 14 Nov Hour Test Review Exam 2 Review 16 Nov Second Hour Test: Chap. 7-11 Exam Answers 19 Nov Chapter 13: Newton Newton Method 21 Nov Chapter 14: Iterated Function Systems Examples: Yale Course Nov. 28, 30 Chapter 15: Complex Functions Dec. 1, 3, 5 Chapter 16: Julia Sets Additional Notebooks Tues., Dec 11 Final Exam: 5:30- 7:30 pm

### Topics: Sept/October

 Date Topics Notebooks 27 &29, August Chapter II: Babylonian Root Method 31 August Chapter III: Orbit Examples Orbits: NestList 4 September Chapter Three: Orbits under Iteration Iteration 6 September Chapter IV: Graphical Analyis & Cobwebs Mathematica: Cobwebs 10 September Many Cobwebs In Class:10 Sept. 12 September V: Rates Of Convergence Examples Function Definition: Cases Cases 19 September Fixed Point Theorem Notes 24 September Bifurcation: Chap 6 Bifurcation Cobwebs 28 September Homework II answers Answers in Mathematica Cantor Map Cantor Map 3 October Cantor/Hour Exam Review Review 10 October First Hour Exam 15 October First Hour Exam Answers Written Answers Computational Ans. 19 October Function: Cantor is non-wandering set Cantor Sequence Space Notes Lecture Homework Chap. 7: 8,10,11,14,15,21; Chap. 9:2,6,7,10,12,14,17,18 Due: Oct. 29 24 October Sequences & Qc Iterates Quad Cantor Seq. Tues., Dec 11 Final Exam: 5:30- 7:30 pm

Neal W. Stoltzfus   Fall 2007