MATH 2030

Dynamical Systems

Fall 2007


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