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Discrete Dynamical Systems
Math 2030-1
Louisiana State University
Spring Semester, 2011
Prof. Stephen Shipman
Place: Room 226 of Tureaud Hall
Time: Monday, Wednesday, and Friday from 1:40 to 2:30
Office: Room 314 of Lockett Hall
Telephone: 225/578-1674
Email: shipman@math.lsu.edu
Office Hours: Monday 9:30 to 11:30, Thursday 1:30 to 3:30 or by appointment
For a PDF version of the basic course information on this page,
click here: 2030syl.pdf
Textbook
A First Course in Chaotic Dynamical Systems, by Robert Devaney.
Course Description
Dynamical systems with discrete time and in one spatial dimension; complex dynamics; quadratic maps; chaos; structural stability; bifurcation theory.
Prerequisite
The prerequisite for this course is Math 1552, the second semester of calculus.
Course Content
The subject of dynamical systems lends it self very well to a fruitful interplay between computational experiment and mathematical theory. This makes the subject an ideal medium for learning to read and write rigorous mathematics. Learning the rigorous definitions of concepts and proving of theorems will be the main objective of the course; this will be emphasized primarily in the second part of the course. The emphasis throughout is on sound logical thinking and communication, and students' work on assignments and the final exam will be held to high standards in this area. In addition, computer experiments will be assigned for the purpose of thoughtful exploration of ideas in discrete dynamics.
Links to web sites on discrete dynamical systems
Orbit diagram java applet
Cobweb diagrams
Davaney's java applets
Devaney's Mandelbrot set explorer
Assignments
The "final due date" is the last day on which revisions to the assignment can be submitted. Between the date of assignment and this date, the assignment may be, and should be, submitted and revised multiple times.
Final due date |
Section |
Problems to do |
| Fri., Feb. 25
| Chapter 3
| 1, 2, 3, 7adh, 10, 11ac, 14, 17
|
| Fri., Mar. 18
| Chapter 6
| 6-14, Problem 2 below
|
| Mon., Mar. 28
| Chapter 9
| 1, 4, 7, 8, 9, 10, 12, 14, 19, 18a,b,d,g,i
|
| Mon., Apr. 11
| Chapter 10
| 2, 7, 9, 13, 17
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| Fri., May 6
| Chapter 14
| 1,3
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| Tue., May 10
| Final Exam
| 10:00-12:00
|
Problems
1. Prove the following statement: Let real numbers c and x be given, with c>1/4. Then Qnc(x) → ∞ as n → ∞.
2. Prove the following statement: The family of iterating functions Fλ(x) = λx(x-1) of the real variable x undergoes a period-doubling bifurcation at λ=1.
Final Exam
The final exam is on Tuesday, May 10, from 10:00 to noon.
Evaluation
Evaluation of performance in the course is based on scores on the assignments and the final exam as follows:
- Assignments: 70%
- Final exam: 30%
Grading scale: A---at least 90%; B---at least 80%; C---at least 70%; D---at least 60%.
Ethical Conduct
Students may discuss problems with each other and other people and consult other literature; however, all work that is turned in must ultimately be that of the submitter alone. If a student receives aid on an assigned problem from discussions with people or other sources, he or she must begin from scratch in writing the solution so that the result is the product of his or her own understanding alone.
Students must abide by the LSU
Code of Student Conduct.
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