Syllabus for MA 537, Spring 2008

1. Instructor: J. E. Franke

Office: HA 205
Office Hours: 9:00 - 10:00 MWF and 1:15 - 2:00 Tues./Th. or by appointment
Phone Number: 515-2381
E-mail address: franke@math.ncsu.edu
Homepage: http://www.math.ncsu.edu/~franke

2. Goals and Objectives:

MA 537 is an introduction to nonlinear dynamics and chaos. Students will

experiment with chaotic dynamical systems and fractals in the computer lab.

develop their proof skills in the area of analysis as it applies to dynamical systems and fractals.

understand the concepts of periodic orbits, dense orbits, hyperbolicity, symbolic dynamics, topological conjugacy, bifurcation, fractals, and chaos.

3. Textbook:

A First Course in Chaotic Dynamical Systems, Theory and Experiment, by R. Devaney. Published by Addison and Wesley, $58.

4. Topics and estimated days allocated to each topics:

Chapter 1&2	Dynamical Systems History and Examples	1 week
Chapter 3	Orbits	1 week
Chapter 4	Graphical Analysis	1 week
Chapter 5	Fixed and Periodic Points	1 week
Chapter 6	Bifurcations	2 weeks
Chapter 7	Quadratic Family	1 week
Chapter 8	Transition to Chaos	1 week
Chapter 9	Symbolic Dynamics	2 weeks
Chapter 10	Chaos	1 week
Chapter 11	Sarkovskii's Theorem	1 week
Chapter 12	Role of Critical Orbit	1 week
Chapter 13	Newton's Method	1 week
Chapter 14	Fractals	1 week

5. Tentative schedule of reading assignments

Read the sections to be covered for the week.

6. Tentative schedule of homework due dates, quizzes and tests

Homework is due on Friday after it is assigned.
The first test will be in February and the second will be in April.
The final is on Wednesday, April 30 at 8:00 am. It is a 3 hour test.

7. Determination of grades:

Homework: 10%

Projects: 10%

Test 1 20%

Test 2 20%

Final: 40%

Range	Grade
97.6 <= X <= 100	A+
92.3 <= X < 97.6	A
90.0 <= X < 92.3	A-
87.6 <= X < 90.0	B+
82.3 <= X < 87.6	B
80.0 <= X < 82.3	B-
77.6 <= X < 80.0	C+
72.3 <= X < 77.6	C
70.0 <= X < 72.3	C-
67.6 <= X < 70.0	D+
62.3 <= X < 67.6	D
60.0 <= X < 62.3	D-
X < 60	F

8. Policy on incomplete grades and late assignments: Late homework assignments will not be graded.

9. Policy on absences (excused and unexcused) and scheduling makeup work:

The attendance policy is consistent with the Academic Regulations which can be found at http://www2.ncsu.edu/unity/project/www/ncsu/provost/info/academic_regulations/attend/reg.htm (link)
In addition, the following clarifications are used in this course: Excused absences are required for making up a missed test.

10. Course Prerequisites / Restrictive Statements:

MA 341 and MA 405.
More information is available at : http://www2.acs.ncsu.edu/reg_records/crs_cat/MA.html (link)

11. Academic Integrity Statement:

Students are expected to follow university guidelines available at http://www.ncsu.edu/provost/academic_regulations/integrity/reg.htm (link)

12. NC State policy on working with students with disabilities:

Reasonable accommodations will be made for students with verifiable disabilities. In order to take advantage of available accomodations, students must register with Disability Services for Students at 1900 Student Health Center, Campus Box 7509, 515-7653. For more information on NC State's policy on working with students with disabilities, please see the Academic Accommodations for Students with Disabilities Regulation (REG02.20.1). Information can be found at http://www2.ncsu.edu/ncsu/stud_affairs/counseling_center/dss/ (link)

13. Statement on laboratory safety or risk assumption in courses requiring physical activity or field trips:

None

14. Statement on "pass-through" charges e.g. , lane rental at bowling alley, field trip costs, etc.:

None

Further Information:

NCSU Academic Regulations can be found at http://www2.ncsu.edu/unity/project/www/ncsu/provost/info/academic_policies/ (link)

15. Homework

Problems	Due date
Linear Difference Equations Solutions to Linear Difference Equations	1/18
Bottom of page 25 Quad	1/25
Newton's Method Page 27 # 12, 13, 14,15, 16, 17, 18 Page 34 # 2 a,b, 4 e,f	2/1
Page 50 # 1 a,b,c, 2 a,c,f, 4 a,f,g, 5, 6, 7, 8, 9 Attracting Cycles	2/8
Implict Function Theorem Page 67 #1 a. Show there is a tangent bifurcation	2/15
Tangent Birfuration Page 67 #1 d. Show there is a pitchfork bifurcation Pitchfork Bifurcation and Period Doubling Bifurcation, only the Pitchfork part Transcritical Bifurcation	2/22
Pitchfork Bifurcation and Period Doubling Bifurcation, only the Period Doubling part	2/29
Page 80 # 8	3/14
Page 80 # 9-15, Repeated Period Doubling	3/28
Page 112 # 10-13, Quad Cubed Bifurcations	4/4
Page 151 # 1, 2, 3, 4, 6, 7	4/18
Windows in Logistic	4/21
Project	4/25

16. Bifurcation Theorems