Syllabus for MA  537, Spring 2013

1. Instructor:  J. E. Franke
Office:  SAS 3222
Office Hours:  9:00 - 10:00 MWF 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
3. Textbook:
 
Discrete Chaos by S Elaydi.  Published by Chapman & Hall, $84.
4. Topics and estimated days allocated to each topics:
 
 
Chapter 1 Stability of 1-D Maps
 3 weeks
Chapter 2 Attraction and Bifurcation
 5 weeks
Chapter 3 Chaos in 1-D
 4 weeks
Chapter 6 Fractals 1 week
Chapter 7 Julia and Mandelbrot Sets
  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 Monday, May 6 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
Page 13 # 7, 8, 10 also in 10 use Phaser to plot the solutions to both the differential equation and difference equation.
 1/11
Page 13 # 3, 4 1/18
Page 23 # use Phaser on 2 and 4,  also do 6,7,9
 1/28

Page 34 # 2, 6, 11, 16, 17a, 18
 2/1
Page 41 # 4, 6, 8
Page 52 # 2, 4
 2/8
Term Project 1.  Page 53 # 11.
 2/15
Page 68 # 1, 4c, 6 minimal periods r < t, 12 prove without assuming f is increasing. 2/22

Page 80 # 7, 9 on R, 11
 2/25
Implicit Function Theorem

 3/15
Tangent Bifurcation
Transcritical Bifurcation
 3/22
Pitchfork & Period Doubling Bifurcation 3/27
Page 92 # 4, 5
Second Term Project		 4/5
Page 103 # 5
Page 127 # 1, 2
Page 142 # 5 		4/12









16. Bifurcation Theorems