M638 DYNAMICAL SYSTEMS

SYLLABUS

POLICIES

ASSIGNMENTS

FINAL PROJECTS

COURSE MATERIAL


        M638 Dynamical Systems / Syllabus

Office: GMCS 503
Office Hours: T TH 1PM - 2PM
e-mail: apalacios AT mail.sdsu.edu

Textbook
Nonlinear Dynamics and Chaos.
Author: Steven H. Strogatz.
Publisher: Westview Press.


Course Outline

  1. Flows on the Line
    • Introduction
    • Stability of fixed points
    • Existence and Uniqueness
    • Potentials
  2. Bifurcations
    • Saddle-node
    • Transcritical
    • Pitchfork
  3. Flows on the Circle
    • Uniform oscillator
    • Nonuniform oscillator
    • Applications
  1. Two Dimensional Flows
    • Phase Portraits
    • Fixed points and stability
    • Conservative Systems
  2. Limit Cycles
    • Poincare-Bendixson Theorem
    • Relaxation oscillators
    • Weakly nonlinear oscillators
  3. Chaos
    • Lorenz Equations
    • Chua's attractor
    • Lyapunov exponents
    • Applications

 

 


References

[1] Chaos. An Introduction to Dynamical Systems. Kathleen T. Alligood, Tim D. Sauer, James A. Yorke.
[3] S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer-Verlag
[4] The nonlinear lab: http://www.apmaths.uwo.ca/~bfraser/nll/version1/
[5] The Chaos HyperTextbook: http://hypertextbook.com/chaos/
[6] MATLAB Tutorial: http://www.math.mtu.edu/~msgocken/intro/intro.html


Grading
  
Homework and Quizzes
40 %
Midterm Exam
30 %
Final Project ( topics )
Oral Presentation + Written report + Attendance
30 %


Grading Scale
 
A -- (minus)
90% and above
B -- (minus)
80% and above
C -- (minus)
65% and above
D -- (minus) 55% and above

 

 

 









*Note: Exam dates listed above are tentative and will be confirmed in class. The instructor reserves the right to change these dates if considered necessary.

  • Exams, Homework, and Quizzes are considered individual work. Copying someone else work is considered cheating and will be penalized.
  • Quizzes may or may not be announced. If a quiz is given at the beginning of class and you are late, you will not be able to take this quiz earlier.If a quiz is given at the end of the hour, you will not be able to take this quiz earlier.



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