M537 ORDINARY DIFFERENTIAL EQUATIONS

SYLLABUS

POLICIES

ASSIGNMENTS


        M537 ODE's / Syllabus

Office: GMCS 589
Office Hours: T TH 10AM - 11AM
e-mail: palacios AT euler.sdsu.edu

Textbook
Differential Equations, Dynamical Systems and An Introduction to Chaos
Author: M. Hirsch, S. Smale, and R. Devaney
Publisher: Elsevier Press

Cell Phones: Please turn off your cell phones during class. NO TEXTING.

Course Outline

  1. First Order Equations
    • Introduction
    • Logistic Population Model
    • Bifurcations
    • Poincare Maps
  2. Planar Linear Systems
    • Linear Systems
    • Eigenvalues and Eigenvectors
    • Linearity Principle
  3. Phase Portraits
    • Real Eigenvalues
    • Complex Eigenvalues
    • Repeated Eigenvalues
    • Change of Coordinates

  1. Classification
    • Trace-Determinant Criterion
    • 3D Parameter Space
    • Conservative Systems
  2. Higher Dim. Linear Algebra
    • Eigenvalues and Eigenvectors
    • Bases and Subspaces
    • Repeated Eigenvalues
  3. Higher Dim. Linear Systems
    • Harmonic Oscillators
    • The Exponential Matrix
    • Nonautonomous Linear Systems
  4. Nonlinear Systems
    • Existence and Uniqueness
    • Equilibria
    • Periodic Solutions
    • Applications

 

 


References

 
[1] S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer-Verlag
 
[2] MATLAB Tutorial: http://www.math.mtu.edu/~msgocken/intro/intro.html
   
[3] ODE Software for MATLAB

 


Grading
Homework
45 %
Midterm Exam
25 %
Final Exam
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.



Important Dates

Withdrawal (fees refunded) Day: September 14
Last Day of Classes December 9



Milk Splash