APPM 5460 Dynamical Systems and Differential Equations Spring 2016

News

 About the Course

 

 

Instructor:J.D. Meiss 
Class:MWF 10:00ECCR 116
Office Hr:M&F1-2, W11-12ECOT 236
Text:Differential Dynamical Systems,
J.D. Meiss

$87 list, (30% off if you are a member of SIAM, or 20% off with code--ask me!)

Course Materials

  1. Syllabus
  2. Lecture Schedule and HW
  3. Typos in the Text (second printing)
  4. Projects Topic selection due Feb 26. 
  5. Some Resources in Dynamical Systems

Outline

  • Dynamics and Modelling
  • Linear Systems (Mostly a review)
    • Eigenvalues and Vectors
    • Exponentials of Operators
    • Floquet Theory
    • Stability
  • Existence and Uniqueness
    • Contraction Maps
    • Lipschitz Functions
  • Dynamical Systems
    • Flows, Stability
    • Lyapunov Functions
    • Topological Conjugacy
    • Attractors and Omega Limit Sets
    • Poincare Maps
  • Invariant Manifolds
    • Stable and Center Manifolds
    • Normal Form Theory
  • The Phase Plane
    • Topological Phase Portraits
    • Poincare Bendixson Theory
    • Index Theory
  • Chaotic Dynamics
    • Lyapunov Exponents
    • Hyperbolicity
    • Strange Attractors
    • Homoclinic Bifurcations
  • + at least one addtional topic
    • Bifurcations
    • Perturbation Theory
    • Hamiltonian Systems

Grading

Grades in the course will be based on:

  1. homework sets (assigned roughly bi-weekly during the semester).
  2. class participation (extra points for helping me to make this class a lively one)
  3. projects (written project due at the end of the semester).

Homework Ground rules for the homework sets are as follows. You may use any reference book from the library. You are encouraged to discuss the homework problems with other students in the class, and even to work on the problems together, until you get to the point that you understand how to solve the problem. Each student is required to write up and to submit his/her own homework set. You are not permitted to copy another student's homework, even if you worked on the problems together.

Projects: A list of possible projects is here. You should select your project and have it approved by me by Feb 26. Projects will consist of a 25 minute presentation to the class during the last week of the semester or the final exam period and a written report. Project can involve computation, but need not.

Policies