Winter 2006 Math 635
What, When, and Where:
Course Description:
Dynamical systems, bifurcation theory, and applications.
Text:
Lectures:
MWF 10:00-10:50 133 TMCB
Office Hours:
MWF 9:00-9:50 306 TMCB
Grading Scheme:
50% Homework Assignments
50% Term Project
Course Schedule: (subject to change)
Jan 09 Review of ODE Theory
Jan 11 1D Dynamics, Logistic equation
Jan 13 1D Stability and Bifurcation Theory
Jan 16 More on Bifurcations
Jan 18 Insect Outbreak
Jan 20 Linear Systems
Jan 23 2D Classification of Linear Systems
Jan 25 The Romeo and Juliet Problem
Jan 27 Phase Portraits and Vector Fields
Jan 31 Fixed Points and Linearization
Feb 01 Rabbits vs. Sheep
Feb 03 Conservative Systems
Feb 06 Index Theory
Feb 08 Limit Cyles
Feb 10 Poincare Benxison Theorem
Feb 13 Traping Regions
Feb 15 Regular Perturbation Theory I
Feb 17 Regular Perturbation Theory II
Feb 20 Singular Perturbation Theory I
Feb 22 Singular Perturbation Theory II
Feb 24 Dimensional Analysis
Feb 27 Boundary Layer Analysis I
Mar 01 Boundary Layer Analysis II
Mar 03 Matlab Exploration
Mar 06 Calculus of Variations I
Mar 08 Calculus of Variations II
Mar 10 Matlab Exploration
Mar 13 Hamiltonian Mechanics I
Mar 15 Hamiltonian Mechanics II
Mar 17 Matlab Exploration
Mar 20 Traveling Wave Solutions I
Mar 22 Traveling Wave Solutions II
Mar 23 Matlab Exploration
Mar 27 Finite Difference Method
Mar 29 Galerkin Method
Mar 31 Matlab Exploration
Apr 03 Spectral Stability
Apr 05 Student Lecture
Apr 07 Student Lecture
Apr 10 Student Lecture
Apr 12 Student Lecture
Apr 14 Student Lecture
Apr 17 Student Lecture
Assignments:
Assignment #1 (Due 01/20/06)
2.2 #1,3,5,13
2.7 #1,3,4
Assignment #2 (Due 02/06/06)
3.1 #1
3.2 #1,3
3.4 #1,6
3.7 #6 (counts as 5 problems)
Assignment #3 (Due 03/27/06)
(pdf)
Assignment #4 (Due 04/10/06)
(pdf)