APPM 5460
Lectures and Homework

Week Date Chapter Topic Secs. HW Problems Due
I 11-Jan 1: Modeling Models 1.2-4 #1 Ch1: 1,3,5,9,10
Ch2: 2,4,6,7,9
1/27
  13-Jan   Phase Plane, Nullclines 1.5-7      
  15-Jan 2: Linear Systems Matrix ODEs 2.1      
II 18-Jan MLK HOLIDAY
  20-Jan   2D Systems, Exponentials 2.2-3      
  22-Jan   etA for Complex, Uniqueness 2.4-5      
III 25-Jan   Semisimple-Nilpotent 2.6      
  27-Jan   Stability 2.7     HW 1 Due
  29-Jan   Floquet Theory I 2.8 #2 Ch 2: 11,14,15abf,19,23
Ch 3: 4,5,8
2/12
IV 1-Feb   Floquet Theory II 2.8      
  3-Feb 3: Existence & Uniqueness Function Space Preliminaries 3.1-2      
  5-Feb   Existence & Uniqueness 3.3      
V 8-Feb   Existence & Uniqueness II        
  10-Feb   Dependence upon initial conditions 3.4      
  12-Feb   Maximal Interval of Existence 3.5     HW 2 Due
VI 15-Feb 4: Dynamical Systems Flows & Vector Fields 4.1-2      
  17-Feb   Global Existence & Linearization 4.3-4 #3 Ch 3: 11, 12
Ch 4: 1b, 2c,3a-d,6, 8, 9
3/2
  19-Feb   Stability 4.5      
VII 22-Feb No lecture: JDM out of town        
  24-Feb No lecture: JDM out of town        
  26-Feb   Lyapunov Functions 4.6     Project selection due
VIII 29-Feb   Lyapunov & Conjugacy 4.7      
  2-Mar   Conjugacy       HW 3 Due
  4-Mar   Hartman-Grobman 4.8 #4 Ch 4:16,17,18
Ch 5:1,3,4,9
3/18
IX 7-Mar   Omega Limits 4.10      
  9-Mar   Attractors 5.1-2      
  11-Mar 5: Invariant Manifolds Heteroclinic Orbits 5.1-2      
X 14-Mar   Stable Manifolds I 5.3      
  16-Mar   Stable Manifolds II 5.4      
  18-Mar   Center Manifolds & Examples 5.5     HW 4 Due
  21-Mar SPRING BREAK
XI 28-Mar 7: Chaos Defining Chaos 7.1     Project Proposal Due
  30-Mar   Lyapunov Exponents I 7.2 #5   Ch 7: 1,4,5,6,9,11abd 4/13
  1-Apr   Lyapunov Exponents II        
XII 4-Apr   Strange Attractors and Dimension 7.3      
  6-Apr   Box Counting & Hausdorff Dimension        
  8-Apr   Transport        
XIII 11-Apr 8: Bifurcation Theory Saddle-Node, Non-bifurcation theorem 8.1-2      
  11-Apr 11AM (Newton Lab) Poincare-Bendixson Theorem 6.6      
  13-Apr   Unfolding 8.3     HW 5 Due
  15-Apr   Saddle-Node Theorem 8.4      
XIV 18-Apr   JDM Out of town        
  20-Apr   Saddle-Node in R^n 8.6      
  22-Apr   Hopf Bifucation 8.8      
XV 25-Apr   Cusp and Taken's Bogdanov 8.9-10      
  27-Apr   Student Presentations: John Nardini, Dylan Abrahamsen        
  29-Apr   Student Presentations: Jacob Cook, Arnold Braker       Project Due
XVI 3-May Final Exam 1:30-4:00 Project Presentations
Lewis Baker, Kaitlyn Garifi, Joy Mueller, Jacob Mink, Richard Schwiezer, Peter Shaffery, Sarah Smith