Institute for Mathematical Science
Stony Brook University
office: Math Tower 4103
phone: (631) 6328266
email: remus.radu@stonybrook.edu
The PDF version of the schedule is available for print here.
Date  Topic  Notes  Assignments 
Jan 26  Introduction: differential equations & dynamical systems  
Jan 28  First order autonomous equations Differential equations in dimension one: equilibrium & stability 
Z3.13.2 S2.12.4 

Feb 2  Stability, Lyapunov function & examples  S2.42.7 Notes Bb 
HW1 (due Feb 11) 
Feb 4  Existence & uniqueness of solutions Bifurcations, normal forms 
Z3.2, S2.5  
Feb 9  Bifurcations: saddlenode, transcritical & examples  Z3.3, S3.13.2 Notes Bb 
HW2 (due Feb 18) 
Feb 11  Bifurcations: transcritical, pitchfork, hysteresis  S3.33.4  
Feb 16  Dimension two: Linear systems  Z5, S5.15.2  
Feb 18  Classification of linear systems  S5.2, 6.16.2  HW3 (due Feb 25) 
Feb 23  Nonlinear systems: sinks, saddles, sources, stability, hyperbolicity HartmanGrobman theorem; Examples 
S6.36.5  
Feb 25  Stable/unstable manifolds, closed orbits, limit cycles An example of Hopf bifurcation 
S7.1, 8.2  HW4 (due Mar 8) 
Mar 1  Conservative systems, energy and nonlinear centers  S6.5  
Mar 3  Gradient systems, Lyapunov functions and examples  S7.2, Z6.2  
Mar 8  Dulac's criterion, Bendixon's negative criterion  S7.17.3 Z6.36.4 
HW5 (due Mar 24) 
Mar 10  PoincaréBendixon theorem  Z6.46.5  
Mar 15  Spring break (no class)  
Mar 17  Spring break (no class)  
Mar 22  Applications of PoincaréBendixon theorem  S7.3  
Mar 24  Bifurcations in twodimensional systems  S8.18.2  Practice problems 
Mar 29  Hopf bifurcations Review 
S8.28.3  Project Topics 
Mar 31  Midterm (1:002:20pm, in class)  Midterm  
Apr 5  Hopf bifurcations; Examples  Notes Bb DHS Ch. 8 

Apr 7  Homoclinic bifurcations; Lorenz system  S8.4, S9.2  
Apr 12  Lorenz system & properties  S9.2, Notes Bb  
Apr 14  Dissipative systems, attractors, examples  S9.3, Notes Bb  HW6 (due Apr 21) 
Apr 19  Lorenz attractor
Stable manifold of the origin: (Video & Lorenz System Example by Alex Vladimirsky) 
S9.3  
Apr 21  A model for the Lorenz attractor Poincaré map 
DHS Ch. 14 Pictures 

Apr 26  Chaotic attractor Reading (see Figures 6, 7): A new twist in knot theory Animation several trajectories (Video) 
DHS Ch. 14 Pictures 
HW7 (due May 5) 
Apr 28  Discrete dynamical systems Chaos 
S10 DHS Ch. 15 

May 3  Discrete dynamical systems; Examples  S10 DHS Ch. 15 

May 5  Fractals and dimension Threedimensional ODEs  Open Problems 
S11  
May 16  Projects  due at 5:30pm in Math Tower 4103 