Chapter: Corresponding Textbook Sections 
Hrs 
Topics 
I. OneDimensional Flows:
2.02.5, 2.8, 3.03.5, 4.04.4.

9 
 A geometric way of thinking (the phase line)
 Fixed points and stability
 Population growth
 Nondimensionalization
 Linear stability analysis
 Existence and uniqueness
 Bifurcations
 Saddlenode bifurcation, normal form
 Transcritical bifurcation, normal form
 Chemical kinetics
 Pitchfork bifurcation, normal form
 Overdamped bead on a rotating hoop
 Dimensional analysis and scaling
 Overdamped pendulum (with steady applied torque)

II. TwoDimensional Flows:
5.05.2, 6.06.5, 6.7, 7.07.3, 8.08.3, 8.7

17 
 Linear systems
 Classification of linear systems
 Stability language
 The phase plane
 Existence and uniqueness
 Fixed points and linearization
 Two competing species ("rabbits versus sheep")
 The effect of small nonlinear terms
 Conservative systems
 Pendulum: undamped and damped
 Limit cycles
 Ruling out closed orbits
 PoincareBendixson Theorem
 Bifurcations in two dimensions: saddlenode, transcritical and pitchfork bifurcations
 Hopf bifurcations
 Oscillating chemical reactions
 Poincare maps

III. Chaos:
10.010.3,9.29.5,10.410.5

11

 Onedimensional maps
 Fixed points and linear stability analysis
 The logistic map
 Invariant sets, attractors, chaos
 Liapunov exponents
 Ruelle plots
 Lorenz equations
 Doubling map
