Nonlinear Dynamics
Chaos, Bifurcations, and Phase Space Analysis
Introduction to Nonlinear Dynamics
The transition from linear to nonlinear systems and fundamental notation.
Existence and Uniqueness Theorems
The mathematical foundations of when solutions to ODEs are guaranteed to exist.
State Variables & Phase Space
Visualizing system evolution through trajectories and phase portraits.
One Dimensional ODEs
Techniques for analyzing flows on a line and fixed point stability.
One Dimensional Bifurcations
How system qualitative behavior changes as parameters vary.