Explore a comprehensive overview of dynamical systems in this 32-minute video lecture. Delve into nonlinear dynamics, linearization at fixed points, eigenvalues and eigenvectors, bifurcations, invariant manifolds, and chaos. Learn about the Duffing equation as a nonlinear example, understand stable and unstable manifolds, and examine discrete-time dynamics through population models. Discover techniques for integrating dynamical system trajectories and grasp the concepts of chaos and mixing. Gain valuable insights from Steve Brunton, an expert in the field, as he guides you through these complex topics that describe the changing world around us.