Topics in Modern Dynamics

Dynamics here means more than rigid bodies and Lagrangians, it's the unifying language for any system that evolves in a state space, whether that's a coupled oscillator, a neuron firing, a population playing a game, or a microswimmer at low Reynolds number. You move through phase-space geometry and stability into nonlinear dynamics and chaos, then apply the same tools to networks, neurodynamics, evolutionary games, and even the physics engines behind computer games, mixing analytical work with simulations. It's a capstone-flavored elective that takes the ODE and vibrations material you already know and shows how the same machinery cuts across biology, economics, and robotics, which is most of where modern ME research actually lives.