Dynamics of Nonlinear Systems
MIT OpenCourseWare offers this graduate-level introduction to nonlinear deterministic dynamical systems, covering nonlinear ordinary differential equations and planar autonomous systems. The curriculum builds up the fundamental theory behind existence and uniqueness of solutions, including Picard iteration, the contraction mapping theorem, and the Bellman-Gronwall lemma, before moving into stability analysis of equilibria via Lyapunov's first and second methods. Later sessions cover feedback linearization and apply the theory to nonlinear circuits and control systems, connecting abstract mathematics to electrical and mechanical engineering practice. Materials include lecture notes, problem sets, and exams drawn from MIT's Electrical Engineering and Computer Science, Mechanical Engineering, and Aeronautics and Astronautics departments, free to access with no certificate offered. The course assumes prior exposure to linear systems and differential equations and suits students moving from linear to nonlinear control theory.