Nonlinear Dynamics and Chaos
MIT's graduate course on nonlinear dynamical systems, covering bifurcations, phase plane analysis, limit cycles, strange attractors, and chaos in both continuous and discrete systems. The approach favors geometric intuition over heavy formalism, using computational demonstrations to show how simple nonlinear equations can produce complex behavior, from the Lorenz system to period-doubling routes to chaos. Materials include full lecture notes, problem sets with solutions, and exams drawn from the course as taught in MIT's mechanical engineering and mathematics departments. Applications span mechanical vibrations, population biology, and other physical systems where linear methods break down. Offered through MIT OpenCourseWare under a Creative Commons license, the course is free to access with no certificate offered, aimed at students who already have a background in differential equations and want a rigorous but visually grounded treatment of chaos theory.