Nonlinear Dynamics and Waves
A graduate-level MIT OpenCourseWare course covering nonlinear oscillations and wave phenomena across mechanical, optical, geophysical, fluid, electrical, and flow-structure interaction systems. Topics include weakly nonlinear oscillators, resonance and forced response, self-excited oscillations, bifurcation theory, nonlinear wave propagation, solitons, and pattern formation, with worked examples drawn from vibrating structures, ocean waves, and electrical circuits. The materials include full lecture notes, problem sets with solutions, and exam materials, giving a self-contained path through the mathematics of nonlinear systems as taught at MIT in its Mechanical Engineering and Civil and Environmental Engineering departments. The course assumes familiarity with differential equations and linear systems theory, and builds toward analytical tools like multiple-scales perturbation methods and phase-plane analysis for tackling problems that defy simple linear treatment. As with other MIT OpenCourseWare offerings, all content is free to access and use under a Creative Commons license, with no certificate offered.