Explore nonlinear dynamics and chaos through a comprehensive series of 25 lectures filmed at Cornell University in Spring 2014. Delve into analytical methods, concrete examples, and geometric intuition as you progress from first-order differential equations to complex topics like the Lorenz equations, chaos, and strange attractors. Apply theoretical concepts to real-world scenarios, including airplane wing vibrations, biological rhythms, and chaotic waterwheels. Engage with computer graphics, simulations, and videotaped demonstrations to enhance understanding of nonlinear phenomena. Prerequisite knowledge includes single-variable calculus, with some multivariable calculus and linear algebra concepts introduced as needed. Gain insights into the fascinating world of nonlinear systems and their applications across various scientific disciplines.
Overview
Syllabus
MAE5790-1 Course introduction and overview.
MAE5790-2 One dimensional Systems.
MAE5790-3 Overdamped bead on a rotating hoop.
MAE5790-4 Model of an insect outbreak.
MAE5790-5 Two dimensional linear systems.
MAE5790-6 Two dimensional nonlinear systems fixed points.
MAE5790-7 Conservative Systems.
MAE5790-8 Index theory and introduction to limit cycles.
MAE5790-9 Testing for closed orbits.
MAE5790-10 van der Pol oscillator.
MAE5790-11 Averaging theory for weakly nonlinear oscillators.
MAE5790-12 Bifurcations in two dimensional systems.
MAE5790-13 Hopf bifurcations in aeroelastic instabilities and chemical oscillators.
MAE5790-14 Global bifurcations of cycles.
MAE5790-15 Chaotic waterwheel.
MAE5790-16 waterwheel equations and Lorenz equations.
MAE5790-17 Chaos in the Lorenz equations.
MAE5790-18 Strange attractor for the Lorenz equations.
MAE5790-19 One dimensional maps.
MAE5790-20 Universal aspects of period doubling.
MAE5790-21 Feigenbaum's renormalization analysis of period doubling.
MAE5790-22 Renormalization: Function space and a hands-on calculation.
MAE5790-23 Fractals and the geometry of strange attractors.
MAE5790-24 Hénon map.
MAE5790-25 Using chaos to send secret messages.
Taught by
Cornell MAE
