Linearizing Nonlinear Differential Equations Near a Fixed Point

This video describes how to analyze fully nonlinear differential equations by analyzing the linearized dynamics near a fixed point. Most of our powerful solution techniques for ODEs are only valid for linear systems, so this is an important strategy for studying nonlinear systems. This is a hugely important step towards analyzing nonlinear systems with linear techniques. Playlist: https://www.youtube.com/playlist?list=PLMrJAkhIeNNTYaOnVI3QpH7jgULnAmvPA Course Website: http://faculty.washington.edu/sbrunton/me564/ @eigensteve on Twitter eigensteve.com databookuw.com This video was produced at the University of Washington %%% CHAPTERS %%% 0:00 Overview 3:37 Fixed points of nonlinear systems 5:32 Zooming in to small neighborhood of fixed point 7:03 Solving for linearization with Taylor series 12:10 Computing Jacobian matrix of partial derivatives 15:10 Example of linearizing nonlinear system