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/

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This video was produced at the University of Washington

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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