Linearizing Nonlinear Differential Equations Near a Fixed Point

Learn how to analyze fully nonlinear differential equations by examining the linearized dynamics near a fixed point in this 23-minute video. Explore the crucial strategy of studying nonlinear systems using powerful linear ODE solution techniques. Discover the process of finding fixed points in nonlinear systems, zooming into small neighborhoods around these points, and solving for linearization using Taylor series. Master the computation of Jacobian matrices with partial derivatives and see a practical example of linearizing a nonlinear system. Gain essential skills for tackling complex nonlinear problems through this important step towards applying linear analysis techniques to nonlinear systems.

Overview
Fixed points of nonlinear systems
Zooming in to small neighborhood of fixed point
Solving for linearization with Taylor series
Computing Jacobian matrix of partial derivatives
Example of linearizing nonlinear system