In this video we discuss the concept of the Jacobian matrix. If given a function with multiple inputs and multiple outputs, the Jacobian matrix is a matrix of partial derivatives that measures the sensitivity of each output with respect to each input. This is the multi-dimension extension of the concept of the gradient of a function.

Topics and timestamps:
0:00 – Introduction
0:45 – Derivative
5:53 – Gradient
12:42 – Jacobian
24:15 – Example 1
27:04 – Example 2 (nonlinear to linear ODE)

Lecture notes and code can be downloaded from https://github.com/clum/YouTube/tree/...

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