The Jacobian Matrix

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 github.com/clum/UA-cam/tree/...
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