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/main/Calculus13
All Calculus videos in a single playlist (https://www.youtube.com/playlist?list=PLxdnSsBqCrrGHwNWnP5XVhytcGL9ExuPE)
#Calculus
All Control Theory videos in a single playlist (https://www.youtube.com/playlist?list=PLxdnSsBqCrrF9KOQRB9ByfB0EUMwnLO9o)
#Control #ControlTheory
All Ordinary Differential Equation videos in a single playlist (https://www.youtube.com/playlist?list=PLxdnSsBqCrrHHvoFPxWq4l9D93jkCNIFN)
#ODEs #OrdinaryDifferentialEquations
You can support this channel via Patreon at https://www.patreon.com/christopherwlum or by clicking on the ‘Thanks’ button underneath the video. Thank you for your help!