Numerically Calculating Partial Derivatives

In this video we discuss how to calculate partial derivatives of a function using numerical techniques. In other words, these partials are calculated without needing an analytical representation of the function. This is useful in situations where the function in question is either too complicated to describe with analytical functions or simply does not have an analytical representation (for example the function is a black-box that can only accept inputs and generate outputs). Topics and timestamps: 0:00 – Introduction 0:19 – Review of partial derivatives 8:22 – Newton quotient 23:21 – Symmetric difference quotient 32:04 – Function of 2 variables 54:48 – Function of n variables Lecture notes and code can be downloaded from https://github.com/clum/YouTube/tree/main/Calculus12 All Vector Differential Calculus videos in a single playlist (https://www.youtube.com/playlist?list=PLxdnSsBqCrrF92Lr54CSJkSlpNWPTpkel) A follow-on video shows how this technique can be applied to numerically linearize a dynamic system (https://youtu.be/1VmeijdM1qs) #calculus 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!