The Shadowy World of Umbral Calculus

An introduction to a famously enigmatic area of math, for calculus students of all levels

↓ Info and Timestamps ↓

In this video we use a primer on discrete calculus to motivate an exploration of the idea you saw in the thumbnail, deriving 2 summation methods along the way!

This was made for the 2022 Summer of Math Exposition (#SoME2), an annual jam encouraging new creators like me to make content like this. It's been a really satisfying project to complete, and I'll definitely be making more in the future!

Discord Server:   / discord  
Patreon:   / supware  

0:00 Intro
1:28 Forward Differences
2:49 Summation
5:59 Falling Powers
7:23 Umbral Calculus
9:53 Stirling Numbers
11:39 Umbral Exponentials
13:27 Newton's Forward Difference Formula
14:31 Thanks for watching!

Music:
Chris Haugen - Glacier
Chris Haugen - Northern Lights

#umbral #calculus

Corrections:
7:13 denominator should be (x+1)(x+2)...(x+n+1) - Jose V
13:13 and so ϕ(1/x) = 1/(x+1) - Jose V
13:22 ϕe^-x is undefined, and the other "curious equation" shown means that implicitly applying ϕ to a circle gives a logarithmic spiral - Discord community