Why dont they teach Newtons calculus of What comes next

Another long one. Obviously not for the faint of heart :) Anyway, this one is about the beautiful discrete counterpart of calculus, the calculus of sequences or the calculus of differences. Pretty much like in Alice s Wonderland things are strangely familiar and yet very different in this alternate reality calculus. Featuring the NewtonGregory interpolation formula, a powerful what comes next oracle, and some very offthebeaten track spottings of some alltime favourites such as the Fibonacci sequence, Pascal s triangle and Maclaurin series. 00:00 Intro 05:16 Derivative difference 08:37 What s the difference 16:03 The Master formula 18:19 What s next is silly 22:05 Gregory Newton works for everything 28:15 Integral Sum 32:52 Differential equation Difference equation 36:06 Summary and real world application 39:22 Proof Here is a very nice writeup by David Gleich with a particular focus on the use of falling powers. This is a nice lesson from a Coursera course on t