Why don’t they teach Newton’s calculus of ‘What comes next?’


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Why don’t they teach Newton’s calculus of ‘What comes next?’

Why don’t they teach Newton’s 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 Newton-Gregory interpolation formula, a powerful what comes next oracle, and some very off-the-beaten track spottings of some all-time 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

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