Why Don't They Teach Newton's Calculus of What Comes Next?

Explore the fascinating world of discrete calculus in this 47-minute video lecture on the calculus of sequences and differences. Delve into the Newton-Gregory interpolation formula, a powerful tool for predicting what comes next in a sequence. Discover how familiar mathematical concepts like derivatives, integrals, and differential equations translate to this alternate reality calculus. Encounter unexpected appearances of the Fibonacci sequence, Pascal's triangle, and Maclaurin series. Follow along as the lecture covers topics such as differences, the master formula, summation as integration, and difference equations. Gain insights into real-world applications and enjoy a comprehensive proof at the end. Perfect for mathematics enthusiasts looking to expand their understanding of calculus beyond the continuous realm.

Intro.
Derivative = difference.
What's the difference.
The Master formula.
What's next is silly.
Gregory Newton works for everything.
Integral = Sum.
Differential equation = Difference equation.
Summary and real world application.
Proof.