Discrete Calculus - My Favorite Topic for a Student Seminar Talk

Explore the fascinating world of discrete calculus in this 38-minute lecture by mathematician Michael Penn. Delve into key concepts such as the discrete derivative, falling factorial, and discrete antiderivative. Learn how to apply these principles to various mathematical functions, including exponential and Fibonacci sequences. Discover the discrete fundamental theorem of calculus and its applications. Master the product rule and summation by parts technique through practical examples. Gain valuable insights into this unique branch of mathematics that bridges the gap between continuous and discrete mathematical analysis.

Intro
Motivating Question
The Discrete Derivative
Towards a power rule
The falling factorial
Observation
What about exponential functions?
What about Fibonacci numbers?
The discrete antiderivative
The discrete fundamental theorem of calculus
Some very basic examples
The Product Rule - Summation by Parts
Some more interesting examples