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.