Calculus: Universal Language

3 Credits · Level: Undergraduate

Calculus is one of the greatest of human achievements. It ranks alongside the works of Shakespeare and Michelangelo. Without it, we would have no airplanes or cell phones, no microwaves or ultrasound machines, no GPS or self-driving cars. It underlies the hard sciences, the soft sciences, and much more. Its ability to describe the physical world is unparalleled (Nobel physicist Richard Feynman once remarked that calculus is the language God speaks). But how did we discover (or invent) it? And what are the basic ideas that underlie it? Although it may seem complicated, the calculus is designed to solve a very simple question, known as Zeno's paradox: if a turtle wants to cross the road, it must first traverse half of the distance, then half of the remaining distance, then again half of the remaining distance, and so on. But if that is true, it will never get to the other side, because there will always be half of the remaining distance in front of it. However, we know from experience that turtles do make it across the road. So, how? What exactly is the error in Zeno's thinking? It took almost 2000 years for humanity to figure out how to solve Zeno's question, and to do so, it required that we discover (or invent) the calculus. In this course, we will study the basic ideas of the calculus, and we will learn how humanity figured it all out, starting in ancient Greek times. You do not need any background in mathematics to take this course. This is a course about the history and "why and how" of the calculus, and although we will do various calculations throughout the course in order to understand how it all works, we will introduce everything needed as we go.