Extended description: One book (see below); other materials will be made available in PDF form or with links to online sources.

  • Book: Infinite Powers: How Calculus Reveals the Secrets of the Universe, by Steven Strogatz. A friendly and readable introduction to the big ideas of calculus, to their 2500-year history, to how calculus is really used in the real world, and to how it fits in the larger intellectual tradition. Available through bookfinder.com new or used for less than $15.  
  • Three weekly “assignments”: optional but ideally revealing problems and puzzles, more to be pondered than completed. As always, emphasizing thought, not intricate calculations.

Notes: Please read and/or work on these assignments before class so that we can meaningfully discuss them. We will spend some class time in breakout groups, for which it will be especially helpful to have pondered some of the “homework” problems; see definition above.

Class 1: Getting started, and big ideas.

Reading:Strogatz book, Introduction and Chapter 1.

Class topics: Archimedes and other Greeks bearing gifts. Early history. Cars: speed and distance; acceleration.

Live questions: Areas of curved figures. What, exactly, does a speedometer say? Can we reconstruct distance from speed, and vice versa?

Class 2: Functions and their derivatives

Reading:Chapters 2, 3, 5 of Strogatz book.

Class topics: Check-in on “homework” and reading. More on speed, distance, and acceleration. Functions, constant and nonconstant. The racetrack principle. 

Live questions: If speed is constant, what about distance? What is acceleration? What acceleration exists in our world? How is gravity involved? What is a derivative function?

Class 3: From derivatives to integrals.

Reading: Chapters 4, 6, 7 of Strogatz book.

Class topics: Check-in on “homework” and reading. From rates to amounts, and how they’re related. The Fundamental Theorem of Calculus. Differential equations.

Live questions: What’s the area between a horizontal line and the x-axis? Between any line and the x-axis? What does this have to do with cars and distance?

Class 4: Calculus: why bother?

Reading: More in Strogatz, ideally Chapters 8-11.

Class topics: Check-in on “homework” and readings. What real problems does calculus solve? Optimization. Differential equations.

Live questions: Nature speaks to us in the language of calculus. What do we hear about optimization? About differential equations? About life, the universe, and everything?