An introduction to the concept of the derivative and the integral, through an exploration of day length through the year.
This project is designed as a first-day introduction for new high-school calculus students, giving a high-level overview of the idea of the derivative and the integral. The specific illustration used is a representation of hours of daylight received from January 1, 2017 to December 31, 2017 in Portland, Oregon.
An interactive Shiny app is used for the purpose, with three plots representing the amount of daylight received each day, the change in daylight received each day, and the total daylight received between January 1 and a given date, inclusive. A few simple exercises are included, in the hope of motivating students to think actively about what the derivative and the integral represent in this context.
References:
Daylight data downloaded from the easy-to-use Sunrise Sunset API