Samantha has finished her Ph.D. in meteorology, and has now joined forces with the local Shmoopville weather team. She loves getting in front of the green-screen and showing her weather chops. Sometimes she wears green, pretending to have an invisible torso. Beyond standing in front of the camera, Sam also likes to play around with the weather computers that are used to model the clouds we see on screen. These computer models use changes with respect to time (derivatives) in atmospheric variables like temperature and pressure to guess the weather. Snow in Florida? Tornado in Alaska? There's a model for that.
Differential equations are used to organize and figure out complicated problems. All of these derivative variables, along with some regular old variables, can be tossed into a differential equation. Because of differential equations, we can sit inside, eating cereal in our PJ's, and know exactly what to expect it to be like outside all day.