differential equations

Differential equations are equations that involve derivatives (rates of change) of one or more functions. They are used to model a wide variety of phenomena that involve change, such as the number of people in a population over time, the motion of an object, or the flow of heat through a material. Think of a differential equation like a recipe. All the ingredients and instructions have to be combined in the right order in order to make something new. For example, a differential equation might describe the velocity of a car over time. The equation might include factors such as the car’s acceleration and the friction of the road. As an example, the differential equation for the acceleration of a car is given by dv/dt = a – bv, where v is the velocity of the car, a is the acceleration of the car, and b is the friction of the road. This equation tells us how the velocity of the car changes over time. Fun fact: one of the earliest known uses of differential equations was by the ancient Greek philosopher Aristotle, who used them to describe the motion of the planets.