Study of equations involving derivatives and their applications.
Differential equations let us model how populations of animals, plants, or even humans change over time.
If resources are unlimited, populations can grow according to \( \frac{dy}{dt} = ky \), leading to exponential growth.
In the real world, resources are limited! The logistic equation \( \frac{dy}{dt} = r y (1 - \frac{y}{K}) \) models population growth with a carrying capacity.
These models are used by ecologists, city planners, and even video game designers to predict and manage populations.
Analyzing yeast growth in a lab using the logistic equation.
Predicting how a fish population in a lake will change over several years.