Differential Equations
Study of equations involving derivatives and their applications.
Practical Applications
Modeling Population Growth
How Populations Change
Differential equations are used to predict how populations of animals, bacteria, or even people grow over time.
The Equation
\( \frac{dP}{dt} = rP \)
Where:
- \( P \) is the population,
- \( r \) is the growth rate.
What Can We Learn?
- How fast a population can grow
- When a population might reach a certain size
Examples
Predicting when a new species will overrun an island.
Estimating the spread of a virus in a city.