Study of equations involving derivatives and their applications.
Most real-world equations aren't linear! Nonlinear differential equations can lead to wild and unpredictable behavior, including chaos.
In math, chaos means that tiny changes in starting conditions can lead to huge differences later. Weather prediction is a classic chaotic system.
Few have neat, exact solutions. We often use approximations or computer simulations to study their behavior.
The logistic equation \( \frac{dy}{dt} = r y (1 - \frac{y}{K}) \) models limited population growth.
Studying the Lorenz system gives insight into how weather can be chaotic.
Nonlinear equations can model complex, unpredictable systems like weather and population dynamics.