Modelling physical systems with ODEs
The SIR model has proved incredibly useful in predicting the evolution of certain categories of infectious outbreaks and serves as our introduction to modeling systems with ODEs.
Well, all hell has broken loose. The zomb-pocalypse is happening!
Studying the behaviour of a pendulum beyond the small angle approximation by using numerical methods
You learned that the period of a pendulum was independent from its amplitude. This was true under the small angle approximation. What can we say about the period when we go beyond that approximation?
A pendulum, made with a magnet, is moving over a surface with embedded magnets that are attracting the pendulum. In this lab, we want to model the trajectory of the magnetic pendulum.
Now that we have a working magnetic pendulum model, let's try to find out where the magnet ends up based on its initial position.
"Change is the only constant" - Heraclitus
Ordinary Differential Equations (ODEs) can be used to model any process involving rates of change. Given Heraclitus' insight, you can see why ODEs are such an important tool in mathematical modeling.