Course 3 · Module 2
Differential Equations and Dynamical Systems
This module covers the branch of mathematics in which science writes its laws of change. You'll see how equations that relate a quantity to its own rate of change describe cooling coffee, growing populations, spreading diseases, and the weather, and why some of those systems are chaotic, so that tiny errors grow until prediction fails. You'll finish with the Navier–Stokes problem, where an AI-generated proof and a dispute over credit are being worked through right now.
Module objectives
- Describe how a differential equation relates a quantity to its rate of change and read the behavior of a simple solution.
- Explain how differential equations model weather and epidemics, why chaos limits prediction, and what the Navier–Stokes problem asks.
Lessons
- Lesson 1 Differential Equations: Laws of change: differential equations from planetary orbits to population growth You'll see how science states its laws as rules about how fast things change, and how to get from such a rule to a prediction. You'll step a growing population forward by hand and… 61111h 3m
- Lesson 2 Differential Equations: Weather, epidemics, chaos, and the Navier–Stokes problem You'll see how differential equations model epidemics and the weather, and why chaos puts a horizon on even perfect models. You'll then follow a live case: a claimed solution to… 611111h 33m