A rate law
The simplest ODE assigns a constant rate of change.
du/dt = c
Ordinary Differential Equations: Introduction
Describing how systems evolve over time
Ordinary differential equations describe continuous change by connecting a system's present state to its rate of change.
watchone idea
→manipulateone example
→leave withone intuition
The essential idea: an ODE's solution is a function tracing evolution through time, not a single number.
One Concept · One Example
Ordinary Differential Equations: Introduction
Presented by Charlotte Moser · Coming soon
What to notice
- Time is the independent variable.
- An initial condition selects one trajectory from a family.
- The derivative controls the local direction of motion.
The mathematical structure
A trajectory
Integration turns the rate into a function of time.
u(t) = u₀ + ct
Turn a rate into a trajectory
Use the constant-acceleration example from the slides. Change the rate and initial state, then read the resulting function.
rate law du/dt = 1.0→solution u(t) = 0.0 + 1.0t
An ODE converts a rule for change into a trajectory through time.