Free module · Calculus & mathematical models
Differential Equations & Numerical Models
Turn a rate rule into a path, and learn what a numerical solver actually approximates.
ODEs · initial conditions · Euler steps · PDEs
The building blocks
- A differential equation gives a rate of change.
- An initial value supplies the starting level.
- Read a rate rule
- Advance one small time step
- Check exact solutions, stability and PDEs
Lessons in this module
- Start with a rate rule and an initial value
- Ordinary differential equations: growth and mean reversion
- Euler stepping, convergence and stability
- Partial differential equations and the bridge to current research
Practice and apply
- Check a numerical decay model against its exact solution — y′=−2y, y(0)=1. Take two Euler steps of length .25.
- Advance a level — Start at 10 units. Add 3 units/hour for 2 hours. Find final level.
Work through the practice exercises · Quant development tools