Differential Equations
Courses
ODEs, the integrators that solve them, and the qualitative theory of flows.
Content for this course is still being written. For now, explore the skill map below — every node links to its full page.
Skill map
Each node is a skill; an arrow means "learn this first." Deep-dive links go to the full pages.
Euler Method…
The first-order explicit integrator from a Taylor step.
content coming soon
deep dive ↓Euler Method
Implicit Methods…
Unconditionally stable stepping for stiff systems.
content coming soon
deep dive ↓Implicit Euler Method
Picard Iteration…
Recast an ODE as an integral equation and iterate.
content coming soon
deep dive ↓Picard Iteration
Runge-Kutta…
Fourth-order accuracy from staged slope evaluations.
content coming soon
deep dive ↓Runge-Kutta Method
Bernoulli Equations…
Reduce a nonlinear ODE to a separable one.
content coming soon
deep dive ↓Bernoulli
Numerov's Method…
High-order integrator for y''=g(x)y+s(x).
content coming soon
deep dive ↓Numerov's Method
Adomian Decomposition…
A systematic series method for nonlinear equations.
content coming soon
deep dive ↓Adomian Decomposition