“Know how to solve every problem that has been solved.” “What I cannot create, I do not understand.” — Richard Feynman

Differential Equations

Courses

ODEs, the integrators that solve them, and the qualitative theory of flows.

7 skills 0 questions ← whole tech tree

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.

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deep dive ↓Euler Method
Implicit Methods

Unconditionally stable stepping for stiff systems.

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Picard Iteration

Recast an ODE as an integral equation and iterate.

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deep dive ↓Picard Iteration
Runge-Kutta

Fourth-order accuracy from staged slope evaluations.

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deep dive ↓Runge-Kutta Method
Bernoulli Equations

Reduce a nonlinear ODE to a separable one.

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deep dive ↓Bernoulli
Numerov's Method

High-order integrator for y''=g(x)y+s(x).

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deep dive ↓Numerov's Method
Adomian Decomposition

A systematic series method for nonlinear equations.

content coming soon