Welcome to Qwik DiffEq Lab — you just made one of the best investments in your STEM career.

What You're Getting

Over 6 chapters and 18 hands-on lessons, you'll go from Julia basics to deploying interactive differential equations simulations on the web. This isn't theory-only — every lesson has runnable code, real-world examples, and practical exercises.

Here's the roadmap:

1. Foundations — Julia environment, syntax, arrays & linear algebra

2. ODE Fundamentals — DifferentialEquations.jl, first-order & systems of ODEs

3. Numerical Methods — Solver selection, stiff problems, benchmarking

4. PDEs — Finite differences, heat equation, wave equation

5. Advanced Techniques — Stochastic & delay DEs, parameter estimation

6. Qwik Integration — Build & deploy interactive dashboards with Qwik

How to Succeed

• Go in order. Each chapter builds on the last. Sequential completion is required.

• Run every code block. Reading isn't enough — type it, break it, fix it.

• Use the Student Community chat. Ask questions, share your plots, help others.

• Complete the final project. You'll walk away with a deployed portfolio piece.

Quick Start

Head to Chapter 1, Lesson 1 right now and get your Julia environment set up. You'll be solving your first ODE within the hour.

Let's get to work. 🔬

Most people think chaotic systems require complex code. They don't. Here's the Lorenz attractor — the most famous chaotic system in mathematics — in 15 lines of Julia:

using DifferentialEquations, Plots

function lorenz!(du, u, p, t)
    σ, ρ, β = p
    du[1] = σ * (u[2] - u[1])
    du[2] = u[1] * (ρ - u[3]) - u[2]
    du[3] = u[1] * u[2] - β * u[3]
end

u0 = [1.0, 0.0, 0.0]
p = (10.0, 28.0, 8/3)
tspan = (0.0, 100.0)

prob = ODEProblem(lorenz!, u0, p, tspan)
sol = solve(prob, Tsit5())
plot(sol, idxs=(1, 2, 3), title="Lorenz Attractor", label="")

What's happening:

• lorenz! defines the 3 coupled ODEs (σ=10, ρ=28, β=8/3 are the classic chaotic parameters)

• Tsit5() is a 5th-order Runge-Kutta method — fast and accurate for non-stiff problems

• idxs=(1,2,3) plots the 3D phase space trajectory

Try this: Change u0 by 0.0001 and overlay both solutions. You'll see them diverge — that's sensitive dependence on initial conditions (the "butterfly effect").

This is Lesson 6 material in our full masterclass, where we go deep into phase portraits, solver selection, and building interactive web visualizations with Qwik.

→ Full course: 6 chapters, 18 lessons, from zero to deployed simulations.