Differential Equations in Spreadsheets: Euler, Heun & Runge–Kutta Methods
Slope fields, Euler's method against exact solutions, step size and the order of a method, Heun, RK4 by hand, predator–prey systems, the damped spring as a second-order ODE and stiffness with backward Euler: 8 hands-on labs that solve ODEs cell by cell.
The first lesson is free — no account needed.
About this course
A numerical differential equations course that solves ODEs cell by cell in a spreadsheet, for calculus and engineering students, physics and biology students, teachers and anyone who wants to see what an ODE solver does. You compute a slope field and test a candidate solution, cool a cup of coffee from 90 °C with Euler's method next to the exact solution, halve the step size to read off the order of a method, correct Euler with Heun's predictor-corrector, write one classical RK4 step with four slopes for logistic growth, step a Lotka-Volterra predator-prey system and chart its cycles, rewrite a damped spring as two first-order equations, and find where Euler becomes unstable on a stiff equation and fix it with backward Euler. Every method is a column of formulas, with no add-in or macro. The first lab is free.
Lessons
- Slope Fields: What a First-Order ODE Really SaysFree
- Euler's Method: A Coffee Cools, Step by Step vs Exact Pro
- Step Size & Error: Halving h and the Order of a Method Pro
- Heun's Method (Improved Euler): Predict, Then Correct Pro
- Runge–Kutta (RK4) by Hand: Four Slopes per Step Pro
- Systems of ODEs: Predator–Prey Cycles (Lotka–Volterra) Pro
- Second-Order ODEs as a System: The Spring–Mass–Damper Pro
- Stability & Stiff Equations: When Euler Blows Up Pro