Researched
Partial Differential Equations
D'Alembert's wave equation (1747) begins the use of differential equations to describe continuous fields and media.
Open in the interactive tree →Euler, Bernoulli and Lagrange extended the method to vibrating strings, fluids and heat, and Fourier's heat equation, Maxwell's equations and Schrödinger's equation are all of this kind. Much of physics, weather forecasting and engineering simulation rests on solving such equations.
Prerequisites
Unlocks
- Fourier Analysis1822Fourier created his series to solve the heat equation
- Electromagnetism1831-1865Maxwell's equations are partial differential equations for electric and magnetic fields
- Numerical weather prediction1950Forecasts integrate the PDEs of fluid motion on a grid
- Poincaré Conjecture Proved2003
- Fluid Equations from Atoms2024-2025
- Navier-Stokes ProblemopenThe Navier-Stokes equations are PDEs whose smooth solutions are still unproven