Heat Equation

★★★★☆Undergraduate

📖Definition

Parabolic PDE describing heat diffusion

📐Formulas

∂u/∂t = α∇²u
1D: ∂u/∂t = α ∂²u/∂x²
Fundamental: u = (1/√4παt)exp(-x²/4αt)

✏️Examples

예제 1

Heat conduction in rod

예제 2

Diffusion processes

예제 3

Brownian motion

Applications

Thermodynamics

Finance (Black-Scholes)

Image processing

#열방정식#heat#parabolic#diffusion