Edited just now · Computational documentThe heat equation describes how heat diffuses through a given region over time. It is a fundamental partial differential equation in mathematical physics.∂u∂t=α∇2u\frac{\partial u}{\partial t} = \alpha \nabla^2 u∂t∂u=α∇2uTextFormulaCodeGraphTableResult⌘K for all commands12u = exp(-α*t) * sin(k*x) plot(u, x=0..2π)t = 0.5The solution exhibits sinusoidal behavior in space with exponential decay in time. As time increases, the amplitude diminishes, representing the smoothing effect of heat diffusion.