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The density function of a normal distribution with mean 0 and standard deviation √(2kt) satisfies the heat equation. That is, the function satisfies the partial differential equation You could verify this by hand, or if you’d like, here’s Mathematica code to do it. u[x_, t_] := PDF[NormalDistribution[0, Sqrt[2 k t]], x] Simplify[ D[u[x, t], {t, […] The post Heat equation and the normal distribution first appeared on John D. Cook....