Show that the heat equation u^∼_t∼ = c²u^∼_xx, 0 ≤ x^∼ ≤ L, can be transformed to the “nondimensional” standard form u_t = u_xx, 0 ≤ x ≤ 1, by setting x = x^∼/L, t = c²t^∼/L², u = u^∼/u₀, where u₀ is any constant temperature.