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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §13.2 Partial Derivatives, #36 · Multivariable Calculus · Partial derivatives

Show that … satisfies the _heat equation_

Show that $t^{- 1/2} e^{- x^{2} /4 t}$ satisfies the _heat equation_ $f_{t} = f_{xx}$ .
This $f (x, t)$ is the temperature at position $x$ and time $t$ due to a point source of heat at $x = 0$ , $t = 0$ .

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §13.2 Partial Derivatives, #36

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