Laplace transform techniques are applicable to a wide variety of problems. The Bromwich inversion employing contour integration on the complex s plane is commonly used to invert untabulated transforms. Most physicists believe Laplace inversion must necessarily involve operations on the complex plane. This is not so. An alternative, the Widder inversion, uses real variables exclusively. We have applied Widder’s method to the problem of Landau damping, a notoriously difficult inversion, to illustrate the power of the techique.