We derive a general formula for the Laplacian acting on a function f(r) then demonstrate that the Laplacian is zero in the case that f(r) = 1/r, thereby showing that 1/r is harmonic.

The Laplacian of f(r) and proof that 1 over r is harmonic (MathsCasts)

These MathsCasts were produced by the mathematics support centres at Swinburne University, the University of Limerick and Loughborough University. They were part of a collaborative research project to develop high quality resources and investigate the effectiveness of MathsCasts to support mathematics learning. The full set of resources are available at http://commons.swin.edu.au/s/mathscasts MathsCasts are licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License

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The Laplacian of f(r) and proof that 1 over r is harmonic (MathsCasts)

The Laplacian of f(r) and proof that 1 over r is harmonic (MathsCasts)