We show that div(curl(v)) and curl (grad f) are 0 for any vector field v(x,y,z) and scalar function f(x,y,z).

The curl of the gradient and the divergence of the curl are zero (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 curl of the gradient and the divergence of the curl are zero (MathsCasts)

The curl of the gradient and the divergence of the curl are zero (MathsCasts)