This article offers a simple but rigorous proof that the curl defined as a limit of circulation density is a vector-valued function with the standard Cartesian expression.
References
[1]
E. Purcell, “Electricity and Magnetism, Berkeley Physics Course,” Volume 2, 2nd Edition, McGraw Hill, New York, 1985.
[2]
J. Stewart, “Calculus,” 4th Edition, Brooks/Cole, Stamford, 1999.
[3]
H. M. Schey, “Div, Grad, Curl, and All That: An Informal Text on Vector Calculus,” 4th Edition, W. W. Norton, New York, 2005.
[4]
E. Weisstein, “Wolfram Mathworld.”
http://mathworld.wolfram.com/Curl.html
[5]
K. Hildebrandt, K. Polthier and M. Wardetzky, “On the Convergence of Metric and Geometric Properties of Polyhedral Surfaces,” Geometriae Dedicata, Vol. 123, No. 1, 2005, pp. 89-112. doi:10.1007/s10711-006-9109-5
