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A Simple Proof That the Curl Defined as Circulation Density Is a Vector-Valued Function, and an Alternative Approach to Proving Stoke’s Theorem

DOI: 10.4236/apm.2012.21007, PP. 33-35

Keywords: Curl, Circulation Density

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Abstract:

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

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