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

Author(s)
David McKay

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.

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.

Cite this paper

D. McKay, "A Simple Proof That the Curl Defined as Circulation Density Is a Vector-Valued Function, and an Alternative Approach to Proving Stoke’s Theorem,"*Advances in Pure Mathematics*, Vol. 2 No. 1, 2012, pp. 33-35. doi: 10.4236/apm.2012.21007.

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

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

[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