Share This Article:

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

Abstract Full-Text HTML Download Download as PDF (Size:128KB) PP. 33-35
DOI: 10.4236/apm.2012.21007    8,514 Downloads   14,658 Views   Citations
Author(s)    Leave a comment

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.

Conflicts of Interest

The authors declare no conflicts of interest.

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.

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

  
comments powered by Disqus

Copyright © 2018 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.