Appendix B Vector Calculus in Orthogonal Coordinate Systems

doi:10.1117/3.581869.apB

Book: Field Mathematics for Electromagnetics, Photonics, and Materials Science: A Guide for the Scientist and Engineer

Author(s): Bernard Maxum

Published: 2004

https://doi.org/10.1117/3.581869.apB

Author Affiliations +

Abstract

This appendix first provides a graphical development of first-order vector differential operators in conventional Cartesian and cylindrical coordinates. The focus is in the use made of differential elements of length (DLs) and how DLs become the building blocks for the differential elements of area and volume used in the definitions of gradient, curl, and divergence (and, of course, any combination of these operators). Once this concept is established several tables are presented for detailing the salient parameters associated with other orthogonal coordinate systems. Perspective views of coordinate surfaces are then provided to give graphical views of the coordinate systems.