General Vector and Dyadic Analysis

Remarks on Standard Textbook Defınıtıons of Vector Operators

“…To overcome the deficiencies of the nabla operator Chen-To Tai has introduced a new symbolic (functional) S-operator and its associated operators in [39] (see also [45]) which do not have explicit differential forms and satisfy commutative property. With these operators he has been able to present a systematic treatment of the entire subject of vector analysis, while it can also be extended to dyadic analysis.…”

Fast and Efficient Methods for Circuit-based Automotive EMC Simulation

“…An arbitrary point in space P (x, y, z) is defined by its position vector r = e x x + e y y + e z z, r = | r| = x 2 + y 2 + z 2 (C. 4) from the origin with length r = | r|. An infinitesimal variation of the position vector by d r to a point Q(x+dx, y +dy, z +dz) is also called vectorial path element and can be defined by [33,182] d r = e x dx + e y dy + e z dz, dr = |d r| = (dx) 2 + (dy) 2 + (dz) 2 , (C 5) as is graphically visualized in Figure C. 1.…”

Direct Integration of Field Equations

“…The rationale for adopting the new notation for the divergence and the curl is explained thoroughly in [4], particularly from the historical point of view as discussed in Chapter 8.…”