Tai Chen-To. Generalized Vector and Dyadic Analysis: Applied Mathematics in Field Theory

2nd Edition. — New York: Wiley Interscience, IEEE Press, 1997. — 192 p.In 1994, I had the opportunity to teach a course at the University of Michigan in which I used the method of symbolic vector and the new notations to teach vector analysis. The reaction from the students was very favorable. Similar views have been communicated to me by colleagues from other institutions. My motivation for revising the books principally due to these encouragements.In addition to the overhaul of the notations, the present edition considerably expands the coverage. The method of symbolic vector is now formulated not only in the curvilinear orthogonal system, but also in the general nonorthogonal curvilinear system. The reciprocal base systems, originally introduced by Gibbs, have been used very effectively in the formulation. New vector theorems and ector and dyadic identities have been derived to make the list as complete as
possible. The relationship between dyadic analysis and tensor analysis has also been explained. The transformation of electromagnetic field vectors based on the special theory of relativity is explained by both the conventional method, using differential calculus, and the more sophisticated method due to Sommerfeld, with the aid of four-dimensional vector analysis.