The comprehension, some problems and suggestions to symbolic vector method and some defenses for Gibbs' symbol (Q1580418)

The product model of the Gibbs' operator is true in a Cartesian coordinate system but some mistakes may be made when it is used in other orthogonal coordinate systems. Many scientists made efforts to present various methods to solve this problem. At the beginning of the 1990s, C. T. Tai has presented the concept of symbolic vector and a systematic theory of it, and the problem was solved entirely. In the present paper the authors present the comprehension of Tai's symbolic vector method in vector analysis, next some problems are found and some suggestions are provided to solve them. Some defenses for Gibbs' symbol are given as well.