A systematic treatment of vector analysis

摘要

A systematic method of treating vector analysis is presented. A general definition of an operational expression containing a new symbolic operator, independent of the choice of coordinate system, is the foundation of the subsequent developments which include an algebraic method of deriving vector identities and the formulation of a generalized Gauss theorem. Vector analysis on a surface is formulated in a similar manner by introducing a symbolic operator for a surface. A generalized Gauss theorem for a surface is formulated that enables the deduction of all the important theorems involving the surface gradient, the surface divergence, and the surface curl. The relationship between the present formulation and the classic work of Weatherburn is pointed out.