A note on divergence,rotation, gradient and their associated theorems

In this note, the essence and some supplements for the unified definition of divergence, rotation and gradient advanced by Tai have been presented based on the method of exterior differential form with an expression of vectors of tensors. The main purpose of this note is to introduce the useful expressions and their applications, and to simplify the proofs of many theorems in various field theories, and they are also important because of their utility for establishing a wide class of principles.