R3中矢量场散度和旋度运算关系的建立方法

矢量微积分在经典场论中占有十分重要的地位。R3中的散度和旋度运算是经典矢量场函数的两种基本微分运算，并将其结果和场的源函数联系起来，从而基于亥姆霍兹定理可以唯一地确定空间场分布。关于散度和旋度运算关系的建立，一般均基于其定义关系的直接计算的基础上，其数学上的完整性并没有得到充分的体现。为此，通过对有关问题的初步分析，时矢量微分运算规则的建立给出了若干简洁明了的方法，从而有助于研究工作者对其本质的进一步认识。

Building of the operation rules of curl and divergence for vector field in R 3 space

Vector calculus plays an important role in classic field theories. The o peration of curl and divergence in R 3 are the two fundamental operations o f differ ential, which reveals the relation between the source and the field, determines t he field distribution in space uniquely on the basis of Helmholtz's theorem if b oth of them are specified everywhere. The operation rules' building is usually based on the direct computing for the definition formula, which is by no means complete mathematically. For this reason,the authors in this paper gave a series of methods with which the rules of the vector differential operations were built up, thus c ontributed to a better understanding to the essence of the operation of the curl and the divergence.