散度概念的从头构建法

Building of divergence concept from scratch

不以高斯公式为前提,从头出发计算矢量场穿出无穷小闭合曲面的通量,以此建立散度概念并推导空间直角坐标系中散度的计算公式.给出一个优美的面积分公式,它能根据闭合曲面的形状和大小一般性地计算该曲面包围的空间区域的体积.指出通过计算矢量场穿出无穷小正六面体表面的通量来推导散度的计算公式的时候,人们通常会陷入误解.

Without taking the Gaussian formula as a premise,the flux of the vector field passing through the infinitesimal closed surface is calculated from the beginning,so as to establish the divergence concept and derive the formula for calculating the divergence in the space rectangular coordinate system.Giving a beautiful area division formula,it can generally calculate the volume of the space area enclosed by the surface according to the shape and size of the closed surface.It is pointed out that people often fall into misunderstanding when they calculate the formula of the divergence by calculating the flux of the vector field through the surface of the infinitesimal hexahedron.