摘要
若在某单连通区域V∈R3上,向量函数A是某个数量函数u的梯度,则其旋度rotA在所定义的区域上为零.本文证明了其旋度的任意两个分量在所定义的区域V上为零,另一个分量满足在区域V的边界S上为零与其三个分量在所定义的区域V上为零是等价的,解惑教学中学生的问题.
If a vector function A is gradient of a quantity function u in a simply-connected area V∈ ^3, its rotation rotA is zero in defined area V. In order to solve a problem put up by a student, this paper show that the condition that arbitrary two components of rotA are zero in defined area V and the third component is zero on the boundary S of area V is equivalent to another condition that three components of rotA are zero in defined area V.
出处
《大学数学》
2009年第3期185-186,共2页
College Mathematics
关键词
向量场
梯度
旋度
vector field
gradient
rotation
