摘要
利用格林公式分析和讨论二重积分在极坐标变换下面积元素的对应关系,由此得到一般坐标变换下面积元素的对应关系,指出面积元素是与划分方式和坐标系的选择密切相关的量.利用高斯公式和第二类曲面积分讨论和证明三重积分中球坐标变换下体积元素的对应关系.
In this paper, the area element of a double integral under the polar coordinates is discussed using Greeffs formula. The general relation of the area element between different coordinate systems is given. The results provide a way to show the relation among the area element, the partition of the integral region, and the coordinate system. Furthermore, the conclusions of the volume element in triple integral are discussed using Gauss formula and surface integral of the second type. The discussion in this paper may help both teachers and students better understanding the area element.
出处
《高等数学研究》
2013年第2期10-12,共3页
Studies in College Mathematics
基金
国家自然科学基金资助项目(61170233)
关键词
格林公式
面积元素
高斯公式
雅可比行列式
Green＇s formula, area element, Gauss formula, Jaeobian determinant
