计算第一型曲面积分的截曲线法  

The Intersection Curve Method for Calculating the Surface Integrals of the First Type

作　　者：罗志刚 LUO Zhigang(The School of Science,Hubei University of Technology,Wuhan 430068,China)

机构地区：[1]湖北工业大学理学院,武汉430068

出　　处：《大学数学》2023年第6期83-88,共6页College Mathematics

基　　金：湖北工业大学校内资助项目(337/187)。

摘　　要：用一族曲面去截被积曲面,如果截曲线族覆盖了被积曲面,就可以先在截曲线上作第一型曲线积分,然后对截曲线的参数积分,结果为被积曲面上的第一型曲面积分.文中用微分形式的计算技巧证明了该结论,并且用若干例子说明了该定理的应用.If the intersection curves of a series of surfaces and the surface over which a integral of the first type is defined cover the surface,the integral can be worked out by two steps:firstly integrating along the intersection curves and secondly integrating respect to the parameter of the intersection curves.This theorem is proved by the tricks from the differential forms theory and some examples are provided to illustrate its applications.

关 键 词：曲面积分 微分形式 外微分 截曲线 

分 类 号：O172.2[理学—数学]