摘要
将通常求重积分的截面法推广到了一般情况:用曲面族(对二重积分是曲线族)去截积分区域,先在截得的曲面片上完成积分,然后对曲面族参数积分,就可以求出重积分的值.用微分形式的计算技巧完成了相关定理的证明,并举了若干例子来说明该定理的具体应用.
The usual plane section method to calculate multiple integrals is generalized to curved section version,i.e.with a series of curved surfaces(curves for double integrals)which cover the region of a multiple integral,one can work out the surface integrals of the first type on the curved sections in advance,and then integrate over the parameter of the sections.The theorem is proved by the tricks from the differential forms theory and some examples are given to illustrate our method.
作者
陈坤
罗志刚
CHEN Kun;LUO Zhigang(The School of Science,Hubei University of Technology,Wuhan 430068,China)
出处
《大学数学》
2023年第3期83-87,共5页
College Mathematics
基金
湖北工业大学校内资助项目(337/187)。
关键词
重积分
截面法
微分形式
multiple integrals
section method
differential forms
