多元积分的降维计算法  

A New Method to Calculate Multiple Integrals by Reducing the Dimensions Repeatedly

作　　者：罗志刚 LUO Zhi-gang(The Science School of Hubei University of Techonology,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》2021年第3期110-116,共7页College Mathematics

基　　金：湖北工业大学校内资助项目(337/187)。

摘　　要：在外微分的基础上讨论了多元函数积分号下凑微分、换元和分部积分问题,并得到了一种计算多元函数积分的统一方案:使用凑微分、换元和分部积分等手段将被积式变形成特定形式后应用广义Stokes公式,区域上的积分就能不断转化成边界上的积分,从而实现“降维”.此方案中不必使用通常的化累次积分方法.所举计算实例演示了这些方法的可行性.With exterior differential theory,the methods to calculate multiple integrals such as substitution rules and integration by parts are investigated completely in this paper.In addition,a uniform scheme is obtained to reduce the dimensions of multiple integrals,i.e.making use of the general Stokes formula repeatedly to convert a multiple integral over a region(or mainfold)into a integral along its boundary.It is unnecessary to turn to iterated integrals in the new scheme.Some examples are provided to illustrate the validity of these methods.

关 键 词：重积分 外微分 外微分形式 分部积分法 

分 类 号：O172.2[理学—数学]