论多元积分学中的降维思想  

On Dimensionality Reduction in Multivariate Integrals

作　　者：田卫章[1] TIAN Weizhang(Shangqiu Polytechnic,Shangqiu 476100,China)

机构地区：[1]商丘职业技术学院,河南商丘476100

出　　处：《商丘职业技术学院学报》2021年第6期78-85,共8页JOURNAL OF SHANGQIU POLYTECHNIC

基　　金：2019年度河南省高等教育教学改革研究与实践项目“提升高职院校学生应用能力的数学教学模式的改革与实践”(2019SJGLX739)。

摘　　要：多元函数的积分运算本质上是将积分区域进行降维的一个过程,例如,牛顿-莱布尼茨格林公式将二重积分转化为平面曲线积分,是将积分区域由2维降到1维.斯托克斯公式将二元函数在空间曲面上的积分转化为空间曲线积分,也是将积分区域由2维降至1维.高斯公式将二元函数的三重积分转化为空间曲面积分,是将积分区域由3维降至2维.一般形式的多重积分的计算过程是降低积分重数的过程,也是降低积分区域维数的过程.The integral operation of multivariate functions is a process of reducing the dimension of integral region.For example,Newton-Leibniz's formula of the dimensional transformation is converted into a plane curve integral and the integral region is reduced from 2 dimensions to 1 dimensions.In the Stokes formula,the integral of the two valued function on the surface of space is transformed into the integral of the space curve and the integral region is reduced from 2 dimensions to 1 dimensions.The Gauss formula is used to transform the three integral of the function of the two variables into the integral of the space surface,and the integral region is reduced from the 3 dimension to the 2 dimension.The calculation of multiple integrals in general form is the process of reducing the number of integrals,which is also the process of reducing the dimension of integral region.

关 键 词：区域降维 牛顿-莱布尼茨公式 格林公式 斯托克斯公式 高斯公式 

分 类 号：O172.2[理学—数学]