高维空间第一类曲面积分的计算及中值定理

目前的数学分析教材中,关于曲线积分和曲面积分的内容大多在三维欧氏空间中论述,对于高维空间中的曲面积分问题很少提及,而在许多工程应用中又需要在高维空间中计算曲面积分.讨论了高维欧氏空间中第一类曲面积分问题,推导出将光滑曲面的第一类曲面积分转化为重积分的一般公式,并将三维空间中的第一类曲面积分中值定理推广到高维的情况.

Calculation and Mean Value Theorem of the First Type Curved Surface Integral in High Dimensional Space

In current mathematical analysis textbooks,curved line integral and curved surface integral are discussed only in three dimensional Euclidean space,and the integral theorems in high dimensional space are seldom mentioned even they are useful in many engineering applications.The general formula of the first type integral in high dimensional space is discussed.A general method is presented to convert it to a multiple integral problem for computing.The mean value theorem for curved surface integral in high dimensional space is also proposed and proved.