(n-1)维曲面所围空间体积的计算公式  

Volume Calculation Formula of Areas Enclosed by (n-1)-dimension Surface

作　　者：陈凌蛟 

机构地区：[1]东南大学吴健雄学院,南京210096

出　　处：《大学数学》2014年第4期102-107,共6页College Mathematics

摘　　要：在不使用Green公式的情况下,通过变量代换的办法,将简单闭曲线所围的区域用它的边界表示出来,结合积分换元公式,给出了一种求解曲线所围区域面积的新方法,并且推广到了n维空间,得出了求取n-1维曲面所围空间体积的新公式,并通过应用实例,尤其是对标准n维单纯形体积的计算,显示了本文提供新方法的优势与应用前景.Within variable substitution and the substitution formula for integrals, the author presents a new method to calculate the area of plane figures whose boundary is written in a parametric form. Then this technique is extended to obtain a new formula for measuring the volume of a specific n-dimensional region with the boundary expressed in the parametric form. Furthermore, some applications, including the calculation of volume of the standard n-simplex, are put forward to reveal the value and prospect of the new approach and formula.

关 键 词：重积分 变量代换 边界条件 闭曲面 围成体积 标准n维单纯形 

分 类 号：O172.2[理学—数学]