球坐标系中空间区域分类探讨与应用实例分析

On 3-D Region Classification with Spherical Coordinates

针对球坐标系中三重积分计算的教学与学习过程中出现的有关积分区域确定的问题,定义了球坐标系中的空间区域的类型,分析了一类球坐标系中简单区域的图形特征,结合图形演示,给出了构建其不等式描述形式的过程与方法.针对不符合球坐标系中简单区域图形特征的立体区域,就如何通过有效分割,借助三重积分对积分区域的可加性完成计算过程进行了探讨和实例分析.

To determine the integral regions for triple integrals with spherical coordinates,the classifications of 3-D regions are suggested.For a class of simple regions,the graphic features are analyzed and the processes and methods to build the corresponding description forms of inequalities are proposed.For none simple regions,the ways of dividing them into some simple regions and ways of calculating the related triple integrals are discussed and explored.