微元法在多元积分学中的灵活应用
The Flexible Application of the Differential Element Method in Multivariate Integration Studies

微元法是分析解决物理问题的常用方法，是一种从部分到整体的思维方法，通过将问题分解为众多微小的“元过程”，运用熟悉的物理规律解决问题，从而使问题简单化。微元法中“元”的寻找是解决问题的关键，对一些特殊的积分区域，如圆柱面，圆柱体，球体，本文打破常规的微元分割，找到灵活的“微元(——弧棒，柱壳，球壳)”，实现积分运算的简化。
The differential element method is a commonly used method for analyzing and solving physical problems. It is a way of thinking that moves from part to whole by breaking down problems into numerous small “element processes” and applying familiar physical laws to solve them, simplifying the problem. The search for “elements” in the differential element method is the key to solving problems. For some special integration regions, such as cylindrical surfaces, cylinders, and spheres, this article breaks away from conventional finite element segmentation and finds flexible “differential elements” (arc rods, cylindrical shells, spherical shells) to simplify integration operations.