体积元几何与Jacobi行列式之关系

The Relationship between Volume Element Geometry Related and Jacobi Determinant

在数学分析的学习中我们已经学习了弧长、面积、体积的求解方法,那这些方法是怎样得到的,是我们学习过程中需要探讨的一个非常重要的问题。为了方便我们在学习过程中对这一部分内容的理解、掌握,本文将从坐标变换、向量外积、向量内积三个不同的方面来介绍体积元与Jacobi行列的关系。

In the study of mathematical analysis, we have learned the solving methods of arc length, area and volume, and how to use these methods to find physical quantities such as the mass of an object and the moment of inertia, which is a very important part in our learning process. In order to ensure that we have a better understanding of the content in the learning process, this thesis will introduce the relationship between volume elements and Jacobi rows from three different aspects of coordinate transformation, vector exterior product and vector inner product.