考虑工科本科生教学特点，在弹性力学教学中，抓住数学和力学问题的内在联系，采用矩阵表达的形式阐述直角坐标与极坐标的变换关系，以及物理量（如位移、体力、应力、应变）的坐标变换关系，并利用坐标变换从直角坐标中的基本方程直接导出极坐标中的基本方程。按照这一教学思路，将数学知识与弹性力学有机结合，简化基本方程的推导过程，在对知识点深入和透彻讲解的同时，可与学生共同体会和分享数学与力学完美融合过程中的美学感受。

According to the characteristics of undergraduate teaching in elastic mechanics, the interconnection between mathematics and mechanics problems is captured, the transform relationship between the rectangular coordinates and the polar coordinates is expressed using matrix form, and the coordinate transformation of basic physical quantities, such as displacement, body force, stress, strain, can been expressed by matrix form. Using the coordinate transformation, the basic equations in polar coordinates is directly derived from the ones in rectangular coordinates. In this teaching way, the knowledge of mathematics and mechanics is naturally combined, and the derivation of the basic equations is simplified. Moreover, the aesthetics of mathematics and mechanics can be experienced and enjoyed.

2014年湖北省高等学校省级教学研究项目(2014241)；三峡大学弹性力学精品课程建设项目