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.