关于微分方程教学中方程类型引入的思考

Reflections on the introduction of equation types in the teaching of differential equations

微分方程是大学数学专业必修的重点课程之一.在微分方程教学中,各种类型的微分方程求解方法是微分方程教学的重点.然而,如何让学生认识到每一种微分方程的重要性,是微分方程教材以及课堂教学普遍缺失的.利用线性化的方法,对2种微分方程的引入做了详细的说明.通过这样的说明,可以使学生不用强行死记硬背方程类型,同时也有利于后续微分方程组和微分方程解的稳定性问题课程的讲解.

Differential equation is one of the key courses in mathematics major.In the teaching of differential equations,solving methods of all differential equations are the emphasis of differential equation teaching.How to make students realize the importance of each differential equation,however,is generally lacking in the book and classroom teaching.The introduction of two differential equations is explained in detail by means of linearization. Through this explanation,the students cannot be forced to memorize the equation type.Moreover,it is also helpful to teach the differential equations and the stability of solutions of differential equations.