一类可降阶高阶微分方程的教学设计

Instructional Design for a Class of Higher Order Differential Equations with Reduced Order

给出针对一类可降阶高阶微分方程的一种教学设计.以趣味故事作为实例引入,得出悬链线所满足的一类高阶微分方程,找出通用的求解方法对其求解.使学生对求解方法印象深刻,并对微分方程的应用有一个初步的了解.在教学过程中,步步引导,全程既具有趣味性又具有启发性.

An instructional design for a class of higher order differential equations with reduced order is provided.Starting with interesting stories as examples,a class of higher order differential equations is obtained,and the common method for solving the equations is used.Students are impressed with the solution and have a preliminary understanding of applications of differential equations.The whole process is both interesting and instructive.