基于“悬链线”的可降阶方程的教学设计  

Teaching Design of Reduced-order Differential Equation Based on the Catenary

作　　者：寇冰煜[1] 滕兴虎[1] 张燕[1] 

机构地区：[1]解放军理工大学理学院数学教研中心,江苏南京211101

出　　处：《高等数学研究》2017年第3期15-16,19,共3页Studies in College Mathematics

摘　　要：为有效进行可降阶微分方程的教学,本文从微分方程的发展历史出发,创设问题情境,引入"悬链线与抛物线"问题,通过受力分析建立数学模型,引出悬链线方程与可降阶微分方程的求解.并利用微分学中的泰勒公式,巧妙地释疑了"悬链线与抛物线的混淆"问题.整个过程易于激发学生的学习兴趣,有助于提高学生分析问题解决问题的数学能力.For the effective teaching of the reduced-order differential equation, the question of catenary and parabola are introduced as the background of the development history of differential equations. By the stress analysis of the catenary, a mathematical model is obtained and methods for solving the reduced-order differential equation are introduced. On the other hand, the Taylor’s formula is subtly used to clear up doubts between catenary and parabola. The whole teaching process stimulates easily students’ learning in-terest, and improves their mathematical abilities of analyzing and resolving problems.

关 键 词：微分方程 可降阶 悬链线 泰勒公式 数学模型 

分 类 号：O151[理学—数学]