梯子下滑过程中的微分方程及其求解

由于微积分在物理学中具有广泛的应用，因此在数学分析教学中适时地加强综合应用练习，不仅有利于学生巩固微积分基本概念，而且有助于提高学生分析问题解决问题的能力。但选择此类应用性模型问题时，一定要尽量与实际相符，如在探索物体运动方程时，其物理背景应与物理中的基本定律相符。本文就高等数学教学中常被采用的一个物理模型问题提出质疑，并利用Mathematica给出与实际背景基本相符的运动轨迹。

Differential Equation and its Solution on the Falling Ladder

Calculus has a wide application in Physics. so certain comprehensive exercises in teaching will result in both the solidification of its fundamental concepts and the enhancement of abilities for one's finding and solving problems. You must take note of the accordance with reality when you choose such exercises. If you try to give the mathematical model of an object's motion, it must be accord with the basic physics laws. This paper is to give a revision of the mathematical model about falling ladder, which has the background in physics and usually be found in calculus teaching, and gives a solution by means of the Mathematica.