微分方程教学中强化建模思想的探讨——2016全国大学生数学建模竞赛题启示

Incorporating Mathematical Modeling in Differential Equation Teaching——Inspiration from the 2016 Mathematical Modeling Contest

微分方程可描述物质的运动规律与演变过程,为解决实际问题提供了强有力的工具,在工程实践中具有重要的作用。因此,以具体问题为背景、以问题建模求解为模式进行微分方程讲解,有助于培养学生的创新实践能力。以2016年全国大学生数学建模竞赛的A题“悬浮线模型在系泊系统设计中的应用”为案例,探讨微分方程建模能力培养的重要性及相应教学策略,并以此形式提升学生对知识的求知欲及建模思维,促进创新精神的培养。

Differential equations can characterize laws of motion and evolution process of matter,and provides a powerful tool for solving practical problems and plays an important role in various engineering fields.Therefore,in the process of learning differential equations,it is necessary to develop students’innovative practical ability for combining the theoretical methods of differential equations with specific problems.This study takes question of“the mooring system design based on catenary model”in the 2016 mathematical modeling competition as an example to elaborate the importance and the corresponding teaching strategy.Furthermore,some strategies are provided for training students'mathematics theory and the ability of solving practical problems,improving students'curiosity for knowledge and innovation spirit,promoting the formation of the mathematical modeling thinking.