数学建模思想融入微积分课程中的两个教学插件

Two Instruction Units for the Calculus Permeated by the Idea of Mathematical Modeling

本文讨论了可融入微积分课程教学中的两个数学模型插件。第一个是研究市场调节下平衡价格的阻尼振荡模型，使用了二阶线性常系数微分方程的课程知识；第二个是在引进社会福利因素时商品的最优定价模型，使用了定积分和微分法的课程知识。在模型建立过程中，强调了建模假设的修改与完善技巧。

Two instruction units which can be inserted into the teaching of the calculus are discussed. The first is refered to the vibration model with retardation for the market equilibrium price, where the knowledge of the second order linear ordinary differential equation is used. The second is refered to the optimal pricing model of the price under the frame of the social welfare, where the concept of the definite integral is exploited. The improvement of the model hypotheses is emphasized during the modeling.