浅谈函数逼近的插值法课程思政融入——数值方法在天气预报中的应用与思考

A Brief Discussion on the Integration of Ideological and Political Education into the Course of Function Approximation: Interpolation and Curve Fitting—The Application and Reflection of Numerical Methods in Weather Forecasting

摘要: 本文阐述了函数逼近的插值法在天气预报中的应用，重点介绍了牛顿插值法及其应用举例，讲授中融入思政内容。针对牛顿插值法的教学过程中学生缺乏学习动力、难以理解方法实际价值的问题，引入天气预报“动态数据”场景，对比拉格朗日插值，突出牛顿插值法的递推增量优势。通过抽样访谈的“量质结合”评估模式表明，该方法提升了学生的问题分析能力与跨学科迁移能力，并自然融入“迭代递推、科学精神”等思政元素。通过教学反思发现，教学中需要优化时间分配及强化差商表理解，后续将拓展国产卫星案例，实现算法教学与科技报国情怀的有机融合，进一步探索更多数值方法与行业应用的结合点，让数学课堂教学既有公式的严谨，也有应用的温度，更有育人的深度。

Abstract: This article describes the application of interpolation methods for function approximation in weather forecasting, focusing on the Newton interpolation method and its application examples, with ideological and political education integrated into the teaching. To address the problems of students’ lack of learning motivation and difficulty in understanding the practical value of the method in the teaching process of Newton interpolation, a “dynamic data” scenario of weather forecasting is introduced, and a comparison with Lagrange interpolation is made to highlight the recursive incremental advantages of Newton interpolation. Through a “quantitative and qualitative combined” evaluation model based on sampling interviews, it is shown that this method improves students’ problem-solving abilities and interdisciplinary transfer capabilities, while naturally integrating ideological and political elements, such as “iterative recursion and scientific spirit”. Teaching reflection reveals that time allocation needs to be optimized and the understanding of the divided difference table needs to be strengthened in teaching. In the future, we will expand to domestic satellite cases to achieve an organic integration of algorithm teaching and the feeling of serving the country with scientific and technological dedication, and further explore the combination of more numerical methods with industry applications, so that mathematics classroom teaching has both the rigor of formulas, the warmth of applications, and the depth of education.