定积分微元法的教学探析与思考  

Exploration and Reflection on the Teaching of Differential Element Method of Definite Integral

作　　者：李灵晓[1] 黄元元[1] 王锋叶[1] Li Lingxiao;Huang YuanYuan;Wang FengYe(School of Mathematics and Statistics,Henan University of Science and Technology,Henan Luoyang 471000)

机构地区：[1]河南科技大学数学与统计学院,河南洛阳471000

出　　处：《科技风》2024年第1期25-28,共4页

基　　金：国家自然科学基金(12101193);河南省高等教育教学改革研究与实践立项项目(2021SJGLX381);2023年高等学校大学数学教学研究与发展中心项目“基于信息技术和学科交叉的高等数学课程教学创新与实践”(项目编号:CMC20230205);智慧教学背景下高等数学课程创新型数学体系的构建与优化设计研究(2023)。

摘　　要：本着教育数学的思路,结合分析和比较三种微元法观点探析定积分微元法的主要思想,总结出定积分微元法的使用特点及判定方法,并运用微元分析法解决曲边扇形面积和变力对质点的冲量两个问题,该方法类似可推广到其他几何、物理及经济问题.According to the idea of educational mathematics,this paper analyzes the main ideas of definite integral differential element method,combined with the analysis and comparison of three viewpoints of differential element method.The application characteristics and judgment methods of definite integral and differential element method are summarized.The differential element analysis method is used to solve the two problems of the sector area of the curved edge and the impulse of the variable force to the mass point.This method is similar and can be extended to other geometric,physical and economic problems.

关 键 词：高等数学 定积分 微元法 高阶无穷小 教育数学 

分 类 号：G642[文化科学—高等教育学]