数学教育学报2024，Vol.33Issue(1)：64-70,7.
中美大学微积分教材之微分方程内容的比较研究
Comparative Study of Differential Equations in Calculus Textbooks of Chinese and American Universities
摘要
Abstract
A comparative study of the contents of differential equations in 5 sets of calculus textbooks for Chinese and American universities found that there are many significantly different aspects in the two types of textbooks,such as the content layout,the number of exercises,mathematical representation methods,the use of mathematical software,the degree of emphasis on mathematical modeling,the processing of secondary or higher required content,and the number and types of real world problems solved by the differential equation models.In addition,American textbooks have many practices worth learning from in terms of ideological and method guidance on mathematical modeling and breakthroughs in difficult mathematical modeling problems.However,a major defect in Chinese textbooks is that most of the knowledge required to solve the"differential equations without primary analytical solutions"is not included in the textbooks.Then,three inspirations are obtained:first,the textbook writers'misunderstanding of knowledge points may lead to deviations in the guiding ideology;second,the cultivation and the training of mathematical abilities are not always beneficial;third,the exercises have many invisible functions that need to be developed and utilized.Finally,three revision suggestions are put forward for Tongji Textbook:add direction field,Euler method and other important content;delete overly formal content such as higher-order differential equations;and adjust the arrangement position of power series solutions to differential equations and other contents.关键词
大学教材/微积分/微分方程/比较研究/数学建模Key words
university textbooks/calculus/differential equation/comparative study/mathematical modeling分类
社会科学引用本文复制引用
潘建辉,胡学刚,朱伟,邓志颖,陈继林..中美大学微积分教材之微分方程内容的比较研究[J].数学教育学报,2024,33(1):64-70,7.基金项目
重庆市高等教育教学改革研究重大项目——政产学研用深度融合的协同育人模式研究与实践(221018) （221018）
重庆市研究生教育教学改革重点项目——新工科背景下"五维一体"研究生数学课程思政体系的综合研究与实践(YJG212022) （YJG212022）
重庆市高等教育教学改革研究项目——大学数学"前移式问题解决"教学模式的实验研究(213161) （213161）
重庆市研究生课程思政示范课程项目——决策理论与决策支持(YKCSZ23121) （YKCSZ23121）
重庆邮电大学金课建设基金项目——《实变函数》线下金课(XJKXX20201-15) （XJKXX20201-15）
