首页|中美大学微积分教材之微分方程内容的比较研究

中美大学微积分教材之微分方程内容的比较研究

扫码查看
原文链接
  • 国家科技期刊平台
  • NETL
  • NSTL
  • 万方数据
对中美大学微积分5套教材中微分方程内容的比较研究发现,中美教材在内容的编排位置、习题数量、数学表征方式、数学软件的使用、对数学建模的偏重程度、对次要或较高要求内容的处理方式,以及微分方程模型解决的实际问题数量和类型等都存在差异.美国教材在数学建模的思想方法指导和数学建模难点突破方面,有许多做法值得借鉴.中国教材存在一个重大缺陷,就是求解"无初等解析解的微分方程"所需的大部分知识均未编入教材.由此得到3点启示:一是教材编写者对知识点的认识偏差可能会导致编写指导思想上的偏差;二是数学能力的培养和训练并非都是有益的;三是习题除了具有提供练习的显性功能外,还有许多隐性功能有待开发利用.针对同济教材,建议:增加方向场、欧拉方法等重要内容;删去高阶微分方程等过于形式化的内容;调整微分方程的幂级数解法等的编排位置.
Comparative Study of Differential Equations in Calculus Textbooks of Chinese and American Universities
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.

university textbookscalculusdifferential equationcomparative studymathematical modeling

潘建辉、胡学刚、朱伟、邓志颖、陈继林

展开 >

重庆邮电大学 理学院,重庆 400065

重庆邮电大学 教务处,重庆 400065

重庆市天星桥中学,重庆 400038

大学教材 微积分 微分方程 比较研究 数学建模

重庆市高等教育教学改革研究重大项目重庆市研究生教育教学改革重点项目重庆市高等教育教学改革研究项目重庆市研究生课程思政示范课程项目重庆邮电大学金课建设基金项目

221018YJG212022213161YKCSZ23121XJKXX20201-15

2024

数学教育学报
天津师范大学 中国教育学会

数学教育学报

CSTPCD北大核心
影响因子：2.296
ISSN：1004-9894
年,卷(期)：2024.33(1)
  • 23