中美大学微积分教材之微分方程内容的比较研究OA北大核心CSTPCD

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.