A Comparative Study On The Content And Structure Of One-element Calculus Between China And The United States

In recent years,the international comparative study of teaching materials is a hot topic in educational research.In this article the author hopes to find out the characteristics of the two countries' calculus and the direction of the reform in calculus in China's Applied Colleges and universities through the comparison between the Chinese and American.This paper first studies the development history of calculus textbooks in China and the United States,and finds some historical factors in the differences between the two countries.Then we compare the two classic calculus textbooks of China and the United States: the higher mathematics published by the Department of mathematics of Tongji University and the American textbook ”Thomas' Calculus”as the object.In the process of comparing the content and structure of the single variable calculus in the teaching materials and the writing characteristics,we found the differences of the two textbooks in China and the United States,and the enlightenment can provide some constructive suggestions for the reform of the calculus in the authors' school.The main research results are as follows:1.Through the history of the development of Chinese and American calculus,it is always the main stream to attach importance to intuition and to attach importance to the application in the whole history,and the course of calculus in our country are more theoretical and systematic.Since the popularization of higher education in the United States is 20 years earlier than that of our country,especially after the 1985,the United States has made a series of effective changes to the calculus teaching materials to adapt to the mass education.Therefore,there are many aspects in the American calculus which deserve our country to study.2.Through studying the structural characteristics of the two textbooks,I find that the two countries have different emphasis on the four modules of function,limit,differential and integral.Through the comparison of function modules,it is found that Chinese calculus textbooks pay much attention to the nature of functions,but it is lack of system.In the limit module,there is too much concern about the existence in Chinese textbooks.In the integral module,the compilation of Chinese textbooks does not conform to the law of cognition,nor does it conform to the history of the development of calculus.Moreover,there are many repetitions in the calculation methods of the indefinite integral and the definite integral,and the processing of the American calculus teaching materials is just right.3.In the comparison of the introduction methods,it is found that China's introduction is relatively simple,while the American's is more flexible.When we studied the introduced method of the fundamental theorem of calculus,it is found that the two calculus textbooks in China and the United States have a great difference in the positioning of the fundamental theorem of calculus.The fundamental theorem of the American textbook is the bond between the integral and the derivative,but it is just a formula in our country.From the comparison of the way of handling exponential functions,the second important limit formula in Chinese calculus textbooks is the core of proving the derivation formula of exponential function,but it is ignored in the Unite States.In the application comparison of exponential functions,the United States pays more attention to the practical application of exponential functions.The selection of examples is not only novel but also closely linked with modern science and technology.Finally,this paper gives a series of suggestions on the compilation of calculus textbooks for Applied Universities in China.