一元微积分理论近期发展内容的比较分析  

A Comparative Analysis on Recent Developments of Single Variable Calculus Theory

作　　者：李红玲[1] LI Hongling(Liberal-arts and Science College, Suqian College, Suqian 223800, China)

机构地区：[1]宿迁学院文理学院,江苏宿迁223800

出　　处：《河南教育学院学报（自然科学版）》2021年第2期34-40,共7页Journal of Henan Institute of Education(Natural Science Edition)

基　　金：江苏省教育科学“十三五”规划课题“‘教育科学’视角下数学学科教学改革研究——以中小学‘微积分’知识模块为例”(D/2020/01/30)。

摘　　要：从两个方面对一元微积分理论的近期发展内容进行比较分析。一是通过对RANGE、张景中、林群和沈卫国各自提出的4种导数定义进行对比,指出其直观形象且不使用极限的共同点,以及应用时简洁程度及适用范围的差异性;二是通过对RANGE、LAX、张景中和萧树铁各自给出的4种微积分基本定理证明过程进行对比,分析其在定积分定义方式与顺序、定理证明条件与方法的差异性,指出其中不够完善的方面。最后提出建议:前沿的探究可以为教学提供新的思考角度与素材,数学教育工作者应积极关注并参与完善。The recent developments of single variable calculus theory are compared and analyzed mainly in two aspects.Firstly,the four definitions of derivative proposed by RANGE,ZHANG Jingzhong,LIN Qun and SHEN Weiguo are compared.The common points are their intuitiveness and the necessity of the limit.The differences are their conciseness and application scope.Secondly,the four proving processes of the fundamental theorem of calculus given by RANGE,LAX,Zhang Jingzhong and Xiao Shutie are compared.There are differences on the definition forms and orders of definite integral.The conditions and methods of theorem proving are different too.And the imperfect aspects are pointed out.Finally,some suggestions are put forward that frontier exploration can provides new perspectives and materials,so mathematics educators should actively pay attention to them and participate in the improvement of them.

关 键 词：一元微积分 导数定义 不用极限 微积分基本定理 定积分定义 对比分析 

分 类 号：O13[理学—数学]