微分积分定义的几种新途径对比分析

Comparison and Analysis on Several New Ways of the Differential and the Integral Definitions

微分与积分的常规定义具有复杂性且两者之间缺乏直观的联系.对于项武义教授、张景中院士与林群院士所给出的新定义进行一一阐述,然后从概念引入、微分与积分之间的联系、定义的应用效果以及微积分基本定理的所指这四个方面进行比较分析.对微积分阐释途径的多元化研究,有助于教改的推进与完善.

The classic definitions of the differential and integral are complex and lack of intuitive link. These new definitions given by Professor Xiang Wuyi , Academician Zhang Jingzhong and Academician Lin Qun are elaborated in detail. The introduction of the con- cepts, the link between the differential and the intqgral, the application effect of the concepts and the connotation of the fundamental theorem of calculus are compared and analyzed. The study on various ways of elaborating calculus is helpful to advance and improve the teaching reform.