微积分中几个著名病态函数的理解与分析  

The Understanding and Analysis on Several Well-known Pathological Functions in Calculus

作　　者：周高军[1] 郑宝杰[1] 

机构地区：[1]河南教育学院数学与统计学院,河南郑州450046

出　　处：《河南教育学院学报（自然科学版）》2014年第4期35-37,共3页Journal of Henan Institute of Education(Natural Science Edition)

基　　金：河南省软科学项目(132400410105);河南省教师教育研究课题(2013-JSJYYB-116)

摘　　要：简要介绍了微积分中4个著名病态函数的历史及其重要性质.对这些函数的了解,一方面可以认识到病态函数在微积分的发展过程中所起的重要作用,另一方面还可以进一步增强对微积分中某些重要概念及结论的理解.Four well-known pathological functions in calculus are discussed, and both the history and the important property of the functions are introduced. The functions have double purposes： on the one hand, they allow us to un- derstand the important role of the pathological functions in the development of calculus ; on the other hand, they ean also further enhance our understanding of the corresponding concepts and conclusions in calculus.

关 键 词：病态函数 DIRICHLET函数 Cauchy函数 RIEMANN函数 WEIERSTRASS函数 

分 类 号：O174.1[理学—数学]