函数的连续性、单调性、可积性及原函数存在性之间的关系  

Relationship Between Continuity,Monotonicity,Integrability and Existence of the Original Function

作　　者：赵秀 李红银 雷飞 ZHAO Xiu;LI Hong-yin;LEI Fei(College of Mathematics and Science,Xingyi Normal University for Nationalities,Xingyi,Guizhou 562400,China)

机构地区：[1]兴义民族师范学院数学科学学院,贵州兴义562400

出　　处：《教育教学论坛》2020年第53期315-317,共3页Education And Teaching Forum

基　　金：2019年度兴义民族师范学院“双一流”重点建设项目“数学与应用数学专业”(兴师发〔2019〕89号);2019年度贵州省省级一流本科专业建设点:数学与应用数学专业(黔教函〔2019〕630号)。

摘　　要：“数学分析”及“高等数学”中有几大类重要函数:连续函数、单调函数、可积函数与存在原函数的函数,它们之间存在着微妙的关系。研究它们之间的相互关系,在对知识的理解、加深、巩固及数学核心素养的提升上有着十分重要的作用。该文作者担任“数学分析”、“复变函数”与“高等数学”教学工作近三十年,同时也为考研辅导班上课,认为明晰这几类重要函数之间的关系意义非凡,故在此分享。There are several kinds of important functions in Mathematical Analysis and Higher Mathematics:continuous function,monotonic function,integrable function and function with original function.There is a subtle relationship between them.The study of the relationship between them plays a very important role in understanding,deepening and consolidating the knowledge and improving students'core quality of mathematics.The author believes it is of great significance to clarify the relationship between these important functions,who has been teaching Mathematical Analysis,Complex Variable Function and Advanced Mathematics for nearly 30 years,and also teaches classes for postgraduate entrance examination.

关 键 词：连续函数 单调函数 可积函数 存在原函数的函数 集合 

分 类 号：O174[理学—数学]