区间上连续函数的性质与构造证明法  

Properties of Continuous Functions on the Interval and Their Proofs with Construction Method

作　　者：丁宣浩[1] 杨宜平[1] 

机构地区：[1]重庆工商大学数学与统计学院,重庆400067

出　　处：《重庆工商大学学报（自然科学版）》2011年第4期410-412,416,共4页Journal of Chongqing Technology and Business University:Natural Science Edition

基　　金：重庆市高等教育教学改革研究项目(093088)

摘　　要：连续函数是"微积分"研究的主要对象;区间上连续函数的性质是"微积分"课程的重要内容;也是被认为很困难的内容;许多教材为了回避困难,不惜先引入定理,在教材的后面部分再给出证明;其实,闭区间上连续函数性质的证明的难度不会超过证明确界定理的难度,而证明这些定理的思想方法可能比这些定理本身更重要;将在确界定理与单调有界定理的基础上,利用构造性方法给出闭区间上连续函数性质的证明;并由此深入讨论一般区间上连续函数的性质。Continuous function is one of the key objects in calculus.Properties of continuous functions on the interval are not only the critical contents in calculus course,but also the difficult ones in calculus course.To avoid these difficulties,many textbooks firstly introduce theorems,and then show the proofs of theorems in the later part.However,proving the properties of continuous functions on closed interval is not more difficult than proving deterministic bounded theorem,the ideas used in proofs are more valuable than these theorems.The proofs of properties of continuous functions on the closed interval based on deterministic bounded theorem and monotonic bounded theorem by using construction method are presented in this article,a further study about the properties of continuous functions on the general interval is conducted.

关 键 词：区间 连续函数 确界定理 单调有界定理 构造法 

分 类 号：G642[文化科学—高等教育学]