介值定理的推广和应用  

Generalization and Applications of Intermediate Value Theorem

作　　者：李娅[1] 薛玉梅[1] LI Ya;XUE Yu-mei(School of Mathematics and Systems Science,Beihang University,Beijing 100191,China)

机构地区：[1]北京航空航天大学数学与系统科学学院,北京100191

出　　处：《教育教学论坛》2018年第14期194-196,共3页Education And Teaching Forum

摘　　要：介值性是有界闭区间上连续函数的重要性质,在很多方面都有广泛的应用。本文对介值定理进一步推广,将此性质拓展到任意区间的一元连续函数以及区域上的多元连续函数,并利用推广后的介值定理去研究它们在理论和实际问题中的应用.Intermediate value is an important property of continuous functions in bounded closed intervals.It has a lot of applications.In this paper,we generalize the Intermediate Value Theorem and extend this theorem to continuous functions of one variable in any intervals and continuous functions of multiple variables.We also study the applications of the generalized theoremon theoretical and practical problems.

关 键 词：有界闭区间 连续函数 介值定理 多元函数 

分 类 号：G642.4[文化科学—高等教育学]