数学分析中一类与存在性有关的错误解法原因剖析  

Analysis of the Causes of a Kind of Incorrect Solutions Related to Existence in Mathematical Analysis

作　　者：江樵芬 徐起 JIANG Qiaofen;XU Qi(College of Mathematics and Informatics,Fujian Normal University,Fuzhou 350117,China)

机构地区：[1]福建师范大学数学与信息学院,福州350117

出　　处：《大学数学》2022年第1期93-100,共8页College Mathematics

基　　金：国家自然科学基金(11971108);福建师范大学2020年校本科教改项目(I202002032)。

摘　　要：从“忽略极限定义中δ对ε的依赖”“忽略介值与中值定理中介值点与中值点对其它因素的依赖”“二元函数中的存在性问题与一致性”等三个方面深入剖析数学分析中一类与存在性有关的错误解法,反思在教学中应注意的地方并给出一些对策与教学建议.From the perspective of“neglecting the dependence ofδonεin the definition of limit”,“neglecting the dependence of existing points in the intermediate value theorem and the mean value theorem on other factors”and“existence and uniformity of binary functions”,we deeply analyze the causes of a kind of incorrect solutions related to existence in mathematical analysis.We also reflect on what we should pay attention to while teaching,and give some countermeasures and suggestions on teaching.

关 键 词：极限定义 中值定理 一致性 

分 类 号：O172.1[理学—数学] O172.2[理学—基础数学]