对多元函数最值问题的思考与教学探讨  

Discussion in Teaching on Minimum and Maximum Values of Functions of Several Variables

作　　者：刘海东[1] 闵啸[1] LIU Hai-dong;MIN Xiao(College of Mathematics,Physics and Information Engineering,Jiaxing University,Jiaxing Zhejiang 314001,China)

机构地区：[1]嘉兴学院数理与信息工程学院,浙江嘉兴314001

出　　处：《西南师范大学学报（自然科学版）》2019年第4期157-160,共4页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11701220)

摘　　要：多元函数的最值问题是高等数学课程的教学难点之一,众多教材重点讲解了如何计算多元函数的最值,而没有深入探究计算函数最值的前提:函数最值的存在性.深入分析了经典教材中的几个实例,证明了这些问题的最小值(或最大值)是存在的,从而打消学生在学习过程中的疑虑,让学生更深刻地理解多元函数最值的存在性.The minimum and maximum value of functions of several variables is one of difficulties in teaching advanced mathematics. In many math books, attentions are only paid to the calculation of minimum and maximum values of functions, while the premise been ignored, that is, existence of minimum and maximum values. In this paper some examples in classic books have been analyzed and it proves that these problems indeed have a minimum(or maximum) value. Then students’ doubts about this part dissipate and they can understand the existence of minimum and maximum values deeply.

关 键 词：多元函数 最值 存在性 

分 类 号：G642[文化科学—高等教育学]