摘要
给出多元函数意义,纠正现今众多文献中康托尔的一个错误.从极值(点)的几何意义逐步推导出(n×n)方程组求解等式条件下n元函数极值点的新方法;用外积得出拉格朗日乘数表达式解决了上个世纪80年代钱伟长提出的乘子是否唯一的问题.给出了不定方程(组)确定显函数组命题.本文指出对应思想方法乃处理问题的重要工具.
This paper gives the meanings of multivariable functions and corrects a wrong conclusion of Cantor set theory in numerous documents. A new method for finding the extreme points is derived based on the geometric meanings of extreme points. It is the extreme points for function of n-variables with （nxn） system of equationson the condition of m-equality constraints.This paper also obtains the formula of Lagrange multiplier by using outer product, which solves an open problem （ if Lagrange multiplies is unique or not） proposed by QIAN Weichang in the 1980s.
出处
《高等数学研究》
2016年第4期22-27,共6页
Studies in College Mathematics
关键词
多元函数
集合论
极值点
拉格朗日乘数
对应
function of n-variables
set theory
extreme point
lagrange muhiplier
correspondence
