多元函数的极限解法.doc

郑州航空工业管理学院 毕 业 论 文（设 计） 09 届 数学与应用数学 专业 0911062 班级 题 目 多元函数的极限解法 姓 名 靳亚洲 学号 091106208 指导教师 王建军 职称 二О一三年 月 日  摘 要：科学生产实际中,存在着很多极值问题需要去解决.有些问题可以用初等的方法可以解决,但是有些问题用初等的方法去解决，有时显得麻烦，有时根本无法解决。因而，我们引入了多元函数的极值问题，本文就以下几个方面，来介绍多元函数的极值，二元函数极值的定义及存在条件、二元函数极值的一阶偏导判别法；条件极值的求解方法及应用（如：代入法、拉格朗日乘数法、标准量代换法、不等式法、二次方程判别式符号法、梯度法、数形结合法等）；n元函数极值的定义及存在条件及存在问题、n元函数的累次极值、向量法求解一类多元函数极值。通过对多元函数极值问题在多元函数条件极值在证明不等式、物理学、生产销售等问题上的探讨与应用，可以让我们对以后的极限问题的学习和实际工作中带来诸多方便。 关键词：多元函数；极值；充要条件 ；方向导数；偏导数；矩阵；驻点；极值；条件极值；拉格朗日乘数法；梯度法；应用 Abstract: Scientific actual production, there are a lot of extreme value problems need to solve some of the problems can be solved with elementary, but some elementary method to solve the sometimes cumbersome, and sometimes can not be solved. Thus, we introduce a multi-function extremum problem, this paper on the following aspects, to introduce multi-function extremum, extreme binary function definitions and the presence of the extreme value of the dual function of a first-order partial derivative of discrimination law ; the Extreme Conditions solution and application (such as: substitution method, Lagrange multiplier method, a standard amount of substitution method, the inequality quadratic equation discriminant symbol method, gradient method, Shuxingjiege law, etc.); the definition of the n-ary function extremum and the existing conditions and problems, n $ function Repeated extreme vector method for solving a class of multi-function extremum. Multi-function conditions of extreme value in proving inequality, physics, production and sales of the extreme value of function problems and application, allows us to bring a lot of convenience on the Limits of study and practical work. Keywords: multi-function; extreme; necessary and sufficient condition; directional derivative; partial derivatives; matrix; stagnation; extreme; extremum condition; Lagrange multiplier method; gradient method; application 目 录 1 绪论 1 1.1研究多元函数极值的意义 1 2二元函数