数学_隐函数定理及其应用[精品].doc

摘 要 隐函数定理是数学分析和高等数学中的一个重要定理，它不仅是数学分析和高等代数中许多问题的理论基础，并且它也为许多数学分支，如泛函分析、常微分方程、微分几何等的进一步研究提供了坚实的理论依据. 隐函数定理有着十分广泛的应用，在经济学、优化理论、条件极值等中均有重要作用. 对本课题的研究，可以加深我们对微分学的认识与理解. 本文简略地论述了隐函数的概念、隐函数定理的内容及证明方法、以及隐函数定理在各个方面的应用. 本文从隐函数定理出发，给出了推论隐函数组定理和反函数组定理以及他们的证明过程. 这些推论使隐函数定理的应用更加广泛. 并针对隐函数定理在计算导数和偏导数、几何应用、条件极值、以及优化理论这几个方面的应用做了系统的论述. 关键词：隐函数定理；应用；优化理论 ；证明 Abstract Implicit function theorem of mathematical analysis and higher mathematics is one of the important theorem, it is not only the mathematical analysis and higher algebra in the theoretical foundation of the many, and it also for many branches of mathematics, such as functional analysis, ordinary differential equation, differential several further research how to provide the solid theoretical basis. Implicit function theorem has a very wide range of application, in ec onomics, optimization theory, such as extreme conditions which is an important role. This topic research, can deepen our understanding of the differential calculus and understanding. This paper briefly discusses the concept of implicit function, the content of the implicit function theorem and prove method, and implicit function theorem in all aspects of the application. This paper, from the implicit function theorem are given, and the corollary of implicit function theorem and the group FanHanShu group theorem and proof of their process. These claims that the application of implicit function theorem and more extensive. And in the light of implicit function theorem in the calculation of the derivative and partial derivative, geometric application, conditional extreme, and the several aspects optimization theory of the application of the system is also discussed in the paper. Key words: implicit function theorem; Application; Optimization theory; proof 目 录 摘要 I Abstract II 绪论 1 第1章 隐函数 2 1. 1 隐函数 2 1. 2 隐函数组的概念 2 1. 3 反函数组的概念 3 第2章 隐函数定理 4 2. 1 隐函数定理 4 2. 2 隐函数组定理 6 2. 3 反函数组定理 7 第3章 隐函数定理的应用 9 3. 1 计算导数和偏导数 9 3. 1. 1 隐函数的导数 9 3. 1. 2 隐