泰勒公式及其在解题目中的应用论文.docVIP

毕 业 设 计（论 文） 题目：泰勒公式及其在解题中的应用 Title: Taylor formula and its application in solving problems 学 院：理学院 专 业：信息与计算科学 姓 名：罗书云 学 号指导教师：蔡奇嵘 二零一二年六月 摘 要 泰勒公式是数学分析中的重要组成部分，它的理论方法已成为研究函数极限和估计误差等方面的不可或缺的工具，它集中体现了微积分“逼近法”的精髓，在近似计算方面有着得天独厚的优势，利用它可以将复杂问题简单化，可以将非线性问题化为线性问题，并且能满足相当高的精确度要求。它是微积分中值定理的推广，亦是应用高阶导数研究函数性态的重要工具。泰勒公式在微积分的各个领域都有着重要的应用，而且泰勒公式“化繁为简”的功能在数学领域的研究方面也起到了很大的作用。文章除了介绍了带佩亚诺余项拉格朗日余项泰勒公式亚诺余项拉格朗日余项ABSTRACT Taylors formula is an important part of mathematical analysis, the theory has become an indispensable tool of the research function limits and estimation error, which embodies the essence of calculus approximation method, It have an unique advantage in the approximate calculation, it also can make complex issues into simplistic, non-linear problem into a linear problem, and can meet the very high accuracy requirements. It is the promotion of the mean value theorem in calculus, is also an important tool for the application of higher order derivatives of the functional state. Taylor formula in the calculus of the various fields have important applications, and the Taylor formula for complex simple function in the mathematical field of research has played a significant role. This article in addition introdution Peano remainder and Lagrange remainder term of Taylor formula commonly used in approximate calculation, the limit inequality proof to determine the function extremum for solving prove, in particular, A detailed introduction of the Taylor formula in the application of the function bump and the inflection point judgment, the judgment of convergence and divergence of series and generalized integral, determinant calculation, and the article discusses a new method to prove that the Taylor formula, further Taylor formula to the more general form. Keywords: Taylor formula; Peano more than; Lagrange remainder; application 目录1. 绪论 1 1.1 综述 1 1.2 泰勒公式的研究背景 2 1.3 泰勒公式的研究意义 2 1.4 泰勒公式的研究目的 2 1.5 本论文所做的工作 3 1