【正文】 畢 業(yè) 設 計（論文） 題 目 ： 輔助函數(shù)在數(shù)學分析上的應用 學 院： 專業(yè)名稱： 學 號： 學生姓名： 指導教師： 2020 年 5 月 5 日 畢業(yè)設計（論文） 輔助函數(shù)在數(shù)學分析中的應用 摘 要 函數(shù)思想自古以來就是數(shù)學界的經典思想，函數(shù)方法已經成為人們解決數(shù)學問題，尤其是難度較大的數(shù)學問題的重要工具．輔助函數(shù)作為函數(shù)重要的一個分類，在數(shù)學分析中也有很大的應用．本文詳略得當?shù)貜目勺鳛檩o助函數(shù)的函數(shù) ，輔助函數(shù)的構造方法和輔助函數(shù)在數(shù)學分析中的應用這三大塊入手，著重介紹輔助函數(shù)法在數(shù)學分析中的運用，同時也會簡略地描述輔助函數(shù)法的定義、輔助函數(shù)的一些常用構造方法與可作為輔助函數(shù)的函數(shù)，以求開拓對此類問題的解決思路． 關鍵詞 輔助函數(shù)，構造方法，數(shù)學分析中的應用 畢業(yè)設計（論文） Application of auxiliary function in mathematical analysis Abstract Function thought since ancient times is the classical ideas of mathematics, a functional approach has bee to solve mathematical problems, particularly important tool for difficult mathematical problems. A classification of auxiliary functions as functions of the important, also has a lot of applications in mathematical analysis. This detail have local from can as auxiliary function of function, auxiliary function of constructed method and auxiliary function in mathematics analysis in the of application this three chunks start, focuses on introduced auxiliary function law in mathematics analysis in the of using, while also will briefly to description auxiliary function law of defines, and auxiliary function of some mon constructed method and can as auxiliary function of function, to pioneering on this class problem of settlement ideas. Keywords Auxiliary function, construction, application of mathematical analysis 畢業(yè)設計（論文） 目錄 1 引言 ................................................................................................................................ 1 研究意義 .............................................................................................................. 1 輔助函數(shù)法的定義 .............................................................................................. 1 2 可作為輔助函數(shù)的函數(shù) ............................................................................................... 2 單調函數(shù) ............................................................................................................... 2 Lagrange 函數(shù) ....................................................................................................... 2 3 輔助函數(shù)的構造方法 ................................................................................................... 5 幾何法 .................................................................................................................. 5 積分意義法 ................................................................................................ 5 三點定拋物線法 ........................................................................................ 6 原函數(shù)法 .............................................................................................................. 7 微分方程法 .......................................................................................................... 8 常數(shù)分離法 .......................................................................................................... 9