大學(xué)畢業(yè)論文--輔助函數(shù)在數(shù)學(xué)分析上的應(yīng)用

1、20142014年5月5日HUBEI POLYTECHNIC UNIVERSITY畢業(yè)設(shè)計(jì)（論文）題 目：輔助函數(shù)在數(shù)學(xué)分析上的應(yīng)用學(xué) 院：專業(yè)名稱：_學(xué) 號(hào)：學(xué)生姓名：指導(dǎo)教師：畢業(yè)設(shè)計(jì)（論文）輔助函數(shù)在數(shù)學(xué)分析中的應(yīng)用摘要函數(shù)思想自古以來就是數(shù)學(xué)界的經(jīng)典思想，函數(shù)方法已經(jīng)成為人們解決數(shù) 學(xué)問題，尤其是難度較大的數(shù)學(xué)問題的重要工具輔助函數(shù)作為函數(shù)重要的一 個(gè)分類，在數(shù)學(xué)分析中也有很大的應(yīng)用本文詳略得當(dāng)?shù)貜目勺鳛檩o助函數(shù)的 函數(shù)，輔助函數(shù)的構(gòu)造方法和輔助函數(shù)在數(shù)學(xué)分析中的應(yīng)用這三大塊入手，著 重介紹輔助函數(shù)法在數(shù)學(xué)分析中的運(yùn)用，同時(shí)也會(huì)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(gòu)造方法與

2、可作為輔助函數(shù)的函數(shù)，以求開拓對(duì)此類 冋題的解決思路.關(guān)鍵詞輔助函數(shù)，構(gòu)造方法，數(shù)學(xué)分析中的應(yīng)用Application of auxiliary function in mathematical analysisAbstractFunction thought since ancient times is the classical ideas of mathematics, a functional approach has become to solve mathematical problems, particularly importa nt tool for difficult ma

3、thematical 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 analy

4、sis 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 defi nes, and auxiliary fun cti on of some com mon con structed method and can as auxiliary functi

5、on of function, to pioneering on this class problem of settlement ideas.KeywordsAuxiliary function, construction, application of mathematical analysis目錄 TOC o 1-5 h z HYPERLINK l bookmark10 o Current Document 1引言1 HYPERLINK l bookmark12 o Current Document 1.1研究意義1 HYPERLINK l bookmark14 o Current Do

6、cument 1.2輔助函數(shù)法的定義12可作為輔助函數(shù)的函數(shù)2 HYPERLINK l bookmark16 o Current Document 2.1單調(diào)函數(shù)22.2 Lagra nge 函數(shù)2 HYPERLINK l bookmark18 o Current Document 3輔助函數(shù)的構(gòu)造方法5 HYPERLINK l bookmark20 o Current Document 3.1幾何法53.1.1積分意義法53.1.2三點(diǎn)定拋物線法6 HYPERLINK l bookmark22 o Current Document 3.2原函數(shù)法7 HYPERLINK l bookmark2

7、4 o Current Document 3.3微分方程法8 HYPERLINK l bookmark26 o Current Document 3.4常數(shù)分離法9 HYPERLINK l bookmark28 o Current Document 4 輔助函數(shù)法在數(shù)學(xué)分析中的運(yùn)用 11 HYPERLINK l bookmark30 o Current Document 4.1證明中值定理11 HYPERLINK l bookmark32 o Current Document 4.2解決有關(guān)不等式與等式的問題 114.2.1不等式的問題 114.2.2證明等式 12 HYPERLINK l b

8、ookmark34 o Current Document 4.3解方程及探討方程的根 12 HYPERLINK l bookmark36 o Current Document 5結(jié)論14 HYPERLINK l bookmark38 o Current Document 致謝15 HYPERLINK l bookmark40 o Current Document 參考文獻(xiàn)16畢業(yè)設(shè)計(jì)（論文） 參考文獻(xiàn)劉勇淺談構(gòu)造輔助函數(shù)的基本方法M 湖北：湖北廣播電視大學(xué).2009, 4.劉士琴.輔助函數(shù)的應(yīng)用J. SCIENCETECHNOLOGYINFORMATION .2011, (29): 157 1

9、59.華東師范大學(xué)數(shù)學(xué)系編.數(shù)學(xué)分析M.北京：高等教育出版社.2001, 7余紅兵，嚴(yán)鎮(zhèn)軍.構(gòu)造法解題M.合肥：中國科學(xué)技術(shù)大學(xué)出版社.2009, 2 元玖東.高等函數(shù)輔助函數(shù)的構(gòu)造及應(yīng)用的應(yīng)用J.山東：濟(jì)南職業(yè)學(xué)院報(bào)，2009, 5： 3-4 王文珍.微積分學(xué)中輔助函數(shù)的應(yīng)用J.陜西：高等數(shù)學(xué)研究.2005.惠存陽.對(duì)微積分中值定理證明中輔助函數(shù)的探討 J.陜西：延安教育學(xué)院學(xué)報(bào).1997, (2)： 2627.常興邦、李娜.輔助函數(shù)的構(gòu)造方法及其應(yīng)用J.河南：商丘職業(yè)技術(shù)學(xué)院學(xué)報(bào)，2009, 2:67.翟修平.構(gòu)造輔助函數(shù)在命題求證中的作用J.江蘇：泰州職業(yè)技術(shù)學(xué)院學(xué)報(bào)，2004, 8:45 47.盛光進(jìn).試析輔助函數(shù)在解題中的作用J.遼寧：錦州師范學(xué)院學(xué)報(bào).2003, 6.王德利.證題中引進(jìn)輔助函數(shù)的幾種方法J.湖北：江漢大學(xué)學(xué)報(bào).1995, 6.王德利.證題中引進(jìn)輔助