高师理科学刊
高師理科學刊
고사이과학간
Journal of Science of Teachers' College and University
2015年
9期
75-78
,共4页
罗尔定理%辅助函数%构造方法
囉爾定理%輔助函數%構造方法
라이정리%보조함수%구조방법
Rolle′s theorem%auxiliary function%construction method
应用罗尔定理证明问题时常通过构造一个与问题相关的辅助函数达到解决问题的目的，这既是证明的需要，也是证明的关键。构造辅助函数没有固定的模式与方法，具有较强的技巧性，是高等数学学习的一个重点内容，也是一个难点问题。给出凑原函数法、乘积因子法、不定积分法、微分方程法、常数k值法等5种常用的罗尔定理应用中构造辅助函数的方法，使辅助函数的构造有章可循，为教学提供参考。
應用囉爾定理證明問題時常通過構造一箇與問題相關的輔助函數達到解決問題的目的，這既是證明的需要，也是證明的關鍵。構造輔助函數沒有固定的模式與方法，具有較彊的技巧性，是高等數學學習的一箇重點內容，也是一箇難點問題。給齣湊原函數法、乘積因子法、不定積分法、微分方程法、常數k值法等5種常用的囉爾定理應用中構造輔助函數的方法，使輔助函數的構造有章可循，為教學提供參攷。
응용라이정리증명문제시상통과구조일개여문제상관적보조함수체도해결문제적목적，저기시증명적수요，야시증명적관건。구조보조함수몰유고정적모식여방법，구유교강적기교성，시고등수학학습적일개중점내용，야시일개난점문제。급출주원함수법、승적인자법、불정적분법、미분방정법、상수k치법등5충상용적라이정리응용중구조보조함수적방법，사보조함수적구조유장가순，위교학제공삼고。
When applying Rolle′s theorem to prove mathematical problems, constructing a problem-related auxiliary function is one of the most common ways,which is not only necessary but critical for the mathematical proof.However,the construction of auxiliary functions usually doesn′t have fixed patterns and methods but needs skillful techniques.It is a key content and difficult point during the process of learning and teaching advanced mathematics.Discussed five common used methods for constructing the auxiliary function when applying Rolle′s theorem,including primitive function method,multiplication factor method,indefinite integration method, differential equation method and constantk-value method.With the help of in-depth understanding of those methods,proposed some guiding principles for the construction of auxiliary functions when using Rolle′s theorem, which provide insights for teaching and learning advanced mathematics in practice.
