中學(xué)數(shù)學(xué)中的不等式問題
Inequality Problems in Mathematics in Middle School



目錄
引言 1
第一章 不等式 2
1.1不等式的由來 2
1.2 不等式的定義 2
1.3不等式的性質(zhì) 2
第二章 求解不等式的方法 4
2.1 絕對值不等式的主要解法 4
2.2 含參不等式的解法 5
2.3 分式不等式的解法 7
2.4 根式不等式的解法 7
第三章 證明不等式的方法與技巧 10
3.1 直接構(gòu)造函數(shù) 10
3.2 函數(shù)變形法 11
3.3 反證法 12
3.4 放縮法 13
3.5 基本不等式法 16
3.6 數(shù)形結(jié)合法 17
第四章 高等數(shù)學(xué)在中學(xué)不等式中的簡單應(yīng)用 20
4.1 柯西不等式 20
4.2 定積分在不等式中的運(yùn)用 22
結(jié)論 24
致謝 25
參考文獻(xiàn)： 26


摘要: 本文主要是通過對例題的分析，然后給出解答，最后得出結(jié)論這種模式來進(jìn)行討論的。而題目的選擇則是通過層層篩選，選出最典型的一兩題進(jìn)行分析，盡量做到精簡。
本文分成了四個大塊對不等式問題進(jìn)行研究討論。首先對不等式的背景進(jìn)行介紹，包括不等式的由來、定義以及性質(zhì)；然后是幾種不同類型不等式的解法；其次介紹了不等式的方法與技巧，主要討論了幾種常見的證明方法；最后，本文介紹了一些高等數(shù)學(xué)中的柯西不等式和定積分的相關(guān)知識，因?yàn)榇蟛糠指咧猩院笫且と氪髮W(xué)校園的，而高中數(shù)學(xué)的難度和大學(xué)數(shù)學(xué)的難度可以說是有一個鴻溝，所以這個介紹將對他們以后大學(xué)數(shù)學(xué)的學(xué)習(xí)起到一點(diǎn)幫助作用。

關(guān)鍵詞:中學(xué)數(shù)學(xué) 不等式問題

Inequality Problems in Mathematics in Middle School
Abstract: This article is mainly discussed through the model that analyse the example first, then give answers, finally,come to the conclusion.The selection of examples is through layers of screening and select the most typical one or two examples for analysis in order to simplify the article as far as possible.
This paper is divided into four large pieces to discuss the issues of inequality.Firstly, it introduces the background information of inequality, including inequality origin, definitions and nature.Then it shows some solutions of several different types of inequality.It also gives the methods and techniques of inequality and mainly discusses several common methods of proof. Finally, this article describes some knowledge of Cauchy Inequality and the definite integral in higher mathematics, because the majority of high school students will enter the university in the future , and there is a gap between the difficulty of high school mathematics and university mathematics so that this introduction would be helpful for their learning of university mathematics.

Key words: Mathematics in Middle School Inequality Problems