数学论文浅析分类讨论思想在数学中的意义及应用.doc

浅析分类讨论思想在数学中的意义及应用 目 录 中文摘要··························································2 外文摘要··························································3 1．分类讨论思想方法的含义 1.1分类讨论思想方法的含义········································4 2．在数学教学中渗透分类讨论思想方法的意义和原则 2.1 什么是数学思想方法和数学思想方法教学的原则··················5 2.2 在数学教学中渗透分类讨论思想方法的意义·······················6 3．数学教学中渗透分类讨论思想方法的实践 3.1 怎样在数学教学中渗透分类讨论思想法····························7 3.2 根据问题中有可能出现的各种情况进行分类讨论····················9 3.3 根据研究对象的不同类型进行分类讨论···························10 3.4 根据曲线类型进行分类讨论·····································11 4. 分类讨论思想在高中数学中的应用 4.1 分类讨论思想在集合中的应用···································12 4.2分类讨论思想在函数中的应用···································12 4.3分类讨论思想在不等式中的应用·································14 4.4分类讨论思想在排列组合中的应用·······························16 4.5 分类讨论思想在数列中的应用···································16 4.6 分类讨论思想在圆锥曲线中的应用·······························17 4.7分类讨论思想在立体几何中的应用·······························18 4.8 分类讨论思想在实际问题中的应用·······························19 结束语····························································20 参考文献··························································21 致谢······························································22 摘要: 分类讨论思想是人们常用的重要思想方法，是重要的数学思想，也是一种逻辑方法。在解数学问题时，通过正确应用分类讨论，可以使复杂的问题得到清晰，完整，严密的解答。本文首先介绍了分类讨论思想，分类讨论的要求与原则，重点讲述了分类讨论思想在高中数学中的具体应用，最后强调了根据问题的特殊性和简单性，避免分类讨论，简化分类讨论过程，从而提高分类讨论的效果。 关键词：分类讨论思想 正确分类 应用 简化分类 Abstract Classified discussion thought is commonly used in an important way of thinking, is an important mathematics thought, but also a logical method.In solving mathematical problems, the correct application of classified discussion, can make the complex problem to be clear, complete, exact solution.This paper first introduces the classified discussion thought, discuss the requirements and principles, focus on classified discussion thought in high school mathematics in the specific application, finally emphasizes the particularity of this problem and simplicity