初等数学解题技巧研究

摘要：初等数学是学生学习高等数学的基础，也是培养学生学习数学兴趣的开始，因此学好初等数学是非常关键的，学好初等数学必须掌握解题，也就是对所学知识的灵活运用，结合大学的学习实践和中学教学改革实际，引用资料和数据从主观上研究“初等数学解题技巧”，首先介绍了初等数学在中国的研究历史,重点以初等数学中极其重要的解题技巧：换元、配方、待定系数、构造等分别论述，以提高观察力和代数变形能力，扩展学生的思维空间。
关键词：换元；因式分解；配方；构造
 

Research on Elementary Mathematics Problem Solving Skills
Abstract: Elementary Mathematics students studying higher mathematics, is fundamental to train students interested in learning mathematics, learn Elementary Mathematics is therefore crucial to study elementary mathematical must master problem-solving, also known as the flexible use of knowledge, combined and practice of the University, and secondary teaching reform reality, cited information and data from a subjective study of "elementary mathematical problem solving skills," first introduced elementary mathematical study of history in China, the primary focus is extremely important in mathematics problem solving skills: - yuan, formulas, coefficients, the structure, which describes respectively, to improve observation and algebra deformation capacity to expand the space of thinking students.
Key words: For yuan; Factorization; Formula; Tectonic
 

目    录
1 配方法................................................................2
2 因式分解中的解题技巧..................................................3
2.1 增补项法..........................................................3
2.2 裂项法............................................................3
2.3 待定系数法........................................................3
2.4 特殊值法..........................................................4
2.5 体换元法..........................................................4
2.6 构造方程法........................................................5
2.7 巧用除法..........................................................5
2.8 利用轮换对称关系..................................................6
2.9 多元变换..........................................................6
2.10 试除法...........................................................6
3换元法...............................................................7
4 判别式法....... .. ......... .. .......................................8
5 待定系数法..... . .. ... ...............................................8
6 构造法............. .... .. ...........................................9
7 反证法............ . .. ... ...........................................10
8 面积法..... . .. .. ...................................................10
9 几何变换法中的解题技巧...............................................11
10客观性题的解题技巧...................................................12
   10.1直接推演法................................. ....................13
   10.2 验证法................................. ........................13
   10.3 特殊元素法................................. ....................13
   10.4 排除、筛选法................................. ...................13
   10.5图解法................................. ........................13
   10.6 分析法................................. ........................13
参考文献................................. ..............................15
致谢...................................................................16