换元思想方法的方法论意义和理解

摘要：在解数学题的过程中，通过剖析思索发现用所知的问题条件难以直接得出结论，或已有的条件之间的关系不明确，无法解决问题，这时候可能需要使用新的变量即“新元”把已有的条件之间的关系明朗化，就是利用所设的“新元”能够把题干中已经给出的分散条件相联系起来，使得提干中隐含的条件露出来，或者是能把题干中条件与结论联系起来。又或者把不常见的形式变成已知的熟悉形式，这样能够简化那些复杂的计算和推证，达到正确解决问题的目的。换元，其实质就是“转化与化归”，它的重点在于如何构造和设元，等量代换是它的主要理论依据，它能够将所研究的问题转移的新元的条件背景中去研究，从而使非标准型问题标准化、复杂问题简单化，从而达到解决问题的目的。92508

毕业论文关键字：数学思想，换元法，解决问题

Abstract: In the process of mathematical problem solving, analytical thinking problems found through the existing conditions is difficult to directly come to the conclusion that or not clear the relationship between the existing situation, can't solve the problem, then generally need to introduce a new variable to clear the relationship between the existing situation, the use of the new variable to be able to relate has given distributed condition, which is revealed under the condition of implicit, or be able to relate condition and conclusion。 Or become known to the familiar form, which can simplify the complicated calculations and inferred, achieve the purpose of correctly solve the problem。 Method of changing variables, its essence is the "reduction", the key lies in constructing and set, theoretical basis is the equivalent substitution, the purpose is to transform the research object, the problem will be moved to a new object to study the background of the knowledge, so that the standard standardization, simplification, problem to achieve the purpose to solve the problem。源F于K优B尔C论V文N网WwW.youeRw.com 原文+QQ752^018766

Keyword：Mathematical thought，method of changing variables，solve the problem

1。引言 4

2。有关换元法的基本知识 4

2。1 换元法的概念 4

2。2 对换元法的理解 4

2。3 换元法的基本形式 4

2。4 换元法在解题中的功能 5

3 常用的换元方法 5

3。1 整体换元思想 5

3。2 倒数换元思想 7

3。3 比值换元思想 8

3。4 三角换元思想 10

4 换元思想方法的方法论意义 11

4。1 换元思想方法是处理数学问题最基本的方法 11

4。2 换元思想方法具有某些数学美的特征 11

4。3 换元思想方法是化归法的一种具体形式 12

5 结论 13

6 参考文献 14

7 感谢 15

1．引言来自优O尔P论R文T网WWw.YoueRw.com 加QQ7520`18766 换元思想方法的方法论意义和理解:http://www.youerw.com/shuxue/lunwen_200192.html