逆向思维在数学分析中的作用.docVIP

摘 要 数学分析是数学殿堂的基石性学科,其内容的广泛性与深刻性包含着形式多样的数学思想与方法,而逆向思维在解决数学分析问题时别开生面.因此,本文就逆向思维在数学分析中作用进行初探. 本论文中,首先阐述逆向思维的内涵及其特征;其次将以数学分析为载体,选取逆向思维作为研究切入点,主要以举例子的形式叙述了逆向思维在数学分析中的具体作用.无论其深化定义、定理的理解,高效的强化解题,批判性命题验证,还是创新性数学品质,无不渗透出笔者最后总结性论述,即逆向思维在数学分析中具有举足轻重的地位. 二十一世纪的信息时代日新月异.数学思维无处不在,无时不有,而逆向思维就是在对数学文化素养的思想研究的基础上,提高数学新意,感受理性美誉,体会数学文化品位,这已成为国内外数学发展的重要趋势. 关键词:逆向思维,作用,数学分析,重要性 The function of reverse thought in mathematical analysis Abstract:Mathematical analysis is the cornerstone of the temple mathematical discipline,breadth and depth of its content contains a variety of mathematical ideas and methods,and the spectacular reverse thinking in solving mathematical analysis of the problem.Therefore,this paper analyzes the role of reverse thought in mathematics carried study. In this thesis,first expounded the connotation and characteristics of reverse thought ,mathematical analysis will be followed by the carrier,select reverse thinking as a research starting point,mainly in the examples given in the form of reverse thought described in mathematical analysis of the specific role. Whether its deepening definitions,theorems understanding and efficient strengthen problem-solving,critical proposition verification,or innovative mathematical quality permeates the author concludes discourse, reverse thought plays a decisive role in the mathematical analysis. Information era of the 21st century rapidly.Mathematical thinking is everywhere and at all times there , but the reverse thought is based on the study of mathematics literacy ideas on improving mathematical ideas, feelings rational reputation,experience culture grade math,which has become an important trend in the development of mathematics at home and abroad.Keywords: reverse thought, function, mathematical analysis,important. 目 录 一、引言 1 二、逆向思维内涵及特征 1 （一）逆向思维的内涵 1 （二）逆向思维的特征 1 三、逆向思维在数学分析中的重要性 2 四、逆向思维在数学分析中四种作用 3 （一）深化定义、定理理解 3 （二）高效强化解题 6 （三）批判性命题验证 11 （四）创新性数学品质 15 五、结束语 15 六、参考文献 17 一、引言 司马光“砸缸救小孩”是一个古老而又优美的传说,