毕业设计论文反例在数学分析学习中的应用.doc

摘 要 本文通过数学分析中的很多定理命题，运用恰当的反例从另一个侧面抓住概念或规则的本质，进而更容易加深对知识的理解.反例思想是数学分析中的重要思想，在概念、性质的理解，问题的研究与论证中都具有不可替代的独特作用.恰当地运用反例，对于正确理解概念、巩固和掌握定理、公式、法则等，培养学生的逻辑思维能力，预防和纠正错误，将起着十分重要的作用.本文针对这个问题，深入细致研究了数学分析中的很多问题的反例.系统的对数学分析中的反例进行总结研究，共分为数列、函数、一元函数导数及其积分、级数、多元函数五个部分，各部分之间并非完全独立.针对多数定理及命题，用逆向思维方法从问题的反面出发，如果有问题，举出反例证实.本文所选的问题和反例比较典型，难度适中，解法精巧，富有启发性.本文对理解数学分析的基本概念，掌握数学分析的基本理论和技巧很有好处. 关键词：数学分析；反例；函数 Abstract There are many theorems and propositions of Mathematical analysis, using appropriate counterexamples from another side can recognize the essence of concept or rules, and it’s easier to deepen the understanding of knowledge. The counterexample of thought is an important thought in Mathematical thought, and it plays an irreplaceable role in the understanding of the concept, nature and the research, reasoning of problems. To understand concepts correctly, consolidate and master theorem, formula and rule, etc, train the logical thinking ability of students and prevent and correct errors, which it’s necessary to use counterexamples felicitously. To the question, this text researches a lot of problems with counterexamples in Mathematical Analysis deeply. The counterexamples are summarized in Mathematical Analysis systematically and there are five sections: sequence of number, function, a circular function derivative and its integral, series, and function of several variables. And every section isn’t independent. We can learn most theorems and propositions with the reverse thinking method. If there’s some problem, you can give the examples to verify from the opposite. The selected problems and counterexamples in this thesis are typical, appropriate difficult, and enlightening. Based on understanding the basic concept of Mathematical Analysis, grasping the basic theory and technique of Mathematical Analysis technique, the thesis is very good. Key words: Mathematical Analysis; Counterexample; Function 目 录 TOC \o 1-3 \h \z HYPERLINK \l _Toc118603129 第一章 绪论 PAGEREF _Toc118603129 \h 1