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调和级数是分析理论中的一个重要发散级数。因其简单的表达形式很容易被学生认为是收敛的。研究了调和级数的一个应用,从而说明了调和级数是发散的。并且给出了一个调和级数在物理学中的例子。更进一步的,本文给出了调和级数的数学证明和一个应用。 相似文献
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乐春红 《楚雄师范学院学报》2009,24(12):34-37
本文在教材中已有的调和级数发散的证明基础上,参照相关的文献,以及在做题中得出的一系列结论,并应用文献中的结论,采用构造方法,给出了几种新的证明方法. 相似文献
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调和级数发散,前n项之和与lnn相当,这是周知的事实,其证明方法甚多,以下给出一个有代表性的证明: 对任意正整数n,总有正整数k,使2~k相似文献
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本文给出了一道极限题的多种证明方法,说明了一题多解的解题方法对于提高学生的学习兴趣,培养学生的综合能力及发散性思维的重要性. 相似文献
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关于P级数∞n=1Σn1p的敛散性的证明,本文则给出一个简单的证法.同时本文还给出调和级数发散的一个更为简洁的证法. 相似文献
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级数是表示函数、进行数值计算的一个有力工具。调和级数作为级数的一个基本成员,结构简单。调和级数的发散及其应用给出了调和级数发散性的4种证明;并分别在比较审敛法和极限比较判别法中,举例说明调和级数在判断无穷级数的敛散性时的标尺作用。 相似文献
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在高等数学范畴中,灵活运用函数的单调性、极值、最值、凸性函数、以及中值定理与泰勒公式、赫尔德不等式、施瓦兹不等式等数学知识,对不等式问题进行分析、构造与转化,是解决不等式的证明问题的常用方法。 相似文献
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翁伟东 《常熟理工学院学报》2003,17(1):33-37
长期以来,民事诉讼中以“客观真实”为证明要求具有明显局限性,确立以“法律真实”为证明要求因其现实意义、可操作价值而更具合理性。追求客观真实作为一种司法理想应是证明目标而非证明要求。而法律真实是证据能够证明的案件事实,是具有高度盖然性的相对真实,人民法院应当据此依法作出裁判。 相似文献
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Usha Kotelawala 《International Journal of Science and Mathematics Education》2016,14(6):1113-1131
This report examines teachers’ self-espoused attitudes and beliefs on proving in the secondary mathematics classroom. Conclusions were based on a questionnaire of 78 US mathematics teachers who had completed at least 2 years of teaching mathematics at the secondary level. While these teachers placed importance on proving as a general mathematical skill, when they discuss their own classrooms, procedural skill consistently surpasses proof-related activities in importance for a majority of high school teachers. Furthermore, teachers labeling their own past experiences in proving as causing anxiety are predictably more likely to put less value on proving. Interestingly, the quantity of past college mathematics courses is a reverse predictor indicating that further study should consider how students perceptions of proving change as they pass through a mathematics major. 相似文献
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章朝庆 《泰州职业技术学院学报》2010,10(3):60-61
积分上限函数及其性质是微积分的基本定理,文章通过构造积分上限函数并结合微分中值定理来证明积分等式、积分不等式,并推出一个新的积分不等式。 相似文献
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Understanding and describing mathematical knowledge for teaching: knowledge about proof for engaging students in the activity of proving 总被引：1，自引：0，他引：1
This article is situated in the research domain that investigates what mathematical knowledge is useful for, and usable in,
mathematics teaching. Specifically, the article contributes to the issue of understanding and describing what knowledge about
proof is likely to be important for teachers to have as they engage students in the activity of proving. We explain that existing
research informs the knowledge about the logico-linguistic aspects of proof that teachers might need, and we argue that this knowledge should be complemented by what we call knowledge of situations for proving. This form of knowledge is essential as teachers mobilize proving opportunities for their students in mathematics classrooms.
We identify two sub-components of the knowledge of situations for proving: knowledge of different kinds of proving tasks and knowledge of the relationship between proving tasks and proving activity. In order to promote understanding of the former type of knowledge, we develop and illustrate a classification of proving
tasks based on two mathematical criteria: (1) the number of cases involved in a task (a single case, multiple but finitely
many cases, or infinitely many cases), and (2) the purpose of the task (to verify or to refute statements). In order to promote
understanding of the latter type of knowledge, we develop a framework for the relationship between different proving tasks
and anticipated proving activity when these tasks are implemented in classrooms, and we exemplify the components of the framework
using data from third grade. We also discuss possible directions for future research into teachers’ knowledge about proof.
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| Andreas J. StylianidesEmail: |
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陈勇勤 《南阳师范学院学报》2007,6(11):32-43
转形问题长期陷入数学求证困境,所得到的各种结果与中外研究者所投入的时间和精力不能成正比。本文列举的中国人的三种解法,各有其特点。既要识别真伪性,也要识别合理性与不合理性。三种解法都以"西方构思"为本源,做出一点点创新(新的未必就不是伪的或不合理的),但都没有突破"西方构思"的基本框架。西方学者刻意追求数学证明,往往又止步在证伪"两个等于"。数学求证有一定的局限性。突破其局限性,不是数学技巧问题,而是数学思维问题。但是,改变数学思维终归替代不了从数学求证转换到非数学求证。 相似文献
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用常微分方程证明了五个函数的幂级数展开式;给出了带有初始条件的一阶线性常微分方程的求解公式,并应用它研究了一阶线性常微分方程解的一个性质;给出了一元函数取极值的新的充分条件。 相似文献
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傅秋桃 《郧阳师范高等专科学校学报》2006,26(3):9-10
泰勒公式是高等数学中的一个重要公式.在此介绍泰勒中值定理在四方面的应用：证明不等式;证明积分等式;求函数的极限;求函数的麦克劳林展开式. 相似文献