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关键词： 数学分析   反例   极限   导数   积分  

摘要： 列举反例作为一种重要的方法,在数学分析教学中起着重要的作用.通过归纳总结,就数学分析中3个重要内容——数列极限、函数导数和函数积分列举了一些重要的反例,从而帮助学生理解和掌握一些较抽象的概念和定理.

关键词： 数学分析   教学:独立学院   思维导图   知识结构图  

摘要： 除了高度抽象性和概括性之外,数学分析学习的难点在于知识的连贯性。本文根据独立学院数学专业学生的特点,分析其学习数学分析的现状,总结教师教学过程中所面临的挑战,从实际出发,探讨适合独立学院学生的教学方法。

关键词： 数学分析   中学数学   课程内容   衔接  

摘要： 数学是我国现行学校课程改革体系中一门重要的课程,数学分析和中学数学的课程与教学出现了部分脱节,数学分析与中学数学存在联系和差异。相对中学数学而言,数学分析包含的知识面更广,内容更深,衔接方面存在问题会影响教学效率与质量。因此,从符号差异、内容重复与脱节问题对数学分析与中学数学的内容衔接方面进行了分析,指出数学分析与中学数学在课程衔接方面需要注意的问题,给教师组织安排课程设置提供一定的参考信息和内容方面的支持。

关键词： 数学分析思想   高中数学解题   应用  

摘要： 高中数学教学的过程应当采取数学分析思想。高中数学本身是一门严谨性及逻辑性较强的学科。开展数学教学活动时,为了正确引导学生,同时进一步扩展学生的数学思路,进一步提高学生的数学能力,在数学解题教学时应融入数学分析思想。这样才能有效提高数学教学质量和教学效果。本文主要是关于数学分析思想在高中数学解题中的应用研究,以供相关专业人士参考和借鉴。

关键词： inclusion force balance   inclusion removal rates   mathematical simulations   steel cleanliness  

摘要： Steel cleanliness is an essential assignment during steelmaking practice to improve the steel quality;this means that the inclusions count during the casting operations must be low. Inclusions removal in the tundish is mainly studied by simulation, assuming that "if an inclusion touches the tundish free surface, it is considered removed," predicting high removal rates for all sizes and showing large discrepancies when compared with the experimental results. Searching for a realistic accordance between inclusions removal rates obtained by mathematical modeling and the experimental results, this work has the main purpose to predict the inclusion removal count at the free surface in a more realistic fashion in a tundish using flow-control devices. The results show an over-estimation up to 80% on the reported removal rates for small inclusions, which is attributed to the use of the Random Walk Model (RWM);however, if the RWM is not used, the inclusions behavior and its removal distribution show severe inconsistencies related to the fluid dynamics. Due to this, a new removal criterion used along with the RWM is applied, predicting more realistic removal rates in agreement with the experimental results and theoretical limits.

关键词： Multi-objective programming   Information entropy   Uncertainty analysis   Mathematical optimization   Agricultural water management   Ecological functions  

摘要： An entropy-based multi-objective interval stochastic programming (EMISP) approach based on interval hierarchical projection, interval information entropy, interval analysis and chance-constrained programming was developed for supporting agricultural water management. EMISP improved upon existing methods through measuring and balancing ecological and economic benefits of irrigated croplands under uncertainty. To demonstrate its applicability, the developed method has been applied to an arid Chinese watershed. The results suggested that grain crops would produce higher ecological benefits than economic crops. A series of benefit- and risk-explicit plans for agricultural water use were generated, which indicated that the relaxation of water availability constraints would generate higher comprehensive benefits, but increase the risks of system infeasibility. The results from the EMISP model were also compared to those from four potential alternative models. These comparisons revealed that EMISP could achieve higher water productivity and comprehensive benefits with controllable water-shortage risks. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： Illicit nominal income (Y-L)   Illicit supply of money (M-I)   Legitimate nominal income   Legitimate supply of money (M-L)   Velocity of circulation of illicit money supply (v(L))   Velocity of circulation of legitimate money supply (v(I))   C30   C39   E26   E52   H11  

摘要： Purpose Over one and half years have passed since the demonetization of Indian economy had occurred on November 8, 2016. The drastic step was initiated by the Prime Minister Narendra Modi with an intention to curb the "huge" circulation of illicit or "black" money of Indian economy by means of withdrawal of high value denominations of Rupees 500 and Rupees 1,000 from the supply of broad money (M3). This step helped to demonetize around 86 per cent value of total money supply leading to an unprecedented chaos in the economy and public life. The long delays in issuing fresh currency notes at the banks and ATMs further deteriorated the sudden economic crisis. Design/methodology/approach This research paper is aimed at exploring the proclaimed "efficacy" of demonetization policy as proposed by Reserve Bank of India by means of a mathematical approach and critically examines the effects of demonetization on the illicit money supply of Indian economy on the basis of macroeconomic theory. Findings From the mathematical model and related estimates, it may be easily deduced that the Indian policymakers deliberately hurled the masses in one of the gravest economic crises with a clear-cut intention of creating a political gimmick, when in reality, the proportion of illegitimate money supply was not even 1 per cent of total legitimate supply of money. Originality/value The analyses and findings related to this paper are based on mathematical modeling and logical interpretations. This paper is free of plagiarism as all the necessary sources and references are properly cited.

关键词： 数学问题   伽利略   实验物理学   比萨斜塔实验   物理学家   天文学家   经典力学   数学分析  

摘要： 伽利略(1564~1642)是享誉世界的意大利物理学家、天文学家,他是经典力学和实验物理学的先驱,著名的"比萨斜塔实验"就出自其手.他还是第一个利用望远镜观察天体取得成功的人.耐人寻味的是,这位实验科学家还对数学情有独钟,不仅数学造诣深厚,具有极强的数学分析、推理能力,而且他首创的"实验+数学"的研究方式,更是成为现代科学研究的范式.下面这几则有关伽利略与数学问题的小故事,就足以说明这位科学巨匠对于数学的浓厚兴趣和精深造诣.

关键词： 小学生   数学分析习惯  

摘要： 数学分析是指人们对题目进行深层次思考以及反复的推敲,了解题目中的含义和要求。从而根据题目要求或给予的已知内容解决题目所求内容。数学的答题过程就是审题,思考,分析解答的过程,要想提高小学生的数学分析能力,就需要在数学教学过程中重视对小学生数学分析能力的培养,可以通过提高学生对题目的总体认知,学会捕捉题目中的关键字,发现题目隐藏题意等能力来增强处理问题信息,准确解决问题的能力。还可以通过对知识点的多方位认识来提高数学分析能力。而这些方式都需要教师在教学过程中采取积极有效的方法来实现。