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关键词： 考研数学   极限   计算方法  

摘要： 函数极限问题是考研数学分析中最常见也是最基本的问题.针对近几年某大学数学分析考研真题中所涉及的函数极限问题认真研究之后,并对其计算方法进行了全面的归纳总结,最典型的计算函数极限的方法有等价无穷小量替换、洛必达法则、导数的定义等.

关键词： 激励计划   深度优化   交互激励计划   自主学习  

摘要： 上海市教育委员会自2012年提出在上海部分高校开展教师教学激励计划试点工作,到正式全面覆盖所有市属高校以来,取得了丰硕成果,使得高校在人才培养上迈上了一个新的台阶。然而,目前的大学教学中仍存在很多没有真正得到解决的问题。鉴于此,从教师教学激励计划出发,深入思考、探讨教师教学激励计划的深度优化,使其能够事半功倍地服务于大学教学。在教师教学激励计划的基础上,提出教师—学生交互激励计划,并以《数学分析》课程为例,探讨教师—学生交互激励计划的可行性,以期让学生能够自发地与教师交流,热爱学习,享受学习,从而从根本上激发大学生的学习热情和学习兴趣,最终形成良好的自主学习习惯。

关键词： Temperature gradient   Temperature distribution   Low temperature   Freezing   Mathematical analysis   Solidification   High temperature   Cooling   Temperature  

摘要： Horizontal directional solidification techniques have been broadly utilized for the freezing of biological matter under conditions in which the freezing rate during solidification must be controlled and known. Directional solidification is used for diverse applications such as fundamental research on freezing of biological materials, cryopreservation of biological matter, and tissue engineering. This study is motivated by our intent to use directional solidification as a simplified model for the study of three-dimensional (3D) cryoprinting. In evaluating directional solidification in the context of 3D cryoprinting, we realized that current mathematical models of directional solidification are not adequately representative for this purpose, because they are simplified and one-dimensional (1D). Here, we introduce an experimentally verified and more representative two-dimensional (2D) mathematical model of directional solidification that can aid in the fundamental study of freezing of biological matter, in particular during 3D cryoprinting. The mathematical model was used to develop correlations between the freezing rates that a layer of an aqueous solution experiences during directional solidification and the various design parameters such as thickness of the sample and temperature gradients in the substrate. Results show that the freezing rates can be higher than those suggested by the previously used simplified 1D mathematical models. The results can be used for developing simplified models of 3D cryoprinting. In addition, the results suggest that many experimental studies on directional solidification of aqueous solutions and biological matter may require readjustment of analysis, in view of these findings.

关键词： Coalescence   Integro-partial differential equations   Numerical analysis   Finite volume scheme   Consistency   Convergence  

摘要： This study presents the convergence analysis of the recently developed finite volume preserving scheme (Forestier-Coste and Mancini, 2012) for approximating a coalescence or Smoluchowski equation. The idea of the finite volume scheme is to preserve the total volume in the system by modifying the coalescence kernel using the notion of overlapping bins (cells). The consistency of the finite volume scheme is examined thoroughly in order to prove second-order convergence on uniform, non-uniform smooth and locally uniform grids independently of the aggregation kernel. The theoretical observations of order of convergence is verified using the experimental order of convergence for analytically tractable kernels. (C) 2019 Elsevier B.V. All rights reserved.

关键词： boundedness   criminal behavior   large time behavior   reaction-advection-diffusion system  

摘要： This paper is concerned with a reaction-advection-diffusion system, which is a continuous version of statistical model for criminal activity proposed by Short et al (Math. Models Methods Appl. Sci., 8 (2008), 1249-1267). From very recently results, it is known that the classical solution of the corresponding initial-boundary value problem exists globally. On the other hand, Rodriguez (Phys. D, 260 (2013), 191-200) asserted the uniform-in-time boundedness of classical solution;however, there is a gap in the proof. In this work, we first solve this open problem by establishing some crucial a priori estimates. Then, invoking the uniform boundedness, we present that the classical solution converges exponentially to the steady state. Our results are consistent with the experiment observation and numerical simulation in the existing literatures.

关键词： 目标位姿   空间坐标系   蒙特卡洛   数学分析  

摘要： 对于冗余度机器人位置级不同运动学反解算法,需要检测算法的有效性、速度和收敛情况。在机器人的工作空间中,人为设置目标位姿的方法缺少全面性论证,通过数学方法论证算法性能,需要较长的研究时间,并且缺少对算法运行速度和收敛性的直观感受。一种简单有效的方式是随机生成多目标位姿。本文详细论述随机生成空间坐标系的数学分析,并编写相关程序实现此功能。

关键词： 数学分析   一笑了之   深层次思考   思维陷阱   数学系   办公室  

摘要： 作为一名纯种数学系的、数学分析屡得满分的办公室工作者,我曾经被这样一道看似简单的题目考倒过:请一次挪动其中一个数字,使101-102=1这个等式成立。当时我百思不得其解,后来在通过百度知晓答案后,也并没有深层次思考,而把此题当成个思维陷阱,一笑了之。

关键词： 数学分析   教学   解题   构造  

摘要： 数学分析选讲教学的重心在于如何让学生“学解”,而不仅是教师在“解”;培养学生如何“数学地思维”。为此,教学中,要引导学生学会“构造”、一题多解、多题一解、深挖核心概念和定理、解题回顾等,学习数学解题主要是有意义的发现学习。

关键词： 数列极限   四则运算法则   数学分析   高等数学教材   理解和运用   归纳总结  

摘要： 数列极限的四则运算法则作为数列极限的基本性质,在求解数列极限值的过程中起着重要的作用。本文归纳总结出在使用这一性质过程经常出现的两个误解,并通过举例加以说明,从而使得学生能正确理解和运用数列极限的四则运算性质,避免出错。在数学分析和高等数学教材中,数列极限是一个重点,也是一个难点。

关键词： 慕课   数学分析   教学  

摘要： 慕课作为基于互联网制作、传播和发展的大规模下在线开放课程,在教学实践中得到了较为广泛的应用。本文分析了慕课的特点,在此基础上从教师和学生两个视角探讨了慕课在数学分析课程教学的准备、课程实施以及评价等环节的具体应用,并就如何提高慕课的应用水平提出了一些建议。