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关键词： 数学分析   细节   教学  

摘要： “数学分析”是数学与应用数学专业学生必修的一门基础课程。但是要使“数学分析”达到理想的教学效果,细节教学尤为重要。文章利用几个例题,分析了在“数学分析”课堂教学中如何注重细节教学,从而使学生更容易理解相应的内容。

关键词： 模块化多电平换流器(MMC)   子模块电容参数   电压波动率   静止无功补偿  

摘要： 远海风电场经MMC-HVDC联网具有一定的技术优势,子模块是模块化多电平换流器(MMC)的重要组成部分,其参数关系到换流器的安全稳定运行。文中在MMC的稳态数学模型基础上,推导了子模块电容能量波动的关系式,以数学分析的方法证明了换流器工作在静止无功补偿方式时模块电压波动最大,设计了全工况下满足电压波动率要求的子模块电容取值,并指出了考虑风电功率波动的子模块电容取值。仿真以南汇柔性直流输电示范工程为背景,验证了发生直流电压极值时换流器的运行方式,以及所设计的电容参数对换流器工况的适应性。

关键词： 基本指数函数   数学分析   本质探究  

摘要： 目前,国内在进行指数函数的教学时,考虑到中学生接受能力的有限性以及知识准备的不足,所以教材中都是采用描述性方法来定义的,定义并没有直接深入其本质。在大学数学中,可以运用数学分析的相关知识,利用指数函数的本质属性来定义它。

关键词： 数学分析   课程思政   科学精神   隐性教育  

摘要： 为了贯彻落实全国高校思想政治工作会议精神,特别是习近平总书记的重要讲话,推动“思政课程”向“课程思政”转变,《数学分析》课程思政改革迫在眉睫。本文首先论述了《数学分析》课程思政的重要性,继而详尽阐述了在教学内容和环节上关于课程思政的几点改革措施,为《数学分析》课程思政改革提供一定的参考价值。

关键词： 华东师大版   数学分析   实指数幂运算性质   证明错误  

摘要： 指出了华东师大版《数学分析》教材中对实指数幂的运算性质的证明过程中的逻辑错误,引入新的技巧来纠正其证明并用该技巧来给出实指数幂运算性质的完整证明(包括教材中“证明留给读者”的部分).

关键词： 微积分   微分几何   数学物理   物理背景   数学分析   理论物理学   物理题   微分方程  

摘要： 常言道:“数学物理不分家”.在物理研究中离不开数学知识,数学研究中离不开物理背景,两者相互依存,相互促进.就像伟大的物理学家、数学家牛顿,在研究物理问题时,创建了很多数学理论,如微积分、广义二项式定理等等,尤其是微积分,促进了数学分析这一分支的产生,并进一步发展为微分几何、微分方程等等,而这些数学理论反过来促进了理论物理学的发展.

关键词： 南水北调中线干渠   藻类繁殖   大气沉降   孢子沉降   累积浓度  

摘要： 针对南水北调中线干渠存在的藻类增殖风险问题,基于氮磷等营养物质及藻类孢子的大气沉降为汇入源的前提假设,采用沃伦韦德尔模型以及河南、山东、京津冀地区氮沉降平均值及全国磷沉降平均值,对中线干渠全线的营养物质累积趋势进行了估算。结果表明,渠水到达监测点三里屯后,渠水中的营养物质累积浓度会超过富营养化阈值;综合考虑大气中藻类孢子沉降的影响,结合藻类增殖的Monod模型,对文献报道的中线藻类数量空间分布数值进行了拟合,估算出中线干渠藻类生长速率在0.21~0.46个/d范围内波动,取得了相对中值误差为23.71%的估测结果;并在此基础上,提出了可提高预测结果精确度的监测方案。

关键词： Population balance equations (PBE)   Cubic spline   Least squares   Janecke phase diagrams   Glauber salt   Lagrange polynomial  

摘要： For the production of sodium sulfate, a brine is crystallized and crystals of glauber salt are generated by this process. The phase data related to the most common sodium sulfate minerals are as follows: mirabilite (Na2SO4 center dot 10H(2)O), tenardite (Na2SO4), glauberite (Na2SO4 center dot CaSO4), astrakanite (Na2SO4 center dot MgSO4 center dot 4H(2)O). The units commonly used to express the phases are moles of salt per 1000 moles of water. These latter units simplify the construction of the commonly employed four-sided Janecke phase diagrams. The cooling temperature or the speed with which the solution is cooled has an effect on the size and purity, as well as the amount of crystals produced. We seek to establish, through the population balance equations (PBE), which process variables can be modified to obtain a specific crystal size, as well as to validate the mathematical model that best predicts the amount of crystals precipitated as a function of temperature. The adjustment by least squares, cubic splines, pitzer equations and Lagrange interpolation is tested. The experimental results agree with the characteristics of the proposed models.

关键词： Blood-feeding behaviour   Infinitesimal generator   Asymptotic behaviour  

摘要： This paper presents an age structured problem modelling mosquito blood-feeding plasticity in a natural environment. We first investigate the analytical asymptotic solution through studying the spectrum of an operator A which is the infinitesimal generator of a C-0-semigroup. Indeed, the study of the spectrum of A per se is interesting. Additionally, we get the existence and nonexistence of nonnegative steady solutions under some conditions. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： economic order quantity (EOQ)   inventory modeling and optimization   mathematical analytic tools and techniques   mathematical solution procedure   permissible delays in payments   supply chain system   trade credit financing  

摘要： Several recent studies in supply chain system and related areas explored various economic order quantity (EOQ) models for noninstantaneous deteriorating items with imperfect quality and trade credit financing. In particular, in the year 2007, Teng et al investigated an EOQ model in which the supplier offers the retailer the permissible delay period M and the retailer, in turn, provides the trade credit period N (with N <= M) to his/her customers. The main purpose of this article is twofold: (a) It modifies the annual total relevant cost TVC(T) in the study of Teng et al and presents the correct derivations of TVC(T) by applying mathematical analytic tools and techniques. (b) It exposes some logical and mathematical problems in the proof of Theorem 1 in Teng et al. It also corrects and overcomes all of the errors and shortcomings by systematically presenting the complete and mathematical solution procedures in order to locate all optimal solutions for the model in Teng et al.