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关键词： 数学分析   教学改革   改革措施  

摘要： 本文对当前大学数学分析课程的教学现状进行了分析,并对当前大学数学分析课程需要进行教学改革的必要性进行了说明.最后,本文对大学数学分析课程的具体改革措施进行了探讨.

关键词： 高中数学   分析和解决问题能力   培养策略  

摘要： 分析和解决问题的能力是指能阅读、理解对问题进行陈述的材料；能综合应用所学数学知识、思想和方法解决问题，包括解决在相关学科、生产、生活中的数学问题，并能用数学语言正确地加以表述．它是逻辑思维能力、运算能力、空间想象能力等基本数学能力的综合体现。

关键词： Asymptotically stable   Exponential time differencing methods   Fractional reaction-diffusion   Pattern formation   Nonlinear time-dependent PDEs   Stability analysis   Super-diffusion  

摘要： The aim of this paper is to examine pattern formation in the sub- and super-diffusive scenarios and compare it with that of classical or standard diffusive processes in two-component fractional reaction-diffusion systems that modeled a predator-prey dynamics. The focus of the work concentrates on the use of two separate mathematical techniques, we formulate a Fourier spectral discretization method as an efficient alternative technique to solve fractional reaction-diffusion problems in higher-dimensional space, and later advance the resulting systems of ODEs in time with the adaptive exponential time-differencing solver. Obviously, the fractional Fourier approach is able to achieve spectral convergence up to machine precision regardless of the fractional order a, owing to the fact that our approach is able to give full diagonal representation of the fractional operator. The complexity of the dynamics in this system is theoretically discussed and graphically displayed with some examples and numerical simulations in one, two and three dimensions. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Cuckoo bird   Brood parasitism   Incubation time   Stability   Hopf bifurcation  

摘要： Although caring and raising children is the duty of all parents, some animals relieve themselves of this labored work by relying on others to raise their young. After the host has made a nest and laid eggs, the parasite locates the nest and lays a few eggs in the host's nest. Several possible interactions occur between the host and parasite in brood parasitism: the parasite does not destroy the host's eggs and the host does not abandon her nest with eggs. Here, we establish a mathematical framework for studying an ecological model on brood parasitism with stage structure of the parasite, where time delay represents the incubation period of the parasite. For the proposed model, we studied the impact of incubation time delay on the coexistence equilibrium. By using corresponding characteristic equations, the local stability behavior of each of the feasible equilibria of the model and existence of Hopf bifurcations at the coexistence equilibrium are established. Further, the global properties of some equilibria are established using Lyapunov-LaSalle invariance principle. The incubation time delay was found to be crucial for establishing stability behavior. When the incubation time delay increased and crossed some critical values, Hopf bifurcation may occur at the coexistence equilibrium. Further, by using normal form and center manifold theories, formulas were established to determine the stability and direction of the Hopf bifurcation. Numerical simulations were conducted to support the theoretical analysis. Our mathematical model could help lay a foundation for further studies on brood parasitism by the cuckoo bird. (C) 2016 Elsevier Inc. All rights reserved.

关键词： 国家精品课程   数学分析   内容分析法.  

摘要： 通过运用文献分析法和内容分析法,对我国2003-2016年7个数学分析精品课程网站的连通性,互动模块的建设和师资队伍的研究,发现这些数学分析精品课程的连通性较好,但大多数授课录象无法观看,精品课程师资队伍结构不合理,反馈性模块建设不足.建议国家建立完善有效的监控机制、提倡名师主讲、建立完善的评价机制.建议在数学分析精品课程建设中,在内容呈现方式、评价等方面建立创新性机制.

关键词： 高中数学   解题技巧   数学分析思想  

摘要： 高中数学所涵盖的知识点和知识面较广、题目难度较大,是学生高考中的一门难以取得高分的科目。数学分析思想则能够帮助学生从繁杂的知识点中跳脱出来,从思想方法和技巧上,帮助学生灵活使用概念和定理,提高解题的效率和正确率。

关键词： Biodiesel   Ultrasound   Transesterification   Rheology   Micro bubbles   Mathematical modelling  

摘要： Ultrasound assisted transesterification has recently been introduced as an effective technology for biodiesel synthesis. However, the behaviour of micro bubbles under ultrasound is affected by operating conditions or rheological properties of reaction mixtures. This paper aims at investigating the changes of micro bubbles characteristics when operating conditions or rheological behaviour of the reaction medium are altered. The mechanistic simulation of micro bubbles was combined with the CFD simulation of reaction mixture to achieve the aims of this work. Continuity and momentum equations of Keller-Miksis model were employed along with reaction, mass and energy balances to simulate different characteristics of micro bubbles such as temperature, pressure, oscillation velocity, maximum radius of micro bubble, equilibrium state of bubble content, diffusion rates of reaction compounds towards bubbles and reaction within bubbles. It was found that among different combinations of reaction temperature, reactants ratio and intensity of ultrasound irradiation, the last one played the most important role. Radius, internal temperature and pressure of bubbles significantly increased with power amplitude due to stronger expansion and greater energy accumulation. At the same time, increase in reaction temperature and alcohol concentration made the bubbles characteristics rather moderate. It was also found that the growth of bubbles radius was reduced by about 4 times as the reaction progressed and the reaction mixture became more viscous and dense. The maximum internal temperature and pressure decreased by about 178 K and 220 bar due to moderate expansion of bubbles. Oscillation velocity was also restricted in this situation. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： 数学研究   台湾地区   数学分析   非线性分析   不等式理论   研究活动   泛函分析   调和分析  

摘要： 数学分析目前岛内数学分析领域的研究活动,大致可分为四大类,即古典分析、泛函分析、调和分析、非线性分析与凸分析。台湾学者在古典分析领域主要研究方向有：不等式理论、可和性理论、逼近论、特殊函数论和复变数函数论等。