教学课程资源库 更多>>

关键词： 数学分析   测试  

摘要： 高校扩大招生后,数学专业基础课的教学大纲是否要作修改已经是业内人士所关注的课题。华东师大与杭州师范学院等高校承担了教育部高教司《世行贷款21世纪初高等理工科教育教学改革》项目课题的研究。为此对在校生进行了一系列数学分析课程的测试。本文对其中一次测试结果作了详细分析,从中可以了解到当前数学专业学生的学习现状,对教师的教学工作有一定的借鉴作用。

关键词： hemodialysis   Kt/V   mathematical analysis   urea rebound  

摘要： Quantifying hemodialysis (HD) treatment requires knowledge of the equilibrated concentrations of the post-HD small molecule rebounds. However, measurement of the equilibrated concentrations is only possible after resting in bed after HD for at least 30 min, and this is often impractical. Therefore, we have analyzed mathematically the time course of post-HD urea rebound, and from this, have derived a new formula for predicting its equilibrated concentration. The blood urea nitrogen (BUN) was measured at 10 time points (immediately following HD, and 0.5, 2.5, 5, 7.5, 10, 15, 20, 25, and 30 min post-HD) in 12 anuric HD patients. The absolute change in the urea rebound (DeqBUN) was approximated (DestBUN) using the equation: DestBUN = b-[1-exp x (-c x time (min))] + a x time (min). After the good correlation between DeqBUN and DestBUN, we compared the value of DeqBUN measured at 30 min (DeqBUN(30)(30)(30)(30)() with that calculated (DestBUN)() using only four sample points (immediately following HD, and 2.5, 5 and 10 min post-HD). Based on this result, we tried to predict post-HD BUN at 30 min (estBUN)()- This study was undertaken to determine whether estBUN) (may be representative of the equilibrated BUN (eqBUN)(), and to compare with Kt/V using estBUN)(30)(30) (and eqBUN)(. There was a significant correlation between DeqBUN and DestBUN (0.97 < r < 0.99, P < 0.001). Thus, there was a significant positive linear correlation between eqBUN)(30)(30) (and estBUN)(30) ((eqBUN)(: 25.7 2.25 mg/dL, estBUN)(: 26.3 2.31 mg/dL;r2 = 0.99, P < 0.001). A Kt/V measurement was obtained with single pool model using BUN just after HD (Kt/V)(), eqBUN)(30)(30)(dp)(30) ((Kt/V)(), and estBUN)(eq)(30) ((Kt/V)(), and with double pool model using Kt/V)(est)(sp) ((Kt/V)() and was compared with them. Though Kt/V)(dp)(sp) (was significantly higher than Kt/V)(eq) ((1.26 0.08 vs. 1.09 0.07, P < 0.001), there were no differences among Kt/V)(, Kt/V)(eq)(est) (and Kt/V)(dp) ((Kt/V)(: 1.06 0.07, Kt/V)(:

关键词： Mayer waves   cardiovascular control   stability  

摘要： The goal of this paper is to explore the low-frequency oscillations of arterial pressure in humans, also called Mayer waves. We carefully describe the cardiovascular control system in order to analyse how its different components may be involved in the occurrence of sustained oscillations. We carry out an analysis of stability leading to the definition of a stability index, which we use to study the influence of each control parameter on the stability of the cardiovascular system. We show that all major components of the control system are probably implicated in the appearance of Mayer waves, substantiating recent clinical results in human as well as experimental findings in rats.

关键词： predator-prey   Beddington-DeAngelis functional response Poincare-Bendixson theorem   Dulac's criterion  

摘要： The dynamics of a predator-prey model with a Beddington-DeAngelis functional response and linear intrinsic growth rate of the prey population is Fully analyzed. Conditions on local and global stability of the interior equilibrium are established. The equilibria type are determined. All possible global asymptotic behaviors of the system are considered, including the determination of the extinction conditions and existence of periodic orbits. It is shown that Mutual interference between predators can alone stabilize predator-prey interactions even when only a linear intrinsic growth rate of the prey population is considered in the mathematical model. Additional biological implications and a set of numerical simulations supporting the analysis are also presented. (C) 2004 Elsevier Inc. All rights reserved.

关键词： 微分中值定理   拉格朗日中值定理   柯西中值定理   高维空间   一元函数   数学分析   罗尔定理   统一形式   导数  

摘要： 微分中值定理是导数应用的基础，一般数学分析教材中给出了一元函数的3大微分中值定理，即罗尔定理、拉格朗日中值定理和柯西中值定理。本文进一步推广高维空间中的微分中值定理，给出3大微分定理在高维空间中的统一形式。下面是本文要用的几个符号。

关键词： 数学软件   Mathematica4.0   数学实验  

摘要： 探讨了利用数学软件Mathematica4.0进行数学分析教学的一个新模式,尝试了以实验、探索、发现为特征的启发式教学法。实验表明,在数学教学中引入数学实验手段,利用数学软件进行多媒体教学,对提高课堂教学质量有一定的效果。

关键词： 数学分析   数学教学   创新能力   教学情境   多媒体教学  

摘要： 一、数学分析课程教学与培养创新能力的重要性 数学分析是数学专业最重要的基础课.课程的目的是通过三到四个学期学习和系统的数学训练,使学生逐步提高数学修养,特别是分析的修养,积累从事进一步学习所需要的数学知识,掌握数学的基本思想方法,最终使学生的数学思维能力和创新能力得到根本的提高.我们在"数学分析"课程教学中采用了分层次教学方法:在每届学生中选择30-40名程度较好的学生组成理科班,其教学内容和教学要求都比普通班要求高.对这个班实行动态管理,对不适合在这个科班学习的学生进行调整,并允许普通班中学习优秀、喜欢数学的学生进入这个班学习,形成竞争机制.多年的实践证明,两种班平行共存的机制有利于提高学生的学习积极性,为优秀学生的成长提供一个好的平台,培养出具有较好的数学修养、基础扎实的人才.高校在制定专业教学计划时,要有一个全盘考虑,在课程教学实施前,教师要做好课程内容的分工与协调工作,教师在课程教学中要严格执行,使不必要的重复现象得到事前控制.在数学分析中,能力比起单单具有一些知识更重要得多.因此,教师应当在传授学生一定数量知识的同时,还应教会学生一定的分析、判断、解题的能力.在数学分析学习实践中,教师要运用已经习得与掌握的数学分析知识(数学分析方法、技能、技巧等),教学生掌握更深一步求知获能的各种实际才能、智慧或本领,使学生获得某种程度的见解、判断力、能动性和创造精神和能力.

关键词： 逆矩阵法   γ能谱   样品   核素含量  

摘要： 当样品含有多种能量的γ射线时, 某一峰下的面积, 不仅记录了该能量的光电效应事件, 而且还包括了更高能量γ射线的Compton散射事件. 这样, 就不能简单地由峰下面积确定相应的γ射线强度, 采用逆矩阵法对γ能谱进行分析可得到较好的结果.

关键词： 数学教育   微积分   教学改革   变换思想   极限思想   数学方法  

摘要： 数学的强大生命力在于对社会进步的贡献,在数学教育中,微积分的教学有其独特的作用。文章认为应结合辩证法,使变换思想和极限思想贯穿整个《数学分析》的教学,抓住《数学分析》的主要数学方法,使学生认清数学分析的实质,是目前行之有效的教改措施。

关键词： 西安联合大学   数列   客户关系管理   王景   高校图书馆   学校图书馆   学报   连续出版物   矩阵   数学分析   吕荣   王军   目录   检索工具