幂级数逐项微分、逐项积分后的收敛域

讨论幂级数的收敛城与逐项微分、逐项积分后所得新幂级数的收敛城之间的关系。     

幂级数逐项求导、逐项积分后收敛域的讨论

本文给出了幂级数逐项求导、逐项积分后的收敛域与逐项求导、逐项积分前的幂级数收敛域的关系及其应用     

求幂级数的和函数的方法

幂级数是级数这一章的主要内容,求幂级数的和函数是幂级数运算中的一个重点和难点,具有一定的技巧性。结合多年的教学实践,介绍了求幂级数的和函数的最基本的方法。     

幂级数分析性质的推广

幂级数的和函数在其收敛区间上具有较好的分析性质。即：连续性、逐项可积性和逐项可微性。文章把连续性和逐项可积性推广到幂级数的收敛域上，并给出幂级数逐项求异与逐项积分后得到的幂级数与原幂级数收敛域之间的关系。     

无穷区间上可积函数列逐项积分的条件

指出无穷区间上一致收敛的函数列未必可逐项积分，并给出无穷区间上可积函数列可逐项积分的一个充分条件。     

幂级数求和的技巧

在求幂级数和的时候,根据幂级数系数的特点,有些题目应该先逐项求导再逐项积分,有的相反,应该先逐项积分再逐项求导,而有的既可以先求导再积分又可以先积分再求导.接下来通过例题的分析,谈一下幂级数求和的技巧,让读者从中获取一些宝贵经验.     

关于函数项级数逐项积分定理的注记

本文进上步研究了函数项级数的逐项积分定理。给出新的逐项积分定理。     

关于幂级数求和的探讨

幂级数求和是无穷级数这一章的重点和难点.本文结合教材中的错例分析了学生的错误及错误原因,并对幂级数求和问题进行了探讨,给出了解决方法.     

对幂级数逐项可导与可积性质应用的探讨

逐项可导性与逐项可积是幂级数的和函数在其收敛区间上的两个重要的分析性质,文章探讨了该性质在求幂级数的和函数、求数项级数的和、求函数的幂级数展开、求积分、求极限等方面的应用。     

几类幂级数的求和公式

本文巧用幂级数逐项微分定理,给出了几类幂级数sun from n=1 to ∞ n(n 1)…(n m-1)x~n,sun from n=1 to ∞(x~n/(n(n 1)…(n m-1)x~n)及sun from n=0 to ∞(a nd)x~n的求和公式。     

例谈探究活动的设计

本文分别就生物学教学中如何进行“观察与测量”、“实验及其模拟”的探究活动设计作了一些阐述。     

几例化学计算中的数列应用

题一:萃取是一种常用的分离、提纯物质的方法.先用一定量CCl4从20 mL碘水(含碘A×10-3mol)中将碘萃取出来,若每次用2mL CCl4,并将每次萃取液(碘的CCl4溶液)收集同一烧杯中.已知在某温度下每次萃取时,碘在CCl4中的物质的量浓度是水中的80倍.假设每次萃取时碘水体积始终为20mL.     

广义幂级数上的GPP-环

设R是交换环,(S,≤)是严格全序幺半群.本文证明了:(1)广义幂级数环[[RS,≤]]是强GPP-环当且仅当R是强GPP-环,且B(R)(R的所有幂等元的集合)的任意S-加标子集C在B(R)中有最小下界.(2)如果(S,≤)满足条件:任意S∈S,s≥0,则环[[RS,≤]]是弱GPP-环当且仅当R是弱GPP-环.     

Dynamic stiffness for thin-walled structures by power series

INTRODUCTION Thin-walled structures have considerable tech-nological importance in many situations of engi-neering practice. The rotary and warping inertia terms should be considered in the analyses of thin-walled structures (Alwis and Wang, 1996), although it is difficult to obtain the analytical solutions of govern-ing differential equations, especially of thin-walled frame and spatial twisted structure. The finite element method (FEM) is widely used for vibration and sta-bility analy…     

函子范畴的Incidence代数的两个例子

以箭图Q₁,Q₂,Q₃为例,构造有限偏序k范畴Γ₁,Γ₂,考虑Γ₁,Γ₂及函子范畴Γ₁^Γ2诱导的incidence代数的两个例子。     

Design considerations for series hybrid active power filter

Some important factors for designing a series hybrid active power filter (SHAPF) are presented in this paper for the case when the load is varied in a wide range and/or the source voltage is seriously distorted. Special design of passive filters, adaptive control of parameter and multi variant control are discussed in detail. The filter is stable, has good performance, and causes small capacitive reactive current. The simulation and experimental results accorded with the theoretical analysis results. Project supported by DELTA Science, Technology and Education Development Fundation for Power Electronics.     

通过实验培养学生创新能力两例

1　实验一设计一个实验 ,能通过观察到的明显现象 ,说明ＣＯ2 与ＮａＯＨ溶液发生了反应。 [实验用品 ]:集气瓶、烧瓶、分液漏斗、长颈漏斗、导管、橡皮管、弹簧夹、烧杯、量筒、水、ＣＯ2 气体、ＮａＯＨ溶液以及你认为所能用到的仪器和药品。 [要求 ]:(1)选用上述实验用品 ,画出设计装置图。 (2 )简述操作并说明能明显观察到的现象 ,证明ＣＯ2 与ＮａＯＨ溶液发生了反应。这道题本身比较简单 ,但它的设计结果却是多种多样的。有的同学设计了如图 1的装置 ,并说明 :当将分液漏斗中的ＮａＯＨ溶液滴入烧瓶时如果看到水槽中水被吸入到烧瓶则…     

Technology in Teacher Education: examples of integration and implementation in early childhood courses

Abstract

This article explores a number of ways in which information and communications technologies (ICT) have been incorporated and integrated in a teacher education program in order to extend opportunities for students to interact with ICT as part of their preparation for becoming early childhood professionals. It describes three examples where ICT have been utilised in different contexts to promote understanding of the implications of technologies in educational settings, to engage students with powerful conceptual ideas and as a means of communication between students on campus and those in remote areas. The examples reveal that both undergraduate and graduate students indicated that they were at a novice stage of use and understanding before embarking on the courses. In addition, the examples show that participation in the courses helped students to come to terms with computer technology as a device that could help them both to acquire new forms of knowledge as well as extend the possibilities for interactions with other early childhood professionals who were located in remote areas. The examples also highlighted the need for teacher educators to become aware of the variety of ways in which ICT can complement and extend teaching and learning contexts in new and dynamic ways rather than be used to perpetuate existing pedagogical strategies that need to be reconceptualized in the information age.