关于微积分的两点思考

从应用的角度来思考什么是微积分,试给出微积分的一个应用模型,再根据给出的模型思考微积分在应用中的要领,从而使初学者对微积分有直观的感知.     

微积分极限思想刍议

极限思想作为高等数学微积分当中最为重要的一种数学思想,主要反映出一个变量和另一个已知量之间无限接近,从而运用该已知量以反映出变量所具有的终极值。高等数学中的微积分形成,正是人们对于极限思想认识在层层深入地认识之后的产物。本文论述了高等数学中微积分极限思想的价值,并探讨了微积分极限思想的具体应用。     

微积分应用的几点思考

作者结合多年的教学经验,从应用的角度对微积分进行思考,并通过具体的实例分析说明微积分在应用中的要领,从而使微积分初学者对微积分有直观的感知,有利于对微积分概念的理解和掌握。     

Evaluating the performance of calculus classes using operational research tools

This paper compares the efficiency of calculus classes. Two kinds of classes are evaluated: the traditional ones and others that use computational methods in teaching. This experiment was performed at Fluminense Federal University, Niterói, Brazil, from 1998 to 2000. The emphasis of this paper is on the quantitative evaluation using two operational research tools: multicriteria decision aid methods (mainly using the MACBETH approach) and data envelopment analysis. The evaluating variables are the level at which students enter the university and the performance of the students after studying calculus.     

Algorithms, the λ calculus and programming

I develop the intuition behind the λ calculus and connect it to computer programming through some basic examples. This fills an often felt gap that teachers and students find between the formal structure of the λ calculus, and the principles and practice of functional programming.     

分数阶微积分及其应用

本文介绍了分数阶微积分的历史、基础知识以及在实际问题中的应用.     

无穷限广义积分的计算方法及技巧

主要介绍无穷限广义积分的计算方法:直接积分法、换元积分法、分部积分法,无穷限广义积分的基本性质及奇函数、偶函数在(-∞, ∞)上的无穷限广义积分的计算。     

对称与和谐在积分中的应用

数学美是一种真实的美,是美的高级形式,是理论思维与审美意识交互的产物。数学积分中蕴藏着和谐美与对称美,有时表现为两者的和谐统一。     

The association of precollege use of calculators with student performance in college calculus

This study investigates how the use of calculators during high school mathematics courses is associated with student performance in introductory college calculus courses in the USA. Data were drawn from a nationally representative sample of 7087 students enrolled in college calculus at 134 colleges and universities. They included information about students’ demographics, standardized test scores, and high school mathematics course enrollment and performance. Factor analysis reduced ten items describing high school calculator usage to two composites: how extensively calculators were employed and teacher-imposed restrictions on their use. Hierarchical linear models predicted students’ college calculus grades, reported by their professor, while controlling for differences between colleges and student backgrounds. The more extensively students had used calculators in high school, the lower their grade in college calculus. However, students earned higher college calculus grades to the extent that their high school teachers had limited calculator use on quizzes and exams and had restricted calculator use until paper-and-pencil methods had been mastered, which offset the negative association of extensive calculator use with grades. The effect sizes of both calculator composites were very small. Overall, the findings raise doubts about any substantial long-term effects on college mathematics performance of calculator use in high school.     

利用微积分证明不等式

不等式证明方法很多,利用微积分的知识证明不等式,使不等式的证明过程简单化,本文列举了8种常用方法.     

极限计算中几类常见错误成因分析及对策

归纳了简单微积分教学中极限运算的几类常见错误，并分析成因提出对策。     

微积分的哲学文化内涵探析

微积分不仅具有实用价值,而且具有深厚的哲学文化内涵。文章揭示了微积分中微分与积分、有限与无限、离散与连续、常量与变量、直线与曲线既对立又统一的辩证关系,旨在加深学生对知识的理解,培养其科学人文精神。     

浅谈微积分基本定理

在一元微积分中,牛顿-莱布尼兹公式是最重要的公式,它建立了微分学与积分学之间的联系.在多元微积分中,也有类似的公式.通过研究场论中三个基本公式的关系,可统一处理多元函数中的相关内容.     

Examining the discourse on the limit concept in a beginning-level calculus classroom

Existing research on limits documents many difficulties students encounter when learning about the concept. There is also some research on teaching of limits but it is not yet as extensive as the research on student learning about limits. This study explores the discourse on limits in a beginning-level undergraduate calculus classroom by focusing on one instructor’s and his students’ discourses through a communicational approach to cognition. The findings indicate that some of the limit-related contexts in which students struggled coincided with those in which the instructor shifted his elements of discourse on limits. The instructor did not attend to the shifts in his discourse, making them implicit for the students. The study highlights that the discrepancies among participants’ discourses signal communicational breakages and suggests that future studies should examine whether teachers’ explicit attention to the elements of their discourse can enhance communication in the classrooms.     

Peer conferences in calculus: the impact of systematic training

This paper describes an intervention for improving the quality of peer assessment conferences in calculus. Although a body of work highlights the learning benefits of peer assessment, few papers have described the nature of student conversations during peer conferences/assessment in detail. This paper provides deeper insight into what those conversations actually look like, and shows the impact of systematic training on conferences. The study took place over two consecutive semesters of introductory college calculus, and analyses show that students had considerably improved conversations after training. The improved conversations consisted of much more on-topic talk and productive feedback; after training, students provided more feedback related to processes (communication and underlying reasoning) than products (correctness or incorrectness).     

关于微积分中值定理的几点注记

首先研究了微积分中值定理的几个性质 ,然后给出了第一积分中值定理的一个新的证明。     

对称法在积分计算中应用的归纳与总结

本文给出积分计算中所采用的常用的对称法,并加以归纳总结     

例说微积分在解初等问题中的应用

以教学过程中积累的多个例子作简单的讨论,展示了微积分学在解决初等问题中的各类应用。     

关于微积分里多元函数极值问题的研究

多元函数极值是微积分课程的一个重要概念 ,文章通过定义并结合具体实例将极值和弱极值概念作一对比 ,以说明它们的区别。同时还指出了条件极值和无条件极值在概念上及求法上的一些区别     

利用Fourier级数展开式计算一个连续无界函数的无穷积分

本文利用Fourier级数展开式得到了一个级数的和,进而又得到了其它级数的和,并利用这些结果计算了一个连续而无界函数的无穷积分,可作为一种方法进行推广。