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辩证思维和形象思维贯穿于微积分数学的全过程,它们是学好微积分的关键,也是大力发展学生教学思维水平的着眼点。 相似文献
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微积分或称数学分析是人类思维的伟大成果之一,是人类经历了2500多年撼人心灵的智力奋斗的结晶.微积分的创立是数学发展中的里程碑,有了这个发明,创造性数学相当普遍地发展到了一个高级水平,为研究变量和函数提供了重要的方法和手段.今天,如果一个人没有微积分方面的知识,就不能说他受过很好的教育. 相似文献
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参数方程在许多学科都有广泛应用,本文旨在探讨大学数学中的参数方程教学,通过三个比较典型的例子展示参数方程与直角坐标和极坐标间的联系与区别以及同工程等学科的关系.建议在教学中参考以提升学生对这类方程描述运动的理解. 相似文献
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本文通过对美国流行微积分教材的研读分析,结合美国大学课堂实践经历,探讨我国高等数学教材的改革热点.文章从内容引入设计、抽象概念的处理、实际问题中的应用、数学文化的融合、习题设置和图表辅助等几个方面分析了美国微积分教材中值得借鉴的教学理念,对高等数学教材改革得到一定的启示. 相似文献
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微积分看作0.9 总被引:3,自引:3,他引:0
林群 《数学的实践与认识》2013,43(7)
由一张示意图入手,把山坡分割为"微分三角形",后者的高简称微分,图中还有小缝.于是,山坡全高=微分的和+小缝的和,或变为:微分的和=全高一小缝的和.当山坡为多项式曲线,小缝的和可以精确计算,特别,可以相继取为小数,0.1,0.01,0.001,….若令全高=1,那么:微分的和=0.9,求出了!如果承认0.9=1,又有:微分的和=全高,此即微积分基本公式.谁想的到这个公式即1=0.9? 相似文献
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微积分(导数与定积分)作为新课标课程的基本内容,07年山东、广东、海南、宁夏四省率先将定积分内容纳入高考.导数的引入为解决函数的性质(单调、极值、最值等)开辟了新的途径,定积分纳入新课程为求中学数学中曲线围成封闭图形的面积带来了生机,拓广了高中数学领域,为数学问题带来了诸多灵性,为学生以后进一步学习高等数学奠定了基础. 相似文献
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米哈伊·列夫舍茨 《数学的实践与认识》2009,39(11)
基于代数和显式一致估计的微积分思想可以追溯到前牛顿时代,或者欧拉和拉格朗日.由于所涉及的数学非常简单,新的方法可以从一些简单的例子出发,直接、自然却严格地建立微分和积分的流线型理论,并不需要连续性、极限和紧性的概念. 相似文献
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我国微积分教学改革方向的思考--兼论美国AP微积分计划给我们的启示 总被引:4,自引:1,他引:3
我国微积分教学在整个高等教育中有着十分重要的地位,经过多年的改革虽然取得了一些成绩,但如何进一步地改革值得思考.美国AP微积分计划在指导思想、课程目标和命题思路对微积分教学的进一步改革有很好的借鉴作用. 相似文献
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Libuše Samková 《International Journal of Mathematical Education in Science & Technology》2013,44(2):230-244
This is a guide to using Maple in teaching fundamental calculus of one, two and three variables (limits, derivatives, integrals, etc.), also suitable for Maple beginners. It outlines one of the ways to effective use of computers in the teaching process. It scans advantages and disadvantages of using Maple in relation to students and teacher. The guide includes hints for creating teaching materials. This article is supported by the author's 10-year experience of teaching calculus with Maple. 相似文献
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Peter K Dunn Chris Harman 《International Journal of Mathematical Education in Science & Technology》2013,44(4):584-596
The note discusses ways in which technology can be used in the calculus learning process. In particular, five MATLAB programs are detailed for use by instructors or students that demonstrate important concepts in introductory calculus: Newton's method, differentiation and integration. Two of the programs are animated. The programs and the graphical user interface have been specifically designed to help the student understand the processes behind these important introductory concepts. Each program has a series of demonstrations that show unusual, difficult or important cases. 相似文献
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Gerhard Sonnert Philip M. Sadler Samuel M. Sadler David M. Bressoud 《International Journal of Mathematical Education in Science & Technology》2013,44(3):370-387
College calculus teaches students important mathematical concepts and skills. The course also has a substantial impact on students’ attitude toward mathematics, affecting their career aspirations and desires to take more mathematics. This national US study of 3103 students at 123 colleges and universities tracks changes in students’ attitudes toward mathematics during a ‘mainstream’ calculus course while controlling for student backgrounds. The attitude measure combines students’ self-ratings of their mathematics confidence, interest in, and enjoyment of mathematics. Three major kinds of instructor pedagogy, identified through the factor analysis of 61 student-reported variables, are investigated for impact on student attitude as follows: (1) instructors who employ generally accepted ‘good teaching’ practices (e.g. clarity in presentation and answering questions, useful homework, fair exams, help outside of class) are found to have the most positive impact, particularly with students who began with a weaker initial attitude. (2) Use of educational ‘technology’ (e.g. graphing calculators, for demonstrations, in homework), on average, is found to have no impact on attitudes, except when used by graduate student instructors, which negatively affects students’ attitudes towards mathematics. (3) ‘Ambitious teaching’ (e.g. group work, word problems, ‘flipped’ reading, student explanations of thinking) has a small negative impact on student attitudes, while being a relatively more constructive influence only on students who already enjoyed a positive attitude toward mathematics and in classrooms with a large number of students. This study provides support for efforts to improve calculus teaching through the training of faculty and graduate students to use traditional ‘good teaching’ practices through professional development workshops and courses. As currently implemented, technology and ambitious pedagogical practices, while no doubt effective in certain classrooms, do not appear to have a reliable, positive impact on student attitudes toward mathematics. 相似文献
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《随机分析与应用》2013,31(2):507-523
Abstract The integration and differentiation of fractional orders are well known concepts for deterministic functions (see Miller, K.S.; Ross, B. An Introduction to Fractional Calculus and Fractional Differential Equations; John Wiley: New York, 1993; I. Podlubny and Ahmed M.A. El-Sayed, On two definitions of fractional calculus Slovak Academy of Sciences Institute of experimental Phys. UEF-03-96 ISBN 80-7099-252-2, 1996; Podlubny, I. Fractional Differential Equations; Acad. Press: San Diego – New York, London etc. 1999; Samko, S.G.; Kilbas, A.A.; Marichev, O. Integral and derivatives of the fractional orders and some of their applications. Nauka i Teknika Minisk 1983). In earlier work, we have studied the fractional calculus for mean square continuous stochastic processes. In this work, we shall study the mean square (m.s.) fractional calculus for stochastic processes which are m.s. Riemann-integrable and prove some its properties. 相似文献
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1加强数学软件在数学教育中的应用数学软件为高等数学教学理论联系实际创造了有利条件.象Maple这样的数学软件在美国的中学数学教育中就已经开始使用了.最近,高等教育出版社推出二部国外原版教材,一部是Finey,Weir等编的《Thomas Calculus》[1],一部是Stewart的《Calculus》[2] 相似文献
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国内外两本微积分教材的比较与启示 总被引:2,自引:1,他引:1
通过中美两国有代表性的两本微积分教材在理论内容、知识应用、习题、现代化教学手段等方面进行比较,分析国外国内两本教材的特点,提出了一些值得思考的问题,给我国高等数学教材改革及教学提供一些启示. 相似文献
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F—fuzzy演绎系统 总被引:1,自引:0,他引:1
本文建立了一种演绎系统FFCS,在该演义系统中可以处理具有模糊性的推理过程,区别与其他对模糊推理进行形式化的逻辑系统,FFCS对模糊假言推理FMP做了完全形式化的处理。 相似文献