Mathematica数学软件包中的积分问题

本文指出了Mathematica软件包在一些积分计算上的错误,并从数学的角度分析了产生这种错误的原因,阐述了数学知识在正确使用数学软件包方面的重要性。     

一道数学竞赛试题的多种解法

对第九届中国大学生数学竞赛预赛(数学类)的一道试题又给出了两种解法,有助于拓宽解题思路.     

关于《A Generalization of Bellman—Gronw all Integral Inequality》一文的错误

《数学研究与评论》1985年第2期发表了Zhang Binggen和Shen Yuyi两人合写的论文《A Generalization of Bellman—Gronwall Integral Ineguality》(以下简称文[1])。必须指出,文[1]的基本结果之一定理2,其结论和证明的思想方法均是错误的。 为讲清楚这点,先将文[1]的定理2叙述如下:     

数学软件在国外工科数学教学中的应用

一、引言工科数学课委会在1996年提出的《关于工科数学系列课程教学改革的建议1）中强调了计算机在工科数学教学中的重要性．该《建议》指出：计算机的广泛使用、数值计算、符号演算以及软件包等计算技术的高速发展,不但代替了许多人工的推导和运算,而且正在改变着人们对数学知识的需求,冲击着传统的观念和方法”．该《建议》将利用计算机进行数学实验（包括数学建模、实用数值方法、常用软件包的使用、数据处理）作为基本知识之一,要求各校根据自身的条件,开展计算机辅助教学,努力探索将计算机引入课堂教学,促进教学内容课程体系改…     

运用Mathematica软件包模拟M/M/1队列

运用Mathematica软件包模拟一个M/M/1队列问题,显现该软件包对于数学研究与教学的重要价值.通过对问题的分析制定模拟方案,利用计算机仿真形象地展示排队过程.其方法适用于一般队列问题.     

关于一道全国大学生数学竞赛试题的思考

针对2013年第五届全国大学生数学竟赛中非数学类的一道预赛题,本文进行了深入地剖析,并探讨了一般情形下求解此类问题的方法及相关结论.     

无界函数的反常积分的计算

运用牛顿‐莱布尼茨公式和无界函数的反常积分的定义证明无界函数的反常积分的计算定理,运用这个定理计算无界函数的反常积分简单快捷,通过举例说明这个定理的应用,并指出多种大学数学参考书中存在的一个共同错误。     

第六届全国大学生数学竞赛预赛一道题的推广

对第六届全国大学生数学竞赛预赛(非数学类)的一道竞赛题进行了推广,探索了高维和高阶形式下的积分与积分定义差值的无穷小的运算性质.     

纠错型小结设计的教学策略浅析

学生在数学学习过程中由于认知水平、思维能力等原因会出现各种各样的错误,利用好错误资源,可以帮助学生认识错误原因,纠正认识偏差,更加深刻地理解知识,探索数学的规律.在教学中进行纠错型小结设计是将学生的典型错误进行分析和纠正,通过正面的错误展示和分析,引导学生重新审视学习内容,完善知识结构,以感悟数学的思想和方法,落实核心素养.     

安全渡河问题的计算机求解和模拟

本文介绍利用数学软件包来求解和利用计算机多媒体制作工具来模拟数学模型课程中安全渡河问题的方法     

On the Optimal Sizing Problem

The paper studies the problem of determining the number and dimensions of sizes of apparel so as to maximize profits. It develops a simple one-variable bisection search algorithm that gives the optimal solution. An example is solved interactively using a Macintosh LC and Math CAD, a mathematical software package.     

Computing the spectral function for singular Sturm–Liouville problems

Algorithms for computing Sturm–Liouville spectral density functions are developed based on several mathematical characterizations. Convergence and error bounds are derived and methods are tested on several examples. The results are compared with those from the existing software package SLEDGE.     

The role of software Modellus in a teaching approach based on model analysis

We discuss some results of a study carried out over the past 4 years to investigate the role of Modellus, a software package, in the development of an approach to teaching calculus for Biology majors. The central idea of the teaching approach is to propose the analysis of a mathematical model for a biological phenomenon at the very beginning of the course, in a way that this analysis is interrelated with some of the mathematical concepts listed in the syllabus. In this paper, we focus on the role of the software during the development of one of the activities proposed to the students, the purpose of which was to discuss the relation between secant lines and the instantaneous rate of change. It was found that this software played two roles in the development of this activity: providing information about the phenomenon and the model; and acting as a trigger, making evident to the student an important aspect that contributed to his understanding. Based on our theoretical perspective of digital technology, we believe that students’ interaction with the software played a fundamental role in the thinking collective composed of humans and media involved in mathematical learning.     

IR Tools: a MATLAB package of iterative regularization methods and large-scale test problems

Numerical Algorithms - This paper describes a new MATLAB software package of iterative regularization methods and test problems for large-scale linear inverse problems. The software package, called...     

Software package for 3D viscous gas flow simulation on multiprocessor computer systems

A parallel software package designed for the numerical simulation of three-dimensional viscous gas flows is presented. The numerical algorithm is based on kinetically consistent difference schemes used on locally refined grids. The software package has been tested in various super-and subsonic flow problems. It provides an opportunity for the direct simulation of turbulent flows. The efficiency of parallelization is analyzed depending on the problem size and the number of processors.     

基于软件测试的软件缺陷预测模型

通过对某武器系统软件测试所得缺陷数据与软件规模之间关系的分析,建立了基于软件测试的软件缺陷预测模型.通过本项研究,可以在武器系统软件研制的初期阶段对软件可能含有的缺陷数量和缺陷等级进行预测,为软件研制过程的质量保证活动策划提供依据.     

OPTAC: a portable software package for analyzing and comparing optimization methods by visualization

A software package for analyzing and comparing optimization methods is presented. This package displays, using different colors, the regions of convergence to the minima of a given function for various optimization methods. It displays also the rate of their convergence as well as the regions of divergence of these methods. Moreover, this package gives quantitative information regarding the total convergence area in a specific domain for various minima.     

风速影响回风换热器换热性能数值仿真及实验研究

针对回风速度对矿井回风换热器换热性能的影响,建立了回风与液滴气液两相流之间热质交换的数学模型,利用CFD仿真软件FLUENT模拟回风速度分别为5 m/s,8 m/s,10 m/s,12 m/s和15 m/s时制热和制冷两种工况下液滴温度的变化,得出了回风速度对回风换热器换热性能的影响规律,最后利用实验测试了制热工况下风速对液滴温度变化的影响,得出的实验结果与仿真结果比较吻合.