基于Mathematica的函数列一致收敛性教学实践  

On Teaching Practice of Uniform Convergence of Function Sequence Based on Mathematica

作　　者：高忠社[1] Gao Zhongshe(School of Mathematics and Statics,Tianshui Normal University,Tianshui 741001,China)

机构地区：[1]天水师范学院数学与统计学院,甘肃天水741001

出　　处：《黑河学院学报》2021年第12期186-188,共3页Journal of Heihe University

基　　金：国家自然科学基金“反常扩散方程的高阶数值算法及其在天水地下水质研究中的应用”(11561060);甘肃省教育科学“十四五”规划2021年度课题“数值分析课程思政教学实践研究”(GS[2021]GHB19332091);天水师范学院2020年度校级教育教学改革项目“数值分析课程思政教学实践研究”(JY202003)。

摘　　要：函数项级数是数学分析教学中的重点、难点内容,函数列是学习函数项级数的基础,也是定义函数项级数收敛性、一致收敛性的基础。根据函数列的定义、收敛点、收敛性、一致收敛性,使用数学软件mathematica作图,并通过实例使用数值和图形分析的方法,分析函数列的一致收敛性与不一致收敛行作图,从而使学生能够更加直观清楚地理解该知识点,提升教学效果。Series of functions are considered to a key and difficult part in teaching of mathematical analysis,and function sequence is the basis of learning series of function,as well as the basis to defining its convergence and uniform convergence.This paper discusses the definition,convergence point,convergence and uniform convergence of function sequence,explores the way of taking the teaching practice by using the mathematica software to draw graphs and by adopting the amount and graph analysis method in several examples;therefore,the uniform convergence and inconsistent convergence of function sequence are presented through graphing analysis,which is helpful for the students to understand the point and to get better teaching effect.

关 键 词：函数列 一致收敛性 MATHEMATICA软件 教学实践 

分 类 号：G642[文化科学—高等教育学]