函数序列一致收敛的判别及MATLAB在其上的应用

AbstractThe theory of uniform convergence of function sequence is an important content ofmathematical analysis.In many lecture notes of mathematical analysis,some methods tojudge the uniform convergence of function sequences are given,but these methods are stillnot comprehensive enough to solve the problem of uniform convergence of most functionsequences.Consequently,the research background and significance of uniform convergenceof function sequences are briefly described in this paper,summarizes six practical methodsfor judging the uniform convergence of function sequences,and gives correspondingexplanations and examples for their applications,so as to facilitate the readers to betterunderstand these methods and provide convenience for dealing with the uniformconvergence of function sequences in the future.At the same time,the paper puts forwardthe application of MATLAB in the judgment of uniform convergence of function sequence,gives the procedure code steps of solving problems,and through several examples,realizesthe effective integration of information technology in mathematical analysis,and is verifiedby experiments.It is important to study the uniform convergence and the convergenceinterval of function sequences.Key words Function sequences;Uniform convergence;MATLAB programme andpicture.