非正常积分的敛散性的判定和计算
关键词：反常积分，敛散性，时间尺度
毕业论文设计说明书外文摘要
Title The calculation ， Convergence and Divergence of improper intergrals
Abstract
The infinite integral that expanding integration interval of the integration of function from a bounded interval to a unbounded one and
the integrals that integrand were expanded from a bounded interval to a unbounded one, this two integrals are what we say improper integral. It is a difficulty to calculate the improper integral and determine its convergence and pergence. This article describes the related definitions and two kinds of forms of the improper integral and summaries calculation solutions and determination solutions of the two integrals. And through access to information, studying other different forms of solutions to calculate and determine the two integrals. At last, the text studies improper integral on time scale, and introduces the two kinds of different forms of the integral, and then describes that how to calculate improper integral on time scale and how to determine the convergence and pergence of this integral. By contrast, find the difference of the improper integral on determining and calculating.
Keywords: improper integral, convergence and pergence, time scale
目 次
1 引言 1
2 反常积分的定义和基本性质 3
2.1 反常积分的定义 3
2.2 无穷积分的性质 3
2.3 瑕积分的性质 5
3 反常积分的敛散性的判定方法 6
3.1 狄利克雷判别法 6
3.2 阿贝尔判别法 6
3.3 对数判别法 7
3.4 根植判别法 8
3.5 比值判别法和拉贝判别法 9
3.6 新对数判别法 10
3.7 基于积分的级数的敛散性判别方法 11
3.8 导数幂乘法 12
3.9 导数自比法 13
4 反常积分的计算 15
4.1 利用定义计算反常积分 15
4.2 利用分部积分法计算反常积分 15
4.3 利用留数定理计算反常积分 16
4.4 利用二重积分理论计算反常积分 17
4.5 利用lagrange中值定理计算反常积分 17
4.6 含参变量的反常积分 19
4.7 几个重要的无穷积分 21
4.8 定积分与瑕积分计算方法的比较[29] 22
5 时间尺度上的反常积分 24
5.1 时间尺度上的反常积分 24
5.2 第一类反常积分 25
5.3 第二类反常积分 26