多元Laplace变换

信息计算科学论文编号:XXLW045 论文字数:4099,页数:19

目   录
 
摘   要 i
Abstract ii
目录 iii
前言 1
第一章 多元Laplace变换 2
1.1多元Laplace变换的概念 2
 1.1.1多元Laplace变换定义 2
 1.1.2 多元Laplace变换存在定理 2
 1.1.3 多元Laplace变换逆变换定义 4
 1.1.4多元Laplace变换逆变换定理 5
第二章 多元Laplace变换的性质 6
2.1线性性质 6
2.2微分性质 6
 2.2.1像原函数的微分性质 6
 2.2.2像函数的微分性质 7
2.3 积分性质 8
 2.3.1像原函数的积分性质 8
 2.3.2像函数的积分性质 8
2.4 卷积性质 8
2.5 其他性质 11
 2.5.1位移性质 10
 2.5.2相似性质 10
 2.5.3延迟性质 10
第三章 多元Laplace变换的应用 11
总  结 13
致  谢 14
参考文献 15

摘要
 Laplace变换是工程技术中应用非常广泛的变换之一。由于其要求条件比Fourier变换要低，所以使得应用范围比Fourier变换更加广泛。
 我们在课程中学习了一元Laplace变换，在此基础上，我们推广其到多元的情形，使其在更广泛的意义下有更多的应用。
 资料中显示目前多元Laplace变换是通过如下方式推广的：
 一元Laplace变换为
 
 多元Laplace变换推广为
 
其中，为复常数。
本文通过如下形式推广Laplace变换

文章在上述Laplace变换的意义下，文章给出了该Laplace变换的存在定理、线性性质、微分性质、积分性质、延迟性质、卷积性质等，并给出了若干应用的例子。

关键词：拉普拉斯变换； 多元Laplace变换；存在性；性质；卷积。

Abstract
 Laplace transform is one of a wide range of transformation in the application of engineering and technology. because of its request conditions is lower than the Fourier transform, it allows application of more extensive than the Fourier transform.
 We learn single-dimensional Laplace in the course , on this basis, we promotion its to diverse circumstances, so that the sense of a wider range of more applications.
Information display, at present, multi-laplace transform through by the following promotion:
 One-dimensional Laplace Transform for

 Promote multi-Laplace transform for

Among them, this constant for the complex.
In this paper, by the following forms of promotion by Laplace transform

The article in the sense of Laplace transform, this paper giving existence theorem for the Laplace transform, linear nature, the nature of differential, integral nature, the nature of the delay, convolution nature, and gives a number of applications examples.

Keywords：Laplace transform; multiple Laplace transform; existence; property; convolution.