作业帮摘要翻译 谢谢了摘 要拉普拉斯变换是复变函数的一部分,它是一种数学积分变换,其核心是把时间函数 与复变函数 联系起来,把
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摘要翻译 谢谢了
摘 要
拉普拉斯变换是复变函数的一部分,它是一种数学积分变换,其核心是把时间函数 与复变函数 联系起来,把时域问题通过数学变换为复频域问题,把时间域的高阶微分方程变换成为复频域的代数方程以便求解.拉普拉斯变换有着广阔的应用空间,拉普拉斯变换在复变函数论及实际应用中都很重要,拉普拉斯积分变换在纯数学以及应用数学中都是一个有力的工具.对某些问题,他比 变换的使用面宽,因为它对像原函数要求的条件比较弱的缘故.拉普拉斯变换具有很多重要的应用,所以研究拉普拉斯变换具有非常实际的应用价值.
拉普拉斯变换是简化计算而建立的实变量函数和复变量间的一种函数变换.对一个实变量函数作拉普拉斯变换并在复数域中作各种运算,再将运算结果作拉普拉斯反演变换来求得实数域中的相应结果,往往比直接在实数域中求出同样的结果在计算上容易的多.
本文主要研究拉普拉斯变换在解微分方程,积分方程以及广义积分计算等方面的应用,并以拉普拉斯变换为工具,介绍拉普拉斯变换在非数学领域内的一些应用.
关键词：拉普拉斯变换,微分方程,积分方程,广义积分
摘 要
拉普拉斯变换是复变函数的一部分,它是一种数学积分变换,其核心是把时间函数 与复变函数 联系起来,把时域问题通过数学变换为复频域问题,把时间域的高阶微分方程变换成为复频域的代数方程以便求解.拉普拉斯变换有着广阔的应用空间,拉普拉斯变换在复变函数论及实际应用中都很重要,拉普拉斯积分变换在纯数学以及应用数学中都是一个有力的工具.对某些问题,他比 变换的使用面宽,因为它对像原函数要求的条件比较弱的缘故.拉普拉斯变换具有很多重要的应用,所以研究拉普拉斯变换具有非常实际的应用价值.
拉普拉斯变换是简化计算而建立的实变量函数和复变量间的一种函数变换.对一个实变量函数作拉普拉斯变换并在复数域中作各种运算,再将运算结果作拉普拉斯反演变换来求得实数域中的相应结果,往往比直接在实数域中求出同样的结果在计算上容易的多.
本文主要研究拉普拉斯变换在解微分方程,积分方程以及广义积分计算等方面的应用,并以拉普拉斯变换为工具,介绍拉普拉斯变换在非数学领域内的一些应用.
关键词：拉普拉斯变换,微分方程,积分方程,广义积分
Abstract
Laplace transform a complex function of the part,it is a mathematical integral transformation,its core is the function of time and complex function linked to the time-domain issue to transformation through complex mathematical problems frequency domain,the domain of high-end time Differential equations transform a complex frequency domain in order to solve the algebraic equation.Laplace transform has broad application of space,Laplace transform the complex function addressed in practical applications are very important,LaPlace integral transformation in pure mathematics and applied mathematics are in a powerful tool.On certain issues,he compared the use of broad transformation because of its original function as the conditions required because of weak.Laplace transform a number of important applications,the study Laplace transform a very practical application.
Laplace transform is to simplify the calculation and the establishment of the function is variable and complex variables of a function transformation.Is a function of variables for Laplace transform and a variety of complex domain,and then computing the results obtained Laplace anti-evolution exchange for real results of the corresponding jurisdictions,often in direct than the actual domain sought The same results in the calculation of the more vulnerable.
This paper studies in Laplace transform of differential equations,integral equations and generalized integral calculation of the application,and Laplace transform as a tool introduced in Laplace transform non-mathematical applications in the field.
Key words:Laplace transform,differential equations,integral equations,generalized integral
Laplace transform a complex function of the part,it is a mathematical integral transformation,its core is the function of time and complex function linked to the time-domain issue to transformation through complex mathematical problems frequency domain,the domain of high-end time Differential equations transform a complex frequency domain in order to solve the algebraic equation.Laplace transform has broad application of space,Laplace transform the complex function addressed in practical applications are very important,LaPlace integral transformation in pure mathematics and applied mathematics are in a powerful tool.On certain issues,he compared the use of broad transformation because of its original function as the conditions required because of weak.Laplace transform a number of important applications,the study Laplace transform a very practical application.
Laplace transform is to simplify the calculation and the establishment of the function is variable and complex variables of a function transformation.Is a function of variables for Laplace transform and a variety of complex domain,and then computing the results obtained Laplace anti-evolution exchange for real results of the corresponding jurisdictions,often in direct than the actual domain sought The same results in the calculation of the more vulnerable.
This paper studies in Laplace transform of differential equations,integral equations and generalized integral calculation of the application,and Laplace transform as a tool introduced in Laplace transform non-mathematical applications in the field.
Key words:Laplace transform,differential equations,integral equations,generalized integral