摘 要:本文首先利用稳定电流场的基本性质,导出拉普拉斯方程.因为拉普拉斯方程描述的是稳态方程,所以不用说初始条件.论文接下来讨论的就是在定解问题中,只有边界条件时,求解方程的边值问题的方法.在解决此类方程时,文中运用了分离变量法、Fourier变换法、Green函数法以及保角变换解法.基于问题的解决,并讨论了拉普拉斯方程在电流场领域的应用.37644 毕业论文关键词:拉普拉斯方程;分离变量法;Fourier变换;格林函数;保角变换
Laplace equation and the exploration of its Solutions
Abstract:Firstly, I use the basic properties of the Laplace equation in steady current field and electric field in this paper, Laplace equation has being derived. Because of the Laplace equation describes the steady state equations, we don’t mention the equation’s initial condition. Next, we discuss the way of resolving these questions of the equation, only when the final condition in the fixed solution question. When resolving the questions like this, I mainly use the means of variable separation, Fourier transformation, Green function and the conformal transformation. Based on resoluving this questions, I also discuss the application of Laplace equation in the current field.
Keywords: Laplace equation; variables separation; Fourier transformation; Green function; the conformal transformation
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