※ [本文轉錄自 FCU_Talk 看板]
作者: vsdavid (飛天豬寶兒) 看板: FCU_Talk
標題: Re: [用功] 林宗志老師的工數提示
時間: Wed Jun 17 20:05:22 2009
(原文吃光光)
※d=偏微分，pi=拍(就是那個拍啦...)
一、Solve following P.D.E. by separation of variable method (15%)
du/dt = 9‧(d^2)u/d(x^2) , 0<x<3 , 0<t
Boundary conditions : ux(0,t) = ux(3,t) = 0
Initial condition : u(x,0) = 3+5cos2pix-3cos3pix
二、Consider the following wave equation (15%*4=60%)
(d^2)u/d(t^2) = 4‧(d^2)u/d(x^2)
1、Solve the equation by separation of variable method(變數分離法)
with boundary conditions : u(0,t) = 0 , u(2,t) = 0 , 0<x<2 , 0<t
initial conditions : u(x,0) = 3sin2pix , ut(x,o) = 4sin4pix
2、Solve the equation by separation of variable method(變數分離法)
with boundary conditions : u(0,t) = 0 , 0<x<∞ , 0<t
initial conditions : u(x,0) = e^-2x , x>0 ,ut(x,o) = x(e^-3x) , x>0
3、Solve the equation by the Laplace transform with respect to t with
initial conditions : u(x,0) = 0 , ut(x,0) = 0
boundary conditions : u(0,t)=(e^-2t)sin2t , and u(x,t) is bounded as
x→∞
4、Solve the equation by the Fourier transform with respect to x
u(x,0)=2(e^-3|x|) , du(x,0)/dt=0 (-∞<x<∞)
三、Solve the following Laplace equation (15%)
(d^2)u/d(x^2) + (d^2)u/d(y^2) = 0
with boundary conditions : u(0,y) = 0 , u(2,y) = 0 ,
u(x,0) = 0 , u(x,3) = f(x)
四、Determine the eigenvalues and eigenfunctions of the following
Sturm-Liourvill problem (10%)
(x^2)y'' + xy' + λy = 0
y(1) = y(e) = 0
打完收工！
我願意用這篇換水源哥的計概以及實習課...
實習助教真的好MAN！
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◆ From: 122.127.179.48