[試題] 99下 林沛群 工程數學 第三次期中考
課程名稱︰工程數學下
課程性質︰系必修
課程教師︰林沛群
開課學院：工學院
開課系所︰機械系
考試日期（年月日）︰100/6/01 (機械之夜那天)
考試時限（分鐘）：90
是否需發放獎勵金：是
試題 :
1.(40%)Solve the following boundary value problem:
d^2 u d^2 u 0 <x< L
─── = k ───
d t^2 d x^2 t>0
u(0,t)=T u(L,t)=0 for t>=0
u(x,0)= 0 for 0<=x<=L
2.A PDE problem is listed below:
d^2 y d^2 y 0 <x< ∞
─── = c^2* ───
d t^2 d x^2 t>0
y(0,t)=0 for t>=0
y(x,0)= f(x)
dy
─(x,0) = 0 for 0<x<∞
dt
(a)Which transform method can be utilized to solve the problem?Explain why.
(b)Derive the solution in analytic expression by the transform method.
(c)Following (b), solve the problem with f(x)=-2*e^(-x) and c=6.
3.(30%)
Solve the Dirichlet problem for rectangle, with the given boundary condition
u(x,0)=0 , u(x,1)= 5 sin(3x) for 0<= x <= π
u(0,y)=sin(πy) , u(π,y)=0 fot 0<= y <= 1
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06/05 18:37, , 1F
06/05 18:37, 1F