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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