课程名称︰工程数学下 课程性质︰系必修 课程教师︰林沛群 开课学院：工学院 开课系所︰机械系 考试日期（年月日）︰100/6/01 (机械之夜那天) 考试时限（分钟）：90 是否需发放奖励金：是 试题 : 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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