作者Brownshale (布朗雪偶)
看板NTU-Exam
标题[试题] 96下 林沛群 工程数学 期末考
时间Mon Jun 30 11:51:43 2008
课程名称︰工程数学
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)︰2008.06.16
考试时限(分钟):120
是否需发放奖励金:是
(如未明确表示,则不予发放)
试题 :
1.(20%) Solve the following PDE
(本题d均表示偏微分符号)
du/dt = d^2 u/dx^2 -∞ < x < ∞, t > 0
1 -1 < = x < = 1
u(x,0) =
0 lxl > 1
2.(30%) Solve the following boundary value problem
(本题d均表示偏微分符号)
d^2 y/d t^2 = 4 d^2 y/d x^2 + 2cos(x) 0 < x < 2π, t > 0
y(0,t) = y(2π,t) for t > = 0
y(x,0) = 0, dy/dt(x,0) = 0 for 0 < = x < = 2π
3.(15%) Determine the differentiability of the function f(z) = ilzl^2
4.(15%) Let f be differentiable on a simply connected domain G. Let Γ be a
closed path in G.
Proof ∫ f(z)dz = 0. (Cauchy's Theorem)
Γ
5.(20%) Evaluate
∞ x^2
∫ ───── dx .
0 (x^2+4)^2
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