課程名稱︰工程數學上
課程性質︰必修
課程教師︰蕭浩明
開課學院：工學院
開課系所︰機械系
考試日期（年月日）︰2016/12/14
考試時限（分鐘）：70
試題 :
-1 1 1
1. (15%) Given that L [－－－－－－－－] = －[2sint - sin2t]
s^4 + 5s^2 + 4 6
-1 e^(-πs)
Find L [－－－－－－－－－]
s(s^4 + 5s^2 + 4)
t
2. (15%) Solve L[∫ u(e^u)(t - u)^2du]
0
t
3. (15%) Solve y' - 2y = ∫ (e^2(t-τ)) cos(3τ) dτ; y(0) = 0
0
4. (15%) Solve y" + y = u(t - π) - u(t - 2π) y(0) = 0, y'(0) = 0
5. (20%) Solve x' + (1/3)x - ((1-2t)/3)x^4 = 0
Hint: Chang of Variables
6. (20%)Solve x" + 16x = f(t); x(0) = 0, x'(0) = 1
where f(t) = cos4t 0 <= t < π
f(t) = 0 t >= π
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