課程名稱︰工程數學
課程性質︰生機系必修
課程教師︰顏炳郎
開課學院：生農學院
開課系所︰生機系
考試日期（年月日）︰108.12.31
考試時限（分鐘）：60
試題 :
(10% for each question)
Find the Laplace transform of f(t).
1. f(t) = 3t - cos^{2}t
t
2. f(t) = e^{-t}∫e^{2τ}cos3τdτ
0
3. f(t) is shown as picture.
f(t)
│
│
├1/a/\
│ / \
│ / \
│/ \
└─-┴─── t
a
Find the inverse Laplace transform of F(s).
4. F(s) = 3e^{-4s} / (s+2)
5. F(s) = (2x+3) / (s^3+2s^2+3s+2)
6. F(s) = ln(s/(s-1))
Using Laplace transform to solve the differential equation.
7. y' - 9y = t; y(0) = 5
8. y'' + 8y' + 16y = t^2e^{-4t}; y(0) = 1, y'(0) = -4
9. y'' + 4y = H(t) - H(t-1); y(0) = y'(0) = 0
10. y'' + y = 1 for 0 ≦ t ＜ π/2 ; y(0) = 1, y'(0) = 0
sint for t ≧ π/2