課程名稱︰工程數學一
課程性質︰必修
課程教師︰王昭男
開課學院：工學院
開課系所︰工程科學與海洋工程學系
考試日期（年月日）︰97/1/14
考試時限（分鐘）：120
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1.Write the following function using unit step functions and find its
Laplace transform (15%)
2 if 0<t<1
f(t) = 0.5t^2 if 1<t<0.5π
sint if t>0.5π
2.determine the solution of the system of linear algebraic equations by (15%)
w+2x+y=6
-3w-10x+y+2z=2
4w-7x+8y-5y=2
-x-2y+z=2
3.solve for y(t) from the simultaneous equations (15%)
t t
y(t) + ∫y(τ)cosh(t-τ)dτ = t+e
0
4.find the inverse matrix of the following matrix (15%)
┌ 1 0 3 ┐
│ 0 2 4 │
└ 3 0 5 ┘
5.find the output voltage response in fig.1 if R=20Ω,L=1H,C=10^-3F,
the input is δ(t-2) (a unit impulse response at time t = 2),
and current and charge are zeros at time t = 0 (15%)
δ(t)
┌────○ ○────┐
│ │
│ │
│ │
＞ Ｓ
＜ Ｓ
＞ Ｓ
＜ R Ｓ L
＞ C Ｓ
＜ Ｓ
│ │ │ │
A ●─────┤ ├─────● B
│ │ │ │
│ │
│ │
└────○ ○────┘
v(t)=?
fig.1
6.if A=[ 1 2 3 4 ], B=[ w x y z ]
find
T T T T
(a) A B (b) AB (c) B A (d) BA (15%)
7. find the value of k that makes the dterminant zero (10%)
│ 1 k k+5 k-3 100 │
│ 0 k k-3 k+5 100 │
│ 0 0 k+5 k-3 100 │ = 0
│ 0 0 0 k-3 k+5 │
│ 0 0 0 0 100 │
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