[試題] 101上 蕭浩明 工程數學 第二次期中考
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）︰2012/12/10
考試時限（分鐘）：110分
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1.solve L[(1-cost)/t] (10%)
2.solve L[te^(-2t)sinwt] (10%)
-1 １ １
3. Give that L [—————] = — [2sint-sin2t]
4 2 ６
s + 5s + 4
-πs
-1 e
Find L [———————]
4 2
s(s + 5s + 4) (15%)
4.solve x"+16x=f(t) ;x(0)=0,x'(0)=1
{ f(t)=cos4t 0≦t<π
{ f(t)=0 t≧π
(15%)
5. Use Laplace Transform to solve y"+2y'+y = f(t); y(0) = 0, y'(0) = 0
(15%)
f(t)
1├ ────
│ │ │
│
─┼───┴───┴───┴───┴───┴─ t
│ 1 2 3 4 5
│ │ │
-1├ ──── (15%)
6. Use Laplace Transform to solve the system of differential equation
╭ x'(t) - 4x + y'''(t) = 6sint
┤
╰ x'(t) + 2x - 2y'''(t) = 0
x(0) = 0, y(0) = 0, y'(0) = 0, y"(0) = 0
(15%)
7. Use Taylor Series Method to solve y"- xy' + y = 0
(10%)
8. Find the recurrence formula and general solution near x = -1 for the
differential equation y" + xy' + (2x-1)y = 0
(15%)
有沒有半張考卷和98年完全一樣的八卦.......
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