[試題] 101上 蕭浩明 工程數學 第二次期中考

[youngluke (luke)]

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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