课程名称︰工程数学上 课程性质︰必修 课程教师︰萧浩明 开课学院：工学院 开课系所︰机械系 考试日期（年月日）︰2012/12/10 考试时限（分钟）：110分 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : 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%) 有没有半张考卷和98年完全一样的八卦....... --

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