作者hellersjoke (heller)
看板NTU-Exam
標題[試題] 101上 李克強 工程數學一 期中考II
時間Fri Dec 7 16:02:09 2012
課程名稱︰工程數學一
課程性質︰必修
課程教師︰李克強
開課學院：工學院
開課系所︰化學工程學系
考試日期（年月日）︰101/12/07
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 :
(一) Find the inverse Laplace Transform of each of the following functions:
(5%) (a) 1 / ( s^2 - 3s + 2 )
(5%) (b) exp( -s ) / ( s + 1 )
(5%) (c) ( 3s + 1 ) / ( s + 1 )( s + 2 )( s + 3 )
(5%) (d) [ 1 - exp( -s )] / s
(15%) (e) 1 / ( s^2 - 1 )^3
(二) (15%) Solve the following problem by the use of Laplace transforms:
y" + 2 y' + 2 y = δ(t-1) , y(0) = 1 , y'(0) = -1
(三) (15%) Use the method of Laplace transforms to obtain the solution of the
simultaneous equations
x' + y' + x = -exp( -t ) ,
x' + 2 y' + 2 x + 2 y = 0 ,
which satisfies the initial conditions x(0) = -1 , y(0) = 1 .
(四) (35%) Find the power series solution around x0 = 0 for the following
ordinary differential equation:
y" - ( x - 3 ) y = 0 .
Get the first
three nonzero terms in each of the
two linearly
independent solutions.
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