作者hellersjoke (heller)
看板NTU-Exam
标题[试题] 101上 李克强 工程数学一 期中考II
时间Fri Dec 7 16:02:09 2012
课程名称︰工程数学一
课程性质︰必修
课程教师︰李克强
开课学院：工学院
开课系所︰化学工程学系
考试日期（年月日）︰101/12/07
考试时限（分钟）：120
是否需发放奖励金：是
（如未明确表示，则不予发放）
试题 :
(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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