作者virgonelson (夏天来了)
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标题[试题] 96下 李克强 工程数学二 期中考
时间Mon Apr 21 09:02:40 2008
课程名称︰工程数学二
课程性质︰必修
课程教师︰李克强
开课学院：理
开课系所︰化工系
考试日期（年月日）︰97/4/1 & 97/4/8 两周
考试时限（分钟）：各50分钟
是否需发放奖励金：是
（如未明确表示，则不予发放）
试题 :
97/4/1
1.
(a) Find the eigenfunctions ψn(x) of the problem: (30%)
y"+λy=0 , y'(0)=0 , y'(1)=0
(b) Find the eigenfunction expansion Σanψn(x) of the function f(x)=x ,0≦x≦1
Calculate the first three coefficients a0 , a1 , a2. (30%)
2. Find the eigenfunctions and the determinantal equations satisfied by the
nonzero eigenvalues of the eigen-problem: (40%)
y"+λy=0 , y(0)-y'(0)=0 , y(1)+y'(1)=0
97/4/8
1. Find the Fourier Series corresponding to the given function: (50%)
f(x)=x , -1≦x＜1 ; f(x+2)=f(x)
2. Find the Fourier Series for the function: (50%)
0, -π ≦x＜ -π/2
f(x)= { 1, -π/2 ≦x＜ π/2
2, π/2 ≦x＜ π
Assume that the function is periodically extended outside the original
interval.
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