[試題] 96下 李克強 工程數學二 期中考
課程名稱︰工程數學二
課程性質︰必修
課程教師︰李克強
開課學院：理
開課系所︰化工系
考試日期（年月日）︰97/4/1 & 97/4/8 兩週
考試時限（分鐘）：各50分鐘
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
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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