1. Find the Fourier series of the function f(x)=f(x+4) ,if -1<x<1,
f(x)=2-x,if 1<x<3 ; graph f(x). Is the given function even or odd?
20points
2. f(x)=e^(-x) u(x) , g(x)=e^(-2x) u(x), where u(x-a)=1 if x>a , otheswise =0.
∞
Find the convolution f＊g(x)=∫ f(t)g(x-t)dt and its Fourier transform.
0
20points
3. Find the half-range Fourier cosine series of f(x)=x (0<x<2π)
15points
∞ sinω π/2 if 0≦x<1
4. Show that ∫ -------cosxω dω = { π/4 if x=1
0 ω 0 if x>1
15points
5. Find Fourier sine transform of f(x)=e^(-2x)
15points
a^2 u a^2 u
6. Solve one dimensional wave equation ------ = 9------ ,
at^2 ax^2
u(0,t)=u(4,t)=ue(x,0)=0 , u(x,0)=2sin(πx)
25points
a^2 u a^2 u a^2 u
7. Solve ----- + 2-----+ 3----- = 0
ax^2 ay^2 axay
15points
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◆ From: 59.117.117.32
※ 編輯: qaz7788123 來自: 59.117.117.32 (04/18 03:05)
※ 編輯: qaz7788123 來自: 59.117.117.32 (04/18 03:06)
※ 編輯: qaz7788123 來自: 59.117.117.32 (04/18 03:06)