作者XX9 ( 佛曰: ....)
看板FCUProblems
标题[考古] 工程数学/廖时三/95下期末考
时间Fri Jan 16 20:37:27 2009
※ [本文转录自 FCU_Talk 看板]
作者: realkirin (Kirin) 看板: FCU_Talk
标题: [考题][工程数学][廖时三]
时间: Sun Jul 8 11:01:34 2007
[工程数学][廖时三][通讯系][95下期末考]
1.) Find the indicial equation and recurrence relation of the following
differential equation:
x^2+y''+x^2y'-2y=0 (20%)
2.) Find all of the singular points and classify each singular point as
regular or irregular
[(9-x^2)y']'+(2+x^2)y=0 (20%)
3.) Suppose f(x)=0,-pi<x<0
1,0<x<pi
find its Fourier series expansion and show that
pi 1 1 1
- =1-(-)+(-)-(-)+... (20%)
4 3 5 7
4.) Assume f(x)=e^-x in [-pi,pi] and f(x+2pi)=f(x), find its complex
Fourier series expansion? (20%)
5.) Assume f(x)=e^-x in [-pi,pi],
find its Fourier cosine series expansion? (20%)
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