[考古] 工程數學/廖時三/95下期末考

[XX9 ( 佛曰: ....)]

※ [本文轉錄自 FCU_Talk 看板]

作者: realkirin (Kirin) 看板: FCU_Talk
標題: [考題][工程數學][廖時三]
時間: Sun Jul  8 11:01:34 2007

[工程數學][廖時三][通訊系][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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