[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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