所屬科目：研究所、轉學考(插大)-應用數學
(a) Find the general solution of by solving the eigenvalues and the corresponding eigenvectors. (10%)
3.Find the steady-state temperature T(x,y) in the thin rectangle plate 0≦xs≦ 10, 0≦y≦20 by solving the Laplace equation. The upper side of the rectangle is kept at u(x) ℃, the lower side is kept at 0℃, and the other two sides are perfectly insulated. Perfectly insulated means no temperature change across the boundary. (20%)
4.Find the Fourier transform of ； otherwise, f(x) =0.(10%)
5. Show thatby Fourier integral of f(x) = 1, if Ixl ＜π, f(x) = 0, if lxl ＞π.(8%)
6.Find all roots of i.(8%)
7.Evalute the integrate by finding the residues. (12%)
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by solving the eigenvalues and the corresponding eigenvectors. (10%) 
. The upper side of the rectangle is kept at u(x) ℃, the lower side is kept at 0℃, and the other two sides are perfectly insulated. Perfectly insulated means no temperature change across the boundary. (20%)
； otherwise, f(x) =0.(10%)
by Fourier integral of f(x) = 1, if Ixl ＜π, f(x) = 0, if lxl ＞π.(8%)
i.(8%)
by finding the residues. (12%)