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%)