所屬科目：研究所、轉學考(插大)◆工程數學
(a) Find the inverse Laplace transform of . (6%)
(b) Solve for f(t) in . (8%)
2. (a) Find the Fourier series of (10%).
(b) Use the Fourier series obtained in 2(a) to find =? (6%)
3. Show that the given complex function is analytic in an appropriate domain.(10%)
4. Evaluate the integral along the indicated contour C: |z| = 2. (10%)
5. Solve the differential equation as follows. (10%).
6. Solve the differential equation as follows. (10%), where and .
7. Find the corresponding eigenvalue and eigenvector of the matrix. (10%)
8. Solve the wave equation , 0<x<L, t>0 subject to the given conditions ,u(0,t)=0,u(L,t)=0 ,t>0,and u(x,0)=x(L-x), ,0<x<L .(10%)
(a) The Stokes’s theorem,
(b) Hermitian matrix.
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. (6%)
. (8%)
(10%).
=? (6%)
is analytic in an appropriate domain.(10%)
along the indicated contour C: |z| = 2. (10%)
, where 
and 
.
, 0<x<L, t>0 subject to the given conditions ,u(0,t)=0,u(L,t)=0 ,t>0,and u(x,0)=x(L-x),
,0<x<L .(10%)