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| 1. |
The differential equation with initial condition is shown as follows:
| (a) |
Solve by UC method. |
| (b) |
Solve by Laplace transform. |
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| 2. |
Solve the system of differential equation:
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| 3. |
Solve the heat equation
with u(0,t)=u(6,t)=0 for all t
and 
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| 4. |
A circular cone S：z = x2+ y2,
0≦z≦4. 
| (a) |
Find a unit normal vector of the surface S. |
| (b) |
What is the Stoke's curl theorem? |
| (c) |
Verifying Stoke's curl theorem by this circular cone S and  .
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| 5. |
| (a) |
Find all Laurent series of f(z) with center 0. |
| (b) |
Compute  , if C：∣z-1∣=
1 and the integral being taken in the counterclockwise sense around
the path C. |
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