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x cosy) (10%) 2. Solve y " + 4 y ' - 2 y - 2 ~ 2 + 3 x - 6 = O (1 0%) 3. Three points in space: A

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(1)

1. Solve y'

=

sin yI(2 y

-

x cosy) (10%) 2. Solve y " + 4 y ' - 2 y - 2 ~ 2 + 3 x - 6 = O (1 0%) 3. Three points in space: A

=

(1, -2, 6), B

=

(3,0, l), C

=

(4,2,4). Use the

principles of vector to find the cosine of the angle between a and the

line from the point A to the midpoint of BC. (1 5%)

4.

Use the matrix method to solve the following simultaneous equations.

x , + 3 xz-2x3

=

-7

5. Please find the general solution of the system y , ' = -Y,

y2'= 2Yl

-Y2

Y ~ ' = ~ Y I +3Y2 -Y3

6 . (6a) please find the Fourier series of periodic function (1 6%)

(6b) Please use the result of (6a) to evaluate 21 and 2-

n=l

n

11=1

n2

(

2

3z - )' , for the curve C is the circle of 7. Please calculate

- ,jiz

- 6 1

radius

-

about

-

3i 2

8. Please find the roots of 1 - i

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