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
-Y2Y ~ ' = ~ 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=1n2
(
23z - )' , for the curve C is the circle of 7. Please calculate
- ,jiz