私立中原大學八十八學年度研究所招生考試命題紙
| 所組別 : | 電子工程學系丙組
| 科目 : | 工程數學
| 考試時間 : | 05月01日第2節
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@Please underline your final answer.
- (10%)Find values of a and b so that the following matrix is orthogonal:
- (10%)Consider the lot of 20 defective and 80 non-defective items form which we choose two items without replacement. What is the probability that the second chosen item is defective?
- (20%)Solve the initial value problem
for y(x).
- (20%)Suppose we wish to construct a tin can in the shape of a cylinder. Let the radius of the circle be r and the height of the cylinder be h, such that the volume is a prescribed value V.The base is to be twice as thick as other sides so its cost per unit area 2r,where r is the cost per unit area of the other sides. Find the
expressions of r and h in terms of V to minimize the material cost subject to volume constraint.
- (20%)Evaluate
zdz,where the contour is the circle 
=2.
- (20%)Use the result that the Fourier tranform of
is 
to solve the following boundary value program:
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