中原大學九十三學年度博士班入學招生考試
93年6月9日8:30~10:00　土木工程學系　 誠實是我們珍視的美德，
我們喜愛「拒絕作弊，堅守正直」的你！
科目：工程數學  
□可使用計算機，惟僅限不具可程式及多重記憶者 □不可使用計算機
1. Express (i) the mathematical Meaning and (ii) the physical meaning of the divergence theorem
(10%)
   
2. Derive the curl theorem by using the divergence theorem (15%)
Hint. Set where is a constant vector
   
3. Integrate (i) along the path , and (ii) along the path as shown in the figure.

 
   
4. Solve the differential equation

where is the Dirac Delta Function (15%)
   
5. For
(1) Find the eigenvalues of A (5%)
(2) Find the eigenvectors of A (10%)
(3) Diagonalize A (10%)
   
6. Consider a partial differential equation
………………………….(1)
p , q , s are constants
(a) If , equation (1) is called a ________equation (2%)
(b) If equation (1) is called a ________equation (2%)
(c) If equation (1) is called a _________equation (2%)
(d) If
B.C.
　　
　　
I.C.
　　

Find the solution of (19%)
   
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