104年 - 104 國立嘉義大學_碩士班招生考試試題_土木與水資源工程學系：工程數學#146477

 1.Solve the following ordinary differential equation. (20%)

(a) by using the associated scalar potential , (10%).

(b) by evaluation of the line integral along thestraight-line path between P₁ and P₂, (5%).

(c) find another path to show path independence of theline integral. (5%)

3. Find the eigenvalue and eigenvector of the matrix (20%)

4. Solve the initial-value problem by the Laplacetransformation.(20%)
， ，

5. Find all unit vectors in the plane orthogonal to . (20%)