私立中原大學八十八學年度博士班招生考試命題紙

所組別： 電機工程學系博士班 科目： 工程數學 考試時間： 06月09日第 1節

　

    1. For a matrix A , with eigenvalues 1,1,and -3.Find the matrix P to let PAP=D,where D is a diagonal matrix. And (15%)

      　　　

    2. With the same matrix as in problem 1,solve the system X'=AX, Where X is a function of t.(10%)

    3. If matrix is an orthogonal matrix, then write the necessary relationships amont a,b,c,d. (15%)

    4. Solve Y''+2tY'-4Y=1;Y(0)=Y'(0)=0.Where Y is a function of t

      5. (Hint:) (20%)

    5. Prove:,for (15%)

    6. Let f(t) be a function having Fourier transform F(w).Write F(w)=R(w)+iX(w). Show that R(w) is an even function and X(w) is an odd function. (10%)

    7. Evaluate 　if　　for　.(15%)

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