107年 - 107 國立中山大學_碩士班招生考試_資工系(乙組)：工程數學#105785

科目：中山◆資工◆工程數學 | 年份：107年 | 選擇題數：0 | 申論題數：9

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所屬科目：中山◆資工◆工程數學

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申論題 (9)

1.The Laplace Transform of f(t) is F(s) (i.e., L[f(t)] = F(s)). Assume that

When s= 3,
Please find A+B+C+D=?
《Hint:L[th(t)]・L[g(t))]=L[f(t)g(t)]》

2. Given one logical circuit (as shown in Figure 1) and the corresponding truth table is provided
in Table 1 as well. We assume the initial state of clk signal is 1. In addition, one value will be
assigned to input D every one clock cycle. The output of this circuit is Q and Q' and the input
sequence of D input is

3.1 Please solve the initial value problems.

3.2 Please verify your answer by using Laplace transformation.

4. Please find the Fourier series of the function f(x) = cos³ 2x+sin⁵ x.

5.1 Please find the eigenvalues and the corresponding eigenvector of the matrix A.

5.2 Find matrix P that makes matrix A diagonal.

5.3 Are the both dragonized as well? If yes, please prove your reason.

6. Let matrix . Please decompose the A by using SVD decomposition.