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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 

選擇:0題,非選:9題 我要補題 回報試卷錯誤
【非選題】
1.

1.The Laplace Transform of f(t) is F(s) (i.e., L[f(t)] = F(s)). Assume that
61e11d81c9ae9.jpg
When s= 3,61e11da590803.jpg
Please find A+B+C+D=?
《Hint:L[th(t)]・L[61e11de8a39da.jpgg(t))]=L[f(t)g(t)]》



【非選題】
2.2. 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
61e11e883d059.jpg61e11e959a7c9.jpg


【非選題】
3.

3. One differential equation y" +3y'+2y=61e11ecaacf85.jpg as y(0)=0 and y'(0)=1.


【題組】3.1 Please solve the initial value problems.


【非選題】
4.【題組】3.2 Please verify your answer by using Laplace transformation.

【非選題】
5.4. Please find the Fourier series of the function f(x) = cos3 2x+sin5 x.

【非選題】
6.

5. Let matrix 61e11f082eb57.jpg


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


【非選題】
7.【題組】5.2 Find matrix P that makes matrix A diagonal.

【非選題】
8.【題組】

5.3 Are the 61e11f2989dea.jpgboth dragonized as well? If yes, please prove your reason.



【非選題】
9.

6. Let matrix 61e11f4179e2d.jpg . Please decompose the A by using SVD decomposition.



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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-阿摩線上測驗

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