102年 - 102 國立中山大學_碩士班招生考試_資工系(乙組)：工程數學#105883

科目：中山◆資工◆工程數學 | 年份：102年 | 選擇題數：0 | 申論題數：11

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所屬科目：中山◆資工◆工程數學

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申論題 (11)

1. Solve the Differential Equation:

(Hint: Is this an exact differential equation?)

(a) (12%) Solve the following differential equation by Laplace Transform and Inverse Laplace Transform

(b) Let f(i)=t and g(t)=cos t. Find the convolution of fand g (i.e., f*g)

(a) Given

(b) Solve the following linear system by using Gauss-Jordon elimination:

Please show step-by-step operations; otherwise, no points will be given.

(c) Find Rank(A),

(d) Find matrix A representing the linear transformation that maps (x₁, x₂) onto (2x₁-5x₂, 3x₁+4x₂)

(a) Give a matrix A representing the state transition probabilities.

(b) At the end of the second cycle, what is the probability that the FSM is in state S1? What is the probability that the FSM is in state S2?

(c) At the end of the 1000th cycle, what is the probability that the FSM is in state S1? What is the probability that the FSM is in state S2? (Hint: You need to convert A to a diagonal matrix)

5. Fourier Series Find the Fourier series of the function , andf(x+4)=f(x).