101年 - 101 國立中山大學_碩士班招生考試_資工系(乙組)：工程數學#105910

科目：中山◆資工◆工程數學 | 年份：101年 | 選擇題數：0 | 申論題數：10

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所屬科目：中山◆資工◆工程數學

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申論題 (10)

1. Please find the solution of y for the first order differential equation.

2. Please find the particular solution of y for the second order differential equation.

3.1 In the integral expression for a ax above, the integrand and the limits define the signal xt). Determine an equation for x(t) that is valid over one period.

3.2 Using the result from (3.1), draw a plot of x() over the range -8 ≤ t ≤ 8 seconds. Label your plot carefully.

3.3 Determine the DC value of x(t).

4.1 Find the DC value ao and other Fourier coefficients for k≠ 0 in the Fourier series representation of x(t).

4.2 Define a new signal as y(t)=2x(t-T₀/2). Use the time shifting property to write down the Fourier series coefficient bo and bx for k * O for the periodic signal y(t) without evaluating any integrals.

5. Find the inverse Laplace transform of

6. 6.1 Find the LU-factorization of the matrix

6.2 Use the result of 6.1 to solve