105年 - 105 國立嘉義大學_碩士班招生考試試題_電機工程學系：工程數學#147200

1. Solve the following systems of equations using Cramer's Rule. (10%)

2. Determine whether the vector, (−3, 3, 7), is a linear combination of the other vectors (1, −1, 2), (2, 1, 0), (−1, 2, 1). If it is, solve for the coefficients of the linear combination. (15%)

(A) Find the Laplace transform of the periodic function f(t) given in Fig. 1. (5%)

(B) Find the inverse Laplace transform of . (5%)

6. Solve . (10%)

7. Calculate the output voltage vo(t) of series RC circuit shown in Fig. 2 if the initial current i(0) = 0. Assume the switch is at “n₂” node from 2 to 3 sec and at “n₁” node for the rest of the time. (Let V₀ = 10 V, R = 2.5 × 10⁵ Ω, and C = 10⁻⁶ pF) (10%)

8. Find the Fourier series of the periodic function f(t) given in Fig. 3. (10%)

9. Solve the given differential equation . (10%)