100年國立暨南大學電機所電子組工程數學線上測驗

5.: If f(x) = x³ + x ; for 0 < x < 2 , we are going to expand f(x) to Cosine series,
Sine series and Fourier series. Choose the correct converges value for different
series?
(A): f(2) = 10 for Sine series
(B): f(2) = 10 for Cosine series
(C): f(2) = 5 for Fourier series
(D): f(−1) = 2 for Sine series
(E): f(−1) = 2 for Fourier series

8.: A differential equation for unknown function y(x)
y´´+ 4y = 0
(1) Find the general solution for y(x) .
(2) Use Laplace Transform Method to find the general solution for y(x) .
(3) Use Power Series Method to find the general solution for y(x) .
(4) Are the answers obtained from (1), (2), and (3) the same?

9.: Find the current i(t) in the RC circuit in the following Figure.
A voltage E(t) is applied. Assume charge and current is zero at t = 0
(Resistance = R , Capacitance = C ) [Use R, C, v₀ , a, b, and t to express the answer]
(1) If applied voltage E(t) = V₀ for t > 0 , Find the current i(t) .
(2) If E(t) = 0 for t < a ( a is positive), and E(t) = V₀ for t > a ; Find the
current i(t) .
(3) If E(t) = V₀ for a < t < b ( a, b are positive) and E(t) = 0 for otherwise; Find
the current i(t) .

模擬測驗