首頁 > 線上測驗 > 100年研究所工程數學歷屆試題(工數1)電機所.電子所. 電信所.光電所.通訊所(二年期) > 100年國立高雄第一科技大學光電所工程數學
(1) Show the set {sin x, sin 2x, sin 3x, sin 4x,} is orthogonal on the interval
[−π ,π] .
(2) Is this set of functions complete?, please explain.
Solve the electrical network as shown below.
(1) By applying Kirchhoff’s law, please show the following system of differential
equations that describes the currents i2(t) and i3(t) in the electrical network.
(2) Use the Laplace transform to obtain the currents i1(t) , i2(t) and i3(t) under
the conditions E(t) = 12V, L = 1 h, R = 5Ω , C = 10−2 f, and i1(0) = 0 ,
i3 (0) = 0 .
Solve the differential equation
( y2 cos t − 3t2 y − 3t2 )dt + (2y sin t − t3 + ln y)dy = 0 , y(0) = e .
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