110年 - 110 國立中山大學碩士暨碩士專班招生考試_機電系碩士班/乙、丙組:工程數學#104304

科目：研究所、轉學考(插大)◆工程數學 | 年份：110年 | 選擇題數：0 | 申論題數：14

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所屬科目：研究所、轉學考(插大)◆工程數學

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申論題 (14)

1. Find the general solution of the first-order ODE: (2x3 + y3)dx -3xy2 dy = 0.(10%)
(a) Represent it as a vector equation y' = Ay + g. (5%)
(b) Find the eigenvalues and eigenvectors of A. (5%)
(c) Find the general solution of the system. (5%)
(d) Find the particular solution. (5%)
(a) Set up the model. (5%)
(b) Find I1(s) and I2(s). (10%)
(c) Find i1(t) and i2(t).(5%)
(a)(3A -2B)T (5%)
(b)(3A-2B)TaT(5%)

5.Find an cigentagi and pecrform diagonalization on the folowing matri. (10%)
61a479d8e68bb.jpg
 
6. Let a = [4, 7, 0], b= [3,-1, 5], c=[-6,2,0], and d = [1,-2, 8]. Find the angle between a and c. Between b and d. (10%)

7. Calculate this line integral by Stokes's theorem for the given F and C. Assume the Cartesian coordinates to be right-handed and the z-component of the surface normal to be nonnegative. F= [0,z3,0], C the boundary curve of the cylinder x2 + y2= 1, x≧ 0,y ≧ 0， 0 ≦z≦1 (10%)

8. Solve y''+ ω2y = r(t), where 61a47a8e79dd0.jpg-periodic and r(t)=3t2(-π＜t＜π).(10%)