作者pattrick (派特瑞克)
看板NTU-Exam
标题[试题] 96下 王昭男 工程数学二 1st期中考
时间Tue May 20 20:41:02 2008
课程名称︰工程数学二
课程性质︰必修
课程教师︰王昭男/谢传璋
开课学院:工学院
开课系所︰工程科学与海洋工程学系
考试日期(年月日)︰2008/4/7
考试时限(分钟):120
是否需发放奖励金:是
(如未明确表示,则不予发放)
试题 :
工程数学(二) 期中考一
┌-2 2 -3┐
1.Find the eigen values and eigen vectors of matrix A = │ 2 1 -6│
└-1 -2 0┘
and then diagonalize it. (20%)
2.Find out what type of conic section the following quadratic form represents
and transform it to principal axes: (15%)
2 2
Q = 4x1 +12x1x2 +13x2 = 16
3 2 ┌2 2┐
3.If p(x) = x - 2x +3x +1 and A = │ │ , find p(A) (15%)
└2 -1┘
4
4.Find the fourier series of f(x) = cos x (15%)
2 if |x|<1
5.Find the fourier integral of f(x) = and then prove that
0 if |x|>1
∞ cosωxsinω π/2 if 0≦x<1
∫ ───────dω = π/4 if x = 1 (15%)
0 ω 0 if x > 1
6.Find the fourier series of f(x) = x^2 , -1<x<1, f(x+2) = f(x)
2
π 1 1 1 1
and prove that ─ = 1 - ─ + ─ - ─ + ─ - ..... (20%)
12 4 9 16 25
hint :∫p(x)f(x)dx = p(x)F1(x) - p'(x)F2(x) + p''(x)F3(x) -
m (m)
+...(-1) p (x) Fm+1(x)
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