課程名稱︰工程數學二
課程性質︰土木系必修
課程教師︰楊德良
開課學院：工學院
開課系所︰土木系
考試日期︰2011年09月02日
考試時限：180分鐘，09:10-12:10
是否需發放獎勵金：是
試題 :
Engineering Mathematics II
2011/9/2
9:10 - 12:10
professor DL Young
2nd Mid-Term Exam
2011 Summer session II
Each problem has 15% with a total of 105
1. Solve x' = ┌ -1 -2 ┐x + ┌ 3 ┐ subject to x(0) = ┌ -4 ┐
└ 3 4 ┘ └ 5 ┘ └ 5 ┘
by the method of eigenvalues and eigenvectors only.
dx
2. Solve ---- = 2x + 8y , x(0) = 2
dt
dy
---- = -x - 2y , y(0) = -1
dt
3. Find (a) L^(-1) {(s^2 - k^2)/(s^2 +k^2)^2 } (b) L^(-1) {e^(-s)/s(s+1)}
4. Solve y''+y =δ(t-2π) with y(0)=0 , y'(0)=1
5. (a) Solve ty'' +y' +ty =0 with y(0)=1 ,y'(0)=0
(b) use (a) to show that L{J_0 (t)} = (s^2 + 1)^(-1/2)
(Hint: lim sF(s) = f(0) )
s→∞
6. Solve y''+4y=0 with y(0) = 1, y(π/4) = 2
by using method of power series solution
2 2
7. Solve 9x y'' + 9x y' + 2y = 0
by using method of power series solution
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