課程名稱︰常微分方程導論
課程性質︰數學系大二必修
課程教師︰林紹雄
開課學院：理學院
開課系所︰數學系
考試日期︰2010年11月30日(二)，14:30-17:20
考試時限：50分鐘
是否需發放獎勵金：是
試題 :
Math 201-24900 (ODE) Quiz No.5 (11/30/2010)
There are problems (A) to (C) with a total of 50 points. Please write down your
computational or proof steps clearly on the answer sheets.
A. (20 points) Consider the function f(t) = 2t*e^(t^2)*cos(e^(t^2)). Does there
exist M > 0 and constant C such that |f(t)| ≦Me^(Ct) as t→∞? Does L[f](s)
exist for s > 0?
B. (10 points) Find the Laplace transform of f(t) = a^[t], where a > 0 is
constant, and [t] is the integer such that [t]≦t＜[t]+1.
2 2
C. (20 points) Apply the Laplace transform to solve a y'' - b y' = -1/2*δ(t)
for all t∈|R, assuming that y(t) satisfies y(-t) = y(t) for t∈|R, and
lim y(t) = 0. a and b are positive constants.
t→∞
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