課程名稱︰工程數學一
課程性質︰必修
課程教師︰邱文英 教授
開課學院：工學院
開課系所︰化工系
考試日期（年月日）︰2010/1/15
考試時限（分鐘）：110分鐘
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
Engineering Mathematics Final Exam
Teacher: Wen-Yen Chiu
Date:2010/01/15
1.(10%) Determine whether lnx processes a Taylor series about x=1, and
find the convergence interval.
2.(10%) Determine the radius of convergence
∞
Σ[(2m!)/m^2]x^m
m=1
3.(15%) Is the corresponding point to the equatino an ordinary point?
a regular singular point? or an irregular singular point?
(a) y"-xy'+2y = 0 at x=0
(b) (x^2-4)y"+y = 0 at x=2
(c) x^2y"+2y'+xy = 0 at x=0
4.(30%) Find a power series solution
(a) y"+3xy'+2y=0 ; y(0)=1,y'(0)=1
(b) y"-(x-2)y'+2y=0 ; y(2)=1,y(2)=-1
(c) (x^2+4)y"+xy=x+2 ; y(0)=1,y'(0)=2
5.(15%) Find a power series solution near x=0
xy"+(x-1)y'-y=0
6.(20%)
(a) Find a power series solution near x=0
xy"+(1-x)y'-y=0
(b) Explain how you find out the solution for s=s2 in part (a)
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