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課程名稱︰應用數學方法
課程性質︰數學系選修、數學研究所選修、應用數學科學研究所選修
課程教師︰薛克民
開課學院：理學院
開課系所︰數學系
考試日期︰2014年06月19日(四)，15:30-18:00
考試時限：150分鐘
是否需發放獎勵金：是
試題 :
National Taiwan University Spring Semester, 2014
MATH 7421 Method of Applied Mathematics
Final exam.
Date: 15:30-17:30, June 19th, 2014
˙Open books
˙total scores: 100 points
Consider the boundary-value problem
2
d u m du n
ε ----- + x ---- - x u = 0, 0<=x<=1, ε<<1, (1)
dx2 dx
u(0) = α, u(1) = β,
where m in Z, n in Z, α in real, β in real are parameters; α≠β≠0.
(a) (40 points) Assume m = n = 1, use the method of matched asymptotic
expansions to determine the first-order asymptotic solution of (1).
(b) (40 points) Verify your result in (a) by employing WKB theory.
(c) (20 points) More generally, under what conditions on m and n will there be
a boundary later at the origin?
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