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Math 401 (Sec. 502)
Spring, 2009
Homework 1 (due January 27)
Q1.
Let
f
(
z
) =
O
(
g
(
z
)) and
F
(
z
) =
O
(
G
(
z
)) as
z
→
0.
(a)
Prove that
f
(
z
)
F
(
z
) =
O
(
g
(
z
)
G
(
z
)).
(b)
Prove that
f
(
z
) +
F
(
z
) =
O
(

g
(
z
)

+

G
(
z
)

).
Q2.
Obtain twoterm expansions for the solutions of the equation (where
0
< ǫ <<
1)
(
z

1)(
z

2)(
z

3) +
ǫ
= 0
.
Q3.
Find the ±rst three terms in the approximate solutions of all the roots
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Unformatted text preview: of these equations (where 0 < ǫ << 1) (a) z 2 + 2 ǫz1 = 0. (b) ǫz 3z + 1 = 0. Q4. Compute the ±rst two terms of all four roots of ǫ 2 z 42 ǫz 3 + z 22 z + 1 = 0 , where 0 < ǫ << 1....
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This note was uploaded on 04/27/2009 for the course MATH 401 taught by Professor Sarkar during the Spring '09 term at Texas A&M.
 Spring '09
 SARKAR
 Math

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