6) (④) f Z=1 f(2)-22-132-1) sangle single 2) 렇 2Tif(20) 2Tif (2) 32-1 f(x)= /3(일) 1 = 2 . . 2Ti(2) = 4: f(2), f(2)=_1 ③ 8 (2), 9(2) =11 == 32-1 22-1 2Tif (20) 2Tif (1) .. 2Ti (-3)=-62 −3 -3 2(5) -1 9(3) 2751 A+B = 4Ti+ F6ⅲ) = -2 L
6) (④) f Z=1 f(2)-22-132-1) sangle single 2) 렇 2Tif(20) 2Tif (2) 32-1 f(x)= /3(일) 1 = 2 . . 2Ti(2) = 4: f(2), f(2)=_1 ③ 8 (2), 9(2) =11 == 32-1 22-1 2Tif (20) 2Tif (1) .. 2Ti (-3)=-62 −3 -3 2(5) -1 9(3) 2751 A+B = 4Ti+ F6ⅲ) = -2 L
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
For q5.b). The answer on the mark scheme is minus phi I. But when I did it I got -2 phi I. Where did I go wrong. The mark scheme is unclear.
Transcribed Image Text:14.1321
1212호
그리
1
2
2
2
(2iti)/ it + (2it D) t
추ㅊ
(2² +1)/ i- i + 2) -~)
11:우리는 이
리실
6 6
8
É2+1) (1) + (-2c+1)10) 2 소
2
f(2)=2
g(2) 1 (2) =
32-1/
>
(A) 6 f(z); f(2)= 1
32-1
f(x)= 1/3(일) 1 = 2
(22-1)(32-1)
1
22-1
9 (33)
2(5) -1
A+le = 4개(+ (6) = -21L
we Z.
D
poles ④
12-1
2Tif(20) 2Tif (2)
21:(2) = 41
2Tif(20) Tif (4)
-3 : 2Ti (-3)=-6Ti
NNGREP
121
single Single
22
![Al
on the circle C defined by |z + 1 = 1/2.
5. Consider the function
f(z) =
1
(2z - 1)(3z - 1)
[6]
(a) Write down all possible Laurent series of the function about the point 0,
indicating their ring of convergence.
[6]
(b) Use Cauchy's integral formula to compute the integral along a positively
oriented square with vertices {1, i,-1,-i}.
[6]
(c) What would the value of the integral be if the integration contour was a
negatively oriented rectangle with vertices {-i, i, -i - 1, i - 1}? Why?
[3]
Page 4 of 5](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F12d366b4-7e59-4d81-8f2b-965d1a83d6f8%2F01bb72ca-a03e-45d6-a77a-1f74a57009b9%2Fzda7tbc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Al
on the circle C defined by |z + 1 = 1/2.
5. Consider the function
f(z) =
1
(2z - 1)(3z - 1)
[6]
(a) Write down all possible Laurent series of the function about the point 0,
indicating their ring of convergence.
[6]
(b) Use Cauchy's integral formula to compute the integral along a positively
oriented square with vertices {1, i,-1,-i}.
[6]
(c) What would the value of the integral be if the integration contour was a
negatively oriented rectangle with vertices {-i, i, -i - 1, i - 1}? Why?
[3]
Page 4 of 5
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