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18mab102t unit 5 tutorial 3a

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SRM Institute of Science and Technology
Kattankulathur
DEPARTMENT OF MEATHEMATICS
18MAB102T ADVANCED CALCULUS &
COMPLEX ANALYSIS
UNIT V Complex Integration
Sl.No.
Tutorial Sheet -3
Answers
Part A
1
Find the residues of
2e
-z
2
Find the residues of at z=ai
2aie
ai
3
Find the residues of
-2
4
Find the residues of
,
5
Find the residues of
1
Part B
6
Using Cauchy’s residues theorem, evaluate where C is a circle │z│=2
4πi
7
Using Cauchy’s residues theorem, evaluate where C is an ellipse
(16/ 5)πi
8
Show that ,(a
2
<1)
9
Evaluate
10
Evaluate
a>│b│

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SRM Institute of Science and Technology Kattankulathur DEPARTMENT OF MEATHEMATICS 18MAB102T ADVANCED CALCULUS & COMPLEX ANALYSIS UNIT –V Complex Integration Sl.No. Tutorial Sheet -3 Part – A Answers 2e-z 1 Find the residues of 2aieai 2 Find the residues of at z=ai -2 3 Find the residues of 4 , Find the residues of 5 1 Find the residues of Part – B 4πi 6 Using Cauchy’s residues theorem, evaluate where C is a circle │z│=2 (16/ 5)πi 7 Using Cauchy’s residues theorem, evaluate 8 ,(a2│b│ where C is an ellipse Co-O ...
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