1. Let Cbe the right-hand semicircle with radius 2 centered at z= 0 given by the parametrization z() = 2e", for -<15. Evaluate the contour integral z dz Withont oreiuesi

Advanced Engineering Mathematics
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Question 1
1.
Let Cbe the right-hand semicircle with radius 2 centered at z=0 given by the
parametrization z(t)= 2e",
, for-Is Evaluate the contour integral
z dz
2.
Without evaluating the integral, show that
z+4
dz=
+1
2i
where C is the arc of the circle z=2 from
z= 2 to z 2i that lies in the first quadrant.
3.
By finding an antiderivative, evaluate the integral, where the contour is
between the indicated limits of integration:
any path
2i
(i+z)° dz
4.
Let C denote the positively oriented circle z-i=2. Evaluate the integral:
dz
+4
C
5.
Let C denote the positively oriented circle z- 1= 3. Evaluate the integral:
z +2z
dz
Transcribed Image Text:1. Let Cbe the right-hand semicircle with radius 2 centered at z=0 given by the parametrization z(t)= 2e", , for-Is Evaluate the contour integral z dz 2. Without evaluating the integral, show that z+4 dz= +1 2i where C is the arc of the circle z=2 from z= 2 to z 2i that lies in the first quadrant. 3. By finding an antiderivative, evaluate the integral, where the contour is between the indicated limits of integration: any path 2i (i+z)° dz 4. Let C denote the positively oriented circle z-i=2. Evaluate the integral: dz +4 C 5. Let C denote the positively oriented circle z- 1= 3. Evaluate the integral: z +2z dz
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