1. Determine the domain of analyticity for the following functions, and conclude that ƒ ƒ(2)dz - O where C is the circle a-1 with positive orientation (counter-clockwise). (A)/(x)- (b)(a)- (c) f(z) - tanz (d) f(z) = Ln(+5) 2. Show that 'dz - 21, where C is the square with vertices 1±1,-1±1 with positive orientation. 3. Show that √(422-4x+5)-³dz = 0 where C is the unit circle [2] - 1 with positive orientation. 4. Find feed for the following contours: (a) The circle |-1-2 with positive orientation. (b) The circle | -1] -with positive orientation. 5. Find fd for the following contours: (a) The circle -2 with positive orientation. (b) The cirlce with positive orientation. 6. Evaluate fdz, where C is the "figure-eight" contour shown. コ The "pure eight co 9. Evaluate fods for the contours given in the following figures. C
1. Determine the domain of analyticity for the following functions, and conclude that ƒ ƒ(2)dz - O where C is the circle a-1 with positive orientation (counter-clockwise). (A)/(x)- (b)(a)- (c) f(z) - tanz (d) f(z) = Ln(+5) 2. Show that 'dz - 21, where C is the square with vertices 1±1,-1±1 with positive orientation. 3. Show that √(422-4x+5)-³dz = 0 where C is the unit circle [2] - 1 with positive orientation. 4. Find feed for the following contours: (a) The circle |-1-2 with positive orientation. (b) The circle | -1] -with positive orientation. 5. Find fd for the following contours: (a) The circle -2 with positive orientation. (b) The cirlce with positive orientation. 6. Evaluate fdz, where C is the "figure-eight" contour shown. コ The "pure eight co 9. Evaluate fods for the contours given in the following figures. C
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![1. Determine the domain of analyticity for the following functions, and conclude that ƒ ƒ(2)dz -
O where C is the circle a-1 with positive orientation (counter-clockwise).
(A)/(x)-
(b)(a)-
(c) f(z) - tanz
(d) f(z) = Ln(+5)
2. Show that 'dz - 21, where C is the square with vertices 1±1,-1±1 with positive
orientation.
3. Show that √(422-4x+5)-³dz = 0 where C is the unit circle [2] - 1 with positive
orientation.
4. Find feed for the following contours:
(a) The circle |-1-2 with positive orientation.
(b) The circle | -1] -with positive orientation.
5. Find fd for the following contours:
(a) The circle -2 with positive orientation.
(b) The cirlce
with positive orientation.
6. Evaluate fdz, where C is the "figure-eight" contour shown.
コ
The "pure eight co
9. Evaluate fods for the contours given in the following figures.
C](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F155158b7-b900-47c4-a397-fbe9c98c96ca%2Faaa0e3d0-36af-4807-9f78-e70c5efb2e4a%2Fap1gn5ab_processed.png&w=3840&q=75)
Transcribed Image Text:1. Determine the domain of analyticity for the following functions, and conclude that ƒ ƒ(2)dz -
O where C is the circle a-1 with positive orientation (counter-clockwise).
(A)/(x)-
(b)(a)-
(c) f(z) - tanz
(d) f(z) = Ln(+5)
2. Show that 'dz - 21, where C is the square with vertices 1±1,-1±1 with positive
orientation.
3. Show that √(422-4x+5)-³dz = 0 where C is the unit circle [2] - 1 with positive
orientation.
4. Find feed for the following contours:
(a) The circle |-1-2 with positive orientation.
(b) The circle | -1] -with positive orientation.
5. Find fd for the following contours:
(a) The circle -2 with positive orientation.
(b) The cirlce
with positive orientation.
6. Evaluate fdz, where C is the "figure-eight" contour shown.
コ
The "pure eight co
9. Evaluate fods for the contours given in the following figures.
C
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