Evaluate (y - x - 3ix²) dz, where C' is the contour joining 0 and 1 + i in the following manners: (a) C is the straight line from 0 to 1 + i. (b) C is the straight line from 0 to i and then the straight line from i to 1+i. (c) C is the parabola y = r². 2² dz, where C'is the contour joining 0 and 1+i in the following Evaluate manners: (a) C is the straight line from 0 to 1 + i. (b) C is the straight line from 0 to i and then the straight line from i to 1 + i. (c) C is the parabola y = 1². 23 ·1+i dz Evaluate *** 2² dz using the formula [²²α = ²3²₁ What is your observation from the answers to questions 1, 2 and 3? From this observation, can you directly argue why 2² dz should be 0 for any closed contour C? Can you find any function other than f(z) = z² that can produce the same result? What kind of functions produce such result?
Evaluate (y - x - 3ix²) dz, where C' is the contour joining 0 and 1 + i in the following manners: (a) C is the straight line from 0 to 1 + i. (b) C is the straight line from 0 to i and then the straight line from i to 1+i. (c) C is the parabola y = r². 2² dz, where C'is the contour joining 0 and 1+i in the following Evaluate manners: (a) C is the straight line from 0 to 1 + i. (b) C is the straight line from 0 to i and then the straight line from i to 1 + i. (c) C is the parabola y = 1². 23 ·1+i dz Evaluate *** 2² dz using the formula [²²α = ²3²₁ What is your observation from the answers to questions 1, 2 and 3? From this observation, can you directly argue why 2² dz should be 0 for any closed contour C? Can you find any function other than f(z) = z² that can produce the same result? What kind of functions produce such result?
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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Question
Solve only 4 no.
Transcribed Image Text:1. Evaluate [(y - z -3i2²) dz, where C' is the contour joining 0 and 1 + i in
the following manners:
(a) C is the straight line from 0 to 1 + i.
(b) C is the straight line from 0 to i and then the straight line from i to 1+i.
(c) C is the parabola y = r².
√²
[2² dz, where C' is the contour joining 0 and 1 + i in the following
2. Evaluate
manners:
(a) C is the straight line from 0 to 1 + i.
(b) C is the straight line from 0 to i and then the straight line from i to 1+i.
(c) C is the parabola y = r².
·1+i
6.² z² dz using the formula
3. Evaluate
·√²
2² dz
=
23
3
4. What is your observation from the answers to questions 1, 2 and 3? From this
observation, can you directly argue why 2²
2² dz should be 0 for any closed
contour C? Can you find any function other than ƒ(z) = z² that can produce
the same result? What kind of functions produce such result?
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