8.) Consider the contour C in the complex plane consisting of the portion of the unit circle from z = -i to z = 1 followed by the line segment from 1 to 2=2+1. iR 2+1 R Compute the following contour integrals directly by the definition. Then verify your answer by finding an appropriate anti-derivative and eval- uating at the endpoints of the countour. a.) /20 2² dz b.)dz (Your final answer should involve Arctan(1/2) which is equivalent to the usual real-valued version of arctangent.)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question

*Should get the same answer for both the contour integrals computed by the definition and the anti-derivative evaluated at the endpoints of the contour

8.) Consider the contour C in the complex plane consisting of the portion
of the unit circle from z = -i to z = 1 followed by the line segment
from 1 to 2=2+1.
iR
2+1
R
Compute the following contour integrals directly by the definition. Then
verify your answer by finding an appropriate anti-derivative and eval-
uating at the endpoints of the countour.
a.)
/20
2² dz
b.)dz (Your final answer should involve Arctan(1/2) which is
equivalent to the usual real-valued version of arctangent.)
Transcribed Image Text:8.) Consider the contour C in the complex plane consisting of the portion of the unit circle from z = -i to z = 1 followed by the line segment from 1 to 2=2+1. iR 2+1 R Compute the following contour integrals directly by the definition. Then verify your answer by finding an appropriate anti-derivative and eval- uating at the endpoints of the countour. a.) /20 2² dz b.)dz (Your final answer should involve Arctan(1/2) which is equivalent to the usual real-valued version of arctangent.)
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 1 steps with 5 images

Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,