Let : C→C be the function defined by ƒ(z) = z and let C be the closed anticlockwise contour whose points lie on the circle {z € C: |z| = 2}. (a) Calculate [ƒ(2) dz. (b) Using part (a), explain why f cannot have an antiderivative on C.

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
Let : C→C be the function defined by
ƒ(z) = z
and let C be the closed anticlockwise contour whose points lie on the circle {z € C:
|z| = 2}.
(a) Calculate [ f(2)
f(z) dz.
(b) Using part (a), explain why ƒ cannot have an antiderivative on C.
Transcribed Image Text:Let : C→C be the function defined by ƒ(z) = z and let C be the closed anticlockwise contour whose points lie on the circle {z € C: |z| = 2}. (a) Calculate [ f(2) f(z) dz. (b) Using part (a), explain why ƒ cannot have an antiderivative on C.
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Similar questions
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,