2. Use Cauchy's residue theorem (Sec. 76) to evaluate the integral of each of these functions around the circle |z| = 3 in the positive sense: exp(-z) (a) (b) z² exp(-z) (z − 1)2; (c) z² exp P(²); (d) z+1 z² - 2z Ans. (a) -2лi; (b) -2лi/e; (c) лi/3; (d) 2лi.

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

question a 

2. Use Cauchy's residue theorem (Sec. 76) to evaluate the integral of each of these functions
around the circle |z| = 3 in the positive sense:
exp(-z)
(a)
(b)
z²
exp(-z)
(z − 1)2;
(c) z² exp
P(²);
(d)
z+1
z² - 2z
Ans. (a) -2лi;
(b) -2лi/e; (c) лi/3; (d) 2лi.
Transcribed Image Text:2. Use Cauchy's residue theorem (Sec. 76) to evaluate the integral of each of these functions around the circle |z| = 3 in the positive sense: exp(-z) (a) (b) z² exp(-z) (z − 1)2; (c) z² exp P(²); (d) z+1 z² - 2z Ans. (a) -2лi; (b) -2лi/e; (c) лi/3; (d) 2лi.
Expert Solution
steps

Step by step

Solved in 1 steps with 1 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,