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.

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.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.4: Ordered Integral Domains

Problem 5E: 5. Prove that the equation has no solution in an ordered integral domain.

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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.

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