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. Complex Integration . Cauchy's theorem and consequences of the theorem . Cauchy Integral formula, Residue theorem 1 Questions 1. Evaluate (² + 1)²dz along the arc of the cycloid x = a(0 sin 0), y = a(1- cos 0) from the point where 1 0 ≤0 ≤2T 2. Evaluate: ²dz + z²dž along the curve C defined by z² +2zz+z² = (2-2i)z+(2+2i) z from the point z = 1 to z=2+2i 1 2πi 3. Evaluate: dz if t> 0 and C is the circle |z| = 3 fcd 2z² +5 4. Evaluate: fc (z+2)³(z² + 4)z² dz where C is the square with vertices at 1+1, 2+1, 2+2i, 1+2i 2 5. Expand f(z) = Z (z-1)(z-2) in a Laurent series valid for 0 < |z-2| < 1 B

. Complex Integration . Cauchy's theorem and consequences of the theorem . Cauchy Integral formula, Residue theorem 1 Questions 1. Evaluate (² + 1)²dz along the arc of the cycloid x = a(0 sin 0), y = a(1- cos 0) from the point where 1 0 ≤0 ≤2T 2. Evaluate: ²dz + z²dž along the curve C defined by z² +2zz+z² = (2-2i)z+(2+2i) z from the point z = 1 to z=2+2i 1 2πi 3. Evaluate: dz if t> 0 and C is the circle |z| = 3 fcd 2z² +5 4. Evaluate: fc (z+2)³(z² + 4)z² dz where C is the square with vertices at 1+1, 2+1, 2+2i, 1+2i 2 5. Expand f(z) = Z (z-1)(z-2) in a Laurent series valid for 0 < |z-2| < 1 B

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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. Complex Integration . Cauchy's theorem and consequences of the theorem . Cauchy Integral formula, Residue theorem 1 Questions 1. Evaluate : (² + 1)²dz along the arc of the cycloid x = a(0 sin 0), y = a(1- cos 0) from the point where 0≤0 ≤ 2T 2. Evaluate: Jdz+z²dž along the curve C defined by 2² +2zz+z² = (2-2i)z +(2+2i) z from the point z = 1 to z=2+2i 1 2πi 3. Evaluate: fcdz if t > 0 and C is the circle |z| = 3 +1) 4. Evaluate: fo 2z² +5 (2+2)³ (2²+4)₂² 5. Expand f(z) = Z (z-1)(z-2) dz where C is the square with vertices at 1+i, 2+i, 2+2i, 1+2i in a Laurent series valid for 0 < 2-2|<1 A BIL
Transcribed Image Text:. Complex Integration . Cauchy's theorem and consequences of the theorem . Cauchy Integral formula, Residue theorem 1 Questions 1. Evaluate : (² + 1)²dz along the arc of the cycloid x = a(0 sin 0), y = a(1- cos 0) from the point where 0≤0 ≤ 2T 2. Evaluate: Jdz+z²dž along the curve C defined by 2² +2zz+z² = (2-2i)z +(2+2i) z from the point z = 1 to z=2+2i 1 2πi 3. Evaluate: fcdz if t > 0 and C is the circle |z| = 3 +1) 4. Evaluate: fo 2z² +5 (2+2)³ (2²+4)₂² 5. Expand f(z) = Z (z-1)(z-2) dz where C is the square with vertices at 1+i, 2+i, 2+2i, 1+2i in a Laurent series valid for 0 < 2-2|<1 A BIL
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