. 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
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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