toán kỹ thuật,lê minh cường,dhbkhcm Hw9 Complex Integral [1] Homework9 Complex Integral Prob9 1 Using the first method to compute 1 j 2z 0 (e )dza) + ∫ 1 j 0 (cosz)dzb) + π ∫ 1 z j (e )dzc) π∫ Prob9 2[.]
Trang 1 Homework9: Complex Integral
Prob9.1: Using the first method to compute :
1 j 2z 0
(e )dz
a) ∫ + b) (cos z)dz ∫01 j+ π 1 z
j
(e )dz
c)
π
∫
Prob9.2: Evaluate : 3 j 2
0 + (z )dz
∫
a) Using the first method
segment from z = 0 to z = 3+ j
Trang 2 Homework9: Complex Integral
Prob9.3: Evaluate : 1 j
0+ (x y)dz +
∫
For the following paths:
a) Along the y-axis: from 0 to j, then along the line y = 1 to 1+j
b) The straight line segment from z = 0 to z = 1+ j
Prob9.4: Evaluate : j 2 2
j(x jy )dz
∫
For the following paths:
a) Half-circle |z| = 1 in the right half-plane.
b) Along the line x = 0
Trang 3 Homework9: Complex Integral
Prob9.5: Using the Cauchy’s Integral Formula to evaluate :
2
sin2z
z 4z 5 C
2
sin2z
z 4z 5 C
b) ∫v + + dz (C: circle |z – j2| = 3 )
2
sin2z
z 4z 5 C
c) ∫v + + dz (C: circle |z – 1 + j2| = 2 )
Trang 4 Homework9: Complex Integral
Prob9.6: Using the Cauchy’s Integral Formula to evaluate :
2
z 1
z (z 2) C
(C: circle |z – 2 – j | = 2 ) (C: circle |z – 1 – j2 | = 2 )
2
z 1
z (z 2) C
b) ∫v +− dz
2
z 1
z (z 2) C
c) ∫v +− dz