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[.]
Homework9: Complex Integral Prob9.1: Using the first method to compute : a) ∫ 1+ j 2z (e )dz b) Prob9.2: Evaluate : ∫ 3+ j ∫ 1+ jπ (cos z)dz c) ∫ jπ (e z )dz (z )dz a) Using the first method b) Using the second method with the path is a straight line segment from z = to z = 3+ j Hw9: Complex Integral CuuDuongThanCong.com [1] https://fb.com/tailieudientucntt Homework9: Complex Integral Prob9.3: Evaluate : ∫ 1+ j (x + y)dz For the following paths: a) Along the y-axis: from to j, then along the line y = to 1+j b) The straight line segment from z = to z = 1+ j Prob9.4: Evaluate : ∫ j −j (x + jy )dz 2 For the following paths: a) Half-circle |z| = in the right half-plane b) Along the line x = Hw9: Complex Integral CuuDuongThanCong.com [2] https://fb.com/tailieudientucntt Homework9: Complex Integral Prob9.5: Using the Cauchy’s Integral Formula to evaluate : a) v∫ sin2z b) v∫ sin2z c) v∫ sin2z C z + 4z +5 C z + 4z + C z + 4z + dz (C: circle |z | = ) dz (C: circle |z – j2| = ) dz (C: circle |z – + j2| = ) Hw9: Complex Integral CuuDuongThanCong.com [3] https://fb.com/tailieudientucntt Homework9: Complex Integral Prob9.6: Using the Cauchy’s Integral Formula to evaluate : a) v∫ z +1 b) v∫ z +1 c) v∫ z +1 C z (z − 2) C z (z − 2) C z (z − 2) dz (C: circle |z | = ) dz (C: circle |z – – j | = ) dz (C: circle |z – – j2 | = ) Hw9: Complex Integral CuuDuongThanCong.com [4] https://fb.com/tailieudientucntt