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Exercises dA (1) Use Cauchy's residue theorem to compute Jo 2+sin (2)...
2. More integrals! Evaluate each integral, using either a Cauchy Integral Formula or Cauchy's Residue Theorem....
2. More integrals! Evaluate each integral, using either a Cauchy Integral Formula or Cauchy's Residue Theorem. Take C to be the circle [2] = 3, oriented counter-clockwise. 1) Sota-1jad: 6) Se TH h) Sorºcos(1/2)da
Jo at 12. Residue theorem. Compute the following integral, 80 (1 +4232(2 points)
Jo at 12. Residue theorem. Compute the following integral, 80 (1 +4232(2 points)
Please do 2 only please do 2 only Exercises (1) Compute for de and c )...
Please do 2 only
please do 2 only
Exercises (1) Compute for de and c ) da where is the ultime center at the origin and oriented once in the counterclockwise (2) Computer da, where I is the circle {: € C: 1:= 3) once in the counterclockwise direction (3) (Mean Value Property of Holomorphic Functions) Supposed w = f(e) is holomorphic on and inside the circle {: € C:- Prove that f(20) == f( 70 +re) de. (4) Under...
solve a and c only 1. Use the residue theorem to evaluate the following integrals: cos...
solve a and c only
1. Use the residue theorem to evaluate the following integrals: cos θ (2+sin θ) 2n 0 0 1+sin2 θ 2x-0820, de (C) Jo 5-4cos
use residue theorem to evaluate the following integrals sin z 21) 20) Cosx dx (r? +...
use residue theorem to evaluate the following
integrals
sin z 21) 20) Cosx dx (r? + 1) X 22) sin mx dx 2(x² + a²² (a > 0, b>0) 23) cos ex - cos bx -dx x?
QUESTION 2. PLEASE USE COMPUTER WRITING SO I CAN READ IT 52 Complex Analysis Exercises (1)...
QUESTION 2.
PLEASE USE COMPUTER WRITING SO I CAN READ IT
52 Complex Analysis Exercises (1) Does the function w = f(2) za have an antiderivative on C? Explain your answer. (2) Is (z dz = 0 for every closed contour I in C? How do you reconcile your conclusion with Cauchy's integral theorem? (3) Compute fc Log(x+3) dz, where is the circle with radius 2. cente at the origin and oriented once in the counterclockwise direction. (4) Let I...
R R 5. To compute 1 = lim 2 COS dr and J = lim 22+1...
R R 5. To compute 1 = lim 2 COS dr and J = lim 22+1 sinc dx simultaneously .22 +1 R R0 R R using Residue Theorem, let f(x) 22 +1 C COSC sinc (1) Show that if z = x + iy, then Rf(R2) = and Sf(R2) = x2 +1 x2 +1 (2) Find Res[f, i]. (3) Show that I = 0 and J (4) Prove I = 0) in the above problem without using Residue Theorem. IT
Please answer all questions and explain every answer. Lab Assignment 1: Complex Numbers 1. Find and...
Please answer all questions and explain every answer.
Lab Assignment 1: Complex Numbers 1. Find and plot all values of V-64. (hint: convert-64 to polar coordinates) 2. Prove that sin2z cos2z 1. hint: use the formulas for complex sin and cos) 3. Prove that cosh2z - sin2. (hint: use the formulas for complex sin and cos) 4. Use matlab to calculate each of the following quantities: cosh2π, tani, cos (ir) 5. Evaluate the following expressions and compare to the computer...
Question of 9 Laurent Series and the Residue Theorem - 9.4 Argument Principle. I want #2 to be answered. Exercises 9.59...
Question of 9 Laurent Series and the Residue Theorem - 9.4
Argument Principle.
I want #2 to be answered.
Exercises 9.59. 1. If f(2) is analytic inside and on the simple closed contour C, and f(z) on C, show that the number of times f(z) C is given by assumes the value a inside f'(2)dz. 1 2πί Jσ f(2)- simple closed contour C except for finite number of poles inside C. Denote the zeros by z1,. . , Zn (none...
EXAMPLE 2 Find sin$(7x) cos”7x) dx. SOLUTION We could convert cos?(7x) to 1 - sin?(7x), but...
EXAMPLE 2 Find sin$(7x) cos”7x) dx. SOLUTION We could convert cos?(7x) to 1 - sin?(7x), but we would be left with an expression in terms of sin(7x) with no extra cos(7x) factor. Instead, we separate a single sine factor and rewrite the remaining sin" (7x) factor in terms of cos(7x): sin'(7x) cos”(7x) = (sinº(7x))2 cos(7x) sin(7x) = (1 - Cos?(7x))2 cos?(7x) sin(7x). in (7x) cos?(7x) and ich is which? Substituting u = cos(7x), we have du = -sin (3x) X...
2. More integrals! Evaluate each integral, using either a Cauchy Integral Formula or Cauchy's Residue Theorem. Take C to be the circle [2] = 3, oriented counter-clockwise. 1) Sota-1jad: 6) Se TH h) Sorºcos(1/2)da
Jo at 12. Residue theorem. Compute the following integral, 80 (1 +4232(2 points)
Please do 2 only
please do 2 only
Exercises (1) Compute for de and c ) da where is the ultime center at the origin and oriented once in the counterclockwise (2) Computer da, where I is the circle {: € C: 1:= 3) once in the counterclockwise direction (3) (Mean Value Property of Holomorphic Functions) Supposed w = f(e) is holomorphic on and inside the circle {: € C:- Prove that f(20) == f( 70 +re) de. (4) Under...
solve a and c only
1. Use the residue theorem to evaluate the following integrals: cos θ (2+sin θ) 2n 0 0 1+sin2 θ 2x-0820, de (C) Jo 5-4cos
use residue theorem to evaluate the following
integrals
sin z 21) 20) Cosx dx (r? + 1) X 22) sin mx dx 2(x² + a²² (a > 0, b>0) 23) cos ex - cos bx -dx x?
QUESTION 2.
PLEASE USE COMPUTER WRITING SO I CAN READ IT
52 Complex Analysis Exercises (1) Does the function w = f(2) za have an antiderivative on C? Explain your answer. (2) Is (z dz = 0 for every closed contour I in C? How do you reconcile your conclusion with Cauchy's integral theorem? (3) Compute fc Log(x+3) dz, where is the circle with radius 2. cente at the origin and oriented once in the counterclockwise direction. (4) Let I...
R R 5. To compute 1 = lim 2 COS dr and J = lim 22+1 sinc dx simultaneously .22 +1 R R0 R R using Residue Theorem, let f(x) 22 +1 C COSC sinc (1) Show that if z = x + iy, then Rf(R2) = and Sf(R2) = x2 +1 x2 +1 (2) Find Res[f, i]. (3) Show that I = 0 and J (4) Prove I = 0) in the above problem without using Residue Theorem. IT
Please answer all questions and explain every answer.
Lab Assignment 1: Complex Numbers 1. Find and plot all values of V-64. (hint: convert-64 to polar coordinates) 2. Prove that sin2z cos2z 1. hint: use the formulas for complex sin and cos) 3. Prove that cosh2z - sin2. (hint: use the formulas for complex sin and cos) 4. Use matlab to calculate each of the following quantities: cosh2π, tani, cos (ir) 5. Evaluate the following expressions and compare to the computer...
Question of 9 Laurent Series and the Residue Theorem - 9.4
Argument Principle.
I want #2 to be answered.
Exercises 9.59. 1. If f(2) is analytic inside and on the simple closed contour C, and f(z) on C, show that the number of times f(z) C is given by assumes the value a inside f'(2)dz. 1 2πί Jσ f(2)- simple closed contour C except for finite number of poles inside C. Denote the zeros by z1,. . , Zn (none...
EXAMPLE 2 Find sin$(7x) cos”7x) dx. SOLUTION We could convert cos?(7x) to 1 - sin?(7x), but we would be left with an expression in terms of sin(7x) with no extra cos(7x) factor. Instead, we separate a single sine factor and rewrite the remaining sin" (7x) factor in terms of cos(7x): sin'(7x) cos”(7x) = (sinº(7x))2 cos(7x) sin(7x) = (1 - Cos?(7x))2 cos?(7x) sin(7x). in (7x) cos?(7x) and ich is which? Substituting u = cos(7x), we have du = -sin (3x) X...
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