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Complex Analysis
IVIatn 401: Homew ork Set # . 1. Apply the Cauchy-Goursat Theorem to show...
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...
Q1. Solve the complex equation: sinz 3i Q2. Study the analyticity of the complex function fusing...
Q1. Solve the complex equation: sinz 3i Q2. Study the analyticity of the complex function fusing Cauchy-Riemann equations: Izl Q3. Evaluate, by using Cauchy's integral formula, the path integral cosh2 z dz (z-1-i(z-4) where C consists of Iz 3 (counterclockwise) Q4. Using the Residue theorem, integrate counterclockwise around the circle C defined by zl 1.5, the following tan z dz Q5. Find, by using parti ial fraction, the Laurent series of the function with center zo 0 for 1< z<3...
please show the work for the solution and use surface z = y and then set...
please show the work for the solution and use surface z = y and
then set up G(x,y,z) = z-y. Thanks!
Use Stokes Theorem to evaluate $F F. dr where F(x, y, z) = ryi+yzj+z?k and C is the intersection of the paraboloid z = x² + y² and the plane z = y with a counterclockwise orientation looking down the positive z-axis. HINT: The polar equation r = 2a sin 0, 0 <O< represents a circle with center (0,...
13. Show step by step how to use the Divergence Theorem to set up the surface...
13. Show step by step how to use the Divergence Theorem to set up the surface integral F. dS := Fonds with outward orientation, where F(x, y, z) = (x, z, y) and S is the surface of the unit sphere x2 + y2 + z2 = 1. Do Not Evaluate.
Complex Analysis A and B plz A) B) = Use Rouche's Theorem to show that 24...
Complex Analysis A and B plz
A)
B)
= Use Rouche's Theorem to show that 24 + 4z +1 has exactly one zero inside |2| 1 Prove that all roots of z? – 523 + 12 = 0 lie between the circles [2] = 1 and |2| = 2
Choose three questions to do The first method: the second method thank you 19-29 INTEGRATION Integrate by the first method or state why it does not apply and then use the second method. (Show...
Choose three questions to do
The first method:
the second method
thank you
19-29 INTEGRATION Integrate by the first method or state why it does not apply and then use the second method. (Show the details of your work.) 19. | Re z dz, C the shortest path from 0 to 1 + i 20. J Re z dz, C the parabola y from 0 to 1 + i 21. | e2z dz, C the shortest path from Ti to...
Use Stoke's Theorem to evaluate ∫CF⋅dr∫CF⋅dr where F=〈e−6x−1yz,e−1y+1xz,e−5z〉F=〈e−6x−1yz,e−1y+1xz,e−5z〉 and CC is the circle x2+y2=9x2+y2=9 on the...
Use Stoke's Theorem to evaluate ∫CF⋅dr∫CF⋅dr where
F=〈e−6x−1yz,e−1y+1xz,e−5z〉F=〈e−6x−1yz,e−1y+1xz,e−5z〉
and CC is the circle x2+y2=9x2+y2=9 on the plane z=6z=6 having
traversed counterclockwise orientation when viewed from above.
The line integral equals
Main Menu Contents Grades Course Contents » ... » PROBLEM SET 12 » stokestheorem-2 Use Stoke's Theorem to evaluate Sc F. dr where F = (e-63 – lyz, e-ly + 1xz, e -52) and C is the circle x2 + y2 = 9 on the plane z= 6 having traversed...
Complex Analysis: 1 + COS Z Define the function 1 f(2)= (z + 1)2(23 +1) (a)...
Complex Analysis:
1 + COS Z Define the function 1 f(2)= (z + 1)2(23 +1) (a) Find all the singularities of f(z) and classify each one as either a removable singulatiry, a pole of order m (and find m), or an essential singularity. (b) Let I = 71+72, where yi and 72 are the directed smooth curves parameterized by TT zi(t) = 2i(1 – 2t), 0 < t < 1 z2(t) = 2eit, 277 < t < 2' respectively. Compute...
Let Ω be an open set and a E Ω with (the closed disc) D(a,p) Ω...
Let Ω be an open set and a E Ω with (the closed disc) D(a,p) Ω Let f є H(Q). We have proved that for any r 〈 ρ, f has a power series expansion in the open disc D(a,r) CO 0 where, for all n0,1,2 7l Here C is the positively oriented circle: z-a+pe.θ, 0-θ-2π. In particular, f has a Taylor series expansion in D(a, r): f" (a) 2-a 0 This results in two consequences (will be shown in...
linear algebra and complex analysis variables please solve this problem quickly 1+i 1. Write in standard...
linear algebra and complex analysis variables
please solve this problem quickly
1+i 1. Write in standard form x+yi. 2. Find the modulus and principal argument of z = 2 + 2/3 i and use it to show z' = -218 3. Give geometrical description of the set {z:2z-il 4} 4. Find the principal argument Arg(z) when a) z = -2-21 b) z=(V3 – )6 5. Find three cubic root of i. 6. Show that f(z) = |z|2 is differentiable at...
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...
Q1. Solve the complex equation: sinz 3i Q2. Study the analyticity of the complex function fusing Cauchy-Riemann equations: Izl Q3. Evaluate, by using Cauchy's integral formula, the path integral cosh2 z dz (z-1-i(z-4) where C consists of Iz 3 (counterclockwise) Q4. Using the Residue theorem, integrate counterclockwise around the circle C defined by zl 1.5, the following tan z dz Q5. Find, by using parti ial fraction, the Laurent series of the function with center zo 0 for 1< z<3...
please show the work for the solution and use surface z = y and
then set up G(x,y,z) = z-y. Thanks!
Use Stokes Theorem to evaluate $F F. dr where F(x, y, z) = ryi+yzj+z?k and C is the intersection of the paraboloid z = x² + y² and the plane z = y with a counterclockwise orientation looking down the positive z-axis. HINT: The polar equation r = 2a sin 0, 0 <O< represents a circle with center (0,...
13. Show step by step how to use the Divergence Theorem to set up the surface integral F. dS := Fonds with outward orientation, where F(x, y, z) = (x, z, y) and S is the surface of the unit sphere x2 + y2 + z2 = 1. Do Not Evaluate.
Complex Analysis A and B plz
A)
B)
= Use Rouche's Theorem to show that 24 + 4z +1 has exactly one zero inside |2| 1 Prove that all roots of z? – 523 + 12 = 0 lie between the circles [2] = 1 and |2| = 2
Choose three questions to do
The first method:
the second method
thank you
19-29 INTEGRATION Integrate by the first method or state why it does not apply and then use the second method. (Show the details of your work.) 19. | Re z dz, C the shortest path from 0 to 1 + i 20. J Re z dz, C the parabola y from 0 to 1 + i 21. | e2z dz, C the shortest path from Ti to...
Use Stoke's Theorem to evaluate ∫CF⋅dr∫CF⋅dr where
F=〈e−6x−1yz,e−1y+1xz,e−5z〉F=〈e−6x−1yz,e−1y+1xz,e−5z〉
and CC is the circle x2+y2=9x2+y2=9 on the plane z=6z=6 having
traversed counterclockwise orientation when viewed from above.
The line integral equals
Main Menu Contents Grades Course Contents » ... » PROBLEM SET 12 » stokestheorem-2 Use Stoke's Theorem to evaluate Sc F. dr where F = (e-63 – lyz, e-ly + 1xz, e -52) and C is the circle x2 + y2 = 9 on the plane z= 6 having traversed...
Complex Analysis:
1 + COS Z Define the function 1 f(2)= (z + 1)2(23 +1) (a) Find all the singularities of f(z) and classify each one as either a removable singulatiry, a pole of order m (and find m), or an essential singularity. (b) Let I = 71+72, where yi and 72 are the directed smooth curves parameterized by TT zi(t) = 2i(1 – 2t), 0 < t < 1 z2(t) = 2eit, 277 < t < 2' respectively. Compute...
Let Ω be an open set and a E Ω with (the closed disc) D(a,p) Ω Let f є H(Q). We have proved that for any r 〈 ρ, f has a power series expansion in the open disc D(a,r) CO 0 where, for all n0,1,2 7l Here C is the positively oriented circle: z-a+pe.θ, 0-θ-2π. In particular, f has a Taylor series expansion in D(a, r): f" (a) 2-a 0 This results in two consequences (will be shown in...
linear algebra and complex analysis variables
please solve this problem quickly
1+i 1. Write in standard form x+yi. 2. Find the modulus and principal argument of z = 2 + 2/3 i and use it to show z' = -218 3. Give geometrical description of the set {z:2z-il 4} 4. Find the principal argument Arg(z) when a) z = -2-21 b) z=(V3 – )6 5. Find three cubic root of i. 6. Show that f(z) = |z|2 is differentiable at...
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