Question

1. Use an antiderivative to show that for every contour C extending from a point zi to a point z2 2 dz= n+1 (n =0, 1,2,...).
0 0
Add a comment Improve this question Transcribed image text
Know the answer?
Add Answer to:
1. Use an antiderivative to show that for every contour C extending from a point zi...
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for? Ask your own homework help question. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions
  • 1. (20 points) Let C be any contour from z = -i to z = i,...

    1. (20 points) Let C be any contour from z = -i to z = i, which has positive real part except at its end points. Then, consider the following branch of the power function zi+l; f(3) = 2l+i (1=> 0, < arg z < Now, evaluate the integral Sc f(z)dz as follows: (a) (5 points) First, explain why f(z) does not have an antiderivative on C, but why the integral can still be evaluated. (b) (5 points) Then, find...

  • Problem 5: Let f(z) = zi = eiLog?, [2] > 0, -T < Arg z <a...

    Problem 5: Let f(z) = zi = eiLog?, [2] > 0, -T < Arg z <a denote the principal branch of the function z', and let C be any contour from –2 to 1 that, except for its endpoints, lies above the real axis. (a) Find an antiderivative of the function f(z); (b) Compute the integralf(z)dz; SOLUTION:

  • 9. Evaluate o (x+ 1)2 by extending the integral into the complex plane and using the contour C sh...

    9. Evaluate o (x+ 1)2 by extending the integral into the complex plane and using the contour C shown below. 9. Evaluate o (x+ 1)2 by extending the integral into the complex plane and using the contour C shown below.

  • 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...

  • Show that . A question from (mathematical physics - Couchy integral formula) c) The Rodrigues formula...

    Show that . A question from (mathematical physics - Couchy integral formula) c) The Rodrigues formula of Legendre polynomials can be converted into the Schlafli integral as (-1)" 1 (1 - 22n Pn(x) = dz 2n 2ni (z - x)n+1 C is a closed contour encircles the point z = x C

  • Problem 6. (1 point) Use the contour diagram of f in the ligure below to decide...

    Problem 6. (1 point) Use the contour diagram of f in the ligure below to decide ir the speciñied directional derivatives below are positive, negative, or approxmately zero 14 (a) At point (-2,2). in direction-i. is.? (b) At point (0,-2) in direction- i f s ? (c) At point ( 1,1), in direction i + s ? a) At point (-1,1), in direction +j f: s ? (e) At point (0,-2), in direction it2j. fd is!? n At point (0,-2),...

  • Show that integral dz/(z-1-i)n+1 =0, if n does not equal 0 and 2 pi i if n = 0 for C the boundary...

    Show that integral dz/(z-1-i)n+1 =0, if n does not equal 0 and 2 pi i if n = 0 for C the boundary of the square 0<=x<=2, 0<=y<=2, taken counterclockwise. [Hint: Use the fact that contours can be deformed into simpler shapes (like a circle) as long as the integrand is analytic in the region between them. After picking a simpler contour, integrate using parametrization.]

  • Problem 3. (i) Show that the Taylor series expansion of the function , with center at 1, is for -1

    Problem 3. (i) Show that the Taylor series expansion of the function , with center at 1, is for -1<1 ii) Explain why the function Log z is analytic in the disk l:-1 iii) For each point z with :-1< 1 consider the straight line segment C starting at 1 and ending at z. Evaluate dz. Hint: You do not need to do any computation. Note that Logz is an antiderivative of 1/z in the disk :-1<1.) (iv) Integrate each...

  • . (a) Show that the function u= 4x2 - 12.xy2 is harmonic and v=12.xy-4v2 is a...

    . (a) Show that the function u= 4x2 - 12.xy2 is harmonic and v=12.xy-4v2 is a harmonic conjugate of u. [Consequently, the function f =u+iv is entire, thus it has an antiderivative and that any contour integral of f is path independent.] (b) Find an antiderivative F(-)= F(x+iy)=P(x, y)+i Q(x, y) of the function f; and (c) evaluate ( f (2) ds , where C is any contour from 0 to 1–2i .

  • EXERCISE 6 Let Zi, Z2,-.., Zi6 be an i.i.d. sample of size 16 from the standard...

    EXERCISE 6 Let Zi, Z2,-.., Zi6 be an i.i.d. sample of size 16 from the standard normal distribution N (0,1). Let Xi,X2,..., X64 be an i.i.d. sample of size 64 from the normal distribution (μ, 1). The two samples are independent. a. What is the distribution of Y, where Y-Σ161 Z2 + Σ-i(X-μ)2? Study List b. Find ΕΥ. c. Find Var(Y) d. Approximate P(Y105)

ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT