4. Find a conformal equivalence from the open unit disc to the set W = {z...
5. Prove that f(z) = (2+1/2) is a conformal map from the half-disc {z = x +iy : 2< 1, y >0} to the upper half-plane. (Hint: The equation f(z) = w reduces to the quadratic equation z2 + 2wz +1 = 0, which has two distinct roots in C whenever w # £1. This is certainly the case if WE H.
4. Set up (but do not solve) the associated v and w problems which homogenize the boundary conditions. Au=0 u(0, y)-f(u), 0 <y< b Vu(a,v) n-g(v), 0<y<b, Vu(r,0) n p(), 0<<a u(z,b)q(z), 0 <r<a. 0<r<a, 0<y < b I
⑤. (a) Find cov(W,Z) for W and Z defined in Problem 1. e loint densitv of random variables 3r, if 0 <yKrK, (, elsewhere. Find cov(X, Y).
IF 4. FIND THE MASS OF A CONICAL FUNNEL Z= 7x+y Oz<4 THE DENSITY PER UNIT AREA IS p=8-2.
4. FIND THE MASS OF A CONICAL FUNNEL Z= Vx+you oz<4 THE DENSITY PER UNIT AREA IS p=8-2. IF
2. (10pts) Find a biholomorphic map between the unit disk A and the region U = {z €C10 < Arg(z) <5).
5. Find the Fourier Transform of g(t) = {o. (1-x?, x<1, 1</z/.
2. (1 point) Determine and sketch or graph the set 2 < 12-1+ i < 4 in the complex plane.
please answer its urgent. develop f(z)=(z(z-3)) into a laurent serkes valid for the following domains develop g(z)= 1/((z-1)(z-2)) into a laurent series valid for the following domains develop h(z)= z/((z+1)(z-2)) into a laurent series valid for the following domains 7) 0 < 1 2 -3/ <3 6) 1८11-4/<4 9) 0시레시 10) 0<l2-2시 ) ۵ < ( 2 + ( ( 3 (2) 02 ( 2 -2) 3.
Question 4 2 pts Find P(-1.47< z< 1.79) = places. Round to 4 decimal