Please show detailed solution Given f(2)=zz – 5z + 7i 1. If z= x +iy u(x,y)=...
1. Write f(z) in the form f(x) = u(x, y) +iv(x, y). (a) f(x) = 23+2+1 (b) f(3) = 2,270. Suppose f(z) = x2 - y2 - 2y +i (2x - 2xy), where z = x + iy, and express () in terms of .
Problem 8. Let f(z) = u(x, y) iv(x, y) be an entire function with real and imaginary parts u(x, y) and v(x, y). Assume that the imaginary part is bounded v(x, y) < M for every z = x+ iy. Prove that f is a constant 1
Please show detailed solution Given: Ux = 3/8 Uxx0 < x < 50,t > 0 u(0,t) = 50, u(50,1)=100, T>0 u(x,0) = 50,0 < x < 50 1. Identify the IBVP case 2. c2= ,1 = 47)2 = To= 3. Find all the values required by the general formula , p= Ti= f(x)=_
transformation. Perform the mappings of lines x- 2 and y 3 under the transformation w = z2 where z = x + iy. Compute the angles between the curves in the u-v plane at the points of intersection. Hence check if the angles between the lines in the z-plane are the same as the angles between the curves in the u-v plane transformation. Perform the mappings of lines x- 2 and y 3 under the transformation w = z2 where...
1. 2. (1 point) Let f(x,y,z) = 4x2 + xy + yz +5z?. Find the linearization L(x, y, z) of f(x,y,z) at the point (-1, -3, -1). L(x,y,z) = -5x-2y+72-3 Find an upper bound for the magnitude El of the error in the approximation f(x, y, z) ~ L(x, y, z) over the box |x +11 30.04, \y +31 < 0.04, 12 +11 30.04. E 3 (1 point) Let f(x, y) = 3 In(x) +2 In(y). Find the linearization L(av)...
[3](4 pts) Let f(x) = u(x, y) + iv(x,y) be differentiable for all z = x + iy. If v(x, y) = x + xy + y2 – x2, for all (x, y), find u(x,y) and express f(x) explicitly in terms of z.
7. Let f:D + C be a complex variable function, write f(x) = u(x, y) +iv(x,y) where z = x +iy. (a) (9 points) (1) Present an equivalent characterization(with u and v involved) for f being analytic on D. (Just write down the theorem, you don't need to prove it.) (2) Let f(z) = (4.x2 + 5x – 4y2 + 3) +i(8xy + 5y – 1). Show that f is an entrie function. (3) For the same f as above,...
2- a) The real part of a complex function f(z) given as, u(x, y) = 3x?y - y. Iff(2) is an analytic function, find v(x,y) and f(z) (15p) b) Find the whether f(z) is analytic or not where f(z) = cos(x) +ie'sinx. (15p)
Use Lagrange multiplier to determine the maximum and minimum values of (f,x,y,z) = x^2 +y^2 +z^2 subject to xyz=4 Detailed solution please. Thank you! 20. Use Lagrange Multiplier to determine the maximum and minimum values of f(x, y, z)-x2 + y2 +12 subject to 20. Use Lagrange Multiplier to determine the maximum and minimum values of f(x, y, z)-x2 + y2 +12 subject to
Given f(x, y, z) = 4yz - x2, and that x, y, z are each differentiable functions of u and v. Suppose (x, y, z) = (-1,0,1) at (u, v) = (1, 2), and that af 09 = 70. au |(1,2) = -50 and av (1,2) What is the value of x,(1, 2)? a) 230/3 b)-230/3 c) 40 d) 110 e) -120