complex variable Problems (108-3)

(See attached file for full problem description) --- - flow around a corner... - components of velocity... --- (See attached file for full problem description)

complex variable problems (108-4)

(See attached file for full problem description) --- - Show the speed of the fluids... - At an interior point of a region of flow... --- (See attached file for full problem description)

Complex Variable Question

(See attached file for full problem description) --- Find the image of the semi-infinite strip x > 0, 0 < y < 2 when w = iz + 1. Sketch the strip and its image. --- (See attached file for full problem description)

Function analytic at origin

Assume that f(z) is analytic at the origin and f(0) = first derivative of f at 0 = 0. Prove that f(z) can be written in the form f(z) = [z^2]g(z), where g(z) is analytic at z = 0.

Function analytic in the open disk

Let g be continuous on the real interval [0,1] and define H(z) := integral (from 0 to 1) [g(t)/(1-z[t^2])]dt, (|z| < 1) Prove that H is analytic in the open disk |z| < 1.

Laurent series expansion

Does the principal branch square root of z have a Laurent series expansion in the domain C{0}? Explain.

Laurent series for a trig function

Find the Laurent series for (z^2)*cos(1/(3z)) in |z| > 0

Function description in detail

Aloha, Please describe in detail the process of solving the problem. I have the answers already, I want to know HOW one arrives at the solutions. f(t) = 10,000 / 10 + 50e ^-0.5t HOW do I obtain the derivative? What is the "e" portion of the problem? I know the derivative = 250,000e^-0.5t/ (10+50e ^-0.5t)^2 Please ...continues

Laurent series for a complex-valued function

Consider f(z) = [(z-i)(z+4)(z-3)]^(-1) restricted to the domain of definition 0 < |z|< infinity How many different Laurent series centered at z_0 = 0 does it have? Explain. Discuss the convergence and divergence sets of each of those Laurent series. Find two non-zero terms of the Laurent series which represents this ...continues

Poles & Singularities

Classify the behavior at infinity (analytic, pole, zero, or essential singularity; if a zero or pole, give its order) of the following functions: f1(z) = (z^3 + i)/z f2(z) = e^(tan(1/z))