Recent content by hadroneater

I'm stuck on a really simple problem because I haven't done MATLAB in a while. I have transfer functions for nth order lowpass Butterworth Filters: H(jw) = 1/(s + w_c)^n I want to plot the 1st to 5th order filters. How do I input H(jw) into matlab? The tf(num, den) is not efficient in that...

^ Up to 3 higher-level math courses can count towards technical electives and I am also trying to do a math minor.

My to-the-point question: If I were to pick between rigour-based real analysis, rigour-based complex analysis or linear programming/optimization, which one would be the most beneficial for pursuing graduate studies in communication systems? My mathematical background: - All the typical EE...

But isn't that only assuming m >= 0?

no takers?

Homework Statement 1. Evaluate \int_{c_{2}(0)} f(z)dz = \int_{c_{2}(0)} \frac{z^{m}}{1+z^{3}}dz Where c_{2}(0) is the circle of radius 2 centered at the origin with positive orientation (ccw). I have done the question myself and compared it with the solution. However, I don't think I am...

Homework Statement Find the contour integral of Log(z). The contour is defined as: x^2 + 4y^2 = 4, x>= 0, y>=0 Homework Equations The Attempt at a Solution parametrize the contour as z(t) = 2cos(t) + isin(t) 0 <= t <= pi/2 The contour integral = ∫Log(z(t))z'(t)dt I am having...

Ah, I see. I just expected the answer to be in some neat closed form.

So I have the image: \left\{ e^{0.5Log(z)} | z = x + i√3/2} z = \sqrt{x^{2} + \frac{3}{4}}*e^{i*arctan(\frac{2x}{sqrt{3})} Log(z) = ln(\sqrt{x^{2} + \frac{3}{4}}) + i*arctan(\frac{2x}{sqrt{3}) How would finding Log(z) help me find the square root of z exactly? Hmm...am I messing up the latex...

Homework Statement Determine the image of the line segment joining e^(i*2*pi/3) to -e^(-i*2*pi/3) under the mapping f = e^(1/2*Log(z)). Homework Equations The Attempt at a Solution The line joining the two points: {z | -0.5 < x 0.5, y = sqrt(3)/2} f = the principle branch of...

Homework Statement This isn't a homework problem but just a fundamental concept that my entire complex analysis course is based on. The set D = ℂ \ non-positive real axis. Why is it considered open and connected (domain)? Homework Equations The Attempt at a Solution When it...

Homework Statement Given that f0 = u(x,y) + i*v(x,y) is analytic in domain D, are these functions analytic in domain D? 1. f1 = (u^2 - v^2) - 2i*u*v 2. f2 = (e^u)cos(v) + i*(e^u)sin(v) 3. f3 = u - i*v Homework Equations cauchy-riemann equations The Attempt at a Solution I kind of...

Homework Statement x(2 - x)y'' - (x - 1)y' + 2y = 0 Find the general solution in terms of a polynomial and a series in powers of x - 1. Homework Equations The Attempt at a Solution Does the question basically ask for a series solution of the ODE at the regular point x = 1? Then y(x) =...

Ah, right. Got it.

Homework Statement (1 - x)y'' + xy' + xy = 0 Find the first 3 nonzero coefficients of the power series expansion about x = 0 if y(0) = -1 and y'(0) = 0Homework Equations The Attempt at a Solution y = \sum^{∞}_{n = 0}c_{n}x^{n} From above, I can say that y(0) = 1 = c_{0} and y'(0) = 0 = c_{1}...