Recent content by csnsc14320

OK, so if I try to map just the square roots to the range (-inf, 0) I get: 1) z^2-1=-R where R ranges from (0, inf). Solving for Z yields z = \pm \sqrt{1-R}, which for R<1 gives (-1,1), and for R>1 gives (-i inf, +i inf) so I get branch cuts from (-1,1) and the imaginary axis. 2) solving...

z+sqrt(z^2-1): 2+sqrt(2^2-1) = 2+sqrt(3) -2+sqrt((-2)^2-1) = -2+sqrt(3) z+isqrt(1-z^2): 2+isqrt(1-2^2) = 2+isqrt(-3) = 2+sqrt(3) -2+isqrt(1-(-2)^2) = -2+isqrt(-3) = -2+sqrt(3) z+sqrt(z+1)sqrt(z-1): 2+sqrt(2+1)sqrt(2-1) = 2+sqrt(3)sqrt(1) = 2+sqrt(3) -2+sqrt(-2+1)sqrt(-2-1) =...

Homework Statement Given that the standard square root sqrt(anything) has a branch cut from (-inf,0), find the branch cuts of the following: z+sqrt(z^2-1) z+isqrt(1-z^2) z+sqrt(z+1)sqrt(z-1)Homework Equations The Attempt at a Solution I understand what branch cuts do (multivalue functions ->...

I have taken data for the transmission vs. wavelength for several types of glasses in the IR. I want to convert this to absorbance so that I can generalize transmission to different thickness glasses. I found an equation online that stated A = 2-Log(T%) (where Log is base 10). But I do not...

For my lab class we have to make some sort of physics demonstration in our machine shop with a budget of ~$600-$1000. I was wondering if anyone on here had some suggestions as to some cool/fun things to make? Things along the lines of Van De Graaf generators, inverted pendulums, etc. can be...

oops! it should read \frac{z^2-1}{(z-1)^2}

i found that it reduces to \frac{z+1}{z-1} but again don't I have to expand this and i have the same problem?

Homework Statement Say whether the indicated point is regular, an essential singularity, or a pole, and if a pole of what order it is. \frac{z^2-1}{(z-1)^2}, z = 1 Homework Equations The Attempt at a Solution Right now I'm just sort of stuck on how to put this into a laurent...

Homework Statement If f(z) is analytic on and inside |z|=1, show \int_{0}^{2\pi} e^{i \theta}f(e^{i \theta}) d\theta = 0 Homework Equations Cauchy's theorem: \oint f(z)dz=0 The Attempt at a Solution I'm not really sure what to do here except setting z=e^{i\theta} and plugging in...

or is this totally wrong?

Homework Statement An isolated metal sphere of radius a has a free charge Q on its surface. The sphere is covered with a dielectric layer with inner radius a and outer radius b Calculate the polarization charge density on the inside and outside of the dielectric. Homework Equations...

Homework Statement The temperature u in a star of conductivity 6 is inversely proportional to the distance from the center: u = \frac{3}{\sqrt{x^{2} + y^{2} + z^{2}}} If the star is a sphere of radius 3, find the rate of heat flow outward across the surface of the star. Homework...

Homework Statement Consider the vector space of square-integrable functions \psi(x,y,z) of (real space) position {x,y,z} where \psi vanishes at infinity in all directions. Define the inner product for this space to be <\phi|\psi> = \int_{-\infty}^{\infty} \int_{-\infty}^{\infty}...

Homework Statement Is the set of all complex solutions to the differential equation \frac{d^2 y}{d x^2} + 2\frac{d y}{d x} - 3 y = 0 If so, find a basis, the dimension, and give the zero vector Homework Equations The Attempt at a Solution I solved the equation and got the...

its a vector space over the complex :D and can have complex entries