Recent content by jtleafs33

E is the electric field vector. it is a function of position and time, so that's just its gradient vector, also a function of position and time.

Homework Statement I put this in the math forum because although it's for my EM waves class, it's a math question. Show that the spin force can be written as: F_{spin}=\frac{-1}{2}Im(\alpha)Im(E\cdot\nabla E^{*})=\nabla\times L_s Find L_s. Where \alpha is complex. I'm using E^{*} to denote...

Got it! It was trivial after I did the substitution you mentioned. Thanks again!

I will be trying it soon.

LCKurtz, I can't find anything like that in my textbook. Did you do that so the solution would satisfy both the nonhomogenous and homogenous parts? I suppose you added the extra function of x because the nonhomogenous boundary conditions only depend on x?

Homework Statement Solve the diffusion equation: u_{xx}-\alpha^2 u_{t}=0 With the boundary and initial conditions: u(0,t)=u_{0} u(L,t)=u_{L} u(x,0=\phi(x) The Attempt at a Solution I want to solve using separation of variables... I start by assuming a solution of the form...

I figured out what I was doing wrong. I realize now the substitutions I was making from the Euler formula don't work over the real line, those are more suited for integration over the unit circle. Once I chose a better way to transform into an integral in Z, this turned out to be a very simple...

Okay, taking your advice. For the example problem, \int^{∞}_{-∞} \frac{e^{it}}{1+t^2} We can directly substitute t=z \oint ^{∞}_{-∞} \frac{e^{iz}}{1+z^2} = \oint ^{\infty}_{-\infty} \frac{e^{iz}}{(1+i)(1-i)} Now since it's clear to see that f(z)→0 as R→∞, we can integrate over the...

Right, this acts like a 'sinc' function, so the Jordan contour is the right selection for integration. So the function is: f(t)=\frac{cos(\alpha t)}{\beta^2+t^2} Let: z=e^{i\alpha t} dz=i\alpha e^{i\alpha t}dt cos(\alpha t)=\frac{z+z^{-1}}{2} Transforming f(t) to f(z)...

Yes I've used the residue theorem to evaluate contour integrals. We've covered so much in this class I had already forgotten that that technique would work. Since this involves a 2\pi periodic function, I'd integrate over the unit circle in the complex plane... Use Euler's formula for the...

Homework Statement Find the Fourier Transform of: f(t)=\frac{cos(\alpha t)}{t^2+\beta^2} Homework Equations F(\omega)=\frac{1}{2\pi}\int^{∞}_{-∞}\frac{cos(\alpha t)exp(i \omega t)}{t^2+\beta^2} The Attempt at a Solution I start with: cos(\alpha t)=\frac{exp(i \alpha t)+exp(-i...

Homework Statement Evaluate the integral: \int^{2\pi}_{0}\frac{d\theta}{(A+Bcos(\theta))^2} a^2>b^2 a>0 The Attempt at a Solution First, I convert this to contour integration along a full sphere in the complex plane. I let: z=e^(i\theta) dz=ie^(i\theta) d\theta=-idz/z...

If v=0, then vx=vy=0. So then, u must be constant, so that it's derivative will also be zero, and thus satisfy the CR conditions?

Homework Statement Can a function which is purely real-valued be analytic? Describe the behavior of such functions? Homework Equations The Cauchy-Riemann conditions ux=vy, vx=-uy The Attempt at a Solution I can't think of any pure real-valued equations off the top of my head which...

Ahh, well at least it's been a nice algebra practice. I got it now, Thanks! :biggrin: