Recent content by mooshasta

I think I get it now, thank you. I didn't realize that one of the independent variables could be the conjugate (T). Thanks!

I still am a little confused how to get to that integral. If S is a function of E, L, and N, doesn't that mean then that: \left( dS \right)_{T,N} = \left( \frac{\partial S}{\partial E} \right)_{L,N} dE + \left( \frac{\partial S}{\partial L} \right)_{E,N} dL But instead I wrote \left(...

As I understand it, then, the heat flow should be \int TdS, since this is the heat part of the equation. So then should I be integrating: T\int^{L_2}_{L_1} \left( \frac{\partial S}{\partial L}} \right)_{T,N} dL Using a Maxwell relation as you said, I see that -\left( \frac{\partial...

Homework Statement Consider a rubber band for which the tension, f, as a function of temperature T and length L is f = \kappa T (L+\gamma L^2), where \kappa and \gamma are positive constants. Determine the heat flow between it and its surroundings when the rubber band is stretched reversibly...

I came across the following statement: \sum_n p(n)e^{-in\theta} \approx exp[-i\theta \langle n\rangle - \theta^2 \langle ( \delta n)^2 \rangle / 2] where \theta is small, \sum_n p(n) = 1, \langle n \rangle = \sum_n p(n)n, and \langle ( \delta n)^2 \rangle = \sum_n p(n)(n-\langle n \rangle)^2...

Thank you! Your hint was just what I needed. For some reason I was forgetting that \frac{dy}{ds} = y' \dot{t}, but now it makes perfect sense. Thanks again :)

Homework Statement I'm given the surface of revolution parametrized by \psi (t, \theta ) = (x(t), y(t)cos \theta, y(t)sin \theta ) where the curve \alpha (t) = (x(t),y(t)) has unit speed. Also given is that \gamma (s) = \psi (t(s), \theta (s)) is a geodesic which implies the following equations...

I know that for a unit-speed \alpha (t), the equation reduces to K = \frac{-y''}{y}, which does clearly represent a sphere. The way the question is worded on my homework seems to point to the fact that that reduction only applies to unit-speed curves, which is why I think that perhaps an...

Homework Statement I'm trying to find a surface of revolution with Gauss curvature K of +1 at all points, which doesn't lie in a sphere. Homework Equations The surface is parametrized as \psi (t, \theta ) = ( x(t), y(t) cos \theta , y(t) sin \theta ) I have the equation K =...

Thank you for your help. I'm trying to solve this without using groups or Lagrange's theorem (we didn't learn any of that in class). I made progress but I still am a little hung up at one (probably extremely trivial) detail. Let S be the set of units {x_1,...,x_n} and let a be a unit of the...

Homework Statement Let q be the number of units in finite ring R. Show that for all a in R, if a is a unit in R then a^q = 1. Is there a way to solve this without using group theory? All I can seem to find information on is when a and m are relatively prime then a^{\phi (m)} = 1 (mod \, m)...

I'm trying to find an algorithm to solve a 4 variable system of nonlinear equations.. the variables are named w,x,y,z and a,b,c,d are constants: a = x - y + z b = w + x c = y * z d = x * y / w Can anyone offer any advice? Much appreciated...

If anyone was curious about this, I found the solution online: http://planetmath.org/encyclopedia/%3Chttp://planetmath.org/?method=l2h&from=collab&id=76&op=getobj

Hey... Could someone help me out with deriving the LaPlacian in spherical coordinates? I tried using the chain rule but it just isn't working out well.. any sort of hint would be appriciated. :) \nabla^2 = \frac{1}{r^2} [ \frac{\partial}{\partial r} ( r^2 \frac{\partial}{\partial r} ) +...

I've encountered a standard problem about single slit diffraction, but there's a slight change to the problem and I don't know how it should be dealt with. The question is: A plane wave of 400-nm light is incident on a 25-µm slit in a screen, as shown in the figure below. At what incident...