Boundary conditions Definition and 418 Threads

Homework Statement The edges of a square sheet of thermally conducting material are at x=0, x=L, y= -L/2 and y=L/2 The temperature of these edges are controlled to be: T = T0 at x = 0 and x = L T = T0 + T1sin(pi*x/L) at y = -L/2 and y = L/2 where T0 and T1 are constants...

how do you prove/show that there really is a vector space defined by certain boundary conditions? unfortunatly this part of pde's was glossed over in my professor's lecture notes and I don't recall him talking about it in class.

I have done most of a question except for the most important part, putting in the boundary conditions, I can't really interpret them. The question is: I managed to solve this, with -c^2 as a separation constant, and I got: T(x,t) = X(x)F(t) = (A_{1} \cos{\frac{cx}{\sqrt{\kappa}}} + A_{2}...

Hey all, Last year, I took my university's undergraduate QM sequence. We mainly used Griffiths' book, but we also used a little of Shankar's. Anyway, I decided to go through Shankar's book this year, in a more formal treatment of QM. After the first chapter, I already have some questions that...

Can someone please help me with this question: Light with frequency \omega in media 1 ,with refractive index n_{1} , is incident (normal) to an interface of media 2, with refractive index n_{2}, and then is incident on a second interface with refractive index n_{3}. Using boundary conditions...

I took an ODE course last year, but I seem to have forgotten some stuff. I need to solve this equation: \frac{d^2u}{dt^2} + {\omega}^2u = f_osin({\mu}t) with the boundry conditions: u(0) = 0, du/dt(0) = 0 When I tried to solve the homogenenous equation first, I got...

"Appropriate boundary conditions"...? I am stumped by a question in my Electromagnetism asignment that asks, after determining the potential (V) and electric field (E) of a hollow conductive sphere containing a point charge system, to "show that E and V satisfy the appropriate boundary...

Im having trouble following how this is derived: The normal component of the electric field is discontinuous by an amount sigma/epsilon_0 at any boundary (when you cross a continuous surface charge). They talk about taking a little box so that the surface integral E dot da = 1/epsilon_0 * sigma...

I'm given the fact that two strings under tension T are joined by a knot of mass m... I'm supposed to find the appropriate boundary conditions. I know that the tensions are the same in both ropes and that the boundary will be continuous. I know the "trick" in this problem is knowing the...

I need a little help getting started here, Show that the boundry conditions X(b)=wX(a) +zX'(a) and X'(b) = yX(a) + dX'(a) on the interval a<=x<=b are symmetric if and only if wd-zy=1 i know that the a set of boundries are symmetric if f '(x)g(x) - f(x)g'(x) = 0 evaluated at x=a and...

I am looking for the general solutions of this equation in z(r) If someone remembers well, this equation arises in surface tension physics. z(r)=\frac{1}{r}\frac{d}{dr}\left[\frac{z_r r}{(1+z_r^2)^{1/2}}\right] subject to the boundary conditions z_r(0)=z_{ro} and z(\infty)=0 I only...

I'm taking solid state, and again and again we use the periodic boundary conditions, that the wavefunction should be unchanged by displacements of the length of the sample, L (assume 1D for simplicity). The argument was that the surface is so far away that it shouldn't have an effect on the...

Hello, Charge density \sigma(\phi) = k \sin 5\phi (where k is a constant is glued over the surface of an infinite cylinder of radius R with axis along the z-direction. Find the potential inside and outside the cylinder. Two things I'm having trouble with: 1. Is the potential of an...

I need to know how different boundary conditions on the DE representing a string under a force can be physically implemented. For example, if you need y(0)= 0, just tie the string to y=0 at that end. If you need y'(0)=0, attatch it so that it can freely slide up and down a pole at x=0. But...

As the thread title says: What's the difference between initial conditions and boundary conditions? Thanks in advance for helpful replies. :)

I'm having trouble with the meaning of the boundary condition in the derivation of fresnels quations, namely that the component of E tangental to the surface is continuous across the boundary. My trouble is, what physically does this corresspond to. Is it something to do with the divergence...

Hello there, I am glad that I found this forum. Because I have a little bit trouble with theoretical physics. The problem is the Green function in theoretical electrodynamic. I try to understand the difference between the Dirichlet Condition and the Neumann Condition. I understand...

This is a homework question so please do not just tell me the answer, but please point me in the right direction. A dipole layer, D(y,z), exists on the plane x=0. Find the boundary conditions (discontinuities, if any) for [phi](x,y,z), E_x(x,y,z), E_y(x,y,z), and E_z(x,y,z) across the...