Conditions Definition and 978 Threads

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.

for example, i want to find the coeffiecients of a function f(x) = ax^2 + bx + c for these given conditions: f(-1) = 3 f(1) = 3 i tried plugging and chugging for the first condition: 3 = a - b + c 3 = a + b + c now i tried subtracting the system to get 0 = 2b so its solved that b...

hello any one can help me with this question thanx (a) Find a recurrence relation for the number of n-digit sequences over the alphabet {0, 1, 2, 3, 4} with at least one 1 and the first 1 occurring before the first 0 (possibly no 0’s). (b) What are the initial conditions? (c)...

Homework Statement The functions u(x,y) and v(x,y) are the real and imaginary parts, respectively, of an analytic function w(z). Assuming that the required derivatives exist, show that \bigtriangledown^2 u=\bigtriangledown^2 v=0 Solutions of Laplace's equation such as u(x,y) and v(x,y)...

Homework Statement Find a quadratic function f(x), that satisfies the given conditions: f(1) = 2, f(-1) = 4, f(3) = 8. Thanks Homework Equations f(x) = k(x-s)(x-t) The Attempt at a Solution I tried entering the points as the the x and f(x) while estimating as what the...

Some new ones here. :cry: :frown: http://news.yahoo.com/s/ap/20070103/ap_on_go_ca_st_pe/detainee_abuse

What were they dependent on?

Homework Statement Sorry if this is the wrong place, I'm new here but I've been given a little paper to write on electromagnetic radiation. I am having trouble finding what the necessary conditions are for the emission of EMR, and kind of don't understand what it's really asking me for...

[FONT="Georgia"]Homework Statement Discuss the motion of a continuous string when the initial conditions are q'(x,0) = 0 and q(x,0) = Asin(3πx/L). Resolve the solution into normal modes. Show that if the string is driven at an arbitrary point, none of the normal modes with nodes at the driving...

If there is a cross member of a bridge with two forces (F and R) acting as contacts at the ends of the member, is there a way to use equilibrium conditions to write the relationships between the forces? The member makes an angle theta with the horizontal (upward and to the right) and has a...

[SIZE="5"]Problem The velocity of a two-dimensional flow of liquid is given by \textbf{V} = \textbf{i}u(x, y) - \textbf{j}v(x, y). If the liquid is incompressible and the flow is irrotational show that \frac{\partial u}{\partial x} = \frac{\partial v}{\partial y} and \frac{\partial...

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}...

Good evening to all you genius people out there, I've been racking my brains for the past 10 minutes and can't come up with anything. The exact wording of the question: Describe how you could use light of a known wavelength to find the distance between two slits. I thought of using...

Why is it when the conditions are adiabatic and reversible about a turbine, the assumption is its isentropic?

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...

The general solution fo the following equations: x'=2x-3y y'=x-2y Is, x=4C1e^2t, y=C1e^2t-3C2e^-2t They ask for me to list a set of initial conditions (xo, yo) for which the solution is stable, i.e, (x, y)-->(0,0) for large t. I don't understand this part of the problem.

I need to write a program that prompts me to enter a positive integer N, after doing so it calculates the factorial of that integer and prints it. I am able to do this with the following code. #include <iostream> using namespace std; int main() { double I, N, Factorial = 1; // Do not...

Two strings with identical mass densities and tensions are attached in the middle by a mass m, an incident pulse is traveling from the left, I need to find the equations of motion for the string on the right. The pulse is y=Aexp[i(kx-wt)] work so far: the mass will act as a moving boundry...

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...

When doing the initial conditions of the velocity of the wave function, why do they have a position (x) derivative (i.e. cF'(x)-cG'(x)=h(x)). It appears in here. http://en.wikipedia.org/wiki/D%27Alembert%27s_formula How someone explain how the c came about and why position derivatives are...

Born's conditions for an acceptable "well-behaved" wavefunction F(x): 1. it must be finite everywhere, i.e. converge to 0 as x -> infinity 2. it must be single-valued 3. it must be a continuous function 4. and dF/dx must be continuous. I'm having difficulty understanding the last...

I have a question about Fourier series that I would like some help with. If there is a function f(t) which does not satisfy all of Dirichlet's conditions then can its Fourier series still represent it? All I've got is that if all of Dirichlet's conditions are satisified by f(t) then the Fourier...

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...

More logic fun! contrapostive confusion, book says one thing, and yet...:Resolved:. Hello everyone! I'm quite confused on this issue. The directions say: Use the contrapositive to rewrite the statements in 45 and 46 in "if-then" form in two ways. So i first look back to see what...

Hi everyone! I have a few questions regarding renormalization in QFT. 1. In Peskin chapter 10, he renormalizes \phi^4 theory using the renormalization conditions in equation (10.19), which basically say that the propagator has a pole at p^2=m^2 and that the 4-point interaction is exact for...

Sir, I have some doubts regarding standing waves. Can anyone who is online now clear my doubts? For the production of standing waves should the 2 interfering waves have the same amplitude, should they be in phase, should they have the same frequency and velocity? I have this doubt because...

so the way book states it, for the sc. lemma to work, |f(z)| has to be less than or equal to 1 and and z has to be less than 1. However, the book seems to use the lemma in some problems even if one of the conditions is not satisfied ... any help with gretaly appreciated also ...if you could...

Hi, World! Nice place here! My first post in this forum. :smile: I've got a short question for a start. If we wish to evaluate the constants for the general solution x(t)=C_1e^{-{\lambda_1}t}+C_2e^{-{\lambda_2}t} of this ODE: \ddot{x}+2{\gamma}\dot{x}+{{{\omega}_0}^2}x=0 we can choose the...

A cook holds a 2 kg cartoon of milk at arm's length. What Force F_{B} must be excerted by the biceps muscle? (Ignore the weight of the forearm) See figure attached. \theta = 75 degrees Please help explain what I'm doing wrong. Correct answer is 312 N. \Sigma\eta = F(sin 75)(.08 m) - (2...

Hi. I'm starting a project on chaos very soon and I was just wondering... One of the distinguishing features of a "chaotic system" is the sensitive dependence on initial conditions. It is stated that if we knew the initial conditions with infinite precision we would also be able to...

Why is there not an Angle-Angle-Angle (AAA) condition for proving triangles are congruent? Is it because, in congruent polygons, the corresponding angles and corresponding sides are equal? If there were an A-A-A method, the corresponding angles would be equal but the sides wouldn't...

Ok, the question I have is attached. What I have done is found the general solution: (Question was seperable, so it was easy) y = x^2 - 2x + c But I don't kwow what/how to do is finding the initial conditions where there are: (a) No solutions (b) more than one solution (c) precisely...

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...

This one got me alittle discombobulated. Initiallly I thought they wanted me to find a particular solution, which I did. But then later I saw it supplied to intial conditions. So I guessed y = Asin(5t)+Bcos(5t) then took derivatives, and applied the intial conditions but also was wrong. Here...

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...

OKay i havn't gotten 1 2nd order Diff EQ right yet! I'm on a role! wee! Find y as a function of t if 81y'' + 126y' + 79y = 0, y(0) = 2, y'(0) = 9 . Here is my work: http://img204.imageshack.us/img204/4605/lastscan5ag.jpg I submitted this and it was wrong...

Ok I have a problem here. I have gotten to the unfortunate point where I feel like I'm nearly done, Mathematica has given me a solution that is correct… but of course, I can't figure out how I was suppose to get from point A to B. I currently have: 2x - 6y\sqrt {x^2 + 1} \frac{{dy}}{{dx}} =...

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...

Does String Theory Satisfy Einstein's Conditions for a Physical Theory? In his autobiography Einstein said: Before I enter upon a critique of mechanics as a foundation of physics, something of a broadly general nature will first have to be said concerning the points of view...

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...

Sketching a graph based on certain conditions... Hello, I'm supposed to sketch a graph of f based on condtions I'm given. However some of the conditions I'm given I'm not sure exactly what is supposed to happen. A little help would be greatly appreciated. Here are the condtions, some of...

If m^2<a<b, & a*b=a perfect square, TPT: b>(m+1)^2

I'm a physics major in Alaska, where it's not uncommon to have temperatures of -40. Are there any interesting experiments or designs that I can do in my freetime that are convenient because of the cold weather? I remember learning briefly about gradients being a source of power. If...

What are the environmental conditions necessary for the operation of an STM and an AFM?

I have a problem that says to prove the superposition of initial conditions gives superposition of corresponding motion for two coupled oscillators. My question is: What do they mean by coupled oscillators? Do they mean coupled pendulums? Double LC circuits? If it's coupled pendulums are...

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 have heard one definition of energy meaning a degree of inertial resistance... can anyone give me a different working condition for the word

Hi there, I was wondering if anyone would be willing and able to help me with this question. Q. Derive the boundary condition satisfied by D at the interface between 2 media. I know that the D field is continuous at the suface, but I need to be able to derive this. If anyone can...