Conditions Definition and 978 Threads

the general equation of a circle has 3 constants , so it is said that 3 conditions , like 3 points (on the circle) are required to specify a circle , but , we require only the center and radius to specify a circle , so how many conditions are actually required ??

Homework Statement Consider the Heat Equation： du/dt=k(d2u/dx2), where d is a partial and d2 is the second partial. The B.C.'s are u_x(0,t)=u(0,t) and u_x(L,t)=u(L,t), where u_x is the partial of u with respect to x. The I.C is u(x,0)=f(x) Now, consider the Boundary Value Problem...

I just started CM (I had 2 classes until now) and the professor said that if you know the position and velocity of say all the particles, then you know how the system will evolve. This, I already read and knew. I've probably a common question so feel free to redirect me to any similar...

Why is it that change in enthalpy (h=e + pv) depends upon pressure as they say, we should measure at standard pressure, while pv=nrt so no matter da presure nrt is the same the product p by change in volume is constant so accordin 2 me we should specify only da temperature change...

For a string with one endpoint attached to a wall and the other to an oscillator (so that it is under boundary conditions), what is the character of waves that are not at a harmonic frequency?

Homework Statement A high temperature, gas cooled nuclear reactor consists of a composite cylindrical wall for which a thorium fuel element (Ka=57 W/m*K) is encased in graphite (Kb= 3 W/m*K) and gaseous helium flows through an annular coolant channel. Consider conditions for which the helium...

Homework Statement Solve the equation u_{x}+2xy^{2}u_{y}=0 with u(x,0)=\phi(x) Homework Equations Implicit function theorem \frac{dy}{dx}=-\frac{\partial u/\partial x}{\partial u/\partial y}The Attempt at a Solution -\frac{u_x}{u_y}=\frac{dy}{dx}=2xy^2 Separating variables...

Hi there, I recently read that the equations of motion for an classical open string naturally give rise to two boundary conditions, namely Dirichlet and Neumann boundary conditions. (i) Could someone explain to me what do these boundary conditions physically mean, in particular for open...

Homework Statement 2) Given a cubic equation y = (x+5)(ax^2 + bx - 2). Give conditions on a and b for the equation to represent the following curve. The curve is attached to the email. http://img35.imageshack.us/img35/8246/question2o.png Homework Equations The Attempt at a Solution...

Greetings all, I have a question in regards to my initial conditions. The problem as given is: ut=uxx with u' = 0 at x=0 and u=0 at x=L I was also given u={1 0<x<L/2, 0 L/2<x<L I understand the set up of the problem and the solving of it for the most part, however I'm having...

Hello all, This is to do with forced longitudinal vibration of a rod (bar). It's basically a problem to do with the linearised plane wave equation (1d). The rod is fixed firmly at one end, and excited at the other by a harmonic force. The wave equation (with constant rho/E instead of...

Homework Statement Find the potential outside of a long grounded conducting cylindrical rod of radius R placed perpendicular to a uniform electric field E0. Homework Equations V(s,\phi) = a_{0}+b_0{}ln(s) + \sum(A_n{}cos(n\phi)+B_n{}sin(n\phi))*(C_n{}s^n{}+D_n{}s^{-n}) The sum being...

hello all, We live in a hot part of the world with the extra bonus of high humidity - around 90%. We don't have A/C, and don't really want to get it (energy use). Evaporative cooling won't do much (towel on head) becuase of water saturation in air. Would a cold wet towel + fan force water...

http://i48.tinypic.com/1o4ow9.jpg why in this circuit they say that in t<0 the voltage on both capacitators is 12 volts?? if both points of each capacitators is connected to the voltage source directy then 12 volts is ok. but here we have a resistor between them this resistor drops...

Homework Statement The problem is given as follows: Solve dy/dt + y = 0.5, y(t=0)=1Homework Equations The Attempt at a Solution I separate the y terms from the t terms, which gives me dy(-y+0.5)=dt I integrate both sides to get -ln(-y+0.5)=t+C C is the constant, I combine the constants from...

For a Sturm-Liouville problem, as in: \frac{d}{{dx}}\left[ {r(x)\frac{{dy}}{{dx}}} \right] + [\lambda p(x) + q(x)]y = 0 I've read in several books that one assumes that p, q and r are continuous, real-valued and bounded in the interval I, r' is continuous, and p>0. But I've never seen...

what is the solution for y in this peculiar ODE ? A\left(y,x\right)=\frac{dy}{dx}+B(x)(1-y) with initial conditions : \frac{dy}{dx}=\left0 \ldots , y=0 \frac{dy}{dx}=\delta(x-x_{0})\ldots,y=1 moreover \int^{\infty}_{-\infty}Adx=\int^{\infty}_{-\infty}Bdx=1

I own an old and small car with only 30HP and a very poor aerodynamic coefficient, Cx=0.51. Based on this and on the rolling coefficient, I just solved out what would be the maximum speed when driving on a leveled road and there is no wind at all. It came out to be 120Kms/hr which can be...

A partial differential equation requires boundary conditions. Consider a 2-dimensional problem, where the variables are 'x' and 'y'. The boundary is the line x=0 and you are given all sorts of information about the function on that line. If you are given just the values of the function on the...

Homework Statement Solve, u_{t} = u_{xx}c^{2} given the following boundary and initial conditions u_{x}(0,t) = 0, u(L,t) = 0 u(x,0) = f(x) , u_{t}(x,0) = g(x)Homework Equations u(x,t) = F(x)G(t) The Attempt at a Solution I solved it, I am just not sure if it is right. u(x,t) =...

What would the boundary conditions be for a fourth order differential equation describing the deflection (elastic curve) of a propped cantilever beam with a uniform distributed load applied? i.e. a beam with a built in support on the left and a simple support on the right. I need 4 obviously but...

My calculus book states that a vector field is conservative if and only if the curl of the vector field is the zero vector. And, as far as I can tell a conservative vector field is the same as a path-independent vector field. The thing is, I came across this...

This is part of a theorem which is left unproved in "Elementary Classical Analysis" by Marsden and Hoffman. Let xn be a sequence in R which is bounded below. Let a be in R. Suppose: (i) For all e > 0 there is an N such that a - e < xn for all n >= N. (ii) For all e > 0 and all M...

If you have the value of a function of many variables, and its 1st-derivatives, at a single point, and a 2nd-order partial differential equation, then haven't you determined the entire function? You can use a Taylor expansion about that point to build the entire function because you have the...

Homework Statement Find general solution of equation (t^3)y' + (4t^2)y = e^-t with initial conditions: y(-1) = 0 and t<0 book answer gives y = -(1+t)(e^-t)/t^4 t not = 0 Homework Equations The Attempt at a Solution (t^3)y' + (4t^2)y = e^-t get integrating...

Homework Statement Solve the differential equation: y' + 2y = te^-2t with initial conditions y(1) = 0? Please show me what I am doing wrong... (or right).. also please don't show me shortcut i need to know where I am going wrong thanks. Homework Equations The Attempt at a...

Homework Statement Find a function H in C such that {\nabla ^2}H = 0 for y>0, H(0,y) = 1 for y<-/pi, H(0,y) = 0 for y>/pi and H(0,y) = -1 for -/pi<y</pi. The Attempt at a Solution I haven't been able to came up with anything. All the conform transformations that I know allow me to...

Homework Statement A dielectric interface is defined as 4x + 3y = 10 m. The region including the origin is free space, where D1 = 2ax - 4ay + 6.5az nC/m2. In the other region, εr2 = 2.5. Find D2 given the previous conditions. Homework Equations an12 = ± grad(f)/|grad(f)| D2n = D1n =...

Homework Statement Use a Gaussian surface and an Amperian loop to derive the electrostatic boundary conditions for the polarisation field P at an interface between electric media 1 and 2 of relative permittivities e1 and e2. (Hint: determine results for D and E first) Homework Equations...

u_t=u_{xx}+2u_x 0<=x<=L, t>=0, u(x,0)=f(x), u_x(0,t)=u_x(L,t)=0 How to do this?

http://www.sciencemag.org/cgi/content/abstract/326/5953/713

I am stuck at the problems of Boundary conditions for two dimensional problem in QM. iIf we have a two-dimensional domain, along the boundary, we can define two directions, one is tangential, the other is normal, assuming that there is no current flowing in and out along the normal direction...

Homework Statement Solve the initial value problem y'' = y' + y where y(0) = 0 and y(1) = 1 derive the power series solution y(x) = \ \ \sum_{n=1}^{\infty}{(F_{n}x^n)/n!} \ \ where {Fn} is the sequence 0,1,1,2,3,5,8,13... of Fibonacci numbers defined by F0 = 0 and F1 = 1 Homework...

Problem: u (sub t) = (1/2)u (sub xx) find the solution u(x,t) of the heat equation for the following initial conditions: u(x,0) = x u(x,0) = x^2 u(x,0) = sinx u(x,0) = 0 for x < 0 and 1 for x>=0 i'm really flying blind here. I've taken differential equations years ago but nothing...

Homework Statement Show that the conditions for a bound state, Eqn1 and Eqn2, can be obtained by requiring the vanquishing of the denominators in Eqn3 at k=i\kappa. Can you give the argument for why this is not an accident? Homework Equations Eqn1: \alpha=q*tan(qa) Eqn2...

What conditions must f satisfy if \lim_{x \to a} \lim_{y \to b} f(x,y)=\lim_{y \to b} \lim_{x \to a} f(x,y) where \lim_{x \to a} f(x,y) and \lim_{y \to b} f(x,y) exists and are finite?

Homework Statement Find the temperature distribution in the long thin bar −a ≤ x ≤ a with a given initial temperature u(x,0) = f(x). The side walls of the bar are insulated, while heat radiates from the ends into the surrounding medium whose temperature is u = 0. The radiation is taken...

Use Green's Functions to solve: \frac{d^{2}y}{dx^{2}} + y = cosec x Subject to the boundary conditions: y\left(0\right) = y\left(\frac{\pi}{2}\right) = 0 Attempt: \frac{d^{2}G\left(x,z\right)}{dx^{2}} + G\left(x,z\right) = \delta\left(x-z\right) For x\neq z the RHS is zero...

Homework Statement A thin conductor plate is in free space. Its conductivity is finite and thickness is approaching zero. Relate the tangential electric field in either side of the conductor. Repeat for tangential magnetic field. How are electric and magnetic fields related. Homework...

I have wandering eyes is one thing I have I only found out a few months ago. I don't know the technical term for it. I was watching a youtube video and they said some people thought they had add when in fact they weren't paying attention because of their eye condition. I have good vision like...

For a string fixed at x=0 and free at x=l I know \frac{dy}{dx}(l,t)=0 (d's are meant to be partials) but what is the other boundry associated with the end of the string? Is the second derivative also equal to 0?

Hi, I need to show this: b_m \geq\sum_{i=1}^n b_i^2 given these three conditions: b_m \geq b_i, for i=1..n (in other words b_m = max(b_i)) and 0 \leq b_i \leq 1 for i=1..n and \sum_{i=1}^n b_i=1 I've been working for hours in this without results...Any clue would be really appreciated...

I hope this is the right place to post this question. I'm trying to figure out how to run a numeric integration for a nonlinear second order ODE with Neumann B.C. I've started programming up Runge Kutta 4, but clearly without a boundary condition on the function, but only on its derivative...

Hey all, I finally figured out how to solve the integral: \int{dp} = \int{6U\eta(\frac{h-\overline{h}}{h^{3}})}{dx} + C using maple and have it export to MATLAB where: h=R+h0-\sqrt{R+x}\sqrt{R-x} \overline{h}=R+h0-\sqrt{R+\overline{x}}\sqrt{R-\overline{x}} how do i find the...

Could someone plase hep me with normal coordinate substitutions with periodic boundary conditions, I can't see where the 1/N cancels in the attached file Thanks Doug

have a bunch of different configurations of a single molecule under some sort of enviromental conditions. They are not of course the same configuration because of fluctations. I have another bunch of different configurations of the same molecule under different or the same conditions (this is...

Homework Statement Given a sequence <xn>n of real numbers. Give the conditions for a real number a not to be a limit point of the sequence. (lim xn not equal to a.) The Attempt at a Solution I'm really not sure if this is the whole answer or if it's only a part of it: For all e>0...

Hi friends, I'm new to CST microwave studio. Just finish constructed a structure of an L-probe patch antenna (from IEEE paper) and just run the simulation by transient time solver, the curve of the return loss(S11) against frequency that i get is different from what showing on the IEEE paper...

Homework Statement Consider the use of cubic splines to interpolate a set of data. Suppose at some stage in the calculation we arrive at the following spline functions for two consecutive intervals \tilde{f_{0}} = x^{3} + ax^{2} + bx + c over the interval -1 \leq x \leq 1 \tilde{f_{1}} =...

Homework Statement I am doing a chemistry extended experimental investigation on the variables affecting a Daniell Cell's voltage. I am required to understand the reasoning behind voltage increase and decrease for particular conditions. I have done extensive research, but am unable to find a...