Delta Definition and 1000 Threads

Like many people on this forum, i am seemingly having a lot of trouble grasping the concepts of Epsilon Delta proofs and the logic behind them. I have read the definition and i realize for e>0 there is a d>0 such that... 0<sqrt((x-1)^2 - (y-b)^2) < d then f(x,y) - L <e (excuse my use of...

Homework Statement \[ \underset{\left|\underline{\xi}\right|=1}{\int}\delta_{0}\left(\underline{\xi}\cdot\underline{z}\right)dS_{\xi}=\intop_{0}^{2\pi}d\varphi\intop_{-r}^{+r}\delta_{0}\left(\varsigma\right)\frac{d\varsigma}{r}=\frac{2\pi}{r}\] The \delta_{0} is the dirac delta function.the...

Hi, I am not really sure whether its over the surface of the sphere or the Volume, the problem and the solution are given below, I want to know how it has been solved. The \delta_{0} is the dirac delta function. \[...

I have been reading papers for my research and I came across this equation twice: \lim_{\eta\to 0+}\frac{1}{x+i \eta} = P\left(\frac{1}{x}\right) - i \pi \delta(x) Where P is the pricipal part. It has been quite a while since I have had complex variables, but might it come from the...

Hi. How do we argue that \nabla^2\frac{1}{r} is a three dimensional delta function? I have seen some people do it using the divergence theorem, i.e. saying that \int_V \nabla\cdot\nabla\frac{1}{r}dv=-\oint_S \nabla\frac{1}{r}\cdot ds=-4\pi if S is a surface containing the origin, but I...

Homework Statement \int_{-\infty}^t (cos \tau)\delta(\tau) d\tau Evaluate the integral. I'm supposed to evaluate this for all t I believe, so I'm concerned with t<0, t=0, t>0. Homework Equations \int_{-\infty}^{\infty} f(x)\delta(x) dx = f(0) The Attempt at a Solution...

Using perturbation theory, I'm trying to solve the following problem \frac{\partial P}{\partial \tau} = \frac{1}{2}\varepsilon^2 \alpha^2 \frac{\partial^2 P}{\partial f^2} + \rho \varepsilon^2 \nu \alpha^2 \frac{\partial^2 P}{\partial f \partial \alpha} + \frac{1}{2}\varepsilon^2 \nu^2...

Im trying to find the number of delta rays though a material and am having some trouble with the units, can anyone help? The number of delta rays through a material is given by N=epsilon(1/E1 - 1/Emax), where epsilon=[2*Pi*A^2*e^4*ne*x]/[m*c^2], where A is unitless, [ne]=cm^-3, and the...

Does anyone has any idea how the spinors of the 3/2 particles look in the helicity basis? Basically, I'm trying to calculate a Feynman diagram for a nucleon Delta scattering, keeping the helicity inices explitly. I've had a look at this...

Homework Statement The problem straight out of the book reads: Prove that the Kronecker delta has the tensor character indicated. Prove also that it is a constant or numerical tensor, that is, it has the same components in all coordinate systems. Without a context the first sentence...

Homework Statement Im having a lot of dificulties evaluating this function, I really need some easy to understand explanation about how to evaluate it by the given values, I would appreciate any help. -Problem one given the function: U(x) = 0 if x < 0 1 if 0 ≤...

I understand most of the logic behind the formal definition of a limit, but I don't understand the the logic behind an epsilon delta proof. The parts I'm having trouble with are these: 1. How does proving that, the distance between the function and the limit is less than epsilon whenever the...

Homework Statement Need to integrate using the dirac delta substitution: \int_{-\infty}^{\infty}\int_{-\infty}^{\infty}\!x^2\cos(xy)\sqrt{1-k^2\sin^2(y)}\, dx\, dy Homework Equations \cos(xy) = \frac{1}{2}\left(e^{ixy} + e^{-ixy}\right) \delta\left[g(t)\right] =...

Homework Statement I have to design a lab to calculate the delta H value of the enthalpy change of ice to liquid water. It has to stay at 0*C Homework Equations Needs to be in lab format but possible q=n(delta H) where n is the molarity The Attempt at a Solution I know the...

Homework Statement By using the substitution u=cosx obtain the value of the integral \int\delta(cosx-1/2)dx between 0 and pi Homework Equations I have no idea how to go any further with this apart from substituting in for u!? The Attempt at a Solution

Hi guys. I play now a bit with EM fields and I have encountered some problems connected with Dirac delta. By coincidence I visited this forum and I thought I could find some help in here. The problem is that in order to get a potential in some point from a single charge you need to just...

The epsilon delta rule states \epsilon_{ijk}\epsilon_{pqk}=\delta_{ip}\delta_{jq}-\delta_{iq}\delta_{jp} I am constantly using this but get stuck when it is applied. For example \epsilon_{ijk}\epsilon_{pqk}A_{j}B_{l}C_{m}=(\delta_{ip}\delta_{jq}-\delta_{iq}\delta_{jp})A_{j}B_{l}C_{m}...

Hi, if I have the confidence interval for the point estimate of an option price A which was found through simulation, can I also find a confidence interval for delta (dA/dS), where S is underlying asset price, without further simulation? thanks, sl

Previously I posted a question on the Dirac delta function and was informed it was not a true function, but rather a distribution. However, I have to admit I still did not understand why its integral (neg inf to pos inf) is unity. I've thought about this and came up with the following...

that is 0 everywhere and 1 at 0. the code I wrote was this: n = -20:1:20; if n==0 imp = 1 else imp = 0; end >> stem (n, imp) ? Error using ==> stem at 40 X must be same length as Y. but i got that error. Using vectors and matrices is useless cause the delta...

Homework Statement A simple harmonic oscillator has a frequency of 3.4 Hz. It is oscillating along x, where x(t) = A cos(ωt + δ). You are given the velocity at two moments: v(t=0) = 1.8 cm/s and v(t=.1) = -19.3 cm/s. 1)Calculate A. 2)Calculate δ. Homework Equations w= 2pi*f = 21.36 rad/s...

Can someone give me quick refresher on what happens when you multiply the heaviside function with the unit impulse? Typically, the unit step function multiplied by anything simply delays it by the offset in the unit step function. The unit impulse function makes the value defined at only one...

Homework Statement How do you show that int[delta(t)]dt from negative infinity to infinity is 1? Homework Equations Dirac delta function defined as infinity if t = 0, 0 otherwise The Attempt at a Solution My teacher said that it has to do with m->infinity for the following...

1. The problem statement Show that: \int_{-\infty}^{\infty} f(x) \delta^{(n)}(x-a) dx = (-1)^n f^{(n)}(a) The Attempt at a Solution I am trying to understand how to prove: \int_{-\infty}^{\infty} f(x) \delta '(x) dx =- f'(x) I know that we need to use integration by parts, but I'm...

A representation of SU(2) is "pseudo-real". Can one form the product \phi^{\dagger i}\rho_{i} , where \phi_i and \rho_i transform in the fundamental representation? If a representation is complex, Krockner delta is an invariant symbol, so you can form such a product. SU(2) is not...

Homework Statement http://i634.photobucket.com/albums/uu67/danilorj/circuito.jpg Above is the picture of the circuit I'm trying to solve. The problem asks to find the current over the resistor of 1 ohm. Homework Equations The Attempt at a Solution Well, I found the equivalent...

Homework Statement Justify the following expretion, in spherical coordinates; delta (vector r) = (1 / r^2 * sin (theta) ) * delta(r) * delta(theta) * delta(phi) Homework Equations The Attempt at a Solution I don't know what it means... please help?

Griffiths' section 1.5.3 states that the divergence of the vector function r/r^2 = 4*Pi*δ^3(r). Can someone show me how this is derived and what it means physically? Thanks in advance.

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Homework Statement im not seeing a factorization for f(x)-L<e and and not sure how to proceed in this case

Homework Statement Starting with the definition of the Dirac delta function, show that \delta( \sqrt{x}) um... i have looked in my book and looked online for a problem like this and i really have no clue where to start. the only time i have used the dirac delta function is in an integral...

Hi I have been trying to learn dirac delta function. but its kind of confusing. I come across 2 contrasting definitions for it. The first one states that the function delta(x-xo) is infinite at x=x0 while the other states that delta(x-x0) tends to infinite as x tends to x0. Now both of them...

Let A, M be a commutative ring and a finitely generated A-module respectively. Let \phi be an A-module endomorphism of M such that \phi (M)\subseteq \alpha\ M where \alpha is an ideal of A. Let x_1,\dots,x_n be the generators of M. Then we know that \displaystyle{\phi(x_i)=\sum_{j=1}^{n}...

Is it possible to calculate Ksp at a certain temperature if you know Ksp at a different temperature and \Delta H?

well, that's the question. They both have the same queark structure. (udd). is it only their different bound states the differentiates them?? thus giving both different masses?

Hey there! I'm faced with this problem: http://img7.imageshack.us/img7/4381/25686658nz9.png It's a 1D nonhomogeneous wave equation with a "right hand side" equaling to the dirac delta function in x * a sinusoidal function in t. I have to find its general solution with the constraints...

Kronecker Delta expression Please, give me an example of this identity using a 3 dimensional matrix R (maybe representing a rotation). My difficulty lies in the indices manipulation. R_{ii'}R{jj'}\delta_{i'j'} = \delta_{ij} I know it is obvious, but I'm really stuck in my...

how to find the second derivitive of delta function?

By definition of the Dirac delta function, we have: \int f(x) \delta(x-a) dx=f(a) This is fair enough. But in ym notes there is a step that goes like the following: \mathbf{\nabla} \wedge \mathbf{B}(\mathbf{r})=-\frac{\mu_0}{4 \pi} \int_V dV'...

Homework Statement Evaluate the integral: Homework Equations To integrate this, should one use a dummy variable to get the delta function only of t, then integrate, then substitute back in after integration?

Homework Statement This is problem 2.46 from Griffith's Electrodynamics. I've already solved the problem but there is one aspect of the solution which bothers me and I can't think of where it is originating. I have found that the potential given in the problem produces an electric field...

I am still very confused about the differences between all the d's and delta's used to represent infinitesimal elements and/or derivatives and never know when and where to use what: - du - \partial u - \delta u For instance what can be simplified exactly in the chain rule and also what to...

I cannot get the answer as from the solution manuel. Please tell me what am I assuming wrong. Thanks

In a book on QM are listed a few properties of the delta function, one of which is: x \delta^{-1}(x) = - \delta(x) I can't figure out how to interpret that? Putting the statement in integral form isn't particularily enlightening looking: f(x) = \int f(x-x') \delta(x') dx' = \int...

I'm posting this here because I'm asking about the mathematical properties of the Dirac delta function, delta(x) which is zero for all non-zero real values of x and infinite when x is zero. The integral (-inf to +inf) of this function is said to be 1. How is this derived?

Homework Statement Three impedance of 10+j6 are delta connected to a three phase 208 V power line. I am to find The Phase currents, and Line currents. I am just learning this so bear with me please. I am correct to assume that the voltage across each impedance is the source voltage of...

Homework Statement Three impedance of 10+j6 are delta connected to a three phase 208 V power line. I am to find The Phase currents, and Line currents. I am just learning this so bear with me please. I am correct to assume that the voltage across each impedance is the source voltage of...

Suppose that one mole of a monatomic perfect gas at 27°C and 1.00 atm pressure is expanded adiabatically (i.e. no heat transfer, so that the temperature must fall) in two different ways: (a) reversibly, to a final pressure of 0.5 atm, and (b) against a constant external pressure of 0.5 atm...

There is an overhead door at work that will start to open but then stops. I don't know all the details because I haven't been out to the door yet, but the information has been given to me by one of my guys. The door is driven by a 3-phase 480 volt motor. I don't know anymore information...

Homework Statement Hi there, i am trying to do a proof that H'(t)= δ(t) Homework Equations We have been given the following: F is a smooth function such that lim (t-->±∞)F(t)=0 Therefore the integral between ±∞ of [H(t)F(t)]'=[H(t)F(t)]∞-∞=0 I understand it up until this point...