Delta Definition and 1000 Threads

I'm going through a list of 12 transformers and trying to determine if they are wye or delta. The schematics I have come across are for power engineering and don't go into too much detail other than the following: The transformers step down ~400V 60Hz AC (three-phase) to ~120V 60Hz AC (single...

Hi All, I have a problem in understanding the concept of dirac delta function. Let say I have a function, q(r,z,t) and its defined as q(r,z,t)= δ(t)Q(r,z), where δ(t) is dirac delta function and Q(r,z) is just the spatial distribution. My question are: 1. How can I find the time derivative...

Homework Statement When constructing an Epsilon Delta proof, why do we need to make a stipulation? For example, in most proofs for limits of quadratic functions, it is stipulated, for example, that δ≤1. Why is this needed anyway? This is my thought process for a quadratic: Prove that lim(x...

I have been wondering exactly how one would express the Dirac delta in arbitrary spaces with curvature. And that leads me to ask if the Dirac delta function has a coordinate independent expression. Is there an intrinsic definition of a Dirac delta function free of coordinates and metrics? Or as...

Homework Statement I have to integrate: \int_0^x \delta(x-y)f(y)dy Homework Equations The Attempt at a Solution I know that the dirac delta function is zero everywhere except at 0 it is equal to infinity: \delta(0)=\infty I have to express the integral in terms of function...

The Fourier series of a delta train is supposedly (1/T) + (2/T ) Ʃcos(nωt) ... where T is period and ω=2*Pi/T ...but when I plot this, it doesn't give me just a spike towards positive infinity, but towards negative infinity as well (see attached pic), so this does not seem to converge to the...

I am testing a cylindrical piece of steel dropping down steel pipe in a vacuum system, and came across a problem comparing the kinematic equation and a standard change in velocity over change in time to determine an acceleration. My derivation shows that the kinematic equation is exactly 2...

Homework Statement L[t^{2} - t^{2}δ(t-1)] Homework Equations L[ t^{n}f(t)] = (-1^{n}) \frac{d^{n}}{ds^{n}} L[f(t)] L[δ-t] = e^-ts The Attempt at a Solution My teacher wrote \frac{2}{s^{3}} -e^{s} as the answer. I got \frac{2}{s^{3}} + \frac{e^-s}{s} + 2 \frac{e^-s}{s^2} + \frac{2e^-s}{s^3}

Integrating the delta function: $$ \frac{4}{\pi^2}\int_0^{\pi}\int_0^{\pi}\delta(x - x_0,y - y_0)\sin nx\sin my dxdy $$ Would the solution be $\frac{4}{\pi^2}\sin nx_0\sin my_0$?

Homework Statement Evaluate the Laplace transform: L{δ(t-∏)tan(t)} Homework Equations The Attempt at a Solution L{δ(t-∏)tan(t)} = ∫ δ(t-∏)tan(t) dt evaluated from 0 to ∞ =tan(∏)e-∏*s = 0 Could someone check my work on this one? I'm suspicious that my transform is just zero...

Can you always put numbers directly into an expression which has the delta triangle against its variables? For example Faraday's Law is always shown with the delta triangle on top and bottom yet these are dropped when you use it for calculations; which leaves me wondering why they are there in...

Homework Statement Consider this situation, V(x)=λδ(x) ,-a<x<a. V(x)=∞,x>a or x<-a. How to find the eigenvalue and eigen wavefuntion of the Hamiltonian. Homework Equations i can only reder to stationary Schrodinger equation. The Attempt at a Solution when it is ouside the well(x>a...

Homework Statement Homework Equations I really wish they existed in my notes! *cry*. All I can think of is that integrating or in other words summing the dirac delta functions for all t, would be infinite? None the less the laplace transform exist since its asked for in the question and i...

I started learning how to do these things today and boy, they take some interesting logic. Anyway, here's my attempt at one: prove that the limit as (x,y) → (0,0) of [(x^2)(siny)^2]/(x^2 + 2y^2) exists Here's what I did: 0<√(x^2 + y^2) < δ, |[(x^2)(siny)^2]/(x^2 + 2y^2) - 0| < ε...

Hi, I'm reading through a paper and have come across what my tutor described as a 'theta function', however it seems to bear no resemblance to the actual 'theta function' I can find online. In the paper it reads: \int^1_0 dz~\theta (s-\frac{4m^2}{z}-\frac{m^2}{1-z}) And apparently this...

I am trying to perform a CFD simulation of a 70 degree sweep Delta Wing at different angles of attack (aoa = 20, 25, 30, 35 degrees). The inlet flow is at 25m/s. I have made a spherical Far-field boundary with the sphere radius of 5 times the root chord length of the delta wing. Because of the...

Homework Statement http://store2.up-00.com/Sep12/JB498124.jpg 2. The attempt at a solution No attempts because i can't understand how to solve it

1. what is the even part of δ(x+3)+δ(x+2) -δ(x+1) +1/2δ(x) +δ(x-1) -δ(x-2) -δ(x-3)? 2. δ= 0 x≠0; ∞ x = 0 1/2 (f(x) + f(-x)) 1/2 (f(x) - f(-x)) Knowing the piecewise definition of the delta function, and knowing 1/2 (f(x) + f(-x)) for even parts of a function. I plug this in...

Homework Statement Find the solution of the equation: α(dy/dt) + y = f(t) for the following conditions: (a) when f(t) = H(t) where H(t) is the Heaviside step function (b) when f(t) = δ(t) where δ(t) is the delta function (c) when f(t) = β^(-1)e^(t/β)H(t) with β<α Homework...

Find the solution of the equation: α(dy/dt) + y = f(t) for the following conditions: (a) when f(t) = H(t) where H(t) is the Heaviside step function (b) when f(t) = δ(t) where δ(t) is the delta function (c) when f(t) = β^(-1)e^(t/β)H(t) with β<α My try for all 3 are as follow: 1...

Hi! I've got a problem with understanding notation in this lecture: http://www.youtube.com/watch?v=FZDy_Dccv4s&feature=BFa&list=PLF4D952FA51A49E66 For example, at 00:44:13, what does all lowercase deltas stand for? He writes: δA=∫(∂L/∂q)δq + (∂L/(∂q dot))δ(q dot) Why lowecase delta? What...

Homework Statement Hi guys ,please look at the integral on the attachement.Does anyone have seen this integral before ? Homework Equations We have the following two properties : ∫δ'(x-x0)f(x) dx =-f'(x0) δ(x^2-a^2)= {δ(x-a) +δ(x+a)}/2a The Attempt at a Solution Please help...

Hi, I first had a question regarding infinitesimals. What does it mean when the infinitesimal is at the beginning of the integral? For example: ∫dxf(x) is this the same as ∫f(x)dx ? My second question was how to convert a summation to an integral and a summation into an integral...

Homework Statement lim (x,y) -> (0,0) xy/sqrt(x^2+y^2) = 0 The Attempt at a Solution my understanding of my actual goal here is kind of poor given ε>0 there exist ∂>0 s.t. 0 < sqrt(x^2 + y^2) < ∂ then 0<|f(x,y) - L| < ε | xy/sqrt(x^2 + y^2) - 0 | < ε (xy * sqrt(x^2 + y^2)) /...

Homework Statement Prove lim x--> -1 1/(sqrt((x^2)+1) using epsilon, delta definition of a limit Homework Equations The Attempt at a Solution I know that the limit =(sqrt(2))/2 And my proof is like this so far. Let epsilon >0 be given. We need to find delta>0 s.t. if...

Homework Statement In the lectures, we considered a dipole, made of two charges ±q at a separation d. Using Dirac's δ function, write the charge density for this dipole. Evaluate the charge (monopole moment), dipole moment, and quadrupole moments Q, p, and Qij in the multipole expansion...

why we haven't any connection other than Delta or star in 3phase

Do you know some example of an operator, other than momentum or position, that has (at least partially) continuous spectrum with eigenvalues s, and the corresponding eigenfunctions obey (\Phi_s,\Phi_s') = \int \Phi_s^*(q) \, \Phi_{s'} (q)~ dq = \delta(s-s')~? EDIT For example...

Homework Statement The question was way too long so i took a snap shot of it http://sphotos-h.ak.fbcdn.net/hphotos-ak-snc7/397320_358155177605479_1440801198_n.jpg Homework Equations The equations are all included in the snapshotThe Attempt at a Solution So for question A I've done what the...

Can someone prove that the change in potential energy is negative work. I have a very basic understanding of the concept. I do not understand where it is derived from.

Prove that \lim_{x\rightarrow} \frac{\sin x}{x} = 1 Solution Given \epsilon > 0 want to find \delta such that \left|\frac{\sin x}{x} - 1 \right| < \epsilon for x, |x | < \delta can I use Taylor expansion of sinx ? but Taylor is an approximation of sin(x) around a certain point ...

Homework Statement How do you find delta X with Voy and Vox? Ex. Problem: Vox = 25.202 Voy = 12.097 Vo = 27.95 ∅ = 25.62° Δx = ? Homework Equations I think Kinematic eq. 2 is supposed to be used in this problem, Δx = Vot + 1/2 at^2 The Attempt at a Solution With Video analysis I was given...

Homework Statement kroenecker delta has one upper and one lower index. except from uppper index and lower index,we have 2 slots for the upper index and 2 slots for the lower index(for a 2 index tensor). Why krenecker delta left or right slot index position doesn't matters? Also why 2 two...

Homework Statement http://postimage.org/image/s7m1kohst/ Homework Equations The Kronecker Delta = 1 ; if i=j The Kronecker Delta = 0 ; i (not equal) j The Attempt at a Solution I have no idea what to do from here, or even if I did this first step right...

Homework Statement I want to show that \lim_{x \rightarrow 0}\frac{1}{x} does not exist by negating epsilon-delta definition of limit. Homework Equations The Attempt at a Solution We say limit exists when: \forall \epsilon > 0, \exists \delta > 0 : \forall x(0< \left| x\right| < \delta...

Homework Statement Show that \delta_n(x) = ne^{-nx} \quad \mathrm{for}\quad x>0 \qquad = 0 \quad \mathrm{for}\quad x<0 satisfies \lim_{n\longrightarrow\infty}\int_{-\infty}^\infty \delta_n(x)f(x)\mathrm{d}x = f(0) The attempt at a solution The hint says to replace the upper limit...

Homework Statement This is an issue I'm having with understanding a section of maths rather than a coursework question. I have a stage of the density function on the full phase space ρ(p,x); ρ(p,x) = \frac {1}{\Omega(E)} \delta (\epsilon(p,x) - E) where \epsilon(p,x) is the...

Hi I would like to know what is the dirac delta function of x^2, I read somewhere it is equal to delta of x itself but why?

Homework Statement I'm wondering why we can't use less than or equal to for the formal definition of the limit of a function: Homework Equations lim x→y f(x)=L iff For all ε>0 exists δ>0 such that abs(x-y)<δ implies abs(f(x) - L)<ε Why not: lim x→y f(x)=L iff For all ε>0 exists...

The Dirac delta function is defined as: \int_{ - \infty }^{ + \infty } {\delta (x - {x_0})dx} = 1 Or more generally the integral is, \int_{ - \infty }^{ + \infty } {\delta (\int_{{x_0}}^x {dx'} )dx} But if the metric varies with x, then the integral becomes, \int_{ - \infty }^{ + \infty }...

Homework Statement Given \nabla\frac{1}{r}, show \nabla\bullet\nabla\frac{1}{r} = -4πδ(r), where δ(r) is the delta dirac function.The Attempt at a Solution I've used divergence theorem and also solved the equation itself, so I know that outright solving is zero and the divergence theorem gives...

Prove that x \frac{d}{dx} [\delta (x)] = -\delta (x) this is problem 1.45 out of griffiths book by the way. Homework Equations I attempted to use integration by parts as suggest by griffiths using f = x , g' = \frac{d}{dx} This yields x [\delta (x)] - \int \delta (x)dx next I tried...

Homework Statement Lim x→a of f(x) = c (Where c is a constant) Homework Equations The Attempt at a Solution I have no idea. I am able to do these if I can manipulate fx-L to equal x-a but I am having trouble with this one. Please help me!

Homework Statement Determine the limit l for a given a and prove that it is the limit by showing how to find δ such that |f(x)-l|<ε for all x satisfying 0<|x-a|<δ. f(x)=x^{4}+\frac{1}{x}, a=1. Homework Equations I claim that \lim\limits_{x\rightarrow 1}x^{4}+\frac{1}{x}=2. The...

Homework Statement Determine the limit l for a given a and prove that it is the limit by showing how to find δ such that |f(x)-l|<ε for all x satisfying 0<|x-a|<δ. f(x)=x^{2}, arbitrary a.Homework Equations I will incorporate the triangle inequality in this proof.The Attempt at a Solution We...

Homework Statement For f(x) = sqrt(27-x), L=4, x_0 = 11 epsilon = 1, find the largest value of delta > 0 in the formal definition of a limit which ensures that |f(x) - L| < epsilon Homework Equations the formal def. of a limit: lim x->x_0 F(x) = L if, for every number epsilon > 0...

Homework Statement Evaluate the following expression: \sum_{j}\sum_{k}\epsilon_{ijk}\delta_{jk} Homework Equations \delta_{ij} = [i = j]The Attempt at a Solution I don't have a solution attempt to this one yet, because somehow I completely missed out on what the permutation thing has to do...

Homework Statement Evaluate the following expression: \sum_{j}\sum_{k}\epsilon_{ijk}\delta_{jk} Homework Equations \delta_{ij} = [i = j] The Attempt at a Solution I don't have a solution attempt to this one yet, because somehow I completely missed out on what the permutation thing...

Homework Statement lim 3 as x->6 lim -1 as x->2 Homework Equations In the first weeks of a calculus class and doing these epsilon delta proofs. As i am looking at two of the problems i have been assigned: Lim 3 as x->6 Lim -1 as x->2 The Attempt at a Solution...

I'd like to show that if there exists some operator \overset {\wedge}{x} which satisfies \overset {-}{x} = <\psi|\overset {\wedge}{x}|\psi> , \overset {\wedge}{x}|x> = x|x> be correct. \overset {-}{x} = \int <\psi|x> (\int<x|\overset {\wedge}{x}|x'><x'|\psi> dx')dx = \int <\psi|x>...