Delta Definition and 1000 Threads

Homework Statement Prove the function f(x)= { 4 if x=0; x^2 otherwise is discontinuous at 0 using epsilon delta. Homework Equations definiton of discontinuity in this case: there exists an e>0 such that for all d>0 if |x-0|<d, |x^2-4|>e The Attempt at a Solution I'm confused...

Homework Statement find \int_{-\infty}^{+\infty} x(t) \delta (\beta t - t_{0}) dt for x(t) = e^{a t} u(t) there is no information conserning a, β, or t_{0}... The Attempt at a Solution assuming that t_{0} is a constant\int_{-\infty}^{+\infty} x(t) \delta (\beta t - t_{0}) dt =...

i am confused on how to find the line currents when there is a line impedance in between the wye source and delta load... is it wrong to directly add the line impedance and the delta load without converting first the delta load to wye...? is there a way that i can find the line currents and...

I'm reading Daniel T. Gillespie's A QM Primer: An Elementary Introduction to the Formal Theory of QM. In the section on continuous eigenvalues, he admits to playing "fast and loose" with the laws of calculus, with respect to the Dirac delta function. I'd like to understand it better, or, if such...

Homework Statement Solve the given symbolic initial value problem: y''-2y'-3y=2\delta (t-1)-\delta (t-3) ;y(0)=2,y'(0)=2 The attempt at a solution Let Y(s):= L{y(t)}(s) Taking laplace transform of both sides: [s^{2}Y(s)-2s-2]-2[sY(s)-2]-3Y(s)=2e^{-s}-e^{-3s}...

Homework Statement An ideal particle of energy E is incident upon a rectangular barrier of width 2a and height V_{0}. Imagine adjusting the barrier width and height so that it approaches V(x)=\alpha \delta(x). What is the relationship between V0, alpha and a? Homework Equations The...

Hi everyone Homework Statement Let's say we observe a rainbow. We know the refraction index of the red and violet light, let's call them n_{1}=1.46 and n_{2}1.47 Now I want to calculate the angle \delta Homework Equations In a square the total angle is 360°, so we have...

What is the difference between a delta-complex and a simplicial complex? Hatcher's book says that simplicial complexes are uniquely determined by their vertices. Could someone clarify this? Thanks.

Homework Statement y[n] - (2/3)y[n-1] = x[n] what is y[n] if x[n] = diracdelta[n] The Attempt at a Solution for some reason, i argued that y[n-1] = diracdelta[n-1] so y[n] = diracdelta[n] + (2/3)diracdelta[n-1] Im pretty sure this is wrong, anybody can help?

Simple Integral: Complex exp --> delta function My Professor has written this down but I'm having some trouble of precisely where this is coming from: \int\psi^*_{f}(\boldsymbol k')\psi_{f}(\boldsymbol k) d^3\boldsymbol r = (2\pi)^3\delta(\boldsymbol k- \boldsymbol k') where \psi_{f} =...

Homework Statement Convolve an arbitary function f(t) with comb(t) [a sum of delta functions that run from -infinity to infinity with spikes at t = nT]. Is the convolution an array of copies of f(t) or is it a set of discrete points such that f(t) is returned at every t = nT? Homework...

Homework Statement Show that \int^{\infty}_{-\infty} e^{-ipt} dt = \delta(t). Homework Equations The Attempt at a Solution I know that I must Fourier transform \delta(t), but not sure how.

I'm looking to fabricate a small version of this device http://energyconservatory.com/products/products7.htm , which is used to measure airflow through a typical residential bath fan. It adjusts to three different known hole sizes, and typically connects to a manometer that has algorithms built...

Homework Statement For example you have a limit approaching 0 from the right cot x=infiniti m=1000 Homework Equations The Attempt at a Solution

Homework Statement Prove that \displaystyle \int_{-\infty}^{\infty} \delta (at - t_0) \ dt = \frac{1}{ | a |} \int_{-\infty}^{\infty} \delta (t - \frac{t_0}{a}) \ dt For some constant a. The Attempt at a Solution Edit: Looking at this again, I really don't understand where this is coming...

Homework Statement #8 (4x+1)/(3x-4)=4.5 Homework Equations The Attempt at a Solution 4<(4x+1)/(3x-4)<5 What do I have to do next?

I just finished up my first class of chemistry, and have a question on something that I just can't figure out. The delta H of formation for diatomic molecules is 0. I just don't understand why this is. If there is a reaction, and O2 is one of the products, why is there no heat released when...

Hi, I have a question about the formulation of the derivative. The definition is f'(x_0)=\lim_{x\rightarrow x_0}\frac{f(x)-f(x_0)}{x-x_0}[/itex] Lets say this limit exists. Can I write the limit in the typical \epsilon-\delta method as such Given the limit exists, then for all...

Homework Statement A \Delta connected induction machine is to start from a source of 480V, 60 Hz. The motor ratings are : 4 poles, \Delta connected, 480V, 60 Hz, X_{ls}\,=\,X_{lr}\,=\,4\,\Omega, X_m\,=\,50\,\Omega, R_s\,=\,0.25\,\Omega, R_r\,=\,0.4\,\Omega. Find the current in the...

why do we require delta and star load connection ? thanks.

Homework Statement Prove the statement http://www.mathhelpforum.com/math-help/vlatex/pics/60_32c8daf48ffa5f233ecc2ac3660e517e.png The Attempt at a Solution I am clueless as to how I would go about doing this, I know the basic properties. I think it has to do with using epsilon...

Homework Statement At 699 K, DeltaG (degree)=-23.25kJ for the reaction H2(g) + I2(g) <-> 2HI(g). Calculate DeltaG for this reaction if the reagents are both supplied at 10.0 atm pressure and the product is at 1.97 pressure. Homework Equations I believe this is the relevant equation G=G(degree)...

Please show me the derivation for the formula relating Gibbs free energy change and the reaction quotient. I didn't find it on Google, so I decided to turn here. Is it really that hard? Thanks for any help.

what is the difference between delta H and q? delta H = delta U + P(delta V) so, delta H = delta U -W delta U=q + W so, q=delta U - W So now is there a difference between the two at all? Why then 2 separate quantities? Thank You

is delta H a state function??(Hess Law?) Is delta H a state function? We know that delta H=delta U+W (at const P) so, we also know that W is path dependent function.So delta H being a sum of delta U and a path dependent function must not be a state function.(point 1) But there is this Hess...

1.>Consider a gas in a vessel with a piston on top.Let it expand to a greater volume. So, delta H=delta U+delta(PV) but delta U is 0 as it is isothermal. now,as the number of moles of gas remains constant,delta(PV) is nR(delta T) which is again 0. SO delta H is 0. Thats what my book says...

Hello Again! My question: Find the bound energy spectrum of the potential that contains two delta-function wells: V(x) = -V_{0}\delta(x-\frac{a}{2}) -V_{0}\delta(x+\frac{a}{2}) under the assumption that the wells are located very far away from each other. Find and plot the associated stationary...

I have a question about delta functions. What I want to believe is the following \int_{-\infty}^{0} \, dt \, f(t) \delta(t) = \frac{1}{2} f(0). It even shows up on Wikipedia (so it must be true!) Here is an argument (I know it isn't a proof). If I use the "delta-sequence" approach and...

Anyone know where I can find a discourse on the dirac delta function in spherical or polar coordinates, in particular why it is the form it is with correction coefficients? Thank you.

Homework Statement Dear all, I have a problem when I using MATLAB to get the Fourier transform of dirac delta function. below is my code.Homework Equations clear all; clc; close all; % t=0:0.002:2; t=0:0.002:4; dt=t(2)-t(1); u=zeros(size(t)); pos0=find(t>=1,1); u(pos0)=1/dt...

Homework Statement Find delta f of f=Z^-1 * Sqrt(9x^2*y^2) at point (1,4,10) Homework Equations f =f+(fx*delta x )+(fydelta y)+(fz*delta z) The Attempt at a Solution fx = 9*2x/(z*(2*sqrt(9x^2*y^2)) =.18 plugging in (1,4,10) fy=2y/(z*(2*sqrt(9x^2*y^2)) =.08 fz=(sqrt(9x^2*y^2) )...

In a given distance apparently regardless of how much work is done (whether the force is large or small) the change in thermal energy is the same since thermal energy change is fk times d. Since Fk is constant as is D the change in thermal energy of the system will remain constant. I'm having...

Homework Statement find an open interval about x0 on which the inequality lf(x)-Ll<\epsilon holds. Then give a value for \delta>0 such that for all x satisfying 0<lx-xol<\delta the inequality lf(x)-Ll<\epsilon holds f(x)=x2 L=3 x0=-2 \epsilon=0.5 Homework Equations The Attempt...

i don't really understand the dirac delta function in 3D. is it right that integral of f(r)d3(r-a)dt = f(a) where a = constant ,r is like variable x in 1D dirac delta function? so why when i have f(r')d3(r-r') , it picks out f(r)? where r is now a constant and r' is a...

Recently in adv calc we have been dealing with the epsilon delta definition for continuity, and my professor said that it is ok to assume that delta<1. I actually used this to show that x^4 satisfies the epsilon delta condition but I'm not quite sure why we can take delta<1. I am sure you guys...

[PLAIN]http://img820.imageshack.us/img820/5817/img8968h.jpg Any hints please, just starting question. Haven't really done any questions like this before

Hello all, I joined this amazing forum just today.I hope that my question will get answered soon. So here it is.I am unable to understand a some steps in calculation. Please help me understand. Here is a linear homogeneous first order differential equation whose solution a research...

Homework Statement Let \vec{A}(\vec{r})and \vec{B}(\vec{r}) be vector fields. Show that Homework Equations \vec{\nabla}\bullet(\vec{A}\vec{B})=(\vec{A}\bullet\vec{\nabla})\vec{B}+\vec{B}(\vec{\nabla}\bullet\vec{A}) This is EXACTLY how it is written in Ch 3 Problem 2 of Schwinger...

Although I am an aspiring physicist, I cannot cope with the physicist's love for vagueness when it comes to yielding math. Exactness is simply not a luxury that can be ignored, certainly not in theoretical physics. But okay, I realize the dirac delta function can be made exact by the use of...

I am confused from a couple of diagrams I have about how to correctly wire 3 small transformers to form a delta wye connection. The transformers are labeled as Primary H1 H2, H1 H2, H1 H2 Secondary X2 X1, X2 X1, X2 X1 My question is in all the diagrams I have the Delta connections...

So I've been told that the Dirac delta functional is a distribution, but I don't see why that's the case. I had an introduction to distributions in my calculus IV course, but as I remember it, a distribution involves and integral containing a the product of a function from the Schwartz space and...

i need help trying to find the laplace transform of te-t\delta(t) i know the laplace transform of te-t is 1/(s+1)2 but i don't know how to find the laplace transform of a product with the Dirac delta

Hi this is my first post here so I'm sorry if my question seems trivial. I haven't worked a lot with the dirac delta function before, so i always thought that the shifting property would only work as: \int\delta(x-h)\;f(x)\;dx=f(h) Now I've been reading some articles and I came across...

I understand that the Dirac delta function can be taken as a distribution. And that one can calculate the Shannon entropy or information content of any distribution. So what is the information content of the Dirac delta function? I think it is probably identically zero, but I'd like to see the...

I'm designing a new spacecraft model, but it does not use Delta wings, like most ships do. I need them to be efficient, because my ship is kinda large. (It's like a hybrid of a rocket, and the Space Shuttle), and so I have two questions: 1) My craft's wings look like really tall right...

Hi folks, I am new to physics forums , an engineer by profession, I have newly developed some interest for pure physics, can someone please enlighten me on the violation of energy conservation by the time energy UP? The way I understand it the principle only puts a LOWER bound. Is...

Homework Statement Show that Re(z) -> Re(z0) as z -> z0 The Attempt at a Solution let epsilon > 0, choose delta = epsilon, so |Re(z) - Re(z0)| = |(z + z')/2 - (z0 + z0')/2| (where z' and z0' are the complex conjugates) |(z + z')/2 - (z0 + z0')/2| = |(z - z0 + z' - z0')/2| < |z -...

Homework Statement Define: f(z) \rightarrow w1 as z \rightarrow z0 and g(z) \rightarrow w2 as z \rightarrow z0 prove that f(z)/g(z) \rightarrow w1/w2 as z\rightarrow z0 The Attempt at a Solution let \epsilon > 0 choose \delta > 0 such that: |f(z) - w1| < ______...

Homework Statement Is my understanding correct? As delta(y) and delta(x) approach X from points to the left and points to the right of X (x is what we wish to find the derivative of) then the x and y values of points to the left and right approach the x and y values of X. And as the...

hi, i don't understand why levi civita symbols is equal to kronecker delta when i was reading the wikipedia on it http://en.wikipedia.org/wiki/Levi-Civita_symbol namely, 1)why does EijkElmn = det [ 9 terms of kronecker delta] how do we know its those 9 terms? like dil dim din etc 2)and since...