Delta Definition and 1000 Threads

first of all i don't know anything about this epsilon and delta method.explain this a bit. secondly i have been given a problem involving this method: f(x)=x^2 given: limit x-->2 [x^2] = 4 a) what is the value of x' such that f(x')= 4 + .01? find \delta=x'-2 b) what is the value of...

Homework Statement I'll post it as an image since the notation will be tricky to type out. It's problem 4. http://img29.imageshack.us/img29/1228/307hw3.jpg Homework Equations Not sure this really applies hereThe Attempt at a Solution This is for a physics course but as you can see it's...

Homework Statement Suppose |f(x)-5|<0.1 when 0<x<5. Find all values \delta>0 such that |f(x)-5|<0.1 whenever 0<|x-2|<\delta Homework Equations The Attempt at a Solution I know that 0<|x-2|<\delta 2-\delta<x<2+\delta \delta=2 but how does this part of the equation help me find...

Homework Statement Integrate exp[abs(x)+3]*delta(x-2) dx, -1, 1 2. The attempt at a solution f(x)=exp[abs(x)+3]*delta(x-2) f(2)=148.4 Integrate exp[abs(x)+3]*delta(x-2) dx, -1, 1 = 0 [b]3. Why is the answer 0?

Hi Everyone, I am trying to solve the partial differential equation given below: \Delta^2\phi(x,y,z)=\frac{qf(x,y,z)}{\epsilon} where f(x,y,z)=1 at one point and zero elsewhere. This is the poisons equation for a point charge inside a conducting box. Can this be solved using the...

I'm having trouble understanding the proof/solution below (please see photo, I also wrote out the problem below). I highlighted the part of my problem in red (in the picture attached). Basically I'm not sure what identity they use to get the Kronecker delta after differentiating or whether they...

Homework Statement I am a bit confused with how to deal with Kronecker Delta. I need to show that P,i = ( P*δij ),j The i and j are subscripts. Homework Equations The Attempt at a Solution P,i = ( P*δij ),j = P,j*δij + P*δij,j I assumed I could get rid of P*δij,j leaving...

Apparently, when convolving, for example: [δ(ω-π) - δ(ω+π)] * (δ(ω+50π)-δ(ω-50π)) the result is δ(ω+49π)-δ(ω-51π)-δ(ω+51π)+δ(ω-49π) where δ() is the Dirac delta function, * the convolution operator and ω the frequency variable How do we get to this? Can you help me on the intuition in...

Probably a trivial question, but does Dirac delta function has (to have always) a physical dimension or is it used just as a auxiliary construct to express e.g. sudden force impulse, i.e. Force = Impulse \times \delta, where 'Impulse' carries the dimension? Any comments would be highly...

Hi, if the definition of a dirac delta (impulse) function is just a sinc function with an infinite height and 0 width, why is it that they are shown and used in Fourier analysis as having a finite height? for example g(t) = cos(2*PI*f0*t) has two impulses of height = 1/2 at f=+/-f0

Hello, I have stumbled upon a couple of proofs, but I can not seem to get an intuitive grasp on the what's and the whys in the steps of the proofs. Strictly logical I think I get it. Enough talk however. Number 1. "Let f be a continuous function on the real numbers. Then the set {x in R ...

does anyone know why djmdkl = dkm when j = l thanks! can i interchange it to djmdkl = dkldjm ? since l = j do the "j" in dkjdjm signify summation? so i get dk1d1m + dk2d2m + dk3d3m ?

Homework Statement For some reason these are just messing me up. I need to prove: 1. \delta(y)=\delta(-y) 2.\delta^{'}(y) = -\delta^{'}(-y) 3.\delta(ay) = (1/a)\delta(y) In 2, those are supposed to be first derivatives of the delta functions Homework Equations Use an integral...

Hi, I was wondering about something a friend told me. He said that we can regularize this product in this form sgn(x)^2 \delta(x)=\frac{\delta(x)}{3} Any guess on how to derive it Thanks.

I am aware that the following operation: mathbf{M}_{ij} \delta_{ij} produces mathbf{M}_{ii} or mathbf{M}_jj However, if we have the following operation: mathbf{M}_{ij} \delta^i{}_j will the tensor M be transformed at all? Thank you for your time.

Homework Statement With the discriminate, why is delta sometimes used? Homework Equations \Delta = b2 - 4ac The Attempt at a Solution I get the logic behind what the discriminate is and how and why it works, but I don't understand why delta is used in the equation. What change is...

in QF, every dirac delta function is accompanied by 2\pi,i.e.(2\pi)\delta(p-p_0) or (2\pi)^3\delta(\vec{p}-\vec{p_0}) the intergral element in QF is \int\frac{d^3p}{(2\pi)^3}\frac{1}{2E_P}, it comes from the integral element \int\frac{d^4p}{(2\pi)^4}(2\pi)\delta(p^2-m^2),I want to know why...

The Relation between Levi-Civita Density and Kroneckers Delta as follows \sum^{3}_{k=1} \epsilon_{mnk} \epsilon_{ijk} = \delta_{mi} \delta_{nj} - \delta_{mj} \delta_{ni} Logically we can satisfy both sides of the expression but Can anyone tell me how to derive this analytically ?

Hello again. Thank you guys. You have been great help... I have another one: Given a potential well- 2a is it's width, and in the middle - there is a delta potential: V(x)= \frac {\hbar^2} {2m} \frac {\lambda} {a} \delta(x) I am looking for the odd solution to this problem. I thought...

Homework Statement Homework Equations The Attempt at a Solution Can I write, say, f(x) \delta(x)=f(2)\delta(x)? Since \delta(x) =0 for x\neq0

let θ(x-x') be the function such that θ = 1 when x-x' > 0 and θ = 0 when x-x' < 0. Show that d/dx θ(x-x') = δ(x - x'). it is easy to show that d/dx θ(x-x') is 0 everywhere except at x = x'. To show that d/dx θ(x-x') is the dirac delta function i also need to show that the integral over the...

Homework Statement Simplify the following expressions involving the Kronecker delta in N dimensions. Where possible, write the final result without indices. C_{ns}\delta_{rn} Homework Equations The Attempt at a Solution I know Kronecker delta is symmetric but that doesn't seem to help. Is...

Could anybody explain me what's the difference between \delta\Gamma^{\rho}_{\mu\nu} and \Delta\Gamma^{\rho}_{\mu\nu}? Thank you

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 =...

Homework Statement A balanced delta load having 18ohm resistance and 24 capacitive reactance in series in each phase is supplied through lines each having 1 ohm resistance and 2 ohm inductive reactance. If the line to line voltage at the sending end is 250 V, find the phase current and line...

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}...

using the convolution theorem with power functions x^{m} we may define via the convolution theorem the product of 2 dirac delta distribution then main idea is to consider the convolution integral \int_{R}dt(x-t)^{m}t^{n} and then apply the Fourier transform with respect to variable 'x'...

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.

Hi All, I'm trying to plot some DiscreteDelta functions in mathematica but unfortunately since the points are singular nothing shows up in the plot. Usually when this comes up I replace the delta functions with very narrow gaussians, graphically it looks even nicer (I'm plotting absorption...

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