Delta Definition and 1000 Threads

Homework Statement a) A charge q1 = q is at r'1 = -Di, and a charge q2 = -3q is at r'2 = Di. Find an expression for the volume charge density p(r). b) An infinitely long wire along the z-axis has a uniform linear charge density \lambda. Find an expression for the volume charge density p(r) in...

Homework Statement prove that the lim as x goes to 4 of x^2 + x -11 = 9 This is the example used on Paul's Online Notes on limits in calculus which can be found here http://tutorial.math.lamar.edu/Classes/CalcI/DefnOfLimit.aspx (I really like this resource.) Homework Equations Paul...

Is this legal? I assumed that delta x is a constant that is approaching zero. So I brought it out. When I took the derivative, the delta x canceled out with the denominator. So I'm left with the derivative of the intergral of f(x) with respect to itself. So I'm essentially trying to find the...

Hi, I am looking for approximations to the delta functoin which I can use on a computer. Although I will never get an exact delta function, I can make an approximation that it can be improved as much as I like. Would you help me to find the approximation of the delta function so that I can...

Homework Statement a.) Given \delta_n=\frac{ne^{-{n^2}{x^2}}}{\pi} Show: x{\frac{d}{dt}\delta_n}=-\delta_n b.) For the finite interval (\pi,-\pi) expand the dirac delta function \delta(x-t) in sines and cosines, sinnx, cosnx, n=1,2,3... They are not orthogonal, they are normalized to...

Hopefully people are still prowling the forums this close to christmas :) I want to show that sin(ax)/x is a representation of a delta function in the limit a->infinty i.e 1) It equals 0 unless x=0 2) integrated from plus minus infinity it equals 1 and 3) multiplying by an arbitrary...

The Solubility Constant for AgI(s) at 25 degrees Celsius is 8.3*10^-17 how do i find \DeltaG(rxn) for [Ag+]=9.1*10^-9 & [I-]=9.1*10^-9 Using the equation: ΔG=ΔGº+RTln(Q) Let K=Our solubility constant: 0=ΔGº+RTlnK ΔGº=-RTlnK Now, ΔG=-RTlnK+RTlnQ ΔG=RTlnQ-RTlnK ΔG=RT(ln(Q/K)) ΔG=-5.67KJ/mol...

does the epsilon delta definition of the limit connect to the uncertainty in measurements like this? like if we measure a quantity time with value a with error of + or - delta then my formula will give me v with value L +or - epsilon or is it unrelated?

NOT A HOME WORK QUESTION how do i know if a delta potential function is given if its solution is even or odd? do i look for symettry or something take this function for example: V(x)= -alpha[delta(x+a) + delta(xa)] i skeched the following graph. since V(-a)=V(a)...

Homework Statement Sodium metal reacts with water to produce hydrogen gas and sodium hydroxide according to the equation: 2 Na(s) + 2 H2O(l) ? 2 NaOH(aq) + H2(g) When 0.030 mol of Na is added to water, the temperature of the calorimeter rises from 25.00C to 37.90C. If the heat...

Homework Statement Let's say we have a wire of finite length L with total charge Q evenly spread along the wire so that lambda=Q/L, linear charge density, is constant. The wire is shaped in x-y plane in some well behaved curve y = f(x). Find the surface charge density sigma(x,y). Homework...

Homework Statement Prove using the Levi-Civita Tensor/Kroenecker Delta that: (AxB)x(CxD) = (A.BxD).C-(A.BxC).D Homework Equations εіјkεimn = δjmδkn – δjnδkm (where δij = +1 when i = j and 0 when i ≠ j) The Attempt at a Solution if E = (AxB) then Ei = εіјkAjBk, and if F =...

I don't understand in the first paragraph of the attached lecture notes. Could anyone help?

I am looking at a problem, part of which deals with expressing delta dirac as a limiting case of gaussian function. I am aware of the standard ways of doing it. In addition, I would also like to know if the following are correct - \delta(x-a) = \lim_{\sigma \rightarrow{0}} \int_{a -...

i need to prove that for every delta i call d=delta e=epsilon 1/|x+1|>e we can choosr any e we want so they took e=1/4 but because the innqualitty needs to work for every delta they took x=min{2,(1+d)/2} for d>2 it takes x= 1+d /2 for d<2 takes x=2 uppon what logic they found this...

Homework Statement I have infinite square well which has a potential V(x)=\frac{\hbar^2}{m}\Omega\delta(x) in x=0, and is 0 in the interval x\in[-a,a]Homework Equations Schrodinger eq.The Attempt at a Solution I solved the time independant Schrodinger eq. by integration around x=0 by some...

So my physics book says "from x(final)=x(initial)+V(initial)t+1/2at^2 observe that when x(final)=x(initial), the time is given by t=-2V(initial)/a" Now if change in x is equal to 0, wouldn't your velocity v(initial)t from above along with your acceleration also be zero? How is the book getting...

This isn't a HW question just something I am curious about. I was looking on wikipedia and found a way to prive the Levi-Citiva Kronecker Delta relation that I hadn't seen before. The site claims \epsilon_{ijk}\epsilon_{lmn} = \det \begin{bmatrix} \delta_{il} \delta_{im} \delta_{in}\\...

\Delta H_{f}\circ=-1670kJ/mol for Al_{2}O_{3} What is \Delta H_{rxn}\circ for 2Al_{2}O_{3}(s)\rightarrow4Al+3O_{2}(g) So clearly we simply multiply -1670*2=-3340kJ/mol. The answer is actually POSITIVE 3340kJ/mol! Can someone please explain to me how this reasoning works? Thank you!

Hello all. So I am trying to integrate a function of this form: \int\intF(x,y)\delta[a(Cos[x]-1)+b(Cos[y]+1)]dxdy The limits of integration for x and y are both [0,2Pi). I know that this integral is only nonzero for x=0, y=Pi. So this should really only sample one point of F(x,y)...

What is the way to show that \lim_{y\rightarrow0}\frac{y}{x^2+y^2}=\pi\delta(x) ?

Homework Statement \int_{0}^{b} \int_{0}^{2\pi} C_{k,m}(r)^2 \left{\begin{array}{cc}cos(m\theta)^2\\sin(m\theta)^2 \end{array}\right} r dr d\theta Homework Equations See above The Attempt at a Solution Ignoring the 'r' integral for a second, the solution that I see written...

Homework Statement Show that the orthogonality relation for the "cosine basis functions" used in the Fourier series is 1/L\intcos[(n*pi*x)/L)]cos[(m*pi*x)/L)]dx = {Sin([n-m]*pi)}/[(n-m)*pi] + {Sin([n+m]*pi)}/[(n+m)*pi] By considering the different integer n and m, show that the right...

Hello, My question is about how dirac-delta function is derived by using this integral, \frac{1}{2\pi }\int_{-\infty}^{\infty}e^{ikx}dk=\delta (x) I couldn't solve this integral. Please help me. Thanks for all of your helps.

Hello, I'm trying to understand the concepts of the change in internal energy (U) or enthalpy (H) of a reaction, given the laws and equations of basic thermodynamics, but I'm getting confused with the following thought experiment. I'm looking at U, since I find it easier to imagine, even...

Homework Statement Pro #2 if you click on this link. http://s1104.photobucket.com/albums/h332/richard78931/?action=view&current=hw4.jpg Homework Equations , The Attempt at a Solution Click here http://s1104.photobucket.com/albums/h332/richard78931/?action=view&current=2a.jpg...

Suppose limx->a f(x) = L does NOT equal 0. Prove that there exists a (delta) d > 0 such that 0<|x-a|<d which implies f(x) does NOT equal 0. Does Anybody Know the Proof For This?

Hi, I have a question about the epsilon / delta definition of limits, for example the limit of x as it approaches c for f(c) = L. As I understand it, epsilon is basically the number of units on either side of L on the y-axis that makes a range between L + epsilon and L – epsilon with L being...

Hi there! I have a problem with one of the questions given to us in the signals and systems course. If anyone could help me I would greatly appreciate it! Homework Statement integral(from -infinity to +infinity) of u0(t) * cos(t) dt u(t) is a step function. Homework Equations...

I was wondering if I integrate the dirac delta function from 0 to infinity where the function it's integrated with is the constant 1, will I get 0.5 or 1? And why? This is not homework so I decided to post this here although I asked this question in class and the teacher (assistant) wasn't...

Homework Statement Hi All. I am given this integral: \int_{-\infty}^{\infty}A\Theta e^{i\omega t}dt I need to show that it's equal to the following: =A(\pi \delta(\omega)+\frac{i}{\omega})Homework EquationsTheta is the Heavyside step function. The Attempt at a Solution The step function...

Homework Statement Using the definition of |x-a|<delta implies |f(x) - L|<epsilon, prove that lim x->0 x^n*sin(1/x) holds for all n belonging to natural numbers. Homework Equations Definition of a limitThe Attempt at a Solution Ok, so when I see "prove for all n belonging to natural numbers" I...

Homework Statement I want to plot the following function into Maple14. \vec{v}=frac{1}{\vec{r^{2}}} \hat{r} **In case the latex is screwed this says v=r^(-2) *r-hat The Attempt at a Solution My code for Maple is the following, but it doesn't seem to work.restart; with(LinearAlgebra)...

[SOLVED] Proofs for Dirac delta function/distribution Homework Statement Prove that \delta(cx)=\frac{1}{|c|}\delta(x) Homework Equations \delta(x) is defined as \delta(x)=\left\{\stackrel{0 for x \neq 0}{\infty for x=0} It has the properties...

Hello! I would like to show the following: u\in C^2(U) \cap C(\bar{U}) satisfies \Delta u(x)>0 for any x\in U, then \max_U u cannot be achieved by any point in U. Here, u\in \mathbb{R}^n, i.e. it's not complex valued. Apparently, one can use the Taylor expansion formula to show this...

Homework Statement I am currently having problems with a similar question, and used that post, but I'm finding it hard to solve for x. the question states. if f(x) = 1/x for every x > 0, there is a positive quantity e (epsilon), find the d(delta) quatity such that if 0 < l x - 3 l < d...

Hi Can somebody help me with this... Is is correct to say that, Integral(delta(0)) = 1 (limits are from -infinity to +infinity) I don't know latex and sorry for the inconvenience in readability. Thanks, VS

I am a first year freshman at UC Berkeley, in Math 1A. We learned the delta-epsilon proof for proving the limit of functions. I won't go through a whole proof or anything, but the general idea is you have a delta that is less than |x-a| (and greater than zero) and an epsilon less than |f(x)-L|...

These problems are from Introductory Quantum Mechanics (Liboff, 4th Ed.) Note: I'm using "D" as the dirac delta function. 3.9 (a) Show that D( sqrt(x) ) = 0 This has me stumped. It is my understanding that the Dirac function is 0, everywhere, except at x=0. So, how can I show this to be...

Hi, I hope this is the right place to ask this Is it possible to expand the Dirac delta function in a power series? \delta(x)=\sum a_n x^n If so, what's the radius of convergence or how can I find it? Thanks.

Suppose I wind up with the relation f(x)\delta (x-x')=g(x)\delta (x-x') true for all x'. Can I safely conclude that f(x) = g(x) (for all x)? Or am I overlooking something? this is a little too close to dividing both sides by zero for comfort.

Homework Statement \int_{-\infty}^{\infty}{u(t)e^{-t}(\delta(t+1)+\delta(t-1))dt Homework Equations \int_{-\infty}^{t}{u(t)dt = \left\{\begin{array}{cc}0,&\mbox{ if } t< 0\\t, & \mbox{ if } t>0\end{array}\right. \int_{-\infty}^{\infty}{f(t)\delta(t-a)dt} = f(a) The...

Homework Statement Proove the limit as x approaches 4 for f(x)=x^2-8x= -16 Homework Equations Definition of Precise Limits The Attempt at a Solution I know that I want x^2-8x+16 (after moving the -16 over per the limit definition) to look like |x-4| Factoring gets me (x-4)(x-4)<e Because...

Homework Statement Prove that lim x->3 of (x^{2}+x-5=7Homework Equations 0<x-c<\delta and |f(x)-L|<\epsilonThe Attempt at a Solution The preliminary analysis. The first equation in the relevant equations becomes 0<x-3<\delta And the second equation becomes |(x^{2}+x-5)-7|<\epsilon...

I'm trying to evaluate the energy shift in a scalar field described by the Klein-Gordon equation caused by adding two time-independent point sources. In Zee's Quantum Field Theory in a Nutshell, he shows the derivation for a (3+1)-dimensional universe, and I'm trying to do the same for an...

I'm not even sure if that's the right name, but my question is when you have a \delta under the integral. For example, \int\limits_{-\infty}^{\infty} ln(x+3) \delta (x+2) \, dx Without the \delta the integral is easy enough (I think) using a u-substitution (u=x+3) then it is (x+3) \ln (x+3) -...

Approximate the function f(x)=\sin(x) using the corresponding Maclaurin polynomial: P_5(x), in a bound \epsilon(0,\delta). Determine a value of \delta>0, so that the rest R_5(x) verifies |R_5(x)|<0.0005 for all x\in{\epsilon(0,\delta)} Well, the first thing that puzzles me a bit is that the...

I'm curious about the use of the Dirac Delta function. I am familiar with the function itself, but have never really seen in used in actual problems. The only problems I've worked with the function are those specifically about the function (ie. Evaluate the Dirac Delta function at x=3). My...

Where can i find the proof of dirac's function properties?

Hello all, My question is as follows: f:[1,\infty) is defined by f(x)=\sqrt{x}+2x (1\leqx<\infty) Given \epsilon>0 find \delta>0 such that if |x-y|<\delta then |f(x)-f(y)|<\epsilon It seems I am being asked to show continuity, and not uniform continuity, so my approach is this, but I am...