Delta Definition and 1000 Threads

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?

Homework Statement Hello. This question is about Fourier transforms and the Delta function. Find the Fourier transform of: g(k)=\frac{10sin(3k)}{k+\pi} Homework Equations f(x)=\frac{1}{2\pi}\int_{-\infty}^{\infty}g(k)e^{(ikx)}dk...

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...

Homework Statement a) Use Y-Δ transformation to simplify the circuit in Figure 2-a to that in Figure 2-b and find the elements and values of Z1, Z2 and Z3 b) Use mesh analysis for the circuit in Fig. 2-b to calculate I1 and I2 Here are the circuits...

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...

Homework Statement For: \lim_{x \to 1^{-}} \frac {1}{1-x^{2}} = \infty Find \; \delta > 0 \; such that whenever: 1-\delta<x<1 \;\; then \; \frac {1}{1-x^{2}} > 100 Homework Equations |x-a| < \delta |f(x)-L| < \epsilon The Attempt at a Solution So as it is set...

Homework Statement Ok so this may get a little drawn out here because my book only gives me one example and I guess I can't decipher its meaning. So here is the example they give: For \;\; \lim_{x \to 2} x^{2} = 4 Find a \;\; \delta > 0 \;\; such that whenever 0 < |x-2|< \delta, \;\;\...

how do we apply dirac delta function?when do we apply?

I want to tell a story about an encounter with Delta Airlines that my parents and I experienced recently. We had scheduled three tickets to San Diego a long time ago. Those who were to fly were my sister, my mother, and my brother. However, my brother found unexpected plans that forbid him to...

for a three phase power generator, you can have sources in series with inductances in either a wye or delta formation by designing the generator differently. from my understanding, if you choose wye instead of delta, then the power produced will be increaced by a factor of the root of 3 in...

Hi, I'm trying to understand the quantum mechanical solution to this potential: V(x) = \left\{\begin{array}{cc}\infty & \mbox{ for } x < 0,\\-\lambda\delta(x-d) & \mbox { for } x > 0\end{array}\right. A particle of mass m is constrained to move on the half straight line \{x \in \mathbb{R}: x...

Homework Statement Hi, I would like to know what is the right way to write continuous deltas standing in a circle of radius a? Homework Equations The Attempt at a Solution I am not sure weather it's δ(r-a) or is it δ(r-a)/|r-a| Thank you

Homework Statement The Identity to prove: Homework Equations Using Integration by parts The Attempt at a Solution I couldn't produce the denominator.

r(x) = x if x \geq 0 and r(x) = 0 if x<0 I have to show that: 1-\[ \int_{- \infty}^{+ \infty} r(x) \varphi ''(x) dx = \varphi(0) \] And 2- that the second derivative of r is the Dirac delta. And I managed to do this by integrating by parts. Howver, I don't get why I can't just write: \[...

http://en.wikipedia.org/wiki/Propagator What does this equation mean: \Big(H_x - i\hbar\partial_t\Big) K(x,t,x',t') = -i\hbar\delta(x-x')\delta(t-t') Wouldn't it be more relevant to emphasize these equations: \Big(H_x - i\hbar\partial_t\Big) K(x,t,x',t') = 0,\quad\quad t\neq t'...

I'm learning how to find delta from a particular epsilon. I'm not understanding a step in the solution for the problem listed below: Here's the problem: lim(x→3)x^2=9 Solution: |x^2-9|<.05 -.05<x^2-9<.05 2.9916..<x<3.0083 2.9916..-3<x-3<3.0083..-3 -.0083..<x-3<.0083.. delta=.0083...

Hi alll, I have an integral which includes a Kronecker delta: I = \int_{u=0}^{a} \int_{v=0}^{a} F(u) G(v) \delta_{u,v} \, \mathrm{d}u \, \mathrm{d}v I know that for a 1D integral there exists the special property: \int F(u) DiracDelta(u-a) = F(a) However, is there something equivalent for...

In the http://en.wikipedia.org/wiki/Hamilton%27s_principle#Mathematical_formulation", I ran across a notation I'm not familiar with. The part I'm unsure about is: \frac{\delta \mathcal{S}}{\delta \mathbf{q}(t)}=0 In the context of the article, what is the meaning of that equation...

Various chemical formulae for the composition of superconductors quote the oxygen content, ie the number oxygen atoms present, as say Osub(10-delta). I would like to know the significance of delta.

Hi, In Srednicki's chapter on cross sections, when he calculating the probability of a particular process from the overlap \langle f\mid i\rangle he comes across: [(2\pi)^4\delta^4(k_{in}-k_{out})]^2 He states this is can be equated as follows: [(2\pi)^4\delta^4(k_{in}-k_{out})]^2=...

Gibbs free energy and Gibbs Free energy under standard conditions; Hi. Is a value of Gibbs free energy (delta G) and Gibbs free energy Under standard conditions (delta G knot) the same if they are both calculated under the same temperature (298K)? cheers

Homework Statement In delta potential barrier problem Schrodinger equation we get \psi(x)=Ae^{kx}, x<0 \psi(x)=Ae^{-kx}, x>0 We must get solution of lim_{\epsilon \rightarrow 0} \int^{\epsilon}_{-\epsilon}\frac{d^2\psi}{dx^2}dx Homework Equations The Attempt at a Solution lim_{\epsilon...

Homework Statement Show that \delta_a^b is a in fact a mixed tensor of valence (1,1).Homework Equations Definition of a (1,1) tensor: \delta'_a^b=\frac{\partial x'^b}{\partial x^c}\frac{\partial x^d}{\partial x'^a}\delta_c^dThe Attempt at a Solution So, I just explicitly put back the...

The problem was to give the charge distribution of a uniformly charged disk of radius R centered at the origin and perpendicular to the z-axis. The professor explained us how to do so (though many parts were unclear to me and I couldn't copy everything that was on the blackboard because we were...