Delta Definition and 1000 Threads

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...

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 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>...

Problem arises from next situation. If we have some distribution (of mass for example) on a ring which is given by \begin{equation} \rho=m\delta(\phi) \end{equation} where phi is azimuthal angle. What is the value of integral ? \begin{equation} \int_0^{2\pi} \! \rho \, \mathrm{d}...

Homework Statement I am using the time differentiation property to find the Fourier transform of the following function: Homework Equations f(t)=2r(t)-2r(t-1)-2u(t-2) The Attempt at a Solution f'(t)=2u(t)-2u(t-1)-2δ(t-2) f''(t)=2δ(t)-2δ(t-1)-?? Can somebody explain what the...

It is better for you to have studied "Feynman lectures on Physics Vol.3", because I cannot distinguish whether the words or expressions are what Feynman uses only or not and in order to summarize my questions here, I have to just quote the contents of the book. However, one thing I notice is...

Homework Statement I need to prove that RC=(VT/2 delta V) Select the circle components of Charging and discharging of a capacitor Measure the resistance of resistor with a multimeter When you run a different frequency the cycle time change run different frequency that T<<tao, T=tao...

The Dirac delta "function" is often given as : δ(x) = ∞ | x = 0 δ(x) = 0 | x \neq 0 and ∫δ(x)f(x)dx = f(0). What about δ(cx)? By u=cx substitution into above integral is, ∫δ(cx)f(x)dx = ∫δ(u)f(u/c)du = 1/c f(0). But intuitively, the graph of δ(cx) is the same as the graph of...

Greetings! I am confused with the difference between Δf, δf, and df. I think Δf is a difference between two values, while df and δf refer to infinitesimal change (but I do not know the difference between the two.) Can anybody explain the difference? I am studying solid state physics (I am...

I originally asked this in the Calculus & Analysis forum. But perhaps this is better suited as a question in Abstract algebra. For the set of all Dirac delta functions that have a difference for an argument, we have the property that: \int_{ - \infty }^\infty {{\rm{\delta (x -...

Hello, I have this question that I've been working on. The question requires me to find the current across an inductor in a Delta circuit, so I want to solve this question using Delta-to-Wye method. so I transformed it using the method and I found the total impedance of the whole circuit, then I...

If you have I=∫∫dxdy [∇x∇y δ(x-y)] f(x)g(y) where ∇x is the derivative with respect to x (and similarly for y), then doesn't it matter which order you take the derivatives? For example: I=∫∫dxdy f(x) ∇x [∇y δ(x-y)] g(y) =∫dx f(x) ∇x[-g'(x)]=∫dx f(x) [-g''(x)] whereas if you take the...

Homework Statement I'm trying to understand a proof of the LC-KD identity involving determinants (see attachment), from the book Introduction to Tensor Calculus and Continuum Mechanics by Herinbockel. What is the author saying in the last line of text? How can we sum the deltas in the upper...

Use the delta-epsilon definition to prove f(x,y) = y/(1+x2) is continuous at (0,0)Attempts:So I'm doing some work and my main issue is finding a bound for the denominator of 1+x2: So work wise I have something looking like: \delta/(|1| + |x2| ). How could I found a good bound?

If I'm not mistaken, measuring the \delta_{CP} from the PMNS matrix may be done by comparing P(\nu_{\alpha} \rightarrow \nu_{\beta}) to P(\overline{\nu_{\alpha}} \rightarrow \overline{\nu_{\beta}}) , where P(\nu_{\alpha} \rightarrow \nu_{\beta}) - P(\overline{\nu_{\beta}} \rightarrow...

1 = 0 <-- What goes fundamentally wrong? Delta distribution 2 \pi a = \iint \delta(a^2 - (x^2+y^2)) \mathrm d x \mathrm d y Differentiating both sides w.r.t. "a" (using chain rule on the RHS) gives \frac{\pi}{a} = \iint \delta'(a^2 - (x^2+y^2)) \mathrm d x \mathrm d y Changing...

Hi Iknow that if we have delta function of one variables function, then we can write it as: \delta (f(x)) = \sum \frac{\delta(x-x0)}{f'(x0)} but how we can write a function of two variables: \delta (f(x,y))