Delta Definition and 1000 Threads

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...

Kronicker Delta, Levi-Civita, Christoffel ... and "tensors" For quick reference in grabbing latex equations: http://en.wikipedia.org/wiki/Levi-Civita_symbol http://en.wikipedia.org/wiki/Kronecker_delta http://en.wikipedia.org/wiki/Christoffel_symbols Wiki warns that the Christoffel...

Hi, On p67 of shankar Principles of QM, he considers the delta functions derivative. He says: \int \delta'(x-x')f(x')dx'= \int \frac{d\delta(x-x')}{dx}f(x')dx'= \frac{d}{dx}\int \delta(x-x') f(x')dx'=\frac{df(x)}{dx} I don't understand how the second equality follows, how can the...

Hi everybody, I'm reading about sigma delta adc, the base theory. I've read about the first order modulator and now the second order, but I have a problem (maybe stupid) with a phrase of my book (Data Converters by F.Maloberti), when he describe the 'passage' from first order to second order...

Homework Statement show that the charge distribution (|\vec{r}|\equiv r ) \rho(r) = Z\delta^3(\vec{r})-\frac{Ze^{-r/R}}{4\pi R^2r} has zero net charge for any Z and R. Explain the meaning of Z. Homework Equations none given, but divergence (gauss) theorem and poisson's equation may...

Homework Statement Prove that \delta(at)=\frac{1}{abs(a)}\delta(t) Hint: Show that \int\phi(t)\delta(at)dt=\frac{1}{abs(a)}\phi(0) (the limits of integration are from -inf to +inf btw, I couldn't find how to put them in..) Homework Equations The Attempt at a Solution Ok. I...

Homework Statement Simplify/Evaluate these expressions involving the Kronecker delta, using Einstein's summation convention: a)\delta_{qr}\delta_{rp}\delta_{pq} b)\delta_{pp}\delta_{qr}\delta_{rq} Homework Equations \delta_{ij}=0 when i =/= j \delta_{ij}=1 when i = j The Attempt at...

Could you help me with the problem? Find delta using the definition of limits, given epsilon = 0,25 lim 1 / (2-x) = -1/3 x->5 Answer should be delta = 1 How can I get it? Thanks.

Can someone tell me how to express a line of charge of charge per unit length \lambda as a delta function volume charge density in cylindrical coordinates?

Just wondering why there can be more than one delta solution for epsilon/delta proofs of a limit. I mean, shouldn't there just be one delta that can be used at any point on the function? Why is it that there is more than one and you choose the minimum delta..? I saw a geometric representation of...

If given δ_ijδ_kk what would the expansion of that be? I thought it was nine but have been told that is incorrect. I know that i=j =1 else zero so I thought that the δ_kk would equal 3 times 3 from the expansion of δ_ij but that isn't the answer

Homework Statement show that the function F:C\rightarrowC z \rightarrow z+|z| is continuous for every z0\in C2. Proof F is continuous at every z0\in C if given an \epsilon > 0 , there exists a \delta > 0 such that \forall z 0 \in C, |z-z 0|< \delta implies |F(z)-F(z0)|< \epsilon. I know...

Homework Statement Calculate DeltaE of a gas for a process in which the gas absorbs 42J of heat and does 14J of work on the surroundings. (ie the gas expands) Homework Equations DeltaH=DeltaE-Q The Attempt at a Solution 42=deltaE-14 DeltaE=+28J This is one of the last...

Homework Statement Im trying to figure out what the difference is between the following two epsilon delta statements and the kinds of functions they satisfy: For all real numbers x and for all delta>0, there exists epsilon>0 such that |x|<delta implies |f(x)|<epsilon vs. there exists...

Homework Statement Prove that as x approaches 0, sin(1/x) has no limit. Homework Equations |x-a|<d and f(x)-L<e The Attempt at a Solution my teacher explained it, but i didnt quite get where the contradiction is at the end. We chose epsilon to be 1/2

Hello everyone, I am stuck when I study Levi-Civita symbol. The question is how to prove \varepsilon_{ijk}\varepsilon_{lmn} = \det \begin{bmatrix} \delta_{il} & \delta_{im}& \delta_{in}\\ \delta_{jl} & \delta_{jm}& \delta_{jn}\\ \delta_{kl} & \delta_{km}& \delta_{kn}\\ \end{bmatrix}...

if \phi is a angular coordinate , between (-\pi,\pi) ¿how much is \delta(\phi-\pi) with \phi=-\pi+\epsilon?

I tried to calculate the volume of a simplex, but got an integral I couldn't do. For simplicity take a 2-simplex (the volume of a 2-simplex is 1/6) V=\int da \int dx \int dy \int dz \mbox{ } \delta(1-a-x-y-z) where the integration limits are over the 4-cube. My reasoning for this formula...

Can someone please explain Epsilon delta definition of limit in detail?

I've come across a very ambiguous statement in my notes on implicit functions (part of the partial derivatives part of the course). I'll write out the preceding explanation but the problematic line is marked by * "Sometimes we can define a function z=z(x, y) only in implicit form, i.e...

Hi! The Dirac delta satisfies \int dx f(x) \delta(x-a) = f(a) But how about \int d^3x f(x) \delta^{(4)}(x-a) Here, x and a are four-momenta, and the integral is over the regular 3-dim momentum. How does the delta behave here?

Homework Statement what does the expression \delta_{ii} mean? Homework Equations \delta_{ij}=1 if i = j and 0 otherwise The Attempt at a Solution What I'm not sure about is if both indices are in the subscript does this mean i can only use it on a term with a subscript or can it also act on...

Homework Statement what is the limit of yb(t) as \delta goes to zero. yb(t) = (b/delta)*exp[-t/RC](exp[delta/RC] - 1)(u(t)-u(t-delta)) b=1. 2. The attempt at a solution I used L'hopitals rule to find the limit of (b/delta)*exp[-t/RC](exp[delta/RC] - 1), which i got to...

Hi there, I'm having trouble understanding how to prove things using the \delta \epsilon definition. I have read a few other threads and sites, but I can't seem to put it together. For example, I came across this problem, if given limx-->af(x) = L, how would I prove (using delta-epsilon and...

Homework Statement Using Dirac delta function in the appropriate coordinates, express the following charge distributions as three-dimensional charge densities p(x). (a) In spherical coordinates, a charge Q uniformly distributed over a spherical shell of radius a. (b) In cylindrical...

Homework Statement For the limit below, find values of δ that correspond to the ε values. Homework Equations epsilon = .5 and epsilon = .05 The Attempt at a Solution These kinds of problems do you have to use a graphing calculator to figure it out? for epsilon = .05 |(9x + x...

How does one deal with a delta squared ? For example, volume is a function of del Diameter and del Length. If i let v = d^2(pi)L/4, and then call the d and L del. d and del L, when i separate for d i get del d^2 So I'm wondering if there are any special rules for squaring a "del"

Homework Statement show x\frac{d}{dx}\delta(x)=-\delta)(x) using the gaussian delta sequence (\delta_n) and treating \delta(x) and its derivative as in eq. 1.151. Homework Equations the gaussian delta sequence given in the book is \delta_n=\frac{n}{\sqrt{\pi}}e^{-n^2x^2} and eq...

Homework Statement evaluate lim2x^2 as x approaches 3 using formal definition (epsilon and delta) of limit Homework Equations The Attempt at a Solution

Im having trouble proving limits of multivariable functions. I understand the principal behind delta-epsilon proofs but I can't get it to work. Once I set up the inequalities I am stuck. The only example in my book seems very convenient though . 3x^2 * abs(y) divided by x^2 + y^2...

Homework Statement Distribution of matter is given in cylindrical coordinates: \rho(\vec{r})=\frac{1}{\rho}\delta(\rho^2-10\rho+9)\delta\left(\frac{z^2-a^2}{z^2+a^2}\right)\delta(\cot(\phi)) where a>0 is a constant. Find the complete mass of the object. Homework Equations The...

Homework Statement How do I calculate delta H given the above info and knowing the specific heat capacity of H2O and that the change in temperature when the 2 react is 6.2 degrees C Homework Equations The Attempt at a Solution Using Q = mcdeltatheta where m=mass and...