Delta Definition and 1000 Threads

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...

Hello, Dirac Delta Function is defined as the function that its amplitude is zero everywhere except at zero where its amplitude is infinitely large such that the area under the curve is unity. Sometimes it is used to describe a function consists of a sequence of samples such as...

Using the defining property of the dirac delta function, \int{dx f(x) \delta(x-c)} show that \delta(ax)=\frac{1}{|a|}\delta(x) I think all I need to do is make the right u substitutions and it will come out right, but I can't think of how to make the substitutions...after a long time working...

Dirac delta function as the limit of a sequence Hi.. If I have a sequence which in some limit tends to infinity for x=0 and goes to zero for x\neq0, then can I call the limit as a dirac delta function? If not, what are the additional constraints to be satisfied?

Homework Statement Let V=x^3 Find dV and \Delta V. Show that for very small values of x , the difference \Delta V - dV is very small in the sense that there exists \varepsilon such that \Delta V - dV = \varepsilon \Delta x, where \varepsilon \to 0 as \Delta x \to 0.Homework Equations...

Claim: \nabla \cdot \frac{\hat{e}_r}{r^2}=4\pi\delta^3(\vec{x}) Anyone know of a proof of this? (or a reference which covers it?) We need to show that \frac{1}{4\pi}\int_0^R{(\nabla \cdot \frac{\hat{e}_r}{r^2})f(r)dr=f(0). The claimed identity can be seen in the solution for...

Homework Statement Evaluate the following integrals: \int^{+\infty}_{-\infty}\delta[f(x)]dx and \int^{+\infty}_{-\infty}\delta[f(x)]g(x)dx Homework Equations \int^{+\infty}_{-\infty}\delta(x)dx=1 \int^{+\infty}_{-\infty}\delta(x)f(x)dx=f(0) \int^{+\infty}_{-\infty}\delta(x-a)f(x)dx=f(a)The...

the question is discuss how you results would change if th balll had bounced off the floor instead of sticked to it. I was having to measure the change in the radius (delta x). So I was thinking about this and I was wondering if there might be a larger difference between initial and final...

I know I haven't entered the formulae with the proper syntax, but I'm extremely exhausted at the time of posting, so please just read it and give advice, forgiving me this once for not using proper form (it's basically in latex code format). Homework Statement Show...

i know how to do basic proofs, but some proofs on the actual limit theorems confuse me. my textbook's choices for delta are very obscure and i have no idea how they even came up with them. for the proof of the limit theorem where the limit of a product of 2 functions is equal to the product...

I'm trying to understand the multiple limit processes involved with the Dirac delta function. Does it matter which process you do first the integral or the delta parameter that approaches zero? The closest theorem I found that addresses the order of taking limits is the Dominate Convergence...

We all know that \frac{1}{2\pi}\int{e^{ik(x-x')}dk=\delta(x-x'). i am working a problem which appears to depend on the statement \int e^{z^*(z-w)}dz^*\propto\delta(z-w) Does anyone know if this is valid? \delta(z-w) is defined in the usual way so that...

Claim: if \psi is a variable grassmann number, then \delta(\psi)=\psi is a Dirac delta function for integrals over \psi. I'm not seeing this. A general function of a grassmann number can be written f(\psi)=a+b\psi because anti-commutativity requires \psi^2=0. According to the wikipedia...

\begin{array}{l} \delta _{jk} A_k \\ \\ \delta _{jk} A_k = \left( {\delta _{1,1} + \delta _{1,2} + \delta _{1,3} + \delta _{2,1} + \delta _{2,2} + \delta _{2,3} + \delta _{3,1} + \delta _{3,2} + \delta _{3,3} } \right)A_k \\ \,\,\,\,\,\,\,\,\,\,\,\,\, = \left( {1 + 0 + 0 +...

Hi all, I'm working through Chandrasekhar's http://prola.aps.org/abstract/RMP/v15/i1/p1_1" and can not understand the steps to progress through Eq. (66) in Chapter 1. The integral is: \prod^{N}_{j=1} \frac{1}{l^{3}_{j}|\rho|}\int^{\infty}_{0} sin(|\rho|r_{j})r_{j}\delta...

Hello. Homework Statement I would like to solve the following: \[\int\limits_{ - \infty }^{ + \infty } {{\rm{d}}x\,f\left( x \right)\frac{{\rm{d}}}{{{\rm{d}}x}}\delta \left[ {a\left( {x - x_0 } \right)} \right]} \] The solution I found in a paper is: \[\int\limits_{ -...

Is delta enthalpy zero for... Homework Statement 1 mol of ideal gas expands isothermally at 274 K ,from pressure 1.1 atm to 1 atm.It absorbs 8.314 J of heat.Find free energy change. Homework Equations dG=dH-T dS...1 dS=dq/T dH=dU+Work done Work done=nRTln(P1/P2)...2 The Attempt at...

Is delta enthalpy zero for... Is delta H, for an isothermal process in which a gas expands? delta H=delta U+work done,correct? delta U is 0,but work done = nCln(V2/V1). So,delta H is not equal to 0.But my book says so.

Homework Statement http://img42.imageshack.us/img42/3537/powersyst.jpg Homework Equations P = I^2 R The Attempt at a Solution Here's what I have so far: I1 = 49.68A<-68.6 degrees (top loop) I2 = 49.68A<-128.6 degrees (bottom loop) I3 = 28.68<-98.6 degrees (triangle loop)...

I'm told that a product of distributions is undefined. See, http://en.wikipedia.org/wiki/Distribution_(mathematics)#Problem_of_multiplication where the Dirac delta function is considered a distribution. Now the Dirac delta function is defined such that, \[ \int_{ - \infty }^{ +...