Delta Definition and 1000 Threads

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 Find negative eigenvalues and corresponding eigenfunctions to the following operator: H:= - \frac{d^2}{dx^2} - \delta_{-r} -2\delta{r} . (The eigenfunction should be twice contiously differentiable, except for possible jump discontinuities at +-r of the first and...

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))

If it's a dirac delta doesn't it mean it's infinite when x=y? Or is it a sort of kronecker where it's equal to one but the indices x and y are continuous? I'm confused.

Is it possible to take the variation of the Dirac delta function, by that I mean take the functional derivative of the Dirac delta function?

I saw this formula while studying Fourier Transform: [Sum of δ(t-lT) from l=-infinity to l= +infinity] = 1/T * [Sum Of exp(jlΩt) from l=-infinity to l=+infinity]. I am having trouble getting this into my head. How do I prove it or understand the physical meaning of this formula?

Hello I'm trying to figure out how to evaluate(in the distribution sense) \delta'(g(x)). Where \delta(x) is the dirac delta function. Please notice that what I want to evaluate is not \frac{d}{dx}(\delta(g(x))) but the derivative of the delta function calculated in g(x). If anyone could post...

Hi all, I read the following: "If g(t) starts with a delta function of strength Y/2, then..." I wonder what that means. Does it mean g(t) = 0.5Yδ(t) ? Thanks

OK, the Dirac delta function has the following properties: \int_{ - \infty }^{ + \infty } {\delta (x - {x_0})dx} = 1 and \int_{ - \infty }^{ + \infty } {f({x_1})\delta ({x_1} - {x_0})d{x_1}} = f({x_0}) which is a convolution integral. Then if f({x_1}) = \delta (x - {x_1}) we get...

hi I really need your help ... for linear time invariant system f(t) =f1(t) (convolution) f2(t) f(t) = ∫f1(t).f2 ( t-T) or f(t) = ∫f1(t-T).f2(t) where f1(t) = delta function = δ(t).δ(t-2) and f2(t) = sine wave = sin ( ∏t ) how i can solve this ... my problem is : how can i...

So far, all I understand is that the definition proves that there's a value of f(x,y) as f(x,y) approaches (x0,y0) which is sufficiently close to but not exactly the value at f(x0,y0). I am probably completely off... but I just don't understand the purpose of proving this. I also don't...

Really couldn't catch the concept on epsilon and delta in limits. Let ∂x=x2 - x1 In finding a gradient the value ∂y is taken at certain value. But in finding area using integral, the ∂y is seen to taken as zero. F(x2)=F(x1) Maybe one multiplication and the other is division.

Hello, I'm dealing with the following equation: A e^{jat} + B e^{jbt} = C e^{jct} \forall t \in \mathbb{R} My book says: given nonzero constants A,B,C, if the above equation yelds for any real t, then the a,b,c constants must be equal. The above statement is prooved by taking the Fourier...

Hello All, I am finding the hardest time in understanding how to work δ & ε Open Set Problems? Can someone please explain this approach to me? Thanks in Advance

hi! i have a question regarding the delta function. if i have a delta distribution with an argument that is a function of multiple arguments, somthimg like: ∫δ(E-p^{2}_{i}/2m)dp^{N}, ranging over +-∞ now, the argument of the delta function vanishes on a sphere. i can evaluate the...

I realize it's not a function in the classical sense, but how would one show that the delta dirac function is a distribution i.e. how do I show it's continuous and linear given that it's not truly a function?

Homework Statement Calculate the value of Go for the formation of 1 mol of phosphorus trichloride from its constituent elements: P2(g) + 3 Cl2(g) ---> 2 PCl3(g) The attempt at a solution I thought of trying delta G = delta H - T deltaS , but I'm lost on where to start...

Hi there, I am trying to integrate this: http://imm.io/oqKi I should get the second line from the integral, but I can't show it. This should somehow relate to the Heaviside step function, or I am completely wrong. Any ideas? Sorry about the url, I fixed it.

Hello team! I saw the other day in a textbook that the Dirac delta function of the form d(x-a) can be written as d(a-x) but the method was not explained. I was wondering if anyone know where this comes from. I've been googling but can seem to find it out. Any help would be appreciated...

Question: Which best describes the delta G for hydrolysis of creatine phosphate under cellular conditions in which the concentration of creatine phosphate, creatine, and phosphate all equal 1 mM at 25 degrees C. The delta G naught for the hydrolysis of creatine phosphate at 25 degrees C is...

Im really just searching for a general explanation! If you are solving a pretty standard left hand side differential equation, but a diracs delta function on the right hand side. I am abit confused about how to interpret this. If this is the case for the right hand side: r(t) = Diracs (t)...

The quark composition of the Δ0 is the same as that of neutron but much heavier and the quark composition of Δ+ is the same as that of proton but also much heavier, so what is the difference between the delta particles and the proton and neutron and where did that extra mass come from?

Homework Statement use the sifting property of the dirac delta function to evaluate the following integrals. a) integral from -inf to inf sin(t) delta(t-pi/2)dt b) integral from 0 to 2 e^(2t) delta(t-1)dt c) integral from 0 to pi e^tan(theta) delta(theta- 3pi/4)d(theta) d)...

I'm having a hard time grasping when I should use this little "function". I'm using Griffith's Intro to Electrodynamics and either he doesn't touch on it enough or I'm missing the point. From what I think I understand I'm to use it when there would be a singularity in a result or calculation(?)...

kron[m_,n_]:=\!\( \*SubsuperscriptBox[\(\[Integral]\), \(0\), \(2\)]\(\(Sin[ \*FractionBox[\(n\ \[Pi]\ x\), \(2\)]]\ Sin[ \*FractionBox[\(m\ \[Pi]\ x\), \(2\)]]\) \[DifferentialD]x\)\) This is the integral over x of sin(n pi x / 2) times sin(m pi x / 2) from 0 to 2. This is one way to...

Homework Statement I need to understand how to integrate \int_{0}^{t}\int_{0}^{s} \delta(\tau-\tau')d\tau d\tau' The solution is min(t,s) Homework Equations See aboveThe Attempt at a Solution min(t,s)

Homework Statement How can i prove this property of Delta, http://e1204.hizliresim.com/w/d/4bw2j.png Homework Equations This is my homework from John David Jackson's Classical Elektrodynamics book The Attempt at a Solution I can't an attempt. Some properties is proved at wiki and...

Homework Statement I just want to make sure I include all the steps in doing this: lim (6x-7) = 11 x->3 Homework Equations The Attempt at a Solution given ε>0, we need to find a δ>0, such that 0< lx-3l < δ then 0 < l (6x-7)-11 l < ε To prove this I need to make 0 < l...

Homework Statement http://gyazo.com/7b2a903b6b3165595b8766d3540f43d9 What is this really saying? I can see that a functino is the inverse Fourier transform of the Fourier transform... and it doesn't matter which way round you integrate. Is that all it's saying. What's the difference...

Homework Statement Use the law of conservation of energy to calculate the temperature increase expected from energy transferred to internal heat of the water. There is more than one way to do this. Consider a mass, m, of water which falls over the cascade. If you wish, you may take the mass...

Hey guys, I found this question and it started bugging me: find the _largest_ δ such that |x - 5| < δ => |1/x - 1/5| < 1/100. This is what I did to try solve the question: From |1/x - 1/5| < 1/100 : I got 1/x > 19/100 and so I wanted x < 100/19 plugging that back into the first...

Hi, Let Z be a r.v. from N(0, σ^2) and let Y = Z^2*exp(Z)/(1 + exp(Z))^2. What is the exptected value of Y, E(Y)? The delta method (Taylor expansion) doesn't work since the errors seem to accumulate. Any suggestions? This is a non-standard problem related to my research and I am totally stuck...

Homework Statement See http://mathworld.wolfram.com/DeltaFunction.html I want to show (6) on that page. I can show it using (7), but we aren't supposed to do that. I already proved (5), and my prof says to use the fact that (5) is true to get the answer. Homework Equations The...

Homework Statement Consider a double delta potential given by V(x) = c_+ \delta (x + \frac{L}{2}) + c_- \delta (x - \frac{L}{2}). The coherence between the amplitude A of an incoming wave from the left and the amplitude F of the outgoing wave to the right is given by: F = A \cdot...

A double delta potential is given by V(x) = c_+ \delta (x + \frac{L}{2}) + c_- \delta (x - \frac{L}{2}). Use the discontinuity relation to find the boundary conditions in x = \pm \frac{L}{2} . The general solutions are: \psi(x) = \begin{cases} Ae^{ikx} + Be^{-ikx} & x < -\frac{L}{2}...

I am doing an assignment about launching a rocket and at the moment I am looking for the delta V of the rocket. I have done a few researches and i found a method of finding the energy of the rocket and find the delta vee of it , but then i found this article and I am not sure if it is delta vee...

It is fairly easy to demonstrate that the Dirac delta function is the Fourier transform of the plane wave function, and hence that: \delta(x)=∫_{-∞}^{∞}e^{ikx}dk (eg Tannoudji et al 'Quantum Physics' Vol 1 p101 A-39) Hence it should be the case that ∫_{-∞}^{∞}e^{ik}dk = \delta(1) = 0...

I'm working on an online EECS course, and to be frank some of it is going straight over my head - but at the same time parts of it are far below my current knowledge, so I want to work and stick with it. The speaker is working through proving current and voltage - to arrive at Kirchoff's...