Delta Definition and 1000 Threads

1.) Laplace transform of differential equation, where L is the Laplace transform of y: s2L - sy(0) - y'(0) + 9L = -3e-πs/2 = s2L - s+ 9L = -3e-πs/2 2.) Solve for L L = (-3e-πs/2 + s) / (s2 + 9) 3.) Solve for y by performing the inverse Laplace on L Decompose L into 2 parts: L =...

I'm trying to get transform the larger circuit into the smaller one and then from there calculate power. My plan was to do the transform and then use kirchhoffs laws to find the current tofind the power. My work so far: Is the sequence of steps I used valid? I'm not focusing on the calculations...

If the question was $$ \int_{∞}^{∞}dxf(x)δ((x - x_1)) = ? $$ The answer would be ##f(x_1)## So the delta function has two roots, I searched the web and some books but I am not sure what approach should I use here. I guess there's sometihng happens when ##x_1 = -x_2##. So I am not sure what...

I have a little question about converting Velocity formula that is derived as, ##\vec{V}=\frac{d\vec{r}}{dt}=\frac{dx}{dt}\hat{x}+\frac{dy}{dt}\hat{y}+\frac{dz}{dt}\hat{z}## in Cartesian Coordinate Systems ##(x, y, z)##. I want to convert this into Polar Coordinate System ##(r, \theta)##...

Can someone explain why I can't simply use a current divider once I've found the equivalent resistance and source current for the entire circuit? This would look like i0 = 0.044*(113.53/210). Req = 113.53. If it helps, the correct answers appear to be: i0 = 8.28 mA, i1 = 23.6 mA, i2 = 35.8 mA...

I have to integrate this expression so I started to solve the delta part from the fact that when n=0 it results equals to 1. And the graph is continuous in segments I thought as the sumation of integers $$ \int_{-(n+1/2)π}^{(n+1/2)π} δ(sin(x)) \, dx $$ From the fact that actually $$ δ(sin(x))=...

While deriving continuity equation in Fluid mechanics, our professor switched the order of taking total time derivative and then applying delta operator to the function without stating any condition to do so(Of course I know it is Physics which alows you to do so) . So,I began to think...

Backstory - I have not been in school for 5ish years, and am returning to take some grad classes in the field of Solid Mechanics. I am freaking out a bit about the math (am rusty). I have not started class yet, but figured I would get my books and start working through problems. This problem...

Let ##\varepsilon > 0## be arbitrary. Now define ##\delta = \text{min}\{\frac{a}{2}, \varepsilon \sqrt{a}\}##. Now since ##a>0##, we can deduce that ##\delta > 0##. Now assume the following $$ 0< |x-a| < \delta $$ From this, it follows that ##0 < |x-a| < \frac{a}{2} ## and ##0 < |x-a| <...

I know it is something simple that I am missing, but for the life of me I am stuck. So, I used the identity ##sin(a)sin(b)+cos(a)cos(b)=cos(a-b)## which gives me $$\int^{\infty}_{-\infty}dx\:f(x)\delta(x-y)=\int^{\infty}_{-\infty}dx\:f(x)\frac{1}{2L}\sum^{\infty}_{n=-\infty}\lbrace...

I understand the concept of Epsilon-Delta proofs, but I can't understand why we have to do them. What's the advantage of using this proof over just showing that the limit from the function approaches from the left and right are the same?

Problem Statement: I am trying to understand how to compute the surface an N-sphere , for large N, to leading order (and exactly) Given a vector J with norm N, with N large, how does one compute the volume integral ? That is, what representation of the delta function. And what is the exact...

Hello everyone, here I have one problem, which I can not understand, can you please help me? In attachment you will find a basic star-delta diagram, with unreal calculation (Z is not real value, it's just for calculation and understanding the princip of star-delta). According to these current...

Hi, I am curious about: $$x^m \delta^{(n)}(x) = (-1)^m \frac {n!} {(n-m)!} \delta^{(n-m)}(x) , m \leq n $$ I understand the case where m=n and m>n but not this. Just testing the left hand side with m=3 and n=4 and integrating by parts multiple times, I get -6. With the same values, the...

Form solid state physics, we know that the volume of k-space per allowed k-value is ##\triangle{\mathbf{k}}=\dfrac{8\pi^3}{V}## ##\sum_{\mathbf{k}}F(\mathbf{k})=\dfrac{V}{(2\pi)^3}\sum_{\mathbf{k}}F(\mathbf{k})\triangle{\mathbf{k}}##...

Using paired t test, how should I pair these results? To calculate the delta values, should I use: downstream - upstream for both sep and apr ? or upstream (sep) - upstream (apr) and downstream (sep) - downstream (apr) ? Thanks

How do you prove 1.85 is valid for all closed surface containing the origin? (i.e. the line integral = 4pi for any closed surface including the origin)

In quantum mechanics, there exist some systems where the potential energy of some particle is a Dirac delta function of position: ##V(x) = A\delta (x-x_0 )##, where ##A## is a constant with proper dimensions. Is there any classical mechanics application of this? It would seem that if I...

Moved from technical math section, so is missing the homework template. How to solve this equation please? I found charakteristic roots ia ##\pm \sqrt{-a^{-k^2}}##. Thank you Moderator note: Edited the LaTeX above to show the exponent correctly.

Homework Statement Hi, I am just stuck in why / how we can write minkowski metric where I would usually write delta. I see that the product rule is used in the first term to cancel the terms in the second term since partials commute for a scalar and so we are left with the d rivative acting...

Homework Statement Consider a particle of mass m moving in a one-dimensional double well potential $$V(x) = -g\delta(x-a)-g\delta(x+a), g > 0$$ This is an attractive potential with ##\delta##-function dips at x=##\pm a##. In the limit of large ##\lambda##, find a approximate formula for the...

I want to know if these functions are related? for example. I can write Dirac delta in term Delta Kronecker from? Where can I learn these?

My function: d2f/dx2 + cf = delta(x) Condition: f is finite and f(50) = f(-50) = 0 Solution: f = C1exp(cx) + C2exp(-cx) Due to condition, f = C1exp(cx) for x<=0 and C2exp(-cx) for x>=0 f(50) = C2exp(-c*50) = 0 = > C2 = 0 Likewise, for C1 I don't know if I might have missed something...

In a book on atmospheric physics I'm reading, the author begins a derivation by examining a fluid element of volume V = δxδyδz. In this context, what purpose is delta δ serving? Is it just a placeholder for an unspecified volume in the x, y, and z directions, or is it referring to an...

Hey guys! How do I derive the general expression for delta p times delta x which is the exception value in the harmonic oscillator. I am supposed to establish delta p and delta x as operators and the express those operators by raising and lowering operators.

So I am making a Delta V calculator. Here it is: https://www.desmos.com/calculator/hib7psndtb Anyone know how to figure out a rocket's Delta V if it launches from in an atmosphere? Also, if I messed up on anything (in the Delta V calculator or isp calculator), please let me know so I could...

In these notes, https://ocw.mit.edu/courses/physics/8-04-quantum-physics-i-spring-2016/lecture-notes/MIT8_04S16_LecNotes10.pdf, at the end of page 4, it is mentioned: (3) V(x) contains delta functions. In this case ψ'' also contains delta functions: it is proportional to the product of a...

I would like to know the solution to Liouville equation ∂ρ/∂t=-{ρ,H} given the initial condition ρ(t=0)=δ(q,p) where δ(q,p) is a dirac delta centered in some point (q,p) in phase space. I have the feeling, but I'm not sure, that the solution is of the form ρ(t)=δ(q(t),p(t)) where q(t) and...

Hi. I was trying to test a code for the diffusion equation, using the analytical solution for infinite media, with a Dirac delta source term: ##q(\mathbf{r},t)=\delta (\mathbf{r}) \delta (t)##. The code is not giving the analytical solution, and there might be several reasons why this is so...

I was taking notes recently for delta y/ delta x and noticed there's more than one way to skin a cat... or is there? I saw the leibniz dy/dx, the triangle of change i was taught to use for "difference" Δy/Δx, and the mirror six ∂f/∂x which is some sort of partial differential or something...

Homework Statement Find ##\langle x \rangle## in the momentum representation I am having trouble understanding some of the steps needed to get to the expression, assistance is greatly appreciated! Homework Equations 3. The Attempt at a Solution [/B] $$\langle x \rangle = \langle \psi | x |...

Dear Everybody, I am having trouble to determine the value of delta when c is strictly greater than 0. Here is the work: The Problem: Find the Limit or prove that the limit DNE. $\lim_{{x}\to{c}}\sqrt{x} for c\ge0$ Proof: Case I: if c>0. Let $\varepsilon>0$ Then there exists $\delta>0$...

Hi So we write ##g_{ab}g^{ac}=\delta^{(4)c}_b ##, but this simply means to replace ##b## with ##c## or vice versa, so, why don't we write ##\delta_{bc}##? Thanks i.e. the affect is not to replace and raise/lower, it is simply to replace, so I'm a bit confused by the notation...

Hi, I am reading the Quantum Mechanics, 2nd edition by Bransden and Joachain. On page 777, the book gives an example of Dirac delta function. $\delta_\epsilon (x) = \frac{\epsilon}{\pi(x^2 + \epsilon^2)}$ I am wondering how I can show $\lim_{x\to 0+} \int_{a}^{b} \delta_\epsilon (x) dx$...

Hi, in some books the ##\nabla## symbol is used for the Laplacian ##\frac{d}{dx^2}+\frac{d}{dy^2}+\frac{d}{dz^2}## while others use the ##\Delta## symbol for this. What is the correct custom for this usage?

Homework Statement Homework Equations For Delta line current = 1.732 times phase current. Line voltage = phase voltage The Attempt at a Solution I don't know how to start this. This is original connection This is new one The voltage should be 3 times because of additive polarity. Not sure...

https://1drv.ms/w/s!Aip12L2Kz8zghV6Cnr8jPcRTpqTX https://1drv.ms/w/s!Aip12L2Kz8zghV6Cnr8jPcRTpqTX My question is in the above link

I previously made a derivation of Neumann potential. It can be found in the pdf file below. I originally made it in the ##dx## method. It involved equations like ##dm=I dS##. My maths teacher told that such an expression has no meaning, at least in elementary calculus. However I argued that my...

Homework Statement I know that we can write ## \int_{-\infinity}^{\infinity}{e^{ikx}dx}= 2\pi \delta (k) ## But is there an equivalent if the interval which we are considering is finite? i.e. is there any meaning in ##\int_{-0}^{-L}{e^{i(k-a)x}dx} ## is a lies within 0 and L? Homework...

Hi, if I have an interval on the x-axis, defined by the parameter L, can this, interval be transformed to a Dirac delta function instead, on the x-axis? Thanks!

If I have a general (not a plain wave) state $$|\psi\rangle$$, then in position space : $$\langle \psi|\psi\rangle = \int^{\infty}_{-\infty}\psi^*(x)\psi(x)dx$$ is the total probability (total absolute, assuming the wave function is normalized) So if the above is correct, does that mean...

Homework Statement Can we use a 3 phase delta supply to a 3 phase synchronous motor who's stator windings are connected in star (wye)? The Attempt at a Solution I was thinking no, since I read in my notes that the rotor has to be supplied with a "continuous current" But I'm not sure. I have...

Remember to use the appropriate packages; these are in similar post if a mod wants to add the link if you choose to use Latex. Here is the PDF \begin{document} \begin{center} {\LARGE Epsilon-Delta Proofs \\[0.25em] Practice} \\[1em] {\large Just for practice, don't use Google to cheat!}...

Hello PF, I was doing the derivation of the Lagrange equation of motion and had to do some calculus of variations. The first step in the derivation is to multiply the integral of ƒ(y(x),y'(x);x)dx from x1 to x2 by δ. and then by the chain rule we proceed. But I cannot understand why we are...

Is the "function" R->R f(x) = +oo, if x =0 (*) 0, if x =/= 0 Lebesgue measureable? Does its Lebesgue Integral exist? If yes, how much is it? (*) Certainly we shoud give a convenient meaning to that writing. -- lightarrow

Homework Statement I am studying for an exam and I never know if I am finding line current / voltage or phase current / voltage. How can I tell? I guess I am confused on what "phase" and "line" represent. For example: If I do the voltage divided by the impedance, then this gives me phase...

Homework Statement Evaluate the integral: $$\int_{-\infty}^{\infty} dx *\dfrac {\delta (x^2-2ax)} {x+b}$$ Homework Equations $$ x^2-2ax=0 $$ The Attempt at a Solution I know that the delta function can only be none zero when $$ x=2a$$ so then I have the following integral...

Homework Statement Show that this is a valid representation of the Dirac Delta function, where ε is positive and real: \delta(x) = \frac{1}{\pi}\lim_{ε \rightarrow 0}\frac{ε}{x^2+ε^2} Homework Equations https://en.wikipedia.org/wiki/Dirac_delta_function The Attempt at a Solution I just...

Homework Statement Homework EquationsThe Attempt at a Solution U is internal energy, but what is u? if its internal energy at a specific state, then why its multiplied by mass? does not makes sense to me...

I am looking for the proof of delta variation of determinant of metric but still I find difficulty ? Can I get the full proof here