Heaviside Definition and 96 Threads

Dear all, I would like to give you the physics context in which this question emerged, but that would be a very long explanation (sorry!). So, since the question is almost self contained, I am just going to tell you what it is. Consider the product Y(x)=H(x)(1-H(x)), where H(x) is the...

Homework Statement I need to find the integral of the following equation.. integral from 0 to 8 of {(2H[x-0]+2H[x-4])*(x/8)}dx The Attempt at a Solution Im am not sure what the integral of the heaviside function is? is it 1 or 0? Any help would be appreciated! Thanks

Hi all: The Heaviside function multiples a random varaible, is that a probability density function? This is my first time knowing about Heaviside, any tutorial and application of it?

Dear Fellows I need to define a function "f" in MATLAB as f is a heaviside unit step function I did it as f = heaviside[abs(-4)] but it is not working as I required.

Homework Statement Compute the Fourier transform of \phi(t)=(e^(-at))H(t) where H(t) is the Heaviside step function Homework Equations The Attempt at a Solution I am stuck in an attempt at the solution, I am confused at how the heaviside step function factors in and think...

Homework Statement (quick sketch of part i. yes i know the graph should specifically end at t=4 lol) Homework Equations u(t-a) = 0 for t>a = 1/2 for t=a = 1 for t>aThe Attempt at a Solution i'm having trouble solving part (ii). i remember a friend of mine saying something like "start with...

Homework Statement [PLAIN]http://img845.imageshack.us/img845/1706/delta.png The Attempt at a Solution This question has come after a chapter on Dirac's delta-function although the question doesn't say use it. Could I use it? If not how do I do it directly?

How would you integrate product of heaviside function and function of x i.e. int[f(x)H(x)dx] Thanks

By considering the wavefunctions within the potential described below, determine the incident, reflected and transmitted amplitudes of each part of the wavefunction at the step boundary (as necessary). For x<0, V = infinity. For 0<x<a, V = 0 For a<x<L, V = V1 For x>L, V = infinity...

Homework Statement given this discrete time signal x[n] = u[n] - u[n-6] find for which n the even part of x is 0The Attempt at a Solution the even part is x' = 1/2(x[n] + x[-n]) = 1/2(u[n] - u[n-6] + u[-n] - u[6-n]) now i find that u[n] + u[-n] is 2 for n = 0 and 1 for n != 0 u[n-6] +...

I wanted to ask if someone can clarify for me when one would use the Heaviside function instead of (or in combination with) the Dirac delta function. Thanks in advance

How do you do a gaussian integral when it contains a heaviside function!? Very few textbooks cover gaussian integrals effectively. This isn't a big deal as they are easy to locate in integral tables, but something I cannot find anywhere is how to handle a gaussian with a heaviside heaviside...

Hi, I'm not really understanding how to convert the piecewise heaviside into a single function. This was on our quiz and the professor didn't really explain how he got the answer. I can't get the tex to work so: f(t)= { 0, 0 <= t < 1 { (t-1) 1 <= 2 { 1, t >= 2 The answer is...

Homework Statement g(x) = [ x^2 + 2 if x<=1 & x + 2 if x>1, I am asked to find the left and right limits, and whether the g(x) is continuous or not. Homework Equations The Attempt at a Solution When I draw the two equations, I get a hyperbola and a line of gradient 1. They...

I'm revising my course text for my exam and came across a Fourier series problem finding the Fourier series of the square wave: http://img574.imageshack.us/img574/5862/eq1.png. It is then calculated that the complex Fourier coefficients are...

This is me questioning a concept, so I did not follow the template. I know that \[\int {u(t-a)dt = tu(t-a)} \] where u(t) is the unit step function. Does this mean that any arbitrary function multiplied by u(t) is just the integral of that function multiplied by u(t), and I don't have to do...

Homework Statement Consider the initial value problem y'' + 1/3y' + 4y = fk(t) with y(0) = y'(0) = 0, fk(t) = 1/2k for 4 - k < t < 4 + k 0 otherwise and 0 < k < 4. (a) Write fk(t) in terms of...

Homework Statement Find the solution to the differential equation using Laplace transforms.Homework Equations y'' - y' - 2y = 12 \theta{(t-\pi)}\sin{t} y(0) = 1 y'(0) = -1 The Attempt at a Solution Using Laplace transforms... \mathcal{L}(y'') = s^2F - s + 1 \mathcal{L}(-y') = -sF-1...

Homework Statement Consider the initial value problem y'' + 1/3y' + 4y = fk(t) with y(0) = y'(0) = 0, fk(t) = piecewise function 1/2k if 4 - k <= t < 4 + k 0 otherwise and 0 < k < 4 (a) Sketch the graph of fk(t). Observe that the area...

What is H(-x)? Is it 1 if x < 0, 0 if x \geq 0. If so what is the Fourier transform of H(-x)exp(x)?

I have a question: given a piecewise function, f(t)= {t when t<=0 ,0 when 0<t<=1, 1-t when t>1. How do express it as a Heaviside function? I have tried to do the solution which is : f(t)= (1-t)*H(t-1)+t*H(t). Here I have considered two non-zero portions of f(t), which are t and 1-t. Is that...

Homework Statement Find the solution for L[y]=H(t-pi/2)sint=q(t) y(0)=0 by using the Green's function. Homework Equations The Attempt at a Solution My problem is that I'm stuck with how to get the Heaviside into the required general solution. Is it anything to do with the fact that the...

Hey guys! I just have a question regarding some notes I've been looking at and trying to understand... Homework Statement Taking the transform: Just wondering, can someone explain to me why the e-3s/s is positive, and not negative because it is originally -u3(t)... Another quick...

Homework Statement how to i take the laplace transform of this , -tH(t-1) so we need to get thr right shift so is it -(t-1 + 1 ) so do i take the laplace transform of -(t+1) so would it be -(1/s^2 + 1/s ) *e^(-s)

Can someone give me quick refresher on what happens when you multiply the heaviside function with the unit impulse? Typically, the unit step function multiplied by anything simply delays it by the offset in the unit step function. The unit impulse function makes the value defined at only one...

Homework Statement What is the Laplace transform of f(t) = 0 for 0 < t < 2 and f(t) = (4-t) for 2 < t < 3 and f(t) = 1 for 3 < t < 4 and f(t) = (5-t) for 4 < t < 5 and f(t) = 0 for t > 5? Homework Equations The Attempt at a Solution f(t) = H(t-2)(4-t) - H(t-3)(4-t) + H(t-3) - H(t-4) +...

Hi, I currently have this problem to solve and I can't seem to figure it out it goes like this Find the Laplace transform of the given function: f(t) = { 0 t<2, (t-2)^2 t>=2 I tried working it out and this is where i get stuck f(t) = (t-2)^2 * u(t-2) I am not sure if I got...

Homework Statement Hi there, i am trying to do a proof that H'(t)= δ(t) Homework Equations We have been given the following: F is a smooth function such that lim (t-->±∞)F(t)=0 Therefore the integral between ±∞ of [H(t)F(t)]'=[H(t)F(t)]∞-∞=0 I understand it up until this point...

Homework Statement the function is with the attachment The question is (i) Express f(t) in terms of the Heaviside function and hence or otherwise find L(f(t)), the Laplace transform of f(t). Homework Equations The Attempt at a Solution Everything is in the attachment...

Homework Statement The function f(t) is defined for t>=0 by f(t) = 1 for 0<= t <= 1 , t-2 for 1 <=t <= 2 and 0 for t >2 Express f(t) in terms of the Heaviside function and hence or otherwise find L(f(t)), the Laplace transform of f(t) Homework Equations The Attempt at a...

in the .pdf article http://repository.dl.itc.u-tokyo.ac.jp/dspace/bitstream/2261/6027/1/jfs080104.pdf i have found the strange representation \delta (x) = -\frac{1}{2i \pi} [z^{-1}]_{z=x} and a similar formula for Heaviside function replacing 1/z by log(-z) , what is the meaning ...

A Question: How was Heaviside able to convert Maxwell's 17 equations down to just 5, and why does Heaviside get ignored for doing so?

[SOLVED] Dirac delta function and Heaviside step function In Levine's Quantum Chemistry textbook the Heaviside step function is defined as: H(x-a)=1,x>a H(x-a)=0,x<a H(x-a)=\frac{1}{2},x=a Dirac delta function is: \delta (x-a)=dH(x-a) / dx Now, the integral: \int...

[SOLVED] Graphing a Heaviside unit function Homework Statement find solution of the following differential eq and graph it: y'' + 4y = \delta(t-2\pi) y(0)=0 y'(0)=0 Homework Equations \delta is the Dirac delta function u_{c} is the Heaviside unit step functionThe Attempt at a Solution I...

Hello, I have a fairly straight forward question regarding an inverse laplace transform. The function follows along with the solution. The solution (provided in my text) has been confirmed by Maple; however, i cannot account for the (1/3) in the solution. Any help would be greatly...

Homework Statement If |x| = -x + 2x*H(x) what is |x - a|? This isn't the actual question, just something I need to know to solve the question. Homework Equations H(x) is the Heaviside function which is: y = 1 if x >= 0 y = 0 if x < 0 The Attempt at a Solution Well, I'm...

Hello. Can someone tell me how is Heaviside (or Unit Step) Function used in real life?

Does anybody knows heaviside function or singularities function such as <x-a>^n ;n=1,2,3... for mechanics i wish to know what does this mean and how to draw the shears stress and moments diagramusing this function.any recommended websites for this is appreaciable too thanx

f(x) = <x-a>^1 - <x-2a>^1 - a<x-3a>^0 this is a diagram of heaviside step function.does anybody has any website regarding this materials so that i can get to learn such as why is it power of one and power of zero plssss thanx very much

Is the square of Heaviside function equal to Heaviside? H(t-t')\times H(t-t')=H(t-t')? Please help me on the above equation.

Could anyone help me out? I've been looking for a Proof to the Heaviside Method all night. The one that deals with the partial fractions stuff. Please either post the PROOF or send me a link to it, thanks very much!

can someone please help me graph this function: u(t)-2u(t-2)+u(t-5) where u(t) is heaviside fcn. i got that it's 1 from 0<t<2 and 1>5 but i don't think that's right but don't know what to do with the 2 in 2u(t-2). thank you.

hey guys, I am having a bit of trouble finding the equation for the following graph. I know it should look something like: u(t)-2u(t-2), but I don't really understand it. Can someone point me in the right direction?

we know that \delta(xa)=(1/a)\delta(x) if the dirac,s delta satisfies this then given the function H(ax) with H the Heaviside step function what relationship is there between H(ax) and H(x) with \frac{dH}{dx}=\delta(x)

Heaviside? HELP hey there peeps, could u guys help me out with heaviside step function..cu zi don't understand anything bout how it works and how to apply to a particular problem... could u guys explain in detail how to solve the next equations using heaviside: exp[-2s] F(s)=...

Help! :confused: Here I am busy doing some Laplace Transforms for my Maths 2 paper on Monday when suddenly to my surprise, an apparent "mistake" appears! GASP! :eek: It's got to do with the Heaviside "cover up" method. To work out a problem, you need to multiply the opposing side by...