# What is Heaviside: Definition and 96 Discussions

Oliver Heaviside FRS (; 18 May 1850 – 3 February 1925) was an English mathematician and physicist who brought complex numbers to circuit analysis, invented a new technique for solving differential equations (equivalent to the Laplace transform), independently developed vector calculus, and rewrote Maxwell's equations in the form commonly used today. He significantly shaped the way Maxwell's equations are understood and applied in the decades following Maxwell's death. His formulation of the telegrapher's equations became commercially important during his own lifetime, after their significance went unremarked for a long while, as few others were versed at the time in his novel methodology. Although at odds with the scientific establishment for most of his life, Heaviside changed the face of telecommunications, mathematics, and science.

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1. ### Antiderivative of Heaviside step function with absolute-value-argument

For ##R<0##, the antiderivative is just a constant, since then ##R-|x|## is negative for all values of ##x##, which in turn implies ##\Theta(R-|x|)## is zero for all values of ##x##. For ##R\geq 0##, and by inspection apparently, the antiderivative is ##(R+x)\Theta(R-|x|)+2R\Theta(x-R)+C.##...
2. ### Fourier sine and cosine transforms of Heaviside function

Hi, I am really struggling with the following problem on the Fourier sine and cosine transforms of the Heaviside unit step function. The definitions I have been using are provided below. I tried each part of the problem, but I'm only left in terms of limits as x -> infinity of sin or cos...
3. ### Indefinite Integration of Heaviside function muliplied by a function

Will it be [{(r-a)/r}*H(r-a)]
4. ### A Second derivative of Heaviside step function

In QFT by peskin scroeder page 30 the action of Klein Gordon Operator on propagator (∂2+m2)DR(x-y)=∂2θ(x0-y0)... how to compute this ∂2θ(x0-y0)?
5. ### Find the Limit of the Heaviside Step Function Added to this Graph

Here's my attempt: I would like to confirm my answers.
6. ### Why is the heaviside function in the inverse Laplace transform of 1?

Homework Statement:: Why is the heaviside function in the inverse laplace transform of 1? Relevant Equations:: N/A This is a small segment of a larger problem I've been working on, and in my book it gives the transform of 1 as 1/s and vice versa. But as I've looked online for help in figuring...
7. ### Confusion about the Heaviside method

So, Heavside's method confused me, I mean, but we can't divide by zero, can we? So, my mind sees it as cheating, and to multiply both sides by zero to cancel zeros, and for the example above(from Thomas Calulus), when x = 1, before you multiply by x-1(=0), you get: 2/0=A/0+B/-1+c/-2, and I think...
8. ### I Length contraction viewed with Heaviside equations

Richard Feynmann, in His lectures on Physics, Vol I, chapter 28. Gives an expression for calculating the E and B field of a moving point charge based on retarded radius; eg: Knowledge of where the charge was at the time when the field was being formed. The Equation was originally derived by...
9. ### A Multi-variable function depending on the Heaviside function

How can I calculate ∂/∂t(∫01 f(x,t,H(x-t)*a)dt), where a is a constant, H(x) is the Heaviside step function, and f is I know it must have something to do with distributions and the derivative of the Heaviside function which is ∂/∂t(H(t))=δ(x)... but I don't understand how can I work with the...
10. ### Converting a Piecewise function to a Heaviside function

Homework Statement Use the Heaviside function as an on the switch over the interval [a,b]. Homework Equations Let the H(x) be the Heaviside function defined as a piece-wise function such that it is zero if x is less than zero, and 1 if it is greater than or equal zero. From that, we can use the...
11. ### Delta property, integration by parts, heaviside simple property proof

Homework Statement I am trying to show that ## \int \delta (x-a) \delta (x-c) dx = \delta (-a-c) ## via integeration by parts, but instead I am getting ##\delta (c-a) ## (or ##\delta (a-c)## depending how I go...). Can someone please help me out where I've gone wrong: struggling to spot it...
12. ### I Heaviside Function: Clarifying H(x-a) & H(a-x)

Hi everyone, I could not figure out whether H(x-a) and H(a-x) are same or different. Please help me to understand this.

45. ### Integral of heaviside, why multiply the result with a heavside function again?

Homework Statement ∫(H(t-2)t)dt from t=0 to t. Homework Equations The Attempt at a Solution It's same as ∫t=2 t (t-2)dt, which is t^2/2-2t+2. But do we have to multiply the answer with H(t-2)?
46. ### MHB Solve f(t) with Heaviside Functions: Find b

Consider the function Then f(t) can be expressed with Heaviside functions as Determine b. Workdone so far... f(t) = 7H(t) + bH(t-5) when t = 5 f(5) = 49 + 7b 15 = 49 + 7b -34 = 7b b = -34/7 http://www.chegg.com/homework-help/questions-and-answers/-q3136934# Is the answer correct...
47. ### Solving ODE with Heaviside Step and Delta function

Homework Statement Find the solution of the equation: α(dy/dt) + y = f(t) for the following conditions: (a) when f(t) = H(t) where H(t) is the Heaviside step function (b) when f(t) = δ(t) where δ(t) is the delta function (c) when f(t) = β^(-1)e^(t/β)H(t) with β<α Homework...
48. ### Solving ODE with Heaviside Step and Delta function

Find the solution of the equation: α(dy/dt) + y = f(t) for the following conditions: (a) when f(t) = H(t) where H(t) is the Heaviside step function (b) when f(t) = δ(t) where δ(t) is the delta function (c) when f(t) = β^(-1)e^(t/β)H(t) with β<α My try for all 3 are as follow: 1...
49. ### Understand Heaviside Functions & Laplace Transforms

Good evening everyone, I have a final exam where one of the questions will most likely be a heaviside function and using Laplase transforms since we just studied it. I am having trouble understanding how the equations are created using piece-wise data. 1. How do you create the heaviside...
50. ### Finding the laplace of a Heaviside system

I need to use Laplace transforms to find the solution to this system of Heaviside functions but I'm not sure where to start because the two different x's in the system are confusing me. Should I start by taking the laplace transforms of both sides where the laplace of H(t-1) = e-s/s These...