# Laplace and inverse laplace transformation of unit step functions u(t).

• thepatient
In summary, the conversation discussed the use of a Laplace transformation chart and how it relates to the unit step function. It was concluded that for the domain t\in [0,\infty), both f(t)=1 and u(t) can be used interchangeably when computing the inverse Laplace transform.
thepatient

## Homework Statement

So I have this laplace transformation chart and was a bit unsure about the laplace and inverse laplace of this.

The unit step function, where u(t) = 0 where t < 0, u(t) = 1 where t > 0.

The laplace transformation chart that I have has two columns, the column on the left shows f(t) and the column on the right shows inverse laplace{f(t)} = F(s) for the corresponding f(t) on the left. Under f(t), both u(t) and 1 are on the same row as F(s) = 1/s. Does this mean that if I take the inverse laplace of 1/s, I can choose between using 1 or u(t)?

Thanks.

The Laplace transform involves the domain $t\in [0,\infty)$. Both $f(t)=1$ and $u(t)$ are the same on this domain, so there's no ambiguity in computing the inverse Laplace transform.

fzero said:
The Laplace transform involves the domain $t\in [0,\infty)$. Both $f(t)=1$ and $u(t)$ are the same on this domain, so there's no ambiguity in computing the inverse Laplace transform.

Thanks.

Thats what I thought.

## 1. What is a unit step function u(t)?

A unit step function, denoted as u(t), is a mathematical function that has a value of 0 for all negative values of t and a value of 1 for all positive values of t.

## 2. What is the Laplace transformation of a unit step function?

The Laplace transformation of a unit step function u(t) is defined as 1/s, where s is a complex variable.

## 3. What is the inverse Laplace transformation of 1/s?

The inverse Laplace transformation of 1/s is a unit step function u(t).

## 4. How is the Laplace transformation of a unit step function used in science?

The Laplace transformation of a unit step function is used in science to solve differential equations and analyze systems in engineering, physics, and other fields.

## 5. What are some properties of the Laplace transformation of a unit step function?

Some properties of the Laplace transformation of a unit step function include linearity, time shifting, and differentiation. It also follows the rule of s-shifting, meaning the transformation of u(t-a) is e^(-as)/s.

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