Laplace Transform Symbol in LaTeX

Written by Admin in Math operators,Math symbols

In this post, we will learn how to write the Laplace transform symbol in LaTeX using different commands.

1. What is Laplace transform?

The Laplace transformOpens in a new tab. of an expression \(f(t)\) is denoted by \(\mathscr{L}\{f(t)\}\) and is defined as the semi infinite integral:

\(\displaystyle\mathscr{L}\{f(t)\}=\int_{t=0}^{\infty}f(t)e^{-st}dt\)

The variable \(s\) used on the right-hand side is a parameter, which is assumed as positive and large enough to ensure that the integral is convergent.

After solving the integral on the right-hand side of the above equation, the resulting value will be in the form of \(s\), which is known as the Laplace transform of \(f(t)\) and denoted \(F(s)\).

2. Laplace symbol in LaTeX

From above you may remark that we used the symbol \(\mathscr{L}\{f(t)\}\) to denote the Laplace transform and you may ask which command in LaTeX produces it? The Laplace transform symbol in LaTeX can be obtained using the command \mathscr{L} provided by mathrsfs packageOpens in a new tab.

The above semi-infinite integral is produced in LaTeX as follows:

% Laplace transform symbol in LaTeX
\documentclass{article}

% Required package
\usepackage{mathrsfs}

\begin{document}

\[
    \mathscr{L}\{f(t)\}=\int_{t=0}^{\infty}f(t)e^{-st}dt
\]

\end{document}

3. Another version of Laplace symbol

Some documents prefer to use the symbol \(\mathcal{L}\{f(t)\}\) to denote the Laplace transform of the function \(f(t)\). In LaTeX, this Laplace transform symbol can be obtained using the command \mathcal{L} provided by amsmath package. The above code becomes:

% Second version of Laplace transform symbol in LaTeX
\documentclass{article}

% Required package
\usepackage{amsmath}

\begin{document}

\[
    \mathcal{L}\{f(t)\}=\int_{t=0}^{\infty}f(t)e^{-st}dt
\]

\end{document}

Compiling this code yields:

\(\displaystyle\mathcal{L}\{f(t)\}=\int_{t=0}^{\infty}f(t)e^{-st}dt\)

We reached the end of this tutorial, and for more math symbols, check this postOpens in a new tab.. If you have any remarks or suggestions, please feel free to reach us via email at admin@latex-tutorial.comOpens in a new tab.

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