Index PrevUp Next

\(\newcommand\DLGray{\color{Gray}} \newcommand\DLO{\color{BurntOrange}} \newcommand\DLRa{\color{WildStrawberry}} \newcommand\DLGa{\color{Green}} \newcommand\DLGb{\color{PineGreen}} \newcommand\DLBa{\color{RoyalBlue}} \newcommand\DLBb{\color{Cerulean}} \newcommand\ds{\displaystyle} \newcommand\ddx{\frac{d}{dx}} \newcommand\os{\overset} \newcommand\us{\underset} \newcommand\ob{\overbrace} \newcommand\obt{\overbracket} \newcommand\ub{\underbrace} \newcommand\ubt{\underbracket} \newcommand\ul{\underline} \newcommand\laplacesym{\mathscr{L}} \newcommand\lap[1]{\laplacesym\left\{#1\right\}} \newcommand\ilap[1]{\laplacesym^{-1}\left\{#1\right\}} \newcommand\tikznode[3][] {\tikz[remember picture,baseline=(#2.base)] \node[minimum size=0pt,inner sep=0pt,#1](#2){#3}; } \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \definecolor{fillinmathshade}{gray}{0.9} \newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}} \newcommand{\sfrac}[2]{{#1}/{#2}} \)

Introduction

Imagine turning a differential equation into an algebra problem instead. That’s exactly what the Laplace transform method does. It unfolds in the same three steps:

Forward transform. Apply the Laplace transform (term-by-term) to a differential equation and get an algebraic equation in $Y(s)\text{.}$
Algebra in the Laplace domain. Isolate $Y(s)$ and prepare it for next step.
Backward transform. Apply the inverse Laplace transform to the prepared $Y(s)$ to turn it back into $y(t)$ as the solution to the original differential equation.

Throughout the chapter, we will examine each step and provide a roadmap like the one below.

PrevTop Next