Laplace Transforms

Authored by: Dalton S. Nelson

The Industrial Electronics Handbook

Print publication date:  March  2011
Online publication date:  April  2016

Print ISBN: 9781439802793
eBook ISBN: 9781439802809
Adobe ISBN:

10.1201/b10602-9

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Abstract

In practice, many engineering and technology problems may be represented as integro-differential equations that need to be solved. Depending on the order of the equation, the solution may be simple or very complex, especially where the standard techniques of integral and differential calculus are used. An alternative is to use the Laplace transform. The Laplace transform allows us to carry out differentiation and integration using purely algebraic manipulations of addition and subtraction, respectively. This transformation is analogous to taking the logarithm of a function [B82]. So, where we had multiplication and division, after “taking logs” of the function, the multiplication becomes addition, and division becomes subtraction. Then, after the various algebraic manipulations in the log form, the results can be transformed back to get the final result. This logarithmic transformation allows for ease and convenience of algebraic manipulation, and the same will be true for the Laplace transform for integro-differential equations. The Laplace transform itself is named after Pierre Simon Laplace (1749–1827), a French mathematician and astronomer, who first used such transforms [KH00].

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