Inverse Laplace Transforms

Inverse Laplace TransformsPrerequisite KnowledgeMethod of Partial FractionsDefinition: Partial FractionsDefinition: Distinct Linear FactorsDefinition: Distinct Quadratic FactorsDefinition: Repeated Linear FactorDefinition: Repeated Quadratic FactorsPracticeUse Technology to Factor ExpressionsUse Technology to Verify Partial FractionsCC BY-NC-SA 4.0

Author: John J Weber III, PhD Corresponding Textbook Sections:

Prerequisite Knowledge

Method of Partial Fractions

Definition: Partial Fractions

Rational expressions can be written as a sum of simpler fractions called partial fractions.

Definition: Distinct Linear Factors

Let be a rational function where\newline and is factorable into distinct linear factors. Then

Definition: Distinct Quadratic Factors

Let be a rational function where and is factorable into distinct quadratic factors. Then

Definition: Repeated Linear Factor

Let be a rational function where\newline and is factorable into -repeated linear factors, i.e., . Then

Definition: Repeated Quadratic Factors

Let be a rational function where and is factorable into -repeated quadratic factors, i.e., . Then

Practice

Rewrite the following rational expressions into a sum of partial fractions:

Use Technology to Factor Expressions

Mathematica

Use Technology to Verify Partial Fractions

Mathematica

Warnings:

  1. Be very careful with the syntax. Syntax is the set of rules on how to write computer code. Every software program has its own unique syntax. Some basic Mathematica syntax is located at: http://www.jjw3.com/TECH_Common_Functions.pdf.
  2. To execute code (including comment codes), press and hold the SHIFT key and press the ENTER key.

CC BY-NC-SA 4.0

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License [http://creativecommons.org/licenses/by-nc-sa/4.0/].

Last Modified: Sunday, 8 November 2020 18:39 EDT