Properties of the Laplace Transform

Properties of the Laplace TransformExpected Educational ResultsProperties of the Laplace TransformTranslation in Theorem: Translation in Investigation 01Investigation 02Hyperbolic FunctionsDefinitionsInvestigation 03CC BY-NC-SA 4.0

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

Expected Educational Results

Properties of the Laplace Transform

Translation in

Theorem: Translation in

If the Laplace transform exists for , then for .

Investigation 01

Prove the above theorem.

Investigation 02

Use the above theorem and the above list of common Laplace transforms to find the Laplace transform following functions:

  1. .
  2. .
  3. .

Hyperbolic Functions

Definitions

Investigation 03

Use the linearity property of the Laplace transform to find the following. Simplify the result into a single term.

  1. .
  2. .
  3. .
  4. .

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 4:26 EDT