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**:

**Section 7.3**– Properties of the Laplace Transform

**Objective 20–1**: I understand the properties of the Laplace transform.**Objective 20–2**: I can utilize the properties of the Laplace transform.

If the Laplace transform exists for , then for .

Prove the above theorem.

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

- .
- .
- .

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

- .
- .
- .
- .

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**Last Modified**: Sunday, 8 November 2020 4:26 EDT