Laplace Transforms

Laplace TransformsExpected Educational ResultsLaplace TransformsCC BY-NC-SA 4.0

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

Expected Educational Results

Laplace Transforms

Definition: Laplace Transforms

Let be a function on . The Laplace Transform of is the function defined as

Note: You will need to know how to evaluate an improper integral; l'Hopital's Rule may be required.

Example 01: Find the Laplace transform of .

Solution:

By the definition of the Laplace Transform

Use the definition of improper integral:

Integrate by parts:

Rewrite rational expressions:

Use FTC-II:

Use Limit Laws:

Use l’Hopital’s Rule for the first two limits:

Evaluate limits:

So, .

NOTE: The more that you can recognize patterns of Laplace transforms, the more helpful Laplace transforms will be.

CC BY-NC-SA 4.0

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Last Modified: Sunday, 8 November 2020 4:12 EDT