Transforms of Discontinuous and Periodic FunctionsExpected Educational ResultsTransforms of Discontinuous and Periodic FunctionsPeriodic FunctionDefinition: Periodic FunctionGraphs of Periodic FunctionsInvestigation 09Laplace Transforms of Periodic FunctionsTheoremInvestigation 10Investigation 11CC BY-NC-SA 4.0

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

**Section 7.6**– Transforms of Discontinuous and Periodic Functions

**Objective 23–1**: I can sketch step and window functions.**Objective 23–2**: I can evaluate the Laplace transform of step and window functions.**Objective 23–3**: I can sketch periodic functions.**Objective 23–4**: I can evaluate the Laplace transform of periodic functions.**Objective 23–5**: I can evaluate the Laplace transform of the Gamma function.

A function is a **periodic function of period ** if for all in the domain of .

Let be a periodic function with period, . Sketch the following. Explain.

- , .
- , .
- , .

If has a period of and is continuous on , then .

Prove the above Theorem.

Evaluate the following Laplace transforms.

- , if , , and has period .
- , if , , and has period .
- , if , and has period .

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**Last Modified**: Sunday, 8 November 2020 22:02 EDT