Transforms of Discontinuous and Periodic FunctionsExpected Educational ResultsTransforms of Discontinuous and Periodic FunctionsUnit Step FunctionDefinition: Unit Step FunctionGraphs of the Unit Step FunctionInvestigation 01Investigation 02Laplace Transform of the Unit Step FunctionInvestigation 03Investigation 04CC 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.

The **unit step function** (a.k.a. *Heaviside step function*) is defined by

Sketch the following step functions.

Sketch the following functions. Explain.

- $

Evaluate the following Laplace transforms.

- Find
- Find

Evaluate the following Laplace transforms.

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