Transforms of Discontinuous and Periodic Functions

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:

Expected Educational Results

Transforms of Discontinuous and Periodic Functions

Periodic Function

Definition: Periodic Function

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

Graphs of Periodic Functions

Investigation 09

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

  1. , .
  2. , .
  3. , .

Laplace Transforms of Periodic Functions

Theorem

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

Investigation 10

Prove the above Theorem.

Investigation 11

Evaluate the following Laplace transforms.

  1. , if , , and has period .
  2. , if , , and has period .
  3. , if , and has period .

CC BY-NC-SA 4.0

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