Step and Delta Functions: Integrals and Generalized Derivatives

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Session Overview

This session looks closely at discontinuous functions and introduces the notion of an impulse or delta function. The goal is to use these functions as the input to differential equations. Step functions and delta functions are not differentiable in the usual sense, but they do have what we will call generalized derivatives, which are suitable for use in DE's.

Session Activities

Read the course notes:

• Introduction (PDF)
• Step and Box Functions (PDF)

Check Yourself

Take the quiz:

• Using Step Functions as Switches (PDF)
• Choices (PDF)
• Answer (PDF)

Session Activities

Read the course notes:

• Delta Functions: Unit Impulse (PDF)

Check Yourself

Take the quizzes:

• Integration with Delta Functions (PDF)
• Choices (PDF)
• Answer (PDF)


• Generalized Derivatives (PDF)
• Choices (PDF)
• Answer (PDF)

Session Activities

Watch the problem solving video:

• Step and Delta Functions: Integration and Generalized Derivatives (00:09:23)

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  Step and Delta Functions: Integration and Generalized Derivatives

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• Transcript (PDF)

Complete the practice problems:

• Practice Problems 24 (PDF)
• Practice Problems 24 Solutions (PDF)

Check Yourself

Complete the problem set:

• Problem Set Part II Problems (PDF)
• Problem Set Part II Solutions (PDF)

(Please note: There is no Problem Set Part I for this session.)

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