Differential Equations

Unit Step and Unit Impulse Response

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Session Overview

In this session we study differential equations with step or delta functions as input. For physical systems, this means that we are looking at discontinuous or impulsive inputs to the system.

Session Activities

Read the course notes:

• Unit Step and Unit Impulse Response: Introduction (PDF)
• Initial Conditions (PDF)
• First Order Unit Step Response (PDF)

Check Yourself

Take the quiz:

• Unit Step Response: Post-initial Conditions  (PDF)
• Choices (PDF)
• Answer (PDF)

Session Activities

Read the course notes:

• First Order Unit Impulse Response (PDF)

Check Yourself

Take the quiz:

• First Order Unit Impulse Response: Post-initial Conditions  (PDF)
• Choices (PDF)
• Answer (PDF)

Session Activities

Read the course notes:

• Second Order Unit Step Response (PDF)
• Second Order Unit Impulse Response (PDF)

Check Yourself

Take the quiz:

• Second Order Unit Impulse Response: Post-initial Conditions (PDF)
• Choices (PDF)
• Answer (PDF)

Session Activities

Read the course notes:

• Higher Order Unit Impulse Response (PDF)

Watch the problem solving video:

• Unit Step and Impulse Response

Complete the practice problems:

• Practice Problems 25 (PDF)
• Practice Problems 25 Solutions (PDF)

Check Yourself

Complete the problem sets:

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

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