Differential Equations

Convolution

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Session Overview

We define convolution and use it in Green’s formula, which connects the response to arbitrary input q(t) with the unit impulse response.

Session Activities

Read the course notes:

• Convolution: Introduction (PDF)
• Definition and Properties (PDF)

Watch the lecture video clips:

• Example: f(t)*1
• Example: Radioactive Dumping

Read the course notes:

• Green’s Formula (PDF)
• Proof of Green’s Formula (PDF)
• Examples (PDF)

Learn from the Mathlet materials:

• Watch the video Exploration of the Convolution Accumulation Applet
• Work with the Convolution: Accumulation Applet

Watch the problem solving video:

• Convolution and Green’s Formula

Complete the practice problems:

• Practice Problems 26 (PDF)
• Practice Problems 26 Solutions (PDF)

Check Yourself

Complete the problem set:

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

(Note: There is no Problem Set Part 1 for this session).

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