Differential Equations

Transfer (System) and Weight Functions, Green's Formula

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Session Overview

This session ties together convolution, Laplace transform, unit impulse response and Green’s formula. They all meet in the notion of a transfer function (also known as a system function). We will define the transfer function and explore its uses in understanding systems and in combining simple systems to form more complex ones.

Session Activities

Read the course notes:

• Transfer (System) and Weight Functions, Green’s Formula: Introduction (PDF)
• Laplace Transform Table (PDF)
• The Transfer Function (PDF)

Check Yourself

Take the quizzes:

• I. Finding p (PDF)

• Choices (PDF)

• Answer (PDF)

• II. Finding p(D) (PDF)

• Choices (PDF)

• Answer (PDF)

Session Activities

Read the course notes:

• Modified Input (PDF)
• Green’s Formula, Laplace Transform of Convolution (PDF)

Watch the lecture video clip:

• Laplace Transform of Convolution

Read the course notes:

• Block Diagrams (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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