Differential Equations

Operations on Fourier Series

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Session Overview

In this session we will learn some tricks to help compute Fourier series, and also see in what sense a periodic function equals its Fourier series.

Session Activities

Read the course notes:

• Operations on Fourier Series: Introduction (PDF)

Complete the practice problem:

• Exercise: Find the Fourier Series (PDF)
• Answer (PDF)

Watch the lecture video clip:

• Even and Odd Functions

Read the course notes:

• Even and Odd Functions (PDF)
• Scaling and Shifting (PDF)
• Integration and Differentiation (PDF)

Watch the lecture video clip:

• Convergence of Fourier Series

Read the course notes:

• Convergence of Fourier Series (PDF)
• The Meaning of Fourier Series (PDF)
• Gibbs Phenomenon (PDF)

Learn from the Mathlet materials:

• Watch the video Exploration of the Fourier Coefficient Applet
• Work with the Fourier Coefficients Applet

Read the course notes:

• Application to Infinite Series (PDF)

Watch the problem solving video:

• Manipulating Fourier Series

Complete the practice problems:

• Practice Problems 22 (PDF)
• Practice Problems 22 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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