Fourier Series: Basics

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Session Overview

We introduce general periodic functions and learn how to express them as Fourier series, which are sums of sines and cosines.

Session Activities

Read the course notes:

• Fourier Series: Basics: Introduction (PDF)
• Periodic Functions (PDF)

Check Yourself

Take the quizzes:

• Cosines with Common Periods (PDF)
• Choices (PDF)
• Answer (PDF)


• Cosines with Common Frequencies (PDF)
• Choices (PDF)
• Answer (PDF)

Session Activities

Watch the lecture video clip:

• Introduction to Fourier Transform (00:10:56)

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  Introduction to Fourier Transform (00:10:56)

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  > Download from Internet Archive (MP4)

• Transcript (PDF)

Read the course notes:

• Fourier Series: Definition and Coefficients (PDF)
• Examples (PDF)

Watch the lecture video clip:

• Fourier Series for Functions with Period 2L (00:06:54)

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  Fourier Series for Functions with Period 2L (00:06:54)

  > Download from iTunes U (MP4)

  > Download from Internet Archive (MP4)

• Transcript (PDF)

Read the course notes:

• Fourier Series for Functions with Period 2L (PDF)

Watch the lecture video clip:

• Orthogonality Relations (00:32:40)

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  Orthogonality Relations (00:32:40)

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• Transcript (PDF)

Read the course notes:

• Orthogonality Relations (PDF)

Watch the problem solving video:

• Computing Fourier Series (00:14:41)

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  Computing Fourier Series

  > Download from iTunes U (MP4)

  > Download from Internet Archive (MP4)

• Transcript (PDF)

Complete the practice problems:

• Practice Problems 21 (PDF)
• Practice Problems 21 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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