Differential Equations

Fourier Series: Basics

« Previous | Next »

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

Read the course notes:

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

Watch the lecture video clip:

• Fourier Series for Functions with Period 2L

Read the course notes:

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

Watch the lecture video clip:

• Orthogonality Relations

Read the course notes:

• Orthogonality Relations (PDF)

Watch the problem solving video:

• Computing Fourier Series

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)

« Previous | Next »