LECTURE NOTES OF WILLIAM CHEN
# FOURIER SERIES AND TRANSFORMS

### Chapter 1 : INTRODUCTION TO FOURIER SERIES >>

### Chapter 2 : ALGEBRAIC BACKGROUND TO FOURIER SERIES >>

### Chapter 3 : FOURIER COEFFICIENTS >>

### Chapter 4 : CONVERGENCE OF FOURIER SERIES >>

### Chapter 5 : FURTHER TOPICS ON FOURIER SERIES >>

### Chapter 6 : INTRODUCTION TO FOURIER TRANSFORMS >>

### Chapter 7 : FURTHER TOPICS ON FOURIER TRANSFORMS >>

This set of notes has been organized in such a way to create a single volume suitable for an introduction to the elementary techniques of Fourier series and transforms.

To read the notes, click the links below for connection to the appropriate PDF files.

The material is available free to all individuals, on the understanding that it is not to be used for financial gain, and may be downloaded and/or photocopied, with or without permission from the author. However, the documents may not be kept on any information storage and retrieval system without permission from the author, unless such system is not accessible to any individuals other than its owners.

- Introduction
- Some Examples of Real Fourier Series

- Introduction
- Complex Inner Product Spaces
- Finite Orthogonal Systems
- Infinite Orthonormal Systems

- Trigonometric Fourier Series
- Exponential Fourier Series

- Pointwise Convergence of Fourier Series
- Introduction to Uniform Convergence
- Uniform Convergence of Fourier Series
- Parseval Identity

- Gibbs Phenomenon
- Differentiation and Integration
- Fourier Series on Other Intervals
- An Application to Partial Differential Equations

- Introduction
- Inverse Fourier Transforms
- Convolutions

- Use of Cauchy's Residue Theorem
- Application to the Heat Equation
- Application to Laplace's Equation