LECTURE NOTES OF WILLIAM CHEN
FOURIER SERIES AND 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.
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Chapter 1 : INTRODUCTION TO FOURIER SERIES >>
- Introduction
- Some Examples of Real Fourier Series
Chapter 2 : ALGEBRAIC BACKGROUND TO FOURIER SERIES >>
- Introduction
- Complex Inner Product Spaces
- Finite Orthogonal Systems
- Infinite Orthonormal Systems
Chapter 3 : FOURIER COEFFICIENTS >>
- Trigonometric Fourier Series
- Exponential Fourier Series
Chapter 4 : CONVERGENCE OF FOURIER SERIES >>
- Pointwise Convergence of Fourier Series
- Introduction to Uniform Convergence
- Uniform Convergence of Fourier Series
- Parseval Identity
Chapter 5 : FURTHER TOPICS ON FOURIER SERIES >>
- Gibbs Phenomenon
- Differentiation and Integration
- Fourier Series on Other Intervals
- An Application to Partial Differential Equations
Chapter 6 : INTRODUCTION TO FOURIER TRANSFORMS >>
- Introduction
- Inverse Fourier Transforms
- Convolutions
Chapter 7 : FURTHER TOPICS ON FOURIER TRANSFORMS >>
- Use of Cauchy's Residue Theorem
- Application to the Heat Equation
- Application to Laplace's Equation