Principles of Fourier Analysis, 2nd Edition

Contents

Preface

Sample Courses

I     Preliminaries

1    The Starting Point

1.1    Fourier’s Bold Conjecture

1.2    Mathematical Preliminaries and the Following Chapters

Additional Exercises

2    Basic Terminology, Notation and Conventions

2.1    Numbers

2.2    Functions, Formulas and Variables

2.3    Operators and Transforms

3    Basic Analysis I: Continuity and Smoothness

3.1    (Dis)Continuity

3.2    Differentiation

3.3    Basic Manipulations and Smoothness

3.4    Addenda

Additional Exercises

4    Basic Analysis II: Integration and Infinite Series

4.1    Integration

4.2    Infinite Series (Summations)

Additional Exercises

5    Symmetry and Periodicity

5.1    Even and Odd Functions

5.2    Periodic Functions

5.3    Sines and Cosines

Additional ...