Table of Contents

Chapter 1. Introduction

Chapter 2. $1$-dimensional waves

Chapter 3. Heat equation in 1D

Chapter 4. Separation of variables and Fourier Series

Chapter 5. Fourier transform

Chapter 6. Separation of variables

Chapter 7. Laplace equation

Chapter 8. Separation of variables

Chapter 9. Wave equation

Chapter 10. Variational methods

Chapter 11. Distributions and weak solutions

Chapter 12. Non-linear equations

Chapter 13. Eigenvalues and eigenfunctions

Chapter 14. Miscellaneous

General appendices