Partial Differential Equations

by Victor Ivrii

Provides a comprehensive online textbook for learning partial differential equations through detailed coverage of wave equations, heat diffusion, and separation of variables techniques.

Chapter 0: Preliminaries
Chapter 1: Introduction
Chapter 2: $1$-Dimensional Waves
Chapter 3: Heat Equation in $1$D
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 in Curvilinear Coordinates
Chapter 9: Wave Equation
Chapter 10: Variational Methods
Chapter 11: Distributions and Weak Solutions
Chapter 12: Nonlinear Equations
Chapter 13: Eigenvalues and Eigenfunctions
Chapter 14: Miscellaneous
General Appendices