Preface
Chapter 1. Introduction
1.1. Notation
1.2. Well-Posed Problems
1.3. Overview

Chapter 2. First-Order Differential Equations
2.1. Noncharacteristic Hypersurfaces
2.2. The Method of Characteristics
2.3. A Priori Estimates
2.4. Exercises

Chapter 3. An Overview of Second-Order PDEs
3.1. Classifications
3.2. Energy Estimates
3.3. Separation of Variables
3.4. Exercises

Chapter 4. Laplace Equations
4.1. Fundamental Solutions
4.2. Mean-Value Properties
4.3. The Maximum Principle
4.4. Poisson Equations
4.5. Exercises

Chapter 5. Heat Equations
5.1. Fourier Transforms
5.2. Fundamental Solutions
5.3. The Maximum Principle
5.4. Exercises

Chapter 6. Wave Equations
6.1. One-Dimensional Wave Equations
6.2. Higher-Dimensional Wave Equations
6.3. Energy Estimates
6.4. Exercises

Chapter 7. First-Order Differential Systems
7.1. Noncharacteristic Hypersurfaces
7.2. Analytic Solutions
7.3. Nonexistence of Smooth Solutions
7.4. Exercises

Chapter 8. Epilogue
8.1. Basic Linear Differential Equations
8.2. Examples of Nonlinear Differential Equations
Bibliography
Index