Contents
Preface ix
Chapter 1. Introduction 1
§1.1. Notation 1
§1.2. Well-Posed Problems 3
§1.3. Overview 5
Chapter 2. First-Order Differential Equations 9
§2.1. Noncharacteristic Hypersurfaces 10
§2.2. The Method of Characteristics 16
§2.3. A Priori Estimates 30
§2.4. Exercises 43
Chapter 3. An Overview of Second-Order PDEs 47
§3.1. Classifications 48
§3.2. Energy Estimates 58
§3.3. Separation of Variables 67
§3.4. Exercises 86
Chapter 4. Laplace Equations 89
§4.1. Fundamental Solutions 90
§4.2. Mean-Value Properties 105
§4.3. The Maximum Principle 112
§4.4. Poisson Equations 133
§4.5. Exercises 143
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