Contents Preface ix Chapter 1. Differential Equations 1 §1.1. Classification of Differential Equations 4 §1.2. Can we write solutions explicitly? 5 §1.3. Differential Equations as Models of Reality §1.4. Named Equations 8 §1.5. When are two equations equivalent? 9 §1.6. Evolution in Time 12 Problems 18 Suggested Reading 22 Chapter 2. Developing PDE Intuition 23 §2.1. The Structure of Linear Equations 23 §2.2. Examples of Linear Equations 30 §2.3. Examples of Nonlinear Equations 35 Problems 41 Suggested Reading 43 Chapter 3. The Story of Solitons 45 §3.1. The Observation 45 §3.2. Terminology and Backyard Study 46 §3.3. A Less-than-enthusiastic Response 47 §3.4. The Great Eastern 49 §3.5. The KdV Equation 49 §3.6. Early 20th Century 52 v and Unreality 7

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