Contents
Preface ix
Chapter 1. Introduction 1
§1.1. The brachistochrone 1
§1.2. The terrestrial brachistochrone 5
§1.3. Geodesics 7
§1.4. Minimal surfaces 14
§1.5. Recommended reading 18
§1.6. Exercises 20
Chapter 2. The First Variation 27
§2.1. The simplest problem 27
§2.2. Euler’s approach 28
§2.3. Lagrange’s approach 32
§2.4. Recommended reading 45
§2.5. Exercises 46
Chapter 3. Cases and Examples 47
§3.1. Special cases 47
§3.2. Case study: Minimal surface of revolution 52
§3.3. Case study: The brachistochrone 59
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