§3.4. Isothermal Parameters 72
§3.5. Harmonic Functions and Minimal Surfaces 75
§3.6. The Weierstrass-Enneper Representations 77
§3.7. The Gauss Map 86
§3.8. Stereographic Projection and the Gauss Map 91
§3.9. Creating Minimal Surfaces from Curves 95
§3.10. To Be or Not To Be Area Minimizing 105
§3.11. Constant Mean Curvature 114
Chapter 4. The Calculus of Variations and Shape 121
§4.1. Introduction 121
§4.2. Minimizing Integrals 124
§4.3. Necessary Conditions: Euler-Lagrange Equations 127
§4.4. Solving the Fundamental Examples 136
§4.5. Problems with Extra Constraints 146
Chapter 5. Maple, Soap Films, and Minimal Surfaces 159
§5.1. Introduction 159
§5.2. Fused Bubbles 159
§5.3. Capillarity: Inclined Planes 166
§5.4. Capillarity: Thin Tubes 172
§5.5. Minimal Surfaces of Revolution 175
§5.6. The Catenoid versus Two Disks 181
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