Chapter 5 • Regular Surfaces

5.1: Parametrized Surfaces

Example 5.1.1: Planes

Example 5.1.2: Graphs of Functions

Example 5.1.3: Spheres

Example 5.1.4: Conics




Example 5.1.5: Surfaces of Revolution

Example 5.1.7: u- and v-Coordinate Curves

Figure 5.4: Coordinate Lines on a Torus

Problem 5.1.5: Loxodromes

5.2 Tangent Planes and Regular Surfaces

Definition 5.2.1: Tangent Vector

Example 5.2.2: The Vertex of a Cone

Definition 5.2.3: Tangent Lines to Curves on a Surface

Proposition 5.2.4: Equation of the Tangent Plane

Example 5.2.5: Tangent Plane to Function Graph

Example 5.2.6: Tangent Plane to Hyperboloid of One Sheet

Problem 5.2.15: Stereographic Projection

Problem 5.2.18: Central Projection

5.4: The Tangent Space and the Normal Vector

Page 157: Unit Normal Vector

Normal Line

Problem 5.4.4: Tangential Surfaces

Problem 5.4.5: Tubes

5.5: Orientable Surfaces

Example 5.5.2: The Möbius Strip

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