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


Ellipsoid

Cone

Hyperboloids

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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