Describing Surfaces Explicitly, Implicitly & Parametrically // Vector Calculus

How can we describe two-dimensional surfaces, even if they are embedded in 3D space? Similar to the three ways to describe curves in 2D, we can do this explicitly, implicitly, or parametrically. In the case of parametrically we get TWO parameters and choose them to try and naturally represent symmetries in the space. We specifically focus on the example of the cone and see how we can use cylindrical coordinates as a base to build out a parameterization of this space.

0:00 Intro to Surfaces
1:23 Descriptions of Curves
3:24 Descriptions of Surfaces
4:24 Cone Example

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