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

MY VECTOR CALCULUS PLAYLIST:
►VECTOR CALCULUS (Calc IV)    • Calculus IV: Vector Calculus (Line Integra...  

OTHER COURSE PLAYLISTS:
►DISCRETE MATH:    • Discrete Math (Full Course: Sets, Logic, P...  
►LINEAR ALGEBRA:    • Linear Algebra (Full Course)  
►CALCULUS I:    • Calculus I (Limits, Derivative, Integrals)...  
► CALCULUS II:    • Calculus II (Integration Methods, Series, ...  
►MULTIVARIABLE CALCULUS (Calc III):    • Calculus III: Multivariable Calculus (Vect...  
►DIFFERENTIAL EQUATIONS:    • How to solve ODEs with infinite series | I...  

OTHER PLAYLISTS:
► Learning Math Series
   • 5 Tips To Make Math Practice Problems Actu...  
►Cool Math Series:
   • Cool Math Series  

BECOME A MEMBER:
►Join:    / @drtrefor  

MATH BOOKS & MERCH I LOVE:
► My Amazon Affiliate Shop: https://www.amazon.com/shop/treforbazett

SOCIALS:
►Twitter (math based):   / treforbazett  
►Instagram (photography based):   / treforphotography