Calculus IV: Vector Calculus (Line Integrals, Surface Integrals, Vector Fields, Greens' Thm, Divergence Thm, Stokes Thm, etc) **Full Course** Describing Surfaces Explicitly, Implicitly & Parametrically // Vector Calculus
Describing Surfaces Explicitly, Implicitly & Parametrically // Vector Calculus Transcript and Lesson Notes
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 parametric
Quick Summary
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 parametric
Key Takeaways
- Review the core idea: 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 parametric
- Understand how Solution fits into Describing Surfaces Explicitly, Implicitly & Parametrically // Vector Calculus.
- Understand how Example fits into Describing Surfaces Explicitly, Implicitly & Parametrically // Vector Calculus.
- Understand how math fits into Describing Surfaces Explicitly, Implicitly & Parametrically // Vector Calculus.
- Understand how Surface fits into Describing Surfaces Explicitly, Implicitly & Parametrically // Vector Calculus.
Key Concepts
Full Transcript
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) https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa OTHER COURSE PLAYLISTS: ►DISCRETE MATH: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS ►LINEAR ALGEBRA: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6 ►CALCULUS I: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m ► CALCULUS II: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n ►MULTIVARIABLE CALCULUS (Calc III): https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd ►DIFFERENTIAL EQUATIONS: https://www.youtube.com/watch?v=xeeM3TT4Zgg&list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1 OTHER PLAYLISTS: ► Learning Math Series https://www.youtube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw ►Cool Math Series: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpiho BECOME A MEMBER: ►Join: https://www.youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/join MATH BOOKS & MERCH I LOVE: ► My Amazon Affiliate Shop: https://www.amazon.com/shop/treforbazett SOCIALS: ►Twitter (math based): http://twitter.com/treforbazett ►Instagram (photography based): http://instagram.com/treforphotography
Lesson FAQs
What is Describing Surfaces Explicitly, Implicitly & Parametrically // Vector Calculus about?
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 parametric
What key concepts are covered in this lesson?
The lesson covers Solution, Example, math, Surface, Integral.
What should I learn before Describing Surfaces Explicitly, Implicitly & Parametrically // Vector Calculus?
Review the previous lessons in Calculus IV: Vector Calculus (Line Integrals, Surface Integrals, Vector Fields, Greens' Thm, Divergence Thm, Stokes Thm, etc) **Full Course**, then use the transcript and key concepts on this page to fill any gaps.
How can I practice after this lesson?
Practice by applying the main concepts: Solution, Example, math, Surface.
Does this lesson include a transcript?
Yes. The full transcript is visible on this page in indexable HTML sections.
Is this lesson free?
Yes. CourseHive lessons and courses are available to learn online for free.
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