Calculus IV: Vector Calculus (Line Integrals, Surface Integrals, Vector Fields, Greens' Thm, Divergence Thm, Stokes Thm, etc) **Full Course** Surface Area for Implicit & Explicit Surfaces // Vector Calculus
Surface Area for Implicit & Explicit Surfaces // Vector Calculus Transcript and Lesson Notes
How can we compute the surface area of a surface? In the previous video (see vector calc playlist below) we derived the surface area when the surface was described parametrically. In this video we focus on when the surfa
Quick Summary
How can we compute the surface area of a surface? In the previous video (see vector calc playlist below) we derived the surface area when the surface was described parametrically. In this video we focus on when the surfa
Key Takeaways
- Review the core idea: How can we compute the surface area of a surface? In the previous video (see vector calc playlist below) we derived the surface area when the surface was described parametrically. In this video we focus on when the surfa
- Understand how Solution fits into Surface Area for Implicit & Explicit Surfaces // Vector Calculus.
- Understand how Example fits into Surface Area for Implicit & Explicit Surfaces // Vector Calculus.
- Understand how math fits into Surface Area for Implicit & Explicit Surfaces // Vector Calculus.
- Understand how surface area fits into Surface Area for Implicit & Explicit Surfaces // Vector Calculus.
Key Concepts
Full Transcript
How can we compute the surface area of a surface? In the previous video (see vector calc playlist below) we derived the surface area when the surface was described parametrically. In this video we focus on when the surface is described explicitly and implicitly, and when those formulas work. The formula only workThe formula for the explicit case could be memorized, but it quickly follows from the implicit case so I usually don't bother. Note that I do skip the formal proof of the formula. The basic ingredients of that proof is to come up with a parameterization (via implicit function theorem) and then plug into the surface area formula for parameterized surfaces. 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 Surface Area for Implicit & Explicit Surfaces // Vector Calculus about?
How can we compute the surface area of a surface? In the previous video (see vector calc playlist below) we derived the surface area when the surface was described parametrically. In this video we focus on when the surfa
What key concepts are covered in this lesson?
The lesson covers Solution, Example, math, surface area, formula.
What should I learn before Surface Area for Implicit & Explicit Surfaces // 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 area.
Does this lesson include a transcript?
Yes. The full transcript is visible on this page in indexable HTML sections.
Is this lesson free?
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