Calculus IV: Vector Calculus (Line Integrals, Surface Integrals, Vector Fields, Greens' Thm, Divergence Thm, Stokes Thm, etc) **Full Course** Computing the Surface Area of an Implicitly Defined Surface
Computing the Surface Area of an Implicitly Defined Surface Transcript and Lesson Notes
In this example, we compute the surface area using the formula for implicit surfaces that we talked about in the previous video of my vector calculus playlist (link below). This paraboloid could be tackled a few ways (pa
Quick Summary
In this example, we compute the surface area using the formula for implicit surfaces that we talked about in the previous video of my vector calculus playlist (link below). This paraboloid could be tackled a few ways (pa
Key Takeaways
- Review the core idea: In this example, we compute the surface area using the formula for implicit surfaces that we talked about in the previous video of my vector calculus playlist (link below). This paraboloid could be tackled a few ways (pa
- Understand how Solution fits into Computing the Surface Area of an Implicitly Defined Surface.
- Understand how Example fits into Computing the Surface Area of an Implicitly Defined Surface.
- Understand how math fits into Computing the Surface Area of an Implicitly Defined Surface.
- Understand how surface area fits into Computing the Surface Area of an Implicitly Defined Surface.
Key Concepts
Full Transcript
In this example, we compute the surface area using the formula for implicit surfaces that we talked about in the previous video of my vector calculus playlist (link below). This paraboloid could be tackled a few ways (parametrically, implicitly or explicitly), but we are going to use the implicit formula thinking of this surface as being above the xy-plane. The double integral that we get actually turns out to be easier to compute in polar coordinates so we make that conversion as well. 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 Computing the Surface Area of an Implicitly Defined Surface about?
In this example, we compute the surface area using the formula for implicit surfaces that we talked about in the previous video of my vector calculus playlist (link below). This paraboloid could be tackled a few ways (pa
What key concepts are covered in this lesson?
The lesson covers Solution, Example, math, surface area, implict.
What should I learn before Computing the Surface Area of an Implicitly Defined Surface?
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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