Calculus IV: Vector Calculus (Line Integrals, Surface Integrals, Vector Fields, Greens' Thm, Divergence Thm, Stokes Thm, etc) **Full Course** Computing the Surface Area of a surface parametrically // Example 1 // Vector Calculus
Computing the Surface Area of a surface parametrically // Example 1 // Vector Calculus Transcript and Lesson Notes
In this video we compute the surface area of the portion of a plane that lies within a cylinder. We've previously derived (see vector calculus playlist below) a formula to compute surface area for a parameterized surface
Quick Summary
In this video we compute the surface area of the portion of a plane that lies within a cylinder. We've previously derived (see vector calculus playlist below) a formula to compute surface area for a parameterized surface
Key Takeaways
- Review the core idea: In this video we compute the surface area of the portion of a plane that lies within a cylinder. We've previously derived (see vector calculus playlist below) a formula to compute surface area for a parameterized surface
- Understand how Solution fits into Computing the Surface Area of a surface parametrically // Example 1 // Vector Calculus.
- Understand how Example fits into Computing the Surface Area of a surface parametrically // Example 1 // Vector Calculus.
- Understand how math fits into Computing the Surface Area of a surface parametrically // Example 1 // Vector Calculus.
- Understand how vector calculus fits into Computing the Surface Area of a surface parametrically // Example 1 // Vector Calculus.
Key Concepts
Full Transcript
In this video we compute the surface area of the portion of a plane that lies within a cylinder. We've previously derived (see vector calculus playlist below) a formula to compute surface area for a parameterized surface, so our first ask is to find an appropriate parameterization of the plane. The key is that because the boundary is this cylinder, it makes sense to use the polar r and theta parameters so that our parameterization respects the boundary and will make the future integral easy to write down. 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 a surface parametrically // Example 1 // Vector Calculus about?
In this video we compute the surface area of the portion of a plane that lies within a cylinder. We've previously derived (see vector calculus playlist below) a formula to compute surface area for a parameterized surface
What key concepts are covered in this lesson?
The lesson covers Solution, Example, math, vector calculus, multivariable calculus.
What should I learn before Computing the Surface Area of a surface parametrically // Example 1 // 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, vector calculus.
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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