Calculus IV: Vector Calculus (Line Integrals, Surface Integrals, Vector Fields, Greens' Thm, Divergence Thm, Stokes Thm, etc) **Full Course** The Surface Area formula for Parametric Surfaces // Vector Calculus
The Surface Area formula for Parametric Surfaces // Vector Calculus Transcript and Lesson Notes
In this video we derive the formula to compute surface area given some surface described parametrically. Thus if you have a parametric description, all you need to do is plug it into this formula. The derivation works by
Quick Summary
In this video we derive the formula to compute surface area given some surface described parametrically. Thus if you have a parametric description, all you need to do is plug it into this formula. The derivation works by
Key Takeaways
- Review the core idea: In this video we derive the formula to compute surface area given some surface described parametrically. Thus if you have a parametric description, all you need to do is plug it into this formula. The derivation works by
- Understand how Solution fits into The Surface Area formula for Parametric Surfaces // Vector Calculus.
- Understand how Example fits into The Surface Area formula for Parametric Surfaces // Vector Calculus.
- Understand how math fits into The Surface Area formula for Parametric Surfaces // Vector Calculus.
- Understand how surface area fits into The Surface Area formula for Parametric Surfaces // Vector Calculus.
Key Concepts
Full Transcript
In this video we derive the formula to compute surface area given some surface described parametrically. Thus if you have a parametric description, all you need to do is plug it into this formula. The derivation works by looking at a tiny section of surface area, and approximating this with a little tangential parallelogram whose area can be computed by the length of the cross product of r_u Delta u and r_v Delta b, the partial derivatives of the position vector with respect to the two parameters u and v. Thus the integral is effectively just summing up these little surface areas and becomes a double integral of the length of that cross product. We will see a concrete example of this in the next video in the vector calculus playlit. 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 The Surface Area formula for Parametric Surfaces // Vector Calculus about?
In this video we derive the formula to compute surface area given some surface described parametrically. Thus if you have a parametric description, all you need to do is plug it into this formula. The derivation works by
What key concepts are covered in this lesson?
The lesson covers Solution, Example, math, surface area, formula.
What should I learn before The Surface Area formula for Parametric 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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