Calculus IV: Vector Calculus (Line Integrals, Surface Integrals, Vector Fields, Greens' Thm, Divergence Thm, Stokes Thm, etc) **Full Course** Divergence Theorem for regions bounded by two surfaces // Vector Calculus
Divergence Theorem for regions bounded by two surfaces // Vector Calculus Transcript and Lesson Notes
In this video we extend the Divergence Theorem to situations where a region has not ONE boundary surface but two. For example, the region between two concentric spheres. This is particularly useful when the divergence is
Quick Summary
In this video we extend the Divergence Theorem to situations where a region has not ONE boundary surface but two. For example, the region between two concentric spheres. This is particularly useful when the divergence is
Key Takeaways
- Review the core idea: In this video we extend the Divergence Theorem to situations where a region has not ONE boundary surface but two. For example, the region between two concentric spheres. This is particularly useful when the divergence is
- Understand how Solution fits into Divergence Theorem for regions bounded by two surfaces // Vector Calculus.
- Understand how Example fits into Divergence Theorem for regions bounded by two surfaces // Vector Calculus.
- Understand how math fits into Divergence Theorem for regions bounded by two surfaces // Vector Calculus.
- Understand how vector calculus fits into Divergence Theorem for regions bounded by two surfaces // Vector Calculus.
Key Concepts
Full Transcript
In this video we extend the Divergence Theorem to situations where a region has not ONE boundary surface but two. For example, the region between two concentric spheres. This is particularly useful when the divergence is zero, which means the right hand side of the divergence theorem is zero, and this gives the result that the flux across the two surfaces must add up to being the same thing! We will use this a lot in the next video on Gauss' Law. 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 Divergence Theorem for regions bounded by two surfaces // Vector Calculus about?
In this video we extend the Divergence Theorem to situations where a region has not ONE boundary surface but two. For example, the region between two concentric spheres. This is particularly useful when the divergence is
What key concepts are covered in this lesson?
The lesson covers Solution, Example, math, vector calculus, multivariable calculus.
What should I learn before Divergence Theorem for regions bounded by two 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, 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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