Calculus IV: Vector Calculus (Line Integrals, Surface Integrals, Vector Fields, Greens' Thm, Divergence Thm, Stokes Thm, etc) **Full Course** Curl, Circulation, and Green's Theorem // Vector Calculus
Curl, Circulation, and Green's Theorem // Vector Calculus Transcript and Lesson Notes
his video is all about Green's Theorem, or at least the first of two Green's Theorem sometimes called the curl, circulation, or tangential form. Consider a smooth, simple, closed curve that encloses a region in the 2D pl
Quick Summary
his video is all about Green's Theorem, or at least the first of two Green's Theorem sometimes called the curl, circulation, or tangential form. Consider a smooth, simple, closed curve that encloses a region in the 2D pl
Key Takeaways
- Review the core idea: his video is all about Green's Theorem, or at least the first of two Green's Theorem sometimes called the curl, circulation, or tangential form. Consider a smooth, simple, closed curve that encloses a region in the 2D pl
- Understand how math fits into Curl, Circulation, and Green's Theorem // Vector Calculus.
- Understand how Circulation fits into Curl, Circulation, and Green's Theorem // Vector Calculus.
- Understand how Circulation Density fits into Curl, Circulation, and Green's Theorem // Vector Calculus.
- Understand how Flow fits into Curl, Circulation, and Green's Theorem // Vector Calculus.
Key Concepts
Full Transcript
his video is all about Green's Theorem, or at least the first of two Green's Theorem sometimes called the curl, circulation, or tangential form. Consider a smooth, simple, closed curve that encloses a region in the 2D plane, together with a Vector Field. One thing we could do is compute the circulation along that curve, which would be a large-scale or global property. Separately, at any point in the enclosed region we could compute the circulation density or curl at that point, which is a small-scale or local property. The power of Green's Theorem is that it relates these two concepts. The circulation or line integral along the curve (i.e. which only depends thus on the boundary of the region) is equal to the double integral over the entire region of the circulation density. Amazing! MY VECTOR CALCULUS PLAYLIST: ►VECTOR CALCULUS (Calc IV) https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa 0:00 Curl vs Circulation 1:48 Derivation 5:00 Green's Theorem 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 Curl, Circulation, and Green's Theorem // Vector Calculus about?
his video is all about Green's Theorem, or at least the first of two Green's Theorem sometimes called the curl, circulation, or tangential form. Consider a smooth, simple, closed curve that encloses a region in the 2D pl
What key concepts are covered in this lesson?
The lesson covers math, Circulation, Circulation Density, Flow, Curl.
What should I learn before Curl, Circulation, and Green's Theorem // 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: math, Circulation, Circulation Density, Flow.
Does this lesson include a transcript?
Yes. The full transcript is visible on this page in indexable HTML sections.
Is this lesson free?
Yes. CourseHive lessons and courses are available to learn online for free.
Continue Learning
Continue this lesson in the app
Install CourseHive on Android or iOS to keep learning while you move.
