Curl, Circulation, and Green's Theorem // Vector Calculus

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

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5.3 hours of video
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Summary

Keywords

math Circulation Circulation Density Flow Curl kth component of curl Green's Theorem Part I vector calculus vector field line integral double integral

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