Divergence, Flux, 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 - Divergence, Flux, and Green's Theorem // Vector Calculus

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What you'll learn

This course includes

5.3 hours of video
Certificate of completion
Access on mobile and TV

Summary

Keywords

math Green's Theorem Vector Calculus Calc 4 Vector Field Flux Flux Density Divergence Definition Proof Motivation Derivation

Full Transcript

In the previous video in our Vector Calculus Playlist (https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa) we saw Part I of Green's Theorem, which related the local property of Curl (aka circulation density) with the global property of Circulation. Circulation, a line integral over a vector field, was compared to a double integral over the area enclosed of the Flux. In this video we look at Part II of Green's Theorem which now contrasts the local property of Divergence (aka Flux Density) with the global property of outward Flux across the boundary of a region. We are going to introduce the concept of Divergence, come up with a formula for it, and discuss the geometric idea behind why Green's Theorem is true. 0:00 Divergence vs Flux 3:50 Divergence Formula 5:22 Derivation of Green's Theorem 7:56 Statement of Green's Theorem 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